Patent Publication Number: US-9410542-B2

Title: Ultrasonic fluid pressure generator

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a National Stage of International Application No. PCT/SG2009/000488 filed Dec. 22, 2009, the contents of which are incorporated herein by reference in their entirety. 
     TECHNICAL FIELD 
     The present invention relates to an ultrasonic fluid pressure generator. It particularly relates to an ultrasonic fluid pressure generator for generating high fluid pressure head for use as a pump, a pressure regulator, a hydraulic actuator or a microfluidic device. 
     BACKGROUND OF THE INVENTION 
     Rotary centrifugal pumps are conventionally used in industrial applications to induce flow of fluids via a pressure difference. The maximum pressure head that can be obtained depends on the external diameter of the impeller and the speed of the rotating shaft. Consequently, for high pressure head applications, a large rotary centrifugal pump is required, leading also to high power consumption. 
     However, it is often not feasible to use a large-sized pump especially where space is a constraint. Furthermore, it is desirable to have as low a power consumption as possible to improve efficiency and save energy. 
     Due to its valveless nature, ultrasonic pumps have been proposed. As shown in  FIG. 1( a )  (prior art), an ultrasonic pump  1  comprises chiefly a tube  2  with a plate  3  positioned at a gap G from the tip  4  of the tube  2 . Either the tube  2  or the plate  3  is ultrasonically vibrated so as to create a displacement D in the gap G. This generates a pressure P in a region of the fluid  5  immediately between the tip  4  and the plate  3 , thereby pushing water into the tube  2  as shown by the block arrow. The pressure P generated is a function of several parameters such as the gap G, internal diameter ID of the tube  2 , vibration amplitude D and vibration frequency ƒ used. In an alternative embodiment, the ultrasonic pump comprises the tube  2  with an insertion rod  6  as shown in  FIG. 1( b )  (prior art). 
     As an example, an ultrasonic pump from Precision and Intelligence Laboratory of the Tokyo Institute of Technology uses a bending disk transducer to vibrate the plate  3 . This achieved a maximum pump pressure of about 2 mH 2 O (or 20 kPa) with a vibration velocity of 1.0 m/s and a gap size of 10 μm, obtaining a maximum flow rate of 22.5 mL/min with input power of 3.8 W. Another ultrasonic pump from the same source uses a vibrating tube  2  (with or without the insertion rod  6 ) to achieve a similar maximum pump pressure. Although prototypes have been developed, the maximum pump pressure is still low for many practical applications, such as micro channel cooling. 
     SUMMARY OF THE INVENTION 
     According to a first aspect, there is provided an ultrasonic fluid pressure generator for generating high pressure head in a fluid. The ultrasonic fluid pressure generator comprises a transducer comprising a piezoelectric actuator and a displacement amplifier, the displacement amplifier having a fluid channel therethrough, the displacement amplifier being connected to the piezoelectric actuator at one end and having a free vibrating tip at another end; a reflecting condenser disposed at the vibrating tip of the displacement amplifier to form a gap between the vibrating tip and a reflecting surface of the reflecting condenser; and a casing configured for establishing a standing wave in the fluid contained within the casing, the transducer and the reflecting condenser being at least in part within the casing. 
     The reflecting condenser is preferably configured for focusing sound waves and improving sound pressure magnitude between the vibrating tip and the reflecting condenser, and may include a rod projecting from the reflecting surface into the fluid channel of the displacement amplifier without contacting the displacement amplifier. The reflecting condenser may further be configured to moveably engage the casing for adjusting pressure magnitude in the fluid. 
     The displacement amplifier preferably has a decreasing external dimension from the end connected to the piezoelectric actuator to the end having the free vibrating tip. 
     The piezoelectric actuator may have a tubular configuration, and preferably comprises a fluid channel therethrough, the fluid channel of the piezoelectric transducer being in fluid connection with the fluid channel of the displacement amplifier. 
     The transducer is preferably affixed to the casing at its nodal position. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Exemplary embodiments will now be described with reference to the accompanying drawings, by way of example only, in which: 
         FIG. 1( a ) (prior art) is a schematic cross-sectional front view of a prior art ultrasonic fluid pump; 
         FIG. 1( b ) (prior art) is a schematic cross-sectional front view of another prior art ultrasonic fluid pump; 
         FIG. 2  is a schematic cross-sectional front view of an exemplary embodiment of an ultrasonic fluid pressure generator according to the present invention; 
         FIG. 3( a )  is a schematic cross-sectional front close-up view of a vibrating tip of the ultrasonic fluid pressure generator of  FIG. 2 ; 
         FIG. 3( b )  is the vibrating tip of  FIG. 3( a )  with a reflecting surface of a reflecting condenser; 
         FIG. 3( c )  is the vibrating tip of  FIG. 3( a )  with a short rod insert; 
         FIG. 3( d )  is the vibrating tip of  FIG. 3( a )  and the reflecting condenser of the ultrasonic fluid pressure generator of  FIG. 2 ; 
         FIG. 4  is a schematic view of alternative embodiments of a casing of the ultrasonic fluid pressure generator; and 
         FIG. 5  is an electric circuit diagram representing a transducer of the ultrasonic fluid pressure generator of  FIG. 2 . 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     An ultrasonic fluid pressure generator  10  capable of generating high pressure head as shown in  FIG. 2 , which is an exemplary embodiment of the invention, will now be described. As a result of the high pressure head that can be produced, the ultrasonic fluid pressure generator  10  may serve not only as a fluid pump, but may also be used as a pressure regulator, a hydraulic actuator or a microfluidic device. 
     As shown in  FIG. 2 , the exemplary embodiment of the ultrasonic fluid pressure generator  10  comprises a transducer  15 , a reflecting condenser  40  and a casing  50  enveloping the transducer  15  and the reflecting condenser  40 . The transducer  15  further comprises a piezoelectric actuator  20  and a displacement amplifier  30 . 
     The transducer  15  is configured for effecting one-dimensional longitudinal vibration in a fluid  12  contained within the casing  50  so that as sound waves propagate in the fluid  12 , pressure patterns are generated in the fluid  12 . Preferably, the transducer  15  has a power consumption as low as 1 Watt, a frequency range of 10 to 100 kHz and a vibration amplitude with an operational vibration velocity range of 0 to 5 m/s. The piezoelectric actuator  20  which serves as a driving component of the transducer  15  may be of a multilayer piezoelectric stack  20  as shown, or have a tubular configuration. Total length of the transducer  15  may be a multiple of a half a wavelength, while length of the piezoelectric actuator  20  is preferably a multiple of a quarter or half of a wavelength. The piezoelectric actuator  20  is preferably clamped between the displacement amplifier  30  and an end-cap  60  as shown. 
     The displacement amplifier  30  of the transducer  15  is connected to the piezoelectric actuator  20  at one end  32  while having a free vibrating tip  34  at another end. The displacement amplifier  30  has a fluid channel  36  therethrough, and is preferably made of a metal such as titanium or an equivalent for generating high vibration velocity while being corrosion resistant. The displacement amplifier  30  is configured to have a decreasing external dimension  38  from the end  32  connected to the piezoelectric actuator  20  to the end having the free vibrating tip  34 . In this way, high vibration amplitude is achieved at the vibrating tip  34  while requiring lower vibration velocity of the piezoelectric actuator  20 . Consequently, less heat is generated by the piezoelectric actuator  20 , thereby improving reliability of the transducer  15 . In the preferred embodiment, the piezoelectric actuator  20  and the end-cap  60  also comprise fluid channels  26  and  66  respectively, wherein all the fluid channels  36 ,  26 ,  66  are in fluid connection with one another, thereby forming a continuous through-hole in the transducer  15  as shown in  FIG. 2 . 
     By providing a displacement amplifier  30  with a vibrating tip  34  of a reduced cross-sectional area compared to the piezoelectric actuator  20 , an overall vibration amplification ratio of about 15 to 20 is obtained. This results in high pressure generation in the fluid  12  as pressure becomes focused at a region  13  of the fluid  12  around a rim  39  of the tip  34  as shown in  FIG. 3( a ) , where arrows indicate direction of fluid flow and dashed lines indicate a maximum pressure region  13 . 
     Impedance of the fluid pressure generator  10  is therefore adjusted by providing the displacement amplifier  30  so as to lower power required of the piezoelectric actuator  20 . Ensuring a smooth decrease in external dimension  38  of the displacement amplifier  30  results in lower overall system energy loss and also reduces bending vibration of the displacement amplifier  30 . 
     The reflecting condenser  40  engages the casing  50  to form a seal  41  between the reflecting condenser  40  and the casing  50 . The reflecting condenser  40  comprises a reflecting surface  42  that is preferably circular in shape and large enough to cover the cross-sectional area of the amplifier tip  34 . The reflecting surface  42  may be flat as shown, or also curved. The reflecting condenser  40  is disposed at the vibrating tip  34  of the displacement amplifier  30  so as to form a gap  46  between the vibrating tip  34  and the reflecting surface  42 , as shown in  FIG. 3( b ) . Downward vertical flow as shown in  FIG. 3( a )  is thus reduced or eliminated by the reflecting surface  42  as can be seen in the absence of downwardly directed arrows in  FIG. 3( b ) . The size of the gap  46  may be adjusted by configuring the reflecting condenser  40  to moveably engage the casing  50  for adjusting pressure magnitude in the fluid region  13 , wherein movement of the reflecting condenser  40  may be actuated by appropriate means such as adjustment screws. 
     While a short rod R alone inserted into the fluid channel  36  of the transducer  15  reduces horizontal flow as shown in  FIG. 3( c ) , too long a rod R by itself will halt fluid flow up the fluid channel  36  as a result of downward flow being greater than upward flow around the rod R. In the preferred embodiment of the fluid pressure generator  10  of the present invention, therefore, the reflecting condenser  40  has a ⊥-shape, comprising a rod  44  together with the reflecting surface  42  as shown in  FIG. 3( d ) . The rod  44  projects from the reflecting surface  42  into the fluid channel  36  of the displacement amplifier  30  without contacting the displacement amplifier  30 . By providing the ⊥-shaped reflecting condenser  40 , useless flow in both the downward and horizontal directions is reduced or eliminated. A well defined flow path is thus created with the use of the ⊥-shaped reflecting condenser  40  together with the displacement amplifier  30 , thereby increasing efficiency. 
     By providing the reflecting surface  42  together with the rod  44 , the rod  44  may be of unlimited length within the fluid channel  36  of the displacement amplifier  30  as downward flow is prevented by the reflecting surface  42 . However, when the length of the rod  44  is a multiple of a quarter of the wavelength, the pressure wave is more focused at the vibrating tip  34 . 
     The ⊥-shaped reflecting condenser  40  also reduces the area of pressure distribution when compared to using only the reflecting surface  42  alone ( FIG. 3( b ) ) or the short rod R alone ( FIG. 3( c ) ). This is due to the ⊥-shaped reflecting condenser  40  providing a corner ring  47  that focuses energy generated by the transducer  15 . In the preferred embodiment as shown in  FIG. 3( d ) , the corner ring  47  has a sharp right angle which focuses pressure between itself  47  and the amplifier tip  34 . This produces a new area of focusing below the vertical flow path that more effectively directs fluid  12  into the fluid channel  36 . Other embodiments of the corner ring  47  such as a concave design may be provided to focus the pressure wave more effectively. 
     As shown in  FIG. 2 , the transducer  15  and the reflecting condenser  40  are enveloped by the casing  50 . The casing  50  is configured for establishing a standing wave in the fluid  12  contained in a liquid cavity  56  within the casing  50 . The liquid cavity  56  is defined or bound by the casing  50 , the displacement amplifier  30 , and the reflecting condenser  40 . The transducer  15  and the reflecting condenser  40  should therefore be at least in part within the casing  50 . For example, in an alternative embodiment, the piezoelectric actuator  20  may be external to the casing  50 . Wavelength of the standing wave established in the liquid cavity  56  may range from zero to infinity in any direction. 
     The casing  50  is provided with at least an inlet  52  for in-flow of the fluid  12 . In the embodiment shown in  FIG. 2 , the casing  50  is also provided with an outlet  54  for liquid out-flow, the outlet  54  being connected to the end-cap  60  of transducer  15  via an out-flow connecting tube  58 . The casing  50  is preferably cylindrical in shape and may have an inner diameter less than a quarter wavelength and a liquid cavity length being multiples of half a wavelength so as to create resonance of the fluid  12  in the cavity  56 . The casing  50  should be made of an acoustically hard material such as aluminium in order to reflect the sound wave generated in the fluid  12 , so as to reduce energy loss induced in the fluid  12 . In the preferred embodiment, the transducer  15  is affixed to the casing  50  to form a seal at a nodal position of the transducer  15  itself. The inlet  52  should be positioned on the casing so as not to affect the standing wave condition created in the fluid  12 . Alternative embodiments of the casing  50  are shown in  FIG. 4 , wherein the casing  50  may be spherical, semi-spherical, stepped, conical, and so forth. 
     By establishing a standing wave condition in the fluid  12 , the casing reduces power consumption required by the transducer  15 . This in turn increases sound pressure at the amplifier tip  34 . In an ideal case, the standing wave condition would not affect power consumption and vibration displacement of the transducer  15  as all the power will be reflected from the boundary. By forming a seal between the casing  50  and the transducer  15 , as well as a seal between the casing  50  and the reflecting condenser  40 , the generated sound wave is confined within the liquid cavity  56 . The displacement amplifier  30  thus forms a first order focusing, the reflecting condenser  40  a second order focusing and the casing  50  a third order focusing. 
     As shown in Table 1 below, with the casing alone, improvement in sound pressure can be up to two times the pressure obtained without the casing  50 , as a result of the casing  50  forming a reflective boundary condition in the fluid  12 . Using the casing  50  together with the reflecting condenser  40 , the sound pressure can be increased by 14 times as the casing  50  and reflecting condenser  40  together restrain and focus the sound wave in a limited space within the casing  50 , thereby producing high static pressure which induces fluid flow towards the outlet  54 . 
     
       
         
           
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                   
                 Pressure magnitude 
                 Pressure 
                   
               
               
                 Condition 
                 (dB) 
                 magnitude (kPa) 
                 Improvement 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 Without casing 
                 193 
                 89 
                 1 
               
               
                 With casing 
                 199 
                 178 
                 ~2 
               
               
                 With casing and 
                 216 
                 1262 
                 ~14 
               
               
                 reflecting 
                   
                   
                   
               
               
                 condenser 
               
               
                   
               
            
           
         
       
     
     To appropriately configure the fluid pressure generator  10  for optimizing performance, the piezoelectric transducer  15  is represented as an electric circuit model as shown in  FIG. 5 , where each section of the transducer  15 , i.e. the displacement amplifier  30 , the piezoelectric actuator  20  and the end-cap  60  are each represented by an appropriate electric circuit component accordingly. 
     In the circuit, Z tip  is the radiation impedance at the amplifier tip  34 . Z end  is the back load from the air. C o  is clamped capacitance of the piezoelectric actuator  20 , R o  is dielectric resistance, φ is electromechanical conversion coefficient (φ=S/L·d 33 /s 33   E ), ν tip  and ν end  are the vibration velocities at the amplifier tip  34  and an end of the actuator  20 , respectively. The parallel and series impedances Z in  FIG. 5  are given by the following expressions: 
     
       
         
           
             
               
                 
                   
                     Z 
                     1 
                   
                   = 
                   
                     j 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ρ 
                       1 
                     
                     ⁢ 
                     
                       c 
                       1 
                     
                     ⁢ 
                     
                       S 
                       1 
                     
                     ⁢ 
                     tan 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         
                           k 
                           1 
                         
                         ⁢ 
                         
                           l 
                           1 
                         
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
             
               
                 
                   
                     Z 
                     
                       1 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       a 
                     
                   
                   = 
                   
                     
                       
                         - 
                         j 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ρ 
                         1 
                       
                       ⁢ 
                       
                         c 
                         1 
                       
                       ⁢ 
                       
                         S 
                         1 
                       
                     
                     
                       sin 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         k 
                         1 
                       
                       ⁢ 
                       
                         l 
                         1 
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
             
               
                 
                   
                     Z 
                     2 
                   
                   = 
                   
                     j 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ρ 
                       2 
                     
                     ⁢ 
                     
                       c 
                       2 
                     
                     ⁢ 
                     
                       S 
                       2 
                     
                     ⁢ 
                     tan 
                     ⁢ 
                     
                       
                         
                           k 
                           2 
                         
                         ⁢ 
                         
                           l 
                           2 
                         
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
             
               
                 
                   
                     Z 
                     
                       2 
                       ⁢ 
                       a 
                     
                   
                   = 
                   
                     
                       
                         - 
                         j 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ρ 
                         2 
                       
                       ⁢ 
                       
                         c 
                         2 
                       
                       ⁢ 
                       
                         S 
                         2 
                       
                     
                     
                       sin 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         k 
                         2 
                       
                       ⁢ 
                       
                         l 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   
                     Z 
                     3 
                   
                   = 
                   
                     j 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ρ 
                       3 
                     
                     ⁢ 
                     
                       c 
                       3 
                     
                     ⁢ 
                     
                       S 
                       3 
                     
                     ⁢ 
                     tan 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         
                           nk 
                           3 
                         
                         ⁢ 
                         
                           l 
                           3 
                         
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
             
               
                 
                   
                     Z 
                     
                       3 
                       ⁢ 
                       a 
                     
                   
                   = 
                   
                     
                       
                         - 
                         j 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ρ 
                         3 
                       
                       ⁢ 
                       
                         c 
                         3 
                       
                       ⁢ 
                       
                         S 
                         3 
                       
                     
                     
                       sin 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         nk 
                         3 
                       
                       ⁢ 
                       
                         l 
                         3 
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
             
               
                 
                   
                     Z 
                     4 
                   
                   = 
                   
                     j 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       ρ 
                       4 
                     
                     ⁢ 
                     
                       c 
                       4 
                     
                     ⁢ 
                     
                       S 
                       4 
                     
                     ⁢ 
                     tan 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         
                           k 
                           4 
                         
                         ⁢ 
                         
                           l 
                           4 
                         
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
             
               
                 
                   
                     Z 
                     
                       4 
                       ⁢ 
                       a 
                     
                   
                   = 
                   
                     
                       
                         - 
                         j 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         ρ 
                         4 
                       
                       ⁢ 
                       
                         c 
                         4 
                       
                       ⁢ 
                       
                         S 
                         4 
                       
                     
                     
                       sin 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         k 
                         4 
                       
                       ⁢ 
                       
                         l 
                         4 
                       
                     
                   
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     In the above expressions, ρ i , c i , S i , k i , l i  (i=1, 2, 3, 4) are density, sound speed, area of cross section, wave number and length for each section respectively, while n is the number of elements in the piezoelectric stack forming the piezoelectric actuator  20 . Before solving the circuit, the following parameters are defined: 
     
       
         
           
             
               
                 
                   
                     Z 
                     5 
                   
                   = 
                   
                     
                       
                         Z 
                         
                           1 
                           ⁢ 
                           a 
                         
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             Z 
                             1 
                           
                           + 
                           
                             Z 
                             2 
                           
                         
                         ) 
                       
                     
                     
                       ( 
                       
                         
                           Z 
                           
                             1 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             a 
                           
                         
                         + 
                         
                           Z 
                           1 
                         
                         + 
                         
                           Z 
                           2 
                         
                         + 
                         
                           Z 
                           
                             2 
                             ⁢ 
                             a 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
             
               
                 
                   
                     Z 
                     6 
                   
                   = 
                   
                     
                       
                         Z 
                         
                           2 
                           ⁢ 
                           a 
                         
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             Z 
                             1 
                           
                           + 
                           
                             Z 
                             2 
                           
                         
                         ) 
                       
                     
                     
                       ( 
                       
                         
                           Z 
                           
                             1 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             a 
                           
                         
                         + 
                         
                           Z 
                           1 
                         
                         + 
                         
                           Z 
                           2 
                         
                         + 
                         
                           Z 
                           
                             2 
                             ⁢ 
                             a 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
             
               
                 
                   
                     Z 
                     7 
                   
                   = 
                   
                     
                       
                         Z 
                         
                           1 
                           ⁢ 
                           a 
                         
                       
                       ⁢ 
                       
                         Z 
                         
                           2 
                           ⁢ 
                           a 
                         
                       
                     
                     
                       ( 
                       
                         
                           Z 
                           
                             1 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             a 
                           
                         
                         + 
                         
                           Z 
                           1 
                         
                         + 
                         
                           Z 
                           2 
                         
                         + 
                         
                           Z 
                           
                             2 
                             ⁢ 
                             a 
                           
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
             
               
                 
                   
                     Z 
                     8 
                   
                   = 
                   
                     
                       Z 
                       1 
                     
                     + 
                     
                       Z 
                       tip 
                     
                     + 
                     
                       Z 
                       5 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
             
               
                 
                   
                     Z 
                     9 
                   
                   = 
                   
                     
                       Z 
                       6 
                     
                     + 
                     
                       Z 
                       2 
                     
                     + 
                     
                       Z 
                       3 
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
             
               
                 
                   
                     Z 
                     10 
                   
                   = 
                   
                     
                       Z 
                       3 
                     
                     + 
                     
                       Z 
                       4 
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
             
               
                 
                   
                     Z 
                     11 
                   
                   = 
                   
                     
                       Z 
                       end 
                     
                     + 
                     
                       Z 
                       4 
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
             
               
                 
                   
                     Z 
                     f 
                   
                   = 
                   
                     
                       
                         
                           Z 
                           8 
                         
                         ⁢ 
                         
                           Z 
                           7 
                         
                       
                       
                         
                           Z 
                           8 
                         
                         + 
                         
                           Z 
                           7 
                         
                       
                     
                     + 
                     
                       Z 
                       9 
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
             
               
                 
                   
                     Z 
                     b 
                   
                   = 
                   
                     
                       
                         
                           Z 
                           
                             4 
                             ⁢ 
                             a 
                           
                         
                         ⁢ 
                         
                           Z 
                           11 
                         
                       
                       
                         
                           Z 
                           
                             4 
                             ⁢ 
                             a 
                           
                         
                         + 
                         
                           Z 
                           11 
                         
                       
                     
                     + 
                     
                       Z 
                       10 
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     The circuit is then solved to obtain important parameters as listed below, where: 
     impedance of vibration system is 
                   Z   =           Z   f     ⁢     Z   b           Z   f     +     Z   b         +     Z     3   ⁢   a                 (   16   )               
velocity at the end is
 
                     v   end     =         Z     4   ⁢   a           Z     4   ⁢   a       +     Z   11         ⁢       Z   f         Z   f     +     Z   b         ⁢       φ   ⁢           ⁢   V     Z               (   17   )               
velocity at the tip  34  is
 
                     v   tip     =         Z   7         Z   7     +     Z   g         ⁢       Z   b         Z   f     +     Z   b         ⁢       φ   ⁢           ⁢   V     Z               (   18   )               
and power consumption of the transducer  15  is
 
     
       
         
           
             
               
                 
                   P 
                   = 
                   
                     
                       1 
                       2 
                     
                     ⁢ 
                     
                       ( 
                       
                         
                           1 
                           
                             R 
                             0 
                           
                         
                         + 
                         
                           
                             Re 
                             i 
                           
                           ( 
                           
                             
                               φ 
                               2 
                             
                             Z 
                           
                           ) 
                         
                       
                       ) 
                     
                     ⁢ 
                     
                       
                         V 
                         2 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     Table 2 below shows experimental performance results of the fluid pressure generator  10  under different conditions. 
     
       
         
           
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                   
                 Power 
                   
                   
               
               
                   
                 consumption 
                 Flow rate 
                 Pressure head 
               
               
                 Condition 
                 (W) 
                 (mL/min) 
                 (mH2O) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 Without casing; 
                 ~6 
                 3.2 
                 0.01 
               
               
                 without reflecting 
                   
                   
                   
               
               
                 condenser 
                   
                   
                   
               
               
                 Without casing; with 
                 ~1.5 
                 9.2 
                 1.6 
               
               
                 flat reflecting 
                   
                   
                   
               
               
                 condenser 
                   
                   
                   
               
               
                 With casing; with ⊥- 
                 ~0.6 
                 9.2 
                 24 
               
               
                 shaped reflecting 
                   
                   
                   
               
               
                 condenser 
               
               
                   
               
            
           
         
       
     
     It can be seen that where a flat reflecting condenser is used without a casing, the ultrasonic pressure generator  10  is effectively the same as the prior art ultrasonic fluid pump as shown in  FIG. 1( a ) (prior art) and achieves only a pressure head of 1.6 mH 2 O. 
     However, by providing the casing  50  together with the ⊥-shaped reflecting condenser  40  in the ultrasonic pressure generator  10  of the present invention, for the same flow rate of 9.2 mL/min, a pressure head of 24 mH 2 O is achieved while power consumption is reduced from 1.5 W to 0.6 W. This is an improvement of 15 times the pressure head that can be obtained by a known ultrasonic pump, while reducing power consumption by 2.5 times. 
     Furthermore, as shown in Table 3 below, in comparison with three different centrifugal pumps, it can be seen that for an equivalent power consumption of around 1 W, the RS M200-S-SUB having small external dimensions of 15.7×15.7×28.5 mm can only reach a pressure head of 1.9 mH 2 O, while the ultrasonic fluid pressure generator  10  of the present invention achieves a maximum pressure head of 30 mH 2 O, an improvement of nearly 16 times for the same power consumption. 
     
       
         
           
               
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                   
                   
                 Power 
                   
               
               
                   
                   
                 consumption 
                 Pressure head 
               
               
                 Device 
                 Dimension (mm) 
                 (W) 
                 (mH 2 O) 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
            
               
                 Centrifugal pump 
                 15.7 × 15.7 × 28.5 
                 0.8-1.5 
                 1.9 
               
               
                 RS M200-S-SUB 
                   
                   
                   
               
               
                 Centrifugal pump 
                  108 × 90 × 88 
                 24 
                 3.1 
               
               
                 SWIFTECH 
                   
                   
                   
               
               
                 MCP655 
                   
                   
                   
               
               
                 ZHEJIANG LEO 
                  383 × 233 × 278 
                 1100 
                 33 
               
               
                 CO., LTD., Micro 
                   
                   
                   
               
               
                 Centrifugal pump 
                   
                   
                   
               
               
                 Ultrasonic Fluid 
                 OD16 × 120 
                 ~1 
                 30 
               
               
                 Pressure Generator 
               
               
                   
               
            
           
         
       
     
     Comparing the ultrasonic fluid pressure generator  10  of the present invention with a centrifugal pump of similar size such as the SWIFTECH MCP655, the centrifugal pump consumes some 24 times more power while achieving a pressure head of about 10 times less. 
     To achieve a similar pressure head as the ultrasonic fluid pressure generator  10  of the present invention, it can be seen that a much bigger centrifugal pump such as the ZHEJIANG LEO CO., LTD., micro centrifugal pump will be required, which consumes over 1000 times the power used by the ultrasonic fluid pressure generator  10  of the present invention. 
     The performance of the ultrasonic fluid pressure generator  10  of the present invention thus greatly exceeds that of all known embodiments of existing ultrasonic fluid pumps, as well as known embodiments of centrifugal pumps having an equivalent size, or power consumption, or pressure head output. 
     It should be appreciated that the invention has been described by way of example only and that various modifications in design and/or detail may be made without departing from the scope of this invention.