Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-10T16:49:34.610Z Has data issue: false hasContentIssue false
  • English
  • Français

Investigation of rarefied flow over backward-facing step in different rarefaction regimes using direct simulation Monte Carlo

Published online by Cambridge University Press:  13 October 2021

D. Nabapure Open the ORCID record for D. Nabapure [Opens in a new window] ,
A. Singh  and
R.C.M. Kalluri
D. Nabapure*
Affiliation:
High-Performance Computing (HPC) Lab, Department of Mechanical Engineering, BITS-Pilani, Hyderabad Campus, 500078, India
A. Singh
Affiliation:
High-Performance Computing (HPC) Lab, Department of Mechanical Engineering, BITS-Pilani, Hyderabad Campus, 500078, India
R.C.M. Kalluri
Affiliation:
High-Performance Computing (HPC) Lab, Department of Mechanical Engineering, BITS-Pilani, Hyderabad Campus, 500078, India
*
E-mail: p20150056@hyderabad.bits-pilani.ac.in
Get access Rights & Permissions [Opens in a new window]

Abstract

Hypersonic aerothermodynamics for a re-entry vehicle approaching the earth’s atmosphere is critical in the exploration of space. These vehicles often encounter various flow regimes due to the density variations and have surface abnormalities. The backward-facing step (BFS) is one such simplified configuration for modeling anomalies around such space vehicles. The present work examines rarefied hypersonic flow over a BFS using the direct simulation Monte Carlo (DSMC) method. The purpose of this research is focused on exploring the various loads encountered by a re-entry vehicle passing through different altitudes covering different rarefaction regimes. The fluid considered was non-reacting air, with the free-stream Mach number as 25, and the Knudsen number considered ranged from 0.05-21.10. The influence of the Knudsen number on flow characteristics has been elucidated graphically in various streamwise directions. The normalised flow properties such as velocity, pressure, temperature and density showed an increasing trend with the Knudsen number due to compressibility and viscous heating effects. In all flow regimes, there was an appearance of flow recirculation. With rarefaction, the recirculation lengths decreased, whereas the boundary layer thickness showed an increase. The aerodynamic surface properties such as pressure coefficient, skin friction, and heat transfer coefficient, by and large, showed an increase with the Knudsen number. When the chemical reactions were accounted for and compared against the non-reacting flows, the velocity, pressure, and density field showed no marked variation; however, considerable variations were observed in the temperature field. Furthermore, the present study also depicts the compressibility factor contour, showing the flow regions that diverge from the ideal gas behaviour.

Keywords

DSMCBackward-facing stepKnudsen numberRarefied gas flows
Type
Research Article
Information
The Aeronautical Journal , Volume 126 , Issue 1298 , April 2022 , pp. 617 - 644
Check for updates
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Royal Aeronautical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Guo, G. and Luo, Q. Flowfield structure characteristics of the hypersonic flow over a cavity: From the continuum to the transition flow regimes, Acta Astronaut., 2019, 161, pp 87–100.CrossRefGoogle Scholar
Gallis, M.A. Bond, R.B. and Torczynski, J.R. A kinetic-theory approach for computing chemical-reaction rates in upper-atmosphere hypersonic flows, J. Chem. Phys. 2009, 131, (12), p 124311.CrossRefGoogle ScholarPubMed
Palharini, R.C. Scanlon, T.J. and Reese, J.M. Aerothermodynamic comparison of two- and three-dimensional rarefied hypersonic cavity flows, J. Spacecr. Rockets, Sep. 2014, 51, (5), pp 1619–1630, doi: 10.2514/1.A32746.CrossRefGoogle Scholar
Morgan, K. Periaux, J. and Thomasset, F. Analysis of Laminar Flow Over a Backward Facing Step. Springer, 1984.CrossRefGoogle Scholar
Chen, L. Asai, K. Nonomura, T. Xi, G. and Liu, T. A review of backward-facing step (BFS) flow mechanisms, heat transfer and control, Ther. Sci. Eng. Prog. 2018, 6, pp 194–216.CrossRefGoogle Scholar
Leite, P.H.M. and Santos, W.F.N. Computational Analysis of a Rarefied Hypersonic Flow over Backward-Facing Steps, J. Thermophys. Heat Transf., Feb. 2019, pp 1–13, doi: 10.2514/1.T5486.Google Scholar
Ahmadian, M.H. Roohi, E. Teymourtash, A. and Stefanov, S. A dusty gas model-direct simulation Monte Carlo algorithm to simulate flow in micro-porous media, Phys. Fluids, Jun. 2019, 31, (6), p 062007, doi: 10.1063/1.5094637.CrossRefGoogle Scholar
Mohammadzadeh, A. Roohi, E. Niazmand, H. Stefanov, S. and Myong, R.S. Thermal and second-law analysis of a micro- or nanocavity using direct-simulation Monte Carlo, Phys. Rev. E Stat. Nonlin. Soft Matter Phys. May 2012, 85, (5 Pt 2), p 056310, doi: 10.1103/PhysRevE.85.056310.CrossRefGoogle ScholarPubMed
Choi, H. Lee, D. and Lee, D. Complex microscale flow simulations using langmuir slip condition, Numer. Heat Transf. A Appl. Sep. 2005, 48, (5), pp 407–425, doi: 10.1080/10407780590957206.CrossRefGoogle Scholar
Hsieh, T.-Y. Hong, Z.-C. and Pan, Y.-C. Flow characteristics of three-dimensional microscale backward-facing step flows, Numer. Heat Transf. A Appl. Mar. 2010, 57, no. 5, pp 331–345, doi: 10.1080/10407780903582992.CrossRefGoogle Scholar
Beskok, A. Validation of a new velocity-slip model for separated gas microflows, Numer. Heat Transf. B Fundam. Dec. 2001, 40, (6), pp 451–471, doi: 10.1080/104077901753306593.CrossRefGoogle Scholar
Celik, B. and Edis, F.O. Computational investigation of micro bacward-facing step duct flow in slip regime, Nanoscale Microscale Thermophys. Eng. Dec. 2007, 11, (3–4), pp 319–331, doi: 10.1080/15567260701715438.CrossRefGoogle Scholar
Rached, J.A. and Daher, N.M. Numerical Prediction of Slip Flow and Heat Transfer in Microchannels, 2007, pp 109–114.Google Scholar
Baysal, O. Erbas, N. and Koklu, M. Control of separated flow past a backward facing step in a microchannel, Microfluid. Nanofluid. Nov. 2004, 1, (1), pp 86–92, doi: 10.1007/s10404-004-0003-x.CrossRefGoogle Scholar
Xue, H. and Chen, S. DSMC simulation of microscale backward-facing step flow, Microscale Thermophys. Eng. Jan. 2003, 7, (1), pp 69–86, doi: 10.1080/10893950390150449.CrossRefGoogle Scholar
Nabapure, D. and Kalluri, R.C.M. DSMC simulation of rarefied gas flow over a 2D backward-facing step in the transitional flow regime: Effect of Mach number and wall temperature, Proc. Inst. Mech. Eng. G J. Aerosp. Eng., 2020, p. 0954410020959872.CrossRefGoogle Scholar
Kursun, U. and Kapat, J.S. Modeling of microscale gas flows in transition regime Part I: Flow over backward facing steps, Nanoscale Microscale Thermophys. Eng. May 2007, 11, (1–2), pp 15–30, doi: 10.1080/15567260701333372.CrossRefGoogle Scholar
Bao, F. and Lin, J. Continuum simulation of the microscale backward-facing step flow in a transition regime, Numer. Heat Transf. A Appl. Apr. 2011, 59, (8), pp 616–632, doi: 10.1080/10407782.2011.561073.CrossRefGoogle Scholar
Darbandi, M. and Roohi, E. DSMC simulation of subsonic flow through nanochannels and micro/nano backward-facing steps, Int. Commun. Heat Mass Transf. Dec. 2011, 38, (10), pp 1443–1448, doi: 10.1016/j.icheatmasstransfer.2011.08.002.CrossRefGoogle Scholar
Mahdavi, A.-M. and Roohi, E. Investigation of cold-to-hot transfer and thermal separation zone through nano step geometries, Phys. Fluids, , Jul. 2015, 27, (7), p 072002, doi: 10.1063/1.4927069.CrossRefGoogle Scholar
Mahdavi, A.-M. Le, N.T.P. Roohi, E. and White, C. Thermal rarefied gas flow investigations through micro-/nano-backward-facing step: Comparison of DSMC and CFD subject to hybrid slip and jump boundary conditions, Numer. Heat Transfer A Appl. Oct. 2014, 66, (7), pp 733–755, doi: 10.1080/10407782.2014.892349.CrossRefGoogle Scholar
Gavasane, A. Agrawal, A. and Bhandarkar, U. Study of rarefied gas flows in backward facing micro-step using Direct Simulation Monte Carlo, Vacuum, Sep. 2018, 155, pp 249–259, doi: 10.1016/j.vacuum.2018.06.014.CrossRefGoogle Scholar
Guo, G. Liu, H. and Zhang, B. Numerical study of active flow control over a hypersonic backward-facing step using supersonic jet in near space, Acta Astronaut. Mar. 2017, 132, pp 256–267, doi: 10.1016/j.actaastro.2016.12.035.CrossRefGoogle Scholar
Paolicchi, L.T.L.C. and Santos, W.F.N. Length-to-depth ratio effects on aerodynamic surface quantities of a hypersonic gap flow, AIAA J. Feb. 2018, 56, (2), pp 780–792, doi: 10.2514/1.J055826.CrossRefGoogle Scholar
Guo, G. and Luo, Q. DSMC investigation on flow characteristics of rarefied hypersonic flow over a cavity with different geometric shapes, Int. J. Mech. Sci. Nov. 2018, 148, pp 496–509, doi: 10.1016/j.ijmecsci.2018.09.022.CrossRefGoogle Scholar
Palharini, R.C. and Santos, W.F. The impact of the length-to-depth ratio on aerodynamic surface quantities of a rarefied hypersonic cavity flow, Aerosp. Sci. Technol. 2019, 88, pp 110–125.CrossRefGoogle Scholar
Jin, X. Wang, B. Cheng, X. Wang, Q. and Huang, F. The effects of Maxwellian accommodation coefficient and free-stream Knudsen number on rarefied hypersonic cavity flows, Aerosp. Sci. Technol. Feb. 2020, 97, p 105577, doi: 10.1016/j.ast.2019.105577.CrossRefGoogle Scholar
Bird, G.A. Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Oxford University Press, New York, 1994.Google Scholar
Zhang, B. Liu, H. and Jin, S. An asymptotic preserving Monte Carlo method for the multispecies Boltzmann equation, J. Computat. Phys. 2016, 305, pp 575–588.CrossRefGoogle Scholar
Roohi, E. and Stefanov, S. Collision partner selection schemes in DSMC: From micro/nano flows to hypersonic flows, Phys. Rep. Oct. 2016, 656, pp 1–38, doi: 10.1016/j.physrep.2016.08.002.CrossRefGoogle Scholar
Roohi, E. Stefanov, S. Shoja-Sani, A. and Ejraei, H. A generalized form of the Bernoulli Trial collision scheme in DSMC: Derivation and evaluation, J. Computat. Phys. Feb. 2018, 354, pp 476–492, doi: 10.1016/j.jcp.2017.10.033.CrossRefGoogle Scholar
Abe, T. Generalized scheme of the no-time-counter scheme for the DSMC in rarefied gas flow analysis, Comput. Fluids, Mar. 1993, 22, (2), pp 253–257, doi: 10.1016/0045-7930(93)90057-G.CrossRefGoogle Scholar
Prasanth, P. and Kakkassery, J.K. Molecular models for simulation of rarefied gas flows using direct simulation Monte Carlo method, Fluid Dyn. Res. 2008, 40, (4), p 233.CrossRefGoogle Scholar
Alexander, F.J. Garcia, A.L. and Alder, B.J. Cell size dependence of transport coefficients in stochastic particle algorithms, Phys. Fluids, May 1998, 10, (6), pp 1540–1542, doi: 10.1063/1.869674.CrossRefGoogle Scholar
Hadjiconstantinou, N.G. Analysis of discretization in the direct simulation Monte Carlo, Phys. Fluids, Sep. 2000, 12, (10), pp 2634–2638, doi: 10.1063/1.1289393.CrossRefGoogle Scholar
Scanlon, T.J. Roohi, E. White, C. Darbandi, M. and Reese, J.M. An open source, parallel DSMC code for rarefied gas flows in arbitrary geometries, Comput. Fluids, Dec. 2010, 39, (10), pp 2078–2089, doi: 10.1016/j.compfluid.2010.07.014.CrossRefGoogle Scholar
White, C. et al. dsmcFoam+: An OpenFOAM based direct simulation Monte Carlo solver, Comput. Phys. Commun. Mar. 2018, 224, pp 22–43, doi: 10.1016/j.cpc.2017.09.030.CrossRefGoogle Scholar
US Standard Atmosphere, US Standard Atmosphere. National Oceanic and Atmospheric Administration, 1976.Google Scholar
Leite, P.H.M. and Santos, W.F.N. Computational analysis of the flow field structure of a non-reacting hypersonic flow over forward-facing steps, J. Fluid Mech. Jan. 2015, 763, pp 460–499, doi: 10.1017/jfm.2014.677.CrossRefGoogle Scholar
Bird, G.A. Simulation of multi-dimensional and chemically reacting flows (past Space Shuttle orbiter), Rarefied Gas Dyn., 1979, pp 365–388.Google Scholar
Bird, G.A. The Q-K model for gas-phase chemical reaction rates, Phys. Fluids, 2011, doi: 10.1063/1.3650424.CrossRefGoogle Scholar
Bird, G. Molecular Gas Dynamics and the Direct Simulation Monte Carlo of Gas Flows, Clarendon, Oxford, 508, p. 128, 1994.Google Scholar
Nabapure, D. Sanwal, J. Rajesh, S. and Murthy, K.R.C. Investigation of Subsonic and Hypersonic Rarefied Gas Flow over a Backward Facing Step, J. Phys. Conf. Ser. 2019, 1276, p 012007.Google Scholar
Nabapure, D. and Kalluri, R. DSMC investigation of rarefied gas flow over a 2D forward-facing step: Effect of Knudsen number, Acta Astronaut. Jan. 2021, 178, pp 89–109, doi: 10.1016/j.actaastro.2020.08.030.CrossRefGoogle Scholar
Nabapure, D. and Ram Chandra Murthy, K. Simulation of flow in single and double-sided lid driven square cavities by direct simulation Monte Carlo method, Thermal Science, 2020, 24, (5 Part A), pp 3031–3045, doi: 10.2298/TSCI180906066N.CrossRefGoogle Scholar
Nabapure, D. and Kalluri, R.C.M. DSMC simulation of rarefied gas flow over a forward-facing step, ICTEA: International Conference on Thermal Engineering, 2019.CrossRefGoogle Scholar
Nabapure, D. and Ram Chandra Murthy, K. Investigation of Rarefied Open Cavity Flows in all Rarefaction Regimes using DSMC Method, in APS Division of Fluid Dynamics Meeting Abstracts, 2020, pp K18-005.Google Scholar
Nabapure, D. et al. DSMC investigation of rarefied gas flow in a four-sided lid driven cavity: Effect of rarefaction and lid velocities, Journal of Computational Science, 49, p. 101276, 2021.CrossRefGoogle Scholar
Nabapure, D. Singh, A. and Murthy, K.R.C. Effect of Mach Number on the rarefied gas flow over a forward-facing step, Theoretical, Computational, and Experimental Solutions to Thermo-Fluid Systems: Select Proceedings of ICITFES 2020, p. 451.Google Scholar
Nabapure, D. and Murthy, R.C. DSMC simulation of rarefied gas flow over a wall mounted cube, Fluids Engineering Division Summer Meeting, 2019, 59032, p V002T02A071.CrossRefGoogle Scholar
Nabapure, D. and Murthy, K.R.C. DSMC simulation of rarefied gas flow over a forward-facing step: Effect of expansion ratio, AIP Conf. Proc. 2021, 2316, (1), p 030032.CrossRefGoogle Scholar
Scanlon, T.J. et al. Open-source direct simulation monte carlo chemistry modeling for hypersonic flows, AIAA J. 2015, 53, (6), pp 1670–1680.CrossRefGoogle Scholar
Karchani, A. and Ejtehadi, O. A review and perspective on a convergence analysis of the direct simulation Monte Carlo and solution verification, Phys. Fluids, Jun. 2019, 31, (6), p 066101, doi: 10.1063/1.5093746.CrossRefGoogle Scholar
Grotowsky, I.M.G. and Ballmann, J. Numerical investigation of hypersonic step-flows, Shock Waves, Mar. 2000, 10, (1), pp 57–72, doi: 10.1007/s001930050179.CrossRefGoogle Scholar
Ejtehadi, O. Roohi, E. and Esfahani, J.A. Detailed investigation of hydrodynamics and thermal behavior of nano/micro shear driven ow using DSMC, Sci. Iran., 2013, p 13.Google Scholar
Schäfer, F. Breuer, M. and Durst, F. The dynamics of the transitional flow over a backward-facing step, J. Fluid Mech., Mar. 2009, 623, p 85, doi: 10.1017/S0022112008005235.CrossRefGoogle Scholar
Deepak, N. Gai, S. and Neely, A. A computational study of high enthalpy flow over a rearward facing step, 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, Orlando, FL, AIAA Paper, 2010, p. 444.Google Scholar
Balaj, M. Akhlaghi, H. and Roohi, E. Rarefied gas flow behavior in micro/nanochannels under specified wall heat flux, Int. J. Mod. Phys. C, Aug. 2015, 26, (08), p 1550087, doi: 10.1142/S0129183115500874.CrossRefGoogle Scholar
Hong, C. and Asako, Y. Some considerations on thermal boundary condition of slip flow, Int. J. Heat Mass Transf. 2010, 53, (15–16), pp 3075–3079.CrossRefGoogle Scholar