Solution Of Viscous Flow Research Articles

DYNAMICAL STRUCTURE OF VISCOUS ACCRETION DISKS WITH SHOCKS

We develop and discuss global accretion solutions for viscous advection-dominated accretion flow (ADAF) disks containing centrifugally supported isothermal shock waves. The fact that such shocks can exist at all in ADAF disks is a new result. Interestingly, we find that isothermal shocks can form even when the level of viscous dissipation is relatively high. In order to better understand this phenomenon, we explore all possible combinations of the fundamental flow parameters, such as specific energy, specific angular momentum, and viscosity, to obtain the complete family of global solutions. This procedure allows us to identify the region of the parameter space where isothermal shocks can exist in viscous ADAF disks. The allowed region is maximized in the inviscid case, and it shrinks as the level of viscous dissipation increases. Adopting the canonical value γ = 1.5 for the ratio of specific heats, we find that the shock region disappears completely when the Shakura-Sunyaev viscosity parameter α exceeds the critical value ~0.27. This establishes for the first time that steady ADAF disks containing shocks can exist even for relatively high levels of viscous dissipation. If an isothermal shock is present in the disk, it would have important implications for the acceleration of energetic particles that can escape to power the relativistic jets commonly observed around underfed, radio-loud black holes. In two specific applications, we confirm that the kinetic luminosity lost from the disk at the isothermal shock location is sufficient to power the observed relativistic outflows in M87 and Sgr A*.

An integrated method for predicting the hydrodynamic resistance of low- [formula omitted] ships

An integrated CFD method is described for predicting the total hydrodynamic resistance at model as well as at full scale of conventional ship forms. The method combines a non-linear potential with a viscous flow solution of the RANS equations. The potential solution is achieved by covering the hull and the free surface with quadrilateral elements while convergence is based on an iterative procedure. A three-block decomposition is introduced to solve the RANS equations in curvilinear co-ordinates and a new conformal mapping technique has been developed to generate grids effectively. To validate the method, experiments have been carried out for a model with three different bulbous bows at the towing tank of NTUA. Computed resistance coefficients for both the models and the 40:1 full scale ships are also compared in order to evaluate the fundamental principles of empirical extrapolation methods.

Analytical approximate solutions for two-dimensional viscous flow through expanding or contracting gaps with permeable walls

Abstract In this paper, the problem of laminar, isothermal, incompressible and viscous flow in a rectangular domain bounded by two moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions is solved analytically by using the homotopy analysis method (HAM). Graphical results are presented to investigate the influence of the nondimensional wall dilation rate α and permeation Reynolds number Re on the velocity, normal pressure distribution and wall shear stress. The obtained solutions, in comparison with the numerical solutions, demonstrate remarkable accuracy. The present problem for slowly expanding or contracting walls with weak permeability is a simple model for the transport of biological fluids through contracting or expanding vessels.

Numerical study and control method of interaction of nucleation and boundary layer separation in condensing flow

The spontaneous nucleation flow in turbine cascade was numerically studied. The model was implemented within a full Navier-Stokes viscous flow solution procedure and the process of condensation was calculated by the quadrature method of moments that shows good accuracy with very broad size distributions. Results were presented for viscous and inviscous flow, showing the influence of boundary layer separation and wake vortices on spontaneous nucleation. The results show that the degree of flow separation in wet steam flow is greater than that in superheated steam flow due to condensation shock and that the loss cannot be neglected. Furthermore, the impact of boundary layer separation and wake vortices on velocity profiles and its implications for profile loss were considered. The calculations showed that layer separation and wake vortices influence nucleation rate, leading to different droplet distributions. A method for controlling homogeneous nucleation and for reducing degree of flow separation in high-speed transonic wet steam flow was presented. The liquid phase parameter distribution is sensitive to the suction side profile of turbine cascade, which impacts the nucleation rate distribution leading to different droplet distributions and affects the degree of flow separation. The numerical study provides a practical design method for turbine blade to reduce wetness losses.

Analytical Solution of Viscous Flow in Porous Media Using ADM and Comparison with the Numerical Runge–Kutta Method

In this article, the problem of laminar viscous flow in a semi-porous channel in the presence of a transverse magnetic field is presented, and the Adomian decomposition method is employed to compute an approximation for the solution of the system of nonlinear differential equations governing on the problem. Then, we consider the influence of the two dimensionless numbers: the Hartmann number (Ha) for the description of the magnetic forces and the Reynolds number (Re) for the dynamic forces. The results of the Adomian decomposition method (ADM) were compared with the numerical method (NM) solution, homotopy perturbation method (HPM), and variation iteration method (VIM). The results reveal that this method is very effective and simple and can be applied for other nonlinear problems.

Simple non-perturbative solution for MHD viscous flow due to a shrinking sheet

The magnetohydrodynamic (MHD) viscous flow due to a shrinking sheet is examined analytically. The series solution is obtained using the Adomian decomposition method (ADM) coupled with Padé approximants to handle the condition at infinity. The numerical solutions agree very well with the results by the homotopy analysis method.

Unsteady viscous flow with variable viscosity in a vascular tube with an overlapping constriction

Numerical solution of the unsteady viscous flow in the neighborhood of an overlapping constriction is obtained under laminar flow conditions with the motivation for modeling blood flow through a local occlusion of artery formed due to arterial disease. The flowing blood is considered to be incompressible, Newtonian with variable blood viscosity. The functional dependence of blood viscosity on haematocrit (percentage volume of red cells) has been duly accounted for in order to improve resemblance to the real situation. The finite-difference technique with staggered grid distribution is employed to solve the governing equations. The recirculation regions are formed in the downstream of the overlapping constriction. It is noticed that the arterial wall shear stress, pressure distribution and flow rate in particular, in the constricted site, are significantly altered. The peak value of wall shear stress decrease with increasing haematocrit parameter. The flow separation region increases with increasing haematocrit parameter. The results are presented graphically and analyzed in detail to study the effects of variable blood viscosity on the flow field. The motion of the arterial wall and its effects on local flow dynamics are considered. The contribution of deformability of the arterial wall is to reduce the wall shear stress in comparison to the consideration of rigid wall. Arterial wall motion causes to diminish the wall shear stress significantly.

A Fictitious Domain Method with the Distributed Lagrange Multiplier for Incompressible Viscous Flow around Moving Particle

This paper discusses the numerical solution of the incompressible viscous flow by the fictitious domain method with distributed Lagrange multiplier. For the analysis of the finite element method, the mixed interpolation based on the bubble function is presented. The way to use the fictitious domain method applied to the Navier-Stokes equation is explained. The incompressible viscous flow with two falling solid particles is presented. Advantage of the fictitious domain method based on distributed Lagrange multiplier is investigated.

Flow in a slowly deforming channel with weak permeability: An analytical approach

The analytical solution of the Navier–Stokes equations for a semi-infinite rectangular channel with porous and uniformly expanding or contracting walls is developed in the present paper. The numerical solution of the resulting problem has been studied by Dauenhauer and Majdalani [E.C. Dauenhauer, J. Majdalani, Exact self-similarity solution of the Navier–Stokes equations for a deformable channel with wall suction or injection, AIAA 3588 (2001) 1–11]. However, for small R (the permeation Reynolds number) and α (the wall expansion ratio), the respective analytical solutions are presented by Majdalani et al. [J. Majdalani, C. Zhou, C.A. Dawson, Two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability, J. Biomech. 35 (2002) 1399–1403] and Boutros et al. [Y.Z. Boutros, M.B. Abd-el-Malek, N.A. Badran, H.S. Hassan, Lie-group method solution for two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability, Appl. Math. Modelling (in press)]. The small R and α may well arise in biomechanics. The Adomian decomposition method (ADM) is used to obtain the solution. The results so obtained are compared with the existing literature (namely, the last two references cited above) and a remarkable improvement leads to an excellent agreement with the numerical results.

On Numerical Solution of the Incompressible Navier‐Stokes Equations with Static or Total Pressure Specified on Boundaries

The purpose of this article is to develop and validate a computational method for the solution of viscous incompressible flow in a domain with specified static or total pressure on the flow‐through boundaries (inflow and outflow). The computational algorithm is based on the Finite Volume Method in nonstaggered boundary‐fitted grid. The implementations of the boundary conditions on the flow‐through parts of the boundary are discussed. Test examples illustrate the main features and validity of the proposed method to study viscous incompressible flow through a bounded domain with specified static pressure (or total pressure) on boundary as a part of well‐posed boundary conditions.

Numerical solution of transonic and subsonic flow of compressible inviscid and viscous fluid

AbstractThe work presents two numerical solutions of compressible flows problems with high and very low Mach numbers. Both problems are numerically solved by finite volume method and the explicit MacCormack scheme using a grid of quadrilateral cells. Moved grid of quadrilateral cells is considered in the form of conservation laws using Arbitrary Lagrangian–Eulerian method. In the first case, inviscid transonic flow through cascade DCA 8% is presented and the numerical results are compared to experimental data. The second case, numerical solution of unsteady viscous flow in the channel for upstream Mach number M∞=0.012 and frequency of the wall motions 100 Hz is presented. The unsteady case can represent a simplified model of airflow coming from the trachea, through the glottal region with periodically vibrating vocal folds to the human vocal tract. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Analytical solution of three-dimensional Navier–Stokes equations for the flow near an infinite rotating disk

In this letter, we will consider variational iteration method (VIM) and Padé approximant, for finding analytical solutions of three-dimensional viscous flow near an infinite rotating disk. The solutions is compared with the numerical (fourth-order Runge–Kutta) solution. The results illustrate that VIM–Padé is an appropriate method in solving the systems of nonlinear equations. It is predicted that VIM–Padé can have wide application in engineering problems (especially for boundary-layer and natural convection problems).

Closed-form exact solutions of MHD viscous flow over a shrinking sheet

In this paper, the magnetohydrodynamic (MHD) flow over a shrinking sheet is solved analytically. The solution is given in a closed-form equation and is an exact solution of the full governing Navier–Stokes equations for the problem. Interesting solution behavior is observed with multiple solution branches for certain parameter domain.

Analytic Solution of Three-Dimensional Viscous Flow and Heat Transfer Over a Stretching Flat Surface by Homotopy Analysis Method

In this paper heat transfer in an electrically conducting fluid bonded by two parallel plates is studied in the presence of viscous dissipation. The plates and the fluid rotate with constant angular velocity about a same axis of rotation where the lower plate is a stretching sheet and the upper plate is a porous plate subject to constant injection. The governing partial differential equations are transformed to a system of ordinary differential equations with the help of similarity transformation. Homotopy analysis method is used to get complete analytic solution for velocity and temperature profiles. The effects of different parameters are discussed through graphs.

Analytical solution for pulsatile viscous flow in a straight elliptic annulus and application to the motion of the cerebrospinal fluid

We present here the analytical solution of transient, laminar, viscous flow of an incompressible, Newtonian fluid driven by a harmonically oscillating pressure gradient in a straight elliptic annulus. The analytical formulation is based on the exact solution of the governing fluid flow equations known as Navier–Stokes equations. We validate the analytical solution using a finite-volume computational fluid dynamics approach. As the analytical solution includes Mathieu and modified Mathieu functions, we also present a stepwise procedure for their evaluation for large complex arguments typically associated with viscous flows. We further outline the procedure for evaluating the associated Fourier coefficients and their eigenvalues. We finally apply the analytical solution to investigate the cerebrospinal fluid flow in the human spinal cavity, which features a shape similar to an elliptic annulus.

Flapping Wing Aerodynamics: Progress and Challenges

It is the objective of this paper to review recent developments in the understanding and prediction of flapping-wing aerodynamics. To this end, several flapping-wing configurations are considered. First, the problem of single flapping wings is treated with special emphasis on the dependence of thrust, lift, and propulsive efficiency on flapping mode, amplitude, frequency, and wing shape. Second, the problem of hovering flight is studied for single flapping wings. Third, the aerodynamic phenomena and benefits produced by the flapping-wing interactions on tandem wings or biplane configurations are discussed. Such interactions occur on dragonflies or on a recently developed micro air vehicle. The currently available two- and three-dimensional inviscid and viscous flapping-wing flow solutions are presented. It is shown that the results are strongly dependent on flapping frequency, amplitude, and Reynolds number. These findings are substantiated by comparison with the available experimental data.

On the analytical solution of viscous fluid flow past a flat plate

In this Letter, we propose a simple approach using HAM to obtain accurate totally analytical solution of viscous fluid flow over a flat plate. First, we show that the solution obtained using HPM is not a reliable one; moreover, we show that HPM is only a special case of HAM and its basic assumptions are restrictive rather than useful. We set ℏ = − 1 for the case of comparison of our results to those obtained using HPM. Afterwards, we introduce an extra auxiliary parameter and a straightforward approach to find best values of this auxiliary parameter which plays a prominent role in the frame of our solution and makes it more convergent in comparison to previous works.

Solution of the laminar viscous flow in a semi-porous channel in the presence of a uniform magnetic field by using the homotopy analysis method

In this paper, the problem of laminar viscous flow in a semi-porous channel in the presence of a transverse magnetic field is presented and the homotopy analysis method (HAM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing the problem. It has been attempted to show the capabilities and wide-range applications of the homotopy analysis method in comparison with the numerical method in solving this problem. The obtained solutions, in comparison with the numeric solutions admit a remarkable accuracy. A clear conclusion can be drawn from the numerical method’s (NM) results that the HAM provides highly accurate solutions for nonlinear differential equations.

Numerical solution of 2D and 3D viscous incompressible steady and unsteady flows using artificial compressibility method

AbstractIn this work, artificial compressibility method is used to solve steady and unsteady flows of viscous incompressible fluid. The method is based on implicit higher‐order upwind discretization of Navier–Stokes equations. The extension for unsteady simulation is considered by increasing artificial compressibility parameter or by using dual time stepping. Turbulence models are eddy‐viscosity SST model and explicit algebraic Reynolds stress model. Results for steady turbulent flow over confined backward‐facing step, unsteady laminar flow around circular cylinder and for unsteady turbulent free synthetic jet are presented. Copyright © 2007 John Wiley & Sons, Ltd.

CFD simulation of propeller and rudder performance when using additional thrust fins

To analyse a possible way to improve the propulsion performance of ships, the unstructured grid and the Reynolds Average Navier-Stokes equations were used to calculate the performance of a propeller and rudder fitted with additional thrust fins in the viscous flow field. The computational fluid dynamics software FLUENT was used to simulate the thrust and torque coefficient as a function of the advance coefficient of propeller and the thrust efficiency of additional thrust fins. The pressure and velocity flow behind the propeller was calculated. The geometrical nodes of the propeller were constituted by FORTRAN program and the NUMBS method was used to create a configuration of the propeller, which was then used by GAMMBIT to generate the calculation model. The thrust efficiency of fins was calculated as a function of the number of additional fins and the attack angles. The results of the calculations agree fairly well with experimental data, which shows that the viscous flow solution we present is useful in simulating the performance of propellers and rudders with additional fins.