Evaluation of Propulsor Aerodynamic Performance for
Powered Aircraft Wind Tunnel Experiments
by
Nina M. Siu
B.S., Massachusetts Institute of Technology, 2011
Submitted to the Department of Aeronautics and Astronautics
in partial fulfillment of the requirements for the degree of
Master of Science in Aeronautics and Astronautics
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
February 2015
c Massachusetts Institute of Technology 2015. All rights reserved.
Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Department of Aeronautics and Astronautics
January 29, 2015
Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Edward M. Greitzer
H. N. Slater Professor of Aeronautics and Astronautics
Thesis Supervisor
Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Alejandra Uranga
Research Engineer, Department of Aeronautics and Astronautics
Thesis Supervisor
Accepted by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Paulo C. Lozano
Associate Professor of Aeronautics and Astronautics
Chair, Graduate Program Committee
2
Evaluation of Propulsor Aerodynamic Performance for
Powered Aircraft Wind Tunnel Experiments
by
Nina M. Siu
Submitted to the Department of Aeronautics and Astronautics
on January 29, 2015, in partial fulfillment of the
requirements for the degree of
Master of Science in Aeronautics and Astronautics
Abstract
This thesis describes a methodology to convert electrical power measurements to
propulsor mechanical flow power for a 1:11-scale, powered wind tunnel model of an
advanced civil aircraft utilizing boundary layer ingestion (BLI); mechanical flow power
is a surrogate for aircraft fuel burn. Back-to-back experiments of BLI and non-BLI
aircraft configurations to assess the BLI benefit directly measured electrical power,
and supporting experiments were performed in a 1×1 foot wind tunnel at the MIT
Gas Turbine Laboratory to convert these measurements into mechanical flow power.
The incoming flow conditions of the powered wind tunnel tests (Reynolds number and
inlet distortion) were replicated. This propulsor characterization was found to convert the electrical power measurements to mechanical flow power with experimental
uncertainty of roughly 1.6%.
Thesis Supervisor: Edward M. Greitzer
Title: H. N. Slater Professor of Aeronautics and Astronautics
Thesis Supervisor: Alejandra Uranga
Title: Research Engineer, Department of Aeronautics and Astronautics
3
4
Acknowledgments
First and foremost, I would like to thank NASA for their financial support throughout
all of the entire N+3 project (Fundamental Aerodynamics program, Fixed Wing
Project, through Cooperative Agreement Number NNX11AB35A), without which
none of this would have been possible. I would also like to thank my thesis advisors,
Professor Edward Greitzer and Dr. Alejandra Uranga for helping to shape my career
and growth not only as a graduate student, but also as an engineer. I express my
deepest gratitude to Professor Mark Drela for always being available to share his
insight and expertise in just about everything.
I would also like to extend thanks to everyone else who has worked on the N+3
project (from MIT, Aurora Flight Sciences, Pratt & Whitney, and NASA), particularly those who partook in the tests at NASA Langley. I also appreciate the assistance
from the many UROPs who helped to complete our numerous tasks. Many of our
experiments would not have been possible without the technical aid of Todd Billings,
Jimmy Letendre, and Dick Perdichizzi, and no words can describe the special thanks
that I give to Dave Robertson for his sage advice in all aspects of life.
To Michael, Neil, Eric, Giulia and Arthur, thank you making me live life a bit
more and for always being there, even when I was down and crippled. To everyone
else in the GTL, ACDL and SPL, thanks for the great camaraderie and for keeping
the department an enjoyable place to work.
Finally, to my relatives in Brookline, I don’t know that I would have survived
the transition to Boston without all of your support. To my parents, Archibald and
Jacqueline, and my sisters, Natasha and Nicole, thank you for all of the support and
encouragement throughout the years.
5
Contents
1 Introduction
17
1.1
Background and Motivation . . . . . . . . . . . . . . . . . . . . . . .
17
1.2
Thesis Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
2 Experimental Setup
25
2.1
Propulsor Turbomachinery . . . . . . . . . . . . . . . . . . . . . . . .
25
2.2
Electronics Hardware and Instrumentation . . . . . . . . . . . . . . .
27
2.3
Wind Tunnel Testing Facility . . . . . . . . . . . . . . . . . . . . . .
29
2.3.1
Distortion Screen Location . . . . . . . . . . . . . . . . . . . .
29
2.3.2
Tunnel Velocity Calibration . . . . . . . . . . . . . . . . . . .
30
Flow Surveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
2.4
3 Experimental Methodology
3.1
33
Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
3.1.1
Mechanical Flow Power . . . . . . . . . . . . . . . . . . . . . .
33
3.1.2
Power Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . .
35
3.2
Performance Map Generation . . . . . . . . . . . . . . . . . . . . . .
37
3.3
Operating Point Determination . . . . . . . . . . . . . . . . . . . . .
38
3.4
Distortion Screen Design . . . . . . . . . . . . . . . . . . . . . . . . .
40
3.4.1
Inlet Distortion Quantification . . . . . . . . . . . . . . . . . .
41
Flow Survey Post-Processing . . . . . . . . . . . . . . . . . . . . . . .
44
3.5.1
Integration and Mass-Averaging . . . . . . . . . . . . . . . . .
45
3.5.2
Traverse Grids
46
3.5
. . . . . . . . . . . . . . . . . . . . . . . . . .
6
3.5.3
PKin Determination . . . . . . . . . . . . . . . . . . . . . . . .
48
3.5.4
PKout Determination . . . . . . . . . . . . . . . . . . . . . . .
48
4 Experimental Results
4.1
4.2
4.3
4.4
51
Flow Surveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
4.1.1
Inlet Flow Fields . . . . . . . . . . . . . . . . . . . . . . . . .
51
4.1.2
Exit Flow Fields . . . . . . . . . . . . . . . . . . . . . . . . .
52
Performance Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
4.2.1
Propulsor Performance in Uniform Inlet Flow . . . . . . . . .
58
4.2.2
Effect of Inlet Distortion on Propulsor Performance . . . . . .
59
4.2.3
Mechanical Flow Power and D8 BLI Benefit . . . . . . . . . .
62
Uncertainty Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
4.3.1
Measurement Uncertainty . . . . . . . . . . . . . . . . . . . .
64
4.3.2
Repeatability . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
Effect of Inlet Swirl Distortion . . . . . . . . . . . . . . . . . . . . . .
66
5 Summary, Conclusions, and Future Work
69
5.1
Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . .
69
5.2
Suggestions for Future Work . . . . . . . . . . . . . . . . . . . . . . .
70
A Five-Hole Probe Calibration
73
A.1 Calibration Procedure . . . . . . . . . . . . . . . . . . . . . . . . . .
73
A.2 Using the Calibration Map . . . . . . . . . . . . . . . . . . . . . . . .
78
A.2.1 Interpolation Method . . . . . . . . . . . . . . . . . . . . . . .
78
A.2.2 Velocity Components . . . . . . . . . . . . . . . . . . . . . . .
81
B Uncertainty Propagation
B.1 Error Propagation
83
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
83
B.2 Overall Efficiency Uncertainty . . . . . . . . . . . . . . . . . . . . . .
86
7
List of Figures
1-1 Schematic of the D8.2 (“Double Bubble” with two engines) aircraft [1]. 18
1-2 Schematic isometric drawings of the two NASA/MIT N+3 1:11-scale,
powered D8 wind tunnel models . . . . . . . . . . . . . . . . . . . . .
20
2-1 MIT GTL 1×1 ft wind tunnel working section setup and station designations with propulsor installed. . . . . . . . . . . . . . . . . . . . .
26
2-2 Aero-naut TF8000 fan . . . . . . . . . . . . . . . . . . . . . . . . . .
27
2-3 Wiring diagram for powering and control of electric motor to drive the
TF8000 rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
2-4 Axial evolution of Cp profile within tunnel working section from an
MTFLOW simulation near cruise condition. Distortion screens are
located 1.5Dfan upstream of the TF8000 fan face at x/Dfan = 0. . . .
30
2-5 Aeroprobe 6 inch, 0.125 inch diameter, conical-head five-hole probe:
zoomed-in front and side views. . . . . . . . . . . . . . . . . . . . . .
32
2-6 Inlet (Station 2) and exit (Station 5) five-hole probe traverse planes. .
32
3-1 Propulsor station designation and control volume for PK evaluation .
35
3-2 Steps of iterative process for determining the operating point. LaRC
measurements of CPE and Reθ are used in conjunction with the propulsor performance map (double boxes) to find φ that balances shaft power. 40
3-3 One-to-one mapping of flow coefficient, φ, to propulsor fan efficiency,
ηf , overall efficiency, ηo , and stagnation pressure rise coefficient, ψ . .
8
41
3-4 Target nominal inlet flow stagnation pressure field C̃pt = (pt − pt∞ )/( 12 ρV∞2 )
from integrated D8 aircraft computations performed by S. Pandya and
A. Huang [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
3-5 Nominal distortion screen design (shading indicates blocked area) . .
42
3-6 Stagnation pressure coefficient profiles, C̃pt = (pt − pt∞ )/( 12 ρV∞2 ), along
centerline of propulsor inlet plane for nominal and heavier distortion
screens and from full-aircraft CFD [2]. . . . . . . . . . . . . . . . . .
43
3-7 Inlet five-hole probe traverse measurement grid: red dots denote measurement locations, centered in cells outlined in black. Total of 600
points: 24 circumferential and 25 radial points. . . . . . . . . . . . . .
47
3-8 Exit five-hole probe traverse grid: red dots denote measurement locations, centered in cells outlined in black. Stator trailing edge profiles
are denoted in green. Total of 814 points: 37 circumferential and 22
radial points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
4-1 Inlet flow surveys: (a), (c), and (e) show the physical design of the
distortion screens; (b), (d), and (f) show the resulting inlet Cpt contours
at Re = 75000 (tunnel velocity V0 = 27 m·s−1 ). . . . . . . . . . . . .
54
4-2 Inlet flow surveys: (a), (c), and (e) show the flow pitch angle, α, and
(b), (d), and (f) show the flow yaw angle, β, at Re = 75000 (tunnel
velocity V0 = 27 m·s−1 ). . . . . . . . . . . . . . . . . . . . . . . . . .
55
4-3 Exit flow surveys: Cpt contours at Station 5 for the three levels of inlet
distortion, at flow coefficient φ = 0.39. . . . . . . . . . . . . . . . . .
56
4-4 Exit flow surveys: (a), (c), and (e) show the flow pitch angle, α, and
(b), (d), and (f) show the flow yaw angle, β, at flow coefficient φ = 0.39. 57
4-5 Propulsor performance metrics versus flow coefficient at four wheel
speeds in uniform inlet flow . . . . . . . . . . . . . . . . . . . . . . .
60
4-6 Propulsor power efficiencies versus flow coefficient at four wheel speeds
in both uniform and distorted inlet flows . . . . . . . . . . . . . . . .
9
61
4-7 Propulsor mechanical flow power versus flow coefficient at four wheel
speeds in uniform inlet flow . . . . . . . . . . . . . . . . . . . . . . .
63
4-8 Propulsor mechanical flow power versus flow coefficient at four wheel
speeds in uniform and distorted inlet flows . . . . . . . . . . . . . . .
63
4-9 Zoomed-in view of overall efficiency versus flow coefficient near the
LaRC cruise operating point. Each point corresponds to a repeated
measurement, and the black error bars denote the measurement uncertainty of each individual traverse. The red dashed and blue dashdotted lines denote the measurement uncertainty, σηo = 0.007, and the
repeatability, uηo = 0.004, about the curve fit (black line). . . . . . . .
66
4-10 Idealized propulsor operating map with variations in inlet swirl angle.
Operation of the left propulsor (green) and right propulsor (blue) is
symmetric about the no-swirl case (black). . . . . . . . . . . . . . . .
67
A-1 Aeroprobe 6 inch long, 0.125 inch diameter, conical-head five-hole
probe (PS5-C318-152) . . . . . . . . . . . . . . . . . . . . . . . . . .
74
A-2 GTL 1 × 1 wind tunnel station definitions . . . . . . . . . . . . . . .
75
A-3 Rotary table setup to control pitch (α) and yaw (β) roll angles with
the Aeroprobe conical-head FHP mounted. . . . . . . . . . . . . . . .
76
A-4 Five-hole probe calibration map for the Aeroprobe conical probe, ReFHP = 12000. 77
A-5 Interpolation for β using measured Cpα and Cpβ values: (a) Step 2, (b)
Step 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A-6 Interpolation for α using measured Cpα and Cpβ values: Step 4.
. . .
78
79
A-7 Interpolation for CpT using local flow angles (α, β): (a) Step 5, (b) Step
6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
79
A-8 Interpolation for CpS using local flow angles (α, β): Step 7. . . . . . .
80
A-9 Conventions for flow velocity components, as measured at the FHP tip. 81
B-1 MIT GTL 1×1 foot wind tunnel testing facility station designations .
84
B-2 Parameter processing sequence for ηo determination . . . . . . . . . .
87
10
List of Tables
1.1
2035 N+3 Phase I goals and estimated D8.5 performance [3] . . . . .
19
2.1
Propulsor Geometric Parameters
. . . . . . . . . . . . . . . . . . . .
26
3.1
Propulsor station designation for performance mapping experiments .
35
3.2
Distortion screen constants . . . . . . . . . . . . . . . . . . . . . . . .
44
A.1 Five-Hole Probe Calibration Coefficients . . . . . . . . . . . . . . . .
74
B.1 Raw data parameters . . . . . . . . . . . . . . . . . . . . . . . . . . .
84
B.2 Variables at each traverse grid element i . . . . . . . . . . . . . . . .
85
11
12
Nomenclature
A
area
ctip
rotor tip chord length
Cp
static pressure coefficient
Cp t
stagnation pressure coefficient
Cp α
FHP pitch angle coefficient
Cp β
FHP yaw angle coefficient
Cp T
FHP stagnation pressure coefficient
Cp S
FHP static pressure coefficient
CPE
electrical power coefficient
CPK
mechanical flow power coefficient
CPS
shaft power coefficient
CX
net streamwise force coefficient
D
diameter
DC60
distortion coefficient within 60◦ section
I
electric current
k
screen pressure drop coefficient
ṁ
mass flow
n̂
unit normal vector
PE
electrical power
PK
mechanical flow power
PS
shaft power
p
static pressure
pt
stagnation pressure
13
q
dynamic pressure
R
radius
Rg
specific gas constant
Re
Reynolds Number
Utip
rotor tip rotational speed
u
repeatability of quantity
v
voltage
V
total velocity vector
V
velocity magnitude
T
temperature
x, y, z
Cartesian coordinates: x is streamwise and z is vertical
x, r, θ
polar coordinates: x is streamwise, r is radial, and θ is circumferential
Greek Characters
α
pitch angle
β
yaw angle
η
efficiency
ν
kinematic viscosity
ρ
air density
σ
measurement uncertainty
φ
flow coefficient
ψ
stagnation pressure rise coefficient
Ω
fan angular velocity, wheel speed
Subscripts
( )0...6
station number
( )∞
LaRC wind tunnel freestream
( )i
index, per traverse element
14
( )atm
atmospheric
( )C
transition duct static pressure tap location
( )f
fan
( )fan
fan face
( )m
electric motor
( )o
overall propulsor
( )ref
reference
( )tot
total
Other Symbols
()
(˜)
mass-averaged quantity
referenced to freestream conditions
Abbreviations
BLI
Boundary Layer Ingestion
CAEP
Committee on Aviation Environmental Protection
CFD
Computational Fluid Dynamics
ESC
Electronic Speed Controller
FHP
Five-Hole Probe
GTL
Gas Turbine Laboratory
LaRC
Langley Research Center
LTO
Landing and Takeoff
MIT
Massachusetts Institute of Technology
MTFLOW
Multi-passage ThroughFLOW
NASA
National Aeronautics and Space Administration
15
16
Chapter 1
Introduction
1.1
Background and Motivation
There is growing interest in using boundary layer ingestion (BLI) propulsion systems for civil aircraft, in which part of the vehicle boundary layer passes through
the propulsion stream. BLI reduces mixing losses in both the wake and the exhaust
jet, thus decreasing the amount of power required to perform a given mission. Analyses of BLI for civil aircraft have found potential aircraft benefits in the range of
5–10% [4, 5, 6].
The work described here is a part of NASA’s N+3 Program, which aims at establishing new concepts for civil aircraft design, determining enabling technologies,
and defining areas that require investment for aircraft entering service in the 2030–35
timeframe. NASA set ambitious goals to reduce the environmental impact of civil aircraft in four different categories [3]: (1) reduction in fuel burn by 70%, (2) reduction
in noise emissions to 71 EPNdB below Stage 4, (3) reduction in LTO NOx emissions
to 80% below CAEP 6, and (4) a maximum required field length of 5000 ft.
During the first phase1 of the N+3 program, a team led by MIT, in partnership
with Aurora Flight Sciences and Pratt & Whitney, developed a conceptual design
for a B737-800 or Airbus A320 class aircraft (180 passengers, 3000 nm range) that
showed major potential for fuel burn reductions [3]. This aircraft, referred to as the
1
Phase I: September 2008 - March 2010
17
D8 (or the “Double Bubble” for its wide, double bubble-shaped fuselage cross section)
has engines flush-mounted on the upper, aft fuselage surface to enable boundary layer
ingestion. The double bubble fuselage structure cross-section can be seen on the lefthand side of Figure 1-1, which also gives side, top, and rear views of the D8.2, a
two-engine version of the D8 aircraft. The estimated performance in the four N+3
goal categories, relative to a baseline Boeing 737-800, for the D8.5, a three-engine
version which incorporates projected 2035 technologies, is presented in Table 1.1 [1].
Of most relevance is the estimated 70% reduction in fuel burn, for which BLI plays
an important role.
Figure 1-1: Schematic of the D8.2 (“Double Bubble” with two engines) aircraft [1].
A major focus of MIT’s second phase of the N+3 program2 is the experimental
2
Phase II: November 2010 - November 2014
18
Table 1.1: 2035 N+3 Phase I goals and estimated D8.5 performance [3]
Metric
737-800 Baseline
N+3 Goals
% of Baseline
D8.5
Fuel Burn (PFEI)
(kJ/kg-km)
7.43
2.23
(70% Reduction)
2.17
(70.9% Reduction)
Noise (EPNdB
below Stage 4)
277
202 (-71 EPNdB
Below Stage 4)
213 (-60 EPNdB
below Stage 4)
LTO Nox (g/kN)
(% Below CAEP 6)
43.28
(31% below CAEP 6)
80% below CAEP 6
10.5 (87.3% below 6)
Field Length (ft)
7680
for 3000 nm mission
5000 (metroplex)
5000 (metroplex)
evaluation of the BLI benefit for the D8 through the first back-to-back experimental
comparison between a BLI and non-BLI airframe/propulsion system for civil aircraft.
In these experiments, 1:11-scale, powered models of the D8.2 aircraft were designed,
constructed and tested in the NASA Langley (LaRC) 14×22 foot Subsonic Wind
Tunnel [7]. To achieve a direct comparison, two D8 models were tested: one with
fans in embedded propulsors, referred to as the integrated (or BLI) configuration,
and the other featuring fans within nacelles, referred to as the podded (or non-BLI)
configuration. Both configurations were powered with ducted fans driven by electric
motors. Isometric drawings of the two are given in Figure 1-2.
For the integrated configuration, there is strong interaction between the airframe
and propulsion systems, and it is difficult to separate (and define) thrust and drag.
Following the power balance framework developed by Drela [8], our principal metric
for assessing the BLI benefit is the mechanical flow power required by the propulsors
at the simulated cruise condition of zero net horizontal (freestream-wise) force, CX ,
on the aircraft. This power is used as a surrogate for fuel burn. Cruise conditions are
of highest interest since most flight time, and thus most fuel burn, occurs at cruise.
For the LaRC wind tunnel experiments, the simulated cruise conditions (CX = 0)
were a tunnel freestream velocity of V∞ = 70 mph, and a model angle of attack of
19
(a) podded, non-BLI configuration
(b) integrated, BLI configuration
Figure 1-2: Schematic isometric drawings of the two NASA/MIT N+3 1:11-scale,
powered D8 wind tunnel models
α = 2◦ .
A direct method to determine the mechanical flow power input would be to take
flow surveys at the inlet and exit planes of the propulsors mounted on the wind
tunnel model. That method, however, is limited by the length of time to complete
sufficiently-detailed surveys and by the complexity of the geometry and flow areas.
Both of these constrain the number of possible operating conditions that can be
examined. The use of a direct method has been described by Lieu [9] and an improved
version of the methodology has been used in more recent 2014 LaRC tunnel entries3 .
A second method of determining PK is to make the conversion from electrical
power measurements via the characterization of the propulsion system in experiments
3
C. Casses, personal communication, Jan 2015
20
outside of the wind tunnel. Characterizing the propulsion system in a smaller and
more controllable environment also allows examination of a wider range of operating
conditions than the direct method. From the range of operating conditions, we can
generate a performance map to use in processing the NASA LaRC 14×22 foot wind
tunnel experimental data into mechanical power. It is this latter method that is
described in this thesis.
The power provided to the propulsors of the wind tunnel D8 model can be quantified at three levels: first is the electrical power provided to the motors, PE , second
is the shaft power, PS = ηm PE , where ηm is the electric motor efficiency, and third
is the net mechanical flow power input to the flow, PK = ηf PS , where ηf is the fan
efficiency. The overall efficiency of the propulsor (from PE to PK ) is thus the product
of the motor and fan efficiencies, ηo = ηf ηm .
A preliminary assessment of the BLI benefit, using electrical power as the metric,
has been presented by Uranga et al [10]. Electrical power is the quantity that is
measured directly in our experiments, but it is not of final interest. For an optimized
fan, shaft power directly relates to specific fuel consumption and hence could be used
as the principal metric. In the current set of experiments, however, our primary
interest is not the turbomachinery design, but rather the aerodynamic benefit of BLI,
so we use the mechanical flow power, PK , as our metric of performance. This quantity
directly evaluates the mechanical power to the stream, and is thus isolated from the
specifics of the particular fan used.
1.2
Thesis Objectives
While there is no simple way to measure mechanical flow power, PK , in the LaRC
14×22 foot wind tunnel experiments, the electrical power input to the propulsion
system is easily accessible. Having said that, however, it is necessary to convert the
electrical power measurements to the desired mechanical flow power. In this a power
efficiency chain can be defined in the conversion of electrical power, PE , to shaft
21
power, PS , and mechanical flow power, PK :
PK = ηo PE = ηf PS = ηf ηm PE .
(1.1)
This thesis describes a process for converting measured electrical power to mechanical flow power and other aerodynamic quantities of interest, including fan efficiency.
A series of wind tunnel experiments has been conducted in the MIT Gas Turbine Laboratory (GTL) 1×1 foot wind tunnel to accomplish this conversion. The propulsors
for the D8 wind tunnel models were tested separately from the full airframe in this
smaller wind tunnel to characterize the performance with inlet conditions representative of both the podded and integrated configuration. Propulsor inlet conditions for
the integrated configuration were simulated using screens to provide representative
non-uniformities (distortions) in stagnation pressure.
Experiments with these screens enabled evaluation of the effect of inlet distortion
on propulsor performance, specifically fan efficiency, and whether there are steep
performance gradients in the operating regimes.
The overall objectives of this thesis are to:
• develop and assess a method of evaluating propulsor mechanical flow power from
electrical power measurements through supporting propulsor characterization
experiments that quantify the power efficiency chain,
• determine the effect of inlet distortion on propulsor performance for the D8
aircraft model (because the fan performance can be altered by the distortion),
• determine the limitations, uncertainties, and possible improvements of this mechanical flow power evaluation method.
This thesis is organized into five chapters: Chapter 2 describes the hardware,
instrumentation, and experimental setup for the propulsor characterization experiments; Chapter 3 discusses the methodology and post-processing method used within
the supporting wind tunnel experiments to quantify the power efficiency chain (ηm , ηf ,
22
and ηo ) and to determine the mechanical flow power, PK ; Chapter 4 discusses the results of the supporting experiments and the experimental uncertainties; and Chapter
5 summarizes the thesis conclusions and provides suggestions for future work.
23
24
Chapter 2
Experimental Setup
This chapter describes the instrumentation and setup of the propulsion system characterization experiments in the MIT GTL 1×1 foot wind tunnel, including details of
the hardware and tunnel testing facilities and flow survey instrumentation. To maintain consistency between primary and supporting experiments, and thus enhance the
ability to link the propulsor operation between the different wind tunnels, the instrumentation was kept the same as much as feasible, for the NASA LaRC and MIT GTL
experiments.
2.1
Propulsor Turbomachinery
The fan for the 1:11-scale D8 wind tunnel model propulsor was the Aero-naut TF8000,
a commercial, off-the-shelf electric ducted fan, typically used for R/C models. The
TF8000 has a five-bladed rotor and four-bladed stator, both fabricated from carbon
composites. The hub of the TF8000 houses the electric motor that drives the rotor. A
1 mm gap surrounds the electrical motor, and allows a small fraction of the total flow
through the propulsor (less than 1%) to cool the motor and exhaust through the plug
at Station 6, as in Figure 2-1, which shows a schematic of the tunnel working section.
The cooling flow is taken into account in the characterization of the propulsion system
using pitot and static probes mounted within the plug cooling flow channel. A frontal
view of the TF8000 is shown in Figure 2-2.
25
0
Kiel probe, pt0
1
1.25 D0
2 D0
2
4
5
1.5 Dfan
wall static tap, pC
z
x
V0
12 in
D0 = 6 in
square-to-round
transition duct
blank/distortion screen
contraction 1
constant area duct contraction 2
propulsor
Figure 2-1: MIT GTL 1×1 ft wind tunnel working section setup and station designations with propulsor installed.
The TF8000 is housed in an aluminum shell that provides the outer casing for
the turbomachinery and the nacelle trailing edge. The aluminum shell was designed
to be inserted into a nacelle external housing for both the podded and integrated
model configurations, so the same propulsors could be installed in both models. The
aluminum shell also allowed for the insertion of the TF8000 into the wind tunnel
working section, as described in Section 2.3. The geometric parameters of the TF8000
and nacelle are provided in Table 2.1.
Table 2.1: Propulsor Geometric Parameters
Description
Parameter
Value
Rotor tip radius
Rtip
0.072 m
Rotor hub radius1
Rhub
0.011 m
1
Afan
0.0159 m2
Rnozzle
0.068 m
Anozzle
0.011 m2
Fan area
Nozzle radius
Nozzle area
1
2
Rotor and fan face measurements are at the rotor blade leading edge.
26
6
Figure 2-2: Aero-naut TF8000 fan
2.2
Electronics Hardware and Instrumentation
A three-phase, brushless electric motor from Lehner Motoren (3060 series, 27 windings) was used to drive the rotor shaft. The motor was controlled by a Schulze
fut-l-40.100 electronic speed controller (ESC) and powered by a 2 kW (53V) Sorenson power supply. To determine the electric power input, PE , the voltage input to
the ESC and the current from the power supply were measured. The motor shaft
rotational speed was determined from the phase voltage difference between two of the
three motor phases.
The NASA LaRC wind tunnel facilities required 30 feet of wire length between the
motor and the ESC (braided wire) and 10 feet of wire between the ESC and the power
supply. The latter length was significantly larger than the Schulze-recommended
maximum length of 1 foot, and a capacitor bank of thirty 330µF individual capacitors
was designed3 to protect the motor controller from voltage fluctuations from the 53V
power supply. A solenoid was placed in the circuit to cut power to the motor in
case of emergency. The electronic components can be seen in the wiring diagram of
Figure 2-3.
3
We wish to acknowledge the guidance of Professor Jeffrey Lang, MIT Department of Electrical
Engineering and Computer Science, to achieve this design.
27
to 53V
power
supply
Vsupply
motor phase
voltage
to servo
(RPM)
to motor controller
30V
solenoid
R
K
B
Electronic
speed controller
(ESC)
–
+
capacitor
denotes measurement
Figure 2-3: Wiring diagram for powering and control of electric motor to drive the
TF8000 rotor
28
2.3
Wind Tunnel Testing Facility
The conduct the propulsor characterization experiments in the MIT GTL 1×1 foot
low-speed, open-circuit wind tunnel, a series of contractions and ducts were attached
to the tunnel exit for installation of the the TF8000 propulsor. Figure 2-1 illustrates
the tunnel working section with a propulsor installed. The initial contraction reduces
the flow path from a 1×1 foot square to a 6 inch diameter circular cross-section.
We will refer to this square-to-round duct as the transition duct. Two constantarea aluminum ducts surround a slot for the insertion of the distortion screens, the
designs of which are described in Section 3.4. The distortion screen slot is 1.25
screen diameters downstream of the end of the transition duct contraction, so there
is negligible interaction between the potential field of the screen and the contraction.
The aluminum duct connects to a second contraction that mates the 6 inch duct
to the 5.7 inch diameter propulsor. The TF8000 fan attaches to this second contraction and exhausts to atmospheric conditions. The junctions between the straight
aluminum ducts and the screen were sealed using petrolatum. Clay was used to seal
all other junctions. Swagelok Snoop liquid leak detector was used to verify the sealing.
2.3.1
Distortion Screen Location
The upstream influence of the fan was analyzed by simulating the flow through the
tunnel working section and the TF8000 turbomachinery using MTFLOW4 [11]. By
determining the TF8000 rotor’s region of upstream influence, we were able to determine a distance upstream of the fan to position the distortion screen such that flow
at the screen’s location would be outside of the potential field of the fan. Figure 2-4
shows the axial evolution of the pressure coefficient. The upstream influence of the
fan is seen 0.5Dfan upstream of the fan face, and more strongly at 0.25Dfan ; however
the radial Cp profile is uniform 1.5Dfan upstream. Therefore, the screen location was
decided to be 1.5Dfan upstream of the fan so flow through the screen would not be
4
MTFLOW (Multi-passage ThroughFLOW) is a design and analysis program for axisymmetric
flows, developed by Drela
29
influenced by the presence of the fan.
0.25 qinl
r/Dfan
Cp (r)
TF8000
rotor and stator
-2
-1.5
-1
-0.5
0
0.5
x/Dfan
1
1.5
Figure 2-4: Axial evolution of Cp profile within tunnel working section from an MTFLOW simulation near cruise condition. Distortion screens are located 1.5Dfan upstream of the TF8000 fan face at x/Dfan = 0.
2.3.2
Tunnel Velocity Calibration
The transition duct was instrumented to measure stagnation and static pressures, and
stagnation temperature of the flow through the wind tunnel. The tunnel “freestream”
stagnation pressure, pt0 , was measured as the average of two kiel probes, located
upstream of the square-to-round contraction. Four wall static pressure taps, axiallylocated 75% of the way down the square-to-round transition duct and equally distributed circumferentially, were averaged to define a reference static pressure, pC .
The axial locations of the kiel probes and wall static taps are shown in Figure 2-1. A
reference dynamic pressure, qC , was defined as the difference between these transition
duct pressures,
qC = pt0 − pC .
(2.1)
In choosing the location of the wall static pressure taps, it was desired to position
them as far down the transition duct as possible to measure a larger qC signal without
being within the upstream influence of distortion screen.
The tunnel velocity at Station 0 (Figure 2-1), V0 , was correlated with the transition duct dynamic pressure, qC , using simultaneous measurements of stagnation and
static pressures at Station 0 and the transition duct pressures. The stagnation and
static pressures at Station 0 were measured using a pitot-static probe located at the
30
center of the Station 0 cross-section with all downstream working tunnel section ducts
and contractions removed. This was done for a range of tunnel velocities, V0 , from
5 to 50 m·s−1 , The calibration factor between the two dynamic pressures at these
locations, qC and q0 , was q0 /qC = 3.86 ± 0.02. The pressure measurements in the
transition duct thus provide a reference tunnel velocity at Station 0,
V0 =
s
2 q0
(pt0 − pC ).
ρ qC
(2.2)
Air density ρ was calculated from measurements of atmospheric pressure, patm , using
a mercury barometer, measurements of flow temperature, To , from a thermocouple
located inside the square-to-round transition duct, and the specific gas constant for
air, Rg = 287 J·kg−1 ·K−1 :
ρ =
patm
.
Rg To
(2.3)
The tunnel mass flow was also calibrated from flow surveys and related to the
dynamic pressure in the transition duct, qC , as described in Section 2.4. Control of
the tunnel velocity provided control of the propulsor operating point.
2.4
Flow Surveys
To evaluate the mechanical flow power input to the flow from the propulsors, area
traverses were performed with a five-hole probe (FHP) at the propulsor inlet and exit
planes, Stations 1 and 5. The traverses were performed using a 6 inch Aeroprobe,
conical-head five-hole probe (DFHP = 0.125 inch), shown in Figure 2-5. The five-hole
probe was calibrated in the MIT GTL 1×1 foot wind tunnel across a range of Reynolds
numbers (ReFHP from 4000 to 12000, based on DFHP ) in uniform flow, between ±30◦
for pitch and yaw flow angles. Details of the calibration procedure are provided in
Appendix A. Motion of the five-hole probe for the cross-sectional area flow surveys
was controlled using a Velmex BiSlide traverse system.
31
6 in
12045-1
DFHP
DFHP = 0.125 in
Figure 2-5: Aeroprobe 6 inch, 0.125 inch diameter, conical-head five-hole probe:
zoomed-in front and side views.
Figure 2-6 denotes the measurement plane locations for the inlet and exit flow
surveys. The propulsor inlet flow fields were determined from five-hole probe traverses
upstream of the TF8000 fan, 3 mm downstream of the second contraction (Station 2),
to characterize the flow downstream of the distortion screens. For purposes of access
to the inlet flow with the FHP the inlet surveys were performed with the TF8000
propulsor removed from the wind tunnel.
The propulsor exit flow fields were determined from five-hole probe traverses at
the exit of the propulsor at Station 5, 3 mm downstream of the nacelle trailing edge,
which was deemed to be as close to the nozzle as possible without risk of FHP collision.
Station
5
2
inlet survey plane
exit survey plane
Figure 2-6: Inlet (Station 2) and exit (Station 5) five-hole probe traverse planes.
32
Chapter 3
Experimental Methodology
This chapter discusses the methodology of propulsion system characterization performed in the MIT GTL 1×1 foot wind tunnel, including definition of the performance metrics of interest and mapping of the performance map to the NASA LaRC
14×22 foot wind tunnel experiments.
3.1
Performance Metrics
3.1.1
Mechanical Flow Power
As defined by Drela [8], PK is the mechanical flow power input from the propulsors.
It is a quantifiable metric for the full aircraft that is independent of the particular
propulsion system and is used as a primary metric for the assessment of BLI benefits
on the D8 aircraft in the LaRC 14×22 foot Subsonic Wind Tunnel experiments. For
the essentially incompressible flow conditions of the experiments, PK can be defined
as the mass flux of stagnation pressure, such that
PK
ZZ
= (pt∞ − pt )V · n̂ dA.
33
(3.1)
PK is reported non-dimensionally relative to the wind tunnel freestream conditions
and airframe dimensions as
CPK ≡
PK
,
1
ρV∞3 Aref
2
(3.2)
where Aref is the wing planform area of 1.088 m2 .
The BLI benefit of the integrated (BLI) relative to the podded (non-BLI) D8
configurations is defined as the difference in mechanical flow power relative to the
podded configuration:
BLI Benefit ≡
CPK ,non−BLI − CPK ,BLI
.
CPK ,non−BLI
(3.3)
The net mechanical flow power for a single propulsor is determined by evaluating
Equation (3.1) for the control volume of Figure 3-1 indicated by the dashed blue
line. This control volume includes the propulsor stream between the propulsor inlet
(Station 2) and exit (Station 5) planes. It follows the inner walls of the propulsor,
so there is zero flux through the side-cylinder (nacelle inner walls). PK can thus be
written as
PK = PKin + PKout .
(3.4)
Figure 3-1 also shows the station number locations for the propulsor characterization tests in the 1×1 foot wind tunnel. A description of each station location is
provided in Table 3.1.
The mechanical flow power through the inlet plane at Station 2 is PKin , and PKout
is the mechanical flow power out of the propulsor at the nozzle plane, Station 5, and
the plug exhaust. Five-hole probe flow surveys described in Section 2.4 are used to
determine PKin and PKout .
34
0
1
z
2
3
6
5
4
n̂
x
n̂
Vfan
CV
Figure 3-1: Propulsor station designation and control volume for PK evaluation
Table 3.1: Propulsor station designation for performance mapping experiments
Station #
0
1
2
3
4
5
6
3.1.2
Description
tunnel freestream, no distortion
fan inlet, downstream of inlet distortion screen
fan face, at rotor hub leading edge
between rotor and stator
stator trailing edge
nozzle exit
plug exit
Power Efficiencies
The conversion from electrical power, PE , to mechanical flow power, PK , can be
represented as a chain of efficiencies, such that
PK
= ηo PE = ηf PS = ηf ηm PE .
(3.5)
The power efficiencies are:
• Electrical motor efficiency, ηm : factor by which the electrical components (motor, motor controller, and all wiring and electronics) convert electrical power,
PE , to shaft power, PS ; PS = ηm PE .
• Aerodynamic fan efficiency, ηf : factor by which the propulsor turbomachinery
motor shaft power, PS , is converted to mechanical flow power, PK ; PK = ηf PS .
The aerodynamic efficiency thus includes duct losses between the propulsor inlet
35
and outlet.
These two efficiencies can be combined into an overall efficiency:
• Overall propulsor efficiency, ηo : the product of the motor and fan efficiencies,
characterizing the propulsor power efficiency, from electrical power to mechanical flow power,
ηo = ηm ηf .
(3.6)
While ηo alone is sufficient to convert PE into PK , it does not provide insight
into the aerodynamics of the flow through the propulsor. Additionally, interchanging
individual components such as the fan or the electric motor alters ηo . Thus, it is
useful to also determine the component efficiencies ηf and ηm separately.
Experiments to determine the motor efficiency, ηm , involve relating the motor
torque, and thus shaft power, to the electrical power input for a range of motor shaft
rotation speeds and loadings. This motor calibration was performed by Casses [12]
and provides a database from which we can determine motor efficiency from the
measured electrical power coefficient
CPE =
PE
,
3
ρUtip Afan
(3.7)
Utip ctip
.
ν
(3.8)
and the rotational Reynolds number,
Reθ =
In Equation (3.8), Utip is the blade tip rotational velocity,
Utip = Ω
2π
Rtip ,
60
(3.9)
Afan is the fan face area (Table 2.1), ctip is the rotor tip chord (ctip = 0.04 m), and ν
is the kinematic viscosity of air (ν = 1.45 × 10−5 m2 s−1 ).
36
The combination of supporting experiments on motor efficiency and overall propulsor efficiency measurements allows the aerodynamic fan efficiency to be deduced as
ηf =
3.2
ηo
.
ηm
(3.10)
Performance Map Generation
The MIT GTL 1×1 foot wind tunnel experiments allowed the creation of a database of
performance characteristics over a range of operating points (a propulsor performance
map) representative of operating conditions seen during the NASA LaRC wind tunnel
experiments. Knowledge of the propulsor operating point allows the power efficiencies
(ηf , ηm , and ηo ) to be inferred from the performance map and determine PK .
The propulsor operating point is determined by the flow coefficient, φ, defined as
the ratio of the axial velocity across the fan face (Station 2 in Figure 3-1), Vfan , to
the rotor tip speed, Utip :
φ =
Vfan
.
Utip
(3.11)
The fan characteristic relates a given φ to the particular non-dimensional stagnation pressure rise across the propulsor,
ψ=
∆pt
,
2
ρ Utip
(3.12)
where ∆pt is the mass-averaged stagnation pressure difference between propulsor inlet
and exit, and ρ is the air density. There is also a dependency on rotational Reynolds
number because the fan characteristics for different wheel speeds do not collapse to
a single characteristic, as will be seen in Section 4.2.1
In addition to φ and Reθ , the performance of the propulsor is also a function
of inlet distortion level. A different performance map is thus measured for each
1
The propulsor mapping experiments found a difference of 0.01 in ψ between the lowest and
highest tested fan speeds (8000 and 13500 RPM). For reference, the pressure rise coefficient at
target conditions is ψ = 0.09.
37
distortion level to capture the effect of distortion on performance. The three power
efficiencies (ηm , ηf , and ηo ) and stagnation pressure rise coefficient, ψ, were determined
as functions of flow coefficient, φ, and rotational Reynolds number, Reθ , such that
for a given level of inlet distortion, we have a set of characteristic functions,
ηm = f ( CPE , Reθ ),
ηo = f ( φ, Reθ ),
ηf = f ( φ, Reθ ),
ψ = f ( φ, Reθ ).
These sets of characteristics fully describe the performance of the propulsor.
3.3
Operating Point Determination
We require a means of translating the measured performance map for the MIT GTL
1×1 foot wind tunnel to the NASA LaRC wind tunnel results. The mass flow and
flow velocity through the propulsor are not directly measured in the LaRC experiments, and thus the flow coefficient of the propulsor is not directly known. We can,
however, determine the operating point from the measured non-dimensional electrical
power, CPE , and fan wheel speed, Reθ , which are recorded in the LaRC wind tunnel
experiments. This enables us to relate the propulsor performance between the two
wind tunnels.
The operating point of the propulsor for the LaRC tests is determined from the
shaft power. A relation between non-dimensional shaft power,
CPS =
PS
,
3
ρUtip Afan
(3.13)
and the performance map characteristics (ηf , ηm , and ηo as functions of φ) can be
derived from the definition of mechanical flow power in Equation (3.1), written in
38
terms of mass-averaged quantities,
PK =
ṁ
∆pt .
ρ
(3.14)
From the power efficiency chain and the definitions of φ and ψ,
ρVfan Afan
∆pt
ρ
Vfan ∆pt
3
ρAfan Utip
.
=
3
Utip ρUtip
(3.15)
φ ψ(φ, Reθ )
PS
.
=
3
ρ Utip Afan
ηf (φ, Reθ )
(3.16)
PK = ηf ηm PE =
The shaft power is represented by
CPS =
For a given wheel speed and distortion level, terms that are dependent on the
measurements from the LaRC experiments, CPE and Reθ , are separated from terms
dependent on the flow coefficient, φ. A unique solution for the flow coefficient, and
thus operating point, exists for a given level of inlet distortion. The iterative process
to determine the operating point, φ, from the LaRC measurements is illustrated in
Figure 3-2.
First, the motor efficiency, ηm , is determined from the LaRC measurements of CPE
and Reθ (wheel speed). It is independent of the propulsor operating point, and thus
determines the left-hand side of Equation (3.16). Second, an initial guess is made for
the flow coefficient, φ, which corresponds to particular values of ηf and ψ, to provide a
value for the right-hand side of Equation (3.16). This one-to-one correlation between
ηf , ηo , and ψ as functions of φ is illustrated in Figure 3-3. The value for φ is adjusted
until Equation (3.16) is satisfied.
With all variables in Equation (3.16) known, the value of CPK can be evaluated. Since the non-dimensionalization of CPK differs from CPE and CPS , the nondimensionalization of the power efficiency chain in Equation (3.5) requires additional
terms relating rotor tip speed to tunnel freestream velocity magnitude and the refer-
39
LaRC data
initial φ
guess
CPE
=
PE
3 A
ρUtip
fan
Reθ
=
Utip ctip
ν
ηm (CPE , Reθ )
Shaft Power
ψ(φ, Reθ )
CPS
ηf (φ, Reθ )
Yes
? φψ
=
ηf
operating
point φ
No
change φ
Figure 3-2: Steps of iterative process for determining the operating point. LaRC
measurements of CPE and Reθ are used in conjunction with the propulsor performance
map (double boxes) to find φ that balances shaft power.
ence fan and wing areas.
CPK
3.4
3
Afan
Utip
= ηf CPS
V∞
Aref
3
Utip
Afan
= ηo CPE
V∞
Aref
(3.17)
Distortion Screen Design
To recreate an inlet flow representative to that ingested by the fan in the LaRC
experiments, two screens were designed, fabricated, and installed 1.5Dfan upstream of
the TF8000 fan. There were also experiments with no distortion, as with the non-BLI,
podded D8 configuration2 . The two screens, referred to as “nominal” and “heavier”
distortions, were designed to bracket the fuselage boundary layer stagnation pressure
profile for the integrated D8 configuration. The desired profile was acquired from
D8 aircraft calculations at the simulated cruise point [2], and the resulting propulsor
inlet plane stagnation pressure flow field is shown in Figure 3-4.
The fuselage boundary layer was approximated as a vertically-stratified stagnation
pressure profile. The distortion screens, made of 0.125 inch-thick steel sheet, had a
2
The “no distortion” inlet conditions in the MIT GTL 1×1 foot wind tunnel contain the tunnel wall boundary layers, which have different flow conditions than the essentially-freestream flow
conditions as seen by the podded propulsors in the LaRC 14×22 foot wind tunnel.
40
CPS =
ηm PE
3
ρUtip
Afan
!
operating
point
φ
ηf
ηo
φ
ψ
flow coefficient
φ
Figure 3-3: One-to-one mapping of flow coefficient, φ, to propulsor fan efficiency, ηf ,
overall efficiency, ηo , and stagnation pressure rise coefficient, ψ
series of horizontal bars of varying thicknesses to produce the stagnation pressure
stratification. The screens were designed by Huang3 from computations using Fluent
and iterated experimentally until the desired distortion level and profile was achieved.
The final design for the nominal screen is shown in Figure 3-5. The design for the
heavier distortion screen looks similar, but has thicker horizontal bars to provide a
greater stagnation pressure drop.
3.4.1
Inlet Distortion Quantification
We could not replicate exactly the inlet flow distortion from the integrated fuselage,
and therefore designed the two distortion screens (nominal and heavier) to bracket
the target distortion level from the integrated D8 configuration CFD calculations [2].
Profiles of the stagnation pressure relative to tunnel freestream conditions (for full
3
Arthur Huang, Research Scientist, MIT Gas Turbine Laboratory
41
C̃pt
Figure 3-4:
Target nominal inlet flow stagnation pressure field
C̃pt = (pt − pt∞ )/( 21 ρV∞2 ) from integrated D8 aircraft computations performed
by S. Pandya and A. Huang [2].
D = 6 inches
Figure 3-5: Nominal distortion screen design (shading indicates blocked area)
aircraft model tests),
C̃pt =
pt − pt∞
,
1
ρV∞2
2
(3.18)
are plotted in Figure 3-6 for the nominal and heavier distortion screens along the
vertical centerline of the inlet flow surveys. The centerline C̃pt profile from the CFD
simulations is also shown. The blue dots correspond to the target (CFD) C̃pt profile,
and the red circles and green squares correspond to the nominal and heavier distortion
profiles respectively. For z/Dfan between 0.9 and 1.0, the 1×1 foot wind tunnel
boundary layer is visible; the CFD at this height has freestream flow, and therefore
C̃pt = 0.0. The heavier distortion profile has a more severe stagnation pressure deficit
42
(in extent and depth) than the target profile, while the nominal distortion profile
oscillates about the target profile.
1
0.9
0.8
CFD
nominal
heavier
z/Dfan
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-1.4 -1.2
-1
-0.8 -0.6 -0.4 -0.2
C˜pt
0
0.2
Figure 3-6: Stagnation pressure coefficient profiles, C̃pt = (pt − pt∞ )/( 12 ρV∞2 ), along
centerline of propulsor inlet plane for nominal and heavier distortion screens and from
full-aircraft CFD [2].
For each screen, an effective stagnation pressure drop coefficient, k, was defined
to quantify the non-dimensional, mass-averaged stagnation pressure drop across the
screen between Stations 2 and 5, relative to the tunnel dynamic pressure, q0 [13]:
k =
pt2 − pt0
(∆pt )screen
= 1 2 .
q0
ρV0
2
(3.19)
Note that in the CFD case, q0 and V0 are the mass-averaged quantities for the flow
through the inlet area, and the stagnation pressure drop is relative to the tunnel
freestream stagnation pressure. Variations in k were within the accuracy of the pressure transducer (σk < 0.01q0 ) across the tested range of tunnel velocities. The pressure drop coefficient is related to the tunnel freestream conditions through q0 , so k
provides the ingested stagnation pressure flux across the inlet plane without requiring
direct inlet flow surveys to be performed for each operating point.
The overall level of distortion for each screen is also quantified using standard
DC60 (Distortion Coefficient) definition,
DC60 =
pt0 − (pt2 )60
,
1
ρV02
2
43
(3.20)
where (pt2 )60 is the mass-averaged stagnation pressure within the 60◦ sector of greatest distortion. This is the bottom-most 60◦ sector (denoted in Figure 4-1b by the
dashed black line) and is the same for all distortion levels. Values for DC60 and
stagnation pressure drop coefficient, k, are provided in Table 3.2 along with the corresponding values from the CFD full-aircraft calculations.
Table 3.2: Distortion screen constants
Distortion Level
DC60
k
σk
None
0.057
0.057
0.004
Nominal
0.664
0.278
0.008
Heavier
0.894
0.389
0.002
CFD
0.721
0.262
–
The nominal distortion DC60 value is lower than that of the CFD DC60 value,
which is bracketed by the nominal and heavier distortion screens, as desired. The
screen constant for the non-distorted case is non-zero, since the measurements for
∆pt include the losses in the tunnel wall boundary layer.
3.5
Flow Survey Post-Processing
At each measurement point in the flow surveys, the five-hole probe (FHP) provided
five pressure measurements: one (p1 ) from a forward-facing port that reads the stagnation pressure when the probe is aligned with the flow, and four static pressures
(p2 . . . p5 ) from ports distributed equally around the angled, conical face of the probe
head. The differences in pressure between two opposing static ports are given as pitch
and yaw pressure coefficients, defined as
p2 − p3
p1 − p
p4 − p5
=
,
p1 − p
Cp α =
(3.21)
Cp β
(3.22)
where p is the average value of the four FHP static pressures. Cpα and Cpβ define the
local flow pitch and yaw angles (α and β). In addition, Cpα and Cpβ , in combination
44
with p1 , determine the stagnation and static pressures, such that
pt = p1 − CpT (p1 − p)
(3.23)
ps = pt − CpS (p1 − p).
(3.24)
The process by which the local flow angle and pressures are determined from the FHP
calibration is covered in detail in Appendix A.
Given the local flow angles and stagnation and static pressures, all velocity components can be found:
2
(pt − p)
ρ
p
= V / 1 + tan2 α + tan2 β
V = |V| =
Vx
r
(3.25)
(3.26)
Vy = −Vx tan β
(3.27)
Vz =
(3.28)
Vr =
Vθ =
Vx tan α
y
z
Vy p
+ Vz p
2
2
2
y +z
y + z2
y
z
− Vy p
Vz p
y2 + z2
y2 + z2
(3.29)
(3.30)
The velocity vector is V = (Vx , Vy , Vz ) in Cartesian coordinates, or V = (Vx , Vr , Vθ )
in polar coordinates, with the origin located along the propulsor centerline.
3.5.1
Integration and Mass-Averaging
The mass-averaged stagnation pressures at the inlet and exit planes are used in determining PK and are the primary quantities of interest. For a general parameter, ξ,
the mass-averaged value of ξ over an area, denoted by ξ, is defined as
ZZ
1
ξ =
ρ V · n̂ ξdA,
ṁtot
(3.31)
where ṁtot is the total mass flow through the traversed area. Equation (3.31) was
evaluated as a summation across all cells using the midpoint integration method, with
45
each measurement point located in the geometric center of a cell i, of area ∆Ai . The
traverse plane is normal to the propulsor axis, so V · n̂ is the axial velocity, Vx , and
the integral becomes
ξ =
1 X
ρi Vxi ξi ∆Ai .
ṁtot i
(3.32)
The total mass flow through the system, ṁtot , is the summation of all of the individual
mass flow contributions through each cell.
ṁtot =
X
ṁi =
i
X
ρi Vxi ∆Ai
(3.33)
i
The net mechanical power input into the flow, PK , is the difference between the
mass-averaged stagnation pressures at the propulsor exit (PKout at Station 5) and
inlet (PKin at Station 2):
PK =
3.5.2
ṁtot
ṁtot
∆pt =
(pt5 − pt1 ).
ρ
ρ
(3.34)
Traverse Grids
Inlet Traverse Grid
The inlet traverse grid had uniform circumferential spacing with 24 spokes. The radial
spacing for the inlet traverse was distributed such that the inlet area was divided into
rings of equal area, with 25 radial locations. The resulting inlet measurement grid is
shown in Figure 3-7. Black lines denote the borders of the cells used in the integration,
and red dots correspond to the measurement locations of the five-hole probe tip. The
blue line denotes the radius of the local tunnel section.
Exit Traverse Grid
The exit grid radial stations were similar to those at the inlet but the grid was tailored
to align with the trailing edge profile of the stator blades, with a higher point density
near the stators. A bifurcation through which the motor power lines ran was located
46
0.8
0.6
0.4
z/R0
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
-0.5
0
0.5
1
y/R0
Figure 3-7: Inlet five-hole probe traverse measurement grid: red dots denote measurement locations, centered in cells outlined in black. Total of 600 points: 24 circumferential and 25 radial points.
immediately downstream of the bottom stator, blocking access for the five-hole probe,
so the exit flow survey did not capture the full 360◦ area.
The exit traverse grid, shown in Figure 3-8, has 37 circumferential spokes and 22
radial locations for a total of 814 points. The black lines denote the borders of the
cells used in the integration, the red dots correspond to the measurement location for
the five-hole probe tip, the blue lines denote the radius of the nacelle trailing edge,
and the trailing edge profiles of the four stators are shown by the heavy green lines.
To test the circumferential grid resolution, a traverse was performed with the
same radial resolution and twice the circumferential density. The radial resolution
was held constant since the spacing was already on the order of the FHP radius. The
difference in measured mass-averaged stagnation pressure between the two circumferential densities was less than 0.1%, within the accuracy of the pressure transducer,
so circumferential spacing was deemed adequate.
47
0.8
0.6
0.4
z/R0
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
-0.5
0
0.5
1
y/R0
Figure 3-8: Exit five-hole probe traverse grid: red dots denote measurement locations,
centered in cells outlined in black. Stator trailing edge profiles are denoted in green.
Total of 814 points: 37 circumferential and 22 radial points.
3.5.3
PKin Determination
The mechanical power inflow to the propulsor, PKin , is determined from the screen
stagnation pressure drop constants in Table 3.2,
1
1
PKin = PK0 − k ρV03 A0 = −k ρV03 A0
2
2
(3.35)
where PK0 is the mechanical flow power upstream of the distortion screen. Since PK
contains the change in stagnation pressure relative to the tunnel freestream stagnation
pressure, PK0 is by definition equal to zero.
Because k is constant for each screen across the range of tested tunnel velocities, this definition of PKin holds for all operating conditions within the scope of the
propulsor characterization experiments. Measurements of upstream tunnel conditions
(V0 ) during the exit flow surveys can thus be used for determination of PKin .
3.5.4
PKout Determination
The mechanical flow power exhausted from the propulsor was determined from fivehole probe exit traverses, as well as measurements inside the plug which accounted
48
for the motor-cooling flow, such that
PKout = (PKout )FHP + (PKout )plug .
(3.36)
The midpoint integration method, described in Section 3.5.1, was again used to evaluate the contribution of the propulsor jet over all traverse grid cells i, such that
(PKout )FHP =
X
i
(pt5 − pt0 )i Vxi ∆Ai .
(3.37)
The motor-cooling flow through the inner plug passage is exhausted at Station 6,
and has a PKout contribution of
(PKout )plug = (pt6 − pt0 ) V6 A6 ,
(3.38)
which accounts for less than 1% of the total PK . In Equation (3.38), pt6 is the
stagnation pressure at the plug exit, V6 is the plug exhaust velocity, and the plug
exhaust area is A6 = 2.34×10−4 m2 ( A6 /Anozzle = 0.022 ). The plug exhaust velocity,
V6 , is assumed to be axial and uniform throughout the plug exit. It is calculated from
the stagnation and static pressures insides of the plug as
V6 =
r
2
(pt6 − p6 ).
ρ
(3.39)
Combining these two contributions, the total mechanical flow power out of the
propulsor is then
PKout =
X
(pt5 − pt0 )i Vxi ∆Ai + (pt6 − pt0 ) V6 A6 .
i
49
(3.40)
50
Chapter 4
Experimental Results
The propulsor characterization and the motor torque calibration were used to generate
propulsor performance maps to analyze the NASA LaRC 14×22 foot wind tunnel
experiment data. The propulsor performance was measured at three wheel speeds1
(8000, 10600, and 13500 RPM) both with and without inlet distortion representative
of simulated cruise condition, as explained in Chapter 3. This chapter presents the
results of the 1×1 foot wind tunnel propulsor performance mapping experiments.
4.1
4.1.1
Flow Surveys
Inlet Flow Fields
The measured non-dimensional stagnation pressure, Cpt , at Station 2 is given in
Figure 4-1 below, all at Re = 75000 (based on a tunnel velocity of V0 = 27 m·s−1 and
reference length ctip ), and is referenced to the tunnel dynamic pressure at Station 0,
upstream of the distortion screen (see Figure 2-1) such that
Cp t =
pt − pt0
,
1
ρV02
2
(4.1)
where pt is the stagnation pressure measured by the five-hole probe.
1
The CX = 0 speed was found to be 11600 RPM for the podded configuration and 11330 RPM
for the integrated configuration in the LaRC experiments.
51
Figure 4-1b shows contours of Cpt for the uniform (no inlet distortion) case. Figures 4-1d and 4-1f show the Cpt contours for the nominal and heavier distortion cases
respectively. Qualitatively, there is a vertically-stratified distortion produced by the
screens, and the heavier distortion screen has a larger region of reduced stagnation
pressure than the nominal distortion screen. As quantiifed in Section 3.4.1, the heavier distortion screen (k = 0.389) produces a stagnation pressure drop 40% greater
than the nominal distortion screen (k = 0.278). Figure 4-2 shows contours of α and
β, the local flow pitch and yaw angles. The flow angles for the non-distorted inflow are
nominally 1◦ . The distortion screens generate regions of additional flow angularity,
up to 2◦ .
The measured flow angles within the outer ring of the inlet traverse grid (points
outside of the wind tunnel jet) contain steep gradients and magnitudes that are nonphysical and significantly greater than the flow angles measured inside of the tunnel
jet (α, β >> 2◦ ). Since the propulsor exhausts to atmosphere, this flow outside of the
tunnel jet is of low velocity, and thus provides low-signal pressure measurements that
are used to determine Cpα and Cpβ (Equations (3.21) and (3.22)). As a result, the
measured flow angles α and β are more sensitive to small changes in the measured
pressures, and are therefore not reliable.
The boundary layer growing along the inner walls of the wind tunnel in the upper
region of the traverse plane has the same profile for all three of the distortion levels.
This can be seen in the centerline C̃pt profiles of Figure 3-6 for the nominal and heavier
distortion cases. The constancy of this upper tunnel wall boundary layer across
distortion levels and the horizontal symmetry within the two distorted cases imply
that there were no unexpected flow structures within the tunnel working section, and
negligible leaks in the junctions between wind tunnel sections.
4.1.2
Exit Flow Fields
The performance of the TF8000 is dependent on the flow coefficient and Reynolds
number, and it is therefore necessary to perform an exit five-hole probe traverse for
the operating points of interest. Contours of the stagnation pressure coefficient at
52
the nozzle exit for each of the distortion screens are shown in Figure 4-3, all with the
propulsor operating at a flow coefficient of φ = 0.39, the simulated cruise condition for
the podded configuration in the NASA Langley 14×22 foot wind tunnel experiments.
Figure 4-4 shows the exit flow pitch and yaw angles. The flow angles near the plug are
dr
roughly 15◦ in magnitude, which is consistent with plug surface angle (tan dx
≈ 15◦ ).
Similar to the inlet flow surveys, the outer ring of the traverse (r > Rnozzle ) is a
low-velocity region outside of the propulsor jet, and therefore contains measured flow
angles that are not reliable.
Wakes of the stator blades and high loss regions near the hub on the suction side
of each stator are visible. With uniform inlet flow conditions, the flow through all four
of the stator passages is qualitatively similar. For the nominal and heavier distortion
cases, the flow through the two lower stator passages has higher losses than the two
upper passages because of the stagnation pressure non-uniformities (i.e. higher rotor
angles of attack in the lower part of the annulus).
53
0
0.8
-0.1
0.6
-0.2
z/R0
0.4
0.2
-0.3
0
-0.4
-0.2
Cp t
-0.5
-0.4
-0.6
-0.6
-0.7
-0.8
-1
-0.5
(a) No distortion screen design
0
y/R0
0.5
-0.8
1
(b) No distortion Cpt
0
0.8
-0.1
0.6
-0.2
z/R0
0.4
0.2
-0.3
0
-0.4
-0.2
-0.5
-0.4
Cp t
-0.6
-0.6
-0.7
-0.8
-1
(c) Nominal distortion screen design
-0.5
0
y/R0
0.5
1
-0.8
(d) Nominal distortion Cpt
0
0.8
-0.1
0.6
-0.2
z/R0
0.4
0.2
-0.3
0
-0.4
-0.2
-0.5
-0.4
-0.6
-0.6
-0.7
-0.8
-1
(e) Heavier distortion screen design
-0.5
0
y/R0
0.5
1
(f) Heavier distortion Cpt
Figure 4-1: Inlet flow surveys: (a), (c), and (e) show the physical design of the
distortion screens; (b), (d), and (f) show the resulting inlet Cpt contours at Re = 75000
(tunnel velocity V0 = 27 m·s−1 ).
54
-0.8
Cp t
5
4
0.8
4
0.6
3
0.6
3
0.4
2
0.4
2
0.2
1
0.2
1
0
0 α [deg]
z/R0
z/R0
5
0.8
0
0 β [deg]
-0.2
-1
-0.2
-1
-0.4
-2
-0.4
-2
-0.6
-3
-0.6
-3
-0.8
-4
-0.8
-4
-1
-0.5
0
y/R0
0.5
1
-5
-1
-0.5
(a) No distortion α
0
y/R0
0.5
1
(b) No distortion β
5
0.8
4
0.8
4
0.6
3
0.6
3
0.4
2
0.4
2
0.2
1
0.2
1
0
0 α [deg]
z/R0
z/R0
5
0
0 β [deg]
-0.2
-1
-0.2
-1
-0.4
-2
-0.4
-2
-0.6
-3
-0.6
-3
-0.8
-4
-0.8
-4
-1
-0.5
0
y/R0
0.5
1
-5
-1
(c) Nominal distortion α
-0.5
0
y/R0
0.5
1
-5
(d) Nominal distortion β
5
5
4
0.8
4
0.6
3
0.6
3
0.4
2
0.4
2
1
0.2
1
0
0 α [deg]
z/R0
0.8
0.2
z/R0
-5
0
0 β [deg]
-0.2
-1
-0.2
-1
-0.4
-2
-0.4
-2
-0.6
-3
-0.6
-3
-0.8
-4
-0.8
-4
-1
-0.5
0
y/R0
0.5
1
-5
(e) Heavier distortion α
-1
-0.5
0
y/R0
0.5
1
(f) Heavier distortion β
Figure 4-2: Inlet flow surveys: (a), (c), and (e) show the flow pitch angle, α,
and (b), (d), and (f) show the flow yaw angle, β, at Re = 75000 (tunnel velocity
V0 = 27 m·s−1 ).
55
-5
2
0.8
0.6
1.5
z/R0
0.4
1
0.2
0
0.5
-0.2
0
-0.4
-0.6
-0.5
-0.8
-1
-0.5
0
y/R0
0.5
1
-1
(a) No distortion
2
0.8
0.6
1.5
z/R0
0.4
1
0.2
0
0.5
-0.2
0
-0.4
-0.6
-0.5
-0.8
-1
-0.5
0
y/R0
0.5
1
-1
(b) Nominal distortion
2
0.8
0.6
1.5
z/R0
0.4
1
0.2
0
0.5
-0.2
0
-0.4
-0.6
-0.5
-0.8
-1
-0.5
0
y/R0
0.5
1
-1
(c) Heavier distortion
Figure 4-3: Exit flow surveys: Cpt contours at Station 5 for the three levels of inlet
distortion, at flow coefficient φ = 0.39.
56
20
20
0.8
0.8
15
10
0.4
0 α [deg]
-1
-0.5
0
y/R0
0.5
1
-5
-10
-0.6
-15
-0.8
0 β [deg]
-0.4
-10
-0.6
0
-0.2
-5
-0.4
5
0.2
z/R0
0
-0.2
10
0.4
5
0.2
z/R0
15
0.6
0.6
-15
-0.8
-20
-1
-0.5
(a) No distortion α
0
y/R0
0.5
1
(b) No distortion β
20
0.8
20
0.8
15
0.6
10
0 α [deg]
-1
-0.5
0
y/R0
0.5
1
-5
-10
-0.6
-15
-0.8
0 β [deg]
-0.4
-10
-0.6
0
-0.2
-5
-0.4
5
0.2
z/R0
0
-0.2
10
0.4
5
0.2
z/R0
15
0.6
0.4
-15
-0.8
-20
-1
(c) Nominal distortion α
-0.5
0
y/R0
0.5
1
-20
(d) Nominal distortion β
20
20
0.8
0.8
15
0.6
15
0.6
10
0.4
0 α [deg]
-5
-0.4
-10
-0.6
-15
-0.8
-1
-0.5
0
y/R0
0.5
1
-20
(e) Heavier distortion α
5
0.2
z/R0
0
-0.2
10
0.4
5
0.2
z/R0
-20
0
0 β [deg]
-0.2
-5
-0.4
-10
-0.6
-15
-0.8
-1
-0.5
0
y/R0
0.5
1
(f) Heavier distortion β
Figure 4-4: Exit flow surveys: (a), (c), and (e) show the flow pitch angle, α, and (b),
(d), and (f) show the flow yaw angle, β, at flow coefficient φ = 0.39.
57
-20
4.2
4.2.1
Performance Metrics
Propulsor Performance in Uniform Inlet Flow
Figure 4-5 shows the TF8000 characteristics for overall propulsor efficiency, ηo , motor
efficiency, ηm , fan efficiency, ηf , and stagnation pressure rise, ψ, versus flow coefficient,
φ. The efficiencies are defined as
ηo = PK /PE
(4.2)
ηm = PS /PE
(4.3)
ηf = PK /PS ,
(4.4)
and the stagnation pressure rise coefficient is
ψ =
∆pt
.
2
ρUtip
(4.5)
Overall efficiency (Figure 4-5a) was calculated from the five-hole probe surveys
at the inlet and exit planes and the monitored electrical power input. The motor
efficiency in Figure 4-5c was determined using the motor calibration map generated
from Casses’ experiments [12]. As seen by the near-constancy of ηm with φ, the motor
efficiency is weakly dependent on the operating condition and strongly dependent on
the wheel speed. This variation in motor operation with wheel speed is the primary
reason for the wide spread of ηo characteristics for different wheel speeds.
Figure 4-5b shows the pressure rise coefficient, ψ, against flow coefficient, φ, for
four wheel speeds in uniform inlet flow conditions. The propulsor operation is stable
over the range of tested operating points, as the ψ-characteristics remain flat. In
particular, there is no evidence of the onset of stall (a turn over of the characteristic)
in the lower range of flow coefficients.
The ratio of the mechanical flow power to shaft power is the fan efficiency, ηf = PK /PS ,
which can also be represented as the ratio of overall propulsor to electric motor efficiencies, ηf = ηo /ηm . Figure 4-5d shows the fan efficiency characteristics across a
58
range of flow coefficients, φ. The fan efficiency as defined here includes aerodynamic
losses through the rotor and stator and other losses through the nacelle flow passage.
The pressure rise and fan efficiency characteristics correlate more closely to single
characteristics than the overall efficiency characteristics. The reason is thought to be
due to Reynolds number effects since the TF8000 rotor blades operated in a transitional regime (Reθ = 100, 000 − 300, 000). The cause of differences in ψ and ηf with
blade Reynolds number, however, has not been fully understood.
4.2.2
Effect of Inlet Distortion on Propulsor Performance
To evaluate the propulsor performance for the integrated (BLI) aircraft configuration,
the pressure rise (ψ) and power efficiencies (ηo , ηm and ηf ) were determined with inlet
distortion representative of the integrated D8 fuselage flow. These metrics are plotted
against flow coefficient in Figure 4-6 for four wheel speeds.
Figure 4-6a compares overall efficiencies for the three levels of distortion: no distortion, nominal distortion, and heavier distortion. The difference in overall efficiency
between all inlet distortion levels is 1-2%. The difference in ηo between the nominal
and heavier distortion cases is less than 1%. Figure 4-6b shows the pressure rise
characteristics for the different distortion levels. Similar to the overall efficiency, the
difference between ψ characteristics is 1-2%. The two distortion cases bracket the
distortion levels for the integrated D8 airframe (Section 3.4.1), and we can thus infer
that the propulsor sensitivity to level of BLI stagnation pressure inlet distortion is
small within the range of the LaRC experiments.
Motor and fan efficiencies for non-distorted and distorted inlet flows are given in
Figures 4-6c and 4-6d. As with the overall efficiency and pressure rise, there is a
1-2% reduction in fan efficiency as a result of the inlet stagnation pressure distortion.
The difference between overall efficiency characteristics for the nominal and heavier
distortion cases directly translate into a 1-2% differences between fan efficiencies,
implying there are not any drops in performance over the range of interest. It can be
noted that the low sensitivity to the level of inlet distortion is representative of levels
seen in transonic fans with BLI distortion [14].
59
The simulated cruise conditions for the first LaRC wind tunnel experiments (2013)
were at φ = 0.38 for the podded configuration and φ = 0.37 for the integrated configuration. These operating points are not near the onset of stall, which is at lower
flow coefficients where the characteristics’ slopes turn over. Even with distortion, the
pressure rise characteristics remain flat over the tested operating range. Overall, for
each of the metrics in the propulsor characterization (ηo , ηf , ψ) the effect of inlet distortion in the form of stagnation pressure non-uniformities is a decrement of roughly
1-2%.
0.75
σ ηo
0.14
0.13
overall efficiency, η
o
pressure rise coefficient, ψ
0.7
0.65
0.6
0.55
8000 RPM
10600 RPM
13500 RPM
12250 RPM
0.5
0.3
0.12
0.11
0.1
0.09
0.08
0.07
0.06
0.35
0.4
flow coefficient, φ
0.05
0.3
0.45
(a) Overall propulsor efficiency
0.45
1
8000 RPM
10600 RPM
13500 RPM
12250 RPM
0.95
0.9
0.95
f
0.85
fan efficiency, η
m
0.35
0.4
flow coefficient, φ
(b) Pressure rise coefficient
1
motor efficiency, η
8000 RPM
10600 RPM
13500 RPM
12250 RPM
0.8
0.75
0.7
0.9
0.85
0.65
0.8
0.6
0.55
0.5
0.3
0.35
0.4
flow coefficient, φ
0.45
0.75
0.3
0.5
(c) Motor efficiency
8000 RPM
10600 RPM
13500 RPM
12250 RPM
0.35
0.4
flow coefficient, φ
0.45
(d) Fan efficiency
Figure 4-5: Propulsor performance metrics versus flow coefficient at four wheel speeds
in uniform inlet flow
60
0.75
8000 RPM
10600 RPM
13500 RPM
12250 RPM
σ ηo
0.13
overall efficiency, η
o
pressure rise coefficient, ψ
0.7
0.14
0.65
0.6
0.55
0.11
0.1
0.09
0.08
0.07
no distortion
nominal distortion
heavier distortion
0.5
0.3
0.12
0.06
0.35
0.4
flow coefficient, φ
0.05
0.3
0.45
(a) Overall propulsor efficiency
0.8
f
0.85
0.95
fan efficiency, η
0.9
m
0.45
1
8000 RPM
10600 RPM
13500 RPM
12250 RPM
no distortion
nominal distortion
heavier distortion
0.95
motor efficiency, η
0.35
0.4
flow coefficient, φ
(b) Pressure rise coefficient
1
0.75
0.7
0.9
0.85
0.65
0.8
0.6
0.55
0.5
0.3
8000 RPM
10600 RPM
13500 RPM
12250 RPM
no distortion
nominal distortion
heavier distortion
0.35
0.4
flow coefficient, φ
0.45
0.75
0.3
0.5
(c) Motor efficiency
8000 RPM
10600 RPM
13500 RPM
12250 RPM
no distortion
nominal distortion
heavier distortion
0.35
0.4
flow coefficient, φ
0.45
(d) Fan efficiency
Figure 4-6: Propulsor power efficiencies versus flow coefficient at four wheel speeds
in both uniform and distorted inlet flows
61
4.2.3
Mechanical Flow Power and D8 BLI Benefit
Since the supporting propulsor characterization experiments were conducted across a
range of operating points, the estimate for the BLI benefit between the podded and
integrated D8 configurations is not limited to the cruise conditions. The mechanical
flow power, CPK , can be determined using the performance maps at other operating
points, subject to the assumption that the inlet distortion in the 1×1 foot wind tunnel
is representative of the actual fuselage boundary layer. The CPK characteristics (referenced to 1×1 foot wind tunnel freestream quantities) versus flow coefficient for the
tested wheel speeds are shown in Figures 4-7 for uniform inlet flow, and in Figure 4-8
for distorted flows. Consistent with the characteristics in Figure 4-5, the CPK characteristics correlate toward a single characteristic, but do not fully collapse. Higher
propulsor flow power is produced at higher wheel speed. The introduction of inlet
distortion is also consistent with the other performance metrics, as the difference between CPK characteristics between all distortion levels is 1-2% in the operating range
of interest.
The performance maps generated in the propulsor characterization experiments
allow the LaRC measurements of electrical power to be converted to the primary
metric of interest, mechanical flow power, CPK . Following the methodology outlined
in Chapter 3, the operating points for the podded and integrated configurations during
the LaRC wind tunnel experiments determine the values of CPK ,non−BLI and CPK ,BLI ,
and therefore the estimate for the BLI benefit in Equation (3.3).
The propulsor mechanical flow power with uniform inlet flow, representative of
the podded configuration, and is found to be CPK (non-BLI) = 0.0486 at the podded
simulated cruise condition of φ = 0.38. For the integrated configuration, the nominal
distortion case best represents the inlet distortion from the D8 fuselage, and gives
CPK (BLI) = 0.0454 at the integrated simulated cruise condition of φ = 0.37.
In the LaRC experiments, the BLI benefit at simulated cruise of the integrated
D8 aircraft relative to the podded aircraft is thus 6.6 ± 2.5%. The uncertainty of
2.5% corresponds to the 95% confidence interval based on repeated runs at simulated
62
cruise condition.2
4
Sref
Afan
3.5
2.5
CPK
V∞
V0
3
3
2
1.5
1
8000 RPM
10600 RPM
13500 RPM
12250 RPM
0.5
0.3
0.35
0.4
flow coefficient, φ
0.45
0.5
Figure 4-7: Propulsor mechanical flow power versus flow coefficient at four wheel
speeds in uniform inlet flow
4
8000 RPM
10600 RPM
13500 RPM
12250 RPM
Sref
Afan
3.5
2.5
CPK
V∞
V0
3
3
2
1.5
1
0.5
0.3
no distortion
nominal distortion
heavier distortion
0.35
0.4
flow coefficient, φ
0.45
0.5
Figure 4-8: Propulsor mechanical flow power versus flow coefficient at four wheel
speeds in uniform and distorted inlet flows
4.3
Uncertainty Analysis
The non-systematic uncertainties in the propulsor performance mapping experiments
(see Section 4.4) can be broken down into two categories: (1) measurement uncer2
uncertainty (repeatability) calculated by N. Titchener and J. Hannon [10].
63
tainty and (2) the repeatability of the experiments. These two sources of error and
the propagation to the final metrics are discussed below.
4.3.1
Measurement Uncertainty
The measurement uncertainties for the 1×1 foot wind tunnel experiments depend
on the accuracies of the pressure and electrical instrumentation. Assuming the measurements are statistically-independent, uncertainties in final performance metrics
(mechanical flow power PK and overall efficiency ηo ) can be found by propagating
the instrumentation accuracies through the calculation of PK and ηo . We will denote
measurement uncertainties with σ.
The uncertainty in mechanical flow power, σPK , is equal to the root-sum-square
of each of the individual measurement uncertainties (i.e. each individual pressure
channel measurement) multiplied by the partial derivative of PK with respect to
that quantity. Since PK is a function of tunnel freestream stagnation pressure, local
stagnation pressure, and local axial velocity, the uncertainty of PK is determined as
σ PK
PK
2
=
∂PK σpt0
∂pt0 PK
2
+
∂PK σpt
∂pt PK
2
+
∂PK σVx
∂Vx PK
2
.
(4.6)
The uncertainty for pt0 above is directly due to the pressure transducer accuracy.
The uncertainties for local stagnation pressure, σpt , and axial velocity, σVx , are determined by propagating the uncertainties from the five-hole probe pressure measurements. The partial derivatives are determined both analytically (e.g. expressions for
the calculation of velocities) and numerically from experimental data (e.g. estimated
curve-slopes in the interpolation from the five-hole probe calibration, accounting for
the calibration angle resolution and probe Reynolds number). A more-detailed account of the error propagation is provided in Appendix B.
Uncertainties for the propulsor overall efficiency, σηo , are derived from uncertainties in PK and in electrical power measurements. From the definition of overall
64
efficiency, ηo = PK /PE ,
σηo
ηo
2
=
σPK
PK
2
+
σPE
PE
2
.
(4.7)
The uncertainty for electrical power measurements [10] across all power levels is
σPE
= 0.011.
PE
(4.8)
The overall propulsor efficiency is the final performance metric to convert electrical power measurements to mechanical flow power. For these experiments, the
uncertainty on the overall efficiency is σηo = 0.7, or fractionally σηo /ηo = 1.2% at simulated cruise conditions. The resulting uncertainty in CPK is then σCPK /CPK = 1.6%,
compared to the BLI benefit of 6.6%.
4.3.2
Repeatability
The repeatability of the measurements describes the distribution of multiple measurements at the same operating conditions. To assess repeatability, multiple traverses
were performed at the operating point of the LaRC experiments that was closest to
simulated cruise conditions (10600 RPM at φ = 0.39). The standard deviation of
these repeated points and the polynomial curve fit through all of the tested operating
conditions give a quantitative estimate of the experimental repeatability, uηo = 0.004
(uηo /ηo = 0.7%). Repeatability is reported here using a 95% confidence interval of
this standard deviation, u = 1.96σ. Figure 4-9 is an expanded (“zoomed in”) view
of the overall efficiency as a function of flow coefficient, showing the measurement
uncertainties (red dashed line) and repeatability (blue dash-dotted line) relative to
the curve fit (solid black line). The repeatability of the experiments is within the
measurement uncertainty as u < σηo .
65
0.7
0.69
0.68
σηo
0.67
η
o
0.66
0.65
u
0.64
0.63
0.62
0.61
0.6
0.37
0.375
0.38
0.385
φ
0.39
0.395
0.4
Figure 4-9: Zoomed-in view of overall efficiency versus flow coefficient near the LaRC
cruise operating point. Each point corresponds to a repeated measurement, and the
black error bars denote the measurement uncertainty of each individual traverse.
The red dashed and blue dash-dotted lines denote the measurement uncertainty,
σηo = 0.007, and the repeatability, uηo = 0.004, about the curve fit (black line).
4.4
Effect of Inlet Swirl Distortion
In addition to uncertainties due to the accuracy of the instrumentation (random errors
that describe the precision of the measurements), there is also uncertainty that is
linked to the inability to fully reproduce the flow conditions of the integrated D8
fuselage boundary layer. This second uncertainty is a systematic error that describes
the accuracy of the power conversion method.
Within the MIT GTL 1×1 foot wind tunnel experiments, inlet distortion was produced only as non-uniformities in stagnation pressure. Fuselage-surface flow visualization during the LaRC experiments also showed non-uniformities in the circumferential
flow direction (non-zero swirl velocities) due to the transverse pressure gradients on
the fuselage. Full integrated D8 aircraft computations showed a nominal swirl angle
of approximately 3◦ over the entire inlet, at the propulsor inlet plane [2]. The absence of this effect in the propulsor mapping experiments introduces an error in the
conversion of electrical power to mechanical flow power for the LaRC experiments.
One aspect is that the pressure rise and fan efficiency characteristics differ for
different swirl velocities, and thus could affect the level of shaft power, from which
66
the propulsor operating point is determined. Equation (3.16) thus becomes
CPS =
PS
3
ρUtip Afan
=
ψswirl φ
ηf,swirl
(4.9)
where ( )swirl denotes conditions in the presence of inlet swirl. The exact effects of
inlet swirl on the pressure rise and fan efficiency have not been established, we can
give rough estimates of the behavior.
An estimate of the effects of inlet swirl can be made based on the assumption
that changes in the performance characteristics with swirl are symmetric about the
no-swirl characteristics. The left and right propulsors are viewed as having the same
swirl magnitude, but in opposite directions due to the co-rotation of the two fans.
The left fan thus sees co-swirl, and the right fan sees counter-swirl. The propulsor
operating map is also taken to be linear about the no-swirl value. This idealized
change in performance is illustrated in Figure 4-10. Non-zero swirl velocities move
the propulsor operation from the no-swirl case (in black) along an assumed throttle
line (in red).
ψ
ηf
left propulsor
right propulsor
throttle
line
co-swirl
counter-swirl
right propulsor
left propulsor
co-swirl
throttle
line
counter-swirl
no swirl
no swirl
φ
φ
(a) Pressure rise
(b) Fan efficiency
Figure 4-10: Idealized propulsor operating map with variations in inlet swirl angle.
Operation of the left propulsor (green) and right propulsor (blue) is symmetric about
the no-swirl case (black).
During the NASA Langley 14×22 foot wind tunnel experiments, there was a 6%
difference in the pressure rise between the left and right propulsors. For symmetric
deviations between the left and right propulsor performances, this difference corre67
sponds to a change in shaft power of approximately 3% from the no-swirl condition
for each of the propulsors. More importantly for our conclusions, the effects of the coswirl and counter-swirl on the two propulsors cancel, with no net effect on determining
the overall BLI benefit.
It is probably not correct to assume the behavior with inlet swirl is symmetric,
but definition of the fan operating point motion with co-swirl and counter-swirl is not
possible without more detailed analyses or experiments that include the inlet swirl
distortion. The assessment of inlet swirl impact was deemed to be outside of the
scope of this thesis.
68
Chapter 5
Summary, Conclusions, and Future
Work
5.1
Summary and Conclusions
A series of powered model experiments have been conducted in the NASA Langley
14×22 foot Subsonic Wind Tunnel to assess the aerodynamic boundary layer ingestion
(BLI) benefit of the Double Bubble (D8) civil transport aircraft. Two 1:11-scale, D8
configuration models, electrically powered using commercial, model aircraft fans, were
tested to provide a back-to-back experimental comparison. One configuration was
podded (non-BLI) configuration, with propulsors operating in nominally uniform flow.
The other was an integrated (BLI) configuration in which the propulsors ingested part
of the fuselage boundary layer and operated with combined circumferential and radial
distortion.
The complex geometry and the small scale of the propulsors made it difficult to
perform direct mechanical flow power measurements. This thesis thus describes a
process for converting the electrical power measurements in the Langley facility to
net mechanical propulsor flow power. In the process, the aerodynamic behavior of
the propulsor in response to inlet flow distortion was assessed in a small (1×1 foot)
wind tunnel in the MIT Gas Turbine Laboratory (GTL), in which the propulsor inlet
stagnation pressure non-uniformities were replicated, and the inlet and exit flow fields
69
measured in detail with a five-hole probe. The conditions of interest included a range
of fan speeds, flow coefficients, and levels of inlet flow distortion.
The efficiency of the fan was determined by combining the propulsor characterization experiments with the results from a series of experiments in which the efficiency
of the electric motor to convert electrical power to shaft power was determined [12].
The propulsor was found to have a fan efficiency degradation of 1-2% in a distortion
representative of that provided by the D8 fuselage boundary layer.
The resulting estimates of mechanical flow power had an uncertainty of approximately 1.6%. This uncertainty is small compared to the 6.6% BLI benefit of the 2013
LaRC experiments, implying that the described method of power conversion through
propulsor characterization experiments is adequate for assessing the BLI benefit for
the D8 aircraft. The experiments were specific to assessment of the BLI benefit for
the D8 model, however the method to convert from electrical power to mechanical
power can be utilized in other powered wind tunnel experiments.
5.2
Suggestions for Future Work
• Inlet flow conditions in the MIT GTL 1×1 foot wind tunnel were tailored to
provide non-uniform stagnation pressure. Flow visualization tests [10] and CFD
simulations [2] showed that the actual D8 fuselage flow also includes some distortion in flow angles. As mentioned in Section 4.4, the generation of swirl
within the turbomachinery test facilities would improve the fidelity of assessing
the TF8000 fan performance.
• The dependence of the performance characteristics on blade Reynolds number
was not fully determined and could be further explored.
• Enhanced accuracy at operating conditions outside of the simulated cruise conditions of the LaRC experiments can be achieved by populating the performance
map with an increased number of fan speeds and operating points.
• Attempts were made to measure the motor torque directly during operation
70
using a small load cell installed on a moment arm attached to the motor, but
were unsuccessful due to size constraints and temperature limits on available
instrumentation. If a way is found to reliably instrument the propulsor for
torque measurements, the fan efficiency could then be determined in real time
during full aircraft wind tunnel tests without the need for separate motor calibration and its associated uncertainty. This would also eliminate any errors
due to the operating point not being perfectly matched between aircraft tests
and supporting experiments.
71
72
Appendix A
Five-Hole Probe Calibration
This appendix describes the procedure for five-hole probe calibration and post-processing.
The five-hole probe (FHP) used in the presented work was calibrated at flow angles
between −30◦ and +30◦ and probe Reynolds numbers between 4000 and 12000. The
output of the calibration is a set of calibration maps, in which values for pitch (α) and
yaw (β) flow angles and stagnation and static pressures are correlated to coefficients
based on the pressure differentials of the different holes (or ports, as they are referred
to). A 6 inch long, 0.125 inch diameter, conical-head FHP from Aeroprobe was used
in the MIT GTL 1×1 foot wind tunnel experiments, and is shown schematically in
Figure A-1.
A.1
Calibration Procedure
The FHP calibration was performed in the MIT GTL 1×1 foot wind tunnel – the
same wind tunnel facilities as the supporting propulsor characterizations experiments
presented in this thesis. A schematic of the tunnel working section for the FHP
calibration is shown in Figure A-2.
There are multiple choices of non-dimensionalization for calibrating a five-hole
probe, depending on the desired sensitivity of either pitch or yaw angle. For decreased
sensitivity to Reynolds number and equal sensitivities to pitch and yaw, the reference
pressure is defined as the pressure differential between the FHP “stagnation” port (1)
73
DFHP
0.125 in
12045-1
6 in
(a) Side view
5
3
1
2
4
(b) Front view, pressure port numbering
Figure A-1: Aeroprobe 6 inch long, 0.125 inch diameter, conical-head five-hole probe
(PS5-C318-152)
and the average of the four FHP “static” ports (2-5) [15]:
p =
1
(p2 + p3 + p4 + p5 ) .
2
(A.1)
The calibration pressure coefficients are defined in Table A.1 below, where p1
through p5 are the pressures from the respective probe ports as shown in Figure
A-1b.
Table A.1: Five-Hole Probe Calibration Coefficients
pitch angle
p4 − p5
p1 − p
p 2 − p3
Cp β =
p1 − p
p1 − pt,ref
Cp T =
p1 − p
pt,ref − pref
Cp S =
p1 − p
Cp α =
yaw angle
stagnation pressure
static pressure
The stagnation and static pressures pt,ref and pref are the known reference pressures
for the calibration, measured at the same tunnel conditions (Station 1 in Figure A-2)
74
Kiel probe
wall static taps
C
y
x
1 × 1 ft
wind tunnel
V
0
1
square-to-round
transition duct
constant area
extension
Figure A-2: GTL 1 × 1 wind tunnel station definitions
using an L-shaped pitot-static probe (United Sensor PAC-12-KL, 0.125 inch probe
diameter).
The incidence angles of the probe are controlled using two Velmex B4800TS rotary
tables, shown in Figure A-3. This setup allows for rotation at a resolution of 0.025◦ in
both pitch and yaw while keeping the tip of the probe at the same location, centered
in the wind tunnel jet. Calibrations used Measurement Specialties ESP-HD pressure
transducers, with an accuracy of ±0.05% of the dynamic pressure at Station 1, or an
absolute accuracy of ±3 Pa1
Before beginning the calibration process, the five-hole probe angle to the flow is
adjusted until opposing ports (p2 with p3 , and p4 with p5 ) read the same pressure
within the accuracy of the pressure transducers, or adjustments in pitch and yaw
angles are within the step resolution of the rotary tables. The resulting position is
defined as the “zero” position, aligned with the flow.
Pitch and yaw calibration angles were varied between −30◦ and +30◦ , in in-
crements of 2.5◦ . The calibration map was taken at four different Reynolds numbers (ReFHP based on the FHP diameter) spanning the speeds of the wind tunnel
(roughly ReFHP ∈ {4000, 7000, 10000, 12000}). A calibration map is thus a series
of (Cpα , Cpβ , CpT , CpS ) values and their corresponding angles (α, β) taken at each
Reynolds number. The discrete one-to-one mappings can be used to determine the
1
N. Titchener, internal project document.
75
α
β
Figure A-3: Rotary table setup to control pitch (α) and yaw (β) roll angles with the
Aeroprobe conical-head FHP mounted.
pitch and yaw angles (α, β), and the stagnation and static pressures from the FHP
pressure readings, and thus the three velocity components. The use of the calibration
maps is discussed in detail in Section A.2
The settling time of the FHP in Figure A-1 was determined by monitoring the
response of the FHP pressure measurement readings to sudden exposure to the tunnel
flow from still conditions. An adequate response time for all the calibration tunnel
velocities to allow the pressure measurement signals to stabilize was found to be 2.5
seconds. Therefore, for each FHP pressure measurement, 2.5 seconds were given to
allow conditions to settle before recording data.
Figure A-4 shows the calibration map for the Aeroprobe conical five-hole probe
at the highest calibration Reynolds number (ReFHP = 12000). Each line represents
a fixed pitch or yaw angle, and zero pitch and yaw correspond approximately to the
origin of the map. Since the design of the probe head is symmetric, the sensitivities
to changes in pitch and yaw angles are expected to be similar, and the resulting
(approximate) squareness of the (Cpα , Cpβ ) map can be seen.
The zero pitch and yaw location on the (Cpα , Cpβ ) map is not exactly at the origin.
This is because the (α, β) = (0,0) position was determined experimentally (rotated
the probe in α and β until Cpα and Cpβ both converged on zero). A finite number
76
of steps in the rotary tables and the accuracy of the pressure transducer limit the
ability to converge on (Cpα , Cpβ ) = (0,0).
5
contours of
increasing α
4
3
Cp β
2
1
contours of
increasing β
0
-1
-2
-3
-4
-2
0
2
4
6
Cp α
Figure A-4: Five-hole probe calibration map for the Aeroprobe conical probe,
ReFHP = 12000.
77
A.2
A.2.1
Using the Calibration Map
Interpolation Method
For a given measurement, all flow quantities (α, β, CpT , CpS ) are given from Cpα , and
Cpβ , which are determined from FHP pressure measurements. A two-level interpolation process using cubic splines is required to get the local flow quantities based on
discrete calibration maps [16]. This process is as follows:
1. From the five FHP pressure measurements, calculate the measured values of
Cpα and Cpβ as defined in Table A.1.
2. Determine a curve relating β and Cpβ by drawing a line at the measured Cpα
on the (Cpα , Cpβ ) map and finding the points of intersection with the β contours. A cubic spline is fitted through these points to get a Cpβ (β) curve. See
Figure A-5a.
3. Using the measured value of Cpβ , interpolate the value of β along the (Cpβ , β)
curve generated in Step 2. See Figure A-5b.
30
5
20
4
3
10
interpolated
β
β
Cpβ
2
1
0
0
-10
-1
measured
Cp β
-20
-2
measured
Cp α
-3
-4
-2
0
2
4
-30
-3
6
-2
-1
0
1
2
3
Cpβ
Cpα
(a) (Cpα , Cpβ ) map: red line denotes measured Cpα
(b) (Cpβ , β) at measured Cpα
Figure A-5: Interpolation for β using measured Cpα and Cpβ values: (a) Step 2, (b)
Step 3.
4. Repeat steps 2-3, this time using Cpβ first, then Cpα , to determine the value of
α. See Figure A-6.
78
30
5
20
4
3
interpolated
α
10
α
Cpβ
2
1
measured
Cp β
0
0
-10
-1
-20
-2
-3
-4
0
-2
2
4
-30
-2
6
Cpα
(a) (Cpα , Cpβ ) map: red line denotes measured Cpβ
measured
Cp α
-1.5
-1
-0.5
0
0.5
Cpα
1
1.5
2
2.5
(b) (Cpα , α) at measured Cpβ
Figure A-6: Interpolation for α using measured Cpα and Cpβ values: Step 4.
5. Using the interpolated local flow angles α and β, define a curve relating yaw
angle and stagnation pressure coefficient by finding the points of intersection of
a line of constant pitch angle through the (CpT , β) data (Figure A-7a) to get a
CpT (β) curve.
6. Use the CpT (β) curve at the interpolated pitch angle (from step 4) to determine the stagnation pressure coefficient (Figure A-7b) that corresponds to the
interpolated β.
0.5
0
0
-0.1
-0.5
-0.2
interpolated
Cp T
-1
-0.3
CpT
CpT
-1.5
-2
-2.5
-0.5
-3
-0.6
-3.5
interpolated
α
-4
-4.5
-30
-0.4
-20
-10
0
α
10
interpolated
β
-0.7
20
-0.8
-30
30
(a) (α, CpT ): lines of constant β (blue) and line
of interpolated α (red)
-20
-10
0
β
10
20
30
(b) (β, CpT ) at interpolated α
Figure A-7: Interpolation for CpT using local flow angles (α, β): (a) Step 5, (b) Step
6.
7. Repeat steps 5 and 6, instead using CpS data to interpolate the static pressure
79
4.5
1.8
4
1.75
3.5
1.7
3
1.65
CpS
CpS
coefficient CpS (Figure A-8).
2.5
1.6
2
1.55
1.5
1
-30
1.5
interpolated
α
-20
-10
0
α
10
interpolated
Cp S
20
-30
30
(a) (α, CpS ): lines of constant β (blue) and line
of interpolated α (red)
interpolated
β
-20
-10
0
β
10
20
30
(b) (β, CpS ) at interpolated α
Figure A-8: Interpolation for CpS using local flow angles (α, β): Step 7.
8. Repeat steps 1–7 for all calibration maps at the four Reynolds numbers.
9. Use the ReFHP = 10000 calibration map to make an initial guess for the local
probe Reynolds number. Linearly interpolate between the four calibration maps
to at this ReFHP guess to get corresponding values for α, β, CpT , and CpS .
10. Use the definition of the stagnation and static pressure coefficients to determine
the local stagnation and static pressures:
pt = p1 − CpT (p1 − p)
p = pt − CpS (p1 − p)
Only one iteration in FHP Reynolds number, using the ReFHP = 10000 calibration
map for the initial guess for local ReFHP , was required for the linear interpolation of
(α, β, CpT , CpS ) in Step 9. Differences in the interpolated values between the four
calibration maps were within the accuracy of the calibration process and pressure
transducer, therefore it was not necessary to repeat the process to converge on the
local Reynolds number.
80
A.2.2
Velocity Components
With the local flow angles α and β known, the local flow velocity components (see
Figure A-9) are determined as follows:
r
y-velocity
2
(pt − ps )
ρ
−1/2
Vx = V 1 + tan2 α + tan2 β
z-velocity
Vz =
Radial velocity
Vr =
Swirl velocity
Vθ =
Total velocity
x-velocity
V =
Vy = −Vx tanβ
Vx tanα
y
z
Vy p
+ Vz p
y2 + z2
y2 + z2
z
y
− Vy p
.
Vz p
y2 + z2
y2 + z2
Note that α and β are defined to describe the motion of the five-hole probe in
pitch and yaw. This is the reason for the negative relation between the horizontal
flow velocity, Vy , and the yaw angle, β.
Vz
origin at
FHP tip
Vy
V
α
−β
Vx
Figure A-9: Conventions for flow velocity components, as measured at the FHP tip.
81
82
Appendix B
Uncertainty Propagation
An important part of any experiment is estimation of the uncertainty, or “error.” Experimental errors can be separated into two categories: (1) measurement uncertainty,
which is the propagation of error due to instrumentation accuracy and resolution to
the final metrics [17], and (2) repeatability, which is error of the distribution of multiple experiments at repeated operating conditions. This appendix details the analysis
of the measurement uncertainty.
B.1
Error Propagation
The measurement uncertainty of the mechanical flow power, PK , is determined via
the propagation of errors in raw measurements due to limitations in instrumentation
accuracy. Raw measurements are data that come directly from the instrumentation
(e.g. pressures from a pressure transducer or temperature from a thermocouple).
The raw measurements recorded in the propulsor characterizations, as well as the
instrumentation used and its associated accuracies, are listed in Table B.1. Other
variables that are not raw measurements (e.g. flow velocity and mass flow) are determined through the manipulation of raw measurements through analytic equations
and experimental calibrations. The variables determined through analytic equations
are given in Table B.2.
For quantities measured using the NI cDAQ, the errors were estimated based on
83
Table B.1: Raw data parameters
Variable
Description
Instrument (σ)
pt0i
tunnel stagnation pressure (×2)
ESP pressure transducer ( 0.05pt0i )
pCi
transition duct static pressure (×4)
ESP pressure transducer ( 0.05pCi )
five-hole probe pressures
ESP pressure transducer ( 0.05p1...5 )
p6
plug static pressure
ESP pressure transducer ( 0.05p6 )
pt6
plug stagnation pressure
ESP pressure transducer ( 0.05pt6 )
atmospheric pressure
mercury barometer (3.4 Pa)
T0
tunnel stagnation temperature
K-type thermocouple (1◦ K)
v
voltage input
NI cDAQ
I
electric current
NI cDAQ
Ω
wheel speed
NI cDAQ ( 25 RPM )
p1 . . . p5
patm
the observed signal outputs during wind tunnel tests. The steadiness of the wheel
speed varied with operating conditions, however the highest fluctuations observed
during all wind tunnel tests corresponded to an error of roughly 25 RPM. Errors in
the voltage and electric current translated into observed fluctuations in the electrical
power input, PE = Iv. As reported in [10], the uncertainty in PE was determined to
be σPE = 0.011PE .
0
1
2
4
5
6
Kiel probe, pt0
wall static tap, pC
z
V0
x
square-to-round
transition duct
blank/distortion screen
Figure B-1: MIT GTL 1×1 foot wind tunnel testing facility station designations
84
Table B.2: Variables at each traverse grid element i
Variable
ρ
pt0
pC
V0
V6
ṁ6
p
Cp α
Equation
Description
patm
Rg T0
air density
1
(pt01 + pt2 )
2
tunnel stagnation pressure
1
(pC1 + pC2 + pC3 + pC4 )
4
r
2 q0
(pt0 − pC )
ρ qC
r
2
(pt6 − p6 )
ρ
transition duct static pressure
tunnel velocity
plug velocity
ρV6 A6
plug mass flow
1
(p2 + p3 + p4 + p5 )
4
average FHP static pressure
p4 − p5
p1 − p
FHP pitch coefficient
p2 − p3
p1 − p
FHP yaw coefficient
pt
p1 − CpT (p1 − p)
local FHP stagnation pressure
ps
pt − CpS (p1 − p)
r
2
(pt − ps )
ρ
local FHP static pressure
Cp β
V
total velocity magnitude
Vx
p
V / 1 + tan2 α + tan2 β
axial velocity
ṁ
ρVx dA
mass flow contribution
PK
Vx (pt − pt0 )dA
PK contribution
PE
Iv
electrical power input
85
For each variable, its error is estimated as the root-sum-square of the individual
errors of each variable on which it is dependent. For example, suppose we have a
variable ζ that depends on N statistically-independent variables xi ,
ζ = f (x1 , x2 , . . . , xN ).
(B.1)
Since it is assumed that that all variables xi are statistically-independent, the error
in ζ (σζ ) is the root-sum-square of the relative errors of each variable,
σζ =
s
∂ζ
σx
∂x1 1
2
+
∂ζ
σx
∂x2 2
2
+ ... +
∂ζ
σx
∂xN N
2
.
(B.2)
In Equation (B.2), σxi is the error of variable xi , and ∂ζ/∂xi quantifies the sensitivity
of ζ to to variable xi .
In instances where an analytic equation cannot be written, the sensitivities are
estimated from trends (curve-slopes) in the data itself. An example instance is the
interpolation of flow angles (α, β) from the five-hole probe calibration maps.
B.2
Overall Efficiency Uncertainty
To assess the uncertainty in the overall propulsor efficiency, the errors of all of the
measurements must be propagated to the final metric. The sequence of processing
these measurements to determine overall efficiency, ηo , is shown in Figure B-2. The
shaded boxes denote raw measurements.
Determination of ηo begins with the five FHP pressure measurements (red), which
are used to interpolate data in the FHP calibration maps to find the local flow angles and stagnation and static pressures. The pressure fields, flow angles, and tunnel
conditions (blue) are used to determine the velocity field which then allows for the
determination of PK , which also includes a contribution from the plug exhaust (yellow). Combining PK with electrical power, PE , allows for the determination of overall
86
Tunnel
Conditions
FHP
p1 . . . p5
Cp α
Cpβ
p1
p
α
β
patm
T0
ρ
pt
ps
V
pt0 , pC , k
Vx
Plug
(exit)
PK
ηo
pt6
p6
PE Electrical
Power
Figure B-2: Parameter processing sequence for ηo determination
efficiency, which is defined as
ηo =
PK
PE
=
PKin + PKout
,
PE
(B.3)
and the uncertainty in ηo is due to errors in PE and PK .
The electrical power is strictly the product of the voltage and electric current
(PE = vI), which are both raw measurements. The mechanical flow power, however,
requires a more complex calculation, as it depends on measurements from the five-hole
probe traverses, tunnel conditions, and plug cooling-flow (for the exit surveys):
PK = f (p1 , . . . , p5 ; pt0 , pC , T0 , patm ; pt6 , p6 ).
The uncertainty in PK is therefore the sum of individual contributions due to each
of these measurements weighted by the sensitivity of PK to each measurement. The
mechanical flow power out of the propulsor has contributions from the nozzle-exit
FHP traverse and the plug exhaust flow, and is
PKout =
X
|
(pt − pt0 )Vx dA + (pt6 − pt0 )V6 A6 .
{z
}
{z
} |
(PK )FHP
(B.4)
(PK )plug
The FHP traverse terms, pt , pt0 , and Vx are determined from expressions given in
Table B.2. Contributions to uncertainty in Vx and pt are not entirely traceable to
87
raw measurements via analytic expressions; some variables (i.e. α, β, CpT , and CpS )
are interpolated from the FHP calibration maps, and thus require estimates for the
sensitivities.
Errors in flow angles α and β can be estimated from the errors in pitch and
yaw angle coefficients. Nominal flow angles of α, β = 10◦ were used in this uncertainty analysis to conservatively represent the average flow angles over the entire
traversed area. Curve-slopes in the FHP calibration map data at the nominal angles
of α, β = 10◦ gave sensitivities to the pitch and yaw coefficients,
δα
δCpα
δβ
δCpβ
≈ 0.25
(B.5)
≈ 0.25.
(B.6)
The sensitivities of CpT and CpS to the flow pitch angle, α, were similarly determined
from the FHP calibration maps at nominal flow angles such that
δCpT
δα
δCpS
δα
≈ 0.5
(B.7)
≈ 0.5.
(B.8)
Using Equations (B.5)–(B.8), errors in the interpolated values of α, β, CpT , and
CpS can be estimated based on Cpα and Cpβ , which are traceable to the FHP pressure
measurements, such that
δα
σC ,
δCpα pα
δβ
σC ,
≈
δCpβ pβ
δCpT δα
σC ,
≈
δα δCpα pα
δCpS δα
σC .
≈
δα δCpβ pβ
σα ≈
σβ
σCpT
σCpS
(B.9)
(B.10)
(B.11)
(B.12)
Equations (B.9)–(B.12) allow the errors of axial velocity, Vx , and stagnation pressure, pt , to be determined using Equation (B.2) at each local traverse grid point i,
88
and therefore provide the error of each traverse point’s mechanical flow power, σPKi .
The FHP traverse contribution to PKout is the sum over all traverse points,
X
(PK )FHP =
PKi ,
(B.13)
i
and the measurements at all of the traverse locations are assumed statisticallyindependent from each other, so the error in (PK )FHP is equal to the root-sum-square
of all traverse point errors,
s
X
σ(PK )FHP =
σP2 Ki
(B.14)
i
The PKout contribution from the plug motor-cooling flow, (PK )plug is dependent on
the plug stagnation and static pressures, as well as the tunnel conditions. Expanding
the sensitivities of (PK )plug to these quantities, the error in (PK )plug is
σ(PK )plug =
q
(pt6 − pt0 )A6 σV6
2
+ V6 A6 σpt6
2
2
+ V6 A6 σpt0 .
(B.15)
Uncertainty in PKout is therefore
σPKout =
q
2
2
σ(P
+ σ(P
.
K )FHP
K )plug
(B.16)
A similar method was used to assess the uncertainty of the mechanical flow power
into the propulsor, PKin ,
1
PKin = −k ρV03 A0 .
2
(B.17)
The error in PKin is thus dependent on errors in the air density, ρ, wind tunnel
velocity, V0 , and the stagnation pressure drop coefficient, k (values for σk are provided
in Table 3.2), and is written as
σPKin =
s
∂PKin
σk
∂k
2
+
89
∂PKin
σρ
∂ρ
2
+
∂PKin
σV0
∂V0
2
.
(B.18)
The uncertainty in measured electrical power [10] is
σPE = 0.011PE .
(B.19)
The error in overall efficiency, ηo , can be determined using the above uncertainties
in PKout , PKin , and PE ,
σηo =
s
1
σP
PE Kout
2
+
1
σP
PE Kin
2
+
PKin + PKout
σ PE
PE2
2
.
(B.20)
In fractional terms, the uncertainty is
σηo
ηo
=
s
σPKout
PKout + PKin
2
+
σPKin
PKout + PKin
2
+
σPE
PE
2
.
(B.21)
The error in overall efficiency was determined to be σηo = 0.007, which at the
simulated cruise condition corresponds to an error of σηo /ηo = 1.2%.
Errors in the fan efficiency, ηf , require the knowledge of uncertainties in the motor
efficiency. These uncertainties in ηm are from a separate experiment performed by
Casses [12], and were not included in this uncertainty analysis.
90
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