Development of Finite Volume Algorithm on Parallel Computer for Prediction of Three-Dimensional Turbulent Compressible Flows

This project aims at developing a general purpose, user-friendly Computer code for numerical prediction of three dimensional, turbulent, compressible flows solving the time-averaged, Navier Stokes equations in body-fitted non-orthogonal coordinate system . A finite volume method [5] has already been developed by the present investigator and others for incompressible flows employing the concept of the Semi-IMplicit Pressure Linked Equations (SIMPLE) of Patankar & Spalding [6], revised for cell-centred variable arrangement and using Cartesian Velocity Components as dependent variables . The same method is proposed to be modified to account for the compressibility effects and hence to achieve a unified aproach for incompressible and compressible flows . Turbulence will be simulated through the Eddy-Viscosity based two equations (K- E) models on which the present investigator has already gained considerable experience [7 - 101 for both 2D & 3D incompressible flows . In order to meet the large Computer storage and CPU demand for real life 3D problems a parallelised version of the code will be generated, compitable to the in-house MK-II FLOSOLVER at NAL for which however the Computer resources and specially the hardware need to be augmented . How to handle irregular flow geometries, modelling turbulence for 3D separated flows and finally the effective utilisation of parallel computers for large CPU and storage-consuming computer codes form the three-major problems to be studied under this research project

Numerical Simulation of Incompressible Turbulent Flow using Linear Eddy Viscosity-based Turbulence Models

The present study focuses on the recent development of an implicit pressure-based finite volume algorithm for numerical solution of Reynolds averaged Navier-Stokes equations (RANS) in an inertial frame of reference for the prediction of unsteady incompressible flow problems. The algorithm uses boundary-conforming, multiblock structured grid with moving boundaries, collocated variable arrangement with momentum equations resolved along cartesian directions, second-order accurate spatial and temporal discretisation schemes for the convective fluxes and a pressure-velocity solution strategy. Effect of turbulence was simulated using appropriate linear eddy viscosity-based turbulence models. The capabilities and limitations of the cost-effective unsteady Reynolds averaged Navier-Stokes (URANS) approach has been demonstrated for few application problems of engineering interest.Defence Science Journal, 2010, 60(6), pp.614-627, DOI:http://dx.doi.org/10.14429/dsj.60.60

The Many Electron Ground State of the Adiabatic Holstein Model in Two and Three Dimensions

We present the complete ground state phase diagram of the Holstein model in two and three dimension considering the phonon variables to be classical. We first establish the overall structure of the phase diagram by using exact diagonalisation based Monte Carlo (ED-MC) on small lattices and then use a new ``travelling cluster'' approximation (TCA) for annealing the phonon degrees of freedom on large lattices. The phases that emerge include a Fermi liquid (FL), with no lattice distortions, an insulating polaron liquid (PL) at strong coupling, and a charge ordered insulating (COI) phase around half- filling. The COI phase is separated from the Fermi liquid by a regime of phase coexistence whose width grows with increasing electron-phonon coupling. We provide results on the electronic density of states, the COI order parameter, and the spatial organisation of polaronic states, for arbitrary density and electron-phonon coupling. The results highlight the crucial role of spatial correlations in this strong coupling problem.Comment: Final versio

Development of a Finite Volume Algorithm for Calculation of Three Dimensional Incompressible Turbulent Recirculating Flows.

This project aims at developing a general purpose, user-friendly computer code for numerical prediction of three-dimensional turbulent separated flows solving the time-averaged, incompressible Navier Stokes equations in bodyfitted nonorthogonal coordinate systems . ,A finite volume method is developed which employs the concept of the Semi Implicit Pressure Linked Equations (SIMPLE) of Patankar & Spalding (1J, revised for cell-centred variable arrangement and 'using' Cartesian velocity components as dependent variables . Two equations (K- E) models of turbulence [21 will be used to simulate the effect of turbulence on time-averaged flow properties . The data structure and the program are so organised that the code, when run on a Vector m/c, may also exploit the hardware -architecture of a Vector processor and consequently the computation is' accelerated . Finally, in order to meet the large Computer-Storage and CPU demand for real-life problems ; a parallelised version of the code will be generated, compatiable to the . in-house MK-II FLOSOLVER at NAL for which also the computer resources and hardware need to be augmented

Studies on the Temporal and Spatial Discretisation Schemes Used in a Pressure Based RANS Algorithm For Incompressible Flow

The present work describes the algebra involved in the two different temporal discretisation and four different spatial discretisation schemes implemented in the RANS code RANS3D developed in the CTFD Division for computation of unsteady turbulent incompressible flow in complex configurations. All the schemes are tested on two simple test problems to show the effect of the discretisation schemes on the numerical accuracy of the flow solution

On the reliability of eddy viscosity based turbulence models in predicting turbulent flow past a circular cylinder using URANS approach

Turbulent flow past circular cylinder at moderate to high Reynolds number has been analysed employing an second-order time accurate pressure-based finite volume method solving two-dimensional Unsteady Reynolds Averaged Navier Stokes (URANS) equations for incompressible flow, coupled to eddy-viscosity based turbulence models. The major focus of the paper is to test the capabilities and limitations of the present turbulence model-based 2D URANS procedure to predict the phenomenon of Drag Crisis, usually manifested in reliable measurement data, as a sharp drop in the mean drag coefficient around a critical Reynolds number. The computation results are compared to corresponding measurement data for instantaneous aerodynamic coefficients and mean surface pressure and skin friction coefficients. Turbulence model-based URANS computations are in general found to be inadequate for correct prediction of the mean drag coefficients, the Strouhal number and also the coefficients of maximum fluctuating lift over the range of flow Reynolds number varying from 104 to 107

Relative assessment of different turbulence models in prediction of airfoil characteristics for a wide range of angle of attack

Simulation of separated flow past an airfoil beyond stall, along with the prediction of stall itself still remains a challenging problem. In practical design and analysis problems of aerodynamics involving turbulent flow, the most widely used methodology is the numerical solution of the Reynolds Averaged Navier Stokes (RANS) in conjunction with appropriate closure models to represent the effect of turbulent stresses. The present paper attempts to compute flow past a symmetric airfoil for a wide range of angles of attack using the code RANS3D developed at NAL Bangalore. The RANS code is coupled to three different eddy viscosity based turbulence models - viz., the low Re version of the k - E model, low Re version of k-w model and the v2 - f model, for which the ability to capture the massive flow separation at and beyond stall has been carefully examined for an operating chord-based Reynolds number of 2 to 3 million and the angle of attack varying from 0 to 25 degrees. Validation against measurement data for instantaneous flow field indicate that all the turbulence models perform almost equally well in pre-stall regimes, while some uncertainties are observed when the flow becomes highly unsteady for high angle of attack. The vortex shedding from the upper surface of the airfoil leading to massive separated flow structure is captured by all the turbulence models. As far as the mean lift and drag coefficients are concerned, reasonable agreement is observed between the low Re k-E low Re k-w model prediction and the measurement data whereas the v2 - f model, in general, has a tendency of overpredicting the aerodynamic coefficients. The Strouhal number, indicating the frequency of the periodic vortex shedding behavior, is observed to be not so sensitive to the turbulence model used for computation

Numerical simulation of incompressible turbulent flow using linear eddy viscosity-based turbulence models

The present study focuses on the recent development of an implicit pressure-based finite volume algorithm for numerical solution of Reynolds averaged Navier-Stokes equations (RANS) in an inertial frame of reference for the prediction of unsteady incompressible flow problems. The algorithm uses boundary-conforming, multi-block structured grid with moving boundaries, collocated variable arrangement with momentum equations resolved along cartesian directions, second-order accurate spatial and temporal discretisation schemes for the convective fluxes and a pressure-velocity solution strategy. Effect of turbulence was simulated using appropriate linear eddy viscosity-based turbulence models. The capabilities and limitations of the cost-effective unsteady Reynolds averaged Navier-Stokes (URANS) approach has been demonstrated for few application problems of engineering interest