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Effects of geometry on simulation of two-phase flow in microchannel with density and viscosity contrast

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Abstract

With respect to the importance of a multiphase flow behaviour in a microchannel, this study is focused on developing a numerical modelling of two-phase flows using lattice Boltzmann method (LBM). This method utilizes a different vision for surveying the behaviour of fluids. The LBM be able to capture fluid motion via a microscopic vision in contrary to classical CFD methods (Navier–Stokes approach). Based on this capability, the LBM is a powerful method for solving complex problems in multiphase and multicomponent fluid dynamics problems. This research attempts to employ the chromo-dynamic model, which is compatible for high-density ratio flow in a microchannel and introduces different approaches to achieve this objective. This study examined both Huang and Lishchuk methods and the obtained results show a sharp interface between two phases by using Haung model. However, utilization of this method can impose some difficulties on stability of calculation. The research tries to eliminate or at least weaken numerical errors caused by density contrast in the interface of different phases from the exertion of an artificial force. A numerical modelling approach comprises an accurate treatment of the surface tension between phases and a passive-scalar heat transfer method. This research used a high-performance simulation to obtain real-time flow visualizations. The proposed method is applied to a new geometry with variable cross section. A correlation introduced between this geometry and dimensionless numbers (Bejan number, Laplace number, Reynolds number). This new correlation defines an operational criterion for a step-contracted microchannel and enables us to capture the delay time between fluctuations. The results are compared to available exact solutions for high-density ratio flow in a microchannel.

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Abbreviations

A :

Surface tension in perturbation operator

A(x):

Local cross-sectional area

a :

Thermal diffusivity

b :

Blue colour for phase 1

\(B_{\text{i}}\) :

Control parameter

\(c\) :

Unit grid velocity for equilibrium state

\(c_{\text{i}}\) :

Lattice velocity vectors (lm/ls), (lattice metre/lattice second)

\(c_{\text{s}}\) :

Lattice sound speed (lm/ls)

\(d\) :

Low-phase position from inlet (m)

D :

Step-contraction length diameter (m)

F :

Colour gradient vector

\(\varvec{G}_{{\mathbf{c}}}\) :

Correction vector for thermal boundary condition

\(g_{\text{i}}\) :

Thermal distribution function

g(x):

Wall profile

\(h\) :

Convection heat transfer coefficient

H :

Channel diameter (m)

k :

Conduction heat transfer coefficient

L :

Channel length (m)

\(\ell\) :

Step-contraction length (m)

M :

Viscosity ratio

\(N_{\text{x}}\) :

Grid divisions in x component direction

\(N_{\text{y}}\) :

Grid divisions in x component direction

\(N_{\text{i}}\) :

Hydraulic distribution function

\(p\) :

Pressure (Pa)

\(\varvec{Q}\) :

Correction vector for hydraulic boundary condition

r :

Red colour for phase 2

\(q\) :

Heat flux (J/s)

\(q^{\prime \prime }\) :

Zero heat flux, adiabatic boundaries (J/s)

R :

Radius of lower density phase (m)

\(\varvec{x}\) :

Position (m)

\(S_{\text{i}}^{\text{k}}\) :

LBM body force

\(t\) :

Dimensionless time

\(\hat{t}\) :

Time (s)

\(T\) :

Temperature (K)

\(\bar{T}\) :

Average temperature (K)

\(\varvec{u}\) :

Velocity vector (m/s)

\(\bar{u}\) :

Average velocity (m/s)

U :

Parasitic velocity, error term (m/s)

\(W_{\text{i}}\) :

Weigh factor

\(Be\) :

Bejan number, dimensionless

\(Eu\) :

Euler number

Kn :

Knudsen number, dimensionless (\(Kn = \frac{{\lambda_{\upalpha} }}{L}\))

\(La\) :

Laplace number, dimensionless

Ma :

Mach number

\(Pr\) :

Prandtl number, dimensionless

\(Re\) :

Reynolds number, dimensionless

\(\alpha_{\text{k}}\) :

Phase fraction

\(\beta\) :

Free parameter for interface thickness controlling in recolouring operator

\(\varphi_{\text{i}}\) :

The angle between the colour gradient and the lattice unit velocity direction

\(\gamma\) :

Density ratio

\(\theta\) :

Dimensionless temperature

\(\bar{\theta }\) :

Average of dimensionless temperature

\(\lambda_{\upalpha}\) :

Mean free path

Γ(x):

Local cross-sectional parameter

\(\tau\) :

Relaxation time for hydraulic distribution function

\(\nu\) :

Kinematic viscosity

\(\mu\) :

Dynamic viscosity

ρ :

Density

σ :

Surface tension

ω :

Relaxation frequency for hydraulic distribution function

\(\omega_{\text{g}}\) :

Relaxation frequency for thermal distribution function

\(\omega_{\text{k}}\) :

Frequency of relaxation

\(\varOmega_{\text{i}}^{\text{k}}\) :

General operator

\(\varOmega_{\text{i}}^{\text{g}}\) :

General operator for heat transfer streaming

\(\left( {\varOmega_{\text{i}}^{\text{k}} } \right)^{\left( 1 \right)}\) :

Collision operator

\(\left( {\varOmega_{\text{i}}^{\text{k}} } \right)^{\left( 2 \right)}\) :

Perturbation operator

\(\left( {\varOmega_{\text{i}}^{\text{k}} } \right)^{\left( 3 \right)}\) :

Recolouring operator

cr:

Critical state

\({\text{e}}\) :

Equilibrium state

K:

Phase colour

in:

Inlet conditions

out:

Outlet conditions

+:

Post streamed indicator

*:

Post-collision

**:

Error elimination step

***:

Recolouring step

References

  1. Sajid MU, Ali HM. Recent advances in application of nanofluids in heat transfer devices: a critical review. Renew Sustain Energy Rev. 2018;103:556–92. https://doi.org/10.1016/j.rser.2018.12.057.

    Article  CAS  Google Scholar 

  2. Dietzel A. Microsystems for pharmatechnology: manipulation of fluids, particles, droplets, and cells. New York: Springer; 2016.

    Google Scholar 

  3. Huh C, Kim J, Kim MH. Flow pattern transition instability during flow boiling in a single microchannel. Int J Heat Mass Transf. 2007;50(5):1049–60.

    CAS  Google Scholar 

  4. Lee J, Mudawar I. Fluid flow and heat transfer characteristics of low temperature two-phase micro-channel heat sinks—part 1: experimental methods and flow visualization results. Int J Heat Mass Transf. 2008;51(17):4315–26.

    CAS  Google Scholar 

  5. Lee J, Mudawar I. Fluid flow and heat transfer characteristics of low temperature two-phase micro-channel heat sinks—part 2. Subcooled boiling pressure drop and heat transfer. Int J Heat Mass Transf. 2008;51(17):4327–41.

    CAS  Google Scholar 

  6. Peles, Y. Two-phase boiling flow in microchannels—instabilities issues and flow regime mapping. ASME Paper No. ICMM2003-1069, 2003.

  7. Shekarchi M, Debicki G, Granger L, Billard Y. Study of leaktightness integrity of containment wall without liner in high performance concrete under accidental conditions—I. Experimentation. Nucl Eng Des. 2002;213(1):1–9.

    CAS  Google Scholar 

  8. Shkarah AJ, Sulaiman MYB, Ayob MRBH. Boiling two phase flow in microchannels: a review. Indian J Sci Technol. 2013;6(10):5514–21.

    Google Scholar 

  9. Simon H, Nahas G, Coulon N. Air–steam leakage through cracks in concrete walls. Nucl Eng Des. 2007;237(15):1786–94.

    CAS  Google Scholar 

  10. Sussman M, Smereka P, Osher S. A level set approach for computing solutions to incompressible two-phase flow. J Comput Phys. 1994;114(1):146–59.

    Google Scholar 

  11. Tadrist L. Review on two-phase flow instabilities in narrow spaces. Int J Heat Fluid Flow. 2007;28(1):54–62.

    CAS  Google Scholar 

  12. Unverdi SO, Tryggvason G. A front-tracking method for viscous, incompressible, multi-fluid flows. J Comput Phys. 1992;100(1):25–37.

    Google Scholar 

  13. Ali R, Palm B, Maqboo MH. Experimental investigation of two-phase pressure drop in a microchannel. Heat Transf Eng. 2011;32(13–14):1126–38.

    CAS  Google Scholar 

  14. Ide H, Kimura R, Kawaji M. Effect of inlet geometry on adiabatic gas-liquid two-phase flow in a microchannel. Heat Transf Eng. 2009;30(1–2):37–42.

    CAS  Google Scholar 

  15. Ide H, Kimura R, Hashiguchi H, Kawaji M. Effect of channel length on the gas–liquid two-phase flow phenomena in a microchannel. Heat Transf Eng. 2012;33(3):225–33.

    CAS  Google Scholar 

  16. Ide H, Kimura R, Kawaji M. Gas–liquid two-phase flow evolution in a long microchannel. Heat Transf Eng. 2013;34(2–3):151–8.

    CAS  Google Scholar 

  17. Wang G, Cheng P. An experimental study of flow boiling instability in a single microchannel. Int Commun Heat Mass Transf. 2008;35(10):1229–34.

    CAS  Google Scholar 

  18. Yang K-S, Jeng Y-R, Huang C-M, Wang C-C. Heat transfer and flow pattern characteristics for HFE-7100 within microchannel heat sinks. Heat Transf Eng. 2011;32(7–8):697–704.

    CAS  Google Scholar 

  19. Bogojevic D, Sefiane K, Walton AJ, Christy JR, Cummins G, Lin H. Investigation of flow distribution in microchannels heat sinks. Heat Transf Eng. 2009;30(13):1049–57.

    CAS  Google Scholar 

  20. Salimpour MR, Sharifhasan M, Shirani E. Constructal optimization of microchannel heat sinks with noncircular cross sections. Heat Transf Eng. 2013;34(10):863–74.

    CAS  Google Scholar 

  21. Bortolin S, Azzolin M, Del Col D. Flow boiling of halogenated olefins inside a square cross-section microchannel. Sci Technol Built Environ. 2016;22(8):1238–53.

    Google Scholar 

  22. Sadeghi E, Bahrami M, Djilali N. Estimation of Nusselt number in microchannels of arbitrary cross section with constant axial heat flux. Heat Transf Eng. 2010;31(8):666–74.

    CAS  Google Scholar 

  23. Achkar G, El Miscevic M, Lavieille P. An experimental study on slug-bubbly condensation flows at low mass velocity in a square-cross-section microchannel. Heat Transf Eng. 2016;37(13–14):1181–9.

    Google Scholar 

  24. Succi S. The lattice Boltzmann equation: for fluid dynamics and beyond. Oxford: Oxford University Press; 2001.

    Google Scholar 

  25. Ma Y, Mohebbi R, Rashidi MM, Mancae M, Yang Z. Numerical investigation of MHD effects on nanofluid heat transfer in a baffled U-shaped enclosure using lattice Boltzmann method. J Therm Anal Calorim. 2018. https://doi.org/10.1007/s10973-018-7518-y.

    Article  Google Scholar 

  26. Ma Y, Mohebbi R, Rashidi MM, Yang Z. MHD forced convection of MWCNT-Fe3O4/water hybrid nanofluid in a partially heated τ-shaped channel using LBM. J Therm Anal Calorim. 2018. https://doi.org/10.1007/s10973-018-7788-4.

    Article  Google Scholar 

  27. Amirshekari M, Nassab SAG, Javaran EJ. Numerical simulation of a three-layer porous heat exchanger considering lattice Boltzmann method simulation of fluid flow. J Therm Anal Calorim. 2018. https://doi.org/10.1007/s10973-018-7794-6.

    Article  Google Scholar 

  28. Bashirnezhad K, Rashidi MM, Yang Z, Bazri S, Yan WM. A comprehensive review of last experimental studies on thermal conductivity of nanofluids. J Therm Anal Calorim. 2015;122(2):863–84.

    CAS  Google Scholar 

  29. Ma Y, Mohebbi R, Rashidi MM, Yang Z. Numerical study of MHD nanofluid natural convection in a baffled U-shaped enclosure. Int J Heat Mass Transf. 2018. https://doi.org/10.1016/j.ijheatmasstransfer.2018.10.072.

    Article  Google Scholar 

  30. Wang G, Cheng P, Wu H. Unstable and stable flow boiling in parallel microchannels and in a single microchannel. Int J Heat Mass Transf. 2007;50(21):4297–310.

    CAS  Google Scholar 

  31. Wu H, Cheng P. Boiling instability in parallel silicon microchannels at different heat flux. Int J Heat Mass Transf. 2004;47(17):3631–41.

    CAS  Google Scholar 

  32. Harlow FH, Welch JE. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys Fluids. 1965;8(12):2182–9.

    Google Scholar 

  33. Hirt CW, Nichols BD. Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys. 1981;39(1):201–25.

    Google Scholar 

  34. Beg OA, Rashidi M, Akbari M, Hosseini A. Comparative numerical study of single-phase and two-phase models for bio-nanofluid transport phenomena. J Mech Med Biol. 2014;14(01):1450011.

    Google Scholar 

  35. Garoosi F, Rohani B, Rashidi MM. Two-phase mixture modeling of mixed convection of nanofluids in a square cavity with internal and external heating. Powder Technol. 2015;275:304–21.

    CAS  Google Scholar 

  36. Rashidi M, Hosseini A, Pop I, Kumar S, Freidoonimehr N. Comparative numerical study of single and two-phase models of nanofluid heat transfer in wavy channel. Appl Math Mech. 2014;35(7):831–48.

    Google Scholar 

  37. Chen S, Doolen GD. Lattice Boltzmann method for fluid flows. Annu Rev Fluid Mech. 1998;30(1):329–64.

    Google Scholar 

  38. Gunstensen AK, Rothman DH, Zaleski S, Zanetti G. Lattice Boltzmann model of immiscible fluids. Phys Rev A. 1991;43(8):4320.

    CAS  PubMed  Google Scholar 

  39. Shan X, Chen H. Lattice Boltzmann model for simulating flows with multiple phases and components. Phys Rev E. 1993;47(3):1815.

    CAS  Google Scholar 

  40. Shao JY, Shu C, Huang HB, Chew YT. Free-energy-based lattice Boltzmann model for the simulation of multiphase flows with density contrast. Phys Rev E. 2014;89(3–1):033309. https://doi.org/10.1103/PhysRevE.89.033309.

    Article  CAS  Google Scholar 

  41. He X, Chen S, Zhang R. A lattice Boltzmann scheme for incompressible multiphase flow and its application in simulation of Rayleigh–Taylor instability. J Comput Phys. 1999;152(2):642–63.

    CAS  Google Scholar 

  42. Martys NS, Chen H. Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice Boltzmann method. Phys Rev E. 1996;53(1):743.

    CAS  Google Scholar 

  43. Latva-Kokko M, Rothman DH. Static contact angle in lattice Boltzmann models of immiscible fluids. Phys Rev E. 2005;72(4):046701.

    CAS  Google Scholar 

  44. Latva-Kokko M, Rothman DH. Diffusion properties of gradient-based lattice Boltzmann models of immiscible fluids. Phys Rev E. 2005;71(5):056702.

    CAS  Google Scholar 

  45. Yuan P, Schaefer L. A thermal lattice Boltzmann two-phase flow model and its application to heat transfer problems—part 1 Theoretical foundation. J Fluids Eng. 2006;128(1):142–50.

    Google Scholar 

  46. Shan X. Simulation of Rayleigh–Bénard convection using a lattice Boltzmann method. Phys Rev E. 1997;55(3):2780.

    CAS  Google Scholar 

  47. Tölke J. Lattice Boltzmann simulations of binary fluid flow through porous media. Philos Trans R Soc Lond A Math Phys Eng Sci. 2002;360(1792):535–45.

    Google Scholar 

  48. Leclaire S, Reggio M, Trépanier J-Y. Numerical evaluation of two recoloring operators for an immiscible two-phase flow lattice Boltzmann model. Appl Math Model. 2012;36(5):2237–52.

    Google Scholar 

  49. Noble DR, Chen S, Georgiadis JG, Buckius RO. A consistent hydrodynamic boundary condition for the lattice Boltzmann method. Phys Fluids. 1995;7(1):203–9.

    CAS  Google Scholar 

  50. Zou Q, He X. On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys Fluids. 1997;9(6):1591–8.

    CAS  Google Scholar 

  51. Connington K, Lee T. A review of spurious currents in the lattice Boltzmann method for multiphase flows. J Mech Sci Technol. 2012;26(12):3857.

    Google Scholar 

  52. Leclaire S, Pellerin N, Reggio M, Trépanier J-Y. Enhanced equilibrium distribution functions for simulating immiscible multiphase flows with variable density ratios in a class of lattice Boltzmann models. Int J Multiph Flow. 2013;57:159–68.

    CAS  Google Scholar 

  53. Leclaire S, Reggio M, Trépanier J-Y. Isotropic color gradient for simulating very high-density ratios with a two-phase flow lattice Boltzmann model. Comput Fluids. 2011;48(1):98–112.

    Google Scholar 

  54. Swift MR, Orlandini E, Osborn W, Yeomans J. Lattice Boltzmann simulations of liquid-gas and binary fluid systems. Phys Rev E. 1996;54(5):5041.

    CAS  Google Scholar 

  55. Huang H, Huang J-J, Lu X-Y, Sukop MC. On simulations of high-density ratio flows using color-gradient multiphase lattice Boltzmann models. Int J Mod Phys C. 2013;24(04):1350021.

    Google Scholar 

  56. Lishchuk S, Halliday I, Care C. Multicomponent lattice Boltzmann method for fluids with a density contrast. Phys Rev E. 2008;77(3):036702.

    CAS  Google Scholar 

  57. Reis T, Phillips T. Lattice Boltzmann model for simulating immiscible two-phase flows. J Phys A: Math Theor. 2007;40(14):4033.

    CAS  Google Scholar 

  58. Morini GL, Spiga M, Tartarini P. The rarefaction effect on the friction factor of gas flow in microchannels. Superlattices Microstruct. 2004;35(3-6):587–99.

    CAS  Google Scholar 

  59. Ipsen DC. Units, dimensions, and dimensionless numbers. New York: McGraw-Hill; 1960.

    Google Scholar 

  60. Awad MM. A new definition of Bejan number. Therm Sci. 2012;16(4):1251–3.

    Google Scholar 

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Authors and Affiliations

  1. Department of Aerospace Engineering, Faculty of Sciences and Technologies, University of Tehran, Tehran, Iran

    Ahmad Reza Ravangard

  2. Department of Mechanical and Aerospace Engineering, Royal Military College of Canada, Kingston, ON, K7K 7B4, Canada

    Ladan Momayez

  3. Shanghai Automotive Wind Tunnel Center, Tongji University, No. 4800, Cao’an Road, Shanghai, 201804, China

    Mehdi Rashidi

  4. Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, No. 4800, Cao’an Road, Shanghai, 201804, China

    Mehdi Rashidi

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  1. Ahmad Reza Ravangard
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  2. Ladan Momayez
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Correspondence to Ladan Momayez.

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Ravangard, A.R., Momayez, L. & Rashidi, M. Effects of geometry on simulation of two-phase flow in microchannel with density and viscosity contrast. J Therm Anal Calorim 139, 427–440 (2020). https://doi.org/10.1007/s10973-019-08342-1

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