Computational Fluid Dynamics Investigation of Two Surfboard Fin Configurations

Computational Fluid Dynamics Investigation of Two Surfboard Fin Configurations.

By: Anthony Livanos (10408690)

Supervisor: Dr Philippa O’Neil

Faculty of Engineering

University of Western Australia

For the fin fanatics of Swaylocks.

Contents Page

• Introduction …………………………………………………………………4

• Hydrodynamic Forces ……………………………………….7

• CFD Analysis Observations .……………………….12

• Conclusion & Review…….…………………………………….18

• Appendix …………………………………………………………………………20

• Bibliography ………………………………………………………………..22

Introduction

As the sport of surfing is continually evolving, surf riding equipment is steadily improving. The surfing industry has lead the surfboard to develop from its origins of tree trunks to highly sophisticated composite structures.

The professional competitive nature of surfing pushes the performance limits higher and higher. There are many variables involved with surfboards and fins in terms of performance such as wave size, board size and the surfer’s ability. All components are inter related and must be optimised as a group, to satisfy the conditions they are being used in and to reach the desired performance.

All the thousands of variables and the definitions of performance make the analysis and comparison of surfboards and fin configurations very difficult. For the purpose of this report, only two different fin configurations have been investigated, the Thruster setup (three fins) and the Single fin setup. The two side fins of the Thruster setup were FCS G5 fins, whilst the rear was an FCS G3000 fin. The fin used for the single fin setup was the JB2 single fin. Both configurations have been put under the same flow conditions.

There is limited experimental evidence available for the relative speeds involved in surfing. For the purpose of this report, a speed of 6 m/s of water relative to the fin has been used in the analysis. Surfboards typically encounter large angles of attack and significant change in directions. This report only simulates straight line flow as the dynamic simulation of turning and manoeuvres is beyond the scope of this report. To simulate the presence of the surfboard, the fins have been modelled in a rectangular domain, attached to a wall surface, representing the bottom of the surfboard.

Since the fin chords are in the order of 0.1m, consequently chord calculated Reynold’s numbers will be in the order of 105 . In this range, separation and boundary layer effects are known to be significant. It is expected the flow will be turbulent with vortices present.

The ultimate goal of this report is to qualitatively investigate the hydrodynamic forces, and fluid behaviour surrounding two different surfboard fin configurations.

The fin properties, configurations and dimensions used in the analysis are as follows:

Figure 1. Thruster and Single fin configurations

Figure 3. Top view of Thruster setup depicting Toe – In.
Figure 2. Front view of Thruster setup depicting Cant.

Figure 4. Thruster setup analysis domain. Front and Side view.

Figure 5. Single fin setup analysis domain. Front and Side view

Fin: / JB2 Single Fin / FCS G5 / FCS G3000
Base Chord (mm): / 155 / 110 / 110
Surface Area (mm ²): / 47, 600 / 20, 100 / 18, 730
Volume (mm ³): / 235, 380 / 53, 800 / 51, 180
Aspect Ratio: / 1.88 / 1.6 / 1.49
Base Thickness/Chord Length ratio (%): / 9.03 / 5.45 / 6.65

Table 1. Summary of Surfboard fin properties

Hydrodynamic Forces

Performance in regards to surfboard fins is not easy to define. Performance is based on a wave-to-wave and surfer-to-surfer basis. Some fins work well in bigger waves, and some fin properties are good for beginners rather than professionals. Fundamentally, the purpose of surfboard fins is to provide greater control over the surfboard.

A greater understanding of the hydrodynamic forces acting on surfboard fins would provide an insight into how to maximise certain properties of the fins in order to achieve greater performance levels. Since fins are foiled bodies, with a large range of angle of attack, they will experience a lifting force acting perpendicularly to the flow, and a drag force acting in parallel with the flow. For visualisation purposes, since the fin is oriented in the vertical plane, the forces will act in primarily the horizontal planes.

Drag forces:

The total drag force acting on a body immersed in a fluid is comprised of three different types of drag: Form (or pressure), Skin Friction (or viscous), and Induced.

Form drag is a result of the difference between the high pressure regions at the leading edge, and the low pressure regions associated with the trailing edge(s). The differences in pressures can be reduced through efficient streamlining of the immersed fin. Studies have shown streamlining the leading edge reduces drag by 45%, whilst streamlining the trailing edge reduces drag by up to 85%.

Rounded leading edges prevent early flow separation, as pre-mature flow separation will lead to the fin stalling and reducing lift dramatically.

Figure 6. Lift and Drag forces.

Skin friction drag is caused by the physical contact between fin and water molecules. This form of friction is similar to the friction

between two bodies. Since the friction is between a solid and a fluid the properties of both the solid and fluid will determine the magnitude of the friction. The surface roughness is a factor affecting friction in terms of the solid fin, and for the fluid it is the fluid’s viscosity dictating the friction. Since the viscosity cannot be changed, changes to the fin surface such as a matte finish or a gloss finish will alter performance.

Along the surface of the fin, a low energy flow region exists known as the boundary layer. The magnitude of skin friction also depends on the state of the boundary layer. Boundary layer and fluid interactions are usually beneficial since the friction between boundary layer and fluid is less than fluid and solid. One method of inducing and retaining boundary layers would be to roughen the surface of the fin, initiating turbulent flow, which is less prone to flow separation, consequently forming a boundary layer.

Induced drag is mainly concerned with the formation of vortices at the fin tips. Vortices are spiralling bodies formed by the ‘leaking’ of pressures at the tip of the fin. A vortice is formed when the high pressure underneath the fin curls around the wing tip to the top side of low pressure. Consequently, the overall pressure above the fin is reduced, and this dramatically reduces the lift generated.

Vortices can be reduced in a few ways. Shortening the chord length will reduce vortices as it provides less opportunity for the formation of vortices. Fins of higher aspect ratios are more efficient because the load bearing distribution is concentrated further away from the tips. Since less load is distributed to the tips vortices are reduced. The introduction of a physical barrier, such as tips on airplane wings also prevents and interrupts the formation of vortices.

In summation, total drag = parasitic drag (form and skin) + induced.

Ideally total drag must be minimised to increase performance, but there are other factors to consider. Certain drags contribute directly to loss of speed, whilst others contribute to fin ‘stability’ and ‘suck’, which are responsible for control and responsiveness of the board on the wave surface. Which drags are positive or negative is another debate in itself, and subject to opinion without the presence of proper evidence.

A qualitative comparison of drag occurring in the two fin configurations can be done using the information given in Table 1. Since the Thruster setup consists of two G5 fins and one G3000, the total surface area and volume is 58930 mm ² and 158, 780 mm ³ respectively. For the Single fin setup, we have a total surface area of 47, 600 mm ² and volume of 235, 380 mm ³.

From this data and assuming that all fins have the same surface roughness, since the Thruster setup has more wetted surface area, it would possess more Skin friction drag than the single fin setup.

From the data it can be observed that the Single fin occupies a larger volume compared the Thruster setup. Theoretically form drag relates to volume but there are other factors involved. The single fin is larger, but has no Cant or Toe-In to add to drag forces. In the simple straight line flow analysis, the Thruster setup would have more form drag due to the side fins being Canted at 4and having a 3.5Toe-In.

In terms of Induced drag, the strength and number of vortices must be considered. The Thruster setup will generate three vortices as compared to the single vortice created by the single fin. It can be assumed that the total induced drag would be more for the Thruster setup. Further investigation with CFD will clarify this issue later in this paper.

Lift forces:

There are quite a few explanations of lift published in resources and available on the internet. Unfortunately, theories are mis-applied and lead to incorrect theories being widely accepted. Theories of lift have been the source of many arguments. The primary reason for this is people choose to believe either a Newtonian point of view, or a Bernoullian point of view.

Incorrectly applying Bernoulli’s theory leads us to the theory which is known as the "equal transit time" or "longer path" theory. This theory states that foiled bodies are designed with the upper surface longer than the lower surface in order to generate higher velocities on the upper surface because the molecules of gas on the upper surface have to reach the trailing edge at the same time as the molecules on the lower surface. From Bernoulli, pressure of a fluid is inversely proportional to velocity. The incorrect theory then invokes Bernoulli's equation to explain lower pressure on the upper surface and higher pressure on the lower surface resulting in a lift force.

The correct theory of lift is based on ‘flow turning’ and is actually a combination of both Bernoullian and Newtonian views. When a body is immersed in a moving fluid, the fluid flows around it, with varying velocities depending on shape, size and drag factors. This variation in flow velocities causes variations in pressures. Integrating the pressures over the entire body, not just the top side, equates to the total hydrodynamic force acting on the body. This hydrodynamic force is comprised of lift, perpendicular to the flow direction, and drag, parallel to the flow direction. This makes the basis for the Bernoullian part of lift.

The Newtonian part is based around Newton’s third law of action and reaction. Since this hydrodynamic force is acting on the solid body, the solid body must also be acting on the fluid with the same force. This force acts to ‘turn’ or deflect the fluid. So in essence, both Bernoulli and Newton are correct.

Factors affecting the generation of lift are grouped into two categories; Object and Fluid.

In relation to the object, shape and size will affect the generation of lift. In terms of a fin, this relates to the fin’s foil, thickness, and camber. Over all plan form shape will also affect the lift generated. Plan form of fins can vary in terms of rake and depth. The discussion of how these factors affect the fin are not relevant as the testing is only being done on two sets of fins, with shape and size being constant.

Hydrodynamic forces are definitely proportional to surface area of the fins.

The Coanda effect is definitely an important consideration in regards to analysis of forces on foiled bodies. The Coanda effect states that a moving stream of fluid in contact with a curved surface will tend to follow the curvature of the surface rather than continue to travel in a straight line. Relating back to the theory of lift, this effect would essentially aid in ‘turning’ the air, thus creating more lift. Certain foils would lead to a more pronounced Coanda effect and consequently more lift.

Figure 7. Cross section of a foil, depicting Coanda Effect

With regards to the fluid factors, properties such as viscosity, mass of fluid and velocity of the fluid relative to the immersed body all contribute to the generation of lift. The velocity of the fluid is constant for both trials, but it is known that higher velocities correlate to larger hydrodynamic forces. Fluid viscosity and velocity in terms of surfing are all dictated by the waves and oceans. Since these are constants, other factors must be optimised to achieve greater lift performance.

The Thruster setup derives its name due to the fact it provides a forward thrust. This thrust comes from the two side fins. The overall lift force on the fin is biased slightly forward on an asymmetrical fin to begin with due to the foil. Increasing the Toe-In angle increases forward thrust to an extent, until the fin reaches a stall angle. At this point flow separates from the fin and reduces the lift dramatically.

Since the Single fin setup is only one fin, with no Cant or Toe-In, it will be producing less lift as opposed to the Thruster setup.

The Thruster setup will be providing more lift, but also has increased drag, consequently reducing the lift.

Figure 8. Vector forces of the side fins
providing the forward thrust.

CFD Analysis Observations

Computational Fluid Dynamics (CFD) is the of computers to help analyse and visualise problems in fluid dynamics. CFD can be used in many applications. For the purpose of this report, CFD will provide information to help visualise the fluid dynamics involved with two different fin configurations.

A wide range of information can be extracted using CFD, in both numerical and graphical data. Caution has to be exercised in order to not make first impression assumptions when considering images and data because they can be mis-leading. The results of CFD analysis of both the Thruster and Single fin configurations are depicted below.

Form Drag:

The first set of images is useful to investigate the form drag present in both fin configurations. Extreme form drag would be evident with a very high pressure at the leading edge of the object, and a very low pressure at the trailing edge. From these images it can be seen that a concentrated high pressure exists before the single fin.

Figure 10. Thruster plane cut depicting pressures.
Figure 9. Single fin plane cut depicting pressures.

The Thruster setup also has high pressure build up at the leading edge of all fins, but it is somewhat larger. The inherit angle of attack of the side fins due to their Toe-In could be the contributing factor. Both sets of fins do not display obvious low pressures behind the fins. This is most likely a result of the fins having an efficient trailing foil, reducing the low pressure behind the fin.

Since the Single fin has a lower average pressure at the leading edge, and with both side fins contributing heavily to form dram on the Thruster setup, it can be confirmed that the Single fin has less form drag.

Skin Friction and the Boundary Layer:

Certain Skin friction configurations would lead to types of Boundary layers being formed. A rougher skin would induce turbulent flow, and consequently reduce the chance of flow separation on the fin. Certain Boundary layer configurations have been used to achieve reduced drag in similar sports, such as skins on the hulls of yachts racing in the America’s Cup. CFD is able to provide us with physical properties of the boundary layer such as fluid velocity within the boundary layer, and size of the boundary layer itself.

Figures 11 & 12 provide us with valuable information in regards to the shapes and sizes of the boundary layers of the different fins.

Figure 11. Single fin plane cut, depicting velocity boundary layer profile / Figure 12. Thruster plane cut, depicting velocity boundary layer profile

From Figure 11 it can be seen that the boundary layer exists mainly the concave formed by the rear half of the fin foil. The Thruster side fins have a different shape, with the boundary layer being formed around the outside and inside edges, all over the fin.

CFD would be a useful tool in analysis of boundary layers, because with the aid of probe lines, the exact profile of the boundary layer can be seen. This would be beneficial in running one test, then slightly changing a variable, for example surface roughness, and then running the same test, and viewing the subsequent profiles.

Probe lines have been placed on the surface of the Single fin, and the side and centre fins of the Thruster setup. The probe lines extend out from the fin’s surface about 10 – 12mm, and the velocity profiles are depicted in the graphs below.