scholarly journals Simulation of flow past two tandem cylinders using deterministic vortex method

2012 ◽  
Vol 16 (5) ◽  
pp. 1460-1464 ◽  
Author(s):  
Guo Huang ◽  
Haiming Huan ◽  
Xiaoliang Xu ◽  
Yu Liu
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
Sudden Change ◽  
Vortex Method ◽  
Simulation Method ◽  
Critical Distance ◽  
Navier Stokes ◽  
Tandem Cylinders ◽  
Flow Past

The vortex method is a direct numerical simulation method for solving the Navier-Stokes equations. In order to reveal the influence of Reynolds number and distances between the cylinders, the incompressible flow past a pair of tandem cylinders is solved on the base of the vortex method. The results show that for the flow past two tandem cylinders, there is a critical distance of the tandem cylinders. Over the critical distance, the flow field will have a sudden change, and the drag coefficient, lift coefficient and Strouhal number will also change dramatically. The critical distance will diminish as the Reynolds number rises.

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.

Parameter Extension Simulation of Turbulent Flows in a Compressor Cascade With a High Reynolds Number

2020 ◽  
Author(s):  
Yan Jin
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Simulation Method ◽  
Potential Method ◽  
Navier Stokes ◽  
Reference Solution ◽  
Compressor Cascade ◽  
High Reynolds

Abstract The turbulent flow in a compressor cascade is calculated by using a new simulation method, i.e., parameter extension simulation (PES). It is defined as the calculation of a turbulent flow with the help of a reference solution. A special large-eddy simulation (LES) method is developed to calculate the reference solution for PES. Then, the reference solution is extended to approximate the exact solution for the Navier-Stokes equations. The Richardson extrapolation is used to estimate the model error. The compressor cascade is made of NACA0065-009 airfoils. The Reynolds number 3.82 × 105 and the attack angles −2° to 7° are accounted for in the study. The effects of the end-walls, attack angle, and tripping bands on the flow are analyzed. The PES results are compared with the experimental data as well as the LES results using the Smagorinsky, k-equation and WALE subgrid models. The numerical results show that the PES requires a lower mesh resolution than the other LES methods. The details of the flow field including the laminar-turbulence transition can be directly captured from the PES results without introducing any additional model. These characteristics make the PES a potential method for simulating flows in turbomachinery with high Reynolds numbers.

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.

Unsteady flow past a rotating circular cylinder at Reynolds numbers 103 and 104

1990 ◽  
Vol 220 ◽  
pp. 459-484 ◽  
Author(s):  
H. M. Badr ◽  
M. Coutanceau ◽  
S. C. R. Dennis ◽  
C. Ménard
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Unsteady Flow ◽  
Rotation Rate ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Number Range ◽  
Flow Past

The unsteady flow past a circular cylinder which starts translating and rotating impulsively from rest in a viscous fluid is investigated both theoretically and experimentally in the Reynolds number range 103 [les ] R [les ] 104 and for rotational to translational surface speed ratios between 0.5 and 3. The theoretical study is based on numerical solutions of the two-dimensional unsteady Navier–Stokes equations while the experimental investigation is based on visualization of the flow using very fine suspended particles. The object of the study is to examine the effect of increase of rotation on the flow structure. There is excellent agreement between the numerical and experimental results for all speed ratios considered, except in the case of the highest rotation rate. Here three-dimensional effects become more pronounced in the experiments and the laminar flow breaks down, while the calculated flow starts to approach a steady state. For lower rotation rates a periodic structure of vortex evolution and shedding develops in the calculations which is repeated exactly as time advances. Another feature of the calculations is the discrepancy in the lift and drag forces at high Reynolds numbers resulting from solving the boundary-layer limit of the equations of motion rather than the full Navier–Stokes equations. Typical results are given for selected values of the Reynolds number and rotation rate.

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.

scholarly journals ENTROPIC LATTICE BOLTZMANN SIMULATION OF THE FLOW PAST SQUARE CYLINDER

2004 ◽  
Vol 15 (03) ◽  
pp. 435-445 ◽  
Author(s):  
SANTOSH ANSUMALI ◽  
SHYAM SUNDER CHIKATAMARLA ◽  
CHRISTOS EMMANOUIL FROUZAKIS ◽  
KONSTANTINOS BOULOUCHOS
Keyword(s):  
Reynolds Number ◽  
Lattice Boltzmann ◽  
Large Scale ◽  
Stokes Equations ◽  
Coarse Grained ◽  
Navier Stokes ◽  
Square Cylinder ◽  
Flow Past ◽  
Lattice Boltzmann Simulation ◽  
Decaying Turbulence

Minimal Boltzmann kinetic models, such as lattice Boltzmann, are often used as an alternative to the discretization of the Navier–Stokes equations for hydrodynamic simulations. Recently, it was argued that modeling sub-grid scale phenomena at the kinetic level might provide an efficient tool for large scale simulations. Indeed, a particular variant of this approach, known as the entropic lattice Boltzmann method (ELBM), has shown that an efficient coarse-grained simulation of decaying turbulence is possible using these approaches. The present work investigates the efficiency of the entropic lattice Boltzmann in describing flows of engineering interest. In order to do so, we have chosen the flow past a square cylinder, which is a simple model of such flows. We will show that ELBM can quantitatively capture the variation of vortex shedding frequency as a function of Reynolds number in the low as well as the high Reynolds number regime, without any need for explicit sub-grid scale modeling. This extends the previous studies for this set-up, where experimental behavior ranging from Re ~O(10) to Re ≤1000 was predicted by a single simulation algorithm.1–5

Viscous and inviscid simulations of the start-up vortex

2017 ◽  
Vol 813 ◽  
pp. 53-69
Author(s):  
Paolo Luchini ◽  
Renato Tognaccini
Keyword(s):  
Reynolds Number ◽  
Large Time ◽  
Stokes Equations ◽  
Infinite Plate ◽  
Vortex Method ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Spiral Vortex ◽  
Start Up

Inviscid, unsteady simulations of the roll up of the start-up vortex issuing from a semi-infinite plate are compared with previous simulations of the viscous flow. The inviscid equations were solved by a lumped-vortex method, the two-dimensional, incompressible Navier–Stokes equations in the vorticity–streamfunction formulation modelled the viscous problem. The purpose is to verify whether the irregular behaviour found by the inviscid solution well approximates the unstable evolution of the viscous spiral vortex in the limit of infinitely large time (or equivalently Reynolds number).

scholarly journals Computation of Flow Past an In-Line Oscillating Circular Cylinder and a Stationary Cylinder in Tandem Using a CIP-Based Model

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Yingnan Fu ◽  
Xizeng Zhao ◽  
Xinggang Wang ◽  
Feifeng Cao
Keyword(s):  
Circular Cylinder ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Immersed Boundary ◽  
Navier Stokes Equations ◽  
Order Difference ◽  
Tandem Cylinders ◽  
Flow Past ◽  
Fluid Body ◽  
Cartesian Coordinate

Viscous flow past an upstream in-line forced oscillating circular cylinder with a stationary cylinder downstream at Reynolds number of 100 is investigated using a CIP model. The model is established in a Cartesian coordinate system using a high-order difference method to discretise the Navier-Stokes equations. The fluid-structure interaction is treated as a multiphase flow with fluid and solid phases solved simultaneously. An immersed boundary method is used to deal with the fluid-body coupling. The CFD model is firstly applied to the computation of flow past a fixed circular cylinder for its validation; then flow over two stationary tandem cylinders is investigated and good agreements are obtained comparing with existing ones. Computations are then performed with flow past two tandem cylinders with an upstream in-line oscillating cylinder with a small spacingL=2D. Considerable attention is paid to the spectrum characteristics and vortex modes.

scholarly journals The Sensitivity Analysis for the Flow Past Obstacles Problem with Respect to the Reynolds Number

2012 ◽  
Vol 4 (1) ◽  
pp. 21-35 ◽  
Author(s):  
Kazufumi Ito ◽  
Zhilin Li ◽  
Zhonghua Qiao
Keyword(s):  
Sensitivity Analysis ◽  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Irregular Domains ◽  
Time Step ◽  
Immersed Interface Method ◽  
Navier Stokes Equations ◽  
Flow Past

AbstractIn this paper, numerical sensitivity analysis with respect to the Reynolds number for the flow past obstacle problem is presented. To carry out such analysis, at each time step, we need to solve the incompressible Navier-Stokes equations on irregular domains twice, one for the primary variables; the other is for the sensitivity variables with homogeneous boundary conditions. The Navier-Stokes solver is the augmented immersed interface method for Navier-Stokes equations on irregular domains. One of the most important contribution of this paper is that our analysis can predict the critical Reynolds number at which the vortex shading begins to develop in the wake of the obstacle. Some interesting experiments are shown to illustrate how the critical Reynolds number varies with different geometric settings.

scholarly journals Numerical study of airfoil with wavy leading edge at high Reynolds number regime

2020 ◽  
Author(s):  
William Denner Pires Fonseca ◽  
Rafael Rosario Da Silva ◽  
Reinaldo Marcondes Orselli ◽  
Adson Agrico De Paula ◽  
Ricardo Galdino da Silva
Keyword(s):  
Reynolds Number ◽  
Turbulence Modeling ◽  
Stokes Equations ◽  
Numerical Study ◽  
Lift Coefficient ◽  
Leading Edge ◽  
Numerical Data ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
High Reynolds

In this work, a numerical study of flow around an airfoil with wavy leading edge is presented at a Reynolds number of 3X106. The flow is resolved by considering the RANS (Reynolds Average Navier-Stokes)equations. The baseline geometry is based on the NACA 0021 profile. The wavy leading edge has an amplitude of 3% and wavelength of 11%, both with respect to the airfoil chord. Cases without and with wavy leadingedges are simulated and compared. Initially, studies of the numerical sensitivity with respect to the obtained results, considering aspects such as turbulence modeling and mesh refinement, are carried out as well as bycomparison with corresponding results in the literature. Numerical data such as pressure distribution, shear stress lines on the wing surface, and aerodynamics coefficients are used to describe and investigate the flowfeatures around the wavy leading airfoil. Comparisons between the straight leading edge and the wavy leading edge cases shows an increase of the maximum lift coefficient as well as stall angle for the wavy leading edge configuration. In addition, at an angle of attack near the stall, the present numerical results shows an increase of the drag coefficient with the wavy leading edge airfoil when compared with the corresponding straight leading edge case.

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