﻿ 船舶柴油动力系统的多工况数学建模研究
 舰船科学技术  2024, Vol. 46 Issue (5): 86-89    DOI: 10.3404/j.issn.1672-7649.2024.05.016 PDF

Research on multi working condition mathematical modeling of marine diesel power systems
JIN Gui-yan, LV Lu
Jiangxi University of Technology, Nanchang 330098, China
Abstract: This article studies the power system of ship diesel engines, with a focus on analyzing the power device of ship diesel engines. The relationship curve between the speed and output power of ship diesel generators is given, and the propulsion load of ship diesel engines is constructed. The curve relationship between the torque and speed of ship propellers is analyzed; A mathematical model was constructed for the multi operating conditions of the ship's diesel power system; Simulated the multi operating condition model of marine diesel engines, and analyzed the combustion rate, pressure, and torque in the diesel engine; This article constructs a mathematical model for the multi operating conditions of ship diesel power systems, which is helpful for the rapid development of ship diesel power systems in China.
Key words: ships     diesel power system     mathematical modeling
0 引　言

1 船舶柴油机动力系统 1.1 船舶动力装置

 图 1 船舶柴油机动力系统结构 Fig. 1 Structure of ship diesel power system

 图 2 船舶柴油发电机转速和输出功率之间的关系曲线 Fig. 2 The relationship curve between the speed and output power of ship diesel generators

 图 3 船舶柴油机运行效率和功率之间的曲线关系 Fig. 3 The curve relationship between operating efficiency and power of marine diesel engines
1.2 船舶柴油机推进负载构建

 ${M_p} = {K_Q} \cdot \rho \cdot n_p^2 \cdot {D^5}\text{，}$ (1)
 ${T_p} = {K_T} \cdot \rho \cdot n_p^2 \cdot {D^4}\text{。}$ (2)

 图 4 船舶螺旋桨敞水特性曲线 Fig. 4 Ship propeller open water characteristic curve
 $J = \frac{{{h_p}}}{D}\text{。}$ (3)

 $J' = \frac{J}{{\sqrt {1 + {J^2}} }}\text{。}$ (4)

 $R = av_s^3\text{。}$ (5)

 ${P_p} = {M_p} \cdot \left( {{\text π} {n_p}/30} \right)\text{。}$ (6)

 $T = \left( {1 - t} \right){T_p}\text{。}$ (7)

 $m\frac{{{\rm{d}}{v_s}}}{{{\rm{d}}t}} = {T_p} - R\text{。}$ (8)

 图 5 船舶螺旋桨转矩和转速之间的曲线关系 Fig. 5 The curve relationship between the torque and speed of ship propellers
2 船舶动力系统工况数学模型构建

 $\sum\limits_i {\frac{{{\rm{d}}{Q_i}}}{{{\rm{d}}\varphi }}} = \frac{{{\rm{d}}{Q_f}}}{{{\rm{d}}\varphi }} + \frac{{{\rm{d}}{Q_w}}}{{{\rm{d}}\varphi }}\text{。}$ (9)

 $\frac{{{\rm{d}}W}}{{{\rm{d}}\varphi }} = - {p_z}\frac{{{\rm{d}}{V_z}}}{{{\rm{d}}\varphi }}\text{。}$ (10)

 ${p_z} = \frac{{{m_z}{R_z}{T_z}}}{{{V_z}}}\text{。}$ (11)

 $\sum\limits_j {{h_j}\frac{{{\rm{d}}{m_j}}}{{{\rm{d}}\varphi }} = {h_a}\frac{{{\rm{d}}{m_a}}}{{{\rm{d}}\varphi }} + {h_s}\frac{{{\rm{d}}{m_s}}}{{{\rm{d}}\varphi }} - {h_e}\frac{{{\rm{d}}{m_e}}}{{{\rm{d}}\varphi }}} \text{。}$ (12)

 ${m_z} = {m_a} + {m_f}\text{，}$ (13)
 ${\lambda _z} = \frac{{{m_z} - {g_f}{\chi _k}}}{{{L_0}{g_f}{\chi _k}}}\text{。}$ (14)

 ${R_z} = 29.2647 - \frac{{0.0402}}{{{\lambda _z}}}\text{，}$ (15)
 ${M_z} = 28.9705 - \frac{{0.0403}}{{{\lambda _z}}}\text{。}$ (16)

 $\frac{{{\rm{d}}{Q_w}}}{{{\rm{d}}\varphi }} = {\alpha _w}\left[ {\frac{{4{V_z}}}{D}\left( {{T_z} - {T_w}} \right) + \frac{{{\text π} {D^2}}}{4}} \right]\frac{1}{{21\;600n}}\text{，}$ (17)
 ${\alpha _w} = \xi {D^{ - 0.214}}{\left( {{C_m}{p_z}} \right)^{0.786}}T_z^{ - 0.525}\text{。}$ (18)

 $\frac{{d{m_s}}}{{d\varphi }} = \frac{{{\mu _s}{F_s}}}{{6n}}\sqrt {\frac{{2{k_A}}}{{{k_A} - 1}}} \frac{{{p_A}}}{{\sqrt {{R_A}{T_A}} }}\text{。}$ (19)

 $\frac{{{\rm{d}}{Q_f}}}{{{\rm{d}}\varphi }} = {\eta _{com}}{H_u}{g_f}\frac{{{\rm{d}}\chi }}{{{\rm{d}}\varphi }}\text{。}$ (20)
3 船舶柴油机多工况模型仿真

 ${y_{n + 1}} = {y_n} + f\left( {{t_n},{y_n}} \right){\rm{d}}t\text{。}$ (21)

 ${\rm{d}}\varphi = 6n{\rm{d}}t\text{。}$ (22)

 图 6 100%工况下的燃烧放热率曲线 Fig. 6 Combustion heat release rate curve under 100%operating conditions

 图 7 90%工况下气缸压强曲线 Fig. 7 Cylinder pressure curve at 90% operating condition

 图 8 扫气过程气缸压强变化曲线 Fig. 8 Pressure variation curve of cylinder during scavenging process

 图 9 100%工况下柴油机输出扭矩曲线 Fig. 9 Output torque curve of diesel engine under100% operating conditions
4 结　语

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