Shock-Turbulence Interactions at High Turbulence Intensities: Theory and Direct Numerical Simulations
Abstract
The interaction of turbulence with shock waves, while very common in nature
and engineered systems, is a very difficult problem from a theoretical, numerical
and experimental perspective. A main challenge comes from the two-way coupling
between the shock and turbulence which occurs over a wide range of scales in time
and space. As a result, many investigations have resorted to strong simplifications
such as the linearization of the governing equations or the assumption of mean conditions
across the shock independent of turbulent fluctuations. When the interaction
is strong, a condition that is realized when turbulence is relatively intense, much less
is known about the behavior of both the shock and turbulence. The focus of this
work, thus, is on shock-turbulence interactions (STI) at high turbulent intensities
using high-fidelity direct numerical simulations (DNS) that fully resolve the shock.
Highly accurate methods are developed to simulate a stationary normal shock as
the turbulent flow passes through the domain and used to generate a massive highly
resolved database at a wide range of conditions. The numerical study is guided by
novel theoretical work that result in analytical expressions for thermodynamic jumps
across the shock that, unlike previous results in the literature, depend on turbulence
characteristics. Comparison with DNS data shows that these expressions can indeed
predict quantitatively a number of statistical variables of interest. The theory also
predicts the emergence of new regimes of the interaction which results in distinct
amplification or attenuation of different variables depending on governing parameters.
This previously unseen behavior is verified against DNS as well. Results on the
shock structure are used to validate previous theoretical proposals and extend the
analysis to much stronger interactions which leads to the observation of a new regime
(a vanished regime in addition to the well-known wrinkled and broken regimes) in
which turbulence undergoes a classical spatial decay as it crosses the shock. Finally,
the amplification of turbulence across the shock is studied using our DNS results as
well as the large collection available in the literature. Disagreements in the literature
on Reynolds stresses are resolved by recognizing a special kind of similarity scaling on
two different parameters in two different limits. This analysis reconciles apparently
contradicting results in the literature. This analysis is extended to other quantities
of interest such as enstrophy and mass flux with similar success.
Citation
Chen, Chang-Hsin (2018). Shock-Turbulence Interactions at High Turbulence Intensities: Theory and Direct Numerical Simulations. Doctoral dissertation, Texas A & M University. Available electronically from https : / /hdl .handle .net /1969 .1 /174324.