Laminar flow of an incompressible fluid past a bluff body: the separation, reattachment, eddy properties and drag

1979 ◽  
Vol 92 (1) ◽  
pp. 171-205 ◽  
Author(s):  
F. T. Smith
Keyword(s):  
Circular Cylinder ◽  
Large Scale ◽  
Bluff Body ◽  
Reynolds Numbers ◽  
The Body ◽  
Navier Stokes ◽  
Pressure Drag ◽  
Body Scale ◽  
Flow Situation ◽  
Large Scale Flow

The asymptotic theory for the laminar, incompressible, separating and reattaching flow past the bluff body is based on an extension of Kirchhoff's (1869) free-streamline solution. The flow field (only the upper half of which is discussed since we consider a symmetric body and flow) consists of two basic parts. The first is the flow on the body scalel*, which is described to leading order by the Kirchhoff solution with smooth inviscid separation, but with an$O(Re^{-\frac{1}{16}})$modification to explain fully the viscous separation (hereRe([Gt ] 1) is the Reynolds number). The influence of this$O(Re^{-\frac{1}{16}})$modification is determined for the circular cylinder. The second part is the large-scale flow, comprising mainly the eddy and the ultimate wake. The eddy has length scaleO(Rel*), widthO(Re½l*) and is of elliptical shape to keep the eddy pressure almost uniform. The ultimate wake is determined numerically and fixes the eddy length. The (asymptotically small) back pressure from the eddy acts (on the body scale) both in the free stream and in the eddy, and it has a marked effect at moderate Reynolds numbers; combined with the Kirchhoff solution, it predicts the pressure drag on a circular cylinder accurately, to within 10% whenRe= 5 and to within 4% whenRe= 50. Other predictions, for the eddy length and width, the front pressure and the eddy pressure, also show encouraging agreement with experiments and Navier-Stokes solutions at moderate Reynolds numbers (of about 30), both for the circular cylinder and the normal flat plate. Finally, an analysis in the appendix indicates that, in wind-tunnel experiments, the tunnel walls (even if widely spaced) can exert considerable influence on the eddy properties, eventually forcing an upper bound on the eddy width asReincreases instead of theO(l*Re½) growth appropriate to the unbounded flow situation.

scholarly journals Dynamical effect of the total strain induced by the coherent motion on local isotropy in a wake

2013 ◽  
Vol 720 ◽  
pp. 393-423 ◽  
Author(s):  
F. Thiesset ◽  
L. Danaila ◽  
R. A. Antonia
Keyword(s):  
Circular Cylinder ◽  
Large Scale ◽  
Bluff Body ◽  
Initial Conditions ◽  
Scale Up ◽  
Wake Flow ◽  
Total Strain ◽  
Coherent Motion ◽  
Square Cylinder ◽  
Local Isotropy

AbstractWe assess the extent to which local isotropy (LI) holds in a wake flow for different initial conditions, which may be geometrical (the shape of the bluff body which creates the wake) and hydrodynamical (the Reynolds number), as a function of the dynamical effects of the large-scale forcing (the mean strain, $ \overline{S} $, combined with the strain induced by the coherent motion, $\tilde {S} $). LI is appraised through either classical kinematic tests or phenomenological approaches. In this respect, we reanalyse existing LI criteria and formulate a new isotropy criterion based on the ratio between the turbulence strain intensity and the total strain ($ \overline{S} + \tilde {S} $). These criteria involve either time-averaged or phase-averaged quantities, thus providing a deeper insight into the dynamical aspect of these flows. They are tested using hot wire data in the intermediate wake of five types of obstacles (a circular cylinder, a square cylinder, a screen cylinder, a normal plate and a screen strip). We show that in the presence of an organized motion, isotropy is not an adequate assumption for the large scales but may be satisfied over a range of scales extending from the smallest dissipative scale up to a scale which depends on the total strain rate that characterizes the flow. The local value of this scale depends on the particular nature of the wake and the phase of the coherent motion. The square cylinder wake is the closest to isotropy whereas the least locally isotropic flow is the screen strip wake. For locations away from the axis, the study is restricted to the circular cylinder only and reveals that LI holds at scales smaller than those that apply at the wake centreline. Arguments based on self-similarity show that in the far wake, the strength of the coherent motion decays at the same rate as that of the turbulent motion. This implies the persistence of the same degree of anisotropy far downstream, independently of the scale at which anisotropy is tested.

scholarly journals Gyrotactic swimmers in turbulence: shape effects and role of the large-scale flow

2018 ◽  
Vol 856 ◽  
Author(s):  
M. Borgnino ◽  
G. Boffetta ◽  
F. De Lillo ◽  
M. Cencini
Keyword(s):  
Large Scale ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Preferential Sampling ◽  
Wide Range ◽  
Shape Effects ◽  
Dilute Suspensions ◽  
Large Scale Flow

We study the dynamics and the statistics of dilute suspensions of gyrotactic swimmers, a model for many aquatic motile microorganisms. By means of extensive numerical simulations of the Navier–Stokes equations at different Reynolds numbers, we investigate preferential sampling and small-scale clustering as a function of the swimming (stability and speed) and shape parameters, considering in particular the limits of spherical and rod-like particles. While spherical swimmers preferentially sample local downwelling flow, for elongated swimmers we observe a transition from downwelling to upwelling regions at sufficiently high swimming speed. The spatial distribution of both spherical and elongated swimmers is found to be fractal at small scales in a wide range of swimming parameters. The direct comparison between the different shapes shows that spherical swimmers are more clusterized at small stability and speed numbers, while for large values of the parameters elongated cells concentrate more. The relevance of our results for phytoplankton swimming in the ocean is briefly discussed.

A versatile taxonomy of low-dimensional vortex models for unsteady aerodynamics

2018 ◽  
Vol 858 ◽  
pp. 917-948 ◽  
Author(s):  
Darwin Darakananda ◽  
Jeff D. Eldredge
Keyword(s):  
Large Scale ◽  
Bluff Body ◽  
Point Vortex ◽  
Unsteady Aerodynamics ◽  
Shear Layers ◽  
Point Vortices ◽  
The Body ◽  
Vortex Sheets ◽  
Proposed Model ◽  
Low Dimensional

Inviscid vortex models have been demonstrated to capture the essential physics of massively separated flows past aerodynamic surfaces, but they become computationally expensive as coherent vortex structures are formed and the wake is developed. In this work, we present a two-dimensional vortex model in which vortex sheets represent shear layers that separate from sharp edges of the body and point vortices represent the rolled-up cores of these shear layers and the other coherent vortices in the wake. We develop a circulation transfer procedure that enables each vortex sheet to feed its circulation into a point vortex instead of rolling up. This procedure reduces the number of computational elements required to capture the dynamics of vortex formation while eliminating the spurious force that manifests when transferring circulation between vortex elements. By tuning the rate at which the vortex sheets are siphoned into the point vortices, we can adjust the balance between the model’s dimensionality and dynamical richness, enabling it to span the entire taxonomy of inviscid vortex models. This hybrid model can capture the development and subsequent shedding of the starting vortices with insignificant wall-clock time and remain sufficiently low-dimensional to simulate long-time-horizon events such as periodic bluff-body shedding. We demonstrate the viability of the method by modelling the impulsive translation of a wing at various fixed angles of attack, pitch-up manoeuvres that linearly increase the angle of attack from $0^{\circ }$ to $90^{\circ }$, and oscillatory pitching and heaving. We show that the proposed model correctly predicts the dynamics of large-scale vortical structures in the flow by comparing the distributions of vorticity and force responses from results of the proposed model with a model using only vortex sheets and, in some cases, high-fidelity viscous simulation.

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.

Identification of Bypass Transition Onset Markers Using Direct Numerical Simulation

2018 ◽  
Vol 140 (11) ◽  
Author(s):  
Shanti Bhushan ◽  
D. Keith Walters ◽  
S. Muthu ◽  
Crystal L. Pasiliao
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Direct Numerical Simulation ◽  
Large Scale ◽  
General Purpose ◽  
Navier Stokes ◽  
Bypass Transition ◽  
Flow Parameters ◽  
Rans Models ◽  
Large Scale Flow

Efficacy of several large-scale flow parameters as transition onset markers are evaluated using direct numerical simulation (DNS) of boundary layer bypass transition. Preliminary results identify parameters (k2D/ν) and u′/U∞ to be a potentially reliable transition onset marker, and their critical values show less than 15% variation in the range of Re and turbulence intensity (TI). These parameters can be implemented into general-purpose physics-based Reynolds-averaged Navier–Stokes (RANS) models for engineering applications.

Experimental Measurements and Computational Solutions for Aerodynamic Forces on an Ahmed Body at Various Ground Clearances

2003 ◽  
Author(s):  
Ilhan Bayraktar ◽  
Drew Landman ◽  
Tuba Bayraktar
Keyword(s):  
Large Scale ◽  
Bluff Body ◽  
Ground Plane ◽  
Computational Simulation ◽  
Simulation Method ◽  
Full Scale ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Ground Clearance ◽  
Ahmed Body

Reliable computer solutions to external aerodynamic flow fields on road vehicles are extremely desirable to road vehicle designers. In a previous publication a study was performed to validate a Reynolds-averaged unsteady Navier-stokes solution for the aerodynamic characterization of a large-scale bluff body. In the present study, the external aerodynamics of this body as a function of ground clearance are explored. Experimental force measurements are obtained in a full-scale wind tunnel using an Ahmed body model and test conditions representative of full-scale operating conditions. A Reynolds averaged Navier-Stokes solver is employed for computational simulation of the external flowfield at the same conditions. Experimental and computational force coefficients versus vehicle ground clearance are presented for fixed ground, moving ground, and suction slot road simulations. Experimental results using boundary layer suction are compared to computational results with a moving ground plane in order to better understand the effect of a road simulation method.

Prediction of Unsteady Loading on a Circular Cylinder in High Reynolds Number Flows Using Large Eddy Simulation

2005 ◽  
Author(s):  
Sung-Eun Kim ◽  
L. Srinivasa Mohan
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Turbulent Viscosity ◽  
Reynolds Numbers ◽  
Unstructured Meshes ◽  
Navier Stokes ◽  
Step Method ◽  
Fractional Step Method ◽  
Eddy Simulation ◽  
Large Eddy

Large eddy simulations were carried out for the flow around a hydrodynamically smooth, fixed circular cylinder at two Reynolds numbers, one at a subcritical Reynolds number (Re = 1.4 × 105) and the other at a supercritical Reynolds number (Re = 1.0 × 106). The computations were made using a parallelized finite-volume Navier-Stokes solver based on a multidimensional linear reconstruction scheme that allows use of unstructured meshes. Central differencing was used for discretization of both convection and diffusion terms. Time-advancement scheme, based on an implicit, non-iterative fractional-step method, was adopted in conjunction with a three-level, backward second-order temporal discretization. Subgrid-scale turbulent viscosity was modeled by a dynamic Smagorinsky model adapted to arbitrary unstructured meshes with the aid of a test-filter applicable to arbitrary unstructured meshes. The present LES results closely reproduced the flow features observed in experiments at both Reynolds numbers. The time-averaged mean drag coefficient, root-mean-square force coefficients and the frequency content of fluctuating forces (vortex-shedding frequency) are predicted with a commendable accuracy.

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.

Navier–Stokes solutions of unsteady separation induced by a vortex

2002 ◽  
Vol 465 ◽  
pp. 99-130 ◽  
Author(s):  
A. V. OBABKO ◽  
K. W. CASSEL
Keyword(s):  
Boundary Layer ◽  
Large Scale ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Recirculation Region ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Scale Interaction

Numerical solutions of the unsteady Navier–Stokes equations are considered for the flow induced by a thick-core vortex convecting along a surface in a two-dimensional incompressible flow. The presence of the vortex induces an adverse streamwise pressure gradient along the surface that leads to the formation of a secondary recirculation region followed by a narrow eruption of near-wall fluid in solutions of the unsteady boundary-layer equations. The locally thickening boundary layer in the vicinity of the eruption provokes an interaction between the viscous boundary layer and the outer inviscid flow. Numerical solutions of the Navier–Stokes equations show that the interaction occurs on two distinct streamwise length scales depending upon which of three Reynolds-number regimes is being considered. At high Reynolds numbers, the spike leads to a small-scale interaction; at moderate Reynolds numbers, the flow experiences a large-scale interaction followed by the small-scale interaction due to the spike; at low Reynolds numbers, large-scale interaction occurs, but there is no spike or subsequent small-scale interaction. The large-scale interaction is found to play an essential role in determining the overall evolution of unsteady separation in the moderate-Reynolds-number regime; it accelerates the spike formation process and leads to formation of secondary recirculation regions, splitting of the primary recirculation region into multiple corotating eddies and ejections of near-wall vorticity. These eddies later merge prior to being lifted away from the surface and causing detachment of the thick-core vortex.

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