Search results for: Stokes problem

Authors: Xin Luo, Jin Huang, Pan Cheng

Abstract:

By means of Sidi-Israeli’s quadrature rules, mechanical quadrature methods (MQMs) for solving the first kind boundary integral equations (BIEs) of steady state Stokes problem are presented. The convergence of numerical solutions by MQMs is proved based on Anselone’s collective compact and asymptotical compact theory, and the asymptotic expansions with the odd powers of the errors are provided, which implies that the accuracy of the approximations by MQMs possesses high accuracy order O (h3). Finally, the numerical examples show the efficiency of our methods.

Keywords: Stokes problem, boundary integral equation, mechanical quadrature methods, asymptotic expansions.

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Authors: M.Devakar, T.K.V.Iyengar

Abstract:

In this paper, we investigate the generalized Stokes’ problems for an incompressible couple stress fluid. Analytical solution of the governing equations is obtained in Laplace transform domain for each problem. A standard numerical inversion technique is used to invert the Laplace transform of the velocity in each case. The effect of various material parameters on velocity is discussed and the results are presented through graphs. It is observed that, the results are in tune with the observation of V.K.Stokes in connection with the variation of velocity in the flow between two parallel plates when the top one is moving with constant velocity and the bottom one is at rest.

Keywords: Couple stress fluid, Generalized Stokes’ problems, Laplace transform, Numerical inversion

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Authors: M. Zamani, O. Kahar

Abstract:

Solution to unsteady Navier-Stokes equation by Splitting method in physical orthogonal algebraic curvilinear coordinate system, also termed 'Non-linear grid system' is presented. The linear terms in Navier-Stokes equation are solved by Crank- Nicholson method while the non-linear term is solved by the second order Adams-Bashforth method. This work is meant to bring together the advantage of Splitting method as pressure-velocity solver of higher efficiency with the advantage of consuming Non-linear grid system which produce more accurate results in relatively equal number of grid points as compared to Cartesian grid. The validation of Splitting method as a solution of Navier-Stokes equation in Nonlinear grid system is done by comparison with the benchmark results for lid driven cavity flow by Ghia and some case studies including Backward Facing Step Flow Problem.

Keywords: Navier-Stokes, 'Non-linear grid system', Splitting method.

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Authors: Gunawan Nugroho, Ahmed M. S. Ali, Zainal A. Abdul Karim

Abstract:

Incompressible Navier-Stokes equations are reviewed in this work. Three-dimensional Navier-Stokes equations are solved analytically. The Mathematical derivation shows that the solutions for the zero and constant pressure gradients are similar. Descriptions of the proposed formulation and validation against two laminar experiments and three different turbulent flow cases are reported in this paper. Even though, the analytical solution is derived for nonreacting flows, it could reproduce trends for cases including combustion.

Keywords: Navier-Stokes Equations, potential function, turbulent flows.

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Authors: N. Khatiashvili, K. Pirumova, D. Janjgava

Abstract:

The Stokes equation connected with the fluid flow over the axisymmetric bodies in a cylindrical area is considered. The equation is studied in a moving coordinate system with the appropriate boundary conditions. Effective formulas for the velocity components are obtained. The graphs of the velocity components and velocity profile are plotted.

Keywords: Stokes system, viscous fluid.

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Authors: Raphael Zanella, Todd A. Oliver, Karl W. Schulz

Abstract:

This work deals with the finite element approximation of axisymmetric compressible flows with swirl velocity. We are interested in problems where the flow, while weakly dependent on the azimuthal coordinate, may have a strong azimuthal velocity component. We describe the approximation of the compressible Navier-Stokes equations with H1-conformal spaces of axisymmetric functions. The weak formulation is implemented in a C++ solver with explicit time marching. The code is first verified with a convergence test on a manufactured solution. The verification is completed by comparing the numerical and analytical solutions in a Poiseuille flow case and a Taylor-Couette flow case. The code is finally applied to the problem of a swirling subsonic air flow in a plasma torch geometry.

Keywords: Axisymmetric problem, compressible Navier- Stokes equations, continuous finite elements, swirling flow.

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Authors: A. Giniatoulline

Abstract:

A nonlinear model of the mathematical fluid dynamics which describes the motion of an incompressible viscous rotating fluid in a homogeneous gravitational field is considered. The model is a generalization of the known Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density. An explicit algorithm for the solution is constructed, and the proof of the existence and uniqueness theorems for the strong solution of the nonlinear problem is given. For the linear case, the localization and the structure of the spectrum of inner waves are also investigated.

Keywords: Galerkin method, Navier-Stokes equations, nonlinear partial differential equations, Sobolev spaces, stratified fluid.

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Authors: Ze-Jun Hu, Ting-Zhu Huang, Ning-Bo Tan

Abstract:

To solve saddle point systems efficiently, several preconditioners have been published. There are many methods for constructing preconditioners for linear systems from saddle point problems, for instance, the relaxed dimensional factorization (RDF) preconditioner and the augmented Lagrangian (AL) preconditioner are used for both steady and unsteady Navier-Stokes equations. In this paper we compare the RDF preconditioner with the modified AL (MAL) preconditioner to show which is more effective to solve Navier-Stokes equations. Numerical experiments indicate that the MAL preconditioner is more efficient and robust, especially, for moderate viscosities and stretched grids in steady problems. For unsteady cases, the convergence rate of the RDF preconditioner is slightly faster than the MAL perconditioner in some circumstances, but the parameter of the RDF preconditioner is more sensitive than the MAL preconditioner. Moreover the convergence rate of the MAL preconditioner is still quite acceptable. Therefore we conclude that the MAL preconditioner is more competitive than the RDF preconditioner. These experiments are implemented with IFISS package. 

Keywords: Navier-Stokes equations, Krylov subspace method, preconditioner, dimensional splitting, augmented Lagrangian preconditioner.

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Authors: Mikhail Gritskevich, Sebastian Hohenstein

Abstract:

The paper presents the results of a detailed assessment of several modern Reynolds Averaged Navier-Stokes (RANS) turbulence models for prediction of C3X vane film cooling at various injection regimes. Three models are considered, namely the Shear Stress Transport (SST) model, the modification of the SST model accounting for the streamlines curvature (SST-CC), and the Explicit Algebraic Reynolds Stress Model (EARSM). It is shown that all the considered models face with a problem in prediction of the adiabatic effectiveness in the vicinity of the cooling holes; however, accounting for the Reynolds stress anisotropy within the EARSM model noticeably increases the solution accuracy. On the other hand, further downstream all the models provide a reasonable agreement with the experimental data for the adiabatic effectiveness and among the considered models the most accurate results are obtained with the use EARMS.

Keywords: Discrete holes film cooling, Reynolds Averaged Navier-Stokes, Reynolds stress tensor anisotropy, turbulent heat transfer.

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Authors: M. Saeedi, R. Wuchner, K.-U. Bletzinger

Abstract:

In order to study the aerodynamic performance of a semi-flexible membrane wing, Fluid-Structure Interaction simulations have been performed. The fluid problem has been modeled using two different approaches which are the vortex panel method and the numerical solution of the Navier-Stokes equations. Nonlinear analysis of the structural problem is performed using the Finite Element Method. Comparison between the two fluid solvers has been made. Aerodynamic performance of the wing is discussed regarding its lift and drag coefficients and they are compared with those of the equivalent rigid wing.

Keywords: CFD, FSI, Membrane wing, Vortex panel method.

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Authors: Monika Neda, Elena Nikonova

Abstract:

We present a numerical study of the sensitivity of the so called time relaxation family of models of fluid motion with respect to the time relaxation parameter χ on the two dimensional cavity problem. The goal of the study is to compute and compare the sensitivity of the model using finite difference method (FFD) and sensitivity equation method (SEM).

Keywords: Sensitivity, time relaxation, deconvolution, Navier- Stokes equations.

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Authors: T. V. S. Sekhar, B. Hema Sundar Raju

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Laminar natural-convective heat transfer from a horizontal cylinder is studied by solving the Navier-Stokes and energy equations using higher order compact scheme in cylindrical polar coordinates. Results are obtained for Rayleigh numbers of 1, 10, 100 and 1000 for a Prandtl number of 0.7. The local Nusselt number and mean Nusselt number are calculated and compared with available experimental and theoretical results. Streamlines, vorticity - lines and isotherms are plotted.

Keywords: Higher order compact scheme, Navier-Stokes equations, Energy equation, Natural convection, Boussinesq's approximation and Mean Nusselt number.

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Authors: Ding Guo-hao, Li Hua, Wang Wen-long

Abstract:

A parallel computational fluid dynamics code has been developed for the study of aerodynamic heating problem in hypersonic flows. The code employs the 3D Navier-Stokes equations as the basic governing equations to simulate the laminar hypersonic flow. The cell centered finite volume method based on structured grid is applied for spatial discretization. The AUSMPW+ scheme is used for the inviscid fluxes, and the MUSCL approach is used for higher order spatial accuracy. The implicit LU-SGS scheme is applied for time integration to accelerate the convergence of computations in steady flows. A parallel programming method based on MPI is employed to shorten the computing time. The validity of the code is demonstrated by comparing the numerical calculation result with the experimental data of a hypersonic flow field around a blunt body.

Keywords: Aerodynamic Heating, AUSMPW+, MPI, ParallelComputation

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Authors: Rajendra K. Ray, H. V. R. Mittal

Abstract:

A numerical study is made of laminar, unsteady flow behind a rotationally oscillating circular cylinder using a recently developed higher order compact (HOC) scheme. The stream function vorticity formulation of Navier-Stokes (N-S) equations in cylindrical polar coordinates are considered as the governing equations. The temporal behaviour of vortex formation and relevant streamline patterns of the flow are scrutinized over broad ranges of two externally specified parameters namely dimensionless forced oscillating frequency Sf and dimensionless peak rotation rate αm for the Reynolds-s number Re = 200. Excellent agreements are found both qualitatively and quantitatively with the existing experimental and standard numerical results.

Keywords: HOC, Navier-Stokes, non-uniform polar grids, rotationally oscillating cylinder.

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Authors: Aymen Laadhari

Abstract:

We present in this paper a fully implicit finite element method tailored for the numerical modeling of inextensible fluidic membranes in a surrounding Newtonian fluid. We consider a highly simplified version of the Canham-Helfrich model for phospholipid membranes, in which the bending force and spontaneous curvature are disregarded. The coupled problem is formulated in a fully Eulerian framework and the membrane motion is tracked using the level set method. The resulting nonlinear problem is solved by a Newton-Raphson strategy, featuring a quadratic convergence behavior. A monolithic solver is implemented, and we report several numerical experiments aimed at model validation and illustrating the accuracy of the proposed method. We show that stability is maintained for significantly larger time steps with respect to an explicit decoupling method.

Keywords: Finite element method, Newton method, level set, Navier-Stokes, inextensible membrane, liquid drop.

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Authors: A. Giniatoulline

Abstract:

A model of the mathematical fluid dynamics which describes the motion of a three-dimensional viscous rotating fluid in a homogeneous gravitational field with the consideration of the salinity and heat transfer is considered in a vertical finite layer. The model is a generalization of the linearized Navier-Stokes system with the addition of the Coriolis parameter and the equations for changeable density, salinity, and heat transfer. An explicit solution is constructed and the proof of the existence and uniqueness theorems is given. The localization and the structure of the spectrum of inner waves is also investigated. The results may be used, in particular, for constructing stable numerical algorithms for solutions of the considered models of fluid dynamics of the Atmosphere and the Ocean.

Keywords: Fourier transform, generalized solutions, Navier-Stokes equations, stratified fluid.

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Authors: N. Thongjub, B. Puangkird, V. Ngamaramvaranggul

Abstract:

The numerical simulation of the slip effect via vicoelastic fluid for 4:1 contraction problem is investigated with regard to kinematic behaviors of streamlines and stress tensor by models of the Navier-Stokes and Oldroyd-B equations. Twodimensional spatial reference system of incompressible creeping flow with and without slip velocity is determined and the finite element method of a semi-implicit Taylor-Galerkin pressure-correction is applied to compute the problem of this Cartesian coordinate system including the schemes of velocity gradient recovery method and the streamline-Upwind / Petrov-Galerkin procedure. The slip effect at channel wall is added to calculate after each time step in order to intend the alteration of flow path. The result of stress values and the vortices are reduced by the optimum slip coefficient of 0.1 with near the outcome of analytical solution.

Keywords: Slip effect, Oldroyd-B fluid, slip coefficient, time stepping method.

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Authors: M. A. Tayfun

Abstract:

Occurrences of spurious crests on the troughs of large, relatively steep second-order Stokes waves are anomalous and not an inherent characteristic of real waves. Here, the effects of such occurrences on the statistics described by the standard second-order stochastic model are examined theoretically and by way of simulations. Theoretical results and simulations indicate that when spurious occurrences are sufficiently large, the standard model leads to physically unrealistic surface features and inaccuracies in the statistics of various surface features, in particular, the troughs and thus zero-crossing heights of large waves. Whereas inaccuracies can be fairly noticeable for long-crested waves in both deep and shallower depths, they tend to become relatively insignificant in directional waves.

Keywords: Large waves, non-linear effects, simulation, spectra, spurious crests, Stokes waves, wave breaking, wave statistics.

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Authors: Hnin Hnin Kyi, Khaing Khaing Aye

Abstract:

Acoustic function plays an important role in aerodynamic mechanical engineering. It can classify the kind of air-vehicle such as subsonic or supersonic. Acoustic velocity relates with velocity and Mach number. Mach number relates again acoustic stability or instability condition. Mach number plays an important role in growth or decay in energy system. Acoustic is a function of temperature and temperature is directly proportional to pressure. If we control the pressure, we can control acoustic function. To get pressure stability condition, we apply Navier-Stokes equations.

Keywords: Acoustic velocity, Irrotational, Mach number, Rotational.

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Authors: Lina Wu, Jia Liu, Ye Li

Abstract:

The goal of this project is to investigate constant properties (called the Liouville-type Problem) for a p-stable map as a local or global minimum of a p-energy functional where the domain is a Euclidean space and the target space is a closed half-ellipsoid. The First and Second Variation Formulas for a p-energy functional has been applied in the Calculus Variation Method as computation techniques. Stokes’ Theorem, Cauchy-Schwarz Inequality, Hardy-Sobolev type Inequalities, and the Bochner Formula as estimation techniques have been used to estimate the lower bound and the upper bound of the derived p-Harmonic Stability Inequality. One challenging point in this project is to construct a family of variation maps such that the images of variation maps must be guaranteed in a closed half-ellipsoid. The other challenging point is to find a contradiction between the lower bound and the upper bound in an analysis of p-Harmonic Stability Inequality when a p-energy minimizing map is not constant. Therefore, the possibility of a non-constant p-energy minimizing map has been ruled out and the constant property for a p-energy minimizing map has been obtained. Our research finding is to explore the constant property for a p-stable map from a Euclidean space into a closed half-ellipsoid in a certain range of p. The certain range of p is determined by the dimension values of a Euclidean space (the domain) and an ellipsoid (the target space). The certain range of p is also bounded by the curvature values on an ellipsoid (that is, the ratio of the longest axis to the shortest axis). Regarding Liouville-type results for a p-stable map, our research finding on an ellipsoid is a generalization of mathematicians’ results on a sphere. Our result is also an extension of mathematicians’ Liouville-type results from a special ellipsoid with only one parameter to any ellipsoid with (n+1) parameters in the general setting.

Keywords: Bochner Formula, Stokes’ Theorem, Cauchy-Schwarz Inequality, first and second variation formulas, Hardy-Sobolev type inequalities, Liouville-type problem, p-harmonic map.

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Authors: Igor Nedelkovski, Ilios Vilos, Tale Geramitcioski

Abstract:

Computational simulation of steam flow and heat transfer in power plant condensers on the basis of the threedimensional mathematical model for the flow through porous media is presented. In order to solve the mathematical model of steam flow and heat transfer in power plant condensers, the Streamline Upwind Petrov-Galerkin finite element method is applied. By comparison of the results of simulation with experimental results about an experimental condenser, it is confirmed that SUPG finite element method can be successfully applied for solving the three-dimensional mathematical model of steam flow and heat transfer in power plant condensers.

Keywords: Navier-Stokes, FEM, condensers, steam.

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Authors: Rana Khalid Naeem, Waseem Ahmed Khan, Muhammad Akhtar, Asif Mansoor

Abstract:

The Navier Stokes Equations (NSE) for an incompressible fluid of variable viscosity in the presence of an unknown external force in Von-Mises system x,\ are transformed, and some new exact solutions for a class of flows characterized by equation y f x a\b for an arbitrary state equation are determined, where f x is a function, \ the stream function, a z 0 and b are the arbitrary constants. In three, out of four cases, the function f x is arbitrary, and the solutions are the solutions of the flow equations for all the flows characterized by the equationy f x a\b. Streamline patterns for some forms of f x in unbounded and bounded regions are given.

Keywords: Bounded and unbounded region, Exact solution, Navier Stokes equations, Streamline pattern, Variable viscosity, Von- Mises system

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Authors: Ram N. Singh, Abraham K. George, Dawood N. Al-Namaani

Abstract:

The Euler-s equation of motion is extended to include the viscosity stress tensor leading to the formulation of Navier– Stokes type equation. The latter is linearized and applied to investigate the rotational motion or vorticity in a viscous fluid. Relations for the velocity of viscous waves and attenuation parameter are obtained in terms of viscosity (μ) and the density (¤ü) of the fluid. μ and ¤ü are measured experimentally as a function of temperature for two different samples of light and heavy crude oil. These data facilitated to determine the activation energy, velocity of viscous wave and the attenuation parameter. Shear wave velocity in heavy oil is found to be much larger than the light oil, whereas the attenuation parameter in heavy oil is quite low in comparison to light one. The activation energy of heavy oil is three times larger than light oil.

Keywords: Activation Energy, Attenuation, Crude Oil, Navier- Stokes Equation, Viscosity.

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Authors: Minghui Wang, Shanrui Hu

Abstract:

An inverse problem of doubly center matrices is discussed. By translating the constrained problem into unconstrained problem, two iterative methods are proposed. A numerical example illustrate our algorithms.

Keywords: doubly center matrix, electric network theory, iterative methods, least-square problem.

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Authors: Brian Considine, Aonghus McNabola, John Gallagher, Prashant Kumar

Abstract:

Passive air pollution control devices known as aspiration efficiency reducers (AER) have been developed using aspiration efficiency (AE) concepts. Their purpose is to reduce the concentration of particulate matter (PM) drawn into a building air handling unit (AHU) through alterations in the inlet design improving energy consumption. In this paper an examination is conducted into the effect of installing a deflector system around an AER-AHU inlet for both a forward and rear-facing orientations relative to the wind. The results of the study found that these deflectors are an effective passive control method for reducing AE at various ambient wind speeds over a range of microparticles of varying diameter. The deflector system was found to induce a large wake zone at low ambient wind speeds for a rear-facing AER-AHU, resulting in significantly lower AE in comparison to without. As the wind speed increased, both contained a wake zone but have much lower concentration gradients with the deflectors. For the forward-facing models, the deflector system at low ambient wind speed was preferred at higher Stokes numbers but there was negligible difference as the Stokes number decreased. Similarly, there was no significant difference at higher wind speeds across the Stokes number range tested. The results demonstrate that a deflector system is a viable passive control method for the reduction of ventilation energy consumption.

Keywords: Aspiration efficiency, energy, particulate matter, ventilation.

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Authors: Darwin Gouwanda, S. G. Ponnambalam

Abstract:

Set covering problem is a classical problem in computer science and complexity theory. It has many applications, such as airline crew scheduling problem, facilities location problem, vehicle routing, assignment problem, etc. In this paper, three different techniques are applied to solve set covering problem. Firstly, a mathematical model of set covering problem is introduced and solved by using optimization solver, LINGO. Secondly, the Genetic Algorithm Toolbox available in MATLAB is used to solve set covering problem. And lastly, an ant colony optimization method is programmed in MATLAB programming language. Results obtained from these methods are presented in tables. In order to assess the performance of the techniques used in this project, the benchmark problems available in open literature are used.

Keywords: Set covering problem, genetic algorithm, ant colony optimization, LINGO.

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Authors: Divya Rajavathsavai, Akhilesh Khapre, Basudeb Munshi

Abstract:

The computational fluid dynamics (CFD) study of stirred tank with the air-water interface are carried out in the presence of different types of the impeller and with or without baffles. A multiple reference frame (MRF) approach with the volume of fluid (VOF) method is used to capture the air-water interface. The RANS (Reynolds Averaged Navier-Stokes) equations with k-ε turbulence model are solved to predict the flow behavior of water and air phase which are treated as a different phases. The predicted results have shown that the VOF method is able to capture the interface in the unbaffled tank. While, the VOF method is showing an unfeasible results in the baffled tank with high rotational impeller speed. For continuous stirred tank, the air-water interface is disturbed by the inflow and the level of water is also increased with time.

Keywords: Computational Fluid Dynamics, stirred tank, airwater interface, multiple reference frame, volume of fluid, Reynolds Averaged Navier-Stokes equations.

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Authors: A. Abou El-Azm Aly, F. Nicolleau, T. M. Michelitsch, A. F. Nowakowski

Abstract:

The dispersion of heavy particles line in an isotropic and incompressible three-dimensional turbulent flow has been studied using the Kinematic Simulation techniques to find out the evolution of the line fractal dimension. In this study, the fractal dimension of the line is found for different cases of heavy particles inertia (different Stokes numbers) in the absence of the particle gravity with a comparison with the fractal dimension obtained in the diffusion case of material line at the same Reynolds number. It can be concluded for the dispersion of heavy particles line in turbulent flow that the particle inertia affect the fractal dimension of a line released in a turbulent flow for Stokes numbers 0.02 < St < 2. At the beginning for small times, most of the different cases are not affected by the inertia until a certain time, the particle response time τa, with larger time as the particles inertia increases, the fractal dimension of the line increases owing to the particles becoming more sensitive to the small scales which cause the change in the line shape during its journey.

Keywords: Heavy particles, two-phase flow, Kinematic Simulation, Fractal dimension.

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Authors: Zohreh Orshesh

Abstract:

In this study, a 3D combustion chamber was simulated using FLUENT 6.32. Aim to obtain detailed information on combustion characteristics and _ nitrogen oxides in the furnace and the effect of oxygen enrichment in a combustion process. Oxygenenriched combustion is an effective way to reduce emissions. This paper analyzes NO emission, including thermal NO and prompt NO. Flow rate ratio of air to fuel is varied as 1.3, 3.2 and 5.1 and the oxygen enriched flow rates are 28, 54 and 68 lit/min. The 3D Reynolds Averaged Navier Stokes (RANS) equations with standard k-ε turbulence model are solved together by Fluent 6.32 software. First order upwind scheme is used to model governing equations and the SIMPLE algorithm is used as pressure velocity coupling. Results show that for AF=1.3, increase the oxygen flow rate of oxygen reduction in NO emissions is Lance. Moreover, in a fixed oxygen enrichment condition, increasing the air to fuel ratio will increase the temperature peak, but not the NO emission rate. As a result, oxygen enrichment can reduce the NO emission at this kind of furnace in low air to fuel rates.

Keywords: Combustion chamber, Oxygen enrichment, Reynolds Averaged Navier- Stokes, NO emission

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Authors: Chao Wang, Ting-Zhu Huang Chen Jia

Abstract:

In this paper, we propose a new linear complementarity problem named as bi-linear complementarity problem (BLCP) and the method for solving BLCP. In addition, the algorithm for error estimation of BLCP is also given. Numerical experiments show that the algorithm is efficient.

Keywords: Bi-linear complementarity problem, Linear complementarity problem, Extended linear complementarity problem, Error estimation, P-matrix, M-matrix.

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