Wind Tunnel Exeiment MAE 7A/75A Objective: Measue te Aeodynamic Foces and Moments of a Clak Y-4 Aifoil Unde Subsonic Flo Conditions Measuement Tecniques Pessue Distibution on Aifoil Dag fom Momentum Loss Measued it a Wakefield Flo Aay Diect Measuement it Mecanical Foce
Pocedue Calibate Tunnel / Pitot-Static Tube Measue Pessue Distibution on Aifoil -Diffeent Flo Seeds & Angle-of-Attack Wakefield Measuement of Dag Mecanical Foce Balance Revie of Hydostatic Pessues Demonstation of essue incease it det Weigt of te column WmgρAg Weigt is suoted by te net essue (P-P o )A P o A PP o ρg - Pessue inceases it det - All oints at a given det ae at te same essue PA
Revie of fluid motion Te motion of fluid deends on te Reynolds No. - Lamina - Tubulent Te lamina flo may be esented by steamlines Wen te fluid velocity is lage o en te fluid encountes most obstacles, te flo becomes tubulent Descibing Fluid Beavio at Isotemal Conditions Consevation of Mass Netons Second La of Motion
Consevation of Mass ρ ( ρ) t i j k x y z ρ- density - velocity t - time Constant density: Note: Tis is valid fo unsteady flo Neton s Second La Eule s Equation D ρ ρ ρ( ) ρf Dt t F F essue - body foce e unit mass Assume body foce is due to gavity, and it is consevative g z g acceleation due to gavity
Eule s Equation ) ( ) ( z g t ρ ρ ρ ρ ) ( gz t ρ Vecto identity: Tus Constant density Benoullis Equation Steady Rotational Flo ds gz ρ Conside Flo Along a Steamline Along a steamline const gz ρ
Benoullis Equation Unsteady Iotational Flo φ gz t ρ φ const gz t ρ φ We Measue Flo Velocity Using Benoulli s Eqn: Alications of Benoulli s Equation is detemined exeimentally Pitot tube as invented by a Fencman Heny Pitot in 73
Pessue Distibution Pessue Tas Located Aound Aifoil Suface Povide P(x) Data Integate Tis Data Ove Aifoil Suface to Find Net Foce Vecto & Moment. Aeodynamic Foces in Aifoil Distance, s P(s) τ(s) Pessue Distibution on Body Suface Given as P(s) Sea Stess on Body Suface given as τ(s) P acts nomal to suface τ acts tangential to suface Bot ave Foce/Aea Units
Integating P and τ Distibutions Gives Foce & Moments on Aifoil V M R Total Foce, R, Can Be Resolved into Lift Foce, L and Dag Foce D L acts eendicula to V D acts aallel to V Lift & Dag Foces L N R V α A D L N cosα Asinα D N sinα Acosα c N, A - Nomal, Axial comonents //t cod D,L - Axial, Nomal comonents //t fee steam V
Integate Pessue Ove Suface to Find Net Foce: Dimensionless Pessue Coefficient: C ef ρu Nomal Foce Coefficient: C n ρ V N A san c ( C C L c Neglecting Skin Sea Stess Effects U ) dx Detemine Lift Coefficient fom Nomal Foce Coefficient Use te Geomety to Find L N cosα Asinα Usually A<<N, Tus Can Aoximate C cosα L C N Note Tat te Assumtion A<<N Imlies Dag Foce is Small (I.e. e ae taking C d ~).
Detemine Pitcing Moment Coefficient fom Pessue Coefficient Distibution Use te Geomety to Find C mef c c (C U C L )(x x ef )dx Conventional X ef is Quate-cod Location Cente-of-Pessue Location Is Ten Given as X c c C M LE C N Pat Dag fom Momentum Loss Measued in Wake it Pessue Aay
Dag Coefficient u A B u u A B u(y) y x incomessible Dag Coefficient Mass Consevation Coss Section: (Rate of Flo) AB AA ρb u BB ρb A B ρb dy ρbu udy ( u u) dy
Dag Coefficient Equation of Motion steady Flo: ( ρ dv [ )] Dag Reynolds Tansot Teoem FdV F nda If static essue on AA, BB ae same Equation of Motion Coss Section AB AA BB A B Dag Coefficient Dag ρ nda ρbu ρb ρb u u dy ( u u) dy ρb u( u u) dy u u u ρbu u dy
Dag on Cylinde: Pe unit lengt (b ) Dag Coefficient Dag u u u ρbu u dy Te Dag Coefficient C D Dag Coefficient is comuted fom dag, D: D Cd ρ V Asan Use Pevious Exession fo Dag to Find Cd Fom Momentum Analysis: C d Y c q c Y Y q dy ee q ρv ( ) y Y ~ Wakefield aay idt
Wakefield Pocedue Oeate Tunnel at Desied Floseed & Aifoil Angle-of-Attack Make Sue Wakefield Aay Coves Entie Wake Gate q(y) data Use Teoy to Find Dag Foce, Coefficient Pat 3 Diect Measuement it Mecanical foce Balance
Mecanical Foce Balance Foce Balance Mecanism Mount Aifoil on Small Sting, o cylinde olde Sting Attaces to Load Fame Stain Gauges Used to Measue Foces & Moments on Sting Assembly Mecanical Foce Balance Aifoil & Sting Detail
Mecanical Foce Balance Te lift, dag, and itcing foces on te aifoil can be calculated fom a foce balance measuements of te axial foce A', nomal foce N', and itcing moment P' elative to te sting suot on te balance. Te values of A', N', and P' ae measued fom stain gauge bidges on te foce balance and ae not indeendent. Comensate fo tis inteaction beteen te measued values it matix: N N'*.954-A'*.8-P'*.6 A N'*.68A'*.59 P -N'*.336A'*.9P'*.8 Refeences. Jon D. Andeson, Fundamentals of Aeodynamics, nd Ed.,. 95- and. 8-36, McGa Hill 99.