Strong shock as a stringent test for Onsager-Burnett equations

Jadhav, Ravi Sudam; Agrawal, Amit

doi:10.1103/physreve.102.063111

Cited by 13 publications

(7 citation statements)

References 36 publications

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“…In the present study, the internal structure of a one-dimensional normal shock wave is studied using the recently derived OBurnett equations. In our previous work (Jadhav & Agrawal 2020b), the equations were shown to give smooth shock structures at all Mach numbers with positive entropy generation across the shock and the clear existence of a heteroclinic trajectory for a demanding case of a strong shock (Ma = 134). In the present work, the aim was to verify these claims for a wide range of Mach numbers (3 ≤ Ma ≤ 9) with a special emphasis on the orbital structures in the phase space.…”

Section: Discussionmentioning

confidence: 90%

“…With above critical comments, we now make some important remarks with respect to the OBurnett equations. In our earlier work (Jadhav & Agrawal 2020b), the case of a very strong shock (Ma = 134) was studied using the OBurnett equations wherein several fundamental aspects of the equations were established. Without tweaking the equations in any way, mathematical evidence was put forward for the following important aspects: It is important to note that the conventional Burnett equations and the Grad 13 moment equations do not satisfy all these fundamental aspects.…”

Section: Advantages Of Using the Oburnett Equationsmentioning

confidence: 99%

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Improved theory for shock waves using the OBurnett equations

Jadhav

Gavasane²,

Agrawal

2021

J. Fluid Mech.

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The main goal of the present study is to thoroughly test the recently derived OBurnett equations for the normal shock wave flow problem for a wide range of Mach number ( $3 \leq Ma \leq 9$ ). A dilute gas system composed of hard-sphere molecules is considered and the numerical results of the OBurnett equations are validated against in-house results from the direct simulation Monte Carlo method. The primary focus is to study the orbital structures in the phase space (velocity–temperature plane) and the variation of hydrodynamic fields across the shock. From the orbital structures, we observe that the heteroclinic trajectory exists for the OBurnett equations for all the Mach numbers considered, unlike the conventional Burnett equations. The thermodynamic consistency of the equations is also established by showing positive entropy generation across the shock. Further, the equations give smooth shock structures at all Mach numbers and significantly improve upon the results of the Navier–Stokes equations. With no tweaking of the equations in any way, the present work makes two important contributions by putting forward an improved theory of shock waves and establishing the validity of the OBurnett equations for solving complex flow problems.

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Section: Discussionmentioning

confidence: 90%

Section: Advantages Of Using the Oburnett Equationsmentioning

confidence: 99%

Improved theory for shock waves using the OBurnett equations

Jadhav

Gavasane²,

Agrawal

2021

J. Fluid Mech.

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“…Readers are directed to the above-mentioned studies for a more detailed exploration of the differences and advantages of the OBurnett equations relative to the Burnett equations. This set of equations has been validated for several canonical problems involving non-equilibrium flow conditions Singh et al 2017;Jadhav & Agrawal 2020b; a consolidated account of the different validation cases can be found in Jadhav et al (2023). Specifically, the validation of the OBurnett equations for the force-driven Poiseuille flow problem (Jadhav et al 2017) is particularly relevant in the context of wall-bounded flows in the late-slip/transition regime.…”

Section: Introductionmentioning

confidence: 99%

“…This set of equations has been validated for several canonical problems involving non-equilibrium flow conditions (Jadhav, Singh & Agrawal 2017; Singh et al. 2017; Jadhav & Agrawal 2020 b , 2021; Yadav & Agrawal 2021); a consolidated account of the different validation cases can be found in Jadhav et al. (2023).…”

Section: Introductionmentioning

confidence: 99%

Derivation of extended-OBurnett and super-OBurnett equations and their analytical solution to plane Poiseuille flow at non-zero Knudsen number

Yadav,

Jonnalagadda,

Agrawal

2024

J. Fluid Mech.

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In this work, we analyse wall-bounded flows in the continuum to transition regime with the help of higher-order transport equations (super-set of the Navier–Stokes equation). Towards this, we incorporate second-order in Knudsen number accurate terms in the single-particle distribution function, and with this complete representation, we first derive the second-order accurate extended-OBurnett (EOBurnett) and third-order accurate super-OBurnett (SOBurnett) equations. We then demonstrate that these newly derived equations exhibit unconditional linear stability. We finally validate the equations by solving for plane Poiseuille flow and derive closed-form analytical solutions for the pressure and velocity fields. The pressure and velocity results thus obtained have been compared with direct simulation Monte Carlo (DSMC) data in the transition regime. The results from both the EOBurnett and SOBurnett equations are found to yield better agreement with DSMC data than that obtained from the Navier–Stokes equations. This improved agreement is attributed to the presence of additional terms in the proposed equations, which effectively capture the effect of the Knudsen layer near the wall. The obtained higher-order transport equations and the closed-form solution presented in this work are novel. The ability of the equations to describe the flow in the transition regime should form the basis for conducting further realistic analytical studies of wall-bounded flows in the future.

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“…Recent notable works on improving shock structure prediction results over the classical Navier-Stokes may include: a second-order continuum theory of Paolucci and Paolucci [41], a linear irreversible thermodynamic model of Velasco and Uribe [42], recast Navier-Stokes of Reddy and Dadzie [43], Onsager-Burnett equations of Jadhav and Agrawal [44]. These previous works paid less attention to temperature profile description across the shock layer.…”

Section: Introductionmentioning

confidence: 99%

Accurate Constitutive Relations for Shock Wave Structures in Gases

Reddy

Dadzie

2021

WIT Transactions on Engineering Sciences

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Predicting accurately shock wave structures in gases using an appropriate hydrodynamic model is still a challenge in extended hydrodynamic model development in rarefied gases. In this paper, we identified constitutive equations that provide better agreement for the prediction of shock structure in a monatomic gas in the Mach number range 1.3-4. The results obtained show an improvement upon those obtained previously in the bi-velocity hydrodynamics and are more accurate than in the hydrodynamic models from expansions method solutions to the Boltzmann equation.

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Strong shock as a stringent test for Onsager-Burnett equations

Cited by 13 publications

References 36 publications

Improved theory for shock waves using the OBurnett equations

Improved theory for shock waves using the OBurnett equations

Derivation of extended-OBurnett and super-OBurnett equations and their analytical solution to plane Poiseuille flow at non-zero Knudsen number

Accurate Constitutive Relations for Shock Wave Structures in Gases

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