LITERATURE REVIEW AND OBJECTIVES OF PRESENT WORK

“Studies on Radial Tipped Centrifugal Fan” 22

CHAPTER – 2

LITERATURE REVIEW AND OBJECTIVES OF PRESENT WORK

2.1 Preamble

Turbo – machines are devices in which energy is transferred either to or from, a

continuously flowing fluid by the dynamic action of moving blades of the runner.

Leonardo Da Vinci (1452-1519) was probably the first to coin the idea of lifting

water by centrifugal forces. He has described primitive models of turbomachines by

making some sketches. From his original sketches, a French physicist Denis Papin was

first to describe the centrifugal pump scientifically in 1687. He built first pump in 1705,

which had impeller with blades and a volute. Thus, centrifugal pumps and blowers of

today are made after more than 300 years’ of revolution.

The theoretical treatment of turbo machines requires the knowledge of fluid

dynamics, flow physics and thermodynamics. Spannhake [23] has made pioneering

work in this area and has defined flow physics and associated terminology in his book

entitled “Centrifugal pumps, turbines and propellers” in 1934. His successor Wislieenus

[24] extended his work and documented in “Fluid Mechanics of Turbo machinery” in

1947.

During this period, W. J. Kearton [25] observed breaks in characteristic curves

by carrying accurate tests. His measurements indicated that the flow is far from

uniform, and that on the trailing face of the vane there is an area of “inactive flow”.

This area increases as the capacity is reduced. The effect of this inactive flow is

equivalent to increasing the vane thickness and reducing the passage area. He had

noticed that number of impeller blades has significant effect on fan performance curves.

W. J. Kearton [25] investigated these conditions and has presented his findings in a very

interesting paper, “Influence of the Number of Impeller Blades on the Pressure

Generated in a centrifugal compressor and on its General performance.” He also found

that below the critical flow the velocity distribution was fairly symmetrical and

resembled the velocity distribution obtained with turbulent flow in a pipe. Above the

critical flow the velocity distribution was not symmetrical, but much greater on the side

of the impeller away from the inlet.

Chapter – 2: Literature Review and Objectives of Present Work


He concluded that overall coefficients based upon experience and test results must be

used until more complete information is available.

Austin H. Church [26] has probably made the first attempt to compile the design

methodology for pumps and blowers. While Eck Bruno [14], Kovats [27], William

Osborne [28], Whitfield and Baines [29] had extended the work of Church and

presented detailed analysis of design parameters for centrifugal, axial and cross flow

fans and blowers. Bela Mishra [30] studied design methodology from literature for

centrifugal blower.

Stodola [31] had developed first useful method for slip factor approximation.

He correlated slip factor and finite number of blades. Stodola claimed that average

direction of discharge varies from the blade angle β2 due to number of blades and

relative circulation in vane to vane plane. This is also responsible for the reduction in

output. Several co-relations as well as empirical equations are used in literature to

estimate slip factor. Other slip factor correlations in literature are given by Balje, Stanitz

[9] and Eck Bruno [14]. According to all these researchers, the major cause of slip are

due to relative eddies generated in vane to vane plane. These correlations conclude that

for a given specified machine, the value of slip factor is constant and is dependent of

Impeller geometry only.

A. J. Stepanoff [32] considers hydraulic losses as the most important and but

least known losses in turbo-machines. He adds that the hydraulic losses are caused by

skin friction and eddies. Separation losses occur due to changes in direction and

magnitude of the velocity of flow. The latter group includes shock loss and diffusion

loss.

D. J. Myles [33] accounts impeller and volute losses as a fraction of the dynamic

exit pressure relative to impeller and volute, respectively. They are correlated with a

diffusion factor over a wide volume flow range. The results are applied to other

impellers and volutes. The low volume flow range of operation is also considered.

Dr. Bruno Eck [14] first dealt with impeller friction or disc friction loss

experimentally. He differentiated impeller loss in to two components as impeller entry

loss and friction loss in impeller. The friction loss in impeller consist retardation and

resultant pressure loss.

William C. Osborne [28] states that the actual performance of a centrifugal fan

(at the design point) differs to the ideal fan power which can be predicted by Euler’s



equation. This difference can be accounted for inter blade circulation which results in a

reduction of the work done by the impeller. Other factors which contribute to reduction

in output are internal volumetric leakage and pressure losses within fan assembly.

Mechanical losses also affect fan input power.

J.D. Denton [34] defines loss as ‘any flow feature that reduces efficiency of a

turbo machine’. Further, he categorizes losses as profile loss, secondary loss (End wall

loss) and tip leakage loss as major source of turbo machine losses.

Baines and Whitfield [29] states that the governing equations of continuity,

momentum and energy together constitute a set of partial differential equations which

must be solved across the complete domain for which a prediction of the flow field is

required. Various flow phenomenons occurring inside turbomachine can be numerically

analyzed.

P. J. Roache [35] made quantification of uncertainty in computational fluid

dynamics. His review covers verification, validation and confirmation for

computational fluid dynamics (CFD). It includes error taxonomies, error estimation,

convergence rates, surrogate estimators, nonlinear dynamics, and error estimation for

grid adaptation.

Hsin-Hua Tsuei, Kerry Oliphant and David Japikse [36] have developed method

for rapid CFD modeling for turbo machinery. Their study sensibly guides engineers in

the economical and accurate utilization of their CFD tools. A base for rapid calculations

is established and developed easy-to-use CFD analysis as a base for advanced design

development.

At present, with the help of commercially available CFD softwares, any realistic

flow simulation on a three-dimensional basis is allowing designer to estimate influence

of spatial parameters on performance of the machine before experimental evaluation.

The very basic objective of this work is to propose a streamlined design

methodology for a centrifugal fan to offer highest possible energy efficiency for fume

extraction in SDS-9 texturising machines of a medium scale textile industry.

This objective cannot be achieved without clear understanding of influence of

finite number of blades on fan performance, study of available design methodologies,

slip, fan losses and flow physics through published literature and accordingly the

subsequent sections of this chapter deals with these aspects in more detail.



2.2 Parametric Influence, Performance and Design Methodologies

Few typical studies pertaining to parametric influence, performance and design

methodologies of centrifugal machines are briefly presented here in.

Balje O. E. [6] has observed that optimum efficiency of a centrifugal

blower/fan occurred for slightly backward leaning vanes.

Wosika L. R. [37] experimentally verified that radial and backward leaning

vanes give slightly better efficiencies than forward vanes.

Faulders C. R. [38] proved by experiments that cross flow occurs in vaned

diffuser passages from the suction face of a vane to the pressure face of the next vane.

He further showed that this cross flow can be reduced by increasing the number of

vanes and increasing the radius of curvature of vanes.

Leslie Young and R. A. Nixon [39] concluded that standardized test

arrangement can give useful performance comparison of different pumps working under

standard conditions, but it does not necessarily give a true indication of performance in

service at off design conditions.

Austin Church [26] has done pioneering work to establish design methodology

for pumps, fans and blowers. He found that the type of flow existing in a pump or

blower is always turbulent, it means, the Reynolds number is always well above the

critical value. The flow is seriously disturbed with a resultant loss of head. He has

presented his design with stage compressibility effect, pressure ratio and energy

transfer. He has also considered density changes at various flow sections with respect to

change in temperature and pressure. Thus volume flow rate gets changed continuously.

The dimensions of the air passage are calculated in accordance to this variation in

volume flow. Stage pressure ratio between atmosphere to inlet eye, inlet eye to impeller

inlet, impeller inlet to impeller outlet and impeller outlet to casing outlet are calculated

individually.

Energy transfer by impeller=

∴ Total adiabatic head across the impeller 0.286⁄ . 1

Overall head to be developed by the centrifugal impeller by energy transfer is:

∆∆ 1 1 1 1



K' is overall pressure coefficient which is used on account of the friction and

turbulence occurring in the impeller. Church has found value of K' = 0.5 to 0.65 by

experiments.

Design of volute casing:

The width of volute casing b3 is taken as 2 to 3 times width of impeller at exit

bv = b3 = 2 to 3b2

Volute base circle/inlet radius r3 is kept slightly higher than r2. In determining cross sectional area of the volute at any point, the problem

consists in finding the area of the section that will pass the volume Qф/360 with a

velocity Vu×R = C. If friction is neglected, the flow through the differential section is:

dQф =b×dr×C/r

The total flow past the section becomes:

ф

360

Vave at 360 º = V4

Radius of volute at angle 360º = r4

Radius of volute tongue r 1.075r

Volute tongue angle θ 132 log⁄

tan Church, 1962

Leakage loss 0.03

Blade Profile:

Blade Profile can be made by tangent of circular arc method or by polar

coordinates method. It is observed that the flow of air through the blade passage of a

centrifugal fan is often far from ideal, and the object of design of blade curvature should

be to provide the minimum of flow separation.

When tangent of circular arc method is used, the impeller is divided into a

number of assumed concentric rings, not necessarily equally spaced between inner and

outer radii. The radius Rb of the arc is defining the blade shape between inner and outer

radii as shown in Figure 2.1.

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these diagrams as following:

• The relative discharge angle β3 is less than the blade angle β2 in each case.

• The average relative discharge velocity changes, in the case of backward

curved and radial tipped blades it increases and with forward curved blades

decreases.

• In each case, the average absolute discharge velocity C3 is more acute than C2.

• In each case the angle α3 of the absolute velocity is more acute than α2

(important for the construction of guide mechanisms, it means guide vanes and

others)

Most efforts to determine the optimum number of blades have resulted in only

empirical relations. Some of them are given below:

ECK Bruno [14] has recommended the following relation,

8.5 β2 / 1 1/ 2

This formula gives an approximate indication of number of blades required for

normal radial impellers. Further he states that the optimum number of blades of a radial

impeller can only be truly ascertained by experiments.

The number of blades in a centrifugal fan varies from 2 to 64 depending on the

application, type and size. Less number of blades is not able to fully impose their

geometry on the flow and the average direction of discharge varies from the blade angle

β2, where as too many of them restrict the flow passage and leads to higher losses.

Pfleiaderer [9] has recommended:

6.5 2 1 / 2 1 β1 β2 /2

Stepanoff (Stepanoff, 1962) has suggested that,

1/3 β2 ---------- (For smaller sized fans, the number of blades is

less than that suggested by Stepanoff method.)

During his further course of study, he considered design of impeller as utmost

important. The main design objective is the design of an individual fan for specific

requirements. Prior to designing an impeller, the designer should select the shape of the

impeller according to the specific requirements. Various design parameters for impeller

design are considered as following:



A. Optimum entry and exit breadth b1 and b2

The factors involved in determining the size of the axial breadth b1 of a blade

entry can be readily obtained. Before the introduction of air into the impeller, the air

must be turned through an angle of 90° from the axis of the suction of the intake duct.

This is analogous to a change of direction occurring at a bend. To avoid this detrimental

influence upon the impeller, separation of flow at the bend must be prevented. The most

effective measure to combat separation at this point is to accelerate the main stream.

Therefore the impeller entry area πd1b1, must be smaller than the intake

opening . This change in area will be designated by ξ,

where F1 is the axial intake area and F1' is the impeller ring entrance area. On

account of a reduction in area caused by a hub of diameter do, then

/ 4 1

Where ξ = 1.2: do = hub diameter. Hence,

B. Entry and exit blades angle β1 and β2

For a given volume V and angular velocity ω, at the rotational speed n, with a

fixed value for d1, a minimum velocity w1 will be obtained.

4 /60 1 ⁄

4 /60 1 sin

The minimum value of w1 as a function of the angle β1 is obtained by equating

(dw13/dβ1) =0. Calculation yields the simple result

tan1

√2

The exit angle β2 will be decided by the computer program, based on maximum

efficiency.

C. Ratio of entry and exit diameter: d1/d2

The ratio of entry and exit diameters d1/d2 can be expressed as follows:



/1 tan

Where t = thickness of blades.

D. The radius of curvature Rb

The radius of curvature of blade Rb is calculated from the following formula:

2 cos sin

Wallace [41] studied and said that for a wide range of positive and negative pre

whirl, it is found that stable operations can be extended to low flow rates by

introduction of positive pre whirl.

R. Subramanian [42] mentioned that the sharpness of the blades at entrance

and the roughness number of the blade surface contributes heavily to the vortex noise.

The blade shape is usually obtained by the approximate single arc method. Design of

blade profile by using point to point method will result in a streamlined flow and less

likelihood of separation at the trailing edge of the blades will occur.

Robert Kazar and John Lynch [43] presented CF fan design for energy

conservation with balancing economic considerations.

S. Sundaram [44] observed that the optimization of number of blades of

centrifugal fan impeller involves a maximization problem of multivariable function with

fluid dynamic constraints. Experimental data based on a simple variation in blade

number alone, keeping other parameters constant, will not yield optimum blade

numbers for a global maximum hydraulic efficiency.

Sankaran and Gopalkrishna [45] found that the absolute velocity is not

uniform near the entrance of the impeller but it is affected by the geometry of the

rotating vanes.

Yadav and Yahya [46] have studied flow visualization and the effect of tongue

area on the performance of the volute casings of centrifugal machines with a swirling

flow free from jets and wakes at their inlet. The flow visualization studies by wool tuft

movements were conducted in the volute channel as well as in the exit diffuser. Flow

separation was observed at high inlet swirl angles near the volute tongue as well as in

the exit diffuser. It was found that the volute performance was strongly dependent on

the tongue area at low and high inlet swirl angles. There is an appreciable pressure



recovery in the radial direction of volute but it is negligible in the tangential direction.

The average velocity in the tangential directions is not constant.

Sane and Shevare [47] dealt with the design of radial impeller through the

superposition of two flows. The first being the flow in an impeller with the infinite

number of blades, obtained directly as a solution of Navier Stoke’s equations for axi-

symmetric, incompressible and inviscid flow. The second being a potential perturbation

due to finite number of blades with the first flow as the onset flow.

Patel, Patel and Shah [48] presented the method, which gives the range of

design constants and rapid selection for optimum design. The specified design method

is wide enough to cover the complete range of centrifugal pumps. The method can be

easily computerized. The actual test performance of pumps designed by this method lies

within acceptance limits.

William C. Osborne [28] has made very good attempt to use simple flow

physics to design fans/blowers. He has used empirical relations for eye velocity,

meridian velocity and casing velocity with respect to impeller tip peripheral velocity.

Relative velocity is considered same for inlet and outlet conditions. This is one of the

major limitations of this design. Suction, impeller, volute pressure losses and leakage

losses are calculated separately. He said that the purpose of fan is to move air/gas

continuously against moderate pressures. Although, a little compression may occur, it is

customary to consider fan as incompressible fluid machine. Osborne has used circular

arc method to construct centrifugal fan blade profile. Blade profile construction

methodology is described as under.

Blade Profile:

The flow of air through the blade passage of a centrifugal fan impeller is often

far from ideal, and the object of design of blade curvature should be to provide the

minimum of flow separation. This is probably best achieved for backward curved fans

by having blades of aerofoil section working at low angle of attack. However design is

still somewhat empirical.

Most of blade Profiles are generally made by circular arc method. When this

method is used, impeller inlet and exit blade angles and are joined by smooth

curve or straight line. A circular arc is convenient to manufacture and have a simple

geometrical construction as given in Figure 2.4.

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Sideris and Braembussche [49] presented a set of detailed experimental data

describing the impeller response to a circumferential variation of the outlet pressure.

These data reveals that the outlet volume influences the flow inside the impeller through

the static pressure variation at the impeller exit and signifies the need of re-evaluation of

theoretical prediction methods. It describes the advantages and disadvantages of the

different geometries, the relation between flow and geometry, and the impact on the

downstream or upstream of impeller, the loss mechanisms and some loss prediction

models are presented. The main purpose of this study is to provide an insight into the

flow structure that can be used later to improve the performance or remediate design

problems. The use of CFD is not discussed here but the flow models presented here may

help to get a better understanding of the CFD output.

G. Karadimas [50] made the optimization of rotor and stator aerofoil section

for the assessment of off-design performance, and the operational stability of the fan. In

the recent past, the performance of transonic fans has been significantly improved. In

addition, through the extensive use of advanced aerodynamic computation codes, the

development time required has been considerably reduced. Methods are used for the

definition of airfoils in quasi-three-dimensional flow with boundary layer optimization

to the analysis of three-dimensional inviscid flow for stage operation at the design point

and in off-design conditions. Detail comparison of full-size component test data with

computation results shows the validity of these methods and also identifies those areas

where research is still required.

Kind and Tobin [51] concluded that large values of rotor exit to inlet area ratio

of fans results in separation of the incoming flow. This paper presents the results of

performance measurements of the mean flow field at rotor inlet and rotor exit for three

squirrel-cage fan configurations. The flow-field measurements were taken with a five-

hole probe for total pressure, static pressure, and the three components of velocity.

Measurements were taken for two different casing throat areas and rotors. For each set

of configuration, flow rate was measured in the vicinity of best efficiency point. Flow

patterns are complex and the reverse flow through the rotor blades was observed even at

the best-efficiency operating condition. This was similar to all fan configurations under

study.

Ishida, Ueki and Senoo [52] highlighted secondary flow occurrence.

According to the theory presented by the authors, the tip clearance loss of an un-

shrouded centrifugal impeller mainly consists of two kinds of losses, one is the drag due



to the leakage flow through the blade tip clearance and the other one is the pressure loss

to support the fluid in the thin annular clearance space between the shroud and the

blade tip against the pressure gradient in the meridional plane without blades. The

former is proportional to the leakage flow or the contraction coefficient of leakage flow.

The authors have conducted performance tests using an impeller with 16 backward-

leaning blades in three blade tip configurations having round edge, sharp square edge,

and edge with an end-plate. The experimental tip clearance effects can be predicted by

assuming reasonable contraction coefficients 0.91, 0.73, and 0.53, respectively. The

impeller efficiency is improved by 1.5% by reducing the contraction coefficient from

0.91 to 0.53, providing that the tip clearance ratio at the exit of impeller is 0.1.

Whitfield [53] illustrates how the initial design can be developed without

recourse to empirical loss models and the associated uncertainties. A fully non-

dimensional preliminary design procedure for a centrifugal compressor is presented.

The procedure can be applied for any desired pressure ratio to develop an initial non-

dimensional skeleton design. The procedure is applied to compressor design for

pressure ratios of 2, 6.5 and 8.

Frost and Nilsen [54] proposed a simple model for estimating the contribution

of the volute to the shut-off head of a centrifugal pump or fan. The model is based on an

assumed linear distribution of tangential velocity in the plane of the cutwater, which

satisfies approximately the continuity condition of zero net flow into the outlet duct.

The contribution of the impeller is assumed to be that given by a solid body rotation at

the angular velocity of the pump from the bore of the inlet duct to the impeller tip. The

simple radial equilibrium equation is then used to calculate the static head rise in both

the impeller and volute. The resultant prediction of shut-off head has been compared to

test data on various pump series made available by courtesy of two European

manufacturers. In all of the series, the impeller diameter has been varied between 100

and 90 to 80 percent of its design value and has been tested in the designed volute.

Since a review of the available literature did not show any previous work of a fully

consistent nature on this topic, the proposed model as described in detail is offered as a

fairly accurate prediction technique for design purposes.

Al-Zubaidy [55] described a scheme for computer aided design and

manufacture of radial impeller. It is starting with one-dimensional calculations. The

principle dimensions (for given performance requirements) are optimized using a

suitable optimization algorithm.



Y. Chon, K. I. Kim and K. Kim [56] attempted to design the optimal

centrifugal fan with specific given conditions by using a knowledge based system which

relies on practical experience in the form of knowledge data base rather than

mathematical representation.

Figure 2.5 gives design algorithm proposed by them.

Figure 2.5 Fan Design Process Algorithms [56]

There are a huge number of possible output answers for one piece of input data.

However, this simulation study demonstrates the optimal answers for different design

conditions and input variables.

For the design, comparison, and critical assessment of all fans, pressure

coefficient, volume coefficient, speed coefficient, diameter coefficient, and noise



coefficient have been used as dimensionless coefficients. To get optimum design, a

precise knowledge of losses is of interest for many reasons. Each individual rule set was

combined with the others in the rule base by the inference engine. This inference engine

serves as the control mechanism for the knowledge-based system. It is an essential part

of the knowledge-based system, as well as a major factor in determining the

effectiveness and efficiency of the system. A simulation study demonstrates the

effectiveness of the proposed approach. Though the design has been expressed in a

mathematical form, the results deviate greatly from the experimental results.

Ayder, Braembussche and Brasz [57] said that static pressure distribution

depends on the relative centrifugal forces due to the swirl velocity in the cross section.

Detailed measurements of the swirling flow in a centrifugal compressor volute with

elliptical cross section are presented. They show important variations of the swirl and

through flow velocity, total and static pressure distribution at the different volute cross

sections and at the diffuser exit. The basic mechanism defining the complex three

dimensional flow structures are clarified. The different sources of pressure loss have

been investigated and used to improve the prediction capability of one-dimensional

mean streamline analysis correlations. The tangential flow loss model under

decelerating flow conditions and the friction loss model are confirmed. New empirical

loss coefficients are proposed for the exit cone loss model and the tangential flow loss

model for the case of accelerating flow in the volute.

Pinarbasi and Johnson [58] derived that as the flow progresses through the

impeller, variations in the tangential direction mixes out, but variations in the axial

direction tends to persist. Hot-wire anemometer measurements have been made in the

vane less diffuser of a 1 meter diameter low-speed backswept centrifugal compressor

using a phase lock loop technique. Radial, tangential, and axial velocity measurements

have been made on eight measurement planes through the diffuser. The flow field at the

diffuser entry clearly shows the impeller jet-wake flow pattern and the blade wakes. The

passage wake is located on the shroud side of the diffuser and mixes out slowly as the

flow moves through the diffuser. The blade wakes, on the other hand, distort and mix

out rapidly in the diffuser. Contours of turbulent kinetic energy are also presented on

each of the measurement stations, from which the regions of turbulent mixing can be

deduced.

S. Yedidiah [59] discussed the present state of the knowledge of the manner in

which the impeller geometry affects the development of head. A comparison with the



test results is a very impressive agreement between theory and practice. This paper

discusses the practical significance of the recent finding that the amount of liquid which

is directly affected by a blade appears to be of the same order of magnitude as the

volume which the blade is displacing. The paper discusses, primarily, causes related to

roto-dynamic pumps, but it is emphasized that this finding is also applicable to a wide

spectrum of additional disciplines.

Mishra Bela [30] critically studied the design methodology as suggested by

Eck Bruno [14] and traced out radial tipped centrifugal blower design methodology.

R. J. Kind [60] describes a method for predicting flow behavior and

performance for centrifugal fans of the squirrel-cage type. Measurements have been

made in an automotive HVAC blower having two different centrifugal fans. This work

is intended to improve the performance of a conventional forward-curved centrifugal

fan. Mean velocities and pressure have been measured using a miniature five-hole probe

and a pressure scanning unit connected to an online data acquisition system. The

measurements showed that performance coefficients are strongly influenced by flow

characteristics at the throat region. Fan performance curves are showing a significant

attenuation of unstable nature achieved with the new fan rotor in the surging operation

range. Based on the measured results, design improvements were carried out.

Dilin, Sakai, Wilson and Whitfield [61] made a detailed experimental study at

the Science University of Tokyo for the performance of two radial-flow fan. This study

includes a volute with a full tongue (such that no recirculation flow occurs) and the

same volute but with the tongue cut back to allow flow recirculation. Velocity and

pressure distributions at a wide range of azimuth angles were obtained experimentally

and are presented. At the University of Bath, a computational model, using the k-έ

turbulence model, has been presented to predict the internal flow in both volutes with

particular attention given to the tongue flow. Predicted flow separation by CFD at the

volute tongue has been demonstrated experimentally by laser sheet studies at the

Science University of Tokyo. The performance of the volutes is discussed and the

computational fluid dynamics (CFD) analysis is used to recommend design

improvements for the volute.

H. W. Oh and M. K. Chung [62] said that usual iterative cut-and-try design

process can be avoided by simply assigning the weighting factors in the range between

0 and 1. Designer can easily find the optimum values of the design variables to meet

their particular requirements of centrifugal pump design. The optimized geometric and



fluid dynamic design curves as functions of the non-dimensional specific speed are

presented. An optimal design code for centrifugal pumps has been developed to

determine the geometric and fluid dynamic variables under appropriate design

constraints. The optimization problem has been formulated with a non-linear objective

function to minimize one, two or all of the fluid dynamic losses. The optimal solution is

obtained by means of the Hooke-Jeeves direct search method. The performance analysis

is based on the mean streamline analysis using the present state-of-the-art loss

correlations. The optimized efficiency and design variables of centrifugal pumps are

presented in this paper as a function of non-dimensional specific speed in the range of

0.5 ≤ Ns ≤ 1.3. The diagrams presented can be used efficiently in the preliminary design

phase of centrifugal pumps.

S. M. Yahya ([9] expressed that on account of low pressures developed by fan

and blowers, they are separate class of turbomachines. They must be designed

separately instead of following compressor or pump design for them. Care must be

taken for Impeller and volute casing design. Energy imparted to the fluid by rotating

impeller will raise its static, stagnation pressure and velocities. The stage work and

stagnation pressure rise for a given impeller depend on the whirl or swirl components

(Vu1 and Vu2) of absolute velocity vectors V1 and V2, respectively. Following relations

are used to find out different stage parameters. The mass flow through the impeller is

ρ1 1 ρ2 2

The area of cross section normal to the radial velocity components

A1 = π d1 b1 and A2 = π d2 b2

Therefore m = ρ1 Vr1 ("π"d1 b1) = ρ2 Vr2 ("π"d2 b2)

The stage work is given by the Euler’s equation as

Wst = U2 VU2 - U1 VU1

In the absence of inlet guide vanes, it is reasonable to assume zero whirls at the

entry. This condition gives,

α = 90° so VU1 = 0 hence U1 VU1 = 0

∴ Wst = U2 VU2

The power required to drive the fan is

P = m (Δho)st = m Cp (ΔTo)st = m U2 VU2

Stage pressure rise

(Δpo)st = (p2 -p1) + 1/2 ρ (V22 - V1

2) = po2 - po1



The stage pressure coefficient

ψst = (Δpo)st /1/2 ρ U22 = 2(VU2 / U2)

The degree of reaction in fan stage is,

Δ / Δ

Where (Δp)rotor = 1/2 ρ (U22 - W2

2 + Vr22)

∴ Rr = 1 - 1/2 VU2 / U2

For radial tipped blades VU2 = U2

∴ Rr = 1/2

Stage efficiency ηst = (Δpo)st / ρ U2 VU2

Static pressure is recovered from the kinetic energy of the flow at the impeller

exit by diffusing the flow in a vaneless or vaned diffuser. The spiral casing as a

collector of flow from the impeller or the diffuser is an essential part of the centrifugal

fan and blower. Diffusers are usually employed on blowers with high heads whereas

volutes are commonly used for fans developing low heads. A diffuser or volute casing

operates on the principle of increasing the pressure energy by decreasing kinetic energy

of flow by diffusing this flow in a vane less or vaned space. A partial increase in head

occurs in the diffuser, surrounding the impeller.

Centrifugal fan with vaned diffuser can give slightly higher efficiency compared

to vaneless fan diffuser/volute casing. For majority of centrifugal fans and low pressure

blowers, the higher cost and size that result by employing a vaned diffuser outweigh its

advantages.

Theoretically, the logarithmatic curve of volute casing begins at the impeller

exit, but in practice this is not possible due to sharp edged lip at base circle of casing,

known as the tongue will be formed. Tongue edge is kept blunt and shifted to reduce

shock losses and improve volute performance.

The volute or scroll casing (in the absence of a diffuser) collects and guides the

flow from the impeller to exit. The volute base circle radius is little larger (0.05 to 0.10

times the impeller exit radius) than the impeller or diffuser exit radius. The vane less

space before volute decreases the non-uniformities and turbulence of flow entering the

volute as well as reduces noise level.

The cross-section of the volute passage may be square, rectangular, circular or

trapezoidal. The fabrication of a rectangular volute from sheet metal is simple while

other shapes can be cast. Rectangular section is very common in centrifugal fan and



circular section is widely used for compressor outlet. Two most widely used volute

design methods are discussed below.

• Free vortex design

Here the flow through the volute passage is assumed to be a free vortex flow.

The axial component of vorticity is zero and angular momentum remains constant.

i.e. rVθ = r2Vθ2 = r3Vθ3 = K

So, Vθ K/r

For constant width of casing for b3 b4, the direction of the streamlines remain

constant, i.e., "tanα Vm/V θ constant"

The total volume flow Q supplied by the impeller is uniformly divided at the

volute base circle. Therefore the flow rate at any section of the volute passage, θ degree

away from the starting is,

Qθ = (θ/360) Q

The flow rate through an infinitesimal section of cross section (dr × b) is,

dQθ = Vθ b3 dr

or dQθ = K b3 dr/r

For the full cross section of the volute passage,

θ

So, / θ/360 /

For a rectangular cross section, it is required to determine the radius r4 of the

volute boundary from θ = 0o to θ = 360o

i.e. θ/360 /

• Constant mean velocity design

For obtaining high efficiency, it is necessary to maintain constant velocity of the

fluid in the volute passage at the design point. This would also give uniform static

pressure distribution around the impeller.

In actual practice, the velocity and pressure vary across the cross section of the

volute passage at any given section. So the mean velocity and pressure along the volute

passage are assumed to remain constant.

For a given value of the mean velocity (Vm), the area distribution is obtained as,

Qθ = Vm Aθ = (θ /360) Q

Aθ = (θ /360) ( Q/ Vm)



For a rectangular cross section,

Aθ = b3 (r4 - r3)

Thus the volute radius r4 for given values of r3 and b3 can be determined.

However, this assumption will be violated at the off-design point. Hence free vortex

design theory is preferable for volute casing.

D. V. Bhopea, P. M. Padoleb [63] made stress analysis of fan impeller by

experimental and finite element method. It has shown that the stress pattern in impeller

components is highly complex. The stresses in the impeller components can be reduced,

by using the stiffening rings on the blades. The flow of centrifugal fan has been also

determined by using the set-up as per AMCA and NAFM guidelines. The effect of the

stiffening rings on the stresses, noise and fluid flow has been also investigated and

discussed.

Tahsin Engin, Mesut Gur, Reinhard Scholz [64] studied that centrifugal fan

when handling gases with temperatures exceeding 800 °C, the conventional steel

impellers would not be operated at such elevated temperatures. In their experimental

study, three semi-open centrifugal fan impellers have been designed and fabricated

using ceramic materials to provide high resistance to temperature. Experiments have

been conducted to investigate the performance characteristics of these impellers and the

deteriorations in their performance due to varying tip clearance. Factors have been

determined to estimate the tip clearance losses. Results showed that the simple impeller

geometries of ceramic materials were less sensitive to the varying tip clearance. In

addition, the gas temperature has been found to have almost no influence on the

performance degradation due to the tip leakage flow.

By studying three dimensional flow fields, it has been deduced that the impeller

with backward-curved blades was very sensitive to the tip clearance, whereas the other

two types were not. The impeller with radial tipped blades 90° showed a weak

dependency on tip clearance. However, for the case of fully radial blades

90° , it has been observed that the fan is almost insensitive to the tip clearance.

However, considerable flow separations have been observed at even in design flow

rates in the blade and scroll passages of this type impeller. The non-uniformity of the

flow field in each fan passages differs considerably from each other and intensifies

particularly near the cut-off regions.



Yu-Tai Lee and et al, [65] presented a design method for re-designing the

double-discharge, double-width, double-inlet (DWDI) centrifugal impeller for the lift

fans of a hovercraft. Given the current high performance of impellers, the design

strategy uses a computational method, which is capable of predicting flow separation

and vortex-dominated flow fields, enabling a detailed comparison of all aerodynamic

losses. The design method, assuming a weak interaction between the impeller and the

volute, employs a blade optimization procedure and several effective flow path

modifications. Simplified CFD calculations were performed on fans with two existing

impellers and the newly designed impeller to evaluate the impeller design criterion. The

calculation was made with the impeller/volute coupling calculation and a frozen

impeller assumption. Further refined CFD calculations, including the gap between the

stationary bell-mouth and the rotating shroud, revealed a reduction in the new impeller's

gain in efficiency due to the gap. The calculations also further supported the necessity

of matching the volute and the impeller to improve the fan's overall efficiency.

Measured data of three fans validated CFD predictions in pressure rise at design and

off-design conditions. CFD calculations also demonstrated the Reynolds number effect

between the model- and full-scale fans. Power reduction data were compared between

the measurements and the predictions along with the original design requirements.

O. P. Singh, Rakesh Khilwani, T. Sreenivasulu, M. Kannan [66] investigated

effect of geometric parameters of a centrifugal fan with backward- and forward-curved

blades. Centrifugal fans are used for enhancing the heat dissipation from the IC engine

surfaces. In the process, the fan consumes power generated from the engine. As a first

step, an experimental setup was developed and prototypes of fans were made to carry

out measurements of flow and power consumed by the fan. The fan mounting setup was

such that fan with uniform blades can be tested. Generally, fans have cut blades on the

vehicle due to mounting accessories. Next, a computational fluid dynamics (CFD)

model was developed for the above setup and the results are validated with the

experimental measurement. Further, parametric studies were carried out to quantify the

power coefficient, flow coefficient, efficiency and flow coefficients formulated as

below:

2 2 /30

/30



The parameters considered in this study are number of blades, outlet angle and

diameter ratio. Figure 2.6 shows backward curved blade fan showing how blades are cut

due to mounting accessories and a line diagram depicting fan parameters.

Figure 2.6 Backward Curved Blade Fan Showing how Blades are Cut Due to Mounting Accessories and a Line Diagram Depicting Fan Parameters

[66]

Figure 2.7 shows developed experimental setup for fan testing. The numbers in

the Figure denotes: (1) volute casing, (2) fan (3) tube connected from volute outlet to

the U-tube manometer, (4) low friction torque measurement machine (5) RPM control

switch, (6) torque value displayer unit (7) optical sensor to measure rpm (8) digital

meter for rpm display.



Figure 2.7 Experimental Setup for Fan Testing [66]

Numeric analysis CFD model was used using moving reference frame for

incompressible flow. The governing continuity and momentum equations Reynolds

averaged Navier-stokes equations (RANS) has following form:

0

Where ρ is the density, μ is the dynamic viscosity, U (U, V, W) is the velocity in

x, y and z direction, p is the pressure, primes denote fluctuating components. The

additional term, uiuj is in the momentum equation, is called Reynolds stress tensor.

Further effect of number of blades (Nb) is investigated and discussed. According

to Bruno (Eck, 1972) the number of blades in fan cannot be determined theoretically.

However, it is time consuming and costly to determine Nb experimentally as it requires

large number of prototypes of fan to be made. CFD has become an important tool to

investigate such kind of problems. The performance characteristics of the backward

curved fans for Nb = 12, 14, 16, 18, 20 and 22 blades is shown in Figure 2.8 from the

CFD model.



Figure 2.8 Performance Characteristics for 12 to 22 Blades [66]

Other fan parameters were kept constant. The main purpose of this discussion is

to provide information about the percentage change in fan performance due to fan

blades alone. From 12 blades to 22 blades, the gain in pressure coefficient, efficiency

and flow coefficient is 4%, 5% and 10.6%, respectively. It is to be noted that from 12 to

22 blades, mass of the fan blades increases about 80% whereas the performance has not

improved proportionally. The relative velocity in the blade passage becomes more

uniform due to proper guidance as Nb increases and hence wakes regions decreases.

This could reduce noise generated due to wake formation. Formation of wake region is

one of the major contributors to the fan losses. Further increase in Nb would deteriorate

the fan performance and boundary layer effects may become dominant.

The results suggest that fan with different blades would show same performance

under high-pressure coefficient. However, the difference between the performances

becomes distinct under low pressure coefficients suggesting that the fan performance

testing should not be done on vehicle level where high pressure coefficients is observed

due to various resistances in the system. The results show that increase in flow

coefficient is accompanied by decrease in efficiency and increase in power coefficient.

Effect on the vehicles mileage due to the use of forward and backward fan is also

discussed. In summary, this study presents a systematic and reliable strategy to

investigate the centrifugal fan performance in automotive applications.



Li Chunxia, Wang Song Linga, Jia Y akuib [67] investigated the influence of

enlarged impeller in unchanged volute on G4-73 type centrifugal fan performance.

Comparisons are conducted between the fan with original impeller and two larger

impellers with the increments in impeller outlet diameter of 5% and 10%, respectively,

for numerical and experimental investigations. The internal characteristics are obtained

by the numerical simulation, which indicate that there is more volute loss in the fan with

larger impeller. Experimental results show that the flow rate, total pressure rise, shaft

power and sound pressure level have increased, while the efficiency have decreased

when the fan operates with larger impeller. Variation equations on the performance of

the operation points for the fan with enlarged impellers are suggested. Comparisons

between experimental results and the trimming laws show that the trimming laws for

usual situation can predict the performance of the enlarged fan impeller with less error

for higher flow rate, although the situation of application is not in agreement. The noise

frequency analysis shows that higher noise level with the larger impeller fan is caused

by the reduced impeller–volute gap.

Yi Xie [68] evaluated performance of two shroud designs having parabolic and

cone shape of a backward inclined (BI) commercial centrifugal fan. The considered fan

that is produced by Nicotra Company has diameter about 400 mm and 11 blades. Whole

device with inlet and outlet channel was numerically simulated in steady state, with two

shroud shape. Results for parabolic shape were verified by performance curves obtained

by experimental tests done by Nicotra. There is a separation region under shroud

because of rapid flow direction changes, from axial direction in inlet to radial in

entrance of impeller. Performance curves show that parabolic shape has better flow

guidance than cone shaped one especially in the impeller outlet, which results in

reduction in flow losses due to recirculation from this region to inlet clearance. Because

of this treatment pressure generation and efficiency are about 3 to 4% and almost 6.5%

more, respectively, for parabolic shape.

Jason Stafford, Ed Walsh, Vanessa Egan A. [69] recorded the thermal

performance characteristics of a range of geometrically scaled centrifugal fan designs

by using velocity field and local heat transfer measurement techniques. Complex fluid

flow structures and surface heat transfer trends due to centrifugal fans were found to be

common over a wide range of fan aspect ratios (blade height to fan diameter). Using the

fundamental information inferred from local velocity field and heat transfer



measurements, selection criteria can be determined for both low and high power

practical applications where space restrictions exist.

Sheam-Chyun Lin, Ming-Lun Tsai [70] made investigations for evaluating fan

performance. An 80 mm-diameter backward-inclined centrifugal fan is chosen to serve

as the research subject for demonstration purposes. Numerical results are utilized to

perform detailed flow visualization, torque calculation, efficiency estimation, and noise

analysis. The results indicate that the fan performance curve and the sound pressure

level (SPL) spectrum of the experiment agree with those of numerical simulations. In

addition, this study proposes two modification alternatives based on the flow

visualization at each operating point, having verified the successful enhancement of fan

performance via numerical calculation. Consequently, this study establishes an

integrated aerodynamic, acoustic, and electro-mechanical evaluation scheme that can be

used as an essential tool for fan designers.

Guopeng Liu and Mingsheng Liu [71] developed a simple in-situ fan curve

measurement procedure using the manufacturers fan curve and one point (air flow and

fan head) measurement according to on site conditions and without interrupting normal

system operations. The in-situ method can simplify air flow measurement if the

manufacturers fan curve is available. Fan air flow measurement continues to be

challenging in HVAC systems. The fan performance curve can be represented as a

multiple order polynomial equation. The in-situ method proposed in this paper makes

use of fan performance curves to predict air flow. Under full speed, the fan curve

equation can be represented as a second-order polynomial equation:

· ·

Where H is a fan head [Pa] under full fan speed, Q is an air flow rate [m3/s]

under full fan speed, and a0, a1 and a2 are fan curve coefficients.

Above equation works well at the normal operating region for most of fans used

in AHUs. If the fan runs under partial speed by the variable frequency drive (VFD), the

fan curve can be represented by equations derived by the fan laws.

This paper presents the background theory, methodology, error analysis and

step-by-step procedure developed for the practitioners. This in-situ method has been

experimentally proven in full-scale air handling unit (AHU) systems. The results show

that the fan curve identified using this simplified approach agrees with the fan curve

identified using the point-by-point direct measurement method. Both the error analysis

and the experiment show that the generated in-situ fan curve with least system



resistance most closely matches the measured in-situ curve (cv-RMSE = 4.7%). The

differences of the fan heads predicted by the fan curves are within the experimental

error range.

Beena D. Baloni, S. A. Channiwala, V. K. Mayavanshi [72] made

experimental study using two different designs of volute casing of a centrifugal blower

with backward blade shrouded impeller. The volute casing designs were based on the

principle of “constant angular momentum” and “constant mean velocity”. For both

design of volute, the flow fields were studied at various angular, radial and axial

locations in the volutes. The experiments were conducted with full throttle open

condition at inlet. Analysis was done with the help of three-dimensional probe, which

gave flow parameters such as stagnation pressure, static pressure and flow directions.

Based on the experimental data, analyzed results were presented for the pressure

recovery coefficient and loss coefficient. Outcome of the work was concluded that the

flow within the volute casing based on ‘‘constant mean velocity’’ design concept gives

better flow conditions than that based on the ‘‘constant angular momentum’’. The

gradient of both the flow parameters were less in case of ‘‘constant mean velocity’’

design, suggests more flow uniformity compared to ‘‘constant angular momentum’’

design concept. Variation in the pressure recovery is larger up to 50% of radial distance

from the impeller towards radial outward direction. Value of loss coefficient was

decreased as flow move from suction to exit of volute.

2.3 Slip Factor

Under actual conditions, the relative flow leaving the impeller of a fan, blower,

pump or compressor will receive less guidance from the vanes and hence real flow is

reduced. This difference in guidance is known as slip. If the impeller could be imagined

as being made with an infinite number of infinitesimally thin vanes, then an ideal flow

would be perfectly guided by the vanes and would leave the impeller at the vane angle.

The concept of slip factor is implied to impeller losses. Slip loss is defined as the

ratio of actual and ideal values of the whirl velocity components at exit of impeller as

shown in Figure 2.9. It has significant effect on fan performance.



Figure 2.9 Actual and Ideal Velocity Triangles at Blade Exit [9]

Mathematically,

The slip velocity is given by,

1

The variation between the actual flow and ideal flow and slip exists due to

impeller entry conditions, finite thickness and number of blades, variation in effective

blade camber line, geometry of impeller, mean blade loading, viscosity of the working

fluid, effect of fluid friction, relative and back eddies in the flow, effect of boundary

layer growth and blockage, separation of flow and friction forces on the walls of flow

passages [22].

For the proper design of centrifugal machines, it is essential to estimate the slip

factor correctly. This variation in the actual and ideal whirl components are suggested in

various slip factor correlations of Stodola, Balje, Stanitz, Pfleiderers, Weisner, Bruno-

Eck and Senoo-Nakase. According to them the major cause of slip factor are the

relatives eddies generated within the meridional region that are dependent on the

geometry of impeller only.

On the basis of fewer historical evidences, approach and experience, this

statement has been challenged and found to be partially correct and factual evidences



have proved that the slip factor not only depends on the geometry of the impeller but

also on the specific speed and flow rate and many more parameters.

Stodola [31] has major contribution towards the concept of slip and slip factor.

He had associated the slip factor of a centrifugal impeller with the relative eddy which

exists between the vanes of the impeller.

Mathematically, Slip Factor

Figure 2.10 shows the flow model with slip, as suggested by Stodola. The

relative eddy is assumed to fill the entire exit section of the impeller passage. It is

considered equivalent to the rotation of a cylinder of diameter d = 2r at an angular

velocity ω which is equal and opposite to angular velocity of the impeller.

Mathematically, slip factor,

1sin

1 ⁄ cot

For radial tipped impeller, β2 = 90°

1

Figure 2.10 Relative Eddies within Blade Passage [31]

The above expressions for the given geometry of flow show that the slip factor

increases with the number of impeller blades. Along with this fact it is concluded that

the number of impeller blades is one of the governing parameters for slip losses.



J. F. Peck [73] published report on his experimental study of the flow in a

centrifugal pump. As a result of his study, he came to the conclusion that the slip factor

must be a function not only of the impeller geometry, but also of the flow rate.

According to him, major cause for slip factor were relative eddies as well as back

eddies. Back eddies are dependent on flow rate. Unfortunately, the supporting

experimental data presented by him were not immune to criticism. This has resulted in

rather poor acceptance of Peck’s theory. Continuing his study, further he added the

effect of impeller blade loading on “head slip”.

Prasad, Ganeshan and Prithviraj [74] found that the fluid deviation at

impeller outlet increased with reduction in volume flow. The flow at the impeller outlet

became more and non-uniform at low volumes and the deviation in meridional plane

was found to be more near the back shroud. This phenomenon increases the slip at

impeller exit.

Sh.Yedidiah [75] carried out series of experiments and proved that Peck’s

conclusion was really correct. Besides Peck’s theory, he also took references of Truscott

G. F. (1963) and Weisner F. J. (1967). He presented factual evidences, which proved

that the slip factor for a given impeller is not constant, but varies with the flow rate. A

new model of the flow through an impeller was established, which gave possible

explanation to the observed discrepancies between the existing theory and reality.

Y. Senoo, S. Maruyama and T. Koizumi, Y. Nakase [76] experimentally

determined slip factors for different kinds of impellers. Big differences were recognized

between experimental values and the predicted values based on various co-relations.

Hence as a result, the blowers which were designed using the predicted slip factor did

not accomplish the design goal. They presented the experimental evidences and reasons

for these differences. They studied viscous effects on slip factor of centrifugal blowers.

In this paper the flow in shrouded centrifugal impellers with backward leaning blades is

analyzed assuming that the flow is quasi-two-dimensional, steady, subsonic and

inviscid, and then the slip factor is corrected to include viscous effects such as

blockage of flow passage and variation of blade shape due to boundary layer, as well as

the change of moment of momentum due to the wall shear force inside the impeller. By

incorporating these corrections the slip factor based on inviscid theory agrees well with

experimental slip factor for various impellers in a wide range of specific speed.

However, the experimental slip factor for high specific speed blowers was considerably

smaller than the prediction based on these equations.



H. Harada [77] presented a modified Wiesner’s slip formula which can give

better slip factor for the three-dimensional impeller. The overall performance of two-

and three-dimensional impellers of a centrifugal compressor were tested and compared.

A closed-loop test stand with Freon gas as the working fluid was employed for

the experiments. The inlet and outlet velocity distributions of all impellers were

measured using three-hole cobra probes. Further, it has also been clarified that the

impeller slip factor is affected by blade angle distribution.

Lal and Vasandani [78] studied slip factor effect on designing of impeller and

concluded that slip factor reduces due to non-uniform velocity distribution at impeller

exit.

R. Ajithkumar [22] observed that the advantages of radial fans and blowers

are:

• More operating range

• Reduced manufacturing cost

• High pressure development per stage

He further adds that the performance of fans/blowers depends upon number of

vanes, which are indefinitely thin, and slip factor is a function of number of vanes,

diameter ratio and outlet blade angle and flow conditions after impeller. He concluded

with the following remarks:

• Stage efficiency is function of stage reaction, which depends upon outlet

blade angle. The smaller the blade angle, the larger the frictional losses.

• Flow disturbances are lesser along the exit width for impellers with

higher blade angles.

He found that slip factor is a function of number of vanes, diameter ratio and

outlet blade angle and flow conditions after impeller. When blade angle is smaller,

frictional losses are larger.

S. M. Miner, R. D. Flack and P.E. Allaire [79] found that there is a

recirculation region within the impeller, which causes negative blade loading. More the

flow below the design flow, the more pronounced is the recirculation. While the tongue

stagnation point moves from the discharge side to the impeller side as the flow is

increased from design to above design. At design flow, slip factor ranges from 0.96-0.7

and computational and measured slip factor lies within 10% deviation.



Deepakkumar M [80] developed an experimental method to determine slip

factor.

S. M. Yahya [9] explained that for the proper design of centrifugal machines, it

is essential to estimate the slip factor correctly. Several co-relations as well as empirical

equations are used for estimating the slip factor. These correlations conclude that for a

given specific machine, the value of slip factor is constant and is dependent of Impeller

geometry only.

• Stanitz’s theory

Stanitz suggests a method which is based on the solution of potential flow in the

impeller passages for β2 = 45° to 90°. The slip velocity is found to be independent of

the blade exit angle and the fluid compressibility. This is given by

11.98

1 ⁄ cot

For radial tipped impeller, β2 = 90°

11.98

• Balje’s theory

Balje has suggested an approximate formula for radial-tipped (β2=90°) blade

impellers. Slip factor,

16.2· /

Where,

K. S. Paeng and M. K. Chung [81] developed a new simple but accurate

correlation for the slip factor of centrifugal impellers. The functional form of the

correlation is obtained by investigating the radius of a relative eddy inscribed by two

adjacent vanes and the exit circle of a flow channel in the impeller. Two functions are

introduced to correct the slip factor obtained by the present relative eddy model with

reference to previous analytical results. The proposed correlation is a function of the

number of vanes (Z), vane exit angle (β2) and the inlet and exit radius ratio (r1/r2). This

presented new correlation for the slip factor is:

1 1 ⁄ ⁄ 0.85

Where f = correction factor, re = radius of relative eddy, = exit vane angle



En-Min Goo, Kwang-Yong Kim [82] developed improved slip factor model

and correction method to predict flow through impeller in forward-curved centrifugal

fan by investigating the validity of various slip factor models. Steady and unsteady

three-dimensional CFD analyses were performed with a commercial code to validate

the slip factor model and the correction method. The results show that the improved slip

factor model presented in this paper could provide more accurate predictions for

forward-curved centrifugal impeller than the other slip factor models since the

presented model takes into account the effect of blade curvature. The comparison with

CFD results also shows that the improved slip factor model coupled with the present

correction method provides accurate predictions for mass-averaged absolute

circumferential velocity at the exit of impeller near and above the flow rate of peak total

pressure coefficient.

Frank Kenyery and José A. Caridad [83] said that empirical correlations have

been widely used to estimate the slip factor. Moreover, these correlations provide a

constant value of the slip factor for a given impeller only at the best efficiency point,

which is an important restriction to the pump performance prediction, considering

that slip factor varies with the pump flow rate. Even in the case of the nominal flow rate,

values for the slip factor produced by correlations could have errors as large as 52% as

is illustrated in Table 2.1.

Table 2.1 Values of the slip factor obtained from correlations [83]

Ns Weisner Stodola Stanitz Simulation Results 1156 0.758 0.681 0.505 0.693

Error in% 9 2 27 - 1447 0.778 0.705 0.604 0.703

Error in% 10 0 14 - 1612 0.829 0.799 0.717 0.716

Error in% 14 10 0 - 1960 0.819 0.776 0.717 0.395

Error in% 52 49 45 - 3513 0.762 0.662 0.604 0.550

Error in% 28 17 9 -

From the results stated above, it is clear that considering the slip factor constant

for the whole operation range of the pump is a remarkable mistake. Moreover, the fluid

dynamics of single-phase flow is quite different from that corresponding to two-phase

flow. Therefore, new approaches to estimate slip factor for centrifugal pumps need to be



developed. This work does not attempt to develop a new correlation for the slip factor

but aims to clear up some misunderstanding with respect to its application. Likewise,

the presented methodology could be used as a trend to follow for subsequent models.

Finally, based on the numerical results, a methodology for prediction of the pump head

is presented.

Theodor W. and Von Backstop, [84] presented in one equation a method that

unifies the trusted centrifugal impeller slip factor prediction methods of Busemann,

Stodola, Stanitz, Wiesner, Eck, and Csanady. The simple analytical method derives the

slip velocity in terms of a single relative eddy (SRE) centered on the rotor axis instead

of the usual multiple (one per blade passage) eddies. It proposes blade solidity (blade

length divided by spacing at rotor exit) as the prime variable determining slip.

Comparisons with the analytical solution of Busemann and with tried and trusted

methods and measured data show that the SRE method is a feasible replacement for the

well-known Wiesner prediction method. It is not a mere curve fit, but is based on a fluid

dynamic model: it is inherently sensitive to impeller inner-to-outer radius ratio and does

not need a separate calculation to find a critical radius ratio: and it contains a constant,

F0, that may be adjusted for specifically constructed families of impellers to improve the

accuracy of the prediction. Since many of the other factors that contribute to slip are

also dependent on solidity, it is recommended that radial turbo machinery investigators

and designers investigate the use of solidity to correlate slip factor.

Xuwen Qiu,Chanaka Mallikarachchi, Mark Anderson [85] proposes a

unified slip model for axial, radial, and mixed flow impellers. For many years,

engineers designing axial and radial turbo machines have applied completely different

deviation or slip factor models. For axial applications, the most commonly used

deviation model has been Carter's rule or its derivatives. For centrifugal impellers,

Wiesner's correlation has been the most popular choice. Is there a common thread

linking these seemingly unrelated models? This question becomes particularly

important when designing a mixed flow impeller where one has to choose between axial

or radial slip models. The proposed model in this paper is based on blade loading, it

means, the velocity difference between the pressure and suction surfaces, near the

discharge of the impeller. The loading function includes the effect of blade rotation,

blade turning, and the passage area variation. This velocity difference is then used to

calculate the slip velocity using Stodola's assumption. The final slip model can then be

related to Carter's rule for axial impellers and Stodola's slip model for radial impellers.



This new slip model suggests that the flow coefficient at the impeller exit is an

important variable for the slip factor when there is blade turning at the impeller

discharge. Some validation results of this new model are presented for a variety of

applications, such as radial compressors, axial compressors, pumps, and blowers.

Alberto Scotti Del Greco, Fernando Roberto Biagi, Giuseppe Sassanelli,

Vittorio Michelassi [86] observed that the preliminary design of new centrifugal stages

often relies on one-dimensional codes implementing the concept of slip factor. This

parameter plays a primary role in the stage design process since it directly affects the

calculation of the impeller work coefficient and hence of the components situated

downstream. Classical slip factor correlations may not always provide a satisfactory

accuracy and generally they fail while attempting at covering a design space in a wide

range of flow coefficients and peripheral Mach numbers. In that case the preliminary

design has to be refined with more advanced tools, such as computational fluid

dynamics (CFD). Often this process needs to be repeated several times before the

design cycle ends. In order to predict more effectively the work coefficient as well as to

reduce the number of iterations between 1D/CFD codes during the design activity, a

new correlation has been developed, which is based on a large number of historical data

from both CFD and experimental results. Accurate statistical analyses have shown that

slip factor can be strongly linked to significant flow and geometry parameters by means

of the outlet deviation angle. As the available calibration dataset gets more and more

populated, the presence of specific constants in the structure of the correlation allows

the designer to improve the accuracy of predictions.

Mohamad Memardezfouli, Ahmad Nourbakhsh [87] have compared

experimental slip factors with the calculated theoretical values and found that they are

in good agreement at design point conditions but deviates at off design conditions. In

the present work, the slip phenomenon at the impeller outlet is studied experimentally

for five industrial pumps at different flow rates and the slip factor is estimated for each

of these cases. Theoretical slip factors are calculated using several existing methods

taking into consideration the main geometric parameters of the impeller.

Theoretical blade-to-blade analysis and experimental measurements at the outlet

of radial and mixed-flow impellers have shown a difference between the exit flow angle

β2 and the geometrical blade angle β2'. This angular difference corresponds to an

absolute- tangential velocity difference and characterizes the slip phenomenon in the



flow. The local slip factor at point i along a streamline, at the impeller outlet is defined

by:

⁄

The mean slip factor (called simply ‘‘slip factor”) can be written as:

⁄ · /

In which CU2 is a mass-average value. Its value depends on the calculation

method (two-or three-dimensional calculation). The theoretical slip factor is affected by

the inevitable slip of the non-viscous flow in the impeller channel. This slip in return

depends only on the geometrical parameters.

Figure 2.11 shows impeller discharge velocity diagram showing slip.

Figure 2.11 Impeller Discharge Velocity Diagram [87]

The local slip factor µi in every point of the flow has been calculated by the

potential-flow method. Local slip-factor distribution in the blade to blade channel, for

mean stream surface is shown in Figure 2.12.



Figure 2.12 Local Slip-Factor Distributions in the Blade to Blade Channel for Mean Stream Surface [87]

From Figure 2.12 it is observed that in the blade to blade flow channel the local

slip-factor distribution is non-uniform. Its highest values are located along the pressure

side of the blade. We also notice that the value of the local slip factor can be higher than

1. This means that the streamlines acquire a larger relative flow angle than that of the

blade surface at the same radius. The disadvantage of this method is that it is time-

consuming. This method is used to ascertain the accuracy of the values of the

theoretical slip factor.

The experimental slip factors are compared with the calculated theoretical

values. It was observed that at the design-point condition, the experimental values are in

a good agreement with the theoretical values. However, there are significant

disagreements between the theoretical and experimental values at off-design regiments.

The difference is more apparent at low flow rates. It is also found that the slip factor

depends on the impeller-outlet velocity profile. By defining a flow distortion

coefficient, a correlation is derived for evaluating the slip-factor value for off-design

conditions. Finally, a slip factor table is provided to calculate the slip factor using the

geometry of impeller.

Donghui Zhang, Jean-Luc Di Liberti, Michael Cave [88] presented

a numerical study for the effect of the blade thickness on centrifugal impeller slip

factor. The CFD results show that generally the slip factor decreases as the blade

thickness increases. Changing the thickness at different locations has different effects

on the slip factor. The shroud side blade thickness has more effect on the impeller slip

factor than the hub side blade thickness. In the flow direction, the blade thickness at



50% meridional distance is the major factor affecting the slip factor. The leading edge

thickness has little effect on slip factor. There is an optimum thickness at the trailing

edge for the maximum slip factor. For this impeller, the hub side thickness ratio of 0.5

between the trailing edge and the middle of the impeller gives the highest value of the

slip factor, while the ratio of 0.25 at shroud side gives the highest value of the slip

factor. A blockage factor is added into the slip factor model to include the aerodynamic

blockage effect on the slip factor. The model explains the phenomena observed in the

CFD results and the test data very well.

2.4 Hydraulic, Capacity and Power Losses

Efficiency is the most important performance parameter for all kind of turbo

machines. Over the years, enormous efforts have been made to improve the efficiency.

Clearly, efficiency of any machine depends on the losses occurring in the machine at

different stages. The centrifugal stages, on account of the relatively longer flow

passages and greater turning of flow, suffer higher losses as compared to axial type.

Therefore it is essential to understand the loss mechanisms to predict the actual

performance of a blower/fan.

Overall efficiency of any turbomachine depends on shaft power input and

airpower developed considering various losses occurring at different stages. There are

different types of losses occurring when the fluid passes from inlet duct to outlet duct of

a turbomachine. The major losses are identified and classified into three categories.

They are hydraulic or pressure losses, mechanical or power losses and flow or leakage

losses [28]. Hydraulic losses reduce the available pressure head developed by the

impeller thereby reducing system’s hydraulic efficiency. Hydraulic losses include

pressure losses due to fluid friction, secondary flow, shock and diffusion. Mechanical

losses are encountered mainly due to disc Friction and friction between rotating shaft

and the journal bearing. Leakage losses reduce the quantity of fluid delivered per unit

time and hence reduce the volumetric efficiency. Overall efficiency of any machine

depends on the losses occurring in the machine at different stages. Hence there is a need

to understand the sources of various losses in turbo machine and consequently a

mechanism to be evolved to estimate those losses accurately.

Andre Kovats [27] explains that duct friction loss is a function of viscosity and

has effect of which is proportional to the ratio of mass force (inertia) to shear force (a

dimensional number called Reynolds’s number). When the flow becomes turbulent,



roughness of the wall through which the fluid is flowing should also be accounted for

losses.

When a disc rotates in a casing, the fluid enclosed between the surfaces of the

moving disc and the stationary casing also rotates, with an angular velocity that has a

value between zero to the tangential velocity (u) of the rotating surface. Due to the

centrifugal force of the rotating fluid, the fluid pumped to the outer diameter of the

casing, where it returns to the center along the stationary wall of the casing as shown in

Figure 2.13. This additional flow produces friction loss, which is different from those

produced in ducts. Friction losses in the impeller can be approximately 50% higher than

the duct friction losses. The friction on the shrouds of centrifugal impeller is a source of

appreciable losses. In a diffuser or volute, the velocity head is converted into pressure

head. This process depends on the efficiency of the diffuser, which is a function of the

roughness of the diffuser and the approach conditions.

Figure 2.13 Disc Friction (Right) and Velocity Distribution in Gap ‘S’ For Laminar and Turbulent Flows (e = Boundary Layer Thickness) [27]

Livshits [89] noticed that the losses increase quickly with positive incidence.

Dean and Senoo [90] are the first to develop an analytical model to explain the

losses resulting from the shedding of rotating wakes into the diffuser inlet. Results from

an experimental study of flow behavior at the inlet of a vane less diffuser of a

centrifugal compressor are presented. Measurements from a crossed hot-wire probe are

given for operating points having inlet flow coefficients ranging from 0.006 to 0.019 at

different Reynolds numbers. Instantaneous, time-averaged, and phase-averaged absolute



velocity and flow angle at the diffuser inlet are deduced from the hot-wire signals after

correction for mean density variations. These results show how flow behavior varies in

stable, rotating stall and surge regimes of compressor operation.

A. J. Stepanoff [91] considers hydraulic losses as the most important and but

least known losses in turbo-machines. He writes that the hydraulic losses are caused by

skin friction and eddies. Separation losses occur due to changes in direction and

magnitude of the velocity of flow. The latter group includes shock loss and diffusion

loss.

He further adds that in the channels from the inlet to the discharge nozzle, area

or shape is not constant. It also includes rotating element which upsets the velocity

distribution and complicating the study of hydraulic losses as given in Figure 2.14, 2.15

and 2.16, respectively.

About leakage loss, he adds that the flow through the impeller is greater than the

measured capacity by the amount of leakage, and the ratio of the measured capacity Q

to the impeller capacity Q + QL is the volumetric efficiency.

Figure 2.14 Hydraulic Losses [91]

Figure 2.15 Q-H Curves Obtained by Subtraction of Hydraulic Losses

from Input Head [83]

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Mechanical losses include power lost by friction in the bearings and seals. These

losses can be easily measured.

Austin H. Church [26] states that the equation which forms the basis of pump

and blower design is based on three assumptions,

(1) The fluid leaves the impeller passages tangentially to the vane surfaces,

or there is complete guidance of fluid at the outlet.

(2) The impeller passages are completely filled with actively flowing fluid at

all times.

(3) The velocities of fluid at similar points on all the flow lines are the same.

The head, which is based on these assumptions, is called virtual head. The

deviation of actual conditions from these assumptions is considered as losses.

Circulatory flow is responsible for causing the fluid to leave the wheel at an

angle less than the vane angle as shown in Figure 2.18. (Decrease in β2)

Figure 2.18 Circulatory, Through and Resultant Flows in Vanes Passage

[26] Loss of head due to friction increases approximately as the square of the

velocity. Since the areas remain constant, the velocity is proportional to flow and the

loss increases approximately as the square of the flow. The losses also increase with the

wetted areas of the passages and roughness of the surfaces of the impeller, diffuser or

volute and casing passages.

The type of flow existing in a pump or blower is always turbulent, the Reynolds

number is always well above the critical value. At certain sections in the machine, such

as at the inlet and outlet edge of the vanes in both the impeller and the diffuser and in

the return guide vanes, the flow is seriously disturbed with a resultant loss of head.

These losses are known as turbulence losses or shock losses. This loss is also

proportional to the velocity squared. The angles of the impeller and diffuser vanes are

not correct at off-design operating conditions leading to increase in turbulence losses.



Sudden changes of sections or sharp turns should be avoided or minimized as much as

possible.

Disc friction is the power required to rotate a disc in a fluid. The usual impeller

has enclosed sides, which rotate in the fluid and the power required for this rotation is

supplied by the driver. The fluid in action is thrown out ward by the centrifugal action

and circulates back toward the shaft to be pumped again.

Leakage loss is due to leakage flow of compressed fluid back to the initial

conditions. The leakage has no effect on the head of the pump or blower but it lowers

the capacity and increases the power required to drive the machine.

Mechanical losses include the frictional losses in the bearing and the packing

boxes. They are usually taken to be 2 to 4% of the shaft power, the larger figure being

used for smaller machines. They are nearly constant for a given speed of rotation.

Development of actual head-capacity curve from the virtual as per Figure 2.19

and development of brake horsepower –capacity curve from the virtual as per Figure

2.20 are shown.

Figure 2.19 Actual Head Capacity Curve from the Virtual [26]

Figure 2.20 Development of Actual Brake Horsepower Capacity Curve from the

Virtual [26]



Between the impeller and diffuser (volute) outlets, the losses are much higher as

converting kinetic energy into pressure energy which is inefficient process. About 40-

60% of velocity head appears as pressure, remainder being lost in turbulence and

friction.

R. C. Worster [92] stated that at low flow rates, the volute induces flow

recirculation in the impeller and at high flow rates, the energy losses in the discharge

branch become severe.

D. J. Myles [33] enumerates following observations after measuring losses from

tests on five centrifugal fan impellers of different blade angle, running at constant speed

in a given volute. Impeller and volute losses, expressed as a fraction of the dynamic exit

pressure relative to impeller and volute, respectively, are correlated with a diffusion

factor over a wide volume flow range. The results are applied to other impellers and

volutes. The low volume flow range of operation is also considered.

• Fluid drag increases to high proportions as diffusion through the impeller

becomes excessive.

• As the surface area of the blade in general decreases as the outlet angle

increases.

• A great deal of separation occurs on the high angle blade impellers.

• Leakage disturbs main flow field.

• Diffusion loss becomes more predominant as the specific speed is

increased.

Dr. Bruno Eck [14] first dealt with impeller friction or disc friction loss

experimentally. The process is described as when air adheres firmly to the surface of the

rotating disc and is caused to move in an angular direction with the peripheral velocity

of the disc. In the disc boundary layer, the velocity of the air which starts at a value

equal to that of the peripheral velocity of the disc gradually becomes reduced to the

velocity of the stream. The air carried along the disc is subjected to a centrifugal force,

which tends to project the air from the center towards the outer edge of the impeller as

given in Figure 2.21. This internal motion is at the expenditure of energy, which

therefore can be classified as loss.



Figure 2.21 Circulation Caused by Impeller Friction and Boundary Layer Motion

Due to Impeller Friction [14]

Impeller loss has two components namely Impeller entry loss and friction loss in

impeller. Entry losses arise from a change of direction in the impeller, it means upon

entry into the impeller intake the air is diverted through an angle of approximately 90°

before entry into the blade cascade. These losses are comparable to losses at bends,

which are dependent upon the values of c0 and c1 as given in Figure 2.22.

Figure 2.22 Entry Losses Due to Change of Flow from Axial to Radial Direction

[14] The greatest losses arise from the passage of fluid through an impeller.

Determination of the degree of loss is difficult to calculate since the losses arising from

separation of flow are impossible to access with accuracy. The eddy zones are unstable.



Therefore, one experimental coefficient cannot be applied to different designs of

impeller. The friction loss in impeller consists of Retardation loss and Resultant

pressure loss. Shock losses arise due to variation from the normal volume flow given in

Figure 2.23.

Figure 2.23 Entry Velocity Triangles Showing Shock Loss [14]

Shock losses can be classified into impeller entrance loss and guide vane loss.

The diameter ratio (d1/d2) has a deciding influence on this loss. In order to minimize this

loss, the ratio d1/d2 should be as small as possible. High values of pressure coefficient

(ψ) reduce shock losses. The guide vane loss arises due to the use of guide vanes at the

entry. The change in the normal volume flow causes shift in the values of the velocity

triangle as per Figure 2.24.

Figure 2.24 Velocity Triangle Showing Losses Due to Guide Vanes [14]



Impeller entry losses, friction losses in impeller and shock losses are derived as following: A. Impeller Entry Losses

These losses may arise from a change of direction in the impeller, it means

upon entry into the impeller intake: the air is diverted through an angle of approx

900 before entry into the blade cascade. The entry losses pent can be expressed as

follows: ∆

∆ 2⁄

Where,

1

1775 ⁄ ⁄

b2=Outlet breadth, c2m

= Average outlet peripheral velocity, d2= Outlet

diameter, c1= Absolute velocity at inlet.

B. Friction Losses in the Impeller

Friction losses are the greatest losses arise from the passage of a fluid through

an impeller. Determination of the degree of loss is difficult to calculate. This is

because the losses arising from separation of flow are impossible to assess with

accuracy. However, if there are cases where no separation of flow exists, one can

treat them in a manner applicable to losses arising from pipe friction. From this

assumption, the friction losses in the impeller pimp can be expressed as follows:

∆∆

12 2 4 1 / sin

Where C1: surface roughness: vx: ratio of relative velocity: l: length of curve:

cf=0.004-0.0045: β m : average angle: z: number of blades: b: breadth and

1

sin



C. Shock Losses

The direction of the relative flow will no longer coincide with the blade angle

if the normal volume flow is varied. As a result of any variation from the normal

volume flow, a loss called a "shock loss" arises. This loss pshk is given by,

∆∆ 1

where: V=0 .7 -0 .9and Vx= variation volume flow from the normal volume

flow.

Clearance loss arises due to clearance between the impeller and sealing lip of the

casing. A small quantity of the total volume passed through the impeller will not

emerge in the volume discharge, so that the work done on this quantity to raise its

pressure to that at discharge will be lost. Between the shaft and impeller, there is also a

small clearance through which leakage can occur, but this is neglected because of the

relatively small shaft diameter as shown in Figure 2.25 and 2.26.

Figure 2.25 Clearances Loss [14]

Figure 2.26 Losses for Different Clearances as a Function of the Diameter Ratio

[14]



Diffuser losses are due to conversion of kinetic energy of air discharged by the

impeller into pressure energy in the diffuser or volute. This process is generally

accompanied by huge pressure loss. Because of this, the ratio of the kinetic energy to

the total energy is kept as low as possible.

Bearing loss arises from bearing friction due to bearings used to enclose the

drive shaft. In majority of the cases this loss is exceedingly small. This loss is

proportional to the weight of the rotor and the peripheral velocity of the shaft journal.

The power supplied to the centrifugal fan stage is the power input at the

coupling less the mechanical losses on account of the bearing, seal and disc friction.

The aerodynamic losses occurring in the stage during the flow processes from its entry

to exit are taken into account by the stage efficiency.

For the purpose of fan performance, there are distinct advantages in subdividing

efficiency into appropriate sections according to the type of loss involved. This

subdivision is convenient, for example, if individual losses are examined at a later date

or if only certain losses can be measured.

• Hydraulic Efficiency

All head losses which are taking place between the stage (which means the

impeller inlet and outlet) are considered for the hydraulic efficiency. These include skin

friction losses along with the fluid path from the inlet to the discharge losses due to

sudden change in area or direction of flow and all losses due to eddies.

Considering all the losses in the fan:

η Δ / Δ

• Volumetric Efficiency

Beside the head losses there are capacity losses known as leakage losses. These

take place through the clearance between the rotating and stationary parts of the

machines. The capacity available at the discharge is smaller than that passed through the

impeller by the amount of leakage. The ratio of the two is called the volumetric

efficiency.

η Q

Q QL

• Mechanical Efficiency

Mechanical losses are made up of bearing and transmission losses like gear,



belt and V- belt losses.

ηm Shaft Power / Input Power

• Total/overall Efficiency

If a particle of air from its entry point into the fan to its discharge from the fan

has been traced, it can be found that the pressure losses are entry loss, friction loss in

the impeller, and shock loss. Therefore, fan efficiency can be expressed as the ratio

of actual work done on the air delivered to the work applied at the shaft coupling is

called fan total efficiency.

ηT = Δp Q / Power Required = ηT = ηhyd ηvol ηm

∆

∆ ∆ ∆ ∆

S. Yedidiah [75] states that according to airfoil theory, the head increases with

the amount of flow rate that the airfoil is displacing in a unit of time. When impeller is

cut down to a smaller diameter, an increase in the loss of head occurs due to the casing.

It results in increase in skin friction and shock losses at higher flow rates. Preliminary

studies show that the distribution of the theoretical heads along the outlet edges can

have a profound effect on the overall efficiency.

A. Satyanarayana Reddy [93] concludes that surface roughness reduces

impeller efficiency and also head and overall efficiency. He suggests that efficiency of

fan/blower can be improved by machining and polishing flow passages.

William C. Osborne [28] observes that the actual performance of a centrifugal

fan at the design point differs from that predicted by Euler’s equation at design point

of operation as follow:

Wst = U2 VU2 - U1 VU1

Graphical presentation of actual performance of fan with respect to ideal is

shown in Figure 2.27. Part of this difference can be accounted for by an adjustment for

inter blade circulation as per Figure 2.28 which results in a reduction of the work done

by the impeller.



Figure 2.27 Effect Losses in a Backward Curved Centrifugal Fan [28]

Figure 2.28 Inter Blade Circulation [28]

Other factors, which contribute to reduction in output, are as follows:

1) Internal volumetric leakage between the impeller inlet and casing, and also

where the drive shaft enters the casing.

2) Pressure loss within the fan assembly, which comprises three components:

a. Loss due to turning of air through 90° from axial to radial direction.

b. Loss due to flow separation within the blade passages.

c. Loss due to retardation of flow velocity and eddy formation in the

passages of casing.

3) Power loss due to fluid drag on the reverse surface of the impeller back plate.



The shapes of characteristic curves of centrifugal fan are shown in Figure 2.29.

Figure 2.29 Centrifugal Fan Characteristics [28]

Actual performance of a centrifugal fan differs from that predicted above. This

difference exists due to hydraulic, volumetric and power losses occurring within flow

passage. These losses reduce the work done by the impeller. Losses occur in stationary

as well as moving parts of the fan. The various major losses are:

• Clearance and Leakage Losses

Certain minimum clearances are necessary between the impeller shaft and the

casing, and between the outer periphery of the impeller eye and the casing. Employing

glands minimizes the leakage of the air or gas through the shaft clearance.

On account of the higher peripheral speed and larger shaft diameter, it is very

difficult to provide sealing between the casing and the impeller eye tip. The leakage

through this clearance from the impeller exit gets re-circulated and additional work is

done on a portion of the impeller flow, which does not reach the stage exit. This loss is

governed by the clearance, diameter ratio (d2/d1), and the pressure at the impeller tip.

Static pressure at the impeller exit is high for a higher degree of reaction.

Internal volumetric leakage between the impeller inlet and casing inlet, and also

where the drive shaft enters the casing, is likely to be more serious, and may be given

similar fashion to flow through orifice. Leakage loss is approximated by:

2



Where coefficient of discharge Cd is 0.6 to 0.7.

• Hydraulic or Pressure Losses

Major portion of hydraulic or pressure losses is due to fluid friction in stationary

surfaces and rotating blade passages. The pressure losses that take place along the

various flow passages such as inlet duct, impeller entrance, impeller, volute and outlet

duct are collectively considered as hydraulic losses. Losses due to fluid friction depend

on the friction factor, passage length and square of the fluid velocity. Therefore, a stage

with relatively longer impeller, diffuser and volute passages and higher fluid velocities

shows poor performance.

There is little information available on pressure losses within fan assembly. It is

felt to be reasonable to consider three phases of losses.

• Impeller Entry Losses

Air enters the impeller eye through a reducing section from the casing inlet duct.

Fluid turns through a right angle prior to entering the impeller inlet blade passages. The

loss here may be written:

∆p12

Where ki is a loss factor probably of the order of 0.5 to 0.8 and Vo is the air

velocity at impeller eye.

• Impeller Passage Losses

Pressure loss will occur within the blade passage due to flow separation since

the relative velocity of the air decreases due to passage friction. This loss may be

written as:

∆12 W

(At design point of maximum efficiency kii is in order of 0.2 – 0.3 for sheet

metal blades and rather less for aerofoil section).

• Diffuser or Volute Losses

The diffuser or volute casing is designed with the intention of permitting free

vortex flow conditions. Such kind of perfect flow is not available in practice. There is

almost 2.5 times [28] increase of area from impeller exit blade passage to the volute

casing inlet. There is thus a tendency of retardation of flow velocity, with resultant eddy

formation. However, it is not east to compare flow under these conditions with that at a

sudden enlargement in normal pipe flow. Losses in the diffuser also occur due to



friction and flow separation. It seems reasonable to express this pressure loss as

following:

∆12 V

V4 is average velocity at fan outlet. At maximum efficiency, kiii is of the order of

0.4 and will vary with deviation from design conditions.

• Mechanical or Power Losses

There may be power loss due to fluid drag on the reverse surface of the impeller

back plate. Disc friction loss due to fluid friction around the rotating impeller and losses

in bearings and transmission devices are considered as mechanical or power loss.

The power required to start rotating a disc in a fluid is known as the disc

friction. This power is transformed into heat and may appreciably increase the

temperature of the fluid.

The disc friction loss is due to two actions occurring simultaneously. It includes

actual friction of the fluid on the disc and a pumping action. The fluid, which is in

contact with the disc or near to it, is thrown outward by the centrifugal action and

circulates back towards the shaft which is to be pumped again and again as shown in

Figure 2.30. This may be significant for large fans. The loss may be estimated as:

T ρ ω

5

(Where f is material friction factor in order of 0.005)

Bearing loss or transmission loss occurs when bearings or transmission devices

are incorporated to support the drive shaft and to transmit the power from motor to the

drive shaft of the blower/fan.

Figure 2.30 Circulation Caused by Impeller Disc Friction [26]



V. Sivakumar [21] found that flow coefficients for radial fan and blowers

ranges from 0.25 to 0.3. His conclusions are:

• Increase in vane angle at outlet increases volume flow.

• There is a marked increase in efficiency by the use of vane less diffuser

and also efficient operating range is extended.

• Flow leaving the impeller is not uniform. Flow near back shroud is more

disturbed than the front shroud. This indicates the presence of thick

boundary layer in this region.

• Flow inside the vane less diffuser is smoother than that in the volute

casing (without vane less diffuser) for the same flow coefficient.

• Return flow and hence the separation regions are encountered near the

back shroud at the exit of the diffuser.

• Radial vanes give better efficiency compared to forward curve vanes.

J. H. Bunjes, J. G. H. Opde woerd [94] concludes that:

• Hydraulic friction losses are proportional to impeller relative velocity

head and depend upon the geometry of the passages and the friction

coefficient determined by surface roughness and Reynolds number.

• Blade loading losses results from blade lift, incidence and velocity

distribution.

• Mechanical losses include disc friction loss resulting from the velocity

distribution profile in the space between the impeller shrouds and pump

casing and seal friction and bearing losses.

• Volumetric losses are due to internal leakage in the pumps through the

wear ring clearances and balance drum in the case of multi stage pumps.

• Impeller tip clearance losses are determined by the clearance between the

impeller blade tips and the pump housing.

Kamaleshaiah, Venkatrayulu and Ramamurthy [95] presented an improved

method for predicting the performance of a centrifugal compressor stage. The prediction

method is based on one-dimensional approach with empiricisms for the loss models and

boundary layer growth within the blade channel.

For a given overall geometry of the compressor and inlet flow conditions, the

method evaluates quite rapidly the compressor performance characteristics with a

reasonably acceptable error. The method is validated with a few typical compressor



configurations and their experimental performance maps available in literature. The

predicted characteristics are in close agreement with the experimental results.

R. K. Srivastava [96] concludes that:

• Low specific speed centrifugal pumps are not giving good performance

due to more disc friction and hydraulic losses.

• As specific speed decreases, hydraulic and disc friction losses increases.

• Losses due to over lapping of boundary layers are applicable in low

specific speed pumps.

Farge, Johnson and Maksoud [97] said that reduced static pressure

distribution is little affected by tip leakage. However, the small decrease in the blade-to-

blade pressure gradient close to the shroud can be activated to tip leakage. The effects of

tip leakage have been studied using a 1-m-dia shrouded impeller where a leakage gap is

left between the inside of the shroud and the impeller blades. A comparison is made

with results for the same impeller where the leakage gap is closed. The static pressure

distribution is found to be almost unaltered by the tip leakage, but significant changes in

the secondary velocities alter the size and position of the passage wake. Low-

momentum fluid from the suction-side boundary layer of the measurement passage and

tip leakage fluid from the neighboring passage contributes to the formation of a wake in

the suction-side shroud corner region. The inertia of the tip leakage flow then moves

this wake to a position close to the center of the shroud at the impeller outlet.

Y. Senoo and H. Hayami [98] have discussed about effects of losses on input

power and efficiency as following:

• The input power to the blower/fan is increased due to the additional

moment arising out of disc friction and mechanical friction at the

bearings and seals. These effects may be handled as mechanical

efficiency.

• The effective output power is considerably reduced by pressure losses in

the impeller, in the diffuser and in the casing. Pressure loss in an

impeller is the sum of various kinds of losses such as friction loss,

deceleration loss: secondary flow loss and incidence loss. These losses

are estimated based on experimental data for respective types of

impellers. Further, about 30% or more of the kinetic energy at the exit of



the impeller is not converted into pressure in the diffuser. Such pressure

losses may be handled as hydraulic efficiency.

• If a part of fluid at the impeller exit is leaked outside or returned to the

suction port after it loses the angular momentum, the input power to the

blower/fan is increased in proportion. The effect may be handled as

volumetric efficiency.

Johnson and Farge [99] have presented lecture notes. These lecture notes

provide an overview of the different inlet and outlet volutes for radial impellers. It

describes the advantages and disadvantages of the different geometries, the relation

between flow and geometry, the impact on the downstream or upstream impeller, the

loss mechanisms and some loss prediction models. The main purpose is to provide an

insight into the flow structure that can be used later to improve the performance. The

use of CFD is not discussed but the flow models presented here may help to get a better

understanding of the CFD output. Base on their study, they stated that the impeller

efficiency is reduced by about 8.5% by the hub inlet distortion for this impeller. This is

largely due to separation of the pressure side boundary layer at the leading age that may

be avoided in other impellers.

Gandhi and Subir Kar [100] studied that impeller friction loss can lower the

predicted head and the recirculation can shift the predicted curve to smaller values of

the net pump flow rate. Analysis shows the influence of volute in predicting the pump

performance and yields a modification to the impeller head due to mechanical energy

losses in the volute. The volute flow is equally dependent on the geometry as on the

impeller exit flow conditions. The later one depends on the volute circumferential

pressure distortion. This means that any prediction method should account for this

strong interaction. Swirl is the main source of losses in a volute. Optimum volute

performance requires minimum radial velocity at impeller exit. Simultaneous

optimization of the impeller and the volute is recommended.

J. D. Denton [34] defines loss as ‘any flow feature that reduces efficiency of a

turbo machine’. Further, he categorizes losses as

1. Profile Loss

2. Secondary Loss (End Wall Loss)

3. Tip Leakage Loss



Profile loss is generated in the blade boundary layers well away from end walls.

The extra loss arising at a trailing edge is usually included as profile loss. End wall loss

or secondary loss arises partly from the secondary flows generated when the annulus

boundary layers pass through a blade row. Secondary loss is sometimes taken to include

all the losses that cannot be otherwise accounted for.

Tip leakage loss arises from the leakage of flow over the tips of rotor blades.

The detailed loss mechanisms clearly depend on whether the blades are shrouded or un-

shrouded.

He suggests the following loss coefficients for better understanding of flow in

turbo machines.

• Stagnation pressure loss coefficient ⁄

• Energy or Enthalpy loss coefficient ⁄

• Entropy loss coefficient ·∆

Where p01, p02 are stagnation pressure at inlet to blade row or stage and

exit from blade row or stage, respectively.

p1 is static pressure at inlet to blade row or stage.

h2, h2s are static and isentropic enthalpies at exit from blade row or stage,

respectively.

h01, h1 are stagnation and static enthalpies at inlet to blade row or stage,

respectively.

T2 is static temperature at exit from blade row or stage.

ΔS is change in specific entropy.

He discusses about 2-D losses in Turbo machinery wherein the following losses

are included:

• Blade boundary layer loss

This loss is estimated by a Loss coefficient

0.5 ⁄

2 ∆⁄ 6∆ ⁄ tan tan

Assuming a rectangular velocity distribution and Cd is constant,

S=total entropy, α2, α1 are flow angles measured from axial direction,

⎯V is mean flow velocity and ΔV is change in flow velocity

• Trailing edge loss

It is about 32% of the boundary layer loss or 21% of total loss



• Tip leakage loss

This loss is estimated by the formula

∆ 0.5⁄ 2 ⁄ 1 tan tan⁄

⁄

Where h is blade span, mL is leakage mass flow, mm is main stream

mass flow, Cc is jet contraction coefficient

• He gives the following Loss coefficient for vane less space immediately

after impeller 4 · ∆ cos⁄

Where h= passage height, Δr= radius change, α= swirl angle, Cd=0.5

He briefs the other sources of loss as Loss due to unsteady flow, shock loss and

loss due to windage and cooling flows. Any periodic motion of the shock will increase

loss due to increased entropy generation. Windage loss and disk cooling flows is the

loss due to viscous friction on all parts of the machine other than blade and annulus

boundaries, where it has already been accounted for .It is considered in terms of the

viscous torque on rotating disks and hence called disc friction loss.

Wakes, vortices and separations from one blade row often mix out in the

downstream blade row. When vortex is stretched or compressed longitudinally its

kinetic energy varies as square of its length. When this is dissipated by viscous effects,

it will increase loss.

Unsteady flow can affect generation through dissipation of span wise vortices

shed from a trailing edge as a result of changes in blade circulation.

In his concluding remarks, Dr. J. D. Denton emphasizes that the understanding

of losses will be improved by thinking loss in terms of entropy generation. Tip leakage

loss, subsonic trailing edge loss and losses due to blade surface separation are estimated

using empirical data. End wall loss, transonic trailing edge loss and loss due to mixing

in a downstream blade row can be estimated approximately using empirical

correlations.

V. M. Sharathkumar [101] concluded that circumferential distortion effects

changes total pressure, static pressure, flow angles and conditions of shock less entry.

B. Laksminarayana and A. Basson [102] explains that the leakage mass flow

is one of the important parameters in assessing the aerodynamic loss and its

performance. The leakage mass flow is given by



Where VL= leakage velocity normal to the blade surface

s = the distance along the blade surface

ρ= density of fluid

τ= tip clearance height

dz= span wise distance (measured from end wall)

They noticed that major leakage flow and losses occur beyond mid chord due to

increased loading and decreased blade thickness in this region.

R. H. Aungier [103] suggests the following formulae to estimate Impeller

windage and disk Friction (IDF) and cover seal leakage work input (IL) for covered

impellers:

IDF IL CMD CMC ρ2U2 2 /2m mLIB/m

Where, CMD = Disc torque coefficient for disc parameter

CMC = Disc torque coefficient for cover parameter

ρ2 = gas density at impeller tip

U2 = blade speed at impeller tip=ωr=tangential velocity

m = mass flow

mL= mass flow for leakage

IB = work input coefficient for blade parameter

Further, for calculating Impeller internal losses, he gives the following formulae:

• Adiabatic head loss coefficient

∆ 2 / /13

Where, Cm1= absolute meridional velocity at impeller blade leading edge

Cf = skin friction coefficient

m1, m0=meridional co-ordinates at impeller blade leading edge and at

impeller eye

b1= hub-to-shroud passage width at impeller blade leading edge

αc1, αc2= stream line slope angles with axis

• Incidence loss

∆ 0.4 / sin ⁄

Where W1= relative velocity at impeller leading edge

β1= blade angle with respect to tangent at impeller leading edge



Cm1= absolute meridional velocity at impeller blade leading edge

U2 = blade speed at impeller tip=ωr=tangential velocity

• Entrance diffusion loss

∆ 0.4 2⁄ ∆

ΔqDiff > 0,

Wth = relative velocity at throat

• Impeller friction loss

∆ 2 ⁄ ⁄

2⁄

2⁄

• Blade loading and hub-to-shroud loading losses

∆ ∆ ⁄ 48⁄ (Blade loading loss)

∆ ⁄ 12⁄ (Hub-to-shroud loss)

⁄

2⁄

2⁄

∆ 2 ⁄

Where LSB = splitter blade mean streamline meridional length

d2=diameter at impeller tip: LB = length of blade mean camber line

IB= work input coefficient for blade

Z= effective number of blades = /

ZFB= Number of splitter blades, L= blade streamline meridional

length=m2-m1

• Discharge profile distortion loss

∆ 0.5 1 2

Where λ = tip distortion factor=1/ (1- β2)

∆ ⁄ 0.3 ⁄ / 2⁄

∆ 2 ⁄ ⁄

22⁄ 12⁄

• Wake mixing loss

∆ 0.5 /

: for Deq<2



/2: For Deq >2

⁄

Where A2 =discharge area inside the blades

K. L. Kumar [10] lists following factors, which account for the departure of the

actual flow from the ideal flow:

• Existence of viscosity: viscous resistance, boundary layer formations,

and separation of flow.

• Finite number of blades: flow through bladed channels, secondary flows

in the bladed passages and leakage effects.

• Existence of compressibility, density variations, temperature rise and

shock phenomena.

• Off design operating conditions, velocities and angles different from the

design values.

• Head loss due to frictional effect are expressed as,

Where hf =head lost due to friction and shearing, Q= Volumetric flow

rate,

k= constant.

• Losses due to improper fluid incidences on the blades at the inlet and

lack of complete guidance by the blades are called turning losses.

Turning losses are expressed as

Where ht = head lost in turning due to improper incidence or flow

guidance,

Q= Volumetric flow rate, Qn= designed flow rate, C = a constant

The effect of all losses on the Head- Discharge characteristic of a typical

centrifugal impeller turbo machine is shown in Figure 2.31. The actual characteristic is

lower than the Euler’s characteristic at all values of the discharge. The difference

between them is the largest at very high and very low discharge.



Figure 2.31 Actual and Euler’s H-Q Characteristic Curve [10]

R. J. Kind [60] studied flow behavior and performance of squirrel-cage type

centrifugal fans. Experimental and analytical study has lead to following conclusions:

• The volute can have a strong influence on the overall performance

characteristics of the machine.

• The inlet losses and volute friction losses are relatively unimportant.

Blading losses are, however, very important and are responsible for

approximately half of the overall losses.

• To improve efficiency, one should focus on gap flow and blading losses.

G. L. Morrison, M. T. Schobeiri and K. R. Pappu [104] introduced Five-hole

pressure probe analysis technique. Five-hole pressure probes are becoming more useful

with the development of small inexpensive fast response pressure transducers, computer

controlled traversing systems, and computer based data acquisition and analysis. A

schematic of the end of a five-hole pressure probe is presented in Figure 2.32.



Figure 2.32 Schematic of a Generic Five-Hole Pressure Probe

The probe can be operated in two ways. The most simple in terms of data

analysis is the nulling arrangement where the probe is mounted on a five degree of

freedom traversing system and is oriented such that the X-axis is parallel to the flow

( are both zero). The center pressure tap, P5, then measures the stagnation

pressure and the pressures in the four outer tubes are equal (P1 = P2 = P3 = P4) and

proportional to the static pressure. This nulling technique requires a very sophisticated

traversing system and long data acquisition time since the probe must be pitched and

yawed at each measurement location until the four pressures are equal. This can take a

long time, especially if the probe is small and has a slow time response. This paper

addresses the non-nulling technique in which the pressure probe undergoes an extensive

calibration which is then used to determine the magnitude and direction of the flow with

respect to the coordinates of the probe. The non-nulling technique is performed by

setting the probe at constant pitch and yaw values with respect to the test section,

traversing the probe over the flow field, and measuring the five pressures at each

measurement location. From these five measured pressures, the direction and magnitude

of the flow with respect to the X-axis of the pressure probe are determined There is a

maximum angle the flow can make with respect to the axis of the probe beyond which

the flow separates from the probe. When this occurs the data cannot be reduced to

obtain the velocity since the pressure taps in the separated regions do not vary

significantly or monotonically with flow angle. Most data analysis techniques for the

non-nulling operation of the probe require that the probes are manufactured to exacting

tolerances such that the response in each of the four pressure taps around the perimeter

of the probe (P1, P2, P3 and P4) is completely symmetrical. The objective of this work is



to present a data reduction technique which will compensate for nonsymmetrical probes

and which will establish the range of flow angles a specific probe can be used.

A refinement on the method used to analyze five-hole pressure probe data

obtained using the non-nulling technique has been presented. The use of advanced three

dimensional curve-fit analysis programs has made it possible to obtain relatively simple

analytical expressions for the four calibration functions,

, ), , ), , , , which are required to convert

the pressures measured by a five-hole pressure probe into the magnitude and direction

of the flow with respect to the axis of the probe. These equations are usually simple

algebraic relationships which may have as many as ten coefficients. Though lengthy to

enter into a data reduction program, they are quickly computed and produce excellent

results. The three dimensional graphical presentation of the calibration

curves, , ), , ), , , , obtained directly from

calibration data are invaluable in evaluating the performance of an individual probe and

determining the range of pitch and yaw angles the probe is capable of measuring.

H. W. Oh, K. Y. Kim [105] classifies losses into internal losses and External

losses.

Internal losses

• Entrance loss

∆ /2

Where fent=0.13

V0= Absolute velocity ahead of impeller

• Incidence loss

∆ /2

Where finc=0.5-0.7

Wui= tangential component of the impeller inlet relative velocity

• Diffusion loss

∆ 0.05 /

Where

1 ⁄ . ⁄

⁄ ⁄2 ⁄

W2=relative velocity at impeller exit

U2= tangential impeller speed at exit



W1t= relative velocity at impeller tip inlet

HEuler= Euler head

Zr= number of impeller blades

D1t=diameter of impeller tip at inlet

D2= diameter at impeller exit

• Skin friction loss

∆ 2 ⁄

Where 2 3 8⁄

Cf= skin friction coefficient

Lb= impeller flow length

Dhyd= hydraulic diameter

V1t, V2= absolute velocities at impeller inlet tip and impeller exit,

respectively.

W1, W1h= relative velocities at impeller tip inlet and impeller hub

inlet, respectively.

• Clearance loss

∆ 0.6 ⁄ ⁄ 4 2⁄⁄ /

Where ε = clearance between impeller tip and casing

b2=impeller width at outlet

Vu2=absolute velocity at tangential direction at impeller exit

r1t, r2t = radii at impeller tip inlet and impeller exit, respectively

r1h= radius at impeller inlet hub

Vm1m =Absolute velocity at meridional directions or root-mean-

square position at impeller inlet

• Mixing loss

∆ 1/ 1 1 1⁄ 2⁄

Where α2= absolute flow angle from the meridional direction at

impeller exit

εwake = wake friction of the blade –to-blade space

b* = ratio of vane less diffuser inlet width to the impeller exit width

• Separation loss

∆ 0.61 ⁄ 1.4 2 ⁄



External losses

• Recirculation loss

∆ 4.32 10 sin 3.5 2 /2

• Leakage loss

∆ /2

Where Qcl = volume flow at clearance in m3/s

0.816 2∆ ⁄

∆ /

2⁄

2⁄

Lθ= impeller meridional length

Q* = volume flow including leakage, m3/s

B. P. M. Van Esch, N. P. Kruyt [106] derives various formulae for power and

turbo machine losses as following:

• The shaft power can be written as

∆

Pfluid= Power imparted by the impeller to the fluid = ρg (Q+Qleak)Hinv

Where Hinv= inviscid head

Q = flow rate

Qleak= leakage flow

ΔPdf= power loss due to shear stress at the impeller external surfaces

(disc friction)

• He derives hydraulic power loss in the impeller as

∆ ∆

Where Δ

Hi is head measured between stations located just above and downstream

of impeller

• Further, he gives the following formula for calculating leakage loss:

Leakage loss, ∆

Final value of head= Hi - ΔHhydr,v

• ΔHhydv is the loss of head in volute



∆ ∆ ∆

Where Pnet is net power relates to the pump’s head H & is equal to ρgQH

∆ ∆

On the basis of above calculations the overall power loss is derived as follows:

Overall power loss=∆ ∆ ∆ ∆ ∆ ∆

Where ΔPhydi is Hydraulic power loss in impeller

ΔPhydv is Hydraulic power loss in volute

ΔPleak is Leakage loss

ΔPdf is disk friction loss

ΔPmech is power loss due to friction in bearings and seals

S. M. Yahya [9] enumerates the losses for a centrifugal fan as Impeller entry

losses, Leakage loss, Impeller losses, Diffuser and volute losses and Disc friction loss.

By accounting for the above losses, the actual performance of the fan can be predicted

from that obtained theoretically. The basic mechanism of the losses for a centrifugal fan

is similar to centrifugal compressor stages as shown in Figure 2.33 and 2.34.

Figure 2.33 Variations of Shock Losses with Incidence [9]



Figure 2.34 Losses and Performance Characteristics of a CF Turbo Machine Stage

[9]

2.5 Computational Fluid Dynamics (CFD) Numeric Analysis

Turbo-machines comprise various types of fans, compressors, pumps and

turbines. In the earlier phase of design and development of turbomachines since

perception, many researchers have done their research work by performing laboratory

experiments or by making analysis of actual performance data available. This was a

slow process of development.

In present era of computerization and its development and advancement, virtual

three-dimensional flow analysis is feasible and allowing designer to have better

estimate of influence of spatial parameters on performance of the machine. CFD

provides an accurate alternative to scale model testing, with variations available in

simulation parameters. Advanced solvers contain algorithms which enable robust

solutions of the flow field in a reasonable time. As a result of these factors,

Computational Fluid Dynamics is now an established industrial design tool, helping to

reduce design time scales and improve processes throughout the engineering world.

Various flow phenomenons occurring inside turbomachine can be numerically

analyzed with the help of commercially available CFD software. The set of equations

which describe the processes of momentum, heat and mass transfer are known as the

Navier-Stokes equations. These partial differential equations were derived in the early

nineteenth century and had no analytical solution but it can only be discretized and

solved numerically.

Centrifugal fan design performance can be truly ascertained by experimental

evaluations, but CFD analysis can greatly help in reducing number of experimental



iterations. CFD can also help to understand profile distribution of mass flow, pressure

and velocity at infinitesimal planes of centrifugal fan geometry under study. This could

not be possible merely by experiments and hence CFD analysis and experimental

evaluation are equally important and mutually exclusive.

Here literature review is focused on use of CFD techniques to make virtual

performance analysis of turbo-machines.

P. J. Roache [35] made quantification of uncertainty in computational fluid

dynamics. This review covers verification, validation and confirmation for

computational fluid dynamics (CFD). It includes error taxonomies, error estimation,

convergence rates, surrogate estimators, nonlinear dynamics, and error estimation for

grid adaptation.

Hsin-Hua Tsuei, Kerry Oliphant and David Japikse [36] have developed

method for rapid CFD modeling for turbo machinery. This study draws on a set of

seven different stages, for which much measured data is available, and provides answers

to issues of sufficient depth to sensibly guide engineers in the economical and accurate

utilization of their CFD tools. A base for rapid calculations is established: it is expected

that the design future will focus intensely on agile, easy-to-use CFD as a base for

advanced design development.

Hsin-Hua Tsuei and J. Blair Perot [107] developed advanced turbulence

model for transitional and rotational flows in turbo machinery. It contains turbulence

model which is expected to capture the full details of 3D non-isotropic turbulence for

wide variety of flows. The greater accuracy is expected to be achieved with a

computational cost similar to an enhanced k-ε model while providing detailed Reynolds

stress information for the mean flow.

Hsin-Hua Tsuei [108] explained the role of CFD in turbo machinery designs

process by using a series of typical turbo machinery test cases for centrifugal and axial

turbo machines.

Hsin-Hua Tsuei, Biing-Horng Liou and S. T. John Yu [109] developed direct

calculation method for turbo machinery flows using space-time conservation element

and solution element method. A three-dimensional space-time Conservation Element

and Solution Element (CE/SE) code in cylindrical coordinates has been developed. For

the study, the blade-to-blade flow field was first investigated to address the fundamental

issues associated with rotation, and blade-to-blade loading. The algebraic Baldwin-



Lomax turbulence model was also implemented to address the shock wave-boundary

layer interaction phenomenon.

Akhras, J. Y. Champagne and R Morel [110] studied rotor–stator interaction

in a centrifugal pump equipped with a vaned diffuser. Their work provides the results of

a detailed flow investigation within a centrifugal pump equipped with a vaned diffuser.

Results are presented as animations reconstituting a temporal evolution of the flow

permitting a better comprehension of the complex flow structure existing between the

two interacting blade rows. At the design flow rate, the presence of the vanes seems to

have a limited effect on the impeller flow structure, except when the suction side of the

blades is facing the diffuser vanes.

Mark R. Anderson, Fahua Gu and Paul D. MacLeod [111] have worked on

application and validation of CFD in a turbo machinery design system. Detailed

comparison to test data of 10 different stages is made.

Kwang-Yong Kim, Seoung-Jin Seo [112] has used response surface method

using a three-dimensional Navier-Stokes analysis to optimize the shape of a forward-

curved-blade centrifugal fan. For the numerical analysis, Reynolds-averaged Navier-

Stokes equations with the standard k-ε turbulence model are discretized with finite

volume approximations. The SIMPLE algorithm is used as a velocity–pressure

correction procedure. In order to reduce the huge computing time due to a large number

of blades in forward-curved-blade centrifugal fan, the flow inside of the fan is regarded

as steady flow by introducing the impeller force models. The geometry of fan used is

shown below in Figure 2.35.

Figure 2.35 Geometry of a Forward-Curved-Blade Centrifugal Fan

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Hong Yang, Dirk Nuernberger, Hans-Peter Kersken [117] developed a

three-dimensional hybrid structured-unstructured Reynolds-averaged Navier-Stokes

(RANS) solver to simulate flows in complex turbo machinery geometries. It is built by

coupling an existing structured computational fluid dynamics (CFD) solver with a

newly developed unstructured-grid module via a conservative hybrid-grid interfacing

algorithm, so that it can get benefits from the both structured and unstructured grids.

The unstructured-grid module has been developed with consistent numerical algorithms,

data structure, user interface and parallelization to those of the structured one. The

numerical features of the hybrid RANS solver are its second-order accurate

upwind scheme in space, its SGS implicit formulation of time integration, and its

accurate modeling of steady/unsteady boundary conditions for multistage turbo

machinery flows. The hybrid-grid interfacing algorithm is essentially an extension of

the conservative zonal approach that has been previously applied on the mismatched

zonal interface of the structured grids, and it is fully conservative and also second-order

accurate. Mismatched grids at blocked interface allow users to have great flexibility to

build the hybrid grids even with different structured and unstructured grid generators.

The performance of the hybrid RANS solver is assessed with a variety of validation and

application examples. It is able to cope up with the flows in complex turbo machinery

geometries and to be promising for the future industrial applications.

ANSYS Inc. [118] has given tutorials on multiple rotating reference frames.

This tutorial illustrates the procedure for setting up and solving a problem using the

MRF capability. Some FLUENT features such as specifying different frames of

reference for different fluid zones, setting the relative velocity of each wall and

calculating a solution using the segregated solver are demonstrated in these tutorials.

A. Behzadmehr, Y. Mercadier and N. Galanis [119] have made sensitivity

analysis of entrance design parameters of a backward inclined centrifugal fan using

DOE method and CFD calculations.

A design of experiments (DOE) has been performed to study the effect of the

entrance conditions of a backward-inclined centrifugal fan on its efficiency. The

parameters involved are the base radius of the motor hub, the radius of the fan entry

section, the deceleration factor throughout the entry zone (from the entry of the fan to

the entry of the blade), and the solidity factor. Numerical simulation coupled with the

DOE has been used for the sensitivity analysis of the entrance parameters. The effects

of these parameters and their interactions on the fan efficiency are presented. A linear



regression with three parameters has been performed to establish the efficiency

distribution map. The methodology employed is validated by comparing the predicted

results from the DOE and those from the numerical simulation of the corresponding fan.

Fahua Gu and Mark R. Anderson [120] have developed CFD based through

flow solver in a turbo machinery design system. In this paper an Euler through flow

approach is described and the steps required for constructing stream surface,

modifications for the incidence and deviation and throat area correction are presented.

This solver creates and modifies the machine geometries and predicts the machine

performance at different levels of approximation, including one-dimensional design and

analysis, quasi-three-dimensional methods (blade-to-blade and through flow) and full-

three-dimensional steady-state CFD analysis. The flow injection and extraction

functions are described, as is the implementation of the radial mass distribution. Some

discussion is dedicated to the shock calculation and examples are provided to

demonstrate the pros and cons of the Euler through flow approach and also to

demonstrate the potential to solve for a wider range of flow conditions, particularly

choked and transonic flows which limit stream function based solvers.

Moulay Bel Hassan, Asad Sardar and Reza Ghias [121] have made CFD

simulations of an automotive HVAC blower. It is operating under stable and unstable

flow conditions.

In this study, CFD simulations for different blowers are performed. The

realizable k-ε turbulence model was used on the Reynolds Averaged Navier-Stokes

approach to model complex flow field properly.

Steady state analysis showed good correlation for the stable flow conditions

(high airflow and low pressure), whereas this approach showed large discrepancies for

unsteady flow conditions (low airflow and high pressure). By a transient simulation and

realizable k-ε turbulence model, the CFD results showed good results compared to

experimental test results. The graph shown in Figure 2.39 gives results obtained from

numerical simulation at varying airflow.

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The analysis shows that the converging suction slots located on the impeller

blade about 25% from the trailing edge, significantly improves the static pressure

recovery across the fan. Also it is found that Slots provided at a radial distance of about

12% from the leading and trailing edges marginally improve the static pressure recovery

across fan.

Songling WANG, Lei ZHANG, Zhengren WU and Hongwei QIAN [123]

have done optimization research work on centrifugal fan with different blade number

and outlet blade angle. In the centrifugal fan, the three-dimensional motion of the gas is

thought to be the incompressible and steady flow, and calculated by using three-

dimension Reynolds both conservation Navier-Stokes equations. As the fluid in a state

of turbulence, the standard k −ε equation of the second model was selected as the

turbulence model, and when near wall, the standard wall function was used. Calculating

method was SEGREGATED implicit method, the pressure - speed coupled using the

SIMPLE calculation method, and turbulent kinetic energy, dissipation of turbulence and

the momentum equation all use second-order discrete upwind. Equations include the

continuity equation, the momentum equation and k −ε equation as following:

0

13

Among them Cε1 =1.44, Cε2 =1.92, Cμ =0.09, σk =1.0, σε =1.3.

Three-dimensional flow field of centrifugal fan is numerically simulated based

on the CFD model with the fluent software and then simulated results are verified by

experiments. Efficiency (η) is taken as maximizing function, while blade number and

outlet blade angle are taken variable quantities. Fan impeller geometric parameters are

optimized based on least square method.



Figure 2.41 shows performance curves obtained through numerical simulation

and experiment. Point A shows the status of the design points, It can be seen that the

error of the total pressure of the fan which attained from numerical simulation is less

than 3%, while the efficiency error in the design point is less than 2.3%, so it can be

concluded that the calculation results derived by numerical simulation are accurate

enough to predict the inner flow of the fan and the results could be used as the guide to

optimize the impeller and verify the accuracy of numerical simulations.

Figure 2.41 Performance curves of numerical simulation and experimental results

[123]

The factors that impact fan’s performance are coupled with each other: various

factors have a combined action together to the fan performance. This paper take the

efficiency η as a maximizations goal, take the number of blade of Z and the angle β2 as

the variable quantity, and construct the optimized mathematical model:

,

. 11 14

43 48

In the model, f (x, y) represents the objective function of efficiency η, and

parameters x and y separately represent the number of blade and the angle β2.

It’s approximately parameters can be looked for by least squares

method. And N × M-order algebraic equations with regard to can be obtained as

follow:



, , · 0

The equations can be solved with programming by MATLAB software, and gets

the curved surface fitting expression of efficiency η with regard to Z and β2. The values

of Z and β2 at maximum surface point are solved by search method. 4 × 4 high-order

fitting is used to ensure the fit accuracy. The basic data for fitting obtained through

numerical simulation is shown in Table 2.2.

Table 2.2 Efficiency Value of Different Impeller Parameters [123]

→ 430 440 450 460 470 480 Z ↓ 11 74.7 75.1 74.8 66.5 72.6 70.8 12 75.9 74.6 76.58 75 74.5 73.7 13 75.9 76.7 76.9 76.3 75.5 72 14 76.5 76.7 77 76.8 74.7 73.6

It is clear from Table 2.2 that optimized number of blades is 14 and optimized

impeller exit blade angle is 45°.

Optimized results have shown that the performance of centrifugal fan was

improved by lowering the energy loss. Energy loss occurs due to secondary flow vortex,

volute tongue, the wake-jet and the angle of attack. Numerical simulation can accurately

predict the performance of centrifugal fan and the details of the flow field in the fan. It

also has the important guiding significance in researching interior losses of centrifugal

fans, optimizing impeller and modifying fans.

Choon-Man Jang, Sang-Yoon Lee, Sang-Ho Yang [124] made optimal design

of a centrifugal fan installed in refuse collecting system using response surface method

and three-dimensional Navier-Stokes analysis to increase fan efficiency. The centrifugal

fan is used to increase suction pressure for the moving of a waste through the pipe line

of the system. Two design variables, which are used to define the shape of an inlet

guide, are introduced to increase the efficiency of the fan. In the shape optimization

using the response surface method, data points for response evaluations are selected,

and linear programming method is used for an optimization on a response surface. To

analyze three-dimensional flow field in the centrifugal fan, general analysis code, CFX

with SST turbulence model is employed to estimate the eddy viscosity.

Unstructured grids are used to represent a composite grid system including blade, casing



and inlet guide. Throughout the shape optimization of a centrifugal fan, the fan

efficiency is successfully increased by decreasing local losses in the blade passage. The

result of shape optimization shows that the efficiency of the optimized shape at the

design flow condition is enhanced by 1.42%. It is also found that recirculation

flow region is relatively small compared to the reference one. The reduction of

recirculation region will help to decrease the shaft power of an impeller with increase in

efficiency of the fan.

Wu Yulin, Liu Shuhong and Shao Jie [125] have made numerical simulation

of steady and unsteady internal flows flowing within centrifugal pump. In this study,

experimental measurements and numerical simulations are made to get more

information about the internal flow of a centrifugal pump. The RANS (Reynolds

Averaged Navier-Stokes) turbulent equations with the SST k-ω turbulence model are

applied to simulate its 3D steady passage flow and the DES (Detached Eddy

Simulation) method to simulate unsteady flow. Based on comparison with experimental

data, the unsteady flow simulation is proved to be relatively accurate in predicting the

flow status in the centrifugal model pump.

Song-ling Wang, Lei Zhang, Qian Zhang [126] numerically simulated the

flow field of the G4-73 centrifugal fan with the software of Fluent. The numerical

results show that large-scale vortex in volute was push forward, and the scale and

intensity of vortex change in different circumferential cross section of the volute. A

vortex-broken device was designed based on the idea of decrease flow loss and vortex

noise through breaking large-scale vortex. Experimental results show that after the

device was added, total pressure nearly increases 44 Pa at the design flow conditions.

The average increase in efficiency is found 3% when relative flow is in the rage of 85 to

100% of design flow. This vortex breaking device has a great significance in energy

saving of a power plant.

Chen-Kang Huang and Mu-En Hsieh [127] presented numerical simulation of

backward-curved airfoil centrifugal blowers and compared them with experimentally

measured data. Simulation settings and boundary conditions are used to simulate four

backward curved airfoil centrifugal blowers using the Navier-Stokes equation and finite

volume method (FVM). In GAMBIT, model construction and split were processed. The

fluid volume was split into a rotating fluid volume, a scroll volume, an inlet cone

volume, and an inlet/outlet duct volume. The inlet and outlet ducts were intentionally

set to simulate the actual measuring situation and to provide better boundary conditions



for simulations. In this study, the length of the inlet duct was set to 10 times the

diameter of the inlet duct and the outlet duct length was set to 15 times the diameter of

the outlet duct. Consequently, the flow was assumed fully developed when leaving the

inlet and outlet ducts. The impeller wheel volume was defined as a rotating reference

frame with constant rotational speed, and other blocks were defined in a stationary

frame. This setup is referred to as a “frozen rotor” model. The rotating fluid and scroll

volumes were defined by tetrahedral/hybrid elements, and hex/wedge elements were

selected for the inlet cone and inlet/outlet duct volumes. A typical grid system is shown

in Figure 2.42. Grid independency tests were performed for each model discussed in

this study.

Figure 2.42 Grid system [127]

In this study, four blowers were tested in the Ventilation Systems Laboratory at

the Industrial Technology Research Institute, Hsin-Chu, Taiwan. The laboratory

possesses the facility for fan or blower performance tests in accordance with the

requirements of ANSI/AMCA Standard 210-07/ANSI/ASHRAE Standard 51-07,

Laboratory Methods of Testing Fans for Certified Aerodynamic Performance Rating

(AMCA/ASHRAE 2007). The apparatus complied with AMCA 120/ASHRAE 51.

In this study, the uncertainty in the flow rate and the pressure measurements is

±2.5%. Moreover, the fan input power obtained is within ±5%. Outlet velocity

uniformity results obtained are not different by more than ±7.5%. Velocity profile

results obtained are not different by more than ±7.5%. The rotational speed variation

during the test is controlled within ±1%.



Comparing simulation results with measured data, it was found that the

deviation of the static pressure curve at each specified flow rate was within 4.8% and

the deviation of the efficiency curve was within 15.1%. After the simulation scheme

was proven valid, the effects of blade angle, blade number, tongue length, and scroll

contour were discussed. Several parameter changes are suggested based on these

simulations. An optimized design is presented with a 7.9% improvement in static

pressure and a 1.5% improvement in efficiency. Overall, the whole process simulates

backward-curved airfoil centrifugal blowers effectively and is a powerful design tool

for blower development and improvement.

Yu-Tai Lee [128] has shown impact of fan gap flow on the centrifugal

fan/impeller overall aerodynamic performance. In this paper, local impeller velocity

distributions are obtained by design and CFD analysis. Impeller flow fields with and

without gap are compared and discussed based on CFD solutions. An example for

controlling the gap effect is also given.

Raúl Barrio, Jorge Parrondo and Eduardo Blanco [129] made numerical

analysis of the unsteady flow near-tongue region in a volute-type centrifugal pump

under different operating conditions. Their investigations are presented for unsteady

flow behavior near the tongue region of a single-suction volute-type centrifugal pump.

The flow through the test pump was simulated by commercial CFD software. A

sensitivity analysis of the numerical model was performed for appropriate grid size,

time step size and turbulence model. Validated, model is used to study flow pulsations

and the leakage flow between the impeller–tongue.

Lamloumi Hedi, Kanfoudi Hatem and Zgolli Ridha [130] have also carried

out numerical flow simulation for centrifugal pump. Their flow simulation is focused to

understand volute flow to provide design guidance in efficient volute design. In this

study, viscous Navier-Stokes equations are used to simulate the flow inside vane less

impeller and volute. Flow variations for different volute tongue geometries are studied

in detail. The numerical calculations are compared with experimental data and good

agreement is found.

Mihael Sekavcnik, Tine Gantar and Mitja Mori [131] have studied single-

stage centripetal pump for design features. They made investigations on operating

characteristics curves. Velocity vectors at mid-channel having full pitch-360 deg

approach is shown in Figure 2.43.



Figure 2.43 Velocity Vectors, Mid-Channel, Full Pitch-3600 Approach

[131] Their research paper presents an experimental and numerical investigation on

single-stage centripetal pump (SSCP). A computational fluid dynamics (CFD) model

was developed to establish throttle-closing and throttle-opening performance curves.

The flow conditions obtained with the CFD simulations, confirms that the hydraulic

behavior of the SSCP is influenced by circumferential stall occurring in impeller-stator

flow channels.

Changyun Zhu, Guoliang Qin, [132] applied an optimization strategy called

response surface methodology (RSM) to a centrifugal fan impeller optimization design.

RSM is used to generate an approximated model of objective function, for which a

second-order polynomial function is chosen. The Design of experiment (DOE)

technique coupled with CFD analysis is then run to generate the database. The least-

squares regression method (LS) is used to determine the coefficient of the RSM

function. Finally, the Genetic Algorithms (GA) is applied to the objective function in

order to obtain the optimal configuration. This paper also presents a solution to the

problem of imprecise fitting of second-order RSM model by dividing the zone into

several subzones which is proved to be effective in this paper. The optimization result

shows that RSM is an effective and feasible optimization strategy for the centrifugal fan

impeller design, and the complexity of the objective function and the overall

optimization time could be significantly reduced.



Yu-Tai Lee, Vineet Ahuja, Ashvin Hosangadi, Michael E. Slipper,

Lawrence P. Mulvihill, Roger Birkbeck, and Roderick M. [133] presented a method

for redesigning a centrifugal impeller and its inlet duct. The double-discharge volute

casing is a structural constraint and is maintained for its shape. The redesign effort was

geared towards meeting the design volute exit pressure while reducing the power

required for operating the fan. Given the high performance of the baseline impeller, the

redesign adopted a high-fidelity CFD-based computational approach capable of

accounting for all aerodynamic losses. The present efforts utilizing a numerical

optimization are used to redesign the fan blades, inlet duct, and shroud of the impeller.

The resulting flow path modifications not only met the pressure requirement, but also

reduce the fan power by 8.8%. The new designed impeller matches with the original

volute in a better way.

2.6 Literature Review Conclusions

Lawrence Berkeley National Laboratory [134] assessed the types of energy

conservation measures that industry could adopt to improve their efficiency in cement,

refineries, fertilizers, and textile industry sectors. Surat is a hub for textile industries. It

is recognized that textile industries is distributed in large numbers of plants in the

unorganized sectors and utilizing old and less efficient fume extraction centrifugal fan

in SDS-9 texturising machines. These centrifugal fans are consuming very high energy

and require frequent maintenance. Their redesigning is very much required for energy

conservation. Present literature review has lead to following conclusions.

1. Fume extraction centrifugal fan needs variable flow at constant head under dust

laden conditions. Radial blade fan has characteristics lying between forward and

backward curved fans and self cleaning properties of radial vaned fan make it ideal

for handling dust or grit laden air [20]. Flow coefficients for radial fan and blowers

ranges from 0.25 to 0.3 and radial vanes give better efficiency compared to forward

curve vanes [21]. Radial fans and blowers are having more operating range, less

manufacturing cost and high pressure development per stage [22]. Radial blades are

ideal for dust laden air or gas because they are less prone to blockage, dust erosion

and failure. It has ideal zero slope in H-Q (head-discharge) curve to give variable

discharge at constant head. It has equal energy conversion in impeller and diffuser

which gives higher pressure ratio with good efficiency [9].



2. The survey of literature indicates that specific and focused research work has been

carried out all over the world on local flow physics, aerodynamics and phenomena

of energy transfer. It includes study of various parameters affecting the power, head

and efficiencies. But major lacuna exists towards availability of unified design

procedure for radial blade centrifugal fan design procedure which is also validated

through experiments. Design expressed in a mathematical form, deviates greatly

from the experimental results [14, 26, 28, 29, 56].

3. Most efforts to determine the optimum number of blades have resulted in to

empirical relations. The optimum number of blades of a radial impeller can only be

truly ascertained by experiments. Optimization of number of blades of centrifugal

fan impeller involves a maximization problem of multivariable function with fluid

dynamic constraints. Experimental data based on a simple variation in blade number

alone, keeping other parameters constant, will not yield optimum blade numbers for

a global maximum hydraulic efficiency [14, 44].

4. Slip factor has significant effect on centrifugal fan design and its performance.

Several co-relations as well as empirical equations are used in literature to estimate

slip factor. Empirical correlations used to estimate the slip factors provide a constant

value of the slip factor for a given impeller only at the best efficiency point.

Calculated theoretical values are in good agreement at design point conditions but

deviates at off design conditions. Even in the case of the nominal flow rate, values

for the slip factor produced by correlations could have errors as large as 52% [9, 14,

75, 76, 78, 79, 83, and 87].

5. Actual performance of a centrifugal fan (at the design point) differs to the ideal fan

power which can be predicted by Euler’s equation. This difference exists due to

hydraulic, volumetric and power losses occurring within flow passage. These losses

reduce the work done by the impeller. Losses occur in stationary as well as moving

parts of the fan [9, 28, and 34].

6. Centrifugal fan design performance can be truly ascertained by experimental

evaluations, but CFD analysis can greatly help in reducing number of experimental

iterations. CFD can also help to understand profile distribution of mass flow,

pressure and velocity at infinitesimal planes of centrifugal fan geometry under

study. This could not be possible merely by experiments and hence CFD analysis

and experimental evaluation are equally important and mutually exclusive [36, 108,

112, 115, 118, 121 and 123].



Thus for evolution of energy efficient design, the literature review clearly

focuses towards the need for experimental optimization of number of vanes, assessment

of existing design methodologies, understanding and measuring slip factor, evaluation

of losses and CFD studies for better understanding of flow physics, which will finally

offer experimentally and numerically verified unified design, which will ultimately

meet or surpass the CSWD [4] minimum efficiency requirements for centrifugal fans.



2.7 Objectives of Present Work

The basic objective of present work is to redesign fume extraction centrifugal

fan used in SDS-9 texturising machine to offer best possible energy efficiency. Radial

blades being most suited for offering constant head under dust laden conditions [9, 20,

21, 22], the overall objectives based on the conclusions derived from extensive

literature review are planned as follows for radial tipped centrifugal fan.

1. Optimization of finite number of blades through experimental studies at design

and off design conditions.

2. Experimental determination of slip factor and its variation at different volute

locations along the blade width and to compare existing slip factor correlations

in light of present results.

3. Compilation and experimental evaluation of existing design methodologies for

radial tipped centrifugal fan.

4. To propose unified design methodology for radial tipped centrifugal fan and

design energy efficient forward and backward curved radial tipped centrifugal

fan for SDS-9 texturing machine.

5. To carry out the experimental validation of these fans to ascertain designed and

desired performance.

6. Experimental determination of hydraulic, leakage and power losses and critical

evaluation of existing loss models in the literature.

7. To carry out 3-D CFD studies to understand flow physics in centrifugal fans and

numerically validate the proposed unified design approach for radial tipped

centrifugal fan.

LITERATURE REVIEW AND OBJECTIVES OF PRESENT WORK

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