Validation and uncertainty framework for variable-density mixing experiments

Variable-density mixing (e.g., mixing due to the Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities) is observed in many engineering applications. For example, RT mixing is observed in geophysical flows, stratified oceanic or atmospheric layers, and contaminant mixing, such as oil spills or pollution. Although less common, RM mixing is present in hypersonic combustion, supernova, and inertial confinement fusion. Current computational fluid dynamics models inadequately predict variable-density mixing physics and developments need to be validated with experimental data. However, variable-density experiments are complicated due to the range of spatial mixing scales and inherent coupling of density and velocity. This requires simultaneous measurement of the density and velocity fields and is typically accomplished via simultaneous particle image velocimetry (PIV) and planar laser--induced fluorescence (PLIF) with two distinct measurement systems. This introduces additional error sources to traditional PIV. Correlated density-velocity quantities (e.g., Favre-averaged Reynolds stresses and mass fluxes) are contaminated by both PIV and PLIF uncertainties. Moreover, spatial registration and sheet alignment errors between PIV and PLIF measurements are introduced for all flow quantities and magnified for correlated quantities. The Extreme Fluids Team at Los Alamos National Laboratory (LANL) is conducting multiple variable density validation experiments. The vertical shock tube (VST) is designed to statistically characterize RM mixing, whereas the turbulent mixing tunnel (TMT) investigates RT and Kelvin–Helmholtz mixing. Simultaneous two-component PIV and PLIF diagnostics are used in both facilities. Although the TMT can acquire large ensemble averaged datasets, the ability of acquiring large numbers of dataset realizations from the VST is severely limited. A framework for variable-density uncertainty quantification and validation is presented for both experiments. This framework follows the validation experiment assessment criteria presented by Oberkampf and Smith [1] with a goal of achieving at least a Level 2 completeness level. Both facilities have been designed to accurately describe the experimental conditions. The most difficult issue is quantifying the measurement uncertainties. Instantaneous PIV uncertainties are estimated using the uncertainty surface method [2] the peak ratio method [3], then propagated into the velocity statistics [4]. The effects of spatial registration sheet alignment errors are also assessed and initial uncertainty estimates due to these quantities are presented. Using the same methods as [4], PIV, PLIF, registration and alignment uncertainties are propagated into the Favre-averaged stresses and mass fluxes

Validation methodologies for turbulent variable density flows: A jet case study

Comparisons studies between simulated variable density turbulent flows often consist of direct graphical representations where the level of agreement is determined by eye. This work demonstrates a formal validation methodology using an existing validation framework to examine the agreement between a simulated variable density jet flow and corresponding experimental data. Implicit large eddy simulations (ILES's) of a round jet and a plane jet with density ratio $s = 4.2$ were simulated using the compressible hydrodynamic code xRAGE. The jet growth, characterized by the spreading rates, was compared, and the difference between the simulations and the experiment was examined through jet structure diagnostics. The spreading rates were found to be larger than the experimental values, primarily due to resolution issues in the simulations, a fact that is quantified by the validation metric analysis.Comment: 19 pages, 13 figure

FEDSM2008-55151 ROBUST GRADIENT ESTIMATION USING RADIAL BASIS FUNCTIONS

ABSTRACT Utilization of Radial Basis Functions (RBFs) for gradient estimation is tested over various noisy flow fields. A novel mathematical formulation which minimizes the energy functional associated with the analytical surface fit for Gaussian (GA) and Generalized Multiquadratic (GMQ) RBFs is presented. Error analysis of the wall gradient estimation was performed at various resolutions, interpolation grid sizes, and noise levels in synthetically generated Poiseuille and Womersley flow fields for RBFs along with standard finite difference schemes. To test the effectiveness of the methods with DPIV (Digital Particle Image Velocimetry) data, the methods were compared using the velocities obtained by processing images generated from DNS data of an open turbulent channel. Random, bias and total error were computed in all cases. In the absence of noise all tested methods perform well, with error contained under 10% at all resolutions. In the presence of noise the RBFs perform robustly with a total error that can be contained under 10-15% even with 10% noise using various interpolation grid sizes, For turbulent flow data, although the total error is approximately 5% for finite difference schemes in the absence of noise, the error can go as high as 150% in the presence of as little as 1% noise. With DPIV processed data the error is 25-40% for TPS and MQ methods optimization of the fitting parameters that minimize the energy functional associated with the analytical surface using RBFs results in robust gradient estimators are obtained that are applicable to steady, unsteady and turbulent flow fields. INTRODUCTION Digital Particle Image Velocimetry (DPIV) is a noninvasive optical flow diagnostic tool used to spatially and temporally resolve the velocity field across a variety of applications. Several sources of error are present in the DPIV estimation, including imaging errors as well as systematic errors in the velocity estimation. These sources of error are further compounded when computing important flow parameters which require gradient estimation, such as vorticity [1], shear stress Luf