### Browsing by Subject "Boundary layer"

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Item Direct numerical simulation and global stability analysis of boundary layer flows past roughness elements(2022-08) Ma, RongShow more Understanding wall roughness effects on flows is important in engineering applications. The objective of this dissertation is to increase understanding of roughness effects on transitional and turbulent boundary layers. The rough-wall flow is studied by performing direct numerical simulations (DNS) of the Navier-Stokes equations and global linear stability analyses. DNS of turbulent channel flow with a random-rough bottom wall is performed at friction Reynolds number $Re_{\tau}=400$ and $600$. The rough surface corresponds to the experiments of Flack et al. \cite{flack2019skin}. The computed skin friction coefficients and the roughness functions show good agreement with experimental results. The double-averaging methodology is used to investigate mean velocity, Reynolds stresses, dispersive flux, and mean momentum balance. The roll-up of the shear layer on the roughness crests is identified as a primary contributor to the wall-normal momentum transfer. The mean-square pressure fluctuations are increased within the inner layer and a phenomenological explanation is suggested by examining the dominant source terms in the pressure Poisson equation. The rapid term shows that high pressure fluctuations observed in front of and above the roughness elements are mainly due to the attached shear layer formed above the protrusions. The slow term makes a relatively smaller contribution, and is primarily increased in the troughs and in front of the roughness elements, corresponding to the occurrence of quasi-streamwise vortices and secondary vortical structures. The mean wall shear on the rough surface is highly correlated with the roughness height, and depends on the local roughness topography. Events with comparable magnitudes of the streamwise and spanwise wall-shear stress occur more frequently, corresponding to a more isotropic vorticity field in the roughness layer. The boundary layer transition due to an isolated roughness element is studied using global stability analysis and DNS. The large ratio of element height to displacement boundary layer thickness $(h/\delta^*)$ is considered to model a trip at an early location in the boundary layer. The cubical trip geometries with two aspect ratios ($\eta$) are investigated. Both steady base flows and time-averaged mean flows are able to capture the frequencies of the primary vortical structures and mode shapes. Global stability results highlight that although the varicose instability is dominant for large $h/\delta^*$, sinuous instability becomes more pronounced as $Re_h$ increases for the thin geometry ($\eta=0.5$), due to increased spanwise shear in the near-wake region. Wavemaker results indicate that $\eta$ affects the convective nature of the shear layer more than the type of instability. DNS results show that different instability mechanisms lead to different development and evolution of vortical structures in the transition process. For $\eta=1$, the varicose instability is associated with the periodic shedding of hairpin vortices, and its stronger spatial transient growth indicated by wavemaker results aids the formation of hairpin vortices farther downstream. In contrast, for $\eta=0.5$, the interplay between varicose and sinuous instabilities results in a broader-banded energy spectrum and leads to the sinuous wiggling of hairpin vortices in the near wake when $Re_h$ is sufficiently high. A sinuous mode with a lower frequency captured by dynamic mode decomposition (DMD) analysis, and associated with the ‘wiggling’ of streaks persists far downstream and promotes transition to turbulence. A new regime map is developed to classify and predict instability mechanisms based on $Re_{hh}^{1/2}$ and $d/\delta^*$ using a logistic regression model. Although the mean skin friction demonstrates different evolution for the two geometries, both of the two geometries efficiently trip the flow to turbulence at $Re_h=1100$. An earlier location of a fully-developed turbulent state is established for $\eta=1$ at $x \approx 110h$. The influence of roughness spacing on boundary layer transition over distributed roughness elements is studied using direct numerical simulation and global stability analysis, and compared to the isolated roughness element. Small spanwise spacing $\lambda_z=2.5h$ inhibits the formation of counter-rotating vortices (CVP), as a result, the hairpin vortices are not generated and the downstream shear layer is steady. For $\lambda_z=5h$, the CVP and hairpin vortices are induced by the first row of roughness, perturbing the downstream shear layer and causing transition. Although the periodicity of the primary hairpin vortices seems to be independent on the streamwise spacing, the distributed roughness leads to lower critical $Re_h$ for instability to occur and more significant breakdown of boundary layer compared to the isolated roughness. When the streamwise spacing is comparable to the region of flow separation ($\lambda_x=5h$), the high-momentum fluid hardly moves downward into the cavities and the wake flow has little impact on the following roughness elements. The leading unstable varicose mode is associated with the central low-speed streaks along the aligned roughness elements, and its frequency is close to the shedding frequency of hairpin vortices in the isolated case. For larger streamwise spacing ($\lambda_x=10h$), two distinct modes are obtained from global stability analysis. The first mode shows varicose symmetry, corresponding to the primary hairpin vortex shedding induced by the first-row roughness. The high-speed streaks formed in the longitudinal grooves are also found to be unstable and interacting with the varicose mode. The second mode is a sinuous mode with lower frequency, induced as the wake flow of the first-row roughness runs onto the second row. It extracts most energy from the spanwise shear between the high- and low-speed streaks.Show more Item Discrete roughness effects on high-speed boundary layers(2015-01) Iyer, Prahladh SatyanarayananShow more This dissertation studies the effects of a discrete roughness element on a high-speed boundary layer using Direct Numerical Simulations (DNS) on unstructured grids. Flow past a cylindrical roughness element placed perpendicular to the flow and a hemispherical bump is studied. A compressible linear stability theory (LST) solver for parallel flows is developed based on the algorithm by Malik [33] and validated for a range of Mach numbers ranging from incompressible to Mach 10. The evolution of the perturbations from DNS is validated with the linear stability solver making the DNS algorithm suitable to study transition problems. Flow past a cylindrical roughness element at Mach 8.12 is simulated using DNS and the velocity profiles in the symmetry and wall--parallel planes are compared to the experiments of Bathel et al. [7]. The flow remains steady and laminar, and does not transition. Overall, good agreement is observed between DNS and experiments, thus validating our algorithm to study effect of roughness on high-speed flows. However, differences are observed in the separation region upstream and recirculation region downstream of the roughness. The DNS results are used to quantify possible uncertainties in the measurement technique as suggested by Danehy [20]. The effect of upstream injection (5% of the free-stream velocity) is also simulated to quantify its effects on the velocity profiles to mimic the injection of NO into air in the experiment. While the boundary layer thickness of the flow increases downstream of the injection location, its effect on the velocity profiles is small when the profiles are scaled with the boundary layer thickness.Flow past a hemispherical bump at Mach 3.37, 5.26 and 8.23 are simulated using DNS with the flow conditions matching the experiments of Danehy et al. [19] to understand the different flow features associated with the flow and the physical mechanism that causes the flow to transition to turbulence. It is observed that the Mach 3.37 and 5.26 flows transition to turbulence while the Mach 8.23 flow remains laminar downstream of the roughness element. The roughness element used in this study is large since the boundary layer thickness of the laminar boundary layer at the location of the roughness is smaller than the roughness height.The Mach 3.37 flow undergoes transition closer to the bump when compared to Mach 5.26, in agreement with experimental observations. Transition is accompanied by an increase in C_f and C_h (Stanton number). Even for the case that did not undergo transition (Mach 8.23), streamwise vortices induced by the roughness cause a significant rise in C_f until 20D downstream. Mean Van-Driest transformed velocity and Reynolds stress for Mach 3.37 and 5.26 shows good agreement with available data. The transition process involves the following key elements - Upon interaction with the roughness element, the boundary layer separates to form a series of spanwise vortices upstream of the roughness, and a separation shear layer. The system of spanwise vortices wrap around the roughness element in the form of horseshoe/necklace vortices to yield a system of counter-rotating streamwise vortices downstream of the element. These vortices are located beneath the separation shear layer and perturb it, which results in the formation of trains of hairpin-shaped vortices further downstream of the roughness for the cases that undergo transition. These hairpins spread in the span with increasing downstream distance and the flow increasingly resembles a fully developed turbulent boundary layer. A local Reynolds number based on the wall properties is seen to correlate the onset of transition for the cases considered.To assess the effect of roughness height on transition, a Mach 3.37 flow past a hemispherical bump is studied by varying the boundary layer thickness (k/delta = 2.54, 1.0, 0.25 & 0.125) where k is the roughness height and delta is the laminar boundary layer thickness at the location of the roughness. Transition occurs in all cases, and the essential mechanism of transition appears to be similar. At smaller boundary layer thickness, multiple trains of hairpin vortices are observed immediately downstream of the roughness, while a single train of hairpin vortices is observed at larger delta. This behavior is explained by the influence of the boundary layer thickness on the separation vortices upstream of the roughness element. Also, hairpin vortices that form downstream of the roughness initially scale with the height of the roughness element and further downstream, begin to scale with the boundary layer thickness, thus causing the entire boundary layer to transition. Dynamic Mode Decomposition of the pressure field for k/delta= 1 and 0.125 is used to obtain the frequency of shedding of hairpin vortices.Show more Item High-fidelity unstructured overset simulation of complex turbulent flows(2023-05) Morse, NicholasShow more The goal of this dissertation is to provide insight into the underlying physics of two sets of complex flows: (i) the axisymmetric and appended DARPA SUBOFF and (ii) tabbed jets in crossflow. The accurate simulation of the flow around marine vessels such as the DARPA SUBOFF is critical for maneuvering predictions, which are inherently challenging due to the characteristically large Reynolds numbers, the complex geometries of the hull, appendages, and propeller, and the unsteady flow-fields, which consist of turbulent boundary layers with pressure gradients, curvature, junction flows, and separations. The understanding of jets in crossflow (JICFs) is important for a variety of applications, and there has been significant interest in designing passive devices to control the mixing and penetration characteristics of the jet, although the specific effects of these devices are not well understood. The unstructured overset method of Horne and Mahesh [1,2] provides the flexibility to perform large-eddy simulations (LES) and direct numerical simulations (DNS) to extract valuable physical insights from these flows.First, wall-resolved LES is performed to study flow about the axisymmetric DARPA SUBOFF hull at a Reynolds number of 1.1×10^6 based on the hull length and free stream velocity. To gain an understanding of the streamline curvature and pressure gradient effects of the hull’s turbulent boundary layer (TBL), the axisymmetric Reynolds-averaged Navier-Stokes equations are derived in an orthogonal coordinate system aligned with streamlines, streamline-normal lines, and the plane of symmetry. Analysis in this frame of reference provides a new perspective on curved TBLs, and has numerous practical benefits, including the orthogonality of the streamline-normal coordinate to the hull surface and to the free stream velocity far from the body, which is critical for studying bodies with concave streamwise curvature. In the potential flow outside the boundary layer, the momentum equations in the streamline coordinate frame naturally reduce to the differential form of Bernoulli’s equation and the s-n Euler equation for curved streamlines. In the curved laminar boundary layer at the front of the hull, the streamline momentum equation represents a balance of the streamwise advection, streamwise pressure gradient, and viscous stress, while the streamline-normal equation is a balance between the streamline-normal pressure gradient and centripetal acceleration. At the mid-hull TBL, the curvature terms and streamwise pressure gradient are negligible, and the results conform to traditional analysis of flat plate boundary layers. Finally, the thick stern TBL causes the curvature and streamwise pressure gradient terms to reappear to balance the turbulent and viscous stresses. This balance is used to explain the characteristic variation of static pressure observed for thick boundary layers at the tails of axisymmetric bodies. Next, trip-resolved LES of the DARPA SUBOFF is performed to investigate the extent to which the details of tripping affect the development of TBLs in model-scale studies, which are limited to moderate Reynolds number TBLs. In particular, four cases are studied at length-based Reynolds numbers of 1.1×10^6 and 1.2×10^6: the bare hull and appended SUBOFF with a resolved experimental trip wire geometry, and the same cases tripped using a simple numerical trip (wall-normal blowing), which serves as an example of artificial computational tripping methods often used in practice. When the trip wire height exceeds the laminar boundary layer thickness, LES reveals that shedding from the trip wire initiates transition, and the near field is characterized by an elevation of the wall-normal Reynolds stress and a modification of the turbulence anisotropy and mean momentum balance. This trip height also induces a large jump in the boundary layer thickness, which affects the rate at which the TBL grows and how it responds to pressure gradients and curvature. In contrast, a trip wire height shorter than the laminar boundary layer thickness is shown to initiate transition at the reattachment point of the trip-induced recirculation bubble. The artificial trip reasonably replicates the resolved trip wire behavior. For each case, the inner layer collapses rapidly in terms of the mean profile, Reynolds stresses, and mean momentum balance. This is followed by the collapse of the Reynolds stresses in coordinates normalized by the local momentum thickness, which proves to be a more robust outer scale than the 99% thickness due to its lower sensitivity to the over-tripped wake at the edge of the boundary layer. The importance of tripping the model appendages is also highlighted, due to their lower Reynolds numbers and susceptibility to laminar separations. Finally, DNS of a JICF with a triangular tab at two positions are performed at jet-to- crossflow velocity ratios of R = 2 and 4 with a jet Reynolds number of 2000 based on the jet’s bulk velocity and exit diameter. DNS and dynamic mode decomposition reveal that a tab on the upstream side of the jet produces Lambda-shaped streamwise vortices in the upstream shear layer (USL), while a tab placed 45 degrees from the upstream side produces a tertiary vortex for R = 4, which is not present at R = 2. For the upstream tab, the presence of streamwise vortices curled around the spanwise USL vortices provides an explanation for the improvements in mixing and spreading associated with an upstream tab. This streamwise vortex structure shows remarkable similarities to the ‘strain- oriented vortex tubes’ observed for disturbed plane shear layers. In contrast, the tab placed 45 degrees from the upstream position produces significantly different effects. At R = 4, the jet cross-section is significantly skewed away from the tab and a tertiary vortex is formed, as observed in past experiments on round JICFs at relatively high R and low Reynolds numbers. The 45 degree tab produces asymmetric effects in the wake of the jet at R = 2, but the effect on the jet cross-section is much smaller, highlighting the sensitivity of jets at high R to asymmetric perturbations.Show more Item Local Variation of Heat and Mass Transfer for Flow Over a Cavity and on a Flat Plate(2017-09) Taliaferro, MatthewShow more Boundary layer theory for flat plates is fundamental to our understanding of fluid flow and heat transfer. However, most of the experimental and analytical work for thermal boundary layers focus on streamwise effects. Lateral changes of heat and mass transfer near a lateral singularity in the surface boundary conditions have not been as extensively studied. Lateral heat transfer is studied using OpenFOAM to run numerical simulations for heated strips of varying width, fluids with varying thermal properties, separation lengths, and unheated starting lengths. Turbulent mass transfer is studied using the naphthalene sublimation technique for heated strips of varying depths, widths, and freestream velocities. The lateral edge effect is found to scale with the conduction thickness for both turbulent and laminar boundary layer flows. For laminar boundary layer flow the lateral edge effect extends approximately three conduction thicknesses into the flow, while for turbulent boundary layer flow it extends approximately ten conduction thicknesses into the flow. The results are useful for modeling heat transfer from discrete electronic components. In addition, the results should serve as useful benchmarks for numerical fluid models and computations where lateral transport is important.Show more Item Numerical Simulation of Surface Patterns on Sublimating Ablative Materials(2021-05) Trevino, LorettaShow more Thermal protection systems made of ablative materials are a well-known solution to protect vehicles from high heating environments. As the material changes shape due to the ablation process, several patterns may develop. One pattern that develops is a very regularly ordered diamond-shaped pattern known as crosshatching. The mechanism for which initiates the pattern development is not yet known. This research aims to study the ablation process and its contribution to crosshatching by implementing and validating a camphor sublimating boundary condition into the US3D fluid-solid solver. This work shows that the sublimation process can develop localized deep grooves, leading to the onset of crosshatching. The stability of a sublimating boundary layer is also not well studied. Through this work, it was demonstrated that the presence of camphor in the boundary layer is stabilizing. There are still many open questions on how the camphor presence affects a boundary layer's stability and how it could potentially play a role in the initiation of crosshatching.Show more