Effect of wall roughness on the flow through converging-diverging nozzles

An understanding of the effect of wall roughness on turbulent flows is important in many engineering applications. The roughness can affect both skin-friction and pressure drag through such factors as the thrust ratios, discharge coefficients, and static pressure distributions. The effect of roughness height on the performance of two-dimensional, converging-diverging nozzles is studied computationally. It is observed that while the total thrust decreases as the wall roughness increases, there is a tradeoff between the losses associated with the shock system and those associated with the skin-friction. However, the normalized skin-friction coefficient is seen to be virtually independent of the Mach number variation. An empirical correlation is proposed to fit the observed variation of skin-friction coefficient as a function of the roughness height.