Shock Structures Using the OBurnett Equations in Combination with the Holian Conjecture
In the present work, we study the normal shock wave flow problem using a combination of the OBurnett equations and the Holian conjecture. The numerical results of the OBurnett equations for normal shocks established several fundamental aspects of the equations such as the thermodynamic consistency o...
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MDPI AG
2021-11-01
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| Online Access: | https://www.mdpi.com/2311-5521/6/12/427 |
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| author | Ravi Sudam Jadhav Amit Agrawal |
| author_facet | Ravi Sudam Jadhav Amit Agrawal |
| author_sort | Ravi Sudam Jadhav |
| collection | DOAJ |
| description | In the present work, we study the normal shock wave flow problem using a combination of the OBurnett equations and the Holian conjecture. The numerical results of the OBurnett equations for normal shocks established several fundamental aspects of the equations such as the thermodynamic consistency of the equations, and the existence of the heteroclinic trajectory and smooth shock structures at all Mach numbers. The shock profiles for the hydrodynamic field variables were found to be in quantitative agreement with the direct simulation Monte Carlo (DSMC) results in the upstream region, whereas further improvement was desirable in the downstream region of the shock. For the discrepancy in the downstream region, we conjecture that the viscosity–temperature relation (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>μ</mi><mo>∝</mo><msup><mi>T</mi><mi>φ</mi></msup></mrow></semantics></math></inline-formula>) needs to be modified in order to achieve increased dissipation and thereby achieve better agreement with the benchmark results in the downstream region. In this respect, we examine the Holian conjecture (HC), wherein transport coefficients (absolute viscosity and thermal conductivity) are evaluated using the temperature in the direction of shock propagation rather than the average temperature. The results of the modified theory (OBurnett + HC) are compared against the benchmark results and we find that the modified theory improves upon the OBurnett results, especially in the case of the heat flux shock profile. We find that the accuracy gain is marginal at lower Mach numbers, while the shock profiles are described better using the modified theory for the case of strong shocks. |
| first_indexed | 2024-03-10T04:09:22Z |
| format | Article |
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| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-03-10T04:09:22Z |
| publishDate | 2021-11-01 |
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| spelling | doaj.art-931ab4dfd00743ff8859c0bd16738e032023-11-23T08:15:21ZengMDPI AGFluids2311-55212021-11-0161242710.3390/fluids6120427Shock Structures Using the OBurnett Equations in Combination with the Holian ConjectureRavi Sudam Jadhav0Amit Agrawal1Department of Mechanical Engineering, Indian Institute of Technology—Bombay Powai, Mumbai 400076, IndiaDepartment of Mechanical Engineering, Indian Institute of Technology—Bombay Powai, Mumbai 400076, IndiaIn the present work, we study the normal shock wave flow problem using a combination of the OBurnett equations and the Holian conjecture. The numerical results of the OBurnett equations for normal shocks established several fundamental aspects of the equations such as the thermodynamic consistency of the equations, and the existence of the heteroclinic trajectory and smooth shock structures at all Mach numbers. The shock profiles for the hydrodynamic field variables were found to be in quantitative agreement with the direct simulation Monte Carlo (DSMC) results in the upstream region, whereas further improvement was desirable in the downstream region of the shock. For the discrepancy in the downstream region, we conjecture that the viscosity–temperature relation (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>μ</mi><mo>∝</mo><msup><mi>T</mi><mi>φ</mi></msup></mrow></semantics></math></inline-formula>) needs to be modified in order to achieve increased dissipation and thereby achieve better agreement with the benchmark results in the downstream region. In this respect, we examine the Holian conjecture (HC), wherein transport coefficients (absolute viscosity and thermal conductivity) are evaluated using the temperature in the direction of shock propagation rather than the average temperature. The results of the modified theory (OBurnett + HC) are compared against the benchmark results and we find that the modified theory improves upon the OBurnett results, especially in the case of the heat flux shock profile. We find that the accuracy gain is marginal at lower Mach numbers, while the shock profiles are described better using the modified theory for the case of strong shocks.https://www.mdpi.com/2311-5521/6/12/427normal shockOBurnett equationsHolian conjectureMach numbernon-equilibrium flows |
| spellingShingle | Ravi Sudam Jadhav Amit Agrawal Shock Structures Using the OBurnett Equations in Combination with the Holian Conjecture Fluids normal shock OBurnett equations Holian conjecture Mach number non-equilibrium flows |
| title | Shock Structures Using the OBurnett Equations in Combination with the Holian Conjecture |
| title_full | Shock Structures Using the OBurnett Equations in Combination with the Holian Conjecture |
| title_fullStr | Shock Structures Using the OBurnett Equations in Combination with the Holian Conjecture |
| title_full_unstemmed | Shock Structures Using the OBurnett Equations in Combination with the Holian Conjecture |
| title_short | Shock Structures Using the OBurnett Equations in Combination with the Holian Conjecture |
| title_sort | shock structures using the oburnett equations in combination with the holian conjecture |
| topic | normal shock OBurnett equations Holian conjecture Mach number non-equilibrium flows |
| url | https://www.mdpi.com/2311-5521/6/12/427 |
| work_keys_str_mv | AT ravisudamjadhav shockstructuresusingtheoburnettequationsincombinationwiththeholianconjecture AT amitagrawal shockstructuresusingtheoburnettequationsincombinationwiththeholianconjecture |