Unsteady separation leading to secondary and tertiary vortex dynamics: the sub-- and sub--phenomena

2013 ◽  
Vol 730 ◽  
pp. 19-51 ◽  
Author(s):  
Jiten C. Kalita ◽  
Shuvam Sen
Keyword(s):  
Circular Cylinder ◽  
Vortex Dynamics ◽  
Stokes Equations ◽  
Weak Sense ◽  
Boundary Layer Separation ◽  
Numerical Results ◽  
Navier Stokes ◽  
Compact Finite Difference Method ◽  
Flow Past ◽  
Depth Analysis

AbstractStudies on the$\alpha $- and$\beta $-phenomena, terms coined by Bouard & Coutanceau (J. Fluid Mech., vol. 101, 1980, pp. 583–607) for the flow past an impulsively started circular cylinder, have been confined only to the very early stages of the flow. In this paper, besides making a comprehensive in-depth analysis of these phenomena for a much longer period of time, we report the existence of some tertiary vortex phenomena for the first time, which we term the sub-$\alpha $- and sub-$\beta $-phenomena. The mechanism of unsteady flow separation at high Reynolds numbers for the flow past a circular cylinder developed in the last two decades has been used to understand these flow phenomena. The flow is computed using a recently developed compact finite difference method for the biharmonic form of the two-dimensional Navier–Stokes equations for the range of Reynolds number$500\leq \mathit{Re}\leq 10\hspace{0.167em} 000$. We specifically choose$\mathit{Re}= 5000$to describe the interplay among the primary, secondary and tertiary vortices leading to these interesting vortex dynamics. We also report a$\beta $-like phenomenon which is very similar to the$\beta $-phenomenon, but slightly differs in details. We offer a new perception of the$\alpha $-phenomenon by defining its existence in a strong and weak sense along with a clearer characterization of the$\beta $-phenomenon. Apart from numerical computation, a detailed theoretical characterization using topological aspects of the boundary layer separation leading to the secondary and tertiary vortex phenomena has also been carried out. We compare our numerical results with established experimental and numerical results wherever available and an excellent match with the experimental results is obtained in all cases.

CFD Analysis of Vortex Shedding in a Circular Cylinder: Flow Induced Vibration Design

2006 ◽  
Author(s):  
Nadeem Ahmed Sheikh ◽  
M. Afzaal Malik ◽  
Arshad Hussain Qureshi ◽  
M. Anwar Khan ◽  
Shahab Khushnood
Keyword(s):  
Circular Cylinder ◽  
Vortex Shedding ◽  
Stokes Equations ◽  
Boundary Layer Separation ◽  
The Body ◽  
Navier Stokes ◽  
Structural Vibrations ◽  
Flow Induced Vibration ◽  
Navier Stokes Equations ◽  
Implicit Approach

Flow past a blunt body, such as a circular cylinder, usually experiences boundary layer separation and very strong flow oscillations in the wake region behind the body at a discrete frequency that is correlated to the Reynolds number of the flow. The periodic nature of the vortex shedding phenomenon can sometimes lead to unwanted structural vibrations. The effect of vibrating instability of a single cylinder is investigated in a uniform flow using the power of computational methods. Fluid structure coupling procedure predicts the fluid forces responsible for structural vibrations. An implicit approach to the solution of the unsteady two-dimensional Navier-Stokes equations is used for computation of flow parameters. Calculations are performed in parallel using a domain re-meshing/deforming technique with efficient communication requirements. Results for the unsteady shedding flow behind a circular cylinder are presented with experimental comparisons, showing the feasibility of accurate, efficient, time-dependent estimation of shedding frequency and resulting vibrations.

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 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.

Flow past an impulsively started circular cylinder

1973 ◽  
Vol 60 (1) ◽  
pp. 105-127 ◽  
Author(s):  
W. M. Collins ◽  
S. C. R. Dennis
Keyword(s):  
Circular Cylinder ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Accurate Method ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Secondary Vortex ◽  
Flow Past ◽  
Dependent Flow ◽  
Good Agreement

An accurate method is described for integrating the Navier-Stokes equations numerically for the time-dependent flow past an impulsively started circular cylinder. Results of integrations over the range of Reynolds numbers, based on the diameter of the cylinder, from 5 to ∞ are presented and compared with previous numerical, theoretical and experimental results. In particular, the growth of the length of the separated wake behind the cylinder has been calculated forR= 40, 100 and 200 and is found to be in very good agreement with the results of recent experimental measurements. The calculated pressure distribution over the surface of the cylinder forR= 500 is also found to be in reasonable agreement with experimental measurements for the caseR= 560.For Reynolds numbers up to 100 the equations were integrated until most of the features of the flow showed a close approximation to steady-state conditions. The results obtained are in good agreement with previous calculations of the steady flow past a circular cylinder. ForR> 100 the integrations were continued until the implicit method of integration broke down by reason of its failure to converge. A secondary vortex appeared on the surface of the cylinder in the caseR= 500, but for higher Reynolds numbers, including the caseR= ∞, the procedure broke down before the appearance of a secondary vortex. In all cases the flow was assumed to remain symmetrical.

scholarly journals DynamFluid: Development and Validation of a New GUI-Based CFD Tool for the Analysis of Incompressible Non-Isothermal Flows

Processes ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 777
Author(s):  
Héctor Redal ◽  
Jaime Carpio ◽  
Pablo A. García-Salaberri ◽  
Marcos Vera
Keyword(s):  
Circular Cylinder ◽  
Stokes Equations ◽  
Vertical Channel ◽  
Temperature Fields ◽  
Navier Stokes ◽  
Convection Flow ◽  
Constant Density ◽  
Flow Past ◽  
Isothermal Flows ◽  
Definition Of

A computational fluid dynamics software (DynamFluid) based on the application of the finite element method with the characteristic-based-split algorithm is presented and validated. The software is used to numerically integrate the steady and unsteady Navier–Stokes equations for both constant-density and Boussinesq non-isothermal flows. Benchmark two-dimensional computations carried out with DynamFluid show good agreement with previous results reported in the literature. Test cases used for validation include (i) the lid-driven cavity flow, (ii) mixed convection flow in a vertical channel with asymmetric wall temperatures, (iii) unsteady incompressible flow past a circular cylinder, and (iv) steady non-isothermal flow past a circular cylinder with negligible buoyancy effects. The new software is equipped with a graphical user interface that facilitates the definition of the fluid properties, the discretization of the physical domain, the definition of the boundary conditions, and the post-processing of the computed velocity, pressure and temperature fields.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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.

Self-Excited Oscillation of Transonic Flow Around an Airfoil in Two-Dimensional Channel

1989 ◽  
Author(s):  
Kazuomi Yamamoto ◽  
Yoshimichi Tanida
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Transonic Flow ◽  
Stokes Equations ◽  
Flow Region ◽  
Boundary Layer Separation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Layer Separation ◽  
Excited Oscillation

A self-excited oscillation of transonic flow in a simplified cascade model was investigated experimentally, theoretically and numerically. The measurements of the shock wave and wake motions, and unsteady static pressure field predict a closed loop mechanism, in which the pressure disturbance, that is generated by the oscillation of boundary layer separation, propagates upstream in the main flow and forces the shock wave to oscillate, and then the shock oscillation disturbs the boundary layer separation again. A one-dimensional analysis confirms that the self-excited oscillation occurs in the proposed mechanism. Finally, a numerical simulation of the Navier-Stokes equations reveals the unsteady flow structure of the reversed flow region around the trailing edge, which induces the large flow separation to bring about the anti-phase oscillation.

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