Jeffrey Crouch

Predicting the onset of flow unsteadiness based on global instability

Global-stability theory is used to predict the onset of flow unsteadiness based on steady solutions of the Reynolds Averaged Navier-Stokes equations. The stability problem is formulated for compressible flow at moderately-high Reynolds numbers, using a turbulence model to provide closure for the averaged Reynolds stresses. The approach provides an efficient method for predicting the occurrence of flow unsteadiness for problems of practical interests, and provides a useful indicator for the legitimate range of application of the steady-flow equations. Numerical solutions are presented based on a finite-difference approximation. The steady baseflow solution and the unsteady disturbance equations are solved using the same grid. Results are presented for the onset of vortex shedding about a circular cylinder at low Reynolds numbers, and for shock-induced transonic-buffet onset at high Reynolds numbers. The results for the onset of flow unsteadiness are in very good agreement with experiments and unsteady calculations.

Origin of transonic buffet on aerofoils

Buffeting flow on transonic aerofoils serves as a model problem for the more complex three-dimensional flows responsible for aeroplane buffet. The origins of transonic aerofoil buffet are linked to a global instability, which leads to shock oscillations and dramatic lift fluctuations. The problem is analysed using the Reynolds-averaged Navier–Stokes equations, which for the foreseeable future are a necessary approximation to cover the high Reynolds numbers at which transonic buffet occurs. These equations have been shown to reproduce the key physics of transonic aerofoil flows. Results from global-stability analysis are shown to be in good agreement with experiments and numerical simulations. The stability boundary, as a function of the Mach number and angle of attack, consists of an upper and a lower branch – the lower branch shows features consistent with a supercritical bifurcation. The unstable modes provide insight into the basic character of buffeting flow at near-critical conditions and are consistent with fully nonlinear simulations. The results provide further evidence linking the transonic buffet onset to a global instability.

Cavity noise generation for circular and rectangular vent holes

Flight tests on a Boeing 777 showed the occurrence of a tone generated by circular anti-icing vents on the underside of a slat during approach conditions. Subsequent wind-tunnel tests are conducted with a fullscale 4ft-span section of the slat at Mach numbers ranging from 0.1 to 0.3. The objective of the wind-tunnel tests is to replicate and then alleviate the tone. Six different vent openings are tested including rectangular and circular shapes constrained by maintaining the overall open area of the vents. Tones are observed at a Strouhal number around 0.4 for the different vent geometries, based on the free-stream velocity and the effective streamwise length of the vent opening. The experimental results also show a sudden tone cut-off as the Mach number is increased; the critical Mach number being dependent on the cavity length. A two-dimensional model of the cavity is developed to enable numerical simulation of the flow. The geometric length scales and Mach numbers are chosen to expand on the experiment findings, but the unknown experimental momentum thickness has to be estimated. The numerical simulations are based on a laminar inflow boundary layer with the initial momentum thickness as a variable. General features of the numerical simulations are in good agreement with the experiments. The simulations show tone cut-on at conditions similar to observations on simple cavity geometries. The tone cut-off with increasing Mach number is observed, but the conditions for its occurrence are not clearly defined.

Global Structure of Buffeting Flow on Transonic Airfoils

The flow field associated with transonic airfoil buffet is investigated using a combination of global-stability theory and experimental data. The theory is based on perturbing a steady flow field obtained from the Reynolds-averaged Navier- Stokes equations. Linearized perturbations are described by an eigenvalue problem, with the frequency and growth rate given by the eigenvalue and global-flow structure provided by the eigenfunction. The experiments provide both steady and unsteady information on the airfoil surface and in the flow downstream of the shock. The the- ory and experiment show good agreement for the buffet onset conditions - including the critical angle of attack and the buffet-onset frequency. The post-buffet flow struc- ture is also in good agreement, and shows a shock oscillation phase locked to an oscillating shear layer downstream of the shock.