北航空气动力学答案

北航空气动力学答案 一架低速袄机的平直机翼采用翼型～袄此翼型的～和各是多5-1 NACA2415fxfc 少, 解,此翼型的最大度弯f=2%最大度位置弯xf=40% 最大厚度c=15% 有一小个下的平板翼型～作袄近似～其上的袄集中在弦点上～袄袄。袄袄明若将5-2 α 取弦点袄袄足袄界件～袄条解,点袄在袄～在袄袄足袄界件～条即Cl=2π rad,1 袄v’,v’,,,,2,, 4b 代入袄界件表式 条达v’,v,袄袄袄,,中～v,, ,bdyfdx,v,,袄袄袄袄bv,, 袄升力袄袄袄v,, 袄袄v,,,bv,, 2,,v,,,b, Cy,, 12,v,,b2,2,, 袄Cy,,dCy d,,2, rad,1 小迎角下平板翼型的袄流袄袄～袄袄明袄可以有以下袄形式的解,两5-3 (,) ,袄cos,,2v,, 1(,),sin, , 袄2(,),1,cos,,2v,, sin, 而解,袄足袄界件～解条,不袄足袄界件。条12 解,迎角度袄袄的袄强方程袄弯 1 2,, 袄;, 袄,置袄袄量后～上面方程化袄 ,b,d,0dy,v(,,) *x),dx 袄0dyf,(,)sin,d,,v,(,,) 2,(cos,,cos,1)dx 袄, 袄cos,,2v,, sin,1(,), 袄入方程;, 袄* 左袄袄,0cos,2v,,,sin,d,2,(cos,,cos,1)2v,,co,sd,,, ,02,(co,s,co,s1) ,袄v,, 袄袄袄袄, 0co,sd, co,s,co,s1sin,1v,,, ,,,sin,1, 右袄故方程袄足v,(,,),,v,, 袄于,～ 袄代入方程;, 2(,), *1,cos,,2v,, sin,,,v,, 左袄1,cos,,2v,,sin,d,,,,02,(cos,,cos,1) ,,,,02v,,(1,co,s)d,2,(co,s,co,s1) ,,,, 袄(1,co,s)d,co,s,co,s1 ,d,co,sd,v,,,,)0co,s,co,s1co,s,co,s1, ,(,,0 sin,1v,,0,,) ,(,,sin,1sin,1,袄,右 故方程袄足v,,, 后袄件, 条?袄(,),cos,,2v,, sin, 当袄袄袄后袄袄 袄袄故不袄足后袄袄袄袄的件条co,s,2v,,,,,,0 sin, 0 ? 后袄袄～袄袄1,cos,,(,),,2v,, sin,1,cos,0,2v,,,2v,, sin,0 当极袄袄袄袄取限1,cos, sin,,,, lim 0,sin, ,lim cos,0,sin, 袄cos, 0,0 ,,1 故袄袄袄袄=0 袄足后袄件条 翼型中弧袄方程是 前5-4 NACA2412yf1,[0.80x,x2] 0,x,0.4 8 后袄2[0.20,0.80x,x] 0.4,x,1.0 yf0.0555 袄袄。袄根据薄翼型理袄求～袄～和并与表中袄袄Cy0xFmZ05-1 ,～袄据相比袄。数～1mZ0,,0.05309] xF,0.25[,0,,2.095,C, ～y,2, rad 解,Cy,2,/rad 袄0,,,,1,dyf dx0(1,co,s)d, 取由袄量置袄b(1,cos,) b,1 2 x, 知袄x,0.4 co,sf,0.2 ,f,78.463,1.369rad,0.44, 又1,dyf,[0.8,2x],0.1,0.25x,,8 dx ,[0.8,2x],0.0444,0.111x,0.0555 袄袄0, 1,[,(0.1,0.25x)(1,cos,)d,,,(0.0444,0.111x)(1,co,s)d,]0,f,,f 袄1,f11,{,[0.1,0.25,(1,cos,)](1,cos,)d,,,[0.0444,0.111,(1,cos,)] (1,cos,)d,},f,022 袄,;注意,是焦点～是最大度位置,弯2.095, xFxf 1,dyfmZ0,,(cos2,,cos,)d, 20dx 1,fs,co,s)d, ,,0(0.1,0.25x)(co2,21, ,,,(0.0444,0.111x)(cos2,,cos,)d, 2f袄,0.053 袄袄袄袄袄 Cy,0.985,2, 袄0,,1.90 xF,0.243 mZ0,,0.05 一翼型前段是一平板～后段袄下偏个的平板襟翼～袄袄。5-5 15 袄 袄求袄袄当袄的袄。 袄5Cy 解,AB,AC2,BC2,2AC,BC,cos165,,0.99246,1袄1 BC,sin15,,AB,sin 袄袄7ad ,1,4.98,5,0.08r 袄袄 袄2,15,,1,10 袄dy, ,,,tan,1,0.087 ,dx,AC 袄dy,n2,,0.174 5 ,,,,ta,,dx,BCxh,2bb ,x,(1,cos,) 32 袄袄h,1.916 ,0,, 1,dyfdx1.91 00(1,cos,)d, ,,1, 1.91 , 袄袄袄0.087(1,cos,)d,,1.916 0(,0.1745)(1,cos,)d, ,0.087(,,sin,),1,,(,0.1745)(,,sin,)1.916 , 袄袄,0.0939rd,,5.38 Cy,2,(,,,0),,/180,1.69 ～～一板翼型～个弯袄常。数。 袄袄求,袄袄袄的和b,1yf,kx(x,1)(x,2)5-7 kf,2%3Cy 。mZ 解,袄0, 袄 袄 袄袄袄11,dyfdx0(1,cos,1)d,1 ,1,,0k(3x2,6x,2)(1,cos,1)d,1 ,1,,,0111k[3(,cos,1)2,6,(1,cos,1),2](1,cos,1)d,1 222331k[cos2,1,cos,1,] (1,cos,1)d,1 424,,0 5,,k 8 1,dyfmZ0,,(cos2,1,cos,1)d,1 02dx袄,9k, 32 当袄～ x,1,2k3y,y,,0.02 max333 ,k,0.,0.052袄5,,Cy,2,,3,,,0.052,,0.533 ,1808,mZ,mZ0 191,Cy,,,0.052,,,0.533,,0.179 4324 低速流气以小袄流袄一薄袄翼型～个称5-10 V, ～袄用迎角袄袄和厚度袄袄～求 yC,4(C)x(1,x)2 ? 表面与的函袄系表式。数达CPx ? 的袄 解,袄用薄翼理袄～袄袄袄分解袄迎角袄袄和厚度袄袄。 迎角袄袄,攻角袄将CP(x,) 流袄平板 ～A0,,An,0 故 袄(,),2V,,cot, 2 CP,1,x,,,,2,co,,2,V,2x,, 厚度袄袄,攻角度～流袄袄翼型称0 dyc CPc,,2, 2,10d,x,,d ,,2c(1,2,)d, ,,0x,,1袄,4c 袄[2,2x,1ln,x]1 0 ,, 4c,1,x,, ,,,2,(2x,1)ln,,x, CP,CP,,CPc 1,x x,4c ,,2,,[2,(2x,1)ln1,x 当袄～x] 8c1x,CP,,2,, ,2 有一平直梯形翼～～袄袄～26-1 S,35m4b1,1.5m 求袄机翼的袄袄。 解,袄袄袄4 b1,1.5 袄b0,,b1,6 (b1,b0)l,S,,,2 22 袄l,35,2,9.33 1.5,6 l29.332 袄袄袄袄袄2.49 S35 袄何袄系袄明三角翼的袄从几袄明,6-2 tan,0,, l2 袄袄 S 而tan,0,c0lS,c, 0 2l2c0,,tan,0,,S 2lc0,,4 lc0,2 ;袄, 使用三角袄法袄算袄袄旧数无袄矩形翼的袄量分布～沿展向取袄扭6-8Cy, 袄～～三位置;个,袄求出袄的表式。 达解,根据升力袄理袄的三2,,n=3,(,)263, 角袄解法～可知数 袄?(,),2lV,,Ansin(n,) n,1, 系数可用下式定确An 袄袄?asin,,,Ansin(n,)(,n,sin,) n,1, 袄袄C, y,(,)b(,) 4l 袄袄袄～b(,),const 袄 Cy,,, 袄0,const,,a,const ,,, 将袄袄袄b4l,0.25 , ～袄～袄代入?得;?取三袄,632 (,,sin,)A1sin,,(3,,sin,)A3sin3,,(5,,sin,)A5sin5,,,,asin, 袄袄袄3,,5,,,(,,sin)Asin,(3,,sin)Asin,(5,,sin)Asin,,,sin135a,6666666,,,,, 5,,,(,,sin)Asin,(3,,sin)Asin,,(5,,sin)Asin,,,sin,135a333333,,,,3,,5,, ,(,,sin)Asin,(3,,sin)Asin,(5,,sin)Asin,,,sin135a,2222222, 袄即袄a,0.375A1,1.25A3,0.875A5,0.125,A1,1.83253A5,0.21651,a 0.96651袄1.25A,1.75A,2.25A,0.25,135a,袄解得 7,8,a A3,0.027A1,0.232a A5,0.003a袄袄(,),2lV,(A1sin,,A3sin3,,A5sin5,)袄lV,,a(0.464sin,,0.0554sin3,,0.0076sin5,)袄袄一有度的翼型～袄个弯～～6-80,,,4Cy,2,rad 若此翼型放到一无袄袄袄将个扭的袄袄翼上～袄求此机翼在袄袄袄的。58,Cy 袄 解,Cy,(,,,0)Cy 由于是无袄机翼扭 袄袄0,,0,,,4, 2,Cy,,,4.486/rad,2 Cy,1,1,5,,,,C,y, 袄Cy,0.078,(8,4),0.94 一架重量的袄机～在以巡航平袄6-9G,14700Nh,3000mV,,300km/h ;,～机翼面袄～袄袄～翼型～Y,GS,17m26.2NACA23012袄～无袄袄袄形平面形。袄～求,扭状CL(,Cy)(,0,,1.2,,CL,0.108/,) CDV(,CXi) 解,Cy,,Y 1,V,2S2,G13002,0.90913,(),1.723.6,0.274 袄袄袄袄袄袄,因是无袄袄袄翼 扭1.200, Cy,,57.3,C,y, 1,C, y, 袄袄0.108,57.3,,4.69/rad,0.082/,0.108,57.31,,,6.2 袄Cy,C, y(,,,0) 袄袄袄Cy Cy, 2Cy,,0,2.14 CXi 0.2742,,,0.00385 ,,6.2, 有一架重量的袄翼袄机～机翼袄袄袄形平面形～状～袄6-10 G,7.38,104Nl,15.23m 以的速度在海平面直袄袄行～是袄算其袄阻及根部剖面袄的袄袄。90m/sXi0解,平袄 袄袄G,7.38,10 Xi, GX.S.q, I4 G2 GXI=,, ;,故～27.38x104Xi, 1x1.225x902,,22 代入～得Xi,1507 Y=2,,,.,0,,4 袄0=55.99 矩形机翼～袄袄～～翼袄荷 。袄袄26-11 6l,12mG/s,900N/m算袄机在海平面以平袄袄的袄袄阻力以及袄袄袄升力之比。与v,150km/h 解,矩形机翼 袄袄故0.049 CXi,2Cy,, 袄(1,,) ,900 1,1.225,(150,103/3600)2 2,0.846 Cy,12,v,,S2 袄CXi0.8642,(1,0.049),0.0399 3.14,612l2 Xi,CXi,,v,,S,0.0399,1063.83,,1018.7 2,XiCXi0.0399,,,0.047 ,Cy0.846 一个～袄袄无袄袄机翼在某雷袄下袄袄所得的扭数6-12A=92.5 袄袄～～若其曲袄袄袄。袄～0.084/,CLmax,1.22CL,,0,,1.5,CL 袄他不袄～只是参数减小袄～求此袄袄和～出并画袄机翼A50CLA=5 袄的曲袄。CL 解,无袄直机翼 袄袄扭2.5 袄袄～袄～A=90,,1.5CL,0.084 CLmax,1.22 当袄～袄不袄 袄A=500,,1.5 袄袄CL,,CL, 1,,CL, 袄袄(1,,) 袄CL, ,0.084, 1,,CL, 9,(1,,) 假定袄袄～袄0 袄CL,,CL0.084,,,,0.1012/, 0.084,57.3CL1,1,9,,, 故 袄CL,A,5,CL, 1,,CL,, 5,(1,,)0.1012,0.074/,,4.24/rad0.1012,57.31,5, 二袄翼型在流中袄袄放置～使的最低袄强点出袄在下表面。袄前方流袄赫气它当来数8-4 袄袄～袄点的袄强系袄数。袄用普朗特葛袄渥法袄～求出翼型的袄界袄赫。—数0.3-0.782 解,袄～～袄用普葛法袄～—即～M,,0.3CPmin,,0.782CPmin,1,CPM,,0袄?CPmin,,0.782,M2 , 或用,0.782,CPM,,0,0.32 2 袄袄袄CPM,,0,,0.746 CPmin,,0.746,M 又袄用等袄袄系 袄袄袄,1P0,,,12,,,,,12,,,1,,1,Mmin,1,Mmin,Pmin,2,,,Pmin,,,,,, ,,1P2,,,1,M,,P0,,,12,2,,,,,1,M,,,P,,2,,袄界袄赫袄 袄数Mmin,1 袄 Pmin,2,,,12,,,,1,,,M,,, ,1,P,2,,,,,1, ?CPmin,,,,,1,2,P2,,2,,,12,,,,,,,1,,M,,,,1, 袄立??得～,1,2,2,,2,M,,P,,,M,,,,,1,,,,,,M,,0.654 CPmin,0.987 某翼型在增大到袄～翼型上最大速度点的速度已音速。袄此翼型在达8-6 M,0.8 低速袄最大速度点的袄强系是多少,假袄普朗特葛袄渥法袄可用。数— 解, 袄袄求M,0.8 CPminM,,0,? CP,CPM,,0 2,M, 2CP,2,M,,P,,,P,1,, ,,, 袄袄袄袄,12,,2,,,12,,,,1,M,1,, ,,, 2,,2,M,,,,,1,,,,,, 袄,0.434 6 袄CPminM,,0,,0.4346,,0.82,,0.26076 一展弦比袄袄的矩形机翼～以袄赫数作等速水平袄行～袄求袄机翼的8-9 10M,,0.6升力袄斜率的～此袄果相同机翼在不可袄袄流中的并将与袄行比袄CyCy袄解, 相同翼型在不可袄流中的袄, 袄袄Cy C, y, 1,C,y,C2 y,,5.09 袄袄(1,,) 袄～根据普朗特葛袄渥法袄～袄袄不可袄机翼后掠角袄M,,0.6- 袄是～仍袄矩形翼～展弦比袄小袄～其不可袄袄C,’,,,,80y’C, y’, 1, 袄而 袄C,y,Cy,,,4.86,,’(1,,) 4.86C,C’,,6.075yy0.8,1 二袄平板在千米高度～以袄行～迎角袄。袄分袄用激膨理袄和袄化理9-3 2M,,210,-袄～袄算上下表面袄的袄强差。 解,如袄～用激膨理袄- 下袄～袄袄下～袄袄～P21.69 M1,2107-20P1, 上表面膨袄波～袄表～～袄袄袄’袄～P1,0.1278 5M,,226.38P0, 故从外折袄’,后～袄P2M=110,36.380.07 P0,, 上所以～P20.07,,0.55 P10.1278 故 下CP2P2,(,1),(1.69,1),0.246 422,M,P,,,2 上1,(0.55,1),,0.1607 2.8CP袄下,上袄CP,CPCP0.2464,0.1607,0.407 袄化理袄 2,CP,, B 上袄,CP2,10,/18022,12,3.14159/18,,,,0.2015 1.732 下袄CP0.2015 袄下,上袄CP,CPCP2,0.2015,0.403 有一机翼～平面形如袄所示。袄求超音速前袄和袄音速后袄的袄赫范袄状数9-6 解, 袄前袄袄2c3b 1 sin,, M, 故 袄前袄袄袄 超音速前袄2tan,,M ,,1 即袄袄22c,2c,2M,,M,1,,,1 3b,3b, 后袄,2c4c,arct,,arct 3b 2 后袄M,n,M,co,sM,,1 袄4c,1,,,,3b,2 要袄音速后袄～即M,n,1 袄故 袄袄4c,M,,,, 3b,2 4c216c2 ,所以～袄袄足。 当1,M,,, 29b9b2 有一三角形机翼～前袄后掠角袄袄～袄以9-7 045V,,450m/s,速度袄行。袄考袄袄行高度分袄袄海平面、米和米袄～袄机翼前袄性袄作何袄化。550011000解,前袄tan,1 海平面袄～ V,,1.324 a,340,M,,a tan,,11,1, 20.870.87M,,1 袄 袄21,450,tan,,,,,1,1.0012 h=5500 a=318 318, 袄 0,45,n,,,,1,1.151 9h=11000 a=295 ta,5,29,故前袄分袄是袄音速、音速、超音速。 2