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FLUID MECHANICS

 Volume 6, 2011
Print ISSN: 1790-5087
E-ISSN: 2224-347X

 
 

 

 

 

 

 

 


Issue 1, Volume 6, January 2011

Special Issue: Mathematical Fluid Dynamics - Part I

Editor: Nikos Mastorakis


Title of the Paper: Asymptotic Solutions and Unsymmetric Solutions of a Fifth Order Ordinary Differential Equation

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Authors: Chung-Hsien Tsai, Shy-Jen Guo

Abstract: The objective of this paper is to construct the asymptotic solutions and unsymmetric solutions of a fifth order model equation for steady capillary-gravity waves over a smooth compact bump with the Froude number near 1 and the Bond number near 1/3.

Keywords: Steady capillary-gravity wave, fifth order model equation, bump, Green’s function, asymptotic solution, unsymmetric Solutions


Title of the Paper: Asymptotic Solutions of a Fifth Order Ordinary Differential Equation

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Authors: Chung-Hsien Tsai, Shy-Jen Guo

Abstract: The objective of this paper is to construct the asymptotic solutions of a fifth order model equation for steady capillary-gravity waves over a smooth compact bump with the Froude number near 1 and the Bond number near 1/3.

Keywords: Steady capillary-gravity wave, fifth order model equation, bump, Green’s function, asymptotic solution


Title of the Paper: Analytic Solutions to a Boundary Layer Problem for Non-Newtonian Fluid Flow Driven by Power Law Velocity Profile

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Authors: Gabriella Bognar

Abstract: In this paper the similarity solutions of the Prandtl boundary layer equations describing a non- Newtonian power law fluid past an impermeable flat plate, driven by a power law velocity profile U = Bys (B > 0) have been investigated. It is shown that there are analytical solutions for any n > 0, n ? 2 and any ?1/ 2 £s < 0 . We give a method for the determination of the power series solutions to the momentum equation and we estimate the convergence radius of the proposed solutions.

Keywords: Similarity solution, power series solution, boundary value problem, non-Newtonian fluid flow


Title of the Paper: Computer Modeling of Planet Partial Fragmentation

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Authors: D. V. Voronin

Abstract: It is difficult to explain an origin of all celestial bodies of the Solar system by smooth evolution of the protoplanet cloud. The alternative is the hypothesis of the explosive origin of some bodies. The nuclear explosion in active layer (particles of uranium and thorium oxides, weighed in liquid iron at a planer core) might take place at collision of the protoplanet with an asteroid. Subsequent fragmentation of the planet in conditions of gravitation is numerically simulated. It was found that the structure and composition of fragments may be determined by the cumulative jet, going from a planetary core to its surface for small enough initial velocity of protoplanet rotation. The origin of Io may be so explained, for example. Separation of the great mass of the stone-silicate shell of the planet and the generation of satellites like the Moon occurs at the great enough velocity of rotation.

Keywords: Numerical simulations, active layer, celestial bodies, explosion, cumulative jet, planet rotation


Title of the Paper: A Combined Space Discrete Algorithm with a Taylor Series by Time for Solution of the Non-Stationary CFD Problems

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Authors: Ivan V. Kazachkov

Abstract: The first order by time partial differential equation (PDE) is used as models in applications such as fluid flow, heat transfer, solid deformation, electromagnetic waves, and many others. In this paper we propose the new numerical method to solve a class of the initial-boundary value problems for the PDE using any known space discrete numerical schemes and a Taylor series expansion by time. Derivatives by time are got from the outgoing PDE and its further differentiation (for second and higher order derivatives by time). By numerical solution of the PDE and PDE arrays normally a second order discretization by space is applied while a first order by time is sometimes satisfactory too. Nevertheless, in a number of different problems, discretization both by temporal and by spatial variables is needed of highest orders, which complicates the numerical solution, in some cases dramatically. Therefore it is difficult to apply the same numerical methods for the solution of some PDE arrays if their parameters are varying in a wide range so that in some of them different numerical schemes by time fit the best for precise numerical solution. The Taylor series based solution strategy for the non-stationary PDE in CFD simulations has been proposed here that attempts to optimise the computation time and fidelity of the numerical solution. The proposed strategy allows solving the non-stationary PDE with any order of accuracy by time in the frame of one algorithm on a single processor, as well as on a parallel cluster system. A number of examples considered in this paper have shown applicability of the method and its efficiency.

Keywords: Non-stationary, First Order by Time; Navier-Stokes Equations; Taylor Series; Numerical; Fractional Derivative


Issue 2, Volume 6, April 2011

Special Issue: Mathematical Fluid Dynamics - Part II

Editor: Nikos Mastorakis


Title of the Paper: The Mathematical Models for Penetration of a Liquid Jets into a Pool

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Authors: Ivan V. Kazachkov

Abstract: The peculiarities of a jet penetrating the liquid pool of different density were examined by means of the non-linear and linear mathematical models derived including bending instability. Based on experimental observations reported in the literature for a number of situations, the penetration behaviour was assumed to govern the buoyancy-dominated regime. A new analytical solution of the one-dimensional non-linear model was obtained for the jet penetration in this condition, as function of Froude number, jet/ambient fluid density ratio and other parameters. The solution was analysed for a number of limit cases. Analytical solution of the non-linear second-order equation obtained can be of interest for other researchers as the mathematical result.

Keywords: Jet, Penetration, Pool of Liquid, Non-linear, Analytical Solution, Bifurcation, Bending


Title of the Paper: High Velocity Motion of a Wing in Compressible Fluid Near a Surface

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Authors: M. N. Smirnova, A. V. Zvyaguin

Abstract: The two-dimensional problems of thin body motion in fluid parallel to the boundary at a distance, comparable with the length of the body, are regarded. In particular, resistance and lift forces in thin body motion parallel to free surface and parallel to rigid surface are determined and compared with existing solutions for resistance and lift forces in case of an infinite space. The solution is determined under the assumption of fluid being ideal and compressible. The Chaplygin-Zhukovsky hypothesis of rear-edge-limited solution is taken into consideration. In case of moving near free surface the solution is obtained for a problem of infinite span wing. The solution allows determining drag and lift forces in the limiting cases. It was shown that on Mach number tending to unity both forces infinitely increase. For relatively thin fluid layer above the moving wing the resistance force depends on the distance to the free surface, inclination and Mach number, while for relatively thick fluid layer the force depends on wing length, inclination angle and Mach number as well. In case of moving near rigid surface the solution of a problem is reduced to the Fredholm equation, which is solved numerically. The generalization of Zhukovski solution was obtained, which provides the lift force dependence on the altitude of the flight. The behavior of the lift force is very peculiar: it increases on decreasing altitude above the rigid surface. The screen effect becomes essential on moving wing altitude being smaller than the wing’s length. The effect was detected experimentally before and gave birth to construction of a special flying vehicle named “ecranoplan”. It is shown in the paper that the lift force could increase several orders of magnitude. This effect could be used in developing flying high-speed vehicles, which could be used in the territories of smooth surface: steppes, deserts, lakes, swamps, etc.

Keywords: Wing, compressible fluid, analytical function, Fredholm equation, Dirichlet problem, lift and resistance forces


Title of the Paper: PIV Velocity and Pressure Measurements of the Unsteady Flow Field behind Two Automobile Outside Rear View Mirrors

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Authors: Bahram Khalighi, Richard Lee

Abstract: The unsteady flow fields behind two different automobile outside side rear view mirrors were examined experimentally in order to obtain a comprehensive data base for the validation of the ongoing computational investigation effort to predict the aero-acoustic noise due to the outside rear view mirrors. This study is part of a larger scheme to predict the aero-acoustic noise due to various external components in vehicles. To aid with the characterization of this complex flow field, mean and unsteady surface pressure measurements were undertaken in the wake of two mirror models. Velocity measurements with particle image velocimetry were also conducted to develop the mean velocity field of the wake. Two full-scale mirror models with distinctive geometrical features were investigated.

Keywords: Outside mirror flow. wake behind automobile mirrors, PIV


Title of the Paper: Large Eddy Simulation of Pressure Distribution of Fluid Flow Over Ridges of Circular, Parabolic and Rectangular Shapes

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Authors: A. J. Templeman, M. G. Rasul

Abstract: This paper presents modeling and large eddy simulation of pressure coefficient distribution of the flow of air over ridges of circular, parabolic and rectangular shapes at different Reynolds numbers using computational fluid dynamics (CFD) code FLUENT. The simulated results are compared and discussed with the experimentally measured pressure distributions. The experiments were done in an open circuit blower type wind tunnel. This study found that the pressure coefficient distributions over the three ridges are not unique in character at zero angle of attack for same Reynolds number and its magnitude depends on the geometry of the ridges. The typical potential flow equations are not applicable to predict the distance of pressure dissipation in the downstream direction of the flow.

Keywords: CFD simulation, ridges, pressure coefficient distribution


Title of the Paper: Linear and Weakly Nonlinear Instability of Slightly Curved Shallow Mixing Layers

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Authors: Irina Eglite, Andrei Kolyshkin

Abstract: The paper is devoted to linear and weakly nonlinear stability analysis of shallow mixing layers. The radius of curvature is assumed to be large. Linear stability problem is solved numerically using collocation method based on Chebyshev polynomials. It is shown that for stably curved mixing layers curvature has a stabilizing effect on the flow. Weakly nonlinear theory is used to derive an amplitude evolution equation for the most unstable mode. It is shown that the evolution equation in this case is the Ginzburg-Landau equation with complex coefficients. Explicit formulas for the calculation of the coefficients of the Ginzburg-Landau equation are derived. Numerical algorithm for the computation of the coefficients is described in detail.

Keywords: Linear stability, weakly nonlinear theory, method of multiple scales, Ginzburg-Landau equation, collocation method


Issue 3, Volume 6, July 2011

Special Issue: Numerical Methods in Fluid Mechanics

Editor: Nikos Mastorakis


Title of the Paper: Modeling of High Velocity Flows with Chemical Reactions

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Authors: D. V. Voronin

Abstract: The numerical algorithm for the decision of non-stationary two-dimensional problems of dynamics of compressible multi phase media is developed on the base of the method of particles in cells. With the purpose of elimination of non-physical fluctuations of the numerical decision inherent in methods of this type, there are offered method of integration of the equation of mass conservation and procedure of determination of pressure in nodes of numerical grid. On the base of algorithm some examples of modeling were executed: propagation of gas detonation with cellular structure in tube, explosion in a planet interiors and bubble detonation.

Keywords: Modeling, two-phase media, compressible flows, particle, detonation, explosion


Title of the Paper: Spray Injection and Ignition in a Heated Chamber Modeling

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Authors: V. B. Betelin, A. G. Kushnirenko, V. A. Nerchenko, V. F. Nikitin, N. N. Smirnov

Abstract: Computer simulation of liquid fuel jet injection into heated atmosphere of combustion chamber, mixture formation, ignition and combustion need adequate modeling of evaporation, which is extremely important for the curved surfaces in the presence of strong heat and mass diffusion fluxes. Combustion of most widely spread hydrocarbon fuels takes place in a gas-phase regime. Thus, evaporation of fuel from the surface of droplets turns to be one of the limiting factors of the process as well. The problems of fuel droplets atomization, evaporation being the key factors for heterogeneous mixtures reacting mixtures, the non-equilibrium effects in droplets atomization and phase transitions will be taken into account in describing thermal and mechanical interaction of droplets with streaming flows. In the present lecture processes of non-equilibrium evaporation of small droplets will be discussed. It will be demonstrated, that accounting for non-equilibrium effects in evaporation for many types of widely used liquids is crucial for droplets diameters less than 100 microns, while the surface tension effects essentially manifest only for droplets below 0.1 micron. Investigating the behavior of individual droplets in a heated air flow allowed to distinguish two scenarios for droplet heating and evaporation. Small droplets undergo successively heating, then cooling due to heat losses for evaporation, and then rapid heating till the end of their life time. Larger droplets could directly be heated up to a critical temperature and then evaporate rapidly. Atomization of droplets interferes the heating and evaporation scenario.

Keywords: Combustion, ignition, phase transition, heat flux, evaporation, non-equilibrium, diffusion, mathematical simulation


Title of the Paper: On the Assessment of an Unstructured Finite-Volume DES/LES Solver for Turbomachinery Applications

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Authors: Chiara Bernardini, Mauro Carnevale, Simone Salvadori, Francesco Martelli

Abstract: Improvements in mean flow and performances simulation in turbomachinery has brought research to focus more demanding topics like turbulence effects on turbines. Although overall performances are well predicted by Unsteady-RANS, other phenomena such as aerodynamic noise or transition need more accurate prediction of turbulent flow features. Thus different kinds of equation modeling other than URANS are needed to cope with this issue. The success of Detached-Eddy Simulation and Large-Eddy Simulation applications in reproducing physical behavior of flow turbulence is well documented in literature. Despite that, LES simulations are still computationally very expensive and their use for investigating industrial configurations requires a careful assessment of both numerical and closure modeling techniques. Moreover LES solvers are usually developed on a structured mesh topology for sake of simplicity of high-order schemes implementation. Application to complex geometries like those of turbomachinery is therefore difficult. The present work addresses this issue considering the feasibility of converting an operative in-house URANS solver, widely validated for applicative purposes, into higher resolution DES and LES, in order to face turbulence computation of turbomachinery technical cases. The solver presents a 3D unstructured finite-volume formulation, which is kept in LES approach in order to handle complex geometries and it is developed to perform unsteady simulations on turbine stages. Preliminary assessment of the solver has been performed to evaluate and improve the accuracy of the convective fluxes discretization on an inviscid bump test case. First a DES-based approach has been implemented, as it is less computationally challenging and numerically demanding than LES. A square cylinder test case has been assessed and compared with experiments. Then, a pure LES with a Smagorinsky sub-grid scale model has been evaluated on the test case of incompressible periodic channel flow in order to assess the capability of the solver to correctly sustain a time developing turbulent field.

Keywords: DES, Inflow Boundary, Numerical accuracy, Turbulent channel flow, Unstructured LES


Title of the Paper: Finite Element Model for Wave Propagation Near Shore Based on Extended Boussinesq Equations

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Authors: L. Pinheiro, C. J. Fortes, J. A. Santos, L. Fernandes, M. Walkley

Abstract: This paper describes the numerical model BOUSS-WMH (BOUSSinesq Wave Model for Harbours), a finite element model for nonlinear wave propagation near shore and into harbors. It is based upon an extended version of the Boussinesq equations to which terms were added to generate regular or irregular waves inside the numerical domain, absorb outgoing waves, partially reflect waves at physical boundaries, control numerical instabilities and reproduce energy dissipation due to bottom friction and wave breaking. The paper focuses on the implementation of partial reflection, bottom friction and wave breaking as well as on the model applications to experimental test cases. Results are compared with physical model tests and another numerical model.

Keywords: Wave Propagation, Boussinesq Equations, Harbours, Finite Elements


Title of the Paper: Droplet Simulation, A Case Study: Evaporation

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Authors: Sadegh Torfi, Seyed Mohammad Hosseini Nejad

Abstract: For heat and mass transfer simulation of single droplet in a two-pieces solution with saturated solvent vapor environment, a numerical model is developed by finite volume method and transient SIMPLEC algorithm. I this study, dimensionless equations of motion, heat transfer and mass transfer (based on mass ratio) are solved simultaneously. All the thermodynamic and transitional solution properties have been considered as a function of temperature and concentration. The numerical analysis results are presented for mass transfer of lithium bromide solution droplet in 300K and initial concentration of 50%. Verification of method is done by compare these numerical results with analytical and numerical analysis of other studies. Droplet Growth Chart, average temperature and concentration, variation of drag coefficient diagrams, Nusselt number and flow line, temperature and concentration and temperature distribution contours, penetration rate of mass and the level of tangential velocity at droplet surface as the modeling results are presented.

Keywords: Heat and Mass Transfer, Finite volume, Droplet, Simulation, SIMPLEC Algorithm


Issue 4, Volume 6, October 2011


Title of the Paper: Supersonic and Hypersonic Flows on 2D Unstructured Context: Part I

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Authors: Edisson Sávio De Góes Maciel

Abstract: In this work, numerical simulations involving supersonic and hypersonic flows on an unstructured context are analyzed. The Van Leer and the Radespiel and Kroll schemes are implemented on a finite volume formulation, using unstructured spatial discretization. The algorithms are implemented in their first and second order spatial accuracies. The second order spatial accuracy is obtained by a linear reconstruction procedure based on the work of Barth and Jespersen. Several non-linear limiters are studied, as well two types of linear interpolation, based on the works of Frink, Parikh and Pirzadeh and of Jacon and Knight. Two types of viscous calculation to the laminar case are compared. They are programmed considering the works of Long, Khan and Sharp and of Jacon and Knight. To the turbulent simulations, the Wilcox and Rubesin model is employed. The ramp problem to the inviscid simulations and the re-entry capsule problem to the hypersonic viscous simulations are studied. The results have demonstrated that the Van Leer algorithm yields the best results in terms of the prediction of the shock angle of the oblique shock wave in the ramp problem and the best value of the stagnation pressure at the configuration nose in the re-entry capsule problem. The convective time step is the best choice to accelerate the convergence of the numerical schemes, as reported by Maciel. In terms of turbulent results, the Wilcox and Rubesin model yields good results, proving the good capacity of this turbulence model in simulate high hypersonic flows. This paper is the first part of this work and is related to the theory and inviscid solutions. The second paper of this work is concerned with the laminar and turbulent viscous results.

Keywords: Supersonic and hypersonic flows, Unstructured discretization, Van Leer algorithm, Radespiel and Kroll algorithm, Wilcox and Rubesin turbulence model, Euler and Navier-Stokes equations, Two-dimensions


Title of the Paper: Supersonic and Hypersonic Flows on 2D Unstructured Context: Part II

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Authors: Edisson Sávio De Góes Maciel

Abstract: In this work, numerical simulations involving supersonic and hypersonic flows on an unstructured context are analyzed. The Van Leer and the Radespiel and Kroll schemes are implemented on a finite volume formulation, using unstructured spatial discretization. The algorithms are implemented in their first and second order spatial accuracies. The second order spatial accuracy is obtained by a linear reconstruction procedure based on the work of Barth and Jespersen. Several non-linear limiters are studied, as well two types of linear interpolation, based on the works of Frink, Parikh and Pirzadeh and of Jacon and Knight. Two types of viscous calculation to the laminar case are compared. They are programmed considering the works of Long, Khan and Sharp and of Jacon and Knight. To the turbulent simulations, the Wilcox and Rubesin model is employed. The ramp problem for the inviscid supersonic simulations and the re-entry capsule for the viscous hypersonic simulations are considered. The results have demonstrated that the Van Leer algorithm yields the best results in terms of the prediction of the wall pressure distribution and the shock angle in the inviscid simulations and the best value of the stagnation pressure at the configuration nose in the viscous simulations. Moreover, the Van Leer algorithm in the SS case and using the Wilcox and Rubesin turbulence model predicts the best value of the lift aerodynamic coefficient. Hence, the Wilcox and Rubesin model yielded good results, proving its good capacity to predict high hypersonic flows. This paper is the second part of this work and is concerned with the laminar and turbulent viscous results.

Keywords: Supersonic and hypersonic flows, Unstructured discretization, Van Leer algorithm, Radespiel and Kroll algorithm, Wilcox and Rubesin turbulence model, Euler and Navier-Stokes equations, Two-dimensions


Title of the Paper: Fluid Flow in Channels Between Two Gas Turbines and Heat Recovery Steam Generator – A Theoretical Investigation

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Authors: H. Walter, C. Dobias, F. Holzleithner

Abstract: The paper present the results of a study for a special configuration of a combined cycle power plant. In this plant two gas turbines are installed to feed one Heat Recovery Steam Generator (HRSG). The flue gas flow in the channels between the two gas turbines and the HRSG was analyzed to get a more homogenous flow distribution in front of the first heating surface of the HRSG which is arranged downstream of the gas turbines. In the study a particular attention was placed at the operation conditions where only one gas turbine is in operation.
The results of the investigation have shown that the measures with a higher possibility to get a homogenous flow distribution in front of the first tube bank arranged downstream of the gas turbine have also a higher pressure loss and in last consequence they are linked with a higher loss of gas turbine power respectively a lower efficiency of the combined cycle. The study has also shown that a larger merging area for the flue gas arranged between the merging point of the two flue gas ducts and the entrance into the HRSG results in a more even flow distribution.

Keywords: Numerical simulation, Flue gas channel, Heat recovery steam generator, Channel optimization, Flow distribution


 

   
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