Wyniki wyszukiwania - Biblioteka Nauki

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Tests on a new method for numerical solution to the Navier-Stokes equations. part II: plane unsteady flow around curvilinear contours

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Klonowska-Prosnak M. E. , Kołodziejczyk M.

International Journal of Applied Mechanics and Engineering

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2002

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tom Vol. 7, no 2

619-652

EN

Similarly as the preceding paper of the authors (Klonowska and Kołodziejczyk, 1999) also the present one deals with the new method (Prosnak and Kosma, 1991) for the determination of unsteady, plane flows of viscous incompressible fluids. The novelty of the method consists in elimination of pressure from the system of the Navier-Stokes equations by means of integration of the "total" differential of pressure. Consequently - the order of the system resulting from such an elimination is not increased in comparison with the original one, and no artificial, non-physical boundary conditions occur. The main difference between the present paper and the previous one consists in geometrical properties of the domain of solution. It is infinite, and bounded by a curvilinear contour. Three contours are considered in the paper: a flat plate, a circle, and the NACA 0012 airfoil. The results prove, that also in these cases the method works properly - at least for rather small values of the Reynolds number. Such a limitation is due to the efficiency of the computers being available at the time, when the calculations were made.

2

Remarks on Plane, Steady, Creeping Flows Generated by Singularities

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Klonowska-Prosnak M. E. , Cześnik P.

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2002

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tom Vol. 50, Nr 1

45--69

EN

Two properties of plane, steady, creeping flow generated in the infinite domain around a given contour by a single singularity are investigated in the paper. The first property concerns velocity field. It is shown, that stream uniform at infinity must occur automatically in this case, and formulae for velocity of the stream are derived. The second property concerns similarity of streamline pattern of such flow, and the potential one, generated around the same contour by the same singularity. Investigation of the both properties concerns - in particular: a disc, an ellipse and the airfoil sections NACA 0012, RAE 2822.

3

On Plane, Steady, Creeping Flow, Generated Around an Arbitrary Cylinder by a Translating Flat Plate

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Klonowska-Prosnak M. E. , Prosnak W. J. , Cześnik P.

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2003

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tom Vol. 51, nr 2

113-144

EN

Plane, steady, creeping flow around an arbitrary cylinder situated in vicinity of a flat plate is considered, the flow being generated by translation of this plate along itself with constant speed, perpendicular to generatrices. The stream function of the flow satisfies the biharmonic equation, so that all properties of the flow - such as velocity and pressure fields as well as fields of other stress tensor components - are expressed in terms of the Goursat functions. Hence, the problem of determination of the flow reduces to determination of these functions. The two-step approach is applied to the solution of this problem. The first step consists in conformal mapping of the original domain of solution onto an annulus - by means of a suitable set of mapping functions. The second step consists in development of the two Goursat functions in Laurent series extended by two logarithmic terms each. Unknown coefficients of the series have to satisfy a system of linear algebraic equations, following from boundary conditions. The system is arrived at by means of the pseudospectral method. The so obtained velocity field is applied to generation of streamline patterns. Such a pattern is presented in the paper, and compared with an analogous one, corresponding to potential flow.

4

An approximate method for estimation of fluid motion in a lake containing islands

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Klonowska-Prosnak M. E. , Prosnak W. J. , Cześnik P. P.

Archives of Hydro-Engineering and Environmental Mechanics

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2005

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tom Vol. 52, nr 4

335-349

EN

The physical phenomenon considered in the paper deals with flow in a lake, which contains one or several islands. The flow is generated by rivers, their inlets and outlets being distributed on the shoreline of the lake. The problem to be solved consists in determination of the velocity field - in the domain bounded by the shorelines of the lake and the islands. In fact, it is attempted to arrive solely at an estimation of the field. Consequently, a rather simple physical model of the phenomenon, as well as its simple mathematical description has been applied. In particular, plane, irrotational and steady flow of ideal liquid has been introduced, the inlets and outlets of the rivers being simulated by sources and sinks. Hence, the problem reduces to determination of a complex function, representing the complex velocity field, which satisfies the impermeability condition on all contours representing the shorelines, the field being generated by the singularities already mentioned. Unfortunately, the so formulated problem is "overconditioned" or "too stiff", what means that the impermeability condition on the outer contour cannot be satisfied. Nevertheless, we arrived at a simple method for circumventing this obstacle, the payoff consisting in some modification of this contour. We had this particular modification in mind, applying the word "approximate" in the title of the paper. The paper contains results - in the form of streamline patterns - for lakes containing from 1 to 3 islands. In the relevant figures the distances between the given and the modified exterior contours can be seen distinctly - allowing the reader to draw conclusions, whether the errors due to the modifications are admissible or not. Of course, it depends anyway on the point of view of the user of the results.