Inviscid Steady Flow

Zhu You-lan, Chen Bing-mu, Zhong Xi-chang and Zhang Zuo-min
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Zhu You-lan: Chinese Academy of Sciences, Computing Center
Chen Bing-mu: Chinese Academy of Sciences, Computing Center
Zhong Xi-chang: Chinese Academy of Sciences, Computing Center
Zhang Zuo-min: Chinese Academy of Sciences, Computing Center

Chapter Chapter 4 in Difference Methods for Initial-Boundary-Value Problems and Flow Around Bodies, 1988, pp 235-336 from Springer

Abstract: Abstract Let us consider steady flow, and assume that the medium is a gas whose viscosity and heat conductivity are negligible. The external force acting on the gas will also be neglected. Under these conditions we can derive the basic flow equations in the integral form as follows[36]: 1.1 % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaiqaaeaafa % qaagWabaaabaWaa8GuaeaacqaHbpGCcaWGwbWaaSbaaSqaaiaad6ga % aeqaaOGaamOvaiabgUcaRmaapifabaGaamiCaiaad6gacaWGKbGaeq % 4WdmNaeyypa0JaaGimaiaacYcaaSqaaiabeo8aZbqab0Gaey4kIiVa % ey4kIipaaSqaaiabeo8aZbqab0Gaey4kIiVaey4kIipaaOqaamaapi % fabaGaeqyWdiNaamOvamaaBaaaleaacaWGUbaabeaakiaadsgacqaH % dpWCcqGH9aqpcaaIWaGaaiilaaWcbaGaeq4WdmhabeqdcqGHRiI8cq % GHRiI8aaGcbaWaa8GuaeaacaWGWbGaamOvamaaBaaaleaacaWGUbaa % beaakmaabmaabaGaamyzaiabgUcaRmaalaaabaWaaqWaaeaacaWGwb % aacaGLhWUaayjcSdWaaWbaaSqabeaacaaIYaaaaaGcbaGaaGOmaaaa % aiaawIcacaGLPaaacaWGKbGaeq4WdmNaey4kaSYaa8GuaeaacaWGWb % GaamOvamaaBaaaleaacaWGUbaabeaakiaadsgacqaHdpWCcqGH9aqp % daWdsbqaaiabeg8aYjaadAfadaWgaaWcbaGaamOBaaqabaGcdaqada % qaaiaadIgacqGHRaWkdaWcaaqaamaaemaabaGaamOvaaGaay5bSlaa % wIa7amaaCaaaleqabaGaaGOmaaaaaOqaaiaaikdaaaaacaGLOaGaay % zkaaaaleaacqaHdpWCaeqaniabgUIiYlabgUIiYdGccaWGKbGaeq4W % dmNaeyypa0JaaGimaiaac6caaSqaaiabeo8aZbqab0Gaey4kIiVaey % 4kIipaaSqaaiabeo8aZbqab0Gaey4kIiVaey4kIipaaaaakiaawUha % aaaa!9878! $$\left\{ {\begin{array}{*{20}{c}} {\iint\limits_{\sigma } {\rho {{V}_{n}}V + \iint\limits_{\sigma } {pnd\sigma = 0,}}} \hfill \\ {\iint\limits_{\sigma } {\rho {{V}_{n}}d\sigma = 0,}} \hfill \\ {\iint\limits_{\sigma } {p{{V}_{n}}\left( {e + \frac{{{{{\left| V \right|}}^{2}}}}{2}} \right)d\sigma + \iint\limits_{\sigma } {p{{V}_{n}}d\sigma = \iint\limits_{\sigma } {\rho {{V}_{n}}\left( {h + \frac{{{{{\left| V \right|}}^{2}}}}{2}} \right)}d\sigma = 0.}}} \hfill \\ \end{array} } \right.$$ . Here σ is any closed surface in space; V is the velocity vector of the moving gas, p the pressure, ρ the density, e the specific internal energy (i.e., the internal energy per unit mass of gas), and % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 % qacaWGObGaeyypa0JaamyzaiabgUcaRmaalaaapaqaa8qacaWGWbaa % paqaa8qacqaHbpGCaaaaaa!3CD6! $$h = e + \frac{p}{\rho }$$ the specific enthalpy; n is the unit outward normal to the surface σ; V n =V•n is the normal component of the velocity.

Keywords: Steady Flow; Flow Property; Compression Shock; Expansion Wave; Contact Discontinuity (search for similar items in EconPapers)
Date: 1988
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DOI: 10.1007/978-3-662-06707-9_4

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