scholarly journals Numerical Simulation for Mixed Convective Flow Over a Three-Dimensional Horizontal Backward Facing Step

2004 ◽  
Author(s):  
J. G. Barbosa Saldana ◽  
N. K. Anand ◽  
V. Sarin
Keyword(s):  
Convective Flow ◽  
Three Dimensional ◽  
Step Length ◽  
Expansion Ratio ◽  
The Other ◽  
Step Height ◽  
Streamwise Direction ◽  
Backward Facing Step ◽  
Thermal Features ◽  
Mixed Convective Flow

Laminar mixed convective flow over a three-dimensional horizontal backward-facing step heated from below at a constant temperature was numerically simulated using a finite volume technique and the most relevant hydrodynamic and thermal features for air flowing through the channel are presented in this work. The channel considered in this work has an aspect ratio AR = 4, and an expansion ratio ER = 2, while the total length in the streamwise direction is 52 times the step height (L = 52s) and the step length is equal to 2 times the step height (l = 2s). The flow at the duct entrance was considered to be hydro-dynamically fully developed and isothermal. The bottom wall of the channel was subjected to a constant high temperature while the other walls were treated to be adiabatic. The step was considered to be a thermal conductive block.

scholarly journals Numerical Simulation of Mixed Convective Flow Over a Three-Dimensional Horizontal Backward Facing Step

2005 ◽  
Vol 127 (9) ◽  
pp. 1027-1036 ◽  
Author(s):  
J. G. Barbosa Saldana ◽  
N. K. Anand ◽  
V. Sarin
Keyword(s):  
Convective Flow ◽  
Three Dimensional ◽  
Step Length ◽  
Expansion Ratio ◽  
Step Height ◽  
Streamwise Direction ◽  
Backward Facing Step ◽  
Thermal Features ◽  
Mixed Convective Flow ◽  
Thermally Conducting

Laminar mixed convective flow over a three-dimensional horizontal backward-facing step heated from below at a constant temperature was numerically simulated using a finite volume technique and the most relevant hydrodynamic and thermal features for air flowing through the channel are presented in this work. The channel considered in this work has an aspect ratio AR=4, and an expansion ratio ER=2, while the total length in the streamwise direction is 52 times the step height (L=52s) and the step length is equal to 2 times the step height (l=2s). The flow at the duct entrance was considered to be hydrodynamically fully developed and isothermal. The bottom wall of the channel was subjected to a constant high temperature while the other walls were treated to be adiabatic. The step was considered to be a thermally conducting block.

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.

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.

Eddy structures in a transitional backward-facing step flow

2007 ◽  
Vol 588 ◽  
pp. 43-58 ◽  
Author(s):  
H. P. RANI ◽  
TONY W. H. SHEU ◽  
ERIC S. F. TSAI
Keyword(s):  
Three Dimensional ◽  
Flow Simulation ◽  
Simulated Data ◽  
Numerical Data ◽  
Expansion Ratio ◽  
Transitional Flow ◽  
Backward Facing Step ◽  
Longitudinal Vortices ◽  
Eddy Structures ◽  
Spanwise Flow

In the present study, flow simulation has been carried out in a backward-facing step channel defined by an expansion ratio of 2.02 and a spanwise aspect ratio of 8 to provide the physical insight into the longitudinal and spanwise flow motions and to identify the presence of Taylor–Görtler-like vortices. The Reynolds numbers have been taken as 1000 and 2000, which fall in the category of transitional flow. The present simulated results were validated against the experimental and numerical data and the comparison was found to be satisfactory. The simulated results show that the flow becomes unsteady and exhibits a three-dimensional nature with the Kelvin–Helmholtz instability oscillations and Taylor–Görtler-Like longitudinal vortices. The simulated data were analysed to give an in-depth knowledge of the complex interactions among the floor and roof eddies, and the spiralling spanwise flow motion. Destabilization of the present incompressible flow system, with the amplified Reynolds number due to the Kelvin–Helmholtz and Taylor–Görtler instabilities, is also highlighted. A movie is available with the online version of the paper.

Global stability of the two-dimensional flow over a backward-facing step

2011 ◽  
Vol 693 ◽  
pp. 1-27 ◽  
Author(s):  
Daniel Lanzerstorfer ◽  
Hendrik C. Kuhlmann
Keyword(s):  
Three Dimensional ◽  
Physical Nature ◽  
Expansion Ratio ◽  
Two Dimensional ◽  
Backward Facing Step ◽  
Critical Mode ◽  
Large Step ◽  
Large Expansion ◽  
Amplification Process ◽  
Two Dimensional Flow

AbstractThe two-dimensional, incompressible flow over a backward-facing step is considered for a systematic variation of the geometry covering expansion ratios (step to outlet height) from 0.25 to 0.975. A global temporal linear stability analysis shows that the basic flow becomes unstable to different three-dimensional modes depending on the expansion ratio. All critical modes are essentially confined to the region behind the step extending downstream up to the reattachment point of the separated eddy. An energy-transfer analysis is applied to understand the physical nature of the instabilities. If scaled appropriately, the critical Reynolds number approaches a finite asymptotic value for very large step heights. In that case centrifugal forces destabilize the flow with respect to an oscillatory critical mode. For moderately large expansion ratios an elliptical instability mechanism is identified. If the step height is further decreased the critical mode changes from oscillatory to stationary. In addition to the elliptical mechanism, the strong shear in the layer emanating from the sharp corner of the step supports the amplification process of the critical mode. For very small step heights the basic state becomes unstable due to the lift-up mechanism, which feeds back on itself via the recirculating eddy behind the step, resulting in a steady critical mode comprising pronounced slow and fast streaks.

Buoyancy-assisted mixed convective flow over backward-facing step in a vertical duct using nanofluids

2012 ◽  
Vol 19 (1) ◽  
pp. 33-52 ◽  
Author(s):  
H. A. Mohammed ◽  
A. A. Al-aswadi ◽  
M. Z. Yusoff ◽  
R. Saidur
Keyword(s):  
Convective Flow ◽  
Backward Facing Step ◽  
Mixed Convective Flow ◽  
Vertical Duct

scholarly journals Convective instability and transient growth in flow over a backward-facing step

2008 ◽  
Vol 603 ◽  
pp. 271-304 ◽  
Author(s):  
H. M. BLACKBURN ◽  
D. BARKLEY ◽  
S. J. SHERWIN
Keyword(s):  
Convective Instability ◽  
Three Dimensional ◽  
Nonlinear Effects ◽  
Expansion Ratio ◽  
Base Flow ◽  
Time Interval ◽  
Transient Growth ◽  
Two Dimensional ◽  
Backward Facing Step ◽  
Transient Energy

Transient energy growths of two- and three-dimensional optimal linear perturbations to two-dimensional flow in a rectangular backward-facing-step geometry with expansion ratio two are presented. Reynolds numbers based on the step height and peak inflow speed are considered in the range 0–500, which is below the value for the onset of three-dimensional asymptotic instability. As is well known, the flow has a strong local convective instability, and the maximum linear transient energy growth values computed here are of order 80×103 at Re = 500. The critical Reynolds number below which there is no growth over any time interval is determined to be Re = 57.7 in the two-dimensional case. The centroidal location of the energy distribution for maximum transient growth is typically downstream of all the stagnation/reattachment points of the steady base flow. Sub-optimal transient modes are also computed and discussed. A direct study of weakly nonlinear effects demonstrates that nonlinearity is stablizing at Re = 500. The optimal three-dimensional disturbances have spanwise wavelength of order ten step heights. Though they have slightly larger growths than two-dimensional cases, they are broadly similar in character. When the inflow of the full nonlinear system is perturbed with white noise, narrowband random velocity perturbations are observed in the downstream channel at locations corresponding to maximum linear transient growth. The centre frequency of this response matches that computed from the streamwise wavelength and mean advection speed of the predicted optimal disturbance. Linkage between the response of the driven flow and the optimal disturbance is further demonstrated by a partition of response energy into velocity components.

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