Turbomachinery Design and Theory - sv.20file.org

1 5 Axial Flow Compressors and INTRODUCTIONAs mentioned in Chapter 4, the maximum pressure ratio achieved in centrifugalcompressors is about 4:1 for simple machines (unless multi-staging is used) at anefficiency of about 70 80%. The axial flow compressor, however, can achievehigher pressures at a higher level of efficiency. There are two importantcharacteristics of the axial flow compressor high-pressure ratios at goodefficiency and thrust per unit frontal area. Although in overall appearance, axialturbines are very similar, examination of the blade cross-section will indicate abig difference. In the turbine, inlet passage area is greater than the outlet. Theopposite occurs in the compressor, as shown in Fig. the process in turbine blades can be described as an accelerating flow,the increase in velocity being achieved by the nozzle. However, in the axial flowcompressor, the flow is decelerating or diffusing and the pressure rise occurswhen the fluid passes through the blades.

2 As mentioned in the chapter on diffuserdesign (Chapter 4, Sec. ), it is much more difficult to carry out efficientdiffusion due to the breakaway of air molecules from the walls of the divergingpassage. The air molecules that break away tend to reverse direction and flowback in the direction of the pressure gradient. If the divergence is too rapid, thismay result in the formation of eddies and reduction in useful pressure rise. Duringacceleration in a nozzle, there is a natural tendency for the air to fill the passageCopyright 2003 by Marcel Dekker, Inc. All Rights Reservedwalls closely (only the normal friction loss will be considered in this case).Typical blade sections are shown in Fig. Modern axial flow compressors maygive efficiencies of 86 90% compressor Design technology is a well-developedfield. Axial flow compressors consist of a number of stages, each stage beingformed by a stationary row and a rotating row of shows how a few compressor stages are built into the axialcompressor.

3 The rotating blades impart kinetic energy to the air while increasingair pressure and the stationary row of blades redirect the air in the proper directionand convert a part of the kinetic energy into pressure. The flow of air through thecompressor is in the direction of the axis of the compressor and, therefore, it iscalled an axial flow compressor. The height of the blades is seen to decrease asthe fluid moves through the compressor. As the pressure increases in the directionof flow, the volume of air decreases. To keep the air velocity the same for eachstage, the blade height is decreased along the axis of the compressor. An extrarow of fixed blades, called the inlet guide vanes, is fitted to the compressor are provided to guide the air at the correct angle onto the first row ofmoving blades. In the analysis of the highly efficient axial flow compressor,the 2-D flow through the stage is very important due to cylindrical sketch of a typical axial compressor assembly: the GeneralElectric J85 compressor.

4 (Courtesy of General Electric Co.)Chapter 5188 Copyright 2003 by Marcel Dekker, Inc. All Rights ReservedFigure of an axial compressor and turbine blade passages: turbine and compressor Flow Compressors and Fans189 Copyright 2003 by Marcel Dekker, Inc. All Rights ReservedThe flow is assumed to take place at a mean blade height, where the bladeperipheral velocities at the inlet and outlet are the same. No flow is assumed in theradial VELOCITY DIAGRAMThe basic principle of axial compressor operation is that kinetic energy isimparted to the air in the rotating blade row, and then diffused through passagesof both rotating and stationary blades. The process is carried out over multiplenumbers of stages. As mentioned earlier, diffusion is a deceleration process. It isefficient only when the pressure rise per stage is very small. The blading diagramand the velocity triangle for an axial flow compressor stage are shown in Fig.

5 Enters the rotor blade with absolute velocityC1at an anglea1measuredfrom the axial direction. Air leaves the rotor blade with absolute velocityC2at ananglea2. Air passes through the diverging passages formed between the rotorblades. As work is done on the air in the rotor blades,C2is larger thanC1. Therotor row has tangential velocityU. Combining the two velocity vectors gives therelative velocity at inletV1at an the relative velocity at the rotoroutlet. It is less thanV1, showing diffusion of the relative velocity has taken placewith some static pressure rise across the rotor blades. Turning of the air towardsthe axial direction is brought about by the camber of the blades. Euler s equationFigure diagrams for a compressor 5190 Copyright 2003 by Marcel Dekker, Inc. All Rights Reservedprovides the work done on the air:Wc U Cw22Cw1 5:1 Using the velocity triangles, the following basic equations can be written:UCa tana1 tanb1 5:2 UCa tana2 tanb2 5:3 in whichCa Ca1 C2is the axial velocity, assumed constant through the work done equation [Eq.]

6 ( )] may be written in terms of air angles:Wc UCa tana22tana1 5:4 also,Wc UCa tanb12tanb2 5:5 The whole of this input energy will be absorbed usefully in raising the pressure andvelocity of the air and for overcoming various frictional losses. Regardless of thelosses, all the energy is used to increase the stagnation temperature of the air, the velocity of air leaving the first stageC3is made equal toC1, then thestagnation temperature rise will be equal to the static temperature rise,KTs. Hence:T0s DTs UCaCp tanb12tanb2 5:6 Equation ( ) is the theoretical temperature rise of the air in one stage. In reality,the stage temperature rise will be less than this value due to 3-D effects in thecompressor annulus. To find the actual temperature rise of the air, a factorl, whichis between 0 and 100%, will be used. Thus the actual temperature rise of the air isgiven by:T0s lUCaCp tanb12tanb2 5:7 IfRsis the stage pressure ratio andhsis the stage isentropic efficiency, then:Rs 1 hsDT0sT01 g=g21 5:8 whereT01is the inlet stagnation Flow Compressors and Fans191 Copyright 2003 by Marcel Dekker, Inc.

7 All Rights DEGREE OF REACTIONThe degree of reaction,L, is defined as:L Static enthalpy rise in the rotorStatic enthalpy rise in the whole stage 5:9 The degree of reaction indicates the distribution of the total pressure rise into thetwo types of blades. The choice of a particular degree of reaction is important inthat it affects the velocity triangles, the fluid friction and other :DTA the static temperature rise in the rotorDTB the static temperature rise in the statorUsing the work input equation [Eq. ( )], we get:Wc Cp DTA DTB DTS UCa tanb12tanb2 UCa tana22tana1 ) 5:10 But since all the energy is transferred to the air in the rotor, using the steady flowenergy equation, we have:Wc CpDTA 12 C222C21 5:11 Combining Eqs. ( ) and ( ), we get:CpDTA UCa tana22tana1 212 C222C21 from the velocity triangles,C2 Cacosa2andC1 Cacosa1 Therefore,CpDTA UCa tana22tana1 212C2a sec2a22sec2a1 UCa tana22tana1 212C2a tan2a22tan2a1 Using the definition of degree of reaction,L DTADTA DTB UCa tana22tana1 212C2a tan2a22tan2a1 UCa tana22tana1 12 CaU tana2 tana1 Chapter 5192 Copyright 2003 by Marcel Dekker, Inc.

8 All Rights ReservedBut from the velocity triangles, adding Eqs. ( ) and ( ),2 UCa tana1 tanb1 tana2 tanb2 Therefore,L Ca2U2 UCa22 UCa tanb1 tanb2 Ca2U tanb1 tanb2 5:12 Usually the degree of reaction is set equal to 50%, which leads to this interestingresult: tanb1 tanb2 UCa:Again using Eqs. ( ) and ( ),tana1 tanb2;i:e:;a1 b2tanb1 tana2;i:e:;a2 b1As we have assumed thatCais constant through the stage,Ca C1cosa1 C3cosa3:Since we knowC1 C3, it follows thata1 a3. Because the angles are equal,a1 b2 a3, andb1 a2. Under these conditions, the velocity triangles becomesymmetric. In Eq. ( ), the ratio of axial velocity to blade velocity is called theflow coefficient and denoted byF. For a reaction ratio of 50%,(h22h1) (h32h1), which implies the static enthalpy and the temperatureincrease in the rotor and stator are equal. If for a given value ofCa=U,b2is chosento be greater thana2(Fig.)

9 , then the static pressure rise in the rotor is greaterthan the static pressure rise in the stator and the reaction is greater than 50%.Figure Flow Compressors and Fans193 Copyright 2003 by Marcel Dekker, Inc. All Rights ReservedConversely, if the designer choosesb2less thanb1, the stator pressure rise will begreater and the reaction is less than 50%. STAGE LOADINGThe stage-loading factorCis defined as:C WcmU2 h032h01U2 l Cw22Cw1 U lCaU tana22tana1 C lF tana22tana1 5:13 LIFT-AND-DRAG COEFFICIENTSThe stage-loading factorCmay be expressed in terms of the lift-and-dragcoefficients. Consider a rotor blade as shown in Fig. , with relative velocityvectorsV1andV2at anglesb1andb2. Let tan bm tan b1 tan b2 /2. Theflow on the rotor blade is similar to flow over an airfoil, so lift-and-drag forces willbe set up on the blade while the forces on the air will act on the opposite tangential force on each moving blade is:Fx Lcosbm DsinbmFx Lcosbm1 CDCL tanbm 5:14 where: L lift and D forces on a compressor rotor 5194 Copyright 2003 by Marcel Dekker, Inc.

10 All Rights ReservedThe lift coefficient is defined as:CL L0:5rV2mA 5:15 where the blade area is the product of the chord c and the span Cacosbminto the above equation,Fx rC2aclCL2secbm1 CDCL tanbm 5:16 The power delivered to the air is given by:UFx mh032h01 rCals h032h01 5:17 considering the flow through one blade passage of , h032h01U2 FxrCalsU 12 CaU cs secbm CL CDtanbm 12cs secbm CL CDtanbm 5:18 For a stage in whichbm 458, efficiency will be maximum. Substituting thisback into Eq. ( ), the optimal blade-loading factor is given by:Copt wffiffiffi2pcs CL CD 5:19 For a well-designed blade,CDis much smaller thanCL, and therefore the optimalblade-loading factor is approximated by:Copt wffiffiffi2pcs CL 5:20 CASCADE NOMENCLATUREAND TERMINOLOGYS tudying the 2-D flow through cascades of airfoils facilitates designing highlyefficient axial flow compressors.