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3 Meshing Strategy

CFD uses a series of cells (previously referred to as control volumes), elements and nodes

that combined form the so called mesh. It is at each of these node locations, that CFD

calculates the fundamental equations of fluid dynamics, as mentioned in the previous

section, the shape of the cells greatly impacts the accuracy of the solution due to

discretisation errors, therefore the meshing stage is one of the most crucial stages in the

problem simulation.

3.1 Mesh types

There are 2 types of meshing predominately used in CFD today, namely:

1. structured meshing; and

2. unstructured meshing.

Structured meshing uses hexagonal shaped elements (12 edges and 8 nodes) while

unstructured meshing uses tetrahedron shaped elements (6 edges and 4 nodes). Each

method has advantages and disadvantages and it is imperative that the CFD user

understands which meshing type is applicable for the given problem.

Figure 3-1 Left section unstructured mesh, right section structured mesh

Structured

Unstructured


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Mesh generation, in most cases is the timeliest task in the CFD simulation and can be quit

challenging to generate a mesh that accurately defines the problem. Two available

programs for this study are ANSYS CFX Mesh Generation which generates an unstructured

mesh and ANSYS-ICEM CFD which can generate both a structured and unstructured mesh.Both mesh types have their strengths and weakness and are listed in Table 3-1 and Table

3-2.

Structured Mesh

Strengths Weakness

Allows user high degree of control.

Mesh can be accurately designed to

users requirements

Excessive time spent producing the

mesh compared to unstructured mesh

Hexahedral cells are very efficient at

filling space, support a high amount of

skewness and stretching before

affecting solution

Some geometries dont allow

structured topology due to the high

skewness angles and stretch of cells

that are required.

Grid is flow aligned which helps the

solver converge

Post-processing is easier due to the

logical grid spacing act as excellent

reference points for examining the flow

field.

Figure 3-2 Hexahedral and tetrahedral elements

Table 3-1 Structured; mesh strengths and weaknesses (Quak F.L. 2006)


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Unstructured Mesh

Strengths Weakness

Automated grid generation allows

much less effort by user to define

mesh.

Lack of user control mesh may not

be defined as well as the user may like

in certain areas

Well suited to inexperienced users

Tetrahedral elements do not twist or

stretch well, which will severely impact

accuracy of results.

Will generate a valid mesh for most

geometries

Require excellent CAD surfaces. Small

mistakes in the geometry can lead to

large meshing problems

Users are able to get results for

relatively large mesh size quickly

Post processing software requires

larger computer power to generate

The aim of this study is to find the most optimum and efficient meshing techniques for

underwater vehicles. A preliminary unstructured mesh was created, however the majority of

this study is focused on the optimisation of a structured mesh due to its high level of user

control which allows for simpler validation. Validation will be done through an iterative

process outlined in Figure 3-3 Suboff mesh generation processes (Ackerman 2008)

Structured and unstructured meshing are only discussed in this study, an area of future

development could be an investigation into the effects of a hybrid mesh, that uses a

structured mesh on the critical regions and a unstructured mesh in the less critical regions.

Table 3-2 Unstructured; mesh strengths and weaknesses (Quak F.L. 2006)


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3.2 Geometry

The geometry used in this study was kept the same as that used in the initial study, allowing

for direct comparison of results. Ackerman (2008) explains that testing a submarine body

requires a large domain for the mesh to be tested in, with little or no effects from the domain

Figure 3-3 Suboff mesh generation processes (Ackerman 2008)


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itself. By creating a large domain with a blocking ratio of only 4% (with respect to the hull

frontal area), the domain affects have been minimised.

Figure 3-4 shows the hemispherical inlet, which is located 6.543m upstream of the bow, the

outlet is located 15.246m downstream of the stern end cap, and the far-field boundary is

located 6.534m from the hull centreline.

3.3 Structured Meshing

As mentioned previously a structured mesh uses hexahedron shaped elements to create the

mesh used to simulate the problem. ANSY-ICEM CFD uses hexahedron blocks that theuser manipulates by slicing into a series of smaller blocks.

Figure 3-4 Fluid domain and Suboff geometry (Ackerman 2008)


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Splitting of the blocks allows for the edges of the blocks to be associated to the geometry.

The edges are then given parameters and node spacings that define the mesh. The power

of ANSYS_ICEM CFD comes from these blocks, as they can be split many times to give the

user complete control over the mesh.

Figure 3-5 Initial block to be split into sections

Figure 3-6 Blocks split to capture the geometry


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Associating the vertexes, edges and faces of these blocks to the points, curves and surfaces

of the geometry shape the mesh to geometry.

Figure 3-7 Edges of blocks that can be associated to the geometry

Figure 3-8 Geometry for association of topology


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However, difficulty with a structured mesh comes from trying to adapt a hexagon shaped

element to a curved or complex shape and can result in a poor quality cells. In chapter 3 it

was discussed how the quality of the mesh will greatly affect the results of the simulation, for

this reason it is imperative to ensure the mesh quality is sufficient.

3.4 Mesh Quality

The Quality of the mesh is determined by the shape of the individual cells, if the quality of

one cell is poor it can cause inaccurate result or convergence failure. Key factors that affect

the quality of the cells are skewness, aspect ratio, angles between the adjacent elements of

the cells and determinants. ANSY-ICEM provides the following definitions for the above

quality parameters:

3.4.1 Skewness

For quad elements, the skew is obtained by first connecting the midpoints of each side with

the midpoint of the opposite side, and finding the angle as shown in Figure 3-10 with the

smaller of the two angles used so that is less than 180 degrees. The result is usually

normalized by dividing by 180 degrees

Figure 3-9 Mesh created after association and edge parameters defined


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3.4.2 Aspect Ratio

The aspect ratio is determined by the size of the minimum element edge divided by the size

of the maximum element edge. Thus in Figure 3-11, the aspect ratio is determined by A

divided by B

3.4.3 Minimum Angle

The angle between adjacent elements is found by determining the internal angle deviation

from 90 degrees for each element as shown in Figure 3-12. Various solvers have different

tolerance limits for the internal angle check. If the elements are distorted and the internal

angles are small, the accuracy of the solution will decrease.

3.4.4 Determinants

The determinant is found by dividing the smallest determinant of the Jacobian matrix by the

largest determinant of the Jacobian matrix at each corner of the hexahedron. A determinant

value of unity indicates a perfectly regular mesh element. Zero would indicate that the

Figure 3-10 Skew definition (ANSYS ICEM 2009)

Figure 3-11 Element aspect ratio determination

Figure 3-12 Minimum angle determination

A

B

D

C


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element has 1 or more degenerate edges, and a negative determinant indicates an inverted

element

Table 3-3 of this section shows the recommended values to ensure sufficient mesh quality

for CFD simulations

3.4.5 ANSYS CFX quality criteria

Although the previously mentioned quality factors give an indication of the quality of the

mesh, various CFD solvers will have differing mesh quality requirements to stability and

accuracy; ANSYS CFX has three requirements that must be achieved to minimise

discretization errors and ensure convergence and accuracy, i.e.

1. Minimum orthogonality angle > 10

2. Mesh expansion factor < 20

3. Mesh aspect ratio < 100

Significant orthogonality and non-orthogonality are illustrated Figure 3-13 at Ip1 and Ip2,

respectively. Orthogonality angle involves the angle between the vector s, that joins two

mesh (or control volume) nodes and the normal vector n, for each integration point

associated with that edge.

Mesh expansion factor measures the magnitude of the rate of change of the adjacent

element areas or volumes.

Figure 3-13 Orthognality example (ANSY CFX 2009)


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The mesh aspect ratio is determined by dividing the smallest element edge length by the

largest, usually they must be less than 100, however it is expected and accepted that mesh

aspect ratio within the boundary layer will be of the magnitude 105-106. Table 3-3 shows the

ICEM criteria that if achieved usually results in the ANSYS CFX criteria being achieved, and

the values for the base mesh used in this study.

Key Factor Requirement Base mesh Value

Minimum volume >0 1.22 x10-13

Minimum determinant >0.2 0.37

Minimum angle Preferably > 18, definitely > 9 17.28

Negative volumes or determinants indicate an inverted element and ANSYS CFX solver will

not run.

3.5 Structured Meshing Topologies

3 basic topologies are used that allow the user to adapt the mesh to most types of

geometries to ensure quality meshing is achieved. The author acknowledges Mr. Ronny

Widjaja, for his guidance and contribution to this section

3.5.1 2D Topology

H mesh

mesh

C mesh

3.5.1.1 H mesh

Table 3-3 CFX ICEM Criteria to determine acceptable mesh quality for CFX Solver

Figure 3-14 H type mesh around a cylinder (Widjaja)


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H type mesh is the standard meshing method used in ANSY-ICEM CFD. H mesh can

achieve good results for a simple geometry, however to maintain accuracy for complex

shapes the blocking becomes quit complex.

3.5.1.2 O mesh

O type mesh is ideally suited for circular or curved surfaces; Figure 3-15 H mesh to O meshshows that when an H mesh is used on a circular geometry highly skewed elements exist at

angles of 45 around the geometry, an O type mesh removes this skewness. O type

meshing is not well suited to wake flows, Figure 3-16 O type mesh around cylindershows

that as the O expands to outer edges of the geometry the elements become quite large, and

would not accurately capture the wake region of the flow.

Figure 3-15 H mesh to O mesh

Figure 3-16 O type mesh around cylinder (Widjaja)


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3.5.1.3 C meshC mesh is a combination of an H and C grid, it has the benefit of the O grid where it

accurately models a curved surface, but also allows for refinement of the mesh in the

leeward edge of the geometry. C type meshing is ideally suited for flows where a wakeneeds to be captured and anything that has a bluff leading edge and small finite to infinite

trailing edge such as foils and wings as the mesh reduces to H mesh at these sections

allowing for mesh edges to fully capture the geometry of these critical regions. Often when

creating a C grid for a foil, a triangular block is created which creates a poor quality mesh, a

Quarter O grid or y grid (see Topology creation steps) can be used on triangular blocks to

increase mesh quality.

3.5.2 3D Topology

When these topologies are used in 3D, they combine to give the following topologies

H-H mesh O-O mesh

H-O mesh O-C mesh

H-C mesh C-C mesh

Figure 3-17 C type mesh around cylinder (Widjaja)


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3.6 Topology Used

To successfully mesh a complex shape such as a submarine body, a combination of these

topologies need to be used in the associated regions, to ensure the geometry is represented

accurately by the mesh. The Suboffgeometry can be broken into 3 critical regions where

different topologies are used:

1. The fluid domain which is modelled using a O-C mesh

2. The region adjacent to the appendages which is modelled using a H C mesh

3. The Appendages, 2 methods where used 1) H - Quarter O grid and 2) H and

combination of a Quarter O grid and an O Grid.

3.6.1 Region 1 - Fluid Domain

The fluid domain is meshed using an O-C type mesh. The O grid (transverse) ensures the

bluff leading and trailing edges of the Suboff geometry would be accurately meshed while

still capturing the complex leeward flow of the model. Figure 3-18 and Figure 3-19 show the

bluff edges of the submarine captured by using an O grid.

Figure 3-18 O type mesh in the bow region resulting from the C grid

O Topology


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The C grid (longitudinal) resolves into a H grid to allow refinement of the mesh to fully

capture the effects of the wake.

Figure 3-19 O type mesh used in the stern region resulting from the C

Figure 3-20 C grid used for the fluid domain

C Grid

H Grid

O Topology


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3.6.2 Region 2 - Adjacent to the appendages

The area surrounding the appendages is meshed using an H-C mesh; this was done to allow

the mesh surrounding the leeward and windward sections of the sail to transition smoothly

into the sail, Figure 3-22 shows a H-H mesh that has highly skewed elements in this region,

Figure 3-23 shows how a H-C mesh removes these poor quality elements.

Figure 3-21 O-C Topology O grid in the YZ plane and C grid in the XZ plane

Figure 3-22 H-H mesh used around Suboff sail

C Grid

O Grid

Skewed cells


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3.6.3 Region 3 Appendages

The appendages are a most complex region of the Suboff simulation and thus a large

portion of this study is focused on determining the most effective topology for this region.

The H-C mesh in the region adjacent to the appendages (see 3.6.2.) improved the mesh in

that region but created triangular or degenerate blocks for the appendages. In ICEM CFD, if

the angle between any of the two edges of a hexahedral block is equal to or greater than

180 degrees, then that particular block is called a degenerate block (CADFEM 2009). These

degenerate blocks cause cells with poor angles at the leading and trailing edges of the

appendages.

The initial study used an H-O topology which removed these poor angles at the leading and

trailing edges of the appendages, See Figure 3-25 and Figure 3-27.

Figure 3-23 H-C mesh used around the Sub of sail

Figure 3-24 Degenerate block (CADFEM 2009)

Quality cells


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Figure 3-25 Poor Cells at the leading and trailing edges of the appendages

(Ackerman 2008)

Figure 3-26 Degenerate blocks producing poor quality cells

Poor cells


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An aim of this study was to find a topology that enhanced the quality of the mesh within this

region. Two topologies have evolved from the original H-O topology, both are essentially an

H-O topology, but have varying blocking strategies:

1. H grid combined with a Y-grid on the leading and trailing edges of the

appendages

2. H grid combined with an O-grid on the leading edge and Y- grid on the

trailing edge of the appendages

A y grid or commonly known as a quarter o grid is an alternative method (to an O grid) usedto eliminate degenerate blocks. y gridding replaces degenerate blocks with 3 regular blocks,

refer to the preceding sections for a detailed y grid explanation.

Figure 3-27 Improved cells dues to H-O topology

Figure 3-28 H-O topology removes poor quality cells


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Figure 3-29 Y grid on the leading and trailing edges of the appendages

Figure 3-30 Y topology used on the leading and trailing edges of the appendages

Figure 3-31 O grid on the leading and y grid on the trailing edges of theappendages

Figure 3-32 O and Y topology used on the appendages


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Further refinement can be done to the OY topology by removing the block in mid-span of the

appendage shown in Figure 3-33, The indicated block creates an unnecessary congestion of

elements shown in Figure 3-34, by using a C and y topology as shown in Figure 3-35 ,this

block would be removed thus improving the mesh. However as the OT topology yielded

accuracy, the CY topology was not created, this is an area of recommend future work.

Figure 3-33 Associated vertices, edges and faces

Figure 3-34 Mesh with degenerate blocks removed using an O grid fwd and a y grid

aft

Unnecessary

congestion of

elements


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