Side-Intake Piston Water Jet Propulsor - A Super Efficient Linear Thruster

Transcription

1 White Paper on Marine Propulsion Side-Intake Piston Water Jet Propulsor - A Super Efficient Linear Thruster Prepared by Dr. James C. Huan Optimax Dynamic, LLC April 24, 2013 Contact: james.c.huan@optimaxdynamic.com 1

2 1. ABSTRACT The white paper addresses a revolutionary idea and its feasible mechanism for marine propulsor of piston-cylinder type. The revolutionary idea, by the use of Side-Intake of water, achieved that the piston completes its recovering stroke in atmospheric air in the same time for water intake. The achievement made the current Side-Intake Piston Water Jet Propulsor work the same cycle as an oarsman strikes his oar to expel water and then recovers the oar in the air; however the current system accomplishes that under the vehicle s waterline. Because the recovering stroke completes in air, the energy loss during recovering stroke is negligible. Therefore, the current propulsor is able to unlimitedly attain the ideal efficiency of propulsion. Further, unlike working on nonlinear lifting surface theory, the thrust generation of the piston water jet is straightforward, which is just a linear displacement of water. Because of this, its efficiency will be nearly a constant. In other words, it is able to maintain thrust power proportional to the input power even as the operational state of the vehicle changes. The pistoncylinder setup in the Side-Intake Piston Water Jet Propulsor is also ideal for the maximum use of the vortex ring impulse associated to the impulsive jet flow, which will further increase the propulsion efficiency beyond the efficiency that only takes account of the linear momentum increase within the system. An innovative inner-ring rotational valve is proposed to make the Side-Intake of water achievable. The design of a 4-cylinder Side-Intake Piston Water Jet Propulsor with the Side- Intake idea and the inner-ring rotational valve is also introduced. 2. BACKGROUND For marine vehicle propulsion, propellers or impeller-driven water jets are mostly being used. The principle to generate thrust in water is to use some mechanism to do work in water in the aim to build up the useful water kinetic energy for thrust generation. The useful water kinetic energy for thrust generation comes from the speedup water velocity in line with the thrust direction. Marine propellers or marine impeller-driven water jets all depend on the spin of blades in water to build up the water kinetic energy. Because of the spin of blades in water, the kinetic energy built up in water is contributed not only from the speedup water velocity in line with the thrust axis but also from the swirl of water associated to the spin of the blades, not to mention some radial velocity generation also. Water kinetic energy due to the swirl of water doesn t contribute to the generation of thrust and therefore it is an energy waste. This principleembedded energy waste due to the spin of blades leads to the fact that such propulsors could hardly reach close to the ideal efficiency of propulsion no matter how much design optimization efforts are spent. The highly rotational water kinetic energy not only brings down the efficiency of the propulsor but also the source of blade surface cavitation and the helical vortices in the propulsor wake that generate water noise. Furthermore, the speedup of water velocity in the thrust-producing axis through the spinning of the blades works on the principle of a lifting foil. A foil requires an optimal angle of attack for maximum lift, likewise an optimal pitch angle distribution along blade s radius is required to have a maximum increase of the thrust-producing water kinetic energy. For a given design of propeller or impeller-driven water jet, it could hardly operate in optimal pitch angle distribution at all vehicle s operation conditions, e.g., various manoeuvrs, because in such a system from input power to thrust power is a highly nonlinear relation established through the solution of a highly nonlinear and exquisite fluid dynamic problem. For instance, the nonlinear lifting surface theory may be applied to the solutions to such a fluid dynamic problem. Once the 2

3 exquisite flow condition breaks down, the efficiency drops greatly. That is why a propeller or an impeller-driven water jet can only reach its highest efficiency at the design point. As the vehicle operates at off-design points or conditions, the efficiency of such propulsors degrades greatly. In other words, such propulsors could hardly offer the thrust power that is proportional to the input power. In real life, that fact reflects a weak or sluggish acceleration and manoeuvring of a marine vehicle equipped with such propulsors. Our forefathers had long before understood that to most effectively propel and offer almost linear propulsion power to his boat one should do what oarsmen do commonly seen in boat racing. In one propulsion cycle, an oarsman gives a powerful stroke of his oar to expel or discharge the water, which generates a reaction force, i.e., the thrust on the oar surface to push the boat, and then follows an effortless oar recovering stroke through atmospheric air. The reason of such a propulsion cycle being highly efficient is that the mechanical work done on the oar to expel the water only accelerates the water velocity in line with the thrust and the oar recovering through the air introduces negligible resistive energy loss. There also exists the use of piston or reciprocating water jet propulsors to propel marine vehicles. From the way of expelling or discharging water, such propulsors work in the same principle of oars. Similarly, the primary advantage of a piston water jet propulsor is that the mechanical motion of the piston is in line with the thrust axis and therefore such a motion builds up the water kinetic energy only from the speedup water velocity in line with the thrust generation. Because of this reason, such a propulsor has a nearly constant efficiency at any working condition or vehicle speed. This characteristic of a piston water jet is consistent with the common knowledge that the efficiency of a positive displacement pump is nearly constant and higher than an impeller-driven pump of same power. Unlike the oar recovering through atmospheric air, an issue relating to the efficiency of a piston water jet propulsor is the energy cost in the water intake process during the piston s back (or recovering) stroke. Prior arts of piston water jet propulsor all employ the water intake from the axial direction of the cylinder as the piston takes a back stroke, for example, through the openings on the piston. With the axial intake, the piston during its back stroke moves in a direct headwind of the intake flow, resulting in a large resistance to the piston s motion. The piston s mechanical work to overcome this resistance during the recovering stroke is an energy waste, which negatively affects the efficiency of the propulsor. 3. OBJECTIVES OF INVENTION The primary objective of the invention is to achieve that the piston moves in atmospheric air condition during its recovering stroke for water intake, and therefore leads to a negligible energy loss for water intake for a piston water jet propulsor. Another objective is to invent an open-close valve for the Side-Intake of water that makes the piston s recovering stroke through air achievable. A further objective is to achieve an actual design of the Side-Intake Piston Water Jet Propulsor that embodies the principle of the Side-Intake concept. All these achieved objectives results in the invention of a super efficient linear thruster for marine vehicle. 4. DESCRIPTON OF THE INVENTION 4.1. The Principle of Side-Intake The concept of Side-Intake of water for a piston water jet propulsor can be shown in a schematic diagram in Fig. 1. First, it requires a tube for a piston to do reciprocating motion 3

4 Figure 1: A schematic diagram for the processes of side-intake and discharge. inside. The tube could be, but not limited to, a cylinder; however the author will refer to such a tube as a cylinder for convenience throughout. The concept of the Side-Intake opens intake holes on the side and near the discharging end of the cylinder wall. An open-close valve must be installed to open and close the Side-Intake holes during the piston s strokes for intake and discharge respectively. The discharge end is completed with a jet nozzle. With a piston installed inside the cylinder, the system becomes a one-cylinder Side-Intake Piston Water Jet Propulsor. Fig.1-(a) shows the water intake process. In this process, the valve is in fully open position and the piston takes the back (or recovering) stroke, namely the piston moves toward left as shown in 4

5 the picture. Fig.1-(b) shows the process of water discharge through the jet nozzle for thrust generation. In this process, the valve is in fully closed position and the piston takes the forward (or discharging) stroke, namely the piston moves toward the right as shown in the picture. The principle feature for the Side-Intake concept is the separation of the inside of the cylinder to be a dry and a wet compartment by the piston at any moment during piston s motion. This feature can be explained with Fig.1-(a) and -(b). As shown in Fig.1-(a) and -(b), whether during intake or discharge, the left compartment of the cylinder separated by the piston is always dry and opens to the inside of a vehicle, which is in an atmospheric pressure condition, and on the other hand the compartment to the right of the piston is always wet containing the water. Because the left compartment of the cylinder is always opens to the atmospheric air condition, the piston only confronts atmospheric air during the recovering stroke for water intake, which requires a negligible energy. From hydrodynamic point of view, this characteristic of piston s recovering stroke through air for water intake achieves the same function as an oarsman recovers his oar in the air. However, the current Side-Intake for piston water jet propulsor achieves that function under the vehicle s water line. Following the description of the above, such a piston water jet propulsor, if with just onecylinder, will have no water intake during the discharge and also no water discharge during the water intake. To keep a continuous water intake and discharge, a Side-Intake Piston Water Jet Propulsor will take at least a pair of cylinders in an actual design. Figure 2: A schematic diagram for first principle analysis for a two-cylinder Side-Intake Piston Water Jet Propulsor First Principle Analysis To facilitate an analysis with first principles for a Side-Intake Piston Water Jet Propulsor, a schematic diagram for such a system with two cylinders that could maintain a continuous inflow and jet exit flow is shown in Fig. 2. First principles used in the analysis are the mass, momentum and energy conservation laws in a control volume. The control volume encloses the 5

6 water region from water coming into the system to water leaving out of the system at the jet exit, which is shown by the dash-dotted line in Fig.2. Note that this control volume is a constant at any moment of the pistons motion. Neglecting the elevation difference between the intake and discharge as well as water viscous effect, applying the first principles to this control volume leads to, Q Ap V p T Q V j V ) W p ( i 1 Q ( V 2 2 j 1 U 2 A 2 a ) o V o A j V j (1) (2) (3) U a is the ambient water velocity, which is the same as the vehicle s speed but in the opposite direction when considering the vehicle is fixed. Eqs.(1)-(3) govern the mass flow rate, the thrust generation and the piston s mechanical work added into water. Note that V j and V i are in the thrust axis. As it can be seen, the piston s mechanical work on such a system is the work done on the boundary of the control volume and required only during piston s forward stroke to discharge water as shown by the down-piston in Fig.2. During the piston s back stroke to intake water, as shown by the up-piston in Fig. 2., which moves to the left, the motion of that piston requires a negligible amount of work because the left compartment of the piston is always at atmospheric condition. The useful work is the product of vehicle s speed and the thrust, and therefore the efficiency of the propulsor is, W V V 2 2 useful 2 U a j i propulsor 2 2 (4) Wp V j Vi V j U a The first factor on the right side of Eq. (4) is the well-known ideal efficiency of propulsion for propeller or water jet. The second factor is considered to be the inflow effect on the propulsor efficiency. Because the area of the Side-Intake openings of the valve, A o, is made larger than the piston area, from the law of mass conservation, V i, will be very close to or even a bit less than U a if considering the boundary layer ingestion effect. Thus, the factor of the intake effect of a Side-Intake Piston Water Jet Propulsor could be greater than one and therefore gives a boost to the propulsor efficiency. The energy equation, Eq. (3), for the current Side-Intake Piston Water Jet Propulsor reveals the fundamental difference from those for the propeller and the impeller-driven water jet, or the axial-intake piston water jet. For propeller or impeller-driven water jet, the right side of Eq. (3) will have an additional term for the water kinetic energy due to water swirl velocities and for the axial-intake piston water jet, the right side of Eq. (3) will also have an additional term for the water resistant work on the piston during the intake. These additional and non-trivial energy costs increase the denominator in the efficiency equation, Eq. (4) and answers why the prior arts could hardly reach close to the ideal efficiency even though assuming that the prior and current arts could have the same inflow effect. 6

7 The first principle analysis demonstrated that the current Side-Intake Piston Water Jet Propulsor is able to achieve the ideal efficiency of propulsor in theory. However, it should be acknowledged that the analysis neglects the energy cost in the open and close of the open-close valve for water intake and discharge. For the current art to beat the efficiency of prior arts, a nontrivial question is to design an open-close valve that costs least energy, or at least less than the energy waste in prior arts, during opening and closing in water. An inner-ring rotational valve is invented and discussed in Section 5, which is expected to cost a negligible amount of energy to open and close in water. The above analysis is based on a steady water jet. It should also point out that the efficiency formula by Eq.(4) as well as the ideal efficiency of propulsion as indicated by the first factor on the right side of Eq. (4) or in text books considers only the water linear momentum increase within the system (from in inlet up to the exit) in the useful work calculation, which is true for steady flow systems. In reality, the piston motion is unsteady. Recent studies have proven that the water jet generated from an unsteady piston motion is able to form vortex rings in the jet exit flow, which through entraining the ambient flow mass and being accelerated will result in an additional increase of the axial water momentum. Because of this reason, the vortex rings generated from the water jet of unsteady piston motion will contribute to an additional thrust and therefore give a further increase of the propulsion efficiency, which is not taken into account in Eq.(4) or the ideal efficiency. A brief discussion on vortex ring and unsteady water jet is given in Section 4.3. Figure 3: Vortex ring formation in the wake of a starting jet from the work by Olcay, A.B. and Krueger, P.S. (2008) Water Jet from Unsteady Piston Motion Piston motion naturally has to employ a non-constant velocity profile or a velocity program, which is from velocity zero at the start of discharge to its peak and then back to zero at the end of discharge. Because of the incompressibility of the fluid, the velocity program of the piston motion in turn creates an impulsive water jet or a starting jet at the jet exit. It is a well known phenomenon that vortex rings will be generated when forcing fluid impulsively out of a nozzle into ambient fluid. Piston-cylinder arrangement is, thus, commonly used in experiments by researchers to generate starting jets and study vortex ring dynamics. Fig.3 taken from the work by Olcay, A.B. and Krueger, P.S. (2008) gives a typical view of a vortex ring formation and evolution as a column of water in the cylinder is ejected out by the piston to the ambient water. Vortex ring is a common natural phenomenon in fluid flow and has fascinated scientists for at least hundred years. Examples are puffs from a smoker, mushroom cloud in explosion, wake of fish tail flapping and even in blood flow of a pulsating human heart. The fundamental 7

8 aspects of vortex ring such as its size, evolution, circulation and stability were reported in the studies of Didden (1979), Auerbach (1987), Glezer (1988), and Glezer & Coles (1990). The reviews of researches on vortex rings by Shariff and Leonard (1992) and Lim and Nickels (1995) summarized much of the current understanding of vortex rings. A vortex ring is a concentrated region of flow vorticity with a closed-loop vortex line. In axisymmetric flows without swirl such as a starting jet generated from a piston-cylinder setup, the vortex rings only contain the azimuthal component of vorticity, which induces flow velocity in axial direction only and so does the axial direction impulse or thrust. Recently, there are increasing interests in the study of vortex ring formation in impulsive jet flow in relation to impulse, thrust and propulsive efficiency and its application to marine vehicle propulsion. One early contribution of the researches in this direction was made by Gharib, et al. (1998). Using a piston-cylinder device to study vortex ring formation in starting jets generated from various short to long of the piston stroke to diameter ratio (L/D), Gharib, et al. (1998) observed that for L/D sufficiently less than 4, there is only a single vortex ring in the jet flow, while for L/D larger than 4, the jet flow will generate a pinched-off leading vortex ring followed by a trailing jet. After the leading vortex pinches off, the on-going trailing jet just behaves like a steady jet flow. The L/D ratio can also be viewed as a non-dimensional time scale for completing one piston stroke. Their observation concluded that when this non-dimensional time scale is around the neighborhood of 4, referred to as the formation number in the paper, a pinch-off of the leading vortex ring from a trailing jet will occur, indicating that the vortex ring can no longer absorb any more vorticities emanating from the jet flow. In other words, the leading vortex ring contains the maximum circulation a vortex ring is able to acquire. Again using the piston-cylinder device, Krueger and Gharib (2003) further studied the relative contributions of the leading vortex ring and the trailing jet to the total impulse provided by the impulsive jet flow at various L/D ratios. The thrust of an impulsive or unsteady jet is the time average of the total impulse. The experiment results from Krueger and Gharib (2003) showed that the thrust contributed from the vortex ring is much higher than the thrust contributed from the trailing jet, which represents a steady jet mode, and the maximum thrust of an impulsive jet can be achieved at a L/D ratio just after the leading vortex pinches off or equal to the formation number. According to Krueger and Gharib (2003), the fact that vortex rings contribute to an increase of thrust or total impulse over a steady jet for a given average piston velocity is attributed to ambient flow mass entrainment into the vortex ring and an acceleration of the vortex ring due to the over-pressure at the jet exit. The existence of an over-pressure at the jet exit is the result of the pulsed-motion of the piston. An example of relying fully on the impulse from vortex rings for thrust generation to maneuver an underwater vehicle was found in a synthetic jet design in Krieg and Mohseni (2008). Their synthetic jet design relies on a plunger movement in a cylindrical water cavity to discharge and intake water from the same nozzle opening. Because the water discharge and intake are from the same opening, there is no net change of momentum flux from the jet velocity in the cycle, and therefore the thrust from momentum flux change of jet velocity is zero. However, the device does create a net positive momentum flux because of the impulse supplied by the vortex ring in the jet exit flow. The synthetic jet is thus also called a vortex ring thruster (VRT) in their paper. Because it does not use the linear momentum flux change through the system for thrust generation, a key mechanism in propeller, impeller-driven water jet as well as the current Side-Intake Piston Water Jet Propulsor to create substantial thrust for general motions of a marine vehicle, a VRT can only be used for low-speed marine vehicle maneuvering or for marine vehicle stationing. However, the VRT reported in Krieg and Mohseni (2008) is an actual 8

9 marine vehicle maneuvering device, which proved that vortex ring generated from impulsive jet is able to add additional thrust to the conventional marine propulsion system that relies on the linear momentum flux change in the system. Realizing that optimum vortex ring at the formation number generated from an impulsive jet can greatly increase propulsive efficiency, researches on using impulsive jet as a general marine propulsion system receive great attentions in the world. Most recently, Ruiz et al. (2011) tried to build up an impulsive jet system to be installed in a laboratory-scale submarine vehicle so as to accomplish a self-propelled vehicle with their impulsive jet propulsion system. The goal of their research was to study the propulsion efficiency of impulsive jets under vehicle s selfpropelled condition. In a laboratory-sized model, they used a propeller installed inside a model submarine hull to generate linear momentum flux change for thrust. The impulsive jet flow at the nozzle exit was achieved by a periodic close and open of the openings on the submarine hull in the upstream through a rotating shell on the hull. When the openings are constantly open, the system works in a steady jet mode, which is the same as an impeller-driven water jet. When the openings are periodically open and close during the spin of the propeller, the system works in an impulsive jet mode. The experiment results from Ruiz et al. (2011) showed that the impulsive jet was able to increase propulsive efficiency by over 50% greater than that of the steady jet through an optimum use of vortex ring. Their analysis model also pointed out that a substantial propulsion efficiency enhancement from the impulsive jet by more than 50% over a steady jet are the results of two primary mechanisms: (1) ambient fluid entrainment into the forming vortex ring; (2) the added mass generated by the downstream acceleration of the vortex ring due to the over-pressure created by the pulsing jet flow at the nozzle exit. These findings were in agreement with the analysis from Krueger and Gharib (2003). However, it should point out that their propulsion system whether operates in the impulsive jet mode or in the steady jet mode always has swirl loss because of the use of propeller and the baseline efficiency of their propulsive system in steady jet mode was not measured or provided in the paper. In summary, from the experimental and analytical studies of vortex ring formation in relation to impulse and thrust by Gharib, et al. (1998) and Krueger and Gharib (2003), to an actual design of VRT for low speed UUV maneuvering by Krieg and Mohseni (2008), and to the experiment tests of a self-propelled submarine powered by an impulsive jet propulsion system, though still using propeller, by Ruiz et al. (2011), all proved that impulsive jet or unsteady jet created from a typical piston-cylinder setup can have a substantial increase of thrust over a steady jet with the same power input especially when the impulsive jet operates around the formation number to generate pinched-off vortex rings. 5. A 4-CYLINDER SIDE-INTAKE PISTON WATER JET PROPULSOR There are many ways to design open-close valves to accomplish the current Side-Intake principle. A primary principle for the design of an open-close valve for the current application is of simplicity and minimum energy loss during the valve open and close process. The current design of the Side-Intake Piston Water Jet Propulsor employs an inventive inner-ring rotational valve for open-close actuated by an electric-magnetic actuator. The propulsion system is a 4-cylinder Side-Intake Piston Water Jet Propulsor. In Fig. 3 and Fig. 4, (1) is the jet nozzle; (2) is the 4 cylinders; (3) is the 4 inner ring rotational valves; 9

10 Figure 3: A side, break-away view of the Side-Intake Piston Water Jet Propulsor. Figure 4: A front, break-away view of the Side-Intake Piston Water Jet Propulsor. 10

11 (4) is the ball bearings; (5) is the permanent magnets installed on the inner ring rational valves; (6) is the 4 electrical coil winding pats in the electric-magnetic actuator; (7) is the 4 pistons; (8) is the 4 absorbing springs, one for each piston; (9) is the baffle cap. For this 4-cylinder Side-Intake Piston Water Jet Propulsor, each two piston-cylinder set is synchronized to move together. For example, one pair of the pistons takes the forward stroke to discharge water from the jet nozzle while the other pair is to take the recovering stroke to intake water from the Side-Intake openings. This can be seen in both Fig. 3 and Fig. 4. Each inner ring rotational valve has rows of ball bearings for easy rotation and two or four permanent magnet pads embedded in at 90 o apart along its circumference. The electric-magnetic actuator will make the inner-ring rotational valve to turn 90 o degree to open the valve before the intake stroke takes place and turn back or another 90 o degree to close the valve before the discharge stroke takes place. The rotational motion to open and close the valve cuts across the flow, which introduces resistive energy loss. However, because the inner-ring is made thin and the cross area for flow cutting is small. Comparing to a gross secondary flow generation due to the entire blades spin in propeller or impeller-driven water jet, the cutting motion of the inner ring valve, therefore, only excites a little local secondary flow. In addition, with the use of ball bearings for easy rotation, the energy cost to open and close the valve is expected to be very small. As indicated in Fig. 4, at this particular moment, the up- and down-cylinders have the inner-ring rotational valves in fully open position and the two pistons just start the recovering stroke for water intake, while the cylinders shown in the left and right have the inner-ring rotational valves in fully closed position and the two pistons just start the forward stroke for water discharging. Associated with Fig. 4, the pistons positions can be seen in Fig. 3 at this same moment. Each spring installed behind the piston is to absorb the potential energy from the water during the intake. Because the air behind the cylinder is at atmospheric condition and the cylinder is submerged in water at certain depth of water depending on the waterline level of the vehicle, during the water intake the water hydrostatic pressure will do the work on the piston that adds energy into the system and the spring is designed such that to absorb that energy. That same amount of energy stored in the spring will then return back into water during piston s discharging stroke. That spring is particularly necessary when the current propulsor is applied to powering deeply-submerged vehicles. 6. SUMMARY OF THE INVENTION The current Side-Intake Piston Water Jet Propulsor is characterized by the principle feature of the Side-Intake of water. The principle feature of Side-Intake of water in piston water jet propulsor is the separation of the cylinder into a dry and wet compartment at any time piston moves, and therefore achieves a negligible energy requirement for water intake because the piston just encounters atmospheric air during the recovering stroke. An efficient, simple and reliable inner-ring rotational valve is invented to achieve the Side-Intake of water for the current propulsion system. Further more, the principle of the Side- Intake of water together with the inner-ring rotational valve leads to the invention of the current Side-Intake Piston Water Jet Propulsor. 11

12 The current propulsor can be applied to either surface or underwater vehicles as a general thruster provider. The system can also turn to be a VRT automatically when the system works in the closed mode of the open-close valves for vehicle low-speed maneuvering. The prime mover to drive the piston s motion can either come from internal combustion engine or linear motor. Although it will be not difficult to design a standardized mechanical drive for using internal combustion engines to drive the Side-Intake Piston Water Jet Propulsor, it is preferred to use linear motors that work similar to solenoids to power each of the cylinders. The use of linear motors also eliminates the needs of the rods connecting the pistons and makes the system very compact. The current Side-Intake Piston Water Jet Propulsor together with linear motors as the prime mover offers an ideal propulsion system to a fully electrical powered ship or submarine. Finally, it is necessary to give a summary of the performance advantages of the current Side-Intake Piston Water Jet Propulsor. Through the first principle analysis for steady jet and the discussion on impulsive jet in Section 4, it is not difficult to realize that the current Side-Intake Piston Water Jet Propulsor is the most streamlined configuration to generate thrust in water with the potential not only to achieve the ideal efficiency but also to have a maximum increase of additional efficiency from impulsive jet dynamics, and remain such high efficiency even as the vehicle operation condition changes. The arguments to support this claim are summarized in the following. Firstly, the system eliminates the swirl loss as well as the loss from the recovering stroke of the piston motion so that the system is able to unlimitedly attain the ideal efficiency of propulsion in generating the thrust from the linear momentum increase within the system. Secondly, the system is a piston-cylinder setup, which is a natural and simplest device to generate and manipulate vortex rings for the maximum thrust enhancement from the vortex ring impulse. The thrust enhancement from the vortex ring impulse makes the system possibly reach super efficiency, a term here referred to as the efficiency higher than the ideal efficiency of propulsion. Thirdly, the system is a linear thruster meaning that the thrust power is able to maintain more or less a linear relation to the input power even when the vehicle operation condition changes. This is because of the fact that the linear work of the piston motion is directly exchanged to a linear displacement of water, leading to a linear momentum flux increase or thrust generation. Lastly, unlike existing positive displacement pumps that are generally designed for static pressure head rise but not for great flow rate generation, the piston motion in the current Side-Intake Piston Water Jet Propulsor is in line with the water flow so that the system can best accelerate water and therefore the system can be as compact as or even more compact than a propeller or impeller-driven water jet for generating necessary flow rate. 7. REFERENCES [1] Auerbach, D. (1987), Experiments on the trajectory and circulation of the starting vortex, J. Fluid Mech. Vol. 183, pp [2] Didden, N. (1979), On the formation of vortex rings: rlling-up and production of circulation, Z. Angew. Math. Phys. Vol. 0, pp [3] Gharib, Morteza, Rambod, Edmond and Shariff, Karim, (1998), A Universal Time Scale for Vortex Ring Formation, J. Fluid Mechanics, vol. 360, pp [4] Glezer, A. (1988), The formation of vortex rings, Phys. Fluids, Vol. 31, pp

13 [5] Glezer, A. & Coles, D. (1990), An experimental study of a turbulent vortex ring, J. Fluid Mech. Vol. 221, pp [6] Krieg, Michael and Mohseni, Kamran, (2008), Thrust Characterization of a Bioinspired Vortex Ring Thruster for Locomotion of Underwater Robots, IEEE Journal of Oceanic Engineering, Vol. 33. No. 2, pp [7] Krueger, Paul S. and Ghairb, M. (2003), The significance of vortex ring formation to the impulse and thrust of a starting jet, Physics of Fluids, Vol 15, No.5, pp [8] Lim, T. T. and Nickels, T. B. (1995), Vortex rings, in Vortices in Fluid Flows (edited by S. I. Green), Kluwer. [9] Olcay, A.B. and Krueger, P.S., (2008) Measurement of Ambient Fluid Entrainment During Laminar Vortex Ring Formation, Experiments in Fluids, pp , Vol. 44. [10] Ruiz, Lydia A., Whittlesey, Robert W. and Dabiri, John O., (2011), Vortex-enhanced Propulsion, J. Fluid Mechanics, vol. 668, pp [11] Shariff, K. and Leonard, A. (1992), Vortex Rings, Ann. Rev. Fluid Mech. Vol. 24, pp