Abstract:
A device for transmitting ultrasonic energy to a liquid or pasty medium, comprising an alternating current generator ( 23 ) intended to operate in a frequency range of 1 to 100 kHz, a magnetostrictive or piezoelectric transceiver ( 12 ) capable of producing under the generator output AC voltage longitudinal high frequency mechanical vibrations, a waveguide ( 27 ) in the form of a cylindrical rod capable of being stimulated by said transceiver for generating longitudinal harmonic vibrations, and a cavity resonator ( 17 ) acoustically coupled with the waveguide and in a tubular form for converting said longitudinal harmonic vibrations into transversal vibrations relative to the longitudinal axis ( 14 ), the wave power of which can be injected into the medium to be submitted to sonicating. Said cavity resonator ( 11 ) is designed in such a way the resonance requirement is met both for the longitudinal and transversal self-vibrations of its envelope ( 18 ).

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The invention concerns a device for transmitting ultrasonic energy to a liquid or pasty medium. A device of this type is the subject matter of a co-owned, not published patent application (DE 195 39 195 A1). 
     2. Description of the Related Act 
     In the known devices in this technology (U.S. Pat. No. 4,016,436) there is provided on one side of a tubular shaped hollow chamber resonator a waveguide, which by means of a piezoelectric transducer, which for its part converts electrical alternating current voltage (a.c. voltage, hereafter alternating current) output signals of an alternating current generator into longitudinal mechanical oscillations, is excitable to resonant longitudinal oscillations. Onto this transducer, a hollow chamber resonator is mechanically rigidly acoustically coupled in a flange-shaped area of the transducer. 
     In a further device of similar type (U.S. Pat. No. 5,200,666), ultrasonic energy is transmitted on both ends of the tubular shaped resonator, which is provided for conversion of longitudinal oscillations into transverse oscillations, by means of respectively one transducer. 
     It is also known (U.S. Pat. No. 4,537,511) to employ a tubular shaped hollow chamber resonator, which is closed on both ends and from one side is acted upon by ultrasound transmitted by a transducer. 
     In all of these devices, the length of the hollow chamber resonator is selected similarly in a first approximation according to the equation 
     
       
           L=nc   0 /2 f   r   (A) 
       
     
     in which n represents a whole number, c 0  represents the sound velocity in the rod shaped resonator, and f r  represents the mechanical resonance frequency of the waveguide employed for introduction of ultrasound into the resonator and acoustically coupled with a transducer. The sound velocity c 0 , is provided by the equation 
     
       
           c   0 ={square root over ( E +L /ρ)}  (B) 
       
     
     in which E represents the modulus of elasticity (Young&#39;s Modulus) and ρ represents the specific weight of the resonator material. 
     In so far as sub-optimal results are achieved by the selection of the resonator length according to the first mentioned equation (A), it is conventional to use experimental attempts to determine the correction of the resonator length, which process, however, is only rational or justifiable, when subsequently a larger number of such devices are to be constructed with this optimized length as determined by experimental attempts. Special devices, which are only constructed in small quantities, are thus very expensive. In addition to this, it may occur that during such a process the result is often times relatively far from the theoretical optimum, which is however taken into consideration, since the device can be suitably produced for the intended purpose by employment of a high output frequency generator and transducer. However, these devices are expensive as a result of the necessity of over-dimensioning their electronic supply and transducer. 
     SUMMARY OF THE INVENTION 
     It is thus the object of this invention, to provide a design for the above-mentioned device, which produces an economically high transmission efficiency and, after which it has once been designed, there is no, or at least no significant, requirement for follow-up processing in order to arrive at dimensions for an operation with optimal working efficiency, in particular, a device having a pre-determined design which operates with a working efficiency which is close to the optimal working efficiency. 
     The deviation of the resonator length from the relation (A) could be relatively small, so that the inventive arrangement with respect to the equation (A) produces only a correspondingly minimal improvement, but it could however in practical cases also deviate by almost 40% from the result obtainable by the equation (A), so that, compared with such a case, the inventive design or arrangement provides a substantially improved result. 
     Also, for the closed design of the hollow chamber resonator, by the inventive arrangement of its length L, its outer diameter D, and its wall thickness a very precise tuning to the resonance requirements can be achieved. In the closed configuration of the hollow chamber resonator, this can be flushed with a liquid cooling medium and can be advantageously employed in this case for ultrasonic treatment of molten metals, in order to achieve a high as possible fineness and homogeneity of the grain size in the cooled, “hardened”, condition of the treated material. 
     There can be achieved in particular for the ultrasonic treatment of fluids an advantageous intensification of the cavitation bubble formation in the material being treated. 
     The design of the device provides the advantage of a substantially homogenous distribution of the ultrasonic energy radiated into the material being treated. 
     In the design of the resonator of the inventive device, there is a transport effect along the resonator faults, which leads to the result of a more even or homogenous treatment of the “flowing” material. 
     By the “eccentric” arrangement of the resonator inner chamber as opposed to the central longitudinal access of its outer jacket surface, there is achieved a directionality effect with respect to the radiated ultrasonic field of such a type, that more ultrasound energy is radiated through the thinner walled area of the resonator jacket than through the thicker walled jacket area. The device following the basic concept of the invention and in certain cases embodiments comprised of multiple hollow chamber resonators, overall longitudinally extending rod shaped ultrasound source has the advantage of its space-saving arrangement of the transducer within the resonator elements and offers also the possibility of radiating particularly high sound capacities into the material being treated. In combination herewith, it is advantageous or useful to employ alternating current controlled transducers as the voltage-sound converter and therein to control or drive the transducers adjacent to each other in the longitudinal direction of the ultrasound source counter-phasic or in phase opposition. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Further details and characteristics of the invention can be seen from the description of embodiments on the basis of the drawing. There is shown: 
     FIG. 1 a first embodiment of the inventive device for introduction of ultrasound into a fluid medium, with a magneto-strictive transducer, which by means of a waveguide system is coupled to a cylindrical-tubular shaped hollow chamber resonator, 
     FIG. 1 a  the amplitude distribution of longitudinal and transverse ultrasound oscillations, to which the transducer and resonator are excitable, 
     FIG. 2 an embodiment of an inventive design with piezoelectric transducers positioned or oriented within hollow chamber resonator elements, 
     FIGS. 3 a-   3   e  special design of hollow chamber resonators, which can be employed in devices according to FIG. 1 and 2, 
     FIG. 4 a resonator with cooling system. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     In FIG. 1, reference number  10  refers to an overall device, by means of which ultrasound in the frequency range of 5-50 kHz can be coupled or introduced into a fluid medium  11 , which can be a thin fluid or paste or also fluid-like, for example fine particle powder. The device includes a transducer indicated by reference number  12 , which converts electrical energy in the form of alternating voltage or as the case may be alternating current into (ultra-)sonic energy, via which the overall with  13  indicated waveguide system is brought to longitudinal oscillations, that is, oscillations of which the deflections occur in the direction of the central longitudinal access  14  of the device  10 , of which the amplitude progress or course is given by the . . . indicated distribution curve  16  of FIG. 1A in relation to the geometric measurement or dimensions of the transducer  12 , the waveguide system  13  and a thereto acoustically coupled hollow chamber resonator  17 , which for its part is excited to longitudinal and transverse ultrasound oscillations by longitudinal oscillations of the waveguide system  13 , that is, also to oscillations to the resonator jacket  18  of which the deflections occur radially with respect to the central longitudinal axis  14  of the device  10 . The amplitude distribution of this transverse oscillation, to which the hollow chamber resonator  17  is excitable, is shown in the continuous or solid amplitude-distribution curve  19  in FIG.  1 A. The hollow chamber resonator  17  is so arranged or designed, that with respect to the longitudinal as well also with respect to the transverse own oscillations of its represented embodiment in essentially, that is in a large part along its length L, cylindric-tubular shaped jacket  18  satisfies the resonator condition. 
     For the special embodiment shown in FIG. 1, it is pre-conceived, that the transducer  12  is constructed as a magneto-strictive transducer of already known construction type, of which essentially schematic indicated oscillation body  21  is excited to an ultrasonic oscillation by radiation of its like-wise only schematically indicated field-winding system  22  in the tempo or cycle of the alternating current provided by an alternating current generator  23 . The oscillation body  21  of the transducer  12  is in a sense the strong or rigid oscillation-coupling fixedly connected with a truncated cone-shaped concentrator  24  of the waveguide system  13 , which for its part, that is, through the screw or thread connection  26  fixedly is coupled with a further, basically cylindrically shaped, like-wise as concentrator acting waveguide  27 , with which again the hollow chamber resonator  12  in a sense of a strong acoustic coupling is fixedly connected, whereby this connection can be realized by means of a not-shown threading. 
     The oscillation body  21  of the transducer, the therewith connected concentrator  24  and the further cylindrical waveguide  27  of the waveguide system  13  as well as the hollow chamber resonator  17  are designed based upon the same mechanical resonator frequency, upon which also the frequency of the alternating current used for radiation of the field development system  22  of the transducer  12  is tuned, which is supplied by the generator  23 . 
     In this tuning, the length of the oscillating body  21  of the transducer  12  measured in the direction of the longitudinal access  14  corresponds to a whole number multiple of the half-wave-length of the longitudinal acoustic oscillations in the magneto-strictive transducer material. In a conventional design of the oscillation body  21  the length corresponds to the half-wave-length of its resident longitudinal own oscillation. 
     Also, the axial expansion or extension of the truncated cone-shaped represented concentrator  24  corresponds in a conventional manner to the half-wave length of its longitudinal resonant own oscillation which, because of the material dependency of the oscillation frequency, can have another value than the resonator wave-length in the oscillation body  21  of the transducer. 
     Also, the axial length of the second waveguide  27  or, as the case may be, concentrator of the waveguide system  13  corresponds to the half-resonance-wavelength in the waveguide-material. This second wave-concentrator  27  has, over its entire length, except for a radial outer flange  28  extending only slightly in the axial direction, which is provided for fixing of the waveguide system  13  as well as the hollow chamber resonator  17  on a reactor vessel  29  which contains the fluid medium of  11 , the same outer diameter D o , which corresponds also to the outer diameter of the hollow chamber resonator  17 . 
     The second “cylindrical” wave concentrator  27  is formed as a “massive” cylinder on the side facing the first concentrator  24  and on its side facing the hollow chamber resonator  17  is formed pot-shaped, wherein the thickness δ of the second pot material  31  of the second wave concentrator  27  is the same as the thickness of the cylindrical resonator jacket  28 . The axial depth of the cylindrical pot jacket  31 , which transmits the oscillation concentration to the jacket of the hollow chamber resonator  17 , corresponds to a quarter of the resonator wave-length of the longitudinal oscillation in the material of the second wave concentrator  27 . In accordance therewith the securing flange  28  is provided in a nodal plane of the longitudinal acoustic oscillations, which via the second wave concentrator  27  are transmitted into the hollow chamber resonator  17 , which thereby both for longitudinal as well also as transverse oscillations is resonantly excited, through which action the ultrasonic treatment of the fluid medium  11  results. 
     The hollow chamber resonator  17  is closed off domed or hemispherically shaped at its end position farthest from the transducer  12 , wherein the outer radius R c  of this resonator closure corresponds to the value D 0 /2 and the thickness δ of this hemispherical shaped resonator closure  32  the thickness δ of the cylinder jacket shaped section  18 ′ of the resonator  18 . 
     In order to achieve optimal geometric dimensioning or measurements of the hollow chamber resonator  17 , it is necessary, that this satisfies the resonant condition both for longitudinal as well also for radial oscillation shapes, this under the condition, that the oscillation excitation that occurs by longitudinal acoustic oscillations of the above-mentioned frequency and that also the acoustic resistance of the load of the medium to be treated is adequately taken into consideration. 
     In accordance therewith, the measured length L of the hollow chamber resonator  17  from the ring shaped end surface  31  of the resonator jacket  18 , with which this connects to the cylindrical jacket shaped section  31  of the second wave concentrator  28 , and the farthest away point  34  of the hemispherical shaped resonator closure  32  is so selected, that it satisfies the following equation.                  L   =         C   lR       2        f   r              n        (     1   -       Δ                 L       1   +       1   +     Δ                 L               )           ;                n   =   1       ,   2   ,   3   ,   …           (   1   )                                
     In this equation, f r  represents the “resonance”-frequency, upon which the hollow chamber resonator  17  is to be based. That is generally determined by the frequency of the alternating current generator  23 , with which this works at the greatest effectiveness. 
     C lR  represents the sound velocity within the material of which the hollow chamber resonator is comprised. 
     It is determined by the following equation:                C   lR     =         E        (     1   -   v     )             ρ   R          (     1   +   μ     )            (     1   -     2      v       )                   (   2   )                                
     In this equation, E represents the Young&#39;s Modulus of Elasticity of the resonator material, μ represents the Poisson&#39;s transverse contraction co-efficient of the resonator material and ρ r  represents the thickness of the resonator material. 
     The outer diameter D 0  of the hollow chamber resonator  17  is selected in accordance with the following equation:                D   0     =         C   lr       π                   f   r         +     (     1   +     Δ                 D       )               (   3   )                                
     The size ΔL contained in the equation (1) and the size ΔD contained in Equation 3 satisfies the following relationship:                  Δ                 L     =       a   2         a   2     -       (     1   +     Δ                 D       )     2           ;           (   4   )                 Δ                 D     =             b   2     -     a   2           c   2     -   1         -   1             (     4   ′     )                                
     These relationships provide a very good approximation, when at the same time the secondary condition expressed in the following is satisfied:              L   ≤         δ        (       D   0     -   δ     )       ·     C   lR     ·     ρ   R           D   0          ρ   L          C   L                 (   5   )                                
     from which the wall thickness δ of the resonator is produced. 
     In Equation (5), C lr  represents the sound velocity in the resonator material, C L  represents the sound velocity in the “load” medium subjected to ultrasonic treatment and ρ L  represents the thickness of the medium  11  to be treated. The sizes a and b contained in the Equations (4) and (4′) are, determined at the same time as step point-coordinates of second functions a 1 (y) and a 2 (y), that is by finding a solution for: 
     
       
           a   1 ( b )= a   2 ( b )= a.   
       
     
     These functions will in the following for reasons of simplicity simply be characterized with a 1  and a 2  as functions of the common parameter y. They are implicitly yielded by the following relationships: 
     
       
         ξ( a   1   ,J   n )β( a   1 )+μ( a   1   ,N   n )(1− G ( a   1 ))−μ( y,J   n ) G ( a   1 )+μ( y,N   n )=0  (6/1) 
       
     
                         q        (       a   2     ,     J   n       )            β        (     a   2     )         +       q        (       a   2     ,     N   n       )            (     1   -     G        (     a   2     )         )       -           κ   t          (     a   2     )         κ                   l        (     a   2     )                [         q        (     y   ,     J   n       )            G        (     a   2     )         -     9        (     y   ,     N   n       )         ]         =   0           (6/2)                                K   t   2 ( x )= k   t   2   −k   2 ( x )  (6/3) 
       K   l   2 ( x )= k   l   2   −k   2 ( x )  (6/4) 
     
       
           k   2 ( x )= k   l   2   K   2 ( x )  (6/5) 
       
     
     
       
         
           
             
               
                 
                   
                     k 
                     
                       1 
                       , 
                       t 
                     
                   
                   = 
                   
                     
                       2 
                        
                       π 
                        
                       
                           
                       
                        
                       
                         f 
                         r 
                       
                     
                     
                       C 
                       
                         lR 
                         , 
                         t 
                       
                     
                   
                 
               
               
                 
                   (6/6) 
                 
               
             
             
               
                 
                   
                     
                       κ 
                       2 
                     
                      
                     
                       ( 
                       x 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         
                           ( 
                           
                             1 
                             - 
                             
                               2 
                                
                               v 
                             
                           
                           ) 
                         
                          
                         
                           ( 
                           
                             
                               b 
                               2 
                             
                             - 
                             
                               x 
                               2 
                             
                           
                           ) 
                         
                       
                       - 
                       
                         x 
                         2 
                       
                     
                     
                       
                         ( 
                         
                           1 
                           - 
                           
                             2 
                              
                             v 
                           
                         
                         ) 
                       
                        
                       
                         ( 
                         
                           
                             b 
                             2 
                           
                           - 
                           
                             x 
                             2 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   (6/7) 
                 
               
             
             
               
                 
                   
                     ξ 
                      
                     
                       ( 
                       
                         x 
                         , 
                         
                           Z 
                           n 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         z 
                         
                           N 
                           + 
                           1 
                         
                       
                        
                       
                         ( 
                         x 
                         ) 
                       
                     
                     - 
                     
                       
                         
                           
                             v 
                             2 
                           
                            
                           x 
                         
                         
                           
                             ( 
                             
                               n 
                               + 
                               1 
                             
                             ) 
                           
                            
                           
                             ( 
                             
                               1 
                               - 
                               v 
                             
                             ) 
                           
                         
                       
                        
                       
                         
                           Z 
                           n 
                         
                          
                         
                           ( 
                           x 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   (6/8) 
                 
               
             
             
               
                 
                   
                     q 
                      
                     
                       ( 
                       
                         x 
                         , 
                         
                           Z 
                           n 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                          
                         
                           
                             Z 
                             
                               n 
                               + 
                               1 
                             
                           
                            
                           
                             ( 
                             x 
                             ) 
                           
                         
                       
                       
                          
                         x 
                       
                     
                     - 
                     
                       
                         
                           ( 
                           
                             n 
                             + 
                             1 
                           
                           ) 
                         
                         x 
                       
                       · 
                       
                         
                           Z 
                           
                             n 
                             + 
                             1 
                           
                         
                          
                         
                           ( 
                           x 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   (6/9) 
                 
               
             
             
               
                 
                   
                     μ 
                      
                     
                       ( 
                       
                         x 
                         , 
                         
                           Z 
                           n 
                         
                       
                       ) 
                     
                   
                   = 
                   
                     
                       
                         Z 
                         
                           n 
                           + 
                           1 
                         
                       
                        
                       
                         ( 
                         x 
                         ) 
                       
                     
                     + 
                     
                       
                         
                           v 
                            
                           
                             [ 
                             
                               
                                 ϑ 
                                  
                                 
                                   ( 
                                   x 
                                   ) 
                                 
                               
                               - 
                               
                                 
                                   κ 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   x 
                                   ) 
                                 
                               
                             
                             ] 
                           
                         
                         
                           
                             ( 
                             
                               1 
                               - 
                               v 
                             
                             ) 
                           
                            
                           
                             
                               κ 
                               2 
                             
                              
                             
                               ( 
                               x 
                               ) 
                             
                           
                         
                       
                       · 
                       
                         
                            
                           
                             
                               Z 
                               
                                 n 
                                 + 
                                 1 
                               
                             
                              
                             
                               ( 
                               x 
                               ) 
                             
                           
                         
                         
                            
                           x 
                         
                       
                     
                   
                 
               
               
                 
                   (6/10) 
                 
               
             
           
         
                 
         
             
         
      
     
     with: θ(x=a 1  or a 2 )=1; θ(x=y)=c 2                  G        (   X   )       =         G   1          (     x   ,     N   n       )           G   1          (     x   ,     J   n       )                 (6/11)                                G   1 ( x,Z   n )=μ( x,J   n )[ξ( y,Z   n )+ξ( x,N   n )]−ξ( x,J   n )[μ( y,Z   n )+μ( x,N   n )]  (6/13) 
     
       
         
           
             
               
                 
                   C 
                   = 
                   
                     
                       C 
                       lR 
                     
                     
                       C 
                       t 
                     
                   
                 
               
               
                 
                   (6/14) 
                 
               
             
             
               
                 
                   
                     C 
                     t 
                     2 
                   
                   = 
                   
                     E 
                     
                       2 
                        
                       
                         
                           ρ 
                           R 
                         
                          
                         
                           ( 
                           
                             1 
                             + 
                             v 
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   (6/15) 
                 
               
             
           
         
                 
         
             
         
      
     
     The two first relationships (6/1) and (6/2) form a transcending equilibrium system for the function a 1 (y) and a 2 (y) in which J n  represents the known Bessel functions and N n  represents the likewise known Neumann&#39;s functions. These functions J n  and N n  have as independent variable respectively those variables a 1 , a 2 , or y with which they are associated with the further functions μ(x,Z n ), ξ(x,Z n ) and q(x,Z n ) . In this relationships “x” represents for the possible variables a 1 , a 2 , or y and Z n  represents the respective cylindrical functions namely the Bessel functions J n  or the Neumann&#39;s functions N n . 
     The functions ξ, q and μ are, with corresponding notation, respectively defined by the relationships (6/8), (6/9), and (6/10), wherein the function θ(x) contained in equation (6/10) is given by the following relationship: 
     
       
         θ( x=a   1  or  a   2 )=1 and θ( x=y )= c   2 . 
       
     
     For its part C is determined by the relationship (6/14), in which C lR  represents the sound velocity of the longitudinal oscillations in the resonator and C t  represents the sound velocity of the transverse ultrasonic oscillations in the resonator. This “transversal” sound velocity satisfies for its part the relationship (6/15), in which ρ R  represents the thickness of the resonator material, E represents the Young&#39;s Modulus of Elasticity and v represents the Posson&#39;s transverse contraction constant of the resonator material. 
     The functions β further mentioned in the equations (6/1) and (6/2) of which the variables can once be the function a 1  and once the function a 2 , is indicated in general form by the relationship (6/13). The functions G further contained in the equations (6/1) and (6/2) are given by the relationships (6/11) and (6/12). The function K 2  contained in the equation (6/10) are again given in general form by the relationship (6/7) and defined by the relationship (6/3), (6/4), (6/5) and (6/6), wherein the in the relationship (6/6) C 1R,t  represents on the one hand C 1R  and on the other hand C t . 
     Through the relationship (6/6) the wave count k 1  and k t  of the longitudinal and transverse oscillations of the resonator at the resonator frequency f r  are given. 
     The equation system (6/1) and (6/2) can be evaluated in simple manner by variation of the perimeter y. 
     The further illustrative embodiment of an inventive device for ultrasound treatment of liquid or pasty medium shown in FIG. 2, of which the details will now be made reference to, is analogous in construction and function to that discussed by reference to FIG. 1, so that a discussion can be limited to the differences with respect to the device  10  according to FIG.  1 . Insofar as the same reference numbers are employed for elements of the device  10 ′ according to FIG. 2 as occurred in the description of the device  10  of FIG. 1, this is intended to provide an indication of the constructional similarity and also a cross-reference to the description of the device  10  on the basis of FIG.  1 . 
     In the device  10 ′ according to FIG. 2 the ultrasound source indicated overall with  35  is comprised of a plurality of hollow chamber resonators, which are arranged along a common central longitudinal axis  14 ′ and fixedly connected with each other. Within an “outer” hollow chamber resonator  17 ′, of which the cylindrical jacket  18 ′ is provided with a assembly flange  28  for outer side securing to a centrally schematically indicated reactor vessel  29 , and a “inner” hollow chamber resonator  17 , which likewise is provided at the furthest within the reactor vessel in the represented, special embodiment has the same shape as that on the basis of FIG. 1 described hollow chamber resonator  17 , are provided multiple identically constructed hollow chamber resonators  17 ″ as intermediate elements, of which for simplification basically only one is represented. These “intermediate” hollow chamber resonators  17 ″ are basically of pot-shaped design with a stable floor  36  of thickness L b  and a tubular shaped cylinder jacket  18 ′. The various resonators  17 ,  17 ′ and  17 ″ have the same length L, the same thickness δ of their cylindrical jacket section and the same outer diameter D 0 , corresponding to the criteria of the on the basis of the embodiment according to FIG. 1 described arrangement criteria, wherein the floor thickness L B  must be selected to be small in comparison to the length L, which suffices as the design criteria with respect thereto (for example: L B ≦L/10). 
     The pot shape designed hollow chamber resonators  17 ″ provided between the outer hollow chamber resonator  17 ′ and the hemispherically shaped closed-off hollow chamber resonator  17  are in the area of their floor  36  and in the area of their open end section  37  provided with complimentarily designed outer threading  38  and inner threading  39  of the same axially protrusion L s , which is smaller than the floor thickness L B , by means of which they can be securely screwed together, in such a manner, that the outer floor surface of the one hollow chamber resonator  17 ″ is rigidly supported on an inner ring shoulder  42  of the adjacent hollow chamber resonator  17 ″. The same type of rigid connection is also provided with respect to the outer hollow chamber resonator  17 ′ and the inner, hemispherically shaped closed off hollow resonator chamber  17  with the respective adjacent “intermediate” resonator  17 ″. 
     In coaxial arrangement with the central longitudinal axis  14 ″ of the ultrasound source  35  there is coupled on the floor  36  of one of each of the intermediate-resonators  17 ″ and overall with  42  indicated ultrasound-transducer. Also the inner hollow chamber resonator  17  of the device  10 ′ is closed off by a floor plate  36 , onto which the transducer  42  taken up or received from the adjacent pot shaped hollow chamber resonator  17 ″ is coupled. 
     In the special embodiment according to FIG. 2, there is essentially to the outer hollow chamber resonator  17 ′ not an equivalent own transducer  42  provided. This on the one side pen tubular shaped designed hollow chamber resonator  17 ′ is likewise or at the same time supplied by the transducer  42 , which is rigidly connected to the floor  36  of the adjacent pot shaped resonator  17 ″, for example by means of a schematically indicated threaded connection  43 . 
     As transducer  42  there are employed in the device  10 ′ according to FIG. 2 in suitable manner piezoelectric transducers, which as electromechanical voltage-oscillation converters have an essentially schematically indicated, overall with  44  indicated piezoelectric column, which by driving with an alternating current is excitable to an in the direction of the central longitudinal axis  14 ′ extending “thick” oscillation, that is, longitudinal length changes, which via a transducer block  46 , by means of which the transducer  42  is connected or secured to the floor  36  of the respective adjacent hollow chamber resonator  17 ″ or as the case may be  17 , upon the respective jacket  18  or as the case may be  18 ′ or as the case may be  18 ″ of the respective hollow chamber resonator  17 ″ or as the case may be  17  or  17 ′ is transmissible, whereby this is excitable to longitudinal and transverse oscillations. 
     The device  10 ′ is particularly suitable for the ultrasonic treatment of fluid media in reactor vessels  29  which have a relatively large depth and which contain media in correspondingly large “layer”-thickness. 
     For discussion of a number of variations of resonator designs, which function both in the device  10  according to FIG. 1 as well also in the device  10 ′ according to FIG. 2, references now made to FIGS. 3 a  through  3   e.    
     The hollow chamber resonator  17   a . according to FIG. 3 a  has the base shape of a cylindrical tube, which over the major part of its length has a constant wall thickness δ, which has an outer diameter D 0  and a length L selected according to the relationship (1). In regular intervals, preferably in intervals L/2, wherein L is provided by the relationship (1) for n=1, the hollow chamber resonator  17   a  is provided with external, flange shaped ring ribs  47 , of which the radial height h and their in the direction of the longitudinal axis measured “axial” thickness  1  respectively is small in comparison to the outer diameter D 0  or as the case may be the axial separation L/2 of the ribs  47  to each other. “Small” herein means a fragment or fraction of about {fraction (1/10)}. 
     By means of these ring ribs  47 , which in the longitudinal sectional representation of FIG. 3 a  have a right angle contour with two circular or arch shaped peripheral edges  48 , there is produced, particularly in the area of these edges  48 , a more intensive cavitation-bubble formation in a fluid to be treated and therewith an improvement of the treatment-effectiveness. 
     The same applies in the same sense for the hollow chamber resonators  17   c  and  17   d  according to the FIGS. 3 c  and  3   d  with reference to a spiral shaped running outer rib  49  with for example triangular or trapezoid shaped cross-section (FIG. 3 c ) or for the outer structure of the resonator  17   d  according to FIG. 3 d  designed or constructed in the manner of a multi-phasic treading, in which a star shaped outer contour  51  of the hollow chamber resonator  17   d  results viewed in cross-sectional representation, according to the spiral shaped running concave ridges  52  and these against each other setting off, sharp or pointed, radial outer rib edges  53 ′ or ribs  53 . 
     The hollow chamber resonator  17   e  according to FIG. 3 e  has a resonator form similar to that of resonator  17   a , of which the inner space has a constant radius R i , in which however the outer radius R(z) is spatially varied according to the relationship                R        (   z   )       =       R   0     +     δ                   R   ·     sin        (     z     z   0       )                     (   7   )                                
     along the central longitudinal axis  54  seen as the z-coordinate. 
     In this relationship (7) R 0  refers to the central radius of the jacket  55  of the hollow chamber resonator  17   e , δ R  refers to the amplitude of the radius change and z 0  refers to the period length of the spatial radius variations of the resonator-outer surface  56 , viewed in the direction of the central z-axes  54 . It is understood, that the minimal value of the radius R(z) given by the relationship (7) must be larger than the radius R i  of the inner jacket surface of the hollow chamber resonator  17   e . In this configuration of the hollow chamber resonator  17   e  the periodicity of the “wave” structure of the resonator-outer surface  56  can also be significantly smaller than the resonator length L. 
     In distinction to the variations described on the basis of FIGS. 3 a  and  3   c  through  3   e , which, other than a spiral shaped structure (FIGS. 3 c  and  3   d ) are axially symmetrical with respect to the respective central longitudinal axis, the hollow chamber resonator  17   b  according to FIG. 3 b  has a design departing from the cylindrical symmetrical insofar that the central longitudinal axis  57  of its through-going cylindrical bore  58  outer axial with respect to the central longitudinal axis  59  of the outer cylindrical jacket surface  61  is provided, so that the resonator jacket  64  only with respect to one, with the central longitudinal axis  57  of the resonator hollow chamber  62  as well also the central longitudinal axis  59  of its outer jacket surface  61  containing longitudinal plane  63  is formed symmetrically. 
     In this design of the resonator jacket  64  the thickness thereof varies between a minimal value δ min  and a maximal value δ max . The effect achieved by this design of the resonator jacket  64  is comprised therein, that a directional characteristic of the radiation of the ultrasound waves is achieved, in such a manner, that in the thinner wall areas more ultrasound energy is radiated out than in the thicker wall area. Hollow chamber resonators  17   d  with this design can be employed advantageously for example in corner areas or edge areas of a large volume reactor vessel. 
     In a special design of a device suitable for the treatment of molten metal according to FIG. 1 with “through going”, unitized resonator-hollow chamber  62  this is provided with a, in FIG. 4 schematically simplified representation, cooling system  70 , by means of which the resonator hollow chamber  62  is flushed with cooling liquid. Hereby there is in the entire volume of the material to be treated, which finally is cooled to the point of solidification, a substantially finer and more homogenous distribution of grain size achieved, since because of the cooling a micro-crystal formation occurs first in the immediate vicinity of the resonator, these primary micro-crystals however again diffusing from here into the warmer areas, which finally achieves the homogenous distribution of the particle size in the material. 
     This cooling system  70  includes a, with respect to the central longitudinal axis  14  of the hollow chamber resonator  17 , coaxial introduction tube  71 , which via a supply conduit  72  of the wave guide  27  is connectable to a cooling material source  73 , and a likewise on the wave guide  27  provided outlet conduit  75 , via which cooling medium can flow out of the resonator hollow chamber  62  back to the cooling medium source. 
     The connection opening  76  of the supply conduit  71 , via which the cooling medium flows into the resonator hollow chamber  62 , is provided in immediate vicinity of the hemispherical shell shaped resonator closure  32 .