Helicopter Aerodynamics and Performance Preliminary Remarks
© L. Sankar Helicopter Aerodynamics
1
The problems are many.. Transonic Flow on Advancing Blade Noise
Thrust
Aeroelastic Response
Shock Waves
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
© L. Sankar Helicopter Aerodynamics
2
A systematic Approach is necessary • •
A variety of tools are needed to understand, and predict these phenomena. Tools needed include – Simple back-of-the envelop tools for sizing helicopters, selecting engines, laying out configuration, and predicting performance – Spreadsheets and MATLAB scripts for mapping out the blade loads over the entire rotor disk – High end CFD tools for modeling • Airfoil and rotor aerodynamics and design • Rotor-airframe interactions • Aeroacoustic analyses
– Elastic and multi-body dynamics modeling tools – Trim analyses, Flight Simulation software
• • •
In this work, we will cover most of the tools that we need, except for elastic analyses, multi-body dynamics analyses, and flight simulation software. We will cover both the basics, and the applications. We will assume familiarity with classical low speed and high speed aerodynamics, but nothing more.
© L. Sankar Helicopter Aerodynamics
3
Plan for the Course • PowerPoint presentations, interspersed with numerical calculations and spreadsheet applications. • Part 1: Hover Prediction Methods • Part 2: Forward Flight Prediction Methods • Part 3: Helicopter Performance Prediction Methods • Part 4: Introduction to Comprehensive Codes and CFD tools • Part 5: Completion of CFD tools, Discussion of Advanced Concepts © L. Sankar Helicopter Aerodynamics
4
Text Books • Wayne Johnson: Helicopter Theory, Dover Publications,ISBN-0-486-68230-7 • References: – Gordon Leishman: Principles of Helicopter Aerodynamics, Cambridge Aerospace Series, ISBN 0-521-66060-2 – Prouty: Helicopter Performance, Stability, and Control, Prindle, Weber & Schmidt, ISBN 0-53406360-8 – Gessow and Myers – Stepniewski & Keys © L. Sankar Helicopter Aerodynamics
5
Grading • • • •
5 Homework Assignments (each worth 5%). Two quizzes (each worth 25%) One final examination (worth 25%) All quizzes and exams will be take-home type. They will require use of an Excel spreadsheet program, or optionally short computer programs you will write. • All the material may be submitted electronically.
© L. Sankar Helicopter Aerodynamics
6
Instructor Info. • Lakshmi N. Sankar • School of Aerospace Engineering, Georgia Tech, Atlanta, GA 30332-0150, USA. • Web site: www.ae.gatech. edu/~lsankar/AE6070.Fall2002 • E-mail Address:
[email protected]
© L. Sankar Helicopter Aerodynamics
7
Earliest Helicopter.. Chinese Top
© L. Sankar Helicopter Aerodynamics
8
Leonardo da Vinci (1480? 1493?)
© L. Sankar Helicopter Aerodynamics
9
Human Powered Flight? Weight 160lbf Rotor Radius ~ 6ft Rotor Area 100 sq.ft Desnity 0.00238 slugs. W Ideal Power W 5.33HP 2 A Actual Power Ideal Power/Figure of Merit 5.33/0.8 6.7 HP © L. Sankar Helicopter Aerodynamics
10
D’AmeCourt (1863) Steam-Propelled Helicopter
© L. Sankar Helicopter Aerodynamics
11
Paul Cornu (1907) First man to fly in helicopter mode..
© L. Sankar Helicopter Aerodynamics
12
De La Cierva invented Autogyros (1923)
© L. Sankar Helicopter Aerodynamics
13
Cierva introduced hinges at the root that allowed blades to freely flap
Hinges
Only the lifts were transferred to the fuselage, not unwanted moments. In later models, lead-lag hinges were also used to Alleviate root stresses from Coriolis forces © L. Sankar Helicopter Aerodynamics
14
Igor Sikorsky Started work in 1907, Patent in 1935
Used tail rotor to counter-act the reactive torque exerted by the rotor on the vehicle. © L. Sankar Helicopter Aerodynamics
15
Sikorsky’s R-4
© L. Sankar Helicopter Aerodynamics
16
Ways of countering the Reactive Torque
Other possibilities: Tip jets, tip mounted engines © L. Sankar Helicopter Aerodynamics
17
Single Rotor Helicopter
© L. Sankar Helicopter Aerodynamics
18
Tandem Rotors (Chinook)
© L. Sankar Helicopter Aerodynamics
19
Coaxial rotors Kamov KA-52
© L. Sankar Helicopter Aerodynamics
20
NOTAR Helicopter
© L. Sankar Helicopter Aerodynamics
21
NOTAR Concept
© L. Sankar Helicopter Aerodynamics
22
Tilt Rotor Vehicles
© L. Sankar Helicopter Aerodynamics
23
Helicopters tend to grow in size..
AH-64A
AH-64D
Length
58.17 ft (17.73 m)
58.17 ft (17.73 m)
Height
15.24 ft (4.64 m)
13.30 ft (4.05 m)
Wing Span
17.15 ft (5.227 m)
17.15 ft (5.227 m)
Primary Mission Gross Weight
15,075 lb (6838 kg) 11,800 pounds Empty
16,027 lb (7270 kg) Lot 1 Weight
© L. Sankar Helicopter Aerodynamics
24
AH-64A
AH-64D
Length
58.17 ft (17.73 m)
58.17 ft (17.73 m)
Height
15.24 ft (4.64 m)
13.30 ft (4.05 m)
Wing Span
17.15 ft (5.227 m)
17.15 ft (5.227 m)
Primary Mission Gross Weight
15,075 lb (6838 kg) 11,800 pounds Empty
16,027 lb (7270 kg) Lot 1 Weight
Hover In-Ground Effect (MRP)
15,895 ft (4845 m) [Standard Day] 14,845 ft (4525 m) [Hot Day ISA + 15C]
14,650 ft (4465 m) [Standard Day] 13,350 ft (4068 m) [Hot Day ISA + 15 C]
Hover Out-of-Ground Effect (MRP)
12,685 ft (3866 m) [Sea Level Standard Day] 11,215 ft (3418 m) [Hot Day 2000 ft 70 F (21 C)]
10,520 ft (3206 m) [Standard Day] 9,050 ft (2759 m) [Hot Day ISA + 15 C]
Vertical Rate of Climb (MRP)
2,175 fpm (663 mpm) [Sea Level Standard Day] 2,050 fpm (625 mpm) [Hot Day 2000 ft 70 F (21 C)]
1,775 fpm (541 mpm) [Sea Level Standard Day] 1,595 fpm (486 mpm) [Hot Day 2000 ft 70 F (21 C)]
© L. Sankar Helicopter Aerodynamics 2,915 fpm (889 mpm)
2,635 fpm (803 mpm)
25
Power Plant Limitations • Helicopters use turbo shaft engines. • Power available is the principal factor. • An adequate power plant is important for carrying out the missions. • We will look at ways of estimating power requirements for a variety of operating conditions. © L. Sankar Helicopter Aerodynamics
26
High Speed Forward Flight Limitations • As the forward speed increases, advancing side experiences shock effects, retreating side stalls. This limits thrust available. • Vibrations go up, because of the increased dynamic pressure, and increased harmonic content. • Shock Noise goes up. • Fuselage drag increases, and parasite power consumption goes up as V 3. • We need to understand and accurately predict the air loads in high speed forward flight. © L. Sankar Helicopter Aerodynamics
27
Concluding Remarks • Helicopter aerodynamics is an interesting area. • There are a lot of problems, but there are also opportunities for innovation. • This course is intended to be a starting point for engineers and researchers to explore efficient (low power), safer, comfortable (low vibration), environmentally friendly (low noise) helicopters.
© L. Sankar Helicopter Aerodynamics
28
Hover Performance Prediction Methods
I. Momentum Theory
© L. Sankar Helicopter Aerodynamics
29
Background • Developed for marine propellers by Rankine (1865), Froude (1885). • Extended to include swirl in the slipstream by Betz (1920) • This theory can predict performance in hover, and climb. • We will look at the general case of climb, and extract hover as a special situation with zero climb velocity. © L. Sankar Helicopter Aerodynamics
30
Assumptions • Momentum theory concerns itself with the global balance of mass, momentum, and energy. • It does not concern itself with details of the flow around the blades. • It gives a good representation of what is happening far away from the rotor. • This theory makes a number of simplifying assumptions. © L. Sankar Helicopter Aerodynamics
31
Assumptions (Continued) • Rotor is modeled as an actuator disk which adds momentum and energy to the flow. • Flow is incompressible. • Flow is steady, inviscid, irrotational. • Flow is one-dimensional, and uniform through the rotor disk, and in the far wake. • There is no swirl in the wake. © L. Sankar Helicopter Aerodynamics
32
Control Volume is a Cylinder V
Station1
2 3
4
Total area S© L. Sankar
Disk area A V+v2 V+v3
V+v4
Helicopter Aerodynamics
33
Conservation of Mass Inflow through the top VS Inflow through the side m1 Outflow through the bottom VS - A 4 (V v4 ) A4
© L. Sankar Helicopter Aerodynamics
34
Conservation of Mass through the Rotor Disk Flow through the rotor disk =
m AV v 2 AV v 3 A4 V v 4 Thus v2=v3=v There is no velocity jump across the rotor disk The quantity v is called induced velocity at the rotor disk © L. Sankar Helicopter Aerodynamics
35
Global Conservation of Momentum Momentum inflow through top V 2 S Momentum inflow through the side m1V A 4 v 4V Momentum outflow through bottom 2
S - A 4 V 2 V v 4 A4 Pressure is atmospheric on all the far field boundaries. Thrust , T Momentum rate out Momentum Rate in T A 4 (V v 4 ) v 4 mv 4 Mass flow rate through the rotor disk times Excess velocity between stations 1 and 4 © L. Sankar Helicopter Aerodynamics
36
Conservation of Momentum at the Rotor Disk p2
V+v
Due to conservation of mass across the Rotor disk, there is no velocity jump. Momentum inflow rate = Momentum outflow rate
p 3
V+v Thus, Thrust T = A(p3-p2)
© L. Sankar Helicopter Aerodynamics
37
Conservation of Energy Consider a particle that traverses from Station 1 to station 4
1
2
V+v
3
We can apply Bernoulli equation between Stations 1 and 2, and between stations 3 and 4. Recall assumptions that the flow is steady, irrotational, inviscid. 1 1 2 V v p V 2 2 2 1 1 2 2 p3 V v p V v 4 2 2 v p3 p2 V 4 v 4 2 p2
4
V+v4
© L. Sankar Helicopter Aerodynamics
38
From the previous slide #38, v4 p3 p2 V v 4 2 v4 T A p3 p2 AV v 4 2 From an earlier slide # 36, Thrust equals mass flow rate through the rotor disk times excess velocity between stations 1 and 4
T AV v v 4 Thus, v = v4/2 © L. Sankar Helicopter Aerodynamics
39
Induced Velocities V
The excess velocity in the Far wake is twice the induced Velocity at the rotor disk.
V+v
To accommodate this excess Velocity, the stream tube has to contract.
V+2v © L. Sankar Helicopter Aerodynamics
40
Induced Velocity at the Rotor Disk Now we can compute the induced velocity at the rotor disk in terms of thrust T. T = Mass flow rate through the rotor disk * (Excess velocity between 1 and 4). T = 2 A (V+v) v
2
V T V v- 2 2 2 A There are two solutions. The – sign Corresponds to a wind turbine, where energy Is removed from the flow. v is negative. The + sign corresponds to a rotor or Propeller where energy is added to the flow. In this case, v is positive. © L. Sankar Helicopter Aerodynamics
41
Induced velocity at the rotor disk 2
V T V v- 2 2 2 A In Hover, climb velocity V 0 T v 2 A
© L. Sankar Helicopter Aerodynamics
42
Ideal Power Consumed by the Rotor P Energy flow out - Energy flow in 1 1 2 mV 2v mV 2 2 2 2mvV v T V v 2 V V T T 2 2 A 2
In hover, ideal power
T T 2 A
© L. Sankar Helicopter Aerodynamics
43
Summary • According to momentum theory, the downwash in the far wake is twice the induced velocity at the rotor disk. • Momentum theory gives an expression for induced velocity at the rotor disk. • It also gives an expression for ideal power consumed by a rotor of specified dimensions. • Actual power will be higher, because momentum theory neglected many sources of lossesviscous effects, compressibility (shocks), tip losses, swirl, non-uniform flows, etc. © L. Sankar Helicopter Aerodynamics
44
Figure of Merit • Figure of merit is defined as the ratio of ideal power for a rotor FM Ideal Power in Hover in hover obtained Actual Power in Hover from momentum CT theory and the actual CT T v 2 power consumed by P CP the rotor. • For most rotors, it is between 0.7 and 0.8. © L. Sankar Helicopter Aerodynamics
45
Some Observations on Figure of Merit • Because a helicopter spends considerable portions of time in hover, designers attempt to optimize the rotor for hover (FM~0.8). • We will discuss how to do this later. • A rotor with a lower figure of merit (FM~0. 6) is not necessarily a bad rotor. • It has simply been optimized for other conditions (e.g. high speed forward flight). © L. Sankar Helicopter Aerodynamics
46
Example #1 • A tilt-rotor aircraft has a gross weight of 60,500 lb. (27500 kg). • The rotor diameter is 38 feet (11.58 m). • Assume FM=0.75, Transmission losses=5% • Compute power needed to hover at sea level on a hot day. © L. Sankar Helicopter Aerodynamics
47
Example #1 (Continued) 2
Disk Area A 19 A 1134.12 square feet Density 0.00238 slugs/cubic feet There are two rotors. T 30250 lbf Induced velocity, v
T 2 A
v 74.86 ft/sec Downwash in the far wake 150 ft/sec ! Ideal Power Tv 30250 x 74.86 lb ft/sec Ideal Power 4117 HP Actual Power ideal Power/FM 4117/0.75 Actual power 5490 HP For the two rotors, total actual power 10980 HP There is 5% transmission loss Power supplied by the engine to the shaft 10980 *1.05 11528 HP © L. Sankar Helicopter Aerodynamics
48
Alternate scenarios • What happens on a hot day, and/or high altitude? – Induced velocity is higher. – Power consumption is higher
• What happens if the rotor disk area A is smaller? – Induced velocity and power are higher.
• There are practical limits to how large A can be. © L. Sankar Helicopter Aerodynamics
49
Disk Loading • The ratio T/A is called disk loading. • The higher the disk loading, the higher the induced velocity, and the higher the power. • For helicopters, disk loading is between 5 and 10 lb/ft2 (24 to 48 kg/m2). • Tilt-rotor vehicles tend to have a disk loading of 20 to 40 lbf/ft2. They are less efficient in hover. • VTOL aircraft have very small fans, and have very high disk loading (500 lb/ft 2). © L. Sankar Helicopter Aerodynamics
50
Power Loading • The ratio of thrust to power T/P is called the Power Loading. • Pure helicopters have a power loading between 6 to 10 lb/HP. • Tilt-rotors have lower power loading – 2 to 6 lb/HP. • VTOL vehicles have the lowest power loading – less than 2 lb/HP. © L. Sankar Helicopter Aerodynamics
51
Non-Dimensional Forms Thrust, Torque, and Power are usually expressed in non - dimensional form. T C T Thrust Coefficient 2 AR P C P Power Coefficient 3 AR Q C Q Torque Coefficient 2 AR R In hover, Power Angualr velocity x Torque P Q C P CQ © L. Sankar Helicopter Aerodynamics
52
Non-dimensional forms.. v 1 Induced inflow i R R
T CT 2 A 2
Ideal Power in Hover FM Actual Power in Hover CT CT Tv 2 P CP © L. Sankar Helicopter Aerodynamics
53
Tip Losses R
BR
A portion of the rotor near the Tip does not produce much lift Due to leakage of air from The bottom of the disk to the top.
One can crudely account for it by Using a smaller, modified radius BR, where B = Number of blades.
2CT B 1 b
© L. Sankar Helicopter Aerodynamics
54
Power Consumption in Hover Including Tip Losses..
1 1 CT CP CT FM B 2
© L. Sankar Helicopter Aerodynamics
55
Hover Performance Prediction Methods II. Blade Element Theory
© L. Sankar Helicopter Aerodynamics
56
Preliminary Remarks • Momentum theory gives rapid, back-ofthe-envelope estimates of Power. • This approach is sufficient to size a rotor (i.e. select the disk area) for a given power plant (engine), and a given gross weight. • This approach is not adequate for designing the rotor.
© L. Sankar Helicopter Aerodynamics
57
Drawbacks of Momentum Theory • It does not take into account – Number of blades – Airfoil characteristics (lift, drag, angle of zero lift) – Blade planform (taper, sweep, root cut-out) – Blade twist distribution – Compressibility effects
© L. Sankar Helicopter Aerodynamics
58
Blade Element Theory • Blade Element Theory rectifies many of these drawbacks. First proposed by Drzwiecki in 1892. • It is a “strip” theory. The blade is divided into a number of strips, of width r. • The lift generated by that strip, and the power consumed by that strip, are computed using 2-D airfoil aerodynamics. • The contributions from all the strips from all the blades are summed up to get total thrust, and total power. © L. Sankar Helicopter Aerodynamics
59
Typical Blade Section (Strip) dT r
Tip dr
T b
R
dT
Cut Out
Root Cut-out
Tip
Pb
dP
Cut Out © L. Sankar Helicopter Aerodynamics
60
Typical Airfoil Section V v arctan r
Line of Zero Lift
V+v
r
effective = © L. Sankar Helicopter Aerodynamics
61
Sectional Forces Once the effective angle of attack is known, we can look-up the lift and drag coefficients for the airfoil section at that strip. We can subsequently compute sectional lift and drag forces per foot (or meter) of span.
1 L U T2 U P2 cCl 2 1 D U T2 U P2 cCd 2
UT=r UP=V+v
These forces will be normal to and along the total velocity vector. © L. Sankar Helicopter Aerodynamics
62
Rotation of Forces T
L
Fx
V+v r
D
dT L cos D sin dr 1 U T2 U P2 cCl cos Cd sin dr 2 dFx D cos L sin dr
1 U T2 U P2 cCd cos Cl sin dr 2 dP U T dFx rdFX
© L. Sankar Helicopter Aerodynamics
63
Approximate Expressions • The integration (or summation of forces) can only be done numerically. • A spreadsheet may be designed. A sample spreadsheet is being provided as part of the course notes. • In some simple cases, analytical expressions may be obtained.
© L. Sankar Helicopter Aerodynamics
64
Closed Form Integrations • •
The chord c is constant. Simple linear twist. The inflow velocity v and climb velocity V are small. Thus,
