scholarly journals Computation of Pressure Fields around a Two-Dimensional Circular Cylinder Using the Vortex-In-Cell and Penalization Methods

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Seung-Jae Lee ◽  
Jun-Hyeok Lee ◽  
Jung-Chun Suh
Keyword(s):  
Circular Cylinder ◽  
Solid Body ◽  
Pressure Field ◽  
Stokes Equations ◽  
Computational Cost ◽  
Fixed Time ◽  
Computational Grids ◽  
Penalty Term ◽  
Pressure Fields ◽  
Wide Range

The vorticity-velocity formulation of the Navier-Stokes equations allows purely kinematical problems to be decoupled from the pressure term, since the pressure is eliminated by applying the curl operator. The Vortex-In-Cell (VIC) method, which is based on the vorticity-velocity formulation, offers particle-mesh algorithms to numerically simulate flows past a solid body. The penalization method is used to enforce boundary conditions at a body surface with a decoupling between body boundaries and computational grids. Its main advantage is a highly efficient implementation for solid boundaries of arbitrary complexity on Cartesian grids. We present an efficient algorithm to numerically implement the vorticity-velocity-pressure formulation including a penalty term to simulate the pressure fields around a solid body. In vorticity-based methods, pressure field can be independently computed from the solution procedure for vorticity. This clearly simplifies the implementation and reduces the computational cost. Obtaining the pressure field at any fixed time represents the most challenging goal of this study. We validate the implementation by numerical simulations of an incompressible viscous flow around an impulsively started circular cylinder in a wide range of Reynolds numbers: Re=40, 550, 3000, and 9500.

An Average-Passage Empirical Closure Model for Centrifugal Compressors

2004 ◽  
Author(s):  
Limin Gao ◽  
Guang Xi ◽  
Shangjin Wang
Keyword(s):  
Experimental Data ◽  
Empirical Model ◽  
Stokes Equations ◽  
Computational Cost ◽  
Axial Flow ◽  
Equation System ◽  
Computational Grids ◽  
Navier Stokes ◽  
Sufficient Information ◽  
Centrifugal Compressors

Applying the novel time- and passage-averaging operators, a reduced average-passage equation system is derived to remove the bodyforce and the blockage factor in Adamczyk’s average-passage equations. Like the Reynolds-averaged Navier-Stokes equations the average-passage flow model does not contain sufficient information to determine its solution. Based on the rich throughflow analysis for axial-flow turbomachinery and numerous studies for centrifugal compressors, a semi-empirical model of the deterministic stress is developed for centrifugal compressors in the present study. Finally, the empirical model coupled with the interface approach is applied to predict the time-averaged flow field in a tested centrifugal compressor stage and the results are compared with experimental data. Using the same computational grids, the computational cost with the empirical model is slightly more than that with the mixing plane model, and a good agreement was obtained between the numerical results and experimental data.

A Model for the Coupled Lift and Drag on a Circular Cylinder

2003 ◽  
Author(s):  
Ali H. Nayfeh ◽  
Farouk Owis ◽  
Muhammad R. Hajj
Keyword(s):  
Circular Cylinder ◽  
Stokes Equations ◽  
Quadratic Function ◽  
Phase Relations ◽  
Suitable Model ◽  
Van Der Pol ◽  
Spectral Moments ◽  
Drag Coefficients ◽  
Wide Range ◽  
Lift And Drag

The time-varying coupled lift and drag coefficients acting on a circular cylinder are modeled. Data used for the model are obtained by numerically solving the unsteady Reynolds-Averaged Navier Stokes equations over a wide range of Reynolds numbers. Using spectral moments, we determine the frequency components in the lift and drag coefficients and their phase relations. Using a perturbation technique, we obtain approximate solutions of both the van der Pol and Rayleigh equations. By fitting the amplitude and phase relations, we find that the van der Pol equation is the suitable model for the lift. The Rayleigh equation fails to give the correct phase relation. Because the major frequency in the drag component is twice that of the lift, the drag component is modeled as a quadratic function of the lift. Through analysis with higher-order spectral moments, the correct quadratic relation of the lift that yields the drag is determined. The model and results presented here are a first step in the development of a reduced-order model for vortex-induced vibrations, which includes the motions of the cylinder.

Heat Transfer From a Circular Cylinder at Low Reynolds Numbers

1998 ◽  
Vol 120 (1) ◽  
pp. 72-75 ◽  
Author(s):  
V. N. Kurdyumov ◽  
E. Ferna´ndez
Keyword(s):  
Circular Cylinder ◽  
Energy Equation ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Order Unity ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Prandtl Numbers ◽  
High Degree

A correlation formula, Nu = W0(Re)Pr1/3 + W1(Re), that is valid in a wide range of Reynolds and Prandtl numbers has been developed based on the asymptotic expansion for Pr → ∞ for the forced heat convection from a circular cylinder. For large Prandtl numbers, the boundary layer theory for the energy equation is applied and compared with the numerical solutions of the full Navier Stokes equations for the flow field and energy equation. It is shown that the two-terms asymptotic approximation can be used to calculate the Nusselt number even for Prandtl numbers of order unity to a high degree of accuracy. The formulas for coefficients W0 and W1, are provided.

scholarly journals Computation of Second-order Design Sensitivities for Steady State Incompressible Laminar Flows Using the Extended Complex Variables Method

2020 ◽  
Author(s):  
Mahdi Hassanzadeh
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Stokes Equations ◽  
General Procedure ◽  
Finite Difference Methods ◽  
Computational Cost ◽  
Complex Variables ◽  
Second Order ◽  
Wide Range ◽  
Extended Complex

In the current paper, the general procedure of the first and second-order sensitivity analysis is presented using the extended complex variables method (ECVM). In the traditional complex variables method, only the imaginary step is used for sensitivity analysis. However, in the ECVM, both of the real and imaginary parts are employed to improve the efficiency of the method. To show this, the ECVM is applied to the steady state incompressible laminar flow around a cylinder. The governing Navier-Stokes equations are solved by the finite element method and then the ECVM is employed. The results are validated through comparing with those of obtained by an analytical as well as the finite difference methods and the convergence rate is investigated. It is illustrated that the first-order sensitivity analysis is not influenced by the change of the step length for both of the traditional and extended complex variables methods. However, it is shown that unlike the traditional complex variables method, the ECVM is less dependent on the step size for calculating the second-order sensitivity. This can be considered as an enhancement in the efficiency of this method. Hence, the ECVM is suggested as an appropriate technique for calculating simultaneously the first and second-order sensitivities with high accuracy as well as low computational cost. The proposed method is applicable to a wide range of problems having simple or complex parameters.

scholarly journals Drag and pressure fields for the MHD flow around a circular cylinder at intermediate Reynolds numbers

2005 ◽  
Vol 2005 (3) ◽  
pp. 183-203 ◽  
Author(s):  
T. V. S. Sekhar ◽  
R. Sivakumar ◽  
T. V. R. Ravi Kumar
Keyword(s):  
Circular Cylinder ◽  
Drag Coefficient ◽  
Stagnation Point ◽  
Stokes Equations ◽  
Separation Bubble ◽  
Flow Direction ◽  
Boundary Layer Separation ◽  
Pressure Fields ◽  
Correction Technique ◽  
Rear Stagnation Point

Steady incompressible flow around a circular cylinder in an external magnetic field that is aligned with fluid flow direction is studied forRe(Reynolds number) up to 40 and the interaction parameter in the range0≤N≤15(or0≤M≤30), whereMis the Hartmann number related toNby the relationM=2NRe, using finite difference method. The pressure-Poisson equation is solved to find pressure fields in the flow region. The multigrid method with defect correction technique is used to achieve the second-order accurate solution of complete nonlinear Navier-Stokes equations. It is found that the boundary layer separation at rear stagnation point forRe=10is suppressed completely whenN<1and it started growing again whenN≥9. ForRe=20and 40, the suppression is not complete and in addition to that the rear separation bubble started increasing whenN≥3. The drag coefficient decreases for low values ofN(<0.1)and then increases with increase ofN. The pressure drag coefficient, total drag coefficient, and pressure at rear stagnation point vary withN. It is also found that the upstream and downstream pressures on the surface of the cylinder increase for low values ofN(<0.1)and rear pressure inversion occurs with further increase ofN. These results are in agreement with experimental findings.

Rapid gust response simulation of large civil aircraft using computational fluid dynamics

2017 ◽  
Vol 121 (1246) ◽  
pp. 1795-1807 ◽  
Author(s):  
P. Bekemeyer ◽  
R. Thormann ◽  
S. Timme
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
Computational Cost ◽  
Aircraft Design ◽  
Navier Stokes ◽  
Surface Pressure Distribution ◽  
Wide Range ◽  
Civil Aircraft

ABSTRACTSeveral critical load cases during the aircraft design process result from atmospheric turbulence. Thus, rapidly performable and highly accurate dynamic response simulations are required to analyse a wide range of parameters. A method is proposed to predict dynamic loads on an elastically trimmed, large civil aircraft using computational fluid dynamics in conjunction with model reduction. A small-sized modal basis is computed by sampling the aerodynamic response at discrete frequencies and applying proper orthogonal decomposition. The linear operator of the Reynolds-averaged Navier-Stokes equations plus turbulence model is then projected onto the subspace spanned by this basis. The resulting reduced system is solved at an arbitrary number of frequencies to analyse responses to 1-cos gusts very efficiently. Lift coefficient and surface pressure distribution are compared with full-order, non-linear, unsteady time-marching simulations to verify the method. Overall, the reduced-order model predicts highly accurate global coefficients and surface loads at a fraction of the computational cost, which is an important step towards the aircraft loads process relying on computational fluid dynamics.

Uniform Flow Past a Rotary Oscillating Circular Cylinder

2011 ◽  
Author(s):  
Lue Derek Du ◽  
Charles Dalton
Keyword(s):  
Circular Cylinder ◽  
Vortex Shedding ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Uniform Flow ◽  
Resonance Phenomenon ◽  
Curvilinear Coordinates ◽  
Wake Structure ◽  
Flow Past ◽  
Wide Range

In this paper, we study uniform flow past a rotary oscillating circular cylinder computationally. The objective is to determine the effect the oscillating rotation has on the lift and drag forces acting on the cylinder, on the wake structure, and on vortex shedding. A combination of finite-difference and spectral methods is used to calculate the three-dimensional incompressible unsteady Navier-Stokes equations in primitive variable form in nonorthogonal curvilinear coordinates. Wake turbulence is modeled by an LES technique. The Reynolds number considered is Re = 1.5×104, which is the same as that in the experimental study of Tokumaru & Dimotakis (1991), who suggested this technique as a means of reducing drag. We fix the forcing amplitude at the moderate value of Ω = 2 and vary the forcing frequency in a wide range to study its effect on the flow. The resonance phenomenon and drag reduction effect are carefully examined. The wake structure and vortex shedding process is visualized by means of computational streaklines. These results have a practical application in offshore engineering.

Synthesis and Numerical Analysis on Velocity and Pressure Field of Convex Diamond Film

2011 ◽  
Vol 175 ◽  
pp. 192-195
Author(s):  
Duo Sheng Li ◽  
Xian Liang Zhou ◽  
Dun Wen Zuo ◽  
Xiao Zhen Hua
Keyword(s):  
Numerical Analysis ◽  
Diamond Film ◽  
Pressure Field ◽  
Stokes Equations ◽  
Plasma Jet ◽  
Reaction Chamber ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Pressure Fields

Maths model based on wo-dimensionalhas was built to simulate the velocity and pressure field of the growth of diamond film. Firtstly，the plasma jet flow is supposed as steady state incompressible gas, which meets with Reynolds-averaged Navier–Stokes equations. The model of the growth of convex diamond film considers different convex height of Mo substrate. The velocity and pressure field were simulated by CFD respectively.The simulational results show that, the distributions of velocity and pressure fields were fluctuant in reaction chamber. When convex height of Mo substrate was 9mm, DC plasma jet was smoother than the other heights, thus, we predicts that diamond film easily grows. Meanwhile, we prepared four diamond films in different heights of substrate, by DCPJCVD. Raman spectra were used to investigate the quality of convex diamond film. It was found that, when the height of convex substrate was 9mm, convex diamond film had only diamond characteristic peak. It is obvious that numerical analysis help us predict the distributions of velocity and pressure fields and synthesize high quality convex diamond film.

Geometry Optimization of Textured 3-D Micro-Thrust Bearings

2011 ◽  
Author(s):  
C. I. Papadopoulos ◽  
E. E. Efstathiou ◽  
P. G. Nikolakopoulos ◽  
L. Kaiktsis
Keyword(s):  
Carrying Capacity ◽  
Stokes Equations ◽  
Optimization Problems ◽  
Load Capacity ◽  
Computational Cost ◽  
Load Carrying Capacity ◽  
Thrust Bearings ◽  
Wide Range ◽  
Load Carrying ◽  
Bearing Load

The paper presents an optimization study of the geometry of three-dimensional micro-thrust bearings, in a wide range of convergence ratios. The optimization goal is the maximization of the bearing load carrying capacity. The bearings are modeled as microchannels, consisting of a smooth moving wall (rotor), and a stationary wall (stator) with partial periodic rectangular texturing. The flow field is calculated from the numerical solution of the Navier-Stokes equations for incompressible isothermal flow; processing of the results yields the bearing load capacity and friction coefficient. The geometry of the textured channel is defined parametrically for several width-to-length ratios. Optimal texturing geometries are obtained by utilizing an optimization tool based on genetic algorithms, which is coupled to the CFD code. Here, the design variables define the bearing geometry and convergence ratio. To minimize the computational cost, a multi-objective approach is proposed, consisting in the simultaneous maximization of the load carrying capacity and minimization of the bearing convergence ratio. The optimal solutions, identified based on the concept of Pareto dominance, are equivalent to those of single-objective optimization problems at different convergence ratio values. The present results demonstrate that the characteristics of the optimal texturing patterns depend strongly on both the convergence ratio and the width-to-length ratio. Further, the optimal load carrying capacity increases at increasing convergence ratio, up to an optimal value, identified by the optimization procedure. Finally, proper surface texturing provides substantial load carrying capacity even for parallel or slightly diverging bearings. Based on the present results, we propose simple formulas for the design of textured micro-thrust bearings.

Steady approach of unsteady low-Reynolds-number flow past two rotating circular cylinders

2013 ◽  
Vol 736 ◽  
pp. 414-443 ◽  
Author(s):  
Y. Ueda ◽  
T. Kida ◽  
M. Iguchi
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Stokes Equations ◽  
Low Reynolds Number ◽  
Vortex Method ◽  
The Self ◽  
Circular Cylinders ◽  
Far Field ◽  
Flow Past ◽  
Low Reynolds

AbstractThe long-time viscous flow about two identical rotating circular cylinders in a side-by-side arrangement is investigated using an adaptive numerical scheme based on the vortex method. The Stokes solution of the steady flow about the two-cylinder cluster produces a uniform stream in the far field, which is the so-called Jeffery’s paradox. The present work first addresses the validation of the vortex method for a low-Reynolds-number computation. The unsteady flow past an abruptly started purely rotating circular cylinder is therefore computed and compared with an exact solution to the Navier–Stokes equations. The steady state is then found to be obtained for $t\gg 1$ with ${\mathit{Re}}_{\omega } {r}^{2} \ll t$, where the characteristic length and velocity are respectively normalized with the radius ${a}_{1} $ of the circular cylinder and the circumferential velocity ${\Omega }_{1} {a}_{1} $. Then, the influence of the Reynolds number ${\mathit{Re}}_{\omega } = { a}_{1}^{2} {\Omega }_{1} / \nu $ about the two-cylinder cluster is investigated in the range $0. 125\leqslant {\mathit{Re}}_{\omega } \leqslant 40$. The convection influence forms a pair of circulations (called self-induced closed streamlines) ahead of the cylinders to alter the symmetry of the streamline whereas the low-Reynolds-number computation (${\mathit{Re}}_{\omega } = 0. 125$) reaches the steady regime in a proper inner domain. The self-induced closed streamline is formed at far field due to the boundary condition being zero at infinity. When the two-cylinder cluster is immersed in a uniform flow, which is equivalent to Jeffery’s solution, the streamline behaves like excellent Jeffery’s flow at ${\mathit{Re}}_{\omega } = 1. 25$ (although the drag force is almost zero). On the other hand, the influence of the gap spacing between the cylinders is also investigated and it is shown that there are two kinds of flow regimes including Jeffery’s flow. At a proper distance from the cylinders, the self-induced far-field velocity, which is almost equivalent to Jeffery’s solution, is successfully observed in a two-cylinder arrangement.

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