Chiodi M. An innovative 3D-CFD-Approach towards Virtual Development of Internal Combustion Engines

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66 6 Three-Dimensional Simulation (3D-CFD Simulation)

Reliability of Turbulence Models in the Simulation of IC-Engines

In order to describe the turbulent exchange coefficients, several turbulence models based on

different approaches and different mathematical complexity have been developed. Due to the

“evident” complexity of turbulent processes, all existing turbulence models are rough

representations of the physical phenomena involved. This is a generally recognized fact, which

nonetheless deserves mention here. It is also known that the degree of approximation in a given

turbulence model depends on the nature of the flow to which both it is being applied or has been

validated, and that the characterization of the circumstances which give rise to ‘good’ or

‘inaccurate’ performance must unfortunately be based mainly on experience.

In case of internal combustion engines turbulent phenomena, due to high temperature, velocity

and compositions gradients, reach complex transient structures that are barely comparable to that

of other thermodynamic machines. Actually, there are no devices able to reliably measure the

turbulence within the combustion chamber, i.e. a validation procedure of turbulence models

under real engine conditions is not possible. This introduces a very sensible factor in the

reliability of simulation results, because, as well known, turbulence is the most important

“driving variable” of engine processes (combustion, wall heat transfer, mixture formation, etc.).

Due to previous considerations it would be confusing and probably misleading to try analyzing

and improving turbulence models on considerations of a local turbulent field; in particular it is

well known that the mesh structure, more than the discretization degree, drastically influences

the calculated turbulence. Therefore, at the end it makes more sense to evaluate the turbulence

models from a global point of view, i.e., whether the global results of the 3D-CFD-models

“feeded” by turbulence and directly responsible for the simulation of engine operation (see

Chapter 2.3) are in accordance with both experimental measurements and other simulation

programs (e.g. the working-process analysis) or not. Of course here a separation of the

contributions to the results reliability between the involved process and the turbulence as input

variable is extremely difficult, but in fact no other more promising approaches are available.

6.2.1.4 Combustion Models

Summarily, the simulation of reacting flows requires one more ingredient in order to provide the

connection between the fluid’s mechanical and chemical behavior: in Eq. (6.5) information are

needed for the chemical source term

iii

Mr Z

of each species involved in the chemical

reactions. Reaction mechanisms in internal combustion engines, which involve hydrocarbon

combustion, are a highly complex system with thousands of species and hundreds of competing

reactions. Moreover, the exact chemistry of the combustion processes and the way in which one

reaction step influences another is not well understood yet. Thus, simple “artificial” reaction

6.2 Engine Modeling 67

schemes are often set as approximations to the more complex ones, to make them easier to be

analyzed. Several of this simplified reaction schemes has been proposed, but still exorbitant

CPU-time has limited their application to fundamental research investigations (more details in

Chapters 7, 8 and 9).

The previous considerations explain the reason why in case of a 3D-CFD-simulation of practical

interest, it is more opportune and convenient to implement engine specific combustion models

that actually are limited to heat-release prediction, skipping a detailed analysis of the combustion

mechanisms which are not relevant in the prediction of the engine operating cycle (see Chapter

6.2.2).

6.2.1.5 Wall Heat-Transfer Models

The temperature difference between the fluid and the wall generates a heat-transfer process that

has a remarkably influence on the engine operating cycle (see Chapter 3). In this near-wall

region the flow field is, especially in case of internal combustion engines, extremely complex.

Approaching the wall the temperature changes drastically from the fluid in the region of fully

turbulence development (isotropic turbulence – see Chapter 6.2.1.3) through a turbulent

anisotropic flow field with increasing laminarization degree and a fully laminar flow in the wall-

near region up to the wall itself, where there is no molecular motion due to friction. This flow

field is described by the boundary layer theory that, in case of a simple geometry and stationary

flow, delivers equations for the prediction of the temperature and the velocity profile (coupling

between the thermal boundary layer and the momentum boundary layer) within the near-wall

region. Starting from the temperature gradients, it is possible then to calculate the corresponding

wall heat-transfer.

In the 3D-CFD-simulation the calculation of the wall heat-transfer is commonly based on the

standard “wall function approach”. This approach estimates the temperature and velocity profiles

of the boundary layer according to the theory of a streamed horizontal plate in case of a

stationary flow. Since this assumption is far away from the real transient boundary layer that is

locally found in a combustion chamber, the reliability of the results is very low (more details in

Chapter 10).

6.2.2 Introduction to Engine-Specific 3D-CFD-Models

In theory there is no need to implement models in 3D-CFD-codes which are dedicated to the

reproduction of phenomena that take place in internal combustion engines. A solution of the

68 6 Three-Dimensional Simulation (3D-CFD Simulation)

equation system should also be possible using the fundamental equations in combinations with

models of general validity that have been introduced before. Since the phenomena are extremely

complex and often not adequately understood at a fundamental level, i.e. it is not possible to find

a mathematical formulation based on both basic governing equations and empirical laws of

general validity, it is necessary to introduce 3D-models that are supposed to be valid only for the

simulation of internal combustion engines. This is an irreplaceable process that allows, using

phenomenological approaches, empirical relations and “ad hoc” approximations, to bridge the

gaps in the understanding of critical phenomena [10,11,23,36,60].

In comparison to the models of general validity, engine-specific models are not only functions of

the local physical properties of the fluid but also of the engine relevant parameters. Moreover, in

some cases, it is also convenient to substitute universally-valid models with engine-specific

models of a more simplified and “robust” formulation so that a reduction of the CPU-time and an

increase of the accuracy of the results can be performed.

The following short list reports the main engine processes that can be described by engine-

specific 3D-CFD-models. A few of them will be discussed in details in Chapters 8, 9 and 10:

modeling of the thermo-physical properties of the working fluid

spark ignition modeling

combustion modeling for spark ignition and diesel engines

self-ignition modeling

wall heat transfer modeling

injector spray modeling

6.3 Discretization Practices (Numerical Implementation)

The system of non-linear partial equations – that represent the mathematical description of the

physical problem of the fluid dynamics introduced in this chapter – cannot be analytically

solved. In order to solve this system, some methods (discretization practices) which allow to

approximate the solution in the continuum using a discretized flow field (computational mesh -

see Figure 6.1) are required. Actually, the discretization practice transforms the non-linear

differential equations of the mathematical model into algebraic equations and employs solution

algorithms to obtain the dependent parameters from the discretized equations (numerical

solution) [53,56]. In the following, a brief description of the discretization practices is reported.

In the fini

nodal val

parameter

central no

volume

Gauss di



t,xf

where

From here

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integral

geneous

equired.

(6.55)

70 6 Three-Dimensional Simulation (3D-CFD Simulation)

The second term, which represents the flux of the variable



txf ,

through the surface

the cell, can be expressed in terms of average values of the variable



txf ,

and the velocity



txv ,

over each surface

with the normal vector



txn

of the cell, thus:



HLESWNjAtxntxvtxfdAn

jjjj

,,,,,,,,  )

&&&

(6.56)

where:

.,,,,, HLESWNjAV

(6.57)

The third term, analog to the first one, becomes:



 



.,,

PfPf

VtxctxsdVcs

 

(6.58)

6.3.1 Spatial Flux Discretization

As it has been seen in Eq. 6.56, the discretization of the flux terms in the conservation equations

requires expressing the values of the variables



txf

at the surface positions of the cells. The

manner in which the fluxes of the generic variable



txf ,

are expressed in terms of nodal values



txf

is one of the key factors determining the accuracy and the stability in the 3D-CFD

simulation. There are essentially two main classes of flux approximation in widespread use,

namely low-order and higher-order differencing schemes.

6.3.1.1 Low-Order Differencing Scheme – Upwind Differencing (UD)

The value of the variables



txf

at the surface position is selected from the nearest upwind

neighbor central-node value, e.g. in case of surface H (see Figure 6.5):



 





t

0,,,

txntxviftxf

txf

HHH

HHP

&&&&&

(6.59)

This differencing scheme, which characteristically generates discretized equation forms that are

easy to solve and CPU-time convenient, produces solutions which obey the expected physical

bounds, but sometimes gives rise to smearing of gradients. The latter effect has come to be

6.4 The Role of the 3D-CFD-Simulation in the Engine Development Process 71

known as numerical diffusion. This is a form of a truncation error that diminishes as the grid is

refined, but with a disproportionate increase of CPU-time (see Chapter 7.1.1).

6.3.1.2 Higher-Order Differencing Scheme

Several higher-order differencing schemes have been proposed and implemented in commercial

3D-CFD-codes. By means of an example – the central differencing scheme (CD) – the basic

concept of these differencing schemes will be introduced. The CD-scheme belongs to the

category of second-order differencing schemes, which simply interpolate linearly on the nearest

neighbor values, irrespective of the flow direction, giving in case of surface H (see Figure 6.5):

   

txfgtxfgtxf

HPh

,1,,

&&&



(6.60)

where

is a geometric interpolation factor. Other higher-order differencing schemes are, e.g.

linear upwind differencing (LUD), self-filtered central differencing (SFCD), Gamma

differencing, blended differencing (BD), quadratic upstream interpolation of convective

kinematics (QUICK) and monotone advection and reconstruction scheme (MARS) [53,54,56,

61].

Higher-order differencing schemes, usually better preserve steep gradients, but often they lead to

equations that are more difficult to solve (and, in extreme cases, they may provoke numerical

instabilities). These schemes, also may lead to values without physical meaning (e.g. negative

turbulent kinetic energy, negative species’ mass fraction, etc.). This phenomenon is often called

numerical dispersion. This phenomenon can be partly diminished by grid refinement or by

implementing blending factors in the differencing schemes.

6.4 The Role of the 3D-CFD-Simulation in the Engine

Development Process

The 3D-CFD-simulation represents indisputably the most detailed approach for the investigation

of the engine operating cycle. From its basic concept this approach should allow an unlimited

predictability of engine processes by unrestrictedly varying of any parameter of both the engine

setting and the operating condition. Depending on the chosen degree of mesh discretization it is

possible to fully record the fluid motion and any chemical and thermodynamic phenomena acting

in any part of the 3D-CFD-domain up to a length scale which is not far away from molecular

dimensions.

72 6 Three-Dimensional Simulation (3D-CFD Simulation)

But this is the theory. The practice looks quite different. The computational resources in terms of

the required hardware and the related CPU-time are prohibitive in case of a too fine mesh

discretization. Consequently the 3D-CFD-domain has also to be limited to the part of the engine

of particular interest (usually the combustion chamber and parts of the intake and exhaust

channels), i.e., this procedure introduces boundary conditions that have to reproduce the part of

the engine missing in the 3D-CFD-domain. The setting of the boundary conditions, e.g., due to

the difficulty in determining or measuring the flow field in these regions can be very often a

source of inaccuracy that irremediably compromises the overall quality of the results and

drastically reduces the benefits of such resource investments. Another critical point is

represented by few three-dimensional engine process models that due to the lack of phenomena

understanding at the fundamental physical level, inaccurate mathematical formulations,

numerical dependencies on the mesh structure, ambiguous validation processes, etc., are not able

to ensure a high level of reliability in reproducing and predicting the requested engine processes.

As discussed in Chapter 2 the implementation of the 3D-CFD-simulation in the engine

development process is a quite controversial topic in which expectations, efforts and resource

investments are evaluated in a different manner from developer to developer. Actually, nobody

denies the potentiality of 3D-CFD-simulations but, at the end, pragmatically their

implementations still remain quite limited in comparison to other simulation tools.

With the development of a new 3D-CFD-tool called QuickSim a new approach in the three

dimensional analysis of internal combustion engines has been introduced. This tool tries to take

advantage of the potentiality of the traditional 3D-CFD-approach combined with a remarkable

reduction of the above mentioned drawbacks so that a mayor contribution in engine development

process can be ensured. The future reduction of costs for computational resources and their

increasing performance will surely support this task. The conceptual ideas that have motivated

the development of QuickSim are widely reported in Chapter 7.

Towards an improved 3D-CFD-Simulation

The interest in enhancing the 3D-CFD-simulation from something for few specialists and with

many limitations into a reliable and powerful tool fully integrated into the engine development

process is incredibly high. Future engines, turbocharged, downsized and with innovative

combustion solutions also for alternative fuels, will require a more detailed analysis of the engine

processes in order to better understand the potentialities of the different configurations and then

to properly design the engine towards efficiency exploitation. For this task no other simulation

tool is more adequate then the 3D-CFD-simulation.

However, any engine manufacturer, as introduced in Chapter 2, seeks simulation tools, whose

peculiarities are: fast analysis calculations, reliability, user-friendliness, clear representation of

the results without ambiguity and cost efficiency. Moreover a simulation tool must be well

integrated into the existent engine development process so that the comparison with both

experimental data and other simulation programs can be efficiently set. It can be seen that in the

above listed peculiarities the 3D-CFD-simulation needs a lot of improvements.

7.1 An innovative Fast-Response 3D-CFD-Tool: QuickSim

The aim of this work is to make a contribution to the mentioned changing-step of the 3D-CFD-

simulation by introducing an innovative concept in the simulation of internal combustion

engines. This new concept is the basic idea of the 3D-CFD-program “QuickSim”, a tool that uses

the traditional CFD-code StarCD

from Adapco in background. The programming of QuickSim

has been started in the year 1998 at the very beginning of my activity as research assistant of

Prof. Michael Bargende at both the FKFS (Research Institute for Automotive and Internal

Combustion Engines - Stuttgart) and the IVK-University of Stuttgart. In this chapter the main

features of QuickSim will be analyzed.

M. Chiodi, An Innovative 3D-CFD-Approach towards Virtual Development of

Internal Combustion Engines, DOI 10.1007/978-3-8348-8131-1_7,

74 7 Towards an improved 3D-CFD-Simulation

7.1.1 Fast Analysis

In a 3D-CFD-simulation in each cell of the mesh representing the fluid domain a local numerical

solution of partial differential equations for the conservation of mass, momentum, energy and

several species concentrations used for describing the mixture formation is performed. In the

case of an engine combustion-chamber very often meshes with usually about 500,000 cells, up to

40 “mixture-species-scalars” and very complex and computing time-expensive 3D-models are

implemented. All this requires the solution of a “huge” amount of equations that easily leads to

an exorbitant CPU-time even using PC-clusters (up to several days).

Figure 7.1 and Figure 7.2 show indicatively (status 2008 using a PC equipped with operating

system Linux) the estimated CPU-time for a simulation over a full operating cycle (computation

of a mesh with cylinder and parts of intake and exhaust channels over 720 deg) as a function of

the total number of cells

Cells

in the mesh of the combustion chamber and as a function of its

averaged cell-discretization-length

l , respectively. It is evident that, e.g. halving

l from 1.5

mm to 0.75 mm, the number of the cells in the engine mesh increases by a factor of eight which

causes an increment of CPU-time by approximately a factor of 25 in comparison to the previous

one. Even multi-processor computing allows for transient simulations, in the “best case”, only a

linear reduction of the CPU-time with the number of processors as long as this number is small

(number of processors <~ 6).

Figure 7.1: CPU-time as function of the total

number of cells N

Cells

in the mesh.

Figure 7.2: CPU-time as function of the

averaged cell-discretization-length l

The estimated required time-step

in the simulation in order to obtain a temporally accurate

numerical solution depends on the convective velocity of the processes

in the flow field and

CPU-time, h

0.1 1 10 100 1000

Mesh cells number N

, -

Multi Processors

1 Processor

CPU-time, h

0.1 1 10 100 1000

Av. cell discretization length l

, mm

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Multi Processors

1 Processor

7.1 An innovative Fast-Response 3D-CFD-Tool: QuickSim 75

the averaged cell-discretization-length

of the mesh. Here the Courant number

introduces

the following relation:

7.0d

'

(7.1)

This relation assumes that the chosen time-step

must be set low enough to allow each

involved cell to “capture” the process transition. Usually, in the simulation of internal

combustion engines using meshes with an averaged degree of discretization, setting values of the

time-step

corresponding to a crank angle step M' of about 0.25 deg are a common practice

at middle engine speed. During the exhaust phase, due to high gas velocity in the channel, or

generally at low engine speed this value

M' is usually reduced to about 0.125 deg, i.e. the

simulation of an operating cycle requires from 3,000 up to 6,000 time-steps.

Figure 7.3: Cell discretization l

and characteristic turbulent lengths (integral and

Kolmogorov) – Cylinder displacement: 500 cm

– 5000 rpm – WOT.

Following the Courant number relation, looking for a more fine mesh e.g. by halving

this

implies not only more cells and consequently much more computing time for each time-step, but

also more time-steps required for the simulation of a cycle. A comparison between the cell

discretization

and the length scales of the phenomena occurring in an engine helps

understanding the capability of both the mesh and the implemented 3D-CFD-models to directly

Characteristic turbulent lengths, mm

-3

-2

0.1

Crank an

,de

TDC BDC FTDC BDC TDC

Kolmogorov

length

- l

50,000 cells

- l

500,000 cells

- l

5,000,000 cells

integral

length