ME 425: Aerodynamics

Size: px

Start display at page:

Download "ME 425: Aerodynamics"

Damian Wilcox
6 years ago
Views:

1 3/4/18 ME 45: Aerodnamics Dr. A.B.M. Toiqe Hasan Proessor Deparmen o Mechanical Engineering Bangladesh Uniersi o Engineering & Technolog BUET Dhaka Lecre-6 3/4/18 Fndamenals so Aerodnamics eacher.be.ac.bd/oiqehasan/ oiqehasan@me.be.ac.bd Dr. A.B.M. Toiqe Hasan BUET L-4 T- Dep. o ME ME 45: Aerodnamics Jan Fndamenal principles in Aerodnamics Flid Mechanics: 1. Conseraion o mass. Conseraion o momenm 3. Conseraion o energ Dr. A.B.M. Toiqe Hasan BUET L-4 T- Dep. o ME ME 45: Aerodnamics Jan. 18 1

2 3/4/18 Mass can neiher be creaed nor desroed. Consider a small olme o space conrol olme hrogh hich a lid is loing. For simplici a D lo is considered and he conrol olme is bonded b he sraces and asshoninigre. Accordingohelahe ne olo o mass hrogh he sraces srronding he olme ms be eqal o he decrease o mass ihin he olme. The mass lo rae is eqal o he prodc o densi eloci componen normal o srace and he area o ha Conseraion o Mass The mass lo rae is eqal o he prodc o densi eloci componen normal o srace and he area o ha srace. In ecor orm ρ ρ da m s nˆ V A irs-order Talor series is sed o ealae he lo properies a he aces o he elemen since he properies are a ncion o posiion coninm approach. The ne olo o mass per ni o ime per ni deph is olo +e olo +e area olo +e olo +e inlo e Dr. A.B.M. Toiqe Hasan BUET 3 L-4 T- Dep. o ME ME 45: Aerodnamics Jan olo e inlo e inlo e area inlo e Conseraion o Mass hich ms be eqal he rae a hich he mass conained ihin he elemen decreases mass in de o decrease e 1 mass= densi olme Eqaing he aboe o epressions and diiding b - I -dimension is considered he dierenial orm o he aboe epression comes as Dr. A.B.M. Toiqe Hasan BUET 4 L-4 T- Dep. o ME ME 45: Aerodnamics Jan. 18 hich is knon as dierenial conini eqaion in ecor orm. V V operaor del and here

3 3/4/18 Conseraion o Mass In case o sead los he conini eqaion becomes as- V di V V div Compressible los Incompressible los Dr. A.B.M. Toiqe Hasan BUET L-4 T- Dep. o ME ME 45: Aerodnamics Jan Conseraion o Momenm Linear Momenm Eqaion The ne orce acing on a lid paricle is eqal o he ime rae o change o he linear momenm o he lid paricle. As lid elemen moes in space is eloci densi shape and olme ma change b is mass is consered. Conseraion o momenm can be rien as- F m DV D D direcion : F m D D direcion : F m D D direcion i : F m D V and F F F F 1 The eloci o a lid paricle is in general an eplici ncion o ime as ell as o is posiion. Frhermore he posiion coordinaes o he lid paricle are hemseles a ncion o ime. The deriaie in he aboe epression is reqenl ermed as paricle oal or sbsanial deriaie D/D o eloci. Dr. A.B.M. Toiqe Hasan BUET L-4 T- Dep. o ME ME 45: Aerodnamics Jan

4 3/4/18 4 Conseraion o Momenm Since conecie local oal D D D D D D D D Similarl Area=A A < A A 3 > A Dr. A.B.M. Toiqe Hasan BUET 7 L-4 T- Dep. o ME ME 45: Aerodnamics Jan. 18 Sead lo Veloci increases 1 o Veloci decreases o 3 a Conecie acceleraion Area=A 1 A < A 1 3 Conseraion o Momenm The principal orces ih hich e are concerned are hose hich ac direcl on he mass o he lid elemen he bod orce and hose hich ac on is srace hepressre orces and shear orces. The sress ssem acing on an elemen o he srace is shon in igre: The properies o mos lids hae no preerred direcion in space ha is lids are isoropic. Asa resl Dr. A.B.M. Toiqe Hasan BUET 8 L-4 T- Dep. o ME ME 45: Aerodnamics Jan. 18

5 3/4/18 5 Conseraion o Momenm In general he arios sresses change rom poin o poin coninm approach. Ths he prodce ne orces on he lid paricle hich case i o accelerae. To simpli he illsraion o he orce balance on he lid paricle consider a D lo as indicaed in igre. The reslan orce in - direcion or a ni deph in he -direcion is here is he bod orce per ni mass in - direcion. Incldingloinhe-direcion he reslan orce in he -direcion- Dr. A.B.M. Toiqe Hasan BUET 9 L-4 T- Dep. o ME ME 45: Aerodnamics Jan. 18 F Conseraion o Momenm Use his epression in eqn. 1 or -direcion: D D D F Similarl or - and -direcions D d D d D Dr. A.B.M. Toiqe Hasan BUET 1 L-4 T- Dep. o ME ME 45: Aerodnamics Jan. 18 d These are he basic orm o Naier-Sokes eqaions.

ME 425: Aerodynamics

ME 425: Aerodynamics ME 45: Aerodnamics Dr. A.B.M. Toiqe Hasan Proessor Deparmen o Mechanical Engineering Bangladesh Uniersi o Engineering & Technolog BUET, Dhaka Lecre-7 Fndamenals so Aerodnamics oiqehasan.be.ac.bd oiqehasan@me.be.ac.bd