空气动力学叶片设计终结版资料.docx

此文档收集于网络，如有侵权，请联系网站删除风力机空气动力学叶片设计风能091班 刘宁 学号 090826 已知：空气密度 = 1.225kg/m3，叶轮前额定风速v1=9m/s。设计一台功率3kW，功率系数CP为0.45，用于发电的风力机。要求：（1）叶尖速比取2、3、4、5、6、7、8、9和10；分别得到CP、CQ和CT ，画出曲线；（2）分别采用简化叶素动量理论、葛劳渥方法和维尔森方法，比较结果。解：（1）首先确定风轮扫风面积A和半径RA=P12v13Cp=3000121.225930.45=14.93m3R=A=2.2m（2）综合考虑叶片数对风力机的气动性能、振动、稳定性等影响，选择该风力机叶片数z=3, 采用FX63-137 翼型，由图可以得到Cl=1.32，Cd=0.012，ClCd=110，最佳攻角=6对根部进行修正10,9,8,7,6,6,6,6,6,6。一、叶素动量理论所用公式如下：n=60v12Rt=8r3z1(uv1CL+23CD)94uv12+1v=23v1u=nr30=arctanvu-=-W=sindQ=12W2trdrCLsin-CDcosdP=dQdT=12W2tdrCLcos+CDsinCp=zP12Av12Cq=zQ12RAv12Ct=zQ12Av13 =2Cp =0.5903 Cq =0.2951 Ct =0.9079 n =78.8463 Ra =0.2180 0.4360 0.6540 0.8720 1.0900 1.3080 1.5260 1.7440 1.9620 2.1800Bata =63.3008 50.0362 40.0128 32.8056 27.6901 23.0546 19.4633 16.6199 14.3231 12.4349fai =73.3008 59.0362 48.0128 39.8056 33.6901 29.0546 25.4633 22.6199 20.3231 18.4349t =2.1438 1.9479 1.6969 1.4652 1.2714 1.1143 0.9871 0.8836 0.7982 0.7270修正后t=0.23760.50780.63210.67020.62140.55420.45710.38350.28210.1701W =6.2642 6.9971 8.0722 9.3723 10.8167 12.3548 13.9556 15.6000 17.2754 18.9737zdQ = 3.6025 9.3834 17.7697 29.8816 43.2207 56.1931 65.4238 74.6024 83.7288 92.8030zdP = 29.7448 77.4768 146.7198 246.7252 356.8630 463.9732 540.1890 615.9743 691.3289 766.2527zdT = 5.1217 13.1803 24.9041 41.8894 60.6649 79.0123 92.1811 105.3498 118.5185 131.6872图形 =3 Cp =0.5742 Cq =0.1914 Ct =0.8911 n =118.2694Ra = 0.2180 0.4360 0.6540 0.8720 1.0900 1.3080 1.5260 1.7440 1.9620 2.1800Bata = 55.7723 39.0128 28.5289 22.0546 17.9625 14.3231 11.6126 9.5241 7.8697 6.5288 fai = 65.7723 48.0128 36.5289 29.0546 23.9625 20.3231 17.6126 15.5241 13.8697 12.5288t = 1.3742 1.1313 0.9089 0.7428 0.6219 0.5321 0.4638 0.4104 0.3677 0.3328修正后t=0.38150.43120.48930.54280.56520.53210.46380.41040.36760.3328W = 6.5795 8.0722 10.0802 12.3548 14.7733 17.2754 19.8295 22.4179 25.0298 27.6586zdQ = 1.7292 4.7760 10.1095 18.2506 28.2896 37.2128 43.2536 49.2422 55.1786 61.0629zdP =21.4169 59.1516 125.2073 226.0361 350.3712 460.8859 535.7020 609.8718 683.3953 756.2724zdT =3.6565 10.0403 21.2694 38.4928 59.8554 79.0123 92.1811 105.3498 118.5185 131.6872图形 =4 Cp =0.5890 Cq =0.1472 Ct = 0.9223 n = 157.6926Ra = 0.2180 0.4360 0.6540 0.8720 1.0900 1.3080 1.5260 1.7440 1.9620 2.1800Bata = 49.0362 30.8056 21.0546 15.6199 12.4349 9.5241 7.3925 5.7683 4.4915 3.4623fai = 59.0362 39.8056 29.0546 22.6199 18.4349 15.5241 13.3925 11.7683 10.4915 9.4623t = 0.9739 0.7326 0.5571 0.4418 0.3635 0.3078 0.2665 0.2347 0.2096 0.1893修正后t= 0.2739 0.3326 0.3571 0.4418 0.3635 0.3078 0.2665 0.2347 0.2096 0.1893W = 6.9971 9.3723 12.3548 15.6000 18.9737 22.4179 25.9044 29.4184 32.9509 36.4966zdQ =1.3184 4.1774 9.0052 17.6401 23.2008 27.6987 32.1445 36.5381 40.8795 45.1688zdP =21.7719 68.9834 148.7072 291.2997 383.1263 457.4039 530.8196 603.3735 675.0655 745.8957zdT =3.7038 11.7121 25.3241 49.8208 65.8436 79.0123 92.1811 105.3498 118.5185 131.6872图形 =5 Cp =0.5952 Cq =0.1190 Ct =0.9409 n = 197.1157Ra = 0.2180 0.4360 0.6540 0.8720 1.0900 1.3080 1.5260 1.7440 1.9620 2.1800Bata = 43.1301 24.6901 15.9625 11.4349 8.9314 6.5288 4.7843 3.4623 2.4270 1.5946fai = 53.1301 33.6901 23.9625 18.4349 14.9314 12.5288 10.7843 9.4623 8.4270 7.5946t = 0.7291 0.5086 0.3731 0.2908 0.2371 0.1997 0.1723 0.1514 0.1350 0.1218修正后t=0.142900.20850.27310.29080.27090.19960.17220.15140.13490.1217W = 7.5000 10.8167 14.7733 18.9737 23.2863 27.6586 32.0663 36.4966 40.9420 45.3982zdQ = 0.7362 3.0781 8.2005 14.8485 21.0725 21.9826 25.4714 28.9080 32.2924 35.6246zdP =15.1975 63.5387 169.2743 306.5011 434.9771 453.7634 525.7787 596.7165 666.5770 735.3601zdT =2.5812 10.8013 28.9179 52.6749 75.2368 79.0123 92.1811 105.3498 118.5185 131.6872图形 =6 Cp =0.5701 Cq = 0.0950 Ct =0.9112 n = 236.5389Ra = 0.2180 0.4360 0.6540 0.8720 1.0900 1.3080 1.5260 1.7440 1.9620 2.1800Bata = 38.0128 20.0546 12.3231 8.5241 6.5288 4.4915 3.0193 1.9072 1.0379 0.3402fai = 48.0128 29.0546 20.3231 15.5241 12.5288 10.4915 9.0193 7.9072 7.0379 6.3402t = 0.5656 0.3714 0.2661 0.2052 0.1664 0.1397 0.1203 0.1056 0.0941 0.0848修正后t=0.11560.14140.16600.17520.16640.13970.12030.10560.09400.0847W = 8.0722 12.3548 17.2754 22.4179 27.6586 32.9509 38.2732 43.6147 48.9690 54.3323zdQ =0.6403 2.3773 5.8067 10.5108 15.2657 18.1687 21.0195 23.8181 26.5644 29.2586zdP =15.8596 58.8864 143.8334 260.3566 378.1362 450.0437 520.6583 589.9801 658.0090 724.7449zdT =2.6920 10.0281 24.6582 44.9742 65.8436 79.0123 92.1811 105.3498 118.5185 131.6872图形 =7 Cp =0.5819 Cq =0.0831 Ct =0.9387 n = 275.9620 Ra = 0.2180 0.4360 0.6540 0.8720 1.0900 1.3080 1.5260 1.7440 1.9620 2.1800Bata = 33.6028 16.4633 9.6126 6.3925 4.7843 3.0193 1.7478 0.7890 0.0406 -0.5597fai = 43.6028 25.4633 17.6126 13.3925 10.7843 9.0193 7.7478 6.7890 6.0406 5.4403t = 0.4505 0.2820 0.1988 0.1523 0.1231 0.1031 0.0887 0.0778 0.0693 0.0624修正后t=0.08050.15200.16870.15220.12300.10310.08870.077800.06920.0624W = 8.7000 13.9556 19.8295 25.9044 32.0663 38.2732 44.5063 50.7559 57.0166 63.2851zdQ =0.4802 2.8791 6.7455 10.4962 12.9956 15.4429 17.8379 20.1808 22.4715 24.7099zdP = 13.8757 83.2007 194.9374 303.3255 375.5562 446.2786 515.4926 583.1982 649.3955 714.0843zdT =2.3551 14.1979 33.5439 52.6749 65.8436 79.0123 92.1811 105.3498 118.5185 131.6872图形 =8 Cp =0.5628 Cq =0.0704 Ct =0.9185 n = 315.3852Ra = 0.2180 0.4360 0.6540 0.8720 1.0900 1.3080 1.5260 1.7440 1.9620 2.1800Bata = 29.8056 13.6199 7.5241 4.7683 3.4623 1.9072 0.7890 -0.0531 -0.7099 -1.2364fai = 39.8056 22.6199 15.5241 11.7683 9.4623 7.9072 6.7890 5.9469 5.2901 4.7636t = 0.3663 0.2209 0.1539 0.1174 0.0946 0.0792 0.0681 0.0597 0.0531 0.0478修正后t=0.06280.08920.10390.10730.09460.07920.06800.05960.05310.0478W = 9.3723 15.6000 22.4179 29.4184 36.4966 43.6147 50.7559 57.9117 65.0772 72.2496zdQ =0.4032 1.8837 4.6750 8.3562 11.2922 13.3977 15.4509 17.4520 19.4009 21.2975zdP =13.3164 62.2126 154.4031 275.9799 372.9478 442.4851 510.2985 576.3880 640.7536 703.3953zdT =2.2609 10.6402 26.6717 48.1864 65.8436 79.0123 92.1811 105.3498 118.5185 131.6872图形 =9 Cp =0.5573 Cq =0.0619 Ct =0.9193 n = 354.8083Ra = 0.2180 0.4360 0.6540 0.8720 1.0900 1.3080 1.5260 1.7440 1.9620 2.1800Bata = 26.5289 11.3231 5.8697 3.4915 2.4270 1.0379 0.0406 -0.7099 -1.2949 -1.7636fai = 36.5289 20.3231 13.8697 10.4915 8.4270 7.0379 6.0406 5.2901 4.7051 4.2364t = 0.3030 0.1774 0.1226 0.0932 0.0750 0.0627 0.0539 0.0472 0.0420 0.0378修正后t=0.04970.07380.08220.08610.07490.06270.05380.04720.04200.0378W = 10.0802 17.2754 25.0298 32.9509 40.9420 48.9690 57.0166 65.0772 73.1465 81.2219zdQ =0.3428 1.7205 4.1147 7.4682 9.9668 11.8064 13.5938 15.3291 17.0121 18.6430zdP = 12.7381 63.9242 152.8821 277.4834 370.3206 438.6726 505.0854 569.5587 632.0927 692.6873zdT =2.1639 10.9589 26.5137 48.7166 65.8436 79.0123 92.1811 105.3498 118.5185 131.6872图形 =10 Cp =0.5545 Cq =0.0555 Ct =0.9245 n = 394.2315Ra = 0.2180 0.4360 0.6540 0.8720 1.0900 1.3080 1.5260 1.7440 1.9620 2.1800Bata = 23.6901 9.4349 4.5288 2.4623 1.5946 0.3402 -0.5597 -1.2364 -1.7636 -2.1859fai = 33.6901 18.4349 12.5288 9.4623 7.5946 6.3402 5.4403 4.7636 4.2364 3.8141t = 0.2543 0.1454 0.0998 0.0757 0.0609 0.0509 0.0437 0.0383 0.0340 0.0307修正后t=0.04050.05400.06980.07570.06080.05080.04360.03820.03400.0306W = 10.8167 18.9737 27.6586 36.4966 45.3982 54.3323 63.2851 72.2496 81.2219 90.1998zdQ =0.2992 1.3793 3.8444 7.2270 8.9062 10.5331 12.1079 13.6304 15.1008 16.5190zdP =12.3510 56.9414 158.7121 298.3583 367.6800 434.8470 499.8590 562.7162 623.4186 681.9660zdT = 2.0996 9.7859 27.6360 52.6749 65.8436 79.0123 92.1811 105.3498 118.5185 131.6872图形二、Glauert方法所用公式：r=rv1a=1+3a4a+3a=1-a(4a-1）/r2v=v1(1-a)u=r(1+a)=arctanvudQ=4r3v1(1-a)adrdP=dQdT=dQ(CLcos+CDsin)rCLsin-CDcosCp=zP12Av12Cq=zQ12RAv12Ct=zQ12Av13 =2 Cp = 0.4264 Cq = 0.2132 Ct = 0.9986 n = 78.8463Ra = 0.2180 0.4360 0.6540 0.8720 1.0900 1.3080 1.5260 1.7440 1.9620 2.1800Bata = 55.6365 38.8328 28.3559 21.9012 17.8284 14.2055 11.5085 9.4310 7.7857 6.4524fai = 65.6365 47.8328 36.3559 28.9012 23.8284 20.2055 17.5085 15.4310 13.7857 12.4524t = 1.0538 0.9335 0.7898 0.6683 0.5729 0.4983 0.4394 0.3920 0.3534 0.3214修正t=0.35370.480320.56970.60830.5728 0.49820.43930.39200.3534 0.3214W = 11.2177zdQ = 2.5118 8.1419 15.1224 22.6210 30.2782 37.9501 45.5849 53.1683 60.7004 68.1863zdP = 20.7393 67.2261 124.8625 186.7765 250.0000 313.3451 376.3839 438.9981 501.1889 562.9984zdT = 5.3444 17.2246 32.0191 48.0166 64.4758 81.0997 97.7817 114.4930 131.2350 148.0196图形 =3 Cp = 0.4532 Cq = 0.1511 Ct = 0.8927 n = 118.2694Ra = 0.2180 0.4360 0.6540 0.8720 1.0900 1.3080 1.5260 1.7440 1.9620 2.1800Bata = 50.4276 32.3847 22.4313 16.7770 13.4154 10.3683 8.1309 6.4231 5.0789 3.9946fai = 60.4276 41.3847 30.4313 23.7770 19.4154 16.3683 14.1309 12.4231 11.0789 9.9946t = 0.8415 0.7029 0.5667 0.4642 0.3893 0.3336 0.2910 0.2577 0.2310 0.2091修正t= 0.24630.32280.38040.40410.37920.33350.29100.25760.23090.2091W = 12.1710zdQ = 2.2562 6.7211 11.7520 16.8667 21.9481 26.9780 31.9617 36.9087 41.8268 46.7227zdP = 27.9438 83.2417 145.5498 208.8968 271.8304 334.1259 395.8509 457.1191 518.0315 578.6674zdT = 5.9978 17.8184 31.2361 45.0071 58.8294 72.6576 86.5079 100.4060 114.3756 128.4354图形 =4 Cp = 0.4657 Cq = 0.1164 Ct = 0.8487 n = 157.6926Ra = 0.2180 0.4360 0.6540 0.8720 1.0900 1.3080 1.5260 1.7440 1.9620 2.1800Bata = 45.2206 26.7523 17.6397 12.7978 10.0655 7.4950 5.6237 4.2034 3.0898 2.1938fai = 55.2206 35.7523 25.6397 19.7978 16.0655 13.4950 11.6237 10.2034 9.0898 8.1938t = 0.6745 0.5268 0.4071 0.3254 0.2690 0.2284 0.1981 0.1746 0.1561 0.1410修正t=0.15460.21680.25670.28010.25890.22830.19800.17460.15600.1410W = 13.2335zdQ = 2.0355 5.6553 9.4875 13.2921 17.0466 20.7611 24.4468 28.1119 31.7619 35.4008zdP = 33.6131 93.3882 156.6726 219.4991 281.4992 342.8393 403.7031 464.2260 524.5009 584.5919zdT = 6.6110 18.3656 30.9420 43.5833 56.2216 68.8919 81.6327 94.4731 107.4344 120.5324图形 =5 Cp = 0.4725 Cq = 0.0945 Ct = 0.8293 n = 197.1157Ra = 0.2180 0.4360 0.6540 0.8720 1.0900 1.3080 1.5260 1.7440 1.9620 2.1800Bata = 40.3532 22.1064 13.9130 9.7883 7.5692 5.3722 3.7815 2.5783 1.6371 0.8811fai = 50.3532 31.1064 21.9130 16.7883 13.5692 11.3722 9.7815 8.5783 7.6371 6.8811t = 0.5467 0.4003 0.2993 0.2353 0.1927 0.1627 0.1406 0.1237 0.1104 0.0996修正t=0.1054 0.1608 0.19280.20520.19260.16270.14060.12360.11030.0995W = 14.3665zdQ = 1.8449 4.8445 7.9013 10.9098 13.8783 16.8202 19.7444 22.6565 25.5602 28.4577zdP = 38.0828 100.0000 163.0982 225.1994 286.4750 347.2004 407.5612 467.6735 527.6106 587.4204zdT = 7.1435 18.7987 30.8404 42.8749 54.9378 67.0840 79.3521 91.7680 104.3497 117.1110图形 =6 Cp = 0.4767 Cq = 0.0795 Ct = 0.8212 n = 236.5389Ra = 0.2180 0.4360 0.6540 0.8720 1.0900 1.3080 1.5260 1.7440 1.9620 2.1800Bata = 35.9562 18.3378 11.0165 7.4930 5.6835 3.7774 2.4022 1.3643 0.5536 -0.0969fai = 45.9562 27.3378 19.0165 14.4930 11.6835 9.7774 8.4022 7.3643 6.5536 5.9031t = 0.4484 0.3102 0.2263 0.1759 0.1432 0.1205 0.1039 0.0913 0.0813 0.0733修正t=0.083890.11020.14020.148700.14030.12040.10380.09120.08130.0733W = 15.5608zdQ = 1.6803 4.2167 6.7445 9.2272 11.6807 14.1164 16.5409 18.9578 21.3696 23.7777zdP = 41.6208 104.4484 167.0630 228.5595 289.3337 349.6673 409.7219 469.5912 529.3322 588.9809zdT = 7.5913 19.1316 30.8287 42.5280 54.3059 66.2186 78.3009 90.5760 103.0604 115.7673图形 =7 Cp = 0.4795 Cq = 0.0685 Ct = 0.8192 n = 275.9620Ra = 0.2180 0.4360 0.6540 0.8720 1.0900 1.3080 1.5260 1.7440 1.9620 2.1800Bata = 32.0542 15.2782 8.7363 5.7092 4.2275 2.5505 1.3435 0.4338 -0.2761 -0.8452fai = 42.0542 24.2782 16.7363 12.7092 10.2275 8.5505 7.3435 6.4338 5.7239 5.1548t = 0.3721 0.2453 0.1757 0.1355 0.1099 0.0922 0.0794 0.0697 0.0621 0.0559修正t=0.0721 0.0910 0.11050.12050.10980.09220.079400.06960.06200.0559W = 16.8124zdQ = 1.5377 3.7212 5.8705 7.9826 10.0737 12.1525 14.2238 16.2901 18.3531 20.4137zdP = 44.4370 107.5383 169.6504 230.6875 291.1152 351.1902 411.0478 470.7634 530.3815 589.9302zdT = 7.9632 19.3901 30.8652 42.3817 54.0289 65.8595 77.9053 90.1879 102.7238 115.5271图形 =8 Cp = 0.4814 Cq = 0.8207 Ct = 0.8207 n = 315.3852Ra = 0.2180 0.4360 0.6540 0.8720 1.0900 1.3080 1.5260 1.7440 1.9620 2.1800Bata = 28.6205 12.7737 6.9114 4.2945 3.0777 1.5841 0.5107 -0.2974 -0.9275 -1.4325fai = 38.6205 21.7737 14.9114 11.2945 9.0777 7.5841 6.5107 5.7026 5.0725 4.5675t = 0.3122 0.1977 0.1397 0.1071 0.0866 0.0726 0.0624 0.0548 0.0488 0.0439修正t=0.050350.06860.08520.09120.08660.07250.06240.05470.04870.0439W = 18.1171zdQ = 1.4138 3.3230 5.1903 7.0280 8.8502 10.6638 12.4721 14.2771 16.0798 17.8808zdP = 46.6942 109.7495 171.4197 232.1130 292.2959 352.1934 411.9180 471.5307 531.0673 590.5497zdT = 8.2711 19.5958 30.9303 42.3553 53.9613 65.7973 77.8932 90.2705 102.9468 115.9381图形 =9 Cp = 0.4828 Cq = 0.0536 Ct = 0.8245 n = 354.8083Ra = 0.2180 0.4360 0.6540 0.8720 1.0900 1.3080 1.5260 1.7440 1.9620 2.1800Bata = 25.6081 10.7010 5.4261 3.1504 2.1510 0.8065 -0.1586 -0.8846 -1.4505 -1.9038fai = 35.6081 19.7010 13.4261 10.1504 8.1510 6.8065 5.8414 5.1154 4.5495 4.0962t = 0.2647 0.1621 0.1134 0.0866 0.0699 0.0585 0.0503 0.0441 0.0392 0.0353修正t=0.0472 0.0621 0.07069 0.076590.06980.05840.05020.04400.039230.0355W = 19.4694zdQ = 1.3058 2.9976 4.6474 6.2740 7.8889 9.4976 11.1025 12.7050 14.3058 15.9055zdP = 48.5168 111.3753 172.6772 233.1115 293.1170 352.8881 412.5190 472.0598 531.5396 590.9760zdT = 8.5266 19.7644 31.0137 42.4050 54.0257 65.9218 78.1228 90.6513 103.5269 116.7684图形 =10 Cp = 0.4839 Cq = 0.0484 Ct = 0.8297 n = 394.2315Ra = 0.2180 0.4360 0.6540 0.8720 1.0900 1.3080 1.5260 1.7440 1.9620 2.1800Bata = 22.9642 8.9658 4.1981 2.2092 1.3902 0.1690 -0.7069 -1.3655 -1.8785 -2.2895fai = 32.9642 17.9658 12.1981 9.2092 7.3902 6.1690 5.2931 4.6345 4.1215 3.7105t = 0.2266 0.1350 0.0937 0.0713 0.0575 0.0481 0.0413 0.0362 0.0322 0.0290修正t=0.0322 0.05020.06260.06790.06360.05050.04120.03610.03220.0290W = 20.8636zdQ = 1.2111 2.7275 4.2050 5.6641 7.1144 8.5600 10.0027 11.4437 12.8835 14.3224zdP = 49.9996 112.5997 173.6002 233.8367 293.7102 353.3885 412.9511 472.4398 531.8784 591.2818zdT = 8.7395 19.9067 31.1097 42.5058 54.1781 66.1712 78.5150 91.2343 104.3518 117.8900图形Wilson方法迭代r=rv1a=1+3a4a+3a=1-a(4a-1）/r2v=v1(1-a)u=r