Completed notes of the course

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Compressible fluid dynamics Legend New paragraph / new theorem Demonstration Definition Important Conservation Laws Mass Conservation (Integral Form ) e dm = o 79da+ |giroI ds= o dta.s |, at s Mass Conservation (DIFFERENTIAL LAW ) • |, 79da _ ° 1911 da = o+ |, st . |Il dr + - o 191) da = o 79 + _ ° '911=0 DI + f-ore= o sit sit Dt a • IF WE PASSFROM THE INTEGRAL TO THE DIFFERENTIAL LAW WE can no LONGER ☐C-AL WITH DISCONTINUI TIES LIKE SHOCK WAVES CONTACTSURFACE SLIPLINES DISCONTINUI TIES ARE NOT DIFFERENTI ABLE COMPRESSIBCE incompressi BLE FLOWS - d = |- o 1 DI THE INTEGRALOF THE ☐IVETLCENCE OF VELOCITY IS THEVariation OF THE VOLUMEOVER TIME at mit) • in COMPLESSI BLE FLOW : THE VOLUME OF THE FLU ID DOESN'T CHANCE OVER TIME - ° I = 0 • THE VELOCITY FIELD OF AN INCOMPLESSIB.LE FLOW IS SOLENO/Dal • KEEP in min☐ THATin compressi b.LE FLUIDS DON'T EX'ST: THEY'RE THERMODYNAMICALLY and PHYS/CALLYMEANINGLESS MOMENTUM BALANCE (Integral form ) • dimmi= I d |finda+ |SI 10?ds = |T.su?ds+ |Erdr dt dt nz S S v2 • TSi SURFACE STRESSTENSOR • FI: VOLUMEForces- pressore : Tp= - PI Gravity : [g= - fly= = v'scuusstress.ES : IT= MOMENTUM BALANCE(DIFFERENTIAL Form ) • 2191) + . ° /97±+ PE)= ° IT - SI- = at • in 29 + gsia + - p+ ±_ 0191)+ giro ±= _ ° it - SI- = at at Mass Conservation • gDei + P= ° - SI- - ☐t VISCOUS Stress TENSOR • ti = Il9, 97, Et)= • HYPOTHESIS : 'SOTROPIC newtoniani FLUID THEVISCOUS STRESSTENSOR ISA L'NEAR FUNCTION OF THE Strain RATE TENSOR " I +( y)T - E= 1 2 . - µ= µ (T, P) Dynamic viscusi T> COEFFICIENT . it = un - µ+( y/T ' + ✗/ o =) , aere |= - - - I= ✗IT, p) volume UISCOSITY COEFFICIENT • BULK VISCOSI TY COEFFICIENT : New= 2 3 µ+ ✗ • STOKES ' HYPOTHESIS : µU = 0 it' s Val ID ☐ult For FEW MOLECULES |not Val id,for EXAMPLE ,for CO2) ENERGY BALANCE (INTEGRALForm ) C:…