A novel porous Ffowcs-Williams and Hawkings acoustic methodology for complex geometries

Abstract

Predictive noise calculations from high Reynolds number flows in complex engineering geometry are becoming a possibility with the high performance computing resources that have become available in recent years. Increasing the applicability and reliability of solution methodologies have been two key challenges toward this goal. This dissertation develops a porous Ffowcs-Williams and Hawkings methodology that uses a novel endcap methodology, and can be applied to unstructured grids. The use of unstructured grids allows complex geometry to be represented while porous formulation eliminates difficulties with the choice of acoustic Green's function. Specifically, this dissertation (1) proposes and examines a novel endcap procedure to account for spurious noise, (2) uses the proposed methodology to investigate noise production from a range of subcritical Reynolds number circular cylinders, and (3) investigates a trailing edge geometry for noise production and to illustrate the generality of the Green's function. Porous acoustic analogies need an endcap scheme in order to prevent spurious noise due to truncation errors. 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. The correlation is investigated by examining it pass through multiple exit planes. It is then evaluated by computing the sound emitted by flow over a circular cylinder at Reynolds number of 150 and compared to other endcap methods, such as Shur et al [1]. Insensitivity to end plane location and spacing and the effect of the dynamic convection velocity are computed. Subcritical Reynolds number circular cylinder flows are investigated at Re = 3900, 10000 and 89000 in order to evaluate the method and investigate the physical sources of noise production. The Re = 3900 case was chosen due to its highly validated flow-field and to serve as a basis of comparison. The Re = 10000 cylinder is used to validate the noise production at turbulent Reynolds numbers against other simulations. Finally the Re = 89000 simulations are used to compare to experiment serving as a rigorous test of the methods predictive ability. The proposed approach demonstrates better perfor- mance than other commonly used approaches with the added benefit of computational efficiency and the ability to query independent volumes. This gives the added benefit of discovering how much noise production is directly associated with volumetric noise contributions. These capabilities allow for a thorough investigation of the sources of noise production and a means to evaluate proposed theories. A physical description of the source of sound for subcritical Reynolds number cylinders is established. A 45� beveled trailing edge configuration is investigated due to its relevance to hydrofoil and propeller noise. This configuration also allows for the evaluation of the assumption associated with the free-space Green's function since the half-plane Green's function can be used to represent the solution to the wave equation for this geometry. Similar results for directivity and amplitudes of the two formulations confirm the flexibility of the porous surface implementation. Good agreement with experiment is obtained. The effect of boundary layer thickness is investigated. The noise produced in the upper half plane is significantly decreased for the thinner boundary layer while the noise production in the lower half plane is only slightly decreased.