Benchmark Solutions for Computational Aeroacoustics (CAA) Code Validation

Abstract

NASA has conducted a series of Computational Aeroacoustics (CAA) Workshops on Benchmark Problems to develop a set of realistic CAA problems that can be used for code validation. In the Third (1999) and Fourth (2003) Workshops, the single airfoil gust response problem, with real geometry effects, was included as one of the benchmark problems. Respondents were asked to calculate the airfoil RMS pressure and far-field acoustic intensity for different airfoil geometries and a wide range of gust frequencies. This paper presents the validated solutions that have been obtained to the benchmark problem, and in addition, compares them with classical flat plate results. It is seen that airfoil geometry has a strong effect on the airfoil unsteady pressure, and a significant effect on the far-field acoustic intensity. Those parts of the benchmark problem that have not yet been adequately solved are identified and presented as a challenge to the CAA research community.

The importance of the unsteady Kutta condition when modelling gust–aerofoil interaction

“…Only a few of these papers go on to compare far-field noise predictions with previous results, [30,17], and we see in these far-field results discrepancy between different codes that do or do not have the unsteady Kutta condition imposed. Whilst it has been reported in Sandberg & Sandham [28] and Sandberg et al [29] that the effects of the unsteady Kutta condition on the far-field noise can be neglected, we highlight that this is only shown for flat plates, and not for aerofoils with realistic thickness or camber (such as the cases in [30,17]), and indeed Amiet [3] predicts that the unsteady Kutta condition is not a necessity for flat plates as it is self-imposed by the solution. It has been shown analytically [32] and numerically [13] that introducing non-zero thickness has a significant effect on sound generation for aerofoils of finite chord length, therefore one should be cautious about classifying zero-thickness and nonzero-thickness aerofoils in the same way.…”

“…The unsteady Kutta condition acts to control the unsteady velocities and pressures at the trailing edge, therefore in this paper we pay particular attention to the surface pressure at the trailing edge. Various numerical results that do not impose an unsteady Kutta condition show singular or "spiked" trailing-edge pressures even though the pressure along the remaining aerofoil chord agrees with benchmark solutions [1,17,22,30]. Only a few of these papers go on to compare far-field noise predictions with previous results, [30,17], and we see in these far-field results discrepancy between different codes that do or do not have the unsteady Kutta condition imposed.…”

“…Various numerical results that do not impose an unsteady Kutta condition show singular or "spiked" trailing-edge pressures even though the pressure along the remaining aerofoil chord agrees with benchmark solutions [1,17,22,30]. Only a few of these papers go on to compare far-field noise predictions with previous results, [30,17], and we see in these far-field results discrepancy between different codes that do or do not have the unsteady Kutta condition imposed. Whilst it has been reported in Sandberg & Sandham [28] and Sandberg et al [29] that the effects of the unsteady Kutta condition on the far-field noise can be neglected, we highlight that this is only shown for flat plates, and not for aerofoils with realistic thickness or camber (such as the cases in [30,17]), and indeed Amiet [3] predicts that the unsteady Kutta condition is not a necessity for flat plates as it is self-imposed by the solution.…”

“…2] which compares two different numerical Kutta conditions, which yield different surface pressure results at the trailing edge. A number of numerical methods do not impose the condition [1,15,17,22,30], and instead only a zero-normal velocity condition is imposed.…”

Validating the Harmonic Balance Method for Turbomachinery Tonal Noise Predictions

“…First, the gusts are subtracted from the solution in all boundary cells using Eq. (21). A characteristic analysis can then be performed based only on flow induced disturbances.…”