Numerical Study of the Flow inside the A250 Diffuser Tube

Transcription

1 Numerical Study of the Flow inside the A25 Diffuser Tube G.G.W. Lee, WDE Allan and K. Goni Boulama* Department of Mechanical and Aerospace Engineering Royal Military College of Canada, Kingston, ON, Canada K7K 7B4 * Goni.Boulama@rmc.ca ABSTRACT The tube connecting the exit of the compressor to the inlet of the combustion chamber of the Allison 25 gas turbine has been investigated using the ANSYS CFX Reynolds Averaged Navier Stokes (URANS) Shear-Stress Transport model (SST). The geometry of this tube consists of a conical divergent that transitions into a constant diameter S-shaped duct. The numerical model was validated using data collected on an in-house test rig. The calculated A25 S-shaped diffuser flow features were then compared to those in a constant diameter S-shaped tube with the same inlet cross-sectional area and offset. The A25 S-shaped diffuser was shown to correspond to a more distorted profile of the streamwise velocity and, most importantly, less friction losses, and a significantly higher pressure recovery capability than the S-shaped constant diameter tube. The flow in the A25 S- shaped diffuser tube was also simulated at different Reynolds numbers, showing a continuous decrease of the friction coefficient and an increase of the pressure coefficient as the Reynolds number was increased. 1. INTRODUCTION Flow passages with bends and axially varying crosssectional area are present in a variety of applications, and have been the subject of extensive research. Planar symmetrical and asymmetrical diffusers have been studied using experimental and numerical approaches, revealing different separated flow features depending on the channel divergence angle and Reynolds number [1-3]. El-Behery and Hamed [3] for example used six different RANS models, including the κ-ε, κ-ω and SST models, evidencing striking inconsistencies in both the required computational time and the prediction capability between the different models. Azad [4] reported a review of 29 years experimental research on an 8 conical diffuser. Sparrow et al. [5] noted that some sources state that flow in conical diffusers separates if the divergence angle exceeds 7, while other sources indicate a critical divergence angle of 15. The authors numerically studied divergence angles of 5, 1 and 3, and Reynolds numbers varying from 5 to 33, showing that the flow separated at lower Reynolds numbers for small divergence angles. Furthermore, the extent of the separated flow region was shown to generally decrease as the Reynolds number increased. S-shaped constant cross-section pipes constitute another typical geometry for which the most important early advances are due to Dean, with his discovery that the primary motion along the conduit was accompanied by a secondary motion in the plane of the cross-section [6]. As a consequence, there is an outward shift of the region where the primary motion is greatest, and a decreased flow-rate for a given pressure gradient. Ng et al. [7] reported a study on an S-shaped square duct at high Reynolds numbers, and observed a flow separation at the first bend. A swirl developed at the same location, but was attenuated at the second bend due to the formation of swirl of opposite direction. Additional flow features included the formation of a streamwise vortex or a pair of counter-rotating vortices on the outer wall of the second bend. Silva Lopes et al. [8] used the LES approach in their study of the flow in geometry similar to that of the preceding authors, but at lower Reynolds numbers, focusing attention on the boundary layer structure and the turbulence statistics. They, for example, showed that centripetal forces make the production and destruction of turbulent kinetic energy, as well as the turbulent motions, to increase at the concave wall and decrease at the convex wall. Patankar et al. [9] adopted a κ-ε type model to predict the flow development in a curved pipe, concluding that the prediction capability was not as satisfactory as for laminar flows. Taylor et al. [1] studied laminar and turbulent flows in a constant circular cross-section S-shaped duct and verified the existence of a correlation between the thickness of the boundary layer at the inlet and the development of the flow in the pipe. A number of studies has also been published that dealt with flows in tubes with both cross-sectional area expansion and curvature. Such devices are

2 present in aircraft intake propulsion systems [11-13]. The combination of the cross-sectional area change and curvature exacerbates flow separation and secondary flow problems, and also complicates the investigation. Lee and Yu [12] for example studied an S-shaped diffuser tube similar to the Royal Aeronautical Establishment (RAE) 2129, using two different RANS models, and failed to correctly predict both the onset and extent of flow separation. A comprehensive research on the Allison 25 gas turbine is being conducted by our group, and this paper specifically discusses the flow inside the tube that takes the flow from the compressor to the combustion chamber. This tube has a conical section that transitions into a constant diameter S-shaped duct. To our knowledge no previous study has been published on this geometry. The investigation adopts the RANS ANSYS-CFX SST numerical model, and an experimental rig is also constructed for validation purposes. The flow in the A25 S-shaped diffuser tube is compared to that in a circular constant diameter S-shaped tube. A parametrical study is also proposed for the A25 diffuser illustrating the sensitivity of the detailed flowfields, friction and pressure coefficients to the Reynolds numbers. 2. EXPERIMENTAL SETUP The geometry of the A25 S-shaped diffuser tube and that of the constant diameter S-shaped tube are presented in Fig. 1. All relevant dimensions are indicated (in mm). A service worn sample of the diffuser tube was supplied to us by the manufacturer, our partner Standard Aero Ltd. The top edge of the diffuser tube in the view in Fig. 1a (R* =.5) will herein be referred to as the inner wall of the first bend, while the bottom edge (R* = -.5) will be referred to as the outer wall of the first bend. A flexible traverse system equipped with a Pitot static tube can be mounted at three streamwise locations (1: entrance plane; 2: end of conical section; 3: exit plane), and pressure is measured in the four directions shown in Fig. 1c. The Omega PX139 pressure transducer used is rated for ±.3 psi with an output voltage between.25 V to 4.25 V. A Westinghouse 1.5 hp, 345 rpm motor mated to a Canadian Blower & Forge Co. centrifugal blower is used to generate the desired flow. A 2 m long steel tube is configured to the blower via a plain reducer and a contraction cone. Flow straighteners are placed at the entrance in order to minimize instabilities before the flow enters the test-section, and a 1 m extension tube is placed at the exit of the diffuser tube in order to prevent outlet conditions from affecting the flow in the region of interest [4, 13]. Under the considered conditions, a mass flow-rate of.55 kg/s and a Reynolds number of 8 are obtained. In the following, the radial coordinates z (AA direction) and r (CC direction) are nondimensionalized by the local tube diameter; the axial coordinate x is non-dimensionalized by the total diffuser tube length; and the velocity components are non-dimensionalized by the local bulk velocity. (c) Fig. 1: A25, and (c) Pressure measurement directions. 3. NUMERICAL APPROACH The CFD code ANSYS-CFX is adopted for this study to solve the steady-state Cartesian coordinate Navier- Stokes equations, the general form of which is: (ρu ) + ρu U t ρ t + ρu = (1) = p + μ U + U (2) These equations are discretized using a fully conservative control-volume-based finite-element method, with a hybrid 1 st and 2 nd -order accurate scheme, which switches from the latter to the former in regions of steep gradients, based on the boundedness principle of Barth and Jespersen [14]. The resolution scheme is practically second-order accurate. Pressure-velocity coupling is enforced with a non-staggered grid and the 4 th -order-accurate algorithm of Rhie and Chow [15]. The details of the SST model could be found in [16], and only the two most important equations are reproduced here:

3 (ρk) + ρu k = P t β ρkω + (μ + σ μ ) k (ρω) t + (ρu ω) = αρs βρω + (μ + σ μ ) ω 1 k ω + 2(1 F )ρσ ω (3) (4) where F 1 is equal to zero away from the surface (κ-ε) and equal to one inside the boundary layer (κ-ω). The calculation of the distance from the wall is achieved by the solution of a Poisson equation. The suitability of the SST turbulence model has been thoroughly investigated, and its superior performance compared to the κ-ε and κ-ω models was demonstrated [17], but not reproduced here because of space limitations. 4. VALIDATION 4.1 Grid Resolution Validation The A25 diffuser tube used in the physical experiment is digitized and imported into ICEM, a grid generator compatible with ANSYS-CFX. An illustration of the grid topology is shown in Fig. 2, including a relatively coarse mesh central region and a geometric refinement as the wall is approached. The grid is uniform in the streamwise direction. Other important features are given in Table 1. A and a are the number of nodes along the side of the square central box and from the corner of the central box to the wall. B represents the axial resolution. Refining the mesh from G1 to G3 noticeably affects the results. Grids G4 and G5 returned similar results (see [17]). Considering the significantly larger cost of G5, G4 is therefore considered to be sufficiently resolved and is used in the remainder of this report. 4.2 Comparison with Experimental Data The calculated velocity profiles using grid resolution G4, a Reynolds number of 8, and a turbulence intensity of 5% at the inlet of the computational domain are compared with the experimentally measured data in Fig. 3. At the entrance, the AA line profile is symmetrical and parabolic, it is elongated at.4.2 Z* Station 1 Station 2 Station Fig. 2: Illustration of grid topology. Table 1: Features of some of the tested grids Wall A a B Total spacing (m) G G G G G R* Station 1 Station 2 Station Fig. 3: Development of the streamwise velocity profile AA line and CC line.

4 the end of the conical section, and shows two overshoots at the exit plane. In the CC direction, the profile is gradually distorted toward the outer wall of the first bend. The calculated results are in very good qualitative and quantitative agreement with the experimental data, at all three measurement stations. The numerical model and the implementation adopted in this study are therefore considered to be validated and appropriate for the problem at hand. 5. RESULTS AND DISCUSSION 5.1 A25 Tube vs. Figure 4 compares the radial distribution of the streamwise velocity at the exit plane of the A25 diffuser tube () to that of the constant cross-sectional area S-shaped tube (). Along the AA direction (Fig. 4a), the velocity profile for the is nearly parabolic, markedly different from saddle type distribution calculated for the. In fact, while the general shape of the profile for the remains essentially unchanged through the tube, the velocity profile for the A25 gets Z* R* Fig 4: vs. exit plane streamwise velocity distribution AA line and CC line. significantly altered in the diffusing section of that tube. Along the CC direction (parallel to the offset), Fig. 4b shows that the curvature effect on the flow in both tubes is qualitatively the same (shift of the region of flow with the highest streamwise velocity toward the outer wall of the first bend), though the S- Diffuser profile is much more skewed. Figure 5 compares the friction coefficient variations for the two geometries. For the A25 diffuser tube, the friction coefficients first monotonically decrease as a result of the cross-sectional area expansion. At the end of the conical section, the friction coefficient at R* =.5 experiences a sudden disturbance, then continues its decrease until it closely approaches zero (incipient shear layer separation), and then increases as the curvature of the pipe changes direction. At the opposite wall, the friction coefficient increases sharply when the flow gets accelerated after the first bend, sharply decreases at the second bend, and remains almost constant in the straight exit section. The variations of the friction coefficients in the S- duct are qualitatively quite similar (note the same locations of peaks and troughs). However the friction C f C f Fig. 5: vs. friction coefficients R* =.5 and R* = -.5.

5 coefficient values for the latter are significantly higher throughout the duct, which correlates with a much more important pumping energy requirement than in the case of the A25 S-shaped diffuser tube. The differences in the pressure variations for the two geometries under study are illustrated in Fig. 6. Next to the inner wall of the first bend (Fig. 6a), the pressure coefficient for the increases monotonically, while on the opposite wall (Fig. 6b), it increases over most of the tube, except for a very small portion located at the second bend. Strikingly, the pressure coefficients for the generally decrease throughout the duct, and are negative at the exit of the pipe. These trends are on the one hand consistent with previous observations by Taylor et al. [1], and on the other hand probably constitute the best evidence of the benefit of the S-shaped diffuser over the constant diameter S-shaped geometry. It is also noted that the C p variations in the constant diameter S-shaped tube differ from those in a straight circular pipe (i.e. in the absence of curvatures); the C p in the latter case linearly decrease by virtue of the fully developed flow conditions that would prevail over the entire length of the pipe..8.6 (c) (d) (e) (f) Fig. 7: velocity contours =, =.35, (c) =.51, (d) =.66, (e) =.81, and (f) = 1. C p C p.4.2 (c) (d) Fig. 6: vs. pressure coefficients R* =.5 and R* = -.5. (e) (f) Fig. 8: velocity contours =, =.35, (c) =.51, (d) =.66, (e) =.81, and (f) = 1.

6 Figure 7 shows the development of the velocity contours along the A25. At the entrance, the velocity profile is fully-developed, the region of maximum velocity is centered in the pipe, and velocity values decrease as the wall is approached. At the end of the conical section (Fig. 7b), the contours are slightly shifted upward (toward the approaching convex wall). After the first bend, there is a consistent gradual shift of the region with maximum velocity magnitude toward the outer wall of the first bend, which agrees with previous observations. The distribution is always symmetrical in the direction perpendicular to the offset. For the (Fig. 8), the same initial axisymmetric distribution as for the is observed (Fig. 8a). The same upward shift of the maximum velocity region is also observed at the first bend (Fig. 8b), though slightly more pronounced than in the case of the (Fig. 7b). Then, the core flow region is shifted toward the inner wall of the second bend. This shift is less pronounced than in the case (consistent with Fig. 4b). The same trends with more marked shifts of the maximum flow region have been predicted for more severely bend pipes [1]. The velocity distributions in the cross-sectional plane are shown at different axial locations in Figs. 9 and 1 for the and, respectively. At the entrance of the (Fig. 9a), the outward oriented velocity vectors are illustrative of the area expansion. At the end of the conical section, the velocity vectors are oriented upward, indicating the curvature driven flow away from the concave wall. The direction of the secondary flow swiftly reverses after the first bend, showing an increasingly intense flow toward the outer wall of the first bend, which in this case may better be referred to as the inner wall of the second bend. Two large counter-rotating recirculation zones are also formed. By the exit plane (Fig. 9f), the vortex pair has migrated from the side walls towards the R* =.5 wall. For the (Fig. 1), there is no secondary flow at all at the entrance and in most of the initial straight pipe section (fully-developed flow conditions at the entrance). A significant secondary flow is observed right at the first bend as a consequence of the main flow being diverted away from the concave wall. Fig. 1c shows a formation of a downward secondary flow in the central region of the pipe that intensifies, driven by the increasingly strong axial flow in the region of the outer wall of the first bend (Dean Effect [6]). The ensuing dynamics is rather complex. Ng et al. [7] indicated that the swirl that forms at the first bend is attenuated by a swirl of opposite direction at the second bend. In our case, a pair of counterrotating vortices is observed at the exit plane instead. (c) (d) (e) (f) Fig. 9: secondary velocity vectors at =, =.35, (c) =.51, (d) =.66, (e) =.81, and (f) = 1. (c) (d) (e) (f) Fig. 1: secondary velocity vectors at =, =.35, (c) =.51, (d) =.66, (e) =.81, and (f) = 1.

7 5.2 : Reynolds Number Effects At the inlet of the A25 S-shaped diffuser tube, the streamwise velocity profiles along the AA and CC lines are identical, and flatten along the divergent. These profiles are generally flatter at higher Reynolds numbers. Figure 11 shows the effects of the Reynolds number on the streamwise velocity profile at the exit plane ( = 1). Along the AA line (Fig. 11a), an increasingly pronounced overshoot in the near wall region, and monotonically decreasing velocity magnitudes in the centreline are observed when the Reynolds number is increased. Along the CC line (Fig. 11b), the distortion of the velocity profile is also observed to intensify as the Reynolds number is increased. It is noted that the decreasing slope of the velocity profile at about R* =.3 suggests that a second overshoot may appear should the Reynolds number be further increased. The general variations of the friction coefficients in the A25 S-shaped diffuser shown in Fig. 5 for a Reynolds number of 8 are reproduced at all tested Reynolds numbers (Fig. 12). In particular, the calculated C f values at all four Reynolds numbers Z* K 29K decrease as the flow passage enlarges, closely approaching zero at the outer wall of the first bend for the lowest Reynolds number (Fig. 12 b). At the inner wall of the first bend, the decrease trend is continued after a slight disturbance (Fig. 12 a), while at the opposite wall a sharp increase is observed after the first bend (Fig. 12 b). The Reynolds number effect is hardly discernible at the former wall, while it is important, and non-linear, at the latter wall. Worth noting, the high friction coefficient value at R* = -.5, = 1, and Re = 25 is hardly predictable from a quick inspection of Fig. 11b. Another important comparison to be made at this point is the one with straight constant diameter pipes (i.e. no curvature and no cross-sectional area change). For this case in fact, the friction coefficient is uniform around the circumference, and it decreases hyperbolically when the Reynolds number increases. Finally, Fig. 13 shows the variations of the pressure coefficients for the four Reynolds numbers of this study. Generally, increasing the Reynolds number is shown to result in a non-negligible increase of the C p values near both walls, over the entire diffuser length. C f K 29K K 29K.4 8K 29K R* C f Fig. 11: Effects of Reynolds number on streamwise velocity AA line and CC line Fig. 12: Effects of Reynolds number on friction coefficients R* =.5 and R* = -.5.

8 C p C p Fig. 13: Effects of Reynolds number on pressure coefficients R* =.5 and R*= CONCLUSION 8K 29K 8K 29K A study has been conducted on an S-shaped diffuser as found in the Allison 25 gas turbine. The aim of this paper was to test the prediction capability of the RANS SST model, while gaining an insight into the flow features for this particular geometry. The numerical code was successfully validated by comparing the calculated results to data collected on a purposefully designed test rig. The flow in the A25 diffuser tube was then compared to that in a constant diameter S-shaped pipe with the same inlet diameter, length and offset. The axial variations of the streamwise velocity profiles and the dynamics of the secondary flow (in the plane of the cross-section) were different. Most importantly however, the A25 S-shaped diffuser tube was shown to correspond to significantly lesser friction losses, and much more pressure recovery capabilities. The flow in the A25 diffuser tube was also investigated for its sensitivity to the Reynolds number. Increasing the Reynolds number resulted in an increasingly severe distortion of the streamwise velocity profiles and high pressure coefficients, while the friction coefficients decreased. REFERENCES [1] Vujicic MR, Crnojevic C: Calculation of turbulent flow in plane diffusers, I. J. Num. Meth. Heat Fluid Flow, 17: , 27. [2] Gullman-Strand J, Tornblom O, Lindgren B, Amberg G, Johansson AV: Numerical and experimental study of separated flow in a plane asymmetric diffuser, I. J. Heat Fluid Flow, 25:451-46, 24. [3] El-Behery SM, Hamed MH: A comparative study of turbulence models performance for separating flow in a planar asymmetric diffuser, Computers Fluids, 44: , 211. [4] Azad RS: Turbulent flow in a conical diffuser: A review, Exp. Therm. Fluid Sci., 13: , [5] Sparrow EM, Abraham JP, Minkowycz WJ: Flow separation in a diverging conical duct: Effect of Reynolds number and divergence angle, I. J. Heat Mass Transfer, 52: , 29. [6] Dean WR, Hurst JM: Note on the motion of fluids in a curved pipe, Mathematika, 6:77-85, [7] Ng YT, Luo SC, Lim TT, Ho QW: On swirl development in a square cross-sectioned, S- shaped duct, Exp. Fluids, 41: , 26. [8] Silva Lopes A, Piomelli U, Palma JMLM: Large-eddy simulation of the flow in an S-duct, J. Turbulence, vol. 7, 26. [9] Patankar SV, Pratap VS, Spalding DB: Prediction of turbulent flow in curved pipes, J. Fluid Mech., 67: , [1] Taylor AMKP, Whitelaw JH, Yianneskis M: Developing flow in S-shaped ducts, II Circular cross-section duct, NASA Report CR-3759, [11] Anderson BH: The aerodynamic characteristics of vortex ingestion for the F/A-18 inlet duct, 29 th AIAA Aerospace Sci. conf., AIAA-91-13, [12] Lee KM, Yu SCM: Computational studies of flows in the RAE2129 S-shaped diffusing duct, AIAA Aerospace Sci. conf., AIAA , [13] Kirk AM, Gargoloff JI, Rediniotis OK, Cizmas PGA, Numerical and experimental investigation of a serpentine inlet duct, I. J. CFD, 23: , 29. [14] Barth TJ, Jespersen DC: The design and application of upwind schemes on unstructured meshes, AIAA , [15] Rhie CM, Chow WL: Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J. 21: , [16] Menter FR: Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications, AIAA J., 32: , [17] Lee GGW, Allan WDE, Goni Boulama K: Numerical and experimental analysis of the airflow inside an A25 diffuser tube, ASME Turbo Expo, GT , 212.