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PDHengineer.com Course M-4013
Practicing the Science of Computational
Fluid Dynamics
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PRACTICING THE SCIENCE OF COMPUTATIONAL FLUID DYNAMICS
H.S. Pordal, Ph.D. Staff Consultant
Stress Engineering Services, Inc. www.stress.com (513) 336
6701
December 8, 2006
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Course Summary
This intense course provides a working understanding of
Computational Fluid Dynamics (CFD) and an overview of best
practices. It is designed to provide the engineer with basic
knowledge to apply CFD, identify and solve real life applications.
This course creates an awareness of the potentials and limitations
of this technology. The engineer will be exposed to a wide range of
applications and the course offers high benefits to those who have
little or no exposure to CFD. This course offers engineers involved
in CFD an opportunity to sample the wide range of applications that
can be solved using CFD methods.
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Table of Contents
Table of
Contents................................................................................................................
ii 1.0
Introduction...................................................................................................................
1 2.0 Overview of
CFD..........................................................................................................
2
2.1 What is CFD ?
...........................................................................................................
2 2.2 Why use CFD
?..........................................................................................................
2 2.3 Three steps to CFD
:..................................................................................................
3
3.0 Geometry and Mesh Generation
...................................................................................
4 3.1 Flow domain definition :
...........................................................................................
4 3.2 Mesh generation
technology:.....................................................................................
6 3.3 Best
practices:..........................................................................................................
10
4.0 Solver
Technology......................................................................................................
11 4.1 Governing equations
:..............................................................................................
11 4.2 Boundary
conditions:...............................................................................................
12 4.3
Discretization:..........................................................................................................
13 4.4 Linear solvers:
.........................................................................................................
14 4.5 Best practice:
...........................................................................................................
16
5.0 Post Processing
...........................................................................................................
17 5.1 CFD results
:............................................................................................................
17 5.2 Analysis of CFD results:
.........................................................................................
17
6.0 Role of CFD in the
Industry........................................................................................
21 7.0 CFD Applications, Part-I
............................................................................................
27
7.1 External aerodynamics :
..........................................................................................
27 7.2 Internal flow
computations:.....................................................................................
29 7.3 Compressible flow computations:
...........................................................................
31 7.4 Buoyancy driven
flows:...........................................................................................
33 7.5 CFD for fluid transport
devices:..............................................................................
35 7.6 Flow in a valve:
.......................................................................................................
40 7.7 Flow and heat transfer:
............................................................................................
41
8.0 CFD Applications,
Part-II...........................................................................................
43 8.1 CFD for mixing applications:
..................................................................................
43 8.2 CFD for multiphase
flow:........................................................................................
45 8.3 Application of CFD to combustion
systems:...........................................................
52
9.0 Future of
CFD.............................................................................................................
63 9.1 Limitation of CFD methods
:...................................................................................
64 9.2 Next generation
CFD:..............................................................................................
64
11.0
References................................................................................................................
65
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1.0 Introduction
The role of computational methods in engineering design and
analysis has greatly increased during the last decade. This is due
to improved numerical methods and also due to the advent of faster
computers. The computational resources such as computer memory and
computer speed are now easily available and also affordable. A
desktop personal computer using todays technology can achieve what
a super computer achieved about 10 years ago. As a result, the
number of engineers applying computational methods for solving
engineering problems has also increased dramatically. Mathematical
modeling for engineering systems is on the rise. This has lead to a
rapid growth in the breadth and depth of software available for
analysis.
In this course various aspects related to CFD technology are
discussed. This course provides the engineer with basic knowledge
to identify, apply and solve real life CFD applications. The
mechanics of applying CFD depend on the particular software being
used. However, the general principles and philosophy described in
this course are not specific to a particular software and apply in
general.
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2.0 Overview of CFD
In this Section a general overview of CFD technology and its
merits are discussed.
2.1 What is CFD ? CFD is the process of solving the fluid flow
equations of mass, momentum and energy on a computer as applied to
a particular geometry and flow conditions. The basic flow variables
such as velocity, pressure and temperature are computed at
thousands of locations. The CFD solution is based on the
first-principle of conservation of mass, momentum and energy.
2.2 Why use CFD ? CFD is a leading edge technology applied to a
large number of engineering applications. The benefits of CFD can
be summarized as follows:
CFD methods are applied to gain insight into fluid flow and
thermal processes. Complex flow fields for which measurements are
not always possible can be
analyzed using CFD methods. While measurement probes provide
point data, very often full-field data or data at multiple
locations is required to fully diagnose a problem. CFD provides
data at thousands of locations.
This technology provides a non-intrusive, non-invasive method of
fluid flow and heat transfer analysis.
Process scenarios can be examined in a virtual environment,
without the safety issues of a real process. For a new design, a
number of design concepts can be examined in a virtual
environment.
A number of designs can be explored on the computer reducing cut
and try methods. Figure 2.2.1 indicates the integration of CFD
methods in the design process.
Figure 2.2.1: Role of CFD methods in product design.
New Product Concept
Process Design
Process & PerformanceEvaluation
Prototyping Full Scale Production
CFD Methods
Analysis, Trouble-shooting, Rapid Proto-typing
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2.3 Three steps to CFD : CFD analysis can be broken down into
three main steps, viz. Pre-processing, Solution and
Post-processing. The main steps of performing a CFD analysis are
depicted in Figure 2.3.1. Figure 2.3.1: Steps of performing a CFD
analysis Pre-processing: The first step in performing a CFD
analysis is called Pre-processing. This involves identification of
the flow region of interest, geometric representation of the
region, meshing and definition of flow physics. Proper selection of
the region of interest and appropriate simplifications play a key
role in the success of the calculation. Once the region is defined,
a computer model of the geometry is created. The next step is mesh
definition. The governing equations are solved at discrete
locations in the flow domain. These locations depend on the mesh
resolution. The accuracy of a CFD calculation and computer time
required for a solution are dependent on mesh resolution. User
experience and skill play a crucial role in the choice of a
suitable mesh. Once a mesh is created appropriate boundary
conditions are applied to define regions of inflow, outflow, walls
and other important features. Physical models within the CFD
software are activated to simulate flow physics pertaining to the
application at hand. For example, a turbulence model is activated
to simulate turbulent flow. Selection of appropriate physical
models and their applicability to the flow physics at hand is
critical to the overall accuracy of a CFD solution. Solution: Once
the problem definition is completed it is submitted to the solver
for computation of a solution. This step is the Solution step. The
governing equations are coupled and non-linear in nature. Therefore
a guess-and-correct, iterative strategy is adopted to compute the
solution. Post-processing: The third step is Post-processing,
during which CFD results are analyzed. A CFD solution provides
full-field data; flow variables at thousands, perhaps hundreds of
thousands of locations are available. A representation of the flow
field is created by plotting flow variables in space on a plane or
a line or in a three-dimensional region of interest. The spatial
plots give the analyst a look inside the unit which is unavailable
experimentally. However, the real value of CFD simulation is
frequently found in its ability to provide accurate predictions of
integrated quantities such as heat transfer rates, mass transfer
rates and forces.
PRE-PROCESSING SOLUTION POST-PROCESSING
Geometry Grid Physics generation generation
Iterative solution of governing equations
Analysis Extraction of of results data
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3.0 Geometry and Mesh Generation
In this Section the pre-processing aspect of CFD is discussed.
Once the flow region is identified a flow model of the region is
created and meshed.
3.1 Flow domain definition : The selection of an appropriate
flow domain is key to the success of obtaining a CFD solution. For
internal flows, the flow region is defined by the wetted surfaces
i.e. surfaces that are in contact with the fluid. Consider flow in
a pipe-junction, the flow region is defined by the inner surfaces
of the pipes as depicted in Figure 3.1.1 A section upstream and
downstream of the pipe-junction is included in the flow domain so
that appropriate boundary conditions can be specified. An inflow,
outflow and wall boundaries are specified.
For external flows, such as flow over an automobile, the flow
region includes the region around the automobile. The region ahead,
behind and around the automobile is included in the flow domain so
that appropriate boundary conditions can be imposed as depicted in
Figure 3.1.2. The boundaries at which flow conditions are specified
(inflow/outflow) must be far from the region of interest. For this
reason the flow domain includes a substantially large region ahead,
behind and above the automobile.
Figure 3.1.1: Flow region for pipe-junction (internal flow).
Inflow boundary
Outflow boundary
Outflow boundary
Wall boundaries
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Figure 3.1.2: Flow region for simulation of flow over an
automobile (external flow).
While defining the flow domain appropriate simplifications of
the flow geometry are required. Features that do not affect the
flow behavior in an appreciable manner or are too small to be
resolved are not included in the flow domain geometry. As an
example, consider modeling the overall flow behavior in the room in
which you are currently sitting. The flow domain in this case is
enclosed by the walls, floor and ceiling of the room. Objects in
the room such as tables and chairs can be represented as
rectangular obstacles. The exact shape of the chairs and tables is
not modeled to study the overall flow behavior in the room. Objects
on the table such as a book, a pen, etc. are not included in the
flow model; unless you are specifically interested in the flow
around these objects. These objects are too small to alter the
overall flow in any appreciable manner. If the thickness of an
object is much smaller than the grid size that will be used then
the object can be represented as a thin surface (impermeable
surface of zero thickness). For instance, the thickness of the
chair seat can be ignored and the seat can be modeled as an
impermeable thin object with zero thickness. The inflow and outflow
regions in the room are the supply and return vents. Engineering
judgement along with some understanding of the expected flow
behavior is applied in selecting objects that need to be included
in the flow model.
Inflow boundary Ground
Faraway boundaries (flow can leave or enter the computational
domain)
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Once the flow domain is selected a model of the flow geometry is
created. Most commercial CFD packages include a CAD like geometry
generation engine. Many CFD packages facilitate easy import of
geometry CAD files created by solid modeling packages. A CAD file
created for some other purpose such as manufacturing requires
modification and cannot be used as is for CFD modeling. CAD created
for manufacturing represents the solid region of an object and the
flow region is not included in the CAD. For example, CAD created
for manufacturing a pipe represents the outer and inner surfaces of
the pipe i.e. the solid material of the pipe. Whereas, the flow
domain is the region inside the pipe. In such cases, the flow
domain is created using the information supplied in the CAD
file.
3.2 Mesh generation technology: Once a model of the flow
geometry is created it is then meshed. The mesh defines the
locations at which the flow solution is computed. The common type
of mesh elements used in CFD solvers are hexahedral, tetrahedral,
pyramidal or wedge shaped as depicted in Figure 3.2.1. A mesh
consisting of hexahedral elements arranged in a rectangular region
as depicted in Figure 3.2.2 is known as a single-block structured
mesh. A grid cell in a structured mesh can be identified by a
unique three-dimensional index (i,j,k). A number of structured
blocks can be arranged to define a complex three-dimensional mesh
region; such an arrangement is called a multi-block structured
mesh. The grid cell in each block is identified by a unique
three-dimensional index (i,j,k). Figure 3.2.3 depicts a multi-block
structured mesh.
Figure 3.2.1: Mesh element types for CFD analysis.
Hexahedral element 8 corners, 12 edges and 6 faces
Tetrahedral element 4 corners, 6 edges and 4 faces
Pyramidal/wedge element 5 corners, 8 edges and 5 faces
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Figure 3.2.2: Single-block structured mesh.
Figure 3.2.3: Multi-block structured mesh.
Tetrahedral meshing technology allows relatively easy meshing of
complex geometries. A surface mesh consisting of triangular
elements is first created, this is then used to mesh the inside of
the geometry. The grid structure obtained using tetrahedral meshes
is called unstructured mesh. Unlike a structured mesh, a grid cell
cannot be identified using a single three-dimensional index. A mesh
consisting of tetrahedral elements are very
I
J K Cell I=3, J=3, K=1
Four blocks
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commonly used to mesh complex three-dimensional geometries. For
a given mesh length, the number of mesh elements required to mesh a
region with tetrahedral elements is about 5-6 times the number of
elements required when a hexahedral mesh is created.
Very often to optimize the number of elements and for ease of
mesh generation, a mixed element mesh consisting of hexahedral
elements that transition into pyramids and eventually into
tetrahedral elements are used to mesh complex flow geometries. A
typical tetrahedral mesh is depicted in Figure 3.2.4.
Figure 3.2.4: Tetrahederal mesh.
The mesh quality has a strong influence on the accuracy of the
solution. A poor quality mesh will not only affect the numerical
accuracy but also convergence. Mesh aspect ratio and skewness are
two parameters that influence mesh quality. Figure 3.2.5 depicts
mesh elements with high aspect ratio (width to height ratio).
Figure 3.2.6 depicts skewed mesh elements. Rapid changes in mesh
density can introduce numerical errors. Mesh size variations must
be gradual as depicted in Figure 3.2.7.
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Figure 3.2.5: High aspect ratio mesh elements.
Figure 3.2.6: Skewed mesh elements and rapidly changing mesh
density.
Width to height ratio of cells is large
Skewed cells (flat and thin cells)
Rapid change in mesh density
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Figure 3.2.7: Gradual mesh size variation.
3.3 Best practices: The type, quality and distribution of mesh
elements have a strong influence on the solution. Guidelines for a
quality mesh are as follows:
Select a mesh length that is appropriate for the resolution
desired. Avoid large skewness. Aspect ratio of 10 or higher is not
normally desirable. Rapid changes in mesh density can have an
adverse effect on convergence and
accuracy. A change in mesh size between adjacent cells must be
less than 2.0.
Some CFD software packages are more forgiving and tolerant of
the mesh quality and converge without too much difficult. The
actual degree of grid skewness, grid quality, aspect ratio that can
be tolerated depends on the flow solver and the flow physics of
interest.
Large elements
Small elements
Gradually varying elements
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4.0 Solver Technology
4.1 Governing equations : The governing equations are
conservation equations of mass, momentum and energy. Computational
fluid dynamics (CFD) methods are based on first principles of mass,
momentum and energy conservation as described by the following
equations:
Mass: =+
j
j
xu
t Sm (4.1.1)
Momentum: j
ij
ij
jii
xxP
xuu
tu
=
++
+ Sfi (4.1.2)
Energy: tp
tu
xq
xHu
tH iji
j
j
j
j
+
=+
+ + Sh (4.1.3)
Where is fluid density, t is time, x is coordinate, u is
velocity, P is fluid pressure, H is fluid enthalpy, is shear stress
and 3,2,1,, =kji represent three coordinate directions. Sm is mass
source due to reactions or other mass transfer mechanisms. Sf
represents momentum source due to mass transfer, body forces such
as gravitational force etc. Sh is energy source due to mass
transfer, phase change and energy generation by other mechanisms.
For situations involving additional species, a conservation
equation for each specie is also solved. The transport equation for
specie concentration is described using equation (4.1.4).
Specie: =+
j
j
xu
t Ss (4.1.4)
The conservation equations represent rate of change with time,
convection into volume and sources. For example, the first term in
the mass conservation equation represents rate of change of mass
with time, the second term represents the net mass flux. The term
on the right-hand-side represents mass source. The source may be
due to chemical reactions or any other mechanism by which mass is
created. Turbulence modeling Turbulent flow is characterized by
rapid fluctuations of flow variables about a mean value. The
magnitude of the fluctuations is a fraction of the mean value.
Resolving the fluctuations spatially and temporally is quite
difficult and not practical in most cases. The effect of turbulent
fluctuations is simulated using turbulence models. This involves
the solution of additional equations. A number of approaches are
adopted to simulate turbulent flow behavior. The approaches vary
from simplistic algebraic models for turbulence to complex methods
where the fluctuations associated with the turbulent field are
captured.
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A common approach is to solve Reynolds Averaged Navier Stokes
equations (RANS). In this method, the Navier Stokes equations are
averaged and the effect of turbulence is represented by using an
effective viscosity. Additional equations as defined by the
selected turbulence model are solved to compute turbulence related
quantities. For example, the k-epsilon turbulence model solves an
equation for the turbulent kinetic energy defined by the quantity k
and another equation for epsilon the turbulence dissipation rate. A
number of turbulence models have been developed. However, the
k-epsilon model is applicable to most industrial CFD applications.
Flows with swirl or large regions of separation cannot be
accurately modeled with k-epsilon model. Variants of k-epsilon
model such as RNG or the k-omega model provide an improved solution
for such situations. In some cases, more advanced turbulence models
such as Large Eddy Simulation (LES) are also applied. In this
approach, the large scale turbulent eddies are computed by solving
time dependent Navier-Stokes equations. The smaller eddies are
modeled using a subgrid model. The large scale eddies are dependent
on the flow behavior and geometry; whereas, the small scale eddies
are independent of the large scale eddies and can be represented
using a subgrid model. LES simulations require a very fine grid so
that the large scale eddies can be resolved. A time dependent
solution is required so that the unsteady behavior of the eddies is
accurately captured. The grid requirements and time step
requirements for LES simulations results in large computer
resources. LES simulations cannot be easily applied for industrial
applications. The most sophisticated level of turbulent flow
computations use Direct Numerical Simulations (DNS). In this
approach, the time dependent Navier-Stokes equations are solved
such that the fluctuations associated with turbulence are captured.
This method requires an extremely fine grid and very fine time
steps and is not practical for general CFD application. RANS
methods provide a viable solution to most CFD applications.
4.2 Boundary conditions: The governing equations are selected
based on a problem definition. For example, the energy equation is
not selected and solved for isothermal flows. The governing
equations are solved subject to boundary conditions. The common
surface boundary condition types are velocity specified, pressure
specified, outflow or wall. Velocity, pressure and outflow
specified boundaries are used to model regions through which the
flow can either enter or leave the flow model geometry.
At a velocity boundary, the velocity components are specified
and this type of boundary is used define the inflow into a CFD
model. Pressure boundaries are used to define openings in the flow
model through which the flow can either leave or enter the flow
domain. An outflow boundary is used to represent regions through
which the flow leaves the flow model. Wall boundary conditions are
used to represent solid surfaces of the
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flow model. A no-slip boundary condition for the velocity is
used at walls. For heat transfer applications temperature or heat
flux is specified at wall boundaries.
4.3 Discretization: The governing equations are solved using
numerical methods. The Navier-Stokes equations are discretized
using either Finite Element Methods (FEM), Finite Volume Methods
(FVM) or Finite Difference Methods (FDM). Each discretization
method has its own advantages and disadvantages.
Finite Difference Method (FDM) is the oldest method for
discretization of the governing equations. In this method, the
differential form of the equations is discretized using a Taylor
series expansion. This is best illustrated using a simple example
as described below. A first derivate can be expressed as
follows:
d/dx = (i+1 i-1)/ 2dx, (4.3.1) where i+1 and i-1 are the values
of the variable at the i+1 and i-1 grid points, the grid spacing is
dx. The accuracy of the discretization scheme depends on the
truncation error which is estimated using Taylor series
expansion.
i+1 = i + (d/dx)i dx + (d2/dx2)(dx)2, (4.3.2) Similarly, i-1 is
expressed as a Taylor series expansion about i using equation
(4.3.3). i-1 = i - (d/dx)i dx + (d2/dx2)(dx)2, (4.3.3) Using
equation (4.3.2) and equation (4.3.3) the truncation error
associated with the differencing scheme described in equation
(4.3.1) is estimated to be of order (dx)2. The differencing scheme
in equation (4.3.1) uses the values of the variable on either side
of the point in consideration. In other words, the derivative at
point i uses the values at points i+1 and i-1. This scheme is known
as central differencing and for a first derivative it is second
order accurate i.e. the truncation error is of order (dx)2. A
differencing scheme that uses the value of the variable only from
one-side as illustrated in equation (4.3.4) is called upwind
differencing. Using a Taylor series expansion it can be shown that
the truncation error is of order (dx). This is scheme provides
first order accuracy.
(d/dx)i = (i i-1)/ dx (4.3.4) The increased accuracy associated
with a second order scheme as compared to that of a first order
scheme comes at the price of robustness. At times a second order
scheme can create local oscillations in the solution and this can
result in a solution process that is difficult to converge or
unphysical in nature. The first order scheme is more robust, but
provides lower accuracy and tends to smear out gradients. For
example, a first order scheme if used to resolve a shock-wave can
smear the shock-wave and result in an inaccurate prediction. On the
other hand, a second-order scheme can cause wiggles in the
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solution around the shock-wave and result in an unphysical
situation. To circumvent this difficulty hybrid differencing
schemes have been developed. These provide second order accuracy in
most regions but reduce to a lower order scheme to prevent
unphysical oscillations in the solution. Some such schemes are
MUSCL scheme and flux-limited Van Leer scheme.
Finite Volume Method (FVM) uses a control volume approach. The
governing equations are integrated over a control volume resulting
in a discretized form of the equations. For example, the
integration of continuity equation over the control volume depicted
in Figure 4.3.1 results in the following form of discretized
equation. (.u.A)w (.u.A)e + (.v.A)s (.v.A)n = 0.0, (4.3.5) The
fluxes on the faces are computed using the velocity and density of
the neighboring cells. For upwind differencing, the fluxes are
computed using the upstream values of the variables. The
Navier-Stokes equations are conducive to finite volume
discretization and this method can be applied to any general cell
type (hexahedral, tetrahedral, pyramidal, etc.). The finite volume
method is used in most commercial CFD packages for discretization
of the equations.
Figure 4.3.1: Descretization over a cell.
Finite Element Method (FEM) uses shape functions associated with
the element (cell) type for discretization. Weight functions that
minimize the error or variation of variable over the element are
applied. The Navier-Stokes equations do not naturally lend itself
to this method of discretization. FEM is not commonly used for CFD
calculations, though there are commercially available CFD packages
based on this method.
Some commercially available CFD packages use a hybrid method
that uses the key features of FVM along with FEM.
4.4 Linear solvers: The discretized equations result in a
non-linear and coupled set of algebraic equations. These are
linearized and solved by inverting a matrix. The discretized and
linearized equations in matrix form are represented by equation
(4.4.1).
s
n
e w
u
v
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15
[A] [X] = [R], (4.4.1)
where [X] is the solution vector of flow variables (u,v,w,P,T),
[A] is the coefficient matrix and depends on the solution vector
[X], [R] is the right-hand-side of the discretized equations. The
solution vector [X] is obtained by inverting the matrix [A]. Once
the solution vector is obtained the matrix [A] is updated and the
solution vector recomputed. This process is repeated till equation
(4.4.1) is satisfied to a specified degree. The degree to which the
solution is satisfied is measured by the residual as defined by
equation (4.4.2).
[r] = [R]- [A] [X] (4.4.2)
The coefficient matrix [A] is large and cannot be easily
inverted using conventional methods of linear algebra. The
coefficients of the matrix [A] also depend on the solution vector
[X], so an exact inverse is not necessary. The structure of matrix
[A] is exploited in computing the inverse. It is very often
decomposed into a lower tri-diagonal and upper-tridiagonal matrix
also known as LU decomposition. The approximate inverse of matrix
[A] is computed by inverting [L] and [U].
[A] = [L] [U] + [E], (4.4.3)
where [E] represents the error.
[X] = [L]-1[U]-1[R] [E][X] (4.4.4)
This results in an iterative process of computing the matrix
inverse. The iterations associated with computing the inverse of
the matrix are very often referred to as inner iterations and the
iterations associated with the non-linearity and coupling between
the equations are known as outer iterations.
The linearized system of equations is solved using various
methods of inverting the matrix [A]. Conjugate gradient methods,
algebraic multigrid methods are some such methods. In most
commercial CFD software the matrix inversion process is generally
transparent to the user. However, the user has control over the
outer iterations and this is specified as one of the inputs.
The governing equations are non-linear and coupled. A large
matrix relating all the variables and equations can be created for
the entire mesh. The inversion of this matrix results in a coupled
scheme of solution. This is called coupled direct solution method.
The matrix is too large and complex to be solved directly. Very
often, each equation is solved sequentially resulting in a
segregated solution procedure. A matrix is setup for each equation
and that equation is solved before proceeding to the next. The size
of the matrix in this case is smaller as compared to that for a
coupled system. Segregated solution method is adopted in most
commercial CFD packages.
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The Navier-Stokes equations are coupled non-linear equations and
the final solution is obtained using a guess-and-correct solution
method. Very often, the initial guess is far from the final
solution, the guess-and-correct procedure can lead to divergence of
the solution. This is overcome by under-relaxing the solution. The
variables are allowed to change gradually using an under-relaxation
factor as described by equation (4.4.5).
= *1 + (1-)*2, (4.4.5) where is under-relaxation factor, 1 is
most recently computed solution and 2 is solution at the previous
iteration. The typical under-relaxation factor varies between 0.3
and 1.0. A smaller under-relaxation factor is used for more complex
cases where the non-linearities are strong.
Convergence is assessed by examining the residuals of the
equations. The residual represents the degree to which an equation
is satisfied. Mass flow balance in the flow domain is often used as
the convergence criteria. For incompressible, steady, internal flow
the inflow mass flux must match the outflow mass flux within a
specified tolerance. A tolerance of less than 1% is typically
used.
4.5 Best practice:
Ensure that the boundary conditions are realistic and represent
the flow behavior under investigation.
Check that the appropriate flow models have been selected. For
example, for turbulent flow ensure that a turbulence model has been
selected.
Run the flow solver for few iterations, about 10 to 20
iterations and check the boundary conditions. Verify that the flow
rate specified at the boundary condition is correct and the
direction of flow is correct.
Obtain a solution using first-order accurate differencing
scheme. If necessary, use this as the starting point for a solution
using a second-order differencing scheme.
For solutions that are difficult to obtain or if the solution
diverges reduce the under-relaxation factors.
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5.0 Post Processing
This is the final step of performing a CFD analysis. In this
step, the results are extracted and intepretted.
5.1 CFD results : A CFD solution provides full-field data; flow
variables at thousands, perhaps hundreds of thousands of locations
are available. The velocity components, pressure, density,
temperature and other flow related quantities are available from a
CFD solution. These quantities are available at the mesh locations
used for computing the flow field. The real value of a CFD
simulation is frequently found in its ability to provide accurate
predictions of integrated quantities such as heat transfer rates,
mass transfer rates and forces. The merits of CFD simulation are
realized when the relevant information is extracted from the
simulation results. This to a large degree depends on the ability
and experience of the practitioner.
5.2 Analysis of CFD results: A representation of the flow field
is created by plotting flow variables in space on a plane or a line
or over a three-dimensional region of interest. The spatial plots
give the analyst a look inside the unit which is generally
difficult to obtain. The flow behavior can be analyzed by plotting
the velocity vectors on a selected plane. Plotting the velocity
field over a three-dimensional region can obscure the flow field
and is difficult to view. Flow behavior is analyzed by examining
the velocity vectors on a series of planes as depicted in Figure
5.2.1a and Figure 5.2.1b. The velocity vector arrows indicate the
direction of the flow and the color indicates speed. Regions of
flow recirculation can be identified by plotting the velocity
field. The vectors can be colored with any other quantity such as
temperature. The flow field is also analyzed by examining contours
of quantities of interest such as speed, pressure, temperature,
shear stress. Figure 5.2.2a depicts the pressure distribution;
regions of low and high pressure are identified. Figure 5.2.2b
depicts the shear stress distribution on the surface of the
automobile. Regions of high shear stress indicate areas of high
frictional drag. Line plots to depict the flow behavior or a region
of interest can also be created. Figure 5.2.3 shows the variation
of speed along the centerline of a pipe. The value of a flow
variable at a specific location (point in space) can also be
extracted by probing the CFD solution.
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18
Figure 5.2.1a: Velocity vectors depicting a flow field in
T-junction. Figure 5.2.1b: Velocity vectors depicting flow around
automobile.
Plane 1
Plane 2
Velocity vectors on planes Velocity vectors are colored with
speed (m/s)
Velocity vectors on mid plane Velocity vectors are colored with
speed (m/s)
Wake behind automobile
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19
Figure 5.2.2a: Contours of pressure (Pa). Figure 5.2.2b:
Contours of shear stress (Pa).
High pressure due to impingement of flow
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20
Figure 5.2.3: Variation of speed along the center-line of a
pipe. Integrated quantities such as drag, lift or components of
force can be obtained. CFD is used to compute the lift and drag
over airfoils and wings. In many cases the CFD solution is used to
compute the forces acting on a body immersed in a fluid. For
example, the structural design of turning vanes in a ductwork
depends on the flow induced forces on the vanes. In such a case,
the forces are estimated using a CFD solution. Surface averaged
mean pressure or temperature can also be computed. Mean heat
transfer coefficient over a surface of interest can also be
computed from a CFD solution. Mean quantities over a volume can
also be computed. The mean volumetric concentration of a specie in
a region of interest can be estimated from a CFD solution. A CFD
solution provides a deluge of information. The flow behavior is
analyzed by examining the flow field on planes and lines. Average
quantities derived from the flow field are also computed to analyze
the flow behavior.
Location of line in pipe
Peak pressure due to impingement of flow
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21
6.0 Role of CFD in the Industry
CFD methods are widely applied within various industries to
examine fluid flow and heat transfer behavior. In the Aerospace
industry, CFD is routinely applied for aerodynamic calculations,
such as computation of lift and drag of lifting surfaces. In the
automotive and heavy equipment industries, CFD is applied for
external drag calculations, climate control and under-hood cooling.
The heating and ventilation industry, power generation industry and
chemical process industries, including oil and gas companies,
chemical companies, pulp and paper companies and pharmaceutical
companies are now beginning to apply CFD methods to gain insight
into their various processes. The Aerospace industry has been
applying CFD methods for the longest period of time. CFD methods in
this industry are routinely applied to improve lift and drag of
aerodynamic surfaces. The overall behavior of flow is very well
understood and small improvements (on the order of 1%) are sought
to achieve incremental increases in performance. In general, CFD
methods are applied to understand the overall flow behavior. A
typical CFD study is aimed at comparing different designs. What-if
studies are performed to examine the influence of various
parameters on flow behavior and hence performance. Relative
comparison of various designs is carried out using CFD methods. A
number of conceptual design changes can be examined rapidly in a
virtual laboratory, without actually building a physical model. CFD
study of a full-scale model can be carried out, thus eliminating
scale-up issues. Unlike experimental methods, CFD provides
full-field data. Pressure, velocity, density, temperature and other
quantities of interest are obtained at each and every point in the
simulated flow domain. These benefits make CFD a viable tool for
analysis, design and rapid proto-typing.
CFD technology is now an accepted method of obtaining solutions
to fluid flow and heat transfer problems. It has gained a great
deal of credibility in many industries and has been integrated into
the main stream of design and analysis. In this section, the role
of CFD in various industrial sectors is summarized. The typical
problems solved using CFD methods are also discussed. Aerospace
This industry is engaged in the business of design and fabrication
of airborne/space vehicles. It includes major aircraft
manufacturers, helicopter, hover craft and space systems generation
companies. This industry also includes companies that supply
components/units needed by the aerospace companies such as aircraft
engines, valves, pumps etc. CFD is widely accepted, applied and
regarded as a credible solution method in the Aerospace industry.
In fact, CFD was pioneered in the Aerospace industry. Home-grown
software is widely applied in this industry and most of the CFD
activity is restricted to CFD experts. Applications in this arena
include flows over aerodynamic shapes, wings, fuselage, nacelles
and after-bodies. CFD is widely applied for analysis of
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22
aircraft components/units such as compressors, pumps, turbines,
cross-over elements, nozzles, diffusers and combustion chambers.
CFD also plays a role in heat transfer analysis of space systems.
These systems typically involve complex flow physics such as
radiative heat transfer, micro-convection, multiphase flows and
microgravity effects. Leading-edge applications in this industry
include full aircraft performance simulations and full engine
performance simulations. CFD technology is highly regarded and well
integrated into the design process in the aerospace industry. The
initial hurdle of 'acceptance' does not exist in this industry. In
many cases CFD is the only solution to a problem; for example,
design of re-entry and high Mach number systems. Automotive Major
automobile manufacturing companies and those that supply parts,
components and design/analysis services for the automobile
companies are included in this industrial sector. Design time
scales in the automotive industry are very tight; as a result, CFD
and FEA analysis techniques are widely used to obtain quick
solutions to problems and to evaluate design changes. A typical
analyst in this industry is required to perform CFD analysis along
with FEA analysis. CFD activity is not restricted to CFD experts
only. Typical applications involve flows inside passenger
compartments of automobiles, external flows, design of blowers,
duct work and under-hood flows. Flow problems related to under-hood
cooling are complex and difficult. CFD is also applied for analysis
of catalytic convertors, torque convertors, valve design and heat
exchanger analysis. Limited application work is carried out for
analysis of IC engines. Leading edge applications in this industry
include under-hood flow/heat transfer and simulation of combustion
in IC engines. Chemical Process Industry (CPI) Any industry that is
involved in the business of processing raw materials for the
production of chemicals is classified as CPI. Chemical process
industry can be further classified into various sub-industrial
sectors as follows: Oil & Gas Chemicals Plastics and Fibers
Consumer and health-care products Pharmaceuticals Food Water Metals
Mining Fertilizers
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23
Paper and Pulp Glass manufacturers The chemical process industry
is quite vast and can be divided into various sub-sectors as
outlined in the section above. Some of the larger CP companies have
embraced CFD as a viable technology and derived tremendous benefits
through its application. These companies have a core group of CFD
experts engaged in CFD activity on a full-time basis (similar to
the Aerospace industry; however, work is carried out using
commercial CFD software). The chemical process industry involves a
wide variety of process equipment and a process unit is required to
perform a wide variety of duties. Hence, it becomes essential to
predict its performance under a wide variety of operating
conditions. The flow field involved is very complex and
conventional methods of analysis are not adequate. Computational
fluid dynamics provides a viable tool for analysis and trouble
shooting of such equipment. A typical unit operation processes a
large amount of fluid. Given the economics of most unit operations,
even small improvements in efficiency and performance can result in
a significant increase in revenue and savings in costs.
As the process industries enter the 21st century they face new
challenges. The predominant forces of change include increased
globalization of markets, demands for cleaner environment, higher
customer expectations and increased profitability. There has been a
general thrust to reduce waste and improve efficiency of processes
in general. The traditional approach of taking a product from
laboratory scale to pilot plants and then to production is no
longer attractive. Process and product development are often
initiated simultaneously, as a result, rapid prototyping and
analysis is required. To meet these challenges innovation is
required at all phases of product development. To meet these goals,
Technology Vision 2020, a document highlighting plans for the
chemical process industries for the next 20 years has identified
three enabling technologies. Computational fluid dynamics (CFD) is
one such technology that is expected to lead process companies into
the future. The integration of CFD methods will lead to shortened
product-process development cycles, optimization of existing
processes, reduced energy requirements and efficient design of new
products and processes. Unit operations in the hydrocarbon process
industry handle large amounts of fluid, as a result, small
increments in efficiency lead to large increments in product cost
savings. It is thus essential for not only the research and
development staff in the hydrocarbon process industry but also for
plant managers and production managers to understand the benefits
of CFD so that it can be integrated into the development process.
Applications in the CPI are very complex and cannot be tackled
using an out-of-the-box CFD approach. Judicious simplification and
careful examination of the solution process is required. A CFD
solution is very often augmented by additional calculations and
engineering judgement. Typical applications in this arena involve
flows in mixing devices, stirred tank reactors,
filtration/separation devices, furnaces, dryers and other
equipment. The flow fields are in general very complex, involve
multiple phases, mass transfer, heat transfer and very often
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24
reactions. Careful simplification of the flow physics and
multi-step solution process is required. The industrial sub-sectors
as stated above differ in their core products and processes but the
equipment (unit operation devices) applied is similar. Companies
are in the process of diversifying their products, as a result, the
same process equipment is called on to perform various tasks. Table
6-I summarizes the wide variety of process equipment in the
chemical process industry that can benefit from CFD analysis.
Process Equipment Impact of CFD
Mixing:
Stirred tank reactors, static mixers, jet mixers, emulsification
units.
Examine performance of static mixers. Optimize stirred tank
performance. Predict shear distribution in stirred tank
reactor. Scale-up/scale-down of reactors
Fluid Transport devices:
Pumps, compressors, manifolds, headers, valves, flow
distributors.
Establish envelope of performance. Ensure uniform flow
distribution. Minimize power requirements. Identify and eliminate
sources of
erosion in transport of slurry. Separation units:
Cyclones, scrubbers, precipitators, centrifuges, gravity
separators,
Optimize and predict performance. Take a look-inside the
process. Evaluate design concepts.
Heat generation and heat transfer:
Heat exchangers, boilers, furnaces, process heaters,
burners.
Minimize failure of heat-exchangers. Control formation of
pollutants. Eliminate hot-spots in heaters. Improve flame stability
and burner
efficiency. Improved heat-recovery.
Reactors:
Packed bed, bubble column, fluidized bed.
Improved catalyst utilization. Minimize waste. Reduced operating
costs.
Auxiliary processes:
Filling, packing.
Eliminate plugging, sloshing, spilling.
Table 6-I: Impact of CFD on various processes in the chemical
process industries.
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25
To meet the challenges associated with the operation of a wide
variety of process equipment, suitable analysis tools are required.
The flow fields involved in the chemical process equipment are very
complex and conventional methods of analysis are not adequate.
Experimental measurement is not always possible. While measurement
probes provide point data, very often full-field data or data at
multiple locations is required to fully diagnose a problem. Trouble
shooting as well as improvements in efficiency and performance are
typically achieved by trial and error based on past experience.
Failure of a process equipment can result in undesirable downtime
and loss of revenue. Hence, more adequate techniques of trouble
shooting are required so that downtime can be minimized. CFD has
been accepted as a viable tool for the analysis of process
equipment. Electronics Electronic device manufacturing companies
such as printer manufacturers, computer hardware manufacturers,
silicon wafers suppliers fall under this category. Manufacturing
and polishing of silicon wafers is an important process for the
electronics industry. CFD has been applied for this process.
Chemical vapor deposition is another area of great interest to the
electronics industry. CFD is also applied for analysis of
micro-electronic devices involving fluid flow and heat transfer
such as ink jet printer nozzles. Electroforming, electroplating are
some of the other processes analyzed using CFD. Power Generation
Traditionally this industrial sector refers to those industries
engaged in the business of generating thermal and hydro
electricity. Fuel cells are also part of this industrial segment.
This industry can be divided into two main sub-sectors viz. thermal
power generation industries and water (hydro) power generation
industries. Thermal power generation is normally achieved by
combustion of coal in furnaces, energy generated in the furnace is
used to produce steam for turbines which are coupled to electric
generators. CFD has been applied for analysis of furnaces, burners,
duct-work, electrostatic precipitators, coal mills and particle
classifiers. The main emphasis here is increased efficiency and
lower levels of pollutants. This thrust has given rise to enhanced
combustion models and pollutant prediction models in commercial CFD
software. The flow physics associated with applications in the
power generation industry is quite complex. Hydro-power generation
involves generation of electricity from water. CFD has been applied
for analysis of water turbines, diffusers, inlet vanes and other
auxiliary devices associated with these units.
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26
Fuel cells as an energy source is an emerging technology. The
flow physics involved is very complex and CFD is accepted as a
technology that can provide insight into design configurations and
optimization. CFD software has the capability to analyze the
complex physics associated with this technology.
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27
7.0 CFD Applications, Part-I
7.1 External aerodynamics : The flow over an airfoil is
computed, the boundary conditions are depicted in Figure 7.1.1. A
boundary layer mesh depicted in Figure 7.1.2 is required to
accurately compute the flow solution. The velocity and pressure
distribution are depicted in Figure 7.1.3 and Figure 7.1.4. Figure
7.1.1: Flow over an airfoil, boundary conditions. Figure 7.1.2:
Mesh near surface of airfoil.
Inflow (velocity specified)
Outflow (pressure specified)
Far field boundary (pressure specified)
Far field boundary (pressure specified)
Surface of airfoil (specified as a solid wall)
Fine mesh near surface
Gradually expanding surface mesh
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28
Figure 7.1.3: Velocity (m/s) distribution. Figure 7.1.4:
Pressure (Pa) distribution.
Higher velocity on upper surface
Lower velocity on lower surface
Suction (low pressure) on upper surface
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29
7.2 Internal flow computations: The mixing of two streams in a
T-junction is studied using CFD methods. The basic arrangement is
depicted in Figure 7.2.1. The mixing is studied by examining the
concentration of the side-stream. As depicted in Figure 7.2.2 the
fluid from the side-stream lies towards the lower section of the
main pipe indicating poor mixing. The mixing behavior is improved
by placing a mixing element in the T-junction as depicted in Figure
7.2.3. The concentration of the side-stream for the configuration
with a mixing element is depicted in Figure 7.2.4.
Figure 7.2.1: T-junction.
Figure 7.2.2: Mixing behavior in a T-junction.
Side-stream fluid injection
Main stream fluid Mixing zone
Red color denotes 100% concentration of side stream fluid Blue
color denotes 100% concentration of main stream fluid
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30
Figure 7.2.3: T-junction with mixing element.
Figure 7.2.4: Concentration of side-stream fluid in T-junction
with a mixing element.
Mixing element
Red color denotes 100% concentration of side stream fluid Blue
color denotes 100% concentration of main stream fluid
Dispersion of side-stream due to mixing element resulting in
improved mixing
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31
7.3 Compressible flow computations: The compressible flow of a
gas in a converging-diverging nozzle depicted in Figure 7.3.1 is
computed. Higher order differencing schemes are applied to capture
the discontinuities such as shock-wave in the flow. The total
supply pressure at the inlet and the static pressure at the outlet
are specified. The velocity distribution is depicted in Figure
7.3.2. The Mach number distribution shows acceleration to sonic
velocity at the throat. The flow continues to accelerate to
supersonic conditions in the diverging portion of the nozzle and
decelerates to subsonic conditions through a shock-wave. The
location of the sonic regions and the shock wave are depicted in
Figure 7.3.4. The pressure distribution is depicted in Figure
7.3.5.
Figure 7.3.1: Compressible flow in a converging-diverging
nozzle.
Figure 7.3.2: Velocity (m/s)distribution in the nozzle.
Inflow (Total pressure specified)
Outflow (Static pressure specified)
High velocity region
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32
Figure 7.3.3: Mach number distribution in the nozzle.
Figure 7.3.4: Location of sonic regions in the nozzle.
Figure 7.3.5: Pressure (Pa) distribution in the nozzle.
Sonic region at throat
Supersonic region (ahead of shock wave)
Subsonic region (behind shock wave)
Sonic line at shock wave
Sonic region at throat
Low pressure due to supersonic expansion in the diverging
portion
High pressure region behind shock wave
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33
7.4 Buoyancy driven flows: The natural convection currents
around a heated pin are simulated. The surface of the pin depicted
in Figure 7.4.1 is maintained at a higher temperature than the
surrounding air. Buoyancy driven flows are normally unstable and
exhibit unsteady behavior. In this case, the plume of hot air
rising from the pin sways from one-side to the other as depicted in
Figure 7.4.2. The temperature distribution is depicted in Figure
7.4.3.
Figure 7.4.1: Natural convection around a heated pin.
Figure 7.4.2: Natural convection velocity distribution (m/s)
around the pin.
Heated pin
Bottom wall
Side wall
Bottom wall
Side wall
Open top
Swaying of the plume from side-to-side is observed Red color
denotes a speed of .74 m/s and blue color denotes are region of
zero speed.
Region of high velocity in the center of the plume
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34
Figure 7.4.3: Temperature (K) around the pin.
Swaying of the plume from side-to-side is observed (plume
orientation at two different time instants)
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35
7.5 CFD for fluid transport devices: CFD methods have been
applied for analysis and performance prediction of fluid transport
devices such as pumps, compressors and fans. Pumps are commonly
employed in the process industries for transport of fluids.
Increasing demands for greater productivity very often calls for
the same pump to handle different fluids. In the following study
CFD techniques are employed to predict pump performance under
different operating conditions. Typical flow field is depicted in
Figures 7.5.1a and 7.5.1b. The accuracy of CFD solution is
demonstrated through detailed comparison with experimental data as
shown in Figure 7.5.2.
CFD is applied to study the flow behavior in a reciprocating
pump; a schematic is depicted in Figure 7.5.3. Design changes to
eliminate cavitation are explored. As a first step, flow behavior
in the existing design is examined. Cavitation occurs during the
suction cycle when the fluid is rapidly drawn into the pump. An
analysis representing a snap shot of the flow behavior at the
instant when the piston suction velocity is highest is carried out.
The velocity field in Figure 7.5.4 depicts the flow behavior in the
interior of the pump. The incoming fluid impinges on the wall near
the discharge port of the pump.
Figure 7.5.1a: Pump, velocity distribution Figure 7.5.1b: Pump,
streak lines
Figure 7.5.2: Pump performance curve, comparison of CFD results
with experimental.
0.0
2.0
4.0
6.0
8.0
10.0
12.0
0.0 1.0 2.0 3.0 4.0 5.0
CFD ResultsData
Pres
sure
Ris
e (in
ches
H2O
)
Flow Rate (gpm)
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36
The suction created by the retreating piston creates a helical
flow pattern in the chamber as depicted by stream-lines in Figure
7.5.5. This leads to the generation of strong vortices in the pump
chamber. The pressure plot in Figure 7.5.6 depicts the low-pressure
regions associated with the vortices; red denotes high pressure
areas and blue low pressure. These are the regions where cavitation
occurs.
Design changes to alter the flow pattern and hence eliminate
cavitation are explored. The inlet port of the pump is altered, a
wider inlet port is used. The vortical flow pattern within the pump
chamber is eliminated as depicted in Figure 7.5.7 and Figure 7.5.8.
The pressure profiles in Figure 7.5.9 indicate that overall
pressure within the chamber is well above the cavitation limit.
Design changes to alter the flow pattern and eliminate cavitation
were carried out in a virtual environment
Figure 7.5.3: Schematic of pump layout.
Inlet port Outlet port
Reciprocating piston
Pump chamber
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37
Figure 7.5.4: Velocity field existing design.
Figure 7.5.5: Path lines in pump chamber.
Vortices
Vortices
Helical flow path lines
-
38
Figure 7.5.6: Pressure distribution in pump chamber.
Figure 7.5.7: Velocity field in modified design.
Figure 7.5.8: Path lines in pump chamber.
Low pressure regions
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39
Figure 7.5.9: Pressure distribution in pump chamber. Pneumatic
transport of products in the form of a powder or a liquid slurry is
very common in the process industry. Granular solids of
free-flowing natures may be conveyed through ducts with high
velocity streams. Air-conveyed materials include chemicals,
plastics, pellets, grains and powders of all kinds. Transfer of
catalysts between regenerator and reactor under fluidized
conditions is a common pneumatic solids transport process. The
performance of pneumatic conveyors is sensitive to several
characteristics of the solids such as bulk density and particle
size distribution. Pressure drop, power requirements are key
indicators of performance. Erosion caused by particle impact is an
area of concern. Figures 7.5.10a and 7.5.10b depict particle paths
for heavy and light particles in a pneumatic conveyer junction.
Heavy particles impact the walls of the junction thereby increasing
the risk of erosion.
Figure 7.5.10a: Pneumatic conveying, light particle tracks
Figure 7.5.10b: Pneumatic conveying, heavy particle tracks
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40
7.6 Flow in a valve: CFD methods are applied to study the flow
behavior in valves and compute valve performance parameters such as
flow coefficient. CFD methods are also employed to derive input
information for other solution tools. CFD techniques are employed
to obtain pressure distribution and flow characteristics of a
butterfly valve at various valve openings. The valve positions and
flow behavior are depicted in Figure 7.6.1. The discharge
coefficient vs angle computed using the CFD model is applied as
input to a waterhammer calculation tool. The resulting waterhammer
pressure profile is depicted in Figure 7.6.2.
Figure 7.6.1: Butterfly valve, pressure distribution for various
positions Figure 7.6.2: Butterfly valve, Water-hammer profile
Pressure @ 0 Degrees Pressure @ 45 Degrees Pressure @ 85
Degrees
Relative Head at Valve Valve Position
0.2 0 0.2 0.4 0.6 0.8 1-1
-0.5
0
0.5
1
1.5
TIME (seconds)
Relative head at valve
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41
7.7 Flow and heat transfer: CFD for Heat generation and heat
transfer equipment: Heat transfer equipment such as heat exchangers
are employed throughout a chemical processing plant. Failure of
this equipment can lead to downtime and significant loss of
revenue. Hence, it is essential for this equipment to perform as
reliably as possible. Inefficiencies associated with heat transfer
equipment directly influence production cost. Small increments in
improved efficiency can result in significant reduction of
operating cost and increased revenues. CFD techniques can provide
an insight into the function of these devices and can help identify
areas for improvement. Figure 7.7.1a shows the temperature
distribution over an array of cylinder in cross flow. This is a
very common configuration in heat exchangers. Comparison of CFD
results with experimental data is depicted in Figure 7.7.1b.
Process heaters of various types are employed for endothermic
reactions. The two major types of heaters are direct-fired or
indirect-fired. Direct-fired heaters are typically employed for
hydrocarbon reforming, pyrolysis-type of processes. High process
temperatures are achieved by direct transfer of heat from the
products of combustion of fuels. Heat is released by the process of
combustion which is transferred to fluids inside tubes which are
arranged along the walls and roof of the combustion chamber. Tubes
containing the process fluid are subject to combustion process
gases and high temperatures. If the heating is not uniform then
hot-spots may occur leading to failure; on the other hand,
inadequate heating can lead to lower process fluid temperatures and
inefficiencies. Formation of pollutants such as NOx can be reduced
using design guidance provided by CFD simulations. The combustion
process and heat transfer within direct-fired heaters are very
complex. Simple methods are inadequate to analyze and predict
performance. Experimental
10
20
30
40
50
60
70
0 20 40 60 80 100 120
2x2 Tube Bundle Heat Transfer Coefficients
Tube 1 HTC - CorrelationTube 1 HTC - CFDCore Tube HTC -
CorrelationCore Tube HTC - CFD
Tube
1 H
TC -
Cor
rela
tion
(Btu
/hr/f
t^2-
F)
Inlet Velocity (ft/s)
Figure 7.7.1a: Heat exchanger, temperature distribution Figure
7.7.1b: Comparison of CFD results with data
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42
measurements are difficult and even impossible. Computational
methods such as CFD present a viable approach for analysis of such
equipment. The combustion process and heat transfer in a
direct-fired heater are modeled using computational fluid dynamics.
A vertical-cylindrical radiant process heater is modeled. The tubes
containing the process fluid are arranged helically as a coil along
the walls of the combustion chamber. Firing of fuel is vertical
from the floor. Heat transfer to the process tube and uniformity of
the temperature field are examined and depicted in Figure 7.7.2,
red regions denote high temperature and blue regions correspond to
low temperature. It is observed that the heat transfer to the tubes
is quite uniform. However, the exhaust gas temperature is high,
indicating that a heat recovery unit downstream of the primary
heater may need to be installed to recover waste heat.
Figure 7.7.2: Process heater, temperature distribution.
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43
8.0 CFD Applications, Part-II
8.1 CFD for mixing applications: Mixing processes form the heart
of the chemical process industries. Mixing may involve blending of
two streams of the same fluid but at different temperatures
(thermal mixing) or, it may involve mixing of two or more different
fluids with or without chemical reactions. The degree of mixing
required and the equipment applied depends on the actual
application. Static mixers for fluid-fluid mixing and stirred tanks
are by far the most commonly applied units for mixing.
Stirred tank reactors are very commonly used in the chemical
process industries for a wide range of duties. The primary function
of these vessels is to provide adequate stirring and mixing of a
mixture. The mixing characteristics influence the product quality
and efficiency of the process to a great degree. Stirred vessels
come in various shapes, sizes and are equipped with many different
types of impellers. Very often the same vessel is required to
perform various duties and it is essential for engineers to ensure
that adequate shaft power is available to perform the mixing duty.
More importantly, it is essential to ensure efficient operation of
the vessel for a given duty. This is very often accomplished by
placing the impellers in the vessel at various locations. Empirical
correlations for estimating vessel performance exist. However,
these correlations are unable to predict the performance accurately
and are very often based on the assumption of linear superposition
of data. The following study examines the influence of impeller
location on the flow field. CFD methods are employed to analyze the
flow field and study vessel flow characteristics. Single-phase flow
in a flat-bottom, baffled tank with dual 4-bladed Rushton impellers
is modeled. Rushton impellers are typically employed to generate
radial flow. Figure 8.1.1a shows properly placed impellers in the
vessel. The radial flow field generated by the impellers leads to
formation of four torroidal re-circulation regions. The impellers
in this case operate with little if any interaction between them.
If the impellers are placed closer to each other, a converging flow
pattern is generated. This is depicted in Figure 8.1.1b. The upper
impeller pumps downward and the lower impeller pumps upwards.
However, if the impellers are placed further apart, a diverging
flow pattern as depicted in Figure 8.1.1c is generated. In this
case, the lower impeller pumps downward and the upper impeller
continues to pump radially outwards. Changes in impeller position
lead to a drastic change in the flow pattern. This has a strong
effect on vessel performance, mixing characteristics and hence
product quality and efficiency. Impeller-impeller interaction is a
strong non-linear effect and cannot be predicted by simple
empirical correlations. CFD provides a viable method to analyze and
optimize stirred tank performance. Impeller performance and flow
field characteristics can be successfully predicted using CFD
methods. CFD methods can also be applied to predict shear stress
distribution within a stirred vessel. This is important for
dissolution, emulsification and dispersion. Shear stress
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distribution is also important for biomedical applications where
excessive shear may lead to damage of product and loss of efficacy.
CFD is also applied to study the flow behavior in static mixers.
Static mixer design and element shape and size can be optimized
using CFD methods. Figure 8.1.2 depicts the mixing of two fluids in
a static mixer. Figure 8.1.2: Mixing of fluids in a static
mixer.
Figure 8.1.1a: Stirred tank, radially pumping impellers
Figure 8.1.1b: Stirred tank, closely placed impellers
Figure 8.1.1c: Stirred tank, impellers too far apart
Helical ribbons for mixing
The fluid streams are colored red and blue
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8.2 CFD for multiphase flow: Flow fields in the chemical process
unit operations are complex and often involve multiphase flows.
Multi-fluid flow also referred to as multiphase flows are complex
in nature and difficult to measure and analyze.
A full description of multiphase flow modeling methods is
provided in Appendix A.
CFD Study of Spray Dryer: Drying equipment is usually large and
expensive. As a result, efficiency is an important factor that
influences production and operation cost. In this section the
benefits derived from CFD study of a spray dryer are discussed. CFD
is used to analyze the performance of a tall-form powdered milk
industrial spray dryer in advance of making major structural
changes to the dryer. The risk of lost profit during changeover
(especially if the improvement did not materialize) is minimized.
CFD is applied to examine configuration changes and thus minimize
risk and avoid unnecessary downtime during testing. CFD results can
provide the necessary confidence that the proposed modifications
will work before capital equipment is ordered and field-testing
scheduled. A tall-form powdered milk spray dryer is analyzed. An
Eulerian-Lagrangian model is applied to simulate the flow field in
the spray dryer. The gas phase is simulated using an Eulerian
formulation. The spray drops are simulated using a discrete
particle model. In this case, the drops exchange mass, momentum and
energy with the continuous phase. Full coupling between the phases
is required to produce an accurate simulate. The CFD results are
applied to guide changes in the geometry and process parameters
necessary to improve product quality. Different combinations of
axial and swirling airflows are modeled. Figure 8.2.1 depicts the
velocity field in the dryer. The velocity field is skewed towards
the wall. This is a result of non-uniform pressure distribution in
the air dispersing head. By changing the vane angles of the air
disperser along with nozzle spray patterns it is possible to create
optimum conditions within the dryer thus yielding a product with
desirable qualities and reducing powder buildup on the dryer
walls.
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CFD Study of Cyclone: In this study CFD solutions are applied to
optimize and predict performance of an existing cyclone design.
Eulerian-Lagrangian model is applied to simulate the flow field.
The gas phase is simulated using an Eulerian formulation. The
particles are simulated using a discrete particle model. In this
case, the particles exchange momentum with the continuous phase.
Momentum coupling between the two phases is included. Separation
efficiency for different particle sizes is examined. Figures 8.2.2a
and 8.2.2b depict particle paths for various particle sizes. CFD
techniques are employed to perform what-if analysis for
optimization of the design. The results agree well with tests,
showing a marked fall-off in separation efficiency between 1 m and
10 m size particles.
Figure 8.2.1: Spray dryer, velocity field
Skewed velocity field
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CFD Study of Filling: CFD is used to simulate the filling
process of containers. A number of virtual experiments are
conducted to optimize the filling process. A number of filling
profiles are examined to minimize splashing. An Eulerian-Eulerian
Volume of Fluid (VOF) model is applied. This study involves free
surface tracking so a volume of fluid method is applied to track
the free surface. Inertial effects dominate and surface tension
force effects are negligible; therefore, a surface tension model is
not included. The free surface is tracked at various time instants
and filling profile adjusted to eliminate splashing of fluid. Free
surface shape and location at the start of filling cycle is
depicted in Figure 8.2.3a and Figure 8.2.3b. Red color denotes
liquid and blue gas.
Figure 8.2.2a: Cyclone, path line of 1micron particle Figure
8.2.2b: Cyclone, path line of 10 micron particle
Figure 8.2.3a: Filling process, free surface location. Figure
8.2.3b: Filling process, free surface location. Strong splash. No
splash.
Red color denotes liquid and blue air
Splashing of liquid on sides
Smooth filling
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CFD Study of Drop Injection: Drop and bubble formation are
studied to establish injection characteristics and understand
sparger behavior. In this study, an Eulerian-Eulerian homogenous
flow model is applied to study drop formation from a nozzle. The
inertial forces associated with such flow fields are small and
surface tension effects dominate. Shape, size and frequency of drop
formation are examined. Liquid is injected through an injection
tube, the injected fluid initially collects at the nozzle tip as
depicted in Figure 8.2.4a. As the fluid bubble grows in size the
gravitational force becomes large and necking of fluid takes place
as depicted in Figure 8.2.4b. At this stage, the fluid column is no
longer able to hold the ejected fluid in place and it breaks from
the nozzle forming a drop as depicted in Figure 8.2.4c.
Figure 8.2.4a: Initial collection of fluid at nozzle tip
Figure 8.2.4b: Necking of injected fluid Figure 8.2.4c: Drop
formation
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CFD Study of Centrifuge Separation: Industrial centrifuges are
widely used in the process industries for separation of solids from
liquids and liquid-liquid separation. If the density of the two
fluids is similar, then gravitational separation is no longer
effective, centrifuge separation devices can be effectively
employed under these conditions. In general, centrifuges are used
for thickening, separation and post-treatment. Centrifuge
separators are required to provide better separation quality
materials at lower operating costs. This is achieved by
improvements in existing design as well as developing new ones. In
the present study, design modification to a centrifuge shown in
Figure 8.2.5a are examined using computational fluid dynamics
(CFD). A drift-flux model is applied to simulate the flow field.
The solution is computed in a rotating frame of reference. The
original design results in slugging of material. This behavior is
characterized by the transient flow field observed during the
simulations. Figures 8.2.5a and 8.2.5b depict material density at
two different time instants. As part of design change
investigations, the concentrate outlet port (side port) was closed.
This resulted in high density liquid exiting the low density port;
this situation is undesirable. Next, the side port opening was
reduced. This minimized slugging and a near steady flow field is
observed as shown in Figure 8.2.5c.
Light fluid outlet
Concentrate outlet
Inlet
Concentrate outlet
Heavy Fluid Outlet
Figure 8.2.5a: Centrifuge configuration
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Figure 8.2.5b: Fluid density (original design) Figure 8.2.5c:
Fluid density (modified design) CFD simulation of bubble column
reactor: Bubble columns reactors are used for contact operations
involving gas and liquid. The flow field within such reactors is
very complex. In the present study, gas-liquid flow in an airlift
loop reactor is simulated using an Eulerian-Eulerian two phase flow
model. The bubbles are modeled as a dispersed phase and the liquid
is treated as a continuous phase. Figure 8.2.6 depicts the gas
phase distribution and liquid phase velocity field in the reactor.
CFD solution is used to predict the bubble distribution in the
reactor so that design changes to improve efficacy of the process
can be planned.
Figure 8.2.6: Gas flow distribution. (Courtesy of AEA
Technology)
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CFD study of gas-solid flow in a fluidized catalytic cracking
unit : gas-solid flows are very commonly observed in chemical
process industries. Pneumatic transport of solids, catalytic
cracking are some examples of such flows. In the petrochemical
industries, fluidized bed reactors are employed for catalytic
cracking of hydrocarbons. Figure 8.2.7 depicts gas flow progression
through a FCC riser. The flow field is simulated using an
Eulerian-Eulerian model. The solid phase is treated as a dispersed
phase. A solids pressure model is included to account for
particle-particle interaction. CFD is applied to study the flow
field in devices such as a FCC is unsteady and chaotic. Simulation
of such a flow field requires unsteady flow calculations. Small
time increments are required to simulate such flow fields, as a
result, these calculations can be very time intensive. Simulations
of gas-solid flows in complex three-dimensional reactors can take
months of computational time and are not practically feasible.
However, with the advent of faster computers and parallel
processing capability simulation of gas-solid flows in complex
reactors can become a reality.
Figure 8.2.7: Gas flow progression in a fluidized bed riser.
(Courtesy of AEA Technology)
Flow fields in the chemical process unit operations are complex
and often involve multiphase flows. Analysis of multi-fluid or
multiphase handling devices is not easy; conventional methods are
inadequate and experimental measurement is difficult if not
impossible. Computational Fluid Dynamics (CFD) has been identified
as a viable tool for analysis of such devices and associated flow
fields.
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8.3 Application of CFD to combustion systems: CFD techniques can
be applied for design, analysis and troubleshooting of combustion
systems. Problems associated with high excess air, high stack
temperature, flame impingement, non-uniform temperatures, loss of
efficiency and non-uniform flow distribution can be examined. CFD
techniques provide an insight into combustion systems such as
burners, furnaces, boilers, heaters and reformers. These methods
can also be applied for the analysis of auxiliary components such
as wind-boxes, classifiers, precipitators and scrubbers.
Combustion Modeling Combustion is the process by which heat is
rapidly released by oxidation of a fuel. The main products of
combustion are carbon dioxide and water vapor. Combustion is a very
complex physical process involving strong interactions between the
aerodynamic field, thermal field, turbulence interactions, mixing
and chemical kinetics. These physical processes are tightly coupled
to each other. In many cases, fuel is injected in the form of
particles or droplets. In such cases interaction between the gas
phase and the particulate phase plays an important role. Combustion
models that appropriately account for the above effects have been
developed. Combustion systems involve high temperatures. At these
temperatures heat transfer by radiation plays an important role. An
appropriate radiation model must be included when simulating
combustion systems. Computational models that account for thermal,
prompt and fuel NOx have been developed. Soot and NOx formation are
modeled using semi-empirical mechanisms. These mechanisms are not
very reliable and accurate prediction of absolute quantities of
pollutants is difficult. However, the models can be applied for
relative comparison of designs and also to predict trends. CFD for
Boilers: Boilers are used to convert energy in conventional fuels
(coal, oil and gas) to steam for power generation, heating or
process consumption. There are two main types of boilers. Fire-tube
boilers are those where combustion takes place inside tubes and
steam is generated on the outside. These are typically used in
small package-boilers and also in waste-heat recovery units that
operate at medium or low-pressures. The other types are water-tube
boilers; these are more commonly used. In these units, water
passing through tubes is heated using combustion gases. These are
available in a wide range of capacities, ranging from 5,000 lbs/hr
to as high as 9,000,000 lbs/hr of steam. These units typically
employ natural gas, oil or pulverized coal as fuel. A water-tube
boiler consists of various components such as burners and heater
tubes. Burners of various types are employed to inject, mix and
burn fuel and oxidant. The combustion process is completed in the
furnace section of the boiler; heat is extracted in the radiant and
convection section of a furnace. The radiant section of a furnace
is lined with water-tubes; steam is generated in this section by
radiant heating of the tubes. The convective section consists of
tube banks and heating of fluid in the tubes is accomplished by
passing hot combustion products through the tube bank. This section
is
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also referred to as the superheater section and generates
high-pressure steam. Many boilers also include an economizer unit.
This unit extracts heat from the moderate temperature gases leaving
the superheater section. Air heaters are employed to further
extract heat form the gas before discharging to stacks. This heat
is recycled to the furnace with combustion air. Coal-fired furnaces
employ pulverized coal as the fuel. Pulverized coal is mixed with
air and burnt in the furnace section of the boiler. Various
configurations of coal-fired furnaces exist. In wall-fired
furnaces, swirl-type burners are located on one of the vertical
walls of the furnace. Swirl imparted by the burner to the secondary
stream of air creates a recirculation zone in front of the burner.
This region acts as a flame stabilizer and is the primary
combustion zone in the furnace. Tangentially-fired or T-fired
furnaces are more common. Burners are located on the boiler corners
and fire towards the axis of the furnace. This generates a vortex
in the core of the furnace; combustion takes place in this region.
Coal requiring high residence times and higher temperatures is
burnt in down-fired furnaces. In this case the burners are located
on horizontal walls in the furnace and fire downwards. Cyclone
furnaces differ from the conventional T-fired or wall-fired
furnaces. In a cyclone furnace, coal devolatilization and char
oxidation occurs in a separate cyclone-type chamber. Residence of
coal is increased by generating highly swirling flow in the
chamber. This chamber also retains most of the coal ash and slag.
The flow field within boilers is very complex and involves
interaction between many variables such as fuel characteristics,
firing systems, and heat transfer. CFD methods can be applied to
examine and study complex flow behavior. The furnace enclosure is
one of the most critical components of a boiler. Uniform gas flow
and temperatures are desired in the convective section of the
furnace. Nonuniformities can result in hot-spots and excessive
metal temperatures in the boiler tubes, resulting in failure. CFD
modeling of package gas-fired boiler: A gas-fired boiler as shown
in Figure 8.3.1 is analyzed. The burner is shown in Figure 8.3.2
and consists of a fuel lance. The oxidant is introduced through the
annular space and passes through a set of swirl-vanes. The swirl
imparted by the vanes stabilizes the flame. The temperature plot in
Figure 8.3.3 depicts the high temperature region in the convective
section of the furnace chamber. This is the region where boiler
tubes are most likely to fail. The velocity field in Figure 8.3.4
depicts a low velocity region near the outer surface of the radiant
section. However, the temperatures in this region are acceptable.
Design changes to induce a more uniform temperature field in the
convective section of the furnace can be explored using CFD
methods.
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Figure 8.3.1: Boiler layout.
Figure 8.3.2: Boiler configuration.
Boiler tubes section
Radiant section
Burner
Swirl vanes
Fuel Lance
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Figure 8.3.3: Temperature distribution in boiler (temperatures
in oK).
Figure 8.3.4: Velocity distribution in boiler (velocity in
m/sec) Application of CFD for coal-fired furnace: Coal-fired
furnaces are employed by utilities for power generation. Uniform
flow and temperatures are desired in the furnace. Minimization of
unburned combustible loss in the fly ash from pulverized
coal-firing units, slag formation and deposition are other issues
that affect the performance of such
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devices. NOx formation and unburnt carbon have an environmental
impact. These aspects can be examined using CFD methods. A
coal-fired unit as shown in Figure 8.3.5 is analyzed. The burners
are arranged at