Propellers and Ducted Fans

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1 Propellers and Ducted Fans Session delivered by: Prof. Q. H. Nagpurwala 1

2 To help protect your privacy, PowerPoint prevented this external picture from being automatically downloaded. To download and display this picture, click Options in the Message Bar, and then click Enable external content. Session Objectives In this session the delegates would learn about Types of propellers and ducted fans Working principle of propellers Slip stream, momentum and blade element theories Design procedure for propellers 2

3 Introduction - Propeller A propeller is a device which transmits power by converting it into thrust for propulsion of a vehicle though a fluid by rotating two or more twisted blades about a central shaft, in a manner analogous to rotating a screw through a solid. The blades of a propeller act as rotating wings and produce force through application of Newton's third law of motion, generating a difference in pressure between the forward and rear surfaces of the airfoil-shaped blades. Air propeller Marine propeller 3

4 Application of Propeller P-51 Mustang Toy aircraft Cheyenne EN02 Pilatus Aircraft 4

5 Introduction Ducted Fan A ducted d fan is apropulsion li arrangement whereby apropeller is mounted tdwithin a cylindrical shroud or duct. The duct prevents losses in thrust from the tips of the propeller and if the duct has an airfoil cross-section, section it can provideadditionalthrustof thrust of itsown own. Ducted fan propulsion is used in aircrafts, airboats and hovercrafts. In aircraft application, ducted fans normally have more number of shorter blades than propellers and thus can operate at higher rotational speeds. The operating speed of an unshrouded propeller is limited since tip speeds approach the sound barrier at lower speeds than an equivalent ducted propeller. 5

6 Application of Ducted Fan Edgley EA7 Optica DOAK VZ-4 Bell X-22A Piasecki VZ-8P(B) 6

7 Types of Ducted Fans Duct shapes Accelerating shroud Decelerating shroud Flow decelerating shroud - noise reduction. accelerating shroud - low speed heavily loaded propellers (improves efficiency) Ducted fans are favoured in VTOL and other low-speed designs for their high thrust- to-weight ratio. 7

8 Types of Ducts Based on Mounting 8

9 Slip Stream Theory Continuity equation m T 1 Thrust generated 1AV A 4V 4 m V V 1 Power required P TV 1 m = mass flow rate in kg/s T = thrust in N P = power in Wtt Watts A = area in m 2 V = velocity in m/s =densityinkg/m in 3 Froude analysis of propeller 9

10 Slip Stream Theory Unducted Propeller Cruise condition Static ti condition 10

11 Slip Stream Theory Ducted Propeller cruise condition static tti condition 11

12 Lift distribution - Propeller Blade Tip relieving effect Duct friction effect Unducted propeller Ducted propeller 12

13 Ducted Fan Shape 13

14 Propellers Propeller consists of a number of rotating wings of airfoil shape, designed to convert torque into thrust. Very similar to an aircraft wing, the propeller blades are subjected to the same aerodynamic laws and dinfluences. Velocity Triangle V 1 V r1 U 14

15 Momentum Theory The momentum theory, developed in 1865 by Rankine, is based on the assumption that the propeller functions as a uniform actuator disk Thrust Flow Flow Flow Far in front of the actuator disk, the pressure (p) and the air velocity (V) are considered thesameasinfreeair. 15

16 Momentum Theory ( contd.) Assumptions for momentum theory The flow is assumed to be inviscid and incompressible. All rotation of fluid within the stream tube is neglected. The flow velocity is assumed uniform over each cross section of the stream tube. The pressure is assumed uniform over each cross section of the stream tube. By applying conservation of mass, momentum and energy, one can derive the following relations: Thrust T 2 A V p V V i V i 2 Brake Power P 2 Ap V V i V i Induced Velocity V i V 4 2 T 2A p V 2 16

17 Momentum Theory ( contd.) Brake power can also be expressed as T V V T P 2 A p T P Propulsive efficiency for the propeller V VV V V A TV i i p 1 2 V V V V V V V V A P TV i i i i p i i p i V A T p 17 p

18 Momentum Theory ( contd.) The Advance Ratio, J ; Thrust Coefficient, C T ; Torque Coefficient, C Q ; and Power Coefficient, C P are defined as: T C V V J p T d C p N d p d J 2.. P Q p P d P C 5 2 p Q d N Q C T T P C J J C C Power coefficient can also be given by C C J C T T i and the propulsive efficiency by J C P i

19 Momentum Theory ( contd.) Limitations of momentum theory Does not account for rotation of the fluid within the slipstream There is no physical basis for neglecting slipstream rotation The actual thrust and propulsive efficiency are lower as a result of slipstream rotation The assumptions of uniform flow and uniform pressure result in a one dimensional solution that is not consistent with the results predicted from propeller vortex theory 19

20 Blade Element Theory In 1878 William Froude developed the blade element theory. This theory is based on the calculation of thrust and torque of a number of sections on the propeller blades. Integration over the entire blade length provides total thrust and torque of the propeller. 20

21 Blade Element Theory ( contd.) The resultant air speed V R 2 2 r V Where r = Part of propeller radius Ω = angular velocity [rad/s] The helix angle, a tan V r A large pitch (stagger) angle at the root of the blade and a small pitch angle at the tip will ensure an efficient angle of attack over the entire propeller blade. The variation in pitch angle from hub to tip results in twisted blades. 21

22 Blade Element Theory ( contd.) When the propeller geometry is known, it is possible to calculate the section thrust and torque, as below: 1 2 R 2 dt V c dr C cos C sin R dq V 2 c r dr Where, V R = Resultant Speed c = Chord C l = Lift Coefficient Q = Torque l C l sin C d d cos The total thrust and torque can be calculated by integrating the elemental quantities along the length of the propeller blade. 22

23 Propeller Pitch The flattened outside surface of the cylinder above, showing the pitch triangle and the pitch angle. Also shown is the triangle, corresponding to a different radius station r, which has the same pitch, and thus a larger pitch angle. 23

24 Pitch, Diameter and Number of Blades The propellers are of fixed pitch or variable pitch Pitch, p = 2 R tan The power needed to turn a propeller depends directly on the number of blades and on the diameter by a power of 5. Doubling the diameter increases the necessary power to 2 5 = 32. Changing the number of blades from b 1 to b 2 increases the power consumption to P 2 = P 1 (b 2 /b 1 ) if we keep the same diameter. On the other hand, a change in diameter from D 1 to D 2, changes the power needed to turn the propeller at the same number of rotations per minute to P 2 = P 1 1( (D 2/D 1 1) ) 5 when the number of blades are the same. Putting both trends together (for propellers of the same power consumption) and solving for the new propeller diameter D 2 leads to D =D(b /b 2 ) 1/5 24

25 Propeller Diameter and Tip Speed The above graph can be used to find the tip speed and Mach number for given propeller diameter and flight speed. 25

26 Blade Thickness 26

27 Propeller Characteristics (1) 27

28 Propeller Characteristics (2) Typical propeller efficiency curves as a function of advance ratio (J = V /nd) and blade angle (McCormick, 1979) 28

29 Propeller Characteristics (3) Typical propeller thrust curves as a function of advance ratio (J =V /nd) and blade angle (McCormick, 1979) 29

30 Propeller Characteristics (4) Typical propeller power curves as a function of advance ratio (J = V /nd) and blade angle (McCormick, 1979) 30

31 Propeller Characteristics from CFD 31

32 Ducted vs Unducted Propeller 32

33 Important Definitions p m PA T p PS V J ND T C T 2 N D P C P 3 N D S 4 5 Pitch 2 r V P S tan J C C (Pitch is specified at 75% of the propeller outer radius, R) T P J = Advance ratio N = Rotational speed D = Propeller diameter P A = Available power P S = Shaft power Q = Torque T = Thrust T A = Available thrust V = Flow velocity C T = Thrust coefficient C P = Power coefficient = Blade orientation w.r.t. zero lift line = Overall efficiency p = Propeller efficiency m = Drive motor efficiency 33

34 Design Concepts The ducted fan and propeller design is influenced by Number of blades, B: Small effect on efficiency, ; propeller with more blades performs better. Axial flow velocity, V (flight speed): Large pitch propellers may have a good efficiency at design point, but may run into trouble at low axial velocity blades tend to stall. Diameter: Large diameter tends to give higher efficiency because of increased mass flow rate. Usually the best overall propellers have a pitch to diameter ratio of 1. Lift and Drag Distribution: Instead of C L and C D, it is convenient to specify radial distribution of polar and design angle of attack. The distribution of C L and C D can then be examined. For good performance, L/D should be high. Also it is better to use lower angle of attack for design. Tip section of air propeller operating at M > 0.7 should be designed to operate at small C L (< 0.5). 34

35 Design Concepts ( contd.) Density: No influence on propeller efficiency, but affects size and shape. Force and Power are proportional to density; hence a hydro propeller has smaller dimension than an air propeller. C T and C P are not affected by density, but T and P are. A propeller-engine combination will find different operating points depending di on the density. For air propeller, the performance of propeller and engine depends upon the altitude also. 35

36 Propeller Design Considerations The stress effects on the engine (the gyroscopic moments) increase exponentially with diameter Ground clearance requirements. Propeller strength. Propeller tip speed. Compressibility constraints dictate that the speed at the blade tips should not exceed about Mach knots or 290 meters/second at sea level but compressibility effects start at 250 m/s and if the propeller is close the noise may be extremely uncomfortable at that speed. So, for comfort, the tip speed is usually in the range m/s. Optimum efficiency according to momentum theory versus flight speed for different power loadings P/D² in [W/m²]. 36

37 Design Process Design Specifications: Aircraft Speed, Propeller Thrust, Altitude Select suitable values for: Number of Blades, Rotational Speed, Diameter Calculate: Advance Ratio, Pitch, Thrust and Power Coefficients, Efficiency, at 75% R, Tip Velocity. Estimate the radial variation of blade setting angle () and angle of attack (). Iterateamong the above steps to obtain satisfactory performance parameters. Select appropriate blade profiles. Radially stack the profiles with proper orientation to form the complete 3-D blade. Evaluate performance of the propeller experimentally or through CFD simulations. 37

38 Standard Blade Profiles NACA Profiles Eppler Profiles Selig Profiles Clark Y Profiles RAF 6E Profiles Note: The x-y coordinates along with the respective performance data for all these profiles are well documented. d 38

39 Propeller Design Programs JAVA Prop XFLR5 39

40 Forces and Stresses Acting on Propeller Blades The forces acting on a propeller in flight are : 1. Thrust is the air force on the propeller which is parallel to the direction of advance and induces bending stress in the propeller. 2. Centrifugal force is caused by rotation of the propeller p and tends to throw the blade out from the centre. 3. Torsion or Twisting forces in the blade itself, caused by the resultant of air forces, which tend to twist the blades towards a lower blade angle. 40

41 Propeller Design Example Start Design Case 1 Design Specifications D=0.12 m, B=2, N=15,000 rpm, T=1N P=V/n Assume V=20 m/s N=Speed (rpm) B=No. of blades D=Prop. Dia (m) T=Thrust Thrust (N) P=Linear pitch (m) η =Efficiency J = 0.7 Blade angles, β P=2*Pi*r*tan(β) Calculate performance parameters, C T, C Q, C P, η Assume η= 80% Specifications Diameter=0.12 m Speed=15,000 rpm Thrust=1 N No. of blades=2 CFD analysis Is performance okay? Design accepted End 41

42 Computational Domain Propeller mesh Fluid domain INLET The fluid domain was initially meshed with tetrahedral elements and these were then converted to polyhedra using FLUENT. 42

43 Airfoil Stacking Details Rectangular Cross-section, β= β=11.769, Chord Length = 10.5 mm, Chord Thk = 0.95 mm β=12.9, Chord Length = 10.5 mm, Chord Thk = mm β=14.287, Chord Length = 10.5 mm, Chord Thk = mm Airfoil il Sections: Selig 1210 β=15.986, Chord Length = 10.5 mm, Chord Thk = mm β=18.129, Chord Length = 10.5 mm, Chord Thk = mm β=20.905, Chord Length = 10.5 mm, Chord Thk = mm β=24.625, Chord Length = 10.5 mm, Chord Thk = mm β=29.811, Chord Length = 10.5 mm, Chord Thk = mm β=37.378, Chord Length = 10.5 mm, Chord Thk = 1.3 mm β=43.890, Chord Length = 10 mm, Chord Thk = 1.5 mm 43

44 Propeller Design ( contd.) Calculated : Numerical results: Thrust (N) 1 N Thrust Co-efficient Torque N-m Torque Co-efficient Power Co-efficient 0.2 Power (W) 25 W Case 1: β = o J Speed Thrust Torque Thrust Co- Torque Co- Power Power Co- (rpm) (N) (N-m) efficient efficient (W) efficient Efficiency , , The propeller was designed for an advance ratio, J=0.7, Speed, N=15,000 rpm, Thrust, T = 1N 44

45 Propeller Design ( contd.) Thrust Co-effic cient, CT Thrust Co-efficient for case 1 Thrust Co-efficient for case 1 Design Point- CT Advance Ratio, J ient, CQ Torque Co-effici Torque co-efficient for case 1 Torque Co-efficient Advance Ratio, J Power Co-effic ien t, C P Power Co-efficient for Case 1 Power Co-efficient, CP Design Point- CP Advance Ratio, J y, n Efficienc Efficiency for Case Efficiency for case Advance Ratio, J 45

46 Propeller Design ( contd.) Start Design Case 2 Design Specifications D=0.12 m, B=2, N=10,000 rpm, T=1N β at 75% R Assume, β=25 o N=Speed (rpm) B=No. of blades D=Prop. Dia (m) T=Thrust Thrust (N) P=Linear pitch (m) η =Efficiency J = 1 Blade angles, β P=2*Pi*r*tan(β) Calculate performance parameters, C T, C Q, C P, η Assume η= 80% Specifications Diameter=0.12 m Speed=10,000 rpm Thrust=1 N No. of blades=2 CFD analysis Is performance okay? Design accepted End 46

47 Propeller Design ( contd.) Calculated : Numerical results: Thrust (N) 1 N Thrust Co-efficient Torque N-m Torque Co-efficient Power Co-efficient 0.2 Power (W) 25 W Case 2: β = 25 o Speed Thrust Torque Thrust Co- Torque Co- Power Power Co- J (rpm) (N) (N-m) efficient efficient (W) efficient Efficiency , , The propeller was designed for an advance ratio, J=1, Speed, N=10,000 rpm, Thrust, T = 1N 47

48 Results of Computations Static pressure distribution on the propeller blade (Pa) SS PS Case 2: Beta = 25 deg, Speed = 10,000 rpm 48

49 Results of Computations Velocity distribution on the propeller blade (m/s) SS Case 2: Beta = 25 deg, Speed = 10,000 rpm 49

50 Results of Computations ressure, (Pa a) P Pressure variation across upstream and downstream of the propeller (25 o blade angle) Upstream Downstream Static Pressure,Ps Total Pressure, Pt Dynamic Pressure.Pd Propeller Axial distance, (m) Velocity,(m m/s) Upstream Case 2: β = 25 deg N = 10,000 rpm V = 20 m/s Velocity variation across upstream and downstream of the propeller (25 o deg) Velocity Downstream Axial distance, (m) Propeller 50

51 Results of Computations 0.16 Thrust Co-efficients for Case 2 at 20 and 18 m/s velocities Torque Co-efficient for Case 2 at 20 and 18 m/s Velocities Thrust Co-effic cient, CT Thrust Co-efficient-Case2-20V 0.04 Thrust Co-efficient-Case2-18V Torque Co-efficien nt, CQ Torque Co-efficient-Case2-20V Torque Co-efficient-Case2-18V i C Advance Ratio, J Advance Ratio, J Power Co-efficient for Case 2 at 20 and 18 m/s Velocities 0.6 Efficiency for case 2 at 20 and 18 m/s velocities fficient, CP Power Co-ef Power Co-efficient-Case 2-20V Power Co-efficient-Case 2-18V Efficienc cy, n Efficiency-Case 2-20V Efficiency-Case 2-18V Advance Ratio,J Advance Ratio, J 51

52 Parametric Studies Parametric studies were carried out by changing the blade setting angle β = 28 o, 30 o, 32 o, 34 o, 35 o, 38 o and 40 o β = 28º β = 30º β = 32º β = 35º β = 40º 52

53 Results of Computations ic pressure, (Pa) Stati Static Pressure variation across the propeller Static Pressure Axial position, (m) 28 Case 2: Pressur re, (Pa) β =40deg Speed = 10,000 rpm Variation of Total and dynamic pressure acros the propeller 295 Dynamic Pressure Total Pressure Axial distance, (m)

54 Results of Computations Torque Co-efficien nt, CQ Comparison of Torque Co-efficients i for different blade setting angles Case degree Case2-25 degree Case2-30 degree Case2-35 degree Case2-40 degree Advance Ratio, J 0.25 Comparison of Thrust Co-efficients for different blade setting angles Thrust Co-effic cient, CT Case degree Case2-25 degree Case2-30 degree Case2-35 degree Case2-40 degree Advance Ratio, J 54

55 Results of Computations Comparison of power Co-efficients for different blade setting angles Pow wer Co-efficie ent, CP Advance Ratio, J 55

56 Results of Computations 0.7 Comparison of Efficiencies for different blade setting angles Efficiency y, Case deg Case2-25 deg Case deg Case2-30 deg Case2-32 deg Case2-34 deg Case2-35 deg Case2-38 deg Case2-40 deg Advance Ratio, J Variation of Propeller Efficiency with Advance Ratio 56

57 Results of Computations 0.8 Efficiency versus different blade setting angles iciency, eller Eff Prop Blade setting angle, Beta (deg) Variation of Propeller Efficiency with Blade Setting Angle 57

58 Session Summary The following aspects of ducted fans and propellers have been discussed d in this session: Working principle of propeller and ducted fan Slip stream, momentum and blade element theories Propeller performance parameters Propeller design procedure with design example 58

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