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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of engineering mathematics 23 (1989), S. 261-271 
    ISSN: 1573-2703
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract In this paper exact analytical values of surface singularity distributions for two-dimensional potential flows are presented. A general formulation which provides an alternative to the Milne-Thomson theorem is presented for the circle, then distributions are obtained for flow about an ellipse. These solutions provide useful bench-mark test cases for examining the convergence properties in the development of some panel-method computer codes.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 1241-1262 
    ISSN: 0271-2091
    Keywords: axisymmetric flow ; vortex method ; laminar flow ; entrance length ; steady and oscillating flows ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Steady and oscillating axisymmetric tube flows are modelled using a vorticity transport algorithm. The axisymmetric convective -diffusive Navier-Stokes equations are solved using a splitting technique. Axisymmetric ring vortex filaments are introduced on the walls and subsequently convected and diffused throughout the flow field. An axisymmetric equation similar to the Oseen diffusion equation is used to diffuse the ring vortex filaments. Vorticity is reflected from the tube walls using two techniques. Results are presented for the developing Poiseuille flow and for the developed flow in the form of the entrance length and the axial velocity and vorticity profiles. Good agreement is achieved with a finite difference method in the developing region of Poiseuille flow. The developed flow results are compared with the analytical solutions. The developed profiles of velocity and vorticity have errors of less than 0ċ3 per cent for both methods of dealing with reflection of diffusion at the bounding surfaces and similar accuracy is obtained for the velocity profiles in oscillating flow except at the wall. Oscillating flow is produced with a discretized sinusoidal piston motion. Velocity profiles, boundary layer thickness and entrance length are presented for oscillating flow. Good agreement is achieved for low-Womersley-number non-dimensional frequency. At higher values of this parameter, flows are inaccurately simulated, because the number of piston positions used to discretize the piston motion is inversely proportional to the non-dimensional frequency.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Medical & biological engineering & computing 19 (1981), S. 79-82 
    ISSN: 1741-0444
    Keywords: Haemodynamics ; Modelling ; Pulsatile flow
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: Abstract The one-dimensional equations are used in the calculation of blood flow in arteries. The majority of the treatments use the method of characteristics and because of the nature of the method it is necessary to use a simplified value of the skin friction. A commonly used simplification is to assume the zero frequency value of the skin friction. The effect of the use of this approximation is compared with results using the full linear theory value. It is shown that the phase difference between the skin friction and the flux has an appreciable effect on the velocity wave calculated from a given pressure wave.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Medical & biological engineering & computing 20 (1982), S. 49-57 
    ISSN: 1741-0444
    Keywords: Haemodynamics ; Modelling ; Pulsatile flow
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: Abstract The purpose of this paper is to present standard results on the effect of nonlinearities on the computed pulsatile flow in a cylindrical distensible tube as a first stage in the calculation of flow in a tapered tube and blood flow in arteries. The calculations are made using the pressure-radius relationship of a rubber tube with no longitudinal motion and for a linearised relationship. The one-dimensional equations of motion are solved by the method of finite differences. The values of skin friction that are incorporated are determined from the vorticity and continuity equations for a rigid tube and a correction made to the current diameter at each time step. The accuracy of the results is assessed and the effect of varying parameters investigated. The method is applied to a segment of an infinite tube for which the linear analytical solution is available. The characteristics of the velocity wave calculated from an input pressure wave are presented as departures from the linear theory values of these characteristics, the wave speed, flux and transmission factor per wavelength. Computations are made at values of non-dimensional frequency (Stokes number α) of about 3 and 10. It is concluded that as far as physiological application is concerned (i.e. small amplitude and long wavelength) the results of linear theory are a very good first approximation for the cylindrical tube. At α=10, the relative departure of wave speed is about 0·5 times the relative diameter amplitude ( $${{\hat D} \mathord{\left/ {\vphantom {{\hat D} {\bar D}}} \right. \kern-\nulldelimiterspace} {\bar D}}$$ amplitude/mean diameter) when the pressure-radius relation is linear and the pressure and velocity waves have the same characteristics. At α=3 the corresponding wave speed departure is about 0·1 $${{\hat D} \mathord{\left/ {\vphantom {{\hat D} {\bar D}}} \right. \kern-\nulldelimiterspace} {\bar D}}$$ . The relative departure of the flux is less than 0·05 $${{\hat D} \mathord{\left/ {\vphantom {{\hat D} {\bar D}}} \right. \kern-\nulldelimiterspace} {\bar D}}$$ at α=3 and about 0·5 $${{\hat D} \mathord{\left/ {\vphantom {{\hat D} {\bar D}}} \right. \kern-\nulldelimiterspace} {\bar D}}$$ at α=10. The transmission coefficient has a relative departure of less than 0·05 $${{\hat D} \mathord{\left/ {\vphantom {{\hat D} {\bar D}}} \right. \kern-\nulldelimiterspace} {\bar D}}$$ at α=10 and its relative increase at α=3 is about 0·3 $${{\hat D} \mathord{\left/ {\vphantom {{\hat D} {\bar D}}} \right. \kern-\nulldelimiterspace} {\bar D}}$$ .
    Type of Medium: Electronic Resource
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