Reattachment of Three-Dimensional Flow Adjacent to Backward-Facing Step

2003 ◽  
Vol 125 (3) ◽  
pp. 422-428 ◽  
Author(s):  
J. H. Nie ◽  
B. F. Armaly
Keyword(s):  
Three Dimensional ◽  
Separated Flow ◽  
Streamwise Velocity ◽  
Convection Flow ◽  
Backward Facing Step ◽  
Dimensional Flow ◽  
Line Region ◽  
Two Dimensional Flow ◽  
Streamwise Velocity Component ◽  
Laminar Forced Convection

Numerical simulations for incompressible three-dimensional laminar forced convection flow adjacent to backward-facing step in rectangular duct are performed to examine the reattachment region of the separated flow on the stepped wall. The feasibility of utilizing the two-dimensional flow definition and the limiting streamline definition for identifying the reattachment line/region was examined. The downwash and the “jet-like” flow that develops near the sidewall creates significant spanwise flow adjacent to the stepped wall, making it difficult to identify a reattachment line/region both numerically and experimentally. The use of the line/region that identifies the location on a plane adjacent to the stepped wall where the gradient of the mean streamwise velocity component is zero ∂u/∂y|y=0=0 is recommended for code and apparatus validation of three-dimensional separated flow.

Perspective: Selected Benchmarks From Commercial CFD Codes

1995 ◽  
Vol 117 (2) ◽  
pp. 208-218 ◽  
Author(s):  
C. J. Freitas
Keyword(s):  
Three Dimensional ◽  
Separated Flow ◽  
Policy Statement ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Common Reference ◽  
Reynolds Number Flow ◽  
Flow Problems ◽  
Dimensional Flow ◽  
Two Dimensional Flow

This paper summarizes the results of a series of five benchmark simulations which were completed using commercial Computational Fluid Dynamics (CFD) codes. These simulations were performed by the vendors themselves, and then reported by them in ASME’s CFD Triathlon Forum and CFD Biathlon Forum. The first group of benchmarks consisted of three laminar flow problems. These were the steady, two-dimensional flow over a backward-facing step, the low Reynolds number flow around a circular cylinder, and the unsteady three-dimensional flow in a shear-driven cubical cavity. The second group of benchmarks consisted of two turbulent flow problems. These were the two-dimensional flow around a square cylinder with periodic separated flow phenomena, and the steady, three-dimensional flow in a 180-degree square bend. All simulation results were evaluated against existing experimental data and thereby satisfied item 10 of the Journal’s policy statement for numerical accuracy. The objective of this exercise was to provide the engineering and scientific community with a common reference point for the evaluation of commercial CFD codes.

Simulation of three-dimensional laminar forced convection flow of a radiating gas over an inclined backward-facing step in a duct under bleeding condition

2012 ◽  
Vol 227 (2) ◽  
pp. 332-345 ◽  
Author(s):  
M Atashafrooz ◽  
SA Gandjalikhan Nassab
Keyword(s):  
Heat Transfer ◽  
Forced Convection ◽  
Fluid Dynamic ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Discrete Ordinates ◽  
Convection Flow ◽  
Backward Facing Step ◽  
Forced Convection Flow ◽  
Laminar Forced Convection

This study presents a numerical analysis of three-dimensional laminar forced convection flow of a radiating gas over an inclined backward-facing step in a rectangular duct under bleeding condition. The fluid is treated as a gray, absorbing, emitting, and scattering medium. The three-dimensional Cartesian coordinate system is used to solve the governing equations which are the conservations of mass, momentum, and energy. These equations are solved numerically using the computational fluid dynamic techniques to obtain the temperature and velocity fields, while the blocked-off method is employed to simulate the incline surface. Discretized forms of these equations are obtained by the finite volume method and solved using the SIMPLE algorithm. Since the gas is considered as a radiating medium, besides the convective and conductive terms in the energy equation, the radiative term also presented. For computation of this term, the radiative transfer equation is solved numerically by the discrete ordinates method to find the divergence of radiative heat flux distribution inside the radiating medium. By this numerical procedure, the role of radiation heat transfer on convection flow of a radiating gas which has many engineering applications (for example in heat exchangers and combustion chambers) is studied in detail. Beside, the effects of bleeding coefficient, albedo coefficient, optical thickness, and the radiation–conduction parameter on heat transfer behavior of the system are investigated. Comparison of numerical results with the available data published in the open literature shows a good agreement.

Heat Transfer Enhancement of Separated Convection Flow Adjacent to Backward-Facing Step With Baffle

2006 ◽  
Author(s):  
Jianhu Nie ◽  
Yitung Chen ◽  
Lijian Sun ◽  
Hsuan-Tsung Hsieh
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Three Dimensional ◽  
Constant Heat Flux ◽  
Convection Flow ◽  
Spanwise Direction ◽  
Streamwise Direction ◽  
Backward Facing Step ◽  
Laminar Forced Convection

Simulations of three-dimensional laminar forced convection adjacent to inclined backward-facing step in rectangular duct are presented to examine effects of the baffle on flow and heat transfer distributions. The step height is maintained as constant. A baffle is mounted onto the upper wall and its distance from the backward-facing step is varied. The inlet flow is hydrodynamically steady and fully developed with uniform temperature. The bottom wall is heated with constant heat flux, while other walls are maintained as being thermally adiabatic. Velocity, temperature, Nusselt number, and friction coefficient distributions are presented. A baffle mounted onto the upper wall increases the magnitude of maximum Nuselt number at the stepped wall. One segment of the xu-line developing close to the backward-facing step becomes shorter with the decrease of the distance of the baffle from the backward-facing step. It becomes more relatively uniform in the spanwise direction as the distance decreases. The other segment developing adjacent to the sidewall moves further downstream as the baffle moves in the streamwise direction. The maximum Nusselt number does not appear at the center of the duct, as one may expect. It develops near the sidewall, and it moves further downstream as the location of the baffle moves in the streamwise direction. The friction coefficient at the stepped wall decreases as the distance of the baffle from the inlet increases.

Contracting ducts of finite length

1951 ◽  
Vol 2 (4) ◽  
pp. 254-271 ◽  
Author(s):  
L. G. Whitehead ◽  
L. Y. Wu ◽  
M. H. L. Waters
Keyword(s):  
Stream Function ◽  
Finite Length ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Relaxation Method ◽  
Two Dimensional ◽  
Dimensional Flow ◽  
Hodograph Plane ◽  
Two Dimensional Flow ◽  
Working Section

SummmaryA method of design is given for wind tunnel contractions for two-dimensional flow and for flow with axial symmetry. The two-dimensional designs are based on a boundary chosen in the hodograph plane for which the flow is found by the method of images. The three-dimensional method uses the velocity potential and the stream function of the two-dimensional flow as independent variables and the equation for the three-dimensional stream function is solved approximately. The accuracy of the approximate method is checked by comparison with a solution obtained by Southwell's relaxation method.In both the two and the three-dimensional designs the curved wall is of finite length with parallel sections upstream and downstream. The effects of the parallel parts of the channel on the rise of pressure near the wall at the start of the contraction and on the velocity distribution across the working section can therefore be estimated.

Three-dimensional flow in cavities

1963 ◽  
Vol 16 (4) ◽  
pp. 620-632 ◽  
Author(s):  
D. J. Maull ◽  
L. F. East
Keyword(s):  
Static Pressure ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Large Span ◽  
Dimensional Flow ◽  
Pressure Distributions ◽  
Oil Flow ◽  
Two Dimensional Flow

The flow inside rectangular and other cavities in a wall has been investigated at low subsonic velocities using oil flow and surface static-pressure distributions. Evidence has been found of regular three-dimensional flows in cavities with large span-to-chord ratios which would normally be considered to have two-dimensional flow near their centre-lines. The dependence of the steadiness of the flow upon the cavity's span as well as its chord and depth has also been observed.

Mixed Convection Adjacent to 3-D Backward-Facing Step

2000 ◽  
Author(s):  
A. Li ◽  
B. F. Armaly
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Buoyancy Force ◽  
Three Dimensional ◽  
The Other ◽  
Convection Flow ◽  
Backward Facing Step ◽  
Grashof Number ◽  
Recirculating Flow

Abstract Results from three-dimensional numerical simulation of laminar, buoyancy assisting, mixed convection airflow adjacent to a backward-facing step in a vertical rectangular duct are presented. The Reynolds number, and duct geometry were kept constant at Re = 200, AR = 8, ER = 2, and S = 1 cm. Heat flux at the wall downstream from the step was kept uniform, but its magnitude was varied to cover a Grashof number (Gr) range between 0.0 to 4000. All the other walls in the duct were kept at adiabatic condition. The flow, upstream of the step, is treated as fully developed and isothermal. The relatively small aspect ratio of the channel is selected specifically to focus on the developments of the three-dimensional mixed convection flow in the separated and reattached flow regions downstream from the step. The presented results focus on the effects of increasing the buoyancy force, by increasing the uniform wall heat flux, on the three-dimensional flow and heat transfer characteristics. The flow and thermal fields are symmetric about the duct’s centerline. Vortex generated near the sidewall, is the major contributor to the three dimensional behavior in the flow domain, and that feature increases as the Grashof number increases. Increasing the Grashof number results in an increase in the Nusselt number, the size of the secondary recirculating flow region, the size of the sidewall vortex, and the spanwise flow from the sidewall toward the center of the channel. On the other hand, the size of the primary reattachment region decreases with increasing the Grashof number. That region lifts away and partially detaches from the downstream wall at high Grashof number flow. The maximum Nusselt number occurs near the sidewalls and not at the center of the channel. The effects of the buoyancy force on the distributions of the three-velocity components, temperature, reattachment region, friction coefficient, and Nusselt number are presented, and compared with 2-D results.

The Elliptic Solution of the Secondary Flow Problem

1983 ◽  
Vol 105 (3) ◽  
pp. 530-535 ◽  
Author(s):  
S. Abdallah ◽  
A. Hamed
Keyword(s):  
Flow Field ◽  
Secondary Flow ◽  
Three Dimensional ◽  
Inviscid Flow ◽  
Elliptic Solution ◽  
Dimensional Flow ◽  
Flow Vorticity ◽  
Dependent Variables ◽  
Two Dimensional Flow ◽  
Uniqueness Of The Solution

This paper presents the elliptic solution of the inviscid incompressible secondary flow in curved passages. The three-dimensional flow field is synthesized between 3 sets of orthogonal nonstream surfaces. The two-dimensional flow field on each set of surfaces is considered to be resulting from a source/sink distribution. The distribution and strength of these sources are dependent on the variation in the flow properties normal to the surfaces. The dependent variables in this formulation are the velocity components, the total pressure, and the main flow vorticity component. The governing equations in terms of these dependent variables are solved on each family of surfaces using the streamlike function formulation. A new mechanism is implemented to exchange information between the solutions on the three family surfaces, resulting into a unique solution. In addition, the boundary conditions for the resulting systems of equations are carefully chosen to insure the existence and uniqueness of the solution. The numerical results obtained for the rotational inviscid flow in a curved duct are discussed and compared with the available experimental data.

Cellular flow in a partially filled rotating drum: regular and chaotic advection

2017 ◽  
Vol 825 ◽  
pp. 631-650 ◽  
Author(s):  
Francesco Romanò ◽  
Arash Hajisharifi ◽  
Hendrik C. Kuhlmann
Keyword(s):  
Three Dimensional ◽  
Reynolds Numbers ◽  
Chaotic Advection ◽  
Two Dimensional ◽  
Rotating Drum ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Heteroclinic Connection ◽  
Two Dimensional Flow ◽  
Chaotic Streamlines

The topology of the incompressible steady three-dimensional flow in a partially filled cylindrical rotating drum, infinitely extended along its axis, is investigated numerically for a ratio of pool depth to radius of 0.2. In the limit of vanishing Froude and capillary numbers, the liquid–gas interface remains flat and the two-dimensional flow becomes unstable to steady three-dimensional convection cells. The Lagrangian transport in the cellular flow is organised by periodic spiralling-in and spiralling-out saddle foci, and by saddle limit cycles. Chaotic advection is caused by a breakup of a degenerate heteroclinic connection between the two saddle foci when the flow becomes three-dimensional. On increasing the Reynolds number, chaotic streamlines invade the cells from the cell boundary and from the interior along the broken heteroclinic connection. This trend is made evident by computing the Kolmogorov–Arnold–Moser tori for five supercritical Reynolds numbers.

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