哈工大 空氣動力學(xué) 第1章緒論及基礎(chǔ)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(xué)學(xué)授課教師：授課教師：陳浮陳浮哈爾濱工業(yè)大學(xué)哈爾濱工業(yè)大學(xué) 能源科學(xué)與工程學(xué)院能源科學(xué)與工程學(xué)院推進理論與技術(shù)研究所推進理論與技術(shù)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