Momentum Theory in Forward Flight

Transcription

1 Momentum Theory in Forward Flight In helicopter forward flight the rotor moves through the air with an edgewise velocity component that is parallel to the rotor plane Since the helicopter rotor has to produced both the lifting force and the propulsion force. The rotor must be tilted forward at an AOA relatively to the oncoming flow. Slide 1

2 The Dynamic Pressure varies Radially and Azimuthally V tip =ΩR V tip =ΩR+V V tip =ΩR-V V tip =ΩR Slide 2

3 Force Balance in Hover Thrust Drag Rotor Disk Drag Weight In hover, T= W The drag forces on the individual blades cancel each other out, when summed up. Slide 3

4 Glauert s flow model To start this effort, we will need a very simple inflow model. A model proposed by Glauert (1926) 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. Slide 4

5 Force Balance in Forward Flight Thrust, T Flight Direction Vehicle Drag, D Weight, W Slide 5

6 Force Balance in Forward Flight Flight Direction α T W c.g. Rotor Disk D Slide 6

7 Glauert s flow model Freestream, V Freestream, V Total velocity, V Induced velocity, v i Freestream, V Induced velocity, w Total velocity, V Slide 7

8 Total Velocity at the Rotor Disk Slide 8

9 Conservation laws Conservation of momentum in the direction normal to the disk: Conservation of energy in the same direction Slide 9

10 Conservation laws From the two previous equations we can write: And reach the conclusion that w=2v i, the same result was in the previous cases. Knowing that the mass flow at the disk is ρau: In high speed forward flight V >>v i so: Slide 10

11 Induce velocity We know for the hover case that: Then from the previous equation: Slide 11

12 Non dimensional forms The non-dimensional form using the tip speed ΩR: So that the non-dimensional induced velocity equation can be written as: Slide 12

13 Non dimensional forms Since we already know that: We can write: Which requires a numerical solution Slide 13

14 Approximate Form at High Speed Forward Flight If the advance ratioµis higher than0.2 andαis small,µfar exceeds the inflow ratioλ: Slide 14

15 Variation of Non-Dimensional Inflow with Advance Ratio Notice that inflow velocity rapidly decreases with advance ratio Slide 15

16 Variation of Non-Dimensional Inflow with Advance Ratio Slide 16

17 Power Consumption in Forward Flight The ideal power from Glauert s theory is For the actual power we have to take into account the blade profile power From the equilibrium of forces Tsinα=D so: Where Tv i is the induce power and DV is the Parasitic power Slide 17

18 Power Consumption in Forward Flight The induce power decrease with the advance ratio µ The Parasite power can be calculated: The Parasite power increases with the cube of the forward velocity (or advance ratio µ) Slide 18

19 Power in Forward Flight Available Power Induced Power, Tv i Profile power Slide 19

20 Power Coefficient Induced power Profile Power Parasite Power 1.15 C D is the vehicle parasite drag coefficient and S the reference area. Because there is no agreement on a common reference area it is customary to supply the product C D S=f equivalent flat plate area Slide 20