A consistent direct discretization scheme on Cartesian grids for convective and conjugate heat transfer
A consistent direct discretization scheme on Cartesian grids for convective and conjugate heat transfer
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DOI：
10.1016/j.jcp.2016.05.034
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发表时间：
2016-09
期刊：
影响因子：
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通讯作者：
Norikazu Sato;S. Takeuchi;T. Kajishima;M. Inagaki;N. Horinouchi
中科院分区：
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作者：
Norikazu Sato;S. Takeuchi;T. Kajishima;M. Inagaki;N. Horinouchi
提出了一种新的笛卡尔网格离散格式，即“一致直接离散格式”，用于求解具有对流换热和共轭换热的不可压缩流动。利用表面速度和压力梯度的一致性，即使在固体边界附近，也可以直接离散N-S方程和压力-泊松方程。通过对基本流动问题的验证，发现本方法显著地提高了速度和壁面剪应力的精度。由于速度场和压力场的一致性，数值结果对Courant数的敏感性较小。对于热场，提出了相容直接离散格式的概念，在满足界面热关系的同时，直接离散了流体和固体相的能量方程。根据热边界条件的不同，它具有不同的形式：对流换热的Dirichlet(等温)和Neumann(绝热/等热流)边界条件，以及共轭换热的流固热相互作用。通过将模拟结果与相应热边界条件下的解析解进行比较，验证了这些离散格式的有效性，并证实了本格式对热场也具有较高的精度。共轭热传导问题的一个显着改进是，即使在流体和固体相接近实际物理性质的恶劣条件下，也能保持二阶空间精度和数值稳定性。
A new discretization scheme on Cartesian grids, namely, a “consistent direct discretization scheme”, is proposed for solving incompressible flows with convective and conjugate heat transfer around a solid object. The Navier–Stokes and the pressure Poisson equations are discretized directly even in the immediate vicinity of a solid boundary with the aid of the consistency between the face-velocity and the pressure gradient. From verifications in fundamental flow problems, the present method is found to significantly improve the accuracy of the velocity and the wall shear stress. It is also confirmed that the numerical results are less sensitive to the Courant number owing to the consistency between the velocity and pressure fields. The concept of the consistent direct discretization scheme is also explored for the thermal field; the energy equations for the fluid and solid phases are discretized directly while satisfying the thermal relations that should be valid at their interface. It takes different forms depending on the thermal boundary conditions: Dirichlet (isothermal) and Neumann (adiabatic/iso-heat-flux) boundary conditions for convective heat transfer and a fluid–solid thermal interaction for conjugate heat transfer. The validity of these discretizations is assessed by comparing the simulated results with analytical solutions for the respective thermal boundary conditions, and it is confirmed that the present schemes also show high accuracy for the thermal field. A significant improvement for the conjugate heat transfer problems is that the second-order spatial accuracy and numerical stability are maintained even under severe conditions of near-practical physical properties for the fluid and solid phases.