jet engine fuel system integration in aircraft environment...

INTRODUCTIONFuel pressure surge is an essential topic for modern aircraft and a main driver for airframe fuel system sizing. This phenomenon can occur both during normal and abnormal operations, notably resulting from a sudden change of fluid velocity due to the opening or closure of an engine valve.

During aircraft development phase, Airbus specifies to engine manufacturers a pressure limit at the interface between the engine and airframe based on aircraft fuel system qualification. The verification activities performed by engine manufacturers shall then ensure that the maximum pressure surge will not exceed this requirement.

The purpose of this paper is to present a methodology for accurate prediction of fuel pressure surge on an engine-aircraft integrated environment at early program stage in order to mitigate the risk associated with fuel pressure surge during aircraft development, avoid late airframe fuel system redesign and secure the aircraft entry-into-service.

1. PROJECT OVERVIEW

1.1. ScopeThe area of study is the integration of an engine fuel system with its aircraft environment.

The aircraft engine feed fuel system is generally composed of:

• Boost pumps that pressurize fuel up to the engine inlet • Fuel hydraulic valves (LPSOV, TRV)

The engine fuel system is generally composed of:

• A two stage- pump with a low pressure and a high pressure part

• A Fuel Oil Heat Exchanger (FOHE) that cools the engine oil circuit

• A main fuel filter that prevents fuel contamination • A fuel metering valve that regulates the flow into the

combustion chamber according to the engine thrust power demand

• A High Pressure Shut Off Valve (HPSOV) that shuts down the engine when it stops the flow into the combustion chamber

Jet Engine Fuel System Integration in Aircraft Environment - Methodology for Pressure Surge Simulation through Model-Based

System Engineering

Matthieu HutchisonAirbus Operations SAS

Grégoire Lenoble and Umberto BadialiSiemens PLM Software

Yannick Sommerer, Olivier Verseux, and Eric DesmetAirbus Operations SAS

ABSTRACTAn Airbus methodology for the assessment of accurate fuel pressure surge at early program stages in the complete aircraft and engine environment based on joint collaboration with LMS Engineering is presented. The aim is to comfort the prediction of the fuel pressure spike generated by an engine shutdown in order to avoid late airframe fuel system redesign and secure the aircraft entry-into-service.

CITATION: Hutchison, M., Lenoble, G., Badiali, U., Sommerer, Y. et al., "Jet Engine Fuel System Integration in Aircraft Environment - Methodology for Pressure Surge Simulation through Model-Based System Engineering," SAE Int. J. Aerosp. 7(1):2014, doi:10.4271/2014-01-2135.

2014-01-2135Published 09/16/2014

Copyright © 2014 SAE Internationaldoi:10.4271/2014-01-2135

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Downloaded from SAE International by Gregoire Lenoble, Monday, September 01, 2014

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• Servo valves that support engine performance and power actuators with pressurized fuel.

Figure 1. Aircraft-Engine Typical Fuel System Schematic

Water hammer or pressure surge is defined as the change in pressure, either above or below the normal pressure, caused by a variation of the flow rate in a pipe. The flow rate in the pipe can vary due to valve either closure or opening. These pressure surges are propagated along the pipeline from the source (valve) to the constant pressure boundary (tank).

Fuel pressure surge phenomena in the engine feed line are mainly linked to transient phenomena that could occur during normal or abnormal fuel system operation. The main physical phenomenon causing a surge is the closure of a valve such as the engine HPSOV at high engine power conditions.

1.2. Verification and Validation ProcessPart of the engine requirements specified by Airbus to the engine manufacturer is the maximum allowable pressure surge level caused by engine valve activation, as measured at the engine fuel system inlet. The engine manufacturer shall ensure through a verification and validation process that in every operating condition the pressure level will be within the requirements specified by Airbus. The worst case condition in terms of pressure surge is defined with maximum engine speed and cold de-aerated fuel (see part 2).

Generally this V&V process is divided in a modelling and a test bench phase that are performed at engine manufacturer facilities followed by an actual aircraft flight test campaign. This engine manufacturer process is performed soon in the aircraft program development. During these phases, the engine fuel system is fully representative, whereas the aircraft part is generally not fully characterized at this stage of the program.

Based on Airbus experience, the engine manufacturer fuel spike predictions run non negligible risk of showing significant discrepancy versus test data from the Airbus test aircraft. These inaccuracies raise an aircraft program risk that can only

be mitigated using requalification or redesign and formerly be closed with test aircraft campaign which is late in the program development.

After a deep analysis of the surge phenomenon, it has been pointed out that the pressure surge risk could be mitigated early in a program development by supporting the engine manufacturer V&V and providing simple airframe fuel system characteristics that impact the fuel surge level behavior.

2. PRESSURE SURGE MODELINGLMS Imagine.Lab Amesim is a graphical software package that enables the modelling, simulation and analysis of multi-physic mechatronic systems; both under steady state and fast dynamic conditions. Such systems are modelled as a collection of C code based components that are connected by the user on a sketch. Component behaviour relies on analytical equations or tabulated models -as chosen by the user- thereby allowing for 0D to 1D system analysis. Each component is specified so as to exchange both flux and effort variables at its ports, which ensures energy conservation at system level (Bond-Graph theory [R 1]). The resulting system model is non-linear space and state function, solved by a solver that automatically chooses the most relevant algorithms as a function of the system numerical stiffness.

Part 2 of this paper summarizes the investigation performed by Airbus and LMS Engineering towards a theoretical analysis of the pressure surge phenomenon. This is based on a simplistic and generic system layout, illustrated with Figure 2, which includes a fuel tank, three fuel pumps, and a valve, all connected by rigid pipes.

Figure 2. System layout used for generic Pressure surge phenomenon understanding

2.1. Pressure Surge Theoretical AnalysisThe velocity of a pressure surge wave is calculated as follows:

Equation 1: Sound velocity in a fluid medium

This study has focused on valve closures, which is one of the design cases of an aircraft fuel system. According to the literature, if the valve closure time is less than the wave reflection time, then the maximum pressure rise at the valve happens during the first peak of pressure oscillations, and is given by the Joukowsky formula:

Hutchison et al / SAE Int. J. Aerosp. / Volume 7, Issue 1 (September 2014)


Equation 2: Pressure peak (Joukowsky)

In the case where the pressure wave has enough time to propagate upwards to the constant pressure source, through the entire pipework, and come back to the valve before its full closure, then the pressure surge induced at the valve is given by the Michaud formula:

Equation 3: Pressure peak (Michaud)

It is important to mention that these formulas are applicable on very simplistic pipework which are not characteristic of a complex aircraft fuel system.

Note that as opposed to Equation 2 (Joukowsky), Equation 3 (Michaud) neglects the fluid and pipework elasticity (and therefore assumes incompressible fluid and system structure -pipework), and assumes a linear valve closure profile.

2.2. Fluid PropertiesLooking at the equations above, fluid properties such as bulk modulus and density are shown to have a direct impact on the pressure spike following a rapid valve closure. Similarly, fluid viscosity, thermal conductivity and specific heat play an important role in characterizing other fluid behaviors (frictions, thermal expansion etc…). Therefore, it is critical that fluid properties are represented appropriately, before a model of the fuel system is built. Fluid properties are pre-defined in LMS Amesim THermal Hydraulic library for Jet A and Jet A1 (commonly used fuel for aircraft application), and rely on the use of polynomial expressions that can accurately represent fluid properties variation with temperature and pressure. The use of (polynomial) expressions allows for continuously defined fluid properties, which can therefore be derived when needed (as opposed to tabulated properties) as per Equation 7 for example. These properties have been checked and validated against the CRC of aviation fuel reference properties [R 2] as shown with the example of the Bulk modulus, density and viscosity variation with temperature on Figure 3.

The presence of gas in fluids is also taken into account in LMS Amesim, both in its free air/gas form and vapor form (vaporized version of a fluid experiencing pressure levels below its vapour pressure limit). As shown with Figure 4, each fluid is parameterized with three pressure limits, so as to account for the right phases, in the right proportions. Note that the variations of θ (fraction of undissolved air/gas, case 2) and Φ (vapor mass fraction, case 3) are quasi linear with Pressure variation, with added considerations for continuity (hyperbolic tangent profiles).

Figure 3. LMS Amesim vs. CRC Handbook Jet-A bulk modulus, density and viscosity

The fluid equivalent density is calculated as the combination of individual densities, as shown with Equation 20, Equation 21, Equation 22 and Equation 23, in line with the zones identified on Figure 4, and relying on the fractions defined with Equation 4, Equation 5 and Equation 6.

Equation 4: air/gas content fraction

Equation 5: undissolved air/gas fraction (modified Henry's

Equation 6: vapor mass fraction

Figure 4. Fluid behavior under varying pressure levels



With fluid density defined as per the above, the fluid equivalent bulk modulus can be derived as follows:

Equation 7: Fluid equivalent bulk modulus

Since the worst case condition in terms of overpressure is reached with fully de-aerated fuel (refer to Figure 6), this particular fuel condition is defined as the design case between Airbus and Engine Manufacturers.

2.3. Sensitivity Analysis

Testing ConditionsThe aim of this part is to validate LMS Amesim pressure surge predictions with theoretical behavior expectations. An analysis of the influent parameters has been performed in order to define the best modelling technique to be used and to highlight any potential hard points that would require further investigation.

First, the valve closure rate (or flow rate evolution during its closure) has been analysed. As suggested by theory, it appeared that in the Joukowsky conditions (fast closure) the valve closure profile does not influence the value of the first pressure peak: both linear and exponential profiles have yielded the same pressure peak at the valve. However when the Michaud condition is met (slow closure), the closure time is not the only influencing parameter (see Equation 3), the closure profile also has an impact on the peak pressure observed at the valve inlet, as shown with Figure 5. Again, the Michaud equation is only valid for a linear valve closure.

The impact of the fluid air/gas content and temperature on the overpressure induced by a valve closure has also been quantified, as shown with Figure 6 and Figure 7. This is the direct result of their impact on the sound velocity and bulk modulus, as per Equation 1 and Equation 2.

Figure 5.

Figure 5. (cont.) Influence of the valve closure rate on the overpressure in bar and flow rate in L/min behavior measured at the valve (a: Joukowsy Scenario; b: Michaud Scenario), Red curve: exponential closure; Green curve: Linear Closure; Blue Curve: Theoretical Results

Figure 6. Influence of the fluid air/gas content on the overpressure in barA (Joukowsky scenario)

Figure 7. Influence of the fluid temperature on the overpressure in barA (Joukowsky scenario)

Testing System LayoutThe aircraft industry commonly relies on the use of flexible pipes for integration purposes. In terms of pressure surge particularly, a flexible pipe has the ability to significantly dampen the overpressure ([R 8]) due to its viscoelastic characteristics. This has been investigated with the system



layout shown with Figure 8. The watchful reader will notice that the flexible pipe does not need to be connected directly to the valve where pressure is measured in order to have an impact.

Figure 8. Modified system layout (flexible hose addition)

When a flexible hose is added to a rigid system pipework, it generates a modification of the system hydraulic stiffness. This is modeled in LMS Amesim through a further correction of the fluid bulk modulus βS (already accounting for the presence of air / gas in the liquid), yielding an effective bulk βeff, as shown with Equation 8.

Equation 8: System effective bulk modulus

This bulk modulus modification enables a large reduction of the first pressure peak at the valve inlet, as shown with Figure 9, and as suggested by Equation 2 (in which the speed of sound depends on the system effective bulk). In addition and as a result of the bulk modification as well, the presence of hoses also impacts the system natural modes through a modification of its hydraulic stiffness K_eq = β * A2/V.

Figure 9. Impact of a hose on the pressure peak in barA measured at the valve (Joukowsky); Red Curve: Baseline Pipework; Green Curve: Addition of Flexible Hose

Another way to interpret this reduction in the first pressure peak at the valve is to consider that the hose flexibility generates an under-pressure wave that is reflected backwards, towards the valve. This reflected wave is the result of a sudden change in the acoustic impedance of the pipework as mentioned in [R 9]. This pressure wave attenuation due to a modification in the pipework acoustic impedance has been also observed by Wylie & Al in [R 10]. A detailed theoretical analysis of pressure wave reflection is provided in appendix. It is

important to mention that these reflected waves will have a tremendous impact on the surge value at a specified measurement location. Notably these reflections are not taken into account in the theoretical formula given with Equation 3 and will lead to large modification in the maximum pressure value measured.

In the present test case, the time at which pressure at the valve stops rising is exactly the one needed by a wave to travel from the hose to the valve, as a result of the valve shut off, which supports the theory that the pressure peak is dampened by an under-pressure wave.

Additional investigations have been performed to better understand the impact of the system layout on the overpressure generated by a valve closure, for which the reader is referred to the appendix.

From this part 2, it can be concluded that the theoretical formula for pressure surge calculation are applicable in very particular cases that are not relevant in aircraft/engine integrated environment. The use of a dedicated model is then needed to ensure that the pressure surge phenomenon is accurately quantified at early program stage.

3. AIRCRAFT FUEL SYSTEM MODELThe Airbus / LMS Engineering collaboration has been continued with an actual aircraft and engine fuel system, with a view to be able to mitigate with simulation the risk linked to pressure surge, very early in a program development.

3.1. Airframe NetworkThe architecture of a typical airframe fuel system is depicted with Figure 1, which highlights the presence of two types of components: centrifugal feed pumps, and hydraulic valves.

Centrifugal PumpCentrifugal pumps are modeled in LMS Amesim based on nominal performance. Pressure rise is calculated from similarity laws, allowing for the pump performance to be deduced from known performance in reference operating conditions. Temperature rise through the pump is based on the theoretical hydraulic power Pow = Q * ΔP and overall efficiencies: the amount of power that is not used for fluid pressure rise is converted into temperature rise.

Hose/PipeThe pipe models for rigid or flexible in LMS Amesim are based on pressure and flow rate differential equations, as per Equation 9 and Equation 10. This allows for their capacitive behavior to be taken into account (Equation 9) as well as the fluid inertia and friction (Equation 10). Note that an analogy of the pressure force term of Equation 10 to its mechanical form allows for a hydraulic equivalent inertia to be derived such that Ihyd = ρ * L/A.



Equation 9: Pressure differential equation of a fluid in a given volume

Equation 10: Newton 2nd equation applied to pipes (gravity neglected)

As indicated in section 2.3, the additional smoothness brought to a system by a flexible hose is taken into account through the calculation of an effective bulk modulus, as per Equation 8.

The aircraft fuel system model is then made up of a combination of pumps and fuel lines (both rigid and flexible), as illustrated with Figure 10. It is important to note that the pipe bends were neglected in this study.

Figure 10. Aircraft fuel system model

3.2. Engine Fuel SystemAs illustrated with Figure 1, the engine part of the fuel system is a complex arrangement of many hydraulic components. For the purpose of this article, only two examples will be used to provide an overview of the modeling performed.

Detailed Valve ExampleControl valves are modeled in LMS Amesim based on their hardware configuration and geometrical parameters (Thermo-Hydraulic Component Design -THCD- library approach). Because of this direct reference to hardware geometry and characteristics, models generated in LMS Amesim can reliably predict physical (mechanical, hydraulic…) interactions between parts, and therefore can reliably predict hardware behavior in all its working conditions (within the definition envelope). This modeling approach method is more reliable than using lookup tables (such as Pressure versus Mass flow), which will not be reliable when extrapolating nominal performance.

This modeling relies on a structured approach, in order to make sure that no interface or interaction is missed.

Figure 11. Control valve example

First, all the pressures acting on the valve and the flows going into / out of the valve are listed: inlet and outlet pressures P_in and P_out, as well as the pressure of the intermediate volume of the spool upper part P_int, and the pressure of the dead volume in the spring cavity P_dead.

Second, the physical phenomena at stake inside the valve are identified:

• Valve actuation: flow forces exerted by P_in, P_out, P_int, and P_dead: perpendicular to their acting surfaces, as per the vertical arrows.

• Valve actuation: jet forces acting on the spool as the inlet flow is sucked in (q_valve)

• Annular leakages: q_leak1, q_leak2, q_leak3 • Routing and combination of the various fluid flows q_in,

q_valve, q_leak1, q_leak2, q_leak3 • Variable chamber pressure calculation: P_int, P_dead • Mechanical forces: pre-charge spring and spool mass

dynamics

Jet-forces in LMS Amesim are intended as correction forces to be applied onto a spool, in order to make up for the fact that the pressure field applied on it is not uniform, as illustrated with Figure 12.

Figure 12. Jet force illustration



Third, now that the phenomena at stake are identified, they have to be quantified. In LMS Amesim, this quantification is done with the following equations:

Equation 11: Normal Pressure force calculation

Equation 12: Flow jet forces calculation

Equation 13: Annular leakage volumetric flow

Equation 14: Spool through-flow calculation

The watchful reader will note that Equation 13 accounts for friction, as seen per the use of the μ viscosity parameter.

Variable chamber internal pressures are calculated based on differential Equation 9, with additional care for nominal volume V0 variation as a result of volume sweeping by the pistons.

Note that when results from additional measurement or other numerical models are available, they can be used instead of the above equations. As an example, jet force results available from previous programs have been re-used, instead of using Equation 12, and as shown with Figure 13. Note that the axes have been blurred on purpose.

Figure 13. jet forces mapping example

Finally, the mechanical force exerted by the spring is expressed as per Equation 14, which takes into account both its pre-charge F0 and current position xspring.

Equation 15: Spring force calculation

Fourth, the dynamic equilibrium of the valve spool (and hence its position) is calculated as per

Equation 16: Spool dynamic equilibrium

Dynamically solving for the spool equilibrium allows LMS Amesim to derive its position, and therefore the mass flow going through the valve, using Equation 14. As an example, the type of behavior that can be reproduced with such a model is illustrated with Figure 14. Note that the axes have been blurred on purpose.

Figure 14. Spool dynamic response to pressure step

Volumetric Pump ExampleThe second example chosen for modelling overview is the volumetric gear pump. Again, it is crucial to take into account their detailed geometry in order to model accurately their volumetric flow and associated flow ripple.

For this study, the LMS Amesim standard external gear pump model PEG01 has been improved (based on [R 6]) so as to make it capable of reproducing the behavior of pumps that have a number of teeth that differs from the driving to the driven gear. By default, this PEG01 model dynamically calculates the volumetric flow rate imposed by the pump as per Equation 17.

Equation 17: Gear pump volumetric flow rate

However in the case of asymmetric pumps, the instantaneous pump displacement Qd has been revised, and is calculated as per Equation 20.



Equation 18: Gear pump instantaneous displacement [R 6]

These calculations are based on the gear geometry shown with Figure 15 and characterized with Equation 19.

Figure 15. Gear pump teeth geometry

Equation 19: Gear pump geometry

This pump shaft torque and mass flow are calculated as a function of its shaft speed and gear geometry, assuming no internal fluid compressibility, and grouping all leakages into an overall volumetric efficiency. This modeling has been validated with results from [R 6], as shown with Figure 16.

Similarly to the aircraft fuel system model, the engine fuel system model was then built as a combination of valves, pumps, fuel pipes and heat exchangers. For illustration purposes, an extract of the engine model is shown with Figure 16.

Figure 16.

Figure 16. (cont.) Asymetric gear pump Flow ripple vs Pump Rotation validation ([R 6] reference: top, LMS Amesim model: down)

Figure 17. Engine fuel system model extract

3.3. System ValidationThis part is related to ground test validation and extrapolation to actual aircraft environment for pressure surge prediction in an integrated environment. A fuel system model of the test bench has been set up in order to replicate the results observed. Once this model had been validated, an extrapolation to aircraft architecture was then performed to anticipate the airframe integration impact on pressure surge maximum value. Indeed, in that particular case, the test bench was not fully representative of the airframe fuel system, which implied that the surge measured on test bench would not be identical to the spike observed on the actual aircraft.

Therefore, the engine model described above has been validated based on (ground) test data, as illustrated with Figure 18 (red and green curves) where the axes have been blurred on purpose. It is important to note that the pressure values shown are measured at the inlet of the engine fuel system.

As mentioned above, the second step consisted in adding the actual airframe fuel system to the validated engine model in order to predict a pressure surge consistent with actual aircraft environment and define the compliance to be associated with the specification level.

As expected from Airbus experience, the aircraft configuration yielded a different pressure peak at the aircraft / engine interface (blue curve). The change in system inertia (ρ * L/A) due to a different piping system, different nominal pressure



level as well as a boundary conditions between test bench and actual aircraft environment explain this difference in pressure peak values.

It is important to notice that the steady state pressures as well as the maximum pressure surge value are strongly impacted by the change in test configuration.

Figure 18. Engine fuel system model validation based on ground test data (Red: Ground Test Data; Green Curve: Test Bench Simulation; Blue: Aircraft Configuration Simulation)

This difference in overpressure prediction between test bench and aircraft configuration highlights the need for the airframe manufacturer to support the engine manufacturer V&V process with the provision of airframe fuel system data. This would allow for accurate predictions of fuel pressure surge in an actual aircraft plus engine environment.

4. PRESSURE SURGE V&V PROCESS PROPOSALAs mentioned in the previous parts, knowledge of the entire fuel system from the aircraft tank up to the engine fuel valve is required to perform an accurate analysis of the pressure surge phenomenon in an integrated engine plus airframe environment. In previous programs, the V&V phases performed by engine manufacturer was done without a fully characterized airframe fuel system, which led to discrepancies between the engine manufacturer predicted surge values and the actual test aircraft results. Consequently, the pressure surge risk was not closed until flight test verification which is late in a program development.

In order to mitigate the risk linked to fuel pressure surge at early program stage during the engine manufacturer V&V cycle, a process has been proposed by Airbus that introduces a support from the airframe manufacturer during this critical verification phase.

The following schematic presents the Airbus proposition to support engine manufacturer V&V process and allow thus allow for a closure of the fuel surge risk at early program stages with the anticipation of the airframe integration environment.



5. CONCLUSIONA deep investigation of the pressure surge phenomenon induced by a valve closure has been carried out in an engine plus airframe integrated environment. It has been demonstrated that with a global knowledge of the overall fuel system, simulation and bench testing could be used at early aircraft program stages to mitigate the risk linked to fuel pressure surge. A revised process for the V&V phases has been proposed by Airbus based on this analysis to support the engine manufacturer verification activities and provide accurate surge predictions at early stages and mitigate the risk of potential fuel system redesign and consequent budget overspending.6.

6. REFERENCESR 1. Karnopp D.C., Margolis D.L. & Rosenberg R.C., “Systems

dynamics : a unified approach”, Second Edition, John Wiley & Sons, New-York, USA, 1990.

R 2. Handbook of aviation fuel properties, coordinating research council, inc., 3650 mansell road · suite 140 · alpharetta, ga 30022.

R 3. “Measuring Pressure Wave Velocity in a Hydraulic System”, Lari Kela and Pekka Vähäoja, World Academy of Science, Engineering and Technology 25 2009

R 4. Memoire “Contribution à l'étude des écoulements transitoires en charge” from Chaoui Sabah from Université Colomnel Hadj Lakhdar - Batna

R 5. The Centrifugal Pump, Grundfos Research And Technology.R 6. Manring Noah D., Kasaragadda Suresh B., “The Theoretical

Flow Ripple of an External Gear Pump”, University of Missouri, Columbia, 2003.

R 7. Blackburn J.F., Reethof G. and Shearer J.L., Fluid Power Control, John Wiley and Sons.

R 8. Covas D., Ramos H., The dynamic effect of pipe-wall viscoelasticity in hydraulic transients

R 9. Pierre B., Pressure Waves in Pipelines and Impulse PumpingR 10. Wylie E. B., Suo, L., and Streeter, V. L. (1993). Fluid transients in

systems, facsimile Ed., Prentice Hall, Englewood Cliffs, NJ7.

7. NOMENCLATUREa - Sound wave speed in the fluid (m/s)

A - Cross section (m2)

Cq - Flow coefficient (-)

D - Pipe diameter (m)

e - Pipe Thickness (m)

E - Pipe Material Young Modulus (Pa)

F - Force (N)

L - Pipe length (from the tank to the engine valve) (m)

P - Fluid Pressure (Pa or Bar)

Q or q - Volumetric flow (L/min)

r - Radius (m or mm)

t - Time taken for complete valve closure (s)

U - Speed (m/s)

V - Volume (m3)

wcomp - Wall compliance (-)

x - Position (m)

- Position derivative with time (m/s)

β - Fluid Bulk modulus (Pa or Bar)

γ - Isentropic coefficient (Specific heat ratio) (-)

η - Efficiency (-)

λ - Friction factor (-)

ν - Poisson Modulus (-)

ρ - Fluid density (kg/m3)

DENSITY CALCULATIONSΦ - Vapor mass fraction (-)

θ - Undissolved air/gas fraction (-)

x - Air gas content (-)

ANNULAR LEAKAGE VARIABLESdp - External piston diameter (m)

ecc - Eccentricity (m)

lc - Contact length (m)

rc - Radial clearance (m)

v- - Piston velocity (m/s)

V+ - Envelope velocity (m/s)

μ - Fluid dynamic viscosity taken at mean pressure and upstream temperature (cP)

GEAR PUMP GEOMETRYl - Instantaneous length of action in the gear mesh (m)

m - Addendum (m)

N - Shaft speed (rpm)

p - Distance between two consecutive teeth (m)

ra - Addendum radius (m)

rp - Pitch radius (m)

rb - Base radius (m)

w - Gear width (m)

z - Number of teeth (-)

SUBSCRIPTS0 - Initial

atm - Atmospheric

i - Internal

liq - Liquid

o - Outside

S - Isentropic

sat - At saturation

T - Isothermal

vap - At vaporisation

vol - Volumetric

ACRONYMSCRC - Coordinating Research Council



FOHE - Fuel Oil Heat Exchanger

HP - High Pressure

HPSOV - High Pressure Shut Off Valve

LP - Low Pressure

LPSOV - Low Pressure Shut Off Valve

THCD - Thermal Hydraulic Component Design

THH - Thermal Hydraulic

TRV - Thermal Release Valve

V&V - Verification and Validation

8. CONTACT INFORMATIONMatthieu HutchisonEngine & Nacelle IntegrationEPT30 Powerplant CoCAirbus Operations [email protected]

Umberto BadialiProject Engineer - Fluid and Mechanical TeamLMS EngineeringSiemens PLM [email protected]

Grégoire LenobleBusiness DeveloperLMS EngineeringSiemens PLM [email protected]



9. APPENDIX

9.1. Density Calculations

Equation 20: Fluid density (zone 1)




With the following fractions and unitary volume definitions

Equation 24: liquid volume (zone 3 density definition)

Equation 25: free air volume (zone 2 and 3 density definition, θ=1 in zone 3)

Equation 26: vapour volume (zone 3 density definition)

9.2. Pipe Stiffness Intermediate Calculations

Equation 27: Overall wall compliance definition

Equation 28: Radial wall compliance definition



Equation 29: Linear wall compliance definition

9.3. Hydraulic System Layout Impact on the First Pressure Peak that Follows Water HammerPlugging two pipes of different diameters upstream of the valve has also been shown to yield large reductions in the first pressure peak at the valve, as shown with Figure 19.

Figure 19. Pressure peak reduction as a result of pipe diameter reduction

Remembering the formulation of Newton's second law applied to hydraulic pipes as per Equation 10, and the associated fluid inertia I = ρ * L/A, it becomes clear that the reduction in system hydraulic inertia provided by the pipe diameter change enables the decrease of the valve first pressure peak, through a modification of the volumetric flow rate dQ/dt, and thus of the fluid speed U0. Conversely, the reduction of a pipe diameter (as the wave sees it = traveling away from the valve) yields an increase in the pressure peak.

Again, this behavior may be interpreted as the result of a reflected pressure wave that travels back to the valve, as discussed for flexible hoses. Low pressure waves have been observed indeed in the case of a pipe diameter expansion (when going away from the valve), and high pressure waves in the case of a pipe diameter contraction (going away from the valve). This is illustrated with Figure 20 that shows a plot of pressure versus position, on the two sides of the diameter change, at the same instant t = 1.8s.

Figure 20. High Pressure wave travelling back (i.e. from right to left) at the pipe diameter change



Adding a pump bypass pipe to the system has a very limited impact: only a very long (i.e. lossy) would result in a noticeable impact on the first pressure peak: 5m of bypass pipework yielding a 3.5% reduction in the first pressure peak. This is the direct result of negligible linear friction losses.

Similarly, the addition of a tank return line yields the same -negligible- pressure peak reduction: 4%.

9.4. Transmission, Reflection of a Pressure WavePressure waves propagate, transmit and reflect in fluid-filled pipelines at the speed of sound. Practically, the acoustic velocity in fluid-filled pipelines depends on the fluid density and fluid properties, and on the pipeline diameter and wall thickness and the wall material Young's modulus.

The product of the fluid density and the wave acoustic velocity divided by the cross-sectional area in the fluid-filled pipeline defines the propagation medium acoustic impedance, Z: Z = ρ*a/A

Acoustic interfaces are virtual borderlines between two pipeline sections of different acoustic impedances. Changes in impedance can originate from changes in fluid density, due to pressure or temperature, or acoustic velocity, due to pipeline geometry or material properties. Changes in acoustic impedance can also result from a combination of changes in density and acoustic velocity. Reflection and transmission coefficients for a pressure wave propagating from a medium a to a medium b are described with Figure 21.

Figure 21. Acoustic Interface Schematic Representation Between

The reflection coefficient is the ratio of the reflected pressure wave amplitude, pR, and the incident pressure wave amplitude, pJ. The transmission coefficient is the ratio of the transmitted pressure wave amplitude, pT, and the incident pressure wave amplitude. Reflection and transmission coefficients are defined as pressure ratios.

The influence of an acoustic interface on a square pressure wave propagating from a high acoustic impedance medium a to a low acoustic impedance b is illustrated in Figure 22. Both transmitted and reflected waves conserve square waveforms although the transmitted pressure wave has a lower amplitude and shorter wavelength than the incident pressure wave (T < 1). The reflected pressure wave has the same wavelength as the incident pressure wave but has a negative amplitude (R < 0).

Figure 22. Influence of Acoustic Interface on Pressure Wave Propagation. Interface of Media a & b at L/2 and Za>Zb



Changes in wavelength are due to the difference in acoustic impedance before and after the interface. The pressure wave front propagates in medium b with a lower impedance than medium a, therefore propagating slower in medium b than in medium a and with a lower amplitude.

Influence of an acoustic interface on a square pressure wave propagating from a low acoustic impedance medium a to a high acoustic impedance b is illustrated in Figure 23. Both transmitted and reflected waves conserve square waveforms although the transmitted pressure wave has a greater amplitude and longer wavelength than the incident pressure wave (T > 1). The reflected pressure wave has the same wavelength as the incident pressure wave but has a lower amplitude (R < 1).

Figure 23. Influence of Acoustic Interface on Pressure Wave Propagation. Interface of Media a & b at L/2 and Za<Zb

Changes in wavelength are due to the difference in acoustic impedance before and after the interface. The pressure wave front propagates in medium b with a greater impedance than medium a, therefore propagating faster in medium b than in medium a and with a greater amplitude.

A pressure wave transmits totally from medium a to medium b when acoustic impedances are equal. The reflection coefficient equals zero in such case. Reflected pressure waves relative pressure can be with or without phase change, but their amplitudes are limited by the incident pressure wave amplitude. However, transmitted pressure waves always have the same phase as the incident pressure wave, but their amplitude can be up to twice the incident amplitude.

9.5. Boundary ConditionsPipe walls, tanks or pumps represent static boundary conditions. Pumps and tanks are characterized by fixed pressure values after flow establishment. Pipe walls are characterized by a zero fluid velocity. Static boundary conditions are categorized into open and close by the reflection coefficient value. Another way to categorize boundary conditions is by soft wall or hard wall, corresponding to open and close boundary, respectively.

Reflections of a square incident pressure wave at closed and open boundaries are illustrated in Figure 24. A pressure wave reflects totally without phase change at a close boundary (R = 1), or hard wall. A pressure wave reflects totally with phase change at an open boundary (R = −1) or soft wall. Fluid velocity reflection coefficient, is opposite of pressure reflection coefficient. Thus, fluid velocity signals are phase shifted compared to pressure signals as observed in Figure 24 d) and e).

The transmission coefficient for a closed boundary (R = 1) equals +2. However, the fluid medium does not exist beyond the boundary. Another way to express this is that a pressure wave of the same amplitude as the incident pressure value will reflect totally into the fluid-filled pipeline whereas a pressure wave twice as large will propagate into the physical boundary. Pressure waves generated in fluid-filled pipeline can propagate further into the supporting structure and weaken mechanical parts.



Figure 24. Pressure and Fluid Velocity Waves Reflections From Open or Close boundary conditions

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