Turbulent Flow Around Rectangular Cylinders with Different Streamwise Aspect Ratios

2021 ◽  
Author(s):  
Sedem Kumahor ◽  
Mark F. Tachie
Keyword(s):  
Aspect Ratio ◽  
High Speed ◽  
Second Harmonic ◽  
Cylinder Surface ◽  
Large Aspect Ratio ◽  
Reynolds Stresses ◽  
Square Cylinder ◽  
Mean Flow ◽  
Aspect Ratios ◽  
The Mean

Abstract Turbulent flows around a square cylinder and a rectangular cylinder with a streamwise aspect ratio of 5 in a uniform flow were investigated using time-resolved particle image velocimetry. The Reynolds number based on the cylinder height and oncoming flow velocity was 16200. Similarities and differences in the flow dynamics over the cylinders and in the near wake region were examined in terms of the mean flow, Reynolds stresses and triple velocity correlations. The budget of turbulent kinetic energy as well as temporal and spectral analyses were also performed. The results show that the primary, secondary and wake vortexes are smaller for the square cylinder compared to the large aspect ratio cylinder. There are regions of elevated Reynolds stresses and triple velocity correlations along the mean separating streamlines, and the magnitudes of these statistics are an order of magnitude higher over the square cylinder compared to the large aspect ratio cylinder. The topology of the triple velocity correlations shows low-speed ejection and high-speed sweep events, respectively, transporting instantaneous Reynolds normal stresses away from the mean separating streamline into the free-stream and toward the cylinder surface, regardless of aspect ratio. Near the leading and trailing edges of both cylinders, regions of negative turbulence production are observed and the dominant components contributing to this occurrence are discussed. Temporal autocorrelation coefficients of the streamwise and vertical velocity fluctuations show a periodic trend, with a periodicity that is directly linked to the Kármán shedding frequency and its second harmonic.

Streamwise Aspect Ratio Effects on Turbulent Flow Separations Induced by Forward–Backward-Facing Steps

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Heath Chalmers ◽  
Xingjun Fang ◽  
Mark F. Tachie
Keyword(s):  
Boundary Layer ◽  
Aspect Ratio ◽  
Turbulent Boundary Layer ◽  
Step Height ◽  
Bluff Bodies ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Freestream Velocity ◽  
Aspect Ratios ◽  
The Mean

Abstract Separated and reattached turbulent flows induced by two-dimensional forward–backward-facing steps (FBFS) with different streamwise lengths submerged in a thick turbulent boundary layer (TBL) are investigated using time-resolved particle image velocimetry (TR-PIV). The aspect ratios (AR) of the step range from 1 to 8, and the Reynolds number based on the freestream velocity and step height is 13 200. The thickness of the incoming turbulent boundary layer is 6.5 times the step height. The effects of varying aspect ratio of the steps on the mean flow, principal stretching, Reynolds stresses, triple velocity correlation, two-point autocorrelation, and unsteadiness of turbulent separation bubbles are studied. The results indicate that the mean flow reattaches over the step for FBFS with aspect ratios of 2 and higher. Two local peaks of Reynolds stresses occur irrespective of AR, and for a sufficiently large AR, a third local peak of Reynolds stresses appear in the shear layer emanating from the trailing edge of the bluff bodies. The streamwise decay of Reynolds stresses is slower for smaller AR cases. Incoming coherent structure is strongly disturbed near an inclined edge where principal stretching switches orientation abruptly. The temporal variation of the first proper orthogonal decomposition (POD) mode and reverse flow area over the bluff bodies shows remarkable correlation, which signifies the flapping motion of separation bubble.

Harmonics generation and the mechanics of saturation in flow over an open cavity: a second-order self-consistent description

2017 ◽  
Vol 826 ◽  
pp. 503-521 ◽  
Author(s):  
P. Meliga
Keyword(s):  
Growth Rate ◽  
Second Harmonic ◽  
Open Cavity ◽  
Linear Growth Rate ◽  
Linear Component ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Higher Harmonics ◽  
Self Consistent ◽  
The Mean

The flow over an open cavity is an example of supercritical Hopf bifurcation leading to periodic limit-cycle oscillations. One of its distinctive features is the existence of strong higher harmonics, which results in the time-averaged mean flow being strongly linearly unstable. For this class of flows, a simplified formalism capable of unravelling how exactly the instability grows and saturates is lacking. This study builds on previous work by Mantič-Lugo et al. (Phys. Rev. Lett., vol. 113, 2014, 084501) to fill in the gap using a parametrized approximation of an instantaneous, phase-averaged mean flow, coupled in a quasi-static manner to multiple linear harmonic disturbances interacting nonlinearly with one another and feeding back on the mean flow via their Reynolds stresses. This provides a self-consistent modelling of the mean flow–fluctuation interaction, in the sense that all perturbation structures are those whose Reynolds stresses force the mean flow in such a way that the mean flow generates exactly the aforementioned perturbations. The first harmonic is sought as the superposition of two components, a linear component generated by the instability and aligned along the leading eigenmode of the mean flow, and a nonlinear orthogonal component generated by the higher harmonics, which progressively distorts the linear growth rate and eigenfrequency of the eigenmode. Saturation occurs when the growth rate of the first harmonic is zero, at which point the stabilizing effect of the second harmonic balances exactly the linear instability of the eigenmode. The model does not require any input from numerical or experimental data, and accurately predicts the transient development and the saturation of the instability, as established from comparison to time and phase averages of direct numerical simulation data.

Effects of Streamwise Aspect Ratio on Turbulent Flows Over Forward-Backward Facing Steps

2020 ◽  
Author(s):  
Heath Chalmers ◽  
Xingjun Fang ◽  
Mark F. Tachie
Keyword(s):  
Boundary Layer ◽  
Aspect Ratio ◽  
Turbulent Boundary Layer ◽  
Turbulent Flows ◽  
Separation Bubble ◽  
Step Height ◽  
Stream Velocity ◽  
Mean Flow ◽  
Aspect Ratios ◽  
The Mean

Abstract Separated and reattached turbulent flows induced by two-dimensional forward-backward-facing steps with different streamwise lengths submerged in a thick turbulent boundary layer are investigated using a time-resolved particle image velocimetry. The examined aspect ratios of the step range from 1 to 8, and the Reynolds number based on the free-stream velocity and step height is 13 200. The thickness of the oncoming turbulent boundary layer is 6.5 times the step height. The effects of varying aspect ratio of the steps on the mean flow, Reynolds stresses, triple correlations and unsteadiness of turbulent separation bubbles are studied. It was found that the mean flow reattaches over the step for forward-backward facing steps with aspect ratios of 2 and higher. The temporal variation of the first proper orthogonal decomposition (POD) mode and reverse flow area, which is used to examine the flapping motion of separation bubble, shows remarkable synchronization.

Influence of Wall Proximity on the Wake Dynamics Behind a Square Cylinder

2021 ◽  
Author(s):  
Samuel Addai ◽  
Afua A. Mante ◽  
Sedem Kumahor ◽  
Xingjun Fang ◽  
Mark F. Tachie
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Normal Stress ◽  
Reynolds Shear Stress ◽  
Stream Velocity ◽  
Reynolds Stresses ◽  
Square Cylinder ◽  
Mean Flow ◽  
The Mean ◽  
Wall Proximity

Abstract In the present study, the effects of wall proximity on the wake dynamics behind a square cylinder subjected to a thick upstream turbulent boundary layer were experimentally investigated using particle image velocimetry. The Reynolds number based on the free-stream velocity and the cylinder height (h) was 12750 while the ratio of the turbulent boundary layer thickness to the cylinder height was 3.6. The gap distance (G) between the bottom face of the cylinder and the wall was varied, resulting in gap ratios (G/h) of 0, 0.3, 0.5, 1.0, 2.0 and 8.0. The flow topological differences among the various gap ratios were analyzed in terms of the mean flow and Reynolds stresses. The results show that as the cylinder approaches the wall, the mean flow becomes increasingly asymmetric about the horizontal centerline of the cylinder and the size of the mean separation bubbles in the cylinder wake increases. Also, the magnitudes of the Reynolds stresses decrease with decreasing gap ratio. For G/h > 0, the distributions of the streamwise Reynolds normal stress and Reynolds shear stress are concentrated along the upper and lower separated shear layers, resulting in characteristic double peaks. The distributions of the vertical Reynolds normal stress, however, are concentrated in the wake about the horizontal centerline of the cylinder and reveal only single peaks.

scholarly journals Modeling the Excess Velocity of Low-Viscous Taylor Droplets in Square Microchannels

Fluids ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 162 ◽  
Author(s):  
Thorben Helmers ◽  
Philip Kemper ◽  
Jorg Thöming ◽  
Ulrich Mießner
Keyword(s):  
High Speed ◽  
Process Intensification ◽  
Continuous Phase ◽  
Channel Cross Section ◽  
Optimization Approach ◽  
Mean Flow ◽  
Bypass Flow ◽  
Wall Film ◽  
Proposed Model ◽  
The Mean

Microscopic multiphase flows have gained broad interest due to their capability to transfer processes into new operational windows and achieving significant process intensification. However, the hydrodynamic behavior of Taylor droplets is not yet entirely understood. In this work, we introduce a model to determine the excess velocity of Taylor droplets in square microchannels. This velocity difference between the droplet and the total superficial velocity of the flow has a direct influence on the droplet residence time and is linked to the pressure drop. Since the droplet does not occupy the entire channel cross-section, it enables the continuous phase to bypass the droplet through the corners. A consideration of the continuity equation generally relates the excess velocity to the mean flow velocity. We base the quantification of the bypass flow on a correlation for the droplet cap deformation from its static shape. The cap deformation reveals the forces of the flowing liquids exerted onto the interface and allows estimating the local driving pressure gradient for the bypass flow. The characterizing parameters are identified as the bypass length, the wall film thickness, the viscosity ratio between both phases and the C a number. The proposed model is adapted with a stochastic, metaheuristic optimization approach based on genetic algorithms. In addition, our model was successfully verified with high-speed camera measurements and published empirical data.

Data Analysis Methods for Stereo PIV of a High Aspect Ratio Flexible Cylinder

2007 ◽  
Author(s):  
D. Furey ◽  
P. Atsavapranee ◽  
K. Cipolla
Keyword(s):  
Boundary Layer ◽  
Data Analysis ◽  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Particle Image Velocimetry Data ◽  
Flow Fields ◽  
Mean Flow ◽  
Boundary Flow ◽  
The Mean ◽  
Cylinder Flow

Stereo Particle Image velocimetry data was collected over high aspect ratio flexible cylinders (L/a = 1.5 to 3 × 105) to evaluate the axial development of the turbulent boundary layer where the boundary layer thickness becomes significantly larger than the cylinder diameter (δ/a>>1). The flexible cylinders are approximately neutrally buoyant and have an initial length of 152 m and radii of 0.45 mm and 1.25 mm. The cylinders were towed at speeds ranging from 3.8 to 15.4 m/sec in the David Taylor Model Basin. The analysis of the SPIV data required a several step procedure to evaluate the cylinder boundary flow. First, the characterization of the flow field from the towing strut is required. This evaluation provides the residual mean velocities and turbulence levels caused by the towing hardware at each speed and axial location. These values, called tare values, are necessary for comparing to the cylinder flow results. Second, the cylinder flow fields are averaged together and the averaged tare fields are subtracted out to remove strut-induced ambient flow effects. Prior to averaging, the cylinder flow fields are shifted to collocate the cylinder within the field. Since the boundary layer develops slowly, all planes of data occurring within each 10 meter increment of the cylinder length are averaged together to produce the mean boundary layer flow. Corresponding fields from multiple runs executed using the same experimental parameters are also averaged. This flow is analyzed to evaluate the level of axisymmetry in the data and determine if small changes in cylinder angle affect the mean flow development. With axisymmetry verified, the boundary flow is further averaged azimuthally around the cylinder to produce mean boundary layer profiles. Finally, the fluctuating velocity levels are evaluated for the flow with the cylinder and compared to the fluctuating velocity levels in the tare data. This paper will first discuss the data analysis techniques for the tare data and the averaging methods implemented. Second, the data analysis considerations will be presented for the cylinder data and the averaging and cylinder tracking techniques. These results are used to extract relevant boundary layer parameters including δ, δ* and θ. Combining these results with wall shear and momentum thickness values extracted from averaged cylinder drag data, the boundary layer can be well characterized.

Numerical Modeling of Fluid-Induced Rotordynamic Forces in Seals With Large Aspect Ratio

2012 ◽  
Author(s):  
Alexandrina Untaroiu ◽  
Costin D. Untaroiu ◽  
Houston G. Wood ◽  
Paul E. Allaire
Keyword(s):  
Finite Difference ◽  
Aspect Ratio ◽  
Finite Difference Method ◽  
Difference Method ◽  
Dynamic Properties ◽  
Bulk Flow ◽  
Large Aspect Ratio ◽  
Flow Method ◽  
Dynamic Coefficients ◽  
Aspect Ratios

Traditional annular seal models are based on bulk flow theory. While these methods are computationally efficient and can predict dynamic properties fairly well for short seals, they lack accuracy in cases of seals with complex geometry or with large aspect ratios (above 1.0). In this paper, the linearized rotordynamic coefficients for a seal with large aspect ratio are calculated by means of a three dimensional CFD analysis performed to predict the fluid-induced forces acting on the rotor. For comparison, the dynamic coefficients were also calculated using two other codes: one developed on the bulk flow method and one based on finite difference method. These two sets of dynamic coefficients were compared with those obtained from CFD. Results show a reasonable correlation for the direct stiffness estimates, with largest value predicted by CFD. In terms of cross-coupled stiffness, which is known to be directly related to cross-coupled forces that contribute to rotor instability, the CFD predicts also the highest value; however a much larger discrepancy can be observed for this term (73% higher than value predicted by finite difference method and 79% higher than bulk flow code prediction). Similar large differences in predictions one can see in the estimates for damping and direct mass coefficients, where highest values are predicted by the bulk flow method. These large variations in damping and mass coefficients, and most importantly the large difference in the cross-coupled stiffness predictions, may be attributed to the large difference in seal geometry (i.e. the large aspect ratio AR>1.0 of this seal model vs. the short seal configuration the bulk flow code is usually calibrated for, using an empirical friction factor).

Numerical Study of Deterministic Fluxes in Compressor Passages

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
Feng Wang ◽  
Mauro Carnevale ◽  
Luca di Mare
Keyword(s):  
High Speed ◽  
Numerical Study ◽  
Navier Stokes ◽  
Design Stage ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Radial Profiles ◽  
And Performance ◽  
Stage Matching ◽  
Unsteady Effects

Computational fluid dynamics (CFD) has been widely adopted in the compressor design process, but it remains a challenge to predict the flow details, performance, and stage matching for multistage, high-speed machines accurately. The Reynolds Averaged Navier-Stokes (RANS) simulation with mixing plane for bladerow coupling is still the workhorse in the industry and the unsteady bladerow interaction is discarded. This paper examines these discarded unsteady effects via deterministic fluxes using semi-analytical and unsteady RANS (URANS) calculations. The study starts from a planar duct under periodic perturbations. The study shows that under large perturbations, the mixing plane produces dubious values of flow quantities (e.g., whirl angle). The performance of the mixing plane can be considerably improved by including deterministic fluxes into the mixing plane formulation. This demonstrates the effect of deterministic fluxes at the bladerow interface. Furthermore, the front stages of a 19-blade row compressor are investigated and URANS solutions are compared with RANS mixing plane solutions. The magnitudes of divergence of Reynolds stresses (RS) and deterministic stresses (DS) are compared. The effect of deterministic fluxes is demonstrated on whirl angle and radial profiles of total pressure and so on. The enhanced spanwise mixing due to deterministic fluxes is also observed. The effect of deterministic fluxes is confirmed via the nonlinear harmonic (NLH) method which includes the deterministic fluxes in the mean flow, and the study of multistage compressor shows that unsteady effects, which are quantified by deterministic fluxes, are indispensable to have credible predictions of the flow details and performance of compressor even at its design stage.

Bubble behaviour in a horizontal high-speed solid-body rotating flow

2021 ◽  
Vol 925 ◽  
Author(s):  
Majid Rodgar ◽  
Hélène Scolan ◽  
Jean-Louis Marié ◽  
Delphine Doppler ◽  
Jean-Philippe Matas
Keyword(s):  
Aspect Ratio ◽  
Solid Body ◽  
High Speed ◽  
Lift Coefficient ◽  
Rotating Flow ◽  
Axis Of Rotation ◽  
Large Fluctuations ◽  
The Mean ◽  
Drag And Lift ◽  
The Impact

We study experimentally the behaviour of a bubble injected into a horizontal liquid solid-body rotating flow, in a range of rotational velocities where the bubble is close to the axis of rotation. We first study the stretching of the bubble as a function of its size and of the rotation of the cell. We show that the bubble aspect ratio can be predicted as a function of the bubble Weber number by the model of Rosenthal (J. Fluid Mech., vol. 12, 1962, 358–366) provided an appropriate correction due to the impact of buoyancy is included. We next deduce the drag and lift coefficients from the mean bubble position. For large bubbles straddling the axis of rotation, we show that the drag coefficient $C_D$ is solely dependent on the Rossby number $Ro$, with $C_D \approx 1.5/Ro$. In the same limit of large bubbles, we show that the lift coefficient $C_L$ is controlled by the shear Reynolds number $Re_{shear}$ at the scale of the bubble. For $Re_{shear}$ larger than 3000 we observe a sharp transition, wherein large fluctuations in the bubble aspect ratio and mean position occur, and can lead to the break-up of the bubble. We interpret this regime as a resonance between the periodic forcing of the rotating cell and the eigenmodes of the stretched bubble.

scholarly journals Self-consistent triple decomposition of the turbulent flow over a backward-facing step under finite amplitude harmonic forcing

2019 ◽  
Vol 475 (2225) ◽  
pp. 20190018
Author(s):  
E. Yim ◽  
P. Meliga ◽  
F. Gallaire
Keyword(s):  
Turbulent Flow ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Reynolds Stresses ◽  
Mean Flow ◽  
Backward Facing Step ◽  
Eddy Viscosity Model ◽  
Coherent Interaction ◽  
Self Consistent ◽  
The Mean

We investigate the saturation of harmonically forced disturbances in the turbulent flow over a backward-facing step subjected to a finite amplitude forcing. The analysis relies on a triple decomposition of the unsteady flow into mean, coherent and incoherent components. The coherent–incoherent interaction is lumped into a Reynolds averaged Navier–Stokes (RANS) eddy viscosity model, and the mean–coherent interaction is analysed via a semi-linear resolvent analysis building on the laminar approach by Mantič-Lugo & Gallaire (2016 J. Fluid Mech. 793 , 777–797. ( doi:10.1017/jfm.2016.109 )). This provides a self-consistent modelling of the interaction between all three components, in the sense that the coherent perturbation structures selected by the resolvent analysis are those whose Reynolds stresses force the mean flow in such a way that the mean flow generates exactly the aforementioned perturbations, while also accounting for the effect of the incoherent scale. The model does not require any input from numerical or experimental data, and accurately predicts the saturation of the forced coherent disturbances, as established from comparison to time-averages of unsteady RANS simulation data.

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