發(fā)動機缸內工作過程計算

發(fā)動機工作過程數(shù)值計算作業(yè)缸內封閉過程數(shù)值計算學 院：汽車學院專 業(yè)：動力機械及工程學 號：2023年五月氣缸封閉過程的數(shù)值計算一、根本熱力學模型圖1 發(fā)動機缸內熱力系統(tǒng)在簡化假設的根底上，取氣缸為一個熱力學系統(tǒng)，如圖1所示。這個熱力系dmdmdm；A E BT、PVm及u為缸內瞬時氣體溫度、壓力、體積、燃料質量及比內能。二、簡化假設假定工質為抱負混合氣體；假定缸內各處溫度、壓力及混合氣濃度均勻；用純空氣的氣體常數(shù)代替混合氣氣體常數(shù)；假定掃氣完全，即不考慮剩余廢氣；不計漏氣損失，并假定只有在燃燒始點才有燃油噴入氣缸；按代用燃燒規(guī)律進展噴油，并認為著火延遲等于零；100%。三、根本方程PV=mRT2、壓縮期(ES

)VBdT＝1d mcv

dQ dV〔dw－pd〕dm＝0d3、燃燒期(VB

)VEdT 1

dQ dQ

dV dm ud能量方程：d＝mc v

dw－pd

－ud

－m d〕質量方程：4、膨脹期(VE

dmdmB＝1 dQBd d H du )AOdT＝1d mcv

dQ dV〔dw－pd〕dm＝0d四、其他計算公式1、氣缸瞬時工作容積：2 V()Vh[ 1cos 2

sin2)]2 1 s1 VV h 4 式中：Vh-氣缸行程容積VL-壓縮比-曲柄連桿比sS-活塞行程D-氣缸直徑2、氣缸容積隨曲軸轉角變化率：sinsincos12sin2s h[sin ]d 2 s3、單位曲軸轉角的傳熱量：dQw13A

T)d 6n

i1

i Wii1-活塞i2-氣缸蓋i3-氣缸套A-傳熱外表積i1 A D2；A 1.5A；A 1 4 2 1 3 DT -傳熱外表平均溫度WiT 560K；TW1

548K；TW3

548K-換熱面平均的瞬時傳熱系數(shù)Woschni130T-0.53P0.8D0.2[cc

c

1(PP

)]0.8T1m 2PV 0T式中：Vh

11-活塞行程容積c-氣體速度系數(shù)1壓縮、膨脹階段c1

2.280.308cuc換氣階段 c1

m6.180.417cucmc-燃燒室外形系數(shù)，直噴式燃燒室c=3.24X10-32 2c 6.9m/smP、V1 1

、T分別為壓縮始點的氣缸壓力、容積、溫度。分別1102kPa,0.89L,375KP100kPa0]4、代用放熱規(guī)律：]

m1QB

mBu B0B

H[1e6.908(u

VB)dQd

6.908u

m HB0

VB)m

6.908(

)m1

-燃燒效率,取為100%uH42500kJ/kgum1.080°CAm 3.5421X10-6kgB0 -338°CAVB5、工質內能：u0.14455[(0.097546.4

0.04850.75

)(T273)3106(7.768

3.360.8

)(T273)2104(489.6

)(T273)102

1356.8]式中：-瞬時過量空氣系數(shù)1〕壓縮階段，取104。燃燒階段：L mLLm ()0 Bd mL dQBd L0

m2H dB u膨脹階段： mL =constLm0 B0

L14.3kg/kg0m(-噴入燃料量隨曲軸轉角的變化函數(shù)Bm -每循環(huán)噴油量B0u 0.0485 3.36c ( )V T V

0.14455[3(0.097546.4

)(T273)21062(7.768

0.8)(T273)104(489.6

)102]7、比內能對過量空氣系數(shù)的偏導u0.14455[0.750.04851.75(T273)31060.83.361.8(T273)21040.9346.41.93(T273)102]BmH=mL+mBBdm

1 dQHBd HB

H du五、龍格—庫塔法的計算步驟 ，Ti if(

,T)T”i i 1K1

f(Ti,i

)T”1TK1i

2K,T 1)T”Ki 2 i 2 2

f(,T 1)T”K2 i 2 i 2 2KTK2i

2K,T 2)T”Ki 2 i 2 3 K

f( ,T 2)T”3 i 2 i 2 3TKi 3i

,Ti

K)T”3 4K4

f(

,Ti

K)T”3 41 1步驟十二：(K2K 2K K) 6Ti1

1 2 3TT”i 5

4 6 1

2 3 4 5六、發(fā)動機根本參數(shù)發(fā)動機型號：ZH105W＝16.5排量：Vh

=0.96Ls＝115mm缸徑：D＝105mm燃燒持續(xù)角：80°CA曲柄半徑和連桿長度比s配氣相位：

＝0.3〔上止點前〕12°CA〔下止點后〕38°CA〔下止點前〕55°CA〔上止點后〕12°CA七、程序框圖開頭開頭定義自定義函數(shù)“ysgm文件定義自定義函數(shù)“rsgm文件定義自定義函數(shù)“pzgcm文件調用自定義函數(shù)“ysg庫塔法解微分方程輸出壓縮過程fai，T調用自定義函數(shù)“rsg庫塔法解微分方程輸出燃燒過程fai，T調用自定義函數(shù)“pzgcc微分方程輸出膨脹過程fai，TV-fai曲線、T-fai曲線、P-fai曲線完畢八、源程序〔matlab〕1、壓縮過程functionf=ysgc(fai,T)P1=102023;%壓縮始點氣缸內氣體壓力，單位pam3T1=375;%壓縮始點氣缸內氣體的溫度〔計算得KR=8.314;%J/mol.kML=29;%空氣摩爾質量，單位g/molnL=P1*V1/R/T1;%空氣摩爾量，單位molglmd=10000;%過量空氣系數(shù)c1=2.29;%氣體速度系數(shù)cm=6.9;%活塞平均速度〔計算得m/sc2=3.24*10^-3;%燃燒室外形系數(shù)Vh=0.96/16.5*15.5/1000;%行程容積，單位m3paksai=16.5;%壓縮比lmds=0.3;%曲柄連桿比V=Vh/2*(2/(ksai-1)+1-cos(fai)+1/lmds*(1-sqrt(1-lmds^2*sin(fai)*sin(fai))));%m3A1=pi*D^2/4;%活塞傳熱外表積，單位m2A2=1.5*A1;%氣缸蓋傳熱外表積，單位m2A3=4*V/D;%氣缸套傳熱外表積，單位m2Tw1=560;%活塞外表的平均溫度，單位KTw2=548;%氣缸蓋外表的平均溫度，單位KTw3=548;%氣缸套外表的平均溫度，單位Kn=1800;%發(fā)動機的轉速，單位r/minparef=0.130*T^(-0.53)*(P/100000)^0.8*D^(-0.2)*(c1*cm+c2*Vh*T1*(P-P0)/P1/V1)^0.8;%換熱面平均的瞬時傳熱系數(shù)，單位KJ/m2.s.KdQw_dfai=1/6/n*ref*(A1*(Tw1-T)+A2*(Tw2-T)+A3*(Tw3-T));%單位曲軸轉KJcv=0.14455*(-3*(0.0975+0.0485/lmd^0.75)*(T-273)^2*10^(-6)+2*(7.768+3.36/lmd^0.8)*(T-273)*10^(-4)+(489.6+46.4/lmd^0.98)*10^(-2));%定容比熱，單位KJ/Kg.KdV_dfai=Vh/2*(sin(fai)+lmds*sin(fai)*cos(fai)/(sqrt(1-lmds^2*sin(fai)*sin(fai))));%氣缸容積隨曲軸轉角的變化率f=1000/mL/cv*(dQw_dfai-P/1000*dV_dfai);ysgc[fai,T]=ode45(”ysgc”,[(180+38)/180*pi:5/180*pi:(360-22)/180*pi],375)2、燃燒過程rsgcm文件，源程序如下：functionf=rsgc(fai,T)壓縮始點氣缸內氣體壓力，單位pam3壓縮始點氣缸內氣體的溫度，單位Km氣體常數(shù)，單位J/mol.k空氣摩爾質量，單位g/molmolgc1=2.29;%氣體速度系數(shù)活塞平均速度，單位m/sc2=3.24*10^-3;%燃燒室外形系數(shù)m3yinu=1;%燃燒效率m=1;%燃燒品質指數(shù)柴油理論空燃比gKJ/Kg噴油始點對應的曲軸轉角drfai=80/180*pi;%燃燒持續(xù)角ksai=16.5;%壓縮比曲柄連桿比V=Vh/2*(2/(ksai-1)+1-cos(fai)+1/lmds*(1-sqrt(1-lmds^2*sin(fai)*sin(fai))));%m3QB=yinu*mB0/1000*Hu*(1-exp(-6.908*((fai-faivb)/drfai)^(m+1)));%累積放熱KJdQB_dfai=6.908*yinu*mB0/1000*Hu/drfai*(m+1)*((fai-faivb)/drfai)^(m+1)*exp(-6.908*((fai-faivb)/drfai)^(m+1));%單位曲軸轉角對應的放熱量fai的時刻,Kglmd=mL/1000/(mB+0.0000000001)/L0;%過量空氣系數(shù)mH=mL/1000+mB;%曲軸轉角對應fai的時刻,氣缸內混合氣的質量，單位Kgcv=0.14455*(-3*(0.0975+0.0485/lmd^0.75)*(T-273)^2*10^(-6)+2*(7.768+3.36/定容比熱，單位KJ/kg.KdV_dfai=Vh/2*(sin(fai)+lmds*sin(fai)*cos(fai)/(sqrt(1-lmds^2*sin(fai)*sin(fai))));%氣缸容積隨曲軸轉角的變化率,單位m3活塞傳熱外表積，單位m2氣缸蓋傳熱外表積，單位m2氣缸套傳熱外表積，單位m2發(fā)動機的轉速，單位r/min,paparef=0.130*T^(-0.53)*(P/100000)^0.8*D^(-0.2)*(c1*cm+c2*Vh*T1*(P-P0)/P1/換熱面平均的瞬時傳熱系數(shù)，單位KJ/m2.s.KdQw_dfai=1/6/n*ref*(A1*(Tw1-T)+A2*(Tw2-T)+A3*(Tw3-T));%單位曲軸轉KJdmH_dfai=1/Hu*dQB_dfai;%氣缸內氣體隨曲軸轉角的變化率,Kgu=0.14455*(-1*(0.0975+0.0485/lmd^0.75)*(T-273)^3*10^(-6)+(7.768+3.36/lmd比內能，單位KJ/Kgzdu_zdlmd=0.14455*(0.75*0.0485*lmd^(-1.75)*(T-273)^3*10^(-6)-0.8*3.36*lmd^(-1.8)*(T-273)^2*10^(-4)-0.93*46.4*lmd^(-1.93)*(T-273)*10^(-2));dlmd_dfai=-mL/1000/L0/(mB+0.0000000001)^2/Hu*dQB_dfai;f=1/mH/cv*(dQB_dfai+dQw_dfai-P/1000*dV_dfai-u*dmH_dfai-mH*zdu_zdlmd*dlmd_dfai);rsgc[fai,T]=ode45(”rsgc”,[(360-22)/180*pi:1/180*pi:(360-22+80)/180*pi],843)3、膨脹過程functionf=pzgc(fai,T)P1=102023;%壓縮始點氣缸內氣體壓力，單位pam3T1=375;%壓縮始點氣缸內氣體的溫度，單位KR=8.314;%J/mol.kML=29;%空氣摩爾質量，單位g/molmolmL=nL*ML;%壓縮始點氣缸內氣體質量，單位gKgL0=14.3;%理論空燃比D=0.105;%氣缸直徑，單位mc1=2.29;%氣體速度系數(shù)cm=6.9;%活塞平均速度，單位m/sc2=3.24*10^-3;%燃燒室外形系數(shù)S=0.115;%活塞行程，單位mm3paksai=16.5;%壓縮比lmds=0.3;%曲柄連桿比V=Vh/2*(2/(ksai-1)+1-cos(fai)+1/lmds*(1-sqrt(1-lmds^2*sin(fai)*sin(fai))));%m3A1=pi*D^2/4;%活塞傳熱外表積，單位m2A2=1.5*A1;%氣缸蓋傳熱外表積，單位m2A3=4*V/D;%氣缸套傳熱外表積，單位m2Tw1=560;%活塞外表的平均溫度，單位KKKn=1800;%r/minparef=0.130*T^(-0.53)*〔P/1000)^0.8*D^(-0.2)*(c1*cm+c2*Vh*T1*(P-P0)/P1/V1)^0.8;%KJ/m2.s.KdQw_dfai=1/6/n*ref*(A1*(Tw1-T)+A2*(Tw2-T)+A3*(Tw3-T));%單位曲軸轉角的傳熱量cv=0.14455*(-3*(0.0975+0.0485/lmd^0.75)*(T-273)^2*10^(-6)+2*(7.768+3.36/lmd^0.8)*(T-273)*10^(-4)+(489.6+46.4/lmd^0.98)*10^(-2));%定容比熱dV_dfai=Vh/2*(sin(fai)+lmds*sin(fai)*cos(fai)/(sqrt(1-lmds^2*sin(fai)*sin(fai))));%氣缸容積隨曲軸轉角的變化率f=1/(mL/1000+mB0)/cv*(dQw_dfai-P*dV_dfai);pzgc[fai,T]=ode45(”pzgc”,[(360-22+80)/180*pi:5/180*pi:(540-55)/180*pi],997)九、程序運行結果1、壓縮過程表1 壓縮過程運行數(shù)據結果faiV〔L〕T〔K〕P〔bar〕faiV〔L〕T〔K〕P〔bar〕3.800.89375.001.024.940.47479.002.453.890.87378.301.055.030.43495.832.783.980.85382.131.095.110.39514.833.184.070.82386.531.145.200.35536.303.704.150.80391.561.195.290.31560.614.354.240.77397.271.255.380.27588.165.194.330.74403.741.335.460.24619.396.294.420.70411.061.415.550.20654.807.754.500.67419.301.525.640.17694.839.684.590.63428.591.645.720.15739.7912.284.680.59439.051.795.810.12789.5915.754.760.55450.821.975.900.10843.3420.304.850.51464.072.18注：瞬時容積V、缸內氣體瞬時P是用excel2、燃燒過程表2 燃燒過程運行數(shù)據結果faiV〔L〕T〔K〕P〔bar〕faiV〔L〕T〔K〕P〔bar〕5.900.1006843.3420.306.610.09001268.6057.245.920.0969854.1021.356.630.09331266.8056.265.930.0933865.3022.456.650.09691264.3055.265.950.0899876.7023.616.670.10061261.3054.225.970.0867888.4024.836.680.10441257.8053.165.990.0837900.5026.126.700.10841253.7052.086.000.0808913.0027.476.720.11261249.1051.006.020.0781925.8028.896.740.11691244.1049.916.040.0756939.2030.386.750.12141238.6048.836.060.0732953.0031.946.770.12601232.8047.756.070.0710967.2033.576.790.13071226.6046.686.090.0689981.9035.276.810.13561220.0045.616.110.0671996.9037.026.820.14071213.2044.576.130.06541012.3038.836.840.14581206.1043.546.140.06391027.9040.686.860.15111198.7042.536.160.06261043.7042.566.880.15661191.1041.536.180.06141059.6044.456.890.16221183.3040.566.200.06041075.5046.346.910.16791175.4039.626.210.05961091.2048.216.930.17371167.3038.696.230.05901106.8050.046.950.17971159.1037.796.250.05861122.0051.816.960.18571150.8036.916.270.05831136.8053.496.980.19191142.4036.056.280.05821151.1055.087.000.19821134.0035.226.300.05831164.8056.547.020.20461125.6034.426.320.05861177.8057.867.030.21121117.1033.636.340.05901190.0059.047.050.21781108.7032.886.350.05961201.5060.057.070.22451100.2032.146.370.06041212.1060.907.090.23131091.8031.446.390.06141221.8061.577.100.23821083.5030.756.410.06261230.6062.067.120.24521075.2030.096.420.06391238.5062.407.140.25241066.9029.446.440.06541245.5062.557.160.25951058.8028.826.460.06711251.6062.567.170.26681050.8028.226.480.06891256.8062.417.190.27421042.8027