Control of flow using genetic algorithm for a circular cylinder executing rotary oscillation

We propose here a new approach to optimally control incompressible viscous flow past a circular cylinder for drag minimization by rotary oscillation. The flow at Re = 15000 is simulated by solving 2D Navier-Stokes equations in stream function-vorticity formulation. High accuracy compact scheme for space discretization and four stage Runge-Kutta scheme for time integration makes such simulation possible. While numerical solution for this flow field has been reported using a fast viscous-vortex method, to our knowledge, this has not been done at such a high Reynolds number by computing the Navier-Stokes equation before. The importance of scale resolution, aliasing problem and preservation of physical dispersion relation for such vortical flows of the used high accuracy schemes [Sengupta TK. Fundamentals of computational fluid dynamics. Hyderabad, India: University Press; 2004] is highlighted.For the dynamic problem, a novel genetic algorithm (GA) based optimization technique has been adopted, where solutions of Navier-Stokes equations are obtained using small time-horizons at every step of the optimization process, called a GA generation. Then the objective functions is evaluated that is followed by GA determined improvement of the decision variables. This procedure of time advancement can also be adopted to control such flows experimentally, as one obtains time-accurate solution of the Navier-Stokes equation subject to discrete changes of decision variables. The objective function - the time-averaged drag - is optimized using a real-coded genetic algorithm [Deb K. Multi-objective optimization using evolutionary algorithms. Chichester, UK: Wiley; 2001] for the two decision variables, the maximum rotation rate and the forcing frequency of the rotary oscillation. Various approaches to optimal decision variables have been explored for the purpose of drag reduction and the collection of results are self-consistent and furthermore match well with the experimental values reported in [Tokumaru PT, Dimotakis PE. Rotary oscillation control of a cylinder wake. J Fluid Mech 1991;224:77].     

Large eddy simulation of pulsating flow over a circular cylinder at subcritical Reynolds number

The pulsating cross-flow over a single circular cylinder at the subcritical Reynolds number Re_D = 2580 is studied with the large eddy simulation (LES) technique using the standard Smagorinsky model as well as a dynamic model in which the test filtered quantities are evaluated through a truncated Taylor series expansion. The filtered equations are discretised using the finite volume method in an unstructured, collocated grid arrangement with a second-order accurate method, in both space and time. The predictions are compared against very detailed experiments for mean velocities and Reynolds stresses that were performed in a duct of cross-section 72 mm × 72 mm using the PIV technique. The effects of mesh refinement close to the cylinder as well as of subgrid scale model are also examined. The numerical predictions are in very good agreement with the measurements in terms of mean as well as turbulence quantities. The instantaneous flow patterns of the flow field are examined and the effect of the external flow pulsation on the wake characteristics such as vortex formation length, vortex strength, Strouhal number as well as the lift and drag coefficients is quantified. The vortex formation length is decreased while the mean drag, as well as the rms values of the drag and lift coefficients increase significantly under pulsating flow conditions. The performance of the LES technique is analysed in the light of the wake characteristics.     

Numerical simulation of an oscillating cylinder in a cross-flow at low Reynolds number: Forced and free oscillations

A numerical simulation of the flow past a circular cylinder which is able to oscillate transversely to the incident stream is presented in this paper for a fixed Reynolds number equal to 100. The 2D Navier-Stokes equations are solved by a finite volume method with an industrial CFD code in which a coupling procedure has been implemented in order to obtain the cylinder displacement. A preliminary work is first conducted for a fixed cylinder to check the wake characteristics for Reynolds numbers smaller than 150 in the laminar regime. The Strouhal frequency f_S and the aerodynamic coefficients are thus controlled among other parameters. Simulations are then performed with forced oscillations characterized by the frequency ratio F = f₀/f_S, where f₀ is the forced oscillation frequency, and by the adimensional amplitude A. The wake characteristics are analyzed using the time series of the fluctuating aerodynamic coefficients and their power spectral densities (PSD). The frequency content is then linked to the shape of the phase portraits and to the vortex shedding mode. By choosing interesting couples (A, F), different vortex shedding modes have been observed, which are similar to those of the Williamson-Roshko map. A second batch of simulations involving free vibrations (so-called vortex-induced vibrations or VIV) is finally carried out. Oscillations of the cylinder are now directly induced by the vortex shedding process in the wake and therefore, the time integration of the motion is realized by an explicit staggered algorithm which provides the cylinder displacement according to the aerodynamic charges exerted on the cylinder wall. Amplitude and frequency response of the cylinder are thus investigated over a wide range of reduced velocities to observe the different phenomena at stake. In particular, the vortex shedding modes have also been related to the frequency response observed and our results at Re = 100 show a very good agreement with other studies using different numerical approaches.     

Particle mixing and reactive front motion in unsteady open shallow flow - Modelled using singular value decomposition

Passive and active tracers are used to examine particle mixing and reactive front dynamics in an open shallow flow of water past a circular cylinder. A quadtree grid based Godunov-type shallow water equation solver predicts the unsteady flow hydrodynamics of the wake behind the cylinder. The resulting periodic flow field consisting of a von Kármán vortex street is decomposed and stored over one oscillatory period using Singular Value Decomposition (SVD). Particles are advected according to the reconstructed flow field from the SVD modes, with continuous spatial velocity information obtained via bilinear interpolation. Passive particle dynamics driven by different SVD flow modes is investigated, and it is found that the flow field recovered from the mean flow and the first pair of time varying modes is adequate to represent the complicated dynamical properties induced by the original flow field. Active autocatalytic reaction, A + B → 2B, is incorporated into the particle advection model, assuming surface reaction. Active particles are found to trace out an expanded version of the unstable manifold of the chaotic saddle in the wake, in qualitative agreement with published analytical results. The numerical model is applicable to mixing and transport processes in more complicated shallow environmental flows.     

Effect of tube spacing on the vortex shedding characteristics of laminar flow past an inline tube array: A numerical study

The effect of tube spacing on the vortex shedding characteristics and fluctuating forces in an inline cylinder array is studied numerically. The examined Reynolds number is 100 and the flow is laminar. The numerical methodology and the code employed to solve the Navier-Stokes and continuity equations in an unstructured finite volume grid are validated for the case of flow past two tandem cylinders at four spacings. Computations are then performed for a six-row inline tube bank for eight pitch-to-diameter ratios, s, ranging from 2.1 to 4. At the smallest spacing examined (s = 2.1) there are five stagnant and symmetric recirculation zones and weak vortex shedding activity occurs only behind the last cylinder. As s increases, the symmetry of the recirculation zones breaks leading to vortex shedding and this process progressively moves upstream, so that for s = 4 there is clear shedding from every row. For any given spacing, the shedding frequency behind each cylinder is the same. A critical spacing range between 3.0 and 3.6 is identified at which the mean drag as well as the rms lift and drag coefficients for the last three cylinders attain maximum values. Further increase to s = 4 leads to significant decrease in the force statistics and increase in the Strouhal number. It was found that at the critical spacing there is 180° phase difference in the shedding cycle between successive cylinders and the vortices travel a distance twice the tube spacing within one period of shedding.     

A collocated finite volume embedding method for simulation of flow past stationary and moving body

A simple and conservative numerical scheme is introduced in this paper to simulate unsteady flow around stationary and moving body. Based on the embedding method (immersed boundary (IB) + volume of fluid (VOF)) implemented in the finite-volume framework, flow past the arbitrarily complex geometry can be readily computed on any existing mesh system. Flow variables stored at cell centers, including those residing within the immersed body, are computed where the induced effect on the flow due to the immersed body is realised via a simple acceleration term (forcing function) derived based on the VOF value. In the current work, an identical VOF value is used for all momentum equations, in contrast to that of the pre-existing method, whereby numerical interpolation is required. The method is verified with a number of flow cases, including flow in a 2D square cavity, flow past a stationary and oscillating cylinder and flow induced by a flapping ellipse in an enclosure.     

圆柱绕流的二维数值模拟和尾迹分析

为指导机械设计中参数和布局的选择,研究固定在水流中的圆柱结构件的受力情况和流场分布．利用FLUENT中的三种湍流模型对雷诺数为3900的圆柱绕流进行二维数值模拟并进行对比,得到升力因数、阻力因数、分离角、斯特劳哈尔数和涡街尺寸等参数的模拟结果,与参考文献中的实验结果对比验证二维模拟的预测精度．RKE（Realizable k-ε）和雷诺应力模型（Reynolds Stress Model,RSM）均能在此雷诺数下得出接近实验结果的流场,RSM模型使用POWER LAW离散格式的结果优于QUICK格式．与三维模拟的对比表明二维模拟适合在设计初期的快速估算,能够快速得到合适精度的模拟结果．     

Analysis and control of the near-wake flow over a square-back geometry

A 3D numerical simulation, based on the Lattice Boltzmann method is carried out on the near-wake flow behind a generic square-back blunt body to analyze and establish a method to control the near-wake flow. The flow topology is described by the velocity and the pressure fields. The influence of the wake vortices on the aerodynamic drag is clarified and quantified. In order to reduce this drag, an active open-loop flow control is applied by continuous blowing devices distributed around the base periphery. The blowing effect on the behind body flow is a reduction of the wake section and of the total pressure loss in the wake and an increase of the static pressure on the base of the square body. This control leads to a significant drag reduction of ΔC_x = −29% with a blowing velocity of 1.5V₀. The efficiency is then studied, and we found that the most efficient control is obtained for a blowing velocity of 0.5V₀ and a jet angle of 45°. In this case, a 20% drag reduction is obtained, and the energy needed to control the system is seven times lower than the energy saved by the control.     

A numerical investigation of fluid flow over a rotating cylinder with cross flow oscillation

This paper studies a two-dimensional incompressible viscous flow past a rotating cylinder with cross flow oscillation using a finite element method based on the characteristic based split (CBS) algorithm to solve governing equations including full Navier–Stokes and continuity equations. Dynamic unstructured triangular grid is used employing lineal and torsional spring analogy which is coupled with the solver by an Arbitrary Lagrangian–Eulerian (ALE) formulation. After verifying the accuracy of the numerical code, simulations are conducted for the flow past a rotating cylinder with cross flow oscillation at moderate Reynolds numbers of 50, 100, and 200 considering different non-dimensional rotational speeds based on the free-stream velocity in the range 0–2.5, and various oscillating amplitudes and frequencies. Effects of the oscillation and rotation of the cylinder on the vortex shedding both in lock-on and non-lock-on regions, the mean drag and lift coefficients, and the Strouhal number are investigated in detail. It is found that similar to the fixed cylinder beyond a critical non-dimensional rotational speed the vortex shedding is highly suppressed. In addition, by increasing the rotational speed of the cylinder, the lift coefficient increases while decreasing the drag coefficient. However, in the vortex lock-on region both the lift and the drag coefficients increase significantly.     

Numerical investigations on dynamic stall of low Reynolds number flow around oscillating airfoils

This paper presents a 2D computational investigation on the dynamic stall phenomenon associated with unsteady flow around the NACA0012 airfoil at low Reynolds number (Re_c ≈ 10⁵). Two sets of oscillating patterns with different frequencies, mean oscillating angles and amplitudes are numerically simulated using Computational Fluid Dynamics (CFD), and the results obtained are validated against the corresponding published experimental data. It is concluded that the CFD prediction captures well the vortex-shedding predominated flow structure which is experimentally obtained and the results quantitatively agree well with the experimental data, except when the blade is at a very high angle of attack.     

Flow patterns past two circular cylinders in proximity

Flow patterns past two nearby circular cylinders of equal diameter immersed in the cross-flow at low Reynolds numbers (Re ? 160), were numerically studied using an immersed boundary method. We considered all possible arrangements of the two cylinders in terms of the distance between the two cylinders and the inclination angle of the line connecting the cylinder centers with respect to the direction of the main flow. Ten distinct flow patterns were identified in total based on vorticity contours and streamlines, which are Steady, Near-Steady, Base-Bleed, Biased-Base-Bleed, Shear-Layer-Reattachment, Induced-Separation, Vortex-Impingement, Flip-Flopping, Modulated Periodic, and Synchronized-Vortex-Shedding. Collecting all the numerical results obtained, we propose a general flow-pattern diagram for each Re, and a contour diagram on vortex-shedding frequency for each cylinder at Re = 100. The perfect symmetry implied in the geometrical configuration allows one to use these diagrams to identify flow pattern and vortex-shedding frequencies in the presence of two circular cylinders of equal diameter arbitrarily positioned in physical space with respect to the main-flow direction.     

On restraining the production of small scales of motion in a turbulent channel flow

Since most turbulent flows cannot be computed directly from the incompressible Navier-Stokes equations, a dynamically less complex mathematical formulation is sought. In the quest for such a formulation, we consider nonlinear approximations of the convective term that preserve the symmetry and conservation properties. In particularly, the energy, enstrophy (in 2D) and helicity are conserved. The underlying idea is to restrain the convective production of small scales in an unconditional stable manner, meaning that the approximate solution cannot blow up in the energy-norm (in 2D also: enstrophy-norm). The numerical algorithm used to solve the governing equations preserves the symmetry and conservation properties too. The resulting simulation method is successfully tested for a turbulent channel flow (Re_τ = 180 and 395).     

Eduction of near wall flow structures responsible for large deviations of the momentum-heat transfer analogy and fluctuations of wall transfer rates in turbulent channel flow

In this paper we analyze the flow structures responsible for large local instantaneous deviations of the conventional momentum-heat transfer analogy and large fluctuations of the wall shear stress and the wall heat flux in a forced convection turbulent channel flow at low-Reynolds numbers (Re = 4570, Pr = 0.7). The analysis was carried out using a database obtained from a direct numerical simulation performed with a second-order finite volume code. The ensemble averaged velocity and temperature profiles and profiles of the turbulence intensities and turbulent heat fluxes agree well with direct numerical simulations available in the literature. When the flow was statistically fully developed, we recorded the time evolution of the velocities and temperatures near one wall of the channel. The near wall structures responsible for the extreme values of the deviations were educed by a conditional sampling technique. Results show that extreme values of the wall shear stress and wall heat transfer rates, as well as departures from the conventional analogy between momentum and heat transfer, occur within the high-speed streaks on the wall and are associated with fluctuations of the streamwise pressure gradient. These large fluctuations on the wall are produced by the combined effect of two quasi-parallel counterrotating streamwise vortices.     

Ship motions using single-phase level set with dynamic overset grids

The problem of surface ships free to pitch and heave in regular head waves is analyzed numerically with an unsteady Reynolds averaged Navier Stokes (URANS) approach. The unsteady single-phase level set method previously developed by the authors was extended to include six degrees of freedom (6DOF) motions. The method uses rigid overset grids that move with relative motion during the computation, and the interpolation coefficients between the grids are recomputed dynamically every time the grids move. The motions in each time step are integrated implicitly using a predictor-corrector approach. An earth-based reference system is used for the solution of the fluid flow, while a ship-based reference system is used to compute the rigid-body equations of motion. Predicted results for sinkage and trim and resistance at two Froude numbers (medium, Fr = 0.28 and large, Fr = 0.41) were compared against experimental data, showing good agreement. Pitch and heave motions were computed for near-resonant cases at Fr = 0.28 and 0.41, with regular linear head waves with slope ak = 0.025 and wavelength λ = 1.5L, with L the ship length. The predicted motions compare favorably with existing experimental data. A solution for a large amplitude head wave case (ak = 0.075) was also obtained, in which the transom wave breaks and extreme motions are observed. The medium Froude number case was subject to a verification and validation analysis. A problem with two ships pitching and heaving one behind the other is demonstrated.     

Large-eddy simulation of streamwise-rotating turbulent channel flow

In many engineering and industrial applications the investigation of rotating turbulent flow is of great interest. Whereas some research has been done concerning channel flows with a spanwise rotation axis, only few investigations have been performed on channel flows with a rotation about the streamwise axis. In the present study an LES of a turbulent streamwise-rotating channel flow at Re_τ = 180 is performed using a moving grid method. The three-dimensional structures and the details of the secondary flow distribution are analyzed and compared with experimental data. The numerical-experimental comparison shows a convincing agreement as to the overall flow features. The results confirm the development of a secondary flow in the spanwise direction, which has been found to be correlated to the rotational speed. Furthermore, the findings show the distortion of the main flow velocity profile, the slight decrease of the streamwise Reynolds stresses in the vicinity of the walls, and the pronounced increase of the spanwise Reynolds stresses at higher rotation rates near the walls and particularly in the symmetry region. As to the numerical set-up it is shown that periodic boundary conditions in the spanwise direction suffice if the spanwise extent of the computational domain is larger than 10 times the channel half width.     

Multi-GPU performance of incompressible flow computation by lattice Boltzmann method on GPU cluster

GPGPU has drawn much attention on accelerating non-graphic applications. The simulation by D3Q19 model of the lattice Boltzmann method was executed successfully on multi-node GPU cluster by using CUDA programming and MPI library. The GPU code runs on the multi-node GPU cluster TSUBAME of Tokyo Institute of Technology, in which a total of 680 GPUs of NVIDIA Tesla are equipped. For multi-GPU computation, domain partitioning method is used to distribute computational load to multiple GPUs and GPU-to-GPU data transfer becomes severe overhead for the total performance. Comparison and analysis were made among the parallel results by 1D, 2D and 3D domain partitionings. As a result, with 384 × 384 × 384 mesh system and 96 GPUs, the performance by 3D partitioning is about 3-4 times higher than that by 1D partitioning. The performance curve is deviated from the idealistic line due to the long communicational time between GPUs. In order to hide the communication time, we introduced the overlapping technique between computation and communication, in which the data transfer process and computation were done in two streams simultaneously. Using 8-96 GPUs, the performances increase by a factor about 1.1-1.3 with a overlapping mode. As a benchmark problem, a large-scaled computation of a flow around a sphere at Re = 13,000 was carried on successfully using the mesh system 2000 × 1000 × 1000 and 100 GPUs. For such a computation with 2 Giga lattice nodes, 6.0 h were used for processing 100,000 time steps. Under this condition, the computational time (2.79 h) and the data communication time (3.06 h) are almost the same.     

Two-dimensional side-by-side circular cylinders at moderate Reynolds numbers

In a companion article [1], we described computer simulations of the flow around 2 two-dimensional, tandem circular cylinders in a flow for 1?Re?20. In this article we adopt a similar approach to characterize the flow around side-by-side cylinders with surface-to-surface separation/diameter in the range 0.1 < s/D < 30. The results revealed some distinct and interesting features of the flow, which are completely different than those observed at higher Reynolds numbers.At low Reynolds numbers, 1?Re?5, for all gap spacings, the flow contains no regions of flow separation. At higher Re, four distinct flow behaviors were observed. For very small gap spacings, e.g. 0.1 < s/D < 0.6 at Re = 20, two elongated “detached vortices” form downstream of the cylinders. The drag coefficient increases sharply with the gap spacing. For gap spacings 0.6 < s/D < 0.7 at Re = 20, no vortices form anywhere in the flow. For gap spacings around s/D ≈ 1 separation regions form only on the inside portions of the cylinders. For larger gap spacings s/D > 1 the flow reverts to something similar to that around an isolated cylinder in the flow, i.e. two attached vortices on the rear side of each cylinder. In general, the drag coefficient increases as the gap spacing increases. At higher Reynolds number it is known that the cylinder lift coefficients decrease monotonically with gap spacing. In contrast, at these lower Reynolds number the lift coefficient curves rise to a maximum for 0.3 < s/D < 3 and then decrease monotonically for larger s/D.     

Large-eddy simulation of vortex breakdown in compressible swirling jet flow

Vortex breakdown in a compressible swirling jet flow is investigated by large-eddy simulation (LES) using the approximate deconvolution model. Conditions are chosen similar to recent experimental investigations by Liang and Maxworthy [Liang H, Maxworthy T. An experimental investigation of swirling jets. J Fluid Mech 2005;525:115] for incompressible flow. LES results are presented for two simulations of a swirling jet at Mach number Ma = 0.6 with and without inflow forcing by imposed linear instability disturbances. Both the forced and the self-excited jet show three-dimensional helical waves developing in the jet breakdown zone. The features observed in the two simulations are compared to each other as well as to the experiments with respect to flow statistics and instability behaviour. Both simulations show favourable qualitative agreement with the experiment.     

Direct numerical simulations of transverse and spanwise magnetic field effects on turbulent flow in a 2:1 aspect ratio rectangular duct

Magnetic fields are used extensively to direct liquid metal flows in material processing. Continuous casting of steel uses different configurations of magnetic fields to optimize turbulent flows in rectangular cross-sections to minimize defects in the solidified steel product. Realizing the importance of a magnetic field on turbulent flows in rectangular cross-sections, the present work is aimed at understanding the effect of a magnetic field on the turbulent metal flow at a nominal bulk Reynolds number of ∼5300 (based upon full duct height) (Re_τ = 170, based upon half duct height) and Hartmann numbers (based upon half duct height) of 0, 6.0 and 8.25 in a 2:1 aspect ratio rectangular duct. Direct numerical simulations in a non-MHD 2:1 aspect ratio duct followed by simulations with transverse and span-wise magnetic fields have been performed with 224 × 120 × 512 cells (∼13.7 million cells). The fractional step method with second order space and time discretization schemes has been used to solve the coupled Navier-Stokes-MHD equations. Instantaneous and time-averaged natures of the flow have been examined through distribution of velocities, various turbulence parameters and budget terms. Spanwise (horizontal) magnetic field reorganizes and suppresses secondary flows more strongly. Turbulence suppression and velocity flattening effects are stronger with transverse (vertical) magnetic field.