Modelling and Evaluation of
Jet Engine Fuel System Designs
Master’s thesis in Mobility Engineering

PER SAMUELSSON
HJALMAR STRÖMFELDT

DEPARTMENT OF MECHANICS AND MARITIME SCIENCES

CHALMERS UNIVERSITY OF TECHNOLOGY
Gothenburg, Sweden 2024
www.chalmers.se

www.chalmers.se




Master’s thesis 2024

Modelling and Evaluation of Jet
Engine Fuel System Designs

PER SAMUELSSON
HJALMAR STRÖMFELDT

Department of Mechanics and Maritime Sciences
Chalmers University of Technology

Gothenburg, Sweden 2024



Modelling and Evaluation of Jet Engine Fuel System Designs
PER SAMUELSSON
HJALMAR STRÖMFELDT

© PER SAMUELSSON, HJALMAR STRÖMFELDT 2024.

Supervisor: Niklas Kringstad, GKN Aerospace Sweden AB
Examiner: Professor Tomas Grönstedt, Mechanics and Maritime Sciences

Master’s Thesis 2024
Department of Mechanics and Maritime Sciences
Chalmers University of Technology
SE-412 96 Gothenburg
Telephone +46 31 772 1000

Cover: RM12 engine test, used with permission from GKN Aerospace Sweden AB

Typeset in LATEX, template by Kyriaki Antoniadou-Plytaria
Gothenburg, Sweden 2024

iv



Modelling and Evaluation of Jet Engine Fuel System Designs
PER SAMUELSSON
HJALMAR STRÖMFELDT
Department of Mechanics and Maritime Sciences
Chalmers University of Technology

Abstract
This master thesis investigates the main fuel pump of the RM12 engine used in
the JAS 39 Gripen C/D fighter jet, with the aim of identifying and modelling the
main fuel pump as well as alternative fuel system configurations. The purpose of
this project is to understand performance, efficiency, and limitations of the current
fuel system, as well as to explore potential improvements using alternative fuel
systems and pump architectures. By combining publicly available data, data from
uninstalled accessory rig tests, as well as data from uninstalled engine tests, the
system model compares the performance of different fuel systems at different steady
state operating conditions. The system model predicts pump power usage and fuel
heat sink capability among other parameters. These performance parameters have a
direct impact on aircraft performance and provide insight in design and optimization
of future jet engine fuel systems. The results indicates that a variable displacement
main fuel pump or an electrically driven variable speed main fuel pump may be
well suited with regards to minimizing power extraction and added heat to the fuel.
Further studies of these configurations may therefore be of interest.

Keywords: RM12, pumps, fuel system, main fuel pump, jet engine, afterburner

v





Acknowledgements
We would like to express a special thanks our supervisor Niklas Kringstad at GKN
Aerospace for his guidance and advice throughout the creation of this thesis.

We also acknowledge Victor Isidorsson and the rest of division 7162 at GKN Aerospace
for their openness and kindness towards us.

Thanks to Mikael Stribrand and Johan Öhman for providing insights on the test rig
specifications, and to Eric and Pernilla for carrying out our custom rig test.

Chalmers Library and Jonathan Mårtensson are acknowledged for providing articles
and books that have been essential for the literature study.

We thank Michael Crona and Simon Dinger for their thorough review and feedback.

Lastly, we acknowledge Tomas Grönstedt for taking on the role as examiner for our
thesis.

Per Samuelsson & Hjalmar Strömfeldt, Gothenburg, June 2024

vii





List of Acronyms

Below is the list of acronyms that have been used throughout this thesis listed in
alphabetical order:

ABC Afterburner Fuel Control
ABP Afterburner Fuel Pump
AGB Accessory Gear Box
A/B Afterburner
A/C Aircraft
BEP Best Efficiency Point
CFD Computational Fluid Dynamics
FADEC Full Authority Digital Engine Control
FI Flight Idle
HP High Pressure
IRP Intermediate Rated Power
LP Low Pressure
MFC Main Fuel Control
MFP Main Fuel Pump
MT Maximum A/B Thrust
NH Rotational Speed of the High Pressure Rotor
NPSHr Required Net Positive Suction Head
RPM Rotations Per Minute
SFC Specific Fuel Consumption
WFM Weighted Fuel Main
WFR Weighted Fuel Reheat
w/o Without

ix





Nomenclature

Below is the nomenclature of parameters that have been used throughout this thesis.

Parameters

A Area [m2]
Cd Discharge coefficient [-]
cp Specific heat capacity [J/(kg· K)]
D Diameter [m]
ds Specific diameter [-]
g Gravitational acceleration constant [m/s2]
H Head [m]
h Specific enthalpy [J/kg]
ṁ Mass flow [kg/s]
Ma Mach number [-]
nq Specific speed [m3/4/(min·

√
s)]

p Pressure [Pa]
Q Volume flow [m3/s]
q∗ Normalized volumetric flow rate [-]
Q̇ Heat power [J/s]
Re Reynolds number [-]
U Sliding velocity [-]
u Internal energy [J/kg]
V Mean flow velocity [m/s]
V Specific volume [m3/kg]
Vd Displacement volume [m3/s]
Ẇs Shaft power [J/s]
Ẇv Viscous power [J/s]

xi



ẇs Shaft work [J/kg]
α Swash plate angle [-]
∆H Total dynamic head [m]
η Efficiency [-]
ηm Mechanical efficiency [-]
ηv Volumetric efficiency [-]
µ Dynamic viscosity [Pa· s]
µJT Joule-Thomson coefficient [° C/Pa]
φ Flow coefficient [-]
ψ Head coefficient [-]
ρ Density [kg/m3]
ω Pump shaft rotational speed [rad/s]
ωs Specific speed [-]

xii



Contents

List of Acronyms ix

Nomenclature xi

List of Figures xvii

List of Tables xix

1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Specification of the issue being investigated . . . . . . . . . . . . . . . 4

2 Theory 5
2.1 Fuel system overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.1 Aircraft booster pump . . . . . . . . . . . . . . . . . . . . . . 5
2.1.2 Main fuel pump . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1.2.1 Pumping stages and fuel filter . . . . . . . . . . . . . 6
2.1.2.2 Main fuel control, bypass and servo flow . . . . . . . 6

2.1.3 A/B fuel pump and A/B fuel control . . . . . . . . . . . . . . 8
2.1.4 Oil cooler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.5 Full authority digital engine control . . . . . . . . . . . . . . . 8

2.2 Pump and system curves . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.1 Definition of head . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.2 Pump efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.3 Pump curves . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.4 System curve . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.5 System performance . . . . . . . . . . . . . . . . . . . . . . . 13

2.3 Dimensionless performance parameters . . . . . . . . . . . . . . . . . 13
2.3.1 Head and flow coefficients . . . . . . . . . . . . . . . . . . . . 13
2.3.2 Specific speed and specific diameter . . . . . . . . . . . . . . . 14
2.3.3 Stribeck curve correlations for positive displacement pumps . . 15

2.4 Pump type theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.1 Specific diameter vs. specific speed diagrams . . . . . . . . . . 16
2.4.2 Pump type descriptions . . . . . . . . . . . . . . . . . . . . . 16

2.4.2.1 Pump type classifications . . . . . . . . . . . . . . . 17

xiii



Contents

2.4.2.2 External gear pump . . . . . . . . . . . . . . . . . . 18
2.4.2.3 Axial swash plate piston pump . . . . . . . . . . . . 19
2.4.2.4 Radial centrifugal pump . . . . . . . . . . . . . . . . 20
2.4.2.5 Partial emission pump . . . . . . . . . . . . . . . . . 21

2.5 Flow rate control methods . . . . . . . . . . . . . . . . . . . . . . . . 23
2.5.1 Flow control by recirculation . . . . . . . . . . . . . . . . . . . 24
2.5.2 Flow control by variable displacement . . . . . . . . . . . . . . 24
2.5.3 Flow control by throttling . . . . . . . . . . . . . . . . . . . . 24
2.5.4 Speed flow control . . . . . . . . . . . . . . . . . . . . . . . . 25

2.6 Fuel properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.6.1 Density, viscosity and specific heat capacity . . . . . . . . . . 25
2.6.2 Joule-Thomson coefficient . . . . . . . . . . . . . . . . . . . . 25

3 Methods 27
3.1 Estimation of density, viscosity and specific heat capacity . . . . . . . 27
3.2 Selection of model inputs . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3 Data collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.3.1 Test rig description . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.2 Formulation of test matrix . . . . . . . . . . . . . . . . . . . . 29
3.3.3 Description of collected data . . . . . . . . . . . . . . . . . . . 31

3.4 Identification of Joule-Thomson coefficient . . . . . . . . . . . . . . . 32
3.5 Identification of LP stage head and efficiency curve . . . . . . . . . . 32
3.6 Identification of HP stage volumetric efficiency . . . . . . . . . . . . . 33
3.7 RM12 state estimator formulation . . . . . . . . . . . . . . . . . . . . 34

3.7.1 Calibration of model using HP total efficiency . . . . . . . . . 34
3.8 Selection and implementation of alternative MFP architectures . . . . 36

3.8.1 System with centrifugal HP stage pump . . . . . . . . . . . . 36
3.8.2 System with axial piston HP stage pump . . . . . . . . . . . . 38
3.8.3 Electrically driven system with centrifugal stages . . . . . . . 39

4 Results 41
4.1 Comparison of fuel systems configurations . . . . . . . . . . . . . . . 41

4.1.1 Power usage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.1.2 Fuel temperature rise . . . . . . . . . . . . . . . . . . . . . . . 42
4.1.3 Driving energy . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.1.4 Cooling capacity . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.1.5 Temperature rise due to bypass ratio . . . . . . . . . . . . . . 45
4.1.6 RM12 modeled LP vs. HP stage temperature rise . . . . . . . 47
4.1.7 Throttle valve pressures . . . . . . . . . . . . . . . . . . . . . 47
4.1.8 Electric speed control . . . . . . . . . . . . . . . . . . . . . . . 48

4.2 Further comparison of fuel system characteristics . . . . . . . . . . . 48

5 Discussion 51
5.1 Discussion of results . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.1.1 General findings . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.1.2 Discrepancies affecting result . . . . . . . . . . . . . . . . . . . 52

5.2 Test rig limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

xiv



Contents

5.3 Gear pump total efficiency curve behavior . . . . . . . . . . . . . . . 53
5.4 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

6 Conclusion 55

Bibliography 57

xv



Contents

xvi



List of Figures

2.1 RM12 fuel system functional schematic. . . . . . . . . . . . . . . . . . 6
2.2 MFC bypass control functional schematic. . . . . . . . . . . . . . . . 7
2.3 General example of pump head and efficiency curves. . . . . . . . . . 12
2.4 General example of a system curve. . . . . . . . . . . . . . . . . . . . 12
2.5 General evaluation of the system point of operation. . . . . . . . . . . 13
2.6 Head vs. flow coefficient for a centrifugal pump [9]. . . . . . . . . . . 14
2.7 A Stribeck curve [12]. . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.8 A specific diameter vs. specific speed diagram showing different types

of pumps [15]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.9 Gear pump functional sketch [10]. . . . . . . . . . . . . . . . . . . . . 18
2.10 Gear pump Stribeck-correlated efficiency values. Z is the dynamic

viscosity, N is the rotational speed (rad/s) and P is the pump differ-
ential pressure [13]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.11 Cutaway axial swash plate piston pump schematic [12]. . . . . . . . . 20
2.12 Cutaway schematic layout of a general centrifugal pump [20]. . . . . . 21
2.13 General pump curves and efficiency curves for centrifugal pumps as

a function of specific speed [21]. . . . . . . . . . . . . . . . . . . . . . 22
2.14 Cutaway schematic layout of a partial emission pump [22]. . . . . . . 23

3.1 Extracted kinematic viscocity data for Jet A-1. Derived from [26]. . . 28
3.2 Functional schematic of the test rig. Pressure and flow sensors are

omitted from the image. . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3 Visualization of test matrix selection of NH, WFM and WFR, with

and without A/B flow. . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.4 Normalized outlet pressure correlation. . . . . . . . . . . . . . . . . . 31
3.5 Estimation of the Joule-Thomson coefficient function using linear re-

gression, expressed as a function of the inlet temperature at the by-
pass valve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.6 LP stage pump curves with data points. . . . . . . . . . . . . . . . . 33
3.7 HP stage volumetric efficiency. . . . . . . . . . . . . . . . . . . . . . . 34
3.8 State estimator code flow chart. . . . . . . . . . . . . . . . . . . . . . 35
3.9 HP stage total efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.10 Dimensionless centrifugal HP pump curves. . . . . . . . . . . . . . . . 37
3.11 Axial piston pump total efficiency. . . . . . . . . . . . . . . . . . . . . 38
3.12 Dimensionless electrically driven centrifugal LP stage pump curves. . 39

4.1 Bar plot of the MFP power usage at flight idle. . . . . . . . . . . . . 43

xvii



List of Figures

4.2 Bar plot of the MFP power usage at intermediate rated power. . . . . 43
4.3 Bar plot of the MFP power usage at maximum A/B thrust. . . . . . 44
4.4 Bar plot of the fuel temperature rise over the MFP at flight idle. . . . 44
4.5 Bar plot of average MFP driving energy. . . . . . . . . . . . . . . . . 45
4.6 Bar plot of cooling capacity. Normalized by System 1. . . . . . . . . . 46
4.7 Scatter plot relating volumetric bypass ratio and temperature rise in

System 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.8 LP vs. HP stage temperature increase ratio as a function of the

volumetric bypass ratio in System 1. . . . . . . . . . . . . . . . . . . 47
4.9 Pressure levels before and after the throttle valve in System 3. . . . . 48
4.10 Pump shaft speed vs. volumetric flow delivered to the engine for

System 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

xviii



List of Tables

4.1 Fuel system numbering description. . . . . . . . . . . . . . . . . . . . 41
4.2 Further comparison of fuel system characteristics. . . . . . . . . . . . 49

xix



List of Tables

xx



1
Introduction

1.1 Background

In any jet engine, a fuel system is needed to supply the engine with metered fuel
flow for combustion. However, it may also be utilized to cool other aircraft (A/C)
components and systems. In such cases, the fuel itself is used as a heat sink. De-
pending on the design of the fuel system, fuel properties, and the fuel demand at
different engine operating points, the efficiency of the fuel pumps will differ. The
energy not imparted as hydraulic work on the fluid will instead largely be introduced
as unwanted heat to the fuel system components and the fuel itself. Heating of the
fuel in the pumping system degrade the available cooling capacity, thus limiting
performance. This issue is exacerbated by an increased necessity to cool electrical
components, and a decreased ability of removing heat through the aircraft skin due
to an increasing use of composite materials [1]. By improving the performance and
efficiency of the fuel pumping system, the cooling ability can be enhanced to better
handle increased cooling needs. Furthermore, by reducing the torque power needed
to operate the pumps, the impact on engine performance is reduced, improving A/C
specific fuel consumption (SFC).

The RM12 engine used in the JAS 39 Gripen C/D fighter jet is developed and
maintained by GKN Aerospace Sweden AB. The main fuel pump (MFP) shaft in
the RM12 is connected to the high pressure (HP) rotor shaft through a transmission
[2]. The rotational speed of the pump shafts are thus proportional to the rotational
speed of the HP rotor (NH). Since the NH, and thus the amount of fuel supplied by
the MFP is not directly correlated to the engine fuel demand, the MFP is unable to
provide the exact amount of fuel needed for all engine operating points. In order to
avoid insufficient fuel flow, the pumps are designed to supply a sufficient amount of
fuel at some extreme operating condition, for example during maximum thrust or
during engine relight at specific points of the flight envelope. As a consequence, the
pumping capacity of the MFP is greater than needed for the majority of the engine
operating cycle [3]. Hence, the fuel supplied to the combustion chamber must be
limited by metering the flow. Depending on the type of pump used, this can be
achieved by recirculating excess fuel or by limiting pumping capacity by employing
a throttling valve [4, 5]. These methods of restricting the fuel flow impart an irre-
versible loss of pressure, resulting in heating of the fuel. Alternatively, in order to
minimize these irreversibilities, the amount of fuel supplied by the pumps can be
set to match the engine requirements. This can be achieved by utilizing pumping

1



1. Introduction

systems that supply fuel flows not directly dependent on the NH, e.g. by using a
variable displacement pump or by decoupling the rotational speed of the pump shaft
from the jet engine rotational speeds [6].

The variety of solutions for supplying the engine with fuel also implies a variety
of advantages and disadvantages. Additional factors important to consider when
designing a system include mass, volume, reliability, and cost. An understanding of
how all of these factors are affected based on the design is consequently crucial in
order to properly review and recommend fuel system designs.

In this thesis, different fuel systems are identified and assessed, using the RM12
engine as a basis. The fuel system model will use inputs from an already created
engine performance model operating at different steady state operating points, and
return values such as pump power use, efficiencies, and fuel temperature.

In order to improve A/C performance, it is the interest of GKN Aerospace Swe-
den AB to investigate how the fuel system of the RM12 and possible alternative
fuel systems performs at different conditions corresponding to different points of the
operating cycle, as it informs future engine development. Specifically, a model of
different fuel systems at different operational conditions informs how variations over
the operating cycle of the aircraft/engine affect the sizing and design of accessory
systems and the accessory gearbox.

1.2 Aim
The task is to model the current fuel system of the RM12 engine operating at steady
state conditions, and to identify and model alternative fuel system configurations
using publicly available data along with uninstalled system data derived from ac-
cessory and engine rig tests at varying operating points.

By comparing the performance of different fuel systems, informative knowledge for
the design of future fuel systems is gained. The information gained can be used in fu-
ture investigations of how A/C thrust, fuel heat sink capability, and SFC is affected.

2



1. Introduction

1.3 Limitations
• The project is carried out over approximately 20 weeks, corresponding to 30

ECTS credits.

• No sensitive data is presented in the final report. Classified information is
excluded.

• The inquiry is limited to the fuel pumping system, and since the fuel flow input
is entirely based on the requirements for combustion as defined by the engine
performance model, the fuel flow needed for cooling of other components is
not included in this input. The cooling ability is consequently estimated by
the available fuel temperature increase margin after the pumping stages.

• A detailed investigation of the expected lifespan of components in the pump-
ing system will not be conducted, instead the focus is to evaluate the overall
performance and reliability.

• A mission is modeled as several steady state operating points, each with a
certain time duration. Transient behavior, and by extension the response time
of fuel flow changes, is thereby not included.

• The same constant value input pressure is assumed for all steady state oper-
ating points, as values affecting the input pressure, such as flight altitude and
flight Mach number is classified information.

• The test rig characteristics resemble the currently installed fuel system on the
RM12 engine. Unknown data regarding alternative fuel system designs will to
a larger extent be based on data from other open sources.

• A fuel system configuration utilizing recirculation of fuel back to the fuel tank
will not be considered in order to reduce complexity in possible configurations.

• Pressure losses in the system are handled using system curves. Individual
components (such as filters) will not be modeled explicitly.

• Factors such as weight, volume, reliability, and cost will not be included in the
model. These factors are instead included as part of the evaluation of different
designs.

• The fuel type utilized in the system models is limited to Jet A-1 fuel. No other
fuel type will be investigated.

3



1. Introduction

1.4 Specification of the issue being investigated
In order to achieve the goal described in section 1.2, some fundamental questions
needs to be answered:

• Which types of pumps and flow rate control methods are relevant for use in
the fuel system, and how can they be modeled?

• How much of the energy lost due to pumping inefficiencies and flow restriction
contributes to heating of the fuel and pump system components respectively,
and what are the sources of these inefficiencies?

• How can a fuel system be modeled to obtain the sought after knowledge (such
as efficiencies, and pumping power), for any given steady state operating point?

• In which aspects are different fuel system configurations preferable?

4



2
Theory

2.1 Fuel system overview
The main purpose of a jet engine fuel system is to supply the engine core with a
metered fuel flow for combustion at sufficient pressures in order to generate thrust.
Additionally, it may be tasked with supplying pressurized fuel for afterburner (A/B)
combustion. Furthermore, the fuel system may be required to supply fuel flow for
use as coolant, or to supply pressurized fuel that can be utilized as hydraulic fluid
for use in engine actuation. Actuation may include movement of stator vane angles
or geometry change in the engine outlet nozzle. More specifically, the RM12 fuel
system is used to supply both main and A/B combustion, to supply coolant flow,
and to supply pressurized hydraulic fluid used to move stator vane angles in the
engine compressor and fan.

The fuel system in the RM12 consists of multiple components. A basic functional
schematic of the system is shown in Fig. 2.1. The dotted line designate components
included in the MFP and denotes parts of the fuel system that are considered in this
thesis. The purpose and function of the components shown in Fig. 2.1 are described
below.

2.1.1 Aircraft booster pump
The objective of the booster pump is to transfer fuel from the airframe fuel tank to
the LP pump at all operating conditions. This includes a pressure buildup, helping
the LP pump operate above the required net positive suction head (NPSHr). While
the booster pump plays a crucial role in transferring fuel from the fuel collector
tank to the MFP, investigations regarding the booster pump and its performance
are beyond the scope of this study.

2.1.2 Main fuel pump
The MFP consists of multiple components, integrated in the same housing assembly.
The purpose of the MFP is to supply pressurized flow to the main engine core, and
to pressurize fuel for the A/B before it enters the A/B pump (ABP) and A/B fuel
controller (ABC). Additionally, it provides pressurized servo fuel flow.

5



2. Theory

MFC

ABP 
and 
ABC

Oil
cooler

FADEC

Fuel 
tank

Bypass

HP pumpLP pump

Booster 
pump

To main 
combustion

To A/B combustion

MFP

Fuel 
filter

Servo flow

Figure 2.1: RM12 fuel system functional schematic.

2.1.2.1 Pumping stages and fuel filter

The MFP contains two pumping stages, a LP pump, and a HP pump. The LP
stage is needed to force the fuel through the filter and to ensure cavitation is not
present in the HP stage. The HP stage is necessary to achieve the high pressure
head needed by the engine during operation. The LP pump consists of a centrifugal
impeller with an axial inducer. The inducer allows the LP pumping stage to op-
erate at lower NPSHr, allowing for operation without cavitation for a wider set of
operating conditions. The LP pump serves as an initial pumping stage for both the
ABP and HP pump.

The HP pump consists of a positive displacement gear pump contributing the greater
part of the fuel pressurization. The LP and HP pumps both share the same drive
shaft. The pump drive shaft is driven by the accessory gearbox (AGB), which in turn
is powered by a bevel gear to the engine HP rotor shaft. The rotational speed of the
pumping stages are thus proportional to the rotational speed of the engine HP rotor.

A fuel filter is placed in between the LP and HP pumps. The purpose of this filter is
to remove contaminants in the fuel before it enters sensitive components downsteam
in the fuel system. The filter location downstream of the LP pumping stage is made
possible as the centrifugal pump used in this stage is insensitive to contaminants.

2.1.2.2 Main fuel control, bypass and servo flow

The main fuel control (MFC) is a hydromechanical control system that, based on
inputs from the FADEC, meters the fuel for the engine main combustion by recir-

6



2. Theory

culating excess fuel back to the HP pump inlet through a bypass channel, as seen
in Fig. 2.2. For further information on the FADEC, see Sec. 2.1.5. By controlling
the opening area of a bypass valve based on the pressure differential over a metering
valve, the pressure differential over the metering valve can be set constant. With a
constant pressure differential over the metering valve, the volume flow to the engine
can be precisely controlled by changing the nozzle area of the metering valve. This
concept can be explained by Eqn. 2.1, which is derived from the Bernoulli equation.

Q = CdA2

√√√√√ 2(p1 − p2)
ρ
(
1−

(
A2
A1

)2) (2.1)

where the discharge coefficient Cd is used to account for the valve geometry. The
discharge coefficient is dependent on the area ratio between valve inlet and outlet
as well as the Reynolds number. Q is the volume flow through the area change. p is
the fluid pressure, ρ is the density of the fluid, and A is the orifice area. Notations
1 and 2 represent valve inlet and outlet respectively.

Value changes of the discharge coefficient tend to be quite small despite large changes
in valve area ratio or Reynolds number, assuming the Reynolds number is sufficiently
high [7].

The flow not needed for combustion passes through the bypass valve, where the
flow experiences a pressure drop and is recirculated back to the HP pump inlet. A
functional schematic of the MFC bypass control can be seen in Fig. 2.2.

Figure 2.2: MFC bypass control functional schematic.

The MFC also control the servo flow. This flow supplies hydraulic actuation fluid
to movable systems and internal servo systems in the MFC. During steady state
operation, actuation is typically not needed, however a certain leakage flow is to be
expected and must be taken into account. The servo flow is diverted from the high

7



2. Theory

pressure flow after the HP pump, used, and returned upstream the LP pump.

2.1.3 A/B fuel pump and A/B fuel control
The A/B fuel pump (ABP) is used to pressurize fuel further before it enters the
A/B. A centrifugal, vapor core-controlled pump is used. The amount of pressurized
fuel is controlled by the hydromechanical A/B fuel controller (ABC).

2.1.4 Oil cooler
The oil cooler is placed after the HP pump and MFC. The oil cooler uses fuel as
a heat sink in order to cool oil used in different parts of the engine system. The
temperature of the fuel therefore have an impact on the cooling performance. By
decreasing the fuel temperature for a given engine operational condition, the amount
of cooling available is increased. Note that the fuel temperature also have to stay
below a certain threshold in order to prevent coking. This constitutes an upper fuel
temperature limit, which depends on the type of fuel used [3].

2.1.5 Full authority digital engine control
The full authority digital engine control (FADEC) is the brain of the engine. The
FADEC receives various inputs, from both the pilot and the engine and calculates
the proper subsystem control outputs. In Fig. 2.1, the communication between the
FADEC and MFC/ABC is marked with blue lines.

2.2 Pump and system curves
The use of pump and system curves is a common way of visualizing pump and
system performance, typically as a function of pump/system head versus flow and
pump efficiency versus flow. These terms are defined in the sections below, followed
by a short explanation of pump and system curve plots.

2.2.1 Definition of head
Consider a one-dimensional steady flow through a pump with an incompressible
fluid. Let station 1 and 2 denote the inlet and outlet respectively. Applying the
steady flow energy equation, the total energy imparted to the fluid can be expressed
as the following:

Q̇+ Ẇs + Ẇv = −ṁ(u1 + p1

ρ
+ 1

2V
2

1 + gz1) + ṁ(u2 + p2

ρ
+ 1

2V
2

2 + gz2) (2.2)

8



2. Theory

where Q̇ is the heat power added to the fluid, Ẇs is the added shaft power, Ẇv is
the added viscous power, ṁ is the mass flow, u is the internal energy, V is the mean
flow velocity, and z a height relative some point.

Since the flow is incompressible, ṁ can be removed. Furthermore, by assuming
adiabatic flow and static walls (thus no viscous work), Eqn. 2.2 can be transformed
into the following:

ws = −
(
u1 + p1

ρ
+ 1

2V
2

1 + gz1
)

+ u2 + p2

ρ
+ 1

2V
2

2 + gz2 (2.3)

Where ws is the shaft work transferred to the fluid per unit mass. By dividing
Eqn. 2.3 by the gravitational constant g each term can be expressed as a length,
and by rearranging the equations, we get the following:

ws

g
= p2

ρg
+ 1

2gV
2

2 + z2 −
( p1

ρg
+ 1

2gV
2

1 + z1
)

+ u2 − u1

g
(2.4)

or

ws

g
= ∆H + u2 − u1

g
(2.5)

where

H = p

ρg
+ 1

2gV
2 + z (2.6)

∆H is refered to as the total dynamic head, as it contains pressure, velocity and
elevation head terms. The total dynamic head is a common measurement for the
useful energy imparted to a fluid by a pump, and can be interpreted as the height
difference that can be generated by a pump if the pressure and velocity head is
transformed into potential energy without losses. Note that ∆H is not the only
term on the right hand side of Eqn. 2.5. The second term represent the increase
in specific energy due to the shaft work on the left hand side, and thus represent
pumping losses added as heat to the fluid [8]. This is important when defining effi-
ciency, which is covered in Sec. 2.2.2.

It is also important to note that the height difference between the inlet and outlet
of the pumps covered in this thesis are negligible. It can also be assumed that the
velocity is similar at the inlet and outlet of the pump. Combined with the high
expected pressure differential, ∆H can safely be approximated as ∆p/(ρg). These
assumptions are commonly made with regards to pumps [9].

2.2.2 Pump efficiency
In order to quantify pump efficiency Eqn. 2.5 is revisited. Recall that the equation
show the head form of the energy equation, where the left hand side represent the
shaft work added to the fluid by the pump. The right hand side of the equation

9



2. Theory

contain ∆H, which represent the useful energy added to the fluid, and ∆u/g rep-
resent the part of the shaft work that instead increase the internal energy of the
fluid, expressed as a fluid temperature rise. By defining the total efficiency, η, as
useful work, divided by the total added shaft work using the terms in Eqn. 2.5, the
following can be shown:

η = Useful work
Added work = ∆Hg

ws

= ∆Hgṁ
Ẇs

= ∆HgρQ
Ẇs

(2.7)

By approximating the total dynamic head using the pressure differential and density
as described in Sec. 2.2.1, Eqn. 2.7 can be rewritten as the following:

η = ∆pQ
Ẇs

(2.8)

If the added work is instead expressed as the sum of useful work and the increase
in internal energy of the fluid, assuming that the increase in internal energy results
in a temperature rise ∆T , η can instead equivalently be expressed as:

η = ∆Hg
∆Hg + ∆u =

(
1 + ∆u

∆Hg

)−1
=
(

1 + cp∆T
∆Hg

)−1
(2.9)

Note that Eqn. 2.9 can be evaluated without knowing the mass flow. The total pump
efficiency can also be expressed as the product of other component efficiencies. An
understanding of how component efficiencies behave, and thereby how they affect
the total efficiency of a pump may be important when, for example, the efficiency
performance of a hypothetical pump is modeled. It is common to divide the total
pump efficiency as the product between the volumetric efficiency ηv and the me-
chanical efficiency ηm [10].

The volumetric efficiency is defined as the actual flow rate delivered by the pump
over the ideal theoretical flow rate (see Eqn. 2.11). The actual flow rate may be
lower than the theoretical ideal flow rate through a pump due to leakage flows, in
essence fluid recirculated within the pump.

Q = Qideal −Qleakage (2.10)

ηv = Q

Qideal
= Qideal −Qleakage

Qideal
(2.11)

In a positive displacement pump, the volumetric efficiency can be expressed as ideal
displacement per pump shaft unit of rotation, divided by the actual displacement
per unit of rotation. The ideal displacement is usually easily defined given a known
pump geometry.

ηv = Q

Qideal
= Vdω

Vd,idealω
= Vd

Vd,ideal
(2.12)

where ω is the rotational speed of the pump shaft.

10



2. Theory

The mechanical efficiency is defined as the ideal useful work divided by the actual
shaft work required to drive the pump as can be seen in Eqn. 2.13:

ηm = ∆HgρQideal

Ẇs

(2.13)

Thus multiplying Eqn. 2.11 and 2.13 returns Eqn. 2.7:

η = ηvηm = Q

Qideal

∆HgρQideal

Ẇs

= ∆HgρQ
Ẇs

(2.14)

Note that the division of the total efficiency into volumetric and mechanical com-
ponents is not the only possible way of dividing the total efficiency, and that other
formulations can be used.

The impact of different pump control methods on the total system efficiency is cov-
ered in Sec. 2.5.

2.2.3 Pump curves
A pump curve typically correlate the volume flow through the pump with some type
of quantity, typically ∆H, pump efficiency or pump power. Pump curves are typ-
ically supplied by pump manufacturers or suppliers, and the exact shape of these
curves vary greatly depending on pump model and type. The expected pump curve
shapes are covered for different pump types in Sec. 2.4.2. Sometimes multiple curves
of the same type are shown in the same figure, denoting different pump speeds or
impeller diameters. A general, purely illustrative, example is shown in Fig. 2.3. The
best efficiency point (BEP) is commonly used to denote the flow where the maxi-
mum pump efficiency is located.

Also note that pumps can be connected in either parallel or in series. When pumps
are connected in series, the volume flow is unaffected (assuming identical pumps),
however the collective pump head becomes the addition of each individual pump
head. Thus, a new pump curve for the series connected pumps can be estimated by
simply adding the head value of the individual pump curves at every point.

2.2.4 System curve
A system curve typically show the head resistance at a point of the system as a
function of the volume flow through the system. A general example can be seen in
Fig. 2.4. The head shown at zero flow represent the static resistance, or the resis-
tance that needs to be overcome in order to generate any flow through the system,
this could for example be caused by a height difference or a resistive pressure differ-
ence present in the system. The additional resistance generated beyond the point of
zero flow is called the dynamic resistance, and is typically proportional to the square
of the flow. The curve can be made steeper by increasing the resistance in the system.

11



2. Theory

Figure 2.3: General example of pump head and efficiency curves.

Figure 2.4: General example of a system curve.

12



2. Theory

2.2.5 System performance
Pump and system curves can be combined in order to estimate at which condi-
tions a pumping system operates. When combined, the pump head curve represents
the available head at a certain flow, whereas the system head represents the re-
quired head for a certain flow. The actual operational point of a system operating
at steady state is therefore located at the intersection between the pump and sys-
tem head curves. This concept is demonstrated in Fig. 2.5. Note that the pump
efficiency is lower at the point of operation, as compared to the BEP in the example.

Figure 2.5: General evaluation of the system point of operation.

2.3 Dimensionless performance parameters
Dimensionless performance parameters, derived through dimensional analysis are
commonly used in order to get a comprehensive understanding of the general be-
havior of a pump. Furthermore, dimensionless performance parameter data may be
used in order to predict pump performance at different scales or speeds given limited
empirical data. They may also be used in pump selection schemes [9].

2.3.1 Head and flow coefficients
The flow coefficient is defined as:

13



2. Theory

φ = Q

ωD3 (2.15)

and the head coefficient is defined as:

ψ = g∆H
(ωD)2 (2.16)

where ω is the rotational speed of the pump, and D is the pump characteristic di-
ameter.

The head coefficient ψ can be assumed to only depend on the flow coefficient φ given
the assumption that pump surface finish is of small importance, and a sufficiently
large Reynolds number [9].

The dimensionless head and flow coefficients may be used to collapse pump curve
data for several pump diameters and speeds into a single curve, given dynamic sim-
ilarity. Thus, if dynamic similarity can be assumed, pump performance at different
conditions can be assessed using a single curve. Furthermore, if dynamic similarity
holds true, all dimensionless parameters including efficiency are identical [9]. In
Fig. 2.6, the dimensionless head and flow coefficients are plotted for a centrifugal
pump at different speeds. Note that dynamic similarity does not hold true when
cavitation is present.

Figure 2.6: Head vs. flow coefficient for a centrifugal pump [9].

2.3.2 Specific speed and specific diameter
Specific speed and specific diameter are commonly used together as a means of
assessing which type of pump is appropriate for a given duty, knowing some perfor-
mance parameters. The specific speed is defined as [9, 11]:

ωs = φ1/2

ψ3/4 = ω
√
Q

(g∆H)3/4 (2.17)

14



2. Theory

The definition shown in Eqn. 2.17 is truly dimensionless and defined in SI units.
Note that several other varieties exist, commonly excluding the gravitational con-
stant g, and using non-SI units. Careful inspection of the version used is needed
when comparing empirical data.

The specific diameter is defined as [9, 11]:

ds = ψ1/4

φ1/2 = (D∆Hg)1/4
√
Q

(2.18)

Similar to the specific speed, Eqn. 2.18 is truly dimensionless and uses SI units. The
specific diameter may also take on several forms.

2.3.3 Stribeck curve correlations for positive displacement
pumps

To the authors’ knowledge there is no way of accurately predicting the efficiency
characteristics given a positive displacement pump without some applicable empiri-
cal data, derived from either CFD or experiments. One possible way of approximat-
ing the efficiency behavior of certain types of positive displacement pumps is derived
from the study of tribology by the use of the Stribeck curve. The Stribeck curve is a
general description of how the coefficient of friction between two lubricated surfaces
is altered depending on the relative velocity of the two surfaces, the dynamic viscos-
ity of the fluid and the applied normal load [12]. In Fig. 2.7, the Stribeck curve is
shown, where µf is the coefficient of friction between two sliding surfaces, U is the
relative sliding velocity and W is the applied normal load per unit width. n1 and
n2 mark the approximate boundaries of different boundary lubrication regimes.

Figure 2.7: A Stribeck curve [12].

By assuming that the efficiencies in the pump are largely dependent on the lubrica-
tion conditions within the machine, and that the sliding velocity and applied nor-
mal force can be substituted by the pump rotational speed and pressure differential
respectively, the dimensionless Stribeck number (also known as the dimensionless
viscosity), is formed. The Stribeck number is defined as [13]:

15



2. Theory

Stribeck number = µω

∆p (2.19)

where µ is the dynamic viscosity and ∆p is the pump static pressure increase.

By relating empirical efficiency data with the Stribeck number, it may be possible to
estimate an approximate general efficiency behavior of different types of positive dis-
placement machines, without designing and simulating a detailed pump. Previous
papers modelling efficiency of positive displacement machines utilizing the Stribeck
curve include [13], in which component efficiencies are correlated to the Stribeck
number for multiple gear pumps at differing operational conditions. In [12], a tribo-
logical approach is used to formulate a model of the mechanical efficiency of axial
piston pumps. The model contains coefficients which need to be evaluated using
empirical data. It is stressed that the model itself is not specifically applicable to
any one type of displacement pump, but can be used for different types of positive
displacement types given appropriate empirical data. In [14], the efficiency charac-
teristics of an axial piston motor is described by correlating experimental data to
the Stribeck number for different fluid viscosities.

2.4 Pump type theory
This section covers the theory regarding pump type selection and general descrip-
tions of relevant pump types for use in a jet engine main fuel system covered in this
thesis.

2.4.1 Specific diameter vs. specific speed diagrams
One way to assess the feasibility of different pump types is through the use of spe-
cific diameter versus specific speed diagrams. These diagrams contain contour plots
denoting expected regions suitable for different types of pumps, and their expected
operational efficiency. These diagrams may thus be used to get a general under-
standing of which types of pumps that are feasible for a certain application. Fig. 2.8
show efficiency contour plots for several types of hydraulic pumps.

Note that several other factors that cannot be included in a specific diameter ver-
sus specific speed diagram may affect the choice of pump type. This may include
absolute limitations on flow and head delivered by the pump, cost, weight, size,
reliability and so on. These factors are important to include in any consideration
regarding pump selection.

2.4.2 Pump type descriptions
Descriptions of different pump types used in this thesis, along with explanations for
their selection as applicable fuel system pumps is covered in the sections below.

16



2. Theory

Figure 2.8: A specific diameter vs. specific speed diagram showing different types
of pumps [15].

2.4.2.1 Pump type classifications

The pumps covered in this thesis can be placed into one of two categories; hydro-
static positive displacement pumps or hydrodynamic centrifugal pumps. Positive
displacement pumps impart a discrete pressure increase to the fluid by displacing
a fluid enclosed in a fixed volume. By forcing a flow relative to some system resis-
tance, the pressure of the fluid increases. The flow rate of a positive displacement
pump is therefore largely dependent on the volume of fluid that can be displaced
per unit of time [8]. Centrifugal pumps on the other hand continuously increase
the energy of the fluid through the use of a rotating impeller, which is subsequently
transformed into a pressure. The amount of flow that the pump is able to generate
is thus dependent on the pressure differential over the pump, and vice versa, as the
amount of energy that the impeller is able to impart on a given volume of fluid is
dependent on the flow rate through the pump [16].

The tolerances in positive displacement pumps are typically small, in order to min-
imize internal leakage of trapped fuel. However, some leakage is typically needed in
order lubricate sliding surfaces and thus limit wear. These small tolerances make
positive displacement type pumps vulnerable to vapor and contaminants in the
fluid, which typically does not affect centrifugal pumps to the same extent [3, 8].
Positive displacement pumps can supply useful pressure at both low and high rota-
tional speeds, and have the ability to reprime from completely dry conditions [8].
Centrifugal pumps are typically better suited than positive displacement pumps for
operation at high rotational speeds [17].

17



2. Theory

2.4.2.2 External gear pump

The external gear pump, is a type of positive displacement pump which impart a
displacement on a fluid by entrapping it in the voids between rotating gear teeth
and the pump casing. As the gear teeth interlock, the entrapped fluid is forced to
eject at the outlet. This causes the pressure to rise at the outlet to meet the system
resistance for the imparted flow. A gear pump typically consists of two gears, a driv-
ing gear driven by the pump’s input shaft, and a driven gear [8]. The main types
of internal leakage in a gear pump consist of the radial leakage and axial leakage.
The radial leakage consists of fluid passing over the gear teeth ridges, whereas the
axial leakage consist of fluid escaping back to the inlet at the contact surface of the
gear wheel sides and pump side plates. Fig. 2.9 show the operational principle of
the gear pump, as well as the main types of internal leakage expected in a gear pump.

Figure 2.9: Gear pump functional sketch [10].

Gear pumps have long been favored for use in the HP stage of jet engine fuel sys-
tems. This is due to its ability of supplying sufficiently pressurized fuel at low as
well as high rotational speeds. Another reason for the widespread adoption of gear
pumps is due to their simple design and benign failure modes, and thus safe oper-
ational characteristics. As the pump is worn, the leakages in the pump increase in
a predictable manner, over time degrading in capacity without any sudden failures
[8]. An external gear pump is also used in the RM12 engine fuel system HP stage.

As the external gear pump is a positive displacement machine, the amount of pres-
surized fluid supplied by the pump is largely dependent on the rotational speed
of the pump, with some variations due to leakage flows, which is affected by the
pressure differential and rotational speed of the pump. The gear pump head curve
can thus be idealized as an essentially straight line, with only minor variations in
flow with larger pressure variations, for a certain rotational speed. The efficiency
characteristics of gear pumps can typically be related to the Stribeck number, as

18



2. Theory

mentioned in Sec. 2.3.3. Fig. 2.10 is used here to illustrate how the gear pump
component efficiency curves typically behave and what efficiencies to expect.

Figure 2.10: Gear pump Stribeck-correlated efficiency values. Z is the dynamic
viscosity, N is the rotational speed (rad/s) and P is the pump differential pressure
[13].

However, as the efficiency correlations above all have been derived using hydraulic
oil as the pump fluid medium, the actual operation using jet fuel may prove sub-
stantially different. In [18], the tribological conditions of a gear pump using jet
fuel is modeled. It is found that the low viscosity of the fuel in combination with
tight tolerances needed to ensure good volumetric efficiency give rise to exceedingly
thin lubricating film layers at the submicrometer level. For this reason, the surface
roughness of the contact surfaces may impact the behavior of the pump. Further-
more, in [17] it is stated that a high rotational speed may negatively impact the
mechanical efficiency and thereby the total efficiency due to increased fluid and me-
chanical friction.

2.4.2.3 Axial swash plate piston pump

The axial swash plate piston pump is a variable displacement pump. The pump
contain pistons oriented in parallel and placed axisymmetrically around the pump
shaft axis. The piston cylinders are located in an axially rotating cylinder block
connected to the pump shaft. A piston reciprocates back and forth in each cylinder,
drawing in and expunging liquid once every full rotation. The pump cylinder block
is pushed against a stationary valve plate containing elongated port openings for
the inlet and outlet. The back end of the cylinders are allowed to slide against an
angled stationary swash plate controlling the reciprocating motion of the pistons.
By altering the swash plate angle α, the piston stroke length can be altered. This
allows for adjustment of the volume of displaced fluid relative the pump shaft ro-

19



2. Theory

tation. The amount of displaced fluid per unit time is thus dependent on both the
rotational speed of the shaft, as well as the swash plate angle α. The entire pump
is typically placed in a fluid-filled pump housing. Most commonly, the pump utilize
nine or seven pistons. An odd number is used in order to reduce the amplitude of
flow ripples [19]. A typical axial swash plate piston pump is shown in Fig. 2.11.

Figure 2.11: Cutaway axial swash plate piston pump schematic [12].

Axial piston pumps are able to supply high pressures while operating at high ef-
ficiencies compared to other displacement pumps. It is the most commonly used
pump type in aircraft hydraulic control systems, however the mechanical complex-
ity limits reliability in comparison to the other pump alternatives listed [19].

The axial piston pump has been utilized as a main fuel pump, but only to a lim-
ited extent, according to [3] and [8]. Furthermore, the authors’ of this thesis have
come across information stating that at least one version of the RM6 engine used
in the Saab 35 Draken fighter jet employed a dual variable axial piston pump MFP
configuration with a stated total efficiency of approximately 80% at maximum flow
and pressure. The dual configuration was most likely used to ensure safe operation
despite the high mechanical complexity and relatively low reliability of each pump.

A variable axial piston pump was used to model a variable flow fuel system in [1].
Since the axial piston pump is a positive displacement machine, the pump head and
efficiency curve behavior is similar to the previously discussed external gear pump.

2.4.2.4 Radial centrifugal pump

The radial centrifugal pump is a hydrodynamic type pump with a mean outflow di-
rection parallel to the radial plane relative the pump shaft axis. This type of pump
is used in the LP stage of the RM12 pumping system, paired with an inducer. The

20



2. Theory

radial centrifugal pump has the lowest specific speed of all the common centrifugal
pump types, as can be seen in Fig. 2.8. The centrifugal pump imparts kinetic en-
ergy to the flow by means of an impeller. The flow is collected into a volute at the
impeller periphery. The kinetic energy is subsequently transformed into a pressure
increase. Fig. 2.12 show the basic layout of a centrifugal pump.

Figure 2.12: Cutaway schematic layout of a general centrifugal pump [20].

The basic shapes of the pump head and efficiency curve for general centrifugal
pumps is shown in Fig. 2.13 as a function of specific speed. Note that ηopt, Hopt
represent the efficiency and head BEP, respectively. q∗ express the volumetric flow
rate through the pump, normalized for the flow at the BEP. The specific speed nq

is defined using rotational speed in RPM, volume flow in cubic meters per second
and head in meters, omitting the gravitational constant g.

A centrifugal pump typically requires a separate positive displacement pump for
priming the system at engine start up because of the poor head build up at low
speeds. It may be possible for a centrifugal pump to have self priming capabilities
in a variable speed system granted it can be spun at high speed [3].

2.4.2.5 Partial emission pump

The partial emission pump, also referred to as a forced vortex pump, Barske pump,
tangent pump, or Sundyne pump, is a type of low specific speed centrifugal pump.

21



2. Theory

Figure 2.13: General pump curves and efficiency curves for centrifugal pumps as a
function of specific speed [21].

22



2. Theory

Partial emission pumps are typically comprised of straight impeller blades enclosed
in a constant cross section housing, using one or more conical diffusers, which allow
for a simple and compact design. The straight radial blades are not subjected to any
considerable bending stress by the high centrifugal forces that are present. Addi-
tional advantageous design features of a partial emission pump include that there is
no need for any wear rings or labyrinth seals and the large clearances between blades
and housing decrease required manufacturing tolerances and thus reduce manufac-
turing cost [17, 23]. A visual representation of a partial emission pump can be seen
in Fig. 2.14. This pump design allows for high rotational speed and is capable of
delivering high head and small flow rates. The pump can thus be made to minimize
size and weight.

Figure 2.14: Cutaway schematic layout of a partial emission pump [22].

The pump curve of a partial emission pump is exceedingly flat with a sharp drop-off
close to the maximum flow rate [24]. Partial emission pumps operate at higher effi-
ciencies at lower specific speeds compared to conventional radial centrifugal pumps,
as can be observed in Fig. 2.8.

2.5 Flow rate control methods

Fuel pumps in A/C are typically sized based on three operating points; the ground
engine starting condition, in-flight windmill relight, and the worst-case conditions
for maximum thrust at sea level during takeoff [3]. This implies that the pump will
provide more fuel than the engine requires during other points of operation if the
flow is not limited.

This section describes methods that may be employed to control the amount of flow
delivered to the engine by a fuel pumping system.

23



2. Theory

2.5.1 Flow control by recirculation
Recirculation is a common way of limiting the amount of flow delivered to the com-
bustion chamber by a pump. As the flow delivered by the pump is dependent on
the rotational speed of the pump shaft, the excess fuel can be recirculated back to
the pump inlet, or alternatively back to the fuel tank. The RM12 fuel system uses
this method to limit the fuel delivered by the HP pump by recirculating excess fuel
back to the HP pump inlet, as mentioned in Sec. 2.1.2.2. While this method offers a
simple solution, it adversely affects the temperature increase, as the same fluid may
be passed through the pump several times, heating the fuel in the process. This
issue is especially significant when the rotational speed of the pump is high, and the
engine fuel demand is low, for example during descent. This temperature increase
thus limits the available cooling performance of the fuel. The total efficiency is
also affected, as the amount of fuel pressurized may be many times larger than the
amount of fuel actually used.

In this thesis, only recirculation back to the pump inlet is covered.

2.5.2 Flow control by variable displacement
The amount of fuel delivered can be set independently of the rotational speed of
the pump if a variable displacement pump is employed, for example the axial piston
pump covered in Sec. 2.4.2. This allows for exact control of the amount of fluid
delivered, while at the same time avoiding a decrease in efficiency and excessive
temperature rise. Possible downsides of these methods may include an increase in
mechanical complexity and a weight penalty.

2.5.3 Flow control by throttling
A throttle valve can be used to restrict the discharge flow produced by a hydro-
dynamic pump by increasing the system resistance. This can be visualized by in-
creasing the steepness of the system curve shown in Fig. 2.5, moving the point of
operation to the left. This results in decreased flow rate and increased pressure
build up upstream of the valve. This method offers a simple, lightweight method of
controlling the amount of fuel delivered to the engine at various operating points.
The throttle valve can be placed on the suction side of the pump, however this may
cause low inlet pressures and thus cavitation in the pump. For this reason, the
throttle valve is assumed to be placed after the pump outlet.

This method does however have downsides. By moving the point of operation to
the right, the fuel pressure is increased. This additional increase in pressure is es-
sentially wasted work. Furthermore, the throttling may move the point of operation
further away from the BEP.

24



2. Theory

2.5.4 Speed flow control
Speed flow control implies control by varying the pump shaft rotational speed inde-
pendent of the NH. This allows for precise control of the delivered flow, and may be
utilized with both hydrodynamic rotary and hydrostatic displacement pumps. The
main downside of this method originates from the need to use a variable speed trans-
mission or an electric engine powered by a generator in order to control the shaft
speed. This may significantly increase mechanical complexity, weight and decrease
the power transfer efficiency between engine rotor and pump shaft. According to one
of GKN’s experts in electrical systems, a general constant transmission efficiency for
mechanical systems can be assumed to be approximately 94 %, assuming a constant
gear ratio. Likewise, a variable speed electrical system can be assumed to have a
transmission efficiency of roughly 80 %, considering the combined efficiencies of the
generator, power electronics, and the electrical motor powering a pump shaft.

2.6 Fuel properties
In order to properly estimate the behavior of the fuel system, some knowledge of the
fuel properties is needed. The fuel used is assumed to be Jet A-1. Basic information
regarding important properties is covered in this section.

2.6.1 Density, viscosity and specific heat capacity
The density, viscosity and specific heat capacity of the fuel all vary depending on
the temperature and to a lesser extent pressure. The data used to estimate these
properties are derived from [25, 26].

As the fuel temperature is expected to be well below the critical temperature, and
since no vapour is assumed to be present in the liquid, the density, viscosity and
specific heat capacity is assumed to be adequately described using only temperature
correlations. The actual correlations used are described in Sec. 3.1.

2.6.2 Joule-Thomson coefficient
The Joule-Thomson coefficient, µJT , is defined as the rate of change of temperature
with respect to the pressure at a constant enthalpy, or:

µJT =
(
∂T

∂p

)
h

(2.20)

This coefficient is needed when estimating temperature changes over valves, assum-
ing the process can be considered adiabatic. The Joule-Thomson coefficient is also
needed when assessing which parts of the total temperature change through a pump

25



2. Theory

is due to pumping inefficiencies or simply the temperature change due to compres-
sion, as described in [27].

The Joule-Thomson coefficient can also be expressed in the following manner, ac-
cording to [28]:

µJT = 1
cp

T(∂V
∂T

)
p
− V

 (2.21)

where cp is the specific heat capacity at constant pressure, V is the specific volume,
and

(
∂V
∂T

)
p
is the coefficient of thermal expansion. By entering approximate values

into Eqn. 2.21, a negative value is obtained. This indicates that the fuel should
increase in temperature when expanded at constant enthalpy, for example when
expanded over a valve, and decrease in temperature when compressed at constant
enthalpy.

A correlation for the Joule-Thomson coefficient was established experimentally, as
described in Sec. 3.4.

26



3
Methods

3.1 Estimation of density, viscosity and specific
heat capacity

Two assumptions are made regarding the fuel properties.

• It is assumed that the LP stage is able to pressurize the fuel in such a manner
that no vapor is present due to cavitation.

• The fuel temperature should never approach the critical temperature of the
fuel.

Given these assumptions, pressure is assumed to have a negligible effect on the fuel
properties.

Multiple linear density vs. temperature correlations from multiple sources within the
span of -40 °C to 100 °C is listed in [25]. The source also contains older pressure vs.
temperature data. While the overall behavior of the fuel density with regards to the
temperature is similar in old and new data, the absolute values may differ somewhat,
as the fuel cut included in different fuel type specifications may have changed over
time. This data indicates that the density of jet fuel in general continues to vary in
a linear manner with the temperature beyond 100 °C, at least until a temperature
of 200 °C. Eqn. 3.1, obtained from [26], was used to approximate the density of Jet
A-1 fuel as a function of the temperature in °C.

ρ = −0.8111 · T [°C] + 814.1 [kg/m3] (3.1)

Similarly, the specific heat capacity at constant pressure was estimated using a
linear correlation. The linear correlations differ somewhat, however the correlation
in Eqn. 3.2 obtained from [25] is used, as it coincides well with data for Jet A-1 from
[26], and has a similar slope to other Jet A-1 data listed in [25]. The data used to
create the correlation range from about -10 °C to 160 °C.

cp = 0.00428 · T [K] + 0.723 [kJ/(kg·K)] (3.2)

The kinematic viscosity of jet fuel does not vary linearly with temperature, however
it should not be affected by pressure unless it approach the critical temperature as
stated in [25]. The kinematic viscosity is estimated using plot data from [26] in the

27



3. Methods

temperature range -17 °C to 144 °C.

The dynamic viscosity is estimated by multiplying the kinematic viscosity with the
estimated density. The extracted plot data used to calculate the kinematic viscosity
is shown in Fig. 3.1.

0 20 40 60 80 100 120 140
Fuel temperature [°C]

0.5

1

1.5

2

2.5

3

3.5

4

K
in

em
at

ic
 v

is
co

si
ty

 [m
m

2 /s
]

Kinematic viscosity vs. temperature

Figure 3.1: Extracted kinematic viscocity data for Jet A-1. Derived from [26].

3.2 Selection of model inputs
In order to estimate the behavior of the MFP, data derived using an engine per-
formance model is used. The data supplied by the performance model consists of
multiple engine values (e.g. pressures, temperatures, rotor speeds, mass flows) at
different operating points for several defined simulated flight missions. The simu-
lated flight missions are representative to typical flight data. The inputs to the MFP
model must thus be limited to the variables that can be supplied by the engine per-
formance model. Furthermore, the data supplied by the engine performance model
may be limited in range depending on what operational conditions it is evaluated
for. The range of data supplied by the performance model to the MFP model is
therefore investigated, as it may limit the amount of test data needed to create the
MFP model.

The necessary inputs to the MFP model given by the performance data is limited
to the weighted fuel main (WFM), weighted fuel reheat (WFR) and NH. WFM is
the mass flow rate to the main combustion chamber, and WFR is the mass flow
rate to the A/B. However, in order to describe the MFP behavior, the inlet pressure
and temperature, as well as the required MFP outlet fuel pressure and servo leakage
mass flow is needed.

While the required MFP outlet fuel pressure can be estimated based on the WFM

28



3. Methods

using data from uninstalled engine tests, the servo leakage flow rate as well as inlet
pressure and temperature is currently unavailable. These inputs therefore need to
be estimated when running the MFP model.

The operational limits of the inputs is covered in detail in Sec. 3.3.2.

3.3 Data collection
This section covers motivations and description of data collected from rig tests used
to formulate the model. A description of the test rig is also included.

3.3.1 Test rig description
A test rig normally used for acceptance testing of overhauled MFP units or serviced
MFP units was used to gather test data. An electric motor in the test rig will
drive the MFP at the desired rotational speed. In addition, valves in the rig are
used to control the volumetric flow rate and pressure levels in different parts of the
system. In this way, operating conditions can be set to mirror conditions present
during actual operation. The fluid used in the test rig flow in a closed loop. Fluid
is drawn from a large tank, passed through the MFP and a cooler and subsequently
returned to the tank. The cooler combined with the large volume of the tank en-
sure near constant MFP fluid inlet temperatures, however there is no possibility
of precisely controlling the MFP inlet temperature, and is thus dependent on the
ambient conditions. The test rig contain several sensors sampling several times per
second. This data includes rotational speed, pressure levels, volumetric flow rates
and temperatures in multiple areas of the system. For a schematic overview of the
test rig, see Fig. 3.2.

The test rig is specified to operate using MIL-C-7024 type II fuel system calibration
fluid. While no correlations of the property behavior was available other than den-
sity and viscosity at ambient conditions it is assumed that the properties of this fluid
closely resemble the properties of Jet A fuel in general. It was therefore assumed
that the data gathered using this fluid should be very similar to the hypothetical
data generated had Jet A-1 been used.

3.3.2 Formulation of test matrix
A test matrix was constructed for a custom rig test. The purpose of the custom rig
test was to gather steady state data at operational points not normally investigated.
This data was used, in addition with previously collected data from routine test rig
operation, as a basis for the MFP model. In order to construct a representable
test matrix, the operational limits of the input data was investigated. Since the
behavior of the MFP was to be investigated both with and without activated A/B,
the test data was segregated based on the presence of A/B activation. For the data

29



3. Methods

Figure 3.2: Functional schematic of the test rig. Pressure and flow sensors are
omitted from the image.

containing no A/B activation, test points were selected according to the first image
in Fig. 3.3. Effort was made to properly cover the entire operational area. Likewise,
the test points selected for the data with A/B activation can be seen in the second
image of Fig. 3.3. Here, a suitable WFR was selected based upon the chosen WFM.
Correlations for the maximum and minimumWFR and WFM values was established
for the relevant range in NH. Linear interpolation between maximum and minimum
WFM, given a chosen test WFM was used to predict a suitable WFR value. This
was done in order to cover the majority of the operational area with as few test
points as possible. Thus, each single green point (WFM) in the second image of
Fig. 3.3 correspond to a single yellow point (WFR) for every test point. Notice that
the mass flow rate on the y-axis has been normalized, in this case by the maxi-
mum inlet mass flow present in the data supplied by the performance model. The
rotational speed is given as a percentage of NH. In total 26 test points were selected.

60 70 80 90 100

NH [%]

0

0.05

0.1

0.15

0.2

0.25

0.3

N
or

m
al

iz
ed

 m
as

s 
flo

w
 r

at
e

Test points w/o A/B (17 test points)

WFM
WFM

test

86 88 90 92 94 96 98

NH [%]

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

N
or

m
al

iz
ed

 m
as

s 
flo

w
 r

at
e

Test points with A/B (9 test points)

WFM
WFR
WFM

test

WFR
test

Figure 3.3: Visualization of test matrix selection of NH, WFM and WFR, with and
without A/B flow.

A suitable outlet pressure was selected based on the WFM using a correlation de-

30



3. Methods

rived from uninstalled engine tests. The normalized correlation is shown in Fig. 3.4
for illustrative purposes.

W
FM m

in

W
FM m

ax

WFM

0

P
max

H
P

 o
ut

le
t p

re
ss

ur
e

Outlet pressure correlation

Figure 3.4: Normalized outlet pressure correlation.

As the temperature between the LP and HP stages was needed in order to establish
efficiencies, a small amount of fluid was allowed to exit through the A/B outlet at
test points defined at no A/B activation. This was done to avoid stagnant fluid at
the temperature sensor placed in the A/B channel, therefore ensuring an accurate
temperature measurement after the LP pump and fuel filter. Furthermore, since
there is no temperature sensor in the servo flow channel, the servo flow channel
valve was completely closed so as to not introduce uncertainties in the temperature
measurement of the fluid entering the LP pump.

3.3.3 Description of collected data
In total, 26 test points were evaluated in the test rig. Each test point was run until
no noticeable temperature change was perceived in the A/B channel temperature
sensor, to ensure steady state conditions. This resulted in an approximate mean
runtime of 2 minutes per test point.

Due to limitations in the test rig, the HP stage outlet pressure could not be set to
desired levels at some operating points. Specifically, the pressure at low flow condi-
tions could not be set sufficiently low. Furthermore, some temperature change was
still present for some test points at temperature sensors located in the HP region of
the MFP.

Temperature, volume flow rate and pressure data was collected for the test points
at all available sensor locations of the system. By studying the temperatures and

31



3. Methods

volume flow rates in the oil cooling loop connected to the pump bearings, it was
determined that the heat energy leaving the system was negligible compared to the
heat energy supplied to the fuel.

3.4 Identification of Joule-Thomson coefficient
A correlation for the Joule-Thomson coefficient was established using the temper-
ature and pressure measurements upstream and downstream of the bypass valve,
assuming adiabatic expansion at data points deemed steady state from the custom
rig test. The result can be seen in Fig. 3.5.

30 40 50 60 70 80

Valve inlet temperature [°C]

-8

-7

-6

-5

-4

-3

-2

-1

0

JT
 [
°C

/P
a]

10-7 Joule-Thomson coefficient estimation

Data points
Linear regression

Figure 3.5: Estimation of the Joule-Thomson coefficient function using linear re-
gression, expressed as a function of the inlet temperature at the bypass valve.

The value of the Joule-Thomson coefficient is negative as expected. The linear
regression equation is shown in Eqn. 3.3.

µJT = (2.5972E − 9) · Tinlet[°C]− 5.2027E − 7 [°C/Pa] (3.3)

3.5 Identification of LP stage head and efficiency
curve

To define the LP-stage behavior, work was conducted to express the LP pump and
filter dimensionless head and total efficiency curves, assuming fully turbulent flow

32



3. Methods

and dynamic similarity at all operational points.

The efficiency was estimated at the steady state data points gathered from the cus-
tom rig test using Eqn. 2.9. Having defined an expression for the Joule-Thomson
coefficient, the estimated temperature change due to compression could be removed
from the total temperature change over the LP stage (∆Tpump = ∆Ttotal−∆Tcompression).
The temperature change used to calculate the total efficiency of the LP stage could
thus be estimated using only the estimated temperature rise due to pumping inef-
ficiencies. Similarly, a head coefficient curve was created. In this case, data from
routine operation was used, as it contained a greater amount of steady state data.

Fig. 3.6 shows the estimated head coefficient and efficiency curves as a function of
the flow coefficient, using rotational speed in rotations per second.

0
max

Flow coefficient 

0

max

H
ea

d 
co

ef
fic

ie
nt

 

0%

5%

10%

15%

20%

25%

30%

35%

40%
LP stage pump curves

Figure 3.6: LP stage pump curves with data points.

3.6 Identification of HP stage volumetric efficiency
Due to the limitations in the test rig described in Sec. 3.3.3, it was not possible to
accurately describe the total efficiency of the HP pump using only temperature and
pressure measurements. However, since the ideal displacement per rotation of the
gear pump was known, it was possible to create an estimation of the volumetric ef-
ficiency based on volume flow rate measurements at different rotational speeds from
data collected from the custom rig test, as well as data generated during routine op-
eration. By relating the HP pump efficiency to the Stribeck number the correlation
shown in Fig. 3.7 was created. Note that the estimated volumetric efficiency points

33



3. Methods

0 max
Stribeck number

0

0.2

0.4

0.6

0.8

1

v

HP pump volumetric efficiency

Data points
Estimated function

Figure 3.7: HP stage volumetric efficiency.

closely adhere to the typical volumetric efficiency curve shape as described in [13].

3.7 RM12 state estimator formulation
A state estimator for the RM12 was created using MATLAB. A functional flow chart
of the script can be seen in Fig. 3.8.

The code uses WFM, WFR, and NH as specified by a performance model, as well
as estimations of inlet pressure, temperature and servo leakage mass flow as inputs.
The script operates iteratively until the temperatures in the system converge. First,
pressures and volume flow rates are estimated. These estimations are subsequently
used in combination with efficiency models to estimate temperatures in the system.
As the temperatures changes, fuel, pump, and valve behavior changes. The code
must therefore iterate in order to update both pressures and temperatures as their
behaviors are coupled.

3.7.1 Calibration of model using HP total efficiency
As the total efficiency of the HP stage gear pump could not be evaluated using data
derived from the custom rig test, uninstalled engine test data was instead used to
calibrate the gear pump total efficiency. The data contained values such as WFM,
WFR, NH, inlet temperatures and pressures as well as temperatures and pressures
at both A/B and main outlets. However, an estimation of the servo leakage mass

34



3. Methods

START
Input: NH, WFM, WFR, Pin, 

Tin, servo mass flow rate

Initiate with uniform 
temperature in the entire 

system

Determine system flow rates
and pressures

Calculate flow through HP 
pump using volumetric 

efficiency and NH

Use mass balance after HP 
pump outlet to estimate 

bypass flow

Estimate LP mass flow rate 
assuming mass balance at 

inlets and outlets

Update temperatures

Use LP pump curve to 
estimate fuel 

temperature at LP 
outlet

Use HP pump curves to 
estimate fuel 

temperature after HP 
stage, in the bypass and  

servo channels

Estimate temperature at 
HP pump inlet due to 

mixing of fuel from 
bypass and LP stage 

Check for convergence

Yes No

Return 
system state

New 
iteration

Estimate HP outlet pressure 
using WFM correlation

Estimate LP outlet/HP inlet 
pressure using LP pump 

curve, volume flow, NH, Pin

1

2

3

4

5

6

7

8

9

10

Estimate new 
temperature before LP 
stage due to mixing of 
servo and inlet flows

11

Figure 3.8: State estimator code flow chart.

flow rate was based on ABC and MFC specifications as it was not included in the
engine test data.

The state estimator model was calibrated using the uninstalled engine test data as
inputs. By matching the derived outlet temperatures to the outlet temperatures
supplied by the engine model, using the HP gear pump mechanical efficiency, the
total efficiency could be estimated for each point. In total 20 test data points were
used.

It was found that when the points were plotted against the Stribeck number, the
mechanical and total efficiency did not follow the typical function shape as described
in [13]. Instead, the pressure differential and the rotational speed of the pump was
found to be a better measure for correlating the efficiency. An estimated curve of
the total efficiency curve as a function of the differential pressure times the rota-
tional speed of the pump (in radians per second) was established by simply drawing
straight lines between points. The data points and total efficiency estimation curve
is shown in Fig. 3.9. Note that while most points are placed in close proximity to the
line, four points in the right side of the image are placed considerably further away.
These lines corresponds to high engine flows, with and without A/B activation, and
thus a small amount of bypass flow. The estimation line was placed in between these
points in an effort to avoid overfitting. While these points are placed relatively far
away from the estimated curve, the resulting outlet temperatures using the esti-
mated curve are within 2 °C of the outlet temperature supplied by the uninstalled
engine data at these points. Possible explanations for the efficiency behavior of the
HP stage gear pump are discussed in Sec. 5.3.

35



3. Methods

min max
( p)

0.35

0.4

0.45

0.5

0.55

0.6

tot

HP pump total efficiency

Data points
Estimated curve

Figure 3.9: HP stage total efficiency.

3.8 Selection and implementation of alternative
MFP architectures

Having established a model for the baseline RM12 system, 3 alternative systems
were selected for implementation. The selected systems are described in this section,
along with brief motivations for their selection. Descriptions of their implementa-
tions in code as well as a brief comparison of characteristics is discussed.

3.8.1 System with centrifugal HP stage pump
By replacing the HP gear pump with a centrifugal pump rotating at a higher speed
and controlling the flow with a throttle valve, it may be possible to decrease the total
weight of the system, as the pump diameter can be made considerably smaller at
higher rotational speeds. A maximum pump shaft rotational speed of 30 000 RPM
was estimated using information from [17]. As the pumps need to be able to sup-
ply adequate pressure at the maximum engine flow, the pressure and flow required
at this operational point was used to calculate the specific speed of the HP pump
stage. The estimated specific speed, using the same definition as shown in Fig. 2.8
was estimated to be about 16. This number indicates that a partial emission pump
can be used. However, if two stages are used the specific speed for each stage is
approximately 27. This number indicates that a dual-stage radial centrifugal pump
can be used at a much smaller specific diameter. As more data is available on the
behavior of conventional radial centrifugal pumps it was decided to use a two stage

36



3. Methods

radial centrifugal pump. A maximum total efficiency of 50% was assumed based on
Fig. 2.8. Pump curve shapes were estimated using pump curves shown in Fig. 2.13.
The BEP was assumed to be located at maximum engine flow and pressure. The
resulting estimated dimensionless pump curves can be seen in Fig. 3.10.

0
max

Flow coefficient 

0

max

H
ea

d 
co

ef
fic

ie
nt

 

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

55%
Centrifugal HP pump curves

Figure 3.10: Dimensionless centrifugal HP pump curves.

In essence, this alternative system uses the baseline centrifugal RM12 low pressure
stage with a separate high speed shaft driving a dual-stage centrifugal HP pump.
As this system does not utilize a displacement pump in the MFP, the rotational
speed can be increased, however a separate smaller displacement pump needs to
be used in order to prime and supply sufficient flow and pressure at low rotational
speeds. However, if fuel is used as hydraulic fluid on engine actuation systems, it
may be possible to use a single pump for both actuation and priming purposes,
thereby reducing the potential weight penalty needed to ensure low rotational speed
function. Additionally the use of centrifugal pumps instead of displacement pumps
avoid the use of metal-to-metal contact surfaces, which may increase component life
expectancy and thereby reduce operational cost.

This alternative was implemented similarly to the RM12 system, with some minor
differences. The volumetric flow to the engine was simply set to match the engine
requirement, and the additional pressure generated at this point was expanded af-
ter the pump to the pressure required by the engine. The bypass channel was also
removed.

37



3. Methods

3.8.2 System with axial piston HP stage pump
Another concept utilize a variable axial piston pump instead of a gear pump in the
high pressure stage of the baseline RM12 system. The piston pump is assumed to
rotate at the same rotational speed as the baseline HP pump. By using this type of
pump the flow and pressure to the engine can be set to match the engine requirement
without the use of a bypass or throttle valve, at the cost of increased mechanical
complexity, and possibly a slight increase in weight. The increase in mechanical
complexity may increase cost and reduce reliability.

In order to create an estimation of the total efficiency of the axial piston pump,
open total efficiency data was collected from a multitude of axial piston pumps us-
ing catalogues published by the pump manufacturer Parker [29, 30]. Estimations of
the efficiency behavior depending on the Stribeck number was established for this
data. It was assumed that the maximum total efficiency should not rise beyond 80%.
A basic estimation of the total efficiency curve was created using the same equa-
tion form as shown in [14]. The equation was altered to peak at a total efficiency
of 80%, with a downward slope similar to the data gathered from [29] and [30].
The peak efficiency point was placed at a Stribeck number roughly in between the
points of peak efficiency given by the data points derived from the catalogues and
the empirically determined curve for the piston motor derived in [14]. The resulting
total efficiency curve and data extracted from the catalogues can be seen in Fig. 3.11.

0 0.5 1 1.5 2
Stribeck number 10-6

0

0.2

0.4

0.6

0.8

1

tot

Axial piston pump total efficiency

Catalogue data
Piston motor
Estimated curve

Figure 3.11: Axial piston pump total efficiency.

The axial piston pump was implemented in a similar way to the previously described
centrifugal HP pump system, however no throttling valve was used as the generated

38



3. Methods

pressure and flow should match the required engine conditions.

3.8.3 Electrically driven system with centrifugal stages
The final concept controls the flow by changing the speed of the pump. In this
case, an electrical system is used to power the pumping system at speeds up to 30
000 RPM. The concept utilizes centrifugal pumps at both the LP and HP stages,
mounted on a common shaft. The HP pump is identical to the HP centrifugal pump
described in Sec. 3.8.1 as the maximum pressure, flow and rotational speed are the
same in both concepts. The LP stage uses pump curves derived in a similar manner
as the HP centrifugal pump. The result can be seen in Fig. 3.12. Note that this
curve is a general description. A fuel filter is not included in this curve, and thus
for an actual case the pump curve behavior would be somewhat different.

0
max

Flow coefficient 

0

max

H
ea

d 
co

ef
fic

ie
nt

 

0%

10%

20%

30%

40%

50%

60%

70%

80%

Electric LP stage pump curves

Figure 3.12: Dimensionless electrically driven centrifugal LP stage pump curves.

In this case a specific speed of about 140 (using the same definition as shown in
Fig. 2.8) was derived, assuming maximum pressure at maximum flow, also placing
the BEP at that point. By changing the pump shaft rotational speed, the pumps
can be set to directly generate the required flow and pressure, avoiding losses in
efficiency due to excess pressure buildup. As the pump shaft rotational speed can
be controlled independently of the NH, the centrifugal pumps are able to supply
sufficient pressure even at low NH. There is also a possibility that the centrifugal
stages may be able to prime the system. Because of these reasons, it may be possi-
ble to disregard the use of a displacement pump for starting and priming purposes.
Possible system downsides include increased weight, cost, and possibly reliability, as

39



3. Methods

a result of the use of power electronics.

The implementation of this concept closely matches the implementation of the pre-
vious system with a centrifugal HP stage pump, however for each input operational
point an iterative method (Newton’s method) is used to estimate the rotational
speed needed to precisely match the engine requirement at the HP pump outlet.

40



4
Results

4.1 Comparison of fuel systems configurations
When comparing fuel systems configurations, three key flight operating points are
of interest: flight idle (FI), intermediate rated power (IRP), and maximum A/B
thrust (MT). FI refers to the minimum thrust the engine can maintain in flight to
keep the aircraft operational. FI conditions typically occur at A/C speed reduction
and descent. IRP refers to maximum engine thrust without A/B activation. MT
refers to maximum engine thrust with A/B activation.

Descriptions of the four different system configurations investigated are presented
in Tab. 4.1. These are the same systems described in Sec. 3.8 as well as the baseline
RM12 system. Brief descriptions are included along with a numbering system used
for clarity.

Table 4.1: Fuel system numbering description.

System 1 Mechanically driven radial centrifugal LP pump and external
gear HP pump with bypass (baseline RM12)

System 2 Mechanically driven radial centrifugal LP pump and axial
swash plate piston HP pump w/o bypass

System 3 Mechanically driven radial centrifugal LP pump and double
stage radial centrifugal HP pump with throttle valve

System 4 Electrically driven radial centrifugal LP pump and
double stage radial centrifugal HP pump

System 1, System 2, and System 4 utilize a single shaft to drive both the LP and
HP pumps. System 3 utilize two separate shafts to drive the LP and HP pumps
respectively.

Plots of the MFP power usage, fuel temperature rise, driving energy, and cooling
capacity comparisons between the four fuel system configurations are shown in this
section. Furthermore, scatter plots relating volumetric bypass ratio to temperature
increase, engine volumetric flow to throttle valve pressure levels, engine volumetric
bypass ratio to pump shaft rotational speed and LP vs. HP temperature rise are
presented.

41



4. Results

All data presented in this section have been calculated assuming an inlet tempera-
ture of 42 °C, inlet pressure of 1 bar, and a constant servo leakage mass flow.

4.1.1 Power usage
Achieving a lower pump power usage is desirable, as all power consumption not
transformed to useful hydraulic work (i.e. required flow at required pressure level)
is considered a waste. Several power uses add to the total wasted work performed
by the pump.

• Individual pump inefficiencies.

• Recirculation of fuel.

• Throttling of excess pressure.

• Efficiency of HP rotor to pump shaft power transmission

In Fig. 4.1, 4.2, and 4.3, each bar is adjusted with a corresponding transmission
efficiency to obtain the corrected power extracted from the HP rotor to power the
pumps. The horizontal line marked "useful power" denotes the pressure work be-
tween MFP inlet and outlets, including the outlet leading to the A/B, as well as
the pressure work used in the servo channel. The derived useful power differs at
most by 5 % between different systems. A single line denoting the mean value de-
rived for all systems is therefore used, as it proved unhelpful to present several values.

4.1.2 Fuel temperature rise
The fuel temperature rise across a MFP is calculated by subtracting the main outlet
temperature by the inlet temperature. This temperature rise is an indication of the
system efficiency, as it correlates with work losses. Additionally, achieving a lower
fuel temperature rise is desirable since the fuel can be used as a heat sink in later
stages of the fuel system. The maximum fuel temperature rise for the 4 compared
fuel systems are presented in Fig. 4.4.

4.1.3 Driving energy
A fuel system’s driving energy is a measure of the total work extracted from the HP
rotor to drive the MFP and indicates the pump total power use during a mission,
and subsequently provides an indication of the effect on the SFC, ignoring additional
factors such as added weight. The driving energy shown in Fig. 4.5 is calculated as
a time integral of the power removed from the HP rotor over all missions included
in the performance model. The plot is normalized by the driving energy of System 1.

42



4. Results

Power usage at flight idle

System 1 System 2 System 3 System 4
0

0.2

0.4

0.6

0.8

1

1.2

1.4
P

ow
er

 u
sa

ge
 n

or
m

al
iz

ed
 b

y 
S

ys
te

m
 1

Useful power

Figure 4.1: Bar plot of the MFP power usage at flight idle.

Power usage at intermediate rated power

System 1 System 2 System 3 System 4
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

P
ow

er
 u

sa
ge

 n
or

m
al

iz
ed

 b
y 

S
ys

te
m

 1

Useful power

Figure 4.2: Bar plot of the MFP power usage at intermediate rated power.

43



4. Results

Power usage at max A/B thrust

System 1 System 2 System 3 System 4
0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1
P

ow
er

 u
sa

ge
 n

or
m

al
iz

ed
 b

y 
S

ys
te

m
 1

Useful power

Figure 4.3: Bar plot of the MFP power usage at maximum A/B thrust.

Maximum fuel temperature rise at flight idle

System 1 System 2 System 3 System 4
0

10

20

30

40

50

60

70

80

90

T
 [°

C
]

Figure 4.4: Bar plot of the fuel temperature rise over the MFP at flight idle.

44



4. Results

MFP driving energy usage, nomalized

System 1 System 2 System 3 System 4
0

0.2

0.4

0.6

0.8

1

1.2
D

riv
in

g 
en

er
gy

 u
sa

ge
 n

or
m

al
iz

ed
 b

y 
S

ys
te

m
 1 Useful energy

Figure 4.5: Bar plot of average MFP driving energy.

4.1.4 Cooling capacity

A fuel system’s cooling capacity is a measure of a system’s ability to act as a heat
sink. The maximum allowed temperature the fuel can reach within a fuel system is
assumed to be 150 °C. The cooling power available is calculated as in Eqn. 4.1.

Q̇ = ṁcp(Tmax − T ) (4.1)

Where ṁ is the outlet mass flow, T and Tmax is the outlet and maximum fuel tem-
perature respectively. cp is the fuel specific heat capacity, estimated as the average
of the specific heat capacities evaluated at the outlet temperature and maximum
temperature. Fig. 4.6 show the available cooling capacity of the fuel for each fuel
system calculated as an integral of the cooling power over all flight conditions. The
bars are normalized by the cooling capacity of System 1.

4.1.5 Temperature rise due to bypass ratio

The image shown in Fig. 4.7 is included to illustrate the clear connection between
bypass ratio and temperature increase in System 1.

45



4. Results

Cooling capacity, normalized

System 1 System 2 System 3 System 4
0

0.2

0.4

0.6

0.8

1

1.2
C

oo
lin

g 
ca

pa
ci

ty
 n

or
m

al
iz

ed
 b

y 
S

ys
te

m
 1

Figure 4.6: Bar plot of cooling capacity. Normalized by System 1.

0 5 10 15

Volume flow ratio Q
bypass

/Q
engine

5

10

15

20

25

30

35

40

45

50

55

T
 [
°C

]

Bypass ratio temperature increase

Figure 4.7: Scatter plot relating volumetric bypass ratio and temperature rise in
System 1.

46



4. Results

4.1.6 RM12 modeled LP vs. HP stage temperature rise

The temperature rise in the LP vs. the HP stage for the baseline System 1 can be
seen in Fig. 4.8. This is included to demonstrate how the LP stage affect the total
temperature increase depending on the bypass ratio. A value above 0.5 on the y-axis
indicates a majority of the temperature increase comes from the LP stage. Addi-
tionally, 3 distinct lines can be seen. The decrease in temperature ratio corresponds
to an increase in A/B fuel flow.

0 5 10 15

Volumetric flow ratio Q
bypass

/Q
engine

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

T
LP

 / 
(

T
LP

+
T

H
P

)

LP vs. HP temperature rise ratio

Figure 4.8: LP vs. HP stage temperature increase ratio as a function of the volu-
metric bypass ratio in System 1.

4.1.7 Throttle valve pressures

In Fig. 4.9 the pressure levels on both sides of the throttle valve, that is the generated
pressure and the required engine pressure is shown as a function of the volumetric
engine flow. The difference between the generated pressure and the pressure re-
quired by the system is essentially wasted energy, which helps explain why System
3 exhibits a poor overall efficiency at low engine fuel flows.

47



4. Results

0 Q
max

Engine volumetric flow

0

P
max

P
re

ss
ur

e

Throttle valve pressure levels

Engine system curve
Generated pressure

Figure 4.9: Pressure levels before and after the throttle valve in System 3.

4.1.8 Electric speed control
In contrast to System 3, System 4 change the rotational speed of the pump shaft in
order to match the engine requirements. Fig. 4.10 shows how the rotational speed
changes depending on the engine volumetric flow requirement. The NH is also shown
as a percentage of the maximum speed. Note that at low engine volumetric flows,
the electrically driven pump spins at about one third of the maximum rotational
speed, whereas a pump using a mechanical transmission and constant gear ratio
would spin at about 70 % of the maximum speed.

4.2 Further comparison of fuel system character-
istics

To further evaluate one A/C fuel system against another, an extended comparison
must consider factors such as penalties of adding weight to a system, reliability
problems, cost, and more. Tab. 4.2 presents a brief and estimated comparison of the
systems based of these parameters alone. Further studies has to be done in this area.

Cells containing a "0" indicate no change compared to System 1. Cells containing a
"+" indicate better results than System 1 (e.g., a "+" in weight implies a lighter sys-
tem). Cells containing a "-" indicate worse results than System 1. Multiple symbols

48



4. Results

Table 4.2: Further comparison of fuel system characteristics.

Weight Reliability Cost
System 1 0 0 0
System 2 - - - -
System 3 + ≈ 0 ≈ 0
System 4 - - - - -

within a cell suggest a greater degree of improvement or decline relative to System 1.

0 Q
max

Engine volumetric flow

0

0.5

1

1.5

2

2.5

3

P
um

p 
sh

af
t r

ot
at

io
na

l s
pe

ed
 [R

P
M

]

104

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

N
H

Electric MFP speed control

Figure 4.10: Pump shaft speed vs. volumetric flow delivered to the engine for System
4.

49



4. Results

50



5
Discussion

5.1 Discussion of results
This section contains a brief discussion of the results along with important con-
siderations regarding the interpretation of the results, including discrepancies that
may affect the results. Test rig limitations and a discussion of the gear pump total
efficiency behavior are included. Lastly, possible future work aiming to improve the
models are covered.

5.1.1 General findings
Regarding the power usage, System 1 was surpassed by all other systems at IRP
and MT, and placed second to last in power usage during FI as can be seen in
Fig. 4.1, 4.2, and 4.3. The overall high power usage was expected as a bypass was
used to meter the flow. What was not expected, however, was that while the total
temperature rise in the system seems to increase with the bypass ratio as can be
seen in Fig. 4.7, a majority of the temperature rise during high bypass ratios seems
to originate in the LP stage of the MFP, as can be seen in Fig. 4.8. This is due to a
low LP stage efficiency at low flow coefficients, coupled with a low volumetric flow
rate.

System 3 had a greater power usage than System 1, but only at FI. This is most
likely due to an excess pressure buildup at low engine volumetric flows as can be
seen in Fig. 4.9. While the driving energy for System 3 was lower than System 1 at
IRP and MT, System 3 still required the highest required driving energy over the
entire mission, as can be seen in Fig. 4.5. As throttling of the excess pressure lead
to a temperature increase, coupled with low centrifugal pump efficiencies at low flow
coefficients, System 3 also gave rise to the highest temperature increase at FI. It is
however important to note that due to the assumptions and simplifications made in
establishing the pump curve behavior of the system, it might be possible to decrease
both the temperature rise and power use in the system, by designing pumps with a
flatter pump curve (for example by using a partial emission pump in the HP stage),
or by placing the BEP further to the left on the pump curves.

System 2 and System 4 both had a superior performance compared to System 1 and
System 3. Especially notable for System 4 is the low power usage and temperature
increase at FI, as can be seen in Fig. 4.1 and 4.4. This effect can be explained by
the ability to control the speed to match the engine requirements. It can be seen in

51



5. Discussion

Fig. 4.10, that the pump rotational speed changes in a manner unlike the change in
NH.

While the temperature rise between different systems are large at FI, the overall
cooling capacity for a typical mission was similar for all systems, as seen in Fig. 4.6.
The differences between the different systems will be larger if the maximum allowed
temperature is lowered and/or the inlet temperature is higher if a specific mission
need to operate at FI for an extended time period.

If a decrease in temperature rise and power use is deemed important enough to
warrant the selection of a new MFP, System 2 and System 4 are most likely superior.
However, as can be seen in Fig. 4.2, System 2 is assumed to have a lower reliability,
which needs to be addressed before it can be considered as a viable option. Likewise,
System 4 is likely heavier due to the additional electric components. In order for this
system to be viable, the weight needs to be reduced. This issue might be mitigated
if there is already a need to include a large generator in the aircraft, allowing a
reduction of the additional weight imposed by the MFP. Furthermore, as System 4
is not driven mechanically it can be placed in the aircraft with greater freedom.

5.1.2 Discrepancies affecting result
As mentioned in Sec. 3.3.3, the mean run time of each test point in the test rig was
approximately 2 minutes. Having analyzed the collected data, the HP outlet fuel
and bypass temperature was confirmed to having not reached a completely steady
state for most test points. This was compounded by the inability to set a repre-
sentative outlet pressure due to limitations in the test rig. In order to create a
model, uninstalled engine test data was used to calibrate the total efficiency of the
HP gear pump, with assumed servo flow mass flow rate, temperature behaviors, and
fuel properties etc. Discrepancies between the assumpti