第三章 物理模型的建立

jc posted @ 2010年5月26日 02:13 in 毕业论文(不再更新) , 2702 阅读

     为了模拟板翅式换热器的换热和流动特性,首先设计一台空气——空气板翅式换热器,以作为数值模拟的模型基础和参考。

 

3.1 原始数据

表3-1 原始数据

                                                        热空气                冷空气

入口温度[tex]^{\circ}C[/tex]              180                    40

入口压力[tex]MPa[/tex]                     0.2648            0.1013

入口质量流量[tex]kg/h[/tex]             3200                 5600

换热器效率                                           [tex]\ge 0.75[/tex]

压降[tex]MPa[/tex]                   [tex]\le 0.4[/tex]  [tex]\le 1[/tex]

流动长度[tex]mm[/tex]                      480                    270

 

3.2 平均温度及物性参数计算

首先假设换热器的效率为75%,则:

 

[tex]\because \quad W_{1}=W_{min}[/tex]

[tex]\therefore \quad \eta=\frac{t_{1}^{'}-t_{1}^{''}}{t_{1}^{'}-t_{2}^{''}}[/tex]

 

[tex]t_{1}^{''}=t_{1}^{'}-\eta(t_{1}^{'}-t_{2}^{''})=180-0.75\times(180-40)=75^{\circ}C[/tex]

 

[tex]\because \quad \eta=\frac{W_{2}(t_{2}^{''}-t_{2}^{'})}{W_{1}(t_{1}^{'}-t_{2}^{'})}[/tex]

[tex]\therefore \quad t_{2}^{''}=\eta\frac{W_{2}}{W_{1}}(t_{1}^{'}-t_{2}^{'})+t_{2}^{'}[/tex]

 

假设[tex]c_{p1}=c_{p2}[/tex],则:

 

[tex]t_{2}^{''}=0.75\times \frac{3200}{5600}\times(180-40)+40=100^{\circ}C[/tex]

 

由于[tex]C^{\ast}=\frac{W_{min}}{W_{max}}=\frac{W_{1}}{W_{2}}\approx \frac{q_{m1}}{q_{m2}}=\frac{3200}{5600}=0.571\le 0.5[/tex]

取算术平均温度作为其平均温度:

 

[tex]t_{m1}=\frac{t_{1}^{'}+t_{1}^{''}}{2}=\frac{180+75}{2}=127.5^{\circ}C[/tex]

[tex]t_{m2}=\frac{t_{2}^{'}+t_{2}^{''}}{2}=\frac{40+100}{2}=70^{\circ}C[/tex]

 

根据平均温度[tex]t_{m1}=127.5^{\circ}C \quad t_{m2}=70^{\circ}C[/tex],求冷热空气的物性参数。

 

[tex]\mu_{1}\!=\!1.50619\!\times\! 10^{-6}\!\times\! \frac{(t_{m1}+273)^{1.5}}{t_{m1}\!+\!395}\!=\!1.50619\!\times\! 10^{-6}\!\times\! \frac{(127.5+273)^{1.5}}{127.5+395}\!=\!23.105\!\times\! 10^{-6}Pa\!\cdot\!s[/tex]

 

同理[tex]\mu_{2}20.576\times 10^{-6}Pa\cdot s[/tex]

 

[tex]\lambda_{1}=2.456\times 10^{-4}\times(t_{m1}+273)^{0.823}=2.456\times 10^{-4}\times(127.5+273)^{0.823}=3.4054\times 10^{-2}[/tex]

 

同理[tex]\lambda_{2}=2.9976\times 10^{-2}W/(m^{2}\cdot K)[/tex]

 

[tex]c_{p1}\!=\!1003+0.02t_{m1}+4\times 10^{-4}t_{m1}^{2}\!=\!1012.05J/(kg \cdot K)\!=\!1.0120 KJ/(kg \cdot K)[/tex]

 

同理[tex]c_{p2}=1006.36J/(kg\cdot K)=1.0064KJ/(kg\cdot K)[/tex]

 

[tex]P_{r1}=\frac{\mu_{1}c_{p1}}{\lambda_{1}}=\frac{23.105\times 10^{-6}\times 1012.05}{3.4054\times 10^{-2}}=0.6867[/tex]

 

同理[tex]P_{r2}=0.6954[/tex]

 

 表3-2 冷热空气的物性参数

参数                [tex]\mu \; Pa\cdot s[/tex]        [tex]\lambda \; W/(m^{2}\cdot K)[/tex]        [tex]c_{p} \; KJ/(kg\cdot K)[/tex]        [tex]P_{r}[/tex]

热空气         [tex]23.105\times 10^{-6}[/tex] [tex]3.4054\times 10^{-2}[/tex]                  [tex]1.0120[/tex]                        [tex]0.6867[/tex]

冷空气         [tex]20.576\times 10^{-6}[/tex] [tex]2.9976\times10^{-2}[/tex]                   [tex]1.0064[/tex]                        [tex]0.6934[/tex]

 

3.3 结构参数的计算

表3-3 产品结构尺寸表

                                                                        热侧                                        冷侧

型面                                                                平直型                                平直型

翅片节距[tex]s/mm[/tex]                                2.0                                        2.1

板间距[tex]b/mm[/tex]                                      4.7                                        6.5

翅片层数[tex]N[/tex]                                            7                                           8

翅片厚度[tex]\delta_{f}/mm[/tex]                        0.3                                      0.3

隔板厚度[tex]\delta_{p}/mm[/tex]                                             0.5

侧板厚度[tex]\delta_{s}/mm[/tex]                                               2

封条厚度[tex]b_{s}/mm[/tex]                                                       6

 

换热器高度:

 

[tex]L_{3}=N_{1}(b_{1}+2\delta_{p})+N_{2}b_{2}+2\delta_{s}=7\times(4.7+2\times 0.5)+8\times 6.5+2\times 2=95.9 mm[/tex]

 

翅片高:

 

[tex]h_{1}=b_{1}-\delta_{f1}=4.7-0.3=4.4 mm[/tex]

[tex]h_{2}=b_{2}-\delta_{f2}=6.5-0.3=6.2 mm[/tex]

 

翅片宽:

 

[tex]w_{1}=s_{1}-\delta_{f1}=2.0-0.3=1.7 mm[/tex]

[tex]w_{2}=s_{2}-\delta_{f2}=2.1-0.3=1.8 mm[/tex]

 

水力直径:

 

[tex]d_{h1}=\frac{2w_{1}h_{1}}{w_{1}+h_{1}}=\frac{2\times 1.7\times 4.4}{1.7+4.4}=2.4525 mm[/tex]

[tex]d_{h2}=\frac{2w_{2}h_{2}}{w_{2}+h_{2}}=\frac{2\times 1.8 \times 6.2}{1.8+6.2}=2.79 mm[/tex]

 

翅片面积比:

 

[tex]\varphi_{1}=\frac{A_{f1}}{A_{1}}=\frac{2N_{1}h_{1}L_{1}L_{2}/s_{1}}{2N_{1}(h_{1}+w_{1})L_{1}L_{2}/s_{1}}=\frac{h_{1}}{h_{1}+w_{1}}=\frac{4.4}{4.4+1.7}=0.7213[/tex]

[tex]\varphi_{2}=\frac{A_{f2}}{A_{2}}=\frac{h_{2}}{h_{2}+w_{2}}=\frac{6.2}{6.2+1.8}[/tex]

 

传热面积密度:

 

[tex]\beta_{1}=\frac{A_{1}}{A_{p1}}=\frac{2N_{1}L_{1}L_{2}(h_{1}+w_{1})/s_{1}}{L_{1}L_{2}N_{1}b_{1}}=\frac{2(h_{1}+w_{1})}{b_{1}s_{1}}=\frac{2\times(4.4+1.7)}{4.7\times 2.0\times 10^{-3}}=1298 m^{2}/m^{3}[/tex]

[tex]\beta_{2}=\frac{A_{2}}{A_{p2}}=\frac{2(h_{2}+w_{2})}{b_{2}s_{2}}=\frac{2\times(6.2+1.8)}{6.5\times 2.1\times 10^{-3}}=1172 m^{2}/m^{3}[/tex]

 

 空气流通面积:

 

[tex]A_{c1}=N_{1}{(L_{2}-1.5b_{s})b_{1}-[\frac{L_{2}-1.5b_{s}}{s_{1}}(s_{1}-\delta_{f1})+(\frac{L_{2}-1.5b_{s}}{s_{1}}-1)b_{1}]}=7\times{(270-1.5\times5)\times 4.7-[\frac{270-1.5\times 6}{2}\times(2-0.3)+(\frac{270-1.5\times 6}{2}-1)\times 4.7]}=2.7734\times 10^{-3}m^{2}[/tex]

[tex]A_{c2}=N_{2}{(L_{1}-2b_{s})b_{2}-[\frac{L_{1}-2b_{s}}{s_{2}}(s_{2}-\delta_{f2})+(\frac{L_{1}-2b_{s}}{s_{2}}-1)b_{2}]}=1.1923\times 10^{-3}m^{2}[/tex]

 

空气迎风面积:

 

[tex]A_{y1}=(L_{2}-1.5b_{s})(L_{3}-1.5\delta_{s})=(270-1.5\times 6)\times(95.9-1.5\times 2)\times 10^{-6}=0.024247m^{2}[/tex]

[tex]A_{y2}=(L_{1}-2b_{s})(L_{3}-2\delta_{s})=(480-2\times 6)\times(95.9-2\times 2)\times 10^{-6}=0.043009m^{2}[/tex]

 

孔度:

 

[tex]\sigma_{1}=\frac{A_{c1}}{A_{y1}}=\frac{2.7734\times 10^{-3}}{0.024247}=0.11441[/tex]

[tex]\sigma_{2}=\frac{A_{c2}}{A_{y2}}=\frac{1.1923\times 10^{-3}}{0.043009}=0.0277[/tex]

 

一次传热面积:

 

[tex]A_{p}=2N_{1}(L_{1}--1.5b_{s})(L_{2}-2b_{s})=2\times 7\times(480-1.5\times 6)\times(270-2\times 6)=1.701252[/tex]

 

二次传热面积:

 

[tex]A_{f1}=2N_{1}h_{1}L_{1}\frac{L_{2}-1.5b_{s}}{s_{1}}=2\times 7\times 4.4\times 480\times \frac{270-1.5\times 6}{2.0}=3.858624m^{2}[/tex]

[tex]A_{f2}=2N_{2}h_{2}L_{2}\frac{L_{1}-2b_{}s}{s_{2}}=2\times 8\times 6.2\times 270\times \frac{480-2\times 6}{2.1}=5.969006m^{2}[/tex]

 

3.4 传热计算

质量流量:

 

[tex]g_{m1}=\frac{q_{m1}}{A_{c1}}=\frac{0.889}{2.7734\times 10^{-3}}=320.545 kg/(m^{2}\cdot s)[/tex]

[tex]g_{m2}=\frac{q_{m2}}{A_{c2}}}=\frac{1.556}{1.1923\times 10^{-3}}=1305.041kg/(m^{2}\cdot s)[/tex]

 

雷诺数:

 

[tex]R_{e1}=\frac{g_{m1}d_{h1}}{\mu_{1}}=\frac{320.545\times 2.4525\times 10^{-3}}{23.105\times 10^{-6}}=34024.54[/tex]

[tex]R_{e2}=\frac{g_{m2}d_{h2}}{\mu_{2}}=\frac{1305.041\times 2.79\times 10^{-3}}{20.576\times 10^{-6}}=176956.86[/tex]

 

由雷诺数可知,流体处于充分发展的湍流状态,采用Gnielinsk公式:

 

[tex]f_{1}=(1.58\lnR_{e1}-3.28)^{-2}\!=\!(1.58\ln(34024.54)-3.28)^{-2}\!=\!6.532842\times10^{-3}[/tex]

[tex]f_{2}\!=\!(1.58\ln R_{e2}-3,28)^{-2}\!=\!(1.58\ln(176956.86)-3.28)^{-2}\!=\!3.999600\!\times\!10^{-3}[/tex]

 

[tex]N_{u1}=\frac{(f_{1}/2)(R_{e1}-1000)P_{r1}}{1+12.7(f_{1}/2)^{0.5}(P_{r1}^{2/3}-1))}=88.28[/tex]

[tex]N_{u2}=\frac{(f_{2}/2)(R_{e2}-1000)P_{r2}}{1+12.7(f_{2}/2)^{0.5}(P_{r2}^{2/3}-1))}=277.94[/tex]

 

[tex]\alpha_{1}=\frac{N_{u1}\lambda_{1}}{d_{h1}}=\frac{88.28\times 3.4054\times 10^{-2}}{2.4525\times 10^{-3}}=1225.82W/(m^{2}\cdot K)[/tex]

[tex]\alpha_{2}=\frac{N_{u2}\lambda_{2}}{d_{h2}}=\frac{277.94\times 2.9976\times 10^{-2}}{2.79\times 10^{-3}}=2986.21W/(m^{2}\cdot K)[/tex]

 

翅片参数:

 

[tex]m_{1}=\sqrt{\frac{2\alpha_{1}}{\lambda_{f1}\delta_{f1}}}=\sqrt{\frac{2\times 1225.82}{175\times 0.3\times 10^{-3}}}=216.10m^{-1}[/tex]

[tex]m_{2}=\sqrt{\frac{2\alpha_{2}}{\lambda_{f2}\delta_{f2}}}=\sqrt{\frac{2\times 2986.21}{175\times 0.3\times 10^{-3}}}=337.28m^{-1}[/tex]

 

[tex]m_{1}h_{1}=216.10\times4.4\times 10^{-3}=0.950828[/tex]

[tex]m_{2}h_{2}=337.28\times 6.2\times 10^{-3}=2.092236[/tex]

 

[tex]\eta_{f1}=\frac{tanh(m_{1}h_{1})}{m_{1}h_{1}}=\frac{tanh(0.950828)}{0.950828}=0.7784[/tex]

[tex]\eta_{f2}=\frac{tanh(m_{2}h_{2})}{m_{2}h_{2}}=\frac{tanh(2.091136)}{2.091136}=0.4638[/tex]

 

有效传热面积:

 

[tex]A_{ef1}=A_{p}+\eta_{f1}A_{f1}=1.701252+0.7784\times 3.858624=4.704940m^{2}[/tex]

[tex]A_{ef2}=A_{p}+\eta_{f2}A_{f2}=1.701252+0.4638\times 5.969006=4.469675m^{2}[/tex]

 

两侧总有效传热面积:

 

[tex]A_{1}=A_{p}+A_{f1}=1.701252+3.858624=5.559876m^{2}[/tex]

[tex]A_{2}=A_{p}+A_{f2}=1.701252+5.969006=7.670258m^{2}[/tex]

 

两侧表面效率:

 

[tex]\eta_{01}=1-\frac{A_{f1}}{A_{1}}(1-\eta_{f1})=1-\frac{3.858624}{5.559876}\times(1-0.7784)=0.846207[/tex]

[tex]\eta_{02}=1-\frac{A_{f2}}{A_{2}}(1-\eta_{f2})=1-\frac{5.969006}{7.670258}\times(1-0.4638)=0.582728[/tex]

 

壁面热阻:

 

[tex]R_{w}=\frac{\delta_{p}}{\lambda_{w}A_{p}}=\frac{0.5\times 10^{-3}}{175\times 1.701252}=1.679435\times 10^{-6}K/W[/tex]

 

忽略污垢热阻,则:

 

[tex]\frac{1}{KA}=\frac{1}{\eta_{01}\alpha_{1}A_{1}}+R_{w}+\frac{1}{\eta_{02}\alpha_{2}A_{2}}=2.4999\times 10^{-4}[/tex]

[tex]KA=4000.10W/K[/tex]

 

传热单元数:

 

[tex]NTU=\frac{KA}{W_{min}}=\frac{4000.1}{0.889\times 1.012\times 10^{3}}=4.4462[/tex]

 

德思克近似公式:

 

[tex]\eta_{i}=1-exp{\frac{NTU^{0.22}}{C^{\ast}}[exp(1-C^{\ast}NTU^{0.78})-1]}=0.7503[/tex]

 

[tex]\eta=\frac{(\frac{1-C^{\ast}\eta_{i}}{1-\eta_{i}})^{2}-1}{(\frac{1-C^{\ast}\eta_{i}}{1-\eta_{i}})^{2}-C^{\ast}}=0.9053[/tex]

 

换热器传热热流量:

 

[tex]\Phi=\eta W_{min}(t_{1}^{'}-t_{2}^{'})=0.9053\times 0.889\times 1.012\times 10^{3}\times(180-40)=114.03KW[/tex]

 

流体出口温度:

 

[tex]t_{1}^{''}=t_{1}^{'}-\frac{\Phi}{W_{1}}=180-\frac{114.03}{0.889\times 1.012\times 10^{3}}=53.253^{\circ}C[/tex]

[tex]t_{2}^{''}=t_{2}^{'}+\frac{\Phi}{W_{2}}=40+\frac{114.03}{1.556\times 1.0064\times 10^{3}}=112.818^{\circ}C[/tex]

 

与假设效率误差:

 

[tex]\Delta\eta=|\frac{\eta-\eta_{s}}{\eta_{s}}|=\frac{0.0003}{0.75}=20.71%[/tex]

 

3.5 阻力计算

热侧阻力:

 

[tex]v_{1}^{'}=\frac{RT_{1}^{'}}{p_{1}^{'}}=\frac{287\times(180+273)}{0.2648\times 10^{6}}=0.4910m^{3}/kg[/tex]

 

设[tex]\Delta p_{1}=10000Pa[/tex]:

 

[tex]v_{1}^{''}=\frac{RT_{1}^{''}}{p_{1}^{''}}=\frac{287\times(53.253+273)}{(0.2648-0.01)\times 10^{6}}=0.3675m^{3}/kg[/tex]

[tex]v_{m1}=\frac{v_{1}^{'}+v_{1}^{''}}{2}=\frac{0.4910+0.3675}{2}=0.4292 m^{3}/kg[/tex]

 

由[tex]\delta_{1}=0.1144[/tex],得[tex]\delta^{2}=0.0131[/tex],查图2-4得[tex]K_{1}^{'}=0.46\quad K_{1}^{''}=0.85[/tex]

 

[tex]1-\delta_{1}^{2}+K_{1}^{'}=1-0.0131+0.46=1.4469[/tex]

[tex]\frac{v_{1}^{''}}{v_{1}^{'}}=\frac{0.3675}{0.4910}=0.7485[/tex]

[tex]2(\frac{v_{1}^{''}}{v_{1}^{'}}-1)=-0.5031[/tex]

[tex]4f_{1}\frac{L_{1}}{d_{h1}}\cdot \frac{v_{m1}}{v_{1}^{'}}=4\times 6.532842\times 10^{-3}\times \frac{480\times 2}{2.4525}\times \frac{0.4292}{0.4910}=8.9413[/tex]

[tex](1-\delta_{1}^{2}-K^{''})\frac{v_{1}^{''}}{v_{1}^{'}}=(1-0.0131-0.85)\times 0.7485=0.1025[/tex]

 

设局部阻力损失系数为[tex]\xi_{a}=5[/tex],则局部损失为:

 

[tex]\xi_{a}\frac{v_{m1}}{v_{1}^{'}}=5\times \frac{0.4292}{0.4910}=4.3707[/tex]

 

[tex]\frac{g_{m1}^{2}v_{1}^{'}}{2}=\frac{320.545^{2}\times 0.4910}{2}=25224.9033[/tex]

[tex]\Delta p_{1}\!=\!\frac{g_{m1}^{2}v_{1}^{'}}{2}[(1-\delta_{1}^{2}+K_{1}^{'})+2(\frac{v_{1}^{''}}{v_{1}^{'}}-1)+4f_{1}\frac{L_{1}v_{m1}}{d_{h1}v_{1}^{'}}-(1-\selta_{1}^{2}-K_{1}^{''})\frac{v_{1}^{''}}{v_{1}^{'}}+\xi_{a}\frac{v_{m1}}{v_{1}^{'}}]=3.570156\times 10^{5}[/tex]

 

        压降符合设计要求。冷侧预设[tex]\Delta p_{2}=25300Pa[/tex],采用与热侧相同的计算方式可得[tex]\Delta p_{2}=9.130742\times 10^{5}Pa[/tex],也符合设计要求。

 

 

 

 

 

 

 

 

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lilu 说:
2010年11月30日 03:25

你好,我现在也在做板翅式换热器方面的研究,我是化工方面偏重于工程应用的,真心希望能和你讨论一些问题。email:lilikkkkk@搜狐.com

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jc 说:
2010年12月01日 11:08

呵呵,研究说不上。只是一片普通的本科生毕业论文而已。
很抱歉我已经转行了,现在做我喜欢的IT行业!
换热器数值模拟还是有很多可以发展的领域,尤其是封头的形式对于流动分配的影响。
这个对板翅式换热器的效率影响很大,可以研究一下。

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