T. P. Chiang

A numerical revisit of backward-facing step flow problem

In the present study we take a fresh look at a laminar flow evolving into a larger channel through a step configured in a backward-facing format. We conduct steady three-dimensional Navier–Stokes flow analysis in the channel using the step geometry and flow conditions reported by Armaly et al. This allows a direct comparison with the results of physical experiments, thus serving to validate the numerical results computed in the range of 100⩽Re⩽1000. Results show that there is generally excellent agreement between the present results and the experimental data for Re=100 and 389. Fair agreement for Re=1000 is also achieved, except in the streamwise range of 15⩽x⩽25. The main difference stems from the fact that the roof eddy is not extended toward the midspan in the channel with a span width 35 times of the height of the upstream channel. In the present study we also reveal that the flow at the plane of symmetry develops into a two-dimensional-like profile only when the channel width is increased up to 100 t...

Effect of Reynolds number on the eddy structure in a lid-driven cavity

SUMMARY In this paper we apply a finite volume method, together with a cost-effective segregated solution algorithm, to solve for the primitive velocities and pressure in a set of incompressible Navier‐Stokes equations. The well-categorized workshop problem of lid-driven cavity flow is chosen for this exercise, and results focus on the Reynolds number. Solutions are given for a depth-to-width aspect ratio of 1:1 and a span-to width aspect ratio of 3:1. Upon increasing the Reynolds number, the flows in the cavity of interest were found to comprise a transition from a strongly two-dimensional character to a truly three-dimensional flow and, subsequently, a bifurcation from a stationary flow pattern to a periodically oscillatory state. Finally, viscous (Tollmien‐Schlichting) travelling wave instability further induced

Side wall effects on the structure of laminar flow over a plane-symmetric sudden expansion

Abstract Computational investigations have been performed in order to study the side-wall effect on a fluid downstream of a channel expansion which is plane. The expansion ratio under investigation is 3 and the aspect ratios are 3, 3.5, 3.75, 4, 5, 6, 7, 8, 9, 10, 12, 18, 24, 48, in the three-dimensional analyses. For the flow with a value of Re=60 , results show symmetric nature of the flow when the channel aspect ratio has a value less than 3.5. Beyond this critical aspect ratio, flow symmetry can no longer be sustained due to the Coanda effect. This confirms the experimental observation that a decrease in aspect ratio has a stabilizing effect. Unless the aspect ratio is increased further to a value above 12, flow in the third dimension plays an essential role to characterize the inherent nature of the flow. In this study, we also confine ourselves to studying flow separation, reattachment, and recirculation by employing a theoretically rigorous theory of topology. Much insight into the vortical flow structure can be revealed from limiting streamlines, on which critical points, such as spiral focal points and saddles, are plotted.

On End-Wall Corner Vortices in a Lid-Driven Cavity

We conducted a flow simulation to study the laminar flow in a three-dimensional rectangular cavity. The ratio of cavity depth to width is 1:1, and the span to width aspect ratio (SAR) is 3:1. The governing equations defined on staggered grids were solved in a transient context by using a finite volume method, in conjunction with a segregated solution algorithm. Of the most apparent manifestation of three-dimensional characteristics, we addressed in this study the formation of corner vortices and its role in aiding the transport of fluid flows in the primary eddy and the secondary eddies.

FINITE VOLUME ANALYSIS OF SPIRAL MOTION IN A RECTANGULAR LID-DRIVEN CAVITY

SUMMARY With the purpose of providing physical insight into the developing spanwise flow motion and identifying the presence of Taylor-Gortler-like vortices, we conducted a flow simulation in a rectangular cavity defined by a square cross-section and a spanwise aspect ratio of 3: 1. The governing equations were solved for the transient processes by using a finite volume method in conjunction with segregated solution procedures. In the present work, attention is placed on the spiralling comer vortices near the two end walls and the longitudinal meandering Taylor-Gortler-like vortices. The investigated Reynolds number is taken to be 1500. As a vehicle for the present flow simulation, validation against analytic data was canied out first for a configuration similar to the problem of interest. This study demonstrates the feasibility of the employed computer code.

Topological flow structures in backward-facing step channels

Abstract The present paper is intended to solve the steady-state Navier-Stokes equations for different Reynolds numbers. Through out this paper, the incompressible fluid will be considered in three-dimensional channels with different spans. The flow field under investigation was characterized as having a backward-facing step across which a fully-developed three-dimensional channel flow expanded into the channel with an expansion ratio of 1.9432. Numerical solutions for this backward-facing step problem were obtained on the basis of the step height, 0.9423, various spans, taking on values up to 10, and Reynolds numbers as high as 800. Of the different flow conditions that were considered, we elaborate on the flow topology under the conditions of an intermediate Reynolds number, Re = 389, and the largest width of the channel, 10. Following Lighthill [Lighthill, M., Attachment and separation in three-dimensional flow. In Laminar Boundary Layers , Vol. 2(6), ed. L. Rosenhead, II. Oxford University Press, 1963, pp. 72–82.] [1], we apply topology theory, which provides a rigorous mathematical foundation for studying kinematically possible flows. The present computational results, together with the inferred flow topology, reveal details of the flow structure which suggest a mechanism for the development of strongly three-dimensional flow with increasing Reynolds numbers. The computation of ‘oil-flow’ streamlines improves the visualization of the flow field and helps sketch the complicated flow patterns by clarifying the three-dimensional flow separation just behind the step. The scope of this enhancement to improved visualization of flow structure is also extended to the flow reattachment on the floor as well as the roof recirculatory flow pattern, manifested itself by the upstream separation and downstream reattachment surfaces. Notably addressed is the separation-reattachment phenomenon emanating only from the roof near the two side walls.

Structural development of vortical flows around a square jet in cross-flow

The present computational study is devoted to unfolding the complex process of three–dimensional flow interaction around a square jet in cross–flow. The aim is to provide a clear understanding about the structural development of the entire vortical flow field, which may immensely enhance our knowledge regarding mutual interaction among various vortical structures that takes place around the jet. Careful attempts have been made to capture the detailed mechanism of formation of the near–field horseshoe–vortex system and the roll–up process of the hovering vortices. The rolled–up shear–layer hovering vortices, which wrap around the front and the lateral jet–cross–flow interface, are observed to initiate the Kelvin–Helmholtz–like instability. The present study also clearly displays the inception process of the counter–rotating vortex pair (CVP) from the shear layers that develop on the two lateral side walls of the jet pipe. In order to better understand the complete flow–interaction process and the governing flow physics, the simulation was performed for a moderate value of the Reynolds number (Re = 225), and for a jet–to–free–stream velocity ratio of 2.5. The interaction process between the streamwise wall vortices and the developed upright (or spin–off, or zipper) vortices in the downstream boundary layer is observed to contribute substantially in the structural development of the jet wake. The upright vortices were seen to originate from the tornado–like critical points on the channel floor shear layer, and subsequently the vortices lift themselves away from the channel floor to merge ultimately with the evolving CVP. Importantly, such merging processes are observed to locally enhance the CVP strength. Following the topological theory of Legendre, the depicted map of computed critical points and the separation lines helps to provide additional insight into the flow mechanism. The computed results clearly demonstrate the entire vortical flow–interaction process to its totality, including all the recent experimental predictions that are made for such flows. Notably, as it was experimentally verified for round jets in cross–flow, in the present configuration too, the flow separation on the channel floor is found to be the basic source of inception of the wall and the upright vortices. The separated flow in the vicinity of different wall vortical corelines joins to form the upright vortices.

VORTICAL FLOW OVER A 3-D BACKWARD-FACING STEP

Abstract Numerical simulations of Navier-Stokes equations were performed for incompressible Navier-Stokes flow inside a channel. The flow field under investigation was characterized as having a backward-facing step, with an expansion ratio γ = H / h = 1.9423, over which a fully developed channel flow is suddenly expanded into the channel with a channel width, B, to upstream channel height, h, ratio B /h = 2, 4, 6, and 10. Numerical solutions for this backward-facing step problem were obtained on the basis of span ratios and Reynolds numbers. For the Reynolds numbers considered, Re = 100, 389, 800, we elaborate on the changes in the flow topology according to solutions computed at Re a 389. We use topology theory as a guide to studying flows that are kinematically possible. This theory is mathematically rigorous and helps find critical points, from which we can sketch complicated flow patterns by clarifying the three-dimensional flow separation just behind the step and the flow reattachment on the downstre...

Numerical investigation of vortical evolution in a backward-facing step expansion flow

Abstract A numerical investigation of laminar flow over a backward-facing step is presented for the Reynolds number in the range of 50⩽Re⩽2500. The objective of this numerical investigation is to add to the existing knowledge of the backward-facing step flow to deepen our understanding of the expansion flow structure. We proceed with the analysis by verifying the computer code through the Pearson vortex problem. We then perform a parametric study by varying the Reynolds number, with the aim of determining whether or not there exists a critical Reynolds number, above which reattachment length on the channel floor decreases. We also concentrate on subjects that have been little explored in the flow, examples of which are the onset of a single vortex in the primary eddy and how the recirculating bubble containing flow reversals is torn into smaller eddies. Eddy distortion, leading to mobile saddle points, and the merging of eddies are also discussed in this study.

Bifurcations of Flow Through Plane Symmetric Channel Contraction

Computational investigations have been performed into the behavior of an incompre fluid flow in the vicinity of a plane symmetric channel contraction. Our aim is to de mine the critical Reynolds number, above which the flow becomes asymmetric with re to the channel geometry using the bifurcation diagram. Three channels, which are acterized by the contraction ratio, are studied and the critical Reynolds numbers determined as 3075, 1355, and 1100 for channels with contraction ratios of 2, 4, a respectively. The cause and mechanism explaining the transition from symmetric to metric states in the symmetric contraction channel are also provided. @DOI: 10.1115/1.1467643 #