Proceedings of ASME Turbo Expo 2009: Power for Land, Sea and Air

GT2009
June 8-12, 2009, Orlando, Florida, USA

GT2009-60051

DEVELOPMENT OF A ONE DIMENSIONAL DYNAMIC GAS TURBINE SECONDARY AIR

SYSTEM MODEL – PART II: ASSEMBLY AND VALIDATION OF A COMPLETE NETWORK

C. Calcagni, L. Gallar, V. Pachidis

Cranfield University
School of Engineering
Department of Power and Propulsion
MK43 0AL, Beds, United Kingdom
l.gallarredondo@cranfield.ac.uk

ABSTRACT other. As it would be expected, the system with a longer pipe is

In the first part of this paper the equations and results for found to have a longer settling time. Finally, the work
the transient models developed for the SAS components in concludes with the analysis of the flow evolution in the
isolation have been thoroughly explained together with the secondary air system during a shaft failure event.
assumptions made and the limitations that arose subsequently. This work is intended to continue to address the limitations
This second part explains the work carried out to couple the imposed by some of the assumptions made for an extended and
individual components into a single network with the aim of more accurate applicability of the tool.
assembling a dynamic model for the whole engine air system.
To the authors’ knowledge the models published hitherto NOMENCLATURE
are only valid for steady or quasi steady state. It is then the Speed of sound
case that the differential equations that govern the fluid A Area
movement are not time discretised and thus can be solved in a c Cavity
relatively straightforward fashion. Unlike during transients, the C Characteristic curve
flow is not supposed to reach sonic conditions anywhere within IP Intermediate pressure
the network and most important, flow reversal cannot be IPC Intermediate pressure compressor
accounted for. IPT Intermediate pressure turbine
This study deals with the mathematical apparatus utilised L Length
and the difficulties found to integrate the single components LP Low pressure
into a network to predict the transient operation of the air LPT Low pressure turbine
system. The flow regime – subsonic or supersonic – and its M Mach number
direction have deemed the choice of the appropriate numerical ND Non dimensional
and physical boundary conditions at the components’ interface NGV Nozzle guide vane
for each time step particularly important. The integration is p Pressure
successfully validated against a known numerical benchmark – SAS Secondary air system
the De Haller test. A parametric analysis is then carried out to t Time
assess the effect of the length of the pipes that connect the u Flow velocity (modulus)
system cavities on the pressure evolution in a downstream V Volume
reservoir. Transient flow through connecting pipes is dependent 1,2,3 Stage number
on the fluid inertia and so it takes a certain time for the
information to be transported from one end of the duct to the

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 Greek symbols, subscripts and superscripts: prevent it from recovering from it, yet again limiting the
γ Specific heat coefficient terminal speed of the turbine. The turbine displacement
Density rearwards may seal the outlet ports of the downstream turbine
0 Initial conditions secondary air system cavity. Should this happen the pressure
e Exterior / ambient inside the cavity will increase, exerting a force acting forward
t Total or stagnation that will reduce the frictional force on the tangling structures.
The energy that can be dissipated as friction will then be lower
1 INTRODUCTION and the beneficial effect of the blades tangling with the
The secondary air system (SAS) of a gas turbine is downstream structure may be lost. Hence the need for a SAS
designed to perform several functions important for the safety, dynamics model that may be applied to future shaft-break
reliability, mechanical integrity and performance of the engine. calculations in new engine projects.
The air is bled from the compressor, flows through the internal
cavities of the engine cooling critical components such as discs, 2 1-D NETWORK APPROACH
shafts and bearing chambers and sealing the oil in their interior. The SAS is characterised by complex flow passages: prior
The secondary air is also responsible for determining the end- to its injection back into the main gas path the air meets a
loads on the discs and balancing shaft thrust loads, by adjusting variety of flow components such as small orifices, pre-swirl
the pressure in the cavities. The air is eventually discharged at nozzles and chambers, ducts, cavities, labyrinth seals, etc.
the turbine rims preventing the air of the main gas path from Traditionally the models developed to simulate the SAS
entering the internal turbomachinery cavities. performance have been one dimensional and empirically based,
The air bled from the main gas path although necessary even if the pattern of the flow in the SAS is either 2-D or 3-D,
does not follow the main gas path thermodynamic cycle and partly because the complexity of the flow phenomena limits the
hence impairs the overall engine performance. In order to application of theoretical approaches and partly because for
quantify and minimise its effect, during the design the SAS is engineering purposes the results yielded by a 1D network
typically modelled as a steady one-dimensional gas flow suffice. The usual approach is to represent the SAS as a 1-D
network of nodes and connections that represent the various network of flow components, in which the complex geometry
flow components the air meets along its path. Consistent works of the system is reduced to a discrete model of the flow
based on that approach are those undertaken by Kutz and Speer passages. Typically, each family of flow elements is
[1] and Alexiou and Mathioudakis [2]. characterised by particular flow equations that are derived from
Quasi-steady flow approaches usually suffice for normal either rig tests or CFD studies [3,4].
engine transient events since the SAS response time is small To deal with the complexity of the transient analysis, a
compared with the engine characteristic time. However, during simplified 1-D dynamic model has been developed in the
some failure scenarios and slam accelerations the rapid changes present work. The approach followed consists in modelling the
in the main gas path flow deem the SAS performance to have SAS dynamics as a network of cavities connected by pipes (fig.
an appreciable impact in the outcome of the event. To the 1). The dynamic response of this simplified system is then
author’s knowledge there is not such an approach available in dependent on both the air system capacity and the fluid flow
the literature. inertia through the flow path. Therefore, in order to study the
In particular, in the event of a shaft failure the sudden compressible unsteady gas flow in the system, the volumes are
decoupling between the turbine and the compressor may result considered as pressure vessels with a certain number of
in a hazardous spool over-speed. In those circumstances, the orifices, to model the air system capacity, and the flow paths
engine will work at extreme off-design conditions and various are idealised as round and straight pipes, to account for the air
complex phenomena will influence the terminal speed the system inertia. The limitations of the models developed to
turbine will eventually reach. It is a certification requirement to represent the vessels and ducts of the system are explained in
demonstrate that the speed reached by the free-running turbine the first part of this work [19].
is low enough so that no high energy debris is released from the
engine. 2.1 Component modelling
If the shaft fails behind its axial location bearings the The coupling between the models developed presents
turbine is no longer axially constrained and is free to move some challenges, the main issue being the heavy interrelation
rearwards due to the force imposed by the air across it. Such between components. In fact the gas transfer between the
movement may result in the turbine rotor blades tangling with vessels is affected by the flow inertia and the pressure waves in
any other structure that is located immediately downstream. In the pipes, but in turn the boundary conditions of the transient
the event of an IP shaft failure, the blades of the IPT rotor may flow through the pipes are defined by the charge and discharge
tangle with the LP NGV blade row. Such interaction, if it process of the vessels. The coupling of the components is hence
occurs in a controlled manner, will dissipate energy as friction achieved by means of the boundary conditions. It is therefore
and will reduce the terminal speed that the turbine is able to necessary to find the appropriate formulation of such conditions
reach. Furthermore, it will induce heavy vibrations in the representative of the interaction of the tube with the
engine that will push the compression system towards surge or neighbouring vessels.

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 based on information from inside the domain reaching the
boundary along the negative characteristic.

2.2 De Haller test

Before applying the model to complex networks, the
numerical algorithm proposed is applied to the reservoir
discharge problem described in [7,8] known as the De Haller
problem. As sketched in fig. 2 a pipe of 0.01m diameter and 1m
length is connected to a large reservoir pressurised to 150 kPa.
Figure 1 Generic gas transmission system A valve is fitted at the other end of the pipe to separate it from
the ambient at a pressure of 100 kPa. Initially the valve is
As seen in the first part of the paper [19] , at each boundary closed and the system is in equilibrium. The exact theoretical
of the pipe three boundary conditions have to be imposed. solution of the unsteady flow in the pipe when the valve is
These are split into physical and numerical boundary suddenly opened is derived by assuming the flow is
conditions. The physical boundary conditions are those homoentropic and was produced by Bessel [7]. The solution
physical variables that can be freely imposed at the boundaries shows the existence of pressure waves travelling in the pipe and
and will depend on the way the information transported along reflected at the boundaries. The schematic diagram of the
the characteristics interacts with the boundaries. However, for system and the theoretical and numerical pressure evolutions at
the numerical problem to be unequivocally defined, the values three different locations (inlet, middle point and outlet) along
of all the variables at the boundaries are required and hence the tube are represented in figures 3, 4 and 5, while the
additional conditions of numerical origin, referred to as associated velocity profiles are shown in figure 6. It is possible
numerical boundary conditions, must be added [5,6]. A wide to state that, although the numerical solution slightly rounds off
variety of methods can be used for the definition of the the sharp edges, it tends to follow the theoretical solution quite
boundary conditions, depending on the variables used in the closely. These results therefore validate the model for this
definition of the physical boundary conditions and the method simplifies network
used for the imposition of the numerical conditions. The choice
of the boundary conditions infers some challenges since their
definition can have a remarkable effect on the accuracy,
stability and convergence of the numerical scheme used. The
number of physical boundary conditions that are required is
also dependent on the flow condition at a given boundary.
Namely, for subsonic inflows, the mass flow and energy
conservation equations between the nozzle exit and the tube
inlet section are imposed. The additional numerical condition is
obtained by the discretisation of the compatibility equation that
corresponds to the negative characteristic, C-, approximating
the space derivatives by one-sided second order difference
formulas. For subsonic outflows the tank pressure is imposed as
a physical condition, while a zero order extrapolation in space
and time is used to obtain the two numerical boundary
conditions. In the case that the flow reaches sonic conditions, Table 1 Physical boundary conditions
three physical boundary conditions at the inlet, and three
numerical boundary conditions at the outlet are required. The
resulting system of equations for the left and right boundaries
of the tube is summarised in tables 1 and 2.
For the system of equations to be mathematically closed the
mass flow at the inlet boundary must be specified. The mass
flow is determined by the discharge process of the vessel
connected to that tube end that, as seen in the first part of the
paper, is a function of the outlet pressure, which in this case is
not easily defined. The numerical algorithm proposed for the
inlet boundary involves an iterative procedure to couple the
tank solution with the boundary conditions: the discharging
mass flow must be varied until the nozzle outlet conditions are
equal to the left boundary conditions. As a result, the mass flow Table 2 Numerical boundary conditions
will not just be a function of a state but will be determined

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 A B C

Figure 2 De Haller test layout

Figure 5 Pressure evolutions at the open-end of the pipe

Figure 3 Pressure evolutions at pipe entry

Figure 6 Velocity profile at different locations of the pipe

3 TEST CASES
In order to assess the influence of the main geometric
parameters of the SAS on the dynamic behaviour of the system,
a series of test cases are carried out for the modelling of simple
networks.
Firstly, the response of a vessel of a size similar to a typical
LPT cavity to a step change in boundary pressure has been
analysed, since usually this is the most significant volume in
the air system (fig. 7). Although the real LPT cavity has a
number of different boundaries, the results show that the time
taken for a cavity of this size to adapt to the new pressure is
Figure 4 Pressure evolutions at mid pipe long enough to have a sensible impact on the system behaviour,
also for very rapid transients such as a shaft failure. This
demonstrates that in the particular case of a shaft failure event a
transient model of the SAS is required.

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 LPT cavity continues to increase although the IPC pressure is
lower. As a result, after a certain time the flow in the tube
reverses and the chamber pressures fluctuate around the
equilibrium pressure until the equilibrium state is reached
It is interesting to see what happens if a shorter tube links
the two vessels or even in the limit case, when a mere orifice
between the reservoirs is considered. The pressure evolution for
these two cases is represented in figures 9 and 10 respectively.
As expected, the overshoots are considerably reduced. On the
other hand, the speed of response of the systems is very similar
regardless of the duct length. In fact although a slight increase
can be noticed for the longest pipe the time to reach the target
pressure is almost the same, being the main difference between
Figure 7 Pressure evolution in a vessel corresponding to a step cases the inertia exerted by the tube length on the flow
change in boundary pressure progression that will force the pressure to overshoot. The
amplitude of the overshoots will depend on the length of the
tube. Consequently the settling time, defined as the time to get
to and stay within 10% of the target value, is different for each
system.

Figure 8 Pressure evolutions in the LP SAS. Pipe length 0.6m

Secondly, a simple system is analysed in order to

reproduce the gas transfer between the IPC and LPT cavities,
which are typically connected through the inter-shaft gap in the
IP system. To that end a high pressure vessel and a low pressure Figure 9 Pressure evolutions in the LP SAS. Pipe length 0.06m
vessel similar in size to the air system cavities are considered.
The two chambers are connected by the inter-shaft gap, which
is a long, thin flow conduit. The transient flow through such a
feature may affect the gas transfer between the two chambers
because of the flow inertia and the possible presence of shock
waves pulsating up and downstream of the tube. Therefore, to
quantify the magnitude of the delay in the gas response
associated with the inter-shaft gap, a long tube is considered
between the two vessels. Although in reality the IPC cavity is
continuously fed by the IP compressor and the LPT cavity has
several ports, at this stage this simple approximation suffices. It
is assumed that initially a valve separates the LPT cavity from
the rest of the system which is stagnated. At t=0 the valve is
suddenly opened and the system is allowed to reach equilibrium
(fig.8). The resulting pressure evolution in the LPT cavity
represented in figure 8 oscillates around the final value. In fact,
because of the inertia of the flow through the tube, a finite time
is required for any change at one end of the tube to be
transported to the other end and therefore, the pressure in the
Figure 10 Pressure evolutions in the LP SAS - Orifice

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 IPC CAVITY

Figure 11 Low pressure SAS schematics

V To account for the fact that the LPT cavity is connected to

several chambers that are usually of a smaller size rather than
isolated, a small volume vessel is added to the system analysed
(fig. 12). The predicted pressure evolutions in the three cavities
are represented in figure 13. As would be expected the system
IPC c LPT c now tends to reach a lower target pressure. However, the
pressure overshoots in the LPT cavity are of the same order
than in the two cavities case. It can be seen that the pressure in
the cavity V tends to rapidly assimilate the LPT cavity pressure,
due to its small capacity, and follows its behaviour effortlessly
Figure 12 Three cavities system schematics afterwards. This is due to the fact that, because of the big
difference in the volume capacity between the LPT and the
additional cavity, the response of the latter is very fast and the
pressure in the cavity V tends to oscillate around a final
pressure that is very close to the LPT initial pressure. The
pressure overshoots in the LPT cavity do not seem affected by
the presence of this smaller volume.

4 OVER-SPEED SIMULATIONS
A one-dimensional network has been created to model the
low pressure branch of the secondary air system of a modern
high bypass ratio turbofan engine. The methodology followed
first identifies volumes and their connections in the system.
Then the most significant volumes are considered and the
network is assembled progressively in order to analyse the
effect of the addition of each new cavity to the system while
monitoring the convergence of the numerical algorithm. For the
reasons already discussed, for short pipes the effect of the flow
Figure 13 Pressure evolutions in the three cavities inertia through the path is considered negligible and it is
approximated by an orifice. The final network is sketched in
fig. 11.

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 Once the network has been built, a simulation of the LPT cavity tends to decrease more slowly than the IPT forcing
whole LP SAS is carried out for maximum take-off (MTO) the LPT cavity pressure to be greater at a certain time. After a
conditions in order to compare the results against data obtained delay, due to the flow inertia, the flow in the inter-shaft gap
by a Rolls-Royce stand-alone software for the SAS modelling reverses. When the second surge is triggered, the IPC cavity
based on a steady state 1-D network representation, in which pressure tends to increase again, restoring the initial flow
each flow element is modelled by its characteristic equations. direction in the inter-shaft gap and causing the LPT cavity
Because of the numerous simplifications made in the present pressure to increase again.
SAS model which considers only volumes and tubes in the Since the pressures in the SAS are primarily responsible
network and neglects the vortices in the rotating cavities, for determining end-loads, a series of loads are calculated and
differences between the results provided by the two models are plotted in figure 16, in order to analyse the effect of the
expected. However a comparison is made in order to give an predicted LPT cavity pressure evolution on the gas load on the
idea of the accuracy of the model. While the pressures in the IP turbine. The loads are derived by the imposed pressure
internal volumes are quite similar, some of the mass flows have evolutions for the IPT inlet pressure P42 and outlet pressure
a noticeable deviation when compared with the software data. P44 and the predicted LPT cavity pressure in figure 14. A first
The main differences are due to the fact that the pressure in the
LPT cavity predicted by the steady state software is not IPC cavity
uniform, a situation that is not reproducible by the present
model. In particular, a region of lower pressure is present in the
vicinity of the shaft. Although a perfect agreement with the
software results has not been obtained, the model has been
proven adequate for the transient simulation in order to have a
preliminary measure of the pressure overshoots that may occur
in the LPT cavity during a shaft failure event.
Using the steady state data as the initial conditions, a
notional shaft failure scenario with compressor surge and
recovery is reproduced. In an over-speed scenario the engine
components are subject to extreme off-design conditions.
Usually shaft breaks are accompanied by a prompt surge that
limits the flow available to the free running turbine and
alleviates the over-speed problem. After the initial surge, in
some circumstances, the compressor can recover and a second
surge is then desired in order to rapidly reduce the over-speed.
In addition, the capacity of the turbine immediately
downstream of the over-speeding rotor is considerably reduced Figure 14 Imposed boundary pressure evolutions
because of the high separation regions that appear as a result of
IPC cavity
the highly distorted velocity triangles. All this leads to a rapid
change in the SAS boundary conditions that needs to be
accounted for. In the simulation, allowances are made for the
variation in turbine capacity and for the compressor surge,
using imposed pressure evolutions at the boundaries as shown
in figure 14.
In addition, the failure of the IPT shaft can be accompanied
by the rearwards movement of the IPT disc due to the net gas
load that causes the first SAS outlet port of the LPT turbine to
close. In order to take into account this effect, the
corresponding orifice area is varied with time during the
simulation (port L in fig. 11).
In figure 15 the predicted pressure evolution in the LPT
cavity is represented together with the boundary condition
profiles imposed at the SAS interfaces. As expected, there is an
initial build up of pressure in the LPT cavity as a consequence
of the sudden rise in IPC cavity at the beginning of the surge
sequence and the sealing of the first outlet port in the LPT.
Then the LPT cavity pressure starts to decrease following the Figure 15 Predicted LPT cavity pressure evolutions
IPC cavity pressure. However, because of the increase in
pressure into the downstream turbine stage, the pressure in the

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 downstream structures in reducing the terminal speed would be
limited. Moreover, the transient end-loads predicted,
considering the effect of the SAS dynamics, are considerably
different to those calculated using a crude scaling of the
pressure drop across the IPT remarking the importance to
account for the SAS dynamics effect for new engine projects
which rely on blade tangling to limit the terminal speed in case
of a shaft failure.

ACKOWLEDGMENTS
The authors would like to thank Rolls-Royce plc for the
support provided to this project.

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