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Algebraic Closure
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Enrica Masi – One of the best experts on this subject based on the ideXlab platform.

Algebraic–ClosureBased Moment Method for Unsteady Eulerian Simulations of NonIsothermal ParticleLaden Turbulent Flows at Moderate Stokes Numbers in Dilute Regime
Flow Turbulence and Combustion, 2014CoAuthors: Enrica Masi, Olivier SimoninAbstract:To model unsteady nonisothermal dilute particleladen turbulent flows, an Algebraic–Closurebased moment method (ACBMM) is developed. ACBMM is a Eulerian approach for the dispersed phase conceived to be coupled with direct numerical simulations (DNSs) of the turbulence when an accurate local description of the turbulent mixture is required. It is based on the combination of a conditional probability density function (PDF) approach, which provides local instantaneous Eulerian equations for the loworder moments of the PDF, and appropriate constitutive relations, as Algebraic Closures, which are necessary to close the set of conservation equations. The computed loworder moments are the mesoscopic particle number density, particle velocity and particle temperature and the unclosed higherorder moments are the particle random uncorrelated motion (RUM) stress tensor and the RUM heat flux (RUMHF) which appear in the particle momentum and enthalpy equations, respectively. The RUM stress tensor is closed by an additional transport equation for the trace of the tensor and a polynomial representation for tensor functions modeling its deviatoric part. The polynomial representation is used in the framework of an assumption of equilibrium of the RUM anisotropy and leads to an explicit Algebraic stress model (2ΦEASM). Similarly, the RUMHF is modeled assuming equilibrium of the scaled heat flux and explicit selfconsistent solutions (2ΦEAHFM) are found by analogy with turbulent heat flux models. As 2ΦEAHFM entails the computation of the RUM temperature variance, an additional transport equation is developed for it. By means of an a priori analysis, the Algebraic Closures developed by the present study are assessed against actual particle Eulerian fields which are extracted from particle Lagrangian simulations coupled with DNS of a temporal nonisothermal particleladen turbulent planar jet, for various Stokes numbers. Results show that both 2ΦEASM and 2ΦEAHFM are successful in reproducing the unclosed moments up to moderate turbulentmacroscale Stokes numbers allowing the ACBMM to accurately predict the unsteady nonisothermal dispersed phase.

Development of an Algebraic–Closurebased moment method for unsteady Eulerian simulations of particleladen turbulent flows in very dilute regime
International Journal of Multiphase Flow, 2014CoAuthors: Enrica Masi, Olivier Simonin, E. Riber, P. Sierra, L.y.m. GicquelAbstract:International audienceAn Algebraic–Closurebased moment method (ACBMM) is developed for unsteady Eulerian particle simulations, coupled with direct numerical simulations (DNSs) of fluid turbulent flows, in very dilute regime and up to large Stokes numbers StK (based on the Kolmogorov timescale) or moderate Stokes numbers St (based on the turbulent macroscale seen by the particles). The proposed method is developed in the frame of a conditional statistical approach which provides a local and instantaneous characterization of the dispersedphase dynamic accounting for the effect of crossing between particle trajectories which becomes substantial for StK > 1. The computed Eulerian quantities are loworder moments of the conditional probability density function (PDF) and the corresponding governing equations are derived from the PDF kinetic equation in the general frame of the kinetic theory of gases. At the first order, the computation of the mesoscopic particle number density and velocity requires the modeling of the secondorder moment tensor appearing in the particle momentum equation and referred to as random uncorrelated motion (RUM) particle kinetic stress tensor. The current work proposes a variety of different Algebraic Closures for the deviatoric part of the tensor. An evaluation of some effective propositions is given by performing an a priori analysis using particle Eulerian fields which are extracted from particle Lagrangian simulations coupled with DNS of a temporal particleladen turbulent planar jet. Several millionparticle simulations are analyzed in order to assess the models for various Stokes numbers. It is apparent that the most fruitful are explicit Algebraic stress models (2UEASM) which are based on an equilibrium assumption of RUM anisotropy for which explicit solutions are provided by means of a polynomial representation for tensor functions. These models compare very well with EulerianLagrangian DNSs and properly represent all crucial trends extracted from such simulations

Development of an Algebraic–Closurebased moment method for unsteady Eulerian simulations of particleladen turbulent flows in very dilute regime
International Journal of Multiphase Flow, 2014CoAuthors: Enrica Masi, Olivier Simonin, E. Riber, Patricia Sierra Sanchez, L.y.m. GicquelAbstract:An Algebraic–Closurebased moment method (ACBMM) is developed for unsteady Eulerian particle simulations, coupled with direct numerical simulations (DNSs) of fluid turbulent flows, in very dilute regime and up to large Stokes numbers StK (based on the Kolmogorov timescale) or moderate Stokes numbers St (based on the turbulent macroscale seen by the particles). The proposed method is developed in the frame of a conditional statistical approach which provides a local and instantaneous characterization of the dispersedphase dynamic accounting for the effect of crossing between particle trajectories which becomes substantial for StK > 1. The computed Eulerian quantities are loworder moments of the conditional probability density function (PDF) and the corresponding governing equations are derived from the PDF kinetic equation in the general frame of the kinetic theory of gases. At the first order, the computation of the mesoscopic particle number density and velocity requires the modeling of the secondorder moment tensor appearing in the particle momentum equation and referred to as random uncorrelated motion (RUM) particle kinetic stress tensor. The current work proposes a variety of different Algebraic Closures for the deviatoric part of the tensor. An evaluation of some effective propositions is given by performing an a priori analysis using particle Eulerian fields which are extracted from particle Lagrangian simulations coupled with DNS of a temporal particleladen turbulent planar jet. Several millionparticle simulations are analyzed in order to assess the models for various Stokes numbers. It is apparent that the most fruitful are explicit Algebraic stress models (2UEASM) which are based on an equilibrium assumption of RUM anisotropy for which explicit solutions are provided by means of a polynomial representation for tensor functions. These models compare very well with EulerianLagrangian DNSs and properly represent all crucial trends extracted from such simulations.
Olivier Simonin – One of the best experts on this subject based on the ideXlab platform.

Algebraic–ClosureBased Moment Method for Unsteady Eulerian Simulations of NonIsothermal ParticleLaden Turbulent Flows at Moderate Stokes Numbers in Dilute Regime
Flow Turbulence and Combustion, 2014CoAuthors: Enrica Masi, Olivier SimoninAbstract:To model unsteady nonisothermal dilute particleladen turbulent flows, an Algebraic–Closurebased moment method (ACBMM) is developed. ACBMM is a Eulerian approach for the dispersed phase conceived to be coupled with direct numerical simulations (DNSs) of the turbulence when an accurate local description of the turbulent mixture is required. It is based on the combination of a conditional probability density function (PDF) approach, which provides local instantaneous Eulerian equations for the loworder moments of the PDF, and appropriate constitutive relations, as Algebraic Closures, which are necessary to close the set of conservation equations. The computed loworder moments are the mesoscopic particle number density, particle velocity and particle temperature and the unclosed higherorder moments are the particle random uncorrelated motion (RUM) stress tensor and the RUM heat flux (RUMHF) which appear in the particle momentum and enthalpy equations, respectively. The RUM stress tensor is closed by an additional transport equation for the trace of the tensor and a polynomial representation for tensor functions modeling its deviatoric part. The polynomial representation is used in the framework of an assumption of equilibrium of the RUM anisotropy and leads to an explicit Algebraic stress model (2ΦEASM). Similarly, the RUMHF is modeled assuming equilibrium of the scaled heat flux and explicit selfconsistent solutions (2ΦEAHFM) are found by analogy with turbulent heat flux models. As 2ΦEAHFM entails the computation of the RUM temperature variance, an additional transport equation is developed for it. By means of an a priori analysis, the Algebraic Closures developed by the present study are assessed against actual particle Eulerian fields which are extracted from particle Lagrangian simulations coupled with DNS of a temporal nonisothermal particleladen turbulent planar jet, for various Stokes numbers. Results show that both 2ΦEASM and 2ΦEAHFM are successful in reproducing the unclosed moments up to moderate turbulentmacroscale Stokes numbers allowing the ACBMM to accurately predict the unsteady nonisothermal dispersed phase.

Development of an Algebraic–Closurebased moment method for unsteady Eulerian simulations of particleladen turbulent flows in very dilute regime
International Journal of Multiphase Flow, 2014CoAuthors: Enrica Masi, Olivier Simonin, E. Riber, P. Sierra, L.y.m. GicquelAbstract:International audienceAn Algebraic–Closurebased moment method (ACBMM) is developed for unsteady Eulerian particle simulations, coupled with direct numerical simulations (DNSs) of fluid turbulent flows, in very dilute regime and up to large Stokes numbers StK (based on the Kolmogorov timescale) or moderate Stokes numbers St (based on the turbulent macroscale seen by the particles). The proposed method is developed in the frame of a conditional statistical approach which provides a local and instantaneous characterization of the dispersedphase dynamic accounting for the effect of crossing between particle trajectories which becomes substantial for StK > 1. The computed Eulerian quantities are loworder moments of the conditional probability density function (PDF) and the corresponding governing equations are derived from the PDF kinetic equation in the general frame of the kinetic theory of gases. At the first order, the computation of the mesoscopic particle number density and velocity requires the modeling of the secondorder moment tensor appearing in the particle momentum equation and referred to as random uncorrelated motion (RUM) particle kinetic stress tensor. The current work proposes a variety of different Algebraic Closures for the deviatoric part of the tensor. An evaluation of some effective propositions is given by performing an a priori analysis using particle Eulerian fields which are extracted from particle Lagrangian simulations coupled with DNS of a temporal particleladen turbulent planar jet. Several millionparticle simulations are analyzed in order to assess the models for various Stokes numbers. It is apparent that the most fruitful are explicit Algebraic stress models (2UEASM) which are based on an equilibrium assumption of RUM anisotropy for which explicit solutions are provided by means of a polynomial representation for tensor functions. These models compare very well with EulerianLagrangian DNSs and properly represent all crucial trends extracted from such simulations

Development of an Algebraic–Closurebased moment method for unsteady Eulerian simulations of particleladen turbulent flows in very dilute regime
International Journal of Multiphase Flow, 2014CoAuthors: Enrica Masi, Olivier Simonin, E. Riber, Patricia Sierra Sanchez, L.y.m. GicquelAbstract:An Algebraic–Closurebased moment method (ACBMM) is developed for unsteady Eulerian particle simulations, coupled with direct numerical simulations (DNSs) of fluid turbulent flows, in very dilute regime and up to large Stokes numbers StK (based on the Kolmogorov timescale) or moderate Stokes numbers St (based on the turbulent macroscale seen by the particles). The proposed method is developed in the frame of a conditional statistical approach which provides a local and instantaneous characterization of the dispersedphase dynamic accounting for the effect of crossing between particle trajectories which becomes substantial for StK > 1. The computed Eulerian quantities are loworder moments of the conditional probability density function (PDF) and the corresponding governing equations are derived from the PDF kinetic equation in the general frame of the kinetic theory of gases. At the first order, the computation of the mesoscopic particle number density and velocity requires the modeling of the secondorder moment tensor appearing in the particle momentum equation and referred to as random uncorrelated motion (RUM) particle kinetic stress tensor. The current work proposes a variety of different Algebraic Closures for the deviatoric part of the tensor. An evaluation of some effective propositions is given by performing an a priori analysis using particle Eulerian fields which are extracted from particle Lagrangian simulations coupled with DNS of a temporal particleladen turbulent planar jet. Several millionparticle simulations are analyzed in order to assess the models for various Stokes numbers. It is apparent that the most fruitful are explicit Algebraic stress models (2UEASM) which are based on an equilibrium assumption of RUM anisotropy for which explicit solutions are provided by means of a polynomial representation for tensor functions. These models compare very well with EulerianLagrangian DNSs and properly represent all crucial trends extracted from such simulations.
L.y.m. Gicquel – One of the best experts on this subject based on the ideXlab platform.

Development of an Algebraic–Closurebased moment method for unsteady Eulerian simulations of particleladen turbulent flows in very dilute regime
International Journal of Multiphase Flow, 2014CoAuthors: Enrica Masi, Olivier Simonin, E. Riber, P. Sierra, L.y.m. GicquelAbstract:International audienceAn Algebraic–Closurebased moment method (ACBMM) is developed for unsteady Eulerian particle simulations, coupled with direct numerical simulations (DNSs) of fluid turbulent flows, in very dilute regime and up to large Stokes numbers StK (based on the Kolmogorov timescale) or moderate Stokes numbers St (based on the turbulent macroscale seen by the particles). The proposed method is developed in the frame of a conditional statistical approach which provides a local and instantaneous characterization of the dispersedphase dynamic accounting for the effect of crossing between particle trajectories which becomes substantial for StK > 1. The computed Eulerian quantities are loworder moments of the conditional probability density function (PDF) and the corresponding governing equations are derived from the PDF kinetic equation in the general frame of the kinetic theory of gases. At the first order, the computation of the mesoscopic particle number density and velocity requires the modeling of the secondorder moment tensor appearing in the particle momentum equation and referred to as random uncorrelated motion (RUM) particle kinetic stress tensor. The current work proposes a variety of different Algebraic Closures for the deviatoric part of the tensor. An evaluation of some effective propositions is given by performing an a priori analysis using particle Eulerian fields which are extracted from particle Lagrangian simulations coupled with DNS of a temporal particleladen turbulent planar jet. Several millionparticle simulations are analyzed in order to assess the models for various Stokes numbers. It is apparent that the most fruitful are explicit Algebraic stress models (2UEASM) which are based on an equilibrium assumption of RUM anisotropy for which explicit solutions are provided by means of a polynomial representation for tensor functions. These models compare very well with EulerianLagrangian DNSs and properly represent all crucial trends extracted from such simulations

Development of an Algebraic–Closurebased moment method for unsteady Eulerian simulations of particleladen turbulent flows in very dilute regime
International Journal of Multiphase Flow, 2014CoAuthors: Enrica Masi, Olivier Simonin, E. Riber, Patricia Sierra Sanchez, L.y.m. GicquelAbstract:An Algebraic–Closurebased moment method (ACBMM) is developed for unsteady Eulerian particle simulations, coupled with direct numerical simulations (DNSs) of fluid turbulent flows, in very dilute regime and up to large Stokes numbers StK (based on the Kolmogorov timescale) or moderate Stokes numbers St (based on the turbulent macroscale seen by the particles). The proposed method is developed in the frame of a conditional statistical approach which provides a local and instantaneous characterization of the dispersedphase dynamic accounting for the effect of crossing between particle trajectories which becomes substantial for StK > 1. The computed Eulerian quantities are loworder moments of the conditional probability density function (PDF) and the corresponding governing equations are derived from the PDF kinetic equation in the general frame of the kinetic theory of gases. At the first order, the computation of the mesoscopic particle number density and velocity requires the modeling of the secondorder moment tensor appearing in the particle momentum equation and referred to as random uncorrelated motion (RUM) particle kinetic stress tensor. The current work proposes a variety of different Algebraic Closures for the deviatoric part of the tensor. An evaluation of some effective propositions is given by performing an a priori analysis using particle Eulerian fields which are extracted from particle Lagrangian simulations coupled with DNS of a temporal particleladen turbulent planar jet. Several millionparticle simulations are analyzed in order to assess the models for various Stokes numbers. It is apparent that the most fruitful are explicit Algebraic stress models (2UEASM) which are based on an equilibrium assumption of RUM anisotropy for which explicit solutions are provided by means of a polynomial representation for tensor functions. These models compare very well with EulerianLagrangian DNSs and properly represent all crucial trends extracted from such simulations.