Process Equipment DesignProcess Equipment Design

Problem Statement

• A three-bladed marine propeller of square pitch is used to agitate a polymer solution of density 1500 kg/m3 and viscosity 15.0 centipoises in an unbaffled tank of diameter (Dt) 1.5 m and 2 m deep. The tank is filled up to a height of 1.5 m and the impeller (diameter = 0.3 Dt) is positioned at one impeller diameter above the vessel floor.

• Estimate the speed of the impeller if the power consumed to drive it is 0.425 kW.

• What will be the impeller speed if the tank is fitted with four longitudinal baffles each of width equal to 10 percent of tank diameter?

• Provide the mechanical design of the vessel and impeller

Agitation Equipment

Liquids are most often agitated in

some kind of tank or vessel, usually

cylindrical in form and with a vertical

axis. The top of the vessel may be

open to the air , more usually it is

closed.

The proportions of the tank vary

widely, depending on the nature of

the agitation problem . A

Standardized design such as that

shown in figure, however, is

applicable in many

situations.

THE VESSEL

Usually vessel with rounded bottom is used to eliminate

sharp corners or regions into which fluid currents would not

penetrate. The height of the liquid is approximately equal to

the diameter of the tank. An impeller is located at the center

of all-liquid system.

Impeller

Impeller agitator are divided into two class

1. Axial Flow Impeller 2. Radial Flow Impeller

The Three main type of impeller are

2. Propellers 2. Paddles 3. Turbines

Axial Flow Axial-flow impeller generates currents parallel with axis of the impeller shafts.Axial flow Impeller:

Radial FlowRadial-flow impellers generates currents in a tangential or radial direction to the axis of the impeller shaft.Radial Flow Impeller: Axial Flow Radial

Flow

PropellersA Propeller is an axial-flow, high-speed impeller for liquids of low viscosity. Standard propellers have three blades or encases by a circular guard. A revolving propeller traces out a helix in the fluid. One full revolution moves the liquid a fixed distance. The ratios of this distance to the propeller diameter is known as pitch. Propellers are a member of axial class of impeller agitator.

Turbines Turbines are six or four blades mounted at the end of the agitator shaft. They are member of the radial class of impeller agitators. Turbines diameter is typically 30-50% of the vessel diameter.

PaddlesPaddles are two or four blades mounted on the end on the agitator shafts. They are subset of radial class of impeller agitators. Typically the impeller diameter of paddles is 50-80% of the tank diameter.

BAFFLESBaffles are vertical strips parallel to the wall of the tank.Baffles are needed to prevent vortexing and rotation of the liquid mass as a whole.A baffle width one-twelfth the tank diameter, w = D/12, a length extending from one half the impeller diameter, d/2, from the tangent line at the bottom to the liquid level, but sometimes terminated just above the level of the eye of the uppermost impeller.

DRAFT TUBESA draft tube is a cylindrical housing around and slightly larger in diameter than the impeller. Its height may be little more than the diameter of the impeller or it may extend the full depth of the liquid, depending on the flow pattern that is required. Usually draft tubes are used with axial impellers to direct suction and discharge streams.

The mechanical design of agitator

For a given diameter and height of the tank the approximate value of other parameters like, impeller diameter, baffle width, width of impeller (in case of turbine), and height from the bottom in standard form.

H- Height of the TankD- Diameter of the Tankd-diameter of the impellerW- width of the baffle

Power Consumption in Impeller Agitator

The agitator impeller is, in essence, a pumping device

operating without the typical confines of a casing or

directed inlet and outlet flows. As the impeller blade

rotates, fluid is forced outward from the blade tip. The

movement force is a vector that can be described by

radial and tangential velocity components. If we

assume that the tangential liquid velocity is some

fraction k, of the blade – tip velocity then:

Vu2=k*u2=k*ᴨ*D*N (1)

Where:

Vu2= tangential component velocity of the

liquid leaving the blade tip

u2= velocity of the impeller blade tip

D= diameter of the impeller feet

N=rotational speed of the impeller

The volumetric flow rate through the radial sweep of the impeller is expressed as

q = Vr2*Ap (2)

where Vr2 = radial component velocity of the liquid leaving the blade

tip.Ap = area of the cylinder swept out by the impeller blade tips

By definition: Ap= ᴨ*D*W (3)

Whereq = volumetric flow rate through the impeller w= width of the impeller

by definition the angle at which the fluid leaves the impeller as β2, it can be shown that Vr2= (u2-Vu2)*tanβ2 (4)

Substituting equations (1),(2) and (3) into equation (4) and rearranging yields :

q = ᴨ2*D2*N*W*(1-k)*tanβ2 (5)

An important consideration in the design of an agitated vessel is the power required to drive the impeller.For geometrically similar impellers w is proportional to D. for given k and β2 flow rate will be given as :

q αN*D3 (6)And flow number is define as NQ = q/(N*D3) (7)

Where N- rotational speed of the impellerD- Diameter of the impeller for marine propeller NQ= 0.5When the flow in the tank is turbulent the power requirement can be calculated from the product of the flow q produced by the impeller and the kinetic energy Ek per unit volume of the fluid :

P=q*Ek (where Ek=ρ(Vu2)2/2gc ) (8)

= NQ*N*D3*(ρ / 2gc)*(k*ᴨ*D*N )2

In dimensionless form(9)

ρ = batch liquid density at the average batch temperature

Np= PDelivered *gc/(N3*D5* ρb)= power number

PDelivered = Np (N3*D5* ρb)/ gc (10)

Reynolds numberThe Reynolds number is defined as for agitated batch liquid as : NRe =(D2*N*ρb/µb)

 where:µb = viscosity of the batch liquid at the average temperature

D = agitator cross sectional diameter measured tip to tipN= agitator speed

PMotor = PDelivered /(100- %losses)

Pdesign = PMotor

S1 = Da/Dt ratio of diameter of impeller to tank.

S2 = E/Dt ratio of height of impeller from bottom of the tank to the diameter of the tank

Calculation (a) µsolution = 15cp = 0.015Pa-sec

ρsolution = 1500 kg/m3

Tank Diameter = 1.5 mImpeller diameter =0.3(tank diameter)= 0.3*1.5 =0.45m Depth of the tank = 2m Tank is filled up to a height =1.5m Height of the impeller from the bottom of the tank is =(diameter of impeller)

=0.45mS1= 0.3, S2= 0.3

So we are using curve A for baffled and curve B for unbaffled tank.

Power consumed = .425Kw

Power no. = PDelivered *gc/(N3*D5 *ρb)

= 0.425*9.81/(N3* (.45)5 *1500)

=150.62/(N3)

Reynolds's Number = (D2*N*ρb/µb)

= ((0.45)2 *N*1500/0.015) = 20250N

Solve N by Trial and Graph ( curve B )

trail N NRe Np N(calculated from equ(10))

5 1.01*105 0.5 3.133.13 6.3*104 0.5 3.13So, N= 3.13 rps = 187.8rpm

(b) Now tank is fitted with 4 longitudinal baffle each of width equal to 0.10*(diameter of tank ) = 0.10*1.5 = 0.15m

Power no. = 150.62/(N3)

Reynolds's Number = 20250N

Solve N by Trial and Graph ( curve A )

trail N NRe Np N(calculated from equ(10))

5 1.01*105 0.9 2.572.57 5.2*104 0.9 2.57

So, N = 2.57 rps = 154.2 rpm

References : 1. Unit operation of chemical engineering, McCabe and

Smith edition 5th2. http://www.pdhonline.org/courses/k103/k103Content.p

df3. http://www.pacontrol.com/process-information-book/

Mixing%20and%20Agitation%2093851_10.pdf