# Lattice Boltzmann simulation to laminar pulsating flow past a circular cylinder with constant temperature

- 235 Downloads

## Abstract

In order to investigate the heat transfer characteristics of pulsating flows past a circular cylinder, a Lattice Boltzmann (LB) numerical code based on a 2-dimension-9-velocity frame is developed. The local Nusselt number and the dimensionless viscous force around the cylinder surface are explored in detail. Double Particle Distribution Function model and the second order extrapolation method for the curve boundary of the cylinder are employed in the LB numerical code. Numerical results found that the spatial averaged Nusselt number of the cylinder is oscillating with the same pulsating frequency of the incoming air flows. The heat transfer enhancement is mainly located in the windward side of the cylinder, and the heat transfer enhancement only happens in one half cycle of the pulsation. Whereas the heat transfer in the leeward side of the cylinder is found to be unaffected, and the heat transfer is slightly deteriorated in the other half cycle of the pulsation. Further analysis showed that the heat transfer enhancement is proportional to the magnitude of dimensionless viscous force.

## Keywords

Heat Transfer Nusselt Number Circular Cylinder Lattice Boltzmann Method Heat Transfer Enhancement## List of symbols

*A*Dimensionless pulsation amplitude

*c*Dimensionless lattice speed

- CFD
Computational Fluid Dynamics

*c*_{s}Dimensionless sound speed

*C*_{D}Drag coefficient

*C*_{P}Dimensionless pressure force

*Cτ*Dimensionless viscous force

*d*Diameter of the cylinder (m)

*D*Number of dimensions

*e*_{α}Dimensionless lattice speed in

*α*direction- EPDF
Energy Particle Distribution Function

*f*Pulsation frequency (Hz)

*f*_{α}PDF in

*α*direction*F*_{D}Drag force of the cylinder (N)

- FFT
Fast Fourier transform

*F*_{α}Dimensionless external force in

*α*direction*g*_{α}EPDF in

*α*direction*H*Height of the computational zone (m)

*L*Length of the computational zone (m)

*L*_{r}Grid resolution (m)

- LBM
Lattice Boltzmann method

*Nu*Nusselt number

- \( \left\langle {Nu} \right\rangle \)
Spatial averaged Nusselt number

- \( \overline{{\left\langle {Nu} \right\rangle }} \)
Spatial and period averaged Nusselt number

*Nu*_{r}Relative Nusselt number

*P*Pressure (Pa)

Particle Distribution Function

*Pr*Prandtl number

*Q*Corrector constant

*R*Dimensionless gas constant

*Re*Reynolds number

*St*Strouhal number

*t*Dimensionless time

*t*_{p}Period of a pulsation cycle (s)

*T*Temperature (K)

*u*Velocity component in

*x*direction (m/s)*u*_{ave}Averaged incoming velocity (m/s)

*v*Velocity component in

*y*direction (m/s)- \( \vec{V} \)
Dimensionless velocity vector

*w*_{α}Weight factor in

*α*direction*y*^{*}Modified

*y*coordinate (=2*y*/*H*)*ρ*Dimensionless density

*τ*Dimensionless relaxation time

*ν*Dynamic viscosity (m

^{2}/s)*ν*Dimensionless dynamic viscosity in LBM

*γ*Dimensionless thermal diffusivity in LBM

*δt*Dimensionless lattice time step

*ε*Dimensionless internal energy

*Δ*Intersection parameter

## Subsrcipt

*av*Averaged

*f*Fluid flow particle

*g*Internal energy particle

*in*Incoming

*n*Iteration step

*p*Pulsating case

*pred*Predicted

*s*Steady case

*theo*Theoretical

*w*Cylinder wall

*α*Lattice direction

## Superscript

*eq*Equilibrium state

## Notes

### Acknowledgements

We are grateful for all kind suggestions and discussions on the code development by Professor Yildiz Bayazitoglu in RICE University (U.S.A.). This work was supported by the National Natural Science Foundation of China (51476146, 51476145).

## References

- 1.Bilen K, Akyol U, Yapici S (2001) Heat transfer and friction correlations and thermal performance analysis for a finned surface. Energy Convers Manag 42:1071–1083CrossRefGoogle Scholar
- 2.Dong C, Li D, Zheng YQ et al (2016) An efficient and low resistant circumferential overlap trisection helical baffle heat exchanger with folded baffles. Energy Convers Manag 113:143–152CrossRefGoogle Scholar
- 3.Li GN, Xu ZH, Zheng YQ et al (2016) Experimental study on convective heat transfer from a rectangular flat plate by multiple impinging jets in laminar cross flows. Int J Therm Sci 108:123–131CrossRefGoogle Scholar
- 4.Williamson CHK (1996) Vortex dynamics in the cylinder wake. Ann R Fluid 28:477–539MathSciNetCrossRefGoogle Scholar
- 5.Zukauskas A, Kakac S, Shah RK et al (1987) Handbook of single-phase convective heat transfer, vol 6. Wiley, New York, pp 1–45Google Scholar
- 6.Havemann HA, Rao NNN (1954) Heat transfer in pulsating flow. Nature 174:41CrossRefGoogle Scholar
- 7.Ji TH, Kim SY, Hyun JM (2008) Experiments on heat transfer enhancement from a heated square cylinder in a pulsating channel flow. Int J Heat Mass Transf 51:1130–1138CrossRefGoogle Scholar
- 8.Baffigi F, Bartoli C (2010) Heat transfer enhancement in natural convections between vertical and down inclined wall and air by pulsating jets. Exp Therm Fluid Sci 34:943–953CrossRefGoogle Scholar
- 9.Elshafei EAM, Mohamed MS, Mansour H et al (2008) Experimental study of heat transfer in pulsating turbulent flow in a pipe. Int J Heat Fluid 29:1029–1038CrossRefGoogle Scholar
- 10.Li GN, Zheng YQ, Hu GL et al (2013) Experimental investigation on heat transfer enhancement from an inclined heated cylinder with constant heat input power in infrasonic pulsating flows. Exp Therm Fluid Sci 49:75–85CrossRefGoogle Scholar
- 11.Li GN, Zheng YQ, Hu GL et al (2016) Experimental study of the heat transfer enhancement from a circular cylinder in laminar pulsating cross-flows. Heat Transf Eng 37:535–544CrossRefGoogle Scholar
- 12.Papadakis G, Bergeles G (2001) Numerical simulation of the flow and heat transfer around a cylinder with a pulsating approaching flow at a low Reynolds number. Proc Inst Mech Eng 215:105–119Google Scholar
- 13.Föller S, Selimefendigil F, Polifke W (2008) Linear identification of the unsteady heat transfer of a cylinder in pulsating cross flow. In: Proceeding of the 2nd international conference on jets, wakes and separated flows, vol 1, Berlin, Germany, pp 16–19Google Scholar
- 14.Selimefendigil F, Föller S, Polifke W (2012) Nonlinear identification of unsteady heat transfer of a cylinder in pulsating cross flow. Comput Fluids 53:1–14CrossRefzbMATHGoogle Scholar
- 15.Sumaily GFA, Thompson MC (2013) Forced convection from a circular cylinder in pulsating flow with and without the presence of porous media. Int J Heat Mass Transf 61:226–244CrossRefGoogle Scholar
- 16.Yu JY, Lin W, Zheng XT (2014) Effect on the flow and heat transfer characteristics for sinusoidal pulsating laminar flow in a heated square cylinder. Heat Mass Transf 50:849–864CrossRefGoogle Scholar
- 17.Li GN, Aktas M, Bayazitoglu Y (2015) A review on the discrete Boltzmann model for nanofluid heat transfer in enclosures and channels. Numer Heat Transf Part B 67:463–488CrossRefGoogle Scholar
- 18.Grucelski A, Pozorski J (2015) Lattice Boltzmann simulations of heat transfer in flow past a cylinder and in simple porous media. Int J Heat Mass Transf 86:139–148CrossRefzbMATHGoogle Scholar
- 19.Sun XW, Chan CK, Mei B (2016) LES of convective heat transfer and incompressible fluid flow past a square cylinder. Numer Heat Transf Part A 69:1106–1124CrossRefGoogle Scholar
- 20.Peng Y, Shu C, Chew YT (2003) Simplified thermal lattice Boltzmann model for incompressible thermal flows. Phys Rev E 68:026701CrossRefGoogle Scholar
- 21.Hou S, Zou Q, Chen S (1995) Simulation of cavity flow by the lattice Boltzmann method. J Comput Phys 118:329–347CrossRefzbMATHGoogle Scholar
- 22.Zou Q, He X (1997) On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys Fluids 9:1591–1598MathSciNetCrossRefzbMATHGoogle Scholar
- 23.Liu C, Lin K, Mai H (2010) Thermal boundary conditions for thermal lattice Boltzmann simulations. Comput Math Appl 59:2178–2193MathSciNetCrossRefzbMATHGoogle Scholar
- 24.Guo Z, Zheng C, Shi B (2002) An extrapolation method for boundary conditions in lattice Boltzmann method. Phys Fluids 14:2007–2010CrossRefzbMATHGoogle Scholar
- 25.Fent ZG, Michaelides EE (2008) Inclusion of heat transfer computations for particle laden flows. Phys Fluids 20:1–10Google Scholar
- 26.Barkley D, Henderson RD (1996) Three-dimensional Floquet stability analysis of the wake of a circular cylinder. J Fluid Mech 322:215–241CrossRefzbMATHGoogle Scholar
- 27.Williamson CHK (1996) Three-dimensional wake transition. J Fluid Mech 328:345–407Google Scholar
- 28.Shi JM, Gerlach D, Breuer M (2004) Heating effect on steady and unsteady horizontal laminar flow of air past a circular cylinder. Phys Fluids 16:4331–4345CrossRefzbMATHGoogle Scholar
- 29.Eckert ERG, Soehngen E (1952) Distribution of heat transfer coefficients around circular cylinders in cross flow at Reynolds numbers from 20 to 500. Trans ASME 74:343–347Google Scholar
- 30.Ji TH, Kim SY, Hyun JM (2008) Experiments on heat transfer enhancement from a heated square cylinder in a pulsating channel flow. Int J Heat Mass Transf 51:1130–1138CrossRefGoogle Scholar
- 31.Perwaiz J, Base TE (1992) Heat transfer from a cylinder and finned tube in a pulsating crossflow. Exp Therm Fluid Sci 5:506–512CrossRefGoogle Scholar
- 32.Li GN, Zheng YQ, Hu GL (2015) CFD method study of the influence of pulsating frequency on enhancement of heat transfer from a rectangular flat plate in laminar pulsating flows inside a vertical circular channel. Heat Transf Res 46:903–921CrossRefGoogle Scholar
- 33.Persoons T, Saenen T, Oevelen TV (2012) Effect of flow pulsation on the heat transfer performance of a minichannel heat sink. J Heat Transf 134:091702CrossRefGoogle Scholar