Reduced Order Modeling of a Turbulent Three Dimensional Cylinder Wake (original) (raw)
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AIP Advances, 2021
The turbulent flow past a wall-mounted square cylinder with an aspect ratio of 4 was investigated with the aid of Spalart-Allmaras improved delayed detached-eddy simulation and proper orthogonal decomposition (POD) analysis. The Reynolds number was equal to 12 000 (based on the free-stream velocity and obstacle width). The boundary layer thickness was ∼0.18 of the obstacle height. This study focused on analyzing the vortical structure of the wake and vortex shedding process along the obstacle height. A quantitative comparison of the first-and second-order flow statistics with the available experimental and direct numerical simulation data was used to validate the numerical results. The numerical model coupled with the vortex method of generating the turbulent inflow conditions could successfully reproduce the flow field around and behind the obstacle with commendable accuracy. The flow structure and vortex shedding characteristics near the wake formation region were discussed in detail using time-averaged and instantaneous flow parameters obtained from the simulation. Dipole type mean streamwise vortices and half-loop hairpin instantaneous vortices with energetic motions were identified. A coherent shedding structure was reported along the obstacle using two-point correlations. Two types of vortex shedding intervals were identified, namely, low amplitude fluctuations (LAFs) and high amplitude fluctuations (HAFs) [P. Sattari et al., Exp. Fluids 52, 1149-1167 (2012)]. The HAFs' interval exhibits von Kármán-like behavior with a phase difference of ∼180 ○ , while the LAFs' interval shows less periodic behavior. It was observed that the effect of the LAFs' interval tends to weaken the alternating shedding along the obstacle height. The POD analysis of the wake showed that for the elevations between 0.25 and 0.5 of the obstacle height, the first two POD modes represent the alternating shedding and contribute to 66.6%-57.6% of the total turbulent kinetic energy. However, at the free end of the obstacle, the first two modes have a symmetrical shedding nature and share 36.5% of the kinetic energy, while the rest of the energy is distributed between the alternating and the random shedding processes. A simple low-order model based on the vortex-shedding phase angle and the spectrum of the time coefficients obtained from POD was developed to predict the wake dynamics at the range of elevations where the alternating shedding is dominated.
Turbulence properties in the cylinder wake at high Reynolds numbers
Journal of Fluids and Structures, 2006
The present contribution analyses the turbulence properties in unsteady flows around bluff body wakes and provides a database for improvement and validation of turbulence models, concerning the present class of nonequilibrium flows. The flow around a circular cylinder with a low aspect ratio and a high blockage coefficient is investigated. This confined environment is used in order to allow direct comparisons with realisable 3-D Navier-Stokes computations avoiding 'infinite' conditions. The flow is investigated in the beginning of the critical regime at Reynolds number 140 000. The analysis is carried out by means of 2-D PIV, of 3-C PIV and of high-frequency 2-D PIV. The experimental analysis contributes to confirm the validity of advanced statistical turbulence modelling for unsteady flows around bodies. r (M. Braza).
Analysis of numerically generated wake structures
Wind Energy, 2009
Direct numerical simulations of the Navier-Stokes equations are performed to achieve a better understanding of the behaviour of wakes generated by wind turbines. The simulations are performed by combining the in-house developed computer code EllipSys3D with the actuator-line methodology. In the actuator-line method, the blades are represented by lines along which body forces representing the loading are introduced. The body forces are determined by computing local angles of attack and using tabulated aerofoil coefficients. The advantage of using the actuator-line technique is that it is not needed to resolve blade boundary layers and instead the computational resources are devoted to simulating the dynamics of the flow structures. In the present study, approximately 5 million mesh points are used to resolve the wake structure in a 120-degree domain behind the turbine. The results from the computational fluid dynamics (CFD) simulations are evaluated and the downstream evolution of the velocity field is depicted. Special interest is given to the structure and position of the tip vortices. Further, the circulation from the wake flow field is computed and compared to the distribution of circulation on the blades.
random vortex method for an incompressible flu id in two dimensions is presented. In the random vortex method, the primary variable is vorticity of the flow field. After generation on the cylinder wall, it is followed in two fractional time step in a Lagrangian system of coordinates, namely convection and diffu sion. No closu re model is u sed and the instantaneou s results are calculated without any a priori modeling. Regarding the Lagrangian nature of the method, there is a ve ry good co m patib ility b etween t he nu m er ical m et hod and p hysics o f the flow. T he numerical resu lts are presented for a wide range of R eynolds nu mber, 40-9500. In the initial stages, there is only an unstable symmetrical flow behind the cylinder and the vortex sheding is not started yet. But, in the high Reynolds number flows, two distinctive flow patterns, namely a and b are detected. The mechanism of generation of the primary and the secondary eddies can be rela ted to the produ ction, conve ction and diffu sion of the vort icity field a nd t he time dependent structure of the flow field in the wake zone behind the cylinder. The length of the compu ta tional d omain, d ownstream of the cylinder , is selected 25 time s of the cylinder' s d ia me te r. R egar d in g su ch a le ngth y co m pu ta tion al d o ma in it is po ssib le t o d et ect th e mechanism of generation, pairing and growth of the large scale structure, eddies. Although the inst antane ou s nu mer ical resu lts are calcu late d, no corespondin g compara ble resu lts are availab le. T he refore , th e va lid it y of t he r esu lts in t his sta ge is on ly qu alita tive. F or t he qu antitative comparison of the results, after the establishment of the stationary state, time averaged based indicators su ch as separation angle, drag coefficient, lift coefficient, Strouhal nu mber and ... are calcu lated. The nu merical resu lts accu rately fall within the range of the experimental measurements.
Numerical Simulations of Wake/boundary Layer Interactions
41st Aerospace Sciences Meeting and Exhibit, 2003
Direct and largeeddy simulations of the interaction between t h e wake of a circular cylinder and a flat-plate boundary layer are conducted. Two Reynolds numbers are examined. The simulations indicate t h a t at the iower Reynolds number ihe boundary layer i s buffeted by t h e unsteady K & m h vortex street shed by the cylinder. The fluctuations, however, cannot be seif-sustained due to the low Reynolds-number, and the flow does not reach a turbulent state within the computational domain. In contrast, in t h e higher Reynolds-number case, boundary-layer fluctuations persist after t h e wake has decayed [due, in part, to the higher values of the local Reynolds number Rea achieved in this case); some evidence could b e observed that a self-sustaining turbulence generation cycle was beginning to be established.
Dependence of square cylinder wake on Reynolds number
Physics of Fluids, 2018
The wake of a square cylinder is investigated for Reynolds number Re < 10 7. Two-dimensional (2D) laminar simulation and three-dimensional (3D) large-eddy simulation are conducted at Re ≤ 1.0 × 10 3 , while experiments of hotwire, particle image velocimetry, and force measurements are carried out at a higher Re range of 1.0 × 10 3 < Re < 4.5 × 10 4. Furthermore, data covering a wide Re range, from 10 0 to 10 7 , in the literature are comprehensively collected for discussion and comparison purposes. The dependence on Re of the recirculation bubble size or vortex formation length, wake width, shear-layer transition, time-mean drag force, and Strouhal number is discussed in detail, revealing five flow regimes, each having distinct variations of the above parameters. With increasing Re, while the streamwise recirculation size enlarges at Re < 50 (steady flow regime), the vortex formation length reduces at 50 < Re < 1.6 × 10 2 (laminar flow regime), remains unchanged at 1.6 × 10 2 < Re < 2.2 × 10 2 (2D-to-3D transition flow regime), and decreases at 2.2 × 10 2 < Re < 1 × 10 3 (shear layer transition I regime), approaching asymptotically a constant at Re > 1.0 × 10 3 (shear layer transition II regime). Meanwhile, the wake width decreases with Re in the laminar flow regime, grows in 2D-to-3D transition and shear layer transition I regimes, and levels off in the shear layer transition II regime. The narrowest wake width is identified in the 2D-to-3D transition flow regime, corresponding to a minimum time-mean drag force and a largest Strouhal number. With increasing Re, the shear-layer transition length rapidly declines in the shear layer transition I regime where the transition occurs downstream of the trailing corner of the cylinder. On the other hand, it slowly tapers off in the shear layer transition II regime where the transition takes place upstream of the trailing corner. An extensive comparison is made between the dependence on Re of a circular cylinder wake and a square cylinder wake, with their distinct natures highlighted.
Efficient Turbulence Modeling for CFD Wake Simulations
2014
Wind turbine wakes can cause 10-20% annual energy losses in wind farms, and wake turbulence can decrease the lifetime of wind turbine blades. One way of estimating these effects is the use of computational fluid dynamics (CFD) to simulate wind turbines wakes in the atmospheric boundary layer. Since this flow is in the high Reynolds number regime, it is mainly dictated by turbulence. As a result, the turbulence modeling in CFD dominates the wake characteristics, especially in Reynolds-averaged Navier-Stokes (RANS). The present work is dedicated to study and develop RANS-based turbulence models, that can accurately and efficiently simulate wind turbine wakes. The linear k-ε eddy viscosity model (EVM) is a popular turbulence model in RANS; however, it underpredicts the velocity wake deficit and cannot predict the anisotropic Reynolds-stresses in the wake. In the current work, nonlinear eddy viscosity models (NLEVM) are applied to wind turbine wakes. NLEVMs can model anisotropic turbule...