The development of a next generation high-fidelity modeling code for wind plant applications is one of the central focus areas of the U.S. Department of Energy Atmosphere to Electrons (A2e) initiative. The code is based on a highly scalable framework, currently called Nalu-Wind. One key aspect of the model development is a coordinated formal validation program undertaken specifically to establish the predictive capability of Nalu-Wind for wind plant applications. The purpose of this document is to define the verification and validation (V&V) plan for the A2e high-fidelity modeling capability. It summarizes the V&V framework, identifies code capability users and use cases, describes model validation needs, and presents a timeline to meet those needs.
Compressible jet-in-crossflow interactions are difficult to simulate accurately using Reynolds-averaged Navier-Stokes (RANS) models. This could be due to simplifications inherent in RANS or the use of inappropriate RANS constants estimated by fitting to experiments of simple or canonical flows. Our previous work on Bayesian calibration of a k - ϵ model to experimental data had led to a weak hypothesis that inaccurate simulations could be due to inappropriate constants more than model-form inadequacies of RANS. In this work, Bayesian calibration of k - ϵ constants to a set of experiments that span a range of Mach numbers and jet strengths has been performed. The variation of the calibrated constants has been checked to assess the degree to which parametric estimates compensate for RANS's model-form errors. An analytical model of jet-in-crossflow interactions has also been developed, and estimates of k - ϵ constants that are free of any conflation of parametric and RANS's model-form uncertainties have been obtained. It has been found that the analytical k - ϵ constants provide mean-flow predictions that are similar to those provided by the calibrated constants. Further, both of them provide predictions that are far closer to experimental measurements than those computed using "nominal" values of these constants simply obtained from the literature. It can be concluded that the lack of predictive skill of RANS jet-in-crossflow simulations is mostly due to parametric inadequacies, and our analytical estimates may provide a simple way of obtaining predictive compressible jet-in-crossflow simulations.
We demonstrate a statistical procedure for learning a high-order eddy viscosity model (EVM) from experimental data and using it to improve the predictive skill of a Reynoldsaveraged Navier-Stokes (RANS) simulator. The method is tested in a three-dimensional (3D), transonic jet-in-crossflow (JIC) configuration. The process starts with a cubic eddy viscosity model (CEVM) developed for incompressible flows. It is fitted to limited experimental JIC data using shrinkage regression. The shrinkage process removes all the terms from the model, except an intercept, a linear term, and a quadratic one involving the square of the vorticity. The shrunk eddy viscosity model is implemented in an RANS simulator and calibrated, using vorticity measurements, to infer three parameters. The calibration is Bayesian and is solved using a Markov chain Monte Carlo (MCMC) method. A 3D probability density distribution for the inferred parameters is constructed, thus quantifying the uncertainty in the estimate. The phenomenal cost of using a 3D flow simulator inside an MCMC loop is mitigated by using surrogate models ("curve-fits"). A support vector machine classifier (SVMC) is used to impose our prior belief regarding parameter values, specifically to exclude nonphysical parameter combinations. The calibrated model is compared, in terms of its predictive skill, to simulations using uncalibrated linear and CEVMs. We find that the calibrated model, with one quadratic term, is more accurate than the uncalibrated simulator. The model is also checked at a flow condition at which the model was not calibrated.
The k-ε turbulence model has been described as perhaps “the most widely used complete turbulence model.” This family of heuristic Reynolds Averaged Navier-Stokes (RANS) turbulence closures is supported by a suite of model parameters that have been estimated by demanding the satisfaction of well-established canonical flows such as homogeneous shear flow, log-law behavior, etc. While this procedure does yield a set of so-called nominal parameters, it is abundantly clear that they do not provide a universally satisfactory turbulence model that is capable of simulating complex flows. Recent work on the Bayesian calibration of the k-ε model using jet-in-crossflow wind tunnel data has yielded parameter estimates that are far more predictive than nominal parameter values. In this paper, we develop a self-similar asymptotic solution for axisymmetric jet-in-crossflow interactions and derive analytical estimates of the parameters that were inferred using Bayesian calibration. The self-similar method utilizes a near field approach to estimate the turbulence model parameters while retaining the classical far-field scaling to model flow field quantities. Our parameter values are seen to be far more predictive than the nominal values, as checked using RANS simulations and experimental measurements. They are also closer to the Bayesian estimates than the nominal parameters. A traditional simplified jet trajectory model is explicitly related to the turbulence model parameters and is shown to yield good agreement with measurement when utilizing the analytical derived turbulence model coefficients. Finally, the close agreement between the turbulence model coefficients obtained via Bayesian calibration and the analytically estimated coefficients derived in this paper is consistent with the contention that the Bayesian calibration approach is firmly rooted in the underlying physical description.
The resonance modes in Mach 0.94 turbulent flow over a cavity having a length-to-depth ratio of five were explored using time-resolved particle image velocimetry and time-resolved pressure sensitive paint. Mode-switching occurred in the velocity field simultaneous with the pressure field. The first cavity mode corresponded to large-scale motions in shear layer and in the vicinity of the recirculation region, whereas the second and third modes contained organized structures associated with shear layer vortices. Modal surface pressures exhibited streamwise periodicity generated by the interference of downstream-traveling disturbances in shear layer with upstream-traveling acoustical waves. Because of this interference, the modal velocity fields also exhibited local maxima at locations containing pressure minima and vice-versa. Modal convective (phase) velocities, based on cross-correlations of bandpass-filtered velocity fields, decreased with decreasing mode number as the modal activity resided in lower portions of the cavity. These phase velocities also exhibited streamwise periodicity caused by wave interference. The measurements demonstrate that despite the complexities inherent in compressible cavity flows, many of the most prevalent resonance dynamics can be described with simple acoustical analogies.
Simulations of the flow past a rectangular cavity containing a model captive store are performed using a hybrid Reynolds-averaged Navier–Stokes/large-eddy simulation model. Calculated pressure fluctuation spectra are validated using measurements made on the same configuration in a trisonic wind tunnel at Mach numbers of 0.60, 0.80, and 1.47. The simulation results are used to calculate unsteady integrated forces and moments acting on the store. Spectra of the forces and moments, along with correlations calculated for force/moment pairs, reveal that a complex relationship exists between the unsteady integrated forces and the measured resonant cavity modes, as indicated in the cavity wall pressure measurements. The structure of identified cavity resonant tones is examined by visualization of filtered surface pressure fields.
Reynolds-averaged Navier–Stokes models are not very accurate for high-Reynolds-number compressible jet-in-crossflow interactions. The inaccuracy arises from the use of inappropriate model parameters and model-form errors in the Reynolds-averaged Navier–Stokes model. In this study, the hypothesis is pursued that Reynolds-averaged Navier–Stokes predictions can be significantly improved by using parameters inferred from experimental measurements of a supersonic jet interacting with a transonic crossflow.
Mach 0.94 flow over a cavity having a length-to-depth ratio of five was explored using time-resolved particle image velocimetry (TR-PIV) with a burst-mode laser. The data were used to probe the resonance dynamics of the first three cavity (Rossiter) tones. Bandpass filtering was employed to reveal the coherent flow structure associated with each tone. The first Rossiter mode was associated with a propagation of large scale structures in the recirculation region, while the second and third modes contained organized structures consistent with convecting vortical disturbances. The wavelengths of the second and third modes were quite similar to those observed in a previous study by the current authors using phase-averaged PIV. Convective velocities computed using cross correlations in the unfiltered data showed the convective velocity increased with streamwise distance in a fashion similar to other studies. Convective velocities during cavity resonance were found to decrease with decreasing mode number, consistent with the modal activity residing in lower portions of the cavity in regions of lower local mean velocities. The convective velocity fields associated with resonance exhibited a streamwise periodicity consistent with wall-normal undulations in the resonant velocity fields; however, additional work is required to confirm this is not an analysis artifact.