turbopump i ection* · 2019. 8. 1. · keywords: cfd,turbopump,diffuser, flowseparation,...

International Journal of Rotating Machinery2000, Vol. 6, No. 1, pp. 57-65

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Simulation of Flow in Turbopump Vaneless and VanedDiffusers with Fluid I ection*

ALI OGUT and DIEGO GARCIA PASTOR

Department of Mechanical Engineering, Rochester Institute of Technology, Rochester, NY 14623, USA

(Received 24 April 1998;In finalform 21 July 1998)

In future space missions by NASA there will be a need for "Space Transfer Vehicles" toperform varying orbital transfers and descents. This requires engines capable of producingdifferent levels of thrust. To accomplish this, the turbopumps employed in these enginesshould efficiently provide a wide range of flow outputs. However, current fuel and oxidizerturbopumps with vaned diffusers do not perform efficiently at off-design (low) flow ratesmainly due to flow separation in the vaned diffuser.

This paper evaluates the effectiveness of boundary layer control by fluid injection(blowing) for suppressing or eliminating the flow separation in a vaned diffuser. A 3-D flowmodel including vaneless and vaned diffusers of a liquid hydrogen (LH2) turbopump is studiedusing the CFD code FIDAP. The paper presents the results of the model at design and off-design flow conditions.The model results showed that flow separation occurs at the top or suction surface of the

vaneless diffuser and at the bottom or pressure surface of the vaned diffuser at off-design flowrates. When fluid injection was applied through the bottom surface of the vaned diffuser, theseparated flow region was reduced almost entirely, resulting in an increase in pressurerecovery of up to 21% with varying fluid injection rates. Results also showed that there is anoptimum injection rate which is most effective in reducing or eliminating the region of flowseparation.

Keywords: CFD, Turbopump, Diffuser, Flow separation, Boundary layer control, Fluid injection

INTRODUCTION

The future space missions planned by NASA willuse "Space Transfer Vehicles" to perform orbitaltransfer missions and Lunar/Mars transfers anddescents. In order to do this efficiently, the vehiclemust have a deep-engine throttling capability that

can be obtained by designing a high performanceLiquid Hydrogen (LH2) turbopump which can

efficiently output different flow rates or operate at

off-design conditions.The current designs of turbopumps with vaned

diffusers do not perform efficiently at off-designflow rates due to flow separation and stall in the

This paper was originally presented at ISROMAC-7.Corresponding author.

57

58 A. OGUT AND D.G. PASTOR

vaned diffuser. Particularly, at low flow rates,impeller discharge effects and increased boundarylayer blockage in the vaneless and vaned diffuserslead to flow separation in the vaned diffuser.The subject of this paper is to provide an insight

into the effectiveness of fluid injection as a bound-ary layer control method in suppressing or elim-inating flow separation in the vaned diffuser atoff-design flow conditions. The effectiveness of thismethod will be demonstrated by obtaining a pres-sure recovery significantly higher with fluid injec-tion than without at off-design flow conditions.The intent is to demonstrate the applicability ofboundary layer control by fluid injection methodfor improving the performance of a three-dimen-sional vaned diffuser and to use the results to

modify the diffuser design for improved turbopumpperformance at off-design flow conditions.The model employed here includes the addition

of the vaneless diffuser section to the previouslystudied vaned diffuser model by Ogut and Yoshida(1994), so that a more realistic model which ac-counts for the impeller discharge effects can bestudied. In addition, for the control of boundarylayer, fluid injection is used instead of fluid suction.A finite-element based code, FIDAP was used for

flow analysis.

BACKGROUND

A vaned diffuser is one ofthe basic components of aturbopump. Its function is to convert inlet dynamicpressure (kinetic energy) to a static pressure rise.For subsonic flows this is accomplished by deceler-ating the fluid particles with a continuos increase ofthe diffuser cross-sectional area. The desired effectis to recover as much of the inlet dynamic pressureas possible under a steady flow condition.However, since the diffuser performs in an adverse

pressure gradient field, operating it at off-designconditions, such as at low flow rates, often leads toflow separation and stall.

Lariviere (1989), and Lariviere and Prueger(1989), tlrough experimental work, has shown that

high performance multistage turbopumps withvaned diffusers often develop stall related instabil-ities at low (off-design) flow rates. For efficientoverall pump performance the stall and flowseparation in these diffusers must be prevented.This requires new design concepts and improvedprediction methods which can lead to the necessarydesign modifications in the diffuser geometry.

Diffuser Performance

The subject of fluid-flow in diffusers contains manyreferences. Particularly Kline and Fox (1962)addressed the issue of diffuser stall in detail anddefined four major areas of diffuser stall known as"no appreciable stall", "large transitory stall","fully developed two-dimensional stall", and "jetflow". Based upon N/W1 and 20 of a vaned diffuser,they developed a chart showing these four stallregions. This chart has been useful in the design ofstall-free vaned diffusers.A diffuser performance depends upon its partic-

ular geometry, and because it operates with anadverse pressure gradient field, its efficiency islimited. The geometry of a diffuser is fully specifiedby the aspect ratio b/W1 and any two of the L/N/W1, and the area ratio, W2/WI. The performanceof a diffuser is specified by the pressure recoverycoefficient:

Cp -P -P

where p is the pressure and Vt is the mean throatvelocity. An ideal pressure recovery coefficient canalso be defined and can be shown to be:

Cp,idea (2)

where AR is the area ratio.

Turbulent Flow Model

The turbulent flow can be described at every pointby Navier-Stokes (N-S) equations. For the flow

SIMULATION OF FLOW 59

in a diffuser with the assumptions of steady,incompressible, isothermal and Newtonian flowconditions the time-averaged (the usual overbarsymbol omitted except for the fluctuating quanti-ties) N-S equations for the conservation of massand momentum can be written as:

Obl=0, (3)Ox

---+Oxi

+ + (4),

The addition of -puiu) (known as the Reynoldsstress) to the momentum equation prevents thesolution of the above set of equations. Conse-quently, the two-equations k-c turbulence modelis usually employed to facilitate the solution.The k-c model leads to the use of eddy viscosity

defined by:

pk2

/t- C#-- (5)

along with transport equation for k and e"

P Ui ---xj - -pG-pe (6)

and

p uj -- -Clp-G-c2p- (7)

where G is the shear generation term defined as:

Oui

and modeled as:

G "-’ (0.; 0.;p OXj

-3t-OXiJ OXj" (9)

In these equations: C,, cl, 2, O’k, and crc are takenas 0.09, 1.44, 1.92, 1.0 and 1.3 respectively.The k-e model used is only applicable in fully

turbulent (high Reynolds number) region. The solu-tion is extended to the wall region by employingLaw of the Wall models.The Law of the Wall models are developed by

using the dominant shear analysis. In the near-wallregion the total shear stress containing thecombined effects of laminar and turbulent shear isconstant. In the viscous sublayer (y+< 5), thelaminar shear is dominant:

V’tot ]Z (10)

which by appropriate substitutions and rearrange-ments leads to"

u pu*yu*

which by definition can be expressed as"

u+ y+. (12)

In the fully developed turbulent region justbeyond y+-30, where the turbulent shear isdominant, the total shear is still constant and can

be set equal to -*:

-r* pu* pu’ v’. (13)

Using dimensional reasoning, Eq. (13) can bewritten in the form of a velocity profile"

u+ 1ln(Ey+) (14)

where =0.41 and is known as the von Karmanconstant and E is an empirical constant (roughnessparameter) found to be 9.0 for smooth walls.

Similarly, from dimensional analysis the equa-tions for k and e for the wall region are given by:

k C-0"5b/.2 (15)


and

H*3c (16)

Equations (12), (14), (15) and (16) are the basis ofthe Law of the Wall models. These equations areemployed in the diffuser flow analysis.

injection can improve the performance ofa diffuser.Bahl (1985) investigated the two-dimensionalboundary layer separation and attachment due tosmall blowing through a transverse porous slot. Hiswork showed that higher blowing velocities cancause the formation ofa separation region upstreamof the jet.

Boundary-Layer Control by Fluid Injection

The reduction or elimination of flow separationand stall in a vaned diffuser has been investigatedas an alternative to modifying its geometry. Oneapproach that has been used for correcting flowseparation is boundary layer control by fluid injec-tion. This method consists of near-wall momentumaddition to re-energize the near-wall fluid particleswhich are being retarded in the boundary layer.This can be accomplished in active or passivemanner.

In the case ofthe active method, a fluid is injectedparallel to the wall to augment the shear-layermomentum or normal to the wall to enhance themixing rate. Either a blower or the pressure differ-ential that exits in the passage is utilized to inject thefluid into the retarded region of the boundary layer.Schwendemann and Sanders (1982) showed that

the efficiency of the fluid injection depends on themomentum of the injected fluid and the distancebetween the injection slit and the boundary layerseparation point. It is indicated that for the injec-tion to be effective, this distance must be longenough to allow sufficient time for the mixingprocess to facilitate the momentum transfer fromthe jet to the boundary layer. At the same time itshould be short enough to ensure that the new

boundary layer developing between the wall and thejet does not grow to the point of separating fromthe wall. In addition the jet maximum velocity de-creases with an increase of this distance, whichtends to make the process inefficient.A literature search provided few references on

the use of fluid injection for control of boundarylayer growth in a diffuser. Ball (1983) experimen-tally showed that using either fluid suction or

The FIDAP Code

In this study, FIDAP was used to predict local flowseparation, regions of stagnation, and secondaryflow patterns within the vaneless and vaned dif-fusers of a LH2 turbopump.FIDAP is a finite-element based CFD code. It

provides several turbulence models for solving theReynolds averaged Navier-Stokes equations forturbulent flow. In this study, the solution is madepossible by employing the two-equation k-cturbulence model. Eight-noded brick elements wereselected for the continuum flow to reduce thecomputational time required to obtain a solution.For greater accuracy of turbulent modeling, four-noded quadrilateral elements were chosen for thenear-wall region. These elements invoke the near-wall model within FIDAP that connects the sharpgradients in the near-wall region with the freestream region. The 3-D model consisted of 45,000grid points.

Application

The diffuser flow passage being studied is a scaled-up model (scale factor: 10) of the diffusing cross-over section of a NASA LH2 turbopump (Model:MK49-F). This turbopump has 17 interstage radialcontinuous crossover passages per stage. A passageconsists of a vaneless diffuser, a three-dimensionalvaned diffuser (upcomer), followed by a turningchannel which is followed by a downcomer diffuser.The turbopump vaned diffuser has a square throatarea with 25.4 mm in height, expanding to a squaredischarge area with a height of 42mm with an

half divergence angle of 6 and an axial length of230mm.


In this study, the vaned diffuser along withthe vaneless diffuser and turning channel weremodeled. As indicated earlier, the inclusion of thevaneless diffuser is important since this allowsthe study of impeller discharge effects as well as

the resulting flow structure in the vaneless diffuser.The 3-D mesh plot showing the diffusers withturning channel is given in Fig. 1.The inlet to the vaneless diffuser and the outlet

from it in the circumferential direction are char-acterized by cyclic symmetry so periodic boundaryconditions are used at these planes. In order to

properly simulate impeller outlet (vaneless diffuserinlet) conditions, the flow was introduced into thevaneless diffuser at velocities that would exist at theimpeller blade trailing edge. These velocities were

determined using a meanline pump performanceanalysis program and listed in Table I for the flowrates studied.Although the impeller blade wake effects intro-

duce periodic unsteadiness at the vaned diffuserinlet, the work of Muggli et al. (1996) reported thatno substantial difference can be found between thesteady simulation and the time-averaged of theunsteady simulation of flow in a vaned diffuser of apump. As a result, a steady simulation in the presentstudy was considered to be satisfactory.The model studies were made at design flow rate

with no injection and at 60% off-design flow ratewith and without injection. These off-design flow

top (suction)

hub

reference outlet

iet (impeller discharge)

periodic

i:."..;:

rDAP ?. 06

FIGURE Diffuser mesh.

TABLE Flow parameters

% of Mass flow Re Vr Vodesign flow (kg/s) (m/s) (m/s)

100 3.98 10-4 3.074 105 29.35 517.760 2.39 10-4 1.845 l05 17.61 540.0

TABLE II Slit boundary conditions at off-design flow rate

% of design Injection Injection Vx Vyflow rate flow (kg/s) (m/s) (m/s)

603%7%10%

7.159 x 10-6 7.8 x 10-3 5.46 x 10-3

1.67 x 10-s 1.82 x 10-2 1.274 x 10-2

2.386 x 10-s 2.59 10-2 1.82 x 10.2

rates were selected since the work of Lariviere andPrueger (1989) have shown that stall relatedinstabilities occur in the vaned diffuser in the flowrange less than 76% of the design flow.

Fluid Injection

The fluid injection was applied through the bottomor pressure surface of the vaned diffuser. The fluidwas injected at an angle of 35 from the diffusercenterline through each of the six slits, two beforeand four after the diffuser throat (Fig. 1). Slits were2 mm in width and placed 1.25 cm apart. They were

positioned along the diffuser wall such that theywere shorter in the flow direction and ran the widthof the diffuser.The previous work by Ogut and Yoshida (1994)

showed that injection rates between 3% and 10% ofthe inlet mass flow rate would be effective. Theinjection rates selected in this study were 3%, 7%,and 10% of the inlet mass flow rate. The totalinjection rate was distributed equally across the sixavailable slits with the velocity of the fluid at eachslit being equal. The boundary conditions at slitsare given in Table II for the off-design case.

RESULTS AND DISCUSSION

Flow Patterns Without Injection

In order to establish a baseline model for compar-ison, results corresponding to the design flow rate


were obtained. Under these conditions, velocityprofiles were investigated at various vaned diffuserplanes for evidence of flow separation.

In Fig. 2, the design flow velocity vector plot ofthe entire flow field is shown at a plane 0.8988 mmaway from the shroud side wall. This figure showsthat even at the design flow, the top or suctionsurface of the vaneless diffuser and the bottom or

pressure surface of the vaned diffuser showed someevidence of flow deceleration. The development ofthis weak flow region at the pressure surface of thevaned diffuser is attributed to the upward accele-ration of the main flow into the vaned diffuserthrough the narrowed area between the separatedflow region at the suction surface of the vanelessdiffuser and the leading edge of the vaned diffuser.This resulted in a flow angle pointing towards thetop surface of the vaned diffuser.At 60% of the design flow the same shroud plane

is shown in Fig. 3. It is clear from this figure that thedecelerated flow region became somewhat larger.Figure 4 shows the pressure surface of the vaneddiffuser at the same flow rate. This figure shows thatflow reverses along the hub and shroud walls.

Flow Patterns with Fluid Injection

Various injection rates (3%, 7%, and 10%) weretested. The results showed that both 3%, and 7%injection rates were effective in eliminating the

VECTOR,,LOT

FIGURE 2 2-D view of the shroud plane velocity (designflow).

separated flow region in the vaned diffuser at

60% of the design flow rate with no significantimpact on the region at the suction surface of thevaneless diffuser. Figure 5 shows this result on theshroud wall plane for the 60% case with 3%injection rate. Figure 6 shows the results at thepressure surface at the same flow conditions. Fromthese results it is clear that use of fluid injectioncompletely restores separation-free flow conditions.The possibility of inducing flow separation at the

pressure surface of the vaned diffuser with higherinjection rates was also investigated. It was deter-mined that higher (10%) injection flow rates caninduce flow separation (Fig. 7). This is thought to

LNG 0.000E/0

FIGURE 3 2-D view of the shroud plane velocity (60% ofdesign flow).

0.2132E+00SHROUD

LDINGHUB EDGE

FDAP 7,06-

FIGURE 4 Vaned diffuser bottom plane velocity (60% ofdesign flow).


VECTOR

FIDAP 7.66

FIGURE 5 Vaned diffuser shroud plane velocity (60%-3%injection).

TABLE III Pressure recovery characteristics

Flow Cp (--) Diff. eft. (%)

Ideal condition 0.866 100100% 0.63 7260% 0.56 6460%-3% injection 0.68 7860%-7% injection 0.65 7560%-10% injection 0.55 63

be the result of boundary layer "lift-off" by the flowcoming through the first several injection slits. Inthis case injected flow augments the separated flowregion instead of eliminating it. Bahl (1985) alsoreported that higher blowing velocities causes

formation of a recirculation region.

/VANELEADINGEDGE

FIGURE 6 Vaned diffuser bottom plane velocity (60%-3%injection).

Pressure Recovery Without Fluid Injection

Pressure recovery coefficients for both cases (100%,and 60%) were determined from the vaned diffuserinlet and outlet pressures. These results are shownin Table III. As shown in this table, the pressurerecovery coefficients for the 100%, and 60% of thedesign flow were 0.63, and 0.56, respectively. Theideal pressure recovery coefficient for the vaneddiffuser in this study was determined to be 0.866,which indicates that there is significant room forimprovement.

:_

-.120E+B1,

0.000E-00FOAP 0

FIGURE 7 Vaned diffuser shroud plane velocity (60%-10% injection).

Pressure Recovery with Fluid Injection

With the employment of injection, there was clearevidence of improvement in pressure recovery inthe vaned diffuser. These results are also shown inTable III for the 100%, and 60% of the design flowconditions. As indicated in this table, for the 60% ofthe design flow, the injection rates of 3% achievedthe highest pressure recovery.

These results show that there is a substantialimprovement in pressure recovery over the cases

without injection. Table III also shows the valuesof diffuser efficiency defined as Cp/Cpi for bothcascs.


0.7

0.6

Cp [-] o.

0.4

0.3

10

Injection Rate, %

FIGURE 8 Pressure recovery coefficient.

Optimal Injection Rate

The results in Table III show that the pressurerecovery coefficient, Cp may have an optimal valuecorresponding to a particular fluid injection rate.The Cp values were plotted against the injectionrates and the results are shown in Fig. 8. This figureshows that an injection rate of 3% at 60% of thedesign flow rate may provide the highest pressurerecovery while completely removing the separatedflow region.

CONCLUSIONS

A vaned diffuser operating at off-design flowconditions can experience flow separation.The application of fluid (LH2) injection wasshown to be an effective method for controllingthe growth of the boundary layer and eliminatingthe resulting flow separation in a vaned diffuserat off-design flow conditions.By employment of optimum injection rates,diffuser efficiency was improved by as much as21% at 60% off-design flow conditions.It can also be concluded that there is an ’optimal’injection rate corresponding to the highestpressure recovery at an off-design flow rate.

Higher rates of flow injection can augment theseparated flow region in a vaned diffuser.

NOMENCLATURE

AR area ratiob diffuser throat depth1,2 empirical constants in c

and k equationsC, empirical constant in

viscosity modelCp pressure recovery coefficientCpi ideal pressure recovery

coefficientE empirical constant

(roughness parameter)F body forceG shear generation termk turbulent kinetic energyL diffuser wall lengthLH2 Liquid HydrogenN axial diffuser lengthP fluid pressureRe Reynolds number

ui velocity in/-direction

u+ dimensionless velocity(=u/u*)

u* friction velocity(=*/)/

V vaneless diffuser inletfluid velocity

Vr radial component of velocityVo tangential component of velocityVt diffuser throat fluid velocityW1 diffuser throat width

W2 diffuser exit widthy coordinate distancey+ dimensionless coordinate distance

(= pu*y/#)

Greek Letters

dissipation rate of kdiffuser divergence angleyon Karman constantfluid viscosity


/At

Tk

TrotT*

eddy viscosityfluid densityReynolds stress termturbulent Prandtl numberturbulent Schmidt numbertotal shear stresswall shear stress

Acknowledgment

This work was supported by a grant from NASALewis Research Center, Cleveland, OH, Grant No:NAG3-1153.

References

Bahl, R., 1985. Boundary layer blowing, AIAA Journal, 23(1),157-158.

Ball, W.H., 1983. Experimental investigation of the effects ofwall suction and blowing on the performance of highly offsetdiffusers, AIAA, SAE, and ASME, 19th Joint PropulsionConference.

Kline, S.J. and Fox, R.W., 1962. Flow regime data and designmethods for curved subsonic diffusers, ASME, Journal ofBasic Engineering, 84, 303-312.

Lariviere, B.W., 1989. MK49-F Fuel pump diffuser and cross-over design, Rockwell International, Rocketdyne DivisionR/H 1173-4126.

Lariviere, B.W. and Prueger, G.H., 1989. Performance tests of ahigh velocity ratio diffusing crossover, JANNAF PropulsionMeeting, Cleveland, OH.

Muggli, F.A., Wiss, D., Eisele, K., Zhang, Z., Casey, M.V. andGalpin, P., 1996. Unsteady flow in the vaned diffuser of amedium specific speed pump, ASME/IGTI GT Conference,Birmingham, England.

Ogut, A. and Yoshida, B.R., 1994. CFD Analysis of flow in aturbopump diffuser with wall suction, ASME Fluids Engi-neerin Division Summer Conference, FED-Vol. 196, pp. 295-315.

Schwendemann, M.F. and Sanders, B.W., 1982. Tangentialblowing for control of the strong schock/boundary-layerinteraction on inlet ramps, AIAA Paper No. 82, pp. 1082.

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