Modeling of gas oscillations in a methane pyrolysis reactor using a locally non-equilibrium Navier–Stokes equation

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Abstract

A locally non-equilibrium Navier–Stokes equation, which accounts for the mean free path and relaxation time of microparticles, has been derived based on a modified Newton's law for shear stress in laminar gas flow within a plane-parallel channel. A numerical study of its solution for the case of a harmonic pressure drop along the channel revealed that the velocity variation at every point also exhibits harmonic behavior. It was found that the velocity oscillation amplitude decreases with an increase in the mean free path and relaxation time of the microparticles. For fixed microparticle parameters, the oscillation amplitude decreases with increasing gas viscosity and decreasing channel width. In the limiting case where the channel width becomes comparable to the mean free path, the velocity oscillation amplitude reaches an almost zero value, despite the constant amplitude of the pressure drop oscillations. It is demonstrated that the generation of gas flow oscillations can be utilized to clean the internal surfaces of a methane pyrolysis reactor from carbon deposits, which reduce the efficiency of the process for producing hydrogen and carbon.

About the authors

Yuriy A. Kryukov

Samara State Technical University

Email: yurakryukov1985@mail.ru
ORCID iD: 0000-0002-8505-132X
https://www.mathnet.ru/rus/person115309

Cand. Techn. Sci.; Engineer; Dept. of Physics

Russian Federation, 443100, Samara, Molodogvardeyskaya st., 244

Sergey V. Zaitsev

Samara State Technical University

Email: mr.zaitzev@mail.ru
ORCID iD: 0009-0000-4380-1201
SPIN-code: 1589-9724
Scopus Author ID: 59306743600
ResearcherId: LRV-2214-2024
https://www.mathnet.ru/rus/person202964

Postgraduate Student; Junior Researcher; Dept. of Physics

Russian Federation, 443100, Samara, Molodogvardeyskaya st., 244

Igor V. Kudinov

Samara State Technical University

Author for correspondence.
Email: igor-kudinov@bk.ru
ORCID iD: 0000-0002-9422-0367
SPIN-code: 4122-0072
Scopus Author ID: 35169937500
https://www.mathnet.ru/rus/person44183

Dr. Techn. Sci., Professor; Head of Department; Dept. of Physics

Russian Federation, 443100, Samara, Molodogvardeyskaya st., 244

Timur F. Amirov

Samara State Technical University

Email: tim_amiroff@mail.ru
ORCID iD: 0009-0008-6492-5164
SPIN-code: 4663-5983
https://www.mathnet.ru/rus/person213825

Postgraduate Student; Junior Researcher; Dept. of Physics

Russian Federation, 443100, Samara, Molodogvardeyskaya st., 244

Maksim V. Nenashev

Samara State Technical University

Email: nenashev.mv@samgtu.ru
ORCID iD: 0000-0003-3918-5340
Scopus Author ID: 56462953900
https://www.mathnet.ru/rus/person38904

Dr. Techn. Sci., Professor; Professor; Dept. of Solid Chemical Substance Technology

Russian Federation, 443100, Samara, Molodogvardeyskaya st., 244

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2. Figure 1. Uniform finite difference mesh

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3. Figure 2. Velocity distribution across the channel width at different time instants for $ A_1 = 0.42 $, $ F = A_2 = 0 $, $ {\sf Zh} \geqslant 3.0 $; dots represent the analytical solution according to (31)

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4. Figure 3. Velocity distribution at points $\eta = 0$ (curve 1), $\eta = 0.2$ (curve 2), $\eta = 0.4$ (curve 3), $\eta = 0.6$ (curve 4), $\eta = 0.8$ (curve 5) across the channel width over time for $F = 0$, $A_1 = 0.42$, $A_2 = 10$

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5. Figure 4. Velocity distribution at points $\eta = 0$ (curve 1), $\eta = 0.2$ (curve 2), $\eta = 0.4$ (curve 3), $\eta = 0.6$ (curve 4), $\eta = 0.8$ (curve 5) across the channel width over time for $F = 10$, $A_1 = 0.42$, $A_2 = 10 $

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6. Figure 5. Velocity distribution at points $\eta = 0$ (curve 1), $\eta = 0.2$ (curve 2), $\eta = 0.4$ (curve 3), $\eta = 0.6$ (curve 4), $\eta = 0.8$ (curve 5) across the channel width over time for $F = 50$, $A_1 = 0.42$, $A_2 = 10 $

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