UNIVERSITÀ DEGLI STUDI DI PARMA
DIPARTIMENTO DI INGEGNERIA INDUSTRIALE
Corso di Laurea Magistrale in Ingegneria Meccanica
THREE DIMENSIONAL CFD SIMULATION OF A
TURBOCHARGER TURBINE FOR MOTORSPORT APPLICATIONS
SVILUPPO DI UN MODELLO DI SIMULAZIONE 3D CON UN CODICE DI
CALCOLO CFD DI UNA TURBINA PER SOVRALIMENTAZIONE
DESTINATA AD APPLICAZIONI MOTORSPORT
Company Advisor:
Academic Advisor:
Ing. M. CHIODI (FKFS Stuttgart)
Prof. Ing. A. GAMBAROTTA
Ing. P. ROBERTI (FKFS Stuttgart)
Candidate:
CRISTIAN CAPILUPPI
Anno Accademico 2011-2012
Index
1
Introduction ......................................................................................................................... 1
2
CFD tools: brief outlines ..................................................................................................... 2
3
Turbocharging fundamentals .............................................................................................. 5
3.1
Why turbocharging .......................................................................................................... 5
3.2
Supercharging technology and strategies ........................................................................ 6
3.2.1
Mechanical supercharger versus turbocharger .................................................................. 6
3.2.2
Layouts: the twincharger................................................................................................... 10
3.2.3
Layouts: two stages twin turbocharger ............................................................................. 12
3.2.4
Layouts: the hybrid turbocharger...................................................................................... 14
3.3
Characteristics ............................................................................................................... 15
3.3.1
4
The turbine map ................................................................................................................ 15
Model description ............................................................................................................. 17
4.1
Geometry design ........................................................................................................... 17
4.1.1
Tomography results ........................................................................................................... 19
4.1.2
Previous CAD resetting ...................................................................................................... 21
4.2
Mesh design................................................................................................................... 23
4.2.1
Preparing the surface ........................................................................................................ 23
4.2.2
Surface mesh setting ......................................................................................................... 24
4.2.3
Creating the volume mesh ................................................................................................ 28
4.3
The regions layout ......................................................................................................... 31
4.3.1
Interfaces creation between the parts .............................................................................. 32
4.3.2
Regions .............................................................................................................................. 33
4.3.3
Rotating motion specification ........................................................................................... 35
4.4
4.3.3.1
MRF Approach ............................................................................................................... 35
4.3.3.2
RBM Approach............................................................................................................... 38
The boundaries definition.............................................................................................. 40
4.4.1
Mass flow inlet boundary .................................................................................................. 40
4.4.2
Pressure inlet boundary .................................................................................................... 43
4.5
Boundary and initial fluid conditions ............................................................................ 44
4.5.1
The GT-Power working point............................................................................................. 44
I
4.5.2
4.6
The fluid initial conditions ................................................................................................. 46
Physics definition .......................................................................................................... 47
4.6.1
Gas model .......................................................................................................................... 48
4.6.2
The continuum fluid domain ............................................................................................. 50
5
Simulations results ............................................................................................................ 54
5.1
Mesh size influence ....................................................................................................... 55
5.2
Inlet boundary type influence ........................................................................................ 57
5.3
Inlet geometry influence................................................................................................ 59
5.4
Pressure and Temperature gradients through the blades ............................................... 61
5.5
Gas composition influence ............................................................................................ 65
5.6
Virtual test bench .......................................................................................................... 68
5.6.1
Outlet duct flow analysis ................................................................................................... 68
5.6.2
Building the turbine characteristic .................................................................................... 75
5.6.3
Choking mass flow rate refinement .................................................................................. 84
5.6.4
Ultimate turbine characteristic ......................................................................................... 86
5.7
6
6.1
Time calculation of the flow crossing the blades .......................................................... 93
Industrial CT analysis ....................................................................................................... 98
Technological signs ....................................................................................................... 98
7
Conclusions ..................................................................................................................... 100
8
References ....................................................................................................................... 102
9
Symbols and Abbreviations ............................................................................................ 103
II
Introduction
1
Introduction
This master thesis work has been conducted at the research institute for automotive
engineering and engine technology Stuttgart (FKFS), with the virtual engine development
team. Its main purpose is to give the customers of projects and advanced analysis solutions,
through 3D-CFD tools.
Nowadays, the computational fluid dynamic applied to the optimisation of engines have
arose a leading role in the thermal design of powertrain systems, to compare different
layout solutions with reduced prototyping costs. These kinds of simulations are in facts very
required, since they can interact with the testing and prototyping steps and sustain them. To
complete the versatility of these tools, the 3D-CFD codes can interact with other simulation
approaches. For example, it’s possible to set a complex and detailed three dimensional flow
simulation with quite reliable data resulting from a real time or 1D-CFD analysis. These last
mentioned models are for sure more flexible in time calculation, but they only provide
signals or the mean values of thermal parameters in one spatial coordinate of the system
volume.
This work aim was to insert in this scenario the basis for the three dimensional fluid dynamic
simulation of a turbocharger for motorsport application, starting from the turbine
component.
Several steps in building the model are normally required, nevertheless bringing to its most
reliable behaviour aligned to the calibration values. The work abstracts are exposed along
the following chapters in a structured and methodical way, towards the most understanding
and precise improvement explanation, as well as inspire further development steps.
1
CFD tools: brief outlines
2
CFD tools: brief outlines
Computational fluid dynamics, usually abbreviated as ‘CFD’, defines a branch of fluid
mechanics that uses numerical methods and algorithms to predict physical fluid flows and
heat transfer. Nowadays, the on-going research yields software achieving the accuracy and
speed of complex simulation scenarios (turbulent and unsteady flows): hence, CFD tools can
be used to calculate design mass-flow rates, pressure drops, heat transfer fluxes and fluid
dynamic forces.
Once the fluid and its thermodynamic working properties are defined, CFD software can
simulate the interaction of liquids and gases with surfaces defined by boundary conditions:
this, through the numerical resolution of mathematical equations which govern these
processes, called indeed ‘governing equations’. The way to solve the problem is always by
numerical iteration, both in steady or unsteady flow (for which, the step time definition is
needed too).
After the simulation run, these software furnish advanced graphical interfaces and post
processing tools with the skill to isolate and analyse single specific phenomena for study; for
example the temperature distribution, rather than the kinetic energy or the pressure.
Furthermore, the flow study can be also in only one detailed region of interest and gives the
designers several comprehensive informations.
The CFD is spread in many science fields and for extreme wide range of industries. For
automotive in particular, CFD software provide large help to the cooling systems
prototyping, the passenger’s comfort analysis, the internal combustion simulation or, more
generically the whole intake and exhaust system design (fig.2.1).
2
CFD tools: brief outlines
Fig. 2.1 CFD tools: internal combustion engine application.
Some example applications in which CFD is used are:
Aerospace: aerodynamics, wing design, missiles, passenger cabin
Biology: study of insect and bird flight
Biomedical: heart valves, blood flow, filters, inhalers
Building: clean rooms, ventilation, heating and cooling
Chemistry: mixing, reactions
Electrical: cooling systems
Environmental: pollutant control, fire management
Marine: wind and wave loading, sloshing, propulsion
Mechanical: pumps, fans, heat exchangers
Oceanography: flows in rivers, oceans
Power generation: boilers, combustors, furnaces
Sports equipment: cycling helmets, golf balls
Turbo-machinery: turbines, blade cooling, compressors
3
CFD tools: brief outlines
Fig. 2.2 CFD analysis: example of external and internal flow application.
Especially for the industry, the CFD use for design purposes generally leads to fewer physical
prototypes being necessary during development and less testing: these aspects contain the
costs for physical experiments, which were traditionally the only way to extrapolate
essential engineering data for design.
Nevertheless, the improvement of this technology doesn’t eliminate the necessity to interact
with testing data towards the same models calibration. The last but not the least, the
solutions results and the experimental data set could always contain light gaps, because of
numerical approximations and the use of computational equations (being only the
mathematical representation of the real physics phenomena). The model boundaries
accuracy is anyway depending to the data used for the calibration, which are often
conditioned by measurement strategies and correction factors.
4
Turbocharging fundamentals
3
Turbocharging fundamentals
3.1 Why turbocharging
In the last decades, charging the engine is an almost diffused strategy towards the
performance rise. Historically, this has always been done with a compressor before the
intake airbox increasing the air (or mixture) pressure and introducing an higher mass in the
cylinders; this is a great advantage, leading to the specific power amount. In fact, with the
same displacement it’s possible to have a higher power:
Pe
V mep
n
(3.1)
Eq. (3.1) demonstrates that the two ways to increase the engine effective power (with the
same displacement) is acting on the mean effective pressure, or on the rotational speed. The
second idea is linked to the inertia effect of the rotating parts, being more influent if the
engine rotates faster: the design of lightweight special alloys components is recommended
to contain this effect, but for the costs is mainly in the racing applications applicable.
Therefore, to increase the engine power output, the mean effective pressure has to be
increased, e.g., raising the intake pressure (i.e., supercharging).
Supercharging has many advantages: the first one is to achieve the same power output with
a more compact engine, allowing to downsize it towards the reduction of dimensions, weight
and the manufacturing costs.
5
Turbocharging fundamentals
3.2 Supercharging technology and strategies
3.2.1 Mechanical supercharger versus turbocharger
Fig. 3.1 Ways of charging.
The compressors usually employed are volumetric or centrifugal (fig. 3.1). The first
superchargers were realised with volumetric machines, mechanically driven with belt
transmissions directly from the engine camshaft (in the 1920’s Mercedes Benz became the
automotive supercharging pioneer, for racing engines design).
6
Turbocharging fundamentals
Fig. 3.2 Volumetric compressors for automotive application (Roots and screw type).
This kind of compressor gives pulsating flow to the engine, but it has the benefit to give the
boost pressure to the air as soon as required, without delay. In this solution however, the air
mass flow rate to be boosted is always linked to the compressor displacement and rotational
speed:
Fig. 3.3 Example of volumetric compressor characteristic.
The last but not the least, this kind of compressor connection is always matter of mechanical
losses and the energy spent to rotate it is never recovered. For this ‘energetic’ reason,
another technology came on the market: the turbo supercharger, or simply turbocharger.
7
Turbocharging fundamentals
Fig. 3.4 Turbocharger concept.
The turbocharger is a compact element, in which a radial turbine is linked to the centrifugal
compressor through a shaft. The idea is just exploiting and converting the exhaust gas
residual enthalpy into mechanical energy to let the compressor rotate. In the figure below,
the exhaust energy available for the compressor is represented by the triangle abc (fig 3.5).
8
Turbocharging fundamentals
Fig. 3.5 Exhaust energy available (abc), represented on a pV diagram [2].
This contributes to obtain higher engine efficiency, because this energy is used and not
discharged.
Differently from the mechanically driven volumetric compressor, the turbocharger bane is
the so called “turbo lag”: or rather, the time needed for the turbocharger to generate the
required boost. Many factors contribute to have this exhaust system delay: among which the
rotating parts inertia, friction and compressor load. The traditional mechanical
superchargers don’t suffer of this, because their response is instantaneous to the driver
power request.
Moreover, a turbocharger can provide an appreciable boost to the engine only when the so
called ‘boost threshold’ is overcome. Especially at the low engine rotational speed, lower
exhaust mass flow rate crosses the turbine blades: they can’t spin enough to win the
frictions and the compressor load, so that also the desired response is not reached.
Another difficulty related to the turbocharger efficiency is the heat exchange: the exhaust
gases high temperature generates material stresses and due to its compactness, it could
transfer the heat to the compressor side and make the latter efficiency worse [7], as shown
below.
9
Turbocharging fundamentals
To overcome this issue, the lubricating oil has the additional task to take away part of the
heat power.
Fig. 3.6. Heat transfer in a turbocharger.
.
3.2.2 Layouts: the twincharger
The comparison between the vantages and limits of the mechanical supercharging and the
turbocharging leads to new configurations, sometimes also with the combinations of these
two approaches to mitigate the weaknesses of both the systems.
The volumetric compressor can work at low engine rpm (at its maximum efficiency operating
area): this avoids the use of a turbocharger with turbo lag and gives a better torque
characteristic. On the other hand, a medium size turbocharger can be activated by the
engine control unit when the engine speed is higher. In the series configuration, the
volumetric compressor can be bypassed with a valve or in high power request, it continues
to work and supply the centrifugal compressor inlet, yielding so elevated boost. This layout is
really suitable for the engines in a spread rpm operating, because it can cover a good range.
The twincharger approach was firstly used by Lancia:
10
Turbocharging fundamentals
Fig. 3.7 Lancia Delta S4 rally engine with “Volumex” twincharger (1985).
In these first applications, the electronic control hardware and strategies were not so able to
manage such a complex system. The complexity still nowadays remains one of this layout
disadvantages, even if many progress have been done. But nevertheless, the series market
too presents clear examples of the twincharger application, as the Volkswagen 1.4 l TSI
downsized engine (fig. 3.8).
Fig.3.8 Volkswagen 1.4 TSI twin charged engine.
11
Turbocharging fundamentals
Fig. 3.9 Volkswagen 1.4 TSI twin charged engine.
The turbocharger has a wastegate valve to control the exhaust gas flow through the turbine,
while the roots supercharger can be controlled with an electromagnetic clutch. The intake
air can bypass the latter with the use of a control valve.
3.2.3 Layouts: two stages twin turbocharger
To reduce the turbo lag of a medium-high size turbocharger, this solution employs two
combined turbos. One smaller works at low engine rpm, having low turbolag and providing
already a good torque; at the medium rpm range, both the turbochargers operate together.
They’re in series, so that their boost pressures are multiplied. Since the exhaust mass flow is
continuously variable, the transition from one to the other is done proportionally and not
with an on-off control strategy.
12
Turbocharging fundamentals
An example of this layout was applied on the Opel 2.0 l biturbo Diesel (fig.3.10 and 3.11).
Fig. 3.10 Opel 2.0 l Biturbo Diesel engine
Fig. 3.11 Opel 2.0 l Biturbo Diesel engine.
13
Turbocharging fundamentals
3.2.4 Layouts: the hybrid turbocharger
This is another solution recently conceived and still on design and optimization:. An electric
machine is coupled with the turbocharger and is electronically driven by the engine control
unit: sometimes it works as motor or as generator.
Fig. 3.12 Electric assisted turbocharger example.
During the throttle opening request, it drives the compressor with an optimum response;
meanwhile, when no more power is needed, it can work as a generator collected to the
turbine in order to recover the compressor absorbed power through the exhaust enthalpy. If
at that instant the turbine provides more energy than the necessary, the excess fraction can
be saved in the battery storage and later supplied to the compressor.
The extreme flexibility is evident: indeed, this system has these two advantages. First, by
decoupling the turbine and compressor, the dynamic response limits of the traditional
turbochargers can be overcome. Furthermore, there’s the opportunity to manage the energy
rates in time.
14
Turbocharging fundamentals
3.3
Characteristics
Both the turbine and the compressor are machineries which operating range is defined
through curves, precisely called characteristics. These characteristics are built by testing the
component in laboratory with different conditions of pressure ratio, mass flow rate and
rotational speed. Then, maps are drawn reporting the speed and mass flow rate as pseudodimensional formulations, towards the comparison of different machines size on the same
diagram.
In this paragraph a brief sign about the characteristic building is presented, since in the
results chapter the Manufacturer’s turbine map has been compared to virtual ones.
3.3.1 The turbine map
The most common automotive turbocharger turbine is a radial flow machinery, often
manufactured in Inconel special alloy. The degree of reaction in automotive applications is
generally 0.5 [1]; It means that half of the overall enthalpy change occurs in the stator and
half in the rotor according to the R definition:
R
hrot
hst
hrot
(hin hout ) rot
hin,st hout,rot
(3.2)
The turbine is characterized through the use of custom test benches and a relation between
the corrected mass flow rate and pressure ratio can be described:
15
Turbocharging fundamentals
Fig. 3.13 Nozzle and radial turbine characteristics (respectively, left and right).
As the figure 3.11 shows, the radial turbine can be seen like a simple nozzle for the flow,
with the difference that there’s curves dependence from the rotational speed: particularly,
to obtain the same mass flow rate a higher pressure is required, as the turbine speed grows.
This aspect justification is that the exhaust flow meets more resistance to enter the blades
when the turbine turns fast. Furthermore, it’s to be noticed that reaching the choked flow
conditions, this correlation tends to be less meaningful: every iso-velocity characteristic
tends to be closer to the other. This effect is more pronounced in the axial turbines rather
than in these radial.
Further details on these topics are reported in [1].
16
Model description
4 Model description
4.1 Geometry design
The first simulations were launched with a ‘hand-made’ housing geometry, having no precise
geometry references from the turbocharger producer (as a turbocharger for WRC rally
applications, no data were available on the web due to confidential reasons). The results
were obviously not enough accurate, so that to make a tomography analysis of the real
housing has been decided [A1].
Fig. 4.1 Turbine CAD assembly.
17
Model description
Fig. 4.2 The assembly: multi-view of the last step modelled (Catia CAD software).
18
Model description
4.1.1 Tomography results
The housing tomography results were furnished in “stl” format (Stereolitography extension).
So that, the software catiaV5 was not able anymore to modify this file extension and obliged
to directly import the housing in StarCCM+, as part. Since the CT file contained both the
surfaces (internal and external one), with the ‘surface repairing’ tool the external geometry
has been manually ‘peeled’ and removed.
Fig. 4.3 The ‘peeling’ and removing of the external housing surface from CT file.
19
Model description
Fig. 4.4 The ‘peeling’ and removing of the external housing surface from CT file.
Since an STL extension is nothing more than a cloud of points and doesn’t contain any
reference system, it was not possible to make a common rapid prototyping and directly use
this geometry for the CFD importing.
Nevertheless, it has been discovered that Solidworks is able to transform Stereolitography
files into 3D cad files, with the tool ‘Scan to 3D’ (Surface Wizard): once a surface mesh is
created, the file could be into catia V5 imported. The way through the so called ‘reverse
engineering’ was too long in time, so that it has been abandoned. Since every STL file can be
normally opened in Solidworks and saved as IGES, this solution was preferred.
20
Model description
4.1.2 Previous CAD resetting
A huge work of geometry building and manipulation has been done: the CAD housing
previously built has been totally reset in its sections and profiles, according to the reference
stl tomography geometry:
Fig. 4.5 Tomography reference geometry (left) and final CAD (right).
Fig. 4.6. The geometry reset.
21
Model description
In Catia, the main issues were related to the multi-sections solid closure: so that, more
splines were added as guide lines.
Furthermore, to increase the model accuracy and precision, the space between the housing
and the impeller blades has been reduced.
Fig. 4.7 Superposition between the two housing surfaces: the internal is the reset one.
Unfortunately, importing the better geometry in Star CCM+ was more difficult as before; the
necessity to convert it in IGES extension and the reduced spaces between the future
boundaries reminded to reset the tessellating tolerance. Then, other problems in surface
recovering and merging between the parts occurred.
22
Model description
4.2
Mesh design
4.2.1 Preparing the surface
As soon as geometry is imported, Star CCM+ directly creates a surface mesh from it, so
called ‘Initial geometry’. The quality of this mesh is often bad and needs to be refined before
launching the surface mesh generator. So that, before creating the regions from the part it’s
better to use the tool ‘repair parts’: with this surface diagnostics the free edges can be
closed, the no manifold vertices and edges have to be eliminated to let the beginning surface
remeshed. Furthermore, before doing this it’s recommended to check the feature curves
(important to let the surface remesher respect the boundaries definition).
Fig. 4.8 Surface diagnostics tool.
23
Model description
4.2.2 Surface mesh setting
Once repaired, the initial surface can be automatically remeshed. A good surface mesh gives
better region boundaries, from which a more accurate volume mesh could be result. If the
surface is not correctly closed (free edges or intersecting faces), the volume meshing is not
possible. The remesher provides automatically to the closing proximity and poor quality
faces refinement and gives as output the worst face quality, so that the user can investigate
it.
Here the parameters mainly used in this work to set the surface mesher are presented:
Base size
The Base Size value is a characteristic dimension of the model. It should be set prior
to using any relative value parameters: for instance, the base size could be initially
set equal to the diameter of an inlet or whatever size is convenient in order for other
values to be scaled from it. If the mesh size is set with absolute values and not in
dependence of a reference length, no base size is needed.
Surface size
The Surface Size node allows the setting of the cells size next to the surface and
feature curves during surface and volume meshing. The min, max and target value
specifications are available. In this instance, the combination between the min and
target was preferred.
Within this specification, mesh models will try to achieve specified target size in the
absence of refinement from curvature/proximity effects, regardless of the local
triangle size of the input surface. Refinements from curvature and proximity will not
cause the surface size to go below specified minimum size.
Surface proximity
The Surface Proximity option allows the specification of cell refinement for the
surface mesh models based on a search distance (called the Search Floor) and the
number of ‘points in a gap’. That is, the ‘Search floor’ represents the minimum size
gap to be considered: if a gap is found with a distance less than the search floor
24
Model description
value, it will not be considered for proximity to prevent unwanted refinement. The
‘Points in a gap’ value is used for specifying the refinement for surfaces that are in
close proximity to one another: a local size for triangles is determined by dividing the
distance from one face to another across a gap by the specified ‘points in a gap’
parameter, as long as the gap distance is not less than the search floor value.
Automatic Surface Repair
The enable automatic surface repair option provides an automatic procedure for
correcting a range of geometric type problems that may exist in the remeshed
surface once the surface remeshing process is complete. This procedure will
ensure that all triangles created by the process will have a quality equal to or
better than a specified value. This is achieved by allowing the mesher to change
feature edges if required, move feature vertices or avoid projecting vertices in
order to remove or improve faces whose quality is below the specified value . Up
to three different metrics are used: pierced faces (intersecting), surface proximity
and surface quality.
The surface repair follows two mechanisms:
a) Remeshing: growing out the problem area, deleting the local surface and
removing features (if required).
b) Patching: the remeshing procedure, including filling holes;
The remeshing will first be applied to a given problem area and if this succeeds in
eliminating the issue or improving the quality then no further action is taken and
the next problem area is addressed. If the remeshing step did not resolve the
problem, then the patching option will be applied to the original problem
definition.
The surface repair includes two nodes to be set:
o Minimum Proximity: can be used to specify the minimum proximity value
which all faces should have after fixing. It is defined as a percentage of the
average length of the edges in the triangle which is being checked. The
default value of 0.05 is sufficient for most fixing requirements and would
mean that any face of a neighbouring triangle would have to be a distance of
0.05 times the average edge length of initial triangle to pass the check.
25
Model description
o Minimum Quality: it can be used to specify the minimum quality value which
all faces should have after fixing. The minimum quality property for the auto
surface repair is a value that ranges from 0 to 1, with 0 being the worst and 1
being perfect. The quality of a triangle is given by 2*(r/R) where r is the radius
of the circle that fits inside the triangle and R the radius of the circle that
passes through the three corner points of the triangle (the default value is
0.05):
2r
2R
Surface curvature (points/circle)
The Surface Curvature node allows cell refinement to be included for the surface
remesher mesh models, based on the number of points around a circle (#Pts/circle)
and the curvature deviation distance. The number of points around a circle value is
used for the specification of the basic curvature. For example, the default Pts/circle
value of 36 indicates that approximately 36 triangles (for a surface) or cells (for a
volume) would be used around a 360 degree cylindrical surface:
Increasing the value would increase the relative refinement of the cells next to the
curved surface.
26
Model description
Surface grow rate
The surface growth rate parameter controls the rate at which triangle edges sizes can
vary from one cell to its neighbor. The parameter typically only comes into effect
when some sort of refinement (for example, curvature or proximity) is included.
Volumetric control
A volumetric control is a very important tool, both for surface and volume meshing. It
allows the mesh density increasing, based on a volume shape closed part. In the case
of the surface meshing tools, only the surfaces contained within the volumetric
control shape is affected. For volume meshing tools, the entire core and/or prism
layer volume contained within the volumetric control shape can be refined
depending on the options selected.
Once a volumetric control has been created, a supplied relative or absolute size value
determines the size of the cell faces that will be used for the isotropic volumetric
control.
In general, volumetric controls that need to influence the domain boundary should
extend a small distance beyond the geometry itself to ensure that that appropriate
sizes are included.
The size value used in a volumetric control can be less than the global minimum size,
so careful attention should be made to the size value and the units it is specified in
order to avoid generating unwieldy meshes by accident when using small values.
27
Model description
Fig. 4.9 Volumetric control shape applied to the rotating region refinement.
To warranty a finer mesh (both surface and volume), a cylinder shape has been
selected as volumetric control, with a major radius than the outlet diameter: all the
mesh models are included under this control, avoiding too much difference between
the volume cells and the surfaces triangles sizes.
4.2.3 Creating the volume mesh
The models available for the volume mesh creations are the tetrahedral, trimmer and
polyhedral: for this model the third has been chosen, because it was considered more
accurate with the compact and complex geometry to fill. Furthermore, with the same
geometry, the number of polyhedral cells can be five times less than the tetrahedral one.
Moreover, other two models were ticked:
28
Model description
-
Prism mesh layer
The prism layer mesh model is used in conjunction with a core volume mesh to
generate orthogonal prismatic cells next to wall boundaries. A prism layer is mainly
defined in terms of its thickness and the number of cell layers within it.
Fig. 4.10 Prism layer definition mask in Star CCM+ and example applied to this work (inlet boundary).
These layers are largely used because necessary to improve the accuracy of the flow
solution. Indeed, numerical dissipation (represented by errors and discontinuities
embodied by large gradients in a finite volume) is minimized when the flow is aligned
with the mesh. In typical boundary layers, the flow is aligned with the wall, and the
largest gradients tend to be normal to the wall. The use of prism layers is an
approach that greatly improves accuracy, as a result of aligning the flow with the
mesh. In general, however, prism layers are critical to properly resolving turbulent
boundary layers.
-
Extruder
This function has been included for example to create an out duct normal to the
outlet section, since fixing the outlet boundary conditions directly beyond the wheel
29
Model description
was to problematic: the flow vortex is there still too high and needs space to be more
completely developed.
Under the outlet boundary it’s possible to activate the normal extruder mask, to set
the length, the number of layers and their stretching:
Fig. 4.11 Extruder settings.
Here the parameters mainly used in this work to set the volume mesher are presented:
Density (both polyhedral and tetrahedral)
A volume mesh growth and/or density factor can be applied to increase or decrease
the mesh density. The density value (1.0 by default) can be used to change the
overall density of the mesh, everywhere. Increasing the value to say 2.0 would
approximately double the number of cells generated, while decreasing it to 0.5
would approximately halve the number of cells.
The Growth Factor can be used to increase or decrease the mesh density of the core
mesh, by changing the rate at which cells grow from coarse to fine areas. Increasing
the value above the default of 1.0 would mean the cell sizes would grow faster,
30
Model description
resulting in fewer cells. Conversely, decreasing the value below 1.0 would make the
cell sizes grow more slowly, resulting in more cells being created.
For example, if there are two opposing surfaces separated by a gap and the surface
mesh sizes are the same, then the growth factor will have no effect in this instance
and only the density factor could be used to change the volume mesh density. If the
surface mesh sizes differ in one surface to the other, then one or both factors could
be used in this instance to influence the resulting density.
Volume blending (both polyhedral and tetrahedral)
The global volume blending factor can be used to control the mesh density transition,
when volumetric controls are in close proximity to the surface mesh boundary or
interface. This is to avoid sharp transitions in mesh density, which could lead to
numerical instability during the analysis. The default value of 1.0 will provide a
reasonable transition between the cell size used for the volumetric control and the
surface mesh. Decreasing the value (to say 0.5) will provide a smoother transition by
making the local mesh size closer to the boundary/interface surface meshing size,
resulting in less cells in the core mesh (assuming that the volumetric control uses a
cell size smaller than the boundary/interface triangle edge size). Increasing the value
(to say 1.5) will provide a sharper transition by making the local mesh size closer to
the volumetric control mesh size, resulting in more cells in the core mesh (again
assuming that the volumetric control uses a cell size smaller than the
boundary/interface triangle edge size).
4.3
The regions layout
As previously mentioned, several steps of the work required a continuous remaking and
refinement of the imported geometry, but the main layout characteristics were always the
same. In this chapter the model is so explained in its parts and how the interfaces between
31
Model description
them have been set. Furthermore, a brief list of every boundary belonging to them is
presented.
4.3.1 Interfaces creation between the parts
The first step is to import the Iges (or Stp) extension file as a new surface mesh, initialised as
soon as it’s opened. It’s strongly recommended to import the geometry as parts, repairing as
parts and let them imprinting.
Merge/Imprint surfaces tool
Fig. 4.12 Multi-part imprint mask (StarCCM+).
This procedure is the best to create a full precise contact between the parts sharing a
surface and edges. In difference with the single part imprint, the multi-part one is able to
calculate source and destination pairs automatically. The merge angle and tolerance
parameters are to be set in the case in which the tool doesn’t find some parts contact. Once
reset, the merging is activated with the command ‘imprint pair’.
32
Model description
Once the part imprinting is done, it’s possible to create the regions and the interfaces from
these merged and repaired parts.
4.3.2 Regions
The model is composed of three different regions: the housing, the blades region and the
outlet one.
Fig. 4.13 The continuum: housing region (grey), blades region (brown), out duct region (blue).
33
Model description
Wall
boundary
Inlet
boundary
Interface
boundary
Fig. 4.14 Housing region detail.
Wheel
Wall
Interface with Housing
region
External
Wall
Interface with Duct region
Fig. 4.15 Rotating region detail.
34
Model description
Duct
Wall
Interface with
Blades region
Outlet
Fig. 4.16 Outlet duct region detail.
4.3.3 Rotating motion specification
For the rotating systems modelling, StarCCM+ is equipped with two different approaches of
motion definition: the Rigid Body Motion (RBM), or the Moving Reference Frame (MRF). The
first approach consists of the vertices mesh motion according to a specified value, the
second uses the specified rotation to create a constant grid flux and no mesh vertices are
moving.
4.3.3.1
MRF Approach
The MRF approach is the most used for steady state flow analysis, so that it has been
adopted for this case. A rotating reference frame applied to a region permit to generate a
constant grid flux. This has to be defined under the node “tools” (fig. 4.17).
35
Model description
Fig. 4.17 Moving reference frame specification (StarCCM+).
The rotation axis has to be specified in its direction and origin, while the rotation rate can be
set as a constant, or as an interpolation of a data table.
In the previous modelling steps, the rotating speed was set as the working point constant
value, but due to numerical problems and floating points occurred this speed ratio value has
been then defined according to an input ramp given by the user (as csv table).
36
Model description
rotational speed [rpm]
150000
100000
50000
0
0
500
1000
1500
2000
2500
3000
Iteration [-]
Fig. 4.18 Velocity ramp.
This law is importable in StarCCM+, under the node ‘tables’ and then can be reminded to the
motion node with a little script (fig. 4.19).
Fig. 4.19 Script for the velocity ramp remind.
37
Model description
Lots of simulations were done with different length ramps, to find the optimum number of
iterations in which the target value can be reached: it was necessary a trade-off between a
gradual ramp allowing no floating points (but increasing the simulation time) and a steeper
one, which could have saved time in calculus but with floating point occurring. After many
attempts, the value has been set to 160: from 160 to 200, the value remains constant.
For every iteration, the program makes a linear interpolation of the table data; the
simulation can continue for the next iterations over 200, keeping the last value of the table
(so, the target one).
4.3.3.2
RBM Approach
With the rigid body motion the procedure to identify the rotation is slightly different, since
to define the inertia of the rotating part is necessary and also the fact that here the whole
region mesh vertices rotate and not only a simple grid.
It has been decided not to delve into this approach, since it’s born for unsteady flow and
transient analysis. This philosophy could be the starting point to model the whole
turbocharger system: in this case the velocity is not imposed and the turbine is matched
with the compressor; the convergence on the velocity is given by the dynamical equilibrium
between the turbine and the compressor torque, only possible after a transient state.
Once the motion is defined, this has to be applied to the region of interest. In this model, it’s
always referred to the blades region (called precisely ‘rotating’, fig. 4.20).
38
Model description
Fig. 4.20 Rotation motion specification: applying the rotating reference frame to the blades region.
39
Model description
4.4 The boundaries definition
In the previous paragraph the regions layout and the boundaries are listed. Here the aim is
to explain how every chosen boundaries work and the combinations between them,
according to the thermodynamic definition of the global system.
Since as first simply step the turbine could be considered as a simple nozzle, to combine the
inlet/outlet boundaries in a compatible way it’s strongly required.
Along the several modelling steps, two were the layout adopted:
Mass flow specification (mass flow inlet)
Pressure ratio specification (pressure inlet)
The first philosophy has generated better results and a faster speed of convergence, but it
has to be considered as less real in its definitions. Since a mass flow is always generated by a
pressure ratio between the inlet and the outlet of every open system, when possible is
better to fix the boundary pressure conditions and let the system aligning on the mass flow
value.
4.4.1 Mass flow inlet boundary
As previously mentioned, this was the first philosophy adopted to model the flow through
the turbine: this paragraph contains a brief elucidation about this aspect. The mass flow rate
inlet could be combined only with a pressure outlet. This is due to the compatibility of the
physical quantities both required:
40
Model description
Boundary type
Physical quantities required
Mass flow Inlet
Mass flow rate
Static Pressure: used only for supersonic conditions. For subsonic
flow, it’s extrapolated from the adjacent cell.
Total Temperature
Pressure Outlet
Static Temperature: used only for inflow conditions. For the
outflow condition, it’s normally extrapolated from the adjacent cell.
Static Pressure: used in subsonic conditions, whereas a correction
is applied.
Table 4.1 Mass flow inlet boundary approach.
Since the temperatures are higher than the standard value of 298 K, the speed of sound is
higher too:
a
(4.1)
kRT
So that it’s more difficult for the flow to reach the sonic condition of Ma=1. Hence it’s
plausible to consider the flow conditions always as subsonic.
As noticed in the table, in subsonic flow conditions the system requires as inlet data the
mass flow rate and the total temperature; at the same time, at the outlet only the pressure
is required. The temperature outlet specification is redundant, excepting the situation in
which some cell calculates an inflow direction. The thermodynamic reason of this setting
could be justified in the following passages.
Considering as first instance an isentropic expansion, it could be:
1 k
Tout
Tin
p in
p out
k
(4.2)
41
Model description
In which the subscripts ‘in’ ‘out’ are respectively referring to the inlet and outlet sections.
At the inlet section, the flow velocity can be determined since the geometry and the mass
flow rate are known:
.
c
m
ρ A
(4.3)
The density is known too, because it comes from the ideal gas equation (for the physic
definition see the next paragraph):
ρ
p
RT
(4.4)
The inlet static pressure p is determined, since taken from the nearest cells. The inlet static
temperature is related to the total temperature, given by the definition of total isentropic
enthalpy:
Δh tot
Δh st
Δh st
c2
2
Tst
Ttot
c2
2 cp
_
c p ΔT
(4.5)
Since all these quantities are determined, the thermodynamic inlet state is completely
defined.
At the outlet section, the hypothesis of averaged outflow can be done (only some cells will
calculate local inflow velocity vectors).
In this conditions, the density is derived from the same ideal gas equation (the static
pressure is given by the user and the temperature is taken from the nearest cells). Besides
this, if the continuity equation is satisfied the mass flow rate is the same as specified at the
inlet by the user. Having the section area too, the outlet velocity can be calculated.
42
Model description
4.4.2 Pressure inlet boundary
In difference with the first simpler approach, this one is slightly different.
Boundary type
Physical quantities required
Pressure Inlet
(working always in inflow)
Static Temperature: being in inflow, it’s always used.
Static Pressure: used in subsonic conditions.
Pressure Outlet
Static Temperature: used only for inflow conditions. For the
outflow conditions, it’s normally extrapolated from the adjacent
cell.
Static Pressure: used in subsonic conditions, whereas a correction
is applied.
Table 4.2 Pressure inlet boundary approach.
The inlet is here set as a ‘pressure outlet’, which always works in inflow conditions. In fact,
due to the higher inlet pressure rather than the outlet one, a decreasing pressure gradient is
fixed and also the mass flux direction is generated. In this solution, as before mentioned, the
mass flow is calculated as a consequence of fixing the pressure ratio (according to the Saint
Venant formulation for isentropic nozzle outflow). The density on both the boundaries
comes from the ideal gas equation, being the pressures and the temperatures already
known.
43
Model description
4.5
Boundary and initial fluid conditions
4.5.1 The GT-Power working point
The values to set the inlet and outlet boundaries have been extrapolated from a GT-Power
turbocharged engine 1D CFD model (in these kinds of models, the quantities involved are
averages across the flow direction). The data were furnished as averaged on the engine
cycle: in fact, the real engine thermodynamic parameters in dependence of the crank angle
are always pulsating.
In the GT-Power model it’s possible to isolate the turbine component and read the most
important quantities.
3500 rpm engine speed point
Hence, at a precise engine speed value:
Pressure (inlet and outlet)
Temperature (inlet and outlet)
Mass flow rate (the fraction bypassed through the external wastegate is already
subtracted)
Turbocharger rotational speed
Turbine real power
Turbine efficiency
Everything then has been managed in an excel table, calculating the remaining reference
data for the 3D StarCCM+ simulation (as the torque and the power, table 4.3).
p in [bar]
1.830
p out [bar]
1.080
ε
1.7
n t [rpm]
149053
T in [K]
1067
44
Model description
T out [K]
945
R air [J/kg*K]
287.05
Runiv [J/mol K]
8.314
R exh [J/kg*K]
296.93
mexh [g/mol]
28
ρ in [kg/m^3]
0.578
ρ out [kg/m^3]
0.385
mass flow rate [kg/s]
0.12
real power [W]
14900
ideal power [W]
20523
real torque [Nm]
0.955
ideal torque [Nm]
1.316
Efficiency
0.726
delta h [J/kg]
124167
ideal delta h [J/kg]
171028
cp in,out [J/kgK]
1017.8
Delta T[K]
122
ideal Delta T [K]
168
ideal T4[K]
899
Table 4.3 Reference parameters calculations.
The densities are calculated with the ideal gas equation (4.4), where R is the mass constant
of the exhaust gases, calculated as:
R
m exh
(4.6)
(m exh is the molecular mass of the gas mixture and R is the universal gas constant).
With the equation P C
2π n t
(4.7), it’s easy to find the real torque value.
60
To estimate the ideal power and the ideal torque, there’s only to divide both the real
quantities for the turbine efficiency given by GT-Power:
Pideal
Preal
ηt
Cideal
C real
ηt
(4.8)
From the real power and the mass flow rate, the real specific enthalpy variation can be
obtained according to the relation:
45
Model description
.
m hreal (4.9)
Preal
Since, under the hypothesis of ideal gas, the enthalpy difference between inlet and outlet
could be defined as follows
Δh real
_
c p in,out (Tin Tout ) (4.10)
Furthermore, as before, is:
Δh ideal
Δh real
ηt
(4.11)
Then the average specific capacity between inlet and outlet can be extracted.
4.5.2 The fluid initial conditions
The regions fluid must be set in its initial conditions, at least pressure and temperature, to
encourage the calculus convergence. For this reason, under the fluid definition the pressure
and temperature values have been reset and intermediate values between the inlet and
outlet were adopted.
46
Model description
Fig. 4.21 Fluid initial conditions set.
For the n=3500 rpm working point:
p= 1.5 bar;
T=1000 K;
4.6 Physics definition
An important step in a CFD model building is to specify all the parameters and equations
concerning the physical definition of the fluid analysed. In particular, the main points to
focus on are:
Gas model
The continuum fluid domain type
In this paragraph a brief description of these points is presented, just to specify the basics.
Deeper dissertations on these topics are discussed in several books on fundamental of fluid
dynamics.
47
Model description
4.6.1 Gas model
Star CCM+ allows the user to choose trough different real fluid definitions, among them the
simplest one which has been adopted in this work: the ideal gas model.
This model refers to the equation pv
RT , where the constant R is for the specified gas and
related to the universal one by the gas molecular weight (4.6).
By default, the software leaves the setting as compressible gas so that no further
modifications were needed about this aspect.
But another important feature revealing itself fundamental for the correct gas definition is
the specific heat: for a CFD simulation, even in the simplest approach the specific heat
modelling as a constant is too restrictive because this parameter can differ according to the
temperature and the species involved: from the output of QuickSim, an innovative tool
cp [J/kgK]
giving StarCD CFD code more flexibility [5], this quantity trends can be seen in figure 4.22.
cp (T) exhaust species
3300
3200
3100
3000
2900
2800
2700
2600
2500
2400
2300
2200
2100
2000
1900
1800
1700
1600
1500
1400
1300
1200
1100
1000
900
800
200
700
1200
1700
cp-N2 [J/kgK]
cp-H20 [J/kgK]
2200 2700 3200 3700 4200
Temperature [K]
cp-CO2 [J/kgK]
cp-Air [J/kgK]
Fig. 4.22 Exhaust species specific heat.
48
4700
Model description
These kinds of correlations are already included for every chemical species in StarCCM+
database, taken from the Janaf tables and fitted with a five coefficient polynomial (fig. 4.23).
Fig. 4.23 CO2 Specific Heat definition: polynomial fitting the Janaf tables.
A polynomial in T could be defined entirely by the user too, specifying the intervals number,
the input variable ranges (in this case, the Temperature), how many coefficient terms fitting
and the coefficient values: but in this case, the definition of the reference temperature and
the enthalpy of formation should be specified.
49
Model description
4.6.2 The continuum fluid domain
The previous results of this work were obtained with the simplest fluid model: ideal gas. The
type has been selected as single component, the air. The next steps required a better
alignment in the comparison with the GT-Power reference data, so that a new multicomponent fluid definition has been created. The gas model remained ideal, but the mixture
composition depends on the ratio between the exhaust species generated by the
combustion reaction.
Hence, considering that in this full load engine working point the mixture is a little bit richer,
there is no oxygen excess in the exhaust gas and the combustion reaction could be in this
way written:
Cn H m
n
m
O2
4
79
n
21
m
N2
4
m
H 2O
2
nCO 2
79
n
21
m
N2
4
(4.12)
For a common gasoline [3], the mass fraction composition could be 0.86C and 0.14H, or
better:
C 0.86
kg c
kg fuel
and H
0.14
kg H
kg fuel
The molecular weight of the involved species is:
C
H
O
N
g
mol
g
1.008
mol
g
16
mol
g
14
mol
12.011
The molecular weight of the fuel is so:
50
Model description
fuel
n
C
m
H
(4.13)
Since in the reaction there’s only one mole of fuel as reactant, it’s possible to write:
fuel
m fuel
Then is
n
0.072
fuel
m
0.139
fuel
A correct ratio for a common gasoline is
m
1.876 so that it could be defined as C n H1.876 n .
n
From the Heywood tables [2], it’s known that
passages, the value n
fuel
110
g
; making some algebraic
mol
7.912 is obtained. The chemical formula of the gasoline could be
written as C 7.912 H 14.843 .
As consequence, the products are:
7.912CO 2
The sum of the products moles is n exh
7.422H 2 O 43.724N 2
59.058 mol
The moles percentage is:
CO2: 13.40%
H2O: 12.57%
N2: 74%
The products molecular weights are:
51
Model description
CO 2
H 2O
N2
g
mol
g
18.016
mol
g
28.013
mol
44.011
So, the product mass is:
m CO 2
n CO 2 μ CO 2
348.215g
m H 2O
n H 2O μ H 2O
133.715g
m N2
n N2 μ N2
m exh
1706.770g
1224.840g
The mass percentage for each component is:
CO2: 20.4 %
H20: 7.8 %
N2=71.8 %
The mass fraction of each component can be then in StarCCM+ defined, being careful to
order the species with an increasing mass fraction criterion. In fact, for calculation reason,
the highest mass fraction species in the mixture must be at the end: the list order must be
so H20, CO2 and N2.
52
Model description
Fig. 4.24 Gas mixture setting.
In the previous steps with the multi-component mixture set up, this order was not respected
and the ‘Biconjugate gradient stabilized method’ non convergence occurred (for
explanations, see [6] the AMG solver chapter.
53
Simulations results
5 Simulations results
In this section, the simulations results are presented in a structured way to comment on the
tested parameters, whereby the runs and the outputs were so sensitive.
Mesh size
Inlet geometry
Inlet boundary type
Gas composition
Model
optimisation
Fig. 5.1 Factors that have a significant influence on the simulations results and model reliability.
54
Simulations results
5.1
Mesh size influence
Since a coarser mesh can save much computational time, it’s a good thing to optimize the
volume mesh cells size in order to have a trade-off number that ensures good model
reliability too.
Some testing simulations with different kind of surface mesh refinement (and consequently,
volume mesh size too) have been run and they demonstrated a coarser mesh can give the
same results as a finer one. Furthermore, it confirmed a finer mesh can give more instability
in calculations, as it can be seen in the figures 5.2 and 5.3.
Δ=3.6%
Δ=4.7 %
Fig. 5.2 Coarser mesh gave less numerical instability; torque has been estimated by integration of the pressure
forces on the wheel surface.
55
Simulations results
These two simulations were done with the same regions layout and imposing the mass flow
rate at the inlet boundary (not the pressure). It’s to be noticed that the outlet mass flow rate
has been estimated by integration of the term ρc (density*velocity), on the outlet flow area.
Δ=0%
Fig. 5.3 The continuity is well verified: the mass flow rate at the outlet boundary is aligned with the target
imposed at inlet.
The convergence values are more or less the same and the signal dynamic on the torque is
even better with the half of the cells number. For this reason, the setting with 800000 cells
has been abandoned. In the last simulations the optimization brought to have even less than
300000 cells (from 230000 to 255000, depending on the inlet length).
The same tests were done with the pressure inlet boundary rather than the mass flow
specification and the effect was the same: a finer mesh could not bring meaningful
enhancements.
56
Simulations results
Another aspect to be mentioned in this parenthesis is the prism layers: these are necessary
to have reliability in the mass flow rate value and respect the continuity equation. Especially,
the layer thickness must have more or less the same dimensions of the nearest volume cells.
5.2 Inlet boundary type influence
As previously discussed, in this work two approaches for the inlet boundary description were
adopted: one time specifying the mass flow rate, the other time the static pressure. In the
second approach, the simulations were very difficult to converge and the dynamics was
definitely the worst. The figures 5.4 show the comparison between the two strategies
adopted, keeping the same geometry (no additional inlet duct).
Fig. 5.4 With pressure inlet boundary type, the numerical instability is higher.
57
Simulations results
Δ=3.6%
Fig. 5.5 With pressure inlet boundary type, the numerical instability is higher.
When the mass flow is imposed, the torque stable value is reached more or less after 2500
iterations (around 3.6% error in respect of the GT-Power target). Imposing the pressure at
the inlet, the numeric fluctuations hold over: as a consequence of the mass flow bad
dynamic behaviour, the torque too is oscillating.
An explanation of this behaviour could be the following: the pressure inlet specification is
unreliable when the inlet boundary is too much closed to the turbine wheel, region in which
the fluid has more vorticity and difficult to be solved.
Fixing a pressure boundary is anyway a more real approach than imposing the mass flow,
because from a theoretical point of view, the mass flow rate through a nozzle is always a
consequence of a given pressure ratio; but to follow this redline, some geometrical device is
required.
58
Simulations results
In fact, it must be mentioned that all three dimensional CFD models are always set with one
dimensional boundaries: for example, at the inlet and the outlet the p,T quantities are
averaged on the sections. This simplification influences the calculations.
So, to avoid this as more as possible and give more reliability to the model, it’s better to fix
the inlet boundaries farther (as done at the outlet).
5.3
Inlet geometry influence
To obtain the convergence with the pressure inlet boundary type too, an inlet duct has been
created with the extruder mesh tool (as the one built previously for the outlet).
Fig. 5.6 Inlet duct.
The number of layers has been calibrated in function of the duct length, to have the same
layer thickness of the outlet ones (5 mm).
59
Simulations results
Different simulations were run, changing the inlet duct length. Within the trade-off between
inlet duct length and numerical stability, the best compromise was 100 mm, since it has
been verified that 5 mm still gives rise to some problems and 300 mm is too much
conservative, because it doesn’t enhance the convergence so meaningfully in respect of the
100 mm duct case.
Δ=4%
Fig. 5.7 The 100 mm inlet duct proved to be the best compromise to have the best stability.
60
Simulations results
Δ=14.7%
Fig. 5.8 Longer inlet solved numerical problems, but the gap on the torque remains.
From one side (figure 5.7), having a farther pressure inlet generates a better numerical
behaviour, but the mass flow rate value decreased (as a consequence, the torque too). In a
first instance, this was supposed due to the gas friction losses near to the housing wall; but
since the results didn’t change with the length duct variation, this was not retained the
cause anymore.
5.4
Pressure and Temperature gradients through the blades
StarCCM+ allows several reports that the user can easily associate to a derived part. This tool
was very useful in this instance of the work, to investigate how the pressure and the
temperature decrease meanwhile the flow passes across the turbine blades.
Different sections were set as derived, along the x axis direction (fig.5.9).
61
Simulations results
Sections (from x=0)
x=1 mm
x=5 mm
x=10 mm
x=15 mm
x=20 mm
x=25 mm
5.9 Sections specifications under the "Derived parts" option.
62
Simulations results
Each section has been linked with an average surface report: this has the task to read a user
specified quantity for every iteration step and send it to a monitor (from which it’s possible
to export or tabulate the value). Ten reports were created, five for the absolute pressure
monitoring and the others for the temperature.
After the simulations, these outputs were post-processed and it has been possible to realise
the following plots (5.10 and 5.11), demonstrating the gradients through the blade in every
approach: original and 50 mm length inlet as geometry, mass flow or pressure as inlet
boundary type.
1.6%
Inlet
1 mm
5 mm
10 mm
Outlet (545 mm)
Fig.5.10 The inlet pressure value changed with reference to the inlet boundary type adopted.
On the pressure gradient, there’s a little gap between the inlet values: when the pressure
inlet is imposed, the value is correct (1.83 bar, according to the GT-Power reference) but the
mass flow rate is underestimated. On the contrary, imposing the correct mass flow rate the
model overestimated the inlet pressure (1.6%). In the further steps of the model
63
Simulations results
development, to delve on this aspect could bring to a fundamental reduction with the
reference data gap.
Furthermore, the presence of the constant section duct seems to give the flow a sort of back
pressure, obliging it to decrease the velocity.
Fig. 5.11 Specifying the pressure as inlet boundary, the temperatures are higher than in the other approaches.
Concerning the way in which the temperature decreases, the 20K regain is due to the
adiabatic duct presence too (figure 5.11): in fact, at this state of the art no convection heat
exchange was considered and the heat from gas friction losses near the walls was not
dissipated.
64
Simulations results
5.5
Gas composition influence
In the GT-Power reference model, the exhaust mixture gas flows from the engine manifolds
to the turbine: its composition depends by several factors, for example λ and the
combustion efficiency. Hence, in order to better align this model to the reference one, a
multi-component gas mixture simulation has been done in comparison with a pure Nitrogen
gas simulation (species highly concentrated in air and exhaust too).
As in the chapter 4 described, the mixture mass fractions have been estimated simply with
the perfect and complete combustion hypothesis.
Furthermore, even if these rally gasoline engines work with mixtures that are often rich, for
more simplicity calculation a stoichiometric air/fuel ratio (λ=1) has been considered. So,
there are no unburned gas and no oxygen excess.
The results of these two simulations are here in the figures 5.12 and 5.13 reported. Through
their comparison, the model sensitivity on the gas multi-component mixture description is
presented.
65
Simulations results
Δ=5%
Δ=7.5%
Fig. 5.12 Pressure inlet boundary type: with multi-component exhaust mixture, underestimation in mass flow
rate is higher.
66
Simulations results
Δ=9.5%
Δ=13%
Fig. 5.13 Pressure inlet boundary type: the multi-component exhaust mixture introduced a gap reduction on
the torque.
67
Simulations results
5.6 Virtual test bench
5.6.1 Outlet duct flow analysis
This 3D CFD model could be very well used as ‘virtual test bench’: as specified in chapter 1,
the experimental conditions can be applied to this virtual component, which solution is good
to justify the measurements done by test engineers on a real bench and overcome the
aspects that couldn’t be so clearly seen. An application of this is here below explained.
The aim of this analysis was to study the temperature, pressure and velocity profiles at
different distances along the outlet.
To reproduce the laboratory test devices, instead of the classical sections, a series of thirty
punctual sensors has been set on six steps along the x axis (one point on every 2 mm in the
vertical direction, fig. 5.14).
Fig. 5.14 Point sensors position.
68
Simulations results
Taking as example the temperature measurement, this is equal to move an ideal
thermocouple and taking 30 samples for every x. Proceeding in this way, these obtained
profiles are shown in figure 5.14.
Temperature
Fig. 5.15 Outlet temperature profiles.
Fig. 5.16 Outlet temperature profiles.
69
Simulations results
Fig. 5.17 Outlet temperature profiles.
The temperature gradient on the sections is going to decrease approaching to the outlet.
But these are very interesting trends especially because they’re asymmetric and the highest
value of every plot seems to oscillate in the x direction, as if a portion of hot gas were
moving helically.
This is totally confirmed in figure 5.18.
Fig. 5.18 The temperature outlet wall pattern justifies the profiles obtained by point measurement (5.14).
70
Simulations results
The helicoidal reflects the velocity flow trends, as follows.
Velocity
As expected, where the gas reaches the highest velocity the temperature is the lowest. In
figure 5.18, the blue helical is also the track of the fastest flow.
Fig. 5.19 Velocity outlet profiles.
Fig. 5.20 Velocity outlet profiles.
71
Simulations results
Fig. 5.21 Velocity outlet profiles.
The temperature profiles aren’t decreasing near the walls because they have been
considered as adiabatic, hence no heat transfer is contemplated. But on the contrary the
velocity tends to decrease in the proximity of the duct walls and this effect is going to be
more relevant along the duct: this is sensible because no slip option has been selected and
friction effects are taken into account, dissipating kinetic energy.
Moreover, on the z=0 level the velocity magnitude is always from 0.7-1 m/s tends to the rest
at the outlet and the gradient is high as on the 100 mm section, immediately after the
turbine.
72
Simulations results
Pressure
Fig. 5.22 Pressure outlet profiles.
Fig. 5.23 Pressure outlet profiles.
73
Simulations results
Fig. 5.24 Pressure outlet profiles.
In the outlet walls a lower increase in static pressure has been observed: on the rotational
axis the pressure is lower due to the vorticity of the flow. There’s a slightly asymmetry of the
profile on the pressure plots too, but in minor relevance. They are more similar between
them and having more or less the same gradient (from 1.075 to 1.11 bar): only at the out
section the pressure rises more uniformity.
Fig. 5.25 On the duct walls there are practically no remarkable pressure differences.
74
Simulations results
5.6.2 Building the turbine characteristic
The model was calibrated by comparison with data referring to one particular condition
.
( , m) and a quite good reliability has been reached. As following step of this work, the
challenge was to build a virtual turbine characteristic at constant rotational speed and
compare it with the characteristics given by the Manufacturer, in order to quantify shifts. To
build these curves several simulations were run, each of them with a different pressure
ratio.
Fig. 5.26 The Garrett GTR 2560R turbine characteristic.
Among these curves, the 138900 rpm one has been chosen as sample.
The first testing series were conducted with the exhaust gas mixture model, whose
composition has been in chapter 4 described.
75
Simulations results
To move on the x axis, the pressure ratio or more precisely the inlet pressure has been
changed. The inlet temperature has been maintained constant: 1045K, from the GT-Power
reference point used to calibrate the model.
Once the simulation has been run, pressure values have been virtually “measured”
immediately upstream and downstream the turbine, with two surface average reports
(figure 5.27).
Fig. 5.27 Definition of the “virtual” measuring sections.
This has been done in order to insert the real modelled ε values on the turbine map: as a
matter of fact, usually pressures and temperatures are measured not very far from the
turbine housing (figure 5.28).
76
Simulations results
P, T turbine
measurement
Fig. 5.28 Typical turbocharger test bench.
Contrary to the real test bench in figure 5.28, the mass flow rate has been measured on the
upstream turbine cross section, since on this reference the mass flow signal is generally
more accurate than the downstream one (it has less fluctuations).
On the turbine characteristic the reduced mass flow rate must be reported:
.
.
m red
m Tt,in
(5.1)
p t,in
Where the total inlet temperature and pressure are so defined:
Tt,in
Tin
in
c2
2 cp
p t,in
c ρ dc (5.2)
pin
t,in
The reduced mass flow rate has been obtained within a simple Excel sheet:
pressure (y 60mm)
1.59
bar
pressure (x 50mm)
1.16
bar
159247.1
Pa
pressure
tot
16007 Pa epsilon 1.369
77
Simulations results
temperature (y 60mm)
1045.0
K
R_exh
287.84
J/kgK
density
0.529
kg/m^3
Inlet area
0.0019625
m^2
mass flow rate
0.077
kg/s
velocity
74.26
m/s
m rid
temperature
tot
cp
inlet
diameter
1047
K
1319
J/kgK
0.05
m
0.01552 (kg/s)*(K^0.5)/kPa
Table 5.1 Reduced mass flow rate calculation.
Obtained values were inserted in the turbine map (figure 5.29).
Fig. 5.29 Turbine characteristic at 138900 rpm: comparison between the reference data (Target) and the model
output.
78
Simulations results
For lower inlet pressures, the gap between reference and calculated data is very small but it
increases with ε: from 1.6 on, it’s around the 5% (figure 5.30).
E(%)
target - model
100
target
Fig. 5.30 Errors evaluation.
An evaluation of the measurement errors related to the reference curves was done to show
the accuracy range of the experimental data. To this extent, measured points were
highlighted (fig. 5.29).
To estimate the measurement errors on ε, as attempt it has been assumed that both the
pressure sensors have a precision of
0.1% full scale (where the latter is 2 bar for the inlet
and 1 bar at the outlet). The error calculation must follow the errors theory description.
Using the total differential theorem:
Δε
δε
Δp in
δp in
δε
Δp out
δp out
Δp in
p out
p in
p out
2
Δp out
(5.3)
With:
Δpout= 0.001 bar, Δpin= 0.002 bar, pout=1 bar and p in
ε p out the results are:
79
Simulations results
Pressure ratio [-] Epsilon error [-] Epsilon error [%]
1.32534
0.00332534
0.250904674
1.44879
0.00344879
0.238046232
1.56358
0.00356358
0.227911588
1.71452
0.00371452
0.216650724
2.00362
0.00400362
0.199819327
2.60694
0.00460694
0.176718298
Table 5.2 Error on the pressure ratio measurement.
The error bars on ε proved to be very narrow in the plot of fig. 5.29.
The same procedure has been applied for the reduced mass flow rate error calculation.
.
Δ m rid
Tt,in
p t,in
.
.
m
.
Δm
2 Tt,in p t,in
m Tt,in
ΔTt,in
p t,in
2
Δp t,in
(5.4)
.
This valuation was a little bit more complicate, since the m values were not known. Hence,
it has been so obtained:
.
.
m
m red p t,in
Tt,in
(5.5)
The kinetic term to be added to the static pressure and temperature inlet has been
evaluated from the model, having no specifications about the inlet and outlet velocity in the
testing conditions.
Considering:
.
m
1% (assumed from experimental experience)
p t ,in
p in
Tt ,in
Tin
80
Simulations results
m_reduced
mass flow rate
[kg/s*K^0.5/bar]
[kg/s]
1.32534
0.05967734
1.772
m_error [kg/s]
m_reduced error
m_reduced error
[kg/s*K^0.5/bar]
[%]
0.000596773
0.01523991
1.149886835
0.087649838
0.000876498
0.020137809
1.136445193
1.986
0.106933425
0.001069334
0.022349377
1.125346269
2.176
0.129032965
0.00129033
0.024236639
1.113816141
2.356
0.164066783
0.001640668
0.025843366
1.096917068
2.5
0.224992945
0.002249929
0.026874808
1.074992313
Table 5.3 Errors on the reduced mass flow rate.
For the reduced mass flow rate the error is higher, because the mass flow measurement
depends on several parameters [equation 5.5].
Last but not the least, the difference between the real walls and the model has to be
considered: in the real conditions, the housing internal surface roughness is decisive and the
dilation with the temperature could be another aspect not to neglect.
81
Simulations results
With the same procedure, several points at 153600 rpm have been considered: obviously,
changing the velocity ramp in the model (paragraph 4.3.3).
Fig. 5.31 Turbine characteristic at 153600 rpm: comparison between reference data (Target) and the model
output.
The gap on the reduced mass flow rate has been evaluated for this 153600 rpm too. With
the exception of the first point in which the mass flow rate is overestimated, the other two
simulations presented a gap of 5% more or less.
82
Simulations results
Since on the most common test benches the turbine is characterised with air and not engine
exhaust, this could have an influence on the shift obtained. Hence, the 5.31 figure curve has
been rebuilt running simulations with air (fig. 5.32).
Fig. 5.32 Turbine characteristic at 153600 rpm: when the air is selected, the gap with the reference data is
smaller.
As forecast, testing the model with the air has brought a gap reduction (averaged on 3%); for
this reason, the comparison with the experimental data has been taken on with this option.
83
Simulations results
Fig. 5.33 Errors evaluation.
5.6.3 Choking mass flow rate refinement
In the following step of the work, the attention has been focused on a point in choked flow
conditions (ε= 2.88) and many attempts were done to reduce as much as possible the mass
flow rate model error.
In the previous simulations, the walls were all set as adiabatic. But this is not so real in
comparison to a real test bench condition. Hence, setting on the walls a constant external
ambient temperature of 300 K the heat exchange coefficient has been gradually increased
until the reasonable value of 150 W/m^2K, being the limit between natural and forced
convection exchange.
It has been so proved that the convection on the housing and duct walls could give a
beneficial amount on the flow rate: this is logical, since as the flow temperature decreases
84
Simulations results
due to the heat exchange, at the same pressure ratios the average air density must increase
and so the mass flow rate too.
Another meaningful factor for the mass flow convergence is the volume mesh layer
thickness: normally, that’s suggested to have the same size of the nearest internal volume
cells dimension.
Fig. 5.34 Volume mesh layer thickness reduction.
In the previous simulations this was 4 mm thick and in the further it has been set as 2.5mm,
with plain improvements on the results:
85
Simulations results
Factors influencing the reduced mass flow rate
Reduced mass flow rate
[kg/s*K^0.5/bar]
2.48
TARGET
2.47
25 W/m^2K
2.46
2.45
2.44
100 W/m^2K
1.83%
2.27 %
No Convection
2.43
2.42
150 W/m^2K
2.41
100 W/m^2K, 2.5 mm mesh layers
2.4
2.4
2.6
2.8
3
150 W/m^2K, 2.5 mm mesh layers
Pressure ratio [-]
Fig. 5.35 Gap reduction with the layer thickness optimization and the inclusion of convection, in the choked
flow condition.
The best compromise resulted to be the thicker mesh layer combined with the highest
possible convection heat exchange (figure 5.35).
5.6.4 Ultimate turbine characteristic
To investigate these factors effect on other working points, a new series has been simulated
and as before post-processed, showing this trend from which the gap is evaluated (fig. 5.36).
86
Simulations results
Fig. 5.36 Turbine characteristic at 153600 rpm: contribute of thinner layers and convection exchange.
.
87
Simulations results
Error (%) on the reduced mass flow rate
6
5
4
[%]
3
Air, 150 W/m^2K, 2.5 mm layers
2
Air, no convection, 4 mm layers
1
0
-1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
Pressure ratio [-]
Fig. 5.37 Errors on the mass flow rate calculations.
The convection effect allows to improve theoretical results of mass flow rate up to ε=1.8,
reaching the smallest gap of 1.83%. But under this pressure threshold, the alignment seems
to be better without convection exchange (figure 5.37).
The further step was to redefine in a more correct way the convective heat exchange:
.
Q
S (Taverage Twall )
(5.6)
As first attempt, the convection heat flux was introduced only with the variation of the heat
exchange coefficient α, keeping the ambient temperature at 300 K. This was not so
reasonable, since the ambient temperature for the flow means not the laboratory one but is
referring to the walls. Hence, as experience assumption, the external walls surface
temperature has been set 50 K less of the average flow temperature and 30 K less for the
wheel surfaces. Precisely, the turbine wheel has been considered with a less convective heat
88
Simulations results
exchange, compared with the external walls: the former was set to exchange only the 1% of
the turbine power, meanwhile the latter convective ratio is around the 17%.
Torque 2.67876577
rotating speed [rpm]
Turbine power [W]
153600 16076.8
43066
External walls
Q [W]
7.09E+03 % of turbine power 16.47
Surface walls area [m^2]
1.45E-01
T in [K]
8.73E+02
T average [K]
813
Twall [K]
763
alfa convection [W/m^2K]
974.8
Turbine walls
% of turbine power
1.00
Q [W]
430.66
Surface walls area [m^2]
1.05E-02
Twall [K]
783
alfa convection [W/m^2K]
1367.9
Table 5.4 Convective heat exchange calculation on the walls.
The surface walls areas were taken from the StarCCM+ reports; the average temperature
has been evaluated between the inlet and outlet turbine cross sections. Fixing higher walls
temperatures than before forced the ΔT to be more realistic and, in order to obtain the
same power, α has grown (table 5.4).
Therefore, a new characteristic curve was built, but with a different measurement strategy
too. In fact, the test methods are usually conducted not through the average pressure and
temperature calculations on the inlet/outlet cross sections, but with a point sensor
measurement according to the testing prescriptions. As matter of that, two point sensors
have been positioned (figure 5.38).
89
Simulations results
Fig. 5.38 Point sensors placement references on the inlet and outlet turbine cross sections.
The results confirmed the expected forecast.
From the pressure acquisition side, the measurement of the inlet and outlet turbine as
averaged rather than punctual is not so forceful: in fact, the inlet pressure is more or less
uniform on the cross section and the outlet one presents 50 mbar range of variation (from
1.07 to 1.12 bar). On the temperature side, measuring an average value or a punctual one
could generate different results because the temperature distribution can be more variable
than the pressure one.
90
Simulations results
Turbine map: target and 3D-CFD model
2.6
2.5
Reduced mass flow rate [kg/s*K^0.5/bar]
2.4
2.3
2.2
2.1
2
1.9
1.8
1.7
1.6
1.5
1.4
153600 rpm (Target)
1.3
StarCCM+: AIR, alfa 150, 2.5 mm layers
1.2
StarCCM+: AIR, convection optimised , 2.5 mm layers (point
measurements)
1.1
1
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
Pressure ratio [-]
Fig. 5.39 Turbine characteristic at 153600 rpm: effect of the point sensors measurement and error evaluation
on the target test bench curve.
Another important issue that should be considered in the presented comparison is related to
the reduced mass flow rate calculation, i.e. if static or total values of T, p were used.
91
Simulations results
Turbine map: target and 3D-CFD model (static p,T)
2.6
2.5
Reduced mass flow rate [kg/s*K^0.5/bar]
2.4
2.3
2.2
2.1
2
1.9
1.8
1.7
1.6
1.5
153600 rpm (Target)
1.4
1.3
StarCCM+: AIR, convection optimised , 2.5 mm layers
(point measurements)
1.2
StarCCM+: AIR, alfa 150, 2.5 mm layers
1.1
1
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
3.2
Pressure ratio [-]
Fig. 5.40 Turbine characteristic at 153600 rpm: effect of the static reduced mass flow rate evaluation.
If static values of p,T are considered in evaluation of reduced mass flow rate parameter, the
characteristic curve changes as reported in figure 5.40.
This aspect has to be investigated, since up to now no information were available.
92
Simulations results
5.7 Time calculation of the flow crossing the blades
As post processing step, an interesting aspect to delve on is how many revolutions the
turbine makes meanwhile a particle of gas crosses a blades duct. This, obviously, it’s
expected to change in function of the flow velocity entering the turbine wheel (and so, from
the pressure ratio fixed).
The length the gas could cover has been in CAD estimated, drawing two splines and
measuring them, for the description of two different flow paths: in fact, the flow particles
could follow several directions entering the turbine wheel.
Low spline: 34.5 mm
High spline: 33.4 mm
Fig. 5.41 Gas particle track definition in turbine wheel.
93
Simulations results
Since the length is not so different, the green one has been considered for this calculation.
As simulation report, the average flow velocity between the housing and the rotating region
can be calculated: this value, for a pressure ratio of 3 and air without convection influence, is
more or less 420 m/s. So, considering the flow having constant velocity, the time necessary
for the gas particle to pass through the blades vane is:
t
0.0345
420
8.214 10 5 s 82 s
The number of revolutions the wheel does during the whole passage of the particle is given
by:
rev t
30
n
8.214 10
5
30
153600
1.32
For rotational speed of 153600 rpm, the particle makes around one revolution before
leaving the turbine wheel. This parameter influences without doubts the flow helicoids in
the outlet duct and depends on the gas velocity entering the turbine, so from the mass flow
rate and indirectly from the pressure ratio stabilised.
Hence, a relation between the pressure ratio and the number of these revolutions has been
sought; the gas track length is always the same, as the turbine rotational speed (steady
state). From the simulations reports, plotting the average inflow velocity in function of the
increasing pressure ratio a proportion has been found (fig. 5.42).
94
Simulations results
Fig. 5.42 Average radial velocity and particle crossing time depend on the pressure ratio.
Hence the expected results is that as the inlet pressure rises, the flows crosses faster the
turbine wheel and recovers a minor rotational angle, finding itself with a more little
tangential velocity vector. Having simulations results at different pressure ratios, it’s possible
to see the number of revolutions trend (fig. 5.43).
95
Simulations results
Fig. 5.43 The turbine revolutions covered by the particle depend on the pressure ratio fixed.
Making some examples, when the pressure ratio is around 1.5, the gas exits from the turbine
wheel after 2.1 revolutions, meanwhile in chocked flow conditions this number is around
1.3. This is reasonable and the previous expectations are justified.
Lower is the pressure ratio, lower is the average flow velocity and the mass flow rate. Hence,
to cross the same track more time is required and in this longer interval, the turbine covers
more angular distance.
In other words, when the gas flow is in steady state conditions and the turbine speed is
constant, the outflow vorticity depends directly to the upstream pressure and this can be
seen also in the StarCCM+ streamlines scenes. In the following table is reported the
measured flow wavelength for different pressures ratios (fig. 5.44).
96
Simulations results
ε 1.47 : 12 cm
ε 1.98 : 19 cm
ε
2.65 : up to 40 cm
ε
2.88 : up to 40 cm
Fig. 5.44 Pressure ratio influence on the streamlines wavelength.
97
Appendix
6 Industrial CT analysis
Industrial CT (computed tomography) scanning is a process which uses X-ray equipment to
produce three-dimensional representations of components, both externally and internally.
The CT scanning was originally used only for medicine applications, but then it has been
applied in many areas of industry too, for internal inspection of components.
6.1
Technological signs
This device uses x-ray beams, in order to create an image to be captured by a detector. The
part to be analysed is fixed on a rotating stage and the source is too moving along the
vertical/horizontal axis, so that a complete three dimensional scanning can be obtained.
More powerful is the x-ray emission, more it can flow through thicker materials substrates
(for the housing walls depth, a medium voltage machine was needed to have a sufficient
intense beam).
Fig. 6.1 Industrial CT device concept.
98
Appendix
Fig. 6.2 Some machines can have the fixed stage and the source/detector system rotating: the result is the
same.
Some of the main sectors in which CT scanning is used are for example failure analysis, metrology,
assembly analysis and the so called ‘reverse engineering’.
In fact, CT scanning can be useful to analyse every single product or assembly quality, without
destructive test or disassembly. It’s so easier to compare the product with the original CAD, or to test
eventual imperfections in every production piece. Furthermore, generating a file from the CT data
set is particularly useful in reverse engineering applications and product development. Exported CAD
file formats are recognized by many types of software. The CAD file created by CT scanning doesn’t
only show the external components, but the internal as well. This allows for first-time rapid
prototyping of internal components. This last application is just this work aim; having no reference
geometry or design data about the internal surface of the volute, it’s necessary to scan the real
component and extract the reference geometry, from which it’s possible to compare the CAD
previously built.
99
Conclusions
7 Conclusions
This thesis work aim has been the building of a 3D-CFD motorsport turbine model. First, the
housing geometry was CAD designed taking as target the real internal housing surface,
obtained from an industrial CT analysis. Subsequently to the assembly between the internal
housing and the turbine wheel, the CFD model has been set in its regions layout and
interfaces optimization between them.
The model calibration occurred on a single steady state condition, using a GT-Power engine
1D model for the boundary conditions generation. Since in GT-Power a real exhaust flow
involves the turbine, a basic multicomponent exhaust fluid definition was proposed to be
more aligned.
Two main inlet boundary types have been compared: imposing the mass flow rate instead of
the pressure at the turbine inlet, the numerical system response is better; but in order to
consider the mass flow as a consequence of a given pressure ratio, the pressure inlet
approach has been for the further steps preferred. According to these first options, the
mesh size and the inlet length influences on the simulations have been estimated: coarser is
the volume mesh, more is the numerical stability. The same could be said about the inlet
length variation; in fact, it has been proved that too short inlet ducts generate mass flow
divergence, so that it’s recommended to fix the inlet and outlet boundary conditions as
further as possible to the wheel region.
In the second part of the work, a ‘virtual’ test bench has been built: varying the pressure
ratio and calculating the mass flow rate, different turbine model characteristic were
extracted. In particular, the alignment with the experimental conditions is very important,
especially the reference temperature. The gap between the experimental turbine map and
the model one has been reduced with the introduction of the convective heat exchange and
the optimisation of the walls volume mesh layers thickness. Furthermore, the comparison
with the experimental map valued with static p,T quantities has brought to an additional
refinement.
Other investigations have been conducted, as the turbine outflow characterization and its
wavelength variation in function of the inlet turbine pressure.
100
Conclusions
This state of the art is considered a good starting point for the next development: especially,
to check the complete alignment with the Manufacturer’s declared testing conditions.
Another two relevant effects could be the axial turbine positioning to the housing and a
more detailed definition of the heat exchange with the walls.
101
References
8 References
[1] N. Watson, M.S. Janota - Turbocharging the internal combustion engine – Ed. Wiley
(1982).
[2] J. Heywood – Internal combustion engines fundamentals – Ed. McGraw-Hill (1988).
[3] G. Ferrari – Motori a combustione interna – Ed. Il Capitello (1988).
[4] C. Caputo – Le turbomacchine – Ed. Cea (1994).
[5] M. Chiodi – An innovative 3D-CFD approach towards virtual development of internal
combustion engines – Ed. Vieweg+Teubner (2010).
[6] StarCCM+ user guide - www.cd-adapco.com
[7] S. Shaaban, J.R. Seume - Analysis of turbocharger non-adiabatic performance - 8th
International Conference on Turbochargers and Turbocharging (London 2006).
102
Symbols and Abbreviations
9 Symbols and Abbreviations
Symbol
a
Description
Unit
Speed of sound
Ma
m/s
Mach number: ratio between the flow velocity and the speed sound
-
Ratio between the specific heat capacity at constant pressure and constant
k
volume
-
c
Flow velocity
m/s
ε
Pressure ratio
-
mep
Mean effective pressure
Abbreviation
Description
in, out
Inlet and Outlet subscripts
st, tot
Static and Total conditions subscripts
CFD
1D,3D
t
exh
Pa
Computational Fluid Dynamics
One dimensional, three dimensional
Turbine subscripts
Exhaust mixture subscripts
103