Venkat Raman

Development of a dynamic model for the subfilter scalar variance using the concept of optimal estimators

The concept of optimal estimators, recently introduced by Moreau et al. [Phys. Fluids 18, 1 (2006)] is used as an a priori tool to discuss the accuracy of subfilter models. Placed in the framework of large-eddy simulation of combustion problems, this work focuses on the subfilter models used to evaluate the subfilter variance of a conserved scalar, the mixture fraction. The a priori tests are performed using 5123 direct numerical simulation data of forced homogeneous isotropic turbulence. First, the performance of the most commonly used models for the subfilter variance is studied. Using optimal estimators, the Smagorinsky-type model [Pierce and Moin, Phys. Fluids 10, 3041 (1998)] is shown to have the best set of parameters. However, the conventional dynamic formulation of the model leads to large errors in the variance prediction. It was found that assumptions used in the model formulation are not verified. A new dynamic procedure based on a Taylor series expansion is then proposed to improve the predict...

Numerical errors in the computation of subfilter scalar variance in large eddy simulations

Subfilter scalar variance is a key quantity for scalar mixing at the small scales of a turbulent flow and thus plays a crucial role in large eddy simulation of combustion. While prior studies have mainly focused on the physical aspects of modeling subfilter variance, the current work discusses variance models in conjunction with the numerical errors due to their implementation using finite-difference methods. A priori tests on data from direct numerical simulation of homogeneous turbulence are performed to evaluate the numerical implications of specific model forms. Like other subfilter quantities, such as kinetic energy, subfilter variance can be modeled according to one of two general methodologies. In the first of these, an algebraic equation relating the variance to gradients of the filtered scalar field is coupled with a dynamic procedure for coefficient estimation. Although finite-difference methods substantially underpredict the gradient of the filtered scalar field, the dynamic method is shown to ...

Bayesian analysis of syngas chemistry models

Syngas chemistry modelling is an integral step toward the development of safe and efficient syngas combustors. Although substantial effort has been undertaken to improve the modelling of syngas combustion, models nevertheless fail in regimes important to gas turbine combustors, such as low temperature and high pressure. In order to investigate the capabilities of syngas models, a Bayesian framework for the quantification of uncertainties has been used. This framework, given a set of experimental data, allows for the calibration of model parameters, determination of uncertainty in those parameters, propagation of that uncertainty into simulations, as well as determination of model evidence from a set of candidate syngas models. Here, three syngas combustion models have been calibrated using laminar flame speed measurements from high pressure experiments. After calibration the resulting uncertainty in the parameters is propagated forward into the simulation of laminar flame speeds. The model evidence is then used to compare candidate models for the given set of experimental conditions and results. Additionally, the technique MUM-PCE, an interesting uncertainty minimisation method for kinetics models, has been compared to the Bayesian method for this application to the prediction of syngas laminar flame speeds. This comparison shows the importance of model form error and experimental error representations in the uncertainty quantification context, for these choices significantly affect uncertainty quantification results.

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.

Modeling of the subfilter scalar dissipation rate using the concept of optimal estimators

In this work, modeling of the subfilter scalar dissipation rate is addressed. First, the best set of quantities to write a model is determined using the concept of optimal estimators. This study shows that the best approach is to assume a proportionality between the turbulent time scale and turbulent scalar mixing time scale. It is shown that the turbulent time scale should be defined by the subfilter kinetic energy. To define the coefficient appearing in this model, a dynamic determination based on a global subfilter equilibrium assumption between the dissipation and the production terms leads to the best results.

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

Adjoint-based sensitivity analysis of flames

Simulation of chemically reacting flows using detailed chemistry introduces a large number of chemistry model parameters. While not all significantly affect the target outcomes of a simulation, the parameters that do are not always known a priori. In order to improve simulations for specified target outcomes, termed quantities of interest (QoIs), the sensitivity of these QoIs to the model parameters are needed. However, evaluating the sensitivities is computationally expensive, especially for complex fuels that may involve many parameters. For these simulations, the forward sensitivity method requires the solution of an additional number of governing equations proportional to the number of parameters. Here, an adjoint sensitivity approach is formulated where the computational cost scales as the number of QoIs and not the number of parameters. Specifically, adjoint equations are derived for laminar, incompressible, variable density reacting flow and applied to hydrogen flame simulations. From the solution of the corresponding adjoint equations, sensitivity of the QoIs to chemistry model parameters is calculated. The one-dimensional simulation results show that the adjoint sensitivity results closely match those of forward sensitivity methods, thus providing validation of the adjoint method. The two-dimensional simulation results indicate the most sensitive parameters for two QoIs, flame tip temperature and NOx emission. For these tests, the adjoint method reduces computational expense compared to forward sensitivity methods by a factor proportional to the number of QoIs over the number of parameters, here 2/172. Such savings can be more drastic for cases that involve complex fuels, such as combustion of jet fuel, requiring thousands of chemistry model parameters. Further, this sensitivity information can be used in development of experiments by pointing out which are the critical chemistry model parameters.

Numerical Investigation of Shock-Train Response to Inflow Boundary-Layer Variations

A dataset of normal shock trains in a rectangular cross-section channel has been created from direct numerical simulations in an effort to quantify the impact of inflow confinement ratio on the sho...

Experimental and Computational Studies of Mixing in Supersonic Flow

A preliminary combined experimental and computational investigation is conducted on the mixing characteristics of a strut-based hypermixer in a Mach 3 freestream. The hypermixing flow-field is generated by an injection pylon with expansive wedges to enhance the streamwise vorticity. Two different scalar visualization techniques are used to examine the underlying mixing processes. Planar laser scattering of condensed carbon dioxide gas is used to visualize the freestream flow, whereas two-photon planar laser-induced fluorescence (PLIF) of krypton gas is used to mark the injected jet fluid. The experimental results are compared directly to a large-eddy simulation (LES) of the same flow-field. The results obtained are complimentary because the experimental data can aid in the validation of LES models, and the simulations provide information about the thermodynamic property variations that affect the interpretation of the krypton PLIF signal.

RANS models for scalar transport in ablating compressible boundary layers

DNS of a high temperature flow over a modeled ablator surface is used to investigate models for turbulent scalar flux and chemical source term closures. Two different Mach numbers of 0.6 and 1.2 are considered. The ablating surface is described using a 1-D quasisteady model. Results show that the simple gradient diffusion scalar flux model, which uses an isotropic coefficient for the components of the flux, provides a poor match for the DNS scalar flux. Allowing anisotropy in the flux coefficient, as in the generalized gradient diffusion model, provides a much better match. Further, the simple laminar closure for the chemical source term introduces significant errors. The large fluctuations of temperature close to the ablator cause significant fluctuations in the chemical source term.