Three Dimensional Stochastic Estimation Applied to Cavity Flow Fields

Abstract

In this paper, we present analysis of a supersonic cavity flow field dataset using the Stochastic Estimation Technique. The dataset used in the present work is generated through the use of Large Eddy Simulations and involves both uncontrolled and controlled cases. We employ the modified estimation technique that combines the Proper Orthogonal Decomposition and the stochastic estimation to reduce the order of the problem numerically and physically. Earlier work in this area has been applied to two dimensional CFD and experimental datasets, with the wall pressure sensors located in close proximity or on the plane of the estimated flow field. Here, we explore the use of this technique to analyze flow field estimation off the plane containing the wall pressure sensors and will look at the contributions from linear and nonlinear terms in the estimation process. I. Introduction The Stochastic Estimation technique, as it has recently been applied (v. Taylor and Glauser [1], Hudy et al. [2] and Murray and Ukeiley [3]-[6] to name a few), is a useful way of estimating the state of the flow field in the interior of the flow domain (off the walls) using data acquired from wall mounted sensors. The method relies on the computation of the interior flow field using statistical information only. The method is based on mean-square estimation techniques (Stochastic Estimation) was originally developed in the turbulence community [7] as a conditional technique to examine coherent structures, but, has since evolved into a method to analyze instantaneous flow fields based on the work of Cole, Glauser and Guzzenic [7]. In the recent past, this method has also been applied to analyze cavity flow fields [3]-[6]. These works exploit the presence of strong coherence in the flow field due to the existence of a feedback loop in the cavity that sustains the oscillating cavity flow field. One of the early applications using a supersonic CFD dataset showed that the quadratic term was essential to reproduce the structure of the flow field accurately. Since then the method has been applied to show the relationship between the surface pressure signatures and vortical structures in the shear layer over the cavity and examine the correlations between the wall pressures and the turbulent structure in the flow field that gives rise to the unsteady pressure signals on the walls. In these applications, as in the case of the computational datasets, the datasets have been two-dimensional, or, in the case of experimental datasets, the estimated flow field has been in close proximity to the same plane as that of the pressure sensors (within the thickness of the laser sheet). Recent work using small mass blowing concepts to control surface dynamic loads in cavity flows has shown that a reduction of the spanwise coherence in the shear layer plays a dominant role the reduction of the dynamic loads on the cavity walls. Here, we examine if the Stochastic Estimation method is applicable to such flow fields. Since these control concepts operate by modifying the large scale coherent features of the flow field, while the stochastic estimation method relies on the existence of such coherence, such an examination is essential to understand the applicability of this technique in these controlled flow fields. Furthermore, as has been shown recently, understanding the three dimensionality of the structure of these flow fields is essential to understanding the effect of flow control. Here we also examine if the Stochastic Estimation is able to estimate the 3D flow structures in regions away from the plane containing the sensors.