38

3. CFD MODELING

The geometry was modeled using the academically available 3D modeling software CATIA

(V5R19). A 3D mesh was generated using the sweep and CFX mesh applications of ANSYS

(12.0). The symmetry of the geometry was taken advantage of and only a quarter of the vehicle was

modeled. This reduced the number of mesh elements and resulted in a lower computational time for

the simulation.

Figure 22 shows the geometry that was used for the simulation. The vertical thruster nozzle and

horizontal thrusters were removed so an objective analysis could be performed on the

hydrodynamic behaviour of the hull form.

Figure 22: Underwater vehicle hull

The CFD analysis was undertaken using ANSYS - CFX 12.0. The turbulence model used for the

analysis was the standard k- and SST model. The convergence was restricted to within 10-4 and the

computations were carried out on a HP Compaq dc7800 quad processor with 4.00 GB of RAM.

3.1. MESH APPLICATION

The 3-D hull was imported into the Design Modeler section of ANSYS. The domain that represents

the water was created around the hull. It extends eight hull lengths behind, two lengths forward and

eight widths on either side of the vehicle as shown by Figure 23. The size of the water domain has

been chosen to reduce the effect the boundary conditions have on the underwater vehicle.

All of the rectangular volumes of the geometry were meshed using the sweep method. ANSYS Inc

(2009) states that a volume is not a sweepable volume if there is a completely contained internal

void in the body, if the sweep application cannot find a source and target to sweep along, or if there

is a hard sizing control used on the body that does not contain the same properties for the source and

39

the target. The sweep method produces a mesh containing mainly hexagons which are preferred by

the CFX Solver.

Figure 23: Mesh methods

The volume containing the ROV hull, as illustrated by Figure 23, was meshed using the CFX

method. This method uses a combination of tetrahedra, pyramids and prisms and is able to mesh

irregular shapes and is most commonly used when meshing complex geometries.

3.1.1. MESH PARTICULARS

The mesh particulars for each volume, shown by Figure 23, are outlined by Table 5.

Table 5: Mesh particulars

Volume Vehicle hull Rectangular sections

Method CFX (unstructured) Sweep (structured)

Element form Tetrahedral Hexagonal

Element size (mm) 4 - 25 25

Inflation

(boundary) layer

20 layers and minimum

height of 1 x 10-5

mm for

SST turbulence model

N/A

The interfaces between the sweep and CFX mesh have to be the same magnitude so ANSYS can

transfer information accurately between the two mesh types. If there is a discontinuity between the

40

mesh interfaces then ANSYS will interpolate data between elements. This will cause errors to

develop as the simulation is solved and will render the solution meaningless.

Figure 24 shows the interfaces between the sweep and CFX mesh, for the simulation performed for

this report. The connections line up so data can be transferred between nodes accurately with

minimal amount of interpolation.

Figure 24: Mesh connections

The sweepable bodies have a bias on the mesh to increase the number of mesh elements closest to

the vehicles hull.

41

3.2. CFX PRE

Once the mesh was produced it was imported into CFX Pre where the settings for CFX Solve are

applied. A run was performed using the k- turbulence model and a set of results was obtained that

was used as initial conditions for subsequent runs. The turbulence model was then changed to SST

to predict the turbulence around the hull more accurately.

Figure 25 illustrates the boundaries applied to the water domain in CFX Pre. The walls that define

the limit to the water domain are defined as being smooth walls. This reduces the drag effect they

have on the simulation. The water enters through the inlet and exits through the outlet. The

underwater vehicles hull is a non slip surface with a roughness of 1.5 x 10-2

mm. This roughness

represents the roughness of the fiberglass hull.

Figure 25: CFX Pre

The underwater vehicle is considered to be sufficiently submerged so each simulation was run in the

steady state condition with no free surface effect. The inlet velocity of the water was varied from

0.5 knots to 4 knots.

42

3.3. CFX SOLVER

The mesh was partitioned into four, thus allowing a larger mesh to be produced. A definition file of

about 4 x 106 elements was run using the AMC Research License and took up to 6 hours to

converge using the SST turbulence model. All runs converged to within 10-4

before the simulation

stopped.

43

3.4. CFX POST

Once the CFX Solver had produced a results file, it was imported into CFX Post to interpret the

simulation. Images, data and other information relevant to specific areas of interest within the

simulation were derived from CFX Post.

3.4.1. PRESSURE DISTRIBUTION

The pressure distribution, as shown in Figure 26, indicates that there exists a high pressure region at

the forward section of the vehicle and a low pressure region at the aft section of the vehicle as

predicted by Figure 13 in Chapter 2 of this report.

Figure 26: Pressure contours

3.4.2. VELOCITY DISTRIBUTION

The velocity distribution, as shown in Figure 27, indicates that separation is occurring at the low

pressure regions as illustrated by Figure 26. The separation is occurring because the fluid close to

the surface of the hull has low momentum and is unable to overcome the pressure differential. This

results in vortices forming in the areas indicated by Figure 27, which contribute to increasing the

drag coefficient. This is consistent with Figure 11 of Chapter 2 of this report.

44

Figure 27: Velocity vectors

3.4.3. BOUNDARY LAYER THICKNESS

The boundary layer thickness was determined using the turbulent equation developed by Horner

(1965) and is shown by Equation (3.1).

(3.1)

where

= Total boundary layer thickness (m)

x = Dimension is direction of flow (m)

Rx = Reynolds number

As Figure 28 shows, the boundary layer thickness is at a minimum before the bow of the vessel and

increases as the flow travels towards the stern. The boundary layer is thicker for the lower speed,

which is due to the lower momentum that causes the flow to separate earlier from the surface of the

vehicle. At the operating speed of 2 knots, the boundary layer is 1 x 10-5

mm thick at amidships.

The following y+ section outlines the importance of predicting the boundary layer thickness.

45

Figure 28: Total boundary layer thickness

3.4.4. Y-PLUS

The SST turbulence model requires a mesh node close to the boundary layer to accurately predict

the turbulence. Figure 29 shows the y+ distribution over the surface of the underwater vehicle. The

y+ is below 2 as required when using the SST Turbulence model. It also shows the y+ decreases

along the length of the vehicle which indicates that the boundary layer thickness is increasing as

predicted by Figure 28.

Figure 29: y+ distribution on surface of AMC II UV

46

3.4.5. GRID INDEPENDENCE

Moinuddin and Thomas (2007) outline that when conducting a CFD analysis, it is essential to

undertake a grid refinement process by gradually reducing the mesh size used for the analysis. It is

usual to find that as the mesh size is reduced the results converge for a specific quantity of interest.

Further reducing the mesh size has virtually no effect on the results. Once the result has converged

it is known as the grid independent result. To be meaningful, any results obtained using a CFD

package should be grid independent.

The drag coefficient is useful to quantify and compare different hull forms and determine their

hydrodynamic resistance. The force required for Equation (3.2) was derived from the CFD

simulations.

(3.2)

where

CD = Drag coefficient

F = Force opposing direction of movement (N)

= Density of fluid (kg/m3)

= Velocity in direction of movement (m/s)

A = Projected area of body (m2)

The drag coefficient was calculated using Equation (3.2) and the convergence behaviour is shown

by Figure 30. It shows the drag coefficient has converged with the 5,110,127 element mesh. The

data used to develop Figure 30 is presented by Appendix 1.

Figure 30: Grid independent result for the drag coefficient

47

3.4.6. VALIDATION

Unfortunately, due to construction delays, model testing was not undertaken on the AMC II UV.

Therefore, alternative methods for validating the CFD are presented.

The AMC II UV, shown by Figure 31(b), is assumed to be that of an elongated cylinder. The

Hoerner (1965) drag coefficient equation for an elongated cylinder is shown by Equation (3.3)

where the diameter and length of the vehicle is 0.35 m and 0.856 m.

(3.3)

where

d = diameter (m)

l = length (m)

The drag coefficient developed using the Hoerner equation for an elongated cylinder is similar to

the 0.29 obtained using CFD on the AMC II UV.

Experimental results for the AMC I UV, Figure 31(a), the NSTL AUV, Figure 32(a) and the

REMUS AUV Figure 32(b) have also been used to validate the CFD for the AMC II UV. The drag

coefficient at the Reynolds number of 7.62 x 105 is shown for each vehicle on Figure 31 and Figure

32.

Figure 31: AMC underwater vehicles

48

Figure 32: Other underwater vehicles

The drag coefficient at different Reynolds number obtained by Saiju et al (2006) for the NSTL

AUV, Prestero (2001) for the REMUS AUV and the AMC I and II UV are presented by Figure 33.

As expected the drag coefficient for the AMC II UV is less than the AMC I UV for all Reynolds

numbers. The AMC I UV has a flat side profile and cumbersome guardrails which contribute

significantly to the drag of the vehicle. The drag of the NSTL and REMUS AUVs is expected to be

less than the AMC II UV because they have a higher aspect ratio.

Figure 33: Drag coefficient at different Reynolds numbers

49

3.5. DISCUSSION

The NSTL and REMUS AUVs investigated by Saiju et al (2006) and Prestero (2001) have a high

aspect ratio. Therefore, as shown by Figure 14 in Chapter 2, the dominant resistance force is due to

skin friction. The main contributor to skin friction is the surface roughness of the body. As a result,

the surface roughness of the underwater vehicles needs to be small.

On the other hand, the low aspect ratio of the AMC II UV means that the dominant resistance force

is due to form drag. The surface roughness still contributes to the drag coefficient as it creates a

turbulent boundary layer and induces vortices. A material with a smooth surface finish will be

suitable for construction of the hull. Fiberglass is a material that is cheap, readily available, easy to

work with and has a smooth surface finish.

A Reynolds number of 7.62 x 105 corresponds to a vehicle speed of 2 knots and a drag coefficient of

0.29 for the AMC II UV. The cross sectional area of the vehicle is 0.1225 m2 and the density of the

water is 1000 kg/m3. Thus, drag is calculated by Equation (3.4) as;

(3.4)

The two forward thrusters will be positioned in the horizontal direction developing 43.16 N which

is sufficient to overcome the resistive force of 18.8 N at 2 knots.