北航CFD講義課

1、三維時(shí)間相關(guān)可壓縮流的Navier-Skokes方程:t.x-:z:R :S+:y（1）（向量形式）式中,PuPu2 + pPuvPwuPvE =PuvF =Pv2 + pG =PuvPwPwuPvwPw2 + pe -(e + p u1 1(e + p v1I(e 十 p-000u 二XXyxzxxyyyzyxzyzzzXXv xyw xzu yx v yyw yzzxV zy w zzIL_ qx其中,XX-:uqyIL- qz：:v ：:u ：:wxz 一xyzx二 yx-:zzzyz zyqxk 遼exqyk 遼-k遼z為了方程封閉，必須引入4個(gè)關(guān)系式（9個(gè)自變量P,u,v,w,e P

2、,T,»,k）:4, p =、RT2 七 Ju2 v2w22,=C1T C2in putNAVIER-STOKES EQUATIONS-Coupled system of five non-linear differential equations of second order, in space and time-Describe conservation of mass, momentum and en ergy-Describe wave propagation phenomena damped by viscosityEULER EQUATIONS-Coupled syst

3、em of five non-linear differential equations of first order, in space and time-Describe conservation of mass, momentum and en ergy-Describe wavepropagation(convective)phe nomenaIsen tropic, irrotati onal flowsPOTENTIAL EQUATIONS-SINGLE sec on d-order non-I in ear differe ntial equati on-Describe con

4、servation of mass and energy-Momentum conservation not fully satisfied in prese nee of shocksClassification of various flow modelsFig” 3. Surface pressure disuibuiion on a upical mtlhary uircrah. Surfoce pressure contours. Q = 002 (nRer Arlincer. 398&1 reprinted wiih permission of Japan Society

5、cf Computational Fj；m1 Dynamics)Fi缶 LE土 b. Surface prt$sme comparison, h) Measurements; (b Predittions匚ul'brik 1990-rcpdrtiea 二:：鼻 permission of (he Meteorologies J Office, U.K.)FOR EACH ELEMENT OF FLUID :Con servati on of mass Newt on' s sec ond law of moti onCon servati on of en ergy Equat

6、i on of state- Continuity Equati on:f Euler Equationt Navier-Stokes Equati on En ergy Equati onI Solve the equationsplus boun dary con diti onsVelocity Distributi on Pressure'、Den sity''Temperature ''u(x,y, z,t) v(x,y, z,t) w(x,y, z,t) P(x,y,乙t)P(x,yzt)T(x,y,z,t)IDeduce flow beha

7、viorflow separati on flow rates heat tran sfer forces on bodies (skin friction, drag, lift ) efficie ncies(turb ine, diffuser )Overview of computati onal fluid dyn amicsReal worldPhysics-levelsApproximatio napproximati onStead in essDyn amicalapproximati onSpatialapproximati onMathematicalmodelVNume

8、ricalDiscretizatio nsimulatio n耳1tech niq uesResoluti on of discrete system of equati onsEquati on discretizati on Defin iti onofnu merical schemeComputati onal ModelsSpace discretizati on Mesh defi niti on年代機(jī)型CPU時(shí)間費(fèi)用計(jì)算流體力學(xué)不同發(fā)展階段所求解的四種基本方程1. 線性小擾動(dòng)方程（6070年代）（1 - M J xx yy zz" 式中 u , I 二 V , = w2. 全位勢(shì)方程 （70年代中80年代初）i a丿XXZZ* *x y2axy* *22 yza* *Z X2azx3. Euler方程 （80年代）-U:E:F:G 小0 t x yz4. 平均N-S方程 （90年代）-U :E :F :G :R :S :T+ + + = + + jL、L、txyrL、L、L、zxyz70VAX75020小時(shí)$1000080IBM303320分鐘$100090Cray-220秒$10求解二維翼型粘性繞流三維機(jī)翼繞流場(chǎng)的數(shù)值模擬若在60年代，在I