Uncertainty Quantification Based Receptivity Modelling of Crossflow Instabilities Induced by Distributed Surface Roughness in Swept Wing Boundary Layers

Abstract

A high fidelity methodology based on the rapid solution of a linearised Navier-Stokes equation set is used to model the role of distributed surface roughness in generating stationary crossflow disturbances on swept wing flows. The technique is based on a stochastic description of surface roughness linked to high precision measurement data for both anodised aluminium and painted surfaces. A Monte Carlo analysis of laminar-turbulent transition is demonstrated for data from the AERAST wind tunnel test which was designed to show control of stationary cross-flow disturbances through the forced excitation of a sub-dominant disturbance mode generated by the artificial placement of periodically distributed roughness elements. The method provides both the roughness induced naturally occurring and forced control mode disturbance amplitudes for initialisation of a simulation based on solution of the non-linear parabolised stability equations. Monte-Carlo based uncertainty quantification analysis enables propagation of uncertainties from the roughness field through the receptivity phase, to ultimately providing bounds on the predicted transition location.

On predicting receptivity to surface roughness in a compressible infinite swept wing boundary layer

“…Crossflow disturbances were most affected by surface roughness variations located close to the leading-edge of the swept wing, while the effects of curvature were found to feature prominently in the receptivity calculations. These observations are consistent with the results of previous receptivity studies performed on different wing geometries 19 . Additionally, the conclusions regarding receptivity being strongest about the leading-edge, reflect experimental observations 16 .…”

“…In fact they are likely to be very different. However, given the observations of previous investigators 19 , we might expect that a Monte-Carlo type analysis (where we compute the receptivity to many roughness strips) will establish a constant mean amplitude…”

“…Numerical discretisation is based on using a fully implicit second-order accurate three-point backward differencing scheme along the x-direction, whilst a two point secondorder accurate (Keller-Box 40 ) method is utilised in the wall normal y-direction. The method has previously been employed to successfully undertake full compressible instability studies on infinite swept wing bodies 19,20,37,41 . For the subsequent LNS and ALNS receptivity analysis, the base boundary-layer profiles were interpolated and mapped on to the {x, y}-grid, where up to N x = 16000 points were used along the x discretised direction, while 51 optimally distributed nodes, with clustering within the boundary-layer were determined to be sufficient in y to generate accurate receptivity calculations.…”

“…Our primary concern relates to outlining the most efficient means of undertaking the Monte-Carlo type analysis conducted by Mughal and Ashworth 19 , who used the direct LNS route. The adjoint linearised Navier-Stokes (ALNS) route is naturally suited for this purpose.…”

Stability of an Infinite Swept Wing Boundary Layer with Surface Waviness

“…Base flow solutions of the CoBL set of equations have previously been utilised for both PSE and receptivity analysis [23,24], for a range of model flow systems. This particular method for generating boundary layer flow profiles is also utlised in this investigation as a means of validating, where possible, a new approach for generating boundary layers.…”