Three-Dimensional Recirculation Flow in a Backward Facing Step

1994 ◽  
Vol 116 (2) ◽  
pp. 228-232 ◽  
Author(s):  
Chiang Shih ◽  
Chih-Ming Ho
Keyword(s):  
Velocity Field ◽  
Aspect Ratio ◽  
Recirculation Zone ◽  
Three Dimensional ◽  
Laser Doppler Anemometer ◽  
Separation Region ◽  
Two Dimensional ◽  
Small Aspect Ratio ◽  
Backward Facing Step ◽  
Recirculation Flow

The flow field behind a small aspect ratio (channel width/step height = 3) backward-facing step is examined using laser Doppler anemometer. All three velocity components inside the separation region are surveyed in detail. The velocity profile just upstream of the step is laminar and two-dimensional. The velocity field reveals that the reattachment and the flow in the recirculation zone are highly three-dimensional due to the small aspect ratio.

scholarly journals Surface, size and topological effects for some nematic equilibria on rectangular domains

2020 ◽  
Vol 25 (5) ◽  
pp. 1101-1123 ◽  
Author(s):  
Lidong Fang ◽  
Apala Majumdar ◽  
Lei Zhang
Keyword(s):  
Aspect Ratio ◽  
Point Defects ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Bifurcation Diagrams ◽  
Variable Formula ◽  
Limiting Profile ◽  
Switching Dynamics ◽  
Line Defects ◽  
Carry Over

We study nematic equilibria on rectangular domains, in a reduced two-dimensional Landau–de Gennes framework. These reduced equilibria carry over to the three-dimensional framework at a special temperature. There is one essential model variable, [Formula: see text], which is a geometry-dependent and material-dependent variable. We compute the limiting profiles exactly in two distinguished limits: the [Formula: see text] 0 limit relevant for macroscopic domains and the [Formula: see text] limit relevant for nanoscale domains. The limiting profile has line defects near the shorter edges in the [Formula: see text] limit, whereas we observe fractional point defects in the [Formula: see text] 0 limit. The analytical studies are complemented by some bifurcation diagrams for these reduced equilibria as a function of [Formula: see text] and the rectangular aspect ratio. We also introduce the concept of ‘non-trivial’ topologies and study the relaxation of non-trivial topologies to trivial topologies mediated via point and line defects, with potential consequences for non-equilibrium phenomena and switching dynamics.

Laminar Mixed Convection Adjacent to Three-Dimensional Backward-Facing Step

2001 ◽  
Vol 124 (1) ◽  
pp. 209-213 ◽  
Author(s):  
A. Li and ◽  
B. F. Armaly
Keyword(s):  
Nusselt Number ◽  
Mixed Convection ◽  
Reverse Flow ◽  
Three Dimensional ◽  
Flow Region ◽  
The Other ◽  
Backward Facing Step ◽  
Number Range ◽  
Grashof Number ◽  
Recirculation Flow

Simulations of three-dimensional laminar buoyancy-assisting mixed convection adjacent to a backward-facing step in a vertical rectangular duct are presented to demonstrate the influence of Grashof number on the distributions of the Nusselt number, and the reverse flow regions that develop adjacent to the duct’s walls. The Reynolds number, and duct’s geometry are kept constant: heat flux at the wall downstream from the step is kept uniform but its magnitude varied to cover a Grashof number range of 0–4000; all the other walls in the duct are kept at adiabatic condition; and the flow, upstream of the step, is treated as fully developed and isothermal. Increasing the Grashof number results in increasing the Nusselt number; the size of the secondary recirculation flow region adjacent to the stepped wall; the size of the reverse flow region adjacent to the sidewall and the flat wall; and the spanwise flow from the sidewall toward the center of the duct. On the other hand, the size of the primary recirculation flow region adjacent to the stepped wall decreases and detaches partially from the heated stepped wall as the Grashof number increases. Details are presented and discussed.

Three-Dimensional Simulation of Gas Flow in Microducts

2005 ◽  
Author(s):  
Abhishek Agrawal ◽  
Amit Agrawal
Keyword(s):  
Aspect Ratio ◽  
Knudsen Number ◽  
Gas Flow ◽  
Flow Direction ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Streamwise Velocity ◽  
Theoretical Development ◽  
Width Ratio ◽  
Two Dimensional

Three-dimensional lattice Boltzmann method based simulations of a microduct have been undertaken in this paper. The objective is to understand the different physical phenomena occurring at these small scales and to investigate when the flow can be treated as two-dimensional. Towards this end, the Knudsen number and aspect ratio (depth to width ratio) are varied for a fixed pressure ratio. The pressure in the microduct is non-linear with the non-linearity in pressure reducing with an increase in Knudsen number. The pressure and velocity behaves somewhat similar to two-dimensional microchannels even when the aspect ratio is unity. The slip velocity at the impenetrable wall has two components: along and perpendicular to the flow. Our results show that the streamwise velocity near the centerline is relatively invariant along the depth for aspect ratio more than three, suggesting that the microduct can be modeled as a two-dimensional microchannel. However, the velocity component along the depth is never identically zero, implying that the flow is not truly two-dimensional. A curious change in vector direction in a plane normal to the flow direction is observed around aspect ratio of four. These first set of three-dimensional results are significant because they will help in theoretical development and flow modeling at micro scales.

Vortex merger in rotating stratified flows

2002 ◽  
Vol 455 ◽  
pp. 83-101 ◽  
Author(s):  
DAVID G. DRITSCHEL
Keyword(s):  
Aspect Ratio ◽  
Initial Conditions ◽  
Random Noise ◽  
Three Dimensional ◽  
Separation Distance ◽  
Two Dimensional ◽  
Initial Separation ◽  
Weak Exchange ◽  
First Results ◽  
Asymmetric Vortices

This paper describes the interaction of symmetric vortices in a three-dimensional quasi-geostrophic fluid. The initial vortices are taken to be uniform-potential-vorticity ellipsoids, of height 2h and width 2R, and with centres at (±d/2; 0, 0), embedded within a background flow having constant background rotational and buoyancy frequencies, f/2 and N respectively. This problem was previously studied by von Hardenburg et al. (2000), who determined the dimensionless critical merger distance d/R as a function of the height-to-width aspect ratio h/R (scaled by f/N). Their study, however, was limited to small to moderate values of h/R, as it was anticipated that merger at large h/R would reduce to that for two columnar two-dimensional vortices, i.e. d/R ≈ 3.31. Here, it is shown that no such two-dimensional limit exists; merger is found to occur at any aspect ratio, with d ∼ h for h/R [Gt ] 1.New results are also found for small to moderate values of h/R. In particular, our numerical simulations reveal that asymmetric merger is predominant, despite the initial conditions, if one includes a small amount of random noise. For small to moderate h/R, decreasing the initial separation distance d first results in a weak exchange of material, with one vortex growing at the expense of the other. As d decreases further, this exchange increases and leads to two dominant but strongly asymmetric vortices. Finally, for yet smaller d, rapid merger into a single dominant vortex occurs – in effect the initial vortices exchange nearly all of their material with one another in a nearly symmetrical fashion.

A Method to Predict Rudder Stall Inception from Two-dimensional Airfoil Data

2014 ◽  
Vol 58 (01) ◽  
pp. 1-19
Author(s):  
Michael J. Hughes ◽  
Young T. Shen
Keyword(s):  
Aspect Ratio ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Theoretical Formulation ◽  
Stall Inception ◽  
Low Aspect Ratio ◽  
Aspect Ratios ◽  
Flow Similarity ◽  
Naca 0015 ◽  
Naca 0012

The behavior of the force on a rudder changes significantly after the inception of stall, requiring different mathematical formulae to compute rudder forces prior-and poststall. Determining the inception angle at which stall occurs is important for predicting the rudder force on a maneuvering ship. A method to compute the inception angle of stall on a rudder is presented in this article. The theoretical formulation is based on a flow similarity approach, which relates three-dimensional rudder stall inception with two-dimensional airfoil data. Rudders are low-aspect ratio wings, and the three-dimensional lift is based on the low-aspect ratio wing theory. The two-dimensional airfoil stall data are obtained from National Advisory Committee for Aeronautics (NACA) reports. The derived theory is first validated with wind tunnel data from foils with a NACA 0015 profile of aspect ratios 1, 2, and 3. The theory is also validated with data from foils with a NACA 0012 profile and an aspect ratio of 2, 3, and 6.

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