Abstract
The thermal stability of a vibrationally non-equilibrium molecular gas with a fixed vibrational energy flowing in a circular tube with a constant surface temperature was theoretically analyzed. The analysis determined the boundaries for the existence of the vibrationally non-equilibrium gas state. It was shown that the upper bound for the existence of a vibrationally non-equilibrium state of a molecular gas increases linearly with increasing Reynolds number over the investigated range, 0 ≤ Re ≤ 550. It also increases when the length of the tube relative to its radius is decreased, and when the non-dimensional quantity, \({\delta ={\frac{\rho\varepsilon_{\rm eq}({\rm T}_{\rm S}){\rm r}_{0}^{2}}{\lambda\tau({\rm T}_{\rm S}){\rm T}_{\rm S}}}}\), is decreased. In this non-dimensional quantity, ρ is the density of the gas, TS is the tube surface temperature, τ is the gas vibrational relaxation time, ε eq is the gas vibrational energy at TS, and λ is the gas coefficient for heat conduction. To obtain a large storage of excess vibrational energy, low values of δ must be used.
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Abbreviations
- ε :
-
Excess gas vibrational energy
- ε eq :
-
Equilibrium gas vibrational energy
- ε c :
-
Critical excess gas vibrational energy
- T:
-
Gas translational temperature
- TS :
-
Tube surface temperature
- Tmax :
-
Maximum gas translational temperature along tube axis
- Tv :
-
Gas vibrational temperature
- τ :
-
Gas vibrational-relaxation time
- λ:
-
Gas heat-conduction coefficient for equilibrium degrees of freedom
- CV :
-
Gas specific-heat capacity for equilibrium degrees of freedom
- ρ :
-
Gas density
- U:
-
Gas velocity
- P:
-
Gas pressure
- μ :
-
Coefficient of gas viscosity
- r0 :
-
Tube radius
- L:
-
Tube length
- \({\gamma=\frac{{\rm L}}{{\rm r}_{\rm 0}}}\) :
-
Ratio of tube length to tube radius
- εeq(TS):
-
Equilibrium gas vibrational energy at tube surface temperature Ts
- \({\beta=\frac{\varepsilon_{\rm c}}{\varepsilon_{\rm eq} \left({{\rm T}_{\rm s}}\right)}}\) :
-
Non-dimensional critical vibrational energy
- τ(Ts):
-
Gas vibrational relaxation time at tube surface temperature Ts
- \({\delta=\frac{\rho\varepsilon_{\rm eq}\left({\rm T}_{\rm S}\right){\rm r}_{\rm 0}^{\rm 2}}{\lambda\tau\left({\rm T}_{\rm S}\right){\rm T}_{\rm S}}}\) :
-
Non-dimensional quantity containing gas parameters
- \({\phi_{\rm f}}\) :
-
Heat flux out of the gas by flow
- \({\phi_{\rm s}}\) :
-
Heat flux out of the gas by conduction
- \({\phi=\phi_{\rm f}/\phi_{\rm s}}\) :
-
Non-dimensional heat flux
- Re:
-
Reynolds number
References
Uvarov AV, Osipov AI, Pilipuk SA, Sakalov AI (1994) Convictivnaya Neostoychivast Neravnavisnava Gasa. Khimicheskaya Fizika 13: 217–224
Mukin RV, Osipov AI, Uvarov AV (2007) Stability of an inhomogeneous vibrationally- nonequilibrium flow in a waveguide. Fluid Dyn 42: 126–132
Kulaga EV, Osipov AI, Uvarov AV, Younis SM (1997) Thermal explosion in a vibrationally nonequilibrium gas. Chem Phys Rep 16: 759–772
Younis SM (2007) Boundaries of thermal stability of a vibrationally nonequilibrium flowing gas considering constant energy pumping power. J Phys Nat Sci 1: 1–5
Raizer YP (1991) Gas discharge physics. Springer, Berlin, p 100
Capitelli M, Ferreira C, Gordiets B, Osipov A (2000) Plasma kinetics in atmospheric gases. Springer, Berlin, p 105
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Younis, S.M. Analysis of the Thermal Stability of a Vibrationally Non-Equilibrium Molecular Gas with Fixed Vibrational Energy Flowing in a Circular Tube. Arab J Sci Eng 36, 137–143 (2011). https://doi.org/10.1007/s13369-010-0016-6
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DOI: https://doi.org/10.1007/s13369-010-0016-6