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Boundary Layer Approximation

The Experts below are selected from a list of 234 Experts worldwide ranked by ideXlab platform

Serafim Kalliadasis – 1st expert on this subject based on the ideXlab platform

  • Boundary Layer Approximation
    , 2012
    Co-Authors: Serafim Kalliadasis, Christian Ruyerquil, Benoit Scheid, Manuel G Velarde

    Abstract:

    We derive the BoundaryLayer equations for falling liquid films. The assumptions used in their derivation are similar in spirit to those in the classical BoundaryLayer theory in aerodynamics. The key in their derivation is the elimination of the pressure by integrating the y-component of the momentum equation where the inertia terms are neglected while at the same time maintaining the inertia terms in the x- and z-components of the momentum equation. We introduce the “Shkadov scaling,” which makes apparent the balance between all forces necessary to sustain strongly nonlinear waves, and we show that the speed of single-hump solitary waves for an isothermal film shows a steep increase as a function of the Shkadov parameter δ, precisely at δ≃1 which then demarcates two distinct flow regimes: the “drag-gravity regime” where δ is small and the “drag-inertia” regime where δ=O(1). Finally, we summarize the different levels of Approximations utilized in the description of the falling film problem and the different scalings.

  • dynamics of a reactive falling film at large peclet numbers ii nonlinear waves far from criticality integral Boundary Layer Approximation
    Physics of Fluids, 2004
    Co-Authors: P M J Trevelyan, Serafim Kalliadasis

    Abstract:

    We consider the dynamics of a reactive falling film far from criticality. Our analysis is based on the integral-BoundaryLayer (IBL) Approximation of the equations of motion, energy and concentration, and associated free-surface Boundary conditions. We develop a hierarchy of IBL models starting from a simplified Shkadov approach to large IBL systems based on high-order Galerkin projections. We show that these high-order models correct the deficiencies of Shkadov’s approach and predict correctly all relevant quantities including the critical Reynolds number. We also numerically construct nonlinear solutions of the solitary wave type for a simplified Shkadov Approximation and we show that unlike the long-wave theory in Paper I which leads to branch multiplicity and limit points as well as points where the solitary wave solution branches terminate, the IBL model predicts the existence of solitary waves for all Reynolds numbers.

Igorm Boiko – 2nd expert on this subject based on the ideXlab platform

  • chattering in sliding mode control systems with Boundary Layer Approximation of discontinuous control
    International Journal of Systems Science, 2013
    Co-Authors: Igorm Boiko

    Abstract:

    It has been a widely accepted notion that Approximation of discontinuous control by certain continuous function in a Boundary Layer results in chattering elimination in sliding mode control systems. It is shown through three different types of analysis that in the presence of parasitic dynamics, this approach to chattering elimination would work only if the slope of the continuous nonlinear function within the Boundary Layer is low enough, which may result in the deterioration of performance of the system. A few examples are provided. An approach to robust stability of linear systems from the consideration of the saturating control is proposed.

  • ACC – Analysis of chattering in sliding mode control systems with continuous Boundary Layer Approximation of discontinuous control
    Proceedings of the 2011 American Control Conference, 2011
    Co-Authors: Igorm Boiko

    Abstract:

    It has been a widely accepted notion that Approximation of discontinuous control by certain continuous function in a Boundary Layer results in chattering elimination in sliding mode (SM) control systems. It is shown through three different types of analysis that in the presence of parasitic dynamics, this approach to chattering elimination would work only if the slope of the continuous nonlinear function within the Boundary Layer is low enough, which may result in the deterioration of performance of the system. A few examples are provided.

  • Analysis of chattering in sliding mode control systems with continuous Boundary Layer Approximation of discontinuous control
    Proceedings of the 2011 American Control Conference, 2011
    Co-Authors: Igorm Boiko

    Abstract:

    It has been a widely accepted notion that Approximation of discontinuous control by certain continuous function in a Boundary Layer results in chattering elimination in sliding mode (SM) control systems. It is shown through three different types of analysis that in the presence of parasitic dynamics, this approach to chattering elimination would work only if the slope of the continuous nonlinear function within the Boundary Layer is low enough, which may result in the deterioration of performance of the system. A few examples are provided.

Peter A. Taylor – 3rd expert on this subject based on the ideXlab platform

  • Development of a non-linear mixed spectral finite difference model for turbulent BoundaryLayer flow over topography
    Boundary-Layer Meteorology, 1994
    Co-Authors: Dapeng Xu, Keith W. Ayotte, Peter A. Taylor

    Abstract:

    Further development of the non-linear mixed spectral finite difference (NLMSFD) model of turbulent BoundaryLayer flow over topography is documented. This includes modifications and refinements to the solution procedure, the incorporation of second-order turbulence closures to the model and the three-dimensional extension of the model. Based on these higher order closures, linear limitations, BoundaryLayer Approximation and non-linear effects are discussed. The impact of different turbulence closures on the prediction of the NLMSFD model is also demonstrated. Furthermore, sample results for 3D idealized topography (sinusoidal) are presented. The parameterization of drag over small-scale topography is also addressed.