Turbomachinery simulation challenges and the future

Abstract

Dramatic changes to aircraft design are on the horizon to meet ambitious efficiency and emissions targets. This will bring about changes in the role and design of aero-engines, requiring a greater degree of high fidelity, coupled modelling. To bridge a wide range of spatial and temporal scales, modern turbomachinery design employs a wide range of modelling fidelities during different design stages and for different engine components. High fidelity methods such as Large Eddy Simulation (LES) have been successfully applied to numerous complex flows where traditional Reynolds-Averaged Navier-Stokes (RANS) modelling does not sufficiently represent flow physics to be consistently accurate. Using LES and, for high Reynolds number flows, hybrid LES-RANS, critical knowledge has been extracted and exploited both to inform designs and to improve lower order modelling. It seems certain that uptake of high fidelity methods will continue at a rapid pace. Here we explore some of the future challenges facing turbomachinery simulation using LES. These include use of higher order schemes, internal and external zonalisation and coupling, exploitation of hardware and pre and post-processing. Although these pose technological barriers, these will enable unexplored design space to be traversed with confidence, resulting in cleaner, quieter, and more efficient aircraft.

Full text

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Progress in Aerospace Sciences
journal homepage: www.elsevier.com/locate/paerosci
Turbomachinery simulation challenges and the future
James Tyacke
a,*
, N.R. Vadlamani
b
, W. Trojak
c
, R. Watson
c
, Y. Ma
c
, P.G. Tucker
c
a
Department of Mechanical and Aerospace Engineering, Brunel University London, UK
b
Department of Aerospace Engineering, Indian Institute of Technology Madras, India
c
Engineering Department, University of Cambridge, UK
ARTICLE INFO
Keywords:
LES
Turbomachinery
Multi-fidelity
Coupled
Multi-physics
ABSTRACT
Dramatic changes to aircraft design are on the horizon to meet ambitious efficiency and emissions targets. This
will bring about changes in the role and design of aero-engines, requiring a greater degree of high fidelity,
coupled modelling. To bridge a wide range of spatial and temporal scales, modern turbomachinery design
employs a wide range of modelling fidelities during different design stages and for different engine components.
High fidelity methods such as Large Eddy Simulation (LES) have been successfully applied to numerous complex
flows where traditional Reynolds-Averaged Navier-Stokes (RANS) modelling does not sufficiently represent flow
physics to be consistently accurate. Using LES and, for high Reynolds number flows, hybrid LES-RANS, critical
knowledge has been extracted and exploited both to inform designs and to improve lower order modelling. It
seems certain that uptake of high fidelity methods will continue at a rapid pace. Here we explore some of the
future challenges facing turbomachinery simulation using LES. These include use of higher order schemes, in-
ternal and external zonalisation and coupling, exploitation of hardware and pre and post-processing. Although
these pose technological barriers, these will enable unexplored design space to be traversed with confidence,
resulting in cleaner, quieter, and more efficient aircraft.
1. Introduction
The challenge to reduce pollutants such as CO
2
, NOx and noise in
aviation continues to be a key technology driver. Aside from the air-
frame, civil turbofan aeroengines have been the focus of intense re-
search, to reduce these emissions. The Advisory Council for
Aeronautical Research in Europe (ACARE) set the target of a reduction
in perceived noise level emission of 50% (to those of the year 2000) by
the year 2020 [1]. The EU Flightpath 2050 report [2] states a 75%
reduction in CO
2
, a 90% reduction in NOx and a 65% perceived noise
level reduction relative to year 2000 levels as a goal. Improving recent
aero-engine technologies has enabled significant reductions to be made,
largely through the use of CFD and supporting experimental data.
A wide range of future aircraft designs are under consideration for
the 2030–2035 timeframe, including: slender winged airframes with
trusses, blended wing-flaps with morphing capability, blended wing-
bodies with podded or embedded boundary layer ingesting engines and
subsonic and supersonic jets. Fig. 1 shows some concepts focused on
reducing fuel burn and pollutants including noise. Most will include
some form of gas turbine power system as direct propulsion or as a
means to generate electricity for propulsion or auxiliary systems. Hall
and Crichton [3] present a propulsion system consisting of an ultra-high
bypass ratio turbofan driving two additional fans, embedded within an
S-duct, for an all-lifting body airframe. As part of the Silent Aircraft
project, fuel burn is predicted to be up to 45% less than a Boeing 777
[9]. Hybrid gas-turbine and electric propulsion systems coupled with
airframes including large laminar flow regions are also under con-
sideration by NASA and Boeing. These provide estimates of reductions
in CO
2
(69–81%), NOx (21–42%) and noise (16–37 dB) in the
2030–2035 timeframe [10]. Many enabling technologies are presented
by Ashcraft et al. [4].
Small improvements in efficiency from each component broadly add
up for the whole engine. The number of passenger and cargo flights per
year is forecast to increase over 20 years at 5% and 5.8% respectively
(from 2011 as [5]), magnifying this effect over decades of service.
However, the role that the entire engine, as well as the relative impact
of the core, bypass or potentially open or closed rotor fans will change.
For a modern bypass ratio the core accounts O
1/10th
the total thrust. It
is clear that given the losses generated in such a complex flow path, the
improvements made to the core flow will have a reduced relative
contribution to the overall aircraft efficiency, yet must still efficiently
drive ever larger fans. Large components such as the fan and
https://doi.org/10.1016/j.paerosci.2019.100554
Received 2 April 2019; Received in revised form 15 July 2019; Accepted 16 July 2019
*
Corresponding author.
E-mail address: james.tyacke@brunel.ac.uk (J. Tyacke).
URL: http://brunel.ac.uk/people/james-tyacke (J. Tyacke).
Progress in Aerospace Sciences xxx (xxxx) xxxx
0376-0421/ © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/BY/4.0/).
Please cite this article as: James Tyacke, et al., Progress in Aerospace Sciences, https://doi.org/10.1016/j.paerosci.2019.100554

installation effects however, now have a significant impact on overall
engine and aircraft performance. New low speed fans may be geared
rather than directly driven by the LPT. Great efforts are being made to
improve low speed fan performance, requiring new understanding of
flow, structural and acoustic interactions. The complex 3D shape of
modern fans indicates multi-fidelity, multi-physics numerical simula-
tion will be heavily relied upon. Therefore, coupling at the internal
(core), engine (fan-intake) and external (engine-airframe) scales will
later be considered. Similarly, critical core areas with important cou-
pling such as heat transfer in the turbine will be discussed.
For context, we look back at how we arrived at today's status of
turbomachinery CFD. Early use of velocity triangles in the 1950s pro-
ceeded to throughflow models such as Wu [11] and gradually led to 2D
and 3D Euler and Navier-Stokes solvers. The main move from thousands
to millions of cells was made in the mid 1980s to the mid 1990s using
steady RANS, enabled by consistently improving CPU speeds. It could
be argued, this is where reliance on advances in hardware to improve
solutions was imprinted within the minds of a CFD generation. This has
lead to poor exploitation of available computational resources today
and the delay of algorithmic advances [12]. In the mid-late 1990s,
unsteady CFD saw use, but turbulence modelling had become limiting,
unable to model important flow physics such as secondary flows,
transition and separation. In addition, the importance of coupling of
external and internal flows became apparent. In Abhari and Epstein
[13], hot gas was found to enter turbine blade cooling holes due to high
external pressure fluctuations, underscoring the physical unsteadiness
and coupled nature of such flows which was not captured by numerical
models. Denton and Dawes [14] summarise turbomchinery CFD prac-
tice in the late 1990s by which time 3D multi-stage calculations were
possible, albeit with the limitations of mixing planes (inter-row cir-
cumferential averaging) and approximations including interactions
with secondary gas systems and leakage paths. Looking back these were
not well modelled, the reality being that they are highly unsteady
coupled systems that cannot be designed or modelled in isolation.
Denton [15] discusses several gross limitations in more detail. Denton
[16] studied loss in terms of entropy for a wide variety of mechanisms.
As noted by Denton, a physical understanding may be more valuable
than quantitative prediction based on empiricism. Later Denton and
Nomenclature
Acronyms/labels
ACARE Advisory Council for Aeronautical Research in Europe
AI Artificial intelligence
ASIC Application specific integrated circuit
BL Boundary layer
CBTE Cut-back trailing edge
CFD Computational fluid dynamics
CFL Courant-Friedrichs-Lewy
CPU Central processing unit
DDES Delayed detached-eddy simulation
DES Detached-eddy simulation
DNA Deoxyribonucleic acid
DNS Direct Numerical Simulation
DOF Degrees of freedom
EU European Union
FD Finite difference
FLOPS Floating point operations per second
FPGA Field-programmable gate array
FR Flux reconstruction
FST Freestream turbulence
FV Finite volume
GA Genetic algorithm
GEP Gene expression programming
GPU Graphics processing unit
HPC High performance computing
HPT High pressure turbine
I/O Input/Output
IBM Immersed boundary method
IBMSG Immersed boundary method smeared geometry
IDDES Improved delayed detached-eddy simulation
ILES Implict large-eddy simulation
LE Leading edge
LES Large-eddy simulation
LPT Low pressure turbine
MILES Montonicically integrated large-eddy simulation
ML Machine learning
MPI Message passing interface
NLDE Non-linear disturbance equations
OGV Outlet guide vane
PDE Partial differential equation
RANS Reynolds-Averaged Navier-Stokes
ROI Region of interest
SE Spectral element
SGS Subgrid scale
STG Synthetic turbulence generation
SV Spectral volume
TE Trailing edge
TKE Turbulence kinetic energy
TRL Technology Readiness Level
UQ Uncertainty quantification
VMS Variational multi-scale
VSTG Volume synthetic turbulence generation
WALE Wall-adapting local eddy-viscosity
ZDES Zonal detached-eddy simulation
Greek
δBoundary layer thickness
+
Grid spacing (wall units)
ηKolmogorov length scale (m)
ψLocal time stepping speedup factor
ρDensity (Kg/m
3
)
Roman
CBlade chord
Cp
Pressure coefficient
CT
Thermal time constant
fr
Lund recycling frequency (Hz)
hHeat transfer coefficient (W/m
2
K)
kThermal conductivity (W/mK)
Lt
Integral length scale (m)
Lr
Lund recycling length (m)
NNumber of grid points
pNumerical scheme order
Rij
Reynolds stress, components i,j
Re
Reynolds number
=Re UL /
L x
Flat plate Reynolds number
SBlade span
uc
Characteristic convective velocity (m/s)
Sub/superscript
x,y,z Streamwise, wall normal, spanwise direction
J. Tyacke, et al. Progress in Aerospace Sciences xxx (xxxx) xxxx
2

Pullan [17] study blade endwall secondary flow loss. Cascade mea-
surements were shown to be of limited use. They proposed full stage
calculations with well defined inlet conditions and investigations into
the specific loss sources for a particular design, before design changes.
Today much design is still based on 1D correlations and steady CFD
being performed with little inflow data if any, in an attempt to verify
improvements. A saturation point has been reached whereby un-
certainties in modelling mask well founded design alterations.
Current design systems have high uncertainties, so designs are often
compromised by adding safety margins. These uncertainties range from
problem definition (do we really know the true boundary conditions?)
to modelling errors (discretisation and turbulence modelling). Current
technology makes use of higher favourable and adverse pressure gra-
dients and often high curvature blades, invalidating standard RANS
calibrations. For example, shock boundary layer interaction modelling
has two key deficiencies. (I), the shock foot location and strength and
(II), the subsequent separation behaviour, all of which are unsteady.
Clearly neither of these are in the comfort zone of typical steady RANS
models, historically developed for attached boundary layer flows. The
influence of coupling zones with RANS content also raises fundamental
RANS modelling issues. For example, labyrinth seals generate low Mach
number wake turbulence from seal teeth but a high rotational Reynolds
number and hence a high
Re
boundary layer also develops [18]. Such
Mach number disparities also raise numerical smoothing issues. In rim
seals, the circumferential integral length scale is many times greater
than that of the meridional plane. The implied lengthscales from RANS
can also be wildly inaccurate. Jefferson-Loveday et al. [19] use a Ha-
milton–Jacobi differential equation to modify RANS length scales, im-
proving drag coefficient prediction by 20–30%. An inflow-outflow
condition is also developed to replicate pumping of fluid in and out of a
rim seal [20]. Hence modest increases in geometrical complexity can
have profound flow and modelling impacts. Inflow conditions in tur-
bomachines are seldom well defined for modelling, even by gross
quantities, let alone detailed fields. Even if they were known, as noted
by Spalart [21], the
k
,
k
and S-A models are insensitive to
freestream conditions, which is obviously incorrect from a physical
standpoint. As an engine cycles through different operating conditions,
the geometry changes, so not even the designed geometry is well de-
fined. These may be seen as problems to modelling, or alternatively, an
opportunity to realise large gains! User experience and the decisions
made are often overlooked as one of the key controls over such un-
certainties, which lead to the previous systems suggested to provide
consistency for industrial use [22].
Sandberg and Michelassi [23] suggest extremely accurate CFD is
required to realise order of efficiency 0.1–1.0% gains. From a flow re-
solution standpoint (ignoring problem definition fidelity and
uncertainty), the ideal of Direct Numerical Simulation (DNS), is cur-
rently out of reach for most industrial flows due to high Reynolds
numbers and impractical grid demands as DNS requires
ORe2.65
nodes
[24]. Many detailed data sets have provided physical insights at low
Re
[25–28]. Most current CFD is still comprised of steady RANS modelling
and acheiving improvements of the order of 0.1% seems out of reach.
Modern turbomachinery design employs a wide range of modelling fi-
delities during different design stages and for different engine compo-
nents. The required spectral gap to enable URANS instead of RANS
often doesn't exist [29] and current trends – smaller, faster rotating
components; higher frequency vortex shedding from thinner trailing
edges; greater degree of transonic to supersonic flow with shock-BL
interaction [23] point towards fewer flows able to utilize URANS. In-
deed, turbulence is broadband, and the notional separation of resolved
and modelled scales makes little sense. Currently in gas turbines 80%
losses stem from BL flow [23]. The above suggests (U)RANS may
completely fail for current applications which could result in redesigns
costing millions to hundreds of millions in additional fuel and main-
tenance costs to manufacturers, airlines and adversely impacting the
environment. Most eddy-resolving methods on the other hand, without
largely resorting to DNS, will exceed current accuracy levels with ease
where RANS fails, bringing about great benefits. Extreme resolution is
not necessarily required.
High fidelity methods such as Large Eddy Simulation (LES) have
been successfully applied to a wide range of complex flows where tra-
ditional (U)RANS modelling does not sufficiently represent flow physics
to be consistently accurate [30]. Using LES and, for high Reynolds
number flows, hybrid LES-RANS, critical knowledge has been extracted
and exploited both to inform designs and to improve lower order
modelling. Although LES is often cheaper than rig testing, it is still
considerably more costly than RANS. Hence this ability to improve
lower order models in a more general sense is key.
With adequate problem definition and mesh resolution, low
Reynolds number and wake dominated flows can now be used to re-
place a substantial amount of rig testing. At higher Reynolds numbers,
jet aeroacoustics is one area of application using hybrid LES-RANS [31].
When installed, ultra-high high bypass ratio jets interact strongly with
the airframe [32,33], requiring these to be considered together. Noise
from ultra-high bypass ratio jets installed near 3D wings under flight
conditions has been accurately predicted [32]. Such coupled flows are
difficult to accurately reproduce experimentally. Using LES, sound
sources, length and time scales have been located and quantified in 3D
[34]. Three-dimensional mean flow, turbulence and unsteady data re-
corded provide a wealth of potential knowledge. The most ideal flows
can even be optimised using LES. For example using a genetic algo-
rithm, turbine trailing edge cut-backs [35] (600 geometries), internal
Fig. 1. Future airframe concepts (a) Silent Aircraft Initiative SAX-40 concept [3], (b) NASA N3-X Turboelectric Distributed Propulsion (TeDP) concept [4], (c) NASA/
Boeing SUGAR concept using a Truss-Braced Wing (TBW) [5], (annotations added to [6–8]).
J. Tyacke, et al. Progress in Aerospace Sciences xxx (xxxx) xxxx
3

cooling geometry [36] (10 geometries) and labyrinth seals [37] (80
geometries). The turbomachinery industry is now actively bringing LES
into their design cycles, however cost will remain the long term con-
straint for eddy resolving methods. Areas of high impact are transi-
tional, separated, and mixing flows and those with heat transfer. LES is
expected to allow progress to be made for the more complex geometries
found in industry. Best practices are hence critical and these are being
established using robust and mature technology such as second order
finite volume (FV) methods [31].
Transition modelling can also impact, for example, LPT perfor-
mance or HPT heat transfer prediction. For the LPT Vadlamani [38]
matches the unsteady transitional flow physics of an LPT with passing
wakes. Pichler et al. [39] study LPT rotor stator axial gap effects per-
forming a loss breakdown and identifying unexpected kinetic energy
growth away from the blade. For the HPT, high heat flux unsteadiness
can be observed even before transition due to Klabanoff streaks. If
hybrid LES-RANS is to be used around such leading edges, either sig-
nificant advances in RANS modelling to account for flow acceleration,
curvature and pre-transitional behaviour, or novel LES/RANS zonali-
sation procedures require development.
Heat transfer is becoming more important in the adequate model-
ling of compressors and turbine temperatures have continually risen
[40]. To prevent blades deteriorating, internal and external cooling
flows are introduced. There has been a long standing demand for ac-
curate heat transfer modelling under these chaotic flow conditions.
Such demands can be largely met by LES, yet industrial use remains
low, instead relying on costly experiments that may deliver data late in
the design, where changes are expensive. For example, in 2005, Guo
et al. [41] study film cooling holes injection angle, blowing ratio and
resulting flow anisotropy, naturally resolved using LES. Sewall and Tafti
[42] and Tyacke and Tucker [43] study internal cooling duct ribbed
passages using LES. Such LES can be run for less than $500 compared to
a rig test costing approximately $50,000. Trailing edge cutbacks are
optimised using a perfectly parallel genetic algorithm by Watson and
Tucker [35]. All of these use meshes of the order of 1–10 million cells,
which in the shadow of Exascale computing (demonstrated 2018 [44],
Argonne Labs, Aurora due 2021 [45]) should now be commonplace.
Tyacke and Tucker use flow categorisation to suggest wider application
of eddy-resolving methods [22].
Although flow over isolated blades or mid span sections is per-
formed routinely in academia and is making inroads into industry,
multi-blade and multi-row effects are critical in revealing the true
performance of real systems. Passing blade wakes and tip leakage
vortices can heavily influence the main flow as shown by McNulty et al.
[46]. Forward sweep was found useful to improve stall margin and
reduce loss, highlighting the need for reliable 3D design and validation
tools. Typical RANS performs poorly outside of a working range and
Uncertainty Quantification could be used in future to provide con-
fidence and quantitative evidence of risk in design. Saito et al. [47]
study a two stage compressor with stator LE and TE leakage flow using
DES with a 450 million cell mesh (104 blades). Yamada et al. [48] study
stall in a seven stage axial compressor using 2 billion cells (650 million
in the first two stages). Here stall cells in the first two stages grow to 1/
3
rd
annulus. In the
5 6th
stages, leading edge separation leads to ro-
tating stall and large scale blockage in up and downstream rows.
Clearly full annulus eddy-resolving calculations meet significant cost
constraints and accurately predicting the sensitive flow physics in a
compressor is essential to predict design and off-design performance.
We are now at a point where turbomachines and their interaction
with future airframes need to radically change to meet new targets,
putting designers in unknown territory. With ever shrinking design
cycles and rapidly dropping computational cost, high fidelity simula-
tion is now being absorbed into industry to supplant experiments, in-
form design tools and reveal unsteady flow physics in astonishing de-
tail. In this paper we review some promising methods, note key
challenges and identify paths forward.
The paper is structured as follows. Firstly, aspects of zonalisation
and coupling are discussed along with some significant challenges fa-
cing the use of high fidelity methods in turbomachinery. The potential
of high order schemes in terms of accuracy, cost, SGS modelling and its
current uses is considered. Validation of high-fidelity methods and their
use in lower order model development are examined. Barriers and
suggestions on how to move forward are then discussed before sum-
marising.
Fig. 2. Recent uses of LES to reveal flow physics and to improve high and low order modelling at a range of scales.
J. Tyacke, et al. Progress in Aerospace Sciences xxx (xxxx) xxxx
4

2. Zonalisation and coupling
Fig. 2 shows current LES use at sub-component level (A), component
level (B), installation effects (C), and large scale coupled systems (D).
Each requires some variation in modelling methodology. Zonalisation
and coupling of these zones is hence a critical issue in terms of both
turbulence and geometry modelling fidelity [22]. Both these aspects are
used to deal with multi-scale flow. Geometry representation is here
considered more fluid in terms of fidelity, using immersed boundaries
and body forces as well as traditional body fitted meshes. Fig. 3 shows
such a hierarchy. Furthermore, design now requires multiphysics
modelling. As noted by Dawes [49], geometry links different dis-
ciplines, perhaps requiring geometry definition in terms of level sets,
allowing simple geometry modification during design. Combined phy-
sical modelling may include conjugate heat transfer for film, cut back
trailing edge and internal cooling as [50–53], finite element analysis
and aeroelasticity, acoustics [31,34,54–63], particle transport (volcanic
ash [64,65], sand), water droplets (rain, steam turbines), ice accretion
and shedding [66] and reacting flows [67] among others.
Where it does not make sense to integrate software aimed at dif-
ferent physics, coupling software can be advantageous. CHIMPS, used
for the Stanford whole engine simulations [68] where RANS is used for
the compressor and turbine and coupled with and LES for the com-
bustor is one example. The MpCCI library [69] also offers multiple grid
functionality including interpolation with user defined methods. Other
available software includes CORBA [70], designed for heterogeneous
computing and interdisciplinary coupling and OpenPALM developed by
Cerfacs and ONERA. Using OpenPALM, conjugate heat transfer for a
combustor is performed by Duchaine et al. [71] and for a cooled turbine
blade [72], combustor LES coupled with radiation modelling is also
performed by Poitou et al. [73]. Aspects of zonalisation and coupling
are now presented. Note, here, the term coupling does not refer to
linking of different codes.
2.1. Hybrid RANS-LES turbulence modelling
LES can be selectively used for low Reynolds number flows such as
those found in the LPT. The use of LES for high Reynolds number flows
is generally still restricted to academia. For these, hybrid LES-RANS
methods appear to be a clear path forward. The most well known and
commonly used is Detached Eddy Simulation (DES) with its variants
such as Delayed DES (DDES) [74], Improved DDES (IDDES) [75]. This
has seen success for massively separated (wake type) flows. For more
general cases Deck [76] suggests a zonalised approach to widen its use
for flows with no clear separation point and later improvements [77].
However, as DES relies on RANS for the entire boundary layer, it in-
herits many of the deficiencies in the underlying RANS model which is
typically a linear eddy viscosity model and can rely heavily on the grid
filter. Aside from this, turbine blade film cooling is achieved with
complex arrays of jets emanating from the wall. These inject locally
large scale unsteadiness into an assumed (under DES) quasi-steady
boundary layer flow. Recently, Sreekanth and Woodruff [78] in-
troduced a RANS-LES zonalisation, whereby discontinuities in turbu-
lence quantities can be avoided by substitutions in the governing
equations. This avoids the well known log-layer mismatch but requires
further testing.
Other well established zonal approaches such as Tucker and
Davidson [79] require more input via the user or a control system, but
allow explicit turbulence modelling and filter definition. Here, use of
RANS in the inner layer only, brings a significant reduction in com-
putational cost, a more diluted RANS contribution (< 1% of the
boundary layer) and allows more fine tuned control over RANS and LES
content if required. This may be required in transitional flow or zones
prone to separation, however, this approach has been quite robust in its
basic form [80,81]. The recent implementation of this zonalisation
using a blending function [57] naturally enables the definition of RANS,
LES and hybrid LES-RANS zones and synthetic turbulence generation
between RANS and LES zones. For sensitive flow regions such as low
surface curvature separation and transition in compressors and tur-
bines, on-the-fly modifications could be applied using zonal informa-
tion and flow metrics. In the HPT where the Reynolds number is high
and hybrid LES-RANS is required, embedded LES zones may also be
useful. For example near the leading edge where there is rapid eddy
distortion, high flow curvature and leading edge transition, or down-
stream of film cooling holes where significant large scale mixing takes
place near the heated surface. Sagaut et al. [82] use LES only in the
transition, trailing edge and wake region of a T106 LPT blade. RANS is
used elsewhere, with Non-Linear Disturbance Equations (NLDE) [83]
used to extract fluctuations from RANS to provide to the LES zone. Non-
reflecting boundary conditions are also applied at the LES interface to
avoid spurious acoustic fields.
Significant performance penalties have been observed for com-
pressor blade roughness [84], especially near the leading edge, the
thickened boundary layer effecting blockage due to shock interaction.
The fine scale topology of roughness elements can have significant ef-
fects on transition, drag and heat transfer [85,86]. Such topology and
degree of roughness will vary over each component and over the life of
the engine due to manufacturing variation, abrasion and accretion of
debris from pollutants and dust, determined by flow paths and tem-
peratures. Any near wall modelling should attempt to reflect this. As
noted, local boundary layers are coupled with the passage flow, the
effect being at the sub-component level.
2.2. Turbulence interfaces
Another aspect is the availability of data indicating inflow condi-
tions. For example, even for carefully carried out academic experi-
mental turbomachinery studies, even mean flow data is often lacking.
The supply of critical integral scales of turbulence is severely lacking.
This forces us to attempt to insert suitable mean flow and turbulent
content at boundaries of domains and interfaces between modelling
regions.
Sufficiently accurate inlet turbulence can be critical in some zones.
Thomas et al. [92] study surface temperatures of high pressure turbine
vanes downstream of a combustor. Unsteady combustor turbulence was
required, constant 2D inlet conditions producing persistent secondary
structures generating incorrect surface temperatures. Inflow turbulence
should be of sufficient form and detail to generate the correct down-
stream flow. An example for an LPT in Fig. 4, shows types of turbulence
content needed. This includes freestream turbulence based on a tur-
bulence spectrum, wake and boundary layer turbulence, with the cor-
rect level and distribution of correlated fluctuations. These can be
generated separately and combined [38], however this is not ideal for
everyday use. A key inflow requirement, particularly for turbo-
machinery, where components are axially close, is that real turbulence
develops rapidly and in a short distance. The inclusion of synthetic
turbulence must ensure realistic conditions at, for example, the leading
edge of a blade rather than the inlet face itself, or an arbitrary mea-
surement location. Ideally methods also adhere to physical require-
ments such as avoiding continuity errors (being divergence free for
incompressible flow) or acoustic contamination. The capability to re-
produce anisotropic Reynolds stresses is also desirable, particularly for
Fig. 3. Turbulence modelling and geometry representation hierarchy. (In the
current discussion (U)RANS is not considered high fidelity and is greyed out).
J. Tyacke, et al. Progress in Aerospace Sciences xxx (xxxx) xxxx
5

boundary layer flows. Table 1 indicates advantages and disadvantages
of common approaches. Previous reviews of inflow generation methods
are provided by Sagaut et al. [82], Keating et al. [93] and Tabor and
Baba-Ahmadi [94]. The most pragmatic and general approach appears
to be the use of synthetic turbulence rather than use of precursor si-
mulations, random perturbations or boundary layer flow where Lund
type recycling (Lund et al. [91]) is often used. For recycling methods,
spurious periodic signals from recycling (
f U L/
rc r
) can arise. Other
limitations relate to appropriate scaling for different flows, for example
for compressible flow or those with strong pressure gradients. In
practical terms, there are two broad considerations - (I) the turbulence
generation method including its capabilities and limitations, and (II),
how this is applied to the flow. The latter point also eludes to the
application of these methods to RANS/LES modelling interfaces.
Schlüter et al. [95] interface RANS-LES-RANS for a compressor-com-
bustor-turbine simulation. On the fly time averaging and scaling of
precursor LES fluctuations using RANS is used to interface upstream
and downstream regions. Shur et al. [96] focus on matching boundary
layer stresses by overlapping RANS to LES regions, enabling a fast
switch to resolved LES from upstream RANS. Forcing terms have also
been used to reduce the development length for resolved turbulence,
however, this must be used with care, especially if considering acous-
tics, where forcing could contaminate the acoustic field. In this regard,
the STG approach of Shur et al. [97] with a damping layer shows
promise. A potentially infinite time series based on correlated Fourier
modes is generated a priori. This avoids frequencies appearing in the
Fig. 4. Wake, freestream and boundary layer turbulence required at an LPT inlet to capture correct transition and turbulence development.
Table 1
Turbulent inflow approaches.
Method Synthetic Eddy Method [87–89]Synthetic Fluctuation Method
Required Inputs
Rij
,
Li
,
U
,
Neddy
Rij
,
Li
,
U
Recovery Length
15 20
20
Anisotropic Capability Yes Not in all directions
Precursor/Real Time Real time Real time
Approximate Cost Low Low
Divergence Free/Continuity met Not generally No
Ideal Use Cases Simple turbulence, hybrid RANS/LES Complex geometries, simple turbulence
Method Digital Filtering [90]Lund recycling [91]
Required Inputs
Rij
,
Li
,
U
Inflow recycling length,
u
,δ, initialisation
Recovery Length
10 20
0 5
Anisotropic Capability Yes Yes
Precursor/Real Time Real time Real time
Approximate Cost Implementation dependent Low
Divergence Free/Continuity met No Yes
Ideal Use Cases Structured Cartesian grids Low pressure gradient boundary layers
Method STG/VSTG Precursor Simulation
Required Inputs
Rij
,
Li
,
U
,
dwall
Mesh, BCs
Recovery Length
0 5
0
Anisotropic Capability Approximated by scaling Yes
Precursor/Real Time Precursor Precursor
Approximate Cost Low High, Low at run time
Divergence Free/Continuity met Yes Yes
Ideal Use Cases Aeroacoustics, non-reflecting boundaries, RANS/LES coupling Simple geometries, complex turbulence
J. Tyacke, et al.
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flow related to recycling of inflow turbulence. Forcing can be applied
over a volume rather than at a plane or face. At the downstream end of
the volume, statistics should match the defined statistics. This has been
shown to greatly reduce acoustic contamination for compressible flow
when passing from RANS to an LES region [97]. Sponge regions can be
used to isolate traditional characteristic boundary conditions from flow
unsteadiness. Where domains can be numerically extended, this could
avoid use of non-reflective treatments which are often sensitive to
tuning parameters. One aspect which appears not to have been tackled
is synthesis of inflow turbulence generated by upstream passing wakes.
These introduce significant mean and turbulence profile variation. It is
possible predicted RANS lengthscales and mean velocities can be in-
corporated into VSTG methods to reflect this. For example, Shur et al.
[97] provide lengthscale functions for channel, boundary layer and
shear layer flows.
An alternative, as noted in Section 2.4 is to model additional com-
ponents at lower geometrical and/or turbulence modelling fidelity to
generate suitable inflow or outflow conditions. For example, upstream
bypass geometry for jet flow or downstream guide vanes for Fan-inlet
coupling or Fan-OGV interaction. This also enables adequate coupling
of different components and zones.
2.3. Blade rows
The flow through single or multiple blade rows contains both de-
terministic and chaotic flow leading to tonal and broadband noise.
Rotor tip leakage and wake flow can impinge on downstream stators
leading to upstream and downstream propagating acoustic waves.
These, along with entropy and vorticity waves, can create a feed back
loop within the flow. Prime numbers are often used for rotors and
stators to avoid resonance and fatigue, requiring, ideally, full annulus
calculations for real geometries. Changes to blade counts to enable
single passage domain periodicity to be imposed changes throat areas,
loading and associated flow frequencies. Aside from this, long wave-
length disturbances such as compressor stall cells may span several
passages making full annulus calculations the only solution. Using
URANS and GPUs, Pullan et al. [98] revealed the route to compressor
spike stall, this being caused by flow scales much larger than modelled
turbulence.
For blade row calculations, cost reduction using ideally single pas-
sages remains challenging for multi-blade and multi-row calculations.
These usually require sliding planes, where suitable interpolation is
necessary to couple different zones whilst propagating numerous scat-
tered waves. Reducing the cost by modelling a single passage is possible
but not without issues. Standard periodic boundaries produce non
physical synchronous vortex shedding. This makes some sense for
URANS, but for eddy-resolving approaches, there is no physical syn-
chronicity. Phase lag boundary conditions can corrupt turbulent spectra
as the entire broadband flow cannot be adequately represented and
stored [99]. Blade row, secondary flow, wake, boundary layer and
shock interactions all contribute to the complex flow field. A detailed
investigation is undertaken by Mouret [100]. Alternatively the com-
putational time plane can be inclined, however this also has physical
and numerical limitations, potentially requiring more than a single
passage [101] and requires awkward post processing. Again, time in-
clining indicates a lagged time shift which is still non-physical. Hollow,
‘soft vanes' which contain Helmholtz resonators may be used in future
to control rotor-stator noise [4], which again may invalidate attempts
to reduce modelled section size. Clearly the cost of resolving full an-
nulus calculations and multi-stage calculations is limiting, indicating
component and system level studies are necessary at different fidelity
levels. With time, each will naturally progress up the geometry and
turbulence modelling hierarchy.
2.4. Use of body forcing
The use of immersed boundary methods (IBM) and similar ap-
proaches such as IBM-smeared geometry (IBMSG), assuming an infinite
number of blades [102], enable greater annulus sectors to be modelled
at reduced cost. This allows the full annulus to be modelled at lower
fidelity and cost, or could be used to enclose a body fitted mesh region,
placing the effect of periodic boundaries far from the region of interest
(ROI). Fig. 5, shows examples of increasing fidelity, which could be
used to reduce flow development cost or place numerical boundaries far
from the ROI. Here multiple arrows represent the equivalent infinite
series of blades (IBMSG), dashed lines approximate geometry (IBM) and
full lines wall resolved geometry.
Alternatively, positioning of key components can be studied such as
fan-inlet or rotor-stator axial location without re-meshing. Cao et al. use
an IBM to study fan-intake interaction under high incidence [103].
Either a suppressed level of post-separation distortion or an increase in
the separation-free operating range was found. Fan inlet distortion can
also be modelled using a localised version of IBMSG. Fig. 6(a) shows a
body fitted mesh contrasted with a background mesh with localised
IBMSG (Fig. 6(b)) to generate blade passages at reduced cost. A
1/3
rd
annulus distortion generator is also added using a classical IBM (
=u0
).
An instantaneous flow for the rotor with inlet distortion is shown in
Fig. 6(c). Fig. 7 shows total pressure distribution at the rotor inlet for
two fan speeds. IBMSG is in good agreement with experiments, body
fitted mesh and IBM results.
An aeroengine mounted to an airframe poses a huge range of scales
from wall streaks and blade wakes, to the largest jet plume scales of the
order of the jet diameter. Such multi-scale simulation is enabled with
multi-fidelity turbulence and geometry modelling. Internal turbulence
is generated using body forcing in the bypass duct of an aeroengine
mounted on a pylon-wing-flap geometry (Fig. 2 frame D) to study the
Fig. 5. Potential blade row geometrical fidelity combinations with identical inflow,(a) IBM rotor with IBMSG stators, (b) body-fitted rotor blade in ROI with
surrounding IBM blades and IBM staors, (c) fully body-fitted rotor and stator.
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effect on jet flow [104]. It was found to promote the weaker, inner
shear layer transition to turbulence. The effect of which is much weaker
than the dominant outer shear layer. This is particularly so with in-
creasing bypass ratio nozzles, which become closer and closer to single
stream jets.
As shown in Fig. 8, using body forcing, plasma actuators have been
modelled, indicating the voltage required to eliminate intake separation
is outside current technology levels [105]. Body forcing clearly has
wide application in scoping studies, active flow control, introducing
complex geometry into high fidelity simulations, representing geometry
of disparate scales and imposing engine realistic boundary conditions.
Although body forcing itself may be considered a low fidelity method, it
is a key enabler for high-fidelity simulation of complex systems.
2.5. Heat transfer
Turbine inlet temperatures can reach 1500–1750 K, exceeding the
melting point of the blade material, and have risen by approximately
7 K per year since the 1950s [40]. Since the 1960s, air from the com-
pressor has been used to cool blades internally via turbulence inducing
ribs and pins, the air of which exits to envelop the blade externally via
film cooling holes. This has enabled vastly extended periods of
operation, at the expense of compressor air and efficiency. It is desir-
able to lower the temperature at the blade root, where the stress is high
and the tip, which is easily damaged by abrasion. Further damage can
result from creep, fracture, fatigue and corrosion (enhanced by high
temperature). These numerous coupled elements are indicated in Fig. 9.
For creep, a rise of 10 K can halve the life of a turbine blade [40].
Careful control of cooling and temperature distribution throughout the
engine cycle is therefore critical.
Ceramic matrices incorporating supporting fibres are likely to be
used to help protect turbine blades [4], presenting new composite
material properties, life and surface roughness challenges. This will
require the accurate modelling of thermal and structural interfaces
between materials and advances in turbulence modelling of a variety of
surface finishes, which may change throughout blade life. Here, smaller
more canonical cases can inform models used for design verification at
larger scale.
For many years, it has been possible for LES to be used in industry to
study internal cooling of turbine blades due to large scale separation
and mixing [30,43]. For a two-pass duct, less than 10 million cells were
required. Note that inflow turbulence is not needed here due to rapid
development of large scales. This is shown in the left of Fig. 10 in ad-
dition to complex 3D corner flows. LES can be used to obtain accurate
Fig. 6. (a) body fitted mesh (62 million nodes), (b) IBMSG background mesh (12 million nodes), (c) localised IBMSG Q-criterion iso-surface coloured by pressure
showing IBM generated inflow distortion near the fan face.
Fig. 7. Total pressure distribution at the rotor inlet.
J. Tyacke, et al. Progress in Aerospace Sciences xxx (xxxx) xxxx
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heat transfer coefficients, removing the large uncertainty in measure-
ments or RANS modelling. This is displayed to the right of Fig. 10,
where the range of Nusselt number prediction using different RANS or
SGS models, is reduced by a factor of four. Mayo et al. [107] study high
rotation number effects on flow and heat transfer using simplified ducts
of only 1 million cells. Real multi-pass geometries are highly complex,
adapted to fit within blade structural constraints. These have been
tackled successfully [108] using meshes up to 100 million cells, LES
responding physically to the rapidly changing duct geometry and
blockages such as pedestal banks in the trailing edge cut back. This
removes the need for re-calibration of RANS models, which will not be
general and may lead to poor heat transfer prediction. The same ar-
guments can be made for trailing edge cut backs, an optimisation of
which is reported by Watson and Tucker [35] using less than 1 million
cells per case. LES should at least be used to check a final design before
rig testing, which may not even be required.
Harnieh et al. [109] study film cooling of a Nozzle Guide Vane
(NGV) in a fully coupled sense with internal passages producing coolant
jets with the correct swirl and mixing with the external flow. Also, in
contrast, a constant steady mass flow boundary condition is imposed at
the coolant holes (with no resolved internal flow), adversely affecting
heat transfer prediction. This is attributed to lack of swirl at the coolant
holes exits and mixing at the internal-external flow interface. As noted
in the introduction, hot gas can enter cooling holes, hence a re-
presentative plenum or inlet/outlet boundary condition with the cor-
rect mean flow characteristics may be required to capture this more
effectively without resolving detailed internal geometry.
Conjugate heat transfer analysis is becoming important not only for
turbines (for example, internal and film cooling) but for compressors
[99], where adiabatic boundary conditions are no longer enough to
accurately predict performance. The disparity in solid and fluid time
scales (
=c c h k/
T p 2
) is often
O(1000 10000)
posing significant chal-
lenges in computational cost. One potential solution is that of solving
the fast varying fluid and the slow varying solid in the frequency and
time domains or disparate spatial scales using the block-spectral
method of He [110]. The selective use of different methods in focused
regions can hence bring about large overall benefits in accuracy, cost
and flow detail, often unobtainable experimentally. The key is to make
the combination of these methods more integrated within the solver,
requiring a commitment to development, such that minimal user in-
tervention is needed.
2.6. Particle transport
In a study to measure volcanic ash deposition of real engine geo-
metries, Kim et al. [64] find turbine inlet and vane surface temperature
to be key parameters. This is also influenced by blockage of cooling
holes by dust that may or may not be deposited. This seems to in-
validate any steady modelling, as the blade may deteriorate resulting in
geometric changes and particles may rebound. Also important is that
ash was also deposited on the temperature probes. Instrumentation
effects on turbine blades have recently been studied using LES by Ubald
[111,112]. This could be extended to study debris and fouling effects on
measurement uncertainty. Cheng et al. [113] study turbine cooling hole
Fig. 8. Intake lip under crosswind conditions (a) without and (b) with plasma actuator to control separation.
Fig. 9. Turbine blade cooling paths (left), structural/environmental factors (right) (modified from [106]).
J. Tyacke, et al. Progress in Aerospace Sciences xxx (xxxx) xxxx
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dust deposition, noting the difficulty of particle resuspension and pre-
deposited particles that may significantly affect results. Grant and Ta-
bakoff [114] use a Monte Carlo method to model particle rebound
dynamics material removal from stationary and rotating blades. Par-
ticle size, relative location and restitution ratio are chosen from sta-
tistical models. Key erosion of the compressor blades includes the cut-
ting back of the leading edge, thinning of the trailing edge and tip
damage. This poses geometrical representation challenges and ques-
tions URANS validity at the trailing edge. To deal with geometry
changes, Dawes [115] has suggested the use of implicit geometry via
level sets to allow rapid re-meshing using unstructured meshes. For
structured meshing, Ali et al. [116] use level sets to determine mesh
blocking topologies. Alternatives may also include the use of immersed
boundaries in wear regions which could be eroded. This would also
require additional corrections such as wall distance calculation for
turbulence modelling.
3. Potential of higher order discretisation
3.1. Computational benefits
Higher-order (
>O2
) methods offer the potential to achieve the
same or better accuracy than second order methods for a reduced
computational cost, which is highly attractive. For example, using
fewer cells and local, compute intense operations as in FR methods.
This more efficiently utilises available floating point operations (FLOPs)
on modern computing architectures. For comparative purposes, in d
dimensions, FV methods have one DOF per cell, and nodal high-order
methods have
O p( )
d
[117]. A side effect of higher computational den-
sity is that parallel partitions can be as small as one cell. This also better
enables typical MPI latency hiding where computation is carried out
whilst communication is performed.
Fig. 11(a) displays the vast difference between the estimated
number of DOF, required throughout a civil aeroengine for a
2nd
and
Fig. 10. LES of internal cooling passages.
Fig. 11. (a) Potential of high order to reduce cost (DOF to resolve the boundary layer at different Reynolds numbers throughout the engine), (b) available modern
architectures and uses.
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4th
-order finite difference (FD) scheme. The use of the
4th
-order scheme
reduces the LES cost to below that of a
2nd
-order hybrid LES-RANS
solution. Use of the proposed IBM however are not currently compa-
tible with higher order methods, the external flow generating numeri-
cally problematic oscillations within IBM zones. Here additional
smoothing may be sufficient where low geometry fidelity is required.
Current finite volume solvers running on CPUs may only attain
5 10%
of their peak performance. This is the theoretical maximum
work throughput, for numerical simulation, generally measured in
floating point operations per second (FLOPS). On idealised geometries,
FR methods can reach
58%
peak performance [118], potentially offering
a large cost saving. It should be noted however, although this clearly
showcased the potential scalability and computational efficiency of FR
methods, very little useful data was recorded. The Reynolds number in
the Low Pressure Turbine (LPT) is low and accurate prediction of un-
steady phenomena are already tractable for industry using FD or FV
methods. In practical terms, the more beneficial route for the LPT
would be to reduce the computational cost (using fewer degrees of
freedom at high order) to obtain the same or better accuracy than other
methods.
3.2. Accuracy and cost
The accuracy and cost of a simulation is linked to the numerical
algorithms employed. Here two codes are contrasted. These are a
compact finite difference scheme (code A), and an optimised flux re-
construction scheme (code B). Particulars of each code are detailed in
Table 2.
To contrast these, the well known Taylor-Green Vortex from the
high order workshop is chosen. This reflects flow transition and decay
found in many turbomachinery zones and highlights sensitivities in the
spatial schemes chosen.
As far as is practically possible, cases are setup identically using
643
degrees of freedom and run for 20 time units. The 4-stage Runge-Kutta
scheme is used for each code with a small time step of
10 3
s to isolate
differences due to the spatial scheme.
Fig. 12 plots the variation of
dk dt/
and enstrophy with time
(Fig. 12(a) and (b) respectively). The benefit from using higher order
schemes is clear. Dissipation is greatly reduced, which may become
more important as greater regions of the engine are modelled, requiring
resolution of eddies over long distances. On a single CPU core, Code A
using an explicit
4th
-order FD takes 0.52 s/iteration and 0.92 s/iteration
using the
4th
-order compact scheme. Code B takes 0.97 s/iteration on a
CPU core and 0.019 s/iteration on a GPU.
3.3. SGS modelling
As with RANS, common SGS models are based on local flow quan-
tities and are of similar form. The Smagorinsky eddy-viscosity model,
which is similar to the RANS mixing length model, is provided in
Equation (1). This forms the basis for the most widely used SGS models.
It contains a
2
term, akin to a dissipative truncation error. Moin et al.
[119,120] show numerical errors can dominate SGS modelling at low
order. A non-dissipative numerical scheme admits the sensible use of an
SGS model. At high order, SGS modelling can dominate the numerical
scheme, destroying any accuracy advantage. For industrial codes, high
numerical smoothing can occur, an example being the Roe smoother at
low Mach number [121]. In this case, an additional SGS model is in-
appropriate, and Implicit LES (ILES) is preferable [30].
= =µ C S S S( ) | |, | | (2 )
t smag sij
,221
2
(1)
With regards to SGS modelling itself, the standard Smagorinsky
model has several negative traits including, being purely dissipative
(dependent on
Cs
) and a non-vanishing eddy viscosity at walls. This can
delay or even prevent transition to turbulence [122]. It is soley based
on local variables, does not generate an anisotropic eddy viscosity to
represent anisotropic turbulence and along with many other turbulence
models has questionable validity in the inertial subrange at low Rey-
nolds numbers [123]. Typically a range of length scales of at least
=L/ 1000
i
is needed before any such range can be detected. Large
regions of a gas turbine do not meet this criterion [124]. Even so, the
Smagorinsky model forms the basis for many widely used models due to
its simplicity. Examples include the Germano dynamic model to modify
Cs
based on resolution, using a test filter (usually
2
), requiring aver-
aging procedures on
µSGS
for stability [125]. Hughes [126] presents the
Variational Multiscale Method (VMS) in which an additional filter is
used to define the interaction between the smallest resolved scales and
sub-grid scales. Vreman modifies the Smagorinsky model to better suit
transitional flows [127]. The Wall-adapting local eddy-viscosity
(WALE) model [128] and σ-model [129], fix gross failures of the
Smagorinsky model. These are contrasted for transitional and endwall
flow of a compressor blade by Scillitoe [122,130]. Many other func-
tional and structural SGS models exist, some allowing non-local and
non-equilibrium effects to be introduced via transport equations [131].
However, these often do not display good agreement with true subgrid
stresses [132]. Non-linear SGS models allow modelling of energy
backscatter and anisotropy, but are not widely used due to instability
without additional dissipative elements that form mixed models [133].
It can be shown mathematically that some high order numerical
schemes contain both dissipative terms and non-linear terms akin to the
Clark model of explicit nonlinear SGS models [134]. Typically they also
dissipate energy at high wave numbers, moving higher still with order.
This appears a desirable trait, whereby sufficient dissipation occurs
near the grid limit, allowing maximum resolution of grid scales as de-
monstrated by Wiart and Hillewaert [135]. This is particularly im-
portant for wave propagation in areas such as aeroacoustics where
dispersion and aliasing can contaminate fields. An explicit SGS model,
with questionable validity at low Reynolds numbers, is thus likely to
create more problems than it solves. Most high order solvers appear
tuned not to require an explicit SGS model, becoming Implicit LES
(ILES) or Montonicity preserving ILES (MILES) [191].
3.4. Current uses
An insight into academic high order method penetration is gleaned
from the International High Order Workshop [136]. Here, flows are
classed into Verification and Validation, Advanced, and Computational
Challenges as shown in Table 3. Flow physics challenges include tran-
sition, laminar separation, transition and reattachment, transonic flow
and shock capturing, and inlet turbulence. These can all be sensitive to
numerical properties, so careful scheme selection is required.
Based on FR, Dawes et al. [137,138] provides examples of more
industrially relevant flows with relative computational costs to achieve
similar accuracy to second order methods. The time step is local and
adaptive through the duration of the simulation requiring close atten-
tion to parallel load-balance. Table 4 summarises the cases. The speed
up of local time stepping over uniform time stepping is denoted ψ. The
aeroacoustic models obtain a large speed up but the Octree mesh dis-
tribution is clearly non-ideal for the jet, but convenient for the time
stepping scheme used. The jet case benefits from an additional 50%
Table 2
Code details. (Note, FD = finite difference, E = explicit, C = compact,
FR = flux reconstruction, DG = discontinuous Galerkin, SD = spectral differ-
ence, RK= Runge-Kutta).
Code A Code B
Spatial scheme FD,
4
th
order (E)/(C),
2nd
order (E) FR,
4
th
order DG/SD
Temporal Scheme Explicit,
4
th
order RK Explicit,
4
th
order RK
Data structure Structured Unstructured
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increase in far-field sound cut-off frequency moving from
2nd
to
3rd
order. Similarly
Cp
distributions on the landing gear indicate a benefit
at
3rd
order. By use of mesh, hardware and points-per-wavelength
scalings, Dawes estimates the HOTnewt solver is approximately
2.9 × faster to an equivalent second order solver such as ONERA/
CEDRE. Given the efficient hardware, the cost is estimated to be
29 × cheaper. This is an example where building from the ground up
using new technologies, progress can be made. It is far more difficult
however to take mature codes and re-invent them.
Marty et al. [139] use the elsA solver of ONERA with AUSM+(P)
with a high-order MUSCL extension to reach
3rd
and
5th
order. This is
applied to study the laminar separation bubble of the T106C LPT in
conjunction with the WALE SGS model. Zonal-DES is also applied to a
transonic compressor with a shock near the blade tip. Zonal-DES is also
applied to a fan rotor in order to assess fan wake-OGV interaction and
noise. Higher order MUSCL interpolation resolved more small scales,
however, whatever the order of MUSCL interpolation, ZDES compared
well with averaged and unsteady statistics, indicating larger scales were
most important. This aligns with the fact that large scales are more
efficient at generating noise [140].
Vadlamani et al. [141] use the COMP-SQUARE solver to study
surface roughness effects on transitional boundary layers using a
6th
order compact FD scheme. Numerical instabilities are treated using a
10th
order non-dispersive filter. Using similar numerics [142], study
non-equilibrium turbulence of a backward facing ramp. Non-equili-
brium flow is found to be dependent on scales relating to boundary
layer and wake turbulence. Suggested mechanisms are phase de-co-
herence and inter-scale spreading of disturbances.
Other higher order codes (with scheme type in brackets) suitable for
turbomachinery application include Cenaero Argo (DG) [143], PyFr
(FR) [144], NASA GFR (FR) [117], Incompact3D (FD) [145], Nektar
+ +
(SE) [146]. This is not an exhaustive list. Clearly, there is also a vast
array of established FV and FD codes, which may be suited to complex
geometry flows.
4. Validation
The flow physics targeted by high-fidelity simulation requires more
stringent validation than mean or bulk quantities. Tyacke and Tucker
[22] indicate turbomachinery LES lags airframe validation levels.
Turbomachinery mainly reaches mean flow with some Reynolds
stresses and airframe validation predominantly reaches second order
moments and spectral analysis. Integrated quantities were are also
lacking for turbomachinery, likely due to access. High-fidelity CFD
provides three-dimensional fields of high order statistics unlimited by
access. Rather than replicating mean profiles from experiments, high-
fidelity simulation data now far exceeds that provided by experiments
[32]. Measurements simply cannot match the quantity of detailed data
obtained due to access limitations and disturbance of the flow. This is
problematic as detailed multi-variable correlations are difficult if not
impossible to obtain. There is also variation between experimental fa-
cilities. Mc Croskey [147] compares 40 NACA 0012 data sets from
different facilities, concluding there is unacceptable variation and that
“no single existing experiment is adequate”. Difference between noise
test facilities can vary by several decibels [31]. It seems useful to
compare with multiple data sets if possible. Measured mean flow and
Reynolds stresses can have 5% and 8% errors respectively [148]; 10%
[149] for skin friction; 1.76% [153], 3% [150] for Reynolds stresses;
7% for pressure [151]. Heat transfer measurements are notoriously
difficult to define and control, errors often in the range of 2–10% [152];
12% [149]; 7–12% [150]; 8% [151]; 3.4–6.66% [153]. Even so, cases
are often not sufficiently well defined for LES to be rigorously validated.
Fig. 12. Taylor-Green vortex results, (a)
dk dt/
, (b) Enstrophy. Legend nomenclature as Table 2. (For interpretation of the references to colour in this figure legend,
the reader is referred to the Web version of this article.)
Table 3
High order workshop test cases, with basic details in brackets.
Verification and Validation Advanced Computational Challenges
Vortex transport (DNS) Inviscid bow shock (2D) High-Lift Common Research Model (RANS)
Smooth Gaussian bump (Steady inviscid) Inviscid Strong Vortex-Shock Wave Interaction (2D) NASA Rotor 67 (RANS)
Laminar Joukowski airfoil at
Re
= 1000 (Steady laminar) Heaving and pitching airfoil (DNS)
RANS Joukowski airfoil (Steady RANS) Common Research Model (Steady RANS)
Taylor-Green vortex at
Re
= 1600 (LES/DNS) Tandem Spheres
Re
= 3900 (LES)
Plane channel at
Ret
= 550 (LES/DNS) T106 LPT Cascades
Re
= 60–80,000(LES/DNS)
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For example, inflow turbulence is rarely recorded. If provided it is in-
complete, stating only turbulence intensity, or turbulence grill details.
Experimental facilities can have various limitations, including unknown
upstream flow within pipes; wake generating bars instead of blades;
wind tunnel contractions and walls; additional flight stream shear
layers in aeroacoustics; heat conductance into substrates (O10%
[148,154]); and small scale geometrical irregularities from manu-
facture, tape and surface roughness. High-fidelity practitioners usually
aim to model the real flow. However, it is impossible for CFD to iden-
tically match these due to computational resource, nor should the CFD
be forced to inherit such deficiencies.
Researchers more widely use high-fidelity simulation but industry
holds significant but inaccessible measurement databases. Publicly
available detailed inflow traverses are hence required to properly
capture inflow turbulence dynamics. These could then be fed into
synthetic turbulence generators or reduced order models to more pre-
cisely match experiment conditions.
Duchaine et al. perform uncertainty quantification on a cooled
turbine blade. Varying the coolant temperature in all holes, the LES
data range with 95% confidence intervals overlaps measured data. It is
hence important for both experiments and CFD to incorporate errors,
confidence intervals or error probability distributions routinely. Rather
than picking one superior dataset, we can be confident in validation
where data overlaps.
5. Lower order model development
The limited design space covered due to computational cost of high-
fidelity methods at high Reynolds numbers limits what is achievable in
design. High fidelity methods can be used to supplement experiments to
gain deeper flow physics insight. Lower fidelity geometry modelling has
been discussed in previous sections. Here, we consider lower fidelity
turbulence modelling (RANS), which forms the basis for the majority of
current CFD. Typically RANS provides some trend data, even if absolute
accuracy is poor. A key application of detailed high-fidelity data is then
to improve lower fidelity methods such as RANS and rapid design tools
that may be lower than 2D.
Many RANS defects are known, but there are not many general
fixes. Spalart discusses numerous turbulence modelling issues and fal-
lacies [155] which should narrow potential fruitful avenues. Tucker
[29] provides a broad review of current turbomachinery turbulence
modelling defects and treatments. Issues include forwards and back-
wards transition; compressive/extensive strain, which can lead to sup-
pression of leading edge separation and over-predicted heat transfer
[156] and downstream accuracy degradation; curvature and rotational
effects, eddy-viscosity models requiring sensitisation to curvature and
additional body forces for rotation, both using a variety of terms and
implementations indicating unreliable performance; freestream turbu-
lence decay, which can incorrectly grow downstream in the absence of
suitable destruction terms [132]; roughness, a simple model by Aupoix
and Spalart [157] offsetting the wall distance, however surface
roughness topology is known to be of significant importance, skin
friction being 25% higher than sand grain roughness. This would ap-
pear difficult to effectively model in a meaningful way. Lack of the
assumed alignment between the Reynolds stress and mean strain-rate
tensors is found for compressor secondary flow [158] and labyrinth seal
flows [18]. Monier [158] tests the quadratic constitutive relation (QCR)
to improve modelled anisotropy, mainly seeing benefits upstream of the
blade. Applied to a tip gap leakage flow, Monier [159] finds little im-
provement using the QCR. Case dependency is typical of RANS and its
variety of proposed fixes. The use of URANS requires the existence of a
spectral gap between unsteady large scales and modelled stochastic
turbulence. Tucker provides many examples where such a gap is ten-
uous in turbomachinery [80]. Rapid eddy distortion can also occur
around turbine blade and fan leading edges with inlet distortion or
boundary layer ingestion.
Non-local non-linear effects are clearly important from a physical
standpoint, however most RANS closures are based on local quantities,
often with some convective element. In combination with the numerous
issues noted above, manual analysis seems out of reach.
Further advances in RANS modelling may be achieved in the near
future through the use of machine learning. The temptation is to use ML
as a black box to try and force an LES solution out of RANS equations.
We should instead be gaining and exploiting an understanding of the
spatio-temporal changes in turbulence for different flows. Wu et al.
[160] find the difference between the RANS and LES Reynolds stresses.
This is then used to correct the RANS stress field. Forward propagation
is then used (i.e. re-solve RANS with turbulent PDEs frozen) to get an
improved velocity/pressure field. Here, training flows need to be close
to test flows. How this is defined is an open research area. Wu et al.
[161] later shows that any errors in the stress field are amplified at
higher Reynolds numbers, hence modification to the eddy viscosity
appears more general.
Weatheritt and Sandberg [162] use Gene Expression Programming
(GEP) to build algebraic equations based on eddy resolving data whose
terms can be studied. Weatheritt et al. [163] use similar techniques to
suggest a non-linear expression for the Reynolds stress to improve
prediction of the wake of an HPT blade where the Boussinesq approx-
imation is found to be invalid. Great care is needed however, to prevent
non-realizable or unstable solutions. However, regions of flow can be
chosen and others ignored to train such models, in a sense calibrating a
fix to a given range of flows. In many situations the complexity of the
turbulence may render RANS too simple a palliate, even with AI for any
substantial design parameter range.
A pragmatic approach is to identify trust regions based on flow
physics to identify regions where RANS is known to be untrustworthy,
for example breakdown of the Boussinesq hypothesis as Ling [164].
Later Ling [165] explores more general breakdown of assumptions
using support vector machines, Adaboost decision trees and random
forests. This gave a point by point breakdown of specific RANS as-
sumptions with high or low uncertainty. Classifiers were then able to
generalise to flows on which they were not trained. This may be more
meaningful to a design engineer, trying to minimise computational cost.
Unreliable RANS zones would then be more suited to LES modelling or
lead to naturally flow adaptive model corrections. Further to this Ling
[166] embeds Galilean invariance into a model to correct anisotropy
trained on LES of channel flow, a duct, square cylinder, perpendicular
and inclined jets in cross-flow and a converging-diverging channel. This
improved predictions over baseline RANS on new cases including a
wavy wall with separation and duct secondary flows. ML is still in its
Table 4
Industrially oriented test cases ([137,138]).
Case Setup details Performance details
T106 LPT blade 4
th
order,
= ×Re 1.1 105
,
=S C0.075
,
×0.11 106
cells
=8
Transonic turbine blade (VKI-LS59)
3rd
order,
= ×Re 8.5 105
,
=S C0.042
,
×0.107 106
cells,
×1.37 108
DOF
=8
NASA SMC001 chevron jet nozzle mixed
2nd
-
3rd
order,
×7.66 106
cells,
×671 106
DOF 29
×
speedup
BANC II landing gear aero-acoustic test case
3 order
rd
, wall modelled,
×11 106
cells,
×862 106
DOF
=35
J. Tyacke, et al.
Progress in Aerospace Sciences xxx (xxxx) xxxx
13

infancy and turbulence is highly non-linear and complex. Rather than
blindly relying on ML, it seems prudent to take smaller steps towards
improvements guided by knowledge.
6. Major barriers and how to overcome them
6.1. Pre-processing
Parallel solvers and the use of High Performance Computing (HPC)
is now common place. In 2009, Dawes [49] notes key changes required
to CFD workflows, most notably the use of massively parallel processing
of all aspects, including pre-processing, solution and post-processing.
Still today, the solver is often the main parallel part of the process
chain. As a rule of thumb, the largest cases usually translate to a run
time of one to two months depending on HPC occupancy rates, larger
cases use larger facilities and so the rule holds. Most human time is now
spent in pre-processing and post-processing.
Zonalisation and coupling at geometry level and turbulence mod-
elling shifts significant time and effort into pre-processing. For example,
one needs to perform mesh generation, and potentially IBM/IBMSG
definition, synthetic turbulence inflow setup, RANS-LES zoning, nu-
merical smoothing zoning and numerical flow instrumentation.
Currently this requires significant manual effort which may outweigh
the runtime of the simulation unless automation is increased sig-
nificantly. Meshing for example is generally a human-led operation.
The more complex the simulation, the longer it takes to generate, with
specific attention paid to important flow regions for LES using a range
of resolution criteria. For example, for boundary layers
=
+
x100
,
=
+
z20
,
=N2000
grid points per
3
, more generally, resolution of
90% TKE. For a wide range of flows this is not simple to automate, as it
is not based solely on geometry and requires flow information.
Fortunately, turbomachinery offers fairly distinct geometrical compo-
nents and flows, where topological similarities can be leveraged and
rules defined in advance. Many pre-processing operations also require
nodal searches. For large meshes, which continue to grow, these can
become prohibitively expensive at run time, where mesh partitioning
and parallel reductions complicate searches. These operations should
clearly be separated from the solver and can be faster sequentially than
in parallel where MPI communication can saturate. K-dimensional-trees
(KDTREEs) can help in many circumstances. It may be beneficial to
completely separate the solver from input and initialisation via a
greater degree of pre-processing as solvers are set for significant and
rapid change.
6.2. Eddy resolving meshes
Chapman [167] estimated that when computing power reaches
1014
FLOPS, LES would begin to compliment and perhaps replace some rig-
testing. This was exceeded by a factor of ten in 2008 with IBM's
Roadrunner. It should be noted that the use of overset meshes in regions
of interest to avoid high cell counts away from boundaries is required to
meet the grid point requirements of Chapman [167,168]. Most current
meshes do not achieve this, for example structured meshes generally
fan out from a boundary and do not coarsen in 3D, becoming larger
than necessary. Choi and Moin [24] also recently reached similar re-
quirements for wall resolved LES.
1
Choi and Moin estimate the number
of grid points Nrequired for a boundary layer scale approximately as
ReL
2.65
, for DNS,
ReL
2
, for wall resolved LES and
ReL
, for hybrid LES-RANS
(wall modelled LES). Clearly, boundary layer adapted meshes will have
the greatest impact at the highest Reynolds numbers where wall mod-
elled LES is needed such as the engine fan or airframe wing, or at lower
Reynolds numbers where wall resolved LES is necessary to capture
transition such as the LPT.
The roadmap in the NASA 2030 report ([12]Fig. 1) study indicates,
both wall modelled and wall resolved LES as low TRL for complex 3D
flows at realistic
Re
when written in 2014. Large scale parallel mesh
generation is indicated as high TRL, however the authors would argue
this is not the case for LES of coupled turbomachinery-airframe flows.
In this case, specifically flow adapted meshes are required to capture
but not over-resolve key flow regions. In any case, an efficient com-
putational mesh and modelling approach go hand in hand. Complexity
is only set to increase, requiring more human input on each modelled
element. To aid structured mesh generation Ali et al. [116], leverage
level sets to gain useable block topologies for complex seals, an in-
stalled engine and an aircraft. Still, the mesh generation process needs
much more parallelism and automation, possibly including adaptive
methods that maintain mesh quality. Quality itself is poorly defined in
the LES context and is related to underlying numerical schemes and
modelling.
For current FV, large meshes mostly stem from connectivity
(structured and unstructured) related to the boundary layer mesh. For
hybrid structured-unstructured meshes, the surface mesh streamwise
and cross-stream spacings are linked to final wall normal spacing and
chosen aspect ratio at the structured-unstructured interface. For de-
veloping boundary layers, the estimates of Chapman [168] assumes
hanging nodes, without which mesh density propagates outwards. This
suggests use of non-conformal/hanging node/polyhedral meshes to
match cell size with developing boundary layers and localised wake and
transitional flow. For LES, the cell aspect ratio for the inner layer is
normally assumed using wall units (for example,
=
+
x100
,
=
+
z20
giving an aspect ratio of 5). Streamwise and cross-stream spacings could
then be linked to the wall normal distribution, connectivity being an-
other issue. Alternatively, the inner and outer layers can be considered
separately. Fig. 13(a) shows a schematic indicating the disparity in
mesh required through a boundary layer. The transition between these
is non-trivial and example mesh topologies are indicated, though the
transition would be more gradual. Two mesh requirements, particularly
for boundary layers, are anisotropic elements and a gradual three-di-
mensional growth to isotropic cells. Where triangular or tetrahedral
elements are required for connectivity, cell skewness limits aspect ratio
and growth rate. Hence hanging nodes are attractive if they adhere to
the above requirements to avoid sudden changes in cell size as in Octree
meshes. Such a mesh is generated by Addad et al. [169] for a flat plate.
For developing boundary layers, the boundary layer thickness and
hence mesh requires a local scaling as indicated in Fig. 13(b) where a
number of notional boundary layer mesh units are distributed based on
the boundary layer thickness. For more general cases, mesh adaptation
may be required at run time. Ideally the level of resolution in each
direction should be the same, implying that for anisotropic flow, there
is an optimal filter width in each direction. Toosi and Larsson [170]
estimate sources of error based on two different grids. The optimum
grid is assumed to have an optimal mesh and cell anisotropy distribu-
tion while achieving a uniform error. This provides a systematic pro-
cedure without resorting to adjoint methods, which are problematic for
unsteady flow.
An example boundary layer mesh schematic and mesh filter scale to
resolve 90% TKE with typical zonalised boundary layer mesh dis-
tribution for a compressor endwall are shown in Fig. 13. For boundary
layers with correctly varying cell size, savings on the order of 10–100
times may be achievable [171]. In addition, boundary layer mesh may
not be required in separated zones, offering further savings.
One benefit of FR methods is a greater resilience to mesh distortion.
For an inviscid convecting vortex passing through a distorted mesh
shown in Fig. 14(a), using a
4th
order FR scheme the mean error (point
averaged
l2
norm) shown in Fig. 14(b) maintains order of accuracy,
rather than degrading as with finite volume. Although promising, the
use of higher order methods has major challenges before they become
widely adopted. Not least of these is the requirement to use higher
order meshes. At boundaries, a
pth
order scheme requires the boundary
1
We note Chapman's outer layer estimates are optimistic.
J. Tyacke, et al. Progress in Aerospace Sciences xxx (xxxx) xxxx
14

mesh to be
Cp
continuous [172]. This may also require further im-
provements to geometry representation such as CAD. Unfortunately,
even for established FV methods, complex geometry LES mesh gen-
eration can take weeks or months. This is then exacerbated with high
order requirements. This bottleneck will not be easy to eliminate.
Subsequent processing of lower order meshes may offer a non-ideal
answer. One could mesh a compatible FV mesh and morph this to high
order geometry, requiring only one extra pre-processing step. Such an
approach which does not require CAD is presented by Ims et al. [173].
6.3. Time integration
Stability is a critical requirement for industrial use. A key aspect
after spatial decomposition is the sequential bottle neck of time in-
tegration for thousands or millions of time steps. This limitation is also
noted by Löhner [174]. Higher order methods generally have even
more stringent CFL limits than second order. For explicit time stepping,
the time step scales roughly as
p1/
after allowing for increases in cell
Fig. 13. (a) Idealised boundary layer mesh distribution unit (not to scale), (b) example developing boundary layer mesh unit distribution (not to scale), (c) ideal
cross-stream mesh spacing based on boundary layer and resolved turbulence kinetic energy estimates.
Fig. 14. Invicid convecting vortex (a) warped mesh (average skew angle
15o
), (b) mean error reduction with degrees of freedom (DoF).
J. Tyacke, et al. Progress in Aerospace Sciences xxx (xxxx) xxxx
15

size [175]. Spiegel et al. [117] note
p2
CFL scaling for explicit time
integration and
p5
becomes too expensive. These exacerbate the
number of time steps required for large simulations or those with long
or disparate time scales. For example, the blade passing frequency in a
compressor is 1000 times greater than a surge [99], or for conjugate
heat transfer, the thermal time constant of the solid is generally much
greater than the fluid.
For implicit time stepping, memory utilization may be limiting at
high order as the bandwidth of matrices grows, scaling with
p6
[176].
Using implicit time stepping near walls, explicit elsewhere (as Shoeybi
et al. [177]) and dynamic load balancing (at relatively few time in-
stants), may in future help alleviate higher order memory requirements
and achieve good load balance. Vermeire and Nadarajah [178] obtain
speedups of over
×50
and a memory reduction of over 50%. Space-time
cells or local time stepping may also be useful to allow more efficient
time integration on a per cell basis. Lu et al. [179] achieve a speed up of
up to
×100
over uniform time stepping. Other avenues are to perform
parallel time integration such as the Parallel method [180] which in-
volves a fine time step parallel correction to a sequential coarse time
step solution. Alternatively the multigrid reduction in time (MGRIT)
algorithm [181] involves a relatively non-intrusive wrapper to obtain a
multigrid method in time.
6.4. Post-processing and data storage
A common issue for high fidelity simulation is that computational
cost limits the simulation period. This is obvious for jet aeroacoustics,
where low frequency resolution is limited by the number of periods
data is collected. Similarly for high order correlations, low sampling
times can limit confidence. Criteria for statistical convergence under a
range of flow conditions are required. For example, initial transients
need to be separated from periodic or pulsatile behaviour. Morton et al.
[182] use deep dynamical modelling based on Koopman theory to ex-
tend time series with low relative error, based on short time samples, to
assess potential flow control. This may allow the relatively short si-
mulations to be extended somewhat, drastically reducing cost, or at
least made more useful. For example, noise reduction concepts could be
assessed based on dynamic models. However, further testing for more
general 3D cases and caution is required.
Clearly we can and do store vast amounts of data when performing
simulations.
2
Using neural networks, data encoding/decoding may re-
duce storage requirements by orders of magnitude [183]. The useable
data is unfortunately largely wasted, as uncompressed, large datasets
are computationally expensive and cumbersome to analyse. In the near
term, with billions of DOF, visualisation and data co-processing may be
required in real time owing to storage limitations. Furthermore, ten-
sorial quantities such as
4th
order space-time correlations used in
aeroacoustics can multiply dimensionality of data compounding storage
issues and impeding comprehension. Tens of Terabytes are easily ex-
ceeded. Targeting Exascale, Ross et al. [184] from Argonne National
Laboratory indicate the growing I/O gap between memory and com-
pute performance and solutions ranging from hardware to low and high
level software. Aids to HPC data analysis include Adaptable IO System
(ADIOS) [185], a framework for I/O and data analysis, and Do It
Yourself (DIY) [186], a library of functions for developing parallel
analysis functionality. Some degree of on-the-fly modal representation
of energetic scales may be useful as suggested by Dawes [137] to be
reconstructed later. We tentatively suggest a notional Use Factor,
UF = knowledge/cost. This is independent of the magnitude of data
stored, emphasising the importance of effective analysis techniques.
Due to sheer volume, any data that is stored may ultimately only be
exploited using machine learning for such large data sets, to provide
intelligible engineering insights and outputs.
For long term or large storage requirements, a glimmer of hope has
appeared perhaps in using DNA as a storage medium. Depending on
encoding technology, this enables
×2.2 103
PB/Kg of DNA [187] with a
raw limit of
106
TB
mm/3
[188], transforming the ultimate storage limits
and stable for centuries. The process to read and write has recently been
automated by Microsoft and the University of Washington, taking
around a day to write the word ‘hello’ [189], set to reduce significantly
but likely requiring tiered storage and databases depending on data size
and usage frequency. As data ages, access frequency usually drops as
newer, better, more detailed data becomes available. Integrated data-
bases were indicated as low TRL by the NASA 2030 report. Data from
multi-fidelity simulation and experiments also needs merging. The
source or age of data is relatively unimportant – it is the accuracy and
uncertainty characteristics that should inform the engineer.
6.5. Hardware and algorithmic coupling
The rapid development of computing hardware opens up the pos-
sibility of using these tools not only on high performance computing
(HPC) platforms, but on local desktops and distributed networks using
combinations of CPUs, GPUs, Application-Specific Integrated Circuits
(ASICs) and Field-Programmable Gate Arrays (FPGAs). The hierarchical
nature of most computing systems involves compute units, multi-level
memory systems and inter-connects between these at the chip and
system level as shown in Fig. 11(b). This presents a highly case and
algorithm dependent load balancing and code abstraction problem.
There is then a link between the equations to be solved, the algorithms
employed and the hardware that can efficiently be used.
Data structures are critical to code efficiency. A benefit of structured
data (for example,
i j k, ,
indexing) is that vectorisation is easily lever-
aged, multiplying the rate at which computation takes place on a CPU.
However, for unstructured meshes with various elements, matrix op-
erations are more efficient. To simplify code structure, NASA have used
Fortran derived datatypes for different elements so that higher level
operations are identical [117]. Matrix sparsity is evaluated and they are
stored in a compressed format, Fortran 2003 type-bound procedure
pointers then utilise compatible sparse matrix algorithms. Un-
fortunately it is not easy for compilers to automatically optimise such
routines with derived types and at least code profiling, and most likely
manual optimisations must be performed.
Abstraction for current hardware has been successfully demon-
strated with projects such as PyFR [144] where low level modules
target different hardware architectures and are linked with high level
matrix operations. The OpenSBLI project [190] allows high level PDE
specification, with parallel code generated for a range of architectures.
Given the rapidly changing architectures of today, code modularity and
maintainability is key. To release the potential of all computational
power, low level alterations to assembly code can be required to sur-
rounding libraries, which may not be sustainable. The coupling of
multi-physics codes may offer ways to utilise different compute archi-
tectures more efficiently by tailoring codes and algorithms to different
types of chip. Computational scientists therefore need to be involved
throughout the entire code development cycle to help make bold
choices early on and to further optimise in later stages.
7. Paths forward
In the near term, we should consider the benefits and disadvantages
of each method and apply them where suited. Fig. 15 suggests where
different methods may be applied indicated using FV, FD and FR. As the
current workhorse, FV offers a great deal of flexibility and robustness. A
key enabler is the increased use of hybrid LES-RANS to alleviate grid
demands. Zonalisataion and treatment of transitional, accelerating and
separated flows on low curvature surfaces, require attention to remedy
deficiencies present in any RANS content. Methods to alleviate
2
It is assumed input and output are as parallel as the solver, using for ex-
ample HDF5 libraries and is hence not discussed.
J. Tyacke, et al. Progress in Aerospace Sciences xxx (xxxx) xxxx
16

computational demands should be incorporated, such as highly adapted
boundary layer meshing and improvements to time stepping proce-
dures. Mixed geometrical fidelity offers a great range of flexibility in
use, accuracy and computational cost.
Currently we may use high order with reduced cost for exploratory
flows and flow physics and limit use of FV to industrial cases, where
more modelling is used, leveraging the hierarchy in Fig. 3. Wave pro-
pagation for jets/fan acoustics seems an obvious use for higher order
methods, potentially reducing mesh requirements for FV based LES. FR
could also be used to explore numerical requirements in different zones,
with these being implemented in similar more tractable schemes. The
reduction in cost may also be useful for improving RANS modelling by
studying simple geometries but where RANS is challenged by flow
physics.
In the medium term,
4th
order appears to provide a significant in-
crease in accuracy for minimal effort in mesh modification and coding.
It is also less severe than
>O4
in regards to stability issues and
memory requirements (particularly if implicit time stepping is em-
ployed). If FR is not used, there is a limited increase in stencil size and
hence MPI data halo. When higher order methods mature, order can be
increased, and this should be planned in current code iterations with
increased modularity. For FR this should be fairly trivial.
Long term, the use of higher order methods largely depends on
development of CFD as a whole. As noted, pre-processing is currently
limiting the use of these methods along with practical limitations in the
amount of RAM or storage available (i.e. cost). It is hoped time in-
tegration (or even parallelism) will see significant advances, which
would counter or alleviate the number of (sequential) computed time
steps required. Storage and post-processing of large simulation data is
also becoming a bottle neck. Data encoding may drastically reduce
storage requirements and allow greater details to be extracted with only
a slight loss in fidelity. To extract knowledge from vast databases, data
mining and machine learning, although young in CFD analysis, seem
the only likely way to inform designs by reliable quantitative data.
8. Summary and outlook
The role and design of aero-engines is set to change rapidly with
future aircraft. With this, highly coupled systems arise throughout at a
range of scales. To model these requires great flexibility and mixed fi-
delity predictive simulation. Although current high fidelity methods
have become mature and more widespread, FV methods in particular
are more limited in accuracy but rich in application and user experi-
ence. Moving forward, higher order methods offer tantalising ad-
vantages. Great hurdles, particularly in the context of turbomachinery
application, remain. However, great computational savings can still be
made by optimising LES mesh and time stepping to obtain the required
accuracy at reduced cost. The variety in modelled physics, and corre-
sponding greater internal and external coupling, demands a degree of
flexibility in the code base for use of different algorithms and hardware.
This runs counter to current industrial practice in which a single code is
developed over decades. However it seems certain that uptake of high
fidelity methods will continue at a rapid pace. Over the next 10 years,
these and future predictive methods will enable unexplored design
space to be traversed with confidence.
Appendix A. Supplementary data
Supplementary data to this article can be found online at https://
doi.org/10.1016/j.paerosci.2019.100554.
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