scholarly journals Validation of a Model for Estimating the Strength of a Vortex Created from the Bound Circulation of a Vortex Generator

Energies ◽  
2019 ◽  
Vol 12 (14) ◽  
pp. 2781 ◽  
Author(s):  
Martin O. L. Hansen ◽  
Antonis Charalampous ◽  
Jean-Marc Foucaut ◽  
Christophe Cuvier ◽  
Clara M. Velte
Keyword(s):  
Boundary Layer ◽  
Vortex Generator ◽  
Tip Vortex ◽  
Navier Stokes ◽  
Wall Boundary Layer ◽  
Normal Distance ◽  
Engineering Models ◽  
Induced Flow ◽  
High Reynolds ◽  
The One

A hypothesis was tested and validated for predicting the vortex strength induced by a vortex generator in wall-bounded flow by combining the knowledge of the Vortex Generator (VG) geometry and the approaching boundary layer velocity distribution. In this paper, the spanwise distribution of bound circulation on a vortex generator was computed by integrating the pressure force along the VG height, calculated using Computational Fluid Dynamics (CFD). It was then assumed that all this bound circulation was shed into a wake to fulfill Helmholtz’s theorem which then curls up into one primary tip vortex. To validate this, the trailed circulation estimated from the distribution of the bound circulation was compared to the one in the wake behind the vortex generator, determined directly from the wake velocities at some downstream distance. In practical situations, the pressure distribution on a vane is unknown and consequently other estimates of the spanwise force distribution on a VG must instead be applied, such as using 2D airfoil data corresponding to the VG geometry at each wall-normal distance. Such models have previously been proposed and used as an engineering tool to aid preliminary VG design. Therefore, it is not the purpose of this paper to refine such engineering models, but rather to validate their assumptions, such as applying a lifting line model on a VG that has a very low aspect ratio and is placed in a wall boundary layer. Herein, high Reynolds number boundary layer measurements of VG-induced flow were used to validate the Reynolds-Averaged Navier–Stokes (RANS) model circulation results, which were used for further illustration and validation of the hypothesis.

Free-stream coherent structures in parallel boundary-layer flows

2014 ◽  
Vol 752 ◽  
pp. 602-625 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Coherent Structures ◽  
Free Stream ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Homotopy Continuation ◽  
Boundary Layer Flows ◽  
Navier Stokes Equations ◽  
High Reynolds

AbstractOur concern in this paper is with high-Reynolds-number nonlinear equilibrium solutions of the Navier–Stokes equations for boundary-layer flows. Here we consider the asymptotic suction boundary layer (ASBL) which we take as a prototype parallel boundary layer. Solutions of the equations of motion are obtained using a homotopy continuation from two known types of solutions for plane Couette flow. At high Reynolds numbers, it is shown that the first type of solution takes the form of a vortex–wave interaction (VWI) state, see Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666), and is located in the main part of the boundary layer. On the other hand, here the second type is found to support an equilibrium solution of the unit-Reynolds-number Navier–Stokes equations in a layer located a distance of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}O(\ln \mathit{Re})$ from the wall. Here $\mathit{Re}$ is the Reynolds number based on the free-stream speed and the unperturbed boundary-layer thickness. The streaky field produced by the interaction grows exponentially below the layer and takes its maximum size within the unperturbed boundary layer. The results suggest the possibility of two distinct types of streaky coherent structures existing, possibly simultaneously, in disturbed boundary layers.

Analysis of the Sutton Model for Aero-Optical Properties of Compressible Boundary Layers

2005 ◽  
Vol 128 (2) ◽  
pp. 239-246 ◽  
Author(s):  
Eric Tromeur ◽  
Eric Garnier ◽  
Pierre Sagaut
Keyword(s):  
Boundary Layer ◽  
Density Field ◽  
The Other ◽  
Navier Stokes ◽  
Eddy Simulation ◽  
Compressible Boundary Layers ◽  
Optical Effects ◽  
Large Eddy ◽  
The One ◽  
Reference Tool

In order to assess the capability of the Sutton model to evaluate aero-optical effects in a turbulent boundary layer, large-eddy simulation (LES) evolving spatially and Reynolds averaged Navier-Stokes (RANS) computations are carried out at Mach number equal to 0.9. First aerodynamic fields are proved to compare favorably with theoretical and experimental results. Once validated, the characteristics of the boundary layer allow us to obtain information concerning optical beam degradation. On the one hand, the density field is used to compute phase distortion directly and, on the other hand, by means of the Sutton model. Therefore, LES and RANS simulations allow us to study optical models and the validity of their assumptions. Finally, LES is proved to be considered as a reference tool to evaluate aero-optical effects.

Numerical Computation of Suspended Sediment Around a Marine Pipeline Close to the Flat Seabed

2011 ◽  
Author(s):  
Muk Chen Ong ◽  
Lars Erik Holmedal ◽  
Dag Myrhaug
Keyword(s):  
Suspended Sediment ◽  
Settling Velocity ◽  
Suspended Sediments ◽  
Navier Stokes ◽  
Suspended Sediment Transport ◽  
Flow Simulations ◽  
Reynolds Number Flow ◽  
Normal Distance ◽  
Number Flow ◽  
High Reynolds

The purpose of this paper is to investigate suspended sediment transport around a marine pipeline near the seabed by solving the Unsteady Reynolds-Averaged Navier-Stokes (URANS) equations with the standard k-ε model. High Reynolds number flow simulations are considered in the present study. The suspended sediments are seeded upstream of the pipeline. Particle trajectories of the suspended sediments downstream of the pipeline have been visualized by using a Lagrangian approach. Effects of the gap (i.e. the normal distance between the pipeline and the seabed) and the sediment weight (i.e. taking into account sediment settling velocity) have been investigated and discussed.

Tip Vortex Cavitation Inception Scaling for High Reynolds Number Applications

2009 ◽  
Vol 131 (7) ◽  
Author(s):  
Young T. Shen ◽  
Scott Gowing ◽  
Stuart Jessup
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layer Thickness ◽  
Reynolds Numbers ◽  
Present Theory ◽  
Full Scale ◽  
Tip Vortex ◽  
Tip Vortex Cavitation ◽  
Cavitation Inception ◽  
High Reynolds

Tip vortices generated by marine lifting surfaces such as propeller blades, ship rudders, hydrofoil wings, and antiroll fins can lead to cavitation. Prediction of the onset of this cavitation depends on model tests at Reynolds numbers much lower than those for the corresponding full-scale flows. The effect of Reynolds number variations on the scaling of tip vortex cavitation inception is investigated using a theoretical flow similarity approach. The ratio of the circulations in the full-scale and model-scale trailing vortices is obtained by assuming that the spanwise distributions of the section lift coefficients are the same between the model-scale and the full-scale. The vortex pressure distributions and core sizes are derived using the Rankine vortex model and McCormick’s assumption about the dependence of the vortex core size on the boundary layer thickness at the tip region. Using a logarithmic law to describe the velocity profile in the boundary layer over a large range of Reynolds number, the boundary layer thickness becomes dependent on the Reynolds number to a varying power. In deriving the scaling of the cavitation inception index as the ratio of Reynolds numbers to an exponent m, the values of m are not constant and are dependent on the values of the model- and full-scale Reynolds numbers themselves. This contrasts traditional scaling for which m is treated as a fixed value that is independent of Reynolds numbers. At very high Reynolds numbers, the present theory predicts the value of m to approach zero, consistent with the trend of these flows to become inviscid. Comparison of the present theory with available experimental data shows promising results, especially with recent results from high Reynolds number tests. Numerical examples of the values of m are given for different model- to full-scale sizes and Reynolds numbers.

The Local Analytic Numerical Method for the Double Vortex Combustor Flow

1985 ◽  
Author(s):  
J. He ◽  
B. Q. Zhang
Keyword(s):  
Reynolds Number ◽  
Analytic Solutions ◽  
Navier Stokes ◽  
Hyperbolic Function ◽  
Navier Stokes Equation ◽  
One Dimensional ◽  
New Type ◽  
High Reynolds ◽  
The One ◽  
Coarse Grids

A new hyperbolic function discretization equation for two dimensional Navier-Stokes equation in the stream function vorticity from is derived. The basic idea of this method is to integrat the total flux of the general variable ϕ in the differential equations, then incorporate the local analytic solutions in hyperbolic function for the one-dimensional linearized transport equation. The hyperbolic discretization (HD) scheme can more accurately represent the conservation and transport properties of the governing equation. The method is tested in a range of Reynolds number (Re=100~2000) using the viscous incompressible flow in a square cavity. It is proved that the HD scheme is stable for moderately high Reynolds number and accurate even for coarse grids. After some proper extension, the method is applied to predict the flow field in a new type combustor with air blast double-vortex and obtained some useful results.

Numerical Study of the Tip Clearance Flow Development in a Propulsion Pump Stage

1996 ◽  
Author(s):  
Yu-Tai Lee ◽  
Chunill Hah ◽  
James Loellbach
Keyword(s):  
Vortex Structure ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Tip Clearance ◽  
Tip Vortex ◽  
Navier Stokes ◽  
Tip Clearance Flow ◽  
Clearance Flow ◽  
High Reynolds

This paper summarizes a numerical investigation of the fundamental structure of the rotor tip-clearance vortex and its interaction with a passage trailing-edge vortex in a single-stage stator-rotor pump. The flow field of a highly-loaded rotor measured in a high Reynolds number pump facility (HIREP) is used for comparison. The numerical solution was obtained by solving the three-dimensional Reynolds averaged Navier-Stokes equations. The calculated results are visualized in order to understand the details of the tip-vortex structure. The study shows that the tip geometry should be accurately represented to predict the tip-vortex structure correctly.

Tip Vortex Cavitation Inception Scaling for High Reynolds Number Application

2003 ◽  
Author(s):  
Young T. Shen ◽  
Stuart Jessup ◽  
Scott Gowing
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layer Thickness ◽  
Reynolds Numbers ◽  
Present Theory ◽  
Full Scale ◽  
Tip Vortex ◽  
Tip Vortex Cavitation ◽  
Cavitation Inception ◽  
High Reynolds

Tip vortices that are generated by marine lifting surfaces such as propeller blades, ship rudders, hydrofoil wings, and anti-roll fins can lead to cavitation. Prediction of the onset of this cavitation depends on model tests at Reynolds numbers much lower than those for the corresponding full-scale flows. The effect of Reynolds number variations on the scaling of tip vortex cavitation inception is investigated using a theoretical flow similarity approach. The ratio of the circulations in the full-scale and model-scale trailing vortices is obtained by assuming that the spanwise section lift coefficient distributions are the same between model and full-scale. The vortex pressure distributions and core sizes are derived using the Rankine vortex model and McCormick’s assumption about the dependence of the vortex core size on the boundary layer thickness at the tip region. Using a logarithmic law to describe the velocity profile in the boundary layer over a large range of Reynolds number, the boundary layer thickness becomes dependent on the Reynolds number to a varying power. In deriving the cavitation inception scaling in the traditional scaling format of σif / σim = (Ref/Rem)n, the values of n are not constant and depend on the values of Ref and Rem themselves. This contrasts traditional scaling for which n is treated as a fixed value that is independent of Reynolds numbers. At very high Reynolds numbers, the present theory predicts the value of n to approach zero, consistent with the trend of these flows to become inviscid. Comparison of the present theory with available experimental data shows promising results, especially with recent results from high Reynolds number tests. Numerical examples are given of the values of n for different model to full-scale sizes and Reynolds numbers.

Modelling of spanwise mixing in compressor through-flow computations

1997 ◽  
Vol 211 (3) ◽  
pp. 243-251 ◽  
Author(s):  
J Dunham
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Navier Stokes ◽  
Streamline Curvature ◽  
Wall Boundary Layer ◽  
Through Flow ◽  
Compressor Design ◽  
Multistage Compressors ◽  
End Wall

Although three-dimensional Navier-Stokes computations are coming into use more and more, streamline curvature through-flow computations are still needed, especially for multistage compressors, and where codes which run in minutes rather than hours are preferred. These methods have been made more realistic by taking account of end-wall effects and spanwise mixing by four aerodynamic mechanisms: turbulent diffusion, turbulent convection by secondary flow, spanwise migration of aerofoil boundary layer fluid and spanwise convection of fluid in blade wakes. This paper describes the models adopted in the DRA streamline curvature method for axial compressor design and analysis. Previous papers are summarized briefly before describing the new part of the model—that accounting for aerofoil boundary layers and wakes. Other changes to the previously published annulus wall boundary layer model have been made to enable it to cater for separations and end bends. The resulting code is evaluated against a range of experimental and computational results.

A Numerical Computation of a Confined Rotating Flow

1970 ◽  
Vol 37 (2) ◽  
pp. 480-487 ◽  
Author(s):  
Hsien-Ping Pao
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Side Wall ◽  
Reynolds Numbers ◽  
Bottom Boundary Layer ◽  
Navier Stokes ◽  
Bottom Boundary ◽  
Small Reynolds Numbers ◽  
Viscous Core ◽  
High Reynolds

A numerical investigation of a viscous incompressible fluid confined in a closed circular cylindrical container is made. The top and side wall are in rotation with a constant angular velocity, and the bottom is held fixed. A numerical scheme using the full Navier-Stokes equations is developed. For small or moderate Reynolds numbers (Re = ΩL2/ν), the convergence of iteration is quite rapid. When the Reynolds number increases, the flow in the bottom boundary layer and the viscous core is intensified. An initial value problem is also investigated for Re = 1000 and 5000. The flow development of the bottom boundary layer and the viscous core is clearly exhibited. Some experimental investigation is also made. The numerical solution agrees very well with the analytic solution for small Reynolds numbers and with the experimental observation for moderate and high Reynolds numbers.

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