Shape optimization of Hydrofoils to maximize lift and minimize drag Sayan Saha 1, Mainak Lodh 2 and Sayani Sen 3 Department of Mechanical Engineering, Future Institute of Technology , Maulana Abul Kalam University of Technology, Kolkata -700152, India Abstract This paper presents the numerical investigations of water flow over 3D symmetrical and unsymmetrical hydrofoil. Steady flow of water over the hydrofoil s is simulated using the k -µ transport equation -based model. The results focus on change in lift and drag forces as a consequence of change of shape, profile of the foil, angle of attack and flow velocity of water around it.
The foils are tested at different angles of attack and different velocit ies of flow. Standard k -› model without any modifications are us ed for simplicity. This is done to determine the most efficient foil shape which generates sufficient lift force while producing as little drag force as possible. After determining the most efficient shape, the power required to operate these foils on a bo at was also calculated so as to get an idea of the reduction of required power.
Keywords Hydrofoil, lift, drag, k -µ transport equation, numerical study, Ansys, shape of hydrofoil . Introduction A hydrofoil is simply a wing or a vane placed underneath the hull of a boat, the primary function of which is to lift the hull of the boat out of the water. In doing so, the drag force created by the friction between the hull of the boat and the water is greatly reduced, allowing the boat to travel fa ster while using much less propulsion power. The primary objective of using a hydrofoil in a boat is to make it more efficient. Whil e flattening the hull reduces the contact area between the hull and the water and helps to speed up the boat greatly, it mak es the boat unsteady. The boat becomes very hard to control even in slightly windy conditions a nd is prone to flipping over, if exposed to a wave of sufficient size. Since a hydrofoil lifts the hull clear off the water, there is no danger of flipping over due to loss of control. While a hydrofoil reduces the drag created by the hull of the boat with water due to fluid friction, it cannot eliminate the drag entirely. The drag force of the hull is simply replaced by the drag force endured by the hydrofoil its elf during its motion through the water. Currently, Hydrofoils are mainly used in water sports where these are used as appendages to existing watercrafts like surfing boards and catamarans. The reason hydrofoils are used so less is because current designs limit their use to lightweight water crafts as construction of hydrofoils require expensive carbon composite materials. Methodology Steady state numerical analysis was conducted for each foil shape . Based on the lift and drag forces generated by the foil under varying conditions of angle of attack and flow velocity of water around the foil, the foil shape was changed accordingly and the same analysis was performed on the newer shape. The goal is to develop a shape capable of generating more than 10000 N of lift force while producing as little drag force as possible. Firstly, a NACA0012 foil was numerically analysed. After obtaining the lift and drag forces from that foil, its shape was altered. In th is way 7 subsequent foil iterations have been generated all of which has been examined in exactly the same conditions. After obtaining the most efficient foil shape the power required to propel the foil through freshwater was calculated. CFD setup The steady flow field was solved with the help of commercially available ANSYS CFD 16.0. The inlet consisted of a specified velocity component of flow of water while the out let was set up as a constant pressure boundary. The remainingsides of the enclosur e were defined as a static no slip wall. The standard 2 equation k -µ transport model having the values of C1 and C2 epsilons as 1.44 and 1.92 respectively along with Prandlt number as 1. Hybrid initialization was used to initialize the case and 100 iterati ons of the calculations were performed to obtain the necessary data. For the analysis, a 2D mesh with triangular mesh elements was selected the minimum edge length of which is 4.0555e -003 m. Validation Before analysing the hydrofoils in ANSYS CFD a tex tbook mathematical problem from page 15 -11 of the book, Fluid Mechanics and Hydraulic Machines by Sukumar Pati was recreated in ANSYS CFD. The results obtained from the software closely matched those from the book. Results and Discussions The NACA0012 foil or foil 1 was tested in ANSYS CFD at 2 different speeds of water flow i.e. 5m/s and 10 m/s and at three different angles of attacks of 0 °, 5 °, and 10 °. Each of the foils have a span of 1.5 m and a maximum chord length of 0.5 m. Fig. 1 (NACA 0012 / Foil 1) After testing this foil in ANSYS CFD, upper and lower cambers having radius 3 m and 9 m respectively were added in order to make the foil profile more aggressive to generate higher lift force. The resultant foil shape came in the form of foil 2. Fig. 2 (Foil 2) Adding upper and lower cambers increased the lift force generated. This shape w as further modified to generate even higher lift forces by reducing the radius of upper and lower cambers to 1 m and 1.5 m respectively. The resultant shape obtained was named foil 3. Fig. 3 (Foil 3) While making the upper and lower cambers more aggressive increased the lift forces, the drag forces generated were also substantially higher. For this reason, the lower portion of the shape was changed so that it may be partially symmetrical to the upper camber in order to incur lower drag forces. The new shape was named as foil 4. Fig. 4 (Foil 4) This shape reduced the drag forces generated while suffering an acceptable loss of the li ft force. The lower symmetrical part of this shape was reduced to increase the lift. Furthermore, the circular front end was changed to an elliptical shape and the chord length was also reduced to 0.35 m. The upper and lower camber radius values were changed to 0.75 m and 2 m respectively This new shape is foil 5. Fig. 5 (Foil 5 ) The upper and lower camber radiuses of foil 5 were changed to 1 m and 2.5 m respectively in order to make the foil even thinner so as to reduce the drag forces produced. This shape is named as foil 6. Fig. 6 (Foil 6)The upper camber radius of foil 6 is increased to 1.75 m in orde r to make the foil even thinner , reducing drag. This new foil shape is named as foil 7. Fig. 7 (Foil 7) Foil 7 was so thin that it isn’t practical. Even though the drag force is reduced by making the foil thinner, the lift force gets substantially reduced as well. To solve this issue the upper camber radius of foil 7 was decreased to 1 m. The new foil shape is foil 8. Fig. 8 (Foil 8) The side by side comparison of the foils under varying conditions of flow velocity of water and angle of attack are presented in the following graphs. Fig. 9 (Lift and Drag forces of all the foils at 0 ° angle of attack and 5 m/s) Fig. 10 (Lift and Drag forces of all the foils at 0 ° angle of attack and 10 m/s) Fig. 11 (Lift and drag forces of all the foils at 5 ° angle of attack and 5 m/s) Fig. 12 (Lift and drag forces of all the foils at 5 ° angle of attack and 10 m/s) Fig. 13 (Lift and drag forces of all the foils at 10 ° angle of attack and 5 m/s) Fig. 1 4 (Lift and drag forces of all the foils at 10 ° angle of attack and 10 m/s) The lift and drag force data of foil 8 (since it provides the best results) under varying conditions of flow velocity of water and angle of attack is presented in the tabular form a s follows. 050010001500 0 50001000015000 1 2 3 4 5 6 7 8 Foil nos.Lift Drag 0200040006000 0 200004000060000 1 2 3 4 5 6 7 8 Foil nos.Lift Drag 0500100015002000 0 50001000015000 1 2 3 4 5 6 7 8 Foil nos.Lift Drag 02000400060008000 0 200004000060000 1 2 3 4 5 6 7 8 Foil nos.Lift Drag 0100020003000 0 5000100001500020000 1 2 3 4 5 6 7 8 Foil nos.Lift Drag 050001000015000 0 20000400006000080000 1 2 3 4 5 6 7 8 Foil nos.Lift DragTable 1 (Lift, drag produced and power required by two foil 8 hydrofoils) Angle of attack (±) Speeds Monitors 5 m/s 6 m/s 7 m/s 8 m/s 9 m/s 10 m/s 0° 5325.94 7670.008 10440.52 13637.92 17261.864 21331.64 Lift (N) 158.8 228.58 310.08 404.028 510.34 629.08 Drag (N) 1.064 1.838 2.908 4.332 6.156 8.432 Power (hp) 2.5 ° 7918.256 11405.72 15527.58 20284.294 25676.238 31703.36 Lift (N) 369 526.44 711.16 923.116 1162.16 1428.274 Drag (N) 2.472 4.234 6.672 9.898 14.02 19.144 Power (hp) 5° 10486.66 15105.71 20565.84 26866.392 34008.28 41990.714 Lift (N) 594.44 850.54 1151.8 1498.04 1889.3 2325.46 Drag (N) 3.984 6.8408 10.808 16.064 22.792 31.172 Power (hp) 7.5 ° 12953.46 18661.18 25408.59 33194.904 42020.3 51886.56 Lift (N) 894.736 1282.16 1738.34 2263.306 2856.92 3503.02 Drag (N) 5.996 10.312 16.31 24.27 34.466 46.956 Power (hp) 10 ° 15173.92 21858.25 29766.87 38896.89 49243.66 60808.6 Lift (N) 1254.74 1798.91 2440.46 3178.96 4014.114 4945.76 Drag (N) 8.408 14.468 22.898 34.09 48.426 66.28 Power (hp) An optimal combination of speed, required power and angle of attack is required, such th at the foiled boat can take off with the lowest combination of speed and power. For stability purposes, it is assumed that two foil 8 hydrofoils are attached to the boat hull. The take -off speeds are calculated by means of interpolation from the data obtained fr om ANSYS CFD. The variation of speed power and angle of attack is presented in the following graph. Fig. 15 (Variation of speed and power required with angle of attack of foil) From the graph, we may conclude that the lowest combination of speed and power can be found at approximately 3.6 ° angle of attack where the required speed to achieve lift -off will be around 6.5 m/s and power required is around 6.5 hp . From the concepts of Newtonian physics, required power is calculated by multiplying the drag force with the flow velocity of water. Conclusions 1. Unsymmetrical foil shapes generate higher lift and drag forces than a symmetrical foil. 2. Making the foil profile more aggressive yields higher lift forces but suffers from high drag forces as well. 3. With hydrofoils a boat uses only around 5 – 25% of power it originally required to travel through water. 4. Since required power is so low, the fuel efficiency will be substantially high. 5. Since required power is low, if full power is used, the hydrofoils will enable the boat to move at much higher speeds. 0246810 0° 2.5° 5° 7.5° 10° speed (m/s) and power (hp) angle of attackspeed powerAcknowledgements This project is supported by all the faculty members of the department of Mechanical Engineering of Future Instit ute of Technology. We express our sincerest gratitude to Prof. Bivas Mandal for guiding us with resources and ideas. References 1. Numerical Modelling of unsteady cavitating flows around a stationary hydrofoil ( Hindawi Publishing Corporation International Journal of Rotating Machinery Volume 2012, Article ID 215678,17 pages:10.1155/2012/215678). 2. 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