[物理学与PDEs]第4章第3节 一维反应流体力学方程组 3.1 一维反应流体力学方程组

1、 一维粘性热传导反应流体力学方程组

$$\beex \bea \cfrac{\p\rho}{\p t}&+\cfrac{\p}{\p x}(\rho u)=0,\\ \cfrac{\p}{\p t}(\rho u) &+\cfrac{\p}{\p x}\sez{ \rho u^2+p-\sex{\cfrac{4}{3}\mu+\mu'}\cfrac{\p u}{\p x} }=\rho F,\\ \cfrac{\p}{\p t}\sex{\rho E+\cfrac{1}{2}\rho u^2}& +\cfrac{\p}{\p x}\sez{ \sex{\rho E+\cfrac{1}{2}\rho u^2+p}u-\sex{\cfrac{4}{3}\mu+\mu'}u\cfrac{\p u}{\p x} }\\ &=\cfrac{\p}{\p x}\sex{\kappa\cfrac{\p T}{\p x}}+\rho{\bf F}\cdot{\bf u},\\ \cfrac{\p }{\p t}(\rho Z)&+\cfrac{\p}{\p x}(\rho Zu) =-\bar k(\rho,p,Z)\rho Z; \eea \eeex$$ 或 $$\beex \bea \cfrac{\p\rho}{\p t}&+\cfrac{\p}{\p x}(\rho u)=0,\\ \cfrac{\p u}{\p t} &+u\cfrac{\p u}{\p x} +\cfrac{1}{\rho}\cfrac{\p p}{\p x} -\cfrac{1}{\rho }\cfrac{\p }{\p x}\sez{\sex{\cfrac{4}{3}\mu+\mu'}\cfrac{\p u}{\p x}}=F,\\ T\cfrac{\p S}{\p t}&+Tu\cfrac{\p S}{\p x} -\cfrac{1}{\rho}\sex{\cfrac{4}{3}\mu+\mu'}\sex{\cfrac{\p u}{\p x}}^2 =\cfrac{1}{\rho}\cfrac{\p}{\p x}\sex{\kappa\cfrac{\p T}{\p x}} -\cfrac{\p S}{\p Z}\bar k(\rho,p,Z)TZ,\\ \cfrac{\p Z}{\p t}& +u\cfrac{\p Z}{\p x}=-\bar k(\rho,p,Z)Z. \eea \eeex$$

 

 

2.  一维理想反应流体力学方程组

$$\beex \bea \cfrac{\p\rho}{\p t}+\cfrac{\p}{\p x}(\rho u)&=0,\\ \cfrac{\p u}{\p t} +u\cfrac{\p u}{\p x} +\cfrac{1}{\rho}\cfrac{\p p}{\p x} &=F,\\ \cfrac{\p S}{\p t}+u\cfrac{\p S}{\p x}&= -\cfrac{\p S}{\p Z}\bar k(\rho,p,Z)Z,\\ \cfrac{\p Z}{\p t} +u\cfrac{\p Z}{\p x}&=-\bar k(\rho,p,Z)Z. \eea \eeex$$