Abstract:
Two or more disks of single or multiple materials of any given diameter and thickness whether homogeneous, tapered or contoured in a constant, linear or non-linear fashion in the axial direction with one or more openings in the disk(s) to create a fluid flow channel from the periphery of the disk(s) to the center near the shaft or vice versa and spaced a distance apart by a bracket, spacer or location along the shaft, used to comprise a disk assembly of a bladeless compressor, pump or turbine. Embodiments of this invention include the non-constant treatment of the assembly outer diameter, fluid flow channel inner and/or outer diameters as well as the differentiation in gap size between disks of the assembly.

Description:
FIELD OF THE INVENTION  
       [0001]     This invention relates to the geometric shape and/or configuration of the fluid flow channels and overall assembly of a disk and/or bracket assembly or assemblies on the rotor(s) of bladeless (disk) turbine(s), bladeless (disk) compressor(s) and/or bladeless (disk) pump(s). This invention offers improvements in the fluid flow channel design as well as improvements to geometry created by groups of disks and/or brackets in a single assembly to increase the efficiency of energy extraction or infusion between the working mechanical components and the working fluid or vice versa whether the working fluid be compressible, incompressible, Newtonian or non-Newtonian in nature.  
       BACKGROUND  
       [0002]     Microturbines are gas turbines generally implemented for electrical power generation applications. Relatively small in comparison to standard power plants, they can be located on sites with space limitations for power production. Microturbines are composed of a compressor, combustor, turbine, alternator, possibly a reheater or recuperator, and generator assembled in any number or order on one, two or three spools. Waste heat recovery can be used in combined heat and power systems to achieve energy efficiency levels greater than 80 percent. Such combinations include but are not limited to combined power and water heating cycles or combined power, heating-ventilation-air-conditioning and water heating systems. In addition to stationary and portable electrical power generation, microturbines offer an efficient and clean solution to direct mechanical drive markets such as compression, machine tools and air conditioning.  
         [0003]     In the commercial and government electrical power markets, independence from the power grid is being sought to lessen the production burden on central power companies and traditional power sources. This move will begin to decentralize the power sources and assure service to all areas under United States sovereignty. Such decentralization protects the power supply from failure by providing for individual consumers such as homes and businesses. Furthermore, power service is commonly affected by storms, hurricanes, tornadoes, earthquakes and other natural disasters which interrupt power service to thousands of individuals in surrounding areas. Terrorist activities, nuclear meltdowns, acts of God or the public enemy; fires; floods; riots; strikes; shortage of labor, inability to secure fuel and/or material supplies, affect power supply and account for shortages thereof as well. Existing and future laws or acts of the Federal or of any State or Territorial Government (including specifically but not exclusively any orders, rules or regulations issued by any official agency or such government) or other unpredictable occurrences also provide service barriers creating situations prone to a lack of power and inappropriate service for consumers. Beyond the discomfort of the power loss, some residents find themselves in desperate circumstances fighting extreme cold or heat.  
         [0004]     The benefits of microturbines are to provide power to individual consumers through individual micro power plants at a reasonable cost with a reasonable payback period of the consumer&#39;s investment over the life of the product. Eight benefits of microturbines as reported by the World Watch Institute (“Micropower: The next electrical era”, Worldwatch Paper 151, July 2000) are given as: 
        1. Modularity—By adding or removing units, micropower system size can be adjusted to match demand.     2. Short Lead Time—Small-scale power can be planned, sited and built more quickly than larger systems, reducing the risks of overshooting demand, longer construction periods and technological obsolescence.     3. Fuel Diversity and reduced volatility—Micropower&#39;s more diverse, renewables-based mix of energy sources lessens exposure to fossil fuel price fluctuations.     4. “Load-growth insurance” and load matching—Some types of small-scale power, such as cogeneration and end-use efficiency, expand with growing loads; the flow of other resources, like solar and wind, can correlate closely with electricity demand.     5. Reliability and resilience—Small plants are unlikely to all fail simultaneously; they have shorter outages, are easier to repair, and are more geographically dispersed.     6. Avoided plant and grid construction and losses—Small-scale power can displace construction of new plants, reduce grid loss, and delay or avoid adding new grid capacity or connections.     7. Local and community choice control—Micropower provides local choice and control and the option of relying on local fuels and spurring community economic development.     8. Avoid emissions and other environmental impacts—Small-scale power generally emits lower amounts of particulates, sulfur dioxide and nitrogen oxides, heavy metals, and carbon dioxide, and has a lower cumulative environmental impact on land and water supply and quality.        
 
         [0013]     Technology trends as witnessed by U.S. Pat. No. 6,324,828 (Willis et al.); U.S. Pat. No. 6,363,712 (Sniegowski et al.); U.S. Pat. No. 6,392,313 (Epstein et al.); U.S. Pat. No. 6,526,757 (MacKay); and U.S. Pat. No. 6,814,537 (Olsen) demonstrate the implementation of conventional radial compressors and turbines in creating microturbines to power the electrical generation system currently on the market and in development. In particular, Olsen demonstrates a method for a rotor assembly with conventional turbine allowing interchangeability.  
         [0014]     A bladeless turbine design was first patented by Nikola Tesla (U.S. Pat. No. 1,061,206) in 1913 for use as a steam turbine to extract energy from a working fluid. This original patent included the grouping of a series of disks and blades with identical passage holes symmetrically grouped around the rotor. The working fluid was introduced at pressure and temperature through a form of nozzle at an angle on the outer perimeter of the disks. With only the passage holes in the disks as an outlet for the working fluid, it was forced across the disks radially and angularly inward to exit through an axially located outlet which path resulted in reduction of pressure and temperature of the working fluid and the consequent rotation of the rotor assembly. This configuration is known as a Tesla, bladeless and/or disk turbine, compressor and/or pump. The general concept has been widely implemented as a pump, witnessed in U.S. Pat. No. 3,644,051 (Shapiro); U.S. Pat. No. 3,668,393 (Von Rauch); and U.S. Pat. No. 4,025,225 (Durant) and a turbine, witnessed in U.S. Pat. No. 1,061,206 (Tesla); U.S. Pat. No. 2,087,834 (Brown et al.); U.S. Pat. No. 4,025,225 (Durant); U.S. Pat. No. 6,290,464 (Negulescu et al.); U.S. Pat. No. 6,692,232 (Letourneau); and U.S. Pat. No. 6,726,443 (Collins et al.). In form without brackets between the disks, the bladeless turbine is referred to as a Prandtl Layer turbine as witnessed in U.S. Pat. No. 6,174,127 (Conrad et al.); U.S. Pat. No. 6,183,641 (Conrad et al.); U.S. Pat. No. 6,238,177 (Conrad et al.); U.S. Pat. No. 6,261,052 (Conrad et al.); and U.S. Pat. No. 6,328,527 (Conrad et al.)  
         [0015]     Standard practice among individual researchers and hobbyists is to combine multiple disks each of identical outer radius and chamber size in the same turbine, compressor or pump assembly. This method is referred to as a constant-geometry disk assembly and is witnessed in U.S. Pat. No. 1,061,206 (Tesla); U.S. Pat. No. 3,644,051 (Shapiro); U.S. Pat. No. 3,668,393 (Von Rauch); U.S. Pat. No. 4,025,225 (Durant); U.S. Pat. No. 4,201,512 (Marynowski et al.); U.S. Pat. No. 6,227,795 (Schmoll, III); U.S. Pat. No. 6,726,442 (Letourneau); U.S. Pat. No. 6,726,443 (Collins et al.); and U.S. Pat. No. 6,779,964 (Dial).  
         [0016]     It has been found by others that variations in the disk shape, referred to here as disk bending, gap differentiation, variation in outer diameters of disks within a single assembly and variation in diameter of flow chambers from one disk to the next alter the performances of the disk assembly. Those are listed as follows: 
        (1) Disk bending—U.S. Pat. No. 1,445,310 (Hall); U.S. Pat. No. 2,087,834 (Brown et al.); U.S. Pat. No. 4,036,584 (Glass); U.S. Pat. No. 4,652,207 (Brown et al.)     (2) Gap differentiation—U.S. Pat. No. 2,087,834 (Brown et al.); U.S. Pat. No. 4,402,647 (Effenberger)     (3) Outer diameter variation—U.S. Pat. No. 5,419,679 (Gaunt et al.); U.S. Pat. No. 6,261,052 (Conrad et al.)     (4) Flow chamber diameter variation—U.S. Pat. No. 2,626,135 (Serner); U.S. Pat. No. 3,273,865 (White); U.S. Pat. No. 5,446,119 (Boivin et al.); U.S. Pat. No. 6,183,641 (Conrad et al.); U.S. Pat. No. 6,238,177 (Conrad et al.); U.S. Pat. No. 6,261,052 (Conrad et al.)        
 
         [0021]     The variations in the assemblies just described pertain to the disks in the assembly only. Only in U.S. Pat. No. 2,626,135 (Serner); U.S. Pat. No. 4,402,647 (Effenberger); and U.S. Pat. No. 5,466,119 (Boivin et al.) are the spacers, hereto referred as brackets, and gaps between the disks approached in design. Serner takes the bridge of the disk and bends it to induce higher efficiency in energy translation from the fluid to the rotor or vice versa. Effenberger tapers the disks to achieve a desired effect on the gap, but shows no interest in deviating from standard practice in bracket design or outer diameter variation. Boivin et al. include one spacer with a knife-shaped deformable portion to compensate for adjustments when combining a turbomolecular bladeless pump with a stator.  
         [0022]     Most of the above methods are implemented for incompressible fluids or steam. In the instance a bladeless configuration is implemented with ideal or near-ideal gases, such as air, the kinematic viscosity effect is considerably lessened. Furthermore, variations in fluid flow design through the disks and brackets do not geometrically coincide with standard assembly designs.  
         [0023]     The variations in the assemblies just described are shown to be linear variations with no apparent scientific method for choosing said variations or combining any of the methods. It appears they were accomplished at random or through empirical methods. Furthermore, all of the variations described above remain linear in appearance proving to have a constant rate of increase or decrease from one disk to another when they are not retained at constant geometric values. No coordinates or variables are firmly established upon which to base the above variations or any others which may occur in the future. Furthermore, all of the above mentioned efforts focus on the mechanical devices, whereas the optimization of the fluid flow and its characteristics are largely ignored.  
         [0024]     It is these issues which have brought about the present invention.  
       SUMMARY OF THE INVENTION SUMMARY OF THE INVENTION  
       [0025]     A bladeless turbine, compressor or pump working with a compressible or incompressible fluid relies on the viscosity and impingement of the fluid to propel the disk assembly through the extraction of energy or vice versa from the rotor to the fluid. Likewise, when energy is added into the working fluid from the disk assembly, it is through impingement and viscosity of the fluid the energy is transferred. Thus, as a working fluid with lower kinematic viscosity is implemented, the ability of the disks to extract or infuse energy into or from the fluid system is proportionally decreased whether this variational relationship be constant, linear or non-linear in nature.  
         [0026]     Individual researchers and hobbyists will reduce the distance between disks in a given assembly to increase the likelihood of energy exchange between the mechanical and fluid systems as the viscosity decreases. When the working fluid is compressible rather than incompressible the viscosity changes by several factors. For example, the kinematic viscosity of an incompressible fluid could be on the order of 1 e−1 while the kinematic viscosity of a compressible fluid could be on the order of 1 e−6. The inability to reduce the distance between disks by such a great factor—assuming a linear relationship between the effects—as the kinematic viscosity is reduced leads to the conclusion that the mechanical system must work harder to increase the pressure and temperature gradients to obtain similar mass flow rates as with incompressible fluids.  
         [0027]     The most common implementation of bladeless turbines, compressors and pumps is with incompressible fluids for this very reason. One can gain satisfactory performance with an incompressible fluid running the bladeless device in a range from 0-25,000 RPM. When implementing a compressible fluid, this range of rotational speed accomplishes very little compression and mass flow comparatively. To obtain the design point of bladeless devices with compressible flow, they must be run at speeds up to 100,000 RPM and beyond.  
         [0028]     Running a rotational device at high RPM as just described brings the outer diameter of the rotor near to stalling speed by approaching, reaching or surpassing the speed of sound under its operating conditions. For this reason, only smaller bladeless turbines, compressors and pumps ranging in size from 1 nanometer to around 150 centimeters in diameter are suited for working at high rotational speeds.  
         [0029]     A disk working at such high rotational speeds with a compressible fluid inherently causes the bridge, holding the hub of the disk to the working surface of the disk and creating the flow chamber, to become an object with which the fluid will collide. Said collision is another method, perhaps the primary method at such high speeds, through which energy is exchanged from the working fluid to the mechanical system or vice versa. The low kinematic viscosity of the compressible working fluid at high RPM having a lesser effect on energy transfer. The importance of these phenomena is reversed in incompressible working fluids running with a bladeless rotor at low RPM.  
         [0030]     An object of this invention is to define the reference system and the variables necessary to produce variation in rotor assembly and fluid flow channel design beyond those standardly used in prior art.  
         [0031]     An object of the invention is to improve rotor performance at high rotational speeds through implementing the variation in outer diameter of the disk assembly in any given configuration on a rotor.  
         [0032]     An object of the invention is to improve rotor performance at high rotational speeds through implementing the variation in outer and/or inner diameter of the fluid flow channels in any given configuration on a rotor.  
         [0033]     A further object of the invention is to provide improved flow channel and assembly geometry combinations to maximize efficiency and improve performance at high RPM with a compressible fluid through the constant, linear and/or non-linear assembly geometry combinations maximizing energy extraction or infusion to and/or from the working fluid.  
         [0034]     Further, an object of the invention is to provide a variation in gap widths between disks of the rotor assembly which, based on the implementation of the bladeless turbine, compressor or disk, will maximize the efficiency of energy transfer within various performance parameters.  
         [0035]     Finally, an object of the invention is to provide several alternate rotor configuration geometries capable of improving the disk performances at high RPM. 
     
    
     DESCRIPTION OF THE DRAWINGS  
       [0036]      FIGS. 1   a ,  1  b,  1   c ,  1  d, &amp;  1   e : Prior art in outer diameter and flow channel geometry;  
         [0037]      FIGS. 2   a ,  2   b  &amp;  2   c : Descending outer diameter with various fluid flow channel geometries;  
         [0038]      FIG. 3   a ,  3   b : Ascending outer diameter with various fluid flow channel geometries;  
         [0039]      FIG. 4 : Variation in gap/bracket width;  
         [0040]      FIGS. 5   a ,  5   b  &amp;  5   c : Converging/Diverging concave fluid flow channels;  
         [0041]      FIGS. 6   a ,  6   b  &amp;  6   c : Converging/Diverging convex fluid flow channels;  
         [0042]      FIGS. 7   a  &amp;  7   b : Convex/Concave non-linear outer diameter geometries; 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0043]     All figures discussed and shown below assume cylindrical coordinates, (x, r, θ) as a point of reference and axisymmetry in the shaft and disk assemblies. Thus the origin of the x-axis is assumed to represent a shaft of any given diameter. The r-axis demonstrates the radial direction of a rotor and assembly. As the inner or outer diameter of any component is discussed, “diameter” being a colloquial term, these consequently appear as radii in each of the diagrams. The angular direction of the θ-axis is not shown due to the assumed general axisymmetry of the assemblies. However, general axisymmetry of a round disk does not limit in any fashion the scope of this invention regarding possible variations of the geometric properties of single components, the rotor and/or the assembly on the θ-axis as discussed in this document. It is only intended by the statements in this paragraph to note the given figures of this document sufficiently describe the desired parameters of variation beyond the prior art and do not limit the possible embodiments in any fashion.  
         [0044]      FIG. 1  establishes a datum of prior art along with the following definitions necessary in discussion of the present invention:  
                                             Definition List 1                Term   Definition                       Gap   Distance between disks in a rotor               assembly whether spaced by a bracket,               spacer or disk placement on a shaft.           Hub   The material filling the distance between               the axis and inner diameter of the fluid               flow chambers, nominal in value with               constant, linear or non-linear behavior in               relation to each other and/or a central               axis while grouped with and similar to               the diameter of the shaft in order of               magnitude.           n   Number of open disks with fluid flow               chambers. Generally equal to m.           m   Number of brackets, spacers and/or               location distance(s) separating the disks               in a bladeless turbine, compressor or               pump rotor assembly. Generally equal               to n.           R IDChannel     Inner diameter of the fluid flow channel               physically defined by the hub(s) of the               disk assembly.           R ODChannel     Outer diameter of the fluid flow channel               physically defined by the inner most               diameter of the working surface(s) of the               disk assembly.           R ODDisk     Outer diameter of the disk assembly               physically defined by the outer               diameter(s) of the disks in the assembly.           ∇   First-order multi-dimensional               differential representing the first-order               variation in a variable as a function of               each of the standard Cartesian, spherical               or cylindrical coordinates.           ∇ 2     Second-order multi-dimensional               differential representing the second-               order variation in a variable as a function               of each of the standard Cartesian,               spherical or cylindrical coordinates.                        
         [0045]      FIG. 1   a  demonstrates Tesla&#39;s original bladeless turbine concept (U.S. Pat. No. 1,061,206) with the flow direction running from the periphery, outer diameter [ 6 ], of the blades to the center of the assembly parallel to the axis [ 1 ] through fluid flow chambers with the working fluid [ 8 ] exiting through an open end disk [ 4 ] and blocked by a closed end disk [ 5 ] at the opposite end. A rotor assembly consisting of a shaft [ 1 ], any number of open disks [ 2 ], n, with a nominal amount of fluid flow chambers evenly spaced by any number of brackets, spacers or disk location(s) [ 3 ], m, on the shaft [ 1 ]. In this prior art, the outer diameter [ 6 ] of the assembly of disks is constant described as ∇R ODDisk =∇ 2 R ODDisk =0, as well as the inner [ 1 ] and outer [ 7 ] diameters of the flow channel ∇R ODChannel =∇ 2 R ODChannel =∇R IDChannel =∇ 2 R IDChannel =0. For purposes of clarity, the figures in this document assume the distance between the axis and inner diameter of the fluid flow chambers to be nominal in value with constant, linear or non-linear behavior in relation to each other and/or a central axis—the material between the two is referred to as the Hub of the disk, bracket or assembly group—while grouped with and similar to the diameter of the shaft [ 1 ] in order of magnitude. In U.S. Pat. No. 1,061,142 Tesla shows the standard design of  FIG. 1   a  can be used to propel fluid through having it flow from the center to the periphery, opposite the direction shown in  FIG. 1   a . Flow from the center to the periphery is further demonstrated by Serner (U.S. Pat. No. 2,626,135).  
         [0046]      FIGS. 1   b  and  1   c  demonstrate variations from Tesla&#39;s original design used in prior art primarily by Serner (U.S. Pat. No. 2,626,135) and White (U.S. Pat. No. 3,273,865) with the flow direction running from the periphery, outer diameter [ 16 ] &amp; [ 26 ] of the blades to the center of the assembly parallel to the axis [ 11 ] &amp; [ 21 ] through fluid flow chambers with the working fluid [ 18 ] &amp; [ 28 ] exiting through an open end disk [ 14 ] &amp; [ 24 ] and blocked by a closed end disk [ 15 ] &amp; [ 25 ] at the opposite end.  FIG. 1   d  demonstrates a flow direction opposite that of  FIG. 1   b  with the flow direction running parallel to the axis [ 31 ] through fluid flow chambers beginning with an open end disk [ 34 ] with the working fluid [ 38 ] exiting at the periphery, outer diameter [ 36 ] of the blades as forced by a closed end disk [ 35 ].  FIGS. 1   b ,  1   c  and  1   d  demonstrate a rotor assembly consisting of a shaft [ 11 ], [ 21 ] &amp; [ 31 ] which does not extend into the assembly, any number of open disks [ 12 ], [ 22 ] &amp; [ 32 ], n, with a nominal amount of fluid flow chambers evenly spaced by any number of brackets, spacers or disk location(s) [ 13 ], [ 23 ] &amp; [ 33 ], m, on the shaft [ 11 ], [ 21 ] &amp; [ 31 ]. In this prior art, the outer diameter [ 16 ], [ 26 ] &amp; [ 36 ] of the assembly of disks is constant described as ∇R ODDisk =∇ 2 R ODDisk =0, as well as the inner [ 11 ], [ 21 ] &amp; [ 31 ] diameters of the flow channel ∇R IDChannel =∇ 2 R IDChannel =0. The variation from Tesla&#39;s original design lies in the outer diameter [ 17 ], [ 27 ] &amp; [ 37 ] described as being linear in its variation gradually decreasing as the working fluid flow progresses along the axis. In this document, such geometry will be defined as a constant negative axial gradient, −∂R ODChannel /∂x=constant, ∂R ODChannel /∂r=0, ∂R ODChannel /∂θ=0 and ∇ 2 R ODChannel =0 assuming cylindrical coordinates, or linear variation in the axial direction.  
         [0047]      FIG. 1   e  demonstrates Gaunt et al.&#39;s variation in outer diameter (U.S. Pat. No. 5,419,679) with the flow direction running parallel to the axis [ 41 ] through fluid flow chambers beginning with an open end disk [ 44 ] with the working fluid [ 48 ] exiting at the periphery, outer diameter [ 46 ] of the blades as forced by a closed end disk [ 45 ]. A rotor assembly consisting of a shaft [ 41 ] which does not extend into the disk assembly, any number of open disks [ 42 ], n, with a nominal amount of fluid flow chambers evenly sized and spaced by any number of brackets, spacers or disk location(s) [ 43 ], m, on the shaft [ 41 ]. In this prior art, the outer diameter [ 46 ] of the assembly of disks varies, increasing in size as the fluid flow progresses, described as being linear in its variation. In this document, such geometry will be defined as a constant positive axial gradient, ∂R ODDisk /∂x=constant, ∂R ODDisk /∂r=0, ∂R ODDisk /∂θ=0 and ∇ 2 R ODDisk =0 assuming cylindrical coordinates, or linear variation in the axial direction. Furthermore, the variation in inner or outer diameter of the fluid flow chambers are given as zero such that ∇R ODChannel =∇ 2 R ODChannel =∇R IDChannel =∇ 2 R IDChannel =0.  
         [0048]     According to the present invention, the following variations in disk assembly and fluid flow channel geometry are defined as prior art for bladeless turbines, compressors and pumps:  
                                         Definition List 2            Term   Definition               ∇R ODDisk =∇ 2 R ODDisk =0   Constant outer diameter of the           disk assembly, from disk to disk.       ∇R ODChannel =∇ 2 R ODChannel =0   Constant outer diameter of the           flow channel.       ∇R IDChannel =∇ 2 R IDChannel =0   Constant inner diameter of the           flow channel.       ∂R ODDisk /∂x= constant   Linearly increasing outer diameter           of the disk assembly, from disk to           disk, along the flow direction of           the axis.       −∂R ODChannel /∂x= constant   Linearly decreasing outer diameter           of the fluid flow channel along           the flow direction of the axis.                  
 
         [0049]     According to the present invention, the following variations in disk assembly and fluid flow channel geometry are defined as capable of improving the performances of bladeless turbines, compressors and pumps:  
                                             Definition List 3                Term   Definition                       ∇R ODDisk ≠0,   Non-constant outer diameter of the disk           ∇ 2 R ODDisk ≠0   assembly, from disk to disk, varying               linearly or non-linearly with a positive or               negative gradient on any one, two or               three of the standard cylindrical axes.               Excluding the one possibility of               ∂R ODDisk /∂x= constant.           ∇R ODChannel ≠0,   Non-constant outer diameter of the fluid           ∇ 2 R ODChannel ≠0   flow channel in the disk assembly,               through the disk and/or disk-bracket-               disk, varying linearly or non-linearly with               a positive or negative gradient on any               one, two or three of the standard               cylindrical axes. Excluding the one               possibility of −∂R ODChannle /∂x= constant               channel.           ∇R IDChannel ≠0,   Non-constant inner diameter of the fluid           ∇ 2 R IDChannel ≠0   flow channel in the disk assembly,               through the disk and/or disk-bracket-               disk, varying linearly or non-linearly with               a positive or negative gradient on any               one, two or three of the standard               cylindrical axes.           ∂R ODDisk /∂x&lt;0   Linearly decreasing outer diameter of the               disk assembly, from disk to disk, along               the flow direction of the axis.           ∂R ODChannel /∂x&gt;0   Linearly increasing outer diameter of the               fluid flow channel along the flow               direction of the axis.                      
 
         [0050]      FIGS. 2   a ,  2   b  &amp;  2   c  demonstrate a bladeless turbine, compressor or pump whose flow direction [ 58 ], [ 68 ] &amp; [ 78 ] is shown running from the axis [ 51 ], [ 61 ] &amp; [ 71 ] through the open-end disk [ 54 ], [ 64 ] &amp; [ 74 ] and the assembly of disks [ 52 ], [ 62 ] &amp; [ 72 ] and expelling along the periphery, outer diameter [ 56 ], [ 66 ] &amp; [ 76 ] of the disk assembly. The geometry shown in  FIGS. 2   a ,  2   b  &amp;  2   c  is also valid for flow beginning at the periphery, outer diameter [ 56 ], [ 66 ] &amp; [ 76 ], of the blade assembly [ 52 ], [ 62 ] &amp; [ 72 ] to the center of the assembly parallel to the axis [ 51 ], [ 61 ] &amp; [ 71 ] through fluid flow chambers with the working fluid [ 58 ], [ 68 ] &amp; [ 78 ] exiting through an open end disk [ 54 ], [ 64 ] &amp; [ 74 ] and blocked by a closed end disk [ 55 ], [ 65 ] &amp; [ 75 ] at the opposite end insomuch as the geometry does not represent prior art. A rotor assembly consisting of a shaft [ 51 ], [ 61 ] &amp; [ 71 ], any number of open disks [ 52 ], [ 62 ] &amp; [ 72 ], n, with a nominal amount of fluid flow chambers evenly spaced by any number of brackets, spacers or disk location(s) [ 53 ], [ 63 ] &amp; [ 73 ], m, on the shaft [ 51 ], [ 61 ] &amp; [ 71 ]. In one embodiment, the outer diameter [ 56 ], [ 66 ] &amp; [ 76 ] of the assembly of disks is variable described as ∇R ODDisk ≠0 and ∇ 2 R ODDisk ≠0. This is valid for all possibilities of constant, linear and/or non-linear variations with the single exception of ∂R ODDisk /∂x=constant but including ∂R ODDisk /∂x&lt;0 as demonstrated in  FIGS. 2   a ,  2   b  &amp;  2   c .  FIG. 2   a  demonstrates the outer diameter [ 66 ] variation on the disks decreasing towards the closed end disk along with inner [ 61 ] and outer [ 67 ] diameters of the flow channels at ∇R ODChannel =∇ 2 R ODChannel =∇R IDChannel =∇ 2 R IDChannel =0.  FIGS. 2   b  &amp;  2   c  demonstrate a combination of geometries where the outer diameter of the disk assembly [ 66 ] &amp; [ 76 ] varies decreasingly toward the closed end disk along with variation in the inner [ 61 ] &amp; [ 71 ] and/or outer [ 67 ] &amp; [ 77 ] diameters of the flow channels at ∇R ODChannel ≠0 and/or ∇R IDChannel ≠0 where the second differential of each, ∇ 2 R ODChannel  and ∇ 2 R IDChannel , may have a negative, positive or zero value. Furthermore,  FIGS. 2   a ,  2   b  &amp;  2   c  represent the option of varying geometry through combining second order variations in geometry while the first order variations are zero such that ∇R ODChannel =0, ∇ 2 R ODChannel ≠0, ∇R IDChannel =0, ∇ 2 R IDChannel ≠0, ∇R ODDisk =0 and ∇ 2 R ODDisk ≠0 with any combination of these components possible in the embodiment of this invention.  
         [0051]      FIGS. 3   a  &amp;  3   b  demonstrate a bladeless turbine, compressor or pump whose flow direction [ 88 ] &amp; [ 98 ] is shown running from the axis [ 81 ] &amp; [ 91 ] through the open-end disk [ 84 ] &amp; [ 94 ] and the assembly of disks [ 82 ] &amp; [ 92 ] and expelling along the periphery, outer diameter [ 86 ] &amp; [ 96 ] of the disk assembly. The geometry shown in  FIGS. 3   a  &amp;  3   b  is also valid for flow beginning at the periphery, outer diameter [ 86 ] &amp; [ 96 ], of the blade assembly [ 82 ] &amp; [ 92 ] to the center of the assembly parallel to the axis [ 81 ] &amp; [ 91 ] through fluid flow chambers with the working fluid [ 88 ] &amp; [ 98 ] exiting through an open end disk [ 84 ] &amp; [ 94 ] and blocked by a closed end disk [ 85 ] &amp; [ 95 ] at the opposite end insomuch as the geometry does not represent prior art. A rotor assembly consisting of a shaft [ 81 ] &amp; [ 91 ], any number of open disks [ 82 ] &amp; [ 92 ], n, with a nominal amount of fluid flow chambers evenly spaced by any number of brackets, spacers or disk location(s) [ 83 ] &amp; [ 93 ], m, on the shaft [ 81 ] &amp; [ 91 ]. In one embodiment, the outer diameter [ 86 ] &amp; [ 96 ] of the assembly of disks is variable described as ∇R ODDisk ≠0 and ∇ 2 R ODDisk ≠0. This is valid for all possibilities of constant, linear and/or non-linear variations with the single exception of ∂R ODDisk /∂x=constant but including ∂R ODDisk /∂x&lt;0 as demonstrated in  FIGS. 3   a  &amp;  3   b .  FIGS. 3   a  &amp;  3   b  demonstrate a combination of geometries where the outer diameter of the disk assembly [ 86 ] &amp; [ 96 ] varies increasingly towards the end disk of the assembly along with variation in the inner [ 81 ] &amp; [ 91 ] and/or outer [ 87 ] &amp; [ 97 ] diameters of the flow channels at ∇R ODChannel ≠0 and/or ∇R IDChannel ≠0 where the second differential of each, ∇ 2 R ODChannel  and ∇ 2 R IDChannel , may have a negative, positive or zero value. Furthermore,  FIGS. 3   a  &amp;  3   b  represent the option of varying geometry through combining second order variations in geometry while the first order variations are zero such that ∇R ODChannel =0, ∇ 2 R ODChannel ≠0, ∇R IDChannel =0, ∇ 2 R IDChannel ≠0, ∇R ODDisk =0 and ∇ 2 R ODDisk ≠0 with any combination of these components possible in the embodiment of this invention.  
         [0052]      FIG. 4  demonstrates a bladeless turbine, compressor or pump whose flow direction [ 108 ] is shown running from the axis [ 101 ] through the open-end disk [ 104 ] and the assembly of disks [ 1   02 ] and expelling along the periphery, outer diameter [ 1   06 ] of the disk assembly. The geometry shown in  FIG. 4  is also valid for flow beginning at the periphery, outer diameter [ 1   06 ], of the blade assembly [ 1   02 ] to the center of the assembly parallel to the axis [ 101 ] through fluid flow chambers with the working fluid [ 1   08 ] exiting through an open end disk [ 1   04 ] and blocked by a closed end disk [ 1   05 ] at the opposite end insomuch as the geometry does not represent prior art. For purposes of clarity, a rotor assembly consisting of a shaft [ 1   01 ], any number of open disks [ 1   02 ], n, with a nominal amount of fluid flow chambers evenly spaced by any number of brackets, spacers or disk location(s) [ 1   03 ], m, on the shaft [ 101 ] are shown at constant geometry to demonstrate the gap width variation, ∂Gap 1 /∂x . . . ∂Gap m /∂x. In one embodiment, the outer diameter [ 1   06 ] of the assembly of disks is variable described as ∇R ODDisk ≠0 and ∇ 2 R ODDisk ≠0. This is valid for a combination of gap width variation, ∂Gap m /∂x, with all possibilities of random, constant, linear and/or non-linear variations. Gap width variation as outlined in  FIG. 4  is possible with a combination of geometries including but not limited to a constant geometry as depicted, all gradients except gap width are zero, and/or where the outer diameter of the disk assembly [ 1   06 ] varies with or without variation in the inner [ 101 ] and/or outer [ 1   07 ] diameters of the flow channels at ∇R ODChannel ≠0 and/or ∇R IDChannel ≠0 where the second differential of each, ∇ 2 R ODChannel  and ∇ 2 R IDChannel , may have a negative, positive or zero value. Furthermore,  FIG. 4  represent the option of varying geometry through combining second order variations in geometry while the first order variations are zero such that ∇R ODChannel =0, ∇ 2 R ODChannel ≠0, ∇R IDChannel =0, ∇ 2 R IDChannel ≠0, ∇R ODDisk =0 and ∇ 2 R ODDisk ≠0 with any combination of these components possible in the embodiment of this invention.  
         [0053]      FIGS. 5   a  &amp;  5   b  demonstrate a bladeless turbine, compressor or pump whose flow direction [ 118 ] &amp; [ 128 ] is shown running from the axis [ 111 ] &amp; [ 121 ] through the open-end disk [ 114 ] &amp; [ 124 ] and the assembly of disks [ 112 ] &amp; [ 122 ] and expelling along the periphery, outer diameter [ 116 ] &amp; [ 126 ] of the disk assembly due to impingement on a closed end disk [ 115 ] &amp; [ 125 ]. The geometry shown in  FIG. 5   a  is also valid and demonstrated by  FIG. 5   c  for flow beginning at the periphery, outer diameter [ 116 ] &amp; [ 136 ], of the blade assembly [ 112 ] &amp; [ 132 ] to the center of the assembly turning parallel to the axis [ 111 ] &amp; [ 131 ] through fluid flow chambers with the working fluid [ 118 ] &amp; [ 138 ] exiting through an open end disk [ 114 ] &amp; [ 134 ] and blocked by a closed end disk [ 115 ] &amp; [ 135 ] at the opposite end.  FIGS. 5   a ,  5   b  &amp;  5   c  consist of a rotor assembly including but not limited to a shaft [ 111 ], [ 121 ] &amp; [ 131 ], any number of open disks [ 112 ], [ 122 ] &amp; [ 132 ], n, with a nominal amount of fluid flow chambers evenly spaced by any number of brackets, spacers or disk location(s) [ 113 ], [ 123 ] &amp; [ 133 ], m, on the shaft [ 111 ], [ 121 ] &amp; [ 131 ]. In one embodiment, the outer diameter [ 116 ], [ 126 ] &amp; [ 136 ] of the assembly of disks is variable described as ∇R ODDisk ≠0 and ∇ 2 R ODDisk ≠0, ∇R ODDisk ≠0 and ∇ 2 R ODDisk =0 or ∇R ODDisk =0 and ∇ 2 R ODDisk ≠0. In another embodiment, the outer diameter [ 116 ], [ 126 ] &amp; [ 136 ] of the assembly of disks is constant as shown in the figures described as ∇R ODDisk =0 and ∇ 2 R ODDisk =0. This is valid for all possibilities of constant, linear and/or non-linear and/or random variations.  FIGS. 5   a ,  5   b  &amp;  5   c  demonstrate a combination of geometries where the outer diameter of the fluid flow channel [ 117 ], [ 127 ] &amp; [ 137 ] varies in a concave, nonlinear fashion referenced to the x-axis this may be coupled with variation in the inner diameter [ 111 ], [ 121 ] &amp; [ 131 ] of the flow channel whether ∇R IDChannel ≠0 or ∇R IDChannel ≠0 where the second differential in any combination, ∇ 2 R IDChannel , may have a negative, positive or zero value. This description is not considered limiting in any fashion as to the possible combinations in embodiment of variations in geometry between the inner [ 111 ], [ 121 ] &amp; [ 131 ] and/or outer [ 117 ], [ 127 ] &amp; [ 137 ] diameters of the fluid flow channel geometries and/or the outer assembly diameter [ 116 ], [ 126 ] &amp; [ 136 ].  
         [0054]      FIGS. 6   a  &amp;  6   b  demonstrate a bladeless turbine, compressor or pump whose flow direction [ 148 ] &amp; [ 158 ] is shown running from the axis [ 141 ] &amp; [ 151 ] through the open-end disk [ 144 ] &amp; [ 154 ] and the assembly of disks [ 142 ] &amp; [ 152 ] and expelling along the periphery, outer diameter [ 146 ] &amp; [ 156 ] of the disk assembly due to impingement on a closed end disk [ 145 ] &amp; [ 155 ]. The geometry shown in  FIG. 6   a  is also valid and demonstrated by  FIG. 6   c  for flow beginning at the periphery, outer diameter [ 146 ] &amp; [ 166 ], of the blade assembly [ 142 ] &amp; [ 162 ] to the center of the assembly turning parallel to the axis [ 141 ] &amp; [ 161 ] through fluid flow chambers with the working fluid [ 148 ] &amp; [ 168 ] exiting through an open end disk [ 144 ] &amp; [ 164 ] and blocked by a closed end disk [ 145 ] &amp; [ 165 ] at the opposite end.  FIGS. 6   a ,  6   b  &amp;  6   c  consist of a rotor assembly including but not limited to a shaft [ 141 ], [ 151 ] &amp; [ 161 ], any number of open disks [ 142 ], [ 152 ] &amp; [ 162 ], n, with a nominal amount of fluid flow chambers evenly spaced by any number of brackets, spacers or disk location(s) [ 143 ], [ 153 ] &amp; [ 163 ], m, on the shaft [ 141 ], [ 151 ] &amp; [ 161 ]. In one embodiment, the outer diameter [ 146 ], [ 156 ] &amp; [ 166 ] of the assembly of disks is variable described as ∇R ODDisk ≠0 and ∇ 2 R ODDisk ≠0, ∇R ODDisk ≠0 and ∇ 2 R ODDisk =0 or ∇R ODDisk =0 and ∇ 2 R ODDisk ≠0. In another embodiment, the outer diameter [ 146 ], [ 156 ] &amp; [ 166 ] of the assembly of disks is constant as shown in the figures described as ∇R ODDisk =0 and ∇ 2 R ODDisk =0. This is valid for all possibilities of constant, linear and/or non-linear and/or random variations.  FIGS. 6   a ,  6   b  &amp;  6   c  demonstrate a combination of geometries where the outer diameter of the fluid flow channel [ 147 ], [ 157 ] &amp; [ 167 ] varies in a convex, nonlinear fashion referenced to the x-axis this may be coupled with variation in the inner diameter [ 141 ], [ 151 ] &amp; [ 161 ] of the flow channel whether ∇R IDChannel =0 or ∇R IDChannel ≠0 where the second differential in any combination, ∇ 2 R IDChannel , may have a negative, positive or zero value. This description is not considered limiting in any fashion as to the possible combinations in embodiment of variations in geometry between the inner [ 141 ], [ 151 ] &amp; [ 161 ] and/or outer [ 147 ], [ 157 ] &amp; [ 167 ] diameters of the fluid flow channel geometries and/or the outer assembly diameter [ 146 ], [ 156 ] &amp; [ 166 ].  
         [0055]      FIGS. 7   a  &amp;  7   b  demonstrate a bladeless turbine, compressor or pump whose flow direction [ 178 ] &amp; [ 188 ] is shown running from the axis [ 171 ] &amp; [ 181 ] through the open-end disk [ 174 ] &amp; [ 184 ] and the assembly of disks [ 172 ] &amp; [ 182 ] and expelling along the periphery, outer diameter [ 176 ] &amp; [ 186 ] of the disk assembly due to impingement on a closed end disk [ 175 ] &amp; [ 185 ]. The geometry shown in  FIGS. 7   a  &amp;  7   b  is also valid for flow beginning at the periphery, outer diameter [ 176 ] &amp; [ 186 ], of the blade assembly [ 172 ] &amp; [ 182 ] to the center of the assembly turning parallel to the axis [ 171 ] &amp; [ 181 ] through fluid flow chambers with the working fluid [ 178 ] &amp; [ 188 ] exiting through an open end disk [ 174 ] &amp; [ 184 ] and blocked by a closed end disk [ 175 ] &amp; [ 185 ] at the opposite end.  FIGS. 7   a  &amp;  7   b  consist of a rotor assembly including but not limited to a shaft [ 171 ] &amp; [ 181 ], any number of open disks [ 172 ] &amp; [ 182 ], n, with a nominal amount of fluid flow chambers evenly spaced by any number of brackets, spacers or disk location(s) [ 173 ] &amp; [ 183 ], m, on the shaft [ 171 ] &amp; [ 181 ]. In one embodiment, the outer diameter [ 176 ] &amp; [ 186 ] of the assembly of disks is variable described as ∇R ODDisk ≠0 and ∇ 2 R ODDisk ≠0, ∇R ODDisk ≠0 and ∇ 2 R ODDisk =0 or ∇R ODDisk =0 and ∇ 2 R ODDisk ≠0 where  FIG. 7   a  demonstrates a possible convex non-linear geometry and  FIG. 7   b  demonstrates a possible concave non-linear geometry. The embodiments in  FIG. 7   a  or  7   b  are not considered limiting in any fashion as to the possible combinations in preferred embodiment of variations in geometry between the inner [ 171 ] &amp; [ 181 ] and/or outer [ 177 ] &amp; [ 187 ] diameters of the fluid flow channel geometries and/or the outer assembly diameter [ 176 ] &amp; [ 186 ].  
         [0056]     The above figures depict, but do not limit in concept the intention of the invention, possible flow optimizations through the combination of design and variation of individual fluid flow channel or disk outer diameter geometries for a given disk assembly of a bladeless compressor, pump or turbine. Geometries of individual fluid channels and outer diameter(s) with combinations thereof are recommended in this invention, but not limited as to possible designs or configurations of the fluid channels and outer diameter(s), to be maximized for energy infusion or extraction purposes between the working fluid and the mechanical components. These designs may be oriented on the rotor in any fashion to maximize the efficiency of energy addition or extraction to the compressible or incompressible working fluid.