0
Research Papers: Flows in Complex Systems

Simulation of Compressible and Incompressible Flows Through Planar and Axisymmetric Abrupt Expansions

[+] Author and Article Information
Ali Nouri-Borujerdi

Department of Mechanical Engineering,
Sharif University of Technology,
Tehran 11155-9567, Iran
e-mail: anouri@sharif.ir

Ardalan Shafiei Ghazani

Department of Mechanical Engineering,
Sharif University of Technology,
Tehran 11155-9567, Iran
e-mail: shafiei@mech.sharif.ir

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received February 1, 2019; final manuscript received April 8, 2019; published online May 8, 2019. Assoc. Editor: Svetlana Poroseva.

J. Fluids Eng 141(11), 111107 (May 08, 2019) (11 pages) Paper No: FE-19-1076; doi: 10.1115/1.4043497 History: Received February 01, 2019; Revised April 08, 2019

In this paper, compressible and incompressible flows through planar and axisymmetric sudden expansion channels are investigated numerically. Both laminar and turbulent flows are taken into consideration. Proper preconditioning in conjunction with a second-order accurate advection upstream splitting method (AUSM+-up) is employed. General equations for the loss coefficient and pressure ratio as a function of expansion ratio, Reynolds number, and the inlet Mach number are obtained. It is found that the reattachment length increases by increasing the Reynolds number. Changing the flow regime to turbulent results in a decreased reattachment length. Reattachment length increases slightly with a further increase in Reynolds number. At a given inlet Mach number, the maximum value of the ratio of the reattachment length to step height occurs at the expansion ratio of about two. Moreover, the pressure loss coefficient is a monotonic increasing function of expansion ratio and increases drastically by increasing Mach number. Increasing inlet Mach number from 0.1 to 0.2 results in an increase in pressure loss coefficient by less than 5%. However, increasing inlet Mach number from 0.4 to 0.6 results in an increase in loss coefficient by 70–100%, depending on the expansion ratio. It is revealed that increasing Reynolds number beyond a critical value results in the loss of symmetry for planar expansions. Critical Reynolds numbers change adversely to expansion ratio. The flow regains symmetry when the flow becomes turbulent. Similar bifurcating phenomena are observed beyond a certain Reynolds number in the turbulent regime.

Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

Javadi, A. , and Nilsson, H. , 2015, “LES and DES of Strongly Swirling Turbulent Flow Through a Suddenly Expanding Circular Pipe,” Comput. Fluids, 107, pp. 301–313. [CrossRef]
Zohir, A. E. , and Gomaa, A. G. , 2013, “Heat Transfer Enhancement Through Sudden Expansion Pipe Airflow Using Swirl Generator With Different Angles,” Exp. Therm. Fluid Sci., 45, pp. 146–154. [CrossRef]
Ma, Z. W. , and Zhang, P. , 2012, “Pressure Drops and Loss Coefficients of a Phase Change Material Slurry in Pipe Fittings,” Int. J. Refrig., 35(4), pp. 992–1002. [CrossRef]
Dora, D. T. K. , Panda, S. R. , Mohanty, Y. K. , and Roy, G. K. , 2013, “Hydrodynamics of Gas-Solid Fluidization of a Homogeneous Ternary Mixture in a Conical Bed: Prediction of Bed Expansion and Bed Fluctuation Ratios,” Particuology, 11(6), pp. 681–688. [CrossRef]
Moallemi, N. , and Brinkerhoff, J. R. , 2016, “Numerical Analysis of Laminar and Transitional Flow in a Planar Sudden Expansion,” Comput. Fluids, 140, pp. 209–221. [CrossRef]
Cole, D. R. , and Glauser, M. N. , 1998, “Flying Hot-Wire Measurements in an Axisymmetric Sudden Expansion,” Exp. Therm. Fluid Sci., 18(2), pp. 150–167. [CrossRef]
Fearn, R. M. , Mullin, T. , and Cliffe, A. K. , 1990, “Nonlinear Flow Phenomena in a Symmetric Sudden Expansion,” J. Fluid Mech., 211(1), pp. 595–608. [CrossRef]
Durst, F. , Pereira, J. C. F. , and Tropea, C. , 1993, “The Plane Symmetric Sudden-Expansion Flow at Low Reynolds Numbers,” J. Fluid Mech., 248(1), pp. 567–581. [CrossRef]
Battaglia, F. , and Papadopoulos, G. , 2006, “Bifurcation Characteristics of Flows in Rectangular Sudden Expansion Channels,” ASME J. Fluids Eng., 128(4), p. 671. [CrossRef]
Smyth, R. , 1979, “Turbulent Flow Over a Plane Symmetric Sudden Expansion,” ASME J. Fluids Eng., 101(3), p. 348. [CrossRef]
Aloui, F. , and Souhar, M. , 2000, “Experimental Study of Turbulent Asymmetric Flow in a Flat Duct Symmetric Sudden Expansion,” ASME J. Fluids Eng., 122(1), pp. 174–177. [CrossRef]
Escudier, M. P. , Oliveira, P. J. , and Poole, R. J. , 2002, “Turbulent Flow Through a Plane Sudden Expansion of Modest Aspect Ratio,” Phys. Fluids, 14(10), pp. 3641–3654. [CrossRef]
Casarsa, L. , and Giannattasio, P. , 2008, “Three-Dimensional Features of the Turbulent Flow Through a Planar Sudden Expansion,” Phys. Fluids, 20(1), p. 015103.
Hawa, T. , and Rusak, Z. , 2001, “The Dynamics of a Laminar Flow in a Symmetric Channel With a Sudden Expansion,” J. Fluid Mech., 436(1), pp. 283–320. [CrossRef]
Back, L. H. , and Roschke, E. J. , 1972, “Shear-Layer Flow Regimes and Wave Instabilities and Reattachment Lengths Downstream of an Abrupt Circular Channel Expansion,” ASME J. Appl. Mech., 39(3), p. 677. [CrossRef]
Lantornell, D. , and Pollard, A. , 1986, “Some Observations on the Evolution of Shear Layer Instabilities in Laminar Flow Through Axisymmetric Sudden Expansions,” Phys. Fluids, 29(1986), pp. 2828–2835. [CrossRef]
Sheen, H. J. , Chen, W. J. , and Wu, J. S. , 1997, “Flow Patterns for an Annular Flow Over an Axisymmetric Sudden Expansion,” J. Fluid Mech., 350, pp. 177–188. [CrossRef]
Hammad, K. J. , Ötügen, M. V. , and Arik, E. B. , 1999, “A PIV Study of the Laminar Axisymmetric Sudden Expansion Flow,” Exp. Fluids, 26(3), pp. 266–272. [CrossRef]
Mullin, T. , Seddon, J. R. , Mantle, M. D. , and Sederman, A. J. , 2009, “Bifurcation Phenomena in the Flow Through a Sudden Expansion in a Circular Pipe,” Phys. Fluids, 21(1), p. 014110.
So, R. M. C. , 1987, “Inlet Centerline Turbulence Effects on Reattachment Length in Axisymmetric Sudden-Expansion Flows,” Exp. Fluids, 5(6), pp. 424–426.
Gould, R. D. , Stevenson, W. H. , and Thompson, H. D. , 1990, “Investigation of Turbulent Transport in an Axisymmetric Sudden Expansion,” AIAA J., 28(2), pp. 276–283. [CrossRef]
Devenport, W. J. , and Sutton, E. P. , 1993, “An Experimental Study of Two Flows Through an Axisymmetric Sudden Expansion,” Exp. Fluids, 14(6), pp. 423–432. [CrossRef]
Battaglia, F. , Tavener, S. J. , Kulkarni, A. K. , and Merkle, C. L. , 1997, “Bifurcation of Low Reynolds Number Flows in Symmetric Channels,” AIAA J., 35(1), pp. 99–105. [CrossRef]
Drikakis, D. , 1997, “Bifurcation Phenomena in Incompressible Sudden Expansion Flows,” Phys. Fluids, 9(1), pp. 76–87.
Kadja, M. , and Bergeles, G. , 2002, “Numerical Investigation of Bifurcation Phenomena Occurring in Flows Through Planar Sudden Expansions,” Acta Mech., 153(1–2), pp. 47–61.
Mishra, S. , and Jayaraman, K. , 2002, “Asymmetric Flows in Planar Symmetric Channels With Large Expansion Ratio,” Int. J. Numer. Methods Fluids, 38(10), pp. 945–962.
Zarghami, A. , Maghrebi, M. J. , Ubertini, S. , and Succi, S. , 2011, “Modeling of Bifurcation Phenomena in Suddenly Expanded Flows With a New Finite Volume Lattice Boltzmann Method,” Int. J. Mod. Phys. C, 22(9), pp. 977–1003.
Quaini, A. , Glowinski, R. , and Čanić, S. , 2016, “Symmetry Breaking and Preliminary Results About a Hopf Bifurcation for Incompressible Viscous Flow in an Expansion Channel,” Int. J. Comput. Fluid Dyn., 30(1), pp. 7–19.
Praveen, T. , and Eswaran, V. , 2017, “Transition to Asymmetric Flow in a Symmetric Sudden Expansion: Hydrodynamics and MHD Cases,” Comput. Fluids, 148, pp. 103–120.
Guevel, Y. , Girault, G. , and Cadou, J. M. , 2014, “Parametric Analysis of Steady Bifurcations in 2D Incompressible Viscous Flow With High Order Algorithm,” Comput. Fluids, 100, pp. 185–195.
Patel, S. , and Drikakis, D. , 2005, “Effects of Preconditioning on the Accuracy and Efficiency of Incompressible Flows,” Int. J. Numer. Methods Fluids, 47(8–9), pp. 963–970.
Dačtekin, I. , and Ünsal, M. , 2011, “Numerical Analysis of Axisymmetric and Planar Sudden Expansion Flows for Laminar Regime,” Int. J. Numer. Methods Fluids, 65(9), pp. 1133–1144.
Sanmiguel-Rojas, E. , and Mullin, T. , 2012, “Finite-Amplitude Solutions in the Flow Through a Sudden Expansion in a Circular Pipe,” J. Fluid Mech., 691, pp. 201–213.
Duwig, C. , Salewski, M. , and Fuchs, L. , 2008, “Simulations of a Turbulent Flow Past a Sudden Expansion: A Sensitivity Analysis,” AIAA J., 46(2), pp. 408–419.
De Zilwa, S. R. N. , Khezzar, L. , and Whitelaw, J. H. , 2000, “Flows Through Plane Sudden-Expansions,” Int. J. Numer. Methods Fluids, 32(3), pp. 313–329.
Guo, B. , Langrish, T. A. G. , and Fletcher, D. F. , 2001, “Numerical Simulation of Unsteady Turbulent Flow in Axisymmetric Sudden Expansions,” ASME J. Fluids Eng., 123(3), p. 574.
Zambrano, H. , Sigalotti, L. D. G. , Peña-Polo, F. , and Trujillo, L. , 2015, “Turbulent Models of Oil Flow in a Circular Pipe With Sudden Enlargement,” Appl. Math. Model., 39(21), pp. 6711–6724.
Drewry, J. E. , 1978, “Fluid Dynamic Characterization of Sudden-Expansion Ramjet Combustor Flowfields X,” AIAA J., 16(4), pp. 313–319.
Issa, R. I. , Gosman, A. D. , and Watkins, A. P. , 1986, “The Computation of Compressible and Incompressible Recirculating Flows by a Non-Iterative Implicit Scheme,” J. Comput. Phys., 62(1), pp. 66–82.
Emmert, T. , Lafon, P. , and Bailly, C. , 2006, “Numerical Study of Aeroacoustic Oscillations in Transonic Flow Downstream a Sudden Duct Enlargement,” AIAA Paper No. 2006-2555.
Mularz, E. J. , Bulzan, D. L. , and Chen, K. H. , 1993, “Spray Combustion Experiments and Numerical Predictions,” National Aeronautics And Space Administration Lewis Research Center, Cleveland, OH, Report No. NASA-E-7647.
Shuen, J.-S. , Chen, K.-H. , and Choi, Y. , 1992, “A Time-Accurate Algorithm for Chemical Non-Equilibrium Viscous Flowsat All Speeds,” 28th Joint Propulsion Conference and Exhibit, Nashville, TN, p. 3639.
Launder, B. E. , and Spalding, D. B. , 1972, Lectures in Mathematical Models of Turbulence, Academic Press, London, UK.
Hoffmann, K. A. K. A. , Chiang, S. T. , and Chung, T. J. , 2000, Computational Fluid Dynamics Volume III, Engineering Education System, Wichita, KS.
Liou, M. S. , 2006, “A Sequel to AUSM—Part II: AUSM+-Up for All Speeds,” J. Comput. Phys., 214(1), pp. 137–170.
Weiss, J. M. , and Smith, W. A. , 1995, “Preconditioning Applied to Variable and Constant Density Flows,” AIAA J., 33(11), pp. 2050–2057.
Van Leer, B. , Lee, W. T. , and Roe, P. , 1991, “Characteristic Time-Stepping or Local Preconditioning of the Euler Equations,” AIAA Paper No. A91-40726.
Turkel, E. , Radespiel, R. , and Kroll, N. , 1997, “Assessment of Preconditioning Methods for Multidimensional Aerodynamics,” Comput. Fluids, 26(6), pp. 613–634.
Li, Z. , and Xiang, H. , 2013, “The Development of a Navier–Stokes Flow Solver With Preconditioning Method on Unstructured Grids,” Eng. Lett., 21(2), pp. 89–94.
Edwards, J. R. , and Liou, M.-S. , 1998, “Low-Diffusion Flux-Splitting Methods for Flows at All Speeds,” AIAA J., 36(9), pp. 1610–1617.
Kermani, M. J. , Gerber, A. G. , and Stockie, J. M. , 2003, “Thermodynamically Based Moisture Prediction Using Roe's Scheme,” Fourth Conference of Iranian Aerospace Society, Tehran, Iran, pp. 27–29.
Roe, P. , 1986, “Characteristic-Based Schemes for the Euler Equations,” Annu. Rev. Fluid Mech., 18(1), pp. 337–365.
Liou, M. S. , 1996, “A Sequel to AUSM: AUSM+,” J. Comput. Phys., 129(2), pp. 364–382.
Poinsot, T. J. , and Lelef, S. K. , 1992, “Boundary Conditions for Direct Simulations of Compressible Viscous Flows,” J. Comput. Phys., 101(1), pp. 104–129.
Okong'o, N. , and Bellan, J. , 2002, “Consistent Boundary Conditions for Multicomponent Real Gas Mixtures Based on Characteristic Waves,” J. Comput. Phys., 176(2), pp. 330–344.
Kim, S.-E. , and Choudhury, D. , 1995, “A Near-Wall Treatment Using Wall Functions Sensitized to Pressure Gradient,” Separated and Complex Flows, 1995: Presented at the 1995 ASME/JSME Fluids Engineering and Laser Anemometry Conference and Exhibition, Hilton Head, SC, pp. 273–279.
Abbott, D. E. , and Kline, S. J. , 1962, “Experimental Investigation of Subsonic Turbulent Flow Over Single and Double Backward Facing Steps,” ASME J. Basic Eng., 84(3), p. 317.
Furuichi, N. , Takeda, Y. , and Kumada, M. , 2003, “Spatial Structure of the Flow Through an Axisymmetric Sudden Expansion,” Exp. Fluids, 34(5), pp. 643–650.
Guo, B. Y. , Hou, Q. F. , Yu, A. B. , Li, L. F. , and Guo, J. , 2013, “Numerical Modelling of the Gas Flow Through Perforated Plates,” Chem. Eng. Res. Des., 91(3), pp. 403–408.
Bae, Y. , and Kim, Y. I. , 2014, “Prediction of Local Loss Coefficient for Turbulent Flow in Axisymmetric Sudden Expansions With a Chamfer: Effect of Reynolds Number,” Ann. Nucl. Energy, 73(1), pp. 33–38.

Figures

Grahic Jump Location
Fig. 1

An enlarged view of a typical computational grid with quadrilateral mesh cells

Grahic Jump Location
Fig. 2

Fluid flow through: (a) planar and (b) axisymmetric sudden expansion

Grahic Jump Location
Fig. 3

Maximum transversal velocity and reattachment length as a function of mesh cells number for the planer channel with W1/W2 = 0.5 and Re =47.7

Grahic Jump Location
Fig. 4

Velocity profile at different cross sections and data of Durst for planar sudden expansion with W1/W2 = 0.5: (a) Re = 47.7 and (b) Re = 400

Grahic Jump Location
Fig. 5

Axial pressure distribution of incompressible flow as a function of mesh cells number for axisymmetric sudden expansion with R1/R2 = 0.33 and Re = 41,000

Grahic Jump Location
Fig. 6

Axial velocity distribution at different radial positions and data of Cole and Glauser [6] for axisymmetric sudden expansion with R1/R2 = 0.33 and Re = 41,000

Grahic Jump Location
Fig. 7

Turbulent kinetic energy at different axial positions and data of Cole and Glauser [6] for axisymmetric sudden expansion with R1/R2 = 0.33 and Re = 41,000

Grahic Jump Location
Fig. 8

Reynolds stress at different axial positions and data of Cole and Glauser [6] for axisymmetric sudden expansion with R1/R2 = 0.33 and Re = 41,000

Grahic Jump Location
Fig. 9

Axial pressure distribution of compressible flow as a function of mesh cells number for axisymmetric sudden expansion with R1/R2 = 0.67 and Min = 0.67

Grahic Jump Location
Fig. 10

Distribution of Mach number at different cross section of the axisymmetric expansion and data of Drewry [38] for R1/R2 = 0.67 and Min = 0.67

Grahic Jump Location
Fig. 11

Streamlines of the planar sudden expansion flow for W1/W2 = 0.5 with: (a) Re = 100 and (b) Re = 400

Grahic Jump Location
Fig. 12

Reattachment length as a function of W1/W2 for planar sudden expansion

Grahic Jump Location
Fig. 13

Critical Reynolds number of the onset of bifurcation as a function of W1/W2

Grahic Jump Location
Fig. 14

Reattachment length of the incompressible flow through axisymmetric expansions as a function of diameter ratio for different Reynolds numbers

Grahic Jump Location
Fig. 15

Pressure loss coefficient of the incompressible flow through axisymmetric expansions as a function of diameter ratio for different Reynolds numbers

Grahic Jump Location
Fig. 16

Reattachment length of the incompressible flow through axisymmetric expansions as a function of diameter ratio for different inlet Mach numbers

Grahic Jump Location
Fig. 17

Pressure loss coefficient of the compressible flow through axisymmetric expansions as a function of diameter ratio for different inlet Mac numbers

Grahic Jump Location
Fig. 18

The total-pressure ratio of the incompressible flow through axisymmetric expansions as a function of diameter ratio for different inlet Mach numbers

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In