Iowa State University Capstones, Theses and Graduate Theses and Dissertations Dissertations 2011 Turbulent flow separation in three-dimensional asymmetric diffusers Elbert Jeyapaul Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/etd Part of the Aerospace Engineering Commons Recommended Citation Jeyapaul, Elbert, "Turbulent flow separation in three-dimensional asymmetric diffusers" (2011). Graduate Theses and Dissertations. 10258. https://lib.dr.iastate.edu/etd/10258 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Turbulent flow separation in three-dimensional asymmetric diffusers by Elbert Jeyapaul A dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Major: Aerospace Engineering Program of Study Committee: Paul A. Durbin, Major Professor Zhi J. Wang Hui Hu Alric P. Rothmayer James C. Hill Iowa State University Ames, Iowa 2011 Copyright c Elbert Jeyapaul, 2011. All rights reserved. ii TABLE OF CONTENTS LIST OF TABLES . iv LIST OF FIGURES . v NOMENCLATURE . x ACKNOWLEDGEMENTS . xii ABSTRACT . xiii CHAPTER 1. OVERVIEW . 1 1.1 Separation definition . .2 1.2 Background . .3 1.3 Asymmetric diffuser . .4 1.4 Reynolds number dependence . .6 1.5 Outline of the Thesis . .6 CHAPTER 2. DIFFUSER SERIES . 8 2.1 Quasi 1-D analysis . .8 2.2 Computational model . 11 2.2.1 Codes and Numerics . 12 2.2.2 Inflow profile generation . 14 2.2.3 Computing resources . 15 CHAPTER 3. EDDY-RESOLVING SIMULATIONS . 16 3.1 Detached Eddy Simulations . 16 3.1.1 Validation . 18 3.1.2 Study of flow separation . 21 iii 3.1.3 Vortical flow features . 22 3.2 Large Eddy Simulations . 24 3.2.1 Verification . 27 3.2.2 Diffuser series . 30 3.3 Comparison of LES and DES . 35 CHAPTER 4. SINGLE POINT CLOSURE MODELS . 38 4.1 Linear eddy-viscosity models (LEVM) . 38 4.1.1 Anomalies in predicting 3-D separation . 39 4.2 Sensitizing Cµ to flow separation . 42 4.2.1 Modeling parameters . 43 4.3 Importance of Anisotropy . 46 4.4 Anisotropy-resolving models . 46 4.5 Explicit Algebraic Reynolds Stress Model(EARSM) . 49 4.5.1 Formulation . 50 4.5.2 Implementation and Numerics . 51 4.5.3 Diffuser flow prediction . 52 4.5.4 Mean flow comparison . 53 4.5.5 Comparison of Reynolds stress . 55 4.5.6 Separation in the diffuser family . 55 4.5.7 General quasi-linear model . 56 4.5.8 Square duct prediction . 56 4.5.9 EARSM variants . 61 CHAPTER 5. CONCLUSION . 66 5.1 Future work . 67 BIBLIOGRAPHY . 70 iv LIST OF TABLES Table 2.1 Family of diffusers generating same adverse pressure gradient . 10 Table 2.2 Computational resource for each Eddy-resolving and RANS simulation 15 r Table 4.1 ARSM coefficients for different linear Πij models . 59 Table 4.2 ARSM coefficients for the calibrated LRR and other linear Πij models 64 v LIST OF FIGURES Figure 1.1 Dimensions of Cherry's diffuser 1 (Cherry et al., 2008) . .5 Figure 2.1 Area distribution(a) and streamwise pressure gradient(b) used in gen- erating the diffuser series . 10 Figure 2.2 Outline of the diffuser domain used for simulations. Shown in side and top view. 11 Figure 2.3 Mesh distribution in the diffuser showing every 4th node. 12 Figure 2.4 Flow domain with inlet mapping . 14 Figure 2.5 Primary and Secondary velocity profile in the fully-developed rectangu- lar channel of A=3.33. Statistics were averaged over 50 flow-through times. 15 Figure 3.1 Power spectrum of instantaneous streamwise velocity. The 4 probe points are located at the centroid of cross-sectional planes that are equally spaced from inlet to outlet. The -5/3 slope line is in red. 17 Figure 3.2 The ratio of the resolved-to-modeled turbulent energy in the baseline diffuser DES. 18 Figure 3.3 Streamwise velocity predicted using SAS and experimental measure- ments of Cherry et al. (2006) at transverse planes. Contour lines are spaced 0.1 m/s apart. The zero-streamwise-velocity contour line is thicker than the others. 19 Figure 3.4 Variation of mean streamwise velocity along spanwise z-lines. B is the width of the diffuser at that x-location. The solid lines are DES, and dashed k − ! SST model compared with experimental data. 20 vi Figure 3.5 Secondary flow in baseline diffuser predicted by DES. (a) The wall lim- iting streamlines indicate the separation structure. (b) secondary flow at transverse planes having streamwise vortices, the separation line is in red. 21 Figure 3.6 Separation bubble(a) and Intermittency(b) in the A2.5 diffuser pre- dicted using the DES model. 22 Figure 3.7 Secondary flow show a similarity in pattern at different inlet aspect ra- tios. The foci is formed earlier in the A2.5 diffuser and moves downstream 22 Figure 3.8 (a)Limiting streamlines for A2.5 diffuser on the wall show a steady sepa- ration surface from the top wall, The side wall has a complex separation- attachment flow. (b)The vortex cores show a vortex originating from foci F3 on left and multiple vortices close to the double-sloped edge . 23 Figure 3.9 Secondary flow streamlines in transverse planes of A2 diffuser. The blue line indicates the location of separation surface. 24 Figure 3.10 Power spectrum of instantaneous streamwise velocity predicted by LES. The 4 probe points are located at the centroid of cross-sectional planes that are equally spaced from inlet to outlet. The -5/3 slope line is in red. 26 Figure 3.11 The quality of the LES assessed using the metric of (a) Ratio of resolved to total Turbulent kinetic energy and (b) LES IQν parameter . 27 Figure 3.12 Contour lines of mean streamwise velocity and streamwise RMS velocity at various transverse planes. The DNS is to the left and LES on the right on each of Figures (a) and (b). Each line is spaced by 0.1 and the zero velocity line is bold. 28 Figure 3.13 Comparison of mean flow velocities, resolved kinetic energy, and Reynolds stresses along z/B=1/2 by LES of baseline diffuser. DNS are solid and LES are dashed. 31 Figure 3.14 Comparison of mean flow velocities, resolved kinetic energy, and Reynolds stresses along z/B=1/4 by LES of baseline diffuser. DNS are solid and LES are dashed. 32 vii Figure 3.15 Comparison of mean flow velocities, resolved kinetic energy, and Reynolds stresses along z/B=3/4 by LES of baseline diffuser. DNS are solid and LES are dashed. 33 Figure 3.16 Comparison of mean flow velocities, resolved kinetic energy, and Reynolds stresses along z/B=7/8 by LES of baseline diffuser. DNS are solid and LES are dashed. 34 p−pref Figure 3.17 Coefficient of pressure Cp = 2 variation along the bottom wall 0:5ρUbulk of baseline diffuser predicted by LES, x/L is the non-dimensional diffuser length. The experimental Cp has been shifted by -0.02 to provide a better comparison. 35 Figure 3.18 Separation surface predicted by LES for the diffuser series . 35 Figure 3.19 Secondary flow predicted by LES at the diffuser exit plane x/H=15 of the diffuser series. The cross-sections are shown in different scale, in real the areas are same. 36 Figure 3.20 Fraction of cross-sectional area separated predicted by DES and Exper- iments for the baseline diffuser . 37 Figure 4.1 Primary and secondary flow predicted using the k − ! SST model. The transverse velocity in (b) is normalized by Ubulk ............. 40 Figure 4.2 Separation surface predicted by SST model in the series of diffusers. 41 Figure 4.3 Anomalous separation surface predicted by SST in diffusers with sym- metric side slope angles. 42 Figure 4.4 Sensitivity of 2-D diffuser flow separation to variations in Cµ value. The separation line is in bold. 43 Figure 4.5 Scatter of Eigen values of Velocity gradient tensor predicted by SST and SAS models for the baseline diffuser. 44 Figure 4.6 Contours of Helicity in transverse plane of baseline diffuser predicted by SST and SAS models . 45 viii Figure 4.7 WALE parameter evaluated using SST-predicted flow field of baseline diffuser. 45 Figure 4.8 DNS data reported for aij (a) Lumley invariant map for flow anistropy along mid-plane of diffuser z/B=0.5(b) The complete Reynolds stress tensor uiuj plotted at x/H=4 at diffuser midplane (z/B=0.5) . 47 Figure 4.9 A plot of aij invariants at various streamwise locations (x/H) from DNS results . 47 Figure 4.10 Variation of Reynolds stress anisotropy(aij) invariants along the span of the baseline diffuser midplane (z=0.5B) from DNS results . 48 Figure 4.11 Secondary flow predicted by DNS and comparison to BEARSM. The magnitudes of the Mean or secondary flow are colored. The streamlines do not show direction. 54 Figure 4.12 Secondary flow predicted by DNS and BEARSM at diffuser exist x/H=15. The flow indicate the presence of 4 vortices. 54 Figure 4.13 Visualization of 3-D flow invariants from LES of baseline diffuser. Re- gions of 0 have no 3D influence on anisotropy. 55 Figure 4.14 Separation topology in the family of diffusers predicted using an anisotropy- resolving BEARSM and LES .