A Bayesian Approach to Non-Deterministic Hypersonic Vehicle Design

Mantis, George; Mavris, Dimitri N.

doi:10.4271/2001-01-3033

Cited by 6 publications

(6 citation statements)

References 25 publications

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“…V.) We acknowledge the decreased fidelity of these runs as a result of the reduced geometric description as well as the relatively simple chemical model in Eqn. 1to (3). Indeed, certain physical features and phenomena are eroded or otherwise not representable in a two-dimensional setting.…”

Section: Large-eddy Simulations For the Hifire Direct Connect Rigmentioning

confidence: 99%

“…While UQ in general has received substantial attention in the past decades, UQ for scramjet applications is much less developed but gaining traction in recent years [3][4][5][6][7][8][9][10][11]. A comprehensive assessment of uncertainty in such systems has been prohibitive due to the high cost of simulating turbulent reacting flows compounded with the multi-query nature of UQ investigations that generally requires some form of exploration in the stochastic space.…”

Section: Introductionmentioning

confidence: 99%

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Uncertainty Propagation Using Conditional Random Fields in Large-Eddy Simulations of Scramjet Computations

Huan

Safta

Vane

et al. 2019

AIAA Scitech 2019 Forum

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The development of scramjet engines is crucial for attaining efficient and stable propulsion under hypersonic flight conditions. Design for well-performing scramjet engines requires accurate flow simulations in conjunction with uncertainty quantification (UQ). We advance computational methods in bringing together UQ and large-eddy simulations for scramjet computations, with a focus on the HIFiRE Direct Connect Rig combustor. In particular, we perform uncertainty propagation for spatially dependent field quantities of interest (QoIs) by treating them as random fields, and numerically compute low-dimensional Karhunen-Loève expansions (KLEs) using a finite number of simulations on non-uniform grids. We also describe a formulation and procedure to extract conditional KLEs that characterize the stochasticity induced by uncertain parameters at given designs. This is achieved by first building a single KLE for each QoI via samples drawn jointly from the parameter and design spaces, and then leverage polynomial chaos expansions to insert input dependencies into the KLE. The ability to access conditional KLEs will be immensely useful for subsequent efforts in design optimization under uncertainty as well as model calibration with field variable measurements.

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Section: Large-eddy Simulations For the Hifire Direct Connect Rigmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Uncertainty Propagation Using Conditional Random Fields in Large-Eddy Simulations of Scramjet Computations

Huan

Safta

Vane

et al. 2019

AIAA Scitech 2019 Forum

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show abstract

“…Thus any module of the scramjet model can be treated as a black box with a PDF shaped input and a correspondingly PDF shaped output. Each modules output is propagated to the following module via Bayes's theorem with respect to the also PDF shaped model uncertainty [3]. This uncertainty is expressed by the error vectors E i whose elements " i;j ; represent the quantified uncertainty in the modules output flow parameters.…”

Section: Modeling Approachmentioning

confidence: 99%

Probabilistic Aspects of Scramjet Design

Schütte¹,

Staudacher²

2009

Journal of Propulsion and Power

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Scramjet design is characterized by a multitude of design variables influencing a highly nonlinear and complex system. Methods such as mean line calculations, high fidelity computational fluid dynamics, and empirical studies are generally used to derive aircraft engine performance. Because of the high complexity and the incomplete knowledge of hypersonic flow regimes, the question of robust design arises in the given context and leads to the need of probabilistic methodology. In this paper a probabilistic approach to scramjet engine design assessing both inflow and model uncertainty is presented. The two different types of uncertainty are quantified with respect to their different nature by use of a two-step bootstrap methodology. A descriptive sampling Monte Carlo method is employed to propagate the quantified uncertainties through the engine model to exemplify the high sensitivity of net thrust vector to present uncertainties and to analyze the correlation between the parameters variations. Nomenclature A = area, m 2 E i = error vector of the ith component, i 2 0; 31; 4; 7 ;9 (see Fig. 1) F net;x , F net;y = net thrust in x and y directions, N G i = vector of geometrical parameters of the ith component, i 2 0; 31; 4; 7 ;9 (see Fig. 1) h = duct height, m L = segment length, m Ma = Mach number _ m = mass flow, kg s 1 n = surface normal vector p = static pressure, Pa px, px j y = probability of x; probability of x assuming y Re x = Reynolds number S fuel = vector of fuel parameters (see Fig. 1) T = static temperature, K v = velocity, m s 1 X i = vector of deterministic flow parameters of the ith component, i 2 0; 31; 4; 7 ;9 (see Fig. 1) X i = vector of probabilistic flow parameters of the ith component, i 2 0; 31; 4; 7 ;9 (see Fig. 1) = ramp angle, deg = boundary-layer displacement thickness, m = mean value x = spline describing the geometry of the nozzle expansion ramp = flow density, kg m 3

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“…The objective of the present paper is to use the recent approach devoted to probabilistic learning on manifolds [1] to the challenges presented by large-eddy simulations (LES) of reactive flows inside a scramjet combustor. While investigations adopting probabilistic approaches for scramjet applications are growing in recent years [2][3][4][5][6][7][8], substantial challenges remain in characterizing and predicting combustion properties for turbulent flows under extreme conditions especially in conjunction with uncertainty quantification. We are particularly interested in employing and enabling probabilistic methods with LES, since these simulations, while computationally more demanding, can allow us to access some turbulence details and features often not available through models involving additional simplifications, such as with Reynolds-averaged Navier-Stokes (RANS).…”

Section: Introductionmentioning

confidence: 99%

“…formed for Q2 and Q 3 with respect to the number N of data points with N = {50, 100, 200, 450, 512} and ν sim = N × n MC = 51, 200 (Section VI. C.1).…”

mentioning

confidence: 99%

Enhancing Model Predictability for a Scramjet Using Probabilistic Learning on Manifolds

et al. 2019

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The computational burden of Large-eddy Simulation for reactive flows is exacerbated in the presence of uncertainty in flow conditions or kinetic variables. A comprehensive statistical analysis, with a sufficiently large number of samples, remains elusive. Statistical learning is an approach that allows for extracting more information using fewer samples. Such procedures, if successful, would greatly enhance the predictability of models in the sense of improving exploration and characterization of uncertainty due to model error and input dependencies, all while being constrained by the size of the associated statistical samples. In this paper, we show how a recently developed procedure for probabilistic learning on manifolds can serve to improve the predictability in a probabilistic framework of a scramjet simulation. The estimates of the probability density functions of the quantities of interest are improved together with estimates of the statistics of their maxima. We also demonstrate how the improved statistical model adds critical insight to the performance of the model.

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A Bayesian Approach to Non-Deterministic Hypersonic Vehicle Design

Cited by 6 publications

References 25 publications

Uncertainty Propagation Using Conditional Random Fields in Large-Eddy Simulations of Scramjet Computations

Uncertainty Propagation Using Conditional Random Fields in Large-Eddy Simulations of Scramjet Computations

Probabilistic Aspects of Scramjet Design

Enhancing Model Predictability for a Scramjet Using Probabilistic Learning on Manifolds

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