1、HW1繞圓柱的有環(huán)量流動(dòng)W(z) = VgZeiaMe】。ir 1+ -Inz2nz 2n令z = reie 且 r2 = x2 + y2W(z) = VooZe-MMeia2nzirInz 2njqe-i(e-a)2nrir#ln(reie)=的 +第*cos(0-卻*部(0-a)-&lnr)令a2 =2nVoo通過建立適當(dāng)?shù)淖鴺?biāo)系,或者坐標(biāo)旋轉(zhuǎn)，使無窮遠(yuǎn)處來流方向與x軸正方向平行，及a =0.則cos。=sine =壽0 = acos ( x/sqrt(x2 + y2) 00 pi0 = 2pi - acos ( x/sqrt(x2 + y2) O0 0即要求環(huán)量逆時(shí)針方向，考查流場(chǎng)中駐點(diǎn)

2、(流場(chǎng)中速度為零 的點(diǎn))情況。設(shè)圓柱表面駐點(diǎn)的幅角為Os根據(jù)參考資料【1】可知，sinOs =二4nVcoa當(dāng)0 vV 1時(shí)，0 V Sines 1有兩個(gè)駐點(diǎn)，分別分布在第一和第二象限，4nvcoa兩個(gè)駐點(diǎn)關(guān)于y軸對(duì)稱。參數(shù)情況 v=2;M=2*pi*v;a=l;t=7; sin0s = 0.2785源程序如下：%變量聲明V無窮遠(yuǎn)來流速度，M偶極子強(qiáng)度a無渦量時(shí)流函數(shù)為零的圓周，t渦量強(qiáng)度stheta滯止點(diǎn)角度正弦值streamf流函數(shù)值potf勢(shì)函數(shù)值%function stheta= Compot() clear;clc;v=2;M=2*pi*v;a=l;t=7;stheta = t/ (

3、4*pi*v*a) syms x y b=3;streamf=t/(2*pi)*log(a);z=v*(sqrt(xA2+yA2)-aA2/sqrt(xA2+yA2)*y/sqrt(xA2+yA2)一 t/ (2*pi)*log(sqrt(xA2+yA2)-streamf;h=ezplot(z,-b,b,-b,b);set (h, color, 1r1);z=v*(sqrt(xA2+yA2)-aA2/sqrt(xA2+yA2)*y/sqrt(xA2+yA2)一t/ (2*pi)*log(sqrt(xA2+yA2)-streamf;h=ezplot(z,-b,b,-b,b);set (h, co

4、lor, 1r1);hold on;endk=3;for potf=-k:0.5:kz2=(v*sqrt(xA2+yA2)+M/(2*pi*sqrt(xA2+yA2)*x/sqrt(xA2+yA2)+t/(2*pi) atan(y/x)-potf;h=ezplot (z2, 10W-6) ,b,-b,b);set (hf 1 color, g, Linestyle, 1-1);hold onendfor potf=-k:0.5:kz2=(v*sqrt(xA2+yA2)+M/(2*pi*sqrt(xA2+yA2)*x/sqrt(xA2+yA2)+t/(2*pi) atan(y/x)-potf;h

5、=ezplot(z2, -bz-10A(-6),-bz b);set (hf 1 color, g, Linestyle, 1-1);hold onendfor potf=k+l:1:20z2=(v*sqrt(xA2+yA2)+M/(2*pi*sqrt(xA2+yA2)*x/sqrt(xA2+yA2)+t/(2*pi) atan(y/x)-potf;h=ezplot (z2, 10W-6) ,b,-b,b);set (hf 1 color, g, Linestyle, 1-1);hold onfor potf=-20:1:-k-1z2=(v*sqrt(xA2+yA2)+M/(2*pi*sqrt

6、(xA2+yA2)*x/sqrt(xA2+yA2)+t/(2*pi) atan(y/x)-potf;h=ezplot(z2, -bz-10A(-6),-bz b);set (hf 1 color, g, Linestyle, 1-1);end hold onend0r/4TTvaNX當(dāng)L= 1時(shí)，松Os = 1有一個(gè)駐點(diǎn)，在y軸上。 4nvcoa參數(shù):v=2;M=2*pl*v;a=l;t=4*pi*v*a;源程序如下：function stheta= Compot()clear;clc;v=2;M=2*pi*v;a=l;t=4*pi*v*a;stheta = t/(4*pi*v*a) syms

7、 x y b=3;streamf=t/(2*pi)*log(a);z=v*(sqrt(xA2+yA2)-aA2/sqrt(xA2+yA2)*y/sqrt(xA2+yA2)一t/ (2*pi)*log(sqrt(xA2+yA2)-streamf;h=ezplot(z,-b,b,-b,b);set (h, color, 1r1);hold onfor streamf=-8:0.5:8z=v*(sqrt(xA2+yA2)-aA2/sqrt(xA2+yA2)*y/sqrt(xA2+yA2) 一t/ (2*pi)*log(sqrt(xA2+yA2)-streamf;h=ezplot(z,-b,b,-b,

8、b);set (h, color, 1r1);hold on;endfor potf=-10:1:10z2=(v*sqrt(xA2+yA2)+M/(2*pi*sqrt(xA2+yA2)*x/sqrt(xA2+yA2)+t/(2*pi) atan(y/x)-potf;h=ezplot (z2, -b,-10A(-6),-bzb);set (hz 1 color, g, Linestyle, 1-1);hold onendfor potf=-10:1:10z2=(v*sqrt(xA2+yA2)+M/(2*pi*sqrt(xA2+yA2)*x/sqrt(xA2+yA2)+t/(2*pi) atan(

9、y/x)-potf;h=ezplot(z2,10A(-6),br-b,b);set (hz 1 color, g, Linestyle, 1-1);hold onendhold on3/4tt 歸二 1AX當(dāng)1時(shí)，在圓柱面上沒有駐點(diǎn)。4nVcoa參數(shù):v=1.5;M=2*pi*v;a=l;t=25;= 1.32634nVcoa源程序如下:function stheta= Compot()clear;clc;v=l.5;M=2*pi*v;a=l;t=25;stheta = t/ (4*pi*v*a) syms x y b=3;for streamf=-4:0.5:4z=v*(sqrt(xA2+y

10、A2)-aA2/sqrt(xA2+yA2)*y/sqrt(xA2+yA2)一t/ (2*pi)*log(sqrt(xA2+yA2)-streamf;h=ezplot(z,-b,b,-b,b);set (h, color, 1r1);hold on;endstreamf=t/(2*pi)*log(a);z=v*(sqrt(xA2+yA2)-aA2/sqrt(xA2+yA2)*y/sqrt(xA2+yA2)一t/ (2*pi)*log(sqrt(xA2+yA2)-streamf;h=ezplot(z,-b,b,-b,b);set (h, color, b1);hold onfor potf=-10:1:10z2=(v*sqrt(xA2+yA2)+M/(2*pi*sqrt(xA2+yA2)*x/sqrt(xA2+yA2)+t/(2*pi) atan(y/x)-potf;h=ezplot(z2, -b,-10A(-6),-bz b);set (hz 1 color, g, Linestyle, 1-1);hold onendfor potf=-10:1:10z2=(v*sqrt(xA2+yA2)+M/(2*pi*sqrt(xA2+yA2)*x/sqrt(xA2+yA2)+t/(2