Compressible ideal-gas turbulence subjected to homogeneous shear is investigated
at the rapid distortion limit. Specific issues addressed are (i) the interaction
between kinetic and internal energies and role of pressure-dilatation; (ii) the modifications
to pressure-strain correlation and Reynolds stress anisotropy and (iii) the effect
of the composition of velocity fluctuations (solenoidal vs. dilatational). Turbulence
evolution is found to be strongly influenced by gradient Mach number, the initial
solenoidal-to-dilatational ratio of the velocity field and the initial intensity of the
thermodynamic fluctuations. The balance between the initial fluctuations in velocity
and thermodynamic variables is also found to be very important. Any imbalance
in the two fluctuating fields leads to high levels of pressure-dilatation and intense
exchange.
For a given initial condition, it is found that the interaction via the pressuredilatation
term between the momentum and energy equations reaches a peak at an
intermediate gradient Mach number. The energy exchange between internal and kinetic
modes is negligible at very high or very low Mach number values due to lack of
pressure dilatation. When present, the exchange exhibits oscillations even as the sum
of the two energies evolves smoothly. The interaction between shear and solenoidal
initial velocity field generates dilatational fluctuations; for some intermediate levels of
shear Mach number dilatational fluctuations account for 20% of the total fluctuations.
Similarly, the interaction between shear and initial dilatation produces solenoidal oscillations. Somewhat surprisingly, the generation of solenoidal fluctuations increases
with gradient Mach number. Larger levels of pressure-strain correlation are seen with
dilatational rather than solenoidal initial conditions. Anisotropies of solenoidal and
dilatational components are investigated individually. The most interesting observation
is that solenoidal and dilatational turbulence tend toward a one componential
state but the energetic component is different in each case. As in incompressible shear
flows, with solenoidal fluctuations, the streamwise (1,1) component of Reynolds stress
is dominant. With dilatational fluctuations, the stream-normal (2,2) component is
the strongest. Overall, the study yields valuable insight into the linear processes in
high Mach number shear flows and identifies important closure modeling issues.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/6014 |
| Date | 17 September 2007 |
| Creators | Lavin, Tucker Alan |
| Contributors | Girimaji, Sharath S. |
| Publisher | Texas A&M University |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Thesis, text |
| Format | 5988166 bytes, electronic, application/pdf, born digital |
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