Influence of upstream disturbances on the primary and secondary instabilities in a supersonic separated flow over a backward-facing step

2020 ◽  
Vol 32 (5) ◽  
pp. 056102 ◽  
Author(s):  
Stefan Hickel ◽  
Bas van Oudheusden
Keyword(s):  
Separated Flow ◽  
Backward Facing Step ◽  
Secondary Instabilities

Time-Dependent Laminar Backward-Facing Step Flow in a Two-Dimensional Duct

1988 ◽  
Vol 110 (3) ◽  
pp. 289-296 ◽  
Author(s):  
F. Durst ◽  
J. C. F. Pereira
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Separated Flow ◽  
Flow Region ◽  
Reynolds Numbers ◽  
Steady State Flow ◽  
Backward Facing Step ◽  
Step Flow ◽  
Recirculating Flow ◽  
State Flow

This paper presents results of numerical studies of the impulsively starting backward-facing step flow with the step being mounted in a plane, two-dimensional duct. Results are presented for Reynolds numbers of Re = 10; 368 and 648 and for the last two Reynolds numbers comparisons are given between experimental and numerical results obtained for the final steady state flow conditions. In the computational scheme, the convective terms in the momentum equations are approximated by a 13-point quadratic upstream weighted finite-difference scheme and a fully implicit first order forward differencing scheme is used to discretize the temporal derivatives. The computations show that for the higher Reynolds numbers, the flow starts to separate on the lower and upper corners of the step yielding two disconnected recirculating flow regions for some time after the flow has been impulsively started. As time progresses, these two separated flow regions connect up and a single recirculating flow region emerges. This separated flow region stays attached to the step, grows in size and approaches, for the time t → ∞, the dimensions measured and predicted for the separation region for steady laminar backward-facing flow. For the Reynolds number Re = 10 the separation starts at the bottom of the backward-facing step and the separation region enlarges with time until the steady state flow pattern is reached. At the channel wall opposite to the step and for Reynolds number Re = 368, a separated flow region is observed and it is shown to occur for some finite time period of the developing, impulsively started backward-facing step flow. Its dimensions change with time and reduce to zero before the steady state flow pattern is reached. For the higher Reynolds number Re = 648, the secondary separated flow region opposite to the wall is also present and it is shown to remain present for t → ∞. Two kinds of the inlet conditions were considered; the inlet mean flow was assumed to be constant in a first study and was assumed to increase with time in a second one. The predicted flow field for t → ∞ turned out to be identical for both cases. They were also identical to the flow field predicted for steady, backward-facing step flow using the same numerical grid as for the time-dependent predictions.

Experiments on Backward-Facing Step Flows Preceding a Filter

2007 ◽  
Author(s):  
S. Yao ◽  
C. Krishnamoorthy ◽  
F. W. Chambers
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Separated Flow ◽  
Reynolds Numbers ◽  
Velocity Profiles ◽  
Step Height ◽  
Reattachment Point ◽  
Backward Facing Step ◽  
Air Filters ◽  
Air Filter

The resistance of automotive air filters alters upstream pressure gradients and thereby affects flow separation, the velocity distributions over the filter, and the performance of the filter. Air filters provide a resistance sufficient to alter flows, but not enough to make face velocities uniform. The backward-facing step flow is an archetype with a separation that resembles those found in automotive air filter housings. To gain insight to the problem of separation and filters, experiments were conducted measuring velocity fields for air flows in a 10:1 aspect ratio rectangular duct with a backward-facing step with and without the resistance of an air filter mounted downstream. The expansion ratio for the step was 1:2. The filter was mounted 4.25 and 6.75 step heights downstream of the step; locations both upstream and downstream of the nominal 6 step-height no-filter reattachment point. Experiments were performed at four Reynolds numbers between 2000 and 10,000. The Reynolds numbers were based on step height and inlet maximum velocity. The inlet velocity profiles at the step were developed. A Laser Doppler Anemometer (LDA) was used to measure velocity profiles and map separated regions between the step and the filter. The results indicate that the filter tends to decrease the streamwise velocity on the non-separated side of the channel and increase it on the separated, step, side compared to the no-filter flow. Non-separated flow tends to separate due to the deceleration and separated flow reattaches before the filter, whether the filter is placed at 4.25 or 6.75 step heights. The literature shows that without a filter the reattachment location depends on the Reynolds number in the laminar and transitional regimes, but is constant for turbulent flow. However, the area of the reversed flow may vary with Reynolds number for turbulent flow. With the filter at 4.25 step heights, the area of reversing flow is reduced significantly, and the Reynolds number has little effect on the main properties of the flow. With the filter at 6.75 step heights, the reversing flow area decreases as the Reynolds number increases though the reattachment point is fixed just upstream of the filter.

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