Abstract:
Continuous, chaotic convection mixer, convection heat exchanger and convection reactor 
     The invention relates to a device ( 1 ), in particular for mixing, for heat exchange or for carrying out reactions, having one or more through-flow elements ( 2 ) which have a center line ( 3 ) in the direction of flow, wherein the element(s) ( 2 ) is/are at least partially shaped or arranged such that the curve ( 9 ) formed by the center line(s) ( 3 ) approximately satisfies the following parametric representation:          ϑ        (   t   )       =     (               (     -   1     )       [   t   ]            a        (   t   )            (       cos        (     2      π                 t     )       -   1     )                   c        (   t   )          t                 a        (   t   )            sin        (     2      π                 t     )               )                             
     the parameters and constants having the following meaning: 
     ∂(t) position vector in a Cartesian coordinate system, 
     t parameter along the curve ( 9 ), −∞≦t≦+∞, 
     [t] integral fraction of t, 
     a(t) a radius of curvature ( 10 ), where 0&lt;|a(t)|&lt;∞, 
     c(t) a spacing parameter, where 0&lt;|c(t)|&lt;∞.

Description:
BACKGROUND OF THE INVENTION 
     The invention relates to a device, in particular for mixing, for heat exchange or for carrying out reactions, having one or more through-flow elements which have a center line in the direction of flow. Devices of the said type are known, specifically as continuous, chaotic convection mixers or convection heat exchangers or convection reactors for Newton and non-Newton fluids. 
     In addition, a multiplicity of types of mixer/heat exchanger are also known. Static mixers have stationary built-in components at which the mixing operation is accelerated. In other types of mixer (mixing vessel, agitated tubular reactor), the mixing is undertaken by movable built-in components. Chaotic mixers and heat exchangers (J. Fluid Mech., 1989, Vol. 209, pp 335-357, Experimental Thermal and Fluid Science, 1993, Vol 7, pp 333-344, Wo 94/12270) use the secondary flows induced by inertia in curved tubes or channels for the purpose of mixing. 
     In the case of static mixers, recirculation zones can lead to deposits on the built-in components. Furthermore, overheating of the fluid (hot spots) can occur locally in the recirculation zones. Mixing systems with moving built-in components have the disadvantage that they are of more complicated construction than static mixers. As a rule, they require a drive and a controller. In the case of complex thermal and rheological fluids, effects such as local overheating and degradation of the fluid can occur because of the high shear rates at the agitating elements. In the known chaotic mixers (WO 94/12270), separation regions can occur on the basis of the flow guidance in the case of relatively large volumetric flows. It is then possible for deposits and local overheating to occur in said recirculation zones. 
     SUMMARY OF THE INVENTION 
     It was therefore the object of the invention to find a device of the type mentioned at the beginning which requires no built-in components and can be built simply and compactly. Furthermore, the aim is to be able to achieve a good mixing and heat exchanging effect—without the disadvantages discussed above—over a wide range of viscosity and volumetric flow. 
     This object is achieved according to the invention by means of a device of the type mentioned at the beginning, wherein the through-flow element(s) is/are at least partially shaped or arranged such that the curve formed by the center line(s) approximately satisfies the following parametric representation:          ϑ        (   t   )       =     (               (     -   1     )       [   t   ]            a        (   t   )            (       cos        (     2      π                 t     )       -   1     )                   c        (   t   )          t                 a        (   t   )            sin        (     2      π                 t     )               )                            
     the parameters and constants having the following meaning: 
     ∂(t) position vector in a Cartesian coordinate system, 
     t parameter along the curve ( 9 ), −∞≦t≦+∞, 
     [t] integral fraction of t, 
     a(t) a radius of curvature ( 10 ), where 0&lt;|a(t)|&lt;∞, 
     c(t) a spacing parameter, where 0&lt;|c(t)|&lt;∞. 
     The subject matter of the invention is thus a device, in particular for mixing, for heat exchange, or for carrying out reactions, having one or more through-flow elements which have a center line in the direction of flow, wherein the through-flow element(s) is/are at least partially shaped or arranged such that the curve formed by the center line(s) approximately satisfies the following parametric representation:          ϑ        (   t   )       =     (               (     -   1     )       [   t   ]            a        (   t   )            (       cos        (     2      π                 t     )       -   1     )                   c        (   t   )          t                 a        (   t   )            sin        (     2      π                 t     )               )                            
     the parameters and constants having the following meaning: 
     ∂(t) position vector in a Cartesian coordinate system, 
     t parameter along the curve ( 9 ), −∞≦t≦+∞, 
     [t] integral fraction of t, 
     a(t) a radius of curvature ( 10 ), where 0&lt;|a(t)|&lt;∞, 
     c(t) a spacing parameter, where 0&lt;|c(t)|&lt;∞. 
     In this case, a parameter range t for a through-flow element defines a so-called loop of 360° from one whole number to the next whole number, and a double loop to the next whole number but one. 
     A device is preferred which is composed of several loops. Connection of the loops can be produced by means of methods known to the person skilled in the art for detachable (flanges) or undetachable (welding, soldering) connections. It is also possible for the individual loops to be interconnected via known connecting pieces, straight or curved tubes. As many different devices according to the invention as desired can be produced in this way. a(t) and c(t) can vary or be the same along the curve or from loop to loop in such a device. In a preferred embodiment, one or each through-flow element and/or one or each loop satisfies the parametric representation exactly or partially exactly or completely. 
     Also preferred is an embodiment in which the through-flow elements are shaped or arranged such that the curve formed by the center line(s) satisfies the parametric representation over the entire device. The through-flow elements or the loops preferably have a circular, rectangular or elliptical cross section. They do not lie in one plane in space, but are arranged in space progressively, one behind another. The center line can be a line of symmetry as regards to the cross-sectional area. In the case of symmetrical or approximately symmetrical cross sections, curves which interconnect identical sites on the circumference of individual through-flow elements in the direction of flow, for example specific comers of individual elements in the case of square elements, are to be considered as equivalent to the curve from the center lines, i.e. said curves (edges in the direction of flow) likewise satisfy the parametric representation. Slight deviations of the curves from the parametric representation, particularly within the scope of normal production and/or assembly tolerances, are not deleterious. 
     The device can consist of one piece or be composed of several parts. The design and production can be performed in accordance with the well-established methods. As materials, consideration is given to all metallic or nonmetallic materials familiar to the person skilled in the art, depending on the design and type of the flowing fluids: plastics, steels (stainless or acid-resistant), glass, ceramic or special materials. 
     The multiples of the diameter of the tube specified in German DIN 2605 T1 are preferably used as radii of curvature a(t) of the center line. A typical design consists, for example, of a tube with the outside diameter D=40 mm. Design 5 of the standard uses a bending radius of 100 mm. A lead (spacing parameters c(t)) of 100 mm per loop of 360° then proves to be advantageous. The number of loops is determined by the mixing task. A typical number of loops is 4 to 8. The wall thicknesses d are usually in the range from 0.5 to a few mm, in the case of extreme pressures up to 10 mm and more. In particular embodiments, the or each through-flow element has an outside diameter D in the range from 1 to 200 mm, preferably 5 to 100 mm, particularly preferably 10 to 50 mm, and the radius of curvature a(t) is selected from the range from 1*D to 7*D, preferably 2*D to 5*D. The spacing parameter c(t) is advantageously selected from the range from −20*D to +20*D, preferably −10*D to +10*D, particularly preferably from −5*D to +5*D, it being the case that it is always ≠0. 
     The advantages of the device according to the invention are to be seen essentially in that it is of simple design and easy to produce, and in that no separation regions occur in the flow guidance. A further important advantage is that a very compact design is produced on the basis of the law of formation. By contrast with static mixers with built-in components, the device according to the invention can be cleaned easily, for example using go-devils. By contrast with the chaotic mixer disclosed in WO 94/12270, the device according to the invention has the advantage that it can be effectively assembled to form compact modules, for example in multipath heat exchangers. Such an arrangement also results, moreover, in an improved heat exchange for the casing fluid owing to a large incident flow surface and intensive vortexing. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Novel features and advantages of the present invention in addition to those mentioned above will become apparent to persons of ordinary skill in the art from a reading of the following detailed description in conjunction with accompanying drawings wherein similar reference characters refer to similar parts and in which 
     FIG. 1 is a perspective view of a device according to the present invention; 
     FIG. 2 is a perspective view of another device, according to the present invention; 
     FIG. 3 is a diagrammatic view illustrating mixing two fluids of different viscosities, according to the present invention; 
     FIG. 4 is a cross-sectional view of a portion of a device shown in FIG. 2; 
     FIG. 5 is a perspective view of still another device, according to the present invention; 
     FIG. 6 is a perspective view of another device, according to the present invention; 
     FIG. 7 shows a perspective representation of the bending device according to the invention with a tube at the start of the bending operation; 
     FIG. 8 shows a perspective representation of the bending device according to the invention with a tube after a loop has been bent; 
     FIGS. 9A, B shows a representation of the bending device according to the invention, with two columns per three molded parts each, in a side view and in a sectional side view; 
     FIG. 10 shows a representation of the bending device according to the invention, in plan view; and 
     FIG. 11 shows a heat exchanger with double loops produced in accordance with the invention. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The device according to the invention is further explained below with the aid of the exemplary embodiments represented perspectively in FIGS. 1,  2 ,  5 ,  6 . FIG. 3 shows the result of a numerical experiment, and FIG. 4 a detail from FIG. 2 in cross section. There is no intention to limit the invention in any way, in particular to these embodiments. 
     FIG. 1 shows the device  1  according to the invention, which is formed from a single tube  2  with a circular cross section, which has a center line  3  in the direction of flow (arrow) which forms a curve  9 . Also illustrated is a Cartesian coordinate system  8  with the spatial directions x,y and z. However, the device  1  can also be conceived as being reduced to four loops  6   a ,  6   b ,  6   c ,  6   d  and two straight tubes  15 , the loops  6  being arranged alternately offset one behind another. Straight tubes  15  are added at the beginning and end of the loop arrangement. Dividing lines  17  drawn in mark the transitions between the individual loops  6  and tubes  15 . The spacing of the loops  6   a ,  6   c  and  6   b ,  6   d  situated one behind another is represented by a distance  7  which corresponds in the illustrated case to 2*c(t), i.e. double the lead. The projection of the curve  9  of the circular elements  6   a ,  6   b ,  6   c ,  6   d  onto the xz plane characterizes the radius a(t)  10 , which can also vary along the curve. In FIG. 2, the device  1  comprises, at least partially, individual through-flow elements  16  with a rectangular cross section, which are interconnected via flanges  5 . FIG. 4 shows a cross section through such a detail. It is shown here how the center lines  3  of the elements  16  form a curve  9 . Likewise represented is a curve  12  which is equivalent to the curve  9  and connects comer points of the individual elements  16 . In the case of a correspondingly shaped or bent square element  16 , an edge  4  of said element  16  can also form a curve  9  which is equivalent to the center line  3  and satisfies the parametric representation. 
     FIG. 3 shows the result of a numerical experiment for mixing two fluids  13 ,  14  whose viscosities differ by a factor of five, for example HCl  13  and water glass  14 , in the device  1  represented in FIG.  1 . In this example, the initial condition was selected so that the low-viscosity fluid  13  (HCl) is located in the core, and the fluid  14  (water glass) of higher viscosity is located in the outer region of the inlet (bottom left). The gray levels represented in the legend mark the concentration (volumetric fractions, black=1, white=0) of the low-viscosity fluid  13 . It is clearly to be seen that the mixing operation makes progress in the chaotic mixing elements, i.e. in the loops  6 . Effective thorough mixing has already been set up in this case after the traversal of three loops  6 . The concentration of the two fluids is approximately uniform over the entire cross section, approximately at 0.5. 
     FIG. 5 shows a preferred embodiment of the device  1  according to the invention, in which two loop pairs  6   a,b  and  6   c,d  are connected by means of a straight pipe  15 . In the further preferred embodiment in accordance with FIG. 6, loop pairs  6   a,b  and  6   c,d  are connected by means of S-shaped tube lengths  18 . The person skilled in the art can thereby produce in a simple way virtually any number of different, compact chaotic convection mixers which mix very effectively. 
     In the following, mixers according to the invention, as represented in FIGS. 1,  5  and  6 , are characterized by way of example with the aid of three sets of parameters. No limitation is thereby intended. 
     FIG. 1 
     
       
         
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 loop 
                 t 
                 a(t) 
                 c(t) 
               
               
                   
                   
               
             
             
               
                   
                 6a 
                 0-1 
                 5*R 
                 3*R 
               
               
                   
                 6b 
                 1-2 
                 5*R 
                 3*R 
               
               
                   
                   
               
               
                   
                 inside radius R = 1 mm (R = (D − 2*d)/2)  
               
             
          
         
       
     
     FIG. 5 
     
       
         
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 loop 
                 t 
                 a(t) 
                 c(t) 
               
               
                   
                   
               
             
             
               
                   
                 6a 
                 0-1 
                 5*R 
                  5*R 
               
               
                   
                 6b 
                 1-2 
                 5*R 
                  5*R 
               
               
                   
                 6c 
                 0-1 
                 5*R 
                 −5*R 
               
               
                   
                 6d 
                 1-2 
                 5*R 
                 −5*R 
               
               
                   
                   
               
               
                   
                 inside radius R = 20 mm; the loops 6b and 6c are connected by a straight element (tube 15).  
               
             
          
         
       
     
     FIG. 6 
     
       
         
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 loop 
                 t 
                 a(t) 
                 c(t) 
               
               
                   
                   
               
             
             
               
                   
                 6a 
                 0-1 
                 5*R 
                  5*R 
               
               
                   
                 6b 
                 1-2 
                 5*R 
                  5*R 
               
               
                   
                 6c 
                 0-1 
                 5*R 
                 −5*R 
               
               
                   
                 6d 
                 1-2 
                 5*R 
                 −5*R 
               
               
                   
                   
               
               
                   
                 inside radius R = 20 mm; the loops 6b and 6c are connected by an element (tube 18) curved in the shape of an S.  
               
             
          
         
       
     
     The object of the invention is, furthermore, a method for producing a device according to the invention in which a tube is bent around [t] cylindrical molded parts which are arranged alternately, to form two mutually parallel columns, a guide groove with the radius of curvature a(t) and a lead ½* c(t) being recessed into each molded part on the circumference, and the tube being bent around the first molded part of the first column and subsequently around the first molded part of the second column, and subsequently the further molded parts being alternately plugged onto the first and second columns, and the tube being bent around said further molded parts. 
     The object of the invention is, furthermore, a device for carrying out said method, having a base plate on which at least two cylindrical molded parts are arranged parallel to one another at a spacing (b) to form two columns, the at least two cylindrical molded parts having on the circumference a guide groove with a radius of curvature a(t) and a lead of ½* c(t) for bending the tube, and being able to be plugged together individually to form the columns. 
     These objects are described in more detail below with the aid of FIGS. 7 to  10 . No limitation of any kind is thereby intended. 
     In order to guide the flow in and around a double loop  6   a ,  6   b  of the device  1  according to the invention in accordance with claim  1 —termed “chaotic mixer” or “CM” below—, it is advantageous to produce said device without joining techniques. For this purpose, a length of tube  2  is brought onto the length of the mixing path and suitably shaped in a modularly configured bending device  22 . 
     The bending device  22  comprises, inter alia, several preferably cylindrical molded parts  23  which can be plugged into one another and are arranged to form two columns  29 ,  32  extending parallel to one another. The number of molded parts  23  is equal to the number [t] of the loops  6   a ,  6   b  . . . The columns  29 ,  32  made from molded parts  23  are fastened to a base plate  30  at a spacing b from one another. A guide groove  31  which advantageously has at least a quarter of the tube cross section, preferably half the tube cross section, with a lead of ½* c(t) is recessed, for example by milling or via a casting method, into the molded parts  23  on the circumference for the purpose of guiding the tube  2  during bending. The molded parts  23  can be plugged into one another and rotated with respect to one another, with the result that the transition of the guide groove  31  (milling) from a first molded part  23  on a first column  29  to the following one on the second column  32  is smooth. For this reason, the first molded part  23  of the second column  32  or its groove  31  is raised by the measure corresponding to the lead. The molded parts  23  have a complete groove  31  of at least 90°, preferably 180°, 360° being particularly preferred. 
     Two types of molded parts are required to bend a CM  1  according to FIG.  1 : a) left-hand helical ones and b) right-hand helical ones, i.e. the lead of the guide groove  31  of the molded parts  23   a ) has the opposite sign to that of  b ). 
     In each case, one type (a), or b)) occurs in a column  29 ,  32  of molded parts  23  plugged into one another. As a result, after the tube  2  is bent around the molded parts  23   a ) and  b ), a double loop  6   a ,  6   b  is produced in the shape of an eight and having a defined lead. Depending on the mutual spacing b of the columns  29 , 32 , the shape of the double loops  6   a ,  6   b  can deviate from the shape shown in FIG.  1 . 
     The bending operation is as follows: 
     The tube end starting from which the bending operation of a CM element is to proceed is fixed to the base plate  30  by means of a bearing  30   a  (FIG.  7 ). 
     The tube  2  is bent around the molded part  23   a ) with the aid of a guide roller  34  which is fastened to a lever  36 , the lever  36  being plugged onto the upper end of the column  29  of molded parts  23   a ), and being capable of displacement in height. After the tube  2  has been bent sufficiently around said molded part  23   a ) (FIG. 7, dashed and dotted), a molded part  23   b ) is plugged onto the column  32 . The lever  36  is likewise plugged on the top of column  32 , and the tube  2  is then bent further in the other direction (FIG.  8 ). It is to be borne in mind in this operation that before it is bent further the tube  2  bears without any pressure against each newly plugged-on molded part  23 , or lies without any pressure in the guide groove  31  thereof, since otherwise deformations of the entire CM element occur when the molded parts  23  are taken out. The tube is thus to be deformed beyond the elastic range. Subsequently, a further molded part  23   a ) is plugged together with the lever  36  onto the column  29 , and bent further as previously described. These operations are repeated until the desired number of loops  6   a ,  6   b  . . . . have been produced. 
     After termination of the entire bending operation, the molded parts  23  are screwed out of the CM element. Owing to this mode of procedure, the molded parts  23  can be repeatedly used as matrices and can be used to produce several, identical CM elements  6   a ,  6   b  . . . . The first molded part  23  into which the tube  2  is inserted differs from the remainder in that the guide groove  31  extends a little horizontally at the start and makes a transition to the required lead only later, on the circumference. This greatly improves the insertion of the tube  2  into the molded part  23 . 
     The following points remain to be considered: 
     The tube inside and outside diameters are to be selected in accordance with the requirements. They can have an outside diameter ranging from 2 mm to 500 mm. 
     Corrosion-resistant metals or suitable plastics satisfying the requirements are to be selected as tube material, it being necessary, as the case may be, for plastic tubes to be heated for the bending operation. 
     The molded parts  23  should be produced from a suitable material which does not lead to problems with the material of the tube during the bending operation such as, for example, corrosion. 
     The tube cross section should not be deformed substantially because of the bending operation. A circular cross section is ideal. Slight deviations can be tolerated. 
     If the CM is pressure-loaded during operation, it is to be ensured that the thermal load during bending does not depress the strength too strongly. 
     The tube should be filled with a suitable filler during bending. 
     Transitions from the bent tube to a straight length of tube should be configured without discontinuity such as kinks, that is to say tangentially. 
     The columns  29 ,  32  made from molded parts  23  plugged into one another are to be held in a base plate  30  of suitable thickness. The spacing b between the columns  29 ,  32  is determined, inter alia, by the dimensions and bending properties of the tubes used. 
     The principal dimensions of the CM elements can lie within the following ranges: spacing b: 10 mm to 5000 mm, diameter D CM : 5 mm to 3000 mm, lead angle a, which is correlated with the lead c(t), (FIG.  9 B), per molded part 23:1 to 60 degrees. 
     The advantages of this method according to the invention are to be seen essentially in that it is possible, by virtue of the modular design and the reciprocating way in which the molded parts are plugged on relative to a column, for tubes of “arbitrary” length to be bent in endless fashion to form chaotic mixers. 
     FIG. 11 shows by way of example how three cm elements  37  produced according to the invention can be assembled to form a compact, effectively operating heat exchanger  38 .