Search results for: Navier Stokes equations

Authors: M. Breška, I. Peruš, V. Stankovski

Abstract:

The number of Ground Motion Prediction Equations (GMPEs) used for predicting peak ground acceleration (PGA) and the number of earthquake recordings that have been used for fitting these equations has increased in the past decades. The current PF-L database contains 3550 recordings. Since the GMPEs frequently model the peak ground acceleration the goal of the present study was to refit a selection of 44 of the existing equation models for PGA in light of the latest data. The algorithm Levenberg-Marquardt was used for fitting the coefficients of the equations and the results are evaluated both quantitatively by presenting the root mean squared error (RMSE) and qualitatively by drawing graphs of the five best fitted equations. The RMSE was found to be as low as 0.08 for the best equation models. The newly estimated coefficients vary from the values published in the original works.

Keywords: Ground Motion Prediction Equations, Levenberg-Marquardt algorithm, refitting PF-L database.

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Authors: Saqib Mahmood, Rolf Radespiel

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This paper aims at numerically analysing the effect of an active flow control (AFC) by a vortex generator jet (VGJ) submerged in a boundary layer via Chimera Grids and Detached- Eddy Simulation (DES). The performance of DES results are judged against Reynolds-Averaged Navier-Stokes (RANS) and compared with the experiments that showed an unsteady vortex motion downstream of VGJ. Experimental results showed that the mechanism of embedding logitudinal vortex structure in the main stream flow is quite effective in increasing the near wall momentum of separated aircraft wing. In order to simulate such a flow configuration together with the VGJ, an efficient numerical approach is required. This requirement is fulfilled by performing the DES simulation over the flat plate using the DLR TAU Code. The DES predictions identify the vortex region via smooth hybrid length scale and predict the unsteady vortex motion observed in the experiments. The DES results also showed that the sufficient grid refinement in the vortex region resolves the turbulent scales downstream of the VGJ, the spatial vortex core postion and nondimensional momentum coefficient
RVx .

Keywords: VGJ, Chimera Grid, DES, RANS.

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Authors: Nisha Goyal, R.K. Gupta

Abstract:

Einstein vacuum equations, that is a system of nonlinear partial differential equations (PDEs) are derived from Weyl metric by using relation between Einstein tensor and metric tensor. The symmetries of Einstein vacuum equations for static axisymmetric gravitational fields are obtained using the Lie classical method. We have examined the optimal system of vector fields which is further used to reduce nonlinear PDE to nonlinear ordinary differential equation (ODE). Some exact solutions of Einstein vacuum equations in general relativity are also obtained.

Keywords: Gravitational fields, Lie Classical method, Exact solutions.

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Authors: Qianhong Zhang, Wenzhuan Zhang

Abstract:

This paper is concerned with the global asymptotic behavior of positive solution for a system of two nonlinear rational difference equations. Moreover, some numerical examples are given to illustrate results obtained.

Keywords: Difference equations, stability, unstable, global asymptotic behavior.

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Authors: D. K. Tiwari, Mukesh Kumar Awasthi, G. S. Agrawal

Abstract:

The effect of an axial electric field on the capillary instability of a cylindrical interface in the presence of heat and mass transfer has been investigated using viscous potential flow theory. In viscous potential flow, the viscous term in Navier-Stokes equation vanishes as vorticity is zero but viscosity is not zero. Viscosity enters through normal stress balance in the viscous potential flow theory and tangential stresses are not considered. A dispersion relation that accounts for the growth of axisymmetric waves is derived and stability is discussed theoretically as well as numerically. Stability criterion is given by critical value of applied electric field as well as critical wave number. Various graphs have been drawn to show the effect of various physical parameters such as electric field, heat transfer capillary number, conductivity ratio, permittivity ratio on the stability of the system. It has been observed that the axial electric field and heat and mass transfer both have stabilizing effect on the stability of the system.

Keywords: Capillary instability, Viscous potential flow, Heat and mass transfer, Axial electric field.

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Authors: Bhanu Gupta, Sanjay K. Srivastava

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In this paper, we shall present sufficient conditions for the ψ-exponential stability of a class of nonlinear impulsive differential equations. We use the Lyapunov method with functions that are not necessarily differentiable. In the last section, we give some examples to support our theoretical results.

Keywords: Exponential stability, globally exponential stability, impulsive differential equations, Lyapunov function, ψ-stability.

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Authors: Cheng-Chung Yang, Jr-Ming Miao, Fuh-Lin Lih, Tsung-Lung Liu, Ming-Hui Ho

Abstract:

The operation performance of a valveless micro-pump is strongly dependent on the shape of connected nozzle/diffuser and Reynolds number. The aims of present work are to compare the performance curves of micropump with the original straight nozzle/diffuser and contoured nozzle/diffuser under different back pressure conditions. The tested valveless micropumps are assembled of five pieces of patterned PMMA plates with hot-embracing technique. The structures of central chamber, the inlet/outlet reservoirs and the connected nozzle/diffuser are fabricated with laser cutting machine. The micropump is actuated with circular-type PZT film embraced on the bottom of central chamber. The deformation of PZT membrane with various input voltages is measured with a displacement laser probe. A simple testing facility is also constructed to evaluate the performance curves for comparison. In order to observe the evaluation of low Reynolds number multiple vortex flow patterns within the micropump during suction and pumping modes, the unsteady, incompressible laminar three-dimensional Reynolds-averaged Navier-Stokes equations are solved. The working fluid is DI water with constant thermo-physical properties. The oscillating behavior of PZT film is modeled with the moving boundary wall in way of UDF program. With the dynamic mesh method, the instants pressure and velocity fields are obtained and discussed.Results indicated that the volume flow rate is not monotony increased with the oscillating frequency of PZT film, regardless of the shapes of nozzle/diffuser. The present micropump can generate the maximum volume flow rate of 13.53 ml/min when the operation frequency is 64Hz and the input voltage is 140 volts. The micropump with contoured nozzle/diffuser can provide 7ml/min flow rate even when the back pressure is up to 400 mm-H2O. CFD results revealed that the flow central chamber was occupied with multiple pairs of counter-rotating vortices during suction and pumping modes. The net volume flow rate over a complete oscillating periodic of PZT

Keywords: valveless micropump、PZT diagraph、contoured nozzle/diffuser、vortex flow.

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Authors: Shafiq R. Qureshi, Syed Noman Danish, Muhammad Saeed Khalid

Abstract:

Fossil fuels are the major source to meet the world energy requirements but its rapidly diminishing rate and adverse effects on our ecological system are of major concern. Renewable energy utilization is the need of time to meet the future challenges. Ocean energy is the one of these promising energy resources. Threefourths of the earth-s surface is covered by the oceans. This enormous energy resource is contained in the oceans- waters, the air above the oceans, and the land beneath them. The renewable energy source of ocean mainly is contained in waves, ocean current and offshore solar energy. Very fewer efforts have been made to harness this reliable and predictable resource. Harnessing of ocean energy needs detail knowledge of underlying mathematical governing equation and their analysis. With the advent of extra ordinary computational resources it is now possible to predict the wave climatology in lab simulation. Several techniques have been developed mostly stem from numerical analysis of Navier Stokes equations. This paper presents a brief over view of such mathematical model and tools to understand and analyze the wave climatology. Models of 1st, 2nd and 3rd generations have been developed to estimate the wave characteristics to assess the power potential. A brief overview of available wave energy technologies is also given. A novel concept of on-shore wave energy extraction method is also presented at the end. The concept is based upon total energy conservation, where energy of wave is transferred to the flexible converter to increase its kinetic energy. Squeezing action by the external pressure on the converter body results in increase velocities at discharge section. High velocity head then can be used for energy storage or for direct utility of power generation. This converter utilizes the both potential and kinetic energy of the waves and designed for on-shore or near-shore application. Increased wave height at the shore due to shoaling effects increases the potential energy of the waves which is converted to renewable energy. This approach will result in economic wave energy converter due to near shore installation and more dense waves due to shoaling. Method will be more efficient because of tapping both potential and kinetic energy of the waves.

Keywords: Energy Utilizing, Wave Shoaling Phenomenon

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Authors: Bin Yu, Minghui Wang, Juntao Zhang

Abstract:

By the real representation of the quaternionic matrix, an iterative method for quaternionic linear equations Ax = b is proposed. Then the convergence conditions are obtained. At last, a numerical example is given to illustrate the efficiency of this method.

Keywords: Quaternionic linear equations, Real representation, Iterative algorithm.

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Authors: Mukesh Kumar Awasth, Mohammad Tamsir

Abstract:

The effect of porous medium on the capillary instability of a cylindrical interface in the presence of axial electric field has been investigated using viscous potential flow theory. In viscous potential flow, the viscous term in Navier-Stokes equation vanishes as vorticity is zero but viscosity is not zero. Viscosity enters through normal stress balance in the viscous potential flow theory and tangential stresses are not considered. A dispersion relation that accounts for the growth of axisymmetric waves is derived and stability is discussed theoretically as well as numerically. Stability criterion is given by critical value of applied electric field as well as critical wave number. Various graphs have been drawn to show the effect of various physical parameters such as electric field, viscosity ratio, permittivity ratio on the stability of the system. It has been observed that the axial electric field and porous medium both have stabilizing effect on the stability of the system.

Keywords: Capillary instability, Viscous potential flow, Porous media, Axial electric field.

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Authors: Ali Khaleel Kareem, Shian Gao, Ahmed Qasim Ahmed

Abstract:

A numerical investigation of unsteady mixed convection heat transfer in a 3D moving top wall enclosure, which has a central rotating cylinder and uses either artificial roughness on the bottom hot plate or smooth bottom hot plate to study the heat transfer enhancement, is completed for fixed circular cylinder, and anticlockwise and clockwise rotational speeds, -1 ≤ Ω ≤ 1, at Reynolds number of 5000. The top lid-driven wall was cooled, while the other remaining walls that completed obstructed cubic were kept insulated and motionless. A standard k-ε model of Unsteady Reynolds-Averaged Navier-Stokes (URANS) method is involved to deal with turbulent flow. It has been clearly noted that artificial roughness can strongly control the thermal fields and fluid flow patterns. Ultimately, the heat transfer rate has been dramatically increased by involving artificial roughness on the heated bottom wall in the presence of rotating cylinder.

Keywords: Artificial roughness, Lid-driven cavity, Mixed convection heat transfer, Rotating cylinder, URANS method.

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Authors: M. Karami Khorramabadi, M. M. Najafizadeh, J. Alibabaei Shahraki, P. Khazaeinejad

Abstract:

Analytical solution of the first-order and third-order shear deformation theories are developed to study the free vibration behavior of simply supported functionally graded plates. The material properties of plate are assumed to be graded in the thickness direction as a power law distribution of volume fraction of the constituents. The governing equations of functionally graded plates are established by applying the Hamilton's principle and are solved by using the Navier solution method. The influence of side-tothickness ratio and constituent of volume fraction on the natural frequencies are studied. The results are validated with the known data in the literature.

Keywords: Free vibration, Functionally graded plate, Naviersolution method.

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Authors: Kyoungwoo Park, Ji-Won Han, Hyo-Jae Lim, Byeong-Sam Kim, Juhee Lee

Abstract:

Shape optimization of the airfoil with high aspect ratio of long endurance unmanned aerial vehicle (UAV) is performed by the multi-objective optimization technology coupled with computational fluid dynamics (CFD). For predicting the aerodynamic characteristics around the airfoil the high-fidelity Navier-Stokes solver is employed and SMOGA (Simple Multi-Objective Genetic Algorithm), which is developed by authors, is used for solving the multi-objective optimization problem. To obtain the optimal solutions of the design variable (i.e., sectional airfoil profile, wing taper ratio and sweep) for high performance of UAVs, both the lift and lift-to-drag ratio are maximized whereas the pitching moment should be minimized, simultaneously. It is found that the lift force and lift-to-drag ratio are linearly dependent and a unique and dominant solution are existed. However, a trade-off phenomenon is observed between the lift-to-drag ratio and pitching moment. As the result of optimization, sixty-five (65) non-dominated Pareto individuals at the cutting edge of design spaces that is decided by airfoil shapes can be obtained.

Keywords: Unmanned aerial vehicle (UAV), Airfoil, CFD, Shape optimization, Lift-to-drag ratio.

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Authors: A. Pérard Lecomte, G. Fokoua, A. Mehel, A. Tanière

Abstract:

Automotive experimental measurements in wind tunnel are often conducted on reduced scale. Depending on the study, different similitude parameters are used by researchers to best reproduce the flow at full scale. In this paper, two parameters are investigated, which are Reynolds number and upstream velocity when dealing with airflow of typical urban speed range, below 15 m.s-1. Their impact on flow structures and aerodynamic drag in the wake of a heavy truck model are explored. To achieve this, Computational Fluid Dynamics (CFD) simulations have been conducted with the aim of modeling the wake airflow of full- and reduced-scaled heavy trucks (1/4 and 1/28). The Reynolds Average Navier-Stokes (RANS) approach combined to the Reynolds Stress Model (RSM) as the turbulence model closure was used. Both drag coefficients and upstream velocity profiles (flow topology) were found to be close one another for the three investigated scales, when the dynamical similitude Reynolds is achieved. Moreover, the difference is weak for the simulations based on the same inlet air velocity. Hence, for the relative low velocity range investigated here, the impact of the scale factor is limited.

Keywords: Aerodynamics, CFD, heavy truck, recirculation area, scale effects, similitude parameters.

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Authors: Yang Liu, Jinfeng Wang, Hong Li, Wei Gao, Siriguleng He

Abstract:

A new numerical scheme based on the H1-Galerkin mixed finite element method for a class of second-order pseudohyperbolic equations is constructed. The proposed procedures can be split into three independent differential sub-schemes and does not need to solve a coupled system of equations. Optimal error estimates are derived for both semidiscrete and fully discrete schemes for problems in one space dimension. And the proposed method dose not requires the LBB consistency condition. Finally, some numerical results are provided to illustrate the efficacy of our method.

Keywords: Pseudo-hyperbolic equations, splitting system, H1-Galerkin mixed method, error estimates.

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Authors: Mahmoud Zarrini, R.N. Pralhad

Abstract:

In this chapter, we have studied Variation of velocity in incompressible fluid over a moving surface. The boundary layer equations are on a fixed or continuously moving flat plate in the same or opposite direction to the free stream with suction and injection. The boundary layer equations are transferred from partial differential equations to ordinary differential equations. Numerical solutions are obtained by using Runge-Kutta and Shooting methods. We have found numerical solution to velocity and skin friction coefficient.

Keywords: Boundary layer, continuously moving surface, shooting method, skin friction coefficient.

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Authors: Mohamed M. Mousa, Aidarkhan Kaltayev

Abstract:

Based on the homotopy perturbation method (HPM) and Padé approximants (PA), approximate and exact solutions are obtained for cubic Boussinesq and modified Boussinesq equations. The obtained solutions contain solitary waves, rational solutions. HPM is used for analytic treatment to those equations and PA for increasing the convergence region of the HPM analytical solution. The results reveal that the HPM with the enhancement of PA is a very effective, convenient and quite accurate to such types of partial differential equations.

Keywords: Homotopy perturbation method, Padé approximants, cubic Boussinesq equation, modified Boussinesq equation.

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Authors: Mohana Sundaram Muthuvalu, Jumat Sulaiman

Abstract:

In this paper, application of the complexity reduction approach based on half- and quarter-sweep iteration concepts with Jacobi iterative method for solving composite trapezoidal (CT) algebraic equations is discussed. The performances of the methods for CT algebraic equations are comparatively studied by their application in solving linear Fredholm integral equations of the second kind. Furthermore, computational complexity analysis and numerical results for three test problems are also included in order to verify performance of the methods.

Keywords: Complexity reduction approach, Composite trapezoidal scheme, Jacobi method, Linear Fredholm integral equations

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Authors: Keke Gao, Tao Lin, Yonghui Xie, Di Zhang

Abstract:

Complicated unsteady flow in axial turbines produces high-frequency unsteady aerodynamic exciting force, which threatens the safe operation of turbines. This paper illustrates how negative-bowed stator reduces the rotor unsteady aerodynamic exciting force by unsteady flow field. With the support of three-dimensional viscous compressible Navier-Stokes equation, the single axial turbines with 0, -10 and -20 degree bowed stator are comparably investigated, aiming to identify the flow field structure difference caused by various negative-bowed degrees. The results show that negative-bowed stator strengthens the turbulence kinetic energy, which is further strengthened with the increase of negative-bowed degree. Meanwhile, the flow phenomenon including stator wakes and passage vortex is shown. In addition, the interaction of upstream negative-bowed wakes contributes to the reduction of unsteady blade load fluctuation. Furthermore, the aerodynamic exciting force decreases with the increasing negative bowed degree, while the efficiency is correspondingly reduced. This paper provides the reference for the alleviation of the harmful impact caused by unsteady interaction with the method of wake control.

Keywords: Unsteady flow, axial turbine, wake, aerodynamic force, loss.

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Authors: Li Ge

Abstract:

In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using Leray-Schauder theory:

Keywords: impulsive differential equations, impulsive integraldifferential equation, boundary value problems

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Authors: jianhua Hou, Changqing Yang, and Beibo Qin

Abstract:

A numerical method for solving nonlinear Fredholm integral equations of second kind is proposed. The Fredholm type equations which have many applications in mathematical physics are then considered. The method is based on hybrid function  approximations. The properties of hybrid of block-pulse functions and Chebyshev polynomials are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of nonlinear. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.

Keywords: Hybrid functions, Fredholm integral equation, Blockpulse, Chebyshev polynomials, product operational matrix.

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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: Li Ge

Abstract:

In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using leray-Schauder theory:

Keywords: impulsive differential equations, impulsive integraldifferentialequation, boundary value problems

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Authors: Li Ge

Abstract:

In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using leray-Schauder theory:

Keywords: impulsive differential equations, impulsive integraldifferentialequation, boundary value problems

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Authors: Fadi Awawdeh, H.M. Jaradat

Abstract:

In this paper, we establish existence and uniqueness of solutions for a class of inverse problems of degenerate differential equations. The main tool is the perturbation theory for linear operators.

Keywords: Inverse Problem, Degenerate Differential Equations, Perturbation Theory for Linear Operators

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Authors: A. M. Sagir

Abstract:

This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y''' = f(x, y, y', y''), y(α)=y₀, y'(α)=β, y''(α)=η with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non – stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep, Self starting, Third Order Ordinary Differential Equations.

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Authors: Sameerah Jamal, Abdul Hamid Kara, Ashfaque H. Bokhari

Abstract:

Equations on curved manifolds display interesting properties in a number of ways. In particular, the symmetries and, therefore, the conservation laws reduce depending on how curved the manifold is. Of particular interest are the wave and Gordon-type equations; we study the symmetry properties and conservation laws of these equations on the Milne and Bianchi type III metrics. Properties of reduction procedures via symmetries, variational structures and conservation laws are more involved than on the well known flat (Minkowski) manifold.

Keywords: Bianchi metric, conservation laws, Milne metric, symmetries.

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Authors: M. Amiri

Abstract:

In this work, functionally graded materials (FGMs), subjected to loading, which varies with time has been studied. The material properties of FGM are changing through the thickness of material as power law distribution. The conical shells have been chosen for this study so in the first step capability equations for FGM have been obtained. With Galerkin method, these equations have been replaced with time dependant differential equations with variable coefficient. These equations have solved for different initial conditions with variation methods. Important parameters in loading conditions are semi-vertex angle, external pressure and material properties. Results validation has been done by comparison between with those in previous studies of other researchers.

Keywords: Impulsive semi-vertex angle, loading, functionally graded materials, composite material.

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Authors: Sachin Kumar, Y. K. Gupta, J. R. Sharma

Abstract:

In the present article, a new class of solutions of Einstein field equations is investigated for a spherically symmetric space-time when the source of gravitation is a perfect fluid. All the solutions have been derived by making some suitable arrangements in the field equations. The solutions so obtained have been seen to describe Schwarzschild interior solutions. Most of the solutions are subjected to the reality conditions. As far as the authors are aware the solutions are new.

Keywords: Einstein's equations, General Relativity, PerfectFluid, Spherical symmetric.

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Authors: Tang Wei, Yang Xiaofeng, Gui Yewei, Du Yanxia

Abstract:

Complex lifting entry was selected for precise landing performance during the Mars Science Laboratory entry. This study aims to develop the three-dimensional numerical method for precise computation and the surface panel method for rapid engineering prediction. Detailed flow field analysis for Mars exploration mission was performed by carrying on a series of fully three-dimensional Navier-Stokes computations. The static aerodynamic performance was then discussed, including the surface pressure, lift and drag coefficient, lift-to-drag ratio with the numerical and engineering method. Computation results shown that the shock layer is thin because of lower effective specific heat ratio, and that calculated results from both methods agree well with each other, and is consistent with the reference data. Aerodynamic performance analysis shows that CG location determines trim characteristics and pitch stability, and certain radially and axially shift of the CG location can alter the capsule lifting entry performance, which is of vital significance for the aerodynamic configuration design and inner instrument layout of the Mars entry capsule.

Keywords: Mars entry capsule, static aerodynamics, computational fluid dynamics, hypersonic.

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