Proceedings of ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition

GT2017
June 26-30, 2017, Charlotte, NC, USA

GT2017-63240

FACING THE CHALLENGES IN CFD MODELLING OF

MULTISTAGE AXIAL COMPRESSORS

Lorenzo Cozzi, Filippo Rubechini, Michele Pio Astrua, Andrea Schneider, Andrea
Marconcini, Andrea Arnone Silingardi
Università degli Studi di Firenze Ansaldo Energia
Via di Santa Marta 3 Via Lorenzi 8
50139 Firenze, Italy 16152 Genova, Italy
Lorenzo.Cozzi@tgroup.unifi.it Pio.Astrua@ansaldoenergia.com

ABSTRACT NOMENCLATURE
Multistage axial compressors have always been a great chal- CFD computational fluid dynamics
lenge for designers since the flow within these kind of machines, GT gas turbine
subjected to severe diffusion, is usually characterized by com- IGV inlet guide vane
plex and widely developed 3D structures, especially next to the 𝑚̇ mass flow rate
endwalls. The development of reliable numerical tools capable NRBC non-reflecting boundary conditions
of providing an accurate prediction of the overall machine per- OGV outlet guide vane
formance is one of the main research focus areas in the multi- p pressure
stage axial compressor field. RBC reflecting boundary conditions
This paper is intended to present the strategy used to run RANS Reynolds-averaged Navier-Stokes
numerical simulations on compressors achieved by the collabo- T temperature
ration between the University of Florence and Ansaldo Energia. Greek
All peculiar aspects of the numerical setup are introduced, such α exit flow angle
as rotor/stator tip clearance modelling, simplified shroud leakage β total pressure ratio
model, gas and turbulence models. Special attention is payed to Subscripts
the mixing planes adopted for steady-state computations because 0 stagnation property
this is a crucial aspect of modern heavy-duty transonic multi- ref reference quantity
stage axial compressors. In fact, these machines are character-
ized by small inter-row axial gaps and transonic flow in front INTRODUCTION
stages, which both may affect non-reflectiveness and fluxes con- Multistage axial compressor often put a strain on CFD mod-
servation across mixing planes. Moreover, the high stage count elling, especially when dealing with off-design operating condi-
may lead to conservation issues of the main flow properties form tions. However, the need for increasing efficiency and operating
inlet to outlet boundaries. Finally, the likely occurrence of part- range of existing machines pushed the diffusion of CFD tools
span flow reversal in the endwall regions affects the robustness able to handle multistage computational domains within indus-
of non-reflecting mixing plane models. trial R&D departments [1] [2] [3]. Multistage 3D steady-state
The numerical setup has been validated on an existing ma- RANS simulations started to appear and be used in the 1990’s
chine produced and experimentally tested by Ansaldo Energia. [4], but some decisive aspects of this kind of analysis are still
In order to evaluate the impact on performance prediction of the open. Probably the most crucial one is the way to model the in-
mixing planes introduced in the steady-state computation, un- terface between stator and rotor rows, in which a circumferential
steady simulations of the whole compressor have been per- averaging of some sort must be introduced to remove the effects
formed at different operating conditions. These calculations have of unsteadiness that are inherent in turbomachinery applications.
been carried out both at the compressor design point and close to The averaging process is performed at the interface between ad-
the surge-line to evaluate the effect of rotor/stator interaction jacent rows in relative motion, called “mixing plane”. The first
along the compressor working line. example of multirow steady-state simulation with the use of mix-
ing planes was published by Denton [5]. In case of small inter-

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 row gaps and/or shock systems reaching the mixing plane, both one-equation model [21], the two-equation k−ω model devel-
typically encountered in modern axial compressors, the unreal- oped by Wilcox [22] and Menter’s shear stress transport model
istic reflections due to a simple circumferential averaging of the [23].
flow are enhanced and can lead to inaccurate results. To over- One of the most challenging issues which arise in multistage
come this issue, Giles developed a non-reflecting boundary con- axial compressor simulations is the need for being able to predict
ditions theory [6], which started to be used by other authors (e.g. the stall margin with a certain level of accuracy with a steady-
[7]) in the 1990’s. Even though mixing plane models with non- state analysis. Especially for compressors with a high stage
reflecting boundary conditions have been used for decades, count, due to mechanical issues, the rear stages tend to have a
fluxes conservation and model robustness are still open issues, high clearance to blade span ratio. This leads to more complex
as demonstrated by several recent publications concerning these and fundamentally unsteady 3D flow structures in the clearance
topics [8] [9] [10]. Furthermore, the extension to the real gas case region, especially when increasing the overall pressure ratio to
of a non-reflecting mixing plane model is rarely addressed in the move the operating point towards the surge line. In this case a
open literature (e. g. [8]). Steady-state multistage analysis is reliable stall margin prediction through steady-state simulations
nowadays a standard for industrial design and design-validation becomes even more demanding. Even if unsteady simulations
purposes, but understanding the limitations of this kind of mod- could be an appropriate answer to these issues, the time and com-
elling is important for contemporary designers as pointed out by putational effort needed is currently not suitable for industrial
Denton [11]. Some experiences in accounting for unsteady ef- design and design-validation purposes, even using a simplified
fects in turbomachinery can be found in [12] and [13]. As the phase-lagged approach as the one implemented in TRAF code
computational cost of unsteady simulations on high stage count [24]. To face the industrial need for a robust computational setup
turbomachines is not yet suitable for industrial needs, assessing to run steady-state simulations of multistage axial compressors,
the level of accuracy of steady-state approximation still has a the algebraic Baldwin-Lomax model has been chosen as turbu-
great interest. lence closure between all the options available in the code. More
In the framework of the collaboration between Ansaldo En- complex one- and two-equation turbulence models have been
ergia and the University of Florence, an advanced numerical tested on several geometries belonging to compressors already
setup for steady-state multistage axial compressor simulations running on-site, leading to a significant underestimation of the
has been developed. This numerical setup has been used to pro- stall margin. Furthermore, for some machines with high clear-
vide CFD results in recent publications of Ansaldo Energia [14] ance to blade span ratios, non-algebraic models have shown con-
[15]. Within this work some key aspects of the compressor mod- vergence issues in steady-state computation even next to the de-
elling are addressed, such as mixing plane model, shroud leak- sign operating condition.
ages and rotor tip clearances. Moreover, a model validation
Gas Models
against experimental measurement on multistage axial compres-
Two different gas models are implemented in TRAF code:
sor is presented. Finally, the results of unsteady full-annulus
perfect and real gas one. In the real gas version [25], the analytic
computations of a whole 15-stage compressor at two different
relationships used to determine thermodynamic properties re-
operating conditions, namely design and near-stall, are compared
quired by the solver for the perfect gas model are replaced with
with steady-state analyses to evaluate the influence of mixing
the local interpolation of gas data from property tables. In order
plane models on performance prediction.
to reduce the computational cost, the gas tables are external to
the flow solver and must be generated before running the code,
COMPUTATIONAL FRAMEWORK
using commercial or in-house developed databases.
The solver used to obtain the results presented in this work
As far as axial compressors of heavy-duty gas turbines are
is the TRAF code [16], in its parallelized version. TRAF is a
concerned, the working fluid is intended to be air operating in
steady/unsteady, multigrid/multiblock flow solver for the 3D
thermodynamic conditions far away from the critical ones, both
Reynolds-averaged Navier-Stokes equations. For time accurate
in terms of pressure and temperature. Between the categories of
calculations a dual-time stepping method [16] [17] is adopted
gas behaviors classified in [26], the most suitable for modelling
and the coupling between consecutive rows is handled by means
the fluid evolving in the compressor of an industrial gas turbine
of sliding interface planes.
is the thermally perfect gas. Such kind of gas obeys the thermal
Numerical Scheme and Turbulence Models equation of state and is characterized by the fact that specific in-
A cell-centered finite volume scheme is used for the space ternal energy, specific enthalpy and the specific heats are only
discretization. Both scalar [18] and matrix [19] artificial dissipa- functions of temperature. As shown in [27] for gas turbine appli-
tion models are available in the code. To minimize the amount of cations, the use of a real gas model which considers the specific
artificial diffusion inside the shear layers, these terms are heat variation with temperature allows a good prediction of the
weighed with an eigenvalue scaling. The matrix artificial dissi- thermodynamic behaviour of the working fluid. This real gas
pation model has been used for the results presented in this work. model is the standard adopted to run simulations of compressors
Several turbulence closures are implemented in TRAF code: the designed by Ansaldo Energia.
algebraic Baldwin–Lomax model [20], the Spalart–Allmaras

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 Computational Grids and Boundary Conditions The non-reflecting mixing plane model has been recently
Elliptic H-type grids have been used for all simulations pre- extended to the real gas case, making it ready to be used as stand-
sented within this work. Each block has typical dimensions of ard model for full compressor steady-state analysis. The exten-
141×65×81 grid points in streamwise, pitchwise, and spanwise sion consisted in removing all the assumptions present in Giles’
directions, respectively. The grid spacing has been chosen to ob- and Saxer’s theory which was developed for the perfect gas case.
tain a y+ value lower than 2.0 for the first grid point above the The key differences from the perfect gas version are an iterative
wall. procedure to compute mixed-out quantities from the mean fluxes
As far as boundary conditions are concerned, the radial dis- of the governing conservative variables through the interface and
tributions of total temperature, total pressure and flow angles are the use of numerical derivatives instead of analytical expressions
prescribed at the computational domain inlet, while the outgoing in some of the terms within the transformation matrix from prim-
Riemann invariant is taken from the interior. On the domain out- itive to conservative variables.
let section, the static pressure spanwise distribution is enforced,
while density and momentum components are extrapolated.
Mixing Plane Models
In the case of multirow steady-state computations, mixing-
planes are introduced to handle the coupling between adjacent
rows. Data exchange through the common interface plane of con-
secutive rows is obtained by an appropriate calculation of phan-
tom cell values, keeping the spanwise distribution while averag-
ing in the pitchwise direction. Two main mixing plane models
are available in the TRAF code: a robust reflecting model and a
more accurate non-reflecting one.
In the former, the boundary conditions imposed in each phantom
cell on one side of the interface are obtained by averaging in the
pitchwise direction the values of the governing conservative var-
iables of the grid cells at the same span on the other interface
side; if the adjacent grids do not match in spanwise direction (e.
g. different number of cells or nodes distribution) an interpola-
tion of the pitchwise averaged values is performed. Robustness
and capability of handling flow reversals across the interface are
the main positive aspects of this mixing plane model, both mak- Figure 1: Normalized mass flow development along compressor me-
ing it attractive for industrial purposes. By imposing as boundary ridional channel using reflecting (RBC) and non-reflecting (NRBC)
condition a constant value for the conservative governing varia- mixing plane model
bles for all the grid cells at the same span, reflections of the main In the development of the non-reflecting model, particular
quantities of interest arise next to the interface. In some particu- attention has been paid to mass flow and total temperature con-
larly demanding cases, as transonic compressor rows with a servation across the interface; for other quantities, such as total
shock system which reaches the interface or machines with small pressure and entropy, the non-conservation through the mixing
inter-row axial gaps, the effects of reflections are enhanced. plane is due to the mixing process itself and cannot be avoided.
To avoid non-physical reflections next to the mixing planes of The need for good mass flow conservation properties is particu-
the computational domain a non-reflecting model based on the larly important for compressors with a high stage count, in which
theory developed by Giles [6] [28] and Saxer [29] has been im- even a relatively low error at each interface can lead to unac-
plemented in the TRAF code. The main issue concerning this ceptable mass flow evaluations in the rear part of the machine.
model is that, when the normal velocity across the interface at a This can result in a wrong stage matching and overall perfor-
certain span has a very small value, it tends to be unstable and mance prediction.
can lead to an abrupt divergence of the simulation. This situation The results in terms of mass flow conservation of steady-
is typically verified inside the boundary layer next to the channel state simulations at design point, performed on the 15-stage
endwalls and in presence of a flow reversal across the mixing AE94.3A GT compressor produced by Ansaldo Energia, using
plane. To face this issue and increase the robustness of the model, the mixing plane models available, are shown in Figure 1. In de-
it is possible to use the reflecting model for a certain percentage sign conditions, the compressor of this F-class GT has a pressure
of the channel span next to the endwalls. If there are no flow ratio of about 18:1 and an inlet mass flow around 680 kg/s (see
reversals across the mixing planes interfaces within the compu- [15] for further details). The computational domain includes the
tational domain, the use of the reflecting model for 1÷2% of the IGV and the OGV of the compressor, which is characterized by
channel span next to hub and tip endwalls is usually enough to five air extractions along the meridional flow path. The conser-
assure the stability of the computation. vation of mass flow obtained with the non-reflecting model is
comparable to that of the reflecting one. The different inlet mass

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 flow predicted by the two models is mainly due to the modifica- the cavity flow effect while, in the other, wall boundary condi-
tions in the shock structure in front of the first transonic rotor tions have been imposed on the cavity inlet and outlet areas on
caused by reflection. the hub endwall. The same inlet and outlet boundary conditions
for the computational domain have been used for both cases.
Shroud Leakage Model
Seal cavities under stator rows are a common feature in
heavy-duty multistage axial compressors. In general, the flow
structures which arise inside shrouded cavities are quite complex
and typically characterized by axial, radial, and circumferential
non-uniformities. Their impact on the main flow path must be
taken into account to properly predict the overall compressor
performance, but a detailed 3D solution of all the cavities would
lead to a significant growth of the computational cost and possi-
ble convergence issues, especially in steady-state simulations.
Both these aspects make this option not attractive for industrial
design purposes. Anyway, the effects of seal cavity flows on the
mainstream may be reliably taken into account using a simplified
one-dimensional correlation-based cavity model. This is the
strategy which has been chosen for the TRAF code in which a
simplified shroud leakage model has been implemented. This
model took inspiration from the work presented by Wellborn et
al. [30] and a detailed description of it is provided in [31]. A one-
dimensional model of shrouded cavity flow is used to estimate
the leakage mass flow, total enthalpy variation, and change in
angular momentum having as inputs some geometric parameters
and the flow conditions at the interface connecting cavity and Figure 3: Normalized total temperature profile at stator row exit
meridional flow path. The influence of the shroud cavity on the
primary flow is considered by imposing coupled source/sink The results of these numerical simulations in terms of total pres-
boundary conditions at the cavity/mainstream interface. sure and temperature outlet radial distributions are shown in Fig-
ure 2 and Figure 3, respectively. The interaction between the
shroud leakage flow and the primary flow results in a loss in total
pressure and a rise in total temperature. Both effects are localized
next to the hub endwall region and their extension depends on
the reinjected cavity flow penetration within the primary flow
path.
Clearance Models
A reliable evaluation of the behavior in design and off-de-
sign conditions of a multistage axial compressor cannot be at-
tained without properly modelling the rotor tip clearances. The
value of the radial gap between the blade tip and the machine
case of the rotor rows has a strong influence on the compressor
operating range and stall margin [32] [33]. Several models of in-
creasing complexity are currently available.
Simplified periodicity boundary condition
The simplest and most commonly used clearance model is
the one in which periodicity boundary conditions are enforced
between the two airfoil sides within the clearance region, ob-
tained by extending the grid from the blade tip to the casing while
maintaining the tangential blade thickness. All the conservative
Figure 2: Normalized total pressure radial distribution at stator row variables values for each phantom cell on one side of the grid are
exit interpolated, at the same axial position, from the corresponding
cells on the other side. This boundary condition is just an approx-
To show the impact of the model on a steady-state analysis,
imation of the real configuration in this area, but can lead to re-
two different single-row simulations have been performed on a
ally good results especially for thin blades at tip and reasonable
compressor vane of an existing Ansaldo Energia gas turbine. The
values of the clearance thickness, as shown in [34].
first has been run using the shroud leakage model to account for

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 Pinched grid An example of axial compressor blade with clearance mesh is
The need for being able to face cases with high clearances, represented in Figure 5.
in which the simplified periodicity method may result in fluxes Models comparison
conservation errors, forced the introduction of a more realistic To compare the clearance models already introduced three
model. By pinching the grid (e. g. [35] [36]) in the clearance re- steady-state computations on a compressor blade row have been
gion, the use of periodicity boundary conditions between the two performed. The blade used for the test has a clearance to channel
grid sides in this area is no longer an approximation. The positive span ratio of 1%. Within the 80 cells in the grid spanwise direc-
aspects of this solution are the good conservation properties and tion, 16 have been used to discretize the clearance region. This
the fact that a pinched grid allows the solution of the flow field choice is the result of a trade-off between resolution in this zone
within the clearance region. The only drawback related with this and computational cost. A useful parameter to check the differ-
model is the unavoidable local alteration of the blade tip geome- ence between the flow field predictions obtained with the three
try that becomes slightly spiky. An example of pinched grid for models is the relative blade-to-blade flow angle at domain outlet
the blade of an axial compressor is shown in Figure 4. section. An outlet radial distribution of flow angle for the test
case is shown in Figure 6. The slight differences between the dis-
tributions are located, as expected, next to the tip endwall in the
last 15% of the channel span. The maximum difference regis-
tered between the three curves is lower than 0.5°.

Figure 4: Compressor blade pinched grid

Meshed clearance region

The most advanced model that can be used without intro-
ducing any approximation or geometry modification is a meshed
clearance region. In this case, a structured O-type grid allows a
detailed solution of the flow field inside the clearance. The only
disadvantage of this solution is the higher computational cost due Figure 6: Radial exit flow angle distribution for the different clear-
to the additional clearance block which is added to the computa- ance models
tional domain. Another possible way to highlight differences between the avail-
able models is a blade-to-blade visualization of the streamlines
in the clearance region. Such kind of representation is shown in
Figure 7 and Figure 8. In the former, a comparison between pe-
riodicity boundary conditions and clearance mesh model is pre-
sented, while the latter shows the pinched grid case. Both perio-
dicity and pinched grid models led to a good match of the
streamlines direction obtained using the more complex and de-
tailed clearance mesh one. These results confirmed that the use
of a simplified periodicity boundary condition for the clearance
region is an appropriate approximation, especially for axial com-
pressor blades which are commonly really thin at tip section,
making this kind of modelling attractive for industrial design
purposes. For routine multistage axial compressor simulations,
Figure 5: Compressor blade with meshed clearance the simplified model is used for clearance values lower than

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 2.5% while, for higher levels, the other options are adopted to Two full-compressor steady-state simulations have been
avoid possible fluxes conservation issues. performed at the operating condition experimentally tested (de-
sign point), using the available mixing plane models.

Figure 7: Blade-to-blade streamline visualization in the clearance

region for periodicity and meshed clearance model

Figure 9: Average static pressure rise along the meridional channel

at machine casing

Figure 8: Blade-to-blade streamline visualization in the clearance

region for the pinched grid model

EXPERIMENTAL VALIDATION OF THE SETUP

In order to assess the reliability of the computational setup
developed within the collaboration between the University of
Florence and Ansaldo Energia, a comparison with experimental
data has been carried out. The experimental data come from a
test campaign handled on an upgraded version of the AE94.3A
GT compressor of Ansaldo Energia fleet. In this configuration,
at design operating conditions, the 15-stage compressor has a
pressure ratio of about 19:1 and an inlet mass flow around 735
kg/s. Six measurement stations have been positioned upstream
of some of the compressor stator rows. Pressure and temperature
static probes have been placed along the meridional flow path at Figure 10: Average static temperature rise along the meridional
the machine casing. For each measuring station, three probes channel at machine casing
have been positioned at different, equally spaced, circumferen-
Figure 9 shows the pressure rise along the compressor meridio-
tial locations, both for pressure and temperature measurements.
nal channel predicted by the numerical simulations and meas-
The values compared with the numerical results are obtained by
ured on-site. The numerical mean pressure values reported are
averaging the data acquired from the probes at the same axial
obtained through a pitchwise averaging process of the 3D solu-
position.
tion. In the front part of the machine, up to the third pressure

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 probe, a really good agreement with experimental results is ob- Design Conditions
served. In this part of the compressor, the analyses with different The first comparison between steady and unsteady analyses
mixing plane models result in a similar predicted pressure rise has been carried out at compressor design operating conditions.
development. Some differences between numerical computa- The results in terms of stage total-to-total pressure ratio are re-
tions and experimental data arise in the second part of the ma- ported in Figure 11. In general, a really good agreement between
chine, especially for the 4th and 5th probe, while for the last one, steady-state results with non-reflecting boundary conditions and
closer to the compressor discharge in which the static pressure time-averaged unsteady ones is observed. In the front stages of
distribution is enforced as boundary condition, a better agree- the compressor, the steady-state simulation with reflecting
ment is obtained. boundary conditions tends to overestimate the pressure ratio with
Simulations results in terms of temperature rise at the casing respect to the full-annulus analysis. On the contrary, it leads to
along the meridional channel are compared with experimental an underestimation in the rear part of the machine. The discrep-
data in Figure 10. In this case again, a pitchwise average has been ancies between the reflecting steady-state case and the others are
performed on the 3D solutions. Excluding the 2 nd and 3rd probe, even more enhanced when it comes to mass-averaged values of
a general overestimation of the measured values is observed for total temperature at row interfaces, shown in Figure 12. Both
both the computations. Between the two mixing plane models, steady-state curves well match the unsteady one up to the end of
the non-reflecting one gets closer to the experiments, mostly pre- the second stage. Downstream of this stage the curve of the
dicting a lower temperature level than the one resulting from the steady-state reflecting case starts to diverge from the others, pro-
other. gressively overestimating the total temperature.

COMPARISON WITH UNSTEADY RESULTS

Due to really high computational cost, unsteady simulations
of a full axial compressor with high stage count are not suitable
for industrial design purposes. Anyway, unsteady analyses can
give feedbacks on the reliability of steady-state simulations,
which are used as a standard for routine design procedures. In
order to assess the impact on performance prediction of the mix-
ing planes, full-annulus unsteady simulations of the whole 15-
stage standard AE94.3A compressor have been performed in two
different operating conditions: design point and near-stall. Both
IGV and OGV rows have been included in the computational do-
main. The same boundary conditions have been used for steady
and unsteady computations.
The choice of performing a full-annulus unsteady analysis
of a compressor with more than 2000 blades instead of a less,
computationally speaking, demanding phase-lagged one, has
been taken because, especially for near-stall conditions, the in-
teractions between non-adjacent rows may be crucial for the
stage matching. In fact, these interactions are not taken into ac-
count in a phase-lagged approach, in which only two blade pass-
ing frequencies, the ones referring to the upstream and down-
stream adjacent rows, are considered in the evaluation of the Figure 11: Normalized total-to-total stage presure ratio at design
boundary conditions to be enforced in each computational block, point
while other perturbations are mixed out at the inter-row inter- Despite the proved good agreement in terms of mean total tem-
faces [24]. The typical block size of structured H-type grid used perature between the unsteady and the steady non-reflecting
for a blade passage is around 0.75 million of cells, resulting in cases, the shapes of the radial distribution of this parameter differ
more than 1.5 billion grid points within the full-annulus compu- for the last stages of the machine, as shown in Figure 13, which
tational domain. The time-sampling of the unsteady computa- displays the computed distributions downstream of the last stage
tions was imposed considering a trade-off between accuracy and stator row. The radial profile obtained through the unsteady sim-
computational costs, adopting 25 time divisions for each blade ulation is more uniform than the steady one. Something similar
passage of the row with the highest blade count. Both the oper- has already been observed in literature [37] [38] when comparing
ating conditions investigated through an unsteady analysis re- experimental temperature profiles in rear stages of multistage ax-
quired 3 periods to reach periodicity starting from a steady-state ial compressors with steady-state CFD analyses. The more uni-
solution, each requiring around 7 days using a parallel process form radial temperature profile experimentally measured after
involving 200 Intel® E5-2680 V2 CPUs. The difference in terms several stages is associated with the so called “radial mixing”
of computational time with respect to a steady simulation is con- phenomenon. By accounting for all the interactions between the
siderable, the latter requiring about 2 hours running on 32 CPUs. rows in terms of wakes, potential effects and secondary flows

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 propagation along the flow path, a full-annulus unsteady simula- Near-stall Conditions
tion seems to better predict the effects of radial mixing. A possi- The use of a relatively light and fast steady-state approach
ble explanation could be associated with a major limitation of with non-reflecting boundary conditions led to a really good ap-
mixing planes, that is their smoothing-out of actual non-uniform- proximation of time-averaged unsteady results for compressor
ities by pitch-averaging the flow between adjacent rows. On the design point. To assess the impact of the steady-state approxima-
contrary, the time-accurate calculation allows the growth and the tion also in off-design, a near-stall condition at compressor nom-
transport of any secondary flow structure throughout the domain, inal speed has been considered. To determine an operating point
thus enhancing the mixing inherently associated with the stream- close to compressor surge line, various steady state analyses have
wise vorticity. been performed by progressively increasing the outlet static
pressure. The run with higher back-pressure which managed to
converge established the near-stall outlet boundary condition,
and the same one was adopted for the unsteady simulation as
well. The comparison results in terms of predicted total-to-total
stage pressure ratio are shown in Figure 14. A really good agree-
ment between unsteady and steady non-reflecting case is ob-
served for the last five stages of the compressor while, for the
front part, some slight discrepancies arise. The reflecting steady-
state model generally shows a less accurate match of unsteady
results than the non-reflecting one.

Figure 12: Normalized mass-averaged total temperature at row

interfaces at design point

Figure 14: Normalized total-to-total stage presure ratio at near-stall

condition
The values of mass-averaged total temperature at row interfaces
for the compressor at near-stall conditions are reported in Figure
15. In this case, an even better match between steady-state non-
reflecting simulation results and unsteady ones is achieved. Only
some slight differences can be found between the two curves in
the central stages of the compressor. As seen for the design point,
also in this operating condition the steady state analysis with re-
flecting boundary conditions tends to overestimate the unsteady
results immediately after the first two front stages.
As shown in Figure 16, the differences in terms of total temper-
Figure 13: Normalized radial total temperature distribution at last
ature radial distribution observed at design conditions are en-
stage stator row outlet at design point hanced getting closer to compressor stall at nominal speed. The

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 steady distribution has an increased non-uniformity in the CONCLUSIONS
spanwise direction with respect to design point, while the un- In this work, an advanced numerical setup for steady-state
steady curve is also in this case more uniform. multistage axial compressor simulations adopted by Ansaldo En-
ergia, developed in collaboration with the University of Flor-
ence, has been presented. Some crucial aspects of the compressor
modelling have been addressed, namely mixing planes, shroud
leakages and rotor tip clearances. Concerning the mixing planes,
a recently implemented, strongly conservative model with non-
reflecting boundary conditions extended to the real gas case has
been presented, showing some results in terms of mass flow con-
servation on a multistage axial compressor of Ansaldo Energia
fleet. Some typical features that have relevant influence on per-
formance such as shroud leakage and clearance modelling have
been included within this paper. The shroud leakage model
adopted has been tested on a single-row case, to assess the influ-
ence of cavity flows on mainstream. All available clearance
models have been presented and compared, showing that for
compressor blades a simplified periodicity boundary condition
can lead to a good approximation of clearance flows.
The numerical setup has been validated on a compressor de-
signed and experimentally tested by Ansaldo Energia. To deter-
mine the influence of mixing plane models on performance pre-
diction, unsteady full-annulus simulations of a whole 15-stage
compressor have been performed at two different operating con-
ditions: design point and near-stall. The comparison between
steady and unsteady computations demonstrated a really good
Figure 15: Normalized mass-averaged total temperature at row agreement in terms of averaged values, especially when using
interfaces at near-stall condition the non-reflecting mixing plane model for the steady state anal-
ysis. Some interesting differences between steady and unsteady
results arose in the radial distribution of total temperature at com-
pressor outlet, showing that the unsteady analysis predicts a
smoother temperature profile. Bearing in mind that experimental
measurements on axial compressors have always shown more
spanwise mixing than CFD results, the present outcome seems
of particular interest, and deserves further investigations. Alt-
hough a possible explanation has been provided, a comparison
with experimental data will be necessary to reinforce it.

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