<p>Fluids conveyed in deformable conduits are often encountered in  microfluidic applications, which makes fluid--structure interactions (FSIs) an unavoidable phenomenon. In particular, experiments reported the existence of FSI instabilities in compliant microchannels at low Reynolds numbers, Re, well below the established values for rigid conduits. This observation has significant implications for new strategies for mixing at the microscale, which might harness FSI instabilities in the absence of  turbulence. In this thesis, we conduct research on the modeling and stability of microscale FSIs. Understanding the steady response, the dynamics and the stability of these FSIs are the three major objectives. This thesis begins with the analysis of the steady-state scalings and the linear stability of a previously derived mathematical model, through which we emphasize the power of reduced modeling in making the FSI problems tractable. Next, we turn to a more realistic problem regarding FSIs in a common configuration of low-Re flows through long, shallow rectangular three-dimensional microchannels. Through a scaling analysis, which takes advantage of the geometric separation of scales, we find that the flow can be simplified under the lubrication approximation, while the wall deforms like a variable-stiffness Winkler foundation at the leading order. Coupling these dominant effects, we obtain a new fitting-parameter-free flow rate--pressure drop relation for a thick-walled microchannel, which rationalizes previous experiments. Then, we derive a one-dimensional (1D) steady model, at both vanishing and finite Re, by coupling the reduced flow and deformation models. To satisfy the displacement constraints along the channel edges, weak tension is introduced to regularize the underlying Winkler-foundation-like mechanism. This model is then made dynamic by introducing flow unsteadiness and the elastic wall's inertia. We conduct a global stability analysis of this system by perturbing the non-flat steady state with infinitesimal perturbations. We identify the existence of globally unstable modes, typically in the weakly inertial flow regime, whose features are consistent with experimental observations. The unstable eigenmodes oscillate at frequencies close to the natural frequency of the wall, suggesting that the instabilities are resonance phenomena. We also capture the transient energy amplification of perturbations through a linear non-normality analysis of the proposed reduced 1D FSI model.</p>

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A numerical method for modeling a low Reynolds number turbine blade, the L1M, is presented along with the pitfalls encountered. A laminar solution was confirmed to not accurately predict the flow features known in low Reynolds number turbine blade flow. Three fully turbulent models were then used to try to predict the separation and reattachment of the flow. These models were also found to be insufficient for transitioning flows. A domain was created to manually trip the laminar flow to turbulent flow using a predictive turbulence transition model. The trip in the domain introduced an instability in the flow field that appears to be dependent on the discretization order, turbulence model, and transition location. The method was repeated using the Pack B blade and the same obstacles were apparent. The numerical method developed was then used in an optimization technique developed to design a wind tunnel simulating periodic flow conditions using only 2 blades. The method was first used to predict a c_p distribution for the aft loaded L1A research blade provided by the U.S. Air Force. The method was then extended to a larger domain emulating the 2 blade, 2D wind tunnel. The end-wall geometry of the tunnel was then changed using previously defined control points to alter the distribution of c_p along the suction surface of the interior blades. The tunnel c_p's were compared to the computationally acquired periodic solution. The processed was repeated until an acceptable threshold was reached. The optimization was performed using the commercially available software iSIGHT by Engineous Solutions. The optimization algorithms used were the gradient based Successive Approximation Method, the Hooke Jeeves, and Simulated Annealing.

Experimental investigations were conducted with and without the presence of the surface-mounted obstacle to quantify its effects on the far wake. The obstacle chosen for this study was a 3:2 elliptical nose NACA 0020 tail wing-body (Rood body), approximately of height equal to the boundary layer thickness at one of the measurement locations of the flow. The experiments were performed by varying the Reynolds number of the flow and manipulating the pressure gradient distributions using a NACA 0012 airfoil placed within the wind tunnel test section. The measurements were acquired utilizing a spanwise traversing boundary layer rake and a point pressure sensing microphone array. The findings reveal that the presence of the obstacle introduces disruptions in the flow, such as vortex and jet regions in the wake. However, the overall flow behavior remains consistent with that of an undisturbed turbulent boundary layer, for varying Reynolds numbers and pressure gradients. Notably, an adverse pressure gradient and lower Reynolds number both accentuate the prominence of the jet and vortex region within the wake, with the trend reversing towards the other end of the spectrum. This behavior is akin to the larger turbulent boundary layer under adverse pressure gradients and lower Reynolds numbers. Furthermore, the presence of obstacles induces an increase in the overall level of the wall pressure spectrum by approximately 2 dB, regardless of the flow condition. Additionally, it leads to a deviation in the slope of the mid-frequency range of the autospectra compared to the smooth wall case. Specifically, the mid-slope frequency of an undisturbed turbulent boundary layer is steeper than that observed in the disturbed wake flow caused by the obstacle. / Master of Science / The interaction between turbulence and aerodynamic surfaces gives rise to wall-pressure fluctuations, which in turn induce structural vibrations and acoustic noise. On surfaces turbulent flows meet, antennae, flaps, and other frequently mounted measuring devices. The flow in their wake is impacted by the coherence of a turbulent boundary layer being disrupted by these impediments mounted on aerodynamic surfaces. They also alter the nature of the pressure fluctuations that are generated on the surface of interest. The far wake of a Rood Body obstacle was studied using a point pressure sensing microphone array and a spanwise traversing boundary layer rake. Experimental measurements were taken for a range of Reynolds numbers and pressure gradient environments at the Virginia Tech Stability Wind Tunnel. Results show that the boundary layer rake measurements resolve the presence of the obstacle wake successfully, by characterizing the wake structures and confirming the presence of jet and vortex regions in the wake of the obstacle. Surface pressure measurements reveal that the presence of the obstacle causes the low-frequency content of the wall pressure to be less dominant than the no obstacle case, while the high-frequency content becomes more dominant in the presence of the obstacle. The presence of obstacles also increases the overall levels of the wall pressure spectrum by approximately 2 dB.

A wing with a Wortmann FX-63-137-ESM airfoil section has been used to study some unique problems encountered in wing aerodynamics in the range of Reynolds numbers between 50,000 and 500,000. The wind-tunnel testing conducted in the 6'x 6' Stability tunnel included strain-gauge data, pressure data, and flow-visualization studies. The laminar separation bubble which frequently occurs on the upper surface of the wing is found to dominate its performance and gives rise to a hysteresis loop for lift and drag. Changes in airfoil performance due to positive flap or control surface deflections resemble changes witnessed at higher Reynolds numbers. Negative deflections are seen to considerably change the stall behavior and the flow over the airfoil. This is due to the considerably greater effect on the separation bubble for negative flap deflections. The structure and mechanism of the laminar separation bubble can also be altered by the introduction of selected acoustic disturbance and increased free-stream turbulence. The wind-tunnel test-section environment is, therefore, capable of considerably altering wing performance in this regime. / Ph. D. / incomplete_metadata

There is increasing interest in design methods and performance prediction for turbine engines operating at low Reynolds numbers. In this regime, boundary layer separation may be more likely to occur in the turbine flow passages. For accurate CFD predictions of the flow, correct modeling of laminar-turbulent boundary layer transition is essential to capture the details of the flow. To investigate possible improvements in model fidelity, both two-dimensional and three-dimensional CFD models were created for the flow over several low pressure turbine blade designs. A new three-equation eddy-viscosity type turbulent transitional flow model originally developed by Walters and Leylek was employed for the current RANS CFD calculations. Flows over three low pressure turbine blade airfoils with different aerodynamic characteristics were simulated over a Reynolds number range of 15,000-100,000, and predictions were compared to experiments. The turbulent transitional flow model sensitivity to inlet turbulent flow parameters showed a dependence on free-stream turbulence intensity and turbulent length scale. Using the total pressure loss coefficient as a measurement of aerodynamic performance, the Walters and Leylek transitional flow model produced adequate prediction of the Reynolds number performance in the Lightly Loaded blade. Furthermore, the correct qualitative flow response to separated shear layers was observed for the Highly Loaded blade. The vortex shedding produced by the separated flow was largely two-dimensional with small spanwise variations in the separation region. The blade loading and separation location was sufficiently predicted for the Aft-Loaded L1A blade flowfield. Investigations of the unsteady flowfield of the Aft-Loaded L1A blade showed the shear layer produced a large separation region on the suction surface. This separation region was located more downstream and significantly reduced in size when impinged upon by the upstream wakes, thus improving the aerodynamic performance consistent with experiments. For all cases investigated, the Walters and Leylek transitional flow model was judged to be sufficient for understanding the separation and transition characteristics, and superior to other widely-used turbulence models in accuracy of describing the details of the transitional and separated flow. This research characterized and assessed a new model for low Reynolds number turbine aerodynamic flow prediction and design improvement. / Ph. D.

Differences in the aerodynamic performance data obtained at different test facilities were observed for the Wortmann FX-63-l37 airfoil. Earlier investigations found that the size of the hysteresis loop was affected by the tunnel environment and that single strut mounting of a three dimensional wing model interfered negligibly with the wing. Theoretical and experimental evaluations of a half wing model mounted with an end plate gap were done. Vortex panel method was used in the theoretical evaluation. The results from this indicated an effect of reduced aspect ratio with increase in end plate gap size. Tests were conducted in the VPI Stability Tunnel at low Reynolds numbers for different gap sizes including sealed gap. Results from the experiments showed that even very small gaps produce substantial changes in zero lift angle of attack (αu) and the change in αu, was reduced as Reynolds number increased. Sealed gap test results did not show such a behavior. Flow visualization of the flow through the gap showed a significant flow through the gap even at very low Reynolds number and small gap size. / Master of Science

The onset of fluid-elastic instability in cylinder arrays is usually thought to depend primarily on the mean flow velocity, the Scruton number and the natural frequency of the cylinders. Currently, there is considerable evidence from experimental measurements and computational fluid dynamic (CFD) simulations that the Reynolds number is also an important parameter. However, the available data are not sufficient to understand or quantify this effect. In this study we use a high resolution pseudo-spectral scheme to solve 2-D penalized Navier-Stokes equations in order to accurately model turbulent flow past cylinder array. To uncover the Reynolds number effect we perform simulations that vary Reynolds number independent of flow velocity at a fixed Scruton number, and then analyze the cylinder responses. The computational complexity of our algorithm is a function of Reynolds number. Therefore, we developed a high performance parallel code which allows us to simulate high Reynolds numbers at a reasonable computational cost. The simulations reveal that increasing Reynolds number has a strong de-stabilizing effect for staggered arrays. On the other hand, for the in-line array case Reynolds number still affects the instability threshold, but the effect is not monotonic with increasing Reynolds number. In addition, our findings suggest that geometry is also an important factor since at low Reynolds numbers critical flow velocity in the staggered array is considerably higher than the in-line case. This study helps to better predict how the onset of fluid-elastic instability depends on Reynolds number and reduces uncertainties in the experimental data which usually do not consider the effect of Reynolds number. / Thesis / Master of Science (MSc)

The interest toward Mars exploration has been considerably increasing due to also the successful deployment of the Perseverance rover and the continuous tests developed by SpaceX's launch vehicle, Starship. While the Mars 2020 mission is currently in progress, the first controlled flight on another planet have been proven in April 2021 with the vertical take-off and landing of the Ingenuity rotorcraft on Mars. In addition, the rotorcraft Dragonfly is expected to achieve the same endeavor in Titan, the largest moon of Saturn, by 2036. Continuous efforts have been oriented toward the development of new technologies and aircraft configurations to improve the performance of current proposed designs to achieve powered flight in different planetary bodies. This thesis work is a preliminary study to develop a comprehensive analysis over the generation of optimum airfoil geometries to achieve vertical flight in environments where low Reynolds numbers and Mach number equal to 0.2 and 0.5.

Low Reynolds number airfoil analysis has become increasingly significant as urban air mobility vehicles and unmanned aerial vehicles surge in popularity. The Green Raven project at KTH Aero aims to use reflex airfoils where little data is available beyond classical analysis. Viscous formulations of the panel method and computational fluid dynamics (CFD) have been used to simulate lift, drag and moments for the MH61 and MH104 airfoils at different angles of attack (AOAs). XFOIL and CFD turbulence models such as Spalart-Allmaras (SA), k-w Shear Stress Transport (SST) with and without damping coefficients were used. The strengths and limitations of each model were used to justify results. Due to clear computational advantages, XFOIL produced adequate results and is tailored toward use in initial design stages where repeated measurements are crucial. The SA turbulence stood out as the model produced accurate results in a reasonable time. The abundance of published CFD material comparing different turbulence models increased the credibility of the results. The two airfoils had similar lift and drag characteristics at AOAs of 0-6 deg while the MH104 was superior near stall. However, due to the lack of experimental data of the airfoils no particular model could be commended or verified.