8.5 Injection Boundary 注入边界[cfd-8-5]

注入速度和其他流动变量由给定的质量流量 $\dot{m}$ 与注入温度 $T_{inj}$ 算出。这里我们假设质量流沿垂直于边界的方向注入。对流通量用式(2.21)计算，并把逆变速度 $$V$$ 取为注入速度，即en

The injection velocity and other flow variables are computed from the given mass flow rate $\dot{m}$ and the injection temperature $T_{inj}$ . We will assume here that the mass is injected perpendicular to the boundary. The convective fluxes are evaluated using Eq. (2.21) with the contravariant velocity $$V$$ set equal to the injection velocity, i.e.,

V=V_{inj}=\frac{\dot{m}}{\rho_{inj}}\,. \tag{8.37}

速度分量利用面法向量按下式求值en

Velocity components are evaluated using the face normal vector as

\vec{v}_{inj}=-\vec{n}\,V_{inj} \tag{8.38}

（见图8.8）。式(8.37)中的密度 $\rho_{inj}$ 是 $T_{inj}$ 和边界压力 $$p_b$$ 的函数。因此，对于完全气体有en

(see Fig. 8.8). The density $\rho_{inj}$ in Eq. (8.37) is a function of $T_{inj}$ and of the pressure at the boundary $$p_b$$ . Hence, in the case of perfect gas we have

\rho_{inj}=\frac{p_b}{R\,T_{inj}}\,. \tag{8.39}

对于图8.8a中所描绘的单元中心格式， $$p_b$$ 可以直接取为边界单元内的压力，即 $$p_b=p_2$$ 。中位对偶单元顶点格式则需要由定义相应面面积的各点插值 $$p_b$$ （即由图8.8b中的 $$(i,2)$$ 和 $$(i+1,2)$$ 插值）。为此可以利用式(8.8)、(8.11)-(8.13)之类的公式。虚单元（点）中的值由域内作零阶外推或线性外推得到。en

For the cell-centred scheme sketched in Fig. 8.8a, $$p_b$$ can be set identical to the pressure in the boundary cell, i.e., $$p_b=p_2$$ . The median-dual cell-vertex scheme requires an interpolation of $$p_b$$ from the points defining the particular face area (i.e., from $$(i,2)$$ and $$(i+1,2)$$ in Fig. 8.8b). Formulae like (8.8), (8.11)-(8.13) can be utilised for this purpose. Values in the dummy cells (points) are obtained by 0-th order or by linear extrapolation from the interior.

图8.8:结构化单元中心格式(a)与单元顶点对偶控制体格式(b)的注入边界条件

图8.8:结构化单元中心格式(a)与单元顶点对偶控制体格式(b)的注入边界条件。虚单元(点)记为1和0。计算对流通量的位置用菱形标出。