Shock-wave structure based on the Navier-Stokes-Fourier equations

Area of Science:

• Fluid dynamics
• Thermodynamics
• Statistical mechanics

Background:

• Plane shock waves are fundamental phenomena in fluid dynamics.
• Understanding shock wave structure in dilute gases is crucial for various applications.
• The Navier-Stokes-Fourier constitutive equations provide a macroscopic framework for fluid behavior.

Purpose of the Study:

• To investigate plane shock waves in dilute gases using established physical principles.
• To evaluate the applicability of the soft sphere model in describing shock wave phenomena.
• To analyze the relationship between gas properties (viscosity, thermal conductivity) and temperature within shock waves.

Main Methods:

• Utilizing the Navier-Stokes-Fourier constitutive equations for theoretical analysis.
• Employing the soft sphere model to represent gas molecular interactions.
• Comparing theoretical predictions with experimental data for normalized density profiles.

Main Results:

• The Navier-Stokes-Fourier equations were successfully applied to model plane shock waves.
• The soft sphere model demonstrated a good fit with experimental normalized density profiles.
• Viscosity and thermal conductivity were found to be proportional to a power of temperature.

Conclusions:

• The soft sphere model is a suitable approach for describing shock waves in dilute gases.
• The temperature dependence of viscosity and thermal conductivity is a key factor in shock wave structure.
• This research validates macroscopic equations for microscale phenomena.