scholarly journals Numerical Investigation of Vortex Induced Vibration for Submerged Floating Tunnel under Different Reynolds Numbers

Water ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 171 ◽  
Author(s):  
Ruijia Jin ◽  
Mingming Liu ◽  
Baolei Geng ◽  
Xin Jin ◽  
Huaqing Zhang ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Numerical Model ◽  
Stokes Equations ◽  
Flow Direction ◽  
Great Influence ◽  
Large Reynolds Number ◽  
Vortex Induced Vibration ◽  
Force Coefficients ◽  
Submerged Floating Tunnel ◽  
Lock In

A 2D numerical model was established to investigate vortex induced vibration (VIV) for submerged floating tunnel (SFT) by solving incompressible viscous Reynolds average Navier-Stokes equations in the frame of Abitrary Lagrangian Eulerian (ALE). The numerical model was closed by solving SST k-ω turbulence model. The present numerical model was firstly validated by comparing with published experimental data, and the comparison shows that good achievement is obtained. Then, the numerical model is used to investigate VIV for SFT under current. In the simulation, the SFT was allowed to oscillate in cross flow direction only under the constraint of spring and damping. The force coefficients and motion of SFT were obtained under different reduced velocity. Further research showed that Reynolds number has not only a great influence on the vibration amplitude and ‘lock-in’ region, but also on the force coefficients on of the SFT. A large Reynolds number results in a relatively small ‘lock-in’ region and force coefficient.

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 The acoustic impedance of a laminar viscous jet through a thin circular aperture

2019 ◽  
Vol 864 ◽  
pp. 5-44 ◽  
Author(s):  
David Fabre ◽  
Raffaele Longobardi ◽  
Paul Bonnefis ◽  
Paolo Luchini
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Axisymmetric Flow ◽  
Classical Problem ◽  
Base Flow ◽  
Large Reynolds Number ◽  
Linear Perturbation ◽  
Circular Aperture ◽  
Vena Contracta ◽  
Numerical Resolution

The unsteady axisymmetric flow through a circular aperture in a thin plate subjected to harmonic forcing (for instance under the effect of an incident acoustic wave) is a classical problem first considered by Howe (Proc. R. Soc. Lond. A, vol. 366, 1979, pp. 205–223), using an inviscid model. The purpose of this work is to reconsider this problem through a numerical resolution of the incompressible linearized Navier–Stokes equations (LNSE) in the laminar regime, corresponding to $Re=[500,5000]$. We first compute a steady base flow which allows us to describe the vena contracta phenomenon in agreement with experiments. We then solve a linear problem allowing us to characterize both the spatial amplification of the perturbations and the impedance (or equivalently the Rayleigh conductivity), which is a key quantity to investigate the response of the jet to acoustic forcing. Since the linear perturbation is characterized by a strong spatial amplification, the numerical resolution requires the use of a complex mapping of the axial coordinate in order to enlarge the range of Reynolds number investigated. The results show that the impedances computed with $Re\gtrsim 1500$ collapse onto a single curve, indicating that a large Reynolds number asymptotic regime is effectively reached. However, expressing the results in terms of conductivity leads to substantial deviation with respect to Howe’s model. Finally, we investigate the case of finite-amplitude perturbations through direct numerical simulations (DNS). We show that the impedance predicted by the linear approach remains valid for amplitudes up to order $10^{-1}$, despite the fact that the spatial evolution of the perturbations in the jet is strongly nonlinear.

Direct numerical simulation of high-speed transition due to an isolated roughness element

2014 ◽  
Vol 748 ◽  
pp. 848-878 ◽  
Author(s):  
Pramod K. Subbareddy ◽  
Matthew D. Bartkowicz ◽  
Graham V. Candler
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
High Speed ◽  
Large Scale ◽  
Stokes Equations ◽  
Roughness Element ◽  
Dynamic Mode Decomposition ◽  
Large Reynolds Number ◽  
Dynamic Mode ◽  
Low Dissipation

AbstractWe study the transition of a Mach 6 laminar boundary layer due to an isolated cylindrical roughness element using large-scale direct numerical simulations (DNS). Three flow conditions, corresponding to experiments conducted at the Purdue Mach 6 quiet wind tunnel are simulated. Solutions are obtained using a high-order, low-dissipation scheme for the convection terms in the Navier–Stokes equations. The lowest Reynolds number ($Re$) case is steady, whereas the two higher $Re$ cases break down to a quasi-turbulent state. Statistics from the highest $Re$ case show the presence of a wedge of fully developed turbulent flow towards the end of the domain. The simulations do not employ forcing of any kind, apart from the roughness element itself, and the results suggest a self-sustaining mechanism that causes the flow to transition at a sufficiently large Reynolds number. Statistics, including spectra, are compared with available experimental data. Visualizations of the flow explore the dominant and dynamically significant flow structures: the upstream shock system, the horseshoe vortices formed in the upstream separated boundary layer and the shear layer that separates from the top and sides of the cylindrical roughness element. Streamwise and spanwise planes of data were used to perform a dynamic mode decomposition (DMD) (Rowley et al., J. Fluid Mech., vol. 641, 2009, pp. 115–127; Schmid, J. Fluid Mech., vol. 656, 2010, pp. 5–28).

Analytical and numerical studies of the structure of steady separated flows

1966 ◽  
Vol 24 (1) ◽  
pp. 113-151 ◽  
Author(s):  
Odus R. Burggraf
Keyword(s):  
Reynolds Number ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Low Reynolds Number ◽  
Reynolds Numbers ◽  
Total Power ◽  
Large Reynolds Number ◽  
Boundary Velocity ◽  
Displacement Thickness ◽  
Low Reynolds

The viscous structure of a separated eddy is investigated for two cases of simplified geometry. In § 1, an analytical solution, based on a linearized model, is obtained for an eddy bounded by a circular streamline. This solution reveals the flow development from a completely viscous eddy at low Reynolds number to an inviscid rotational core at high Reynolds number, in the manner envisaged by Batchelor. Quantitatively, the solution shows that a significant inviscid core exists for a Reynolds number greater than 100. At low Reynolds number the vortex centre shifts in the direction of the boundary velocity until the inviscid core develops; at large Reynolds number, the inviscid vortex core is symmetric about the centre of the circle, except for the effect of the boundary-layer displacement-thickness. Special results are obtained for velocity profiles, skin-friction distribution, and total power dissipation in the eddy. In addition, results of the method of inner and outer expansions are compared with the complete solution, indicating that expansions of this type give valid results for separated eddies at Reynolds numbers greater than about 25 to 50. The validity of the linear analysis as a description of separated eddies is confirmed to a surprising degree by numerical solutions of the full Navier–Stokes equations for an eddy in a square cavity driven by a moving boundary at the top. These solutions were carried out by a relaxation procedure on a high-speed digital computer, and are described in § 2. Results are presented for Reynolds numbers from 0 to 400 in the form of contour plots of stream function, vorticity, and total pressure. At the higher values of Reynolds number, an inviscid core develops, but secondary eddies are present in the bottom corners of the square at all Reynolds numbers. Solutions of the energy equation were obtained also, and isotherms and wall heat-flux distributions are presented graphically.

Particle Arrestance Modeling Within Fibrous Porous Media

1999 ◽  
Vol 121 (1) ◽  
pp. 155-162 ◽  
Author(s):  
James Giuliani ◽  
Kambiz Vafai
Keyword(s):  
Reynolds Number ◽  
Numerical Model ◽  
Stokes Flow ◽  
Stokes Equations ◽  
Angular Position ◽  
Past Research ◽  
Particle Growth ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Fibrous Medium

In the present study, particle growth on individual fibers within a fibrous medium is examined as flow conditions transition beyond the Stokes flow regime. Employing a numerical model that solves the viscous, incompressible Navier-Stokes equations, the Stokes flow approximation used in past research to describe the velocity field through the fibrous medium is eliminated. Fibers are modeled in a staggered array to eliminate assumptions regarding the effects of neighboring fibers. Results from the numerical model are compared to the limiting theoretical results obtained for individual cylinders and arrays of cylinders. Particle growth is presented as a function of time, angular position around the fiber, and flow Reynolds number. From the range of conditions examined, particles agglomerate into taller and narrower dendrites as Reynolds number is increased, which increases the probability that they will break off as larger agglomerations and, subsequently, substantially reduce the hydraulic conductivity of the porous medium.

On Vortex Induced Vibration in Two-Degree-of-Freedoms of Flexible Cylinders

2011 ◽  
Author(s):  
Weiping Huang ◽  
Weihong Yu
Keyword(s):  
Natural Frequency ◽  
Current Velocity ◽  
Coupling Effect ◽  
Great Influence ◽  
Cross Flow ◽  
Flexible Cylinder ◽  
Fluid Structure ◽  
Vortex Induced Vibration ◽  
Flow Vortex ◽  
Lock In

In this paper, an experimental study on the in-line and cross-flow vortex-induced vibration (VIV) of flexible cylinders is conducted. The relationship of two-degree-of-freedoms of vortex-induced vibration of flexible cylinders is also investigated. The influence of natural frequency of flexible cylinders on vortex shedding and VIV are studied through the experiment in this paper. Finally, A nonlinear model, with fluid-structure interaction, of two-degree-of-freedom VIV of flexible cylinders is proposed. It is shown that the ratio of the frequencies and amplitudes of in-line and cross flow VIV of the flexible cylinders changes with current velocity and Reynolds number. The natural frequency of flexible cylinder has great influence on the vortex-induced virbation due to the strong fluid-structure coupling effect. Under given current velocity, the natural frequency of flexible cylinder determines its forms of vibration (in circular or ‘8’ form). The ratio of the VIV frequencies is 1.0 beyond the lock in district and 2.0 within the lock in district respectively. And the ratio of the VIV amplitudes is 1.0 beyond the lock in district and 1/3 to 2/3 within the lock in district. The results from this paper indicates that in-line vibration should be considerated when calculating the vibration response and fatigue damage.

scholarly journals On the uniqueness of steady flow past a rotating cylinder with suction

2000 ◽  
Vol 411 ◽  
pp. 213-232 ◽  
Author(s):  
E. V. BULDAKOV ◽  
S. I. CHERNYSHENKO ◽  
A. I. RUBAN
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Cross Flow ◽  
Rotation Velocity ◽  
Rotating Cylinder ◽  
Large Reynolds Number ◽  
Order Unity ◽  
Flow Past ◽  
Exponentially Small

The subject of this study is a steady two-dimensional incompressible flow past a rapidly rotating cylinder with suction. The rotation velocity is assumed to be large enough compared with the cross-flow velocity at infinity to ensure that there is no separation. High-Reynolds-number asymptotic analysis of incompressible Navier–Stokes equations is performed. Prandtl's classical approach of subdividing the flow field into two regions, the outer inviscid region and the boundary layer, was used earlier by Glauert (1957) for analysis of a similar flow without suction. Glauert found that the periodicity of the boundary layer allows the velocity circulation around the cylinder to be found uniquely. In the present study it is shown that the periodicity condition does not give a unique solution for suction velocity much greater than 1/Re. It is found that these non-unique solutions correspond to different exponentially small upstream vorticity levels, which cannot be distinguished from zero when considering terms of only a few powers in a large Reynolds number asymptotic expansion. Unique solutions are constructed for suction of order unity, 1/Re, and 1/√Re. In the last case an explicit analysis of the distribution of exponentially small vorticity outside the boundary layer was carried out.

scholarly journals Numerical studies of viscous incompressible flow between two rotating concentric spheres

2004 ◽  
Vol 2004 (2) ◽  
pp. 91-106 ◽  
Author(s):  
E. O. Ifidon
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Outer Sphere ◽  
Navier Stokes ◽  
Large Reynolds Number ◽  
Stable Configuration ◽  
Axially Symmetric ◽  
Closed Curves ◽  
Concentric Spheres ◽  
Flow Variables

The problem of determining the induced steady axially symmetric motion of an incompressible viscous fluid confined between two concentric spheres, with the outer sphere rotating with constant angular velocity and the inner sphere fixed, is numerically investigated for large Reynolds number. The governing Navier-Stokes equations expressed in terms of a stream function-vorticity formulation are reduced to a set of nonlinear ordinary differential equations in the radial variable, one of second order and the other of fourth order, by expanding the flow variables as an infinite series of orthogonal Gegenbauer functions. The numerical investigation is based on a finite-difference technique which does not involve iterations and which is valid for arbitrary large Reynolds number. Present calculations are performed for Reynolds numbers as large as 5000. The resulting flow patterns are displayed in the form of level curves. The results show a stable configuration consistent with experimental results with no evidence of any disjoint closed curves.

Laminar flow in a curved pipe with varying curvature

1976 ◽  
Vol 73 (4) ◽  
pp. 735-752 ◽  
Author(s):  
S. Murata ◽  
Y. Miyake ◽  
T. Inaba
Keyword(s):  
Reynolds Number ◽  
Flow Direction ◽  
Circular Cross Section ◽  
Outer Side ◽  
Large Reynolds Number ◽  
Phase Lag ◽  
Mean Flow ◽  
Curved Pipe ◽  
Curved Pipes ◽  
Centre Line

The steady laminar motion of fluid through pipes of circular cross-section, the curvature of whose centre-line varies locally, is analysed theoretically. The flow in three kinds of pipes whose centre-lines are specified by \[ \hat{y} = a(1+\kappa^2\hat{x}^2)^{\frac{1}{2}},\quad\hat{y} = a\tan h\kappa\hat{x}\quad{\rm and}\quad\hat{y} = a\sin\kappa\hat{x} \] are treated as the examples of once-, twice- and periodically-curved pipes, respectively. The analysis is valid for any other two-dimensionally curved pipes, when centre-line curvature is small. At very small Reynolds number, the position of maximum axial velocity shifts towards the inner side of the pipe section; at large Reynolds number, on the contrary, it tends to the outer side, owing to centrifugal force. Furthermore, in the latter case, adaptation of the flow follows the change of mean-flow direction, with a phase lag.

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