Numerical Study of the Steady-State Tip Vortex Flow Over a Finite-Span Hydrofoil

1998 ◽  
Vol 120 (2) ◽  
pp. 345-353 ◽  
Author(s):  
Chao-Tsung Hsiao ◽  
Laura L. Pauley
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Vortex Core ◽  
Axial Velocity ◽  
Stokes Equations ◽  
Numerical Study ◽  
Angle Of Attack ◽  
Tangential Velocity ◽  
Tip Vortex ◽  
Finite Span

The flow over a finite-span hydrofoil creating a tip vortex was numerically studied by computing the full Navier-Stokes equations. A good agreement in pressure distribution and oil flow pattern was achieved between the numerical solution and available experimental data. The steady-state roll-up process of the tip vortex was described in detail from the numerical results. The effect of the angle of attack, the Reynolds number, and the hydrofoil planform on the tip vortex was investigated. The axial and tangential velocities within the tip-vortex core in the near-field wake region were greatly influenced by the angle of attack. A jet-like profile in the axial velocity was found within the tip-vortex core at high angle of attack, while a wake-like profile in the axial velocity was found at low angle of attack. Increasing the Reynolds number was found to increase the maximum axial velocity, but only had a slight impact on the tangential velocity. Finally, a swept hydrofoil planform was found to attenuate the strength of the tip vortex due to the low-momentum boundary layer traveling into the tip vortex on the suction side.

Effect of wall-mounted V-baffle position in a turbulent flow through a channel

2019 ◽  
Vol 29 (10) ◽  
pp. 3908-3937 ◽  
Author(s):  
Younes Menni ◽  
Ahmed Azzi ◽  
Ali J. Chamkha ◽  
Souad Harmand
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Rectangular Channel ◽  
Simple Algorithm ◽  
Two Dimensions ◽  
Large Reynolds Number ◽  
Constant Property ◽  
Content Type

Purpose The purpose of this paper is to carry out a numerical study on the dynamic and thermal behavior of a fluid with a constant property and flowing turbulently through a two-dimensional horizontal rectangular channel. The upper surface was put in a constant temperature condition, while the lower one was thermally insulated. Two transverse, solid-type obstacles, having different shapes, i.e. flat rectangular and V-shaped, were inserted into the channel and fixed to the top and bottom walls of the channel, in a periodically staggered manner to force vortices to improve the mixing, and consequently the heat transfer. The flat rectangular obstacle was put in the first position and was placed on the hot top wall of the channel. However, the second V-shaped obstacle was placed on the insulated bottom wall, at an attack angle of 45°; its position was varied to find the optimum configuration for optimal heat transfer. Design/methodology/approach The fluid is considered Newtonian, incompressible with constant properties. The Reynolds averaged Navier–Stokes equations, along with the standard k-epsilon turbulence model and the energy equation, are used to control the channel flow model. The finite volume method is used to integrate all the equations in two-dimensions; the commercial CFD software FLUENT along with the SIMPLE-algorithm is used for pressure-velocity coupling. Various values of the Reynolds number and obstacle spacing were selected to perform the numerical runs, using air as the working medium. Findings The channel containing the flat fin and the 45° V-shaped baffle with a large Reynolds number gave higher heat transfer and friction loss than the one with a smaller Reynolds number. Also, short separation distances between obstacles provided higher values of the ratios Nu/Nu0 and f/f0 and a larger thermal enhancement factor (TEF) than do larger distances. Originality/value This is an original work, as it uses a novel method for the improvement of heat transfer in completely new flow geometry.

scholarly journals A Numerical Study of Chemical Reaction in a Nanofluid Flow Due to Rotating Disk in the Presence of Magnetic Field

2021 ◽  
Author(s):  
Muhammad Ramzan ◽  
Poom Kumam ◽  
Kottakkaran Sooppy Nisar ◽  
Ilyas Khan ◽  
Wasim Jamshed
Keyword(s):  
Differential Equation ◽  
Radial Velocity ◽  
Chemical Reaction ◽  
Axial Velocity ◽  
Numerical Study ◽  
Tangential Velocity ◽  
Rotating Disk ◽  
Partial Differential ◽  
Suction Parameter ◽  
Matlab Programming

Abstract In this paper, a numerical study of MHD steady flow due to the rotating disk with chemical reaction was explored. Effect of different parameters such as Schmidt number, chemical reaction parameter, Prandtl number, Suction parameter, heat absorption/generation parameter, Nano-particle concentration, Reynold number, Magnetic parameter, skin friction, shear stress, temperature distribution, Nusselt number, mass transfer rate, radial velocity, axial velocity, and tangential velocity was analyzed and discussed. For the simplification of non-linear partial differential equations (PDEs) into the nonlinear ordinary differential equation (ODEs), the method of Similarity transformation was employed, and the resulting partial differential equation was solved by using finite difference method through MATLAB programming. This work's remarkable finding is that with the expansion of nanoparticle concentration radial velocity, tangential velocity and temperature of the fluid was enhanced but reverse reaction for axial velocity. Furthermore, the present results are found to be in excellent agreement with previously published work.

On the Axisymmetric Vortex Flow Over a Flat Surface

1969 ◽  
Vol 36 (3) ◽  
pp. 614-619 ◽  
Author(s):  
E. W. Schwiderski
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Numerical Study ◽  
Lower Boundary ◽  
Tangential Velocity ◽  
Slow Motion ◽  
Boundary Layer Separation ◽  
Local Boundary ◽  
Self Similar

The numerical study of the interaction of a potential vortex with a stationary surface recently published by Kidd and Farris [1] is extended through a transformation of the boundary-value problem to Volterra integral equations. The new calculations verified the results by Kidd and Farris and improved the bounds of the critical Reynolds number Nc, beyond which no self-similar vortex flows exist, to 5.5 < Nc < 5.6 The breakdown of the self-similar motions develops through an instability in the lower boundary layer, which is indicated by two inflection points in the tangential velocity profile. At the critical Reynolds number the lower inflection point reaches the surface and indicates the beginning of boundary-layer separation in the wake-type flow. If the Stokes linearization is applied, one arrives at a new Stokes paradox. However, this “paradox” can be resolved by correcting the free-stream pressure distortion of the Stokes approximation. The new slow-motion approximation is nonlinear and yields an integral which is also free of the Whitehead paradox. The properties of the new exact solution confirm the novel flow features previously detected in almost self-similar motions, which were constructed by adjustable local boundary-layer approximations.

Fluid Flow and Lateral Fluid Dispersion in Bounded Granular Beds

2002 ◽  
Author(s):  
Azita Soleymani ◽  
Eveliina Takasuo ◽  
Piroz Zamankhan ◽  
William Polashenski
Keyword(s):  
Reynolds Number ◽  
Porous Media ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Numerical Results ◽  
Transition To Turbulence ◽  
Wide Range

Results are presented from a numerical study examining the flow of a viscous, incompressible fluid through random packing of nonoverlapping spheres at moderate Reynolds numbers (based on pore permeability and interstitial fluid velocity), spanning a wide range of flow conditions for porous media. By using a laminar model including inertial terms and assuming rough walls, numerical solutions of the Navier-Stokes equations in three-dimensional porous packed beds resulted in dimensionless pressure drops in excellent agreement with those reported in a previous study (Fand et al., 1987). This observation suggests that no transition to turbulence could occur in the range of Reynolds number studied. For flows in the Forchheimer regime, numerical results are presented of the lateral dispersivity of solute continuously injected into a three-dimensional bounded granular bed at moderate Peclet numbers. Lateral fluid dispersion coefficients are calculated by comparing the concentration profiles obtained from numerical and analytical methods. Comparing the present numerical results with data available in the literature, no evidence has been found to support the speculations by others for a transition from laminar to turbulent regimes in porous media at a critical Reynolds number.

scholarly journals Tip Vortex Cavitation on an Oscillating Hydrofoil

1997 ◽  
Vol 119 (4) ◽  
pp. 752-758 ◽  
Author(s):  
O. Boulon ◽  
J. P. Franc ◽  
J. M. Michel
Keyword(s):  
Steady State ◽  
Vortex Core ◽  
Oscillation Frequency ◽  
Strong Influence ◽  
Tip Vortex ◽  
Tip Vortex Cavitation ◽  
Cavitation Inception ◽  
Time Required ◽  
Oscillation Frequencies ◽  
The University

This paper discusses tests conducted in the hydrodynamic tunnel of the University of Grenoble on a 3D oscillating hydrofoil. Visualization of unsteady tip vortex cavitation indicates a strong influence of the water nuclei content. The investigation was focused on the influence of the oscillation frequency on tip vortex cavitation inception. For very low nuclei content, cavitation inception is strongly delayed as compared to the steady-state results at very small oscillation frequencies. This delay is significantly reduced by nuclei seeding. The results can be explained by assuming that the time required for the inception of cavitation in the tip vortex corresponds to the time necessary for a cavitation nucleus to be captured by the vortex core.

scholarly journals Numerical study of flow across an ellipse and a circle placed in a uniform stream of infinite extent

2020 ◽  
Author(s):  
Adnan Anwar ◽  
Mudassar Razzaq ◽  
Liudmila Rivkind
Keyword(s):  
Reynolds Number ◽  
Numerical Study ◽  
Angle Of Attack ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Reynolds Number Flow ◽  
Infinite Extent ◽  
Number Flow ◽  
Conforming Finite Element Method ◽  
Drag And Lift

As an example of an aerodynamics prototypical study, we examined a two-dimensional low Reynolds number flow over obstacles immersed in a stream of infinite extent. The Navier Stokes equation is being discretized by non conforming finite element method approach. The resulting discretized nonlinear algebraic system is being solved by using the fixpoint method and the Newton method and multigrid method for the linear sub-problem employed. The magnitude of the uniform upstream velocity under the study of the problem for Reynolds number in the range 1 < Re < 100 and the angle of attack of the upstream velocity at α = -5; 0; 5 degrees performed. Analysis of the resulting drag and lift forces acting on obstacles with respect to the angle of attack of the upstream velocity and the Reynolds number is made. Moreover, the influence of one obstacle on the resulting drag and lift coefficients of other obstacles determined. The results are being presented in a graphical and vector form.

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.

Laminar Fully Developed Flow in Periodically Converging-Diverging Microtubes

2008 ◽  
Author(s):  
M. Bahrami ◽  
M. Akbari ◽  
D. Sinton
Keyword(s):  
Reynolds Number ◽  
Axial Velocity ◽  
Flow Resistance ◽  
Numerical Study ◽  
Numerical Results ◽  
Geometrical Parameters ◽  
Fully Developed Flow ◽  
Proposed Model ◽  
Axial Velocity Profile ◽  
Flow Approximation

Laminar fully developed flow and pressure drop in linearly varying cross -section converging-diverging microtubes have been investigated in this work. These microtubes are formed from a series of converging-diverging modules. An analytical model is developed for frictional flow resistance assuming parabolic axial velocity profile in diverging and converging sections. Frictional flow resistance is found to be only a function of the geometrical parameters. To validate the model, a numerical study is carried out for the Reynolds number ranging from 0.01 to 100, for various taper angles and maximum-minimum radius ratios ranging from 0.5 to 1. Comparisons between the model and numerical results show that the proposed model predicts the axial velocity and the flow resistance accurately. As expected, the flow resistance is found to be effectively independent of the Reynolds number from numerical results. Parametric study shows that the effect of radius ratio is more significant than the taper angle. It is also observed that for small taper angles, flow resistance can be determined accurately by applying the local Poiseuille flow approximation.

Effect of Hydrofoil Planform on Tip Vortex Roll-Up and Cavitation

1995 ◽  
Vol 117 (1) ◽  
pp. 162-169 ◽  
Author(s):  
D. H. Fruman ◽  
P. Cerrutti ◽  
T. Pichon ◽  
P. Dupont
Keyword(s):  
Reynolds Number ◽  
Incidence Angle ◽  
Pressure Coefficient ◽  
Tangential Velocity ◽  
Leading Edge ◽  
Velocity Profiles ◽  
The Other ◽  
Tip Vortex ◽  
Trailing Edge ◽  
Cavitation Inception

The effect of the planform of hydrofoils on tip vortex roll-up and cavitation has been investigated by testing three foils having the same NACA 16020 cross section but different shapes. One foil has an elliptical shape while the other two are shaped like quarters of ellipses; one with a straight leading edge and the other with a straight trailing edge. Experiments were conducted in the ENSTA, Ecole Navale and IMHEF cavitation tunnels with homologous foils of different sizes to investigate Reynolds number effects. Hydrodynamic forces as well as cavitation inception and desinence performance were measured as a function of Reynolds number and foil incidence angle. Laser Doppler measurements of the tangential and axial velocity profiles in the region immediately downstream of the tip were also performed. At equal incidence angle and Reynolds number, the three foils show different critical cavitation conditions and the maximum tangential velocity near the tip increases as the hydrofoil tip is moved from a forward to a rear position. However, the velocity profiles become more similar with increasing downstream distance, and at downstream distances greater than one chord aft of the tip, the differences between the foils disappear. The rate of tip vortex roll-up is much faster for the straight leading edge than for the straight trailing edge foil and, in the latter case, a significant portion of the roll-up occurs along the foil curved leading edge. The minimum of the pressure coefficient on the axis of the vortex was estimated from the velocity measurements and correlated with the desinent cavitation number for the largest free stream velocities. The correlation of data is very satisfactory. At the highest Reynolds number tested and at equal lift coefficients, the straight leading edge foil displays the most favorable cavitation desinent numbers.

Numerical study of three-dimensional Kolmogorov flow at high Reynolds numbers

1996 ◽  
Vol 306 ◽  
pp. 293-323 ◽  
Author(s):  
Vadim Borue ◽  
Steven A. Orszag
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Eddy Viscosity ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Large Reynolds Number ◽  
Kolmogorov Flow ◽  
Turbulence Decay ◽  
High Reynolds

High-resolution numerical simulations (with up to 2563 modes) are performed for three-dimensional flow driven by the large-scale constant force fy = F cos(x) in a periodic box of size L = 2π (Kolmogorov flow). High Reynolds number is attained by solving the Navier-Stokes equations with hyperviscosity (-1)h+1Δh (h = 8). It is shown that the mean velocity profile of Kolmogorov flow is nearly independent of Reynolds number and has the ‘laminar’ form vy = V cos(x) with a nearly constant eddy viscosity. Nevertheless, the flow is highly turbulent and intermittent even at large scales. The turbulent intensities, energy dissipation rate and various terms in the energy balance equation have the simple coordinate dependence a + b cos(2x) (with a, b constants). This makes Kolmogorov flow a good model to explore the applicability of turbulence transport approximations in open time-dependent flows. It turns out that the standard expression for effective (eddy) viscosity used in K-[Escr ] transport models overpredicts the effective viscosity in regions of high shear rate and should be modified to account for the non-equilibrium character of the flow. Also at large scales the flow is anisotropic but for large Reynolds number the flow is isotropic at small scales. The important problem of local isotropy is systematically studied by measuring longitudinal and transverse components of the energy spectra and crosscorrelation spectra of velocities and velocity-pressure-gradient spectra. Cross-spectra which should vanish in the case of isotropic turbulence decay only algebraically but somewhat faster than corresponding isotropic correlations. It is verified that the pressure plays a crucial role in making the flow locally isotropic. It is demonstrated that anisotropic large-scale flow may be considered locally isotropic at scales which are approximately ten times smaller than the scale of the flow.

Sign in / Sign up

Export Citation Format

Share Document