Computational Study of Miniature Tube for Biomedical Application

Computational Study of Miniature Tube for Biomedical Application | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Computational Study of Miniature Tube for Biomedical Application ZEYAULLAH ANSARI, Ramesh Babu Pallekonda This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1884965/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Needle-free injection devices are novel inventions to provide medications to patients without puncturing their skin with a needle. The present work focuses on the computational study of fluid flow characteristics inside the shock tube designed for liquid-type drug delivery and also evaluates these computational and analytical results with experimental observations. To observe primary and reflected shock pressure and shock Mach number for achieving the controlled microjet velocity to accelerate the drugs. ANSYS fluent has been utilized to solve the governing equations of energy, continuity, and momentum where density-based implicit solver is used to perform the transient analysis of the shock tube. Two combinations of gases (nitrogen-air and helium-air as a driver and driven section gas) have been considered for the CFD analysis. Four pressures ranging from 25-50 bar in the driver section and 1 bar in the driven area are considered as an initial condition to perform the simulations. The obtained results showed that the pressure and temperature ratios and Mach numbers are more significant for the helium-air model than for the nitrogen-air model at different operating pressures. These results are validated using analytical calculations, which also agree well with experimental results. Further, the microjet velocity has been calculated. The maximum value of microjet velocity for the nitrogen-air model is 62 m/s, whereas for the helium-air model is 106 m/s. The microjet velocity is more significant for the helium-air combination; hence the penetration depth on the target surface will be more effective on helium than nitrogen. Shock Wave Miniature Tube Biomedical Needle-less drug delivery CFD Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Full Text Tables Table 1 Parameters and values obtained from CFD simulation at 25 bar of operating pressure Parameters Values for Nitrogen Values for Helium x 1 0.1330 m 0.1421 m x 2 0.1560 m 0.1547 m t 1 0.000035 sec 0.000035 sec t 2 0.000070 sec 0.000049 sec Δx (x 2 -x 1 ) 0.023 m 0.0126 m Δt (t 2 -t 1 ) 0.000035 sec 0.000014 sec Initial temperature, T 1 300 K 300 K Primary shock temperature, T 2 475 K 674 K Reflected shock temperature, T 5 696 K 1120 K Driven pressure, P 1 (bar) 1 1 Driver pressure, P 4 (bar) 25 25 Primary shock pressure, P 2 (bar) 4.11 7.9 Reflected shock pressure, P 5 (bar) 13.9 35.1 Table 2 Values for standard parameters Parameters Values Specific heat ratio of air () 1.4 Specific heat ratio of nitrogen () 1.4 Specific heat ratio of helium 1.6 Gas constant (R) 287 J/Kg K Room temperature (T) 298 K Speed of the air (a 1 ) = 346 m/s Table 3 Results obtained from CFD simulations at 25-50 bar Filling pressure, Filling gas combination Mach No, 25 Nitrogen-Air 1.89 4.11 13.9 1.58 2.32 Helium-Air 2.60 7.9 35.02 2.24 3.73 32 Nitrogen-Air 2.03 4.82 15.80 1.71 2.53 Helium-Air 2.76 8.80 42.03 2.45 4.18 42 Nitrogen-Air 2.10 4.70 16.95 1.75 2.68 Helium-Air 2.96 10.10 50.03 2.68 4.70 50 Nitrogen-Air 2.18 5.45 19.35 1.88 2.79 Helium-Air 3.10 11.05 56.20 2.83 5.06 Table 4 CFD, analytical, and experimental results comparison at 25-50 bar Driver sections filled pressure, P 4 (bar) Parameters Shock Mach number, M s Reflected pressure, P 5 (bar) Fluctuation (%) P2/P1 T2/T1 T5/T1 CFD Analytical Exp. (Battula et al., 2016) CFD Analytical Exp. (Battula et al., 2016) M s P 5 Analytical 25 Nitrogen-Air 1.89 1.91 1.51 13.90 13.02 20 1.04 0.10 4.14 1.62 2.34 Helium-Air 2.60 2.59 - 35.02 34.22 - 0.38 2.30 7.76 2.23 3.73 32 Nitrogen-Air 2.03 1.99 1.75 15.80 14.90 23 1.95 6.00 4.51 1.68 2.49 Helium-Air 2.80 2.76 - 42.03 41.24 - 1.40 1.90 8.84 2.41 4.14 42 Nitrogen-Air 2.10 2.084 2.0 17.95 17.30 35 0.96 2.00 4.96 1.76 2.66 Helium-Air 2.96 2.95 - 50.30 50.03 - 0.23 0.50 10.14 2.63 4.64 50 Nitrogen-Air 2.18 2.15 2.3 19.35 19.20 40 1.39 0.70 5.29 1.82 2.79 Helium-Air 3.10 3.08 - 56.50 56.20 - 0.64 0.53 11.05 2.78 4.99 Table 5 Microjet velocity comparison at 25-50 bar Filled gas pressure, P4 Operating gas Microjet velocity, (m/s) CFD Analytical Experimental values, m/s (Battula et al., 2016) 25 Nitrogen-Air 50.9 51.3 63.2 Helium-Air 83.90 82.72 - 32 Nitrogen-Air 56.21 54.58 68.0 Helium-Air 91.68 90.81 - 42 Nitrogen-Air 58.22 58.82 83.6 Helium-Air 100.29 100.02 - 50 Nitrogen-Air 62.20 61.96 89.4 Helium-Air 106.30 106.01 - Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-1884965","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":127449644,"identity":"144d3ab1-1b27-4c5e-8f43-d4f8e12f3b04","order_by":0,"name":"ZEYAULLAH ANSARI","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0klEQVRIiWNgGAWjYLCCBLb/dvxgRgHxWpiTJRtADAOirWFjZtxwAMQgRot8+/GHHx6UsTEbn1+d+OGBAYM8v9gB/FoYexKSJRLO8fCZ3Xi7WQLoMMOZsxPwa2FmSDggkdgmwWx24+wGkJYEg9sEtLDxP2z+kdhmwLh5xtnNP4jSwiORzAa0JYFxA3/vNuJskZB4xmaRcO5AssQN3m0WCQYShP0i35/++OaPsgN2/P1nN9/8UWEjzy9NQAuSfWCVEsQqBwH+A6SoHgWjYBSMgpEEAPGAQsV8+eooAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0001-7779-3537","institution":"National Institute of Technology Meghalaya","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"ZEYAULLAH","middleName":"","lastName":"ANSARI","suffix":""},{"id":127449645,"identity":"12ba6b10-bbbd-44d2-b9b8-f2759d301e2c","order_by":1,"name":"Ramesh Babu Pallekonda","email":"","orcid":"","institution":"NIT Meghalaya: National Institute of Technology Meghalaya","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Ramesh","middleName":"Babu","lastName":"Pallekonda","suffix":""}],"badges":[],"createdAt":"2022-07-22 09:58:06","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-1884965/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-1884965/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":25936947,"identity":"d1c5559c-cc27-4fd6-b176-f33e60e11cb1","added_by":"auto","created_at":"2022-09-01 15:26:35","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":50641,"visible":true,"origin":"","legend":"\u003cp\u003eShock tube with initial boundary condition\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-1884965/v1/9af31086c9114d9b92dddc33.png"},{"id":25936167,"identity":"7710cebf-0cbc-4458-962f-2b3bf0de1764","added_by":"auto","created_at":"2022-09-01 15:21:35","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":131018,"visible":true,"origin":"","legend":"\u003cp\u003eShock wave flow field after instant rupture\u003cstrong\u003e \u003c/strong\u003eof the diaphragm\u003cstrong\u003e\u0026nbsp;\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-1884965/v1/3dc3e6c62242b61caead6f33.png"},{"id":25936168,"identity":"d808b029-436b-4e2f-81b7-05c11467f4f6","added_by":"auto","created_at":"2022-09-01 15:21:35","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":29911,"visible":true,"origin":"","legend":"\u003cp\u003ePressure distribution after bursting the diagram\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-1884965/v1/b9c56ca476067d37e0cdfa1b.png"},{"id":25936170,"identity":"8050d52a-27b5-4088-9480-02174e530759","added_by":"auto","created_at":"2022-09-01 15:21:35","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":35921,"visible":true,"origin":"","legend":"\u003cp\u003eTemperature distribution after reflection from the end wall\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-1884965/v1/d716196d03c408c52d160003.png"},{"id":25936949,"identity":"c92bff9e-55ed-440d-84cc-dbc11131d946","added_by":"auto","created_at":"2022-09-01 15:26:35","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":166418,"visible":true,"origin":"","legend":"\u003cp\u003eDistance-time graph comparison for 25 bar pressure of nitrogen and helium as driver gases\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-1884965/v1/4453f3c09174fcc7122413b3.png"},{"id":25936174,"identity":"93bca3e7-ecdb-4089-9669-3f127d626e41","added_by":"auto","created_at":"2022-09-01 15:21:35","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":275875,"visible":true,"origin":"","legend":"\u003cp\u003ePressure-distance graph comparison at 25 bars\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-1884965/v1/034fc09056a1b4186f56974b.png"},{"id":25936172,"identity":"ddb2f351-ea78-488e-89bb-0d35f8f0eab8","added_by":"auto","created_at":"2022-09-01 15:21:35","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":226278,"visible":true,"origin":"","legend":"\u003cp\u003eTemperature-distance graph comparison at 25 bars\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-1884965/v1/f9120ea144edab0f87e4a78a.png"},{"id":25936956,"identity":"d1de64e9-b79e-4be5-9c27-fe64501157a8","added_by":"auto","created_at":"2022-09-01 15:26:35","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":170589,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of diaphragm pressure ratios to Mach No. for nitrogen and helium gases\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-1884965/v1/40096afe2e0cfa5a01d230df.png"},{"id":25937466,"identity":"6751e7ca-283d-4113-92f9-e4d038075db0","added_by":"auto","created_at":"2022-09-01 15:31:35","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":257326,"visible":true,"origin":"","legend":"\u003cp\u003eError bar of Mach No. for nitrogen gas\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-1884965/v1/b1c60ea9c8c7c97c1ece8ccb.png"},{"id":25937465,"identity":"43dcfe33-99ec-47c8-b0fb-017684596e4e","added_by":"auto","created_at":"2022-09-01 15:31:35","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":257788,"visible":true,"origin":"","legend":"\u003cp\u003eError bar of reflected shock pressure for nitrogen gas\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-1884965/v1/a0c2aad544333fda7784b56d.png"},{"id":25936954,"identity":"fbd810cf-cb2c-42ae-8562-a4b8a2085aad","added_by":"auto","created_at":"2022-09-01 15:26:35","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":257166,"visible":true,"origin":"","legend":"\u003cp\u003eError bar of microjet velocity for nitrogen gas\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-1884965/v1/c28bb6318e81af79b7980900.png"},{"id":25936179,"identity":"044da031-7f89-418c-988d-ab41d51379c1","added_by":"auto","created_at":"2022-09-01 15:21:35","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":226021,"visible":true,"origin":"","legend":"\u003cp\u003eError bar of Mach No. for helium gas\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-1884965/v1/fccc81abb03fb2b4b5813617.png"},{"id":25936950,"identity":"4206d30d-3f13-4ed5-bcf6-a279fd974897","added_by":"auto","created_at":"2022-09-01 15:26:35","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":237499,"visible":true,"origin":"","legend":"\u003cp\u003eError bar of reflected shock pressure for helium gas\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-1884965/v1/31a5230372d644a97c1f172e.png"},{"id":25936175,"identity":"21ae4488-a85a-4717-89c3-e2bc4be7a8ee","added_by":"auto","created_at":"2022-09-01 15:21:35","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":226241,"visible":true,"origin":"","legend":"\u003cp\u003eError bar of microjet velocity for helium gas\u003c/p\u003e\u003cp\u003e\u0026nbsp;\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-1884965/v1/4f77e5131195f2389d9b2ed8.png"},{"id":28583247,"identity":"7a870209-7190-4906-9b05-4652a1bcdf26","added_by":"auto","created_at":"2022-11-03 00:13:16","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":772862,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1884965/v1_covered.pdf"},{"id":25937467,"identity":"a7098124-0f43-47f8-b930-17e44d750524","added_by":"auto","created_at":"2022-09-01 15:31:48","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":540005,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1884965/v1_covered.pdf"}],"financialInterests":"","formattedTitle":"Computational Study of Miniature Tube for Biomedical Application","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-1884965/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."},{"header":"Tables","content":"\u003cp\u003e\u003cstrong\u003eTable 1\u003c/strong\u003e Parameters and values obtained from CFD simulation at 25 bar of operating pressure \u0026nbsp;\u003c/p\u003e\n\u003ctable border=\"0\" cellpadding=\"0\" cellspacing=\"0\" width=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"44.35612082670906%\"\u003e\n \u003cp\u003e\u003cstrong\u003eParameters\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"28.616852146263913%\"\u003e\n \u003cp\u003e\u003cstrong\u003eValues for Nitrogen\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"27.027027027027028%\"\u003e\n \u003cp\u003e\u003cstrong\u003eValues for\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003eHelium\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"44.35612082670906%\"\u003e\n \u003cp\u003ex\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"28.616852146263913%\"\u003e\n \u003cp\u003e0.1330 m\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"27.027027027027028%\"\u003e\n \u003cp\u003e0.1421 m\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"44.35612082670906%\"\u003e\n \u003cp\u003ex\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"28.616852146263913%\"\u003e\n \u003cp\u003e0.1560 m\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"27.027027027027028%\"\u003e\n \u003cp\u003e0.1547 m\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"44.35612082670906%\"\u003e\n \u003cp\u003et\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"28.616852146263913%\"\u003e\n \u003cp\u003e0.000035 sec\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"27.027027027027028%\"\u003e\n \u003cp\u003e0.000035 sec\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"44.35612082670906%\"\u003e\n \u003cp\u003et\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"28.616852146263913%\"\u003e\n \u003cp\u003e0.000070 sec\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"27.027027027027028%\"\u003e\n \u003cp\u003e0.000049 sec\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"44.35612082670906%\"\u003e\n \u003cp\u003e\u0026Delta;x (x\u003csub\u003e2\u003c/sub\u003e-x\u003csub\u003e1\u003c/sub\u003e)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"28.616852146263913%\"\u003e\n \u003cp\u003e0.023 m\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"27.027027027027028%\"\u003e\n \u003cp\u003e0.0126 m\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"44.35612082670906%\"\u003e\n \u003cp\u003e\u0026Delta;t (t\u003csub\u003e2\u003c/sub\u003e-t\u003csub\u003e1\u003c/sub\u003e)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"28.616852146263913%\"\u003e\n \u003cp\u003e0.000035 sec\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"27.027027027027028%\"\u003e\n \u003cp\u003e0.000014 sec\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"44.35612082670906%\"\u003e\n \u003cp\u003eInitial temperature, T\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"28.616852146263913%\"\u003e\n \u003cp\u003e300 K\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"27.027027027027028%\"\u003e\n \u003cp\u003e300 K\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"44.35612082670906%\"\u003e\n \u003cp\u003ePrimary shock temperature, T\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"28.616852146263913%\"\u003e\n \u003cp\u003e475 K\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"27.027027027027028%\"\u003e\n \u003cp\u003e674 K\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"44.35612082670906%\"\u003e\n \u003cp\u003eReflected shock temperature, T\u003csub\u003e5\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"28.616852146263913%\"\u003e\n \u003cp\u003e696 K\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"27.027027027027028%\"\u003e\n \u003cp\u003e1120 K\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"44.35612082670906%\"\u003e\n \u003cp\u003eDriven pressure, P\u003csub\u003e1\u0026nbsp;\u003c/sub\u003e(bar)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"28.616852146263913%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"27.027027027027028%\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"44.35612082670906%\"\u003e\n \u003cp\u003eDriver pressure, P\u003csub\u003e4\u0026nbsp;\u003c/sub\u003e(bar)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"28.616852146263913%\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"27.027027027027028%\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"44.35612082670906%\"\u003e\n \u003cp\u003ePrimary shock pressure, P\u003csub\u003e2\u0026nbsp;\u003c/sub\u003e(bar)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"28.616852146263913%\"\u003e\n \u003cp\u003e4.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"27.027027027027028%\"\u003e\n \u003cp\u003e7.9\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"44.35612082670906%\"\u003e\n \u003cp\u003eReflected shock pressure, P\u003csub\u003e5\u0026nbsp;\u003c/sub\u003e(bar)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"28.616852146263913%\"\u003e\n \u003cp\u003e13.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"27.027027027027028%\"\u003e\n \u003cp\u003e35.1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cstrong\u003eTable 2\u003c/strong\u003e Values for standard parameters \u0026nbsp;\u003c/p\u003e\n\u003ctable border=\"1\" cellpadding=\"0\" cellspacing=\"0\" width=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"64.44444444444444%\"\u003e\n \u003cp\u003e\u003cstrong\u003eParameters\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"35.55555555555556%\"\u003e\n \u003cp\u003e\u003cstrong\u003eValues\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"64.44444444444444%\"\u003e\n \u003cp\u003eSpecific heat ratio of air ()\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"35.55555555555556%\"\u003e\n \u003cp\u003e1.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"64.44444444444444%\"\u003e\n \u003cp\u003eSpecific heat ratio of nitrogen ()\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"35.55555555555556%\"\u003e\n \u003cp\u003e1.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"64.44444444444444%\"\u003e\n \u003cp\u003eSpecific heat ratio of helium\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"35.55555555555556%\"\u003e\n \u003cp\u003e1.6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"64.44444444444444%\"\u003e\n \u003cp\u003eGas constant (R)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"35.55555555555556%\"\u003e\n \u003cp\u003e287 J/Kg K\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"64.44444444444444%\"\u003e\n \u003cp\u003eRoom temperature (T)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"35.55555555555556%\"\u003e\n \u003cp\u003e298 K\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"64.44444444444444%\"\u003e\n \u003cp\u003eSpeed of the air (a\u003csub\u003e1\u003c/sub\u003e)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"35.55555555555556%\"\u003e\n \u003cp\u003e\u0026nbsp;= 346 m/s\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cstrong\u003eTable 3\u003c/strong\u003e Results obtained from CFD simulations at 25-50 bar\u0026nbsp;\u003c/p\u003e\n\u003ctable border=\"1\" cellpadding=\"0\" cellspacing=\"0\" width=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"18.138801261829652%\"\u003e\n \u003cp\u003e\u003cstrong\u003eFilling pressure,\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.028391167192428%\"\u003e\n \u003cp\u003e\u003cstrong\u003eFilling gas combination\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"14.037854889589905%\"\u003e\n \u003cp\u003e\u003cstrong\u003eMach No,\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.35646687697161%\"\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"12.302839116719243%\"\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"10.56782334384858%\"\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"10.56782334384858%\"\u003e\n \u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" width=\"18.138801261829652%\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.028391167192428%\"\u003e\n \u003cp\u003eNitrogen-Air\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"14.037854889589905%\"\u003e\n \u003cp\u003e1.89\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.35646687697161%\"\u003e\n \u003cp\u003e4.11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"12.302839116719243%\"\u003e\n \u003cp\u003e13.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"10.56782334384858%\"\u003e\n \u003cp\u003e1.58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"10.56782334384858%\"\u003e\n \u003cp\u003e2.32\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"28.131021194605008%\"\u003e\n \u003cp\u003eHelium-Air\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"17.148362235067438%\"\u003e\n \u003cp\u003e2.60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"13.872832369942197%\"\u003e\n \u003cp\u003e7.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.028901734104046%\"\u003e\n \u003cp\u003e35.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"12.909441233140655%\"\u003e\n \u003cp\u003e2.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"12.909441233140655%\"\u003e\n \u003cp\u003e3.73\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" width=\"18.138801261829652%\"\u003e\n \u003cp\u003e32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.028391167192428%\"\u003e\n \u003cp\u003eNitrogen-Air\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"14.037854889589905%\"\u003e\n \u003cp\u003e2.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.35646687697161%\"\u003e\n \u003cp\u003e4.82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"12.302839116719243%\"\u003e\n \u003cp\u003e15.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"10.56782334384858%\"\u003e\n \u003cp\u003e1.71\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"10.56782334384858%\"\u003e\n \u003cp\u003e2.53\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"28.131021194605008%\"\u003e\n \u003cp\u003eHelium-Air\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"17.148362235067438%\"\u003e\n \u003cp\u003e2.76\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"13.872832369942197%\"\u003e\n \u003cp\u003e8.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.028901734104046%\"\u003e\n \u003cp\u003e42.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"12.909441233140655%\"\u003e\n \u003cp\u003e2.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"12.909441233140655%\"\u003e\n \u003cp\u003e4.18\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" width=\"18.138801261829652%\"\u003e\n \u003cp\u003e42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.028391167192428%\"\u003e\n \u003cp\u003eNitrogen-Air\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"14.037854889589905%\"\u003e\n \u003cp\u003e2.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.35646687697161%\"\u003e\n \u003cp\u003e4.70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"12.302839116719243%\"\u003e\n \u003cp\u003e16.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"10.56782334384858%\"\u003e\n \u003cp\u003e1.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"10.56782334384858%\"\u003e\n \u003cp\u003e2.68\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"28.131021194605008%\"\u003e\n \u003cp\u003eHelium-Air\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"17.148362235067438%\"\u003e\n \u003cp\u003e2.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"13.872832369942197%\"\u003e\n \u003cp\u003e10.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.028901734104046%\"\u003e\n \u003cp\u003e50.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"12.909441233140655%\"\u003e\n \u003cp\u003e2.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"12.909441233140655%\"\u003e\n \u003cp\u003e4.70\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" width=\"18.138801261829652%\"\u003e\n \u003cp\u003e50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.028391167192428%\"\u003e\n \u003cp\u003eNitrogen-Air\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"14.037854889589905%\"\u003e\n \u003cp\u003e2.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.35646687697161%\"\u003e\n \u003cp\u003e5.45\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"12.302839116719243%\"\u003e\n \u003cp\u003e19.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"10.56782334384858%\"\u003e\n \u003cp\u003e1.88\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"10.56782334384858%\"\u003e\n \u003cp\u003e2.79\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"28.131021194605008%\"\u003e\n \u003cp\u003eHelium-Air\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"17.148362235067438%\"\u003e\n \u003cp\u003e3.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"13.872832369942197%\"\u003e\n \u003cp\u003e11.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"15.028901734104046%\"\u003e\n \u003cp\u003e56.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"12.909441233140655%\"\u003e\n \u003cp\u003e2.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"12.909441233140655%\"\u003e\n \u003cp\u003e5.06\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cstrong\u003eTable 4\u003c/strong\u003e CFD, analytical, and experimental results comparison at 25-50 bar\u0026nbsp;\u003c/p\u003e\n\u003ctable border=\"1\" cellpadding=\"0\" cellspacing=\"0\" width=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" valign=\"top\" width=\"9.21875%\"\u003e\n \u003cp\u003e\u003cstrong\u003eDriver sections filled pressure, P\u003csub\u003e4\u003c/sub\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e(bar)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"2\" valign=\"top\" width=\"11.09375%\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eParameters\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"3\" valign=\"top\" width=\"23.90625%\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eShock Mach number, M\u003csub\u003es\u003c/sub\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"3\" valign=\"top\" width=\"24.21875%\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eReflected pressure, P\u003csub\u003e5\u003c/sub\u003e (bar)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\" width=\"11.09375%\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eFluctuation (%)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.71875%\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eP2/P1\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.875%\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eT2/T1\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.875%\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eT5/T1\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"7.465618860510806%\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eCFD\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"12.573673870333987%\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eAnalytical\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"10.019646365422396%\"\u003e\n \u003cp\u003e\u003cstrong\u003eExp.\u0026nbsp;\u003c/strong\u003e(Battula et al., 2016)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"7.858546168958743%\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eCFD\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"12.573673870333987%\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eAnalytical\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"10.019646365422396%\"\u003e\n \u003cp\u003e\u003cstrong\u003eExp.\u0026nbsp;\u003c/strong\u003e(Battula et al., 2016)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.8762278978389%\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eM\u003csub\u003es\u003c/sub\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.8762278978389%\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eP\u003csub\u003e5\u003c/sub\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"3\" valign=\"top\" width=\"25.73673870333988%\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eAnalytical\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" valign=\"top\" width=\"9.23317683881064%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.11111111111111%\"\u003e\n \u003cp\u003eNitrogen-Air\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"5.94679186228482%\"\u003e\n \u003cp\u003e1.89\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"10.015649452269171%\"\u003e\n \u003cp\u003e1.91\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"7.981220657276995%\"\u003e\n \u003cp\u003e1.51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.259780907668231%\"\u003e\n \u003cp\u003e13.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"10.015649452269171%\"\u003e\n \u003cp\u003e13.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"7.981220657276995%\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"5.477308294209703%\"\u003e\n \u003cp\u003e1.04\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"5.477308294209703%\"\u003e\n \u003cp\u003e0.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.729264475743349%\"\u003e\n \u003cp\u003e4.14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.885758998435055%\"\u003e\n \u003cp\u003e1.62\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.885758998435055%\"\u003e\n \u003cp\u003e2.34\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"12.241379310344827%\"\u003e\n \u003cp\u003eHelium-Air\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.551724137931035%\"\u003e\n \u003cp\u003e2.60\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.03448275862069%\"\u003e\n \u003cp\u003e2.59\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"8.793103448275861%\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.896551724137931%\"\u003e\n \u003cp\u003e35.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.03448275862069%\"\u003e\n \u003cp\u003e34.22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"8.793103448275861%\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.0344827586206895%\"\u003e\n \u003cp\u003e0.38\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.0344827586206895%\"\u003e\n \u003cp\u003e2.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"7.413793103448276%\"\u003e\n \u003cp\u003e7.76\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"7.586206896551724%\"\u003e\n \u003cp\u003e2.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"7.586206896551724%\"\u003e\n \u003cp\u003e3.73\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" valign=\"top\" width=\"9.23317683881064%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.11111111111111%\"\u003e\n \u003cp\u003eNitrogen-Air\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"5.94679186228482%\"\u003e\n \u003cp\u003e2.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"10.015649452269171%\"\u003e\n \u003cp\u003e1.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"7.981220657276995%\"\u003e\n \u003cp\u003e1.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.259780907668231%\"\u003e\n \u003cp\u003e15.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"10.015649452269171%\"\u003e\n \u003cp\u003e14.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"7.981220657276995%\"\u003e\n \u003cp\u003e23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"5.477308294209703%\"\u003e\n \u003cp\u003e1.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"5.477308294209703%\"\u003e\n \u003cp\u003e6.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.729264475743349%\"\u003e\n \u003cp\u003e4.51\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.885758998435055%\"\u003e\n \u003cp\u003e1.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.885758998435055%\"\u003e\n \u003cp\u003e2.49\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"12.241379310344827%\"\u003e\n \u003cp\u003eHelium-Air\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.551724137931035%\"\u003e\n \u003cp\u003e2.80\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.03448275862069%\"\u003e\n \u003cp\u003e2.76\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"8.793103448275861%\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.896551724137931%\"\u003e\n \u003cp\u003e42.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.03448275862069%\"\u003e\n \u003cp\u003e41.24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"8.793103448275861%\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.0344827586206895%\"\u003e\n \u003cp\u003e1.40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.0344827586206895%\"\u003e\n \u003cp\u003e1.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"7.413793103448276%\"\u003e\n \u003cp\u003e8.84\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"7.586206896551724%\"\u003e\n \u003cp\u003e2.41\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"7.586206896551724%\"\u003e\n \u003cp\u003e4.14\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" valign=\"top\" width=\"9.23317683881064%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.11111111111111%\"\u003e\n \u003cp\u003eNitrogen-Air\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"5.94679186228482%\"\u003e\n \u003cp\u003e2.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"10.015649452269171%\"\u003e\n \u003cp\u003e2.084\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"7.981220657276995%\"\u003e\n \u003cp\u003e2.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.259780907668231%\"\u003e\n \u003cp\u003e17.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"10.015649452269171%\"\u003e\n \u003cp\u003e17.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"7.981220657276995%\"\u003e\n \u003cp\u003e35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"5.477308294209703%\"\u003e\n \u003cp\u003e0.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"5.477308294209703%\"\u003e\n \u003cp\u003e2.00\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.729264475743349%\"\u003e\n \u003cp\u003e4.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.885758998435055%\"\u003e\n \u003cp\u003e1.76\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.885758998435055%\"\u003e\n \u003cp\u003e2.66\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"12.241379310344827%\"\u003e\n \u003cp\u003eHelium-Air\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.551724137931035%\"\u003e\n \u003cp\u003e2.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.03448275862069%\"\u003e\n \u003cp\u003e2.95\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"8.793103448275861%\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.896551724137931%\"\u003e\n \u003cp\u003e50.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.03448275862069%\"\u003e\n \u003cp\u003e50.03\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"8.793103448275861%\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.0344827586206895%\"\u003e\n \u003cp\u003e0.23\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.0344827586206895%\"\u003e\n \u003cp\u003e0.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"7.413793103448276%\"\u003e\n \u003cp\u003e10.14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"7.586206896551724%\"\u003e\n \u003cp\u003e2.63\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"7.586206896551724%\"\u003e\n \u003cp\u003e4.64\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" valign=\"top\" width=\"9.23317683881064%\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.11111111111111%\"\u003e\n \u003cp\u003eNitrogen-Air\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"5.94679186228482%\"\u003e\n \u003cp\u003e2.18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"10.015649452269171%\"\u003e\n \u003cp\u003e2.15\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"7.981220657276995%\"\u003e\n \u003cp\u003e2.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.259780907668231%\"\u003e\n \u003cp\u003e19.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"10.015649452269171%\"\u003e\n \u003cp\u003e19.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"7.981220657276995%\"\u003e\n \u003cp\u003e40\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"5.477308294209703%\"\u003e\n \u003cp\u003e1.39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"5.477308294209703%\"\u003e\n \u003cp\u003e0.70\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.729264475743349%\"\u003e\n \u003cp\u003e5.29\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.885758998435055%\"\u003e\n \u003cp\u003e1.82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.885758998435055%\"\u003e\n \u003cp\u003e2.79\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"12.241379310344827%\"\u003e\n \u003cp\u003eHelium-Air\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.551724137931035%\"\u003e\n \u003cp\u003e3.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.03448275862069%\"\u003e\n \u003cp\u003e3.08\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"8.793103448275861%\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.896551724137931%\"\u003e\n \u003cp\u003e56.50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"11.03448275862069%\"\u003e\n \u003cp\u003e56.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"8.793103448275861%\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.0344827586206895%\"\u003e\n \u003cp\u003e0.64\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"6.0344827586206895%\"\u003e\n \u003cp\u003e0.53\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"7.413793103448276%\"\u003e\n \u003cp\u003e11.05\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"7.586206896551724%\"\u003e\n \u003cp\u003e2.78\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"7.586206896551724%\"\u003e\n \u003cp\u003e4.99\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cstrong\u003eTable 5\u003c/strong\u003e Microjet velocity comparison at 25-50 bar\u003c/p\u003e\n\u003ctable border=\"1\" cellpadding=\"0\" cellspacing=\"0\" width=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" valign=\"top\" width=\"19.375%\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eFilled gas pressure, P4\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd rowspan=\"2\" valign=\"top\" width=\"20.78125%\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eOperating gas\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"3\" valign=\"top\" width=\"59.84375%\"\u003e\n \u003cp\u003e\u003cstrong\u003eMicrojet velocity,\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;(m/s)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"27.41514360313316%\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eCFD\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"33.15926892950392%\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eAnalytical\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"39.425587467362924%\"\u003e\n \u003cp\u003e\u003cstrong\u003eExperimental values, m/s\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e(Battula et al., 2016)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" width=\"19.375%\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"20.78125%\"\u003e\n \u003cp\u003eNitrogen-Air\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.40625%\"\u003e\n \u003cp\u003e50.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"19.84375%\"\u003e\n \u003cp\u003e51.3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.59375%\"\u003e\n \u003cp\u003e63.2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"25.775193798449614%\"\u003e\n \u003cp\u003eHelium-Air\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"20.348837209302324%\"\u003e\n \u003cp\u003e83.90\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"24.612403100775193%\"\u003e\n \u003cp\u003e82.72\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"29.26356589147287%\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" width=\"19.375%\"\u003e\n \u003cp\u003e32\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"20.78125%\"\u003e\n \u003cp\u003eNitrogen-Air\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.40625%\"\u003e\n \u003cp\u003e56.21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"19.84375%\"\u003e\n \u003cp\u003e54.58\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.59375%\"\u003e\n \u003cp\u003e68.0\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"25.775193798449614%\"\u003e\n \u003cp\u003eHelium-Air\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"20.348837209302324%\"\u003e\n \u003cp\u003e91.68\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"24.612403100775193%\"\u003e\n \u003cp\u003e90.81\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"29.26356589147287%\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" width=\"19.375%\"\u003e\n \u003cp\u003e42\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"20.78125%\"\u003e\n \u003cp\u003eNitrogen-Air\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.40625%\"\u003e\n \u003cp\u003e58.22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"19.84375%\"\u003e\n \u003cp\u003e58.82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.59375%\"\u003e\n \u003cp\u003e83.6\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"25.775193798449614%\"\u003e\n \u003cp\u003eHelium-Air\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"20.348837209302324%\"\u003e\n \u003cp\u003e100.29\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"24.612403100775193%\"\u003e\n \u003cp\u003e100.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"29.26356589147287%\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"2\" width=\"19.375%\"\u003e\n \u003cp\u003e50\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"20.78125%\"\u003e\n \u003cp\u003eNitrogen-Air\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"16.40625%\"\u003e\n \u003cp\u003e62.20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"19.84375%\"\u003e\n \u003cp\u003e61.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"23.59375%\"\u003e\n \u003cp\u003e89.4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" width=\"25.775193798449614%\"\u003e\n \u003cp\u003eHelium-Air\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"20.348837209302324%\"\u003e\n \u003cp\u003e106.30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"24.612403100775193%\"\u003e\n \u003cp\u003e106.01\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" width=\"29.26356589147287%\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Shock Wave, Miniature Tube, Biomedical, Needle-less drug delivery, CFD","lastPublishedDoi":"10.21203/rs.3.rs-1884965/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1884965/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Needle-free injection devices are novel inventions to provide medications to patients without puncturing their skin with a needle. The present work focuses on the computational study of fluid flow characteristics inside the shock tube designed for liquid-type drug delivery and also evaluates these computational and analytical results with experimental observations. To observe primary and reflected shock pressure and shock Mach number for achieving the controlled microjet velocity to accelerate the drugs. ANSYS fluent has been utilized to solve the governing equations of energy, continuity, and momentum where density-based implicit solver is used to perform the transient analysis of the shock tube. Two combinations of gases (nitrogen-air and helium-air as a driver and driven section gas) have been considered for the CFD analysis. Four pressures ranging from 25-50 bar in the driver section and 1 bar in the driven area are considered as an initial condition to perform the simulations. The obtained results showed that the pressure and temperature ratios and Mach numbers are more significant for the helium-air model than for the nitrogen-air model at different operating pressures. These results are validated using analytical calculations, which also agree well with experimental results. Further, the microjet velocity has been calculated. The maximum value of microjet velocity for the nitrogen-air model is 62 m/s, whereas for the helium-air model is 106 m/s. The microjet velocity is more significant for the helium-air combination; hence the penetration depth on the target surface will be more effective on helium than nitrogen.","manuscriptTitle":"Computational Study of Miniature Tube for Biomedical Application","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2022-09-01 15:21:33","doi":"10.21203/rs.3.rs-1884965/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"7fa88956-280e-4431-ad6b-0eef014e7aeb","owner":[],"postedDate":"September 1st, 2022","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2022-11-03T00:12:54+00:00","versionOfRecord":[],"versionCreatedAt":"2022-09-01 15:21:33","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-1884965","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-1884965","identity":"rs-1884965","version":["v1"]},"buildId":"-HB7Z8yhvgn0wM9Nzuekk","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}