Gas Turbine Engineering Handbook 2 Episode 6 pps

Centrifugal Section of an Impeller The flow in this section of the impeller enters from the inducer section andleaves the impeller in the radial direction.. The flow in this section is n

Figure 6-18 Velocity profiles through a centrifugal compressor.

The function of an inducer is to increase the fluid's angular momentumwithout increasing its radius of rotation In an inducer section the bladesbend toward the direction of rotation as shown in Figure 6-19 The inducer

is an axial rotor and changes the flow direction from the inlet flow angle tothe axial direction It has the largest relative velocity in the impeller and, ifnot properly designed, can lead to choking conditions at its throat as shown

in Figure 6-19

There are three forms of inducer camber lines in the axial direction Theseare circular arc, parabolic arc, and elliptical arc Circular arc camber linesare used in compressors with low pressure ratios, while the elliptical arcproduces good performance at high pressure ratios where the flow hastransonic mach numbers

Figure 6-19 Inducer centrifugal compressor

Because of choking conditions in the inducer, many compressors porate a splitter-blade design The flow pattern in such an inducer section

incor-is shown in Figure 6-20a Thincor-is flow pattern indicates a separation on thesuction side of the splitter blade Other designs include tandem inducers Intandem inducers the inducer section is slightly rotated as shown in Figure6-20b This modification gives additional kinetic energy to the boundary,which is otherwise likely to separate

Centrifugal Section of an Impeller

The flow in this section of the impeller enters from the inducer section andleaves the impeller in the radial direction The flow in this section is not com-pletely guided by the blades, and hence the effective fluid outlet angle doesnot equal the blade outlet angle

To account for flow deviation (which is similar to the effect accounted for

by the deviation angle in axial-flow machines), the slip factor is used:

where V2 is the tangential component of the absolute exit velocity with afinite number of blades, and V21 is the tangential component of theabsolute exit velocity, if the impeller were to have an infinite number ofblades (no slipping back of the relative velocity at outlet).

With radial blades at the exit,

Inertia and centrifugal forces cause the fluid elements to move closer toand along the leading surface of the blade toward the exit Once out of theblade passage, where there is no positive impelling action present, these fluidelements slow down

Causes of Slip in an Impeller

The definite cause of the slip phenomenon that occurs within an impeller

is not known However, some general reasons can be used to explain why theflow is changed

Figure 6-21 Forces and flow characteristics in a centrifugal compressor

Coriolis circulation Because of the pressure gradient between the walls

of two adjacent blades, the Coriolis forces, the centrifugal forces, and thefluid follow the Helmholtz vorticity law The combined gradient that resultscauses a fluid movement from one wall to the other and vice versa Thismovement sets up circulation within the passage as seen in Figure 6-22.Because of this circulation, a velocity gradient results at the impeller exitwith a net change in the exit angle

Boundary-layer development The boundary layer that developswithin an impeller passage causes the flowing fluid to experience a smallerexit area as shown in Figure 6-23 This smaller exit is due to small flow(if any) within the boundary layer For the fluid to exit this smaller area,its velocity must increase This increase gives a higher relative exit velocity

Figure 6-22 Coriolis circulation

Figure 6-23 Boundary-layer development

Since the meridional velocity remains constant, the increase in relativevelocity must be accompanied with a decrease in absolute velocity.

Although it is not a new approach, boundary-layer control is being usedmore than ever before It has been used with success on airfoil designs when

it has delayed separation, thus giving a larger usable angle of attack Control

of the flow over an airfoil has been accomplished in two ways: by using slotsthrough the airfoil and by injecting a stream of fast-moving air

Separation regions are also encountered in the centrifugal impeller asshown previously Applying the same concept (separation causes a loss inefficiency and power) reduces and delays their formation Diverting the slow-moving fluid away lets the separation regions be occupied by a faster stream

of fluid, which reduces boundary-layer build-up and thus decreases separation

To control the boundary layer in the centrifugal impeller, slots in theimpeller blading at the point of separation are used To realize the fullcapability of this system, these slots should be directional and converging

in a cross-sectional area from the pressure to the suction sides as seen inFigure 6-24 The fluid diverted by these slots increases in velocity andattaches itself to the suction sides of the blades This results in moving theseparation region closer to the tip of the impeller, thus reducing slip andlosses encountered by the formation of large boundary-layer regions Theslots must be located at the point of flow separation from the blades Experi-mental results indicate improvement in the pressure ratio, efficiency, andsurge characteristics of the impeller as seen in Figure 6-24

Leakage Fluid flow from one side of a blade to the other side is referred

to as leakage Leakage reduces the energy transfer from impeller to fluid anddecreases the exit velocity angle

Number of vanes The greater the number of vanes, the lower the vaneloading, and the closer the fluid follows the vanes With higher vane load-ings, the flow tends to group up on the pressure surfaces and introduces avelocity gradient at the exit

Vane thickness Because of manufacturing problems and physicalnecessity, impeller vanes are thick When fluid exits the impeller, the vanes

no longer contain the flow, and the velocity is immediately slowed Because

it is the meridional velocity that decreases, both the relative and absolutevelocities decrease, changing the exit angle of the fluid

A backward-curved impeller blade combines all these effects The exitvelocity triangle for this impeller with the different slip phenomenon changes

is shown in Figure 6-25 This triangle shows that actual operating conditionsare far removed from the projected design condition

Several empirical equations have been derived for the slip factor (seeFigure 6-26) These empirical equations are limited Two of the morecommon slip factors are presented here.

Stodola Slip Factor

The second Helmholtz law states that the vorticity of a frictionless fluiddoes not change with time Hence, if the flow at the inlet to an impeller isirrotational, the absolute flow must remain irrotational throughout theimpeller As the impeller has an angular velocity !, the fluid must have anangular velocityÐ! relative to the impeller This fluid motion is called therelative eddy If there were no flow through the impeller, the fluid in the

Figure 6-24 Percent design flowÐlaminar flow control in a centrifugal pressor

com-Figure 6-25 Effect on exit velocity triangles by various parameters.

Figure 6-26 Various slip factors as a function of the flow coefficient

impeller channels would rotate with an angular velocity equal and opposite

to the impeller's angular velocity

To approximate the flow, Stodola's theory assumes that the slip is due tothe relative eddy The relative eddy is considered as a rotation of a cylinder

of fluid at the end of the blade passage at an angular velocity ofÐ! about itsown axis The Stodola slip factor is given by

 ˆ 1 Z 1 Vsin 2

m2cot 2

U2

264

37

where:

2ˆ the blade angle

Z ˆ the number of blades

Vm2ˆ the meridional velocity

U2ˆ blade tip speed

Calculations using this equation have been found to be lower than mental values

experi-Stanitz Slip Factor

Stanitz calculated blade-to-blade solutions for eight impellers andconcluded that for the range of conditions covered by the solutions, U is

a function of the number of blades (Z), and the blade exit angle ( 2) isapproximately the same whether the flow is compressible or incompressible

further improvement in efficiency will be gained only by improving thepressure recovery characteristics of the diffusing elements of these machines,since these elements have the lowest efficiency.

The performance characteristics of a diffuser are complicated functions ofdiffuser geometry, inlet flow conditions, and exit flow conditions Figure 6-27

Figure 6-27 Geometric classification of diffusers

shows typical diffusers classified by their geometry The selection of anoptimum channel diffuser for a particular task is difficult, since it must bechosen from an almost infinite number of cross-sectional shapes and wallconfigurations In radial and mixed-flow compressors the requirement ofhigh performance and compactness leads to the use of vaned diffusers asshown in Figure 6-28 Figure 6-28 also shows the flow regime of a vane-island diffuser.

Matching the flow between the impeller and the diffuser is complexbecause the flow path changes from a rotating system into a stationaryone This complex, unsteady flow is strongly affected by the jet-wake ofthe flow leaving the impeller, as seen in Figure 6-29 The three-dimensionalboundary layers, the secondary flows in the vaneless region, and the flowseparation at the blades also affects the overall flow in the diffuser

The flow in the diffuser is usually assumed to be of a steady nature toobtain the overall geometric configuration of the diffuser In a channel-typediffuser the viscous shearing forces create a boundary layer with reducedkinetic energy If the kinetic energy is reduced below a certain limit, the flow

in this layer becomes stagnant and then reverses This flow reversal causes

Figure 6-28 Flow regions of the vaned diffuser

separation in a diffuser passage, which results in eddy losses, mixing losses,and changed-flow angles Separation should be avoided or delayed toimprove compressor performance.

The high-pressure-ratio centrifugal compressor has a narrow yet stableoperating range This operating range is due to the close proximity of thesurge and choke flow limits The word ``surge'' is widely used to expressunstable operation of a compressor Surge is the flow breakdown periodduring unstable operation The unsteady flow phenomena during the onset

of surge in a high-pressure-ratio centrifugal compressor causes the mass flowthroughout the compressor to oscillate during supposedly ``stable'' operations.The throat pressure in the diffuser increases during the precursor period

up to collector pressure Pcol at the beginning of surge All pressure traces(except plenum pressure) suddenly drop at the surge point The suddenchange of pressure can be explained by the measured occurrence of backflowfrom the collector through the impeller during the period between the twosudden changes

Figure 6-29 Jet-wake flow distribution from an impeller

Scroll or Volute

The purpose of the volute is to collect the fluid leaving the impeller ordiffuser, and deliver it to the compressor outlet pipe The volute has animportant effect on the overall efficiency of the compressor Volute designembraces two schools of thought First, the angular momentum of the flow

in the volute is constant, neglecting any friction effects The tangentialvelocity V5 is the velocity at any radius in the volute The following equa-tion shows the relationship if the angular momentum is held constant

Assuming no leakage past the tongue and a constant pressure around theimpeller periphery, the relationship of flow at any section Qto the overallflow in the impeller Q is given by

of the double-vortex in the symmetrical volute Where the impeller is charging directly into the volute, it is better to have the volute width largerthan the impeller width This enlargement results in the flow from the

dis-impeller being bounded by the vortex generated from the gap between theimpeller and the casing.

At flows different from design conditions, there exists a circumferentialpressure gradient at the impeller tip and in the volute at a given radius

Figure 6-30 Flow patterns in volute

At low flows, the pressure rises with the peripheral distance from the volutetongue At high flows, the pressure falls with distance from the tongue Thiscondition results because near the tongue the flow is guided by the outer wall

of the passage The circumferential pressure gradients reduce efficiency awayfrom the design point Nonuniform pressure at the impeller discharge results

in unsteady flows in the impeller passage, causing flow reversal and ation in the impeller

separ-CentrifugalCompressor PerformanceCalculating the performance of a centrifugal compressor in both design andoff-design conditions requires a knowledge of various losses encountered

in a centrifugal compressor

The accurate calculation and proper evaluation of losses within a fugal compressor is as important as the calculation of the blade-loading para-meters If the proper parameters are not controlled, efficiency decreases Theevaluation of various losses is a combination of experimental results and theory.The losses are divided into two groups: (1) losses encountered in the rotor, and(2) losses encountered in the stator

centri-A loss is usually expressed as a loss of heat or enthalpy centri-A convenient way

to express them is in a nondimensional manner with reference to the exitblade speed The theoretical total head available (qtot) is equal to the headavailable from the energy equation

qthˆ 1

U2 2

plus the head, which is lost because of disc friction (
qdf) and resulting fromany recirculation (
qrc) of the air back into the rotor from the diffuser

The adiabatic head that is actually available at the rotor discharge is equal

to the theoretical head minus the heat from the shock in the rotor (
qsh), theinducer loss (
qin), the blade loadings (
qbl), the clearance between therotor and the shroud (
qc), and the viscous losses encountered in the flowpassage (
qsf)

Therefore, the adiabatic efficiency in the impeller is

imp ˆqqia

The calculation of the overall stage efficiency must also include lossesencountered in the diffuser Thus, the overall actual adiabatic head attainedwill be the actual adiabatic head of the impeller minus the head lossesencountered in the diffuser from wake caused by the impeller blade (
qw),the loss of part of the kinetic head at the exit of the diffuser (
qed), andthe loss of head from frictional forces (
qosf) encountered in the vaned orvaneless diffuser space

Rotor losses are divided into the following categories:

Shock in rotor losses This loss is due to shock occurring at the rotorinlet The inlet of the rotor blades should be wedgelike to sustain a weakoblique shock, and then gradually expanded to the blade thickness to avoidanother shock If the blades are blunt, a bow shock will result, causing theflow to detach from the blade wall and the loss to be higher

Incidence loss At off-design conditions, flow enters the inducer at anincidence angle that is either positive or negative, as shown in Figure 6-31

A positive incidence angle causes a reduction in flow Fluid approaching

a blade at an incidence angle suffers an instantaneous change of velocity atthe blade inlet to comply with the blade inlet angle Separation of the bladecan create a loss associated with this phenomenon

Disc friction loss This loss results from frictional torque on the backsurface of the rotor as seen in Figure 6-32 This loss is the same for a given

size disc whether it is used for a radial-inflow compressor or a radial-inflowturbine Losses in the seals, bearings, and gear box are also lumped in withthis loss, and the entire loss can be called an external loss Unless the gap is

of the magnitude of the boundary layer, the effect of the gap size is gible The disc friction in a housing is less than that on a free disc due to theexistence of a ``core,'' which rotates at half the angular velocity

negli-Diffusion-blading loss This loss develops because of negative velocitygradients in the boundary layer Deceleration of the flow increases theboundary layer and gives rise to separation of the flow The adverse pressuregradient that a compressor normally works against increases the chances ofseparation and causes significant loss

Figure 6-31 Inlet velocity triangles at nonzero incidents

Clearance loss When a fluid particle has a translatory motion relative

to a noninertial rotating coordinate system, it experiences the Coriolis force

A pressure difference exists between the driving and trailing faces of animpeller blade caused by Coriolis acceleration The shortest and least resis-tant path for the fluid to flow and neutralize this pressure differential isprovided by the clearance between the rotating impeller and the stationarycasing With shrouded impellers, such a leakage from the pressure side to thesuction side of an impeller blade is not possible Instead, the existence of apressure gradient in the clearance between the casing and the impellershrouds, predominant along the direction shown in Figure 6-33, accountsfor the clearance loss Tip seals at the impeller eye can reduce this lossconsiderably

This loss may be quite substantial The leaking flow undergoes a largeexpansion and contraction caused by temperature variation across the clear-ance gap that affects both the leaking flow and the stream into which itdischarges

Skin friction loss Skin friction loss is the loss from the shear forces

on the impeller wall caused by turbulent friction This loss is determined byconsidering the flow as an equivalent circular cross section with a hydraulicdiameter The loss is then computed based on well-known pipe flow pressureloss equations

Figure 6-32 Secondary flow at the back of an impeller

Stator Losses

Recirculating loss This loss occurs because of backflow into the ler exit of a compressor and is a direct function of the air exit angle As theflow through the compressor decreases, there is an increase in the absoluteflow angle at the exit of the impeller as seen in Figure 6-34 Part of the fluid isrecirculated from the diffuser to the impeller, and its energy is returned tothe impeller

impel-Wake-mixing loss This loss is from the impeller blades, and it causes

a wake in the vaneless space behind the rotor It is minimized in a diffuser,which is symmetric around the axis of rotation

Figure 6-33 Leakage affecting clearance loss

Vaneless diffuser loss This loss is experienced in the vaneless diffuserand results from friction and the absolute flow angle.

Vaned diffuser loss Vaned diffuser losses are based on conical diffusertest results They are a function of the impeller blade loading and the vanelessspace radius ratio They also take into account the blade incidence angle andskin friction from the vanes

Exit loss The exit loss assumes that one-half of the kinetic energy ing the vaned diffuser is lost

leav-Losses are complex phenomena and as discussed here are a function ofmany factors, including inlet conditions, pressure ratios, blade angles, andflow Figure 6-35 shows the losses distributed in a typical centrifugal stage ofpressure ratio below 2:1 with backward-curved blades This figure is only aguideline

Compressor Surge

A plot showing the variation of total pressure ratio across a compressor as

a function of the mass flow rate through it at various speeds is known as aperformance map Figure 6-36 shows such a plot

The actual mass flow rates and speeds are corrected by factors (p=)and (1=p), respectively, to account for variation in the inlet conditions oftemperature and pressure The surge line joins the different speed lines where

Figure 6-34 Recirculating loss

the compressor's operation becomes unstable A compressor is in ``surge''when the main flow through the compressor reverses its direction and flowsfrom the exit to the inlet for short time intervals If allowed to persist, thisunsteady process may result in irreparable damage to the machine Lines

of constant adiabatic efficiency (sometimes called efficiency islands) are alsoplotted on the compressor map A condition known as ``choke'' or ``stonewalling'' is indicated on the map, showing the maximum mass flow ratepossible through the compressor at that operating speed

Compressor surge is a phenomenon of considerable interest, yet it is notfully understood It is a form of unstable operation and should be avoided inboth design and operation Surge has been traditionally defined as the lowerlimit of stable operation in a compressor and involves the reversal of flow.This reversal of flow occurs because of some kind of aerodynamic instabilitywithin the system Usually a part of the compressor is the cause of theaerodynamic instability, although it is possible that the system arrangementcould be capable of augmenting this instability Figure 6-36 shows a typical

Figure 6-35 Losses in a centrifugal compressor

performance map for a centrifugal compressor with efficiency islands andconstant aerodynamic speed lines The total pressure ratio can be seen tochange with flow and speed Compressors are usually operated at a workingline separated by some safety margin from the surge line.

Surge is often symptomized by excessive vibration and an audible sound;however, there have been cases in which surge problems that were not audiblehave caused failures Extensive investigations have been conducted on surge.Poor quantitative universality of aerodynamic loading capacities of differentdiffusers and impellers, and an inexact knowledge of boundary-layer behaviormake the exact prediction of flow in turbomachines at the design stagedifficult However, it is quite evident that the underlying cause of surge isaerodynamic stall The stall may occur in either the impeller or the diffuser

Figure 6-36 Typical compressor performance map

When the impeller seems to be the cause of surge, the inducer section

is where the flow separation begins A decrease in the mass flow rate, anincrease in the rotational speed of the impeller, or both can cause the com-pressor to surge

Surge can be initiated in the diffuser by flow separation occurring atthe diffuser entrance A diffuser usually consists of a vaneless space withthe prediffuser section before the throat containing the initial portion of thevanes in a vaned diffuser The vaneless space accepts the velocity generated

by the centrifugal impeller and diffuses the flow so that it enters the vaneddiffuser passage at a lower velocity, avoiding any shock losses and resultantseparation of the flow When the vaneless diffuser stalls, the flow will notenter the throat A separation occurs, causing the flow to finally reverse andsurge the compressor Stalling of the vaneless diffuser can be accomplished

in two waysÐby increasing impeller speed or decreasing the flow rate.Whether surge is caused by a decrease in flow velocity or an increase inrotational speeds, either the inducer or vaneless diffuser can stall Whichstalls first is difficult to determine, but considerable testing has shown thatfor a low-pressure-ratio compressor, the surge initiates in the diffuser sec-tion For units with single-stage pressure ratios above 3:1, surge is probablyinitiated in the inducer

Most centrifugal compressors have for the most part impellers with ward leaning impeller blades Figure 6-37 depicts the effects of impellerblade angle on the stable range and shows the variance in steepness of theslope of the head-flow curve

back-The three curves are based on the same speed and show actual head back-Therelationship of ideal or theoretical head to inlet flow for different bladeangles would be represented by straight lines For backward leaning blades,the slope of the line would be negative The line for radial blades would

be horizontal Forward leaning blades would have a positively sloped line.For the average petrochemical process plant application, the compressorindustry commonly uses a backward-leaning blade with an angle ( 2) ofbetween about 55±75 (or backward leaning angle of 15±35), because

it provides a wider stable range and a steeper slope in the operating range.This impeller design has proven to be about the best compromise betweenpressure delivered, efficiency, and stability Forward leaning blades are notcommonly used in compressor design, since the high exit velocities lead tolarge diffuser losses A plant air compressor operating at steady conditionsfrom day to day would not require a wide stable range, but a machine in aprocessing plant can be the victim of many variables and upsets So morestability is highly desirable Actually, the lower curve in Figure 6-37 appears

to have a more gentle slope than either the middle or upper curve This

comparison is true in the overall sense, but it must be remembered that thenormal operating range lies between 100% flow (Q) and flow at surge, plus

a safety margin of, usually, about 10% The right-hand tail ends of all threecurves are not in the operating range The machine must operate with asuitable margin to the left of where these curves begin their steep decent ortail-off, and in the resultant operating range, the curve for backward leaningblades is steeper This steeper curve is desirable for control purposes Such

a curve produces a meaningful change in pressure drop across the orifice for

a small change in flow The blade angle by itself does not tell the overallperformance story The geometry of other components of a stage will con-tribute significant effects also

Most centrifugal compressors in service in petroleum or petrochemicalprocessing plants use vaneless diffusers A vaneless diffuser is generally asimple flow channel with parallel walls and does not have any elementsinside to guide the flow

Forward Leaning Blade β 2 > 90°

Radial Blade

β 2 = 90°

Backward Leaning Blade β 2 < 90°

When the inlet flow to the impeller is reduced while the speed is heldconstant, there is a decrease in the relative velocity leaving the impeller andthe air angle associated with it As the air angle decreases, the length of theflow path spiral increases The effect is shown in Figure 6-38.

If the flow path is extended enough, the flow momentum at the diffuserwalls is excessively dissipated by friction and stall With this greater loss, thediffuser becomes less efficient and converts a proportionately smaller part

of the velocity head to pressure As this condition progresses, the stage willeventually stall This could lead to a surge

Vaned diffusers are used to force the flow to take a shorter, more efficientpath through the diffuser There are many styles of vaned diffusers, withmajor differences in the types of vanes, vane angles and contouring, andvane spacing Commonly used vaned diffusers employ wedge-shaped vanes(vane islands) or thin-curved vanes In high head stages, there can be two tofour stages of diffusion These usually consist of vaneless spaces to deceleratethe flow, followed by two or three levels of vaned blades in order to preventbuild-up of boundary layer, which causes separation and surging of thecompressor Figure 6-38 indicates the flow pattern in a vaned diffuser Thevaned diffuser can increase the efficiency of a stage by two to four percen-tage points, but the price for the efficiency gain is generally a narroweroperating span on the head-flow curve with respect to both surge andstonewall Figure 6-39 also shows the effect of off-design flows

Excessive positive incidence at the leading edge of the diffuser vane occurswhen the exit flow is too small at reduced flow, and this condition brings on astall Conversely, as flow increases beyond the rated point, excessive negative

Impeller Eye Blade Diffuser O.D.

Paths of Particle in Diffuser

Normal Condition Good Flow Angle Relatively Short Flow Path.

Minimum Friction Loss

Near Surge Shallow Flow Angle.

Long Flow Path High Frictional Loss Possibility of Flow Re-entering the Impeller.

Impeller O D

Figure 6-38 Flow trajectory in a vaneless diffuser

m2cot 2< /small>

U2< /small>

26 4

37

where:

2< /small>ˆ the blade angle

Z... instability Figure 6- 36 shows a typical

Figure 6- 35 Losses in a centrifugal compressor

performance... ofhigh performance and compactness leads to the use of vaned diffusers asshown in Figure 6 -28 Figure 6 -28 also shows the flow regime of a vane-island diffuser.

Matching the flow between