Finite Volume Discrete Ordinate Method Research Articles

Benchmark Test Cases for Non-Gray Radiative Heat Transfer Calculation using FSK Look-Up Table

Three test cases in the categories of homogeneous non-isothermal, non-homogeneous isothermal and non-homogeneous non-isothermal have been developed to validate the two-dimensional interpolation technique for calculation of non-gray radiative heat flux on the walls of the system. The participating gases H 2 O and CO 2 of different mole fractions and temperatures are considered in different zones of the test cases. HITEMP-2010 database has been used to calculate the absorption coefficients of H 2 O and CO 2 at different mole fractions and temperatures. Further, the random variation of absorption coefficients with spectrum has been reordered in smooth monotonically increasing smooth function using full spectrum k-distribution method (FSK). A look-up table is developed for different mole fractions and temperatures of gases H 2 O and CO 2. The calculation of absorption coefficients at thermodynamic states other than look up table has been performed using two dimensional interpolation techniques. The geometry of test cases have been divided into three zones whose conditions on the first and last zones are same as available in look-up table while interpolation is used for the middle zone. The radiative transfer equation is solved numerically by finite volume discrete ordinate method (FVDOM). The results have been compared with FSK method and have been found that interpolation techniques are giving satisfactory results with extremely less computational resource and time.

Radiative heat transfer calculation for mixture of gases using full spectrum k-distribution method

The full spectrum k-distribution method is used to obtain radiative heat flux and divergence of radiative heat flux for two test cases, containing mixture of CO 2 and H 2 O at different concentration and temperature keeping pressure constant. The k-distribution for mixture of gases is obtained from individual gas k-distribution using three different mixing models, viz., superposition, multiplication and hybrid model. Further, the radiative transfer equation (RTE) is solved by the finite volume discrete ordinate method (FVDOM) to obtain the radiative flux and the radiation source term. The results obtained were compared with the FSK from spectral addition and LBL method. The multiplication mixing model provides better accuracy compared to other mixing models considered in the present study.

Large-eddy simulation of wind-driven flame in the atmospheric boundary layer

The interaction between the natural ambient winds found in the atmospheric boundary layer (ABL) and buoyant flames is crucial in broad applications in the scientific and engineering fields. Unlike the buoyancy-driven pool fires in still air that have been studied extensively, the complexity of physics changes significantly in wind presence. This study aims at analysing the characteristics of boundary-layer turbulence in the presence of large fires. The eddy dissipation concept, finite volume discrete ordinate method, and one k-equation model are used for combustion, thermal radiation, and sub-grid scale closure using the Large-Eddy Simulation (LES), respectively. A numerical model on simple cases is validated first to assess its capability to reproduce available experimental observations for a purely buoyant fire in still air. A forced-flow boundary layer combustion in a small chamber with a smooth inflow is further considered. In general, good agreement between the simulation results and available experimental data was achieved for temperature and velocity profiles. The unsteady inflow condition used to consider incoming atmospheric turbulence is generated through a precursor simulation. The wind interaction with the line fire changes the atmospheric boundary layer profile affecting the heat transfer ahead of the flame, thereby creating counter-rotating structures downstream. It is shown that the buoyancy-dominated flow due to the flame reaction induced local pressure variation and perturbed shear flow near the ground, thereby altering the wind speed through which the plume rises. Richardson number was also used as a dominant non-dimensional group to analyse the variation of enhanced flow vertical velocity with distance from the fire source. Thus, it is understood that the pronounced longitudinal shear spreading at the surface affects the behaviour of short term or puff releases, suggesting the shedding of small eddies during the combustion process.

Numerical and experimental study of cedar façade fire

SummaryThis article presents a large eddy simulation and experimental study of cedar façade behavior exposed to a 900 kW window spilled flame. The experiments used for validation were carried out in the Building Research of Institute of Japan in Tsukuba according to JIS A 1310 method. The compartment fire was modeled by using the modified eddy dissipation model with a diffusion mixing time scale for the near wall laminar region of combustion model, oneEqEddy model of turbulence model, pyrolysis chemistry mode of pyrolysis model, and finite volume discrete ordinates method of radiation model. The fire flame is treated as optically thin, and a fixed radiant fraction 0.35 is used to calculate the radiation source term. The pyrolysis model of cedar was modeled and optimized according to the results of fire propagation apparatus test. The influence of cedar parameters on time‐to‐pHRR (peak HRR), pHRR, and (total heat release rate) THR curves of facade fire were clarified by a series of simulation varying from thermal density, conductivity, heat capacity, and pyrolysis reaction parameters. It indicates the simulation results show a reasonable good quantitative agreement with experimental measurements. The activation energy of cedar pyrolysis shows a great influence on the time‐to‐pHRR, low pHRR, and THR of cedar facade.

McrtFOAM: A mesh-agglomeration Monte Carlo ray-tracing solver for radiative transfer in gray semitransparent solids

Monte Carlo ray-tracing method has become a promising technique for solving radiative transfer. However, large memory footprint or long CPU time hampers its further utilization. In this work, a Monte Carlo ray-tracing method radiation solver called mcrtFOAM is developed in the framework of open source CFD toolbox OpenFOAM. The radiative source term is calculated based on the radiation distribution factor to avoid repeated ray tracing. In addition, a mesh-agglomeration technique is used to overcome the problem of memory catastrophe for storing a huge radiation distribution factor matrix caused by a large number of mesh elements. The key principle is to agglomerate the refined mesh elements to the coarse ones, and the calculation of radiation distribution factor as well as radiative source term is carried out in the coarse mesh, while the procedure of ray tracing as well as solving the heat conduction is performed in the refined mesh. After validation of the algorithm code within a cubic enclosure, a coupled conductive–radiative heat transfer problem within a cylindrical enclosure filled with gray semitransparent solids is also tested. To test the present solver in realistic industrial systems, a coupled conductive–radiative heat transfer within a tomographic porous structure with gray surfaces is further investigated. All results are compared with previous studies and the solutions by the Finite Volume Discrete Ordinate Method (FVDOM) in OpenFOAM, and they all show great satisfaction. When the mcrtFOAM solver is used for solving the radiative transfer equation, it is found that the CPU time and the memory footprint consumed by the present mcrtFOAM solver with mesh-agglomeration technique are far less than that without this technique. Convincing first implementation exercises indicate that both significant memory and CPU benefits can be expected for configurations of industrial interest These findings will contribute greatly to achieve the calculation of coupled heat transfer involving radiation within large number of mesh elements.

Effectively modeling surface temperature and evaluating mean radiant temperature in tropical outdoor industrial environments

Radiant heat gain severely endangers thermal comfort and dramatically increases building energy consumptions in a tropical outdoor urban environment. To rapidly evaluate outdoor thermal features, this paper presents a three-dimensional integrated numerical model to assess building surface temperature and mean radiant temperature (MRT) in typical outdoor industrial environments of Singapore. For proper accounting of solar irradiance and radiant heat fluxes, Perez all-weather model and finite volume discrete ordinates method (fvDOM) are integrated into numerical code. Under the climate conditions of Singapore, i.e., light wind and intense solar irradiance, the model adopts a daily-average convection coefficient to simplify air dynamics to solve the surface energy balance equation so that the model efficiency can be significantly improved. Surface thermal load computed using the model has been validated by the on-site measurement for a contemporary and a matured industrial building on two sunny days. By comparing simulated and measured results, the corresponding coefficient of determination (R2) and the refined index of agreement (RIA) are respectively > 0.99 and > 0.8 to indicate that the model agrees well with the measurement. Also, the model is used to predict the MRT map around the industrial environment and to demonstrate that tree shading reduces mean MRT of 6.3 °C for daily-average and 13.29 °C at noon in a street canyon under a 25% greenery coverage ratio.

Analysis of radiation heat transfer and temperature distributions of solar thermochemical reactor for syngas production

This paper investigated radiation heat transfer and temperature distributions of solar thermochemical reactor for syngas production using the finite volume discrete ordinate method (fvDOM) and P1 approximation for radiation heat transfer. Different parameters including absorptivity, emissivity, reflection based radiation scattering, and carrier gas flow inlet velocity that would greatly affect the reactor thermal performance were sufficiently investigated. The fvDOM approximation was used to obtain the radiation intensity distribution along the reactor. The drop in the temperature resulted from the radiation scattering was further investigated using the P1 approximation. The results indicated that the reactor temperature difference between the P1 approximation and the fvDOM radiation model was very close under different operating conditions. However, a big temperature difference which increased with an increase in the radiation emissivity due to the thermal non-equilibrium was observed in the radiation inlet region. It was found that the incident radiation flux distribution had a strong impact on the temperature distribution throughout the reactor. This paper revealed that the temperature drop caused by the boundary radiation heat loss should not be neglected for the thermal performance analysis of solar thermochemical reactor.

Assessment of the capabilities of FireFOAM to model large-scale fires in a well-confined and mechanically ventilated multi-compartment structure

This article presents a large eddy simulation study of a pool fire in a well-confined and mechanically ventilated multi-room configuration. The capabilities of FireFOAM are assessed by comparing the numerical results to a well-documented set of experimental data available from Propagation d’un Incendie pour des Scénarios Multi-locaux Elémentaires. The eddy dissipation concept, finite volume discrete ordinate method, and one k-equation model are used for combustion, thermal radiation, and sub-grid scale closure, respectively. The main boundary conditions are imposed based on the experimental profiles. A detailed comparison is made with available experimental data. Good agreement between the large eddy simulation results and experimental values is achieved for temperatures, velocity, CO2 volume concentrations, and pressures for most compartments. There are some noticeable underpredictions of temperature in the outlet room. Overall, FireFOAM is shown to have good predictive capabilities for the present confined large-scale fire scenario.

PMMA壁面の上方向への燃え拡がりのLarge eddy simulation

A fully coupled fluid-solid approach for flame spread simulations has been developed using FireFOAM. Radiative heat transfer and soot treatment are fully coupled with the pyrolysis calculations. For gaseous combustion, the newly extended eddy dissipation concept (EDC) for the large eddy simulation (LES) is used. Due to low Reynolds number, the laminar combustion model based on viscous diffusion is presented and coupled with the EDC model. The soot model is based on the laminar smoke point concept recently extended to turbulent fires using the partially stirred reactor (PaSR) concept. For radiation, the finite volume discrete ordinate method (FVDOM) is used with the gaseous absorption coefficients evaluated using the polynomial coefficient of temperature. In the solid region, one dimensional diffusion equation for sensible enthalpy is solved. The effect of in-depth radiation is taken into account using the relatively simple formation according to Beer's law. The Arrhenius type pyrolysis model developed by FM Global is used along with their measurements of the PMMA physical properties as input data. The validation study has been conducted with the published experiment. The predictions are in very good agreement with the relevant experimental data, demonstrating that the present modelling approach can be used to predict upward flame spread over PMMA with reasonable accuracy. Such a fully coupled predictive tool can be used to aid fundamental studies of the flame spread phenomena such as investigating the effects of width, inclination angles and side walls on flame spread.

Comparison of accuracy and computational expense of radiation models in simulation of non-premixed turbulent jet flames

The accuracy and computational expense of various radiation models in the simulation of turbulent jet flames are compared. Both nonluminous and luminous methane–air nonpremixed turbulent jet flames are simulated using a comprehensive combustion solver. The combustion solver consists of a finite-volume/probability density function-based flow–chemistry solver interfaced with a high-accuracy spectral radiation solver. Flame simulations were performed using various k-distribution-based spectral models and radiative transfer equation (RTE) solvers, such as P-1, P-3, finite volume/discrete ordinates method (FVM/DOM), and line-by-line (LBL) accurate Photon Monte Carlo (PMC) methods, with and without consideration of turbulence–radiation interaction (TRI). Various spectral models and RTE solvers are observed to have strong effects on peak flame temperature, total radiant heat source and NO emission. The P-1 method is found to be the computationally least expensive RTE solver and the FVM the most expensive for any spectral model. For optically thinner flames all radiation models yield excellent accuracy. For optically thicker flames the P-3 and the FVM with advanced k-distribution methods predict radiation more accurately than the P-1 method with any spectral model when compared to the benchmark LBL PMC. The LBL PMC yields exact results with sufficient number of samples and is found to be less expensive than the FVM (for all spectral models) and the P-3 (for some spectral models) in statistically stationary combustion simulations. TRI is found to drop the peak temperature by close to 150K for a luminous flame (optically thicker) and 25–100K for a nonluminous flame (optically thinner).

Large eddy simulation of a turbulent diffusion flame including thermal radiation heat transfer

Experimental data from the literature for a methane flame on a diffuser burner with diameter of 7.1 cm and flow rate of 84.3 mg/s were used to validate the numerical model of FireFOAM, a compressible solver for flame simulation implemented in the CFD package OpenFOAM®. This model employs large eddy simulation for the turbulence modeling and it solves the radiative transfer equation using the finite volume discrete ordinate method. For the methane combustion, the eddy dissipation combustion model with a single-step kinetic equation was employed. The simulations were verified for mesh convergence and spectral analysis was used to verify mesh adequacy for the large eddy simulations. The FireFOAM results were compared to available experimental data and to FDS simulation results for the velocity, mixture fraction, temperature and vorticity fields with good agreement.