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. In conclusion, 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.
For film cooling of combustor linings and turbine blades, it is critical to be able to accurately model jets-in-crossflow. Current Reynolds-averaged Navier-Stokes (RANS) models often give unsatisfactory predictions in these flows, due in large part to model form error, which cannot be resolved through calibration or tuning of model coefficients. The Boussinesq hypothesis, upon which most two-equation RANS models rely, posits the existence of a non-negative scalar eddy viscosity, which gives a linear relation between the Reynolds stresses and the mean strain rate. This model is rigorously analyzed in the context of a jet-in-crossflow using the high-fidelity large eddy simulation data of Ruiz et al. (2015, "Flow Topologies and Turbulence Scales in a Jet-in-Cross-Flow," Phys. Fluids, 27(4), p. 045101), as well as RANS k-ε results for the same flow. It is shown that the RANS models fail to accurately represent the Reynolds stress anisotropy in the injection hole, along the wall, and on the lee side of the jet. Machine learning methods are developed to provide improved predictions of the Reynolds stress anisotropy in this flow.
The development of scramjet engines is an important research area for advancing hypersonic and orbital flights. Progress towards optimal engine designs requires both accurate flow simulations as well as uncertainty quantification (UQ). However, performing UQ for scramjet simulations is challenging due to the large number of uncertain parameters involved and the high computational cost of flow simulations. We address these difficulties by combining UQ algorithms and numerical methods to the large eddy simulation of the HIFiRE scramjet configuration. First, global sensitivity analysis is conducted to identify influential uncertain input parameters, helping reduce the stochastic dimension of the problem and discover sparse representations. Second, as models of different fidelity are available and inevitably used in the overall UQ assessment, a framework for quantifying and propagating the uncertainty due to model error is introduced. These methods are demonstrated on a non-reacting scramjet unit problem with parameter space up to 24 dimensions, using 2D and 3D geometries with static and dynamic treatments of the turbulence subgrid model.
For film cooling of combustor linings and turbine blades, it is critical to be able to accurately model jets-in-crossflow. Current Reynolds Averaged Navier Stokes (RANS) models often give unsatisfactory predictions in these flows, due in large part to model form error, which cannot be resolved through calibration or tuning of model coefficients. The Boussinesq hypothesis, upon which most two-equation RANS models rely, posits the existence of a non-negative scalar eddy viscosity, which gives a linear relation between the Reynolds stresses and the mean strain rate. This model is rigorously analyzed in the context of a jet-in-crossflow using the high fidelity Large Eddy Simulation data of Ruiz et al. (2015), as well as RANS k-e results for the same flow. It is shown that the RANS models fail to accurately represent the Reynolds stress anisotropy in the injection hole, along the wall, and on the lee side of the jet. Machine learning methods are developed to provide improved predictions of the Reynolds stress anisotropy in this flow.
This study presents a detailed analysis of the flow topologies and turbulence scales in the jet-in-cross-flow experiment of [Su and Mungal JFM 2004]. The analysis is performed using the Large Eddy Simulation (LES) technique with a highly resolved grid and time-step and well controlled boundary conditions. This enables quantitative agreement with the first and second moments of turbulence statistics measured in the experiment. LES is used to perform the analysis since experimental measurements of time-resolved 3D fields are still in their infancy and because sampling periods are generally limited with direct numerical simulation. A major focal point is the comprehensive characterization of the turbulence scales and their evolution. Time-resolved probes are used with long sampling periods to obtain maps of the integral scales, Taylor microscales, and turbulent kinetic energy spectra. Scalar-fluctuation scales are also quantified. In the near-field, coherent structures are clearly identified, both in physical and spectral space. Along the jet centerline, turbulence scales grow according to a classical one-third power law. However, the derived maps of turbulence scales reveal strong inhomogeneities in the flow. From the modeling perspective, these insights are useful to design optimized grids and improve numerical predictions in similar configurations.
Large-eddy-simulation (LES) is quickly becoming a method of choice for studying complex thermo-physics in a wide range of propulsion and power systems. It provides a means to study coupled turbulent combustion and flow processes in parameter spaces that are unattainable using direct-numerical-simulation (DNS), with a degree of fidelity that can be far more accurate than conventional engineering methods such as the Reynolds-averaged Navier-Stokes (RANS) approximation. However, development of predictive LES is complicated by the complex interdependence of different type of errors coming from numerical methods, algorithms, models and boundary con- ditions. On the other hand, control of accuracy has become a critical aspect in the development of predictive LES for design. The objective of this project is to create a framework of metrics aimed at quantifying the quality and accuracy of state-of-the-art LES in a manner that addresses the myriad of competing interdependencies. In a typical simulation cycle, only 20% of the computational time is actually usable. The rest is spent in case preparation, assessment, and validation, because of the lack of guidelines. This work increases confidence in the accuracy of a given solution while minimizing the time obtaining the solution. The approach facilitates control of the tradeoffs between cost, accuracy, and uncertainties as a function of fidelity and methods employed. The analysis is coupled with advanced Uncertainty Quantification techniques employed to estimate confidence in model predictions and calibrate model's parameters. This work has provided positive consequences on the accuracy of the results delivered by LES and will soon have a broad impact on research supported both by the DOE and elsewhere.