﻿ 燃料电池-燃气轮机底层循环性能研究
 舰船科学技术  2018, Vol. 40 Issue (8): 76-80 PDF

Research on the performance of SOFC-GT bottom cycle
ZHAN Hai-yang, LIANG Qian-chao, ZHU Run-kai, WEN Qiang
Naval University of Engineering, Wuhan 430033, China
Abstract: The SOFC-GT combined cycle system as the power source of ship has higher efficiency than traditional engine. In this paper, a mathematical model is built for the bottom cycle of SOFC-GT, and its performance is simulated. At present, the power of SOFC is smaller than micro gas turbine. In order to realize the power matching between SOFC and micro gas turbine, a multi stack fuel cell and gas turbine combined cycle is proposed. The system can keep high efficiency under different working conditions by analysing power matching and parameter optimization. It has laid a solid foundation for the application of SOFC-GT combined power system on ships.
Key words: SOFC     micro gas turbine     power matching     modeling and simulation
0 引　言

1 构建系统数学模型

 图 1 系统结构拓扑图 Fig. 1 System structure topology

1.1 燃料电池模型

 ${\rm{C}}{{\rm{H}}_4} + {{\rm{H}}_2}{\rm{O}} \leftrightarrow {\rm{CO}} + 3{{\rm{H}}_2}\text{，}$ (1)
 ${\rm{CO}} + {{\rm{H}}_2}{\rm{O}} \leftrightarrow {\rm{C}}{{\rm{O}}_2} + {{\rm{H}}_2}{\text{。}}$ (2)

 ${r_r} = {K_r}P_{_{C{H_{4,tpb}}}}^\alpha P_{_{{H_2}O,tpb}}^\beta \exp \left( - \frac{{{E_r}}}{{R{T_{fuel}}}}\right){\text{。}}$ (3)

 $\begin{split}{K_r} =& \exp ({A_r}T_{fuel}^4 + {B_r}T_{fuel}^3 + {C_r}T_{fuel}^2 + \\&{D_r}T_{fuel}^{} + {E_r})\text{。}\end{split}$ (4)

 $\begin{split}{K_s} =& \exp ({A_s}T_{fuel}^4 + {B_s}T_{fuel}^3 + {C_s}T_{fuel}^2 + \\&{D_s}T_{fuel}^{} + {E_s})\text{，}\end{split}$ (5)

 $\begin{split} & {{\rm{H}}_2} + {{\rm{O}}^{2 - }} \to {{\rm{H}}_2}{\rm{O}} + 2{{\rm{e}}^ - }\text{，} \\ & \frac{1}{2}{{\rm{O}}_2} + 2{{\rm{e}}^ - } \to {{\rm{O}}^{2 - }} \text{。}\end{split}$ (6)

 $E = {E^0} - \frac{{R{T_{cell}}}}{{4F}}\ln \left(\frac{{{p^2}_{tpb,{{\rm{H}}_2}{\rm{O}}}}}{{{p^2}_{tpb,{{\rm{H}}_2}} \cdot p_{tpb,{{\rm{O}}_2}}^{}}}\right)\text{，}$ (7)
 ${E^0} = 1.272\;3 - 2.764\;5 \times {10^{ - 4}}{T_{cell}}\text{，}$ (8)

 ${v_f}_c = E - {\eta _{ohmic}} - {\eta _{conc}} - {\eta _{act,a}} - {\eta _{act,c}}\text{。}$ (9)

 ${q_{conv}} = hA\left( {{T_{cell}} - {T_{fuel}}} \right)\text{。}$ (10)

 $\begin{split}h =& 0.332\frac{k}{{{D_{fuel,air}}}}{\left( {\frac{{{C_V}\mu }}{k}} \right)^{1/3}} \times \\&{\left( {\frac{{{D_{fuel,air}}M}}{\mu }} \right)^{1/2}}{\left( {\frac{{uP}}{{R{T_{out}}}}} \right)^{1/2}}{\text{。}}\end{split}$ (11)

 ${m_{cell}}{C_{cell}}\left( T \right) \cdot \frac{{d{T_{cell}}}}{{dt}} = - {P_{fc}} - {r_3}\Delta {H_3}\left( T \right) - {q_{conv}}\text{，}$ (12)
 $\begin{split} & {C_{re}}\left( T \right) \cdot \frac{{d{T_{out}}}}{{dt}} = \sum {\left( {G_{in,i}^{air} \cdot h_{_{in,i}}^{air}} \right)} + \sum {\left( {G_{in,i}^{fuel} \cdot h_{_{in,i}}^{air}} \right)} -\\ & \sum {\left( {G_{_{out,i}}^{air} \cdot h_{_{out,i}}^{air}} \right)} - \sum {\left( {G_{_{out,i}}^{fuel} \cdot h_{_{out,i}}^{fuel}} \right)} - {r_r}\Delta {H_r}\left( T \right)-\\ & {r_s}\Delta {H_s}\left( T \right) + {q_{conv}} \text{。}\end{split}$ (13)

1.2 微型燃气轮机模型

 $\Delta p = \frac{{{p_{in}} - {p_{out}}}}{{{p_{in}}}}{\rm{ = }}{\left( {\frac{{{G_{in}}}}{{{G_0}}}} \right)^2} \cdot \sigma {\text{。}}$ (14)

 ${G_{{\rm{in}}}} = {G_{{\rm{out}}}}{\text{，}}$ (15)

 $\begin{split} {\pi _C} = {f_1}\left({G_{in}}\frac{{{p_0}\sqrt {{T_{in}}} }}{{{p_{in}}\sqrt {{T_0}} }},{n_c}\frac{{\sqrt {{T_0}} }}{{\sqrt {{T_{in}}} }}\right) \text{，}\\ {\eta _C} = {f_2}\left({G_{in}}\frac{{{p_0}\sqrt {{T_{in}}} }}{{{p_{in}}\sqrt {{T_0}} }},{n_c}\frac{{\sqrt {{T_0}} }}{{\sqrt {{T_{in}}} }}\right) \text{。}\end{split}$ (16)

 $N{e_C} = {{{c_{pa}}{T_{in}}(\pi _C^{{m_a}} - 1)} / {{\eta _C}}}\text{，}$ (17)

 ${T_{out}} = {{{T_{in}}[1 + (\pi _C^{{m_a}} - 1)} / {{\eta _C}}}]\text{。}$ (18)

 $\begin{split} {\varepsilon _T} = {f_3}\left(\frac{{{G_{{\rm{in}}}}\sqrt {{T_{{\rm{in}}}}} }}{{{p_{{\rm{in}}}}}},\frac{{{n_T}}}{{\sqrt {{T_{{\rm{in}}}}} }}\right)\text{，} \\ {\eta _T} = {f_4}\left(\frac{{{G_{{\rm{in}}}}\sqrt {{T_{{\rm{in}}}}} }}{{{p_{{\rm{in}}}}}},\frac{{{n_T}}}{{\sqrt {{T_{{\rm{in}}}}} }}\right) \text{。}\end{split}$ (19)

 $N{e_T} = {c_{pg}}{T_{{\rm{in}}}}(1 - \varepsilon _T^{ - {m_g}}){\eta _T}\text{，}$ (20)

 ${T_{{\rm{out}}}} = {T_{{\rm{in}}}}[1 - (1 - \varepsilon _T^{ - {m_g}}){\eta _T}]\text{。}$ (21)
1.3 换热器模型

 $\Delta {T_{lc}} = \frac{{T_1'- T_2''}}{{\ln \left( {{{T_1'' - T_2'} / {T_1'- T_2''}}} \right)}}\left( {\frac{{T_1'' - T_2'}}{{T_1'- T_2''}} - 1} \right)\text{。}$ (22)

 $P = \frac{{T_2'' - T_2'}}{{T_1'- T_2'}},R = \frac{{T_1'- T_1''}}{{T_2'' - T_2'}}\text{。}$ (23)
 图 2 温度修正系数 Fig. 2 Temperature correction factor

 $\varPhi = {q_{m1}}{c_{p1}}\left( {T_1'- T_1''} \right) = {q_{m2}}{c_{p2}}\left( {T_2'' - T_2'} \right)\text{。}$ (24)
2 性能研究

 图 3 电堆连接体结构 Fig. 3 Structure of SOFC

 图 4 电堆性能参数 Fig. 4 Test curve

 图 5 变工况效率特性曲线 Fig. 5 The efficiency of SOFC-GT at off-design condition

 图 6 系统效率特性曲线 Fig. 6 The efficiency of SOFC-GT at off-design condition

 图 7 系统功率特性曲线 Fig. 7 The power of SOFC-GT at off-design condition

3 结　语

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