A simple direct heating thermal immersed boundary-lattice Boltzmann method for its application in incompressible flow

Abstract A simple direct heating thermal immersed boundary-lattice Boltzmann method for buoyancy-driven incompressible flow with complex geometry boundaries is developed to simulate natural convection with curved boundary. In the newly developed method, both Dirichlet and Neumann boundary conditions in macroscopic equation are deduced into a novel mesoscopic discrete heat source. The mesoscopic discrete heat source consists of simplified explicit discrete heat source scheme which reduces the computational complexities and is introduced into lattice Boltzmann equation for temperature field, which extends the idea of the previous direct forcing IB-LBM. Both isothermal boundary condition (i.e. Dirichlet boundary condition) and constant heat flux boundary condition (i.e. Neumann boundary condition) are considered in our simulations. The efficiency and accuracy of the present method are demonstrated by simulating both two dimensional and three dimensional thermal flow with curved boundaries. Numerical results indicate that the efficiency and accuracy of the present method are well consistent with experimental and the other numerical results. The present method has also been successfully applied to three dimensional simulations of natural convection in a thin annulus with adiabatic wall at both vertical sides.

[1]  M. Yoshino,et al.  A thermal immersed boundary–lattice Boltzmann method for moving-boundary flows with Dirichlet and Neumann conditions , 2018, International Journal of Heat and Mass Transfer.

[2]  Yang Li,et al.  Axisymmetric lattice Boltzmann model for multiphase flows with large density ratio , 2018, International Journal of Heat and Mass Transfer.

[3]  Wei Zhang,et al.  Forced convection for flow across two tandem cylinders with rounded corners in a channel , 2019, International Journal of Heat and Mass Transfer.

[4]  Yikun Wei,et al.  A novel two-dimensional coupled lattice Boltzmann model for incompressible flow in application of turbulence Rayleigh–Taylor instability , 2017 .

[5]  Yikun Wei,et al.  Simulations of natural convection heat transfer in an enclosure at different Rayleigh number using lattice Boltzmann method , 2016 .

[6]  Joo-Sik Yoo,et al.  Dual free-convective flows in a horizontal annulus with a constant heat flux wall , 2003 .

[7]  Sheng Chen.  Simulating compositional convection in the presence of rotation by lattice Boltzmann model , 2010 .

[8]  Wenming Yang,et al.  Novel immersed boundary methods for thermal flow problems , 2013 .

[9]  J. Wu,et al.  Implicit velocity correction-based immersed boundary-lattice Boltzmann method and its applications , 2009 .

[10]  Zuchao Zhu,et al.  Quantification of wake unsteadiness for low-Re flow across two staggered cylinders , 2019, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science.

[11]  Zuchao Zhu,et al.  Effects of vortex structure on performance characteristics of a multiblade fan with inclined tongue , 2019, Proceedings of the Institution of mechanical engineers. Part A, journal of power and energy.

[12]  P. Bhatnagar,et al.  A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems , 1954 .

[13]  Xiao-Dong Niu,et al.  Study of multiple steady solutions for the 2D natural convection in a concentric horizontal annulus with a constant heat flux wall using immersed boundary-lattice Boltzmann method , 2015 .

[14]  H. Liang,et al.  An efficient phase-field-based multiple-relaxation-time lattice Boltzmann model for three-dimensional multiphase flows , 2017, Comput. Math. Appl..

[15]  C. Shu,et al.  An efficient immersed boundary method for thermal flow problems with heat flux boundary conditions , 2013 .

[16]  Z. Feng,et al.  Proteus: a direct forcing method in the simulations of particulate flows , 2005 .

[17]  Xiao-Dong Niu,et al.  An Efficient Immersed Boundary-Lattice Boltzmann Method for the Simulation of Thermal Flow Problems , 2016 .

[18]  Hong-Liang Yi,et al.  Eccentricity effect on bifurcation and dual solutions in transient natural convection in a horizontal annulus , 2015 .

[19]  Xiaolei Yang,et al.  A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations , 2009, J. Comput. Phys..

[20]  Z. Chai,et al.  A lattice Boltzmann analysis of the conjugate natural convection in a square enclosure with a circular cylinder , 2019, Applied Mathematical Modelling.

[21]  Zhenhua Chai,et al.  Phase-field-based lattice Boltzmann modeling of large-density-ratio two-phase flows. , 2018, Physical review. E.

[22]  Chang Shu,et al.  A simplified thermal lattice Boltzmann method without evolution of distribution functions , 2017 .

[23]  Raffaele Tripiccione,et al.  LBE SIMULATIONS OF RAYLEIGH-BÉNARD CONVECTION ON THE APE100 PARALLEL PROCESSOR , 1993 .

[24]  Y. Qian,et al.  Lattice BGK Models for Navier-Stokes Equation , 1992 .

[25]  Yan Peng,et al.  A momentum exchange-based immersed boundary-lattice Boltzmann method for simulating incompressible viscous flows , 2006 .

[26]  H Liang,et al.  Lattice Boltzmann simulation of three-dimensional Rayleigh-Taylor instability. , 2016, Physical review. E.

[27]  Chuguang Zheng,et al.  A coupled lattice BGK model for the Boussinesq equations , 2002 .

[28]  I. Karlin,et al.  Lattice Boltzmann method for thermal flow simulation on standard lattices. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  G. Doolen,et al.  Discrete Boltzmann equation model for nonideal gases , 1998 .

[30]  Y. Qian,et al.  A bounce back-immersed boundary-lattice Boltzmann model for curved boundary , 2020 .

[31]  Z. Chai,et al.  Lattice Boltzmann modeling of three-phase incompressible flows. , 2016, Physical review. E.

[32]  Yue-Hong Qian,et al.  Simulating thermohydrodynamics with lattice BGK models , 1993 .

[33]  M. Y. Ha,et al.  An immersed boundary-thermal lattice Boltzmann method using an equilibrium internal energy density approach for the simulation of flows with heat transfer , 2010, J. Comput. Phys..

[34]  Hui Yang,et al.  A novel two-dimensional coupled lattice Boltzmann model for thermal incompressible flows , 2018, Appl. Math. Comput..

[35]  A. Salsac,et al.  Minuet motion of a pair of capsules interacting in simple shear flow , 2020, Journal of Fluid Mechanics.

[36]  C. Shu,et al.  Simulation of incompressible viscous flows around moving objects by a variant of immersed boundary-Lattice Boltzmann method , 2009 .

[37]  Richard J Goldstein,et al.  An experimental and theoretical study of natural convection in the annulus between horizontal concentric cylinders , 1976, Journal of Fluid Mechanics.

[38]  Zuchao Zhu,et al.  Experimental investigations on the performance and noise characteristics of a forward-curved fan with the stepped tongue , 2019, Measurement and Control.

[39]  Xiaowen Shan,et al.  SIMULATION OF RAYLEIGH-BENARD CONVECTION USING A LATTICE BOLTZMANN METHOD , 1997 .

[40]  Yi Li,et al.  Fluidization characteristics of particles in a groove induced by horizontal air flow , 2020 .

[41]  Y. Hassan,et al.  A direct-forcing immersed boundary method for the thermal lattice Boltzmann method , 2011 .

[42]  Z. Feng,et al.  The immersed boundary-lattice Boltzmann method for solving fluid-particles interaction problems , 2004 .

[43]  Application of differential quadrature method to simulate natural convection in a concentric annulus , 1999 .

[44]  Chiang Juay Teo,et al.  Thermal lattice Boltzmann flux solver and its application for simulation of incompressible thermal flows , 2014 .