Siddharth Thakur

Computational techniques for complex transport phenomena

1. Introduction 2. Numerical scheme for treating convection and pressure 3. Computational acceleration with parallel computing and multigrid methods 4. Multiblock methods 5. Two-equation turbulence models with non-equilibrium, rotation, and compressibility effects 6. Volume-averaged macroscopic transport equations 7. Practical applications References Index.

Second-order upwind and central difference schemes for recirculating flow computation

Two-dimensional driven cavity flows with the Reynolds number ranging from 102 to 3.2 x 10 3 are used to assess the performance of second-order upwind and central difference schemes for the convection terms. Three different implementations of the second-order upwind scheme are designed and tested in the context of the SIMPLE algorithm, with the grid size varying from 21 x 21 to 161 x 161 uniformly spaced nodes. Converged solutions are obtained for all Reynolds numbers. Although these different implementations of the second-order upwind scheme have the same formal order of accuracy, significant differences in numerical accuracy are observed. It is demonstrated that better performance can be obtained for the second-order upwind scheme if the discretization is cast in accordance with the finite volume formulation. Although both the second-order upwind and central difference schemes exhibit no oscillations in the solution, the upwind scheme is more accurate. In assessing and comparing the performance of these schemes, the distribution of cell Reynolds number is discussed and its impact on numerical accuracy illustrated.

Some implementational issues of convection schemes for finite-volume formulations

Abstract Two higher-order upwind schemes—second-order upwind and QUICK—are examined in terms of their interpretation, implementations, as well as performance for a recirculating flow in a lid-driven cavity, in the context of a control-volume formulation using the SIMPLE algorithm. The present formulation of these schemes is based on a unified framework wherein the first-order upwind scheme is chosen as the basis, with the remaining terms being assigned to the source term. The performance of these schemes is contrasted with the first-order upwind and second-order central difference schemes. Also addressed in this study is the issue of boundary treatment associated with these higher-order upwind schemes. Two different boundary treatments—one that uses a two-point scheme consistently within a given control volume at the boundary, and the other that maintains consistency of flux across the interior face between the adjacent control volumes—are formulated and evaluated.

Modeling of Fluid Dynamics and Heat Transfer Induced by Dielectric Barrier Plasma Actuator

Glow discharge at atmospheric pressure using a dielectric barrier discharge can inducefluid flow, and can be used for active control of aerodynamics and heat transfer. In thepresent work, a modeling framework is presented to study the evolution and interaction ofsuch athermal nonequilibrium plasma discharges in conjunction with low Mach numberfluid dynamics and heat transfer. The model is self-consistent, coupling the first-principles-based discharge dynamics with the fluid dynamics and heat transfer equations.Under atmospheric pressure, the discharge can be simulated using a plasma–fluid insteadof a kinetic model. The plasma and fluid species are treated as a two-fluid system coupledthrough force and pressure interactions, over decades of length and time scales. Themultiple-scale processes such as convection, diffusion, and reaction/ionization mecha-nisms make the transport equations of the plasma dynamics stiff. To handle the stiffness,a finite-volume operator-split algorithm capable of conserving space charge is employed.A body force treatment is devised to link the plasma dynamics and thermo-fluid dynamics.The potential of the actuator for flow control and thermal management is illustratedusing case studies.

Development of pressure-based composite multigrid methods for complex fluid flows

Abstract Progress in the development of a multiblock, multigrid algorithm, and a critical assessment of the κ-e two-equation turbulent model for solving fluid flows in complex geometries is presented. The basic methodology employed is a unified pressure-based method for both incompressible and compressible flows, along with a TVD-based controlled variation scheme (CVS), which uses a second-order flux estimation bounded by flux limiters.Performance of the CVS is assessed in terms of its accuracy and convergence properties for laminar and turbulent recirculating flows as well as compressible flows containing shocks. Several other conventional schemes are also employed, including the first-order upwind, central difference, hybrid, second-order upwind and QUICK schemes. For better control over grid quality and to obtain accurate solutions for complex flow domains, a multiblock procedure is desirable and often a must.Here, a a composite grid algorithm utilizing patched (abutting) grids is discussed and a conservative flux treatment for interfaces between blocks is presented.A full approximation storage-full multigrid (FAS-FMG) algorithm that is incorporated in the flow solver for increasing the efficiency of the computation is also described. For turbulent flows, implementation of the κ-e two-equation model and in particular the wall functions at solid boundaries is also detailed.In addition, different modifications to the basic k-e model, which take the non-equilibrium between the production and dissipation of κ and e and rotational effects into account, have also been assessed.Selected test cases are used to demonstrate the robustness of the solver in terms of the convection schemes, the multiblock interface treatment, the multigrid speedup and the turbulence models.

A COMPUTATIONAL AND EXPERIMENTAL INVESTIGATION OF TURBULENT JET AND CROSSFLOW INTERACTION

The flowfield induced by a single circular jet exhausting perpendicularly from a flat plate into a crossflow has been investigated numerically. The flow regime investigated corresponds to that encountered in a modern gas-turbine combustor. Reynolds-averaged solutions were obtained using a pressure-based Navier-Stokes solver. The standard k -epsilon turbulence model with and without nonequilibrium modification was employed. Two different momentum flux ratios, J, between the jet and the free stream are investigated, namely, J = 34.2 and J = 42.2. To aid the evaluation of the computational capability, experimental information also has been obtained, including mean and root-mean-square (RMS) velocity distributions downstream of the jet, and the detailed velocity profile at the jet exit. An evaluation of the different convection schemes reveals that the second-order upwind scheme does a noticeably better job than the first-order scheme to predict the velocity profile at the jet exit while predicting less mixin...The flowfield induced by a single circular jet exhausting perpendicularly from a flat plate into a crossflow has been investigated numerically. The flow regime investigated corresponds to that encountered in a modern gas-turbine combustor. Reynolds-averaged solutions were obtained using a pressure-based Navier-Stokes solver. The standard k -epsilon turbulence model with and without nonequilibrium modification was employed. Two different momentum flux ratios, J, between the jet and the free stream are investigated, namely, J = 34.2 and J = 42.2. To aid the evaluation of the computational capability, experimental information also has been obtained, including mean and root-mean-square (RMS) velocity distributions downstream of the jet, and the detailed velocity profile at the jet exit. An evaluation of the different convection schemes reveals that the second-order upwind scheme does a noticeably better job than the first-order scheme to predict the velocity profile at the jet exit while predicting less mixing than the experimental measurement during the jet and free stream interaction. It appears that turbulence modeling primarily is responsible for the deficiency the accounting for the physics of the jet and free stream interaction.

Validation of a New Parallel All-Speed CFD Code in a Rule-Based Framework for Multidisciplinary Applications

This paper focuses on the validation of a new all-speed Computational Fluid Dynamics (CFD) code called LociSTREAM. This computational package is not just another CFD solver; rather, it integrates proven numerical methods and state-of-the-art physical models to compute all-speed flows using generalized grids in a novel rule-based programming framework called Loci which allows: (a) seamless integration of multidisciplinary physics in a unified manner, and (b) automatic handling of massively parallel computing. The objective is to be able to routinely simulate problems involving complex geometries requiring large unstructured grids with arbitrary polyhedral cells and complex multidisciplinary physics. As a first step towards achieving this objective, a wide range of model test cases are studied here, including incompressible laminar and turbulent flow cases, inviscid compressible flow cases, compressible turbulent flows with wall heat transfer as well as internal turbulent flows in 3D geometries and unsteady computations. Comparison of the code with experimental and prior benchmark numerical results is done to validate the robustness of the code for flows ranging from incompressible to supersonic regimes. A scalability analysis is performed as well to study the efficiency of parallelization.

Large Eddy Simulation of Shear Coaxial Rocket Injector: Real Fluid Effects

The implementation and verification of real-fluid effects towards the high-fidelity large eddy simulation of rocket combustors is reported. The non-ideal fluid behavior is modeled using a cubic Peng-Robinson equation of state; a thermodynamically consistent approach is used to convert conserved into primitive variables. The viscosity is estimated by Chung et al.’s method in the supercritical gas phase. In the transcritical liquid phase, a simple, accurate and efficient method to estimate the viscosity as a function of temperature and pressure is proposed. The highly non-linear coupling of the primitive thermodynamic variables requires special consideration in regions of high-density gradients to avoid spurious numerical oscillations. The characterization of the non-linearity of the equation of state identifies the regions of high sensitivity. In these regions, small relative changes in the pressure lead to significant changes in density and/or temperature, therefore, numerical instabilities tend to be amplified in these regions. To avoid non-physical oscillations, a first-order and second-order essentially non-oscillatory (ENO) schemes are locally applied to the flux computation on the faces identified with a dual-threshold relative density sensor. The evaluation of the sensor and capabilities of the non-oscillatory schemes on canonical test cases are presented. Finally, these schemes are used to model two canonical cases.

CONTROLLED VARIATION SCHEME IN A SEQUENTIAL SOLVER FOR RECIRCULATING FLOWS, PART I: THEORY AND FORMULATION

The formalism of the total variation diminishing (TVD) schemes is utilized to design a convection scheme for incompressible recirculating flows. The scheme has been named the controlled variation scheme (CVS). Even though the CVS does not possess the TVD property for sequential solution algorithms, due to the appearance of source terms, the concept of controlled variation fluxes can be effective in suppressing spurious oscillations that commonly occur in convection-dominated viscous flows, by injecting a nonlinear numerical diffusion, similar to the original TVD schemes, into the central difference scheme. This is demonstrated by using the one-dimensional linear convection-diffusion equation with and without a source term as model problems. The formulation and an efficient implementation of the CVS in a sequential pressure-based solver for incompressible steady-state Navier-Stokes equations is presented in this work. The applications of the CVS for two-dimensional laminar and turbulent flows is presented ...

Turbulence-Chemistry Interaction and Heat Transfer Modeling of H 2 /O 2 Gaseous Injector Flows

Reliable prediction of rocket injector flows introduces significant challenges associated with the complex physics involving recirculation, turbulence, scalar mixing, chemical reactions and wall heat transfer. This work is aimed at assessing the importance of turbulence-chemistry interaction and non-equilibrium effects in experimentally characterized single and multi-element injector flows. By examining the different chemistry models (laminar finite rate, assumed PDF with either flamelet or equilibrium assumption), it was found that for both cases investigated, chemical non- equilibrium is insignificant while substantial turbulence-chemistry interaction is observed. A zonal wall treatment was developed based on a blend of SST low-Re turbulence wall treatment and law- of-the-wall, showing improved predictive capability. A heat flux extraction method was also proposed to estimate heat flux results from adiabatic flamelet model under the consideration that wall heat loss is small compared to the overall energy generated by chemical reactions.