哈工大 空氣動力學 第1章緒論及基礎知識

1、1第一章第一章 緒論及基本概念、知識緒論及基本概念、知識空空 氣氣 動動 力力 學學授課教師：授課教師：陳浮陳浮哈爾濱工業(yè)大學哈爾濱工業(yè)大學 能源科學與工程學院能源科學與工程學院推進理論與技術研究所推進理論與技術研究所23422vpconstLVcAndA 0DDt5611V a 21VV120shDm VVnV78910PRT111213141516DVpRDt22Vpconst11211231112123yxxxxzxyyyyxzyvDvvvvvpRVDtxxxyyxzzxDvvvvvvpRVDtxyxyyyzz1111223yxzzzzzyvvDvvvvpRVDtxzxyyzzzz17

2、0,0uuau xf xtx1121nnnnjjnnjjjjnnnjjjuuuuuutOtOttttuuuOxxx11110,0nnnnnnnnjjjjjjjjjjtuuauuuuuuaOtxxtxuf 181922VpgzconstDVpRDt0Vt222sin0.5pppCV22222220uuuuxyz2020V 20DVpRDt21LV222324a 或aLa39301010acmcm250, , ,limmdmx y z tdmd 260limppdpKd 211111dddpaKdpddp 2dVdMaVyT(y+ y)xyT(y)Qy yyyQdTqSdy qT 27yFhv(y

3、)ABxvFdVSdyffdtgddvdtdtdyddtdvvdy dtdyvdtddy T 28bRm或00, , ,limlimbbbxyzmRRdRR x y z tR iR jR kmd RdRdbbdRR, , ,R x y z tgk ZXYkdbdRg npnnpnp0, , ,limnnSppx y z tS nnpnnp dsp dsdVdynpnnpnp0dV dy 0npnnpp n29pRT, ,T p, ,u h s, ,0pp Tuu Tf T p, q w uu T hupu TRTh T11qdupdqdhdp21212121TTconstTpppppTp co

4、nstqduCduC dTuC dTC TuCTTdTdTqdhCdhC dThC dTC ThCTTTdT 3011ppvpvvpvkRppChudhdudC dTC dTRdTCCRkRCkCCk5321.4722vpCRuRTRTkCR 2222exp32exp1312exp111exp312exp1vevevvevvveppvveveveveTTTcRRRTTTccTRTuRTRTccTcTTkkk TRTTTTTT NONONNeOOeNONOe31revqdsT21122211111lnln111lnlnvvppqdsdTdTdsdupdCRsCRTTTTqdupdqCdsTpdp

5、dpdsdhdTRsCRTTTpTpqdhdp 1111212222221211111111222222221111111110lnlnlnlnlnln10lnlnlnlnlnln1kkvvkkkkppkCTTTTTCRTRTkTTTCTppTTTpTkpCRconstTppRTkTTpT0ds 111lnlnlnlnkkkkkkvpvscTCcTpCcpCRTpC32RRcossinsincosLNADNA212qv/2wLDMpfLDMppLDMCCCCCq Sq Sq SlqqLDMcccq cq cq c33ZXYAOBdAAdAC, ,A x y zxiyjzkAAAdAdxdydz

6、xyzdAdxidyjdzkAxixiyjzkixixxxxjikZr XYOr=constr+dr=const =const +d =constd eeererered, ,rzA rzrezerzdAdrerd edzerrzrrrrzrrzAAAdAdrddzrzeArrezeererrrreArrezeerredAdrerd edzedArreeee 34RenRRdRdRdn1dRPP1Q =const + d =constijkijkxyzxyzijkxyz ddxdydzidxjdykdzijkxyzxyzddR110ddRdRconst等勢面cos ,cosRRddRe dR

7、nddnendRdn nn + d =const間最小距離間最小距離RRdddRe dRedR 1rzrzddRdrerd edzeeeerrzddrddzrz 35VVVVijkVijkxyzxyzyxzyxzyxzijkvvvixxxVvvvjyyyvvvkzzzxyzyxzyxzyxzivjvkvvvvVijkxxxxxvvvVijkyyyyvvvVijkzzzzVDSA11()()2211()()2211()()2210(2yxxxzyxzyyyyxxzzyyxxzzzzyvvvvvVVVxxyxzxxxVvvvVvVvyyyyxyyzVvVvVvvvzzzzxzyzvx1)()211

8、()0()2211()()022xxzyyxzyxzzvvvyxzvvvvyxyzvvvvzxzy360limsA ndsA dsn VVdsn0001111lim1limlimstssV t ndsdddV ndsdtdttV ndsdVdt Vds nyyzxzxvvvvvvyzzxxyxyzijkVijkxyzvvv AALndAV ndAV dr 37sssn dsdn adsadnadsad a2222222xyz n222221111rzrzrrrrrrrzeeeeeerrzrrzeeeeeeeeerrrrrrrzrrr 2222222221111,111zrrrreerrzzrr

9、rrrz2VVVV 383921212111212111, , , , ,x y z tx y z txxyyxyzzttzt高階項212121212121212121212121limlimlimlimttttttttxxyyzzttxttyttzttt21212121lim12ttDDttttt 點與 點趨向重合212121212121212121limlimlimxyzttttttxxyyzzVVVttttttxyzDVVVVDtxyzttDVDtttV VVtVVt40, , ,Ix y z t d22IdIVdVIedIrV d (t) (t+ t)SS2nV t 3S1ndAdAV

10、 t 2 1 00010202030201030000000,tttII ttI ttt dt dtt dt dtttdtt dt d rrrrrrrr 0201030000000,limlimlimlimtttttttdtt dt dDI tIDttttt rrrr410200,limttttdddttt rrdtV ndA ADddV ndADtt0103120000,limlim,ttSSStt dt dtttdStdStdS rrrV nrV nrV nADVDttDddV ndADtt42sAa ndsadV ndAV d DdVdDtt F 00DFDDFDF dFV dFFV d

11、DtDtDtDtDDFF ddDtDtVVV 00DDdVV dV dDttDtDD0VV=0DtDtDddDt 43ZXYnpnnpnp0, , ,limnnSppx y z tS nnpnnnppnnnnpSpSpp ZXYnpnzpypxpcxxyyzznnxxyyzznnDVmR mpApApApADtR mpApApApA nxxyyzzxyzxyzpp np np ninjnknipjpkp0nnxxyyzzpApApApAcos,cos,cos,xnxnynynznznAAn xnAAAn ynAAAn znA xxxxyxzyyxyyyzzzxzyzzpipjpkppipjpk

12、ppipjpkpnxxxyyxzzxxxyyyyzzyxxzyyzzzzpi n pn pn pj n pn pn pk n pn pn pzxpzypzzpxxpxypyzpxzpyypyxp44xxxyxznxyzyxyyyzzxzyzzppppnnnpppn Ppppxxxyxzyxyyyzzxzyzzppppppppp,xyxzyxyzzxzypppppp,xxyyzzpppPxypxpZXYMG2G1GG3MG1G2GG31r2r3rrA B C nxxyyzzxxnyynzznpp np np nAnAAnAAnA123nnxxyyzzrpArpArpArpA1230 xxyyzz

13、rrp nrrp nrrp n,xyzAAA123,0GGGGxxGyyGzzGGGrrx i rry j rrz kx nipy njpz nkprx iy jz kn1232131321230GxGyGznrrnrrnrrnrrnrrnrrn rn rn rx ny nz n 00,xxxxyxzxyyxyzzyzxxzxyzyyxyyyzxyyxyzzyzxxzzzxzyzzpipjpkpk ppippj ppipjpkppipjpkppppppppipjpkp45xxyyzznnppppnxxxyyxzzxxxyyyyzzyxxzyyzzzzxxxyyyzzzpi n pn pn pj

14、 n pn pn pk n pn pn pin pjn pkn pnnnxyznnpnpinjnknpnppn 100010001pppI VDSAyv111()()0(222x11()()2211()()22yxxxzyxzyyyyxxzzyyxxzzzzvvvvvVVVxxyxzxxxVvvvVvVvyyyyxyyzVvVvVvvvzzzzxzyzxzxyyxzyxzzxxxyxzzyyxyyyzzxyxzxzyzzvvv1)()y2xzvvvv11()0()2yx2yzvvvv11()()02zx2zy000 4611()()221 0 011()()0 1 0220 0 111()()22yxxxzxxxyxzyyyxzyxyyyzzxzyzzyxzzzvvvvvxxyxzpppvvvvvpaSbIpppabyxyyzpppvvvvvzxzyzxdVdVdydy1()2y