High Reynolds number turbulent boundary layers over both smooth and rough surfaces subjected to a systematically defined family of continually varying, bi-directional pressure gradient distributions are investigated in both wind tunnel experiments and steady 2D and 3D Reynolds Averaged-Navier-Stokes (RANS) computations. The effects of pressure gradient, pressure gradient history, roughness, combined roughness and pressure gradient, and combined roughness and pressure gradient history on boundary growth and the behavior of the underlying surface pressure spectrum are examined. Special attention is paid to how said pressure spectra may be effectively modeled and predicted by assessing existing empirical and analytical modeling formulations, proposing updates to those formulations, and assessing RANS flow modeling as it pertains to successful generation of spectral model inputs.
It is found that the effect of pressure gradient on smooth wall boundary layers is strongly non-local. The boundary layer velocity profile, turbulence profiles, and associated parameters and local skin friction at a point that has seen non-constant upstream pressure gradient history will be dependent both on the local Reynolds number and pressure gradient as well as the Reynolds number and pressure gradient history. This shows itself most readily in observable downstream lagging in key observed behaviors. Steady RANS solutions are capable of predicting this out-of-equilibrium behavior if the pressure gradient distribution is captured correctly, however, capturing the correct pressure gradient is not as straightforward as may have previously been thought. Wind tunnel flows are three-dimensional, internal problems dominated by blockage effects that are in a state of non-equilibrium due to the presence of corner and juncture flows. Modeling a 3D tunnel flow is difficult with the standard eddy viscosity models, and requires the Quadratic Constitutive Relation for all practical simulations. Modeling in 2D is similarly complex, for, although 3D effects can be ignored, the absence of two walls worth of boundary layer and other interaction flows causes the pressure gradient to be captured incorrectly. These effects can be accounted for through careful setup of meshed geometry.
Pressure gradient and history effects on the pressure spectra beneath smooth wall boundary layers show similar non-locality, in addition to exhibiting varying effects across different spectral regions. In general, adverse pressure gradient steepens the slope of the mid-frequency region while favorable shallows it, while the high frequency region shows self-similarity under viscous normalization independent of pressure gradient. The outer region is dominated by history effects. Modeling of such spectra is not straightforward; empirical models fail to incorporate the subtle changes in spectral shape as coherent functions of flow variables without becoming overly-defined and producing non-physical spectral shapes. Adopting an analytical formulation based on the pressure Poisson equation solves this issue, but brings into play model inputs that are difficult to predict from RANS. New modeling protocols are proposed that marry the assumptions and limitations of RANS results to the analytical spectral modeling.
Rough surfaces subjected to pressure gradients show simplifications over their smooth wall relatives, including the validity of Townsend's outer-layer-Reynolds-number-similarity Hypothesis and shortened history effects. The underlying pressure spectra are also significantly simplified, scaling fully on a single outer variable scaling and showing no mid-frequency slope pressure gradient dependence. This enables the development of a robust and accurate empirical model for the pressure spectra beneath rough wall flows. Despite simplifications in the flow physics, modeling rough wall flows in a steady RANS environment is a challenge, due to a lack of understanding of the relationship between the rough wall physics and the RANS model turbulence parameters; there is no true physical basis for a steady RANS roughness boundary condition. Improvements can been made, however, by tuning a shifted wall distance, which also factors heavily into the mathematical character of the pressure spectrum and enables adaptations to the analytical model formulations that accurately predict rough wall pressure spectra.
This work was sponsored by the Office of Naval Research, in particular Drs. Peter Chang and Julie Young under grants N00014-18-1-2455, N00014-19-1-2109, and N00014-20-2821. This work was also sponsored by the Department of Defense Science, Mathematics, and Research for Transformation (SMART) Fellowship Program and the Naval Air Warfare Center Aircraft Division (NAWCAD), in particular Mr. Frank Taverna and Dr. Phil Knowles. / Doctor of Philosophy / Very near to a solid surface, air or water flow tends to be highly turbulent: chaotic and random in nature. This is called a boundary layer, which is present on almost every system that involves a fluid and a solid with motion between them. When the boundary layer is turbulent, the surface of the solid body experiences pressures that fluctuate very rapidly, and this can fatigue the structure and create noise that radiates both into the structure to passengers and out from the structure to observers far away. These pressure fluctuations can be described in a statistical nature, but these statistics are not well understood, particularly when the surface is rough or the average pressure on the surface is changing. Improving the ability to predict the statistics of the pressure fluctuations will aid in the design of vehicles and engineering systems where those fluctuations can be damaging to the structure or the associated noise is detrimental to the role of the system. Wind turbine farm noise, airport community noise, and air/ship-frame longevity are all issues that stand to benefit from improved modeling of surface pressure fluctuations beneath turbulent boundary layers.
This study aims to improve said modeling through the study of the effects of changing average surface pressure and surface roughness on the statistics of surface pressure fluctuations. This goal is accomplished through a combination of wind tunnel testing and computer simulation. It was found that the effect of gradients in the surface pressure is not local, meaning the effects are felt by the boundary layer at a different point than where the gradient was actually applied. This disconnect between cause and effect makes understanding and modeling the flow challenging, but adjustments to established modeling ideas are proposed that prove more effective than what exists in the literature for capturing those effects. Roughness on the surface causes the flow to become even more turbulent and the surface pressure fluctuations to become louder and more damaging. Fortunately, it is found that the combination of roughness with a gradient in surface pressure is actually simpler than equivalent smooth surfaces. These simplifications offer significant insight into the underlying physics at play and enable the development of the first analytically based model for rough wall pressure fluctuations.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/115587 |
| Date | 16 September 2022 |
| Creators | Fritsch, Daniel James |
| Contributors | Aerospace and Ocean Engineering, Devenport, William J., Roy, Christopher John, Woolsey, Craig A., Tyson, William Conrad, Lowe, Kevin T. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
| Format | ETD, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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