Steady Level Forward Flight I Introductory Remarks Lakshmi Sankar 2002 1 The Problems are Many Transonic Flow on Advancing Blade Noise Thrust Shock Waves Aeroelastic Response Unsteady Aerodynamics 0 Main Rotor Tail Rotor Fuselage Flow Interference 90 Tip Vortices Blade Tip Vortex interactions V 180 270 Dynamic Stall on Retreating Blade Lakshmi Sankar 2002 2 The Dynamic Pressure varies Radially and Azimuthally V 180 Vtip R Retreating Side Advancing Side Vtip R V 90 270 Vtip R V R Reverse Flow Region Lakshmi Sankar 2002 Vtip R 0 3 Consequences of Forward Flight The dynamic pressure and hence the air loads have high harmonic content Above some speed vibrations can limit safe operations On the advancing side high dynamic pressure will cause shock waves and too high a lift unbalanced To counter this the blade may need to flap up or pitch down to reduce the angle of attack Low dynamic pressure on the retreating side The blade may need to flap down or pitch up to increase angle of attack on the retreating side This can cause dynamic stall Total lift decreases as the forward speed increases as a consequence of these effects setting a upper limit on forward speed Lakshmi Sankar 2002 4 Forward Flight Analysis thus requires Performance Analysis How much power is needed Blade Dynamics and Control What is the flapping dynamics How does the pilot input alters the blade behavior Is the rotor and the vehicle trimmed Airload prediction over the entire rotor disk using blade element theory which feeds into vibration analysis aeroelastic studies and acoustic analyses We will look at some of these elements Lakshmi Sankar 2002 5 Steady Level Forward Flight II Performance Lakshmi Sankar 2002 6 Inflow Model To start this effort we will need a very simple inflow model A model proposed by Glauert is used This model is phenomenological not mathematically well founded It gives reasonable estimates of inflow velocity at the rotor disk and is a good starting point It also gives the correct results for an elliptically loaded wing Lakshmi Sankar 2002 7 Force Balance in Hover Thrust Drag Rotor Disk Drag Weight In hover T W That is all No net drag or side forces The drag forces on the individual blades Cancel each other out when Lakshmi Sankar 2002 summed up 8 Force Balance in Forward Flight Thrust T Vehicle Drag D Flight Direction Weight W Lakshmi Sankar 2002 9 Simplified Picture of Force Balance T Rotor Disk referred to As Tip Path Plane Defined later TPP c g Flight Direction D T sin TPP D T cos TPP W W Lakshmi Sankar 2002 10 Recall the Momentum Model V V v V 2v Lakshmi Sankar 2002 11 Glauert s Conceptual model Freestream V Freestream V Induced velocity v Freestream V 2v Lakshmi Sankar 2002 12 Total Velocity at the Rotor Disk V cos TPP Free strea m Tot al V sin TPP V vel oci ty Induced Velocity v Total Velocity V cos TPP 2 V sin TPP v Lakshmi Sankar 2002 2 13 Relationship between Thrust and Velocities In the case of hover and climb recall T 2 A V v v Induced Velocity Total velocity Glauert used the same analogy in forward flight Lakshmi Sankar 2002 14 In forward flight T 2 Av V cos TPP V sin TPP v 2 This is a non linear equation for induced velocity v which must be iteratively solved for a given T A and tip path plane angle TPP It is convenient to non dimensionalize all quantities Lakshmi Sankar 2002 15 2 Non Dimensional Forms T 2 A R Edgewise Freestream Component V cos TPP V Tip Speed R R is called advance ratio CT Non dimensinal inflow ratio i v R Glauert equation in non dimensional form becomes C T 2 i 2 tan TPP i Lakshmi Sankar 2002 2 16 Approximate Form at High Speed Forward Flight If advance ratio is higher than 0 2 and if tip path plane angle is small far exceeds inflow ratio i so that C T 2 i 2 tan TPP i 2 2 i CT i 2 In practice advance ratio seldom exceeds 0 4 because of limitations associated with forward speed Lakshmi Sankar 2002 17 Variation of Non Dimensional Inflow with Advance Ratio CT i 2 i C T 2 i 2 tan TPP i2 2 Notice that inflow velocity rapidly decreases with advance ratio Lakshmi Sankar 2002 18 Power Consumption in Forward Flight We can compute Ideal Power from Glauert s theory as Thrust times normal velocity at the rotor disk The actual power will include blade profile power due to viscous drag on the blade We will compute it later P T V sin TPP v Profile Power Recall Tsin TPP D Thus P Tv DV Profile Power Induced Power Parasite Power Lakshmi Sankar 2002 19 Power Consumption in Level Flight P Tv DV Blade Profile Power The induced power Tv decreases with advance ratio as discussed earlier 1 1 Parasite Power DV V 2C D S V V 3C D S 2 2 The parasite power increases as the cube of the velocity or advance ratio and dominates power consumptio n in high speed forward flight Here C D is vehicle parasite drag coefficien t and S is the reference area C D is based on Because there is no agreement on a common reference area it is customary to supply the product C D S This product is called f the equivalent flat plate area 1 Lakshmi Sankar 2002 Parasite Power V 3 f 2 20 Power Induced Power Consumption in Forward Flight Induced Power Tv V Lakshmi Sankar 2002 21 Pow Par asi te Power er Parasite Power Consumption in Forward Flight V Lakshmi Sankar 2002 22 Profile Power Consumption in Forward Flight We will later derive C d 0 Profile Power A R 1 3 2 8 where Cd 0 Average Drag Coefficient of the Airfoil Power 3 Blade Profile Power V Lakshmi Sankar 2002 23 ed Po we r T er Pow Par asi te In du c Tot al Power Pow er Power Consumption in Forward Flight v Blade Profile Power V Lakshmi Sankar 2002 24 Non Dimensional Expressions for Contributions to Power P 3 A R C P C P i C P parasite C P 0 Recall C P Pi Tv Tv T v CT i 3 2 A R A R R 1 V 3 f 1 1 f 3 Pparasite V 3 f C P parasite 2 3 2 2A A R C P i We will later show from blade element theory that C P 0 1 f 3 C d 0 Thus C P CT i 1 3 2 2A 8 C d 0 1 3 2 8 Lakshmi Sankar 2002 25 Empirical Corrections The performance theory above does not account for Non uniform inflow effects Swirl losses Tip Losses It also uses an average drag coefficient To account for these the power coefficient is empirically corrected Lakshmi Sankar 2002 26 Empirical Corrections Power Coefficent Uncorrected 1 f 3 C d 0 2 CT i 1 3 2A 8 Profile …
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