Marvin E. Goldstein

An Exact Form of Lilley's Equation with a Velocity Quadrupole/Temperature Dipole Source Term

There have been several attempts to introduce approximations into the exact form of Lilleys equation in order to express the source term as the sum of a quadrupole whose strength is quadratic in the fluctuating velocities and a dipole whose strength is proportional to the temperature fluctuations. The purpose of this note is to show that it is possible to choose the dependent (i.e. the pressure) variable so that this type of result can be derived directly from the Euler equations without introducing any additional approximations.

Algebraic/transcendental disturbance growth behind a row of roughness elements

This paper is a continuation of the work begun in Goldstein et al . ( J. Fluid Mech. , vol. 644, 2010, p. 123), who constructed an asymptotic high-Reynolds-number solution for the flow over a spanwise periodic array of relatively small roughness elements with (spanwise) separation and plan form dimensions of the order of the local boundary-layer thickness. While that paper concentrated on the linear problem, here the focus is on the case where the flow is nonlinear in the immediate vicinity of the roughness with emphasis on the intermediate wake region corresponding to streamwise distances that are large in comparison with the roughness dimension, but small in comparison with the distance between the roughness array and the leading edge. An analytical O ( h 2 ) asymptotic solution is obtained for the limiting case of a small roughness height parameter h . These weakly nonlinear results show that the spanwise variable component of the wall-pressure perturbation decays as x −5/3 ln x when x → ∞ (where x denotes the streamwise distance scaled on the roughness dimension), but the corresponding component of the streamwise velocity perturbation (i.e. the wake velocity) exhibits an O ( x 1/3 ln x ) algebraic/transcendental growth in the main boundary layer. Numerical solutions for h = O (1) demonstrate that the wake velocity perturbation for the fully nonlinear case grows in the same manner as the weakly nonlinear prediction – which is considerably different from the strictly linear result obtained in Goldstein et al . (2010).

The Long Range Persistence of Wakes Behind a Row of Roughness Elements

We consider a periodic array of relatively small roughness elements whose spanwise separation is of the order of the local boundary-layer thickness and construct a local asymptotic high-Reynolds-number solution that is valid in the vicinity of the roughness. The resulting flow decays on the very short streamwise length scale of the roughness, but the solution eventually becomes invalid at large downstream distances and a new solution has to be constructed in the downstream region. This latter result shows that the roughness-generated wakes can persist over very long streamwise distances, which are much longer than the distance between the roughness elements and the leading edge. Detailed numerical results are given for the far wake structure.

Boundary-layer transition at high free-stream disturbance levels : beyond Klebanoff modes

We consider a nominally uniform flow over a semi-infinite flat plate and show how a small slowly modulated (predominantly streamwise) disturbance of the upstream flow is amplified by leading-edge bluntness effects and eventually develops into a small-amplitude but nonlinear spanwise motion far downstream from the edge. This motion is then imposed on the viscous boundary layer at the surface of the plate – causing an order-one change in its profile shape, which can reduce the wall shear to zero and thereby causes the boundary layer to separate. The present study is similar to an earlier steady flow analysis, but the unsteady effects now cause the upstream boundary layer to develop inflectional profiles which can support rapidly growing inviscid instabilities that give rise to transition before the separation can occur.

Hybrid Reynolds-Averaged Navier-Stokes/Large Eddy Simulation Approach for Predicting Jet Noise

Hybrid acoustic prediction methods have an important advantage over the current Reynolds-averaged Navier-Stokes based methods in that they only involve modeling of the relatively universal subscale motion and not the configuration-dependent larger-scale turbulence. Unfortunately, they are unable to account for the high-frequency sound generated by the turbulence in the initial mixing layers. This paper introduces an alternative approach that directly calculates the sound from a hybrid Reynolds-averaged Navier-Stokes/large eddy simulation flow model (which can resolve the steep gradients in the initial mixing layers near the nozzle lip) and adopts modeling techniques similar to those used in current Reynolds-averaged Navier-Stokes based noise prediction methods to determine the unknown sources in the equations for the remaining unresolved components of the sound field. The resulting prediction method would then be intermediate between the current noise prediction codes and previously proposed hybrid noise prediction methods.

Ninety-Degree Acoustic Spectrum of a High Speed Air Jet

Tam and Auriault successfully predicted the acoustic spectrum at 90 deg to the axis of a high-speed air jet by using an acoustic equation derived from ad hoc kinetic theory-type arguments. It is shown that similar predictions can be obtained by using a rigorous acoustic analogy approach together with actual measurements of the relevant acoustic source correlations. This puts the result on a firmer basis and enables its extension to new situations and to the prediction of sound at other observation angles.

A Hybrid RANS/LES Approach for Predicting Jet Noise

Hybrid acoustic prediction methods have an important advantage over the current Reynolds averaged Navier-Stokes (RANS) based methods in that they only involve modeling of the relatively universal subscale motion and not the configuration dependent larger scale turbulence. Unfortunately, they are unable to account for the high frequency sound generated by the turbulence in the initial mixing layers. This paper introduces an alternative approach that directly calculates the sound from a hybrid RANS/LES flow model (which can resolve the steep gradients in the initial mixing layers near the nozzle lip) and adopts modeling techniques similar to those used in current RANS based noise prediction methods to determine the unknown sources in the equations for the remaining unresolved components of the sound field. The resulting prediction method would then be intermediate between the current noise prediction codes and previously proposed hybrid noise prediction methods.

Boundary-layer effect in panel flutter

The present note shows that if the supersonic Mach number is not too large, an analytical expression can be obtained for the generalized aerodynamic force relating the pressure fluctuation at the surface of a flexible plate to the plate displacement in the presence of an adjacent boundary layer. The low supersonic Mach numbers are the ones of maximum interest since it is in this Mach number region that the boundary layer has the most influence. In this respect, Dowell (1971) has already shown that the presence of a boundary layer causes about a 300% increase in flutter dynamic pressure at a Mach number of about 1.2, while it causes only about a 20% increase at a Mach number of 2.