The calculation of turbulent recirculating flows in general orthogonal coordinates

Many flows of practical interest, such as those that are bounded by curved surfaces, could be calculated in curvilinear coordinates more accurately, conveniently, and economically than in Cartesian coordinates. A calculation procedure is developed by representing the conservation equations in general orthogonal coordinates and so obtaining appropriate finite-difference equations. These equations are written in a similar manner to their Cartesian counterparts, thus enabling the procedure of Gosman and Pun (Imperial College Report HTS/73/2) to be adapted. The viability of such a procedure depends upon the ability to generate an orthogonal grid appropriate to a given flow geometry and consequently a grid-generation procedure is also developed: it is based on the solution, by an iterative finite-difference technique, of Laplace's equation for the Cartesian coordinates of the orthogonal grid nodes. The combined procedures are tested and demonstrated by calculating the flow properties in a diffuser of sufficient divergence to cause recirculation.