In the ordinary process of estimating uncertainty in model predictions one usually looks to some set of calibration experiments from which the model can be parameterized and then the resulting discrete set of model parameters are used to approximate the joint probability distribution of parameter vectors. That parameter uncertainty is propagated through the model to obtain predictive uncertainty. A key observation here is that usually, the modeler will attempt to find a unique “best” vector of parameters to match each calibration experiment and these “best” parameter vectors are used to estimate parameter uncertainty. In the work presented here, it is shown how for complex models — having more than a few parameters — it can happen that each experiment can befit equally well by a multitude of parameter vectors. It is also shown that when these large numbers of candidate parameter vectors are compiled the resulting model predictions may manifest substantially more variance than would be the case without consideration of the non-uniqueness issue. The contribution of non-uniqueness to prediction uncertainty is illustrated on two very different sorts of model. In the first case Johnson-Cook models for a titanium alloy are parameterized to match calibration experiments on three different alloy samples at different temperatures and strain rates. The resulting ensemble of parameter vectors are used to predict peak stress in a different experiment. In the second case, an epidemiological model is calibrated to history data and the parameter vectors are used to calculate a quantity of interest and uncertainty of that quantity.

Remote sensors in the infrared region can be used to study the progression of fireballs generated from experiments involving high explosives (HE). Developing an improved understanding of HE fireballs can be used to validate and improve computational physics codes that simulate such events. In this paper, Bayesian approaches are studied to estimate time-dependent optimal fireball parameters and their uncertainties using Fourier transform infrared (FTIR) spectroscopy. The optical signal measured by an FTIR sensor provides information on the fireball due to thermal emission, particulate emission/absorption, and HE gas product emission/absorption from the fireball. FTIR sensors have the advantage of being able to capture and measure the radiance in a large part of the infrared spectrum. The parameters to be estimated from the fireball include temperature and size, soot quantity, gas species concentrations (e.g., H 2 O, CO 2 , CO), and information on the presence of metals. In general, this inverse optimization problem is difficult due to the estimated quantities being correlated, the low spectral resolution of the FTIR sensor, and the intervening atmosphere absorbing the radiation emitted from the fireball. Bayesian calibration and Bayesian model averaging are applied to address these difficulties and to quantify the uncertainty in the estimated optimal parameter values. The fireball parameter settings are evaluated by the fit of a simplified spectral model to FTIR data. The overall problem will be presented together with a description of the Bayesian approaches. In this paper, the Bayesian approaches are applied to artificially generated FTIR data to illustrate the approach.

The extreme pressures and temperatures of the gas produced by detonating a High Explosive (HE) make it difficult to use experimental measurements to estimate the Equation Of State (EOS), the physics model that relates pressure, temperature, and density of the gas. Instead of measuring pressure directly one measures effects like the acceleration of metals driven by the HE. Typically one fits a few free parameters in a fixed functional form to measurements from a single experiment. The present work uses the optimization tool F_UNCLE to incorporate data from multiple experiments into a single EOS model for the gas produced by detonating the explosive PBX 9501. The model is verified by comparison to an experiment from outside the set of calibration data. The uncertainty in the EOS is also is examined to determine how each calibration experiment constrains the model and how the uncertainty arising from all calibration experiments affects predictions. This work identifies an EOS for HE detonation products and uncertainty about the EOS.

CFD is a valuable tool for showing compliance with peak temperatures in dry cask storage systems (DCSS). When demonstrating compliance, it is valuable to quantify the uncertainty in the simulation result as a function of the computational mesh and simulation inputs. USNRC was a participant in a CFD validation test using the TN-32B cask, with extensive temperature measurements throughout the DCSS, including measurements on the cask surface and in fuel bundles. This paper discusses validation and uncertainty quantification of a CFD model using experimental data. Uncertainty quantification follows the procedures outlined in ASME V&V20-2009 [1]. Sources of uncertainty that were examined in the analysis include iterative uncertainty, spacial discretization, and uncertainty due to approximately twenty input parameters. Input parameters investigated include environmental conditions, material properties, decay heat, and the spacing of the many small gaps in the installation. The uncertainty in gap size was found to be a particularly large source of uncertainty in this particular installation. Results of a “base case” using the conservative estimates outlined in the updated final safety analysis report (UFSAR) [2] are presented, as well as a “best estimate case” that uses more realistic values. These results are compared to experimentally measured values, which fall within the uncertainty band of the analysis. This work is also the subject of an upcoming NUREG/CR.

In the power plant industry, the turbine inlet temperature (TIT) plays a key role in the efficiency of the gas turbine and, therefore, the overall — in most cases combined — thermal power cycle efficiency. Gas turbine efficiency increases by increasing TIT. However, an increase of TIT would increase the turbine component temperature which can be critical (e.g., hot gas attack). Thermal barrier coatings (TBCs) — porous media coatings — can avoid this case and protect the surface of the turbine blade. This combination of TBC and film cooling produces a better cooling performance than conventional cooling processes. The effective thermal conductivity of this composite is highly important in design and other thermal/structural assessments. In this article, the effective thermal conductivity of a simplified model of TBC is evaluated. This work details a numerical study on the steady-state thermal response of two-phase porous media in two dimensions using personal finite element analysis (FEA) code. Specifically, the system response quantity (SRQ) under investigation is the dimensionless effective thermal conductivity of the domain. A thermally conductive matrix domain is modeled with a thermally conductive circular pore arranged in a uniform packing configuration. Both the pore size and the pore thermal conductivity are varied over a range of values to investigate the relative effects on the SRQ. In this investigation, an emphasis is placed on using code and solution verification techniques to evaluate the obtained results. The method of manufactured solutions (MMS) was used to perform code verification for the study, showing the FEA code to be second-order accurate. Solution verification was performed using the grid convergence index (GCI) approach with the global deviation uncertainty estimator on a series of five systematically refined meshes for each porosity and thermal conductivity model configuration. A comparison of the SRQs across all domain configurations is made, including uncertainty derived through the GCI analysis.

In this work, a dynamic physics-based model developed for the prediction of biohydrogen production in a compact tubular photobioreactor was calibrated experimentally. The spatial domain in the model was discretized with lumped control volumes, and the principles of classical thermodynamics, mass, species and heat transfer were combined to derive a system of ordinary differential equations whose solution was the temperature and mass fraction distributions across the entire system. Two microalgae species, namely, Acutodesmus obliquus and Chlamydomonas reinhardtii strain ccI25 were cultured in triplicate with different culture media via indirect biophotolysis. Experimental biomass and hydrogen concentrations were then used to adjust the specific microalgae growth and hydrogen production coefficients based on residual sum of squares and the direct search method.

V&V constitutes a powerful framework to demonstrate the capability of computational tools in several technological areas. Passing V&V requirements is a needed step before applications. Let’s focus hereafter to the area of (transient) Nuclear Thermal-hydraulic (NTH) and let’s identify V1 and V2 as acronyms for Verification and Validation, respectively. Now, V1 is performed within NTH according to the best available techniques and may not suffer of important deficiencies if compared with other technological areas. This is not the case of V2. Three inherent limitations shall be mentioned in the case of Validation in NTH: 1. Validation implies comparison with experimental data: available experimental data cover a (very) small fraction of the parameter range space expected in applications of the codes; this can be easily seen if one considers data in large diameter pipe, high velocity and high pressure or high power and power density. Noticeably, the scaling issue must be addressed in the framework of V2 which may result in controversial findings. 2. Water is at the center of the attention: the physical properties of water are known to a reasonable extent as well as large variations in values of quantities like density or various derivatives are expected within the range of variation of pressure inside application fields. Although not needed for current validation purposes (e.g. validation ranges may not include a situation of critical pressure and large heat flux) physically inconsistent values predicted by empirical correlations outside validation ranges, shall not be tolerated. 3. Occurrence of complex situations like transition from two-phase critical flow to ‘Bernoulli-flow’ (e.g. towards the end of blow-down) and from film boiling to nucleate boiling, possibly crossing the minimum film boiling temperature (e.g. during reflood). Therefore, whatever can be mentioned as classical V2 is not or cannot be performed in NTH. So, the idea of the present paper is to add a component to the V&V. This component, or step in the process, is called ‘Consistency with Reality’, or with the expected phenomenological evidence. The new component may need to be characterized in some cases and is indicated by the letter ‘C’. Then, the V&V becomes V&V&C. The purpose of the paper is to clarify the motivations at the bases of the V&V&C.