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Title:Modeling of shock boundary layer interactions and stability analysis using particle approaches
Author(s):Tumuklu, Ozgur
Director of Research:Levin, Deborah A.
Doctoral Committee Chair(s):Levin, Deborah A.
Doctoral Committee Member(s):Elliott, Gregory S.; Rovey, Joshua L.; Theofilis, Vassilis
Department / Program:Aerospace Engineering
Discipline:Aerospace Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Direct simulation Monte Carlo method
Hypersonic Flows
Shock wave boundary layer interactions
Linear stability and residuals algorithm
Proper orthogonal decomposition
Doak's momentum potential theory
Ellipsoidal statistical BGK method
Abstract:Hypersonic flow separation and laminar shock wave boundary layer interactions (SWBLIs) have received considerable attention since these interactions can lead to laminar to turbulent transition, unsteadiness, and localized high pressure and heating regions. Accurate predictions of these phenomena, particularly when thermochemical nonequilibrium is present, play a crucial role for design purposes. In this regard, many experimental, theoretical, and numerical works have been conducted over the decades. In this work, numerical investigations of SWBLIs for hypersonic flows over a double wedge and cone and ”tick-shaped” model configurations have been conducted to investigate the origin of SWBLIs and to compare with measurements in the Hypervelocity Expansion Tube (HET), Calspan-University at Buffalo Research Center (CUBRC), and T-ADFA free-piston shock tunnel facilities using particle approaches to model the Boltzmann equation. The Boltzmann transport equation is the most general formulation of binary gas flows for a wide Knudsen number spectrum including rarefied, slip, continuum regimes. The direct simulation Monte Carlo (DSMC) method, a well-known stochastic approach to solving the Boltzmann equation, provides high-fidelity molecular transport and thermal nonequilibrium, commonly seen in strong shock-shock interactions and inherently captures rarefaction effects such as velocity slip and temperature jump without a priori specific model. Therefore, the DSMC method has been applied to SWBLIs in order to take all these effects into account. However, DSMC becomes prohibitively expensive for calculations in the continuum regime. In order to potentially reduce the computational costs related to DSMC computations for low Knudsen number flows, the ellipsoidal statistical Bhatnagar-Gross-Krook (ES-BGK) model of the Boltzmann equation was developed and applied to shock dominated flows. The DSMC method has been used for modeling shock dominated separated hypersonic flows at Mach 7 for a unit Reynolds number of 4.15 × 105 m−1 previously studied in the HET over a double wedge configuration to investigate the impacts of thermochemical effects on SWBLIs by changing the chemical composition. The DSMC simulations are found to reproduce many of the classical features of Edney Type IV strong shock interactions. A comparison of simulated heat flux with measurements reveals that the calculated surface heating profiles were found to be time-dependent and in disagreement with experiments at later flow times, especially for the 2D wedge model. Further investigations using a three-dimensional model, taking the pressure relief into account, indicate that the simulated 3D heat fluxes, shock structure, and triple point movement were found to be in fair agreement with the experimental heat flux values, especially in the aft part of the wedge, and the shock tracking measurements. Nonetheless, both the 2D and 3D cases do not reach steady state for the duration of the experiment. To reduce 3D effects and to investigate time-dependency more closely, shock-dominated hypersonic lam- inar flows over a double cone are investigated using time-accurate DSMC combined with the residuals algorithm (RA) for unit Reynolds numbers gradually increasing from 9.35×104 to 3.74×105 m−1 at a Mach number of about 16. The main flow features, such as the strong bow-shock, location of the separation shock, the triple point, and the entire laminar separated region show a time-dependent behavior. As the Reynolds number is increased, larger pressure values in the under-expanded jet region due to strong shock interactions form more prominent λ-shocklets in the supersonic region between two contact surfaces. A Kelvin-Helmholtz instability arising at the shear layer results in an unsteady flow for the highest Reynolds number. These findings suggest that consideration of experimental measurement times is important when it comes to deter- mining the steady state surface parameters even for a relatively simple double cone geometry at moderately large Reynolds numbers. Further studies have been conducted to analyze the unsteadiness of the double cone flows using a com- bination of DSMC calculations, linear global instability analysis and momentum potential theory (MPT). Close to steady state linear analysis reveals the spatial structure of the underlying temporally stable global modes. Application of the MPT (valid for both linear and nonlinear signals) to the highest Reynolds number DSMC results shows that large acoustic and thermal potential variations exist in the vicinity of the sepa- ration shock, the λ-shock patterns, and the shear layers. It is further shown that the motion of the bow shock system is highly affected by non-uniformities in the acoustic field. At the highest Reynolds number considered here, the unsteadiness is characterized by Strouhal numbers in the shear layer and bow-shock regions. Lastly, a modal analysis with window proper orthogonal decomposition (WPOD) has been applied to hypersonic separated flows with different chemical composition over the double wedge near steady state in order to correlate POD modes with global modes, to predict future states without running computationally demanding simulations, and to eliminate statistical noise inherent to the DSMC method. Thermochemical nonequilibrium effects are found to change the shock structures, the size of the separation region, and the required time to reach steady state. The temporal analysis of POD modes shows that the decay rate of the least damped eigenmode for the chemically reacting air case is found to be smaller in comparison to the non-reacting air case. For the first time, steady state solutions for an unsteady, chemically reacting hypersonic flow are predicted using the WPOD method.
Issue Date:2018-09-21
Rights Information:Copyright 2018 Ozgur Tumuklu
Date Available in IDEALS:2019-02-06
Date Deposited:2018-12

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