Turbulent boundary layer

Turbulent flow is a complex three dimensional system of velocity and pressure fluctuations in a fluid that creates vorticity, eddies and other flow structures. In this study we are specifically concerned with the surface pressure fluctuations below a turbulent boundary layer which is one of the primary sources of panel vibration on aircraft fuselages and ship hulls as well a major issue in ship hydrodynamics. The most accepted analytical approaches to describe the surface pressure fluctuations are the Chase model [1] for the surface pressure wavenumber spectrum and Goody’s model [2] for the pressure spectrum at a point. The most accurate numerical approach to use is Direct Numerical Simulations (DNS) [3]. In this study we compared Chase and Goody’s models against DNS of a turbulent channel flow in the space–time and wavenumber-frequency domains and estimated regions of convergence between the analytical models and the DNS data.

The objective of this thesis is to review recently developed empirical and analytical models for the surface pressure and wavenumber spectra for fully developed boundary layers to highlight the effect of assumptions about the turbulence length scales and show how the effects of mean flow Reynolds number has on the spectra shape. The Goody model is used as a reference model to compare the spectra shape as it characterizes the basic physical features of the wall-pressure spectrum under a zero-pressure gradient turbulent boundary layer and scales as a function of Reynolds number. The turbulence length scales of the comparison models are modified to observe the effects on the shape of the spectra. A new model is also considered that also scales as a function of Reynolds number and is compared to the Goody model.

The reduction of drag and sound pressure levels (SPL) are desirable traits in many fluidics’ applications ranging from high-speed transportation to energy generation. Inspiration has been found in some species of owls that possess boundary layer control surface treatments on their wings that appear to reduce SPL while in flight. This modification of the flow over the wings is known as the development of a modified boundary layer (MBL). Virginia Tech is working in collaboration with Florida Atlantic University to investigate this reduction in SPL experimentally but requires the assistance of RANS simulation to obtain drag results. This thesis investigates the drag effects of the rod style geometries being evaluated at VT to mimic the MBL of an owl. In doing this it was found that the height of the rods has a direct correlation with the amount of drag induced by the presence of the rods in the flow field.

Shear sheltering is defined as the effect of the mean flow velocity profile in a boundary layer on the turbulence caused by an imposed gust. In aeroacoustic applications turbulent boundary layers interacting with blade trailing edges or roughness elements are an important source of sound, and the effect of shear sheltering on these noise sources has not been studied in detail. Since the surface pressure spectrum below the boundary layer is the primary driver of trailing edge and roughness noise, this thesis considers the effect that shear sheltering has on the surface pressure spectrum below a boundary layer. This study presents a model of the incoming turbulence as a vortex sheet at a specified height above the surface and shows, using canonical boundary layers and approximations to numerical results, how the mean flow velocity profile can be manipulated to alter the surface pressure spectrum and hence the associated trailing edge noise. The results from this model demonstrate that different mean velocity profiles drive significant changes in the unsteady characteristics of the flow. The surface pressure fluctuations results also suggest that boundary layers where the shear in the mean velocity profile is significant can be beneficial for the reduction of trailing edge noise at particular frequencies.

Surface pressure fluctuations developed by turbulent flow within a boundary layer is a major cause of flow noise from a body and an issue which reveals itself over a wide range of engineering applications. Modified boundary layers (MBLs) inspired by the down coat of an owl’s wing has shown to reduce the acoustic effects caused by flow noise. This thesis investigates the mechanisms that modified boundary layers can provide for reducing the surface pressure fluctuations in a boundary layer. This study analyzes various types of MBLs in a wall jet wind tunnel through computational fluid dynamics and numerical surface pressure spectrum predictions. A novel surface pressure fluctuation spectrum model is developed for use in a wall jet boundary layer and demonstrates high accuracy over a range of Reynolds numbers. Non-dimensional parameters which define the MBL’s geometry and flow environment were found to have a key role in optimizing the acoustic performance.

Aircraft engine fan trailing edge noise prediction is very challenging. To achieve a better understanding of the physics of the propagation problem, the fan has been modeled as an infinite cascade of blades and acoustic monopoles and dipoles have been placed at the trailing edges. The flow has been computed using the Transonic Small Disturbance equation. As soon as the critical Mach number is exceeded by the free stream, a supersonic region that joins two consecutive blades appears. It completely blocks the sound and limits the study to entirely subsonic flow. In this type of flow, a sound propagation simulator has been implemented. The linearized form of Howe's equation is solved by a high frequency method. The ray caustic problem which causes regular ray tracing failure is fixed by interpolating the field on a preset grid. Results are compared with the analytical solution in uniform flow and computations in realistic flow are presented.

The effect of applied periodic straining field on the behavior of coherent vortical structures in the turbulent boundary layer is studied. In particular, the coherent vortical longitudinal structures in the turbulent boundary layer in the form of isolated vortices or in the form of pairs of counter-rotating vortices is considered. The effect on the pressure fluctuations on the wall due to the applied periodic strain is studied. A numerical method using Contour Dynamics technique and incompressible, inviscid equations of motion is developed to determine the evolution of these structures in time. The pressure fluctuations on the wall are calculated making use of the unsteady Bernoulli's equation. The various parameters associated with the coherent structures in the turbulent boundary layer such as the strength of the vortices, their distance from the wall, separation distance between counter-rotating vortices, the frequency of the applied straining field, the magnitude of the straining field and the stretching rate are varied to study the resultant pressure fluctuations. It is observed that at low applied frequencies, there are high modulations in the surface pressure fluctuations, and at higher applied frequencies of straining field there is reduction in surface pressure fluctuations in the boundary layer.