Pratik Donde

A multivariate quadrature based moment method for LES based modeling of supersonic combustion

The transported probability density function (PDF) approach is a powerful technique for large eddy simulation (LES) based modeling of scramjet combustors. In this approach, a high-dimensional transport equation for the joint composition-enthalpy PDF needs to be solved. Quadrature based approaches provide deterministic Eulerian methods for solving the joint-PDF transport equation. In this work, it is first demonstrated that the numerical errors associated with LES require special care in the development of PDF solution algorithms. The direct quadrature method of moments (DQMOM) is one quadrature-based approach developed for supersonic combustion modeling. This approach is shown to generate inconsistent evolution of the scalar moments. Further, gradient-based source terms that appear in the DQMOM transport equations are severely underpredicted in LES leading to artificial mixing of fuel and oxidizer. To overcome these numerical issues, a semi-discrete quadrature method of moments (SeQMOM) is formulated. The performance of the new technique is compared with the DQMOM approach in canonical flow configurations as well as a three-dimensional supersonic cavity stabilized flame configuration. The SeQMOM approach is shown to predict subfilter statistics accurately compared to the DQMOM approach.

Large eddy simulation based studies of reacting and non-reacting transverse jets in supersonic crossflow

Jet in supersonic cross ow (JISC) provide e cient mixing and ame stabilization in supersonic combustion. A LES-DQMOM based comprehensive methodology was developed and calculated sonic jet in Mach 2.0 cross ow with momentum ratio of 0.5, 1.03, and 1.52. JISC con guration were matched to experiment from Air Force Research Laboratory. After careful validation of the code, ow feature of non-reacting and reacting JISC were studied including shock structures and interaction of vortical structures. Turbulence-chemistry interactions are modeled using a DQMOM based combustion model. High temperature region near the wall upstream of the jet and the recirculated ow behind the barrel shock from the jet provided suitable condition of auto-ignition and ame stability.

A multivariate quadrature based moment method for supersonic combustion modeling

The joint probability density function (PDF) of thermochemical variables can be used for accurately computing the combustion source term. Quadrature based methods provide a computationally ecient and robust approach for estimating the PDF. The direct quadrature method of moments (DQMOM) is well suited for multivariate problems like combustion. Numerical implementation of DQMOM however leads to errors in estimating the PDF. In this work, a new quadrature based approach called semi-discrete quadrature method of moments (SeQMOM) that overcomes this problem is developed. A decoupling procedure allows extension of this method to multivariate problems. SeQMOM is then used for studying an experimental Mach 2.2 supersonic cavity based combustor. Development of predictive models for supersonic combustion is a critical step in design and development

Large Eddy Simulation of Supersonic Combustion using Direct Quadrature Method of Moments

Modeling of the reaction source term in large eddy simulations (LES) leads to the combustion modeling problem. In supersonic combustion, typical closures based on conserved scalar approaches cannot be used. Transport of the joint filtered density function (FDF) of the thermochemical composition vector leads to a better prediction of the reaction source term. Direct quadrature method of moments (DQMOM) is an Eulerian method for solving the FDF transport equation. In this work, we show that DQMOM introduces errors in predicting higher moments of scalars, and hence in estimating the reaction source term. We propose a semi-discrete DQMOM approach that overcomes this problem. Moments of a conserved scalar computed using the proposed method agree well with moments predicted by solving the exact moment transport equations.

Supersonic combustion studies using a multivariate quadrature based method for combustion modeling

The joint probability density function (PDF) of thermochemical variables can be used for accurately computing the combustion source term. Quadrature based methods such as the direct quadrature method of moments (DQMOM) provide a computationally ecient and robust approach for estimating the PDF. Numerical implementation of DQMOM can however lead to an erroneous estimation of the PDF. An alternative semi-discrete quadrature method of moments (SeQMOM) was recently developed by the authors. This method solves a linear system of equation for evaluating the PDF, while making sure that moments of the PDF are accurately represented. In this work, SeQMOM is used for studying the eect of various model parameters in an experimental supersonic hydrogen jet. Development of predictive models for supersonic combustion is a critical step in design and development of scramjet engines. In subsonic ows, combustion models are often formulated based on the conserved scalar approach. 1 However, the coupling between the energy and velocity elds in the high-speed ow regime precludes the direct use of low-Mach number mixture fraction based combustion models. One approach to overcome this problem is the transported probability density function (PDF) method. Here, the joint-PDF of the gas phase thermochemical vector is obtained by solving a transport equation. Typically, ow solvers employing the Reynolds-averaged Navier Stokes (RANS) or large eddy simulation (LES) methodology are coupled to a solver that evolves the PDF transport equation. This hybrid PDF approach has been successfully used for a wide range of combustion problems. 2{9 The PDF transport equation is high-dimensional spanning N + 5, where N is the number of species in the chemistry mechanism. Consequently, the usual

Supersonic cavity flame stabilization studies using a multivariate quadrature based moment method

In supersonic combustion, typical closures based on conserved scalar approaches cannot be used. Transport of the joint probability density function (PDF) of the thermochemical composition vector leads to a better prediction of the reaction source term. The quadrature approximation allows us to develop computationally ecient Eulerian moment methods for solving the PDF transport equation. In this work, we use the direct quadrature method of moments (DQMOM) for simulating a supersonic cavity-stabilized ame. Numerical implementation of DQMOM leads to an erroneous evolution of the PDF. We develop an alternate semi-discrete quadrature method of moments (SeQMOM) for multivariate PDFs that overcomes this problem. SeQMOM is further used for simulating turbulent mixing using the Reynolds-averaged Navier Stokes (RANS) formulation.

Large Eddy Simulation/Eulerian Probability Density Function Approach for Simulating Hydrogen-Enriched Gas Turbine Combustors

To describe partially-premixed combustion inside hydrogen-rich combustors, a novel quadrature-based probability density function (PDF) approach is studied here. The PDF approach is comprehensive in describing multiple combustion regimes, and multiple inlet streams. The methodology is implemented in the context of the large eddy simulation (LES) approach. The main bottleneck in utilizing the PDF approach is that the PDF transport equation, which needs to be evolved along with the LES equations, is high-dimensional and intractable using conventional discretization techniques. In order to ensure that the PDF approach is easily transferred to existing industrial flow solvers, a quadrature-based Eulerian method for solving the PDF transport equation is considered here. The corresponding Eulerian equations are implemented in the open source OpenFOAM code using an unstructured grid system. Simulations of an experimental high-pressure combustor demonstrate that the PDF approach significantly changes the reaction structure compared to laminar chemistry assumption.Copyright

Sensitivity analysis for Eulerian PDF methods

The joint probability density function (PDF) of thermochemical variables can be used for accurately computing the combustion source term in turbulent ows. Evolution of the PDF in physical and composition spaces is governed by a transport equation which requires modeling of sub-lter mixing process. Mixing models used in PDF methods are known to have a substantial impact on reactions, and can therefore signiantly inuence ame stabilization in turbulent combustors. A systematic approach is required for studying the eect of variations in the mixing model constant on reactions. The objective of this work is to develop a sensitivity based frame-work to study this problem. The approach presented here is developed in the context of the direct quadrature method of moments (DQMOM), which is an Eulerian method for solving the PDF transport equation. Governing equations for the corresponding dierential sensitivity analysis are formulated and implemented in a practical large eddy simulation (LES) solver. The DQMOM-sensitivity approach is then used for studying an experimental supersonic combustor. Large eddy simulation (LES) has emerged as a potentially accurate tool for the simulation of complex turbulent reacting ows, including internal