CFD ASSIGNMENT

Computational Modelling and Flow Analysis in a

Complex Manifold Configuration under Steady State
Turbulent Flow Conditions
Preamble

The purpose of this assignment is to expose the students to some of the key concepts and practicalities
of Computational Fluid Dynamics (CFD).

For this task, a case study that is representative in terms of its computationally challenging nature, but
also suitable for a Module-level assignment, is selected: that of the flow analysis in a complex manifold
configuration under steady-state turbulence conditions. Manifolds are relevant in internal combustion
engine technology but also in other applications. The main role of an intake manifold is to provide a
uniform and stable intake of air for the engine, thus ensuring intake uniformity in each cylinder. Failing
to meet this requirements effects emissions, engine vibrations and torque output.

Inlet manifolds are of course three-dimensional, and it is common to import geometries into the solver
that are created using various computer-aided design software packages. Three-dimensionality, complex
geometric features, as well as other complications, like pulsatile flow conditions, have been removed
from this exercise: our emphasis here is on the “CFD workflow”.

The instructions that follow briefly describe the steps the students must take to complete the process.
Moreover, where necessary, they provide background information and theory describing the concepts
behind the tools.

Although dealing with a simplified case, we have tried to make the experience as realistic as possible –
the level of task definition provided would be representative for an industrial engineer using CFD for
design or R&D purposes, or a researcher using CFD for analysis and research. If there is a piece of
information in the specification that you think is missing, it is probably missing for a reason.

Acknowledgements
The ESI Group (Paris, France), developers of the CFD-ACE+ multiphysics software platform, are
kindly acknowledged for allowing the use of the software for this assignment.
2
 DOs and DON’Ts
DOs

 Explore. Try different things. You cannot break the software, so going outside the instructions
provided and attempting things you find interesting will only enhance your experience.

 The manuals of CFD-ACE (or any software of this type) are endless sources of information
(available on MOODLE). Use them wisely: it is probably not prudent to attempt to read them
cover to cover.

 Doing the work and the computations in a consistent manner is important. Demonstrating that
you have done so is equally important. Be very meticulous with the report. You are to structure
your report as a technical/scientific paper which means that the space available is limited and
the format is strictly prescribed.

 You are given (available on MOODLE) a small number of very well-defined tutorials outlining
the various aspects of the work you will need to do. Complete the tutorials (and explore) before
you engage with the main tasks.

DON’Ts
 The ESI Group has kindly permitted us to use one of the most complete Multiphysics/multiscale
solvers (CFD-ACE+) for this assignment. Interaction with this very mature code, used routinely
in industry of all types all around the world, will offer you as realistic an experience as possible
regarding organizing and conducting CFD studies.

 Remember what you have been told, repeatedly, regarding plagiarism.

3
Introduction
The purpose of this exercise is to familiarise the students with state-of-the-art CFD software. In this lab,
the flow distribution in a 2D inlet manifold configuration under steady-state turbulent flow conditions
will be pursued, and different design modifications will be expected as part of this computer lab.
In practical applications, inlet manifolds usually operate at high velocities and therefore high
Reynolds numbers. This means that laminar flow conditions are not applicable. To address this issue, it
is commonplace to introduce turbulence models in the computations. For the geometry defined in the
next section, conduct a computation at a low Reynolds number to account for laminar flow characteristics
(base case). Once this is completed, conduct simulations at a much higher Reynolds number, say starting
at 10,000 (based on inlet diameter and bulk inflow velocity). Subsequent calculations should include
Reynolds numbers in the range between 1×103 and 1×105. Based on the results of these calculations,
show and comment:
 Do flow features change at these high Reynolds numbers? If yes, how so?
 How does the pressure drop from inlet to exit(s) change with Reynolds number? How do these
compare with that of the laminar computation?
 Evaluate the intake uniformity via the use of a suitable metric, such as the intake manifold flow
coefficient.
 What are the hypotheses and limitations behind these turbulent computations?
 Are your computations grid-independent?
 How do grid requirements differ for turbulent-specific computations compared to those for
laminar ones?
 Comment regarding convergence criteria in turbulent computations like the ones you are
conducting.
 How high, in Reynolds number, could you go in such computations?
 Explore a different design configuration of your choice (for instance, you may want to alter the
design of the regulator cavity, location/diameter/length of the inlet/outlets, and/or add an
additional outlet). Please do not forget to justify your choice of alternative designs.

The order that tasks are to be completed during this assignment is predefined by the nature of the work
you are asked to complete, and falls under the following headers:
o Geometry Definition
o Grid Generation
o Computation
o Post-processing and Visualization
o Preparing the report
The sections that follow are similarly organized around these themes. In summary, for the first section
(Geometry Definition and Grid Generation), you are asked to define an intake manifold and then to
construct a mesh.
The third part (Computation) explains how the solver should be setup and provides the pertinent
elements of the theory behind the numerical solver. Visualization, which is described in a very
rudimentary fashion, involves examining the flow fields obtained. This latter section is, truly, open to
interpretation: we would like you to show initiative and explore alternative ways to interrogate and
compare your results. Finally, your report must capture all of the above. Exercise judgment regarding
what to include and what to reference only or outright exclude form your report. A common mistake such
reports suffer from is inclusion of software-specific trivialities (like menu snapshots): remember that an
important aspect that any report should convey is reproducibility, and this involves the capacity to repeat
a study using different tools. Place emphasis on governing equations and formal algorithms, not on
software-specific terminology.

4
Geometry Definition and Grid Generation

You shall use the programme CFD-GEOM for this task.

Build an inlet manifold that looks like this:

Regulator chamber
Inlet

Outlet Outlet Outlet

The dimensions given are enough to construct this geometry. Finally, construct an unstructured triangular
mesh with roughly 20,000 - 50,000 elements. Remember, you will be required to construct more than
one mesh, to demonstrate grid independence for the base case.

5
Computation
You shall use the programme CFD-ACE+ for this task.

Introduction to CFD–ACE+1
CFD–ACE+ is a Computational Fluid Dynamics (CFD) and Multiphysics solver. In the sequel, a short
description of the main functionality of the software is given.

Flow Module
Although CFD-ACE+ has many physical modules or models, we will only concentrate on the Flow and
Turbulence (Turb) module. The Flow module is the heart of CFD-ACE+ and is used in most simulations.
It enables the user to model virtually any gas or liquid system. When coupled with other modules, like
chemistry/mixing, stress, two–fluid, this can be used to solve problems in a very wide variety of
application areas. Both internal and external flows, at any speed, can be simulated yielding numerical
solutions of the pressure and velocity fields.

Flow Module Theory

The governing equations for the Flow Module are based on mathematical statements of the conservation
laws of physics for flow: –
 Fluid mass is conserved, meaning that the system does not lose or gain mass;
 The rate of change of momentum equals the sum of the forces on the fluid (Newton’s Second
Law of Motion).

Mass Conservation
Conservation of mass requires that the rate of change of mass, in a control volume system, is balanced
by the net mass flow into the same control volume (outflow–inflow). Mathematically this is expressed
by:–

where ∂ρ/∂t is the rate of change of mass–density (mass per unit volume) and   ( V) is the convective
term that constitutes the net mass flow across the control volume’s boundaries.

Momentum Conservation
The x–component of the momentum equation, used in CFD-ACE+, is obtained by setting the rate of
change of x–momentum of the fluid particle equal to the total force in the x–direction on the fluid particle
equal to the total force in the x–direction on the element due to surface stresses plus the rate of increase
of x–momentum due to sources:–

Similarly, the y–component of the momentum equation is given by: –

6
Finally, the z–component of the momentum equation is: –

where τ is shear stress, p is pressure and S M is the momentum source term. Note, that when dealing
i

with 2D problems, the latter equation is not used. The above system of conservation laws is generically
called the Navier-Stokes Equations.

The k–ε model

Flows in the laminar regime are completely described by the equations 1-2 above. At values above a
critical Reynolds number, a complicated series of events takes place which eventually leads to a radical
change of the flow character, usually portrayed by random and chaotic behaviour. The motion becomes
intrinsically unsteady even with constant imposed boundary conditions. The velocity and all other flow
properties vary in a random and chaotic way. This regime is called turbulent flow. Most flows of
engineering significance are turbulent, so the understanding of the turbulent flow regime is not just of
theoretical interest. As stated in your lecture notes, a turbulent flow can now be characterised in terms of
the mean values of flow properties (U, V, W, P etc.) and some statistical properties of their fluctuations
(u’, v’, w’, p’ etc.).

In 2D thin shear layers the changes in the flow direction are always so slow that the turbulence can adjust
itself to local conditions. In flows where convection and diffusion cause significant differences between
production and destruction of turbulence, such as in recirculating flows, a compact algebraic prescription
for the mixing length is no longer feasible (see lecture notes). The way forward is to consider statements
regarding the dynamics of turbulence. The k–ε model focuses on the mechanisms that affect the turbulent
kinetic energy. The k-ε model is one of the most widely used models, as it is known to be robust and
applicable to a wide spectrum of problems and possesses the added benefit of not requiring high mesh
resolution near the walls of the domain. It is noted here that wall functions are empirical functions used
in the near wall region and hence allows a relaxation on the mesh resolution. Several versions of the k-
ε model are in use in the literature. They all involve solutions of transport equations for turbulent kinetic
energy and its rate of dissipation. The version adopted in CFD-ACE+ is based on Launder and Spalding
(1974):

Turbulent kinetic energy, k

7
Dissipation rate, ε

where P is a production term, given by:

The five constants used are: C  0.09, C  1.44, C  1.92, k  1.0, 

1 2 
The turbulent dissipation rate is given by:    s   d
1
.
3
The standard k-ε model is a high Reynolds Number model and is not ideally suited to the near-wall
regions where viscous effects dominate the effects of turbulence. Instead, wall functions are used in
cells adjacent to walls. Adjacent to a wall, the non-dimensional wall parallel velocity is defined as:

u   y , u   yv
(4a-b)
u      ln  Ey   , y  y v
1  

In equations 4a-b:

C 0.25 
y  y 

v
u
u y (5a-b)
C 0.25 
where :   0.4, E  9.0 for smooth walls

8
 Numerical Methods: Finite Volume Method [2]
CFD-ACE+ is a pressure correction-based Finite Volume Method (FVM) Navier–Stokes equation flow
solver. Briefly, the finite volume method is probably the most–well established and thoroughly validated
general purpose CFD technique. The numerical algorithm rests on the following steps:–
 Integration of the governing equations of fluid flow over the (finite) control volume (cells) of the
computational domain;
 Discretisation involves the substitution of a variety of finite–difference–type approximations for
the terms in the integrated equations expressing flow processes such as convection, diffusion, and
source terms. This process transforms the integral equations into a set of algebraic equations;
 Solution of the algebraic equations is attained using an iterative approach.

The Laminar Case

Procedure:–
After you have defined the geometry of the manifold in GEOM save it as a .GGD file. Once you have
created your mesh, save your progress again, only this time it will be in the form of a .DTF file. You will
select the physical and chemical phenomena relevant to the problem, assign appropriate boundary
conditions, and solve the problem. The subsequent section will guide you through.

Here are some of the parameters you will need for the gas properties (air at standard temperature and
pressure):–

 Air mass density, ρair = 1.225 kg/m3

 Constant (Dynamic) viscosity, μdynamic = 1.789 105 kg/m–s

 Inlet velocity:
o Base case (laminar case), Uinlet = 0.1 m/s
o Please note that you are expected to increase the value of Uinlet to obtain values of Re
numbers in excess of 1000 for the turbulent computations.

The following describes the step necessary to define the turbulent cases:

9
 In the PT settings tab make sure you
choose the relevant solvers for the
simulation at hand.

In the GUI, make sure you tick the Flow

and Turbulence (Turb) checkbox when
simulating the turbulent cases. For the
laminar case, do not select the
Turbulence (Turb) module.

Next, we select the model options.

In the MO settings tab choose the Non-

Axisymmetric Polar option, and the Steady
time dependence condition in the Transient
Conditions settings. The latter should be an
intuitive choice, since you are focusing on
steady state computations in this lab.

Make sure you have NOT selected the

inclusion of body forces, rotational
reference frames and Chimera options.

For the Flow, Turb and Adv tabs within

the MO settings, keep the default
options.

In the next section, we enter the specified volume conditions for the fluid.

10
 In the VC settings tab choose Gas as the
fluid subtype and enter the relevant density
(Rho) and Dynamic viscosity values given
to you in The Laminar Case description.

Next, define the boundary conditions for the laminar case, and pay attention to the use of
turbulent kinetic energy/turbulent intensity and dissipation rate/hydraulic diameter. For internal
flows, the turbulence intensity can be somewhat large (1-10%). Choose a suitable turbulence
intensity, calculate the inlet turbulent kinetic energy and dissipation rate. Assume a fixed outlet
pressure and update the Turb tab accordingly for the output.

For the inlet conditions, use similar values to the boundary conditions (especially for the
turbulent kinetic energy and dissipation rate), but perturb the component of velocity.

A recommendation regarding Solver Control Settings is offered here; feel free to explore other options.
The only strict requirement is to use the Central Differencing Scheme (and to achieve converged
solutions of course!)

Press the Solver Conditions [SC] tab

to activate the Solver Condition
setting page.
In the Iteration tab:–
 Set the Max. Iterations to 5000;
 Set the Residual Reduction
Ratio to 0.0001.
 Set the Min. Residual to 1E-18

11
In the Spatial Differencing tab set
the Spatial Differencing for both
velocity and turbulence to Upwind.
You may want to explore this choice
further in your report.

In the Solver tab under the Solvers

window:–
 Set the Velocity to CGS to 50
Sweeps with the Criterion of
0.0001, and an ILU(k)
preconditioner.
 Assign the Pressure Correction to
the AMG option, to 50 Sweeps
with the Criterion being 0.1
 Finally, set the Turbulence option
to CGS, 50 Sweeps with the
Criterion of 0.0001, , and an
ILU(k) preconditioner.
 You may want to explore the
choice of these settings in your
report.

Under the Relaxation tab set the

Inertial Relaxation Velocities to
0.1, and that of Turbulence to 0.2.

Keep the Linear Relaxation Pressure,

Density, and Viscosity to 1.

Ensure the Limits window settings

are not changed.

12
 In the Advanced tab keep the values
as they appear on the RHS Figure.

A recommendation regarding Output Settings – feel free to explore other options:

Select the Output

Window. In the Restart
tab and in the “Restart
Data” option select the
“End of Simulation”.
Ensure that the box next
to “Write Restart solution
Data” is ticked.

13
Select the Summaries tab
and check the Mass
Balance Summary and
make sure Include
Interfaces is selected.

14
 Under the Graphic tab,
ensure a suitable selection
of solution fields that you
would like to analyse in
the post-processing.

Once all the settings are in place, you are ready to conduct your simulations. The following figure
shows how a residuals plot should look like for a fully converged solution.

15
Important Note

Grid Independence: You must compute an appropriate number of meshes to demonstrate that your
results are real and not an artefact of discretisation. Exercise judgement (and literature review)
regarding how best to achieve this and how many meshes you need to include.

16
Post-processing and visualisation
You shall use the programme CFD-VIEW for this stage.

One of the challenges in computational modelling is that each simulation generates a vast volume of data
that needs to be manipulated to extract useful information that can be applied to practical science and
engineering problems. For this purpose, we are going to use CFD–VIEW, which is a graphical post–
processor.

The number of plots and comparisons you can generate from your simulations results is practically
infinite. Some recommendations include: streamlines, velocity vectors, flooded or contoured
distributions of quantities like velocity magnitude, pressure, shear etc.

Preparing the report

We shall follow (strictly) the guidelines of IEEE Transactions on Medical Imaging for formatting the
report/paper. You will find all the relevant information on http://www.ieee-tmi.org/authors/submit-a-
manuscript.asp, including template Word files for fast formatting.

The webpage above includes a link for submitting a paper to the journal for review - Do not submit your
paper to the journal!!! Instead:
 Produce a pdf
 Upload it on MOODLE
 Print it
 Attached the assessment and feedback form at the front, after you fill in your name and relevant
information
 Hand it in at the Departmental Reception
 All before by the deadline!

The maximum size of your report is 10 pages, all inclusive. Do not exceed this limit.

Your report is expected to include a brief introduction where you describe computational work reported
on the literature involving inlet manifolds, a Methods section where you outline the numerical analysis
features of the techniques you used; the bulk of your report will of course include your results – figures
and a critical discussion of that the figures show. Other elements (Abstract etc.) must abide to the
specification discussed above.

References
[1] CFD–ACE Modules Manual
[2] Versteeg HK, Malalasekera W. (1995) Introduction to CFD. The finite volume method
[3] Launder BE and Spalding DB. (1974). The numerical computation of turbulent flows, Computer Methods in
Applied Mechanics and Engineering, 3: 269-289.

17