Basis adaptation in Homogeneous Chaos spaces rely on a suitable rotation of the underlying Gaussian germ. Several rotations have been proposed in the literature resulting in adaptations with different convergence properties. In this paper we present a new adaptation mechanism that builds on compressive sensing algorithms, resulting in a reduced polynomial chaos approximation with optimal sparsity. The developed adaptation algorithm consists of a two-step optimization procedure that computes the optimal coefficients and the input projection matrix of a low dimensional chaos expansion with respect to an optimally rotated basis. We demonstrate the attractive features of our algorithm through several numerical examples including the application on Large-Eddy Simulation (LES) calculations of turbulent combustion in a HIFiRE scramjet engine.
Model error estimation remains one of the key challenges in uncertainty quantification and predictive science. For computational models of complex physical systems, model error, also known as structural error or model inadequacy, is often the largest contributor to the overall predictive uncertainty. This work builds on a recently developed framework of embedded, internal model correction, in order to represent and quantify structural errors, together with model parameters,within a Bayesian inference context. We focus specifically on a Polynomial Chaos representation with additive modification of existing model parameters, enabling a non-intrusive procedure for efficient approximate likelihood construction, model error estimation, and disambiguation of model and data errors’ contributions to predictive uncertainty. The framework is demonstrated on several synthetic examples, as well as on a chemical ignition problem.
The computational burden of a 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, will 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, it is shown 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. It is also demonstrated how the improved statistical model adds critical insight to the performance of the model.
The development of scramjet engines is an important research area for advancing hypersonic and orbital flights. Progress toward optimal engine designs requires accurate flow simulations together with uncertainty quantification. However, performing uncertainty quantification for scramjet simulations is challenging due to the large number of uncertain parameters involved and the high computational cost of flow simulations. These difficulties are addressed in this paper by developing practical uncertainty quantification algorithms and computational methods, and deploying them in the current study to large-eddy simulations of a jet in crossflow inside a simplified HIFiRE Direct Connect Rig scramjet combustor. First, global sensitivity analysis is conducted to identify influential uncertain input parameters, which can help reduce the system’s stochastic dimension. Second, because models of different fidelity are used in the overall uncertainty quantification assessment, a framework for quantifying and propagating the uncertainty due to model error is presented. Finally, these methods are demonstrated on a nonreacting jet-in-crossflow test problem in a simplified scramjet geometry, with parameter space up to 24 dimensions, using static and dynamic treatments of the turbulence subgrid model, and with two-dimensional and three-dimensional geometries.
The development of scramjet engines is an important research area for advancing hypersonic and orbital flights. Progress toward optimal engine designs requires accurate flow simulations together with uncertainty quantification. However, performing uncertainty quantification for scramjet simulations is challenging due to the large number of uncertainparameters involvedandthe high computational costofflow simulations. These difficulties are addressedin this paper by developing practical uncertainty quantification algorithms and computational methods, and deploying themin the current studyto large-eddy simulations ofajet incrossflow inside a simplified HIFiRE Direct Connect Rig scramjet combustor. First, global sensitivity analysis is conducted to identify influential uncertain input parameters, which can help reduce the system's stochastic dimension. Second, because models of different fidelity are used in the overall uncertainty quantification assessment, a framework for quantifying and propagating the uncertainty due to model error is presented. These methods are demonstrated on a nonreacting jet-in-crossflow test problem in a simplified scramjet geometry, with parameter space up to 24 dimensions, using static and dynamic treatments of the turbulence subgrid model, and with two-dimensional and three-dimensional geometries.
This study evaluates the applicability of the Octane Index (OI) framework under conventional spark ignition (SI) and “beyond Research Octane Number (RON)” conditions using nine fuels operated under stoichiometric, knock-limited conditions in a direct injection spark ignition (DISI) engine, supported by Monte Carlo-type simulations which interrogate the effects of measurement uncertainty. Of the nine tested fuels, three fuels are “Tier III” fuel blends, meaning that they are blends of molecules which have passed two levels of screening, and have been evaluated to be ready for tests in research engines. These molecules have been blended into a four-component gasoline surrogate at varying volume fractions in order to achieve a RON rating of 98. The molecules under consideration are isobutanol, 2-butanol, and diisobutylene (which is a mixture of two isomers of octene). The remaining six fuels were research-grade gasolines of varying formulations. The DISI research engine was used to measure knock limits at heated and unheated intake temperature conditions, as well as throttled and boosted intake pressures, all at an engine speed of 1400 rpm. The tested knock-limited operating conditions conceptually exist both between the Motor Octane Number (MON) and RON conditions, as well as “beyond RON” conditions (conditions which are conceptually at lower temperatures, higher pressures, or longer residence times than the RON condition). In addition to directly assessing the performance of the Tier III blends relative to other gasolines, the OI framework was evaluated with considerations of experimental uncertainty in the knock-limited combustion phasing (KL-CA50) measurements, as well as RON and MON test uncertainties. The OI was found to hold to the first order, explaining more than 80% of the knock-limited behavior, although the remaining variation in fuel performance from OI behavior was found to be beyond the likely experimental uncertainties. This indicates that the effects of specific fuel components on knock which are not captured by RON and MON ratings, and complicating the assessment of a given fuel by RON and MON ratings alone.