Flow of Wall Jet Near Channel Exit at Moderate Reynolds Number

2010 ◽  
Author(s):  
Md. Abul Kalam Azad ◽  
Roger E. Khayat
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Free Surface ◽  
Boundary Conditions ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Wall Jet ◽  
Channel Exit ◽  
Moderate Reynolds Number ◽  
Layer Region

The wall jet flow near channel exit at moderate Reynolds Number, emerging from a two-dimensional channel, is examined theoretically in this study. Poiseuille flow conditions are assumed to prevail far upstream from the exit. The problem is solved using the method of matched asymptotic expansions. The small parameter involved in the expansions is the inverse Reynolds number. The flow and stress fields are obtained as composite expansions by matching the flow in the boundary-layer region near the free surface, flow in the outer layer region and the flow in the core region. The fluid is assumed to be Newtonian and it is found that the jet contracts downstream from the channel exit. The influence of inertia on the shape of free surface, the velocity and stress is emphasized and the higher order boundary layer is explored. To leading order, the problem is similar to the case of the free jet (Tillett) [1] with different boundary conditions. A similarity solution can be carried out using a similarity variable problem which is then solved as an initial-value problem, where the equation is integrated subject to the boundary conditions and a guessed value of the slope at the origin. The slope is adjusted until reasonable matching is achieved between the solution and the asymptotic form at large θ. The level of contraction is essentially independent of inertia, but the contraction moves further downstream with increasing Reynolds number. The present work provides the correct conditions near exit, which are required to determine the jet structure further downstream. If the jet becomes thin far downstream, a boundary layer formulation can be used with the presently predicted boundary conditions for steady and possibly transient flows.

Flow of Moving Wall Jet Near Channel Exit at Moderate Reynolds Number

2010 ◽  
Author(s):  
Rizwana Amin ◽  
Roger E. Khayat
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Free Surface ◽  
Equations Of Motion ◽  
Outer Region ◽  
Moving Wall ◽  
Moderate Reynolds Number ◽  
Boundary Layer Region ◽  
Asymptotic Development ◽  
Layer Region

The two-dimensional jet flow of a Newtonian fluid at moderate Reynolds Number emerging from a channel where the upper plate is moving is examined theoretically in this study. In this case, the equations of motion are reduced by expanding the flow field about the basic Couette flow. Inertia is assumed to be large enough, allowing asymptotic development in terms of the inverse Reynolds number. A boundary layer forms adjacent to the free surface, and a classical boundary-layer analysis is applied to find the flow in the free surface and the moving wall. The influence of this boundary layer is investigated with the aid of the method of matched asymptotic expansions. The flow and stress fields are obtained as composite expansions by matching the flow in the boundary-layer region near the free surface and the flow both in the inner (boundary-layer) region and in the outer region of the core. The influence of wall velocity on the shape of the free surface, the velocity and stress is emphasized. The formulation allows for the determination of the steady state flow and free surface profiles analytically. The present work provides the conditions near exit, with the help of Higher-order boundary-layer effects (i.e. the cubic term of the inverse Reynolds number), to determine the jet structure further downstream.

Effects of Submergence on Low and Moderate Reynolds Number Free-Surface Flow Around a Matrix of Cubes

2016 ◽  
Vol 138 (5) ◽  
Author(s):  
Z. Ikram ◽  
E. J. Avital ◽  
J. J. R. Williams
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Immersed Boundary ◽  
Surface Boundary ◽  
Reynolds Number Flow ◽  
Eddy Simulation ◽  
Moderate Reynolds Number ◽  
Submergence Depth

The effect of reducing submergence depth at a low and moderate Reynolds number flow is investigated using large eddy simulation (LES) around a matrix of cubes. The submerged body is modeled using an immersed boundary method, while the free-surface is accounted for using a moving mesh. Results show that for reducing the submergence depth, the forces acting on the cube reduce as the force variation increased. Variation in depth is also found to influence the level of damping and redistribution of turbulence near the free-surface boundary. Both submergence depth and Reynolds number are also found to influence the dominant free-surface signature and shedding frequencies from the cube. In the interobstacle region (IOR), the variation of Reynolds number and submergence depth is found to have little effect.

scholarly journals Influence of the hydrofoil inclination angle at free surface flow around junctions

2020 ◽  
Vol 43 ◽  
pp. 103-108
Author(s):  
Costel Ungureanu ◽  
Costel Iulian Mocanu
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Bluff Body ◽  
Three Dimensional ◽  
Free Surface Flow ◽  
Breaking Waves ◽  
Surface Flow ◽  
Vortex Structures ◽  
The Body ◽  
Flow Topology

"Free surface flow is a hydrodynamic problem with a seemingly simple geometric configuration but with a flow topology complicated by the pressure gradient due to the presence of the obstacle, the interaction between the boundary layer and the free surface, turbulence, breaking waves, surface tension effects between water and air. As the ship appendages become more and more used and larger in size, the general understanding of the flow field around the appendages and the junction between them and the hull is a topical issue for naval hydrodynamics. When flowing with a boundary layer, when the streamlines meet a bluff body mounted on a solid flat or curved surface, detachments appear in front of it due to the blocking effect. As a result, vortex structures develop in the fluid, also called horseshoe vortices, the current being one with a completely three-dimensional character, complicated by the interactions between the boundary layer and the vortex structures thus generated. Despite the importance of the topic, the literature records the lack of coherent methods for investigating free surface flow around junctions, the lack of consistent studies on the influence of the inclination of the profile mounted on the body. As a result, this paper aims to systematically study the influence of profile inclination in respect to the support plate."

Effect of small roughness elements on thermal statistics of a turbulent boundary layer at moderate Reynolds number

2015 ◽  
Vol 787 ◽  
pp. 84-115 ◽  
Author(s):  
Ali Doosttalab ◽  
Guillermo Araya ◽  
Jensen Newman ◽  
Ronald J. Adrian ◽  
Kenneth Jansen ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Prandtl Number ◽  
Rough Surface ◽  
Surface Flow ◽  
Unit Mass ◽  
Turbulent Prandtl Number ◽  
Reynolds Analogy ◽  
Moderate Reynolds Number

A zero-pressure-gradient turbulent boundary layer flowing over a transitionally rough surface (24-grit sandpaper) with$k^{+}\approx 11$and a momentum-thickness Reynolds number of approximately 2400 is studied using direct numerical simulation (DNS). Heat transfer between the isothermal rough surface and the turbulent flow with molecular Prandtl number$Pr=0.71$is simulated. The dynamic multiscale approach developed by Arayaet al.(J. Fluid Mech., vol. 670, 2011, pp. 581–605) is employed to prescribe realistic time-dependent thermal inflow boundary conditions. In general, the rough surface reduces mean and fluctuating temperature profiles with respect to the smooth surface flow when normalized by Wang & Castillo (J. Turbul., vol. 4, 2003, 006) inner/outer scaling. It is shown that the Reynolds analogy does not hold for$y^{+}<9$. In this region the value of the turbulent Prandtl number departs substantially from unity. Above this region the Reynolds analogy is only approximately valid, with the turbulent Prandtl number decreasing from 1 to 0.7 across the boundary layer for rough and smooth walls. In comparison with the smooth-wall case, the turbulent transport of heat per unit mass,$\overline{v^{\prime }v^{\prime }{\it\theta}^{\prime }}$, towards the wall is enhanced in the buffer layer, but the transport of$\overline{v^{\prime }v^{\prime }{\it\theta}^{\prime }}$away from the wall is reduced in the outer layer for the rough case; similar behaviour is found for the vertical transport of turbulent momentum per unit mass,$\overline{v^{\prime }u^{\prime }v^{\prime }}$. Above the roughness sublayer (3$k$–5$k$) it is found that most of the temperature field statistics, including higher-order moments and conditional averages, are highly similar for the smooth and rough surface flow, showing that the Townsend’s Reynolds number similarity hypothesis applies for the thermal field as well as the velocity field for the Reynolds number and$k^{+}$considered in this study.

A Method to Calculate Resistance of Ship Taking the Effect of Dynamic Sinkage and Trim and Viscosity of Fluid

2011 ◽  
Vol 121-126 ◽  
pp. 1849-1857
Author(s):  
Chao Bang Yao ◽  
Wen Cai Dong
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Flow Field ◽  
Indirect Method ◽  
Free Surface Flow ◽  
Field Resistance ◽  
Surface Flow ◽  
Equilibrium Equations ◽  
Sinkage And Trim ◽  
Hydrodynamic Equilibrium

A method is presented to calculate the resistance of a ship taking the effect of sinkage & trim and viscosity of fluid. The free surface flow field is evaluated by solving RANS equations with VOF method. The sinkage and trim are computed by hydrodynamic equilibrium equations. The method can be divided into direct and indirect method according to the way to calculate trim of ship. The software Fluent is used to implement this method. With dynamic mesh being used, the position of a ship is updated by the motion of “ship + boundary layer” grid zone. The present methods have been applied to the INSEAN2340 hull for different Froude numbers and are found to be efficient for evaluating the flow field, resistance, sinkage and trim.

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