Hydraulic Modeling of A Curtain-Walled Dissipater by the Coupling of RANS and Boussinesq Equations
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A hybrid numerical method for the hydraulic modeling of a curtain-walled dissipater of reflected waves from breakwa-ters is presented. In this method, a zonal approach that combines a nonlinear weakly dispersive wave (Boussinesq-type equation) method and a Reynolds-Averaged Navier-Stokes (RANS) method is used. The Boussinesq-type equation is solved in the far field to describe wave transformation in shallow water. The RANS method is used in the near field to re-solve the turbulent boundary layer and vortex flows around the structure. Suitable matching conditions are enforced at the interface between the viscous and the Boussinesq region. The Coupled RANS and Boussinesq method successfully resolves the vortex characteristics of flow in the vicinity of the structure, while unexpected phenomena like wave re-reflection are effectively controlled by lengthening the Boussinesq region. Extensive results on hydraulic performance of a curtain-walled dissipater and the mechanism of dissipation of reflected waves are presented, providing a reference for minimization of the breadth of the water chamber and for determination of the submerged depth of the curtain wall.Keywords:
Boussinesq approximation (buoyancy)
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A numerical method,by coupling 2-D Reynold average N-S equation and volume of fluid model(RANS-VOF) with 1-D Boussinesq model,is proposed to study the wave-structure interaction in coastal area.By using this method,the detail of the flow in the vicinity of the structure,including the information of vortex,can be attained.The effect of wave reflection can be effectively avoided by lengthening the computation domain.The model is applied to investigate the hydraulic performances of the curtain-walled wave dissipater.
Hydraulic structure
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An integrated two-dimensional vertical (2DV) model was developed to investigate wave interactions with permeable submerged breakwaters. The integrated model is capable of predicting the flow field in both surface water and porous media on the basis of the extended volume-averaged Reynolds-averaged Navier–Stokes equations (VARANS). The impact of porous medium was considered by the inclusion of the additional terms of drag and inertia forces into conventional Navier–Stokes equations. Finite volume method (FVM) in an arbitrary Lagrangian–Eulerian (ALE) formulation was adopted for discretization of the governing equations. Projection method was utilized to solve the unsteady incompressible extended Navier–Stokes equations. The time-dependent volume and surface porosities were calculated at each time step using the fraction of a grid open to water and the total porosity of porous medium. The numerical model was first verified against analytical solutions of small amplitude progressive Stokes wave and solitary wave propagation in the absence of a bottom-mounted barrier. Comparisons showed pleasing agreements between the numerical predictions and analytical solutions. The model was then further validated by comparing the numerical model results with the experimental measurements of wave propagation over a permeable submerged breakwater reported in the literature. Good agreements were obtained for the free surface elevations at various spatial and temporal scales, velocity fields around and inside the obstacle, as well as the velocity profiles.
Stokes drift
Breakwater
Free surface
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Inviscid flow
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A computational study of natural convection of air in a tall rectangular cavity with 4 :1 aspect ratio is conducted. In an effort to investigate the applicability of the Boussinesq approximation to turbulent flow simulation, the cavity is differentially heated from the sides and is insulated at the ends at a Rayleigh number of 10 9 . Starting from quiescent and isothermal flow conditions, the flow is driven to turbulence without any artificial perturbations. The computer programme developed integrates the two-dimensional, time-dependent Navier-Stokes equations with the Boussinesq approximation and the energy equation by a time-accurate method on a stretched, staggered grid.
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Turbulence Modeling
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A simplified physical model was constructed which simulates the viscous crossflow in a fluid layer near the slots at a fixed streamwise location in a slotted wind tunnel. For low to moderate Reynolds numbers, numerical solutions of the two dimensional, incompressible Navier-Stokes equations in stream function and vorticity, which govern the model flow, were obtained. Fairly general slot geometry was incorporated by means of the Thompson-Thames-Mastin transformation. An approximate factorization scheme with cyclic acceleration parameters was employed to solve a finite difference analog of the stream function equation. The vorticity equation was numerically solved with a modified version of the classical alternating direction implicit scheme. Although no quantitative assessment of solution accuracy can be made, numerical results for variations in incremental wall pressure around the slat are at least qualitatively similar to some experimental results.
Stream function
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