Abstract:
Embodiments of the invention relate to apparatus for modifying the properties of a flow field and to a method of selecting an apparatus to achieve a desired flow field. The invention finds particular application in the control of the mixing of fluids, heat transfer within and between fluids, acoustic noise, oscillations in fluids, microchip cooling, structural vibrations and chemical reactions. Embodiments of the invention comprise a fractal fluid flow modification structure comprising: a plurality of turbulence-creating elements; and a support for holding the turbulence-creating elements in the fluid so as to allow movement of the fluid relative to the turbulence-creating elements, wherein said turbulence-creating elements include at least two different types of element, including a first type of element and a second type of element, and wherein the turbulence-creating elements are arranged in a fractal structure, the first type of element being arranged at a first level in said fractal structure and the second type of element being arranged at a second level in said fractal structure. Since the fluid flow modification structure comprises a plurality of levels of fractal structures, the surface area of the first type of element differs from that of the second type of element: varying the respective surface areas between fractal levels provides a convenient mechanism for controlling turbulence levels in the fluid.

Description:
FIELD OF THE INVENTION 
       [0001]    The present invention relates to apparatus for modifying the properties of a flow field and to a method of selecting an apparatus to achieve a desired flow field. Embodiments of the invention can be used to control the mixing of fluids, heat transfer within and between fluids, acoustic noise, oscillations in fluids, microchip cooling, structural vibrations and chemical reactions. One particular application to which embodiments of the invention are particularly well suited is airbrakes on airborne vehicles. 
       BACKGROUND OF THE INVENTION 
       [0002]    The capability to predict and control flow field characteristics has been the subject of scientific research for a significant period of time. However, as has been realised in the course of many and diverse research projects, flow field behaviour is extremely complex and thus difficult to control by means of artefacts placed within a flow field. 
         [0003]    In the period between 1963 and 1966, Corrsin and co-workers spearheaded a research effort directed towards controlling the turbulence within a conduit by means of a grid comprising a two-dimensional uniform mesh disposed symmetrically within the conduit (as comprehensively described in S. Corrsin, Handbook de Physik (1963) 8:254). This research effort showed that low Reynolds number, essentially isotropic and homogeneous turbulence flow, can be generated downstream of the grid. In the period since 1966, various different shaped grids have been tested, but for each of these grids, the cross section of individual grid elements has been identical to that of other elements in the grid. 
         [0004]    The feature that is common to the measurement data obtained for any of these known two-dimensional grids is that the turbulence levels, that is to say the fluctuations in velocity over time downstream of the grid, has been limited to extremely low levels. Thus the range of control that is achievable with, and applicability of, such grids to applications such as mixing and noise control, is extremely limited. 
         [0005]    It is an objective of the present invention to increase the range within which flow field parameters can be controlled. 
       SUMMARY OF THE INVENTION 
       [0006]    In accordance with a first aspect of the present invention, there is provided fluid flow modification apparatus for creating turbulence in a fluid when said fluid is moving relative to the fluid flow modification apparatus, the apparatus comprising: 
         [0007]    a plurality of turbulence-creating elements, each turbulence-creating element having a first surface portion against which the fluid can flow and a second surface portion along which the fluid can flow, each surface portion having a surface area association therewith; and 
         [0008]    a support for holding the turbulence-creating elements in the fluid so as to allow movement of the fluid relative to the turbulence-creating elements, 
         [0009]    wherein said turbulence-creating elements include at least two different types of element, including a first type of element and a second type of element, and 
         [0010]    wherein the first type of element has a first surface area and the second type of element has a second surface area, different to said first surface area, said first and second surface areas having a relationship selected to control the turbulence-creating characteristics of said fluid flow modification apparatus. 
         [0011]    As described above, in embodiments of the invention, the surface area of the first element differs from that of the second element. The turbulence-creating elements can be defined such that the first surface portion of the first type of element has a first width and the first surface portion of the second type of element has a second width, so that the variation in surface area can be achieved by setting the second width to be different to the first width. Alternatively and/or additionally the turbulence-creating elements can be defined such that the first surface portion of the first type of element has a first length and the first surface portion of the second type of element has a second length so that the variation in surface area can be achieved by setting the second length to be different to the first length. 
         [0012]    As will be expected from the foregoing, since the first surface portion is a surface against which the fluid flows, the first surface portion effectively presents an obstruction to the oncoming fluid, causing the fluid to pass around the turbulence-creating elements. The second surface portion, however, is a surface along which the fluid flows, and therefore presents resistance to the oncoming flow (in the form of friction) as it passes around the elements, leading to development of a shear layer along the second surface portion. The characteristics of the shear layer that is created thereby are dependent on the width of the second surface portion, and since the properties of the shear layer have a significant bearing on the flow field downstream of the fluid flow modification apparatus, the turbulence created by the fluid flow modification apparatus can further be controlled by varying the width of the second surface portion between respective types of elements. 
         [0013]    Embodiments of fluid modification apparatus are referred to herein as grids and because the grids are composed of elements having different surface areas, the levels of turbulence that can be generated downstream of a given grid are greater than is achievable using the classical grids of Corrsin described above. By varying the surface area of the second type of elements, either in absolute terms or compared with that of the first type of elements, the levels of turbulence can be modified. 
         [0014]    Preferably the turbulence-creating elements are arranged such that at least one of said first type of element is attached to at least one of said second type of element. The turbulence-creating elements can be generally elongate and of generally uniform thickness along their length, and can be arranged in a generally planar configuration. 
         [0015]    Preferably the turbulence-creating elements are arranged in a multi-scale configuration. By multi-scale is meant that the thickness and/or length and/or depth of turbulence-creating elements of the first type of turbulence-creating element differs from that (or those) of the second type of turbulence-creating element. This relationship can most conveniently be quantified in terms of a ratio between the types of turbulence-creating elements: in one arrangement the turbulence-creating elements can be arranged in a fractal configuration comprising two or more fractal levels, such that the ratio of thickness and/or length and/or depth of turbulence-creating elements is constant between the fractal levels; in an alternative arrangement the turbulence-creating elements can be arranged in a multi-fractal configuration comprising two or more multi-fractal levels, such that the ratio of thickness and/or length and/or depth of turbulence-creating elements varies between respective multi-fractal levels. 
         [0016]    In the case of a fractal configuration, the ratio of thickness and/or length and/or depth between turbulence-creating elements at different fractal levels can be within the ranges of 1.1 and 3; 1.2 and 2.7; or 1.3 and 2.6. The ratio can be chosen to be 1.35, 1.71, 2.05, 2.35 or 2.58, but any suitable values falling within the afore-mentioned ranges could be selected. 
         [0017]    Conveniently the grids can be described as comprising a plurality of sets of said turbulence-creating elements: in a first arrangement a first said set comprises one of said first type of turbulence-creating elements and a second set comprises a plurality of said second type of turbulence-creating elements. In another arrangement the grid comprises three or more sets of turbulence-creating elements, the structures of at least one of the sets comprising turbulence-creating elements of a surface area different to the surface area associated with another of the sets of structures. 
         [0018]    In a particularly preferred configuration, the turbulence-creating elements are arranged in structures, each said structure including a plurality of elongate members. The structures can include a structure having two elongate members, in which one said elongate member is attached to the other said elongate member part way along respective lengths of respective elongate members so as to form a cross-shaped structure. Alternatively the structures can include a structure having three elongate members, in which a first said elongate member has two ends and is attached to a second elongate member and to a third elongate member at respective ends of the first elongate member so as to attach to the second elongate member and the third elongate member part way along their respective lengths. An I-shaped structure is an example of one such structure. As a further alternative the structures can include a structure having a plurality of elongate members such that each member is in an end-to-end relationship with another elongate member so as to form a polygon (comprising three or more members); a particularly preferred example of this type comprises four elongate members so that the structure is square-shaped. 
         [0019]    The elongate members can be integrally formed with other elongate members of a given structure, or the structures can comprise an attachment point for providing separable interconnection between respective elongate members of the structure. In the latter case the structures might be interconnected so as to form a grid that comprises a plurality of planes. In one arrangement the grids are arranged such that elongate members of the first structure engage with elongate members of at least one second structure; in the case where the structures are fabricated from a planar sheet such engagement between elongate members is inherent in the grid design. 
         [0020]    According to a further aspect of the present invention there is provided a fractal fluid flow modification structure comprising: 
         [0021]    a plurality of turbulence-creating elements; and 
         [0022]    a support for holding the turbulence-creating elements in the fluid so as to allow movement of the fluid relative to the turbulence-creating elements, 
         [0023]    wherein said turbulence-creating elements include at least two different types of element, including a first type of element and a second type of element, and 
         [0024]    wherein the turbulence-creating elements are arranged in a fractal structure, the first type of element being arranged at a first level in said fractal structure and the second type of element being arranged at a second level in said fractal structure. 
         [0025]    In one arrangement each turbulence-creating element comprises two ends, and an end of one turbulence-creating element is joined to an end of another turbulence-creating element such that the turbulence-creating elements are joined in an end-to-end configuration so as to form a given fractal structure. An example of such a fractal structure is a polygon fractal structure, and a particularly preferred polygon fractal structure is a square fractal structure. 
         [0026]    In another arrangement each fractal structure comprises two turbulence-creating elements, one said turbulence-creating element being attached to the other said turbulence-creating element part way along respective lengths of respective turbulence-creating elements. An example of such a fractal structure is a cross-grid fractal structure. 
         [0027]    In yet another arrangement each fractal structure comprises three turbulence-creating elements: in this arrangement a first said turbulence-creating element has two ends and is attached to a second turbulence-creating element and to a third turbulence-creating element at respective ends of the first turbulence-creating element so as to attach both to the second turbulence-creating element and to the third turbulence-creating element part way along their respective lengths. An example of such a fractal structure is an I-shaped fractal structure, and this structure is preferably embodied as a planar fractal structure. 
         [0028]    In arrangements according to this aspect of the invention the turbulence-creating elements can be of uniform or different thickness between fractal levels, and/or of uniform or different depth between fractal levels. 
         [0029]    According to a yet further aspect of the present invention there is provided a fractal fluid flow modification structure comprising: 
         [0030]    a plurality of turbulence-creating elements; and 
         [0031]    a support for holding the turbulence-creating elements in the fluid so as to allow movement of the fluid relative to the turbulence-creating elements, 
         [0032]    wherein said turbulence-creating elements are arranged in an end to end configuration, and 
         [0033]    wherein the turbulence-creating elements are arranged in a fractal structure, the fractal structure having at least two levels. 
         [0034]    In arrangements according to this aspect of the invention the turbulence-creating elements can be of uniform or different thickness between fractal levels, and/or of uniform or different depth between fractal levels. 
         [0035]    According to a yet further aspect of the invention there is provided a computer-implemented method of determining one or more properties related to turbulence in a fluid when said fluid is moving relative to a fluid flow modification apparatus, the fluid flow modification apparatus comprising: 
         [0036]    a plurality of turbulence-creating elements, each turbulence-creating element having a first surface portion against which the fluid can flow and a second surface portion along which the fluid can flow, each surface portion having a surface area association therewith; and 
         [0037]    a support for holding the turbulence-creating elements in the fluid so as to allow movement of the fluid relative to the turbulence-creating elements, 
         [0038]    wherein said turbulence-creating elements include at least two different types of element, including a first type of element and a second type of element, and 
         [0039]    wherein the first type of element has a first surface area and the second type of element has a second surface area, different to said first surface area, said first and second surface areas having a relationship selected to control the turbulence-creating characteristics of said fluid flow modification apparatus, 
         [0040]    said method comprising: 
         [0041]    i) determining said one or more properties for a first set of data relating to said first and second surface areas, wherein said first and second surface areas are related by a first relationship in said first set of data; and 
         [0042]    ii) determining said one or more properties for a second set of data relating to said first and second surface areas, wherein said first and second surface areas are related by a second relationship, different to said first relationship, in said second set of data. 
         [0043]    The method can most conveniently be used when the relationship is a ratio that is varied between said first and second sets of data so as to generate different values for the turbulence properties. Alternatively or additionally the first and second sets of data can include data indicative of an amount of blockage presented by the plurality of turbulence-creating elements to the fluid, and the method includes varying the amount of blockage between said first and second sets of data. 
         [0044]    The method can be applied to determine turbulence intensity in a direction substantially perpendicular to the direction of said relative movement of the fluid and/or turbulence intensity in a direction substantially parallel to the direction of said relative movement of the fluid. To this end the method includes performing a calculation which takes into account said relationship whereby to determine said one or more properties of the fluid. This calculation can proceed according to various expressions, the actual form of which is selected in dependence on the form of the grid. For example, for grids comprising cross-shaped structures, the method includes performing a calculation according to the formula (u′/U) 2 =t r   2 C ΔP f 1 (x/M eff ) so as to determine said one or more properties of the fluid. For grids comprising I-shaped structures, however, the method includes performing a calculation according to the formula (u′/U) 2 =t r C ΔP (T/L max ) 2 f 2 (x/M eff ). 
         [0045]    The computer-implemented method is conveniently performed by a computer, or a suite of computers, adapted to process a set of instructions according to the method and the method can be stored as a computer program, or a suite of computer programs, that holds such a set of instructions. 
         [0046]    Embodiments of the invention can conveniently be applied in a variety of situations involving relative movement between an object and fluid, such as landing of aircraft; in such an application a grid according to the invention is used as an air break and attached to an aircraft wing, the wing comprising: a wing element having a leading edge and a trailing edge; at least one slat comprising a plurality of turbulence-creating elements, wherein the slat acts cooperatively with the wing element to control the speed of the aircraft, wherein said turbulence-creating elements are arranged in a generally planar configuration, and wherein the turbulence-creating elements are arranged in a fractal structure, the fractal structure having at least two levels. 
         [0047]    Further features and advantages of the invention will become apparent from the following description of preferred embodiments of the invention, given by way of example only, which is made with reference to the accompanying drawings. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0048]      FIG. 1   a  is a schematic diagram of a conduit in which fluid modification apparatus according to an embodiment of the invention can operate; 
           [0049]      FIG. 1   b  is a schematic diagram showing side and end view of a wind tunnel section arranged to accommodate fluid modification apparatus according to embodiments of the invention; 
           [0050]      FIGS. 2   a  and  2   b  are schematic diagrams showing fluid modification apparatus according to a first embodiment of the invention; 
           [0051]      FIG. 2   c  is a perspective diagram showing a three dimensional view of a section of the fluid modification apparatus shown in  FIGS. 2   a  and  2   b;    
           [0052]      FIGS. 3   a - 3   e  are schematic diagrams showing different arrangements of the fluid modification apparatus according to the first embodiment shown in  FIG. 2   b;    
           [0053]      FIG. 4  is a schematic diagram showing normalised pressure drop across grids according to the invention; 
           [0054]      FIGS. 5   a  and  5   b  are schematic diagrams showing fluid modification apparatus according to a second embodiment of the invention; 
           [0055]      FIGS. 6   a - 6   j  are schematic diagrams showing different arrangements of the fluid modification apparatus according to the second embodiment shown in  FIG. 5   b;    
           [0056]      FIGS. 7   a ,  7   b  and  7   c  are schematic diagrams showing fluid modification apparatus according to a third embodiment of the invention; 
           [0057]      FIGS. 8   a - 8   g  are schematic diagrams showing different arrangements of the fluid modification apparatus according to the third embodiment shown in  FIG. 7   c;    
           [0058]      FIG. 9  shows a graphical representation of measurement data taken in the axial direction along a centre line of the conduit shown in  FIG. 1   b  for fluid modification apparatus according to various of the first embodiments shown in  FIGS. 3   a - 3   e;    
           [0059]      FIG. 10  shows a graphical representation of measurement data taken in the axial direction along a centre line of the conduit shown in  FIG. 1   b  for fluid modification apparatus according to various of the second embodiments shown in  FIGS. 6   a - 6   e;    
           [0060]      FIG. 11  shows a graphical representation of measurement data taken in the axial direction along a centre line of the conduit shown in  FIG. 1   b  for fluid modification apparatus according to various of the third embodiments shown in  FIGS. 8   a - 8   g;    
           [0061]      FIG. 12  is a schematic flow diagram showing steps involved in a grid selection routine according to an embodiment of the invention; 
           [0062]      FIG. 13  is a schematic flow diagram showing steps involved in a grid selection routine according to another embodiment of the invention; 
           [0063]      FIG. 14  is a schematic diagram showing use of a grid as an airbrake; and 
           [0064]      FIG. 15  is a schematic diagram showing an arrangement comprising a plurality of the airbrakes shown in  FIG. 14  affixed to a portion of a wing. 
       
    
    
       [0065]    In the figures, the same reference numerals are used to refer to the same parts and process steps; in relation to any given part, different embodiments thereof are assigned the same reference number as utilised in other embodiments, incremented by 100. 
       DETAILED DESCRIPTION OF THE INVENTION 
       [0066]    As described above, embodiments of the invention are concerned with controlling the properties of a flow field, the flow field being generated by relative movement between fluid and a body. In a first arrangement this relative movement is generated by fluid F flowing through a conduit such as conduit  101 , shown part-open in  FIG. 1   a . The conduit  101  can be any channel suitable for carrying fluid, of rectangular, circular or other suitable cross-section, and capable of accommodating fluid modification apparatus  100  therein. 
         [0067]    In one arrangement the conduit  101  comprises a wind tunnel, which, as known in the art, typically comprises a contraction section  101   a  for directing the fluid into a test section  101   b , within which fluid modification apparatus  100  is situated, and an exit section  101   c , which acts to diffuse the fluid as it exits the conduit. The wind tunnel facilitates measurement of the effects of the fluid modification apparatus  100  on the flow field. The test section  101   b  of the wind tunnel comprises a rectangular cross section, of width T and height H, and the fluid modification apparatus  100  extends across the full cross section of the test section  101   b.    
         [0068]    Turning now to  FIGS. 2   a  and  2   b , a first embodiment of the fluid modification apparatus  100 , hereinafter referred to as a grid, will be described. The grid  100  comprises a plurality of grid elements that are arranged symmetrically with respect to the axis of the test section  101   b ; the grid elements are selected so as to generate turbulence within fluid flow therethrough and in this embodiment the grid elements are embodied as generally elongate members, substantially uniform along their length, and arranged so as to form a cross-like structure  102   a  shown in  FIG. 2   a.    
         [0069]    In this particular example the grid  100  comprises three structures: the first structure  102   a  is composed of elongate members S 1 b 1  and S 1 b 2 ; the second structure  102   b  is composed of elongate members S 2 b 1  and S 2 b 4 ; and the third structure  102   c  is composed of elongate members S 2 b 2  and S 2 b 3 . For each respective structure the elongate members are interconnected via an attachment point, indicated in  FIG. 2   a  for the first structure  102   a  by reference S 1 A 1 . The attachment point is either embodied as an attachment means that enables respective elongate members to separably attach to one another, or is an integral part of the respective elongate members, and configured such that any given structure is part of one planar sheet. It will be noted that the individual members of a given structure abut those of another structure: the grid  100  is configured such that these abutting members engage with one another so as to prevent relative movement between individual structures while the fluid flows therethrough; when the grid  100  is embodied as an integral planar sheet, prevention of lateral movement is an inherent feature of the grid design. 
         [0070]    Whilst not shown in  FIG. 2   b , the grid  100  also includes a support for engaging the grid  100  with a positioning mechanism within the wind tunnel  101   b , the support being configured so as to enable relative movement between the grid  100  and fluid. 
         [0071]    As can be seen from  FIG. 2   b , and according to a first grid definition (hereinafter referred to as the non-symmetrical definition) the elongate members S 1 b 1  and S 1 b 2  of the first structure  102   a  have a thickness different to that of the members of the second and third structures  102   b ,  102   c , and the thickness of these second and third structures  102   b ,  102   c  is identical. Accordingly, in this example the grid comprises two sets S 1 , S 2  of structures, and respective sets differ from one another by virtue of the thickness of the members of the structures. 
         [0072]    In the example shown in  FIG. 2   b , the first set S 1  comprises one cross structure  102   a  and the second set S 2  comprises two structures  102   b ,  102   c ; alternative arrangements can include three, or more, sets of structures, and the actual number of sets, numbers of structures within a set, and the thickness of individual members of the respective structures, serve to define the nature and degree of blockage presented by the grid  100  to the incoming fluid F. These features can be defined by means of the following grid parameters: Number of sets of structures, N; blockage ratio, σ (i.e. the amount of the cross-sectional area of the conduit  101  is blocked by the grid); ratio of the thickness between the thickest and thinnest members in the grid, t r ; and the effective mesh size, 
         [0000]    
       
         
           
             
               M 
               eff 
             
             ( 
             
               
                 = 
                 
                   
                     4 
                      
                     
                       
                         
                           T 
                           2 
                         
                          
                         
                           ( 
                           
                             1 
                             - 
                             σ 
                           
                           ) 
                         
                       
                       
                         1 
                         / 
                         2 
                       
                     
                   
                   P 
                 
               
               , 
             
           
         
       
     
         [0000]    where P is roughly twice the sum of all of the lengths of members making up the grid  100 ). It is to be noted that according to the foregoing definition of the grid  100 , the elongate members structures S 2 b 1  and S 2 b 4 ; S 2 b 2  and S 2 b 3  making up structures  102   b ,  102   c  respectively of the second set S 2  each form a non-symmetrical cross structure (non-symmetrical in so far as the attachment point is not located half-way along the lengths of respective elongate members). 
         [0073]    According to an alternative definition of the grid  100  (hereinafter referred to as the symmetrical definition), a structure is considered to be a member of a successive set if it is symmetrically disposed around a structure of the previous set; in accordance with this definition the second set S 2  of grid  100  could alternatively be viewed as comprising four symmetrical cross structures, each of the four being disposed in a quadrant of the structure  102   a  of the first set S 1 . According to this symmetrical definition, the elements of the grid  100  are arranged in a fractal configuration, since the grid can be subdivided into parts, each of which is a smaller copy of the whole grid. 
         [0074]    Turning now to  FIG. 2   c , which shows a perspective view of the cross structure  102   a  shown in  FIG. 2   a , it can be seen that fluid F flows against a first surface portion  201  and along, or past, a second surface portion  203  of the grid  100 . Thus the first surface portion  201  presents an obstruction to the incoming flow F, while the second surface portion  203  lies parallel to, and is responsible for, the shear layer that builds up along the second surface portion  203  of each structure. In the arrangement shown in  FIG. 2   c , individual elongate members are shown as having a rectangular cross-section, but it will be appreciated that they can alternatively have a circular cross-section, in which the case the surface portions  201 ,  203 , would comprise curved surface portions. 
         [0075]    In the foregoing description of the first embodiment of the invention, the turbulence generated downstream of the grid  100  is controlled by means of thickness variation between sets S 1 , S 2  of structures, which in terms of  FIG. 2   c  amounts to variation in width  207  of the first surface portion  201 ; however, the turbulence could alternatively be modified by varying the length  205  between sets S 1 , S 2  of structures, or indeed by modifying the width  209  of the second surface portion  203 . It can be expected that selection of a given geometric parameter—for the purposes of modification—will be dependent on the intended use of the grid, since turbulence distribution, homogeneity and magnitude differs with configuration of respective turbulence-creating elements. It should be noted that for clarity purposes the second and third embodiments discussed below are described in the context of the effects of modification of the width (“thickness”) of the first surface portion  201  between sets S 1 , S 2  of structures; however, it should be appreciated that, as for the cross-grids and discussed with reference to  FIG. 2   c , the length  205  or depth  209  of structures of these embodiments could additionally or alternatively be varied. 
         [0076]      FIGS. 3   a - 3   d  show various different grid configurations for which there are three sets of structures and for which the grid is situated within a tunnel having width, T, of 0.46 m: in a first configuration ( FIG. 3   a ), σ is 40%, t r  is 3.3; and M eff =114 mm; in a second configuration ( FIG. 3   b ), σ is 17%, t r  is 5.0; and M eff =57 mm; in a third configuration ( FIG. 3   c ), σ is 21%, t r  is 2.8; and M eff =57 mm; and in a fourth configuration ( FIG. 3   d ), σ is 29%, t r  is 2.0; and M eff =57 mm. 
         [0077]    According to the non-symmetrical definition of a given structure adopted in  FIG. 2   b , in the configurations of  FIGS. 3   a - 3   c , the first set S 1  comprises one structure and the second set S 2  comprises two structures, whereas in the fourth configuration ( FIG. 3   d ) the second set S 2  comprises six structures. In relation to the third set, S 3 , the first configuration ( FIG. 3   a ) comprises four structures, the second and third configurations ( FIGS. 3   b ,  3   c ) comprise twelve structures and the fourth configuration ( FIG. 3   d ) comprises six structures. In each of these four grid configurations ( FIG. 3   a - FIG. 3   d ) the relationship between thicknesses of structures of respective sets can be quantified as a ratio, which in the case of a fractal grid, is constant between respective sets of structures; if t 1  denotes the thickness of structures in the first set S 1 , t 2  denotes the thickness of structures in the second set S 2 , and t 3  denotes the thickness of structures in the third set S 3 , and assuming grid to be a fractal grid (meaning that the ratio is constant between the three sets S 1 , S 2 , S 3 ) then 
         [0000]    
       
         
           
             
               
                 t 
                 1 
               
               
                 t 
                 2 
               
             
             = 
             
               
                 
                   t 
                   2 
                 
                 
                   t 
                   3 
                 
               
               = 
               
                 
                   R 
                   t 
                 
                 . 
               
             
           
         
       
     
         [0000]    As defined above, the ratio between the thickest and the thinnest elongate members is given by 
         [0000]    
       
         
           
             
               
                 
                   t 
                   r 
                 
                  
                 
                   : 
                 
                  
                 
                     
                 
                  
                 
                   
                     t 
                     1 
                   
                   
                     t 
                     3 
                   
                 
               
               = 
               
                 t 
                 
                   r 
                    
                   
                       
                   
                 
               
             
             , 
           
         
       
     
         [0000]    so that 
         [0000]    
       
         
           
             
               t 
               2 
             
             = 
             
               
                 
                   
                     t 
                     1 
                   
                   
                     
                       t 
                       
                         r 
                          
                         
                             
                         
                       
                     
                   
                 
                  
                 
                     
                 
                  
                 and 
                  
                 
                     
                 
                  
                 
                   t 
                   3 
                 
               
               = 
               
                 
                   
                     t 
                     2 
                   
                   
                     
                       t 
                       r 
                     
                   
                 
                 . 
               
             
           
         
       
     
         [0000]    Alternatively the ratio R t  could vary between sets of structures, leading to what is herein referred to as a multi-fractal grid. 
         [0078]      FIG. 3   e  shows a particularly preferred arrangement in which the number of sets is four: again, according to the non-symmetrical definition of the grid  100 , the first set S 1  comprises one structure, the second set S 2  comprises two structures, the third set S 3  comprises four structures and the fourth set S 4  comprises eight structures. 
         [0079]    Turning now to  FIGS. 5   a  and  5   b , a second embodiment of the grid  200  will now be described; in this embodiment the grid elements comprise a plurality of structures  202 , each in the form of the I structure  202   a  shown in  FIG. 5   a ; in the example shown in  FIG. 5   b  there are five such structures: the first structure  202   a  is composed of elongate members S 1 b 1 , S 1 b 2 , S 1 b 3 ; the second structure  202   b  is composed of elongate members S 2 b 1 , S 2 b 2 , S 2 b 3 ; the third structure  202   c  is composed of elongate members S 2 b 4 , S 2 b 5 , S 2 b 6 ; the fourth structure  202   d  is composed of elongate members S 2 b 7 , S 2 b 8 , S 2 b 9 ; and the fifth structure  202   e  is composed of elongate members S 2 b 10 , S 2 b 11 , S 2 b 12 . For each respective structure the elongate members are interconnected via an attachment point, indicated in  FIG. 5   a  for the first structure  202   a  by references S 1 A 1  and S 1 A 2 . As for the first embodiment, the attachment points are either embodied as an attachment means that enables respective elongate members to separably attach to one another, or as an integral part of the respective elongate members, such that any given structure is part of one planar sheet. 
         [0080]    It will be noted that the ends of individual members of the first structure  202   a  abut members of the other four structures: the grid  200  is configured such that individual structures engage with one another at the abutment points so as to prevent relative movement while the fluid flows therethrough (in the case where the grid  200  is manufactured from a planar sheet, suppression of relative movement between sets of structures is inherent). 
         [0081]    The number of structures making up a given set is constrained by a symmetry condition, which specifies that, with the exception of structures in the last set, each unconnected end of an elongate member in a given set is required to abut a structure in the next set. Accordingly, grid elements according to this second embodiment are arranged in a fractal configuration, since the grid  200  comprises a geometric pattern that is repeated at various scales and can be subdivided into parts, each of which is a smaller copy of the grid as a whole. 
         [0082]    As can be seen from  FIG. 5   b , the elongate members S 1 b 1 , S 1 b 2 , S 1 b 3  of the first structure  202   a  have a thickness different to that of the members of the second-fifth structures  202   b  . . .  202   e , and the thickness of these second-fifth structures  202   b  . . .  202   e  is identical. Accordingly, for an example in which the grid  200  comprises two sets S 1 , S 2  of structures, respective sets differ from one another by virtue of the thickness of the members of the structures. 
         [0083]    Whilst the examples shown in  FIG. 5   b  comprise two sets of structures, S 1 , S 2 , the grid  200  can comprise any number of sets of structures within the constraints of the overall grid configuration, namely that none of the elongate members should cross over another elongate member. This constraint gives rise to a set of geometrical constraints for the ratio between thicknesses of members of respective structures (R t , as described above), and the ratio between lengths of members of respective structures, R L , which, for fractal grids, is constant between sets of structures and for multi-fractal grids can vary between sets of structures (in the case of fractal grids 
         [0000]    
       
         
           
             
               
                 L 
                 1 
               
               
                 L 
                 2 
               
             
             = 
             
               
                 
                   L 
                   2 
                 
                 
                   L 
                   3 
                 
               
               = 
               
                 R 
                 L 
               
             
           
         
       
     
         [0000]    where L 1  denotes the length of structures in the first set S 1 , L 2  denotes the length of structures in the second set S 2 , and L 3  denotes the length of structures in the third set S 3 ). For example, in the case of a fractal grid, one such set specifies R L ≦0.6 and R t ≦1. 
         [0084]    The parameter R L  is related to a further grid parameter, namely the fractal dimension D f  of a given grid: 
         [0000]    
       
         
           
             
               
                 D 
                 f 
               
               ≈ 
               
                 
                   log 
                    
                   
                       
                   
                    
                   B 
                 
                 
                   log 
                    
                   
                     ( 
                     
                       1 
                       / 
                       
                         R 
                         L 
                       
                     
                     ) 
                   
                 
               
             
             , 
           
         
       
     
         [0000]    where B is the multiplier between the number of structures in successive sets of structures (when a grid is defined according to the symmetrical definition such that a structure is considered to be a member of a successive set if it is symmetrically disposed around structure of the previous set), and as can be seen from  FIG. 5   b , B=4. 
         [0085]      FIGS. 6   a - 6   e  show various different grid configurations for which there are four sets of structures and for which the grid is situated within a tunnel having a width, T, of 0.46 m: in each configuration the blockage ratio, σ is 25% and the fractal dimension of the grids, D f , is 2.0. In the first configuration ( FIG. 6   a ) t r  is 2.5 and M eff =36.9 mm; in a second configuration ( FIG. 6   b ), t r  is 5.0 and M eff =36.4 mm; in a third configuration ( FIG. 6   c ), t r  is 8.5 and M eff =35.9 mm; in a fourth configuration ( FIG. 6   d ), t r  is 13.0 and M eff =35.7 mm; and in a fifth configuration ( FIG. 6   e ), t r  is 17.0 and M eff =35.5 mm. In each configuration shown in  FIGS. 6   a - 6   e , the first set S 1  comprises one structure, the second set S 2  comprises two four structures, the third set S 3  comprises sixteen structures and the fourth set S 4  comprises sixty-four structures; it will thus be appreciated that according to the symmetrical definition, the number of structures n i  associated with a given set S i , n i =4 (i-1) . 
         [0086]    Further grid configurations according to the second embodiment are shown in  FIGS. 6   f - 6   j :  FIG. 6   f  shows a grid  200  having five sets of structures, and  FIGS. 6   g - 6   j  shows grids having six sets of structures and fractal dimensions D f  of 1.98, 1.87, 1.79 and 1.68 respectively; these latter Figures clearly show the effect of fractal dimension D f  on blockage distribution across the grid  200 . It will be appreciated from the foregoing that a grid can comprise various numbers of structures and indeed sets of structures, and should not be limited to the 2, 3, 4, 5 or 6 sets of structures illustrated in the accompanying figures. 
         [0087]    Turning now to  FIGS. 7   a ,  7   b  and  7   c , a third embodiment of the grid  300  will be described; in this embodiment the grid elements comprise a plurality of structures  302 , each in the form of a polygon. In the examples shown in  FIGS. 7   a - 7   c  the polygon is embodied as a square, but it could alternatively be triangular, rectangular, hexagonal or any other structure comprising members joined in an end-to-end configuration; in the case of the grid elements comprising square structures, and for the example shown in  FIG. 7   a  there are five such structures: the first structure  302   a  is composed of elongate members S 1 b 1 , S 1 b 2 , S 1 b 3 , S 1 b 4 ; the second structure  302   b  is composed of elongate members S 2 b 1 , S 2 b 2 , S 2 b 3 , S 2 b 4 ; the third structure  302   c  is composed of elongate members S 2 b 5 , S 2 b 6 , S 2 b 7 , S 2 b 8 ; the fourth structure  302   d  is composed of elongate members S 2 b 9 , S 2 b 10 , S z b 11 , S 2 b 12 ; and the fifth structure  302   e  is composed of elongate members S 2 b 13 , S 2 b 14 , S 2 b 15 , S 2 b 16 . For each respective structure the elongate members are interconnected via an attachment point, indicated in  FIGS. 7   a  and  7   b  for the first structure  302   a  by references S 1 A 1 , S 1 A 2 , S 1 A 3  and S 1 A 4 . As for the first and second embodiments, the attachment points are either embodied as an attachment means that enables respective elongate members to separably attach to one another, or is an integral part of the respective elongate members, such that the grid  300  is manufactured from one planar sheet. 
         [0088]    In a first arrangement of this third embodiment, shown in  FIG. 7   a , the elongate members of a given structure have the same thickness as that of members of any other structure, since a grid structure comprising grid elements, or elongate members, joined in an end-to-end configuration is itself novel. In an alternative arrangement, and as can be seen from  FIG. 7   c , the elongate members of the first structure  302   a  can have a thickness different to that of the members of the second-fifth structures  302   b  . . .  302   e , and the thickness of these second-fifth structures  302   b  . . .  302   e  is identical. From a review of  FIGS. 7   a  and  7   c  it will be noted that in either arrangement, each of the structures  302   b - 302   e  of the second set S 2  abut two of the elongate members of the structure  302   a  of the first set S 1  (for example, members S 2 b 3  and S 2 b 4  of structure  302   b  abut elongate members S 1 b 2  and S 1 b 2  respectively of the first structure  302   a ). As a result each elongate member of a structure in a given set has two crossing points and the grid  300  is configured such that these crossing points are arranged so as to prevent relative movement between structures while the fluid flows therethrough (in the case where the grid  300  is manufactured from a planar sheet, suppression of relative movement between sets of structures is inherent). 
         [0089]    As for the first and second embodiments, grid elements according to the third embodiment are arranged in a fractal configuration, since the grid comprises a geometric pattern that is repeated at various scales and can be subdivided into parts, each of which is a smaller copy of the grid as a whole. 
         [0090]      FIGS. 8   a - 8   e  show various different grid configurations for which there are four sets of structures and for which the grid is situated within a tunnel having a width, T, of 0.46 m: in each configuration the blockage ratio, σ is 25% and the fractal dimension of the grids, D f , is 2.0. In the first configuration ( FIG. 8   a ) t r  is 2.5 and M eff =26.6 mm; in a second configuration ( FIG. 8   b ), t r  is 5.0 and M eff =26.5 mm; in a third configuration ( FIG. 8   c ), t r  is 8.5 and M eff =26.4 mm; in a fourth configuration ( FIG. 8   d ), t r  is 13.0 and M eff =26.3 mm; and in a fifth configuration ( FIG. 8   e ), t r  is 17.0 and M eff =26.2 mm. It is to be noted that, as for the example of two sets shown in  FIG. 7   c , each elongate member in a given set has two crossing points where the member abuts members of structures within the next set (for all sets for which there is a next set). 
         [0091]    In each configuration shown in  FIGS. 8   a - 8   e , and according to the symmetrical grid definition, the first set S 1  comprises one structure, the second set S 2  comprises four structures, the third set S 3  comprises sixteen structures and the fourth set S 4  comprises sixty-four structures; it will thus be appreciated that for this embodiment, the number of structures n i  associated with a given set S i , n i =4 (i-1) . In the case of a grid comprising triangular structures, the number of structures associated with a given set S i , n i =3 (i-1) ; thus for a grid comprising a closed p-sided structure, the number of structures n i  associated with a given set S i , n i =p (i-1) . The total number of structures in a grid having q sets can then be derived from the following expression: 
         [0000]    
       
         
           
             
               Total 
                
               
                   
               
                
               
                 no 
                 . 
                 
                     
                 
                  
                 structures 
               
             
             = 
             
               
                 ∑ 
                 
                   i 
                   = 
                   1 
                 
                 
                   i 
                   = 
                   q 
                 
               
                
               
                 p 
                 
                   
                     i 
                     - 
                     1 
                   
                    
                   
                       
                   
                 
               
             
           
         
       
     
         [0092]    Further grid configurations are shown in  FIGS. 8   f  and  8   g :  FIG. 8   f  shows a grid  300  having five sets of structures, D f  of 2.0 and t r  of 17.0 and 28.0 respectively; these latter Figures clearly show the effect of fractal dimension thickness ratio, t r , on blockage distribution across the grid  300 . 
         [0093]    Turning back to  FIG. 4 , it can be seen that for a given blockage ratio, σ, the normalised static pressure drop, 
         [0000]    
       
         
           
             
               C 
               
                 Δ 
                  
                 
                     
                 
                  
                 P 
               
             
              
             
               ( 
               
                 
                   where 
                    
                   
                       
                   
                    
                   
                     C 
                     
                       Δ 
                        
                       
                           
                       
                        
                       P 
                     
                   
                 
                 ≡ 
                 
                   
                     2 
                      
                     Δ 
                      
                     
                         
                     
                      
                     P 
                   
                   
                     ρ 
                      
                     
                         
                     
                      
                     
                       U 
                       ∞ 
                       2 
                     
                   
                 
               
               ) 
             
           
         
       
     
         [0000]    achievable across the grid, is significantly greater when using grids according to the invention than is achievable using known grids (which, as described in the introductory section, comprise a plurality of structures of a uniform size). Furthermore, and particularly surprisingly, the inventors have identified that for a given blockage ratio the pressure drop C ΔP  is independent of how the blockage is distributed: in other words, the pressure drop C ΔP  appears to be insensitive to different arrangements of sets of structures having the same blockage ratio. 
         [0094]    In the course of designing these new and inventive grids, many measurements have been performed in order to characterise the flow field downstream thereof. One such set of measurements involves the turbulence field with axial distance away from the grid (i.e. with increasing values of x). In the course of reviewing the flow field data the inventors identified that for each of the embodiments, the flow field downstream of any grid according to that embodiment could be normalised by certain grid parameters, such that, as a fraction of the mean velocity, the turbulence decay is the same irrespective of grid configuration. This effect is shown in  FIG. 9  for the case of grids according to the first embodiment, in respect of which the flow field can be normalised by the effective mesh size M eff  and the thickness ratio t r ; importantly it is to be noted that the flow fields associated with grids according to the prior art (for which the thickness of the elongate members is uniform across the entire grid) can also be normalised by the effective mesh size M eff  and the thickness ratio t r  (these grids are identified by the label “classic”).  FIG. 10  shows normalised turbulence decay for grids according to the second embodiment, and  FIG. 11  shows the logarithmic normalised turbulence decay for grids according to the third embodiment. 
         [0095]    The inventors then realised that these relationships can be used to design a grid configuration selection tool in order to generate a desired turbulence field (u′/U)—in other words, provided the grid can be described by physical parameters thickness ratio, blockage ratio and mesh perimeter (t r , σ and P (by virtue of the definition of the effective mesh size, 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       M 
                       eff 
                     
                     , 
                   
                   = 
                   
                     
                       4 
                        
                       
                         
                           
                             T 
                             2 
                           
                            
                           
                             ( 
                             
                               1 
                               - 
                               σ 
                             
                             ) 
                           
                         
                         
                           1 
                           / 
                           2 
                         
                       
                     
                     P 
                   
                 
                 ) 
               
               ) 
             
             , 
           
         
       
     
         [0000]    the turbulence field downstream of the grid can be predicted. 
         [0096]    For grids according to the first embodiment of the invention the expression that governs this grid selection is as follows: 
         [0000]      ( u′/U ) 2   =t   r   2   C   ΔP   f   1 ( x/M   eff )  (1) 
         [0000]    where f 1 (x/M eff ) is derivable from the empirical data shown in  FIG. 9 . It is to be noted that axial distance from the grid  100  is metered by units of M eff  rather than absolute distance, x. As stated above, for any given blockage ratio, σ, the pressure drop C ΔP  has been found to be substantially constant; accordingly, given C ΔP  and M eff  the turbulence intensity u′/U and indeed axial decay of turbulence intensity can be controlled by varying the thickness ratio, t r . 
         [0097]    Turning again to  FIG. 10 , for the case of grids according to the second embodiment, the expression that governs grid selection is as follows: 
         [0000]      ( u′/U ) 2   =t   r   C   ΔP ( T/L   max ) 2   f   2 ( x/M   eff )  (2) 
         [0000]    where L max  is the length of the elongate member S 1 b 1  of the structure in the first set S 1  and f 2 (x/M eff ) is derivable from the empirical data shown in  FIG. 10 . Again, axial distance from the grid  200  is metered by units of M eff  rather than absolute distance, x and the thickness ratio, t r , is a significant parameter in the control of the magnitude, and axial decay, of turbulence. 
         [0098]    In relation to the grids according to the third embodiment, the inventors identified the following relationship as unifying the turbulence decay downstream of the grids: 
         [0000]        u′   2   =u′   2   peak exp[−( x−x   peak )/ l   turb ]  (3) 
         [0000]    where x peak  is the absolute axial distance downstream of the grid  300  at which the turbulence field is a maximum and l turb  is the distance for which the turbulence persists downstream of the grid  300 . Referring to  FIG. 11 , an interesting unifying feature of the grids emerges when the logarithmic of this expression is taken: 
         [0000]    
       
         
           
             
               
                 
                   ln 
                    
                   
                     ( 
                     
                       U 
                       
                         u 
                         ′ 
                       
                     
                     ) 
                   
                 
                 2 
               
               = 
               
                 
                   
                     ln 
                      
                     
                       ( 
                       
                         U 
                         
                           u 
                           peak 
                           ′ 
                         
                       
                       ) 
                     
                   
                   2 
                 
                 + 
                 
                   [ 
                   
                     
                       x 
                       - 
                       
                         x 
                         peak 
                       
                     
                     
                       l 
                       turb 
                     
                   
                   ] 
                 
               
             
             , 
           
         
       
     
         [0000]    from which it can be seen that the various flow field profiles  1101 ,  1103 ,  1105 ,  1107 ,  1109  converge onto linear portion  1111 , which corresponds to the latter part of this expression, namely 
         [0000]    
       
         
           
             
               
                 x 
                 - 
                 
                   x 
                   peak 
                 
               
               
                 l 
                 turb 
               
             
             . 
           
         
       
     
         [0000]    The point at which the profiles converge onto linear portion  1111  corresponds to the point downstream at which the turbulence field is at a maximum: x peak . The value of this parameter is dependent on the thickness ratio t r  and it can be seen that the higher the thickness ratio t r , the further upstream (i.e. closer to the grid  300 ) the profile converges onto linear portion  1111 . The parameter x peak  is defined by various grid parameters, namely 
         [0000]    
       
         
           
             
               x 
               peak 
             
             = 
             
               75 
                
               
                 
                   
                       
                   
                    
                   
                     
                       t 
                       
                         m 
                          
                         
                             
                         
                          
                         i 
                          
                         
                             
                         
                          
                         n 
                       
                     
                      
                     T 
                   
                 
                 
                   L 
                   
                     m 
                      
                     
                         
                     
                      
                     i 
                      
                     
                         
                     
                      
                     n 
                   
                 
               
             
           
         
       
     
         [0000]    where t min  and L min  are the thickness and length respectively of the smallest structures in the grid  300 , while the distance downstream for which the turbulence persists is governed by l turb , where 
         [0000]    
       
         
           
             
               
                 l 
                 turb 
               
               = 
               
                 0.1 
                  
                 
                     
                 
                  
                 
                   λ 
                   0 
                 
                  
                 
                     
                 
                  
                 
                   
                     U 
                      
                     
                         
                     
                      
                     
                       λ 
                       0 
                     
                   
                   v 
                 
               
             
             , 
           
         
       
     
         [0000]    ν being the kinematic viscosity of the fluid F. 
         [0099]      FIGS. 9 ,  10  and  11  are concerned with turbulence decay and identifying those grid parameters that have a controlling influence thereon. However, another important flow field characteristic is that of homogeneity, which defines the variation in turbulence intensity in the three axial dimensions x, y, z. It has been identified that homogeneity increases with fractal grid dimension, D f , so that for example in the case of grids  200  according to the second embodiment, the grid shown in  FIG. 6   j , having the lowest value of D f , generates the least homogeneous turbulence field, while the grid shown in  FIG. 6   g , having the highest value of D f , generates the most homogeneous turbulence field. It is to be noted that the effect of grid arrangement on homogeneity is completely decoupled from its effect on turbulence decay, as can be seen from  FIG. 10 . 
         [0100]    The following description, together with  FIGS. 12 and 13 , describe how expressions (1)-(3) can be used in a grid selection routine. Starting with expression (1), and referring to  FIG. 12 , grid selection for the first embodiment starts by specifying the mean velocity U des  and desired pressure drop C ΔP, des  (step S 12 . 1 ); from the empirical data relating pressure drop C ΔP  to blockage ratio, σ, a corresponding blockage ratio is identified at step S 12 . 3 . Having established the blockage ratio, σ, a first effective grid size, M eff  is selected, by setting a value for the perimeter P of the grid (step S 12 . 5 ); next a first predefined value of the thickness ratio t r  is selected (step S 12 . 7 ), and these values are inserted into expression (1) for a predefined range of values for x, in order to establish the turbulence velocity values as a function of M eff /x (step S 12 . 9 ). Once the range of turbulence velocity values has been established, the routine returns to step S 12 . 7  for a second predefined value of the thickness ratio t r , and step S 12 . 9  is repeated for this second value. This is repeated for all of the predefined values of thickness ratio t r , whereupon the routine returns to step S 12 . 5  for different values of grid perimeter P, and indeed the routine can return to step S 12 . 1  and the entire process be repeated for a different pressure drop and thus blockage ratio. 
         [0101]    The routine for grids according to the second embodiment is essentially the same as the routine shown in  FIG. 12 , but step S 12 . 9  involves invoking expression (2); in addition, and in view of the fact that expression (2) includes parameter L max , an additional iteration can be invoked outside of step S 12 . 1 , involving varying of L max . 
         [0102]    The output of these routines will be a sequence of values of the turbulence intensity, u′, for grid parameter values set at instances of steps S 12 . 1 , S 12 . 5  and S 12 . 7 , and a particular grid can be selected from a comparison between the predicted turbulence decay field and a desired turbulence decay field. Such a tool is particularly useful for applications such as mixing of fluids (whether it be mixing of different fluids or mixing streams of the same fluids, the streams having different temperatures), where the mixing rate is highly correlated with turbulence intensity. 
         [0103]    Turning now to the selection routine for grids according to the third embodiment, as will be appreciated from the foregoing, the flow downstream of all of these grids  300  converge onto 
         [0000]    
       
         
           
             
               
                 x 
                 - 
                 
                   x 
                   peak 
                 
               
               
                 l 
                 turb 
               
             
             ; 
           
         
       
     
         [0000]    the routine shown in  FIG. 13  can be used to determine the point at which the turbulence field is a maximum (x peak ), in other words the axial distance at which the measurement data converge onto linear portion  1111 , and the associated turbulence intensity can be derived from where this value of x peak  intersects the linear portion  1111 . 
         [0104]    It will be appreciated that expressions (1) and (2) can be rearranged so as to express the thickness ratio, t r , as a function of the other parameters in the expression. When suitably rearranged, the expressions can then be used to identify a thickness ratio as a function of these other parameters such that the amount of turbulence intensity would be specified instead of being the subject of the calculations. As a result, and in order to identify the thickness ratio corresponding to specified sets of turbulence intensities, a slightly modified grid selection algorithm to those shown in  FIGS. 12 and 13  would be used. 
         [0105]    The above embodiments are to be understood as illustrative examples of the invention. Further embodiments of the invention are envisaged. For example, individual structures could be configured as Koch curve structures and, if the cross section of the conduit  101  were circular instead of rectangular, the grids could be configured so as to have a circular, rather than rectangular, profile. 
         [0106]    In relation to the first aspect of the invention, it is assumed that for a grid comprising two or more sets of structures, the surface area (width, length or depth) of elongate members of each respective set of structures is different; it should be appreciated that for grids comprising three or more sets of structures, the surface area of the structures in the third set can be the same as the surface area of one of the other sets. Similarly, for increasing numbers of sets, and provided the minimum condition of two sets having different thicknesses is satisfied, the thickness of a given set of structures can be replicated in respect of different set(s) of structures. 
         [0107]    Whilst in the foregoing embodiments any given grid comprises structures of the same shape, a grid could alternatively comprise a plurality of structures, each of a different shape; for example, the first set S 1  could comprise a cross-shaped structure, the second set S 2  could comprise I-shaped structures, the third set S 3  could comprise polygon-shaped structures etc. In addition or as a further alternative, the orientation of structures could vary between sets: for example the polygon-shaped structures could, in some sets, be rotated by an angular extent relative to a previous set. 
         [0108]    In the arrangements described above, and as exemplified in the appended Figures, any given grid comprises a symmetrical arrangement of fractal structures. However, a grid could alternatively comprise a non-symmetrical distribution of fractal and/or multi-fractal structures, which is to say that the distribution of fractal/multi-fractal structures within the grid can vary in a non-uniform manner. 
         [0109]    As described above, and referring back to  FIG. 2   c , fluid F flows against a first surface portion  201  and along, or past, a second surface portion  203  of the grid  100 ; the turbulence can be modified by varying the width  209  of the second surface portion  203 , essentially introducing flow control via a third dimension. It has been noted by the inventors that varying this third dimension precipitates the decay of the turbulence field downstream of the grid  100 , thereby providing a further means of tuning mixing efficiencies and vibration control. 
         [0110]    It has been noted that the turbulence control can be realised in a particularly economic and efficient manner with grids according to embodiments of the invention: in particular, grids according to embodiments of the invention enable realisation of a given mixing and/or reaction rate using less energy than is required with known configurations. In particular, embodiments of the invention provide an improved mechanism for mixing in so-called micro channels in which there is otherwise no turbulence. Embodiments of the invention provide a means of introducing flow irregularities over a broad range of small-scales down to the micron scale, thereby artificially introducing turbulence and forcing mixing within the channel. In one arrangement the channel dimension and corresponding overall fractal grid size is of the order 1 cm, but channel dimensions of between 2.5 cm and 10 microns (and corresponding grid sizes) fall within the definition of micro channels, and are thus possible applications for embodiments of the invention. Similarly, fractal grids of the micron-scale can be used for microchip cooling technology as an aid to improving heat transfer from the chips (the use of micron chip sizes presents overheating problems). 
         [0111]    In view of the fact that fluid modification apparatus according to embodiments of the invention have a significant effect on flow field parameters such as pressure drop and turbulence intensity, embodiments of the invention can be used in applications such as air braking (e.g. for aeroplanes); aerodynamic control of fluid flow around motor vehicles and motorbikes; control of wind characteristics in sailing applications; among many others: in such applications it will be appreciated that the relative movement is induced by physical movement of the grid relative to the surrounding fluid, in which case the support structure would be affixed, e.g. to the wing of the aeroplane. Alternatively relative movement could be provided by movement on the part of both the grid and the fluid. In addition, fluid modification apparatus according to embodiments of the invention could be used to control of mixing of reacting fluids in vessels and combustion chambers. 
         [0112]    Experimental data taken during landing of an aircraft indicate that, compared with the amount of noise associated with conventional (solid) wing slats and flaps, a reduced amount of noise is generated during landing of an aircraft when the landing slats include fractal airbreaks.  FIG. 14  shows an airbrake comprising a grid  100  according to an embodiment of the invention, the airbrake being hingedly connected to an aircraft wing  1400  between the leading edge  1401  and the trailing edge  1403  thereof. The fixing arrangement for connecting the fractal airbrake  100  to the wing  1400  preferably includes a lowering and raising mechanism, the operation of which can be dependent on airspeed and controlled by an actuation system (such a configuration being employed in conventional leading edge wing slats mechanisms). One example arrangement is illustrated in  FIG. 15 , which shows a plurality of slats having been deployed, each slat comprising fractal airbrakes  100 . As a general design principle, the type of fractal grid and its adaptation can be determined as functions of a number of various fractal, aerodynamic and structural parameters. Indeed, whilst the example shown in  FIG. 15  shows a similar geometrical configuration between respective fractal airbrakes, each or some of the individual fractal airbreaks could alternatively have different configurations, either in terms of structures making up a given airbreak and/or fractal dimension D f  and/or thickness ratio t r . 
         [0113]    Furthermore the fluid modification apparatus can be used to reduce structural vibrations that would otherwise be induced by aerodynamic loading. 
         [0114]    Other applications of embodiments of the invention include heat transfer and/or flow oscillations, specifically as a means to control acoustic noise and/or heat transfer to walls of a channel (since embodiments of the invention improve the mixing within the channel, and thereby flatten the heat transfer profile across a given channel cross section). 
         [0115]    Whilst the measurement data show that the fluid modification apparatus affects the flow field so as to modify the turbulence intensity therein, the fluid modification apparatus can also be used to modify chemical structures within the fluid, for example, if the elongate members were coated with a catalyst material or a material that reacts with the incoming fluid. 
         [0116]    It is to be understood that any feature described in relation to any one embodiment may be used alone, or in combination with other features described, and may also be used in combination with one or more features of any other of the embodiments, or any combination of any other of the embodiments. Furthermore, equivalents and modifications not described above may also be employed without departing from the scope of the invention, which is defined in the accompanying claims.