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1

Exact solutions for the incompressible electrically conducting viscous flow between two moving parallel disks in unsteady magneto hydrodynamic and stability analysis

Balagondar P. M., Kempe Gowda M.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 2

571--579

EN

The main interest of the present investigation is to generate exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous electrically conducting fluid flow motion and stability due to disks moving towards each other or in opposite directions with a constant velocity. Making use of the analytic solution, the description of possible conditions of motion is based on the exact solutions of the Navier-Stokes equations. Both stationary and transient cases have been considered. The stability of motion is analyzed for different initial perturbations. Different types of stability were found according to whether the disks moved towards or away from each other.

2

A 4th-Order Staggered Compact Finite Difference Method for the Three-Dimensional Incompressible Navier-Stokes Equations

Abide S., Chesneau X., Zeghmati B.

Machine Dynamics Research

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2011

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Vol. 35, No. 1

7-18

EN

The objective of this work is the developement and assessment of a fourth-order compact scheme for the three-dimensional unsteady incompressible viscous flows. The equations of the flow are discretized on a staggered grid and using fourth-order compact scheme for the three directions. The accuracy of the method is demonstrated in the Taylor-Green vortex problem. Finally, the turbulent natural convection in a vertical channel is investigated to validate the numerical methods.

3

Calculation of the force on solid body in the unsteady flow of incompressible fluid

Poćwierz M., Styczek A.

Archives of Mechanics

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2010

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Vol. 62, nr 2

103-119

EN

In the paper, a special method to compute the aerodynamic force is presented. This method is especially addressed to the calculation while both the velocity and vorticity fields are found as a result of the vortex method application. In the case of vortex method, the vorticity field is shown as a sum of contributions given by a large number of the vorticity carriers. These carriers of vorticity move and change, but the vorticity distribution given by each of them is known. It means that both the vorticity and induced velocity field connected with them are easy to determine. The velocity field may also contain any potential component. This component assures the fulfillment of the asymptotic condition, and cancels the normal component of the velocity on the rigid body surface [15]. As it is known, the aerodynamic force may be calculated by using the basic definition, but in this case the boundary values of pressure and vorticity or derivatives of velocity field have to be found beforehand. These values are difficult to determine and their properties can be inconvenient. Quartapelle and Napolitano [12] introduced a special method of aerodynamic force calculation. This method does not require any surface integrals. Instead, the areas integrations are held. The integrands consist of vorticity and velocity fields only. The pressure field is excluded by special harmonic projection. The numerical experiment shows that the method of Quartapelle and Napolitano requires improvement in case of complicated, rapidly changing velocity and vorticity fields and the approximation of these fields in the neighborhood of the body not being perfect. However, if the concept of Quartapelle and Napolitano is applied to the area located outside the big sphere surrounding the body and containing the sources of vorticity, where velocity and vorticity fields have suitable properties (which permits to perform analytical calculations), we will get a simple formula for the aerodynamic force. This formula is not limited by additional properties of the pressure and velocity and vorticity fields. The numerical results are in relatively good agreement with the experimental data.

4

Przepływy lepkie w materiałach kapilarno-porowatych

Kucharczyk A.

Zeszyty Naukowe. Budownictwo / Politechnika Śląska

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2006

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z. 109

179-184

PL

W pracy zostały przedstawione bilanse masy, ładunku elektrycznego, pędu, energii, nierówność entropii oraz nierówność rezydualna. Na podstawie tych zależności zostały wyznaczone równania konstytutywne oraz równania na prąd elektryczny oraz na strumień masy i ciepła.

EN

In paper was presented mass, electric charge, momentum and energy balances. With the help of this statements we can calculate physical equations and equations for electric current, heat and mass flux.