J.C. Mandal

Kinetic flux vector splitting for Euler equations

This paper is mainly concerned with the development of a class of new upwind methods and a novel treatment of the boundary condition based on the concept of kinetic flux vector splitting (KFVS) for solving inviscid gasdynamic problems. KFVS utilizes the well-known connection that the Euler equations of motion are the moments of the Boltzmann equation whenever the velocity distribution function is a Maxwellian. After presentation of the analysis of the KFVS method in I-D in detail, it is described how KFVS can be performed in a different manner to construct various upwind methods for higher dimensions depending on the situations. Next, it is shown how the KFVS formulation together with the specular reflection model of the kinetic theory of gases at the solid boundary lead to the development of a new treatment of the flow tangency boundary condition which is robust, upwind and conservative and does not require any further assumptions or the use of fictitious grid points. Finally, the present method is tested on a wide variety of problems to demonstrate its capability in obtaining accurate and wiggle-free solutions.

CFD analysis of single-phase flows inside helically coiled tubes

It has been well established that heat transfer in a helical coil is higher than that in a corresponding straight pipe. However, the detailed characteristics of fluid flow and heat transfer inside helical coil is not available from the present literature. This paper brings out clearly the variation of local Nusselt number along the length and circumference at the wall of a helical pipe. Movement of fluid particles in a helical pipe has been traced. CFD simulations are carried out for vertically oriented helical coils by varying coil parameters such as (i) pitch circle diameter, (ii) tube pitch and (iii) pipe diameter and their influence on heat transfer has been studied. After establishing influence of these parameters, correlations for prediction of Nusselt number has been developed. A correlation to predict the local values of Nusselt number as a function of angular location of the point is also presented.

Computations of laminar and turbulent mixed convection in a driven cavity using pseudo-compressibility approach

Abstract A driven cavity, for two different thermal boundary conditions, has been chosen as a test case to establish the suitability of pseudo-compressibility algorithm for mixed convection flow problems for both laminar and turbulent flow situations. Here shear stress transport eddy viscosity model has been modified to include the buoyancy effects. The flow is computed inside the cavity under the influence of varying buoyancy and inertia forces. The computed results demonstrate the ability of the pseudo-compressibility approach and shear stress transport model to solve complex heat transfer problems.

An upwind method for incompressible ow computations using pseudo-compressibility approach

A new efficient and accurate method has been developed for computing incompressible viscous flows. This method is derived for pseudo-compressibility formulation of incompressible flow following the approach of Harten Lax and van Leer with contact(HLL-C) scheme for compressible flow equations. Several numerical test examples are computed in order to demonstrate the efficacy of the present method.

Simulation of flow inside differentially heated rotating cavity

Purpose – The purpose of this paper is to simulate flow inside differentially heated rotating cavity using two different formulations; one using Navier‐Stokes (NS) equations derived in non‐inertial (rotating) frame of reference and the other using NS equations in inertial frame of reference. Then to compare the results obtained from these formulations to find their merits and demerits.Design/methodology/approach – The NS equations for both non‐inertial and inertial formulations are written in artificial compressibility form before discretizing them by a high resolution finite volume method. The dual time steeping approach of Jameson is used for time accuracy in both the formulations. Arbitrary Lagrangian Eulerian (ALE) approach is used for taking care of moving boundary problem arising in the inertial formulation. A newly developed HLLC‐AC Riemann solver for discretizing convective fluxes and central differencing for discretizing viscous fluxes are used in the finite volume approach. Results for both the ...

An upwind method for incompressible flows with heat transfer

Purpose – The purpose of this paper is to present a novel numerical method to solve incompressible flows with natural and mixed convections using pseudo‐compressibility formulation.Design/methodology/approach – The present method is derived using the framework of Harten Lax and van Leer with contact (HLLC) method of Toro, Spruce and Spears, that was originally developed for compressible gas dynamics equations. This work generalizes the algorithm described in the previous paper to the case where heat transfer is involved. Here, the solution of the Riemann problem is approximated by a three‐wave system.Findings – A few test cases involving incompressible laminar flows inside 2D square cavity for various Rayleigh and Reynolds numbers are considered for validating the present method. The computed results from the present method are found to be quite promising.Originality/value – Although pseudo‐compressibility formulation has been found to have superior performance and has the potential to have numerical trea...

Simulation of Moderator Flow and Temperature Inside Calandria of CANDU Reactor Using Artificial Compressibility Method

Numerical computations of moderator flows inside calandria of the typical CANDU-6 reactor are presented here. The numerical model is based on incompressible Navier–Stokes equations in artificial compressibility formulation with dual time-stepping approach for time-accurate computations. A high-resolution unstructured finite-volume scheme, based on the HLLC-AC Riemann solver for convective fluxes and central differencing type discretization for viscous fluxes, is used here. In order to simulate more realistic flow, the calandria tube matrix is considered directly, in contrast with the usual practice of indirect accounting of tube bundles through porosity modeling. The moderator flows are computed for different operating conditions. The nature of computed flow is found to be dependent on the relative balance between momentum and buoyancy forces as observed by Carlucci. A parametric study is also carried out to investigate the effect of moderator inlet diffuser location, moderator inlet flow velocity, and angle of moderator inlet diffuser. The inlet flow velocity and inlet diffuser location are found to have significant effect on flow features inside the calandria.

High resolution schemes for genuinely two-dimensional HLLE Riemann solver

In this paper, two higher order solution reconstruction techniques based on SDWLS gradients and Barth-Jespersen limiter are investigated to obtain higher order accuracy for a genuinely multidimensional Riemann solver. Due to use of vertex-based framework in the multidimensional Riemann solver, straight forward application of conventional TVD limiters becomes difficult and confusing. Several test examples are solved in order to establish order of accuracy and to demonstrate the efficacy of the proposed reconstruction techniques. The SDWLS gradient technique is found to produce consistently higher order solution accuracy and maintain multidimensional nature of the solutions as compared to Barth-Jespersen limiter.

Convective-pressure flux split algorithm for incompressible flow computation using artificial compressibility formulation

Purpose – The purpose of this paper is to present two low diffusive convective-pressure flux split finite volume algorithms for solving incompressible flows in artificial compressibility framework. Design/methodology/approach – The present method follows the framework similar to advection upwind splitting method of Liou and Steffen for compressible flows which is used by Vierendeels et al. to solve incompressible flow equations. Instead of discretizing the total inviscid flux using upwind scheme, the inviscid flux is first split into convective and pressure parts, and then discretized the two parts differently. The convective part is discretized using upwind method and the pressure part using central differencing. Since the Vierendeels type scheme may not be able to capture the divergence free velocity field due to the presence of artificial dissipation term, a strategy to progressively withdraw the dissipation with time step is proposed here that can ascertain the divergence free velocity condition to the level of residual error. This approach helps in reducing the amount of numerical dissipation due to upwind discretization, which is evident from the numerical test examples. Findings – Upwind treatment of only the convective part of the inviscid flux terms, instead of the whole inviscid flux term, leads to more accurate solutions even at relatively coarse grids, which is substantiated by numerical test examples. Research limitations/implications – The method is presently applicable to Cartesian grid. Originality/value – Although similar formulation is reported by Vierendeels et al., no detailed study of the accuracy is presented. Discretization and solution reconstructions used in the present approach differ from the approach reported by Vierendeels et al. A modification to Vierendeels type scheme is proposed that can help in achieving divergence free velocity condition. Finally the efficacy of the present approach to produce very accurate solutions even on coarse grids is successfully demonstrated using a few benchmark problems.

A genuinely multidimensional convective pressure flux split Riemann solver for Euler equations

A simple inexpensive genuinely multidimensional HLL type Riemann solver for Euler equations of gasdynamics is proposed. The genuinely multidimensional formulation is based on the work of Balsara 17]. In the present approach, the missing contact wave in the HLL type solver is restored using the HLL-CPS formulation of Mandal and Panwar 5]. A few two-dimensional standard test cases are solved to demonstrate the efficacy of the proposed solver. A very simple new genuinely multidimensional HLL type Riemann solver for Euler equations is proposed.Due to the use of closed form expressions for the fluxes, the present method is easier to apply.The contact discontinuity is restored using the HLL-CPS formulation without the need for independently specifying its direction of evolution.Numerical test results demonstrate the efficacy of the present method of its ability to capture accurate solutions.