1第一题一管壳式换热器,单壳程、双管程,用渣油预热原油。渣油的质量流量是,入口温度为,原油的质量流量是入口温度为,求原油的出口温度,换热器的总传热系数,传热效率。换热器的结构参数如下:传热面积A=130m2壳体直径D=0.7m管子规格Φ25×2.5mm管中心距P=32mm,正方形排列管长L=6m管程通道截面积AT=0.0459m2壳程通道截面积AS=0.0525m2渣油侧的污垢热阻R渣油=0.0005m2·K/W原油侧的污垢热阻R原油=0.0001m2·K/W解:1初设出口温度Th2或Tc2。1)设定热容流率较小一侧流体的出口温度。∵Wh=68250㎏/hWc=175000㎏/h显然:Wh〈WcWhCph〈WcCpc即:热流体一侧热容流率较小,所以设热流体一侧出口温度。2)进一步估算冷流体出口温度Tc2=Tc1+Wh/Wc(Th1-Th2)=275+68250/175000(382-328.5)=295.9(℃)故初设:Th2=328.5(℃)Tc2=295.9(℃)2.计算物性参数及传热系数;1)定性温度:Tmc=(Tc2+Tc1)/2=(295.9+275)/2=285.5(℃)Tmh=(Th2+Th1)/2=(382+328.5)/2=355.25(℃)2)计算物性参数:密度、比热、导热系数、粘度。相对密度D式中X=1+t/100;t-定性温度;A密度:D20-20℃时油品相对密度,D20渣油=0.919,D20原油=0.850hkgWh/68250CToh382hkgWc/175000CTco2755.328)275382(5.03825.0)11(12TcThThTh)exp(556.0312.00841.0)(174.0248.0942.02020220XDXXDDXDD1000855.310015525.41001TXTXch2Dh=0.6866同理Dc=0.6227。比热Cp式中,K为油品特性因数,可查取或实测对渣油,K渣油=12.5对原油,K原油=12.5Cph=0.7857Cpc=0.7499导热系数λ单位粘度υ(单位为cSt1cSt=10-6m2/s)注意区别动力粘度和运动粘度,运动粘度单位:cSt式中:z-渣油;y-原油)exp(556.0312.00841.02)^20(174.0248.0942.02020hhhhhhhhXDXDXDXD)/()35.0055.0(318.0)000551.000147.0(7072.02020CkgkcalKDtDCpoCkgKcalCkgKcal)/(/00054.011008.020hCmkcalDto1003.0)00054.01(1008.008864.0)00054.01(1008.02020cchhDTmcDTmh)(hCmKcalcsttba22.1)273ln(expexp1312010090150050273273ln/)22.1ln()22.1ln(ln)273ln()22.1ln(ln222111212111yzyzttttbtba3SI单位为:㎡/s3、据换热器的结构尺寸求a、安排流程:管程:I,h,渣油—热流体,易结垢,粘度大,管内易清洗,热损失少。壳程:O,C原油—冷流体。b、分别计算管程和壳程的流速。注意单位:由(㎏/h)换算为u的单位(m/s)单位是:m/sc、计算Re,Pr准数。其中:di=0.025-2×0.0025=0.02d、计算0,i;6^106013.06^10617.1chKi,,0602.03600hihhhhNAWAWui487.100cAWcu1193.41Pr9.67285Re66.7455Re000hhhphhhphiccehiihhiiCCuddudi69.11Pr0cccpcccpcuCC02718.0025.0)2^025.042^032.0(4)2^42^(400ddpdeo14.0)^/(33.0Pr^8.0Re^023.0wiuuda14.0)^/(33.0Pr^55.0Re^36.00wuudea4e、进行壁温校正:Qc=WcCpc(Tc2-Tc1)Qh=WhCph(Th1-Th2)据:冷侧:Twc>TmcTwc=(Tc1+Tc2)/2+Qc/(0×A0)热侧:Twh<TmhTwh=(Th1+Th2)/2-Qh/(i×Ai)Qc=WcCpc(Tc2–Tc1)=3.18×10^6J/sQH=WhCph(Th1–Th2)=3.3×10^6J/s只估算一侧壁温,认为Twc=Twhf、求K0:1K0=R0+1/0+(d0/di)Ri+(d0/di)1/0=215.41g、求=0.37464、计算TH2:TH2’=TH1-(TH1–TC1)=382-0.3746(382-275)=341.90CTH2’-TH20.1所以重新计算TC2、Tmc、Tmh、物性参数等等。第一次计算数据:48.435PrRe023.0.........365.1352PrRe527.0Re36.033.0^8.0^33.0^05.0^055.0^0002000Re2000ReiiihiecddLLiodnAdnAio2)^(1maxminCCNTUmin)(WCpAKNTU))(^1()(^12max)^min(1max)min(12eeCCCC5Th1Th2TmhD20hXhDhCph382328.5355.250.9194.55250.6866430.785686Tc1Tc2TmcD20cXcDcCpc275295.9285.450.853.85450.6226930.749927λhazbzυhυhAtWh0.08864318.917-2.92961.616731.6167*10^-60.045968250λcaybyυcυcAsWc0.10030922.81-3.68710.6013640.6013*10^-60.0525175000UidiReiPriαiCmax0.6015290.027441.29841.19797435.0817131237.2U0de0Re0Pr0α0KCmin1.4869690.027267256.3911.721811352.365215.271653623.08NTUτεTh2’0.5218890.5637730.374406341.9386第一次迭代过程及结果:Th1Th2TmhD20hXhDhCph382341.9386361.96930.9194.6196930.6805840.792404Tc1Tc2TmcD20cXcDcCpc275290.624282.8120.853.828120.6256960.747185λhazbzυhυhAtWh0.08824518.917-2.92961.5274071.5275*10^-60.045968250λcaybyυcυcAsWc0.10047822.81-3.68710.6206990.6207*10-60.0525175000UidiReiPriαiCmax0.6068840.027946.59739.08365448.6338130757.4U0de0Re0Pr0α0KCmin1.4798330.027264848.612.092231367.653220.13854081.57NTUτεTh2'0.5291620.5726380.377652341.59126第二次迭代及结果:Th1Th2TmhD20hXhDhCph382341.5912361.80.9194.6180.6807360.792235Tc1Tc2TmcD20cXcDcCpc275290.756282.8780.853.828780.6256210.747254λhazbzυhυhAtWh0.08825518.917-2.92961.5295781.5296*10^-60.045968250λcaybyυcυcAsWc0.10047322.81-3.68710.6202070.620210^-60.0525175000UidiReiPriαiCmax0.6067480.027933.53739.13517448.2896130769.4U0de0Re0Pr0α0KCmin1.4800110.027264907.812.082821368.242220.040554070.02NTUτεTh2'0.5290410.5724810.377602341.5966由第二次可以看出Th2’–Th2=0.00540.1结束计算。故原油的出口温度为341.5970C,换热器的总传热系数为220.041W/(㎡·0C),传热效率是0.3776.7第二次大作业用黄金分割法求下面问题的最优解,minf(x)=2xxe,s.t3x2精度要求,将原始区间缩短5倍。解:a=-2b=309017.0)23618034.03abbx1()(09017.123618034.02abax2)()(10249.1xf1)(5246.1xf2)(5246.1xf9219.0xf21)(<)(a=-2b=1.0910781996.0209017.1618034.009017.1a-bbx1)()(09017.0)209017.1(618034.02)a-bax2(1124.1xf1)(10249.1xf2)(1124.181966.0xf10249.109017.0xf12)(<)(a=-0.81966b=1.0901709017.0x1f(-0.09017)=1.1024936067.0a-bax2)(82729.0xf2)(249.1.109017.0fxf82729.036067.0fxf12)()(<)()(舍去[a.1x]a=-0.09017b=1.0901736037.0x182729.0xf1)(63932.0a-bax2)(93638.0xf2)(93638.063932.0fxf82729.036067.0fxf21)()(<)()(舍去[2x.b]a=-0.09017b=0.63932若要求将原始区间缩短5倍。b-a=0.63932+0.9017=0.73102<nl=nolE=50.2=182729.036067.0ff36067.0xx*1*)(8