Transient separation of compressible flows over convex walls.
Date
2011-09-27
Authors
Muritala, Adam Olatunji
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Abstract
This study investigated the shock induced transient separation of compressible flows over
convex walls using both numerical and experimental analysis. The numerical simulations
solved the Reynolds Averaged form of the Navier–Stokes equations, using unstructured
quadrilateral cells. Some results are presented in numerical schlieren images for analysis.
Experiments were conducted in a purpose built shock tube that allows for a large scale
testing an order of magnitude greater than previously examined. The images of the
interactions were captured with schlieren arrangement and later compared to the pictures
from numerical schlieren analysis.
Three flow situations were examined: 30 corner in which the presence of the wall
influences the flow; a 90 corner in which the internal flow features were not affected by
the wall downstream; and a convex circular wall with flow influenced by the wall radius.
The development of instabilities and the break-up of shear layer into vortices are evident
in both experimental and numerical images especially on a 90 corner wall. The flow
over the 30 corner wall developed instability at very low incident shock Mach numbers.
At incident shock Mach 1.5 series of lambda shocks formed above the shear layer with
strong instability under it. The instability developed into a homogenous turbulent flow
after long times of the diffraction process.
The flow behind the diffracting shock Mach number of 1.5 on curved walls did not
separate at small times but separated after long time of diffraction process. A three-shock
configuration was observed in the perturbed region from incident Mach number 1.5 while
two were observed at higher Mach numbers but the upper triple point faded away with
time when the Mach number is approaching 3.0. Both the secondary and recompression shocks exist for the range of incident shock Mach numbers between 1.5 and 2.0.
However, the secondary shock could not be sustained at higher Mach numbers and the
recompression shock was fading away as the diffraction process progresses downstream
before finally disappearing at a later time.
The movement of separation point increases with time for high incident shock Mach
numbers but decreases with time for low incident shock Mach numbers. Separation and
shear angle are independent of the wall radius for high Mach number incident shocks. A
kink that is formed at the lower extremity of the contact surface is proposed to be due to
sudden change in radial velocity as a result of near wall effects which enhanced an
increase in tangential momentum.
For high Mach number incident shocks the flow features are similar for the three
geometries except that two triple points are formed on curved walls. Many flow features
that only appeared at high incident shock Mach numbers in the conventionally sized
shock tubes were observed at low Mach numbers in the present large scale tests.
The final analysis showed that the global flow behaviour behind a diffracted shock wave
is well captured in large scale experimentations and the detailed flow behaviour is
predicted better using SST k- turbulent model.