The development of a new computational scheme for mixed convection with using a scalar potential

流场用原始变量系统或涡量和矢势系统求解。对于混合对流，后一种格式不能适用。在这项工作中，它表明，这一困难可以通过引入一个标量势能来解决。这最初是由Hirasaki和Hellums提出的，但似乎没有实际的计算结果。本文首先求解了Re=81.6时近底开孔矩形通道内的等温二维通流问题。计算得到的速度场与用经典的流函数方法得到的结果吻合得很好，流函数的梯度是在活塞流的开口处给定的。两种解的相关系数均为0.9969。然后将其应用于加热地板和冷却垂直壁的二维混合对流。流函数表示的流场与相同边界条件下水槽中的实验条纹线吻合得很好。这种计算方案也被发现是适用于在一个三维领域。对于一个蓄热系统，有两种流动模式，即捷径模式和曲折模式是稳定的，这取决于阿基米德数Gr/ <Re ^2>。

Flow fields have been solved either with a primitive variable system or with a vorticity and vector potential system. For the mixed convection, the latter scheme can not be suitally applied. In this work, it is shown that this difficulty can be resolved by introducing a scalar potnetial. This was originally proposed by Hirasaki and Hellums but there appears to be no practical computational results. At the beggining, isothermal two-dimensional through-flow in a square rectangular channel with openings near bottom was solved for Re=81.6. Computed velocity field agreed very well with the results obtained by a classical way of stream function whose gradient is given at the openings for a plug flow. Both solutions agreed in that the relative coefficient is 0.9969. Then this was applied to a two-dimensional mixed convection with heating floor and a cooling vertical wall. The flow field shown in a stream function agreed very well with the experimental streak line in a water box with the same boundary conditions. This computational scheme was also found to be applicable in a three-dimensional field. For a heat storage system two flow modes, a short-cut and a tortours modes were found to be stable depending on the Archimedes number Gr/ <Re^2> .