Abstract
In the present work, supersonic flows over an axisymmetric base and a 24-deg compression ramp are investigated using the generalized k - ω (GEKO) model implemented in the commercial software, ANSYS FLUENT. GEKO is a two-equation model based on the k - ω formulation, and some specified model coefficients can be tuned depending on the flow characteristics. Uncertainty quantification (UQ) analysis is incorporated to quantify the uncertainty of the model coefficients and to calibrate the coefficients. The Latin hypercube sampling (LHS) method is used for sampling independent input parameters as a uniform distribution. A metamodel is constructed based on general polynomial chaos expansion (gPCE) using ordinary least squares (OLS). The influential coefficient closure is obtained by using Sobol indices. The affine invariant ensemble algorithm (AIES) is selected to characterize the posterior distribution via Markov chain Monte Carlo sampling. Calibrated model coefficients are extracted from posterior distributions obtained through Bayesian inference, which is based on the point-collocation nonintrusive polynomial chaos (NIPC) method. Results obtained through calibrated model coefficients by Bayesian inference show superior prediction with available experimental measurements than those from original model ones.
Highlights
Uncertainty quantification (UQ) has been applied to computational fluid dynamics (CFD) by improvement of computing performance and reduction of computational cost
uncertainty quantification (UQ) with Bayesian inference is applied to the GEKO turbulence model to estimate the optimized model coefficients and QoIs in supersonic flows over an axisymmetric base and 24-deg compression ramp
The GEKO model was investigated to quantify the uncertainty of its coefficients for supersonic flows over an axisymmetric base and a 24-deg compression ramp
Summary
Uncertainty quantification (UQ) has been applied to computational fluid dynamics (CFD) by improvement of computing performance and reduction of computational cost. UQ is used to estimate the mean value and standard deviation and the probability distributions of QoIs (Quantities of Interest) by considering the probability distributions of input variables such as boundary conditions or applied model coefficients. The Monte Carlo (MC) technique has been the general method used to compute output variables by sampling the random inputs with a specific distribution. The generalized polynomial chaos (gPC) method that was recently proposed by Xiu [1] requires much fewer samples than the MC technique so that studies using UQ can be performed efficiently. Aleatory uncertainty relates to the random components contained in a real system; from the perspective of CFD, examples would include uncertainties in geometry and boundary conditions such as velocity and pressure. Uncertainties caused by the process of model formulation and estimation of model coefficients, such as those used in modeling turbulence or multiphase flow, are typical examples of epistemic uncertainty
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