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Article
Publication date: 2 November 2018

Nikhil Kalkote, Ashwani Assam and Vinayak Eswaran

The purpose of this paper is to solve unsteady compressible Navier–Stokes equations without the commonly used dual-time loop. The authors would like to use an adaptive…

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Abstract

Purpose

The purpose of this paper is to solve unsteady compressible Navier–Stokes equations without the commonly used dual-time loop. The authors would like to use an adaptive time-stepping (ATS)-based local error control instead of CFL-based time-stepping technique. Also, an all-speed flow algorithm is implemented with simple low dissipation AUSM convective scheme, which can be computed without preconditioning which in general destroys the time accuracy.

Design/methodology/approach

In transient flow computations, the time-step is generally determined from the CFL condition. In this paper, the authors demonstrate the usefulness of ATS based on local time-stepping previously used extensively in ordinary differential equations (ODE) integration. This method is implemented in an implicit framework to ensure the numerical domain of dependence always contains the physical domain of dependence.

Findings

In this paper, the authors limit their focus to capture the unsteady physics for three cases: Sod’s shock-tube problem, Stokes’ second problem and a circular cylinder. The use of ATS with local truncation error control enables the solver to use the maximum allowable time-step, for the prescribed tolerance of error. The algorithm is also capable of converging very rapidly to the steady state (if there is any) after the initial transient phase. The authors present here only the first-order time-stepping scheme. An algorithmic comparison is made between the proposed adaptive time-stepping method and the commonly used dual time-stepping approach that indicates the former will be more efficient.

Originality/value

The original method of ATS based on local error control is used extensively in ODE integration, whereas, this method is not so popular in the computational fluid dynamics (CFD) community. In this paper, the authors investigate its use in the unsteady CFD computations. The authors hope that it would provide CFD researchers with an algorithm based on an adaptive time-stepping approach for unsteady calculations.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 2
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 7 November 2016

Ying Chen, Chuanjing Lu, Xin Chen, Jie Li and Zhaoxin Gong

Ultrahigh-speed projectile running in water with the velocity close to the speed of sound usually causes large supercavity. The computation of such transonic cavitating…

Abstract

Purpose

Ultrahigh-speed projectile running in water with the velocity close to the speed of sound usually causes large supercavity. The computation of such transonic cavitating flows is usually difficult, thus high-speed model reflecting the compressibility of both the liquid and the vapor phases should be introduced to model such flow. The purpose of this paper is to achieve a model within an in-house developed solver to simulate the ultrahigh-speed subsonic supercavitating flows.

Design/methodology/approach

An improved TAIT equation adjusted by local temperature is adopted as the equation of state (EOS) for the liquid phase, and the Peng-Robinson EOS is used for the vapor phase. An all-speed variable coupling algorithm is used to unify the computations and regulate the convergence at arbitrary Mach number. The ultrahigh-speed (Ma=0.7) supercavitating flows around circular disk are investigated in contrast with the case of low subsonic (Ma=0.007) flow.

Findings

The characteristic physical variables are reasonably predicted, and the cavity profiles are compared to be close to the experimental empirical formula. An important conclusion in the compressible cavitating flow theory is verified by the numerical result that, at any specific cavitation number the cavity’s size and the drag coefficient both increase along with the rise of Mach number. On the contrary, it is found as well that the cavity’s slenderness ratio decreases when Mach number goes up. It indicates that the compressibility has different influences on the length and the radius of the supercavity.

Originality/value

A high-speed model reflecting the compressibility of both the liquid and the vapor phases was suggested to model the ultrahigh-speed supercavitating flows around underwater projectiles.

Details

Engineering Computations, vol. 33 no. 8
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 6 August 2019

Ashwani Assam, Nikhil Kalkote, Nishanth Dongari and Vinayak Eswaran

Accurate prediction of temperature and heat is crucial for the design of various nano/micro devices in engineering. Recently, investigation has been carried out for…

Abstract

Purpose

Accurate prediction of temperature and heat is crucial for the design of various nano/micro devices in engineering. Recently, investigation has been carried out for calculating the heat flux of gas flow using the concept of sliding friction because of the slip velocity at the surface. The purpose of this study is to exetend the concept of sliding friction for various types of nano/micro flows.

Design/methodology/approach

A new type of Smoluchowski temperature jump considering the viscous heat generation (sliding friction) has recently been proposed (Le and Vu, 2016b) as an alternative jump condition for the prediction of the surface gas temperature at solid interfaces for high-speed non-equilibrium gas flows. This paper investigated the proposed jump condition for the nano/microflows which has not been done earlier using four cases: 90° bend microchannel pressure-driven flow, nanochannel backward facing step with a pressure-driven flow, nanoscale flat plate and NACA 0012 micro-airfoil. The results are compared with the available direct simulation Monte Carlo results. Also, this paper has demonstrated low-speed preconditioned density-based algorithm for the rarefied gas flows. The algorithm captured even very low Mach numbers of 2.12 × 10−5.

Findings

Based on this study, this paper concludes that the effect of inclusion of sliding friction in improving the thermodynamic prediction is case-dependent. It is shown that its performance depends not only on the slip velocity at the surface but also on the mean free path of the gas molecule and the shear stress at the surface. A pressure jump condition was used along with the new temperature jump condition and it has been found to often improve the prediction of surface flow properties significantly.

Originality/value

This paper extends the concept of using sliding friction at the wall for micro/nano flows. The pressure jump condition was used which has been generally ignored by researchers and has been found to often improve the prediction of surface flow properties. Different flow properties have been studied at the wall apart from only temperature and heat flux, which was not done earlier.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 8
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 6 June 2016

Bassem R Girgis, Sarma L Rani and Abdelkader Frendi

The purpose of this paper is to investigate the computational features of the Flowfield Dependent Variation (FDV) method, a numerical scheme built to simulate flows…

Abstract

Purpose

The purpose of this paper is to investigate the computational features of the Flowfield Dependent Variation (FDV) method, a numerical scheme built to simulate flows characterized by multiple speeds, multiple physical phenomena, and by large variations in flow variables.

Design/methodology/approach

Fundamentally, the FDV method may be regarded as a variant of the Lax-Wendroff Scheme (LWS) that is obtained by replacing the explicit time derivatives in LWS by a weighted combination of explicit and implicit time derivatives. The weighting factors – referred to as FDV parameters – may be broadly classified as convective and diffusive parameters which, for example, are determined using flow quantities such as the Mach number and Reynolds number, respectively. Hence, the reference to these parameters and the method as “flow field dependent.” A von Neumann Fourier analysis demonstrates that the increased implicitness makes FDV both more stable and less dispersive compared to LWS, a feature crucial to capturing shocks and other phenomena characterized by high gradients in variables. In the current study, the FDV scheme is implemented in a Taylor-Galerkin-based finite element method framework that supports arbitrarily high order, unstructured isoparametric elements in one-, two- and three-dimensional geometries.

Findings

At first, the spatial accuracy of the implemented FDV scheme is established using the Method of Manufactured Solutions, wherein the results show that the order of accuracy of the scheme is nearly equal to the order of the shape function polynomial plus one. The dispersion and dissipation errors of FDV, when applied to the compressible Navier-Stokes and energy equations, are investigated using a 2-D, small-amplitude acoustic pulse propagating in a quiescent medium. It is shown that FDV with third-order shape functions accurately captures both the amplitude and phase of the acoustic pulse. The method is then applied to cases ranging from low-Mach number subsonic flows (Mach number M=0.05) to high-Mach number supersonic flows (M=4) with shock-boundary layer interactions. For all cases, fair to good agreement is observed between the current results and those in the literature.

Originality/value

The spatial order of accuracy of the FDV method, its stability and dispersive properties, as well as its applicability to low- and high-Mach number flows are established.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 5
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 19 November 2021

M. R. Nived, Bandi Sai Mukesh, Sai Saketha Chandra Athkuri and Vinayak Eswaran

This paper aims to conduct, a detailed investigation of various Reynolds averaged Navier–Stokes (RANS) models to study their performance in attached and separated flows…

Abstract

Purpose

This paper aims to conduct, a detailed investigation of various Reynolds averaged Navier–Stokes (RANS) models to study their performance in attached and separated flows. The turbulent flow over two airfoils, namely, National Advisory Committee for Aeronautics (NACA)-0012 and National Aeronautics and Space Administration (NASA) MS(1)-0317 with a static stall setup at a Reynolds number of 6 million, is chosen to investigate these models. The pre-stall and post-stall regions, which are in the range of angles of attack 0°–20°, are simulated.

Design/methodology/approach

RANS turbulence models with the Boussinesq approximation are the most commonly used cost-effective models for engineering flows. Four RANS models are considered to predict the static stall of two airfoils: Spalart–Allmaras (SA), Menter’s kω shear stress transport (SST), k – kL and SA-Bas Cakmakcioglu modified (BCM) transition model. All the simulations are performed on an in-house unstructured-grid compressible flow solver.

Findings

All the turbulence models considered predicted the lift and drag coefficients in good agreement with experimental data for both airfoils in the attached pre-stall region. For the NACA-0012 airfoil, all models except the SA-BCM over-predicted the stall angle by 2°, whereas SA-BCM failed to predict stall. For the NASA MS(1)-0317 airfoil, all models predicted the lift and drag coefficients accurately for attached flow. But the first three models showed even further delayed stall, whereas SA-BCM again did not predict stall.

Originality/value

The numerical results at high Re obtained from this work, especially that of the NASA MS(1)-0317, are new to the literature in the knowledge of the authors. This paper highlights the inability of RANS models to predict the stall phenomenon and suggests a need for improvement in modeling flow physics in near- and post-stall flows.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 1 May 1997

M. Vahdati and M. Imregun

Presents a finite element/volume method for non‐linear aeroelasticity analyses of turbomachinery blades. The method uses an Arbitrary Lagrangian‐Eulerian (ALE) kinematical…

Abstract

Presents a finite element/volume method for non‐linear aeroelasticity analyses of turbomachinery blades. The method uses an Arbitrary Lagrangian‐Eulerian (ALE) kinematical description of the fluid domain, in which the grid points can be displaced independently of the fluid motion. In addition, it employs an iterative implicit formulation similar to that of the Implicit‐continuous Eulerian (ICE) technique, making it applicable to flows at all speeds. A deforming mesh capability that can move the grid to conform continuously to the instantaneous shape of an aeroelastically deforming body without excessive distortion is also included in the algorithm. The unsteady aerodynamic loads are obtained using inviscid Euler equations. The model for the solid is general and can accommodate any spatial or modal representation of the structure. Determines the flutter stability of the system by studying the aeroelastic time response histories which are obtained by integration of the coupled equations of motion for both the fluid and the structure. Develops and demonstrates in 2D the formulation, which includes several corrections for better numerical stability. The cases studied include NACA64A006 and NACA0012 aerofoils and the EPFL Configuration 4 cascade. Finds the results from the numerical indicate good overall agreement with other published work and hence demonstrates the suitability of an ICED‐ALE formulation for turbomachinery applications.

Details

Engineering Computations, vol. 14 no. 3
Type: Research Article
ISSN: 0264-4401

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Article
Publication date: 1 February 1969

In our first issue Mr E. Phillips described the Post Office system for training counter clerks. He explained that the period of initial classroom instruction does not…

Abstract

In our first issue Mr E. Phillips described the Post Office system for training counter clerks. He explained that the period of initial classroom instruction does not attempt to teach the whole of the job: some infrequently‐occurring items are not taught in the off‐the‐job training school but are learnt on‐the‐job as the occasion arises. Overseas parcels is one such item and the communication technique used by the trainer in this case is the algorithm. Here by way of illustration of how the technique applies to the clerical field is part of the actual algorithm used by the Post Office.

Details

Industrial and Commercial Training, vol. 1 no. 2
Type: Research Article
ISSN: 0019-7858

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Article
Publication date: 30 October 2020

Nikhil Kalkote, Ashwani Assam and Vinayak Eswaran

The purpose of this study is to present and demonstrate a numerical method for solving chemically reacting flows. These are important for energy conversion devices, which…

Abstract

Purpose

The purpose of this study is to present and demonstrate a numerical method for solving chemically reacting flows. These are important for energy conversion devices, which rely on chemical reactions as their operational mechanism, with heat generated from the combustion of the fuel, often gases, being converted to work.

Design/methodology/approach

The numerical study of such flows requires the set of Navier-Stokes equations to be extended to include multiple species and the chemical reactions between them. The numerical method implemented in this study also accounts for changes in the material properties because of temperature variations and the process to handle steep spatial fronts and stiff source terms without incurring any numerical instabilities. An all-speed numerical framework is used through simple low-dissipation advection upwind splitting (SLAU) convective scheme, and it has been extended in a multi-component species framework on the in-house density-based flow solver. The capability of solving turbulent combustion is also implemented using the Eddy Dissipation Concept (EDC) framework and the recent k-kl turbulence model.

Findings

The numerical implementation has been demonstrated for several stiff problems in laminar and turbulent combustion. The laminar combustion results are compared from the corresponding results from the Cantera library, and the turbulent combustion computations are found to be consistent with the experimental results.

Originality/value

This paper has extended the single gas density-based framework to handle multi-component gaseous mixtures. This paper has demonstrated the capability of the numerical framework for solving non-reacting/reacting laminar and turbulent flow problems. The all-speed SLAU convective scheme has been extended in the multi-component species framework, and the turbulent model k-kl is used for turbulent combustion, which has not been done previously. While the former method provides the capability of solving for low-speed flows using the density-based method, the later is a length-scale-based method that includes scale-adaptive simulation characteristics in the turbulence modeling. The SLAU scheme has proven to work well for unsteady flows while the k-kL model works well in non-stationary turbulent flows. As both these flow features are commonly found in industrially important reacting flows, the convection scheme and the turbulence model together will enhance the numerical predictions of such flows.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 10
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 3 May 2019

Jin-Ping Wang, Jian-Fei Zhang, Zhi-Guo Qu and Wen-Quan Tao

Pressure-based methods have been demonstrated to be powerful for solving many practical problems in engineering. In many pressure-based methods, inner iterative processes…

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Abstract

Purpose

Pressure-based methods have been demonstrated to be powerful for solving many practical problems in engineering. In many pressure-based methods, inner iterative processes are proposed to get efficient solutions. However, the number of inner iterations is set empirically and kept fixed during the whole computation for different problems, which is overestimated in some computations but underestimated in other computations. This paper aims to develop an algorithm with adaptive inner iteration processes for steady and unsteady incompressible flows.

Design/methodology/approach

In this work, with the use of two different criteria in two inner iterative processes, a mechanism is proposed to control inner iteration processes to make the number of inner iterations vary during computing according to different problems. By doing so, adaptive inner iteration processes can be achieved.

Findings

The adaptive inner iterative algorithm is verified to be valid by solving classic steady and unsteady incompressible problems. Results show that the adaptive inner iteration algorithm works more efficient than the fixed inner iteration one.

Originality/value

The algorithm with adaptive inner iteration processes is first proposed in this paper. As the mechanism for controlling inner iteration processes is based on physical meaning and the feature of iterative calculations, it can be used in any methods where there exist inner iteration processes. It is not limited for incompressible flows. The performance of the adaptive inner iteration processes in compressible flows is conducted in a further study.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 4
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 7 August 2017

Guo Huang and Haiming Huang

The purpose of this paper is to perform the simulation to explore the gap flow field under a hypersonic air flow. Thermal protection systems of hypersonic vehicles…

Abstract

Purpose

The purpose of this paper is to perform the simulation to explore the gap flow field under a hypersonic air flow. Thermal protection systems of hypersonic vehicles generally consist of thermal insulation tiles, and gaps between these tiles probably cause a severe local aerodynamic thermal effect.

Design/methodology/approach

The discretizations of convection flux term and temporal term in the governing equation with chemical equilibrium, respectively, take AUSM+-up flux-vector splitting scheme and the implicit lower-upper symmetric Gauss–Seidel method. Based on these, the flow field in a deep gap is simulated by means of the computer codes that the authors have written.

Findings

The numerical results show that the heat flux distribution in a gap has a good agreement with experimental results. Importantly, the distribution of heat flux is “U” shaped and the maximum of the heat flux occurs at the windward corner of a gap.

Originality/value

To explore the gap flow field under a hypersonic air flow, which is a chemically reacting, all speed and viscous flow, a novel model with an equivalent ratio of specific heats is presented. The investigation in this paper has a guide for the design of the thermal protection system in hypersonic vehicles.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

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