Chen, Chang-Hsin (2018-12). Shock-Turbulence Interactions at High Turbulence Intensities: Theory and Direct Numerical Simulations. Doctoral Dissertation. Thesis uri icon

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.
  • 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.

publication date

  • December 2018