P ll d D d F Propellers and Ducted Fans

Transcription

PEMP
RMD510
P
Propellers
ll
and
d Ducted
D
dF
Fans
Session delivered by:
Prof Q.
Prof.
Q H.
H Nagpurwala
08
@ M.S. Ramaiah School of Advanced Studies, Bengaluru
1
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Session Objectives
PEMP
RMD510
In this
hi session
i the
h delegates
d l
would
ld learn
l
about
b
 Types of propellers and ducted fans
 Working principle of propellers
 Slip stream, momentum and blade
element theories
 Design procedure for propellers
08
2
Introduction - Propeller
PEMP
RMD510

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
airfoil shaped blades.
Air propeller
08
Marine propeller
3
Application of Propeller
PEMP
RMD510
P-51 Mustang
Toy aircraft
Ch
Cheyenne
EN02
Pilatus Aircraft
08
4
Introduction – Ducted Fan





08
PEMP
RMD510
A ducted
d t d fan
f is
i a propulsion
l i arrangementt whereby
h b a propeller
ll is
i mounted
t d within
ithi
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,
cross section it can provide additional thrust of its own.
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
Application of Ducted Fan
Edgley EA7 Optica
Bell X-22A
08
PEMP
RMD510
DOAK VZ-4
Piasecki VZ-8P(B)
6
Types of Ducted Fans
PEMP
RMD510
Duct shapes
Accelerating shroud
Decelerating shroud
Flow
Fl
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 thrustto eight ratio.
to-weight
ratio
08
7
PEMP
RMD510
Types of Ducts – Based on Mounting
08
8
Slip Stream Theory
PEMP
RMD510
Continuity equation

m  1 A1V1   4 A4V4
Thrust generated

T  m V1
Power required
P  TV1
m = mass flow rate in kg/s
T = thrust in N
P = power in
i Watts
W tt
A = area in m2
V = velocity in m/s
 = density in kg/m3
08
Froude analysis of propeller
9
PEMP
RMD510
Slip Stream Theory – Unducted Propeller
Cruise condition
08
Static
St ti condition
diti
10
Slip Stream Theory – Ducted Propeller
cruise condition
08
PEMP
RMD510
static
t ti condition
diti
11
Lift distribution - Propeller Blade
Tip relieving effect
Unducted propeller
08
PEMP
RMD510
Duct friction effect
Ducted propeller
12
Ducted Fan Shape
08
PEMP
RMD510
13
Propellers
PEMP
RMD510
 Propeller consists of a number of rotating
wings of airfoil shape, designed to convert
torque into
i
thrust.
h
 Very similar to an aircraft wing, the
propeller blades are subjected to the same
aerodynamic
d
i laws
l
andd influences.
i fl
Velocity Triangle
V1
Vr1
U
08
14
PEMP
RMD510
Momentum Theory
The momentum theory, developed in 1865 by Rankine, is based on the assumption that
the propeller functions as a uniform “actuator disk”
Flow
Thrust
Flow
Flow
Far in front of the actuator disk, the pressure (p) and the air velocity (V) are
considered the same as in free air.
08
15
Momentum Theory (… contd.)
PEMP
RMD510
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 Ap  V  Vi Vi
Brake
a e Power
owe
P  2 Ap  V  Vi  Vi
2
V2
T
V
Ind ced Velocity
Induced
Velocit
Vi 


4 2 Ap  2
08
16
PEMP
RMD510
Brake power can also be expressed as
2
V
V
T



P T


 2
4 2 Ap 





Propulsive efficiency for the propeller
TV 2 Ap  V  Vi ViV
V
1

i 


2
P
2 Ap  V  Vi  Vi V  Vi 1  Vi
1
1
T




2
2
4
2

A
V
p


08




V
1
17
PEMP
RMD510
The Advance Ratio, J ; Thrust Coefficient, CT ; Torque Coefficient, CQ ; and Power
Coefficient, CP are defined as:
V
V
J

N .d p 2 . d p
Q
CQ 
  N 2  d 5p
CT 
CP 
T
 2 2 d p4
P
 2  d 5p
3
2
J

J
2
C
T

Power coefficient can also be given by C P  CT  

2

4



and the p
propulsive
p
efficiency
y by
y
08
CT J  1
1 2CT
i 
  

CP  2
4  J2




1
18
PEMP
RMD510
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
08
19
Blade Element Theory
PEMP
RMD510
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
h propeller.
ll
08
20
PEMP
RMD510
Blade Element Theory (… contd.)
The resultant air speed
VR 
r 2  V 2
Where
r = Part of propeller radius
Ω = angular velocity [rad/s]
V
The helix angle,   a tan
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.
blade The
variation in pitch angle from hub to tip results in twisted blades.
08
21
Blade Element Theory (… contd.)
PEMP
RMD510
When the propeller geometry is known, it is possible to calculate the section
thrust and torque, as below:
dT 
1
   V R2  c  dr
d  C l  cos   C d  sin
i  
2
dQ 
1
   V R2  c  r  dr  C l  sin    C d  cos 
2
Where,
VR = Resultant Speed
c = Chord
Cl = Lift Coefficient
Q = Torque
q
The total thrust and torque can be calculated by integrating the elemental
q antities along the length of the propeller blade.
quantities
blade
08
22
Propeller Pitch
PEMP
RMD510
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,
r which has the same pitch,
pitch and thus a larger pitch angle  .
08
23
PEMP
RMD510
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
D bli the
th diameter
di
t increases
i
the
th necessary power to
t 25 = 32.
32
 Changing the number of blades from b1 to b2 increases the power
consumption to P2 = P1(b2 /b1) if we keep the same diameter.
 On the other hand, a change in diameter from D1 to D2, changes the
power needed to turn the propeller at the same number of rotations per
minute to P2 = P1((D2/D1)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 D2 leads to
D2 = D1(b1 /b2)1/5
08
24
Propeller Diameter and Tip Speed
PEMP
RMD510
The above
Th
b
graph
h can be
b used
d tto find
fi d the
th tip
ti speedd andd Mach
M h number
b for
f given
i
propeller diameter and flight speed.
08
25
Blade Thickness
08
PEMP
RMD510
26
Propeller Characteristics (1)
08
PEMP
RMD510
27
PEMP
RMD510
Typical propeller efficiency curves as a function of advance ratio (J = V/nD) and
blade angle (McCormick
(McCormick, 1979)
08
28
PEMP
RMD510
Typical propeller thrust curves as a function of advance ratio (J = V/nD) and
blade angle (McCormick, 1979)
08
29
PEMP
RMD510
Typical
ratio
T i l propeller
ll power curves as a function
f ti off advance
d
ti (J = V/nD)
/ D) andd
blade angle (McCormick, 1979)
08
30
Propeller Characteristics from CFD
08
PEMP
RMD510
31
Ducted vs Unducted Propeller
08
PEMP
RMD510
32
Important Definitions
   
p
J = Advance ratio
m
CT
PA TS  V

p 
J
PS
PS
CP
N = Rotational speed
D = Propeller diameter
PA = Available power
PS = Shaft power
V
J
ND
Q = Torque
T = Thrust
T
CT 
N 2 D 4
P
CP 
N 3 D 5
Pitch  2  r  tan 
(Pitch is specified at 75% of the propeller
outer radius, R)
08
PEMP
RMD510
TA = Available thrust
V = Flow velocity
CT = Thrust coefficient
CP = Power coefficient
 = Blade orientation w.r.t. zero lift line
 = Overall efficiency
p = Propeller efficiency
m = Drive motor efficiency
33
Design Concepts
PEMP
RMD510
• The ducted fan and propeller design is influenced by
– Number of blades, B: Small effect on efficiency, ; propeller with more
blades p
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
Lif andd Drag
D
Distribution:
Di ib i
I
Instead
d off CL and
d CD , it
i is
i convenient
i to
specify radial distribution of polar and design angle of attack. The
distribution of CL and CD 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 CL (< 0.5).
08
34
Design Concepts (… contd.)
PEMP
RMD510
– 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.
propeller
– CT and CP are not affected by density, but T and P are.
– A propeller-engine combination will find different operating points
d
depending
di on the
th density.
d it
– For air propeller, the performance of propeller and engine depends upon
the altitude also.
08
35
Propeller Design Considerations
PEMP
RMD510
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 0.85
0 85
– 560 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 200 – 240 m/s.
m/s
Optimum efficiency according to momentum theory versus flight
speed for different power loadings P/D² in [W/m²].
08
36
Design Process
•
•
•
•
•
•
•
•
08
PEMP
RMD510
Design Specifications:
Aircraft Speed, Propeller Thrust, Altitude
Select suitable values for:
Number of Blades, Rotational Speed, Diameter
Calculate:
Advance Ratio,
Ratio Pitch
Pitch, Thrust and Power Coefficients
Coefficients, Efficiency,
Efficiency  at
75% R, Tip Velocity.
Estimate the radial variation of blade setting angle () and angle of
( )
attack ().
Iterate among 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
Standard Blade Profiles
•
•
•
•
•
PEMP
RMD510
NACA Profiles
E l Profiles
Eppler
P fil
Selig Profiles
Clark Y Profiles
RAF 6E Profiles
Note: The x-y coordinates along with the respective performance
d t for
data
f all
ll these
th
profiles
fil are well
ll documented.
d
t d
08
38
Propeller Design Programs
PEMP
RMD510
• JAVA Prop
• XFLR5
08
39
PEMP
RMD510
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 ppropeller
p
and tends to
throw the blade out from the centre.
3. Torsion or Twisting forces in
the blade itself,, caused byy the
resultant of air forces, which tend to
twist the blades towards a lower
blade angle.
08
40
PEMP
RMD510
Propeller Design Example
Start Design
Case 1
Design Specifications
D=0.12 m, B=2,
N=15,000 rpm,
T=11 N
T
Assume
V=20 m/s
N=Speed (rpm)
B=No. of blades
D=Prop. Dia (m)
T=Thrust
T
Thrust (N)
P=Linear pitch (m)
η =Efficiency
P=V/n
J = 0.7
Blade angles, β
P=2*Pi*r*tan(β)
Assume
η= 80%
Calculate performance
parameters, CT , CQ , CP , η
CFD analysis
Is performance okay?
Specifications
Diameter=0.12 m
Speed=15,000 rpm
Thrust=1 N
No. of blades=2
Design accepted
End
08
41
Computational Domain
PEMP
RMD510
Propeller mesh
Fluid domain
INLET
The fluid domain was initially meshed with tetrahedral elements and these
were then
th converted
t d to
t polyhedra
l h d using
i FLUENT.
FLUENT
08
42
Airfoil Stacking
Details
Rectangular Cross-section, β=10.812
PEMP
RMD510
β=11.769, Chord Length = 10.5 mm, Chord Thk = 0.95 mm
β=12.908, Chord Length = 10.5 mm, Chord Thk =0. 99375mm
Ai f il S
Airfoil
Sections:
ti
Selig 1210
β=20.905,
β
20.905, Chord Length = 10.5 mm, Chord Thk = 1.16875 mm
β=43.890, Chord Length = 10 mm, Chord Thk = 1.5 mm
08
43
PEMP
RMD510
Propeller Design (…contd.)
Calculated :
Thrust (N)
1N
Thrust Co-efficient
0.1642
Torque N-m
0.0238
Torque Co-efficient
0.0326
Power Co-efficient
0.2
P
Power
(W)
25 W
Case 1:
β = 15.798o
Numerical results:
Speed
(rpm)
Thrust
(N)
Torque
(N-m)
0.7
15,000
0.7385
0.02080
0.0539
0.0127
32.6730
0.0795
0.4521
0.9
11,111.1
0.2360
0.00722
0.0314
0.0080
8.4051
0.0503
0.5616
J
Thrust Co
Coefficient
Torque Co
Coefficient
Power
(W)
Power CoCo
efficient
Efficiency
The propeller was designed for an advance ratio, J=0.7, Speed, N=15,000
rpm, Thrust, T = 1N
08
44
PEMP
RMD510
0.09
0.08
0.07
0.06
0 05
0.05
0.04
0.03
0.02
0.01
0
Torque co-efficient for case 1
Torque Co-efficiient, CQ
Thrust Co-effic
cient, CT
Thrust Co-efficient for case 1
Thrust Co-efficient for case 1
Design Point- CT
0
0.2
0.4
0.6
0.8
1
1.2
Advance Ratio, J
0.018
0.016
0.014
0.012
0.01
0.008
0.006
0.004
0.002
0
Torque Co-efficient
0
0.2
0.4
1
1.2
1.4
1.2
1.4
0.6
0.12
0.5
0.1
E ffic ie n c y, n
P o w e r C o -e f ficc ie n t , C P
0.8
Efficiency for Case 1
Pow er Co-efficient for Case 1
0.08
0.06
0.04
Power Co-efficient, CP
0.02
Design Point- CP
0.2
0.4
0.6
0.4
0.3
0.2
Efficiency for case 1
0.1
0
0
0.8
Advance Ratio, J
08
0.6
Advance Ratio, J
1
1.2
1.4
0
0
0.2
0.4
0.6
0.8
1
Advance Ratio, J
45
PEMP
RMD510
Start Design
Case 2
Design Specifications
D=0.12 m, B=2,
N=10,000 rpm,
T=11 N
T
β
at 75% R
Blade angles, β
P=2*Pi*r*tan(β)
J=1
Assume,
β=25o
Assume
η= 80%
η
Calculate performance
parameters, CT , CQ , CP , η
CFD analysis
Is performance okay?
N=Speed (rpm)
B=No. of blades
D=Prop. Dia (m)
T=Thrust
T
Thrust (N)
P=Linear pitch (m)
η =Efficiency
Specifications
Diameter=0.12 m
S d 10 000 rpm
Speed=10,000
Thrust=1 N
No. of blades=2
Design accepted
End
08
46
PEMP
RMD510
Calculated :
Thrust (N)
1N
Thrust Co-efficient
0.1642
Torque N-m
0.0238
Torque Co-efficient
0.0326
Power Co-efficient
0.2
P
Power
(W)
25 W
Case 2:
β = 25o
Numerical results:
J
Speed
(rpm)
Thrust
(N)
Torque
(N-m)
Thrust Co
Coefficient
Torque Co
Coefficient
Power
(W)
Power CoCo
efficient
0.9
11,111.1
0.7461
0.0225
0.0993
0.0250
26.2112
0.1569
0.5693
1
10,000
0.4603
0.0164
0.0756
0.0225
17.1809
0.1411
0.5359
Efficiency
The propeller was designed for an advance ratio, J=1, Speed, N=10,000 rpm,
Thrust, T = 1N
08
47
Results of Computations
PEMP
RMD510
Static pressure distribution on the propeller blade (Pa)
SS
PS
Case 2: Beta = 25 deg, Speed = 10,000 rpm
08
48
PEMP
RMD510
Velocity distribution on the propeller blade (m/s)
SS
Case 2: Beta = 25 deg, Speed = 10,000 rpm
08
49
PEMP
RMD510
Pressure variation across upstream and
o
downstream of the propeller (25 blade angle)
Case 2:
P ressure, (Pa
a)
350
Upstream
300
250
200
150
100
50
0
β = 25 deg
Downstream
N = 10,000 rpm
Static Pressure,Ps
Total Pressure, Pt
D
Dynamic
i Pressure.Pd
P
Pd
V = 20 m/s
-0.3 -0.3 -0.2 -0.2 -0.1 -0.1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Axial distance, (m)
Propeller
Velocity,(m
m/s)
Velocity variation across upstream and
o
downstream of the propeller (25 deg)
Upstream
Velocity
-0.3
08
-0.2
23
22
21
20
19
18
17
16
15
-0.1
0
Propeller
Downstream
0.1
0.2
0.3
0.4
Axial distance, (m)
0.5
50
PEMP
RMD510
0.035
Thrust Co-efficients for Case 2 at 20 and 18 m/s velocities
0.16
0.03
0.14
Thrust Co-effic
cient, CT
Torque Co-efficient for Case 2 at 20 and 18 m/s Velocities
Torque Co-efficien
nt, CQ
0.12
0.1
0.08
0.06
Thrust Co-efficient-Case2-20V
0.04
Thrust Co-efficient-Case2-18V
0.02
0.025
0.02
0.015
0.01
Torque Co-efficient-Case2-20V
0
0
0.2
0.4
0.6
0.8
1
1.2
0 005
0.005
1.4
Advance Ratio, J
T
Torque
Co-efficient-Case2-18V
C ffi i
C
2 18V
0
0
0.2
0.4
0.6
0.8
Advance Ratio, J
1
1.2
1.4
Efficiency for case 2 at 20 and 18 m/s velocities
Power Co-efficient for Case 2 at 20 and 18 m/s Velocities
02
0.2
0.6
0.18
0.5
0.14
0.12
Efficienc
cy, n
Power Co-effficient, CP
0.16
01
0.1
0.08
0.06
Power Co-efficient-Case 2-20V
0.04
0.2
0.4
0.6
0.8
Advance Ratio,J
08
0.2
Efficiency-Case 2-20V
0.1
0
0
0.3
Efficiency-Case 2-18V
Power Co-efficient-Case 2-18V
0.02
0.4
1
1.2
1.4
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Advance Ratio, J
51
PEMP
RMD510
Parametric Studies
Parametric studies were carried out by changing the blade setting angle β
= 28o, 30o, 32o, 34o, 35o, 38o and 40o
β = 28º
08
β = 30º
β = 32º
β = 35º
β = 40º
52
PEMP
RMD510
Static Pressure variation across the propeller
Case 2:
28
27
β = 40 deg
S tatiic pressure, (P a)
26
25
Speed = 10,000 rpm
24
Static Pressure
23
22
21
20
19
18
-0.2
-0.175
-0.15
-0.125
-0.1
-0.075
-0.05
-0.025
0
0.025
Variation of Total and dynamic pressure acros the
propeller
0.05
295
Axial position, (m)
290
P ressurre, (P a)
285
Dynamic Pressure
Total Pressure
280
275
270
265
260
255
-0.2
08
-0.15
-0.1
-0.05
0
Axial distance, (m)
0.05
0.1
53
PEMP
RMD510
C
Comparison
i
off T
Torque Co-efficients
C ffi i t for
f different
diff
t
blade setting angles
0.07
Torque Co-efficien
nt, CQ
0.06
0.05
C
Case1-15-79
1 15 79 d
degree
0.04
Case2-25 degree
0.03
Case2-30 degree
0.02
Case2-35 degree
0.01
0
0
Case2-40 degree
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Advance Ratio, J
Comparison of Thrust Co-efficients for different blade
setting angles
Thrust Co-effic
cient, CT
0.25
0.2
0.15
Case1-15.79 degree
Case2-25 degree
0.1
Case2-30 degree
Case2-35 degree
0.05
Case2-40 degree
0
0
08
0.2
0.4
0.6
0.8
1
1.2
Advance Ratio, J
1.4
1.6
1.8
54
PEMP
RMD510
Comparison of power Co-efficients for different
blade setting angles
Pow
wer Co-efficie
ent, CP
04
0.4
0.35
0.3
0 25
0.25
0.2
0.15
0.1
0.05
0
0
08
02
0.2
04
0.4
06
0.6
0.8
0
8
1
12
1.2
Advance Ratio, J
14
1.4
16
1.6
18
1.8
55
PEMP
RMD510
Comparison of Efficiencies for different blade setting
angles
0.7
Efficiency
y, 
0.6
Case1-15.79 deg
Case2-25 deg
C
Case2-28
2 28 d
deg
Case2-30 deg
Case2-32 deg
Case2-34 deg
g
Case2-35 deg
Case2-38 deg
Case2-40 deg
0.5
0
0.4
0.3
02
0.2
0.1
0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Advance Ratio, J
1.4
1.6
1.8
Variation of Propeller Efficiency with Advance Ratio
08
56
PEMP
RMD510
Efficiency versus different blade setting angles
Prop eller Eff iciency, 
0.8
0.75
0.7
0.65
0.6
0.55
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42
Blade setting angle, Beta (deg)
Variation of Propeller Efficiency with Blade Setting Angle
08
57
Session Summary
PEMP
RMD510
The following aspects of ducted fans and propellers have been
di
discussed
d in
i this
thi session:
i




08
Working principle of propeller and ducted fan
Slip stream, momentum and blade element theories
Propeller performance parameters
Propeller design procedure with design example
58

P ll d D d F Propellers and Ducted Fans

Transcription

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