Topic
Similarity solution
About: Similarity solution is a research topic. Over the lifetime, 2074 publications have been published within this topic receiving 59790 citations.
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TL;DR: In this article, the non-Darcian effects on the flow and vortex instability of a horizontal natural convection boundary flow in a high-porosity medium are examined, and the results indicate that all of these three effects reduce the heat transfer rate.
17 citations
TL;DR: In this article, the stability of similarity solutions with respect to perturbations which preserve the planar geometry was examined under the assumption of local equilibrium at the solid-liquid interface, and it was shown that the solution corresponding to the intermediate value of λ is unstable and the other two solutions are stable.
17 citations
TL;DR: In this article, a simple analytical model of spray jet evaporation in gas-solid suspension flows has been developed, which is based on the extension of similarity correlation from two-phase jets to threephase jets.
17 citations
Dissertation•
01 Jan 2002
TL;DR: In this article, a theoretical and experimental study of the turbulent axisymmetric wake was presented, where an equilibrium similarity solution of the far wake was derived that was found to admit to two different solutions for this flow.
Abstract: This thesis presents a theoretical and experimental study of the turbulent axisymmetric wake. In the theoretical part, an equilibrium similarity solution of the far wake was derived that was found to admit to two different solutions for this flow. The high Reynolds number solution predicts that the flow grows as the cube root of the distance downstream, whereas the low Reynolds number solution grows as the square root of the downstream distance. None of these solutions had unambiguously been confirmed in earlier work. The analysis also provided necessary criteria for when to expect either solution. In the experimental part, data was obtained by hot-wire anemometry using arrays of 13 and 15 probes. For the first time, experimental data was proven to behave like the high Reynolds number equilibrium similarity solution predicted. These multi-point probe rakes were also used to measure cross-spectra in cross-sections of the flow from 10 to 150 disk diameters downstream. The cross-spectra obtained from the measurements were Fourier transformed in the azimuthal direction and used in the kernel for a proper orthogonal decomposition (POD). The POD was shown to order the energetic structure in a highly organized manner, with approximately 56% of the resolved energy in the first mode. The decomposition revealed that the initial wake region from 10 to 30 diameters downstream was dominated by an azimuthal mode-1 type of motion, but also that the importance of this mode vanishes as the flow evolves. Instead the far wake from 30 diameters downstream on was found to be dominated by a mode-2 type of azimuthal motion. This was found to coincide very well with the position at which the similarity solution became valid. This mode-2 dominance continued throughout the whole range of the investigation, with virtually no change in the modal decomposition. The mode-1 was interpreted as a convected structure associated to the vortex shedding in the near wake that was just swept by the probes and dies off downstream, and the mode-2 was postulated to be associated with a global instability manifested as a slow movement of the whole mean velocity field. The findings of the experiment triggered new theoretical investigations, and a re-visit of the classical linear temporal stability analysis. It was found that the theory permits unstable solutions of mode-0, 1, and 2 kind, contrary to the previous view that only azimuthal mode-1 can be unstable.
17 citations
TL;DR: In this article, the assumptions implicit in Leveque's approximation are re-examined, and the analytical solution of the problem with additional boundary conditions, for the temperature field and the boundary layer thickness through the long tube is presented.
Abstract: In the thermal entrance region, a thermal boundary layer develops and also reaches the circular tube center. The fully developed region is the zone in which the flow is both hydrodynamically and thermally developed. The heat flux will be higher near the inlet because the heat transfer coefficient is highest at the tube inlet where the thickness of the thermal boundary layer is zero, and decreases gradually to the fully developed value. In this paper, the assumptions implicit in Leveque’s approximation are re-examined, and the analytical solution of the problem with additional boundary conditions, for the temperature field and the boundary layer thickness through the long tube is presented. From the mathematical side, numerical techniques for solving the problem of fluid–structure interaction with a fully developed laminar incompressible Newtonian flow is described. By defining a similarity variable the governing equations are reduced to a dimensionless equation with an analytic solution in the entrance region. This report gives justification for the similarity variable via scaling analysis, details the process of converting to a similarity form, and presents a similarity solution. The analytical solutions are then checked against numerical solution programming by FORTRAN code obtained via using Runge–Kutta fourth order (RK4) method. Finally, others important thermal results obtained from this analysis, such as; approximate Nusselt number in the thermal entrance region was discussed in detail.
17 citations