{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T03:40:16Z","timestamp":1758685216295,"version":"3.44.0"},"publisher-location":"400 Commonwealth Drive, Warrendale, PA, United States","reference-count":34,"publisher":"SAE International","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>&lt;div class=\"section abstract\"&gt;&lt;div class=\"htmlview paragraph\"&gt;In this work, an investigation of the enthalpy effects on the thermochemical non-equilibrium in hypersonic nozzles is performed. Three different nozzles, with different geometries and stagnation enthalpy conditions are used in this study. The three cases, two of them with stagnation enthalpy conditions of 3.3 MJ\/kg and 7.56 MJ\/kg, use molecular nitrogen as the testing fluid and in the third case, corresponding to the higher enthalpy condition of 23.8 MJ\/kg, the fluid is partially dissociated air composed by five neutral species (N&lt;sub&gt;2&lt;\/sub&gt;, O&lt;sub&gt;2&lt;\/sub&gt;, NO, N and O). A reliable numerical model, previously validated by the authors, using non-equilibrium Navier-Stokes-Fourier equations within a density-based algorithm is here employed in the OpenFOAM framework. After an estimation of the discretization uncertainties by using the Richardson extrapolation method and Roache\u2019s Grid Convergence Index, the results are obtained by using a sufficient independent grid for each case. It was found that the nozzle with the higher non-equilibrium impact on the flow properties, was the one with the higher expansion ratio, with the difference between equilibrium and non-equilibrium of 17% for the Mach number, 35% for the static pressure and 38% for the static temperature. Using three different stagnation conditions, of 4.92 MJ\/kg, 5.98 MJ\/kg, and 7.56 MJ\/kg, for that nozzle, it was revealed that the increasing of the stagnation enthalpy at the reservoir leads to an increment of the degree of non-equilibrium inside the nozzle, reaching its maximum at the nozzle exit. Increasing the stagnation enthalpy in 1.58 MJ\/kg leads to an increment of the non-equilibrium degree in 3.4% for the Mach number, 5.5% for the static pressure and 6.6% for the static temperature.&lt;\/div&gt;&lt;\/div&gt;<\/jats:p>","DOI":"10.4271\/2024-01-1935","type":"proceedings-article","created":{"date-parts":[[2024,3,5]],"date-time":"2024-03-05T21:15:48Z","timestamp":1709673348000},"source":"Crossref","is-referenced-by-count":1,"title":["Computational Modelling of Hypersonic Nozzles: The Influence of Enthalpy on the Flow Thermochemistry"],"prefix":"10.4271","volume":"1","author":[{"given":"Odelma","family":"Teixeira","sequence":"first","affiliation":[{"name":"Universidade da Beira Interior"}]},{"given":"Jose","family":"Pascoa","sequence":"additional","affiliation":[{"name":"Universidade da Beira Interior"}]}],"member":"2796","published-online":{"date-parts":[[2024,3,5]]},"reference":[{"key":"ref0","doi-asserted-by":"crossref","unstructured":"Teixeira ,  O.  and  \n \n Pascoa ,  J. \n Hypersonic Flow Simulation towards Space Propulsion Geometries SAE Int. J. Adv. Curr. Pract. Mobil. 2 2 2020 803 810 https:\/\/doi.org\/10.4271\/2019-01-1873","DOI":"10.4271\/2019-01-1873"},{"key":"ref1","doi-asserted-by":"crossref","unstructured":"Netterfield ,  M.P. \n Validation of a Navier-Stokes Code for Thermochemical Non-Equilibrium Flows 27th Thermophysics Conference 1992","DOI":"10.2514\/6.1992-2878"},{"key":"ref2","doi-asserted-by":"crossref","unstructured":"Grasso ,  F.  and  \n \n Marini ,  M. \n TVD Multigrid Solutions of Three-Dimensional Viscous Hypersonic Flows 33rd Aerospace Sciences Meeting and Exhibit 1995","DOI":"10.2514\/6.1995-470"},{"key":"ref3","doi-asserted-by":"crossref","unstructured":"Grasso ,  F.  and  \n \n Capano ,  G. \n Modeling of Ionizing Hypersonic Flows in Nonequilibrium J. Spacecr. Rockets 32 2 1995 217 224","DOI":"10.2514\/3.26599"},{"key":"ref4","doi-asserted-by":"crossref","unstructured":"Gnoffo ,  P. ,  \n \n Weilmuenster ,  K. ,  \n \n Hamilton ,  H.   II ,  \n \n Olynick ,  D. , and  \n \n Venkatapathy ,  E. \n Computational Aerothermodynamic Design Issues for Hypersonic Vehicles 32nd Thermophysics Conference 1997","DOI":"10.2514\/6.1997-2473"},{"key":"ref5","doi-asserted-by":"crossref","unstructured":"Candler ,  G. \n High Enthalpy Flow Simulation Challenges 29th AIAA, Plasmadynamics and Lasers Conference 1998","DOI":"10.2514\/6.1998-2749"},{"key":"ref6","doi-asserted-by":"crossref","unstructured":"Fuhrmann ,  H.D. ,  \n \n Hildebrand ,  J. , and  \n \n Lalicata ,  T. \n Aerothermodynamic Overview, X-34 J. Spacecr. Rockets 36 2 1999 153 159","DOI":"10.2514\/2.3437"},{"key":"ref7","doi-asserted-by":"crossref","unstructured":"Hollis ,  B. ,  \n \n Horvath ,  T. ,  \n \n Berry ,  S. ,  \n \n Hamilton ,  H.   II  \n et al. \n X-33 Computational Aeroheating Predictions and Comparisons with Experimental Data 33rd Thermophysics Conference 1999","DOI":"10.2514\/6.1999-3559"},{"key":"ref8","doi-asserted-by":"crossref","unstructured":"Sarma ,  G.S.R. \n Physico\u2013Chemical Modelling in Hypersonic Flow Simulation Prog. Aerosp. Sci. 36 3\u20134 2000 281 349","DOI":"10.1016\/S0376-0421(00)00004-X"},{"key":"ref9","doi-asserted-by":"crossref","unstructured":"Anderson ,  J.D.   Jr. \n Hypersonic and High-Temperature Gas Dynamics 2nd Reston,VA American Institute of Aeronautics and Astronautics 2006","DOI":"10.2514\/4.861956"},{"key":"ref10","doi-asserted-by":"crossref","unstructured":"Niu ,  Q. ,  \n \n Yuan ,  Z. ,  \n \n Chen ,  B. , and  \n \n Dong ,  S. \n Infrared Radiation Characteristics of a Hypersonic Vehicle under Time-Varying Angles of Attack Chinese J. Aeronaut. 32 4 2019 861 874","DOI":"10.1016\/j.cja.2019.01.003"},{"key":"ref11","doi-asserted-by":"crossref","unstructured":"Baurle ,  R.A.  and  \n \n Eklund ,  D.R. \n Analysis of Dual-Mode Hydrocarbon Scramjet Operation at Mach 4-6.5 J. Propuls. Power 18 5 2002 990 1002","DOI":"10.2514\/2.6047"},{"key":"ref12","doi-asserted-by":"crossref","unstructured":"Brune ,  A.J. ,  \n \n Hosder ,  S. ,  \n \n Campbell ,  D. ,  \n \n Gulli ,  S.  \n et al. \n Numerical Analysis of an Actively Cooled Low-Reynolds-Number Hypersonic Diffuser J. Thermophys. Heat Transf. 33 1 2019 32 48","DOI":"10.2514\/1.T5437"},{"key":"ref13","doi-asserted-by":"crossref","unstructured":"Hamaidia ,  W. ,  \n \n Zebbiche ,  T. ,  \n \n Sellam ,  M. , and  \n \n Allali ,  A. \n Performance Improvement of Supersonic Nozzles Design Using a High-Temperature Model Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng. 233 13 2019 4895 4910","DOI":"10.1177\/0954410019831862"},{"key":"ref14","doi-asserted-by":"crossref","unstructured":"Teixeira ,  O.  and  \n \n P\u00e1scoa ,  J. \n Catalytic Wall Effects for Hypersonic Nozzle Flow in Thermochemical Non-Equilibrium Acta Astronaut. 203 2023 48 59","DOI":"10.1016\/j.actaastro.2022.11.031"},{"key":"ref15","doi-asserted-by":"crossref","unstructured":"Casseau ,  V. ,  \n \n Palharini ,  R. ,  \n \n Scanlon ,  T. , and  \n \n Brown ,  R. \n A Two-Temperature Open-Source CFD Model for Hypersonic Reacting Flows, Part One: Zero-Dimensional Analysis Aerospace 3 4 2016 34","DOI":"10.3390\/aerospace3040034"},{"key":"ref16","doi-asserted-by":"crossref","unstructured":"Casseau ,  V. ,  \n \n Espinoza ,  D. ,  \n \n Scanlon ,  T. , and  \n \n Brown ,  R. \n A Two-Temperature Open-Source CFD Model for Hypersonic Reacting Flows, Part Two: Multi-Dimensional Analysis Aerospace 3 4 2016 45","DOI":"10.3390\/aerospace3040045"},{"key":"ref17","doi-asserted-by":"crossref","unstructured":"Park ,  C. \n Two-Temperature Interpretation of Dissociation Rate Data for N2 and O2 26th Aerospace Sciences Meeting 1988","DOI":"10.2514\/6.1988-458"},{"key":"ref18","doi-asserted-by":"crossref","unstructured":"Park ,  C. \n Review of Chemical-Kinetic Problems of Future NASA Missions. I - Earth Entries J. Thermophys. Heat Transf. 7 3 1993 385 398","DOI":"10.2514\/3.431"},{"key":"ref19","unstructured":"Landau ,  L.  and  \n \n Teller ,  E. \n On the Theory of Sound Dispersion Phys. Zeitschrift der Sowjetunion 10 34 1936 147 153"},{"key":"ref20","doi-asserted-by":"crossref","unstructured":"Millikan ,  R.C.  and  \n \n White ,  D.R. \n Systematics of Vibrational Relaxation J. Chem. Phys. 39 12 1963 3209 3213","DOI":"10.1063\/1.1734182"},{"key":"ref21","unstructured":"Park ,  C. \n Nonequilibrium Hypersonic Aerothermodynamics New York Wiley International 1990"},{"key":"ref22","doi-asserted-by":"crossref","unstructured":"Greenshields ,  C.J. ,  \n \n Weller ,  H.G. ,  \n \n Gasparini ,  L. , and  \n \n Reese ,  J.M. \n Implementation of Semi-Discrete, Non-Staggered Central Schemes in a Colocated, Polyhedral, Finite Volume Framework, for High-Speed Viscous Flows Int. J. Numer. Methods Fluids 63 1 2010 1 21","DOI":"10.1002\/fld.2069"},{"key":"ref23","doi-asserted-by":"crossref","unstructured":"Kurganov ,  A. ,  \n \n Noelle ,  S. , and  \n \n Petrova ,  G. \n Semidiscrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton--Jacobi Equations SIAM J. Sci. Comput. 23 3 2001 707 740","DOI":"10.1137\/S1064827500373413"},{"key":"ref24","doi-asserted-by":"crossref","unstructured":"Blottner ,  F.G. ,  \n \n Johnson ,  M. , and  \n \n Ellis ,  M. \n Chemically Reacting Viscous Flow Program for Multi-Component Gas Mixtures Albuquerque, NM, and Livermore, CA 1971","DOI":"10.2172\/4658539"},{"key":"ref25","unstructured":"Casseau ,  V. \n An Open-Source CFD Solver for Planetary Entry University of Strathclyde 2017"},{"key":"ref26","doi-asserted-by":"crossref","unstructured":"Wilke ,  C.R. \n A Viscosity Equation for Gas Mixtures J. Chem. Phys. 18 4 1950 517 519","DOI":"10.1063\/1.1747673"},{"key":"ref27","doi-asserted-by":"crossref","unstructured":"Sutton ,  K.  and  \n \n Gnoffo ,  P. \n Multi-Component Diffusion with Application to Computational Aerothermodynamics 7th AIAA\/ASME Joint Thermophysics and Heat Transfer Conference 1998","DOI":"10.2514\/6.1998-2575"},{"key":"ref28","unstructured":"Gupta ,  R.N. ,  \n \n Yos ,  J.M. , and  \n \n Thompson ,  R.A. \n 1989"},{"key":"ref29","doi-asserted-by":"crossref","unstructured":"Gillespie ,  W. ,  \n \n Bershader ,  D. ,  \n \n Sharma ,  S. , and  \n \n Ruffin ,  S. \n Raman Scattering Measurements of Vibrational and Rotational Distributions in Expanding Nitrogen 31st Aerospace Sciences Meeting 1993","DOI":"10.2514\/6.1993-274"},{"key":"ref30","doi-asserted-by":"crossref","unstructured":"Nagamatsu ,  H. ,  \n \n Geiger ,  R. , and  \n \n Sheer ,  R. \n Hypersonic Shock Tunnel ARS J. 29 5 1959 332 340","DOI":"10.2514\/8.4763"},{"key":"ref31","doi-asserted-by":"crossref","unstructured":"Russo ,  G. \n The Scirocco Wind Tunnel Project - Progress Report 1993 5th International Aerospace Planes and Hypersonics Technologies Conference 1993","DOI":"10.2514\/6.1993-5117"},{"key":"ref32","doi-asserted-by":"crossref","unstructured":"Richardson ,  L.F.  and  \n \n Gaunt ,  J.A. \n The Deferred Approach to the Limit Philos. Trans. R. Soc. London. Ser. A, Contain. Pap. a Math. or Phys. Character 226 636\u2013646 299 361 1927","DOI":"10.1098\/rsta.1927.0008"},{"key":"ref33","unstructured":"Roache ,  P.J. \n Verification and Validation in Computational Science and Engineering Albuquerque, NM Hermosa 1998"}],"event":{"name":"AeroTech Conference & Exhibition","start":{"date-parts":[[2024,3,12]]},"number":"345679","location":"Charlotte, North Carolina, United States","acronym":"AEROTECH"},"container-title":["SAE Technical Paper Series"],"original-title":[],"link":[{"URL":"https:\/\/saemobilus.sae.org\/downloads\/papers\/2024-01-1935\/Full%20Text%20PDF","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T03:20:35Z","timestamp":1758684035000},"score":1,"resource":{"primary":{"URL":"https:\/\/saemobilus.sae.org\/papers\/computational-modelling-hypersonic-nozzles-influence-enthalpy-flow-thermochemistry-2024-01-1935"}},"subtitle":[],"proceedings-subject":"SAE Technical Paper Series","short-title":[],"issued":{"date-parts":[[2024,3,5]]},"references-count":34,"URL":"https:\/\/doi.org\/10.4271\/2024-01-1935","relation":{},"ISSN":["0148-7191","2688-3627"],"issn-type":[{"type":"print","value":"0148-7191"},{"type":"electronic","value":"2688-3627"}],"subject":[],"published":{"date-parts":[[2024,3,5]]},"article-number":"2024-01-1935"}}