A dynamic end cap technique for sound computation using the Ffowcs Williams and Hawkings equations

A dynamic end cap methodology is proposed to account for spurious contributions to the far-field sound within the context of the Ffowcs–Williams and Hawkings (FW–H) acoustic analogy. The quadrupole source terms are correlated over multiple planes to obtain a convection velocity which is then used to determine a corrective convective flux at the FW–H porous surface. The proposed approach is first demonstrated for a convecting potential vortex. It is then evaluated by computing the sound emitted by flow over circular cylinders at Reynolds number of 150, 10 000, and 89 000, respectively. The low Re cylinder is used to validate against direct numerical simulation (DNS) and demonstrate insensitivity to end plane location and spacing, the effect of dynamic convection velocity and to compare to commonly used end cap corrections. The Re 100 00 cylinder is used to validate at turbulent Reynolds numbers against other simulations. Finally the Re 89 000 simulations are used to compare to experiment. The proposed approach demonstrates better performance than other commonly used approaches with the added benefit of computational efficiency and the ability to query independent volumes.