Pseudocompressible approximation and statistical turbulence modeling: application to shock tube flows

Area of Science:

• Fluid Dynamics
• Turbulence Modeling
• Computational Fluid Dynamics

Background:

• Turbulent mixing flows in shock tubes present challenges for accurate modeling due to compressibility effects.
• Existing models often struggle to capture the nuances of rapid distortions and diffusion-dissipation in these flows.

Purpose of the Study:

• To derive a pseudocompressible approximation applicable to turbulent mixing flows in shock tubes.
• To investigate the influence of key dimensionless numbers on flow compressibility.
• To analyze the impact of the approximation on statistical turbulence models.

Main Methods:

• Asymptotic analysis was employed to derive the pseudocompressible approximation.
• The analysis considered the roles of turbulent, deformation, stratification, and buoyancy force Mach numbers.
• Direct numerical simulation of a shock tube flow was performed for validation.

Main Results:

• A novel pseudocompressible approximation for shock tube turbulent mixing flows was successfully derived.
• The study identified four critical dimensionless numbers governing flow compressibility.
• The analysis revealed implications for the evolution of density variance, flux, and turbulent energy transport.

Conclusions:

• The derived pseudocompressible approximation offers a more accurate approach for modeling turbulent mixing in shock tubes.
• Understanding the interplay of the identified dimensionless numbers is crucial for improving turbulence models.
• Direct numerical simulations confirmed the validity and utility of the proposed approximation.