Randall J. McDermott

A particle formulation for treating differential diffusion in filtered density function methods

We present a new approach for treating molecular diffusion in filtered density function (FDF) methods for modeling turbulent reacting flows. The diffusion term accounts for molecular transport in physical space and molecular mixing in composition space. Conventionally, the FDF is represented by an ensemble of particles and transport is modeled by a random walk in physical space. There are two significant shortcomings in this transport model: (1) the resulting composition variance equation contains a spurious production term and (2) because the random walk is governed by a single diffusion coefficient, the formulation cannot account for differential diffusion, which can have a first-order effect in reacting flows. In our new approach transport is simply modeled by a mean drift in the particle composition equation. The resulting variance equation contains no spurious production term and differential diffusion is treated easily. Hence, the new formulation reduces to a direct numerical simulation (DNS) in the limit of vanishing filter width, a desirable property of any large-eddy simulation (LES) approach. We use the IEM model for mixing. It is shown that there is a lower bound on the specified mixing rate such that the boundedness of the compositions is ensured. We present a numerical method for solving the particle equations which is second-order accurate in space and time, obeys detailed conservation, enforces the realizability and boundedness constraints and is unconditionally stable.

Computational fluid dynamics modelling of fire

An overview of a methodology for simulating fires and other thermally-driven, low-speed flows is presented. The model employs a number of simplifications of the governing equations that allow for relatively fast simulations of practical fire scenarios. The hydrodynamic model consists of the low Mach number large-eddy simulation subgrid closure with either a constant or dynamic coefficient eddy diffusivity. Combustion is typically treated as a mixing-controlled, single-step reaction of fuel and oxygen. The radiation transport equation is written in terms of a spectrally-averaged grey gas. Applications of the model include the design of fire protection systems in buildings and the reconstruction of actual fires.

The parabolic edge reconstruction method (PERM) for Lagrangian particle advection

We describe a Lagrangian particle advection scheme which is intended for use in hybrid finite-volume (FV) large-eddy simulation/filtered density function (LES/FDF) methods for low-Mach flows, but which may also be applicable to unsteady probability density function (PDF) methods, direct numerical simulation (DNS) or any other situation where tracking fluid particles is of concern. A key ingredient of the scheme is a subgrid reconstruction of the filtered velocity field with desirable divergence properties, which is necessary for accurate evolution of the particle number density. We develop reconstructions for 2D and 3D Cartesian staggered non-uniform grids. The reconstructed velocity field is continuous and piecewise parabolic in the velocity-component direction. In the direction normal to the velocity component the reconstruction is piecewise linear. The divergence of the reconstructed field is bilinear in 2D (trilinear in 3D) within a given cell and consistent with the discrete divergence given by the staggered-grid velocities. Though the reconstructed divergence field may be discontinuous from cell to cell, the norm of the differences between the vertex values of the reconstructed divergence for neighboring cells is minimized. As a consequence, the divergence is everywhere zero for the constant-density case. A two-stage Runge-Kutta scheme is employed for advancement of the particle positions. To assess the performance of the scheme we utilize a set of non-trivial velocity test functions which are designed to mimic realistic flow fields. We show that an advection scheme based on the new velocity reconstruction method is effective at maintaining an accurate particle number density in the particle-tracking limit.

Fire-front propagation using the level set method

Propagation of an outdoor fire front in wildland or in a combination of wildland and structural fuels (the so-called wildland-urban interface or WUI fire), can be modelled as an initial-value problem using either a Lagrangian or an Eulerian description. The equations associated with each description are presented, and the methods used to solve the equations are discussed. Some comparisons between the two methods are also made. The emphasis in this report is on the Eulerian equations and on the level-set numerical method. Earlier studies had presented the Lagrangian formulation, and a method-of-lines solution. Advantages of the Eulerian/level-set method are discussed, and several examples that illustrate these advantages are presented.

The ensemble mean limit of the one-dimensional turbulence model and application to residual stress closure in finite volume large-eddy simulation

In order to gain insight into the one-dimensional turbulence (ODT) model of Kerstein [1] as it pertains to residual stress closure in large-eddy simulation (LES), we develop ensemble mean closure (EMC), an algebraic stress closure based on the mappings and time scale physics employed in ODT. To allow analytic determination of the stress the ODT model is simplified, conceptually, such that eddy events act upon a velocity field linearized by the local resolved scale strain. EMC can account for viscous effects, addressing the laminar flow finite eddy viscosity problem without implementation of the dynamic procedure [2]. The algebraic form of the model lends itself to analysis [3] and we are able to derive a theoretical value for the eddy rate constant. This value is a bound on the rate constant for full ODT subgrid closure and yields good results in LES of decaying isotropic turbulence with EMC.

A velocity divergence constraint for large-eddy simulation of low-Mach flows

The velocity divergence (rate of fluid volumetric expansion) is a flow field quantity of fundamental importance in low-Mach flows. It directly affects the local mass density and therefore the local temperature through the equation of state. In this paper, starting from the conservative form of the sensible enthalpy transport equation, we derive a discrete divergence constraint for use in large-eddy simulation (LES) of low-Mach flows. The result accounts for numerical transport of mass and energy, which is difficult to eliminate in relatively coarse, engineering LES calculations when total variation diminishing (TVD) scalar transport schemes are employed. Without the correction terms derived here, unresolved (numerical) mixing of gas species with different heat capacities or molecular weights may lead to erroneous mixture temperatures and ultimately to an imbalance in the energy budget. The new formulation is implemented in a publicly available LES code called the Fire Dynamics Simulator (FDS). Accuracy of the flow solver for transport is demonstrated using the method of manufactured solutions. The conservation properties of the present scheme are demonstrated on two simple energy budget test cases, one involving a small fire in a compartment with natural ventilation and another involving mixing of two gases with different thermal properties.

A Simple Reaction Time Scale for Under-Resolved Fire Dynamics

A reaction time scale model is developed for use in the eddy dissipation concept (fast chemistry limit) closure of the mean chemical source term in large-eddy simulation of fires. The novel aspect of the model is to consider a scaling regime for coarse mesh resolution based on buoyant acceleration. The model computes local time scales for diffusion, turbulent advection, and buoyant acceleration and takes the minimum of these as the local mixing time. The new model is implemented in the Fire Dynamics Simulator (FDS) and tested by comparing flame height predictions to the Heskestad correlation.

An accurate time advancement algorithm for particle tracking

We describe a particle position time advancement algorithm that is designed for use with several subgrid velocity reconstruction schemes used in LES/FDF methods, and potentially in other applications. These reconstruction schemes yield a subgrid velocity field with desirable divergence properties, but also with discontinuities across cell faces. Therefore, a conventional time advancement algorithm, such as second-order Runge-Kutta (RK2), does not perform as well as it does with a smooth velocity field. The algorithm that we describe, called Multi-Step RK2 (MRK2), builds upon RK2 by breaking up the time step into two or more substeps whenever a particle crosses one or more velocity discontinuities. When used in conjunction with the parabolic edge reconstruction method, MRK2 performs considerably better than RK2: both the final position of an advected particle, and the final area of a 2D infinitesimal area element are second-order accurate in time (as opposed to first-order accurate for RK2). Furthermore, MRK2 has the theoretical advantage that it better preserves the continuity of the mapping between initial and final particle positions.

Modeling flame extinction and reignition in large eddy simulations with fast chemistry

This work seeks to support the validation of large eddy simulation models used to simulate fire suppression. The emphasis in the present study is on the prediction of flame extinction and the prevention of spurious reignition using a fast chemistry, mixing-controlled combustion model applicable to realistic fire scenarios of engineering interest. The configuration provides a buoyant, turbulent methane diffusion flame within a controlled co-flowing oxidizer. The oxidizer allows for the supply of a mixture of air and nitrogen, including conditions for which oxygen-dilution in the oxidizer leads to flame extinction. Measurements to support model validation include local profiles of thermocouple temperature and oxygen mole fraction, global combustion efficiency, and the limiting oxygen index. The present study evaluates the performance of critical-flame-temperature-based extinction and reignition models using the Fire Dynamics Simulator, an open-source fire dynamics solver. Alternate model cases are explored, each offering a unique treatment of extinction and reignition. Comparisons between simulated results and experimental measurements are used to evaluate the capability of these models to accurately describe flame extinction. Of the considered cases, those that include provisions to prevent spurious reignition show excellent agreement with measured data, whereas a baseline case lacking explicit reignition treatment fails to predict extinction.

Proceedings of the first workshop organized by the IAFSS Working Group on Measurement and Computation of Fire Phenomena (MaCFP)

This paper provides a report of the discussions held at the first workshop on Measurement and Computation of Fire Phenomena (MaCFP) on June 10-11 2017. The first MaCFP work-shop was both a technical meeting for the gas phase subgroup and a planning meeting for the condensed phase subgroup. The gas phase subgroup reported on a first suite of experimental- computational comparisons corresponding to an initial list of target experiments. The initial list of target experiments identifies a series of benchmark configurations with databases deemed suitable for validation of fire models based on a Computational Fluid Dynamics approach. The simulations presented at the first MaCFP workshop feature fine grid resolution at the millimeter- or centimeter- scale: these simulations allow an evaluation of the performance of fire models under high-resolution conditions in which the impact of numerical errors is reduced and many of the discrepancies between experimental data and computational results may be attributed to modeling errors. The experimental-computational comparisons are archived on the MaCFP repository [1]. Furthermore, the condensed phase subgroup presented a review of the main issues associated with measurements and modeling of pyrolysis phenomena. Overall, the first workshop provided an illustration of the potential of MaCFP in providing a response to the general need for greater levels of integration and coordination in fire research, and specifically to the particular needs of model validation.