Turbulent boundary layer and metamaterial properties were explored to initiate the viability of controlling acoustic waves driven by pressure fluctuations from flow. A turbulent boundary layer scaling analysis was performed on zero-pressure-gradient turbulent boundary layers over rough surfaces, for 30,000≤〖Re〗_θ≤100,000. Relationships between fluctuating pressures and velocities were explored through the pressure Poisson equation. Certain scaling laws were implemented in attempts to collapse velocity spectra and turbulence profiles. Such analyses were performed to justify a proper scaling of the low-frequency region of the wall-pressure spectrum. Such frequencies are commonly associated with eddies containing the largest length scales. This study compared three scaling methods proposed in literature: The low-frequency classical scaling (velocity scale U_τ, length scale δ), the convection velocity scaling (U_e-U ̅_c, δ), and the Zagarola-Smits scaling (U_e-U ̅, δ). A default scaling (U_e, δ) was also selected as a baseline case for comparison. At some level, the classical scaling best collapsed rough and smooth wall Reynolds stress profiles. Low-pass filtering of the scaled turbulence profiles improved the rough-wall scaling of the Zagarola-Smits and convection velocity laws. However, inconsistent scaled results between the pressure and velocity requires a more rigorous pressure Poisson analysis. The selection of a proper scaling law gives insight into turbulent boundary layers as possible sources for acoustic metamaterials. A quiescent (no flow) experiment was conducted to measure the capabilities of a metamaterial in retaining acoustic surface waves. A point source speaker provided an acoustic input while the resulting sound waves were measured with a probe microphone. Acoustic surface waves were found via Fourier analysis in time and space. Standing acoustic surface waves were identified. Membrane response properties were measured to obtain source condition characteristics for turbulent boundary layers once the metamaterial is exposed to flow. / Master of Science / Aerodynamicists are often concerned with interactions between fluids and solids, such as an aircraft wing gliding through air. Due to frictional effects, the relative velocity of the air on the solid-surface is negligible. This results in a layer of slower moving fluid near the surface referred to as a boundary layer. Boundary layers regularly occur in the fluid-solid interface, and account for a sufficient amount of noise and drag on aircraft. To compensate for increases in drag, engines are required to produce increased amounts of power. This leads to higher fuel consumption and increased costs. Additionally, most boundary layers in nature are turbulent, or chaotic. Therefore, it is difficult to predict the exact paths of air molecules as they travel within a boundary layer. Because of its intriguing physics and impacts on economic costs, turbulent boundary layers have been a popular research topic. This study analyzed air pressure and velocity measurements of turbulent boundary layers. Relationships between the two were drawn, which fostered a discussion of future works in the field. Mainly, the simultaneous measurements of pressure on the surface and boundary layer velocity can be performed with understanding of the Pressure Poisson equation. This equation is a mathematical representation of the boundary layer pressure on the surface. This study also explored the possibility of turbulent-boundary-layer-driven-acoustic-metamaterials. Acoustic metamaterials contain hundreds of cavities which can collectively manipulate passing sound waves. A facility was developed at Virginia Tech to measure this effect, with aid from a similar laboratory at Exeter University. Microphone measurements showed the reduction of sound wave speed across the metamaterial, showing promise in acoustic manipulation. Applications in metamaterials in the altering of sound caused by turbulent boundary layers were also explored and discussed.

Projection methods for the incompressible Navier-Stokes equations (NSE) are efficient, but introduce numerical boundary layers and have limited temporal accuracy due to their fractional step nature. The Pressure Poisson Equation (PPE) reformulations represent a class of methods that replace the incompressibility constraint by a Poisson equation for the pressure, with a suitable choice of the boundary condition so that the incompressibility is maintained. PPE reformulations of the NSE have important advantages: the pressure is no longer implicitly coupled to the velocity, thus can be directly recovered by solving a Poisson equation, and no numerical boundary layers are generated; arbitrary order time-stepping schemes can be used to achieve high order accuracy in time. In this thesis, we focus on numerical approaches of the PPE reformulations, in particular, the Shirokoff-Rosales (SR) PPE reformulation. Interestingly, the electric boundary conditions, i.e., the tangential and divergence boundary conditions, provided for the velocity in the SR PPE reformulation render classical nodal finite elements non-convergent. We propose two alternative methodologies, mixed finite element methods and meshfree finite differences, and demonstrate that these approaches allow for arbitrary order of accuracy both in space and in time. / Mathematics

1 Abstract: Time-dependent and three-dimensional flow of Newtonian fluid is studied in context of two biomechanical applications, flow in cerebral aneurysms and flow in stenotic valves. In the first part of the thesis, the computational meshes obtained from the medical imaging techniques are used for the computation of hemodynamic parameters associated with the rupture potency of the cerebral aneurysms. The main result is the computation within twenty geometries of aneurysms. It is shown that the aneurysm size has more important role in wall shear stress distribution than the fact whether the aneurysm is ruptured or unruptured. The second part of the thesis is addressed to the flow in stenotic valves. It is shown that the method cur- rently used in medical practice is based on assumptions which are too restrictive to be apply to blood flow in the real case. The full continuum mechanics model is presented with physiologically relevant boundary conditions and it is shown that results are consistent with measured data obtained from literature. Then we focus on the obtaining the pressure field from the velocity field. The presented method provides more accurate pressure approximation than commonly used Pressure Poisson Equation. The last chapter of the thesis is dedicated to Nitsche's method for treating slip boundary...

No description available.

In this project, the inverse problem of determining regional pressure variations from measured blood velocity data in the contect of a cardiovascular setting has been approached. A common esimator, the pressure poisson estimator (PPE) has been implemented in a non-variational setting and evaluated for clinically relevant synthetic flow cases, over dynamically varying domains, mimicking or directly representing the intra-cardiac space: A synthetic dynamic domain benchmark problem and a patient specific model of the left ventricle. The results obtained show under ideal condition the capability of the approach to tackle complex domains successfully and to obtain regional pressure fields to a high degree of accuracy when compared to a locally provided state of the art estimator, the stokes estimator (STE). Under noise, results obtained suggest that divergence may occur with finer temporal resolution. Spatially convergence in a setting mimicking an image scenario is observed with minor exceptions though to stem from the specific composition of the flow field between discretizations. The implementation at hand avoids common problems in the non-variational approaches of this estimator stemming from domain complexity and leads to a simple application of the pure neumann boundary conditions required to compute the relative pressure field while avoiding the need to estimate boundary normals or use an embedded approach. The resulting linear system has desirable properties such as symmetry and compliance with the discrete compatibility condition by construction. / Syftet med följande projekt har varit att undersöka metoder för uppskattning av regionala tryckvariationer från uppmätta flödeshastigheter, med direkt tillämpning för förbättrad kardiovaskulär diagnostik. Mer specifikt har en tillgänglig gold-standardmetod; Pressure Poisson Estimatorn (PPE); implementerats i en icke-variationell miljö och utvärderats över en samling testfall med ökande komplexitet och med ökande relevans för det kliniska problemet med kardiovaskulär tryckmätning i det dynamiskt varierande hjärtutrymmet: ett syntetiskt referensproblem med varierande dynamisk rörelse, och en patientspecifik modell av vänster kammare. De erhållna resultaten visar att den icke-variationella implementeringen av PPE framgångsrikt kan hantera komplexa domäner och erhålla regionala tryckfält med hög noggrannhet. PPE-metoden påvisar också konkurrenskraftig noggrannhet i jamförelse med alternativa referensmetoder så som den s.k. Stokes-estimators (STE). Resultat visar också på tillfredställande beteende under realistiska signal-till-brus-förhallanden, likväl som spatiotemporell konvergens vid upplösningar som motsvarar vad som kan förväntas vid klinisk bildgivning. I summering visar våra resultat att vår implementering av PPE undviker vanliga problem i alterantiva icke-variationella implementeringar som annars kan uppkomma vid analys av komplexa flödesdomaner, och att en förenklad men likväl korrekt implementering av de rena Neumann-gränsvillkor som krävs för att beräkna det relativa tryckfältet kan uppnås utan behovet av att uppskatta icke-triviala gränsnormaler. Utöver detta påvisar det resulterande linjära systemet även önskvarda egenskaper såsom numerisk symmetri och överenstämmelse med diskreta kompatibilitetsvillkor.