Simulation of Unsteady Flow Around a Cylinder

2015 ◽  
Vol 3 (2) ◽  
pp. 28-49
Author(s):  
Ridha Alwan Ahmed
Keyword(s):  
Stokes Equations ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Mean Value ◽  
Navier Stokes ◽  
Cylinder Surface ◽  
Navier Stokes Equations ◽  
Flow Around A Cylinder ◽  
Numerical Grid ◽  
Good Agreement

       In this paper, the phenomena of vortex shedding from the circular cylinder surface has been studied at several Reynolds Numbers (40≤Re≤ 300).The 2D, unsteady, incompressible, Laminar flow, continuity and Navier Stokes equations have been solved numerically by using CFD Package FLUENT. In this package PISO algorithm is used in the pressure-velocity coupling.        The numerical grid is generated by using Gambit program. The velocity and pressure fields are obtained upstream and downstream of the cylinder at each time and it is also calculated the mean value of drag coefficient and value of lift coefficient .The results showed that the flow is strongly unsteady and unsymmetrical at Re>60. The results have been compared with the available experiments and a good agreement has been found between them

scholarly journals Instability of transonic flow past flattened airfoils

2013 ◽  
Vol 3 (4) ◽  
Author(s):  
Alexander Kuzmin
Keyword(s):  
Numerical Modeling ◽  
Transonic Flow ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Simulations ◽  
Flow Past ◽  
Coefficient Versus

AbstractTransonic flow past a Whitcomb airfoil and two modifications of it at Reynolds numbers of the order of ten millions is studied. The numerical modeling is based on the system of Reynolds-averaged Navier-Stokes equations. The flow simulations show that variations of the lift coefficient versus the angle of attack become more abrupt with decreasing curvature of the airfoil in the midchord region. This is caused by an instability of closely spaced local supersonic regions on the upper surface of the airfoil.

Rotordynamic Coefficients of Circumferentially-Grooved Liquid Seals Using the Averaged Navier-Stokes Equations

1997 ◽  
Vol 119 (3) ◽  
pp. 556-567 ◽  
Author(s):  
Mihai Arghir ◽  
Jean Freˆne
Keyword(s):  
Coordinate Transformation ◽  
Stokes Equations ◽  
Turbulent Viscosity ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
First Order ◽  
Rotordynamic Coefficients ◽  
High Reynolds ◽  
Good Agreement

The paper presents a method to calculate the rotordynamic coefficients of circumferentially-grooved liquid seals operating in centered position and turbulent flow regimes. The method is based on the integration of the averaged Navier-Stokes equations and uses a coordinate transformation proposed by Dietzen and Nordmann (1987). The effect of the coordinate transformation on the components of the stress tensor is included in the first order transport equations. To ensure grid independent solutions, numerical boundary conditions for the first-order velocities were formulated using the logarithmic law. The perturbation of the turbulent viscosity was also considered. A pressure recovery effect at the exit section was included in the first order mathematical model. The method is validated by calculations for straight and circumferentially-grooved seals. Comparisons with experimental and theoretical results show a good agreement for straight seals and for seals with few grooves, and a reasonable agreement for severe industrial cases (high Reynolds numbers and large number of grooves).

scholarly journals Energy spectrum in the dissipation range of fluid turbulence

1997 ◽  
Vol 57 (1) ◽  
pp. 195-201 ◽  
Author(s):  
D. O. MARTÍNEZ ◽  
S. CHEN ◽  
G. D. DOOLEN ◽  
R. H. KRAICHNAN ◽  
L.-P. WANG ◽  
...  
Keyword(s):  
Energy Spectrum ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Fluid Turbulence ◽  
Theoretical Predictions ◽  
Dissipation Range ◽  
Good Agreement

High-resolution, direct numerical simulations of three-dimensional incompressible Navier–Stokes equations are carried out to study the energy spectrum in the dissipation range. An energy spectrum of the form A(k/kd)α exp[−βk/kd] is confirmed. The possible values of the parameters α and β, as well as their dependence on Reynolds numbers and length scales, are investigated, showing good agreement with recent theoretical predictions. A ‘bottleneck’-type effect is reported at k/kd≈4, exhibiting a possible transition from near-dissipation to far-dissipation.

Steady two-dimensional flow through a row of normal flat plates

1990 ◽  
Vol 210 ◽  
pp. 281-302 ◽  
Author(s):  
D. B. Ingham ◽  
T. Tang ◽  
B. R. Morton
Keyword(s):  
Finite Difference ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Corner Singularities ◽  
Flat Plates ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
Good Agreement

A numerical and experimental study is described for the two-dimensional steady flow through a uniform cascade of normal flat plates. The Navier–Stokes equations are written in terms of the stream function and vorticity and are solved using a second-order-accurate finite-difference scheme which is based on a modified procedure to preserve accuracy and iterative convergence at higher Reynolds numbers. The upstream and downstream boundary conditions are discussed and an asymptotic solution is employed both upstream and downstream. A frequently used method for dealing with corner singularities is shown to be inaccurate and a method for overcoming this problem is described. Numerical solutions have been obtained for blockage ratio of 50 % and Reynolds numbers in the range 0 [les ]R[les ] 500 and results for both the lengths of attached eddies and the drag coefficients are presented. The calculations indicate that the eddy length increases linearly withR, at least up toR= 500, and that the multiplicative constant is in very good agreement with the theoretical prediction of Smith (1985a), who considered a related problem. In the case ofR= 0 the Navier–Stokes equations are solved using the finite-difference scheme and a modification of the boundary-element method which treats the corner singularities. The solutions obtained by the two methods are compared and the results are shown to be in good agreement. An experimental investigation has been performed at small and moderate values of the Reynolds numbers and there is excellent agreement with the numerical results both for flow streamlines and eddy lengths.

scholarly journals A Numerical Investigation of Co-flow Jet Effects on Airfoil Aerodynamic Characteristics

2021 ◽  
Author(s):  
Shima Yazdani ◽  
Erfan Salimipour ◽  
Ayoob Salimipour
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Active Flow Control ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Aerodynamic Characteristics ◽  
Dynamic Stall ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Momentum Coefficient

Abstract The present paper numerically investigates the performance of a Co-Flow Jet (CFJ) on the static and dynamic stall control of the NACA 0024 airfoil at Reynolds number 1.5 × 105. The two-dimensional Reynolds-averaged Navier-Stokes equations are solved using the SST k-ω turbulence model. The results show that the lift coefficients at the low angles of attack (up to α = 15̊) are significantly increased at Cµ = 0.06, however for the higher momentum coefficients, it is not seen an improvement in the aerodynamic characteristics. Also, the dynamic stall for a range of α between 0̊ and 20̊ at the mentioned Reynolds number and with the reduced frequency of 0.15 for two CFJ cases with Cµ = 0.05 and 0.07 are investigated. For the case with Cµ = 0.07, the lift coefficient curve did not present a noticeable stall feature compared to Cµ = 0.05. The effect of this active flow control by increasing the Reynolds numbers from 0.5 × 105 to 3 × 105 is also investigated. At all studied Reynolds numbers, the lift coefficient enhances as the momentum coefficient increases where its best performance is obtained at the angle of attack α = 15̊.

Numerical Solutions of Viscous Flow through a Pipe Orifice at Low Reynolds Numbers

1968 ◽  
Vol 10 (2) ◽  
pp. 133-140 ◽  
Author(s):  
R. D. Mills
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Viscous Incompressible Fluid ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Axially Symmetric ◽  
Navier Stokes Equations ◽  
Low Reynolds Numbers ◽  
Flow Through ◽  
Good Agreement

Numerical solutions of the Navier-Stokes equations have been obtained in the low range of Reynolds numbers for steady, axially symmetric, viscous, incompressible fluid flow through an orifice in a circular pipe with a fixed orifice/pipe diameter ratio. Streamline patterns and vorticity contours are presented as functions of Reynolds number. The theoretically determined discharge coefficients are in good agreement with experimental results of Johansen (2).

Steady flow through a channel with a symmetrical constriction in the form of a step

1980 ◽  
Vol 372 (1750) ◽  
pp. 393-414 ◽  
Keyword(s):  
Asymptotic Theory ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Volumetric Flow Rate ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Uniform Grids ◽  
Flow Through ◽  
Good Agreement

Numerical solutions of the Navier-Stokes equations are given for the steady, two-dimensional, laminar flow of an incompressible fluid through a channel with a symmetric constriction in the form of a semi-infinite step change in width. The flow proceeds from a steady Poiseuille velocity distribution far enough upstream of the step in the wider part of the channel to a corresponding distribution downstream in the narrower part and is assumed to remain symmetrical about the centre line of the channel. The numerical scheme involves an accurate and efficient centred difference treatment developed by Dennis & Hudson (1978) and results are obtained for Reynolds numbers, based on half the volumetric flow rate, up to 2000. For a step that halves the width of the channel it is found that very fine uniform grids, with 80 intervals spaced across half of the wider channel upstream, are necessary for resolution of the solution for the flow downstream of the onset of the step. Slightly less refined grids are adequate to resolve the flow upstream. The calculated flow ahead of the step exhibits very good agreement with the asymptotic theory of Smith (1979 b)for Reynolds numbers greater than about 100; indeed, comparisons of the upstream separation position and of the wall vorticity nearby are believed to yield the best agreement between numerical and asymptotic solutions yet found. Downstream there is also qualitative agreement regarding separation and reattachment as the grid size is refined in the numerical results.

A Numerical Study of Unsteady Laminar Forced Convection From a Circular Cylinder

1976 ◽  
Vol 98 (2) ◽  
pp. 303-307 ◽  
Author(s):  
P. C. Jain ◽  
B. S. Goel
Keyword(s):  
Nusselt Number ◽  
Circular Cylinder ◽  
Forced Convection ◽  
Stokes Equations ◽  
Numerical Study ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Laminar Forced Convection ◽  
Good Agreement

A numerical investigation of an unsteady laminar forced convection from a circular cylinder is presented. The Navier-Stokes equations and the energy equation for an unsteady incompressible fluid flow are solved by the finite difference method. The results are obtained at Reynolds numbers 100 and 200. The temperature field around the cylinder is obtained throughout the region of computation and is shown by isotherms at different times. The variations of the local Nusselt number around the cylinder at different times are computed and shown by graphs. The mean Nusselt number and the Strouhal number are also calculated. The computed results are compared with the other available experimental and theoretical results and are found to be in good agreement with them.

Symmetrical flow past a uniformly accelerated circular cylinder

1974 ◽  
Vol 65 (3) ◽  
pp. 461-480 ◽  
Author(s):  
W. M. Collins ◽  
S. C. R. Dennis
Keyword(s):  
Circular Cylinder ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Method Of Solution ◽  
Small Times ◽  
Accurate Procedure ◽  
Logical Extension ◽  
Good Agreement

The flow normal to an infinite circular cylinder which is uniformly accelerated from rest in a viscous fluid is considered. The flow is assumed to remain symmetrical about the direction of motion of the cylinder. Two types of solution are presented. In the first an expansion in powers of the time from the start of the motion is given which extends the results of boundary-layer theory by taking into account corrections for finite Reynolds numbers. Physical properties of the flow for small times and finite but large Reynolds numbers are calculated from this expansion. In the second method of solution the Navier-Stokes equations are integrated by an accurate procedure which is a logical extension of the solution in powers of the time. Results are obtained forR2= 97·5, 5850, 122 × 103and ∞, whereRis the Reynolds number. This is defined asR= 2a(ab)½/v, whereais the radius of the cylinder,bthe uniform acceleration andvthe kinematic viscosity of the fluid. The methods are in good agreement for small times.The numerical method of integration has been carried to moderate times and various flow properties have been calculated. The growth of the length of the separated wake behind the cylinder forR2= 97·5, 5850 and 122 × 103is compared with the results of recent experimental measurements. The agreement is only moderate forR2= 97·5 but it improves greatly asRincreases. The numerical integrations were continued in each case until the implicit method of integration failed to converge, which terminated the procedure. A secondary vortex appeared on the surface of the cylinder for the caseR2= 122 × 103.

Numerical Modeling of Evolution of Boundary Between Incompressible Gas and Liquid in Two-Dimensional Region

2006 ◽  
Vol 4 ◽  
pp. 224-236
Author(s):  
A.S. Topolnikov
Keyword(s):  
Numerical Modeling ◽  
Interphase Boundary ◽  
Incompressible Liquid ◽  
Stokes Equations ◽  
Numerical Code ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Incompressible Media ◽  
Good Agreement

The paper is devoted to numerical modeling of Navier–Stokes equations for incompressible media in the case, when there exist gas and liquid inside the rectangular calculation region, which are separated by interphase boundary. The set of equations for incompressible liquid accounting for viscous, gravitational and surface (capillary) forces is solved by finite-difference scheme on the spaced grid, for description of interphase boundary the ideology of Level Set Method is used. By developed numerical code the set of hydrodynamic problems is solved, which describe the motion of two-phase incompressible media with interphase boundary. As a result of numerical simulation the solutions are obtained, which are in good agreement with existing analytical and experimental solutions.

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