Three-Dimensional Simulation of Flow Past a Circular Cylinder by Nonlinear Turbulence Model
19 May 2008-Numerical Heat Transfer Part A-applications (Taylor & Francis Group)-Vol. 54, Iss: 2, pp 221-234
TL;DR: In this paper, a nonlinear turbulence model based on the k-e formulation is used to achieve the turbulent closure of flow past a circular cylinder at subcritical Reynolds number Re = 3,900 is performed using three-dimensional, unsteady, Reynolds-Averaged Navier-Stokes (URANS) equations.
Abstract: Numerical simulation of flow past a circular cylinder at sub-critical Reynolds number Re = 3,900 is performed using three-dimensional, unsteady, Reynolds–Averaged Navier-Stokes (URANS) equations. A nonlinear turbulence model based on the k–e formulation is used to achieve the turbulent closure. The results obtained by the simulations are compared with experimental and previously reported numerical results. The grid used for the present simulation is reasonable, and the accuracy obtained is good considering the computational cost involved in carrying out large-eddy simulations (LES) for the same test case. The test flow is also simulated using standard k–e model, and the results obtained by the nonlinear k–e model are found to be better.
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TL;DR: In this article, the authors employed partially-averaged Navier-Stokes (PANS) equations to simulate the flow around a smooth circular cylinder at Reynolds number 3900 and evaluated the importance of discretization and modelling errors on the accuracy of this mathematical model.
Abstract: This study employs Partially-Averaged Navier-Stokes (PANS) equations to simulate the flow around a smooth circular cylinder at Reynolds number 3900. It intends to evaluate the importance of discretization and modelling errors on the accuracy of this mathematical model. Furthermore, the study addresses the effect of the physical resolution, or fraction of turbulence kinetic energy being modelled fk, on the predictions accuracy. To this end, Validation exercises are carried out using five different values of fk which range from typical values for well-resolved Scale-Resolving Simulations (fk ≤ 0.25) to Reynolds-Averaged Navier-Stokes equations ( f k = 1.00 ). Naturally, these exercises require the evaluation of numerical errors, i.e. Verification studies. Consequently, and taking advantage of the ability of PANS to enable the distinction between discretization and modelling errors, spatial and temporal grid refinement studies are carried out to assess the magnitude of the discretization error, as well as its dependence on fk. The outcome confirms the ability of PANS, in combination with fk f k = 1.00 . However, the reduction of fk tends to increase the model dependence on the spatial and temporal resolution. It is demonstrated that similarly to the effect of the spatial and temporal grid resolution on the magnitude of the numerical error, the modelling error diminishes with the physical resolution (fk → 0). The convergence of the predictions with fk is also illustrated.
64 citations
TL;DR: A comprehensive survey of the literature in the area of numerical heat transfer (NHT) published between 2000 and 2009 has been conducted by as mentioned in this paper, where the authors conducted a comprehensive survey.
Abstract: A comprehensive survey of the literature in the area of numerical heat transfer (NHT) published between 2000 and 2009 has been conducted Due to the immenseness of the literature volume, the survey
58 citations
TL;DR: In this paper, the effect of angle of attack over flow structure, force coefficients and wall related flow variables are discussed in detail, and the non-linear k-e turbulence model is validated against DARPA Suboff axisymmetric hull.
Abstract: This paper addresses the Computational Fluid Dynamics Approach (CFD) to simulate the flow over underwater axisymmetric bodies at higher angle of attacks. Three Dimensional (3D) flow simulation is carried out over MAYA Autonomous Underwater Vehicle (AUV) at a Reynolds number (Re) of 2.09×10 6 . These 3D flows are complex due to cross flow interaction with hull which produces nonlinearity in the flow. Cross flow interaction between pressure side and suction side is studied in the presence of angle of attack. For the present study standard k-e model, non-linear k-e model models of turbulence are used for solving the Reynolds Averaged Navier-Stokes Equation (RANS). The non-linear k-e turbulence model is validated against DARPA Suboff axisymmetric hull and its applicability for flow simulation over underwater axisymmetric hull is examined. The non-linear k-e model performs well in 3D complex turbulent flows with flow separation and flow reattachment. The effect of angle of attack over flow structure, force coefficients and wall related flow variables are discussed in detail. Keywords: Computational Fluid Dynamics (CFD); Autonomous Underwater Vehicle (AUV); Reynolds averaged Navier-Stokes Equation (RANS); non-linear k-e turbulence model doi: http://dx.doi.org/10.3329/jname.v8i2.6984 Journal of Naval Architecture and Marine Engineering 8(2011) 149-163
22 citations
Cites methods from "Three-Dimensional Simulation of Flo..."
...Earlier, UDF implementation had been validated for flow past a square cylinder [Ramesh et al (2006)] and for a circular cylinder [Ayyappan and Vengadesan (2008)]....
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TL;DR: The main challenges to prediction of turbulent external flows of practical interest with Reynolds-Averaged Navier–Stokes equations (RANS) and Scale-Resolving Simulation (SRS) models are investigated and bridging models are revealed better suited for prediction.
Abstract: We investigate the main challenges to prediction of turbulent external flows of practical interest with Reynolds-Averaged Navier–Stokes equations (RANS) and Scale-Resolving Simulation (SRS) models. This represents a crucial step toward further developing and establishing these formulations so they can be confidently utilized in engineering problems without reference data. The study initiates by identifying the major challenges to prediction. A literature review is performed to illustrate their effects in RANS and SRS computations. Afterward, we evaluate the impact of the challenges to prediction by analyzing representative statistically steady and unsteady flows with prominent RANS and SRS methods. These include multiple turbulent viscosity and second-moment RANS closures, and hybrid and bridging SRS models. The results demonstrate the potential of the selected SRS models to predict engineering flows. Yet, they also show the importance of considering the challenges to prediction during the setup and conduction of numerical experiments. These can suppress the advantages of using SRS formulations. The data also indicate that only SRS models can confidently predict statistically unsteady flows. In contrast, the results demonstrate that mean-flow quantities of statistically steady flows can be efficiently calculated with RANS closures, especially second-moment closures. Among the selected SRS methods, bridging models reveal better suited for prediction due to their ability to prevent commutation errors and enable the robust evaluation of numerical and modeling errors. This last property allows the use of a new validation technique that does not require reference data.
22 citations
TL;DR: In this paper, the macroscopic turbulence quantities for porous media were computed and analyzed for different Reynolds numbers as well as for different porosity levels, and the results showed that the spatial dispersion of the mean flow is the main contributor to this quantity at low porosities.
Abstract: In this study, fully developed macroscopic turbulence quantities—based on their definitions in some existing turbulence models for porous media as well as those based on definitions introduced in a recently developed model [F.E. Teruel, Rizwan-uddin, A new turbulence model for porous media flows. Part I: Constitutive equations and model closure, Int. J. Heat Mass Transfer (2009)]—are computed and analyzed for different Reynolds numbers as well as for different porosity levels. When computed based on the definition introduced in the new model, these numerically computed, pore-level turbulent quantities provide closure to the formulation. A large set of microscopic turbulent flow simulations of the REV of a porous medium, formed by staggered square cylinders, is carried out to achieve these tasks. For each Reynolds number selected, ten different porosities are simulated in the 5–95% range. The Reynolds number is varied from Re = 103 to Re = 105, covering four different cases of the turbulence flow regime. Numerical results obtained for the macroscopic turbulent kinetic energy based on the new definition show that the spatial dispersion of the mean flow is the main contributor to this quantity at low porosities. Additionally, it is found that for high porosities, the spatial average of the turbulent kinetic energy is the main contributor but the spatial dispersion of the mean flow cannot be neglected. The new definition of the macroscopic dissipation rate is found to asymptotically approach the volume average of this quantity at high Reynolds numbers. It is confirmed that microscopic numerical simulations are consistent with the macroscopic law that states that the macroscopic dissipation rate is determined by the pressure-drop through the REV.
21 citations
References
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TL;DR: In this paper, hot-wire measurements were conducted in the very near wake (x/d⩽10) of a circular cylinder at a Reynolds number based on cylinder diameter.
Abstract: Hot-wire measurements were conducted in the very near wake (x/d⩽10) of a circular cylinder at a Reynolds number based on cylinder diameter, Re
d of 3900. Measurements of the streamwise velocity component with the use of single sensor hot-wire probes were found to be inaccurate for such flowfields where high flow angles are present. An X-array probe provided detailed streamwise and lateral velocity component statistics. Frequency spectra of these two velocity components are also presented. Measurements with a 4-sensor hot-wire probe confirmed that the very near wake region is dominantly two-dimensional, thus validating the accuracy of the present X-array data.
437 citations
"Three-Dimensional Simulation of Flo..." refers methods in this paper
...Cd mean mean drag coefficient Cl rms rms lift coefficient D diameter of cylinder f frequency of vortex shedding K turbulent kinetic energy rmin location of minimum velocity Re Reynolds number St Strouhal number U1 streamwise velocity U2 cross-streamwise velocity U1 free-stream velocity e turbulent kinetic energy dissipation rate Later, Ong and Wallace [10] conducted detailed experiments using an X-array probe hotwire and reported data to verify the LES simulation of BM....
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...Later, Ong and Wallace [10] conducted detailed experiments using an X-array probe hotwire and reported data to verify the LES simulation of BM....
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TL;DR: In this article, it was shown that the spanwise end conditions which control the primary mode of vortex shedding significantly affect the shear-layer instability and contributed to the large discrepancy in quoted values of the critical Reynolds number.
Abstract: Notwithstanding the fact that the instability of the separated shear layer in the cylinder wake has been extensively studied, there remains some uncertainty regarding not only the critical Reynolds number at which the instability manifests itself, but also the variation of its characteristic frequency with Reynolds number (Re). A large disparity exists in the literature in the precise value of the critical Reynolds number, with quoted values ranging from Re = 350 to Re = 3000. In the present paper, we demonstrate that the spanwise end conditions which control the primary mode of vortex shedding significantly affect the shear-layer instability. For parallel shedding conditions, shear-layer instability manifests itself at Re ≈ 1200, whereas for oblique shedding conditions it is inhibited until a significantly higher Re ≈ 2600, implying that even in the absence of a variation in free-stream turbulence level, the oblique angle of primary vortex shedding influences the onset of shear-layer instability, and contributes to the large disparity in quoted values of the critical Reynolds number. We confirm the existence of intermittency in shear-layer fluctuations and show that it is not related to the transverse motion of the shear layers past a fixed probe, as suggested previously. Such fluctuations are due to an intermittent streamwise movement of the transition point, or the location at which fluctuations develop rapidly in the shear layer.Following the original suggestion of Bloor (1964), it has generally been assumed in previous studies that the shear-layer frequency (normalized by the primary vortex shedding frequency) scales with Re1/2, although a careful examination of the actual data points from these studies does not support such a variation. We have reanalysed all of the actual data points from previous investigations and include our own measurements, to find that none of these studies yields a relationship which is close to Re1/2. A least-squares analysis which includes all of the previously available data produces a variation of the form Re0·67. Based on simple physical arguments that account for the variation of the characteristic velocity and length scales of the shear layer, we predict a variation for the normalized shear-layer frequency of the form Re0·7, which is in good agreement with the experimental measurements.
397 citations
"Three-Dimensional Simulation of Flo..." refers methods in this paper
...The three-dimensional Floquet stability analysis reported by Barkley and Henderson [17] and the experiment done by Prasad and Williamson [18] at subcritical Reynolds number showed the dominant spanwise scales having wavelengths of approximately three to four cylinder diameters in the Reynolds number range 180 < Re < 240....
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...The three-dimensional Floquet stability analysis reported by Barkley and Henderson [17] and the experiment done by Prasad and Williamson [18] at subcritical Reynolds number showed the dominant spanwise scales having wavelengths of approximately three to four cylinder diameters in the Reynolds number range 180 Re 240....
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TL;DR: In this paper, the authors simulated flow past a circular cylinder at a Reynolds number of 3.9 X 10 3 using a solver that employs an energy-conservative second-order central difference scheme for spatial discretization.
Abstract: We have simulated flow past a circular cylinder at a Reynolds number of 3.9 X 10 3 using a solver that employs an energy-conservative second-order central difference scheme for spatial discretization. Detailed comparisons of turbulence statistics and energy spectra in the downstream wake region (7.0 < x/D < 10.0) have been made with the results of Beaudan and Moin and with experiments to assess the impact of numerical diffusion on the flowfield. Based on these comparisons, conclusions are drawn on the suitability of higher-order upwind schemes for LES in complex geometries.
397 citations
Additional excerpts
...The same test case was simulated using LES technique by Breuer [12] and by Krevechenko and Moin [13]....
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...Beaudan and Moin [9] (hereafter referred to as BM) were the first to carry out a detailed LES study for the subcritical flow past a circular cylinder at Re ¼ 3,900....
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...This factor was later explained by Mittal and Moin [11]....
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TL;DR: In this paper, the authors investigate the dynamics of the near wake in turbulent flow past a circular cylinder up to ten cylinder diameters downstream, and find that the very near wake is dominated by the shear layer dynamics and is very sensitive to disturbances and cylinder aspect ratio.
Abstract: We investigate the dynamics of the near wake in turbulent flow past a circular cylinder up to ten cylinder diameters downstream. The very near wake (up to three diameters) is dominated by the shear layer dynamics and is very sensitive to disturbances and cylinder aspect ratio. We perform systematic spectral direct (DNS) and large-eddy simulations (LES) at Reynolds number ( Re ) between 500 and 5000 with resolution ranging from 200 000 to 100 000 000 degrees of freedom. In this paper, we analyse in detail results at Re = 3900 and compare them to several sets of experiments. Two converged states emerge that correspond to a U-shape and a V-shape mean velocity profile at about one diameter behind the cylinder. This finding is consistent with the experimental data and other published LES. Farther downstream, the flow is dominated by the vortex shedding dynamics and is not as sensitive to the aforementioned factors. We also examine the development of a turbulent state and the inertial subrange of the corresponding energy spectrum in the near wake. We find that an inertial range exists that spans more than half a decade of wavenumber, in agreement with the experimental results. In contrast, very low-resolution spectral simulation as well as other dissipative LES do not describe accurately the inertial range although they predict low-order statistics relatively accurately. This finding is analysed in the context of coherent structures using a phase averaging technique and a procedure to extract the most energetic (on the average) eigenmodes of the flow. The results suggest that a dynamical model would require of the order of twenty modes to describe the vortex shedding dynamics with reasonable accuracy.
378 citations
"Three-Dimensional Simulation of Flo..." refers methods in this paper
...DNS study by Ma et al. [ 14 ] with a spectral finiteelement method explained the extent of recirculation length (Lr) for two domain sizes in the spanwise directions....
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TL;DR: In this paper, the turbulent flow past a circular cylinder (Re=3900) was computed by large eddy simulation (LES), and the authors investigated numerical and modeling aspects which influence the quality of LES solutions.
Abstract: SUMMARY The turbulent flow past a circular cylinder (Re=3900) was computed by large eddy simulation (LES). The objective was not to investigate the physical phenomena of this flow in detail but to study numerical and modeling aspects which influence the quality of LES solutions. Concerning the numerical method, the most important component is the discretization of the non-linear convective fluxes. Five different schemes were investigated. Also, the influence of different grid resolutions was examined. Two aspects play an important role on the modeling side, namely the near-wall model and the subgrid scale model. Owing to the restriction to low Reynolds numbers in this study, no-slip boundary conditions were used at solid walls. Therefore, only the second aspect was taken into account. Two different subgrid scale models were applied. Additionally, LES computations without any subgrid scale modeling were carried out in order to prove the performance of the models. The results were evaluated by comparison with available experimental data. © 1998 John Wiley & Sons, Ltd.
372 citations
"Three-Dimensional Simulation of Flo..." refers background or methods in this paper
...The same test case was simulated using LES technique by Breuer [12] and by Krevechenko and Moin [13]....
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...In Breuer’s LES work [12], in the time history of the lift coefficient, there was a low-frequency component over a regular periodic component....
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