Proceedinga of FEDSM’98 1998 ASME Fluids Engineering Division Summer Meeting June 21-25,1998, Washington, DC FEDSM98-4967
NUMERICAL AND EXPERIMENTAL INVESTIGATION OF THE FLOW IN ANNULAR DIFFUSER Berge DJEBEDJIAN
* and Jean-Pierre
RENAUDEAUX
..
* Mechanical Power Engineering Department, Faculty of Engineering Mansoura University, El-Mansoura 35516, EGYPT. E. Mail :
[email protected] u ESCPI, Conservatoire National des Arts et Metiers, 5 Boulevard Descartes, 77420 Champs-sur-Mame, FRANCE. E. Mail :
[email protected]
ABSTRACT
2
Numerical calculation of turbulent separatedflow characteristics in an axial steam turbine engine exhaust diEuser having 22 cylindrical struts in its passageis presented.The used numerical code is based on the resolution of the averaged Navier-Stokes equations and a finite volume formulation. Turbulence is simolated by the k-s model and the Reynolds stress model. Computations are performed for turbulent flow in a sector of l/S of exhaust dif&ser (2 struts / 45’ of the total geometry). In this simplified geometry, the presence of 6 struts is neglected. The comparison between the numerical results with the experimenta.l data reveals an important difference for the static pressure recovery coefficient. A small part of this difference is attributed to numericaI reasons: turbulence model, discretization scheme, wall function, swirl treatment in the model,... etc. These numerical factors are already observed in previous work concerning the different types of diffusers. A large part of this difference is attributed to effects of the number of struts neglectedin these calculations.
INTRODUCTION
Annular exhaust difhsers are used in turbomachinery applications; such as axial flow compressors and turbines; to increase the static pressureand reducethe velocity of the discharge flow. These diffusers of central hub deal with flows of varying degrees of swirl. The hub is sometimes supportedby struts. The wake of struts may deteriorate the pressure recovery of the diffuser and therefore, special care should be taken for the design of these struts. In the studies of exhaust diffusers, several interesting features can be observed such as the presenceof the adverse pressure gradient, regions of recirculating flow as well as the wakes of the struts. The existing swirl in the flow stabilizes the flow on the outer wall and prevents separation their. However, excessiveswirls may createrecirculating zone near the hub. Annular diffusers situated downstream of a turbomachine have inlet conditions different from ducted flow inlet conditions. These last conditions concern the annular difhtsers situated downstream of an annular duct or upstream of a ventilator. In turbomachinery inlet conditions, the flow presents a swirl component, a high level of turbulence and a periodical component induced by the presenceof the upstream turbomachine. A higher pressure recovery coefficient C, is obtained in the diffusers situated downstream an axial turbomachine due to the increased turbulent mixing which results in a later onsetof separation. A considerable amount of experimental investigations was carried out on annular diffuser flows with ducted flow inlet conditions (e.g., Sovran
KEYWORDS
Annular Diffuser, Turbulent Flow, k-c model, RSM model. NOMENCLATURE static pressurerecovery coefficient CP
F
mean static pressure
vl a P
mean total velocity swirl angle density
Subscripts
1
outlet
inlet 1
Copyright 01998 by ASME
and Klomp, 1967; L&mann et al., 1979; and Kumar
and Kumar. 1980). On the other hand, little contributions concerning annular diffusers downstream a turbine (e.g., Kruse et al., 1983; and Quest, 1990) or a compressor(e.g., Adenubi, 1976; Pfeil and Going, 1987; and Zierer, 1995) can be found in the literature survey. In the domain of the numerical studies of annular diffuser turbulent flows, few numerical researcheson the swirling flow and the boundary-layer development through annular diffusers of different shapes have been tested. Most of these studies are focused on annular diffusers with ductedflow inlet conditions and without strut (k-E model/RSM model, e.g., Jones and Manners, 1989; Djebedjianet al., 1995; and Shuja and Habib, 1996). Published numerical contributions concerning annular diffusers with turbomachinery inlet conditions are rarely available. Using the algebraic eddy-viscosity model of Baldwin and Lomax and neglecting the presence of exhaust struts, Baskharone (1991) obtained displaced curves for the computed and measuredpressurerecoverycoefficients. From these studies and others in the domain of twodimensional and conical diffusers, it is observedthat the numerically predicted pressurerecovery coefficient is superior to the experimental one. The experimental researches studying the influence of wake of struts on the pressure recovery indicate the importance of strut geometry, stagger angle and swirl angle (Senooet al., 1981, and Kruse et al., 1983), upstream and downstream distances from the edges of strut to the inlet and outlet of diffuser, (Gogolev et al., 1974) and the interaction of strut’s with guide vanes wakes (Desideri and Manfrida, 1995). In the present study, a numerical study has been conducted to make a comparison of the predicted results for the pressure recovery coefficient for an exhaust annular diffuser with experimental data for swirling and non-swirling turbulent flows. EXPERIMENTAL
Fig. 1 Test rig of the axial exhaust
Model Description
The model exhaust diffuser, Fig. 2, consists of three annular diffusers in series with a casing of expanding octagonal shape for the second and third one. There are 22 cylindrical struts (20 inclined and 2 vertical struts) in the exhaust diffuser passagefor the rigidity of the outer casing. The annular diffuser’s inlet casing and hub radii are 0.069 m and 0.14 m, respectively. At the outlet, the radius of the hub is 0.031 m. The length of the diffuser is 0.321 m. The area ratio of the exhaust is 3.47 and the ratio of length-to-inlet height is 4.5.
FACILITY
Fig. 1 shows a cross-section of the test rig. Compressedair passesthrough a single stage turbine and the axial ezrhaust.Behind the exhaust, the flow expands into a condenser followed by a perforated plate. Based on the mean axial velocity and the hydraulic diameter at the diffuser inlet; the average inlet Reynolds number was greater than 5.3*105 for all experiments. Measurementswere carried out with 5 hole probes, static pressuretaps, and hot film probes. The details of the test rig and the measurementsare mentioned in Djebedjian (1997).
Fig. 2 Geometry
Diffuser
of the exhaust
diffuser
Performance
The evaluation of the diffuser performance can be done by many coefficients such as the static pressure recovery coefficient. It is defined as : 2
Copyright 0 1998 by ASME
characteristics that are spatially periodic. In general, the periodicity can be of two types, transitional and rotational. In this cor@uration, rotational periodic conditions were specified on the surfaces I = 1 and I = I-, Fig. 4.
where j5, and jT2 are the mean static pressures at the inlet and the outlet of the diffuser, respectively. p is the density and c, is the mean total velocity at the inlet. NUMERICAL
APPROACH
The used numerical code was based on the resolution of the time-averaged equations of conservation of massand momentum. These equations were discretized along with the suitable transport equations for the turbulence model by a finite-volume method using a non-staggered grid arrangement. In this study, turbulence was simulated by the standard kc model, (Launder and Spalding, 1974), and the Reynolds stressmodel (RSM), (Launder et al., 1975). The facevalues of the unknowns were evaluated by the Quadratic Upstream Interpolation for Convective Kinematics (QUlCK), (Leonard, 1979). The SIMPLE (Semi-Implicit Method for pressure-l&ked muations) algorithm (Patankar, 1980) was used for the pressurevelocity coupling and the line-by-line solution method for solving the linearized equations with an additive correction multigrid for the pressurecorrection
Fig. 3 Sector of the i/8 of the annular diffuser (2 struts / 45” of the total geometry)
Grid Generation
A generalized body-fitted coordinate system that conforms to the physical boundaries of the diffuser was used. The resulted algebraic grid was smoothedby the Poissonequations solver.
fXpZitiOnS.
Boundary
Conditions
Inlet. At the inlet of the diffuser, total pressure, flowqes and turbulence intensity, deduced from measured data, were specified. The inlet turbulent calculated from: dissipation was energy &=Cp o.75k’.5 ll, where the length scale, I, was 5.5 percent of the annular gap. Outlet. Constant static pressure was specified at the diffuser outlet. This specified pressure was determined from measureddata. Walls. The no-slip condition was used for all velocities. The flow close to the wall was handled by the wall function; (Launder and Spalding, 1974).
Fig. 4 Surface grid of the 118 of the annular diffuser, 25 x 27 x SO grid
Geometry Sector For economical reasons of the calculation time, three-dimensional studies were undertaken on a sector of l/8 of annular diffuser (2 struts / 45” of the total geometry),Fig. 3. It doesnot representexactly the real unsymmetrical exhaust and neglects the presence of 6 struts. Consequently, the resulted sector exhibits geometric periodic@ and gives rise to flow
RESULTS AND DISCUSSION Grid Density Study
For this study,three grid sizes (Imaxx J,, x K,-), namely, 11x23~50 grid, 21x23~50 grid and 25 x 27 x 90 grid, Fig. 4, were used. For the swirl angle a= 20”, the coefficient C, predicted by the
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RSM model is plotted in Fig. 5 as a function of the inverse of the mesh size. Two important effects interpose: -The first is the pressure loss effect due to the recirculation region at the outlet of the exhaust. The increment of the mesh size is accompanied by an increment of C, for the studied axisymmetrical diffuser (Djebedjian, 1997). -The second effect is the pressure loss due to the presence of struts in the axial exhaust. The refinement of grid around the struts was not sufEcient to capture this loss as the C, shows an important dependenceon the meshsize.
“” ..-..... “-“---” 09 T’-....... ea........
0
10
..-..“I- .-.,~....”.........”....
20
30 a
0.65 ,
CP 0.6
1 A
I
0
0.55 0.5j-gq -0.45 I 0
!
2
1 4 6 8 1 I (Mesh Size)
Fig. 6 Pressure recovery coefficient as a function of the swirl angle for the numerical predictions without strut and 16 struts
Turbulence
~1~ 1 10 so6
Fig. 5 Grid density effect on the pressurerecovery coefficient C,, for the swirl angle
(“>
Models Study
The experimental and the predicted coefficients C, from the standard k-s model and the RSM model using the coarsest grid 11 x 23 x 50 are plotted for difEerent swirl angles, Fig. 7. The over-estimation of the RSM model is less than that of the k-s model and it can be concluded the superiority of the RSM for the numerical simulation of the treatedcase.
Z=20” 0.7 7 Diffuser
Performance
The computed and measured pressure recovery coefficients C, are presentedin Fig. 6. The numerical results were obtained with the 25 x 27 x 90 grid and the R!SM model for the configurations without and with 16 struts. It can be observedthat the evolution of the curves representing the numerical results is in good agreement with the experimental one and that the pressure loss due to the struts is evident. From previous numerical simulations of turbulent flows in diffusers without strut, an over-estimation of the coefficient C, is usually observed.Beside this fact, the difference between the predicted and experimental C, can be attributed to the following reasons: - The neglected struts proposed to simplify the numerical prediction. - The insufficient number of grids around the struts which can evaluate correctly their infhrences on the pressureloss. - The unsteadinessof the flow (The pressureloss due to the existence of the struts is under-estimated).
CP
o.3 __ -u--Nun -k-s model - 16 struts -A----Num. - RSM model - 16 struts -22struts L -o-Exp. 0.2 -
0
1
’
10
20
a
(“I
Fig. 7 Pressure recovery coefficients predicted by the k-E and the RSM models
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from applying the total geometry of exhaust with the 22 struts.
Number of Struts Effect on The Pressure Recovery Coefficient
The utilization of a 2 struts / 45O sector of the axial exhaust neglects the presence of 6 struts and increases the evaluated pressure recovery coefficient. A simplified approach,which applies a blockage factor and presents a mean to know the neglected head loss in the numerical calculation, is studied. The head loss depends on the configuration and the section of strut. In this study, there are 20 inclined cylindrical struts, i.e. elliptical sections.For a swirling flow with an angle Z and a strut of length L and elliptical section with maximum lengths D and I, (= Dlcos p where p is the angle of inclination of strut), Fig. 8, the projectedsurfaceof the strut A, is given by: A, = l,.L where I,,, is the width perpendicular to the from: calculated velocity Ir. It is I, = D/($n2 Zcos2 p + cos2Zp5
The
Experimental
NUllltiUll
0.8 ?-‘---.,
o.2+Withyt Ol 0
0.05
16
8
0.1
20
22
strutsstrutsstruts
struts 0.15
0.2
0.25
0.3
Struts Blockage Factor
struts
Fig. 9 Variation of the pressure recovery coefficient with the struts blockage factor
blockage factor is defined as the report ~~,,Q!,~ A,, i=l I for n struts (.& is the cross-sectional area of the exhaust at the distancebetweenthe two struts).
CONCLUSIONS
The pressure recovery coefficient of an axial exhaust d&r installed downstream a single-stage turbine was measuredfor different swirl angles. The simplified rotationally periodic sector of 45O of the geometry with 0, 1 and 2 struts was used in the numerical computations. From this variation of the total number of struts, the following major conclusions emerge: - The usedassembleof struts have an important role in decreasingthe pressurerecovery in the exhaust. -The numerical evolution of the coefficient C, with the swirl angle is similar to that measured experimentally. - Depending on the swirl angle, the pressure recovery is more or less influenced by the interaction between the two struts’ wakes. - Using the struts blockage factor approach, the application of the total geomeq of the exhaust is expectedto give good agreement with the measured CP
Fig. 8 Velocity component V’ of the swirling flow and strut width /, perpendicular to V
Fig. 9 shows the variation of C, with the struts blockage factor. The evaluated numerical results were obtained using the RSM model and the 25 x 21 x 90 grid and the experimental data corresponds to the actual exhaust with 22 struts. The C, coefficients for the configuration of 8 struts were obtained by keeping only the first strut of the 45’ sector, Fig. 3, and applying the sameboundary conditions. The variation of C, for a blockagefactor equal to zero representsthe influence of swirl on the pressure recovery in the exhaust without strut. That recovery is maximum when Z= 20’. The flow with Z= 0” is very influenced by the interaction of the wakes of the two struts, while for the other swirling flows, these tendencies are slightly less important. Taking into account the curves slopes of the numerical results, good agreementwith the measuredC, will be resulted
REFERENCES
Adenubi, SO., 1976, “Performance and Flow Regime of Annular Diffusers With Axial Turbomachine Discharge Inlet Conditions,” ASME Journal of Fluids Engineering, Vol. 98, pp. 236-243. Baskharone,E.A., 1991, “Finite Element Analysis of Turbulent Flow in Annular Exhaust Diffusers of
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Gas Turbine Engines,” AWE Journal 01 Fluids Engineering, Vol. 113, pp. 104-l 10. Desideri, U., and Manfiida, G., 1995, “Flow and turbulence Survey for a Model of Gas Turbine Exhaust Diffuser,” ASME Paper 95-GT-139. Djebedjian, B., 1997, “Etude de l’ecoulement tridimensionnel darts un khappement axial de turbine a vapeur,” These de Doctorat, Conservatoire national des arts et metiers, Paris. Djebedjian, B., Gist, M.. Renaudeaux, J.P., and Rayan, M.A., 1995, “Numerical Study of Turbulent Flow through Equiangular Annular Diffusers,” Proceedings of the Fifth International Conference of FluidMechanics, Cairo, Egypt, Vol. 2, pp. 719-729. Gogolev, I.G., Drokonov, A.M., and Drokonov, E.M., 1974, “On Estimating the Effect of a Turbine Stage on Energy Losses in an Annular Diffuser with Shaped Struts,” Fluid Mechanics-Soviet Research, Vol. 3, No. 1, pp. 28-32. Jones, W.P., and Manners, A., 1989, “The Calculation of the Flow through a Two-dimensional Faired Diffuser,” Turbulent Shear Flows-6, Springer, Heidelberg, pp. 18-31. Kmse, H., Quest, J., and Scholz, N., 1983, “Experimentelle Untersuchungen von Nabendiffusoren hinter Turbinenstufen,” h472 Motortechnische Zeitschrifl, Vol. 44, No. 1, pp. 13-17. Kumar, D.S., and Kumar, K.L., 1980, “Effect of Swirl on Pressure Recovery in Annular Diffusers,” Journal ofMechanical Engineering Science, Vol. 22, No. 6, pp. 305-313. Launder, B.E., Reece, G.J., and Rodi, W., 1975, “Progress in the development of a Reynolds-stress closure,” Journal of Fluid Mechanics, Vol. 68, Part 3, pp. 537-566. Launder, B.E., and Spalding, D.B., 1974, “The Numerical Computation of Turbulent Flows,” Computer Methoa!s in Applied Mechanics and Engineering, Vol. 3, Part 3, pp. 269-289. Leonard, B.P., 1979, “A Stable and Accurate Convective Modeling Procedure Based on Quadratic Upstream Interpolation,” Computer Methods in Applied Mechanics and Engineering, Vol. 19, Part 1, pp. 59-98. Lohmann, R.P., Markowski, S.J., and Brookman, E.T., 1979, “Swirling Flow Through Annular Diffusers With Conical Walls,” ASME Journal of Fluids Engineering, Vol. 101, pp. 224-229. Patankar, S.V., 1980, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York. Pfeil, H., and Going, M., 1987, “Measurementsof the Turbulent Boundary Layer in the Diffuser Behind an Axial Compressor,” ASME Journal of Turbomachinery, Vol. 109, pp. 405-412.
Quest, J., 1990, “Test Case E/Du-2 : Annular Diffuser, Test Casesfor Computation of Internal Flows in Aero Engine Components,” (Ed. Fottner, L.), Advisory Group for Aerospace Research and Development (Neuilly-Stir-Seine, France), AGARDAR-275, pp. 309-321. Senoo,Y., Kawaguchi, N., Kojima, T., and Nishi, M., 1981, “Optimum Strut-Configuration for Downstream Annular Diffusers With Variable Swirling Inlet Flow,” ASME Journal of Fluids Engineering, Vol. 103, pp. 294-298. Shuja, S.Z., and Habib, M.A., 1996, “Fluid Flow and Heat Transfer Characteristics in Axisymmetric Annular Diffusers,” Computers & Fluids, Vol. 25, No. 2, pp. 133-150. Sow-an, G., and Klomp, E.D., 1967, “Experimentally Determined Optimum Geometriesfor Rectilinear Diffusers with Rectangular, Conical, or Annular Cross-Section,” Fluid Mechanics of Internal Flow, (Ed. Sovran G.), Elsevier Publication, pp. 270319. Zierer, T., 1995, “Experimental Investigation of the Flow in Diflusers Behind an Axial Flow Compressor,” ASME Journal of Turbomachinery, Vol. 117, pp. 231-239.
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