High-fidelity unstructured overset simulation of complex turbulent flows

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High-fidelity unstructured overset simulation of complex turbulent flows

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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.


University of Minnesota Ph.D. dissertation. May 2023. Major: Aerospace Engineering and Mechanics. Advisor: Krishnan Mahesh. 1 computer file (PDF); xxv, 216 pages.

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Morse, Nicholas. (2023). High-fidelity unstructured overset simulation of complex turbulent flows. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/257091.

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