二維導(dǎo)熱物體溫度場(chǎng)的數(shù)值模擬

1、Ah喩釧復(fù)*灣University(/ Stienw pnd 丁的呦翎廿 Pcfjing金屬凝固過(guò)程計(jì)算機(jī)模擬二維導(dǎo)熱物體溫度場(chǎng)的數(shù)值模擬Solidworks十字接頭的傳熱分析作者:張杰學(xué)號(hào):S20156019學(xué)院:北京有色金屬研究總院專業(yè):材料科學(xué)與工程成績(jī):2015年12月二維導(dǎo)熱物體溫度場(chǎng)的數(shù)值模擬+ 1%Ml,hj-1圖1二維均質(zhì)物體的網(wǎng)格劃分用有限差分法模擬二維導(dǎo)熱物體的溫度場(chǎng)，首先將二維物體劃分為如圖1所示的網(wǎng)格，Ax與與可以是不變的常量，即等步長(zhǎng),也可以是變量（即在區(qū)域內(nèi)的 不同處是不同的），即變步長(zhǎng)？如果區(qū)域內(nèi)各點(diǎn)處的溫度梯度相差很大，則在溫度變 化劇烈處，網(wǎng)格布得密些，在溫度

2、變化不劇烈處，網(wǎng)格布得疏些？至于網(wǎng)格多少，步長(zhǎng) 取多少為宜，要根據(jù)計(jì)算精度與計(jì)算工作量等因素而定 ？在有限的區(qū)域內(nèi)，將二維不穩(wěn)定導(dǎo)熱方程式應(yīng)用于節(jié)點(diǎn)（i , j）可寫成： 刃P、（oT c2T YPCp=人 I 2- +Fi ,jW2f cTTP-T P=+0(叵丫 J； ,j-2TiP j+T： ,j S 丿i ,j, 2(Ax)+ o(Ax)25丿i ,jTiPj-2T Pj+TP+咻y)2 比込X、也y（亦2 2當(dāng)Aj也X、也y較小時(shí)，忽略0（肛）、o2x）、。（與）項(xiàng)。當(dāng)2 = 3時(shí),即X、y方向網(wǎng)格劃分步長(zhǎng)相等？最后得到節(jié)點(diǎn)（i，j）的差分方程：TiPr =TiPj+Fobi； ,j

3、 +昭,j +TPj/TPj_4-4TiPj ）式中假設(shè)邊界為對(duì)流和輻射邊界，對(duì)流用以下公式計(jì)算：PPCpAxTiPjTi卩嚴(yán)0（2巧,j+TiPj汀TiPjd-4TiP）廣心（Tf ,j）MATLAB編程模擬表1計(jì)算機(jī)模擬參數(shù)模擬參數(shù)輸入幾何尺寸/m0.35初始溫度/ C15定溫邊界/ C100密度/kg/m37840導(dǎo)熱系數(shù)/w/（m C）30比熱 /J/(kg C)610工件節(jié)點(diǎn)數(shù)/個(gè)25時(shí)間步長(zhǎng)/min0.1時(shí)間步數(shù)/個(gè)100幾何步長(zhǎng)/mm35在MATLAB中編程求解，程序如下：cic;clear;format Io ng%參數(shù)輸入moni_canshu=xlsread模擬參數(shù)輸入.x

4、lsx,1,B2:B11); %讀取exce中的模擬參數(shù) s=moni_canshu(1);%幾何尺寸,mt0=moni_can shu (2);% 初始溫度，Ctf=mo ni_can shu(3); % 輻射(空氣)邊界，C rou=mon i_ca nshu(4);% 密度,kg/m3 lamda=moni_canshu(5);%導(dǎo)熱系數(shù),w/(m C) Cp=moni_can shu(6);% 比熱,J/(kgC) n=moni_canshu(7);%工件節(jié)點(diǎn)數(shù)，個(gè)1000 dt=60*mo ni_can shu(8); % 時(shí)間步長(zhǎng)，min to s m=moni_canshu(9)

5、;%時(shí)間步數(shù)，個(gè)100 dx=s/( n-1);% 計(jì)算 dx f0=lamda*dt/(rou*Cp*dx*dx); %計(jì)算f0%初始參數(shù)矩陣，初始溫度f(wàn)or iii=1: nfor jjj=1: nTold(iii,jjj)=t0;endendTold(1,:)=tf;Told( n,:)=tf;Told(:,1)=tf;Told(:, n)=tf;%寫文件表頭xlswrite(data.xlsx,坐標(biāo)位置, sheet1：A1); asc=97;for ii=1: nbiaotou仁第nu m2str(ii)點(diǎn);asc=asc+1;xlswrite(data.xlsx：biaotou1：

6、sheet1：char(asc) 1); xlswrite(data.xlsx：biaotou1：sheet1：A num2str(ii+1); end%模擬運(yùn)算for jj=1:2co pyfile( data.xlsx：,data1.xlsx)Tn ew(1：1: n)=tf;Tn ew( n：1: n)=tf;Tn ew(1: n：1)=tf;Tn ew(1: n：n )=tf;for i=2: n-1for j=2: n-1Tn ew(i,j)=Told(i,j)+fO*(Told(i-1,j)-4*Told(i,j)+Told(i+1,j)+Told(i,j-1)+Told(i,j+

7、1); endendTold=T new;p color(Told);% 繪圖shad inginterpcolorma p(jet)p ause(0.1)saveas(gcf,第num2str(jj*0.1) s溫度圖像.jpg); xlswrite(data1.xlsx；Told,sheet1；B2);cop yfile(data1.xlsx：第nu m2str(jj*0.1) s數(shù) 據(jù).xlsx) delete(data1.xlsx);end模擬結(jié)果：坐標(biāo)位置第1點(diǎn)第2點(diǎn)第3點(diǎn)第4點(diǎn)第5點(diǎn)第6點(diǎn)第7點(diǎn)第8點(diǎn)第9點(diǎn)第10點(diǎn)第11點(diǎn)第12點(diǎn)第13點(diǎn)第1點(diǎn)96.2896.2896.2896.2

8、896.2896.2896.2896.2896.2896.2896.2896.2896.28第2點(diǎn)96.2885.7374.9068.6665.9465.0564.8464.8064.7964.7964.7964.7964.79第3點(diǎn)96.2874.9055.9145.0440.3638.8538.4938.4338.4238.4238.4238.4238.42第4點(diǎn)96.2868.6645.0431.6425.9424.1323.7123.6423.6323.6323.6323.6323.63第5點(diǎn)96.2865.9440.3625.9419.8517.9517.5217.4517.4417

9、.4417.4417.4417.44第6點(diǎn)96.2865.0538.8524.1317.9516.0315.5915.5215.5115.5115.5115.5115.51第7點(diǎn)96.2864.8438.4923.7117.5215.5915.1615.0915.0815.0815.0815.0815.08第8點(diǎn)96.2864.8038.4323.6417.4515.5215.0915.0215.0115.0115.0115.0115.01第9點(diǎn)96.2864.7938.4223.6317.4415.5115.0815.0115.0015.0015.0015.0015.00第10點(diǎn)96.286

10、4.7938.4223.6317.4415.5115.0815.0115.0015.0015.0015.0015.00第11點(diǎn)96.2864.7938.4223.6317.4415.5115.0815.0115.0015.0015.0015.0015.00第12點(diǎn)96.2864.7938.4223.6317.4415.5115.0815.0115.0015.0015.0015.0015.00第13點(diǎn)96.2864.7938.4223.6317.4415.5115.0815.0115.0015.0015.0015.0015.00第14點(diǎn)96.2864.7938.4223.6317.4415.51

11、15.0815.0115.0015.0015.0015.0015.00第15點(diǎn)96.2864.7938.4223.6317.4415.5115.0815.0115.0015.0015.0015.0015.00第16點(diǎn)96.2864.7938.4223.6317.4415.5115.0815.0115.0015.0015.0015.0015.00第仃點(diǎn)96.2864.7938.4223.6317.4415.5115.0815.0115.0015.0015.0015.0015.00第18點(diǎn)96.2864.8038.4323.6417.4515.5215.0915.0215.0115.0115.01

12、15.0115.01第19點(diǎn)96.2864.8438.4923.7117.5215.5915.1615.0915.0815.0815.0815.0815.08第20點(diǎn)96.2865.0538.8524.1317.9516.0315.5915.5215.5115.5115.5115.5115.51第21點(diǎn)96.2865.9440.3625.9419.8517.9517.5217.4517.4417.4417.4417.4417.44第22點(diǎn)96.2868.6645.0431.6425.9424.1323.7123.6423.6323.6323.6323.6323.63第23點(diǎn)96.2874.90

13、55.9145.0440.3638.8538.4938.4338.4238.4238.4238.4238.42第24點(diǎn)96.2885.7374.9068.6665.9465.0564.8464.8064.7964.7964.7964.7964.79第25點(diǎn)96.2896.2896.2896.2896.2896.2896.2896.2896.2896.2896.2896.2896.28坐標(biāo)位置第14點(diǎn)第15點(diǎn)第16點(diǎn)第17點(diǎn)第18點(diǎn)第19點(diǎn)第20點(diǎn)第21點(diǎn)第22點(diǎn)第23點(diǎn)第24點(diǎn)第25點(diǎn)第1點(diǎn)96.2896.2896.2896.2896.2896.2896.2896.2896.2896.2896

14、.2896.28第2點(diǎn)64.7964.7964.7964.7964.8064.8465.0565.9468.6674.9085.7396.28第3點(diǎn)38.4238.4238.4238.4238.4338.4938.8540.3645.0455.9174.9096.28第4點(diǎn)23.6323.6323.6323.6323.6423.7124.1325.9431.6445.0468.6696.28第5點(diǎn)17.4417.4417.4417.4417.4517.5217.9519.8525.9440.3665.9496.28第6點(diǎn)15.5115.5115.5115.5115.5215.5916.0317

15、.9524.1338.8565.0596.28第7點(diǎn)15.0815.0815.0815.0815.0915.1615.5917.5223.7138.4964.8496.28第8點(diǎn)15.0115.0115.0115.0115.0215.0915.5217.4523.6438.4364.8096.28第9點(diǎn)15.0015.0015.0015.0015.0115.0815.5117.4423.6338.4264.7996.28第10點(diǎn)15.0015.0015.0015.0015.0115.0815.5117.4423.6338.4264.7996.28第11點(diǎn)15.0015.0015.0015.00

16、15.0115.0815.5117.4423.6338.4264.7996.28第12點(diǎn)15.0015.0015.0015.0015.0115.0815.5117.4423.6338.4264.7996.28第13點(diǎn)15.0015.0015.0015.0015.0115.0815.5117.4423.6338.4264.7996.28第14點(diǎn)15.0015.0015.0015.0015.0115.0815.5117.4423.6338.4264.7996.28第15點(diǎn)15.0015.0015.0015.0015.0115.0815.5117.4423.6338.4264.7996.28第16點(diǎn)

17、15.0015.0015.0015.0015.0115.0815.5117.4423.6338.4264.7996.28第仃點(diǎn)15.0015.0015.0015.0015.0115.0815.5117.4423.6338.4264.7996.28第18點(diǎn)15.0115.0115.0115.0115.0215.0915.5217.4523.6438.4364.8096.28第19點(diǎn)15.0815.0815.0815.0815.0915.1615.5917.5223.7138.4964.8496.28第20點(diǎn)15.5115.5115.5115.5115.5215.5916.0317.9524.1338.8565.0596.28第21點(diǎn)17.4417.4417.4417.4417.4517.5217.9519.8525.9440.3665.9496.28第22點(diǎn)23.6323.6323.6323.6323.6423.7124.1325.9431.6445.0468.6696.28第23點(diǎn)38.4238.4238.4238.4238.4338.4938.8540.3645.0455.9174.9096.28第24點(diǎn)64.7964.7964.7964.7964.8064.8465.0565.9468.6674