# 航空動力裝置控制規律與特性/第一章

## 1.1 氣體動力方程

—般情況下，發動磯各部件中進行的是粘性可壓縮氣體的空間(三元)流動。空間中每一個點上的氣流參數，是由速度向量c， 壓力p，密度ρ，和溫度T表示。這些參數受空間的坐標x、y、z和時間T制約。發動機氣體動力學的題解，以能求出下列關係式描述的整個流動場為前提：

c=c(x,y,z,t);p=p(x,y,z,t);ρ=ρ(x,y,z,t);T=T(x,y,z,t);    (1-1)


${\displaystyle {\frac {\partial \rho }{\partial t}}+div(\rho c)=0}$     (1-2)


${\displaystyle {\frac {\partial \rho }{\partial t}}+{\frac {\partial (\rho c_{x})}{\partial x}}+{\frac {\partial (\rho c_{y})}{\partial y}}+{\frac {\partial (\rho c_{z})}{\partial z}}=0}$     (1-3)


${\displaystyle \rho {\frac {dc}{dt}}=\mathbf {R} -grad\,\mathbf {p} +\mu \Delta c+{\frac {1}{3}}\mu grad(div\,c)}$    (1-4)


${\displaystyle \rho {\frac {dc}{dt}}=\mathbf {R} -grad\,\mathbf {p} +\mu \Delta c}$    (1-5)


${\displaystyle \rho {\frac {\partial c_{x}}{\partial t}}+\rho (c_{x}{\frac {\partial c_{x}}{\partial x}}+c_{y}{\frac {\partial c_{x}}{\partial y}}+c_{z}{\frac {\partial c_{x}}{\partial z}})=X+{\frac {\partial p}{\partial x}}+\mu ({\frac {\partial ^{2}c_{x}}{\partial x^{2}}}+{\frac {\partial ^{2}c_{x}}{\partial y^{2}}}+{\frac {\partial ^{2}c_{x}}{\partial z^{2}}})}$
${\displaystyle \rho {\frac {\partial c_{y}}{\partial t}}+\rho (c_{x}{\frac {\partial c_{y}}{\partial x}}+c_{y}{\frac {\partial c_{y}}{\partial y}}+c_{z}{\frac {\partial c_{y}}{\partial z}})=Y+{\frac {\partial p}{\partial y}}+\mu ({\frac {\partial ^{2}c_{y}}{\partial x^{2}}}+{\frac {\partial ^{2}c_{y}}{\partial y^{2}}}+{\frac {\partial ^{2}c_{y}}{\partial z^{2}}})}$     (1-6)
${\displaystyle \rho {\frac {\partial c_{z}}{\partial t}}+\rho (c_{x}{\frac {\partial c_{z}}{\partial x}}+c_{y}{\frac {\partial c_{z}}{\partial y}}+c_{z}{\frac {\partial c_{z}}{\partial z}})=Z+{\frac {\partial p}{\partial z}}+\mu ({\frac {\partial ^{2}c_{z}}{\partial x^{2}}}+{\frac {\partial ^{2}c_{z}}{\partial y^{2}}}+{\frac {\partial ^{2}c_{z}}{\partial z^{2}}})}$


${\displaystyle \rho c_{p}{\frac {dT}{dt}}=\lambda \Delta T+\mu \Phi }$    (1-7)


${\displaystyle \Phi \approx 0}$，並引入稱之為導溫係數的${\displaystyle a={\frac {\lambda }{c_{p}\rho }}}$後，則得

${\displaystyle {\frac {dT}{dt}}=a\Delta T}$    (1-8)


${\displaystyle {\frac {\partial T}{\partial t}}+c_{x}{\frac {\partial T}{\partial x}}+c_{y}{\frac {\partial T}{\partial y}}+c_{z}{\frac {\partial T}{\partial z}}=a({\frac {\partial ^{2}T}{\partial x^{2}}}+{\frac {\partial ^{2}T}{\partial y^{2}}}+{\frac {\partial ^{2}T}{\partial z^{2}}})}$    (1-9)


1. 表徵進行過程的物體或系統形狀和尺寸的幾何條件
2. 確定初始瞬間氣流狀態的時間(初始的)條件
3. 確定系統邊界上氣流狀態的邊界條件
4. 確定液體的種類，其物理參數和這些參數與溫度關係的物理條件

${\displaystyle G=\rho _{1}c_{1}F_{1}=\rho _{2}c_{2}F_{2}}$    (1-10)


${\displaystyle i_{1}+{\frac {c_{1}^{2}}{2}}+L}$внеш${\displaystyle +Q}$внеш${\displaystyle =i_{2}+{\frac {c_{2}^{2}}{2}}}$    (1.11)