Background Tracking the compressible fluid equations in the unsteady one-dimensional flow of the CO2 gas as an active medium when heated and forced to enter through special nozzles into the cavity of a laser-generating device leads to a supersonic propagation in the thermo-viscous fluid state in a bounded medium. Objective Highlighting theoretically the thermodynamically non-equilibrium properties of molecular gaseous media caused by the change in sign of the second viscosity and the corresponding dispersion parameters, such media are acoustically active, namely carbon dioxide gas under study. Methods of solution The reductive perturbation method of obtaining an exact solution to the Navier–Stokes equations of continuity, momentum, energy, and state takes the form of the Ginzburg–Landau complex cubic equation. For the sake of covering a wider insight into the system's behavior, this equation is solved exactly by the separation of variables, resorting to the factorization method first, then the complex Tanh-function method, and finally the Hamiltonian integral method. Results and Conclusion -After the nozzle exit during expansion, the temperature and pressure drastically reduce in a nonlinear oscillating manner. -There are significant differences in the velocity profiles upstream and downstream of the Shock zone due to the gas entrance in the shock area. Various graphs of the variables that describe the flow dynamics and thermodynamic states of the gas, such as particle velocity, temperature, density, entropy, entropy production, and the rate of change in its internal energy, are illustrated by symbolic software, showing good agreement with the experiment. It is concluded that the effect caused by addressing a negative sign to the volume viscosity, meaning that the gas is allowed to move with less resistivity to its motion, is caused by the transfer of energy from the internal degrees of freedom possessed in and released out of the carbon dioxide as a consequence of thermal excitation, adding up to its translational modes more energy to agitate. The system is thermodynamically unstable because the entropy production <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43994_2025_224_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$\sigma$</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation> is positive, but the rate of internal energy change <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43994_2025_224_Article_IEq2.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">$\frac{{{\text{dU}}}}{{{\text{dt}}}}$</EquationSource> <EquationSource Format="MATHML"><math> <mfrac> <mtext>dU</mtext> <mtext>dt</mtext> </mfrac> </math></EquationSource> </InlineEquation> fluctuates between positive and negative signs, which violate the condition of the tendency to equilibrium.

Flow and thermodynamics predictions of CO2 gas in laser cavities

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2025年8月19日

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Aly Maher Abourabia,
Reda Eid Tolba

摘要

Background

Tracking the compressible fluid equations in the unsteady one-dimensional flow of the CO2 gas as an active medium when heated and forced to enter through special nozzles into the cavity of a laser-generating device leads to a supersonic propagation in the thermo-viscous fluid state in a bounded medium.

Objective

Highlighting theoretically the thermodynamically non-equilibrium properties of molecular gaseous media caused by the change in sign of the second viscosity and the corresponding dispersion parameters, such media are acoustically active, namely carbon dioxide gas under study.

Methods of solution

The reductive perturbation method of obtaining an exact solution to the Navier–Stokes equations of continuity, momentum, energy, and state takes the form of the Ginzburg–Landau complex cubic equation. For the sake of covering a wider insight into the system's behavior, this equation is solved exactly by the separation of variables, resorting to the factorization method first, then the complex Tanh-function method, and finally the Hamiltonian integral method.

Results and Conclusion

-After the nozzle exit during expansion, the temperature and pressure drastically reduce in a nonlinear oscillating manner. -There are significant differences in the velocity profiles upstream and downstream of the Shock zone due to the gas entrance in the shock area. Various graphs of the variables that describe the flow dynamics and thermodynamic states of the gas, such as particle velocity, temperature, density, entropy, entropy production, and the rate of change in its internal energy, are illustrated by symbolic software, showing good agreement with the experiment. It is concluded that the effect caused by addressing a negative sign to the volume viscosity, meaning that the gas is allowed to move with less resistivity to its motion, is caused by the transfer of energy from the internal degrees of freedom possessed in and released out of the carbon dioxide as a consequence of thermal excitation, adding up to its translational modes more energy to agitate. The system is thermodynamically unstable because the entropy production $\sigma$ $σ$ is positive, but the rate of internal energy change $\frac{{{\text{dU}}}}{{{\text{dt}}}}$ $\frac{dU}{dt}$ fluctuates between positive and negative signs, which violate the condition of the tendency to equilibrium.