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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, a flat horizontal plate aligned parallel to a uniform flow with velocity U∞ and temperature T∞ is assumed that a heat source (or sink) of strength Q is at the leading edge of the plate and that the plate is adiabatic everywhere else.
2 citations
TL;DR: In this paper, the nonlinear momentum equation for turbulent far-wake flow downstream of a cylinder is derived from the Reynolds averaged Navier-Stokes equations and solved by iteration and generalized similarity solution.
Abstract: The nonlinear momentum equation for turbulent far-wake flow downstream of a cylinder is derived from the Reynolds averaged Navier–Stokes equations and solved by iteration and generalized similarity solution. The first-order Oseen-type linearization yields for the wake boundary layer width a series, whose terms vary as x
1∕2 , x − 1∕2 , x − 3∕2 etc., where x is the streamwise distance from the center of cylinder. The velocity deficit from the free-stream velocity is similarly obtained as a series and the iteration is carried over to a second-order. This method is then applied to the problem of an array of cylinders. Both turbulent and laminar far-wake flow cases are analyzed. The series solutions broadly extend the earlier findings. The first-order solutions agree in form with those stated in the book of Schlichting (1979).
2 citations
TL;DR: In this paper, an integral method for computing turbulent boundary layers on rotating disks has been developed using a power law profile for the tangential velocity and a new model for the radial profile.
Abstract: An integral method for computing turbulent boundary layers on rotating disks has been developed using a power law profile for the tangential velocity and a new model for the radial profile. A similarily solution results from the formulation. Radical transport, boundary layer growth, and drag on the disk were computed for the case of a forced vortex freestream flow. The results were compared to previous similarity solutions. The method was extended to a Rankine vortex freestream flow. Differential equations for boundary layer parameters were developed and solved for different Reynolds numbers to look at the net entrainment, boundary layer growth, and drag on the disk
2 citations
10 Jul 2018
TL;DR: In this article, a homotopy analysis of the double-diffusive free convection flow with the vertical surfaces is given, where the governing equations are changed into a group of coupled non-linear partial differential equations, making use of reasonable non-similarity transformations.
Abstract: Homotopy analysis is given in this paper, which obtains non-similarity solutions of the double-diffusive free convection flow with the vertical surfaces. The governing equations are changed into a group of coupled non-linear partial differential equations, which is making use of reasonable non-similarity transformations. The effects of some dimensionless parameters of the velocity, temperature or concentration profiles are valid for the whole calculation area with non-similarity solutions.
2 citations
08 Oct 2021
TL;DR: In this paper, the linear stability of similarity solutions of the breakup of viscous liquid threads, in which the viscosity and inertia of the liquid are in balance with the surface tension, was determined using numerical continuation to find the dominant eigenvalues.
Abstract: In this paper we compute the linear stability of similarity solutions of the breakup of viscous liquid threads, in which the viscosity and inertia of the liquid are in balance with the surface tension. The stability of the similarity solution is determined using numerical continuation to find the dominant eigenvalues. The stability of the first two solutions (those with the largest minimum radius) is considered. We find that the first similarity solution, which is the one seen in experiments and simulations, is linearly stable with a complex nontrivial eigenvalue, which could explain the phenomenon of breakup producing sequences of small satellite droplets of decreasing radius near a main pinch-off point. The second solution is seen to be linearly unstable. These linear stability results compare favorably to numerical simulations for the stable similarity solution, while a profile starting near the unstable similarity solution is shown to very rapidly leave the linear regime.
2 citations