CRYOGENIC FRANCIS TURBINES - ebaracryo.com … · 8th International Symposium on Transport...

8th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, ISROMAC-8, March 26-30, 2000, Honolulu, HI, USA

CRYOGENIC FRANCIS TURBINES

Hans E. Kimmel Cryodynamics Division

Ebara International Corporation 350 Salomon Circle

Sparks, NV 89434, USA Fax: (775) 356 2884, E-mail: [email protected]

KEY WORDS: Cryogenic Hydraulic Turbine, Variable Speed Francis Turbine, Multistage Francis Turbine, Hydraulic Turbine Performance, Axial Rotor Oscillations ABSTRACT Cryogenic fluids are liquefied gases with very low temperatures. In many cryogenic liquefaction processes, gases are often expanded from a high to a low-pressure level. Traditionally the expansion has been achieved by reducing the pressure under constant enthalpy across a Joule-Thompson valve. The kinetic energy is mostly transferred into undesirable heat increasing the boil-off losses of the cryogenic liquid. A new application of Francis turbines for cryogenic liquids is presented: The cryogenic submerged turbine generator. Turbine generators convert the hydraulic energy of the cryogenic fluid stream into electric energy, thus reducing the thermodynamic enthalpy of the liquefied gas and increasing the productivity of the gas liquefaction process. The current design of cryogenic Francis turbines is a radial inflow reaction turbine with an induction generator mounted on an integral shaft. The entire unit, including the electric generator is totally submerged in the cryogenic fluid. The turbine generator has no dynamic rotating shaft seal and no coupling between turbine and generator. The economic benefits of power generation with cryogenic turbine generators are significantly increased by a factor dependent on the temperature difference between the liquid and the environment. The colder the cryogenic liquid, the greater the power savings, not only in

the power recovery but also in the total power input of the refrigeration process. Gas liquefaction processes have changes both in volumetric flow and differential pressure during operation. To accomplish a high isentropic efficiency for different input parameters the cryogenic Francis turbines must operate with variable speeds. This paper presents the design and performance of variable speed cryogenic Francis turbines. INTRODUCTION The history of cryogenic expansion machines is more than hundred years old. Early cryogenic expansion machines used reciprocating engines with a piston, bellows or diaphragm (Habets,Kimmel 1998/99). The first rotating expander for cryogenic gases was patented in 1898 under the British Patent No. 26,767 for Edgar C. Thrupp. In 1939 Peter Kapitza built a radial inflow reaction turbine for the expansion of compressed refrigerated air into the condensation phase. Several other designs of turbine expanders were operated in the following decades, but the size of these expanders remained small, in the power range of less than one hundred kilowatts. The construction and operation of large liquefaction plants for natural gas began


approximately twenty years ago and led to the development of cryogenic turbine expanders in the power range above one Megawatt. The purpose of using cryogenic expansion machines is to reduce the enthalpy of the cryogenic fluid by extracting work from the fluid. The reduction of enthalpy lowers the exit temperature of the cryogenic fluid and decreases the boil-off losses due to the inevitable heat transfer from the warm environment. The current design of these liquefied natural gas expanders makes use of the well-established features of hydroelectric Francis turbines. Named after the developer of this turbine type, Francis turbines are radial inflow turbines, which generate shaft torque by changing the angular momentum of the rotating fluid. Although the same principle is used to generate shaft torque in hydroelectric and cryogenic Francis turbines, there are distinctly different features in the overall turbine design due to certain operational requirements. The two most important operational requirements are the cryogenic temperatures and flammable properties of hydrocarbon fluids. Both requirements suggest designs to insulate and separate the machine from the environment. The current design of cryogenic Francis turbines is a radial inflow reaction turbine with an induction generator mounted on an integral shaft. The entire unit, including the electric generator is totally submerged in the cryogenic fluid. The turbine generator has no dynamic shaft seal and no coupling between turbine and generator. The only connections to the environment are the electric power cables and the inlet and outlet piping system. All three connections are sealed with reliable cryogenic static seals. Fig.1 shows the cryogenic Francis turbine outside the containment vessel on the test stand. Fig.2 presents a cross sectional drawing of the current design showing three turbine stages, induction generator, rotating shaft, housing, power cables and containment vessel with inlet and outlet piping. The ball bearings are submerged and lubricated by the cryogenic fluid and a special thrust-balancing device is mounted between turbine and generator to increase the operational life of the bearings. The cryogenic Francis turbine is controlled through the power cables by use of a variable frequency device. This solution allows turbine control without any dynamic seals. The usual control mechanism for hydroelectric turbines, the

variable geometry nozzle vanes, would require dynamic seals. VARIABLE SPEED TURBINE PERFORMANCE The performance prediction and test of variable speed cryogenic Francis turbines face unique problems due to the cryogenic design requirements. The mechanical parts of the turbines are manufactured and assembled under atmospheric temperatures but operated under cryogenic temperatures. Shapes and clearances of the mechanical parts are different at cryogenic temperatures and cannot be accessed once they are submerged in the cold liquid. Thus the mechanical and hydraulic performance of the turbine, as well as the electrical performance of the generator, changes at cryogenic temperatures. The acquisition of test data from turbomachines submerged in cryogenic liquids is limited to sensors operating with eddy current or with piezoelectric methods. Particularly measurements of shaft torque during operation in cryogenic environment encounter problems not yet solved with an acceptable range and accuracy. The data acquisition of performance tests for cryogenic Francis turbines is therefore limited to the following four properties: Pressure, Temperature, Mass or Volumetric Flow and Rotational Speed. Kimmel (1996) suggested to model the hydraulic performance of variable speed Francis turbines through Pressure, Volumetric Flow and Rotational Speed. Additional and more detailed models (Kimmel, 1998) offer a comprehensive description of the cryogenic Francis turbine performance characteristics. MODELING The dynamic behavior of turbines with variable speed is governed by the conservation laws of mass, energy, and momentum. The mass flow across the inlet and the outlet of the turbine are generally the same, so conservation of mass is automatically satisfied. The equation for conservation of energy implies that the sum of static and kinetic energy is constant:

H = Q2 + N2 (1) Static energy is represented with H, the differential head across the turbine. The translatory and rotatory kinetic energies are


represented with the squared values of volumetric flow Q and rotational speed N. The conservation law of angular momentum (Kimmel, 1997) determines shaft torque T, wherein the expression (Q - N) represents the change of angular momentum between inlet and outlet of the turbine runner.

T = Q ( Q - N) (2)

The constants , , and are dependent on the particular design of the turbine, and are also functions of the fluid properties. The hydraulic turbine efficiency is defined by the ratio of shaft power P = TN over hydraulic power HQ, and can be calculated by using the equations (1) and (2), with as density of the fluid. The performance of variable speed cryogenic Francis turbines is best described in a graphical presentation using the Q-H-plane with the volumetric flow Q as abscissa and the differential head H as ordinate. The hydraulic efficiency and the shaft power P are the two most important performance parameters for variable speed turbines. The curves for constant efficiency and for constant shaft power P in the Q-H-plane are shown in Fig.3. The constant efficiency curves derived from equation (1) and (2) are parabolas intersecting at the zero-point. For each efficiency value there are two corresponding parabola curves except for the unique maximum efficiency max . The two zero efficiency curves correspond to the no-load characteristic and to the locked rotor characteristic (Kimmel, 1996). The equation for constant efficiency curves is the following:

H = Q2 , , , , , (3) with as a function of the constants , , , , , and only. The constant shaft power curves in Fig.3, which are shaped like the Greek letter , are also obtained from equation (1) and (2) and represent higher order polynomials. H = Q2 /42 1 1 4 P/ Q3 ½ (4) With increasing power the curves move towards higher values of Q and H. For large values of Q the constant shaft power curves approach asymptotically the two parabolic zero efficiency curves.

Thus the hydraulic performance of variable speed Francis turbines is best described with two sets of curves: the constant shaft power curves and the constant efficiency curves. THRUST BALANCING DEVICE Francis turbines generate a relatively high axial thrust, which can reach several tons on multistage turbines, resulting in heavy bearing loads with reduced efficiency due to friction losses (Kimmel, 1998). High axial forces are also present in centrifugal pumps, and a variety of mechanisms have been developed to balance or reduce these forces. Most of these mechanisms are applicable to turbines and Fig.4 illustrates the design of a thrust-balancing device for cryogenic turbines, described in detail in Kimmel, 1998. The design allows small axial movements of the rotor and consists of a fixed and a variable orifice. The opening of the variable orifice depends on the momentary axial position of the rotor. Fig.4 illustrates the pressure distribution of the fluid flow for the two extreme positions of the variable orifice. The left side demonstrates the variable orifice in the closed position generating a downstream thrust. The right side shows the variable orifice in the open position, producing an upstream thrust. Between these two extreme positions exists a certain position with no thrust on the rotor. The distance between this thrust balanced position and the completely closed position is defined as distance d. The opening of the fluid passage of the variable orifice is directly proportional to the axial rotor position y, with y = 0 for the thrust balanced case, and y = d for the closed position. NON-LINEAR ROTOR OSCILLATIONS The described device is a self-adjusting thrust balancing mechanism and can be compared to a spring with a non-linear spring characteristic. The mass of the rotor assembly and the hydraulic spring form an axially oscillating mechanical system with non-linear damping and spring characteristics. Any fluctuation in the distribution of the fluid pressure or in the electromagnetic field of the induction generator results in an excitation of axial rotor oscillations, as reported by Evrensel, Kimmel et.al.1999. To establish a mathematical model of these non-linear axial rotor oscillations the following assumptions are made:


1. The maximal axial displacement y or the amplitude A is small compared to the distance d.

2. The cryogenic fluid is incompressible and liquid phase only.

3. The forces from fluid inertia are small compared to the forces from fluid pressure and rotor assembly inertia.

The pressure drop p0 across the variable orifice for the balanced position y = 0 can be calculated using Bernoulli’s modified equation for fluid friction with all constants expressed in C. The volumetric flow q across the thrust balancing device can be assumed to be constant for the steady turbine operation.

p0 = C q2 / d2 (5)

The pressure drop p for any position of y = y (t) as a time dependent function is calculated with

p = C q2 / (d-y)2 (6) Since p0 balances the axial thrust in the steady case, any axial displacement y of the rotor causes an axial force proportional to p0 - p. Newton’s second law describes the displacement of the rotor assembly with the mass m and with E (t) as the function for the exciting force.

m d2y/dt2 + Cq2 [ (d y)2 d2 ] = E(t) (7)

Introducing the variable z = y/d, and the constant k = Cq2/md2, equation (7) reduces to:

d2z/dt2 + k (1 z)2 1 = F(t) (8)

with F(t) = E(t)/k . Fig.5 shows the non-linear characteristic of the hydraulic spring for the described thrust-balancing device. The spring force S and the displacement z are scaled and without dimension.

S = (1 z)2 1 (9) For displacements z 0 the spring characteristic is stiffening and it is softening for z 0. In the case of significant forces through fluid damping the equation (8) can be extended to

d2z/dt2 + dz/dt dz/dt + k(1 z)21=F(t)

(10)

with as the scaled damping coefficient. The fluid friction damping forces depend on the square value of the displacement velocity and are always acting in the opposite direction of the displacement velocity. NATURAL FREQUENCY Equation (10) is a non-linear second order differential equation. In the absence of exciting forces, F (t) = 0, and without damping forces, = 0, the natural frequency of the oscillating system can be calculated. Equation (10) reduces to

d2z/dt2 = k 1 (1 z )2 (11)

and the first integral can be obtained using the substitution dz/dt = p(z).

p(z)2 = 2k K + z (1 z)1 (12) The initial condition p(z)=0 for z = z0 determines the integration constant K. The constant K>1 determines the maximum displacement z0. The value K=1 describes the non-oscillating case with no displacement. The quadratic equation (13) for z0 has two real solutions,

z0

2 + z0 (K1) (K1) = 0 (13)

one always positive and the other always negative: z0 = ½ (K 1){1 K3 / ( K– 1½ (14) The positive solution z0 = A 0 is the maximum amplitude A of the oscillation in positive z-direction and the negative solution z0 = B 0 describes the maximum amplitude B in negative z-direction. Amplitude B is always larger than the amplitude A, because of the hydraulic spring characteristic described in Fig.5. Amplitude B is determined by amplitude A and calculated by equation (14) using

K = (1A)1 A = (1+ B)1 + B (15) Equation (12) is a first order differential equation and can be directly integrated with an elliptic integral of the second kind as solution:


(t–t0) =p(z)1dz (2k)½ K+ z(1 z)1-½ dz (16)

t0 is the second integration constant. The natural frequency in Hertz can be calculated by evaluating the definite integral (17) from z = B to z =A: A

½T = pz1dz with T1 (17) B

For an approximate evaluation of the dynamical behavior of the hydraulic spring, equation (16) can be expanded in a third order MacLaurin polynomial with the initial condition t0 = 0 for z = 0.

t(z) = 2k½K1)½{1+ z(1+z)[2(K1)1}z (18)

B is the amplitude for the softening part of the spring characteristic and always larger than A, the amplitude for the stiffening part of the spring characteristic. The value of K is equal for both amplitudes A and B (equation 15), and therefore

t(B) t(A) (19) The time period for the oscillation in the softening spring part is longer than the time period in the stiffening part, as a consequence of the elliptic integral. The natural frequency depends on the amplitude A and increases for increasing values of the amplitude A. The natural frequency of axial rotor oscillations occurs in thrust balanced cryogenic Francis turbines in the case of free turbine rotation without power generation. The performance during the de-energized turbine operation, described in Fig.3 as no-load characteristic with P = 0, allows measuring of the natural frequency of the axial oscillations without exciting electromagnetic forces E(t) from the generator. The described cryogenic eddy current sensors (Evrensel, Kimmel et.al.1999) enable the rotor displacement to be measured during turbine operation. Changes in the displacement characteristic like amplitude and frequency of the oscillation, can be detected and compared with the original characteristic and analyzed by applying the presented model of the non-linear oscillation.

CONCLUSIONS Variable speed cryogenic Francis turbines are subject to particular design, manufacturing and operational requirements as a result of their cryogenic environments and the flammable properties of these liquefied hydrocarbon gases. To predict the performance, and to control and monitor the operation of cryogenic turbines, the application of new and advanced engineering methods are necessary to assure all essential requirements are met. REFERENCES Evrensel, C.A., Kimmel, H.E., Cullen D.M., 1999, Axial Rotor Oscillations in Cryogenic Fluid Machinery. Proceedings of the 1999 ASME Fluids Engineering Division Summer Meeting, July 1999, San Francisco. Habets, G., Kimmel, H.E. 1998/99, Economics of Cryogenic Turbine Expanders, The International Journal of Hydrocarbon Engineering, Dec/Jan 1998/99 Palladian Publications, Farnham, Surrey, UK. Kikuchi, H., Kimmel, H.E., Smith, D.R. 1999, Prediction and Test Verification of Liquid Hammer in De-energized Hydraulic Reaction Turbines, Proceedings of the Fluids Engineering Division , 1999 ASME International Mechanical Engineering Congress and Exposition, Nashville, Tennessee, USA. Kimmel, H.E. 1996, Variable Speed Turbine Generators in LNG Liquefaction Plants, Proceedings of the GASTECH 96, Vienna, Austria, Dec. 1996. Kimmel, H.E. 1998, Power Generation using Thrust Balanced Hydraulic Turbines, Proceedings of the American Power Conference, Vol.60, pg.200 ff, Illinois Institute of Technology, Chicago, April 1998


Fig. 1: Cryogenic Francis Turbine Testing


Fig. 2: Cross Sectional Drawing

Fig. 5: Hydraulic Spring Characteristic


Constant Shaft Power P and Constant Hydraulic Efficiency

Flow

(No

- Loa

d Ch

arac

teris

tic)

= 0;

P =

0

(Locked Rotor Characteristic) = 0; P = 0

Hea

d1 = 2

P 1 =

cons

t.P 2

= co

nst.

P1 < P2

1 = co

nst.

2 = const.max = const.

Fig. 3: Hydraulic Performance of Variable Speed Francis Turbines


Fig. 4: Thrust Balancing Device

CRYOGENIC FRANCIS TURBINES - ebaracryo.com … · 8th International Symposium on Transport...

Documents

Transcript of CRYOGENIC FRANCIS TURBINES - ebaracryo.com … · 8th International Symposium on Transport...