Backpressure propagation mode and balance property in a rectangular duct

The backpressure propagation mode accompanied by shock-train evolution is investigated numerically in a rectangular duct with an open space. On this basis, the balance mechanism and parametric effects of heat transfer and skin friction for backpressure propagation are revealed to understand the nature of force competition better. As a result, the backpressure propagation mode can be classified into two different flow processes with increased backpressure. In addition, balance property mechanism reveals that both the momentum inside the boundary layer and the shear force which transfers the momentum from the outer core flow to boundary layer are combined to resist the adverse pressure gradient. Further, parametric effect indicates that varying wall temperatures and roughness heights lead to different degrees of changes in balance property. According to quantitative results, both wall temperature and roughness height decrease the local boundary-layer momentum at the starting point of original pressure rise and thus the local adverse pressure gradient wins the force competition. In the subsequently continuous flow, the adverse pressure gradient continues to propagate upstream and then is retarded gradually by the boundary layer with a fuller velocity profile until a new force balance is generated.