Modelling of Wall Pressure Fluctuations Induced by Turbulent Boundary Layer Flow

Abstract

Semi-empirical models are used to predict the power spectral density of wall pressure fluctuations in the turbulent boundary layer. From the analysis of current semiempirical models and a large survey of experimental data, it was found that the models proposed by Goody and Smol'yakov have the lowest mean squared error when predicting the power spectral density for wind tunnel experiments. The Rackl and Weston model has the lowest mean squared error when predicting the power spectral density for flight test data. In addition, although current studies of the power spectra obtained in the wind tunnel are similar, they are not generally an accurate representation of flight test experiments. Current advancements in power spectral density wall pressure fluctuation prediction have focused on expanding the range of experiments that can be predicted to include adverse pressure gradient flows, however, favourable pressure gradient flows have not received much attention. An experiment was performed to capture the effects of the favourable pressure gradient on the power spectral density. A model was then created to improve upon some of the limitations of existing models. The proposed model improves upon the prediction of the high-frequency roll-off location, incorporates improvements made by past models, and captures the effects of favourable pressure gradients.

Derivation of an Empirical Model to Estimate the Power Spectral Density of Turbulent Flow Wall Pressure Fluctuations Using Machine Learning Regression Techniques

“…The Goody model would prove to be accurate and broadly applicable [12,15,16], particularly when accounting for the influence of non-zero pressure gradients in the flow field. Several future papers, including Lee (2018) and Thomson (2021), used its general form as a template for new models, and it would eventually be known as "the universal wall pressure spectrum" model [19,43]. For a presentation and in depth discussion of the Smol'yakov and Goody models, please refer to Subsection 3.1.…”

“…in which Re T is the turbulence Reynolds number. When parameterized, Goody's model is the shell of the universal wall pressure spectrum used in the Lee [43] and Thomson models [19], as depicted in Equation 12:…”

“…The Goody model provides a clear versatility advantage in comparison to earlier models, as its generalized universal wall pressure spectrum can be accurately applied when non-zero pressure gradients are present in the flow field [19,43]. Furthermore, the model itself has been shown to be accurate under all Reynolds numbers, though it is inaccurate at supersonic speeds [16,59,60].…”

“…First, the EDA step is explored in greater detail, beginning with the identification of data sources. For this thesis, low Reynolds number, low airspeed wind tunnel test data procured by Nicholas Thomson [19] and Jared Van Blitterswyk [20] was used. Measurements were collected via a microphone array that stored pressure fluctuations in the time domain, along with any ancillary data necessary to evaluate several key flow characterizing parameters, such as U ∞ and Re [19].…”

“…As such, this thesis further investigates the validity of alternative statistical techniques (namely, a regression machine learning analysis) to derive a TBL model. Much of the analysis work was performed in the statistical programming language R, making use of low Reynolds number, low airspeed test data from a closed-loop, acoustic foam coated wind tunnel procured at Carleton University by Nicholas Thomson [19] and Jared Van Blitterswyk [20]. This thesis explores those techniques in greater depth, presents a new model, and explores its accuracy and shortcomings.…”