This report details a new method for propagating parameter uncertainty (forward uncertainty quantification) in partial differential equations (PDE) based computational mechanics applications. The method provides full-field quantities of interest by solving for the joint probability density function (PDF) equations which are implied by the PDEs with uncertain parameters. Full-field uncertainty quantification enables the design of complex systems where quantities of interest, such as failure points, are not known apriori. The method, motivated by the well-known probability density function (PDF) propagation method of turbulence modeling, uses an ensemble of solutions to provide the joint PDF of desired quantities at every point in the domain. A small subset of the ensemble is computed exactly, and the remainder of the samples are computed with approximation of the driving (dynamics) term of the PDEs based on those exact solutions. Although the proposed method has commonalities with traditional interpolatory stochastic collocation methods applied directly to quantities of interest, it is distinct and exploits the parameter dependence and smoothness of the dynamics term of the governing PDEs. The efficacy of the method is demonstrated by applying it to two target problems: solid mechanics explicit dynamics with uncertain material model parameters, and reacting hypersonic fluid mechanics with uncertain chemical kinetic rate parameters. A minimally invasive implementation of the method for representative codes SPARC (reacting hypersonics) and NimbleSM (finite- element solid mechanics) and associated software details are described. For solid mechanics demonstration problems the method shows order of magnitudes improvement in accuracy over traditional stochastic collocation. For the reacting hypersonics problem, the method is implemented as a streamline integration and results show very good accuracy for the approximate sample solutions of re-entry flow past the Apollo capsule geometry at Mach 30.
Tabulated chemistry models are widely used to simulate large-scale turbulent fires in applications including energy generation and fire safety. Tabulation via piecewise Cartesian interpolation suffers from the curse-of-dimensionality, leading to a prohibitive exponential growth in parameters and memory usage as more dimensions are considered. Artificial neural networks (ANNs) have attracted attention for constructing surrogates for chemistry models due to their ability to perform high-dimensional approximation. However, due to well-known pathologies regarding the realization of suboptimal local minima during training, in practice they do not converge and provide unreliable accuracy. Partition of unity networks (POUnets) are a recently introduced family of ANNs which preserve notions of convergence while performing high-dimensional approximation, discovering a mesh-free partition of space which may be used to perform optimal polynomial approximation. In this work, we assess their performance with respect to accuracy and model complexity in reconstructing unstructured flamelet data representative of nonadiabatic pool fire models. Our results show that POUnets can provide the desirable accuracy of classical spline-based interpolants with the low memory footprint of traditional ANNs while converging faster to significantly lower errors than ANNs. For example, we observe POUnets obtaining target accuracies in two dimensions with 40 to 50 times less memory and roughly double the compression in three dimensions. We also address the practical matter of efficiently training accurate POUnets by studying convergence over key hyperparameters, the impact of partition/basis formulation, and the sensitivity to initialization.
In this work, medium scale (30 cm diameter) methanol pool fires were simulated using the latest fire modeling suite implemented in Sierra/Fuego, a low Mach number multiphysics reacting flow code. The sensitivity of model outputs to various model parameters was studied with the objective of providing model validation. This work also assesses model performance relative to other recently published large eddy simulations (LES) of the same validation case. Two pool surface boundary conditions were simulated. The first was a prescribed fuel mass flux and the second used an algorithm to predict mass flux based on a mass and energy balance at the fuel surface. Gray gas radiation model parameters (absorption coefficients and gas radiation sources) were varied to assess radiant heat losses to the surroundings and pool surface. The radiation model was calibrated by comparing the simulated radiant fraction of the plume to experimental data. The effects of mesh resolution were also quantified starting with a grid resolution representative of engineering type fire calculations and then uniformly refining that mesh in the plume region. Simulation data were compared to experimental data collected at the University of Waterloo and the National Institute of Standards and Technology (NIST). Validation data included plume temperature, radial and axial velocities, velocity temperature turbulent correlations, velocity velocity turbulent correlations, radiant and convective heat fluxes to the pool surface, and plume radiant fraction. Additional analyses were performed in the pool boundary layer to assess simulated flame anchoring and the effect on convective heat fluxes. This work assesses the capability of the latest Fuego physics and chemistry model suite and provides additional insight into pool fire modeling for nonluminous, non-sooting flames.
This report describes an assessment of flamelet based soot models in a laminar ethylene coflow flame with a good selection of measurements suitable for model validation. Overall flow field and temperature predictions were in good agreement with available measurements. Soot profiles were in good agreement within the flame except for near the centerline where imperfections with the acetylene-based soot-production model are expected to be greatest. The model was challenged to predict the transition between non-sooting and sooting conditions with non-negligible soot emissions predicted even down to small flow rates or flame sizes. This suggests some possible deficiency in the soot oxidation models that might alter the amount of smoke emissions from flames, though this study cannot quantify the magnitude of the effect for large fires.
A low-Mach, unstructured, large-eddy-simulation-based, unsteady flamelet approach with a generalized heat loss combustion methodology (including soot generation and consumption mechanisms) is deployed to support a large-scale, quiescent, 5-m JP-8 pool fire validation study. The quiescent pool fire validation study deploys solution sensitivity procedures, i.e., the effect of mesh and time step refinement on capturing key fire dynamics such as fingering and puffing, as mesh resolutions approach O(1) cm. A novel design-order, discrete-ordinate-method discretization methodology is established by use of an analytical thermal/participating media radiation solution on both low-order hexahedral and tetrahedral mesh topologies in addition to quadratic hexahedral elements. The coupling between heat losses and the flamelet thermochemical state is achieved by augmenting the unsteady flamelet equation set with a heat loss source term. Soot and radiation source terms are determined using flamelet approaches for the full range of heat losses experienced in fire applications including radiative extinction. The proposed modeling and simulation paradigm are validated using pool surface radiative heat flux, maximum centerline temperature location, and puffing frequency data, all of which are predicted within 10% accuracy. Simulations demonstrate that under-resolved meshes predict an overly conservative radiative heat flux magnitude with improved comparisons as compared to a previously deployed hybrid Reynolds-averaged Navier-Stokes/eddy dissipation concept-based methodology.