An approach to model validation and model-based prediction -- polyurethane foam case study.

Enhanced software methodology and improved computing hardware have advanced the state of simulation technology to a point where large physics-based codes can be a major contributor in many systems analyses. This shift toward the use of computational methods has brought with it new research challenges in a number of areas including characterization of uncertainty, model validation, and the analysis of computer output. It is these challenges that have motivated the work described in this report. Approaches to and methods for model validation and (model-based) prediction have been developed recently in the engineering, mathematics and statistical literatures. In this report we have provided a fairly detailed account of one approach to model validation and prediction applied to an analysis investigating thermal decomposition of polyurethane foam. A model simulates the evolution of the foam in a high temperature environment as it transforms from a solid to a gas phase. The available modeling and experimental results serve as data for a case study focusing our model validation and prediction developmental efforts on this specific thermal application. We discuss several elements of the ''philosophy'' behind the validation and prediction approach: (1) We view the validation process as an activity applying to the use of a specific computational model for a specific application. We do acknowledge, however, that an important part of the overall development of a computational simulation initiative is the feedback provided to model developers and analysts associated with the application. (2) We utilize information obtained for the calibration of model parameters to estimate the parameters and quantify uncertainty in the estimates. We rely, however, on validation data (or data from similar analyses) to measure the variability that contributes to the uncertainty in predictions for specific systems or units (unit-to-unit variability). (3) We perform statistical analyses and hypothesis tests as a part of the validation step to provide feedback to analysts and modelers. Decisions on how to proceed in making model-based predictions are made based on these analyses together with the application requirements. Updating modifying and understanding the boundaries associated with the model are also assisted through this feedback. (4) We include a ''model supplement term'' when model problems are indicated. This term provides a (bias) correction to the model so that it will better match the experimental results and more accurately account for uncertainty. Presumably, as the models continue to develop and are used for future applications, the causes for these apparent biases will be identified and the need for this supplementary modeling will diminish. (5) We use a response-modeling approach for our predictions that allows for general types of prediction and for assessment of prediction uncertainty. This approach is demonstrated through a case study supporting the assessment of a weapons response when subjected to a hydrocarbon fuel fire. The foam decomposition model provides an important element of the response of a weapon system in this abnormal thermal environment. Rigid foam is used to encapsulate critical components in the weapon system providing the needed mechanical support as well as thermal isolation. Because the foam begins to decompose at temperatures above 250 C, modeling the decomposition is critical to assessing a weapons response. In the validation analysis it is indicated that the model tends to ''exaggerate'' the effect of temperature changes when compared to the experimental results. The data, however, are too few and to restricted in terms of experimental design to make confident statements regarding modeling problems. For illustration, we assume these indications are correct and compensate for this apparent bias by constructing a model supplement term for use in the model-based predictions. Several hypothetical prediction problems are created and addressed. Hypothetical problems are used because no guidance was provided concerning what was needed for this aspect of the analysis. The resulting predictions and corresponding uncertainty assessment demonstrate the flexibility of this approach

Atmospheric Flow Validation for Contaminant Transport

Presentation on atmospheric flow validation for contaminant transport.https://digitalcommons.usmalibrary.org/presentations/1015/thumbnail.jp

Statistical validation of engineering and scientific models : bounds, calibration, and extrapolation.

Numerical models of complex phenomena often contain approximations due to our inability to fully model the underlying physics, the excessive computational resources required to fully resolve the physics, the need to calibrate constitutive models, or in some cases, our ability to only bound behavior. Here we illustrate the relationship between approximation, calibration, extrapolation, and model validation through a series of examples that use the linear transient convective/dispersion equation to represent the nonlinear behavior of Burgers equation. While the use of these models represents a simplification relative to the types of systems we normally address in engineering and science, the present examples do support the tutorial nature of this document without obscuring the basic issues presented with unnecessarily complex models

Isothermal by Design: Comparison with an Established Isothermal Nucleation Kinetics Analysis Method

The nucleation kinetics of the alpha form of p‐aminobenzoic acid from ethanolic and aqueous solutions is examined through a comparative examination of temperature‐jump and anti‐solvent drown‐out isothermal crystallization methodologies. Analysis of the data reveals the measured induction times, and the calculated effective interfacial tensions as a function of the supersaturation show broadly equivalent behavior for the aqueous‐ethanol mixed‐solvent drown‐out and temperature‐jump ethanol solution systems, confirming the comparability of the two methodologies. The results also demonstrate poorer agreement with the temperature‐jump pure aqueous system, highlighting the importance of the strength of solvation/desolvation as the key rate‐limiting process for the overall nucleation behavior

Case study for model validation : assessing a model for thermal decomposition of polyurethane foam.

A case study is reported to document the details of a validation process to assess the accuracy of a mathematical model to represent experiments involving thermal decomposition of polyurethane foam. The focus of the report is to work through a validation process. The process addresses the following activities. The intended application of mathematical model is discussed to better understand the pertinent parameter space. The parameter space of the validation experiments is mapped to the application parameter space. The mathematical models, computer code to solve the models and its (code) verification are presented. Experimental data from two activities are used to validate mathematical models. The first experiment assesses the chemistry model alone and the second experiment assesses the model of coupled chemistry, conduction, and enclosure radiation. The model results of both experimental activities are summarized and uncertainty of the model to represent each experimental activity is estimated. The comparison between the experiment data and model results is quantified with various metrics. After addressing these activities, an assessment of the process for the case study is given. Weaknesses in the process are discussed and lessons learned are summarized

CPUF - a chemical-structure-based polyurethane foam decomposition and foam response model.

A Chemical-structure-based PolyUrethane Foam (CPUF) decomposition model has been developed to predict the fire-induced response of rigid, closed-cell polyurethane foam-filled systems. The model, developed for the B-61 and W-80 fireset foam, is based on a cascade of bondbreaking reactions that produce CO2. Percolation theory is used to dynamically quantify polymer fragment populations of the thermally degrading foam. The partition between condensed-phase polymer fragments and gas-phase polymer fragments (i.e. vapor-liquid split) was determined using a vapor-liquid equilibrium model. The CPUF decomposition model was implemented into the finite element (FE) heat conduction codes COYOTE and CALORE, which support chemical kinetics and enclosure radiation. Elements were removed from the computational domain when the calculated solid mass fractions within the individual finite element decrease below a set criterion. Element removal, referred to as ?element death,? creates a radiation enclosure (assumed to be non-participating) as well as a decomposition front, which separates the condensed-phase encapsulant from the gas-filled enclosure. All of the chemistry parameters as well as thermophysical properties for the CPUF model were obtained from small-scale laboratory experiments. The CPUF model was evaluated by comparing predictions to measurements. The validation experiments included several thermogravimetric experiments at pressures ranging from ambient pressure to 30 bars. Larger, component-scale experiments were also used to validate the foam response model. The effects of heat flux, bulk density, orientation, embedded components, confinement and pressure were measured and compared to model predictions. Uncertainties in the model results were evaluated using a mean value approach. The measured mass loss in the TGA experiments and the measured location of the decomposition front were within the 95% prediction limit determined using the CPUF model for all of the experiments where the decomposition gases were vented sufficiently. The CPUF model results were not as good for the partially confined radiant heat experiments where the vent area was regulated to maintain pressure. Liquefaction and flow effects, which are not considered in the CPUF model, become important when the decomposition gases are confined

Sensitivity Analysis and Uncertainty Propagation in a General-Purpose Thermal Analysis Code

Methods are discussed for computing the sensitivity of field variables to changes in material properties and initial/boundary condition parameters for heat transfer problems. The method we focus on is termed the ''Sensitivity Equation Method'' (SEM). It involves deriving field equations for sensitivity coefficients by differentiating the original field equations with respect to the parameters of interest and numerically solving the resulting sensitivity field equations. Uncertainty in the model parameters are then propagated through the computational model using results derived from first-order perturbation theory; this technique is identical to the methodology typically used to propagate experimental uncertainty. Numerical results are presented for the design of an experiment to estimate the thermal conductivity of stainless steel using transient temperature measurements made on prototypical hardware of a companion contact conductance experiment. Comments are made relative to extending the SEM to conjugate heat transfer problems

Data for Crystallisation of a Homologous Series of Single and Mixed n-Alkanes (C16 – C23) from Representative Hydrocarbon Fuel Solvents

The data presented in this article relates to the crystallisation of 8 single n-alkanes, C16H34 – C23H48 in representative diesel solvents dodecane and toluene, as well as a mixture of these 8-alkanes with a composition representative of real diesel fuel in the same solvents. For the single alkane systems, the data was collected over a range of 5 concentrations ranging from 0.09 – 0.311xi, depending upon the system, and 4 concentrations for the 8-alkane mixture, 0.1 – 0.5 xi. Raw average crystallisation and dissolution points as a function of cooling rate (q) from a polythermal methodology are presented. Along with the equilibrium crystallisation and dissolution temperatures, van’t Hoff fitting parameters, relative critical undercooling (uc) values as a function of q as well as the calculated values of KG and αdet