﻿ 水下闭式循环动力系统动态过程数值仿真研究
 舰船科学技术  2017, Vol. 39 Issue (3): 101-106 PDF

1. 中国船舶重工集团公司 第七〇五研究所，陕西 西安 710075;
2. 西北工业大学 航海学院，陕西 西安 710072

Numerical simulation of dynamic process of underwater closed-loop propulsion system
LU Jun1,2, HAN Yong-jun1, GAO Yu-ke1, MA Wei-feng1, GUO Zhao-yuan1, Li Xin1
1. The 705 Research Institute, of CSIC, Xi’an 710075, China;
2. School of Marine Science and Technology, Northwestern Polytechnical University, Xi′an 710072, China
Abstract: The underwater closed-loop propulsion system is characterized by high energy density、high specific power and zero emission, which make it superior in terms of range, speed, depth and stealth. In this paper, the dynamic model of the underwater closed-loop propulsion system is developed. The combustor model is based on the interphase coupling of fuel gas and coolant water. The turbine model takes rotator and volume inertia into account. The condenser model is divided into three zones: superheated, saturated and supercooled region. Using the model, the dynamic behavior of the system is simulated. The results indicate that as long as the ratio of fuel gas to coolant water keep constant during the dynamic process, the combustor temperature will remain stable. As such, the combustor pressure and turbine power output is determined solely by total flux of the work fluid. This conclusion implies the decouple control strategy for the system.
Key words: underwater propulsion     closed-loop     modeling     numerical simulation
0 引　言

 图 1 水下闭式循环动力系统原理图 Fig. 1 Schematic of the underwater closed-loop propulsion system

1 加湿燃烧室模型

1.1 气相模型

 $\frac{{{\rm d}{m_c}}}{{{\rm d}t}} = \frac{{{\rm d}{m_{{{\rm H}_2}}}}}{{{\rm d}t}} + \frac{{{\rm d}{m_{{{\rm O}_2}}}}}{{{\rm d}t}} + \frac{{{\rm d}{m_{{{\rm H}_2}{\rm O}(l),in}}}}{{{\rm d}t}} - \frac{{{\rm d}{m_{c,{\rm out}}}}}{{{\rm d}t}}{\text{，}}$ (1)

 $\frac{{{\rm d}{m_{c,{\rm out}}}}}{{{\rm d}t}} = {A_e}{p_c}{(\frac{2}{{k + 1}})^{\frac{1}{{k - 1}}}}\sqrt {\frac{{2k}}{{{R_g}T(k + 1)}}}{\text{，}}$ (2)

 ${\rm d}{U_c} = {\rm d}{Q_{\rm react}} - {\rm d}{Q_{{H_2}O(l),zf}}\text{，}$ (3)

 ${\rm d}{U_c} = {C_v}{m_c}{\rm d}{T_c} + {C_v}{T_c}{\rm d}{m_c}{\text{，}}$ (4)

 $\frac{{{\rm d}{T_c}}}{{{\rm d}t}} = (\frac{{{\rm d}{Q_{\rm react}}}}{{{\rm d}t}} - \frac{{{\rm d}{Q_{{{\rm H}_2}{\rm O}(l),zf}}}}{{{\rm d}t}} - \frac{{{c_v}T{\rm d}{m_{\rm out}}}}{{{\rm d}t}})/({m_c}\times{c_v})\text{。}$ (5)

1.2 液相模型

 $\frac{{{\rm d}{m_{{{\rm H}_2}{\rm O}(l),c}}}}{{{\rm d}t}} = \frac{{{\rm d}{m_{{{\rm H}_2}{\rm O}(l),{\rm in}}}}}{{{\rm d}t}} - \frac{{{\rm d}{m_{{{\rm H}_2}{\rm O}(l),zf}}}}{{{\rm d}t}}\text{。}$ (6)

 $\frac{{{\rm d}{m_{{{\rm H}_2}{\rm O}(l),c}}}}{{{\rm d}t}} \!=\! N\pi {d_l}{\rho _l}{D_l}Sh\ln (1 + Yw/(1 - Yw)){T_l} \!<\! {T_d}{\text{，}}$ (7)
 $\frac{{{\rm d}{m_{{{\rm H}_2}{\rm O}(l),c}}}}{{{\rm d}t}} \!=\! N\pi {{d}_l}{\lambda _l}Nu\ln (1 \!+\! {c_p}({T_l} - {T_d})/{q_e})/{c_p} {T_l} \!\!=\!\! {T_d}{\text{。}}\!\!\!\!\!\!\!\!$ (8)

 $\begin{split}\\[-12pt]\frac{{{\rm d}{T_l}}}{{{\rm d}t}} = & (\frac{{{\rm d}{Q_{dl}}}}{{{\rm d}t}} + \frac{{{\rm d}{m_{{{\rm H}_2}{\rm O}(l),{\rm in}}}}}{{{\rm d}t}}{q_0} - \frac{{{\rm d}{m_{{{\rm H}_2}{\rm O}(l),zf}}}}{{{\rm d}t}}L)/\\ & ({m_{{{\rm H}_2}{\rm O}(l),c}}\times {c_v}){\text{，}}\end{split}$ (9)

2 汽轮机模型

 $\frac{{{\rm d}({\rho _s}{V_t})}}{{{\rm d}t}} = {m_{t,{\rm in}}} - {m_{t,{\rm out}}}{\text{，}}$ (10)

 $\frac{{{\rm d}({\rho _s}{V_t}{U_s})}}{{{\rm d}t}} = {m_{t,\rm in}}{h_{t,\rm in}} - {m_{t,\rm out}}{h_{t,\rm out}} - {N_t}{\text{，}}$ (11)

 ${N_t} = \frac{k}{{k - 1}}RT_o^*\left[ {1 - {{\left( {\frac{{{p_1}}}{{p_o^*}}} \right)}^{\frac{{k - 1}}{k}}}} \right]{\text{，}}$ (12)

 $J\frac{{{\rm d}{n^2}}}{{{\rm d}t}} = \frac{{1800}}{{{\pi ^2}}}({N_t} - {N_g}){\text{。}}$ (13)

3 壳体冷凝器模型

 ${L_{cd,l}} = {L_{cd}} - {L_{cd,b}} - {L_{cd,g}}{\text{，}}$ (14)

 图 2 控制体示意图 Fig. 2 Control unit of the shell-integrated condenser

 $\Omega \frac{\rm d}{{{\rm d}t}}\int_{{z_A}}^{{z_B}} {\rho {\rm d}z} {\rm{ + }}{\rho _A}\varOmega \frac{{{\rm d}{z_A}}}{{{\rm d}t}} - {\rho _B}\varOmega \frac{{{\rm d}{z_B}}}{{{\rm d}t}} = {\dot m_A} - {\dot m_B}{\text{，}}$ (15)

 $\begin{split}\\[-12pt]\Omega \frac{\rm d}{{{\rm d}t}} & \int_{{z_A}}^{{z_B}} {\left( {h\rho } \right){\rm d}z} - \varOmega {h_B}{\rho _B}\frac{{{\rm d}{z_B}}}{{{\rm d}t}} + \varOmega {h_A}{\rho _A}\frac{{{\rm d}{z_A}}}{{dt}} - \\& \varOmega \left( {{z_B} - {z_A}} \right)\frac{{{\rm d}p}}{{{\rm d}t}} = {h_A}{\dot m_A} - {h_B}{\dot m_B} + q\left( {{z_B} - {z_A}} \right){\text{。}}\end{split}$ (16)
3.1 过冷区模型

${z_A} = {L_{cd,g}} + {L_{cd,b}}$ ${z_B} = {L_{cd}}$ 代入式（15）中，可得过冷区的质量守恒方程为：

 $\begin{split}\displaystyle \frac{\rm d}{{{\rm d}t}}\int_{{L_{cd,g}} + {L_{cd,b}}}^{{L_{cd}}} {\rho dz} {\rm{ + }}\rho \frac{{{\rm d}({L_{cd,g}} + {L_{cd,b}})}}{{{\rm d}t}}-\\[8pt] \quad \quad \rho \displaystyle\frac{{{\rm d}{L_{cd}}}}{{{\rm d}t}} = {{\dot m}_{cd,bout}} - {{\dot m}_{cd,out}} = 0{\text{。}}\end{split}$ (17)

${z_A} = {L_{cd,g}} + {L_{cd,b}}$ ${z_B} = {L_{cd}}$ 代入式（16）中，可得过冷区的能量守恒方程为：

 {equation}{18}\begin{aligned}{A_{cd}}\displaystyle\frac{\rm d}{{{\rm d}t}}\!\! & \int_{{L_{cd,g}} \!+\! {L_{cd,b}}}^{{L_{cd}}} \!\!{\left( {{\rho _{cd,lsa}}h} \right){\rm d}z} \!\!+\!\! {A_{cd}}{h_{cd,lsa}}{\rho _{cd,lsa}}\displaystyle\frac{{{\rm d}\left( {{L_{cd,g}} \!\!+\!\! {L_{cd,b}}} \right)}}{{{\rm d}t}}\!=\\ & \displaystyle {h_{cd,lsa}}{{\dot m}_{cd,\rm bout}} - {h_{cd,\rm out}}{{\dot m}_{cd,out}} + {q_{cd,l}}{L_{cd,l}}{\text{。}}\quad\quad\quad (18)\end{aligned}

 ${h_{cd,lav}} = \frac{{\left( {{h_{cd,\rm out}} + {h_{cd,lsa}}} \right)}}{2}{\text{。}}$ (19)

 \begin{aligned}\frac{\rm d}{{{\rm d}t}}& \int_{{L_{cd,g}} + {L_{cd,b}}}^{{L_{cd}}} {\left( {{\rho _{cd,lsa}}h} \right){\rm d}z} = {\rho _{cd,lsa}}\frac{{{\rm d}{h_{cd,lav}}{L_{cd,l}}}}{{{\rm d}t}} =\\ & {\rho _{cd,lsa}}\left( {{h_{cd,lav}}\frac{{{\rm d}{L_{cd,l}}}}{{{\rm d}t}} + \frac{{{L_{cd,l}}}}{2}\frac{{{\rm d}{h_{cd,\rm out}}}}{{{\rm d}t}}} \right){\text{。}}\end{aligned} (20)

 ${a_b}\frac{{{\rm d}{L_{cd,b}}}}{{{\rm d}t}} + {a_g}\frac{{{\rm d}{L_{cd,g}}}}{{{\rm d}t}} + {a_h}\frac{{{\rm d}{h_{cd,\rm out}}}}{{{\rm d}t}} = {a_q}{\text{，}}$ (21)

3.2 饱和区模型

${z_A} = {L_{cd,g}}$ ${z_B} = {L_{cd,g}} + {L_{cd,b}}$ 代入式（15）中，可得饱和区的质量守恒方程为：

 \begin{aligned}\!\!\!\!\!{A_{cd}}\displaystyle\frac{\rm d}{{{\rm d}t}} & \int_{{L_{cd,g}}}^{{L_{cd,g}} + {L_{cd,b}}} {\rho dz} {\rm{ + }}{\rho _{cd,gsa}}{A_{cd}}\frac{{{\rm d}{L_{cd,g}}}}{{{\rm d}t}}-\\& {\rho _{cd,lsa}}{A_{cd}}\frac{{{\rm d}\left( {{L_{cd,g}} + {L_{cd,b}}} \right)}}{{{\rm d}t}} \!= \!{{\dot m}_{cd,gout}} \!-\! {{\dot m}_{cd,bout}}{\text{。}}\end{aligned} (22)

 ${\rho _{cd,gav}} = {\gamma _{cd,av}}{\rho _{cd,gsa}} + \left( {1 - {\gamma _{cd,av}}} \right){\rho _{cd,lsa}}{\text{。}}$ (23)

 \begin{aligned} \frac{\rm d}{{{\rm d}t}}& \int_{{L_{cd,g}}}^{{L_{cd,g}} + {L_{cd,b}}} {\rho {\rm d}z} = \frac{{{\rm d}\left( {{\rho _{cd,gav}}{L_{cd,b}}} \right)}}{{{\rm d}t}} =\\& \left[ {{\gamma _{cd,av}}{\rho _{cd,gsa}} + \left( {1 - {\gamma _{cd,av}}} \right){\rho _{cd,lsa}}} \right]\frac{{{\rm d}{L_{cd,b}}}}{{{\rm d}t}}{\text{。}} \end{aligned} (24)

 ${b_b}\frac{{{\rm d}{L_{cd,b}}}}{{{\rm d}t}} + {b_g}\frac{{{\rm d}{L_{cd,g}}}}{{{\rm d}t}} - \frac{{{{\dot m}_{cd,\rm gout}}}}{{{A_{cd}}}} = {b_q}\text{。}$ (25)

${z_A} = {L_{cd,g}}$ ${z_B} = {L_{cd,g}} + {L_{cd,b}}$ 代入式（16）中，可得饱和区的能量守恒方程为：

 $\begin{split}\\[-12pt]{A_{cd}} & \displaystyle\frac{\rm d}{{{\rm d}t}}\int_{{L_{cd,g}}}^{{L_{cd,g}} + {L_{cd,b}}} {\left( {h\rho } \right){\rm d}z} + {A_{cd}}{h_{cd,gsa}}{\rho _{cd,gsa}}\displaystyle\frac{{{\rm d}{L_{cd,g}}}}{{{\rm d}t}}-\\& {A_{cd}}{h_{cd,lsa}}{\rho _{cd,lsa}}\displaystyle\frac{{{\rm d}\left( {{L_{cd,g}} + {L_{cd,b}}} \right)}}{{{\rm d}t}}=\\ & {h_{cd,gsa}}{{\dot m}_{cd,\rm gout}} - {h_{cd,lsa}}{{\dot m}_{cd,\rm bout}} + {q_{cd,b}}{L_{cd,b}}{\text{，}}\end{split}$ (26)

 \begin{aligned} \frac{d}{{dt}}& \displaystyle\int_{{L_{cd,g}}}^{{L_{cd,g}} + {L_{cd,b}}} {\left( {h\rho } \right){\rm d}z} = \\& \left[ {{\gamma _{cd,av}}{\rho _{cd,gsa}}{h_{cd,gsa}} + \left( {1 - {\gamma _{cd,av}}} \right){\rho _{cd,lsa}}{h_{cd,lsa}}} \right]\frac{{{\rm d}{L_{cd,b}}}}{{{\rm d}t}}{\text{。}} \end{aligned} (27)

 ${c_b}\frac{{{\rm d}{L_{cd,b}}}}{{{\rm d}t}} + {c_g}\frac{{{\rm d}{L_{cd,g}}}}{{{\rm d}t}} - \frac{{{h_{cd,gsa}}}}{{{A_{cd}}}}{\dot m_{cd,g{\rm out}}} = {c_q}{\text{。}}$ (28)

3.3 过热区模型

${z_A} = 0$ ${z_B} = {L_{cd,g}}$ 代入式（15）中，可得过热区的质量守恒方程为：

 ${A_{cd}}\frac{\rm d}{{{\rm d}t}}\int_0^{{L_{cd,g}}} {\rho dz} \!-\! {\rho _{cd,gsa}}{A_{cd}}\frac{{{\rm d}{L_{cd,g}}}}{{{\rm d}t}} \!=\! {\dot m_{cd,{\rm in}}} \!- \!{\dot m_{cd,g{\rm out}}}{\text{。}}$ (29)

 ${\rho _{cd,gav}} = \frac{{({\rho _{cd,\rm in}} + {\rho _{cd,gsa}})}}{2}{\text{，}}$ (30)

 $\begin{split}\\[-12pt]\frac{{\rm{d}}}{{{\rm{d}}t}}\int_0^{{L_{cd,g}}} \rho dz = & \frac{{\rm{d}}}{{{\rm{d}}t}}\left( {{\rho _{cd,gav}}{L_{cd,g}}} \right) = \\ & \frac{{{L_{cd,g}}}}{2}\frac{{{\rm{d}}{\rho _{cd,{\rm{in}}}}}}{{{\rm{d}}t}} + {\rho _{cd,gav}}\frac{{{\rm{d}}{L_{cd,g}}}}{{{\rm{d}}t}}{\text{。}}\end{split}$ (31)

 $\frac{{{\rm d}{\rho _{cd,\rm in}}}}{{{\rm d}t}} = \frac{{{{\dot m}_{t,{\rm in}}} - {{\dot m}_{cd,\rm in}}}}{{{V_t}}}{\text{。}}$ (32)

 ${{ d}_g}\frac{{{\rm d}{L_{cd,g}}}}{{{\rm d}t}} + \frac{{{{\dot m}_{cd,\rm gout}}}}{{{A_{cd}}}} + {d_m}{\dot m_{cd,\rm in}} = {d_q}{\text{。}}$ (33)

${z_A} = 0$ ${z_B} = {L_{cd,g}}$ 代入式（16）中，可得过热区的能量守恒方程为：

 \begin{aligned} {A_{cd}}\displaystyle \frac{\rm d}{{{\rm d}t}}& \int_0^{{L_{cd,g}}} {\left( {h\rho } \right){\rm d}z} - {A_{cd}}{h_{cd,gsa}}{\rho _{cd,gsa}}\displaystyle \frac{{{\rm d}{L_{cd,g}}}}{{{\rm d}t}} =\\& {h_{cd,in}}{\dot m_{cd,\rm in}} - {h_{cd,gsa}}{\dot m_{cd,\rm gout}} + {q_{cd,g}}{L_{cd,g}}{\text{。}}\end{aligned} (34)

 ${h_{cd,gav}} = \frac{{({h_{cd,\rm in}} + {h_{cd,gsa}})}}{2}{\text{，}}$

 $\begin{split}\\[-12pt] \frac{{\rm{d}}}{{{\rm{d}}t}}\int_0^{{L_{cd,g}}} & {\left( {h\rho } \right){\rm{d}}z} = \frac{{{\rm{d}}\left( {{\rho _{cd,gav}}{h_{cd,gav}}{L_{cd,g}}} \right)}}{{{\rm{d}}t}}\\& {\rho _{cd,gav}}{h_{cd,gav}}\frac{{{\rm{d}}{L_{cd,g}}}}{{{\rm{d}}t}} + \frac{{{L_{cd,g}}}}{{2{V_{tr}}}} \times \qquad\qquad\qquad\quad (35)\\ & \left\{ {\left[ {\frac{{{\rho _{cd,gav}}}}{{{\rho _{cd,{\rm{in}}}}}}\left( {{h_{tr}} - {h_{cd,{\rm{in}}}}} \right) + {h_{cd,gav}}} \right]{{\dot m}_n} - {h_{cd,gav}}{{\dot m}_{cd,\rm in}}} \right\}{\text{。}}\end{split}$

 ${e_g}\frac{{{\rm d}{L_{cd,g}}}}{{{\rm d}t}} + \frac{{{h_{cd,gsa}}}}{{{A_{cd}}}}{\dot m_{cd,\rm gout}} + {e_m}{\dot m_{cd,\rm in}} = {e_q}{\text{。}}$ (36)

 ${e_g} = {\rho _{cd,gav}}{h_{cd,gav}} - {\rho _{cd,gsa}}{h_{cd,gsa}}{\text{，}}$ (37)
 ${e_m} = - \left( {\frac{{{L_{cd,g}}{h_{cd,gav}}}}{{2{V_{tr}}}} + \frac{{{h_{cd,\rm in}}}}{{{A_{cd}}}}} \right){\text{，}}$ (38)
 ${e_q}\!\! =\!\!\! \frac{{{q_{cd,g}}{L_{cd,g}}}}{{{A_{cd}}}}\!\! -\!\! \frac{{{L_{cd,g}}}}{{2{V_t}}}\!\!\left[ {\frac{{{\rho _{cd,gav}}}}{{{\rho _{cd,in}}}}\!\!\left( {{h_{tr}} \!\!-\!\! {h_{cd,\rm in}}} \right) \!\!+\!\! {h_{cd,gav}}} \right]{\dot m_n}{\text{。}}$ (39)
4 仿真结果与讨论

 图 3 系统仿真结果 Fig. 3 Simulation results

5 结　语

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