Title:
Fluid Flow Chambers and Bridges in Bladeless Compressors, Turbines and Pumps
Kind Code:
A1


Abstract:
A disk in a bladeless turbine, compressor or pump comprising of a working surface, a hub for axial mounting and one or more bridges connecting the hub to the working surface. Said disk configuration forming fluid flow chambers in the disk for the entrance or exit of fluid for the purpose of extracting or infusing energy into or from the fluid. Said chambers may vary in size from one to another or may be of geometry other than triangular or trapezoidal, for example tear-drop shaped. Furthermore, this invention includes precise description of non-constant angular and axial geometry of said bridges.



Inventors:
Wilson, Erich Andrew (Springville, UT, US)
Application Number:
11/163415
Publication Date:
12/28/2006
Filing Date:
10/18/2005
Primary Class:
International Classes:
F01D1/36
View Patent Images:



Primary Examiner:
WIEHE, NATHANIEL EDWARD
Attorney, Agent or Firm:
ERICH A WILSON (SPRINGVILLE, UT, US)
Claims:
What is claimed is:

1. A unit with a circular outermost geometry in two of three dimensions consisting of any given material or combination(s) of material(s) fabricated from a single piece of material or combined materials or comprised of more than one individual component(s) joined together in any fashion to achieve the same mechanical function. For conventional purposes, said unit is hereafter referred to as “disk” or “the disk”. The disk may be used separately or in a group of more than one to comprise a single component or multiple components of bladeless compressor(s), pump(s), turbine(s) and/or gas turbine(s) fashioned to be applied separately or in conjunction with one or more similar and/or differing entities.

2. A unit with a circular outermost geometry in two of three dimensions consisting of any given material or combined materials or combination(s) of material(s) fabricated from a single piece of material or comprised of more than one individual component(s) joined together in any fashion to achieve the same mechanical function. For conventional purposes, said unit is hereafter referred to as “disk” or “the disk”. The disk containing one or more passages, hereafter referred to as “chamber(s)”, in its body provides for the transfer of a single-phase, two-phase and/or more than two-phase, compressible and/or non-compressible, Newtonian and/or non-Newtonian working fluid(s) or any combination thereof through the body of the disk. The disk may be used separately or in a group of more than one to comprise a single component or multiple components of bladeless compressor(s), pump(s), turbine(s) and/or gas turbine(s) fashioned to be applied separately or in conjunction with one or more similar and/or differing entities.

3. A unit with a circular outermost geometry in two of three dimensions consisting of any given material or combination(s) of material(s) fabricated from a single piece of material or combined materials or comprised of more than one individual component(s) joined together in any fashion to achieve the same mechanical function. For conventional purposes, said unit is hereafter referred to as “disk” or “the disk”. The disk containing one or more bridge(s), arm(s) and/or bracket(s), hereafter referred to as “bridge(s)”, as part of its geometry whether attached at any location or included within the unit leading to a central hub or shaft location provides for the transfer of a single-phase, two-phase and/or more than two-phase, compressible and/or non-compressible, Newtonian and/or non-Newtonian working fluid(s) or any combination thereof, hereafter referred to as “working fluid”, through the body of the disk between said bridge(s). The disk may be used separately or in a group of more than one to comprise a single component or multiple components of bladeless compressor(s), pump(s), turbine(s) and/or gas turbine(s) fashioned to be applied separately or in conjunction with one or more similar and/or differing entities.

4. The disk(s) in claim 1 is (are) described to be circular in its (their) outermost geometry, when using cylindrical coordinates, in the radial, r, and angular, θ, directions. In the axial, x, direction the disk geometry can be constant, linear, non-linear, step-function and/or random in design whether homogeneous, tapered or contoured as a function of the axial, radial and/or angular properties of the design.

5. The disk(s) in claim 2 is (are) described to be circular in its (their) outermost geometry, when using cylindrical coordinates, in the radial, r, and angular, θ, directions. In the axial, x, direction the disk geometry can be constant, linear, non-linear, step-function and/or random in design whether homogeneous, tapered or contoured as a function of the axial, radial and/or angular properties of the design.

6. The disk(s) in claim 3 is (are) described to be circular in its (their) outermost geometry, when using cylindrical coordinates, in the radial, r, and angular, θ, directions. In the axial, x, direction the disk geometry can be constant, linear, non-linear, step-function and/or random in design whether homogeneous, tapered or contoured as a function of the axial, radial and/or angular properties of the design.

7. The chamber(s) according to claim 2 defined as passing through the disk in the axial, x, direction consist(s) of one or more edges in the radial, r, and/or angular, θ, directions geometrically defined as point(s), round(s), fillet(s), arc(s), line(s), b-spline(s) or any other single, constant, linear, nonlinear, random and/or step-function value.

8. The edge(s) according to claim 5 of the chamber(s) in claim 2 provide(s) closed geometrical configuration for the chamber(s) of the disk allowing for the passage of a working fluid through the chamber(s) demonstrating, but with the exception of previous art geometry demonstrating simple trapezoids and equilateral triangles in the cylindrical radial and angular coordinates whose edges are lines in the cylindrical coordinate system not limited in any fashion or application to, geometry of square(s), triangle(s), trapezoid(s), circle(s), cone(s) and/or tear-drop(s) whose edge(s) are geometrically defined according to claim 5.

9. The chamber(s) of claim 2 are present as part of the disk geometry as a single entity or more than one, thus forming a configuration of chamber(s) on the disk. The chamber(s) configuration consists of one or more chamber(s) of like or varying sizes as well as like or varying geometry regardless of orientation or location on the disk.

10. The bridge(s) of the disk according to claim 3 can be determined to have a median running the length of the bridge defined as a centerline, ℄(x,r,θ), functioning in, but with the exception of previous art geometry demonstrating linear radial behavior and constant angular and axial value (i.e. a straight bridge running from the hub to the body of the disk) not limited in any fashion or application to, all three geometrical dimensions possessing constant, linear, non-linear, random and/or step-function values whether dependent or independent on/from the other dimensions. When more than one bridge(s) is (are) present centerline, ℄(x,r,θ), of each bridge(s) may differ from the others or posses the same behavior.

11. The bridge(s) according to claim 3 consisting of a non-variable, constantly, linearly, non-linearly, step-function and/or random variable thickness and/or width extending in, but not limited to, the angular and/or axial directions as well as a non-variable, constantly, linearly, non-linearly, step-function and/or random length extending in, but not limited to, the radial direction whose centerline, ℄(x,r,θ), varies in angular and/or axial location as it progresses away from the center of the disk according to claim 1.

Description:

FIELD OF THE INVENTION

This invention relates to the geometric shape and/or configuration of the fluid flow chambers of the individual disks and/or brackets in bladeless (disk) turbine(s), bladeless (disk) compressor(s) and/or bladeless (disk) pump(s). This invention offers improvements in the fluid flow chamber design 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

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, 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.

In the commercial, residential 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 general failure to provide for individual consumers such as homes and businesses. Furthermore, power service is commonly affected by storms, hurricanes, tornadoes, earthquakes and other natural disasters through the interruption of power service to thousands of individuals in the 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. 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.

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'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'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.

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.

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 turbine, bladeless turbine, disk turbine, Tesla pump, bladeless pump or disk 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.)

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 may be termed 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 (Latourneau); U.S. Pat. No. 6,726,443 (Collins et al.); and U.S. Pat. No. 6,779,964 (Dial).

It has been found by others that variations in the disk shape through 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.)

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) is an alteration to the fluid chamber on the disk taken into account. 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. For all other designs, the bridge crossing from the hub or shaft to the working surface of the disk and thereby creating the fluid flow chamber is straight in the axial and angular planes.

Variations in fluid flow chamber design and consequentially the bridge portion of the disk extending from the shaft to the surface area of the disk are not considered in the public domain beyond that discussed above. Improvements in the design of the bridge and fluid flow chamber will better optimize the functionality of the overall turbine, compressor or pump assembly.

These issues have brought about the present invention.

SUMMARY OF THE INVENTION

A bladeless turbine, compressor or pump working with a compressible or incompressible fluid relies on the viscosity of the fluid to propel the disk assembly through the extraction of energy. Likewise, when energy is added into the working fluid from the disk assembly energy is transferred. Thus, as a working fluid with lower kinematic viscosity is implemented, the ability of the disks to extract or infuse energy through their working surfaces into or from the fluid system is proportionally decreased whether this variational relationship be constant, linear or non-linear in nature.

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 no longer incompressible, but compressible the viscosity changes by several factors. For example, the kinematic viscosity of an incompressible fluid could be on the order of 1e-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 for compressible fluids as with incompressible fluids.

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 in comparison. To obtain the design point of bladeless devices with compressible flow, they must be run at speeds up to 100,000 RPM and beyond.

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 are suited for working at high rotational speeds.

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.

An object of this invention is to define the reference system and the variables necessary to produce variation in fluid flow chamber design beyond those standardly used in prior art.

An object of the invention is to improve disk performance at high rotational speeds through implementing the variation in outer and/or inner diameter of the flow chambers from one chamber to another in any given configuration on a disk.

A further object of the invention is to provide improved flow chamber geometry to maximize efficiency and improve performance at high RPM with a compressible fluid through the tear-drop shaped chamber that maximizes the energy extraction or infusion to and/or from the working fluid.

Another object of the invention is to define the variables and geometry of flow chamber implemented with incompressible fluids and improve upon them, especially for applications with compressible fluids, through showing the limitations of the conventional practices and providing descriptive means for developing geometries beyond those found in prior art.

Further, an object of the invention is to provide a variation in geometries of the tear-drop shaped flow chamber which, based on the implementation of the bladeless turbine, compressor or disk, will maximize the efficiency of energy transfer within various performance parameters.

Finally, an object of the invention is to provide several alternate geometries capable of improving the disk performances at high RPM.

DESCRIPTION OF THE DRAWINGS

FIG. 1: Cylindrical coordinates used to describe the disk;

FIG. 2: Variables describing the bridge between the hub and the disk with a given angle from the origin, θn;

FIG. 3: Prior art disk with standard four-sided flow chambers;

FIG. 4: Prior art disk with standard three-sided flow chambers;

FIG. 5: Variation in outer diameter of flow chambers;

FIG. 6: Tear-drop flow chambers;

FIGS. 7a, 7b &7c: Variations of tear-drop chamber geometry in FIG. 6;

FIGS. 8a, 8b, 8c &8d: Alternative geometries for flow chambers;

FIG. 9: Equation denoting the relationship between the angle between bridges, 5, and the number of bridges, m.

DETAILED DESCRIPTION OF THE INVENTION

According to the present invention, the best coordinates used to describe the geometry related to a disk are cylindrical coordinates as shown in FIG. 1. The center of the disk is chosen as the origin through which a shaft may or may not be attached or pass. While the disk extends out in the radial direction, [r], has a thickness in the axial direction, [x], and contains fluid flow chambers with bridges connecting the hub to the working surface of the disk at various locations along the angular axis, [θ].

To understand prior art designs of the bridge connecting the hub and working surface of the disk, FIG. 2 denotes the variables necessary to explain the improvements provided in this invention. Again the origin is placed at the center of the disk with the disk extending radially outward in the redirection and a nominal thickness in the x-direction. At a distance, [θn], from the angular origin a bridge is located by its centerline, [℄(r)], of constant angular direction and increasing radial direction. Said bridge is given a physical width, [w(r)], as a function of radial location as well as a decrease in width, [dw(r)], as it distances from the origin. Thus, the following definitions are given:

Definition List 1
TermDefinition
dFirst order differential
mAn integer denoting the number of
bridges of value 1, 2, 3, . . . k − 1, k
nAn integer of value 1, 2, 3, . . . k − 1, k
rRadial direction
RIDInner diameter of the fluid flow chamber
and bridge where they junction with the
hub, a function of angular direction, θ, in
prior art.
RODOuter diameter of the fluid flow chamber
and bridge where they junction with the
working surface of the disk, a function of
angular direction, θ, in prior art.
wBridge width
xAxial direction
δAngular spacing distance of bridges
θAngular direction

Said bridge(s) may be a single unit or more than one unit. In general practice, the number of bridges, m, may vary between two and six or more and are angularly spaced a distance, δ, apart according to the equation in FIG. 9. Each of the bridges and consequential fluid flow chambers has a given outer diameter, ROD, and an inner diameter, RID, which in prior art are constant in value across the chamber and from one chamber to another. Each fluid flow chamber begins with a leading edge at location δm-1+0.5w(r)m-1 and ends with a trailing edge at δm−0.5w(r)m where in prior art w(r)m-1=0.5w(r)m.

FIG. 3 demonstrates the prior art described above consisting of a disk [1] comprised of a working surface [2] one or more bridges [3] connecting the working surface to the hub [4]. The center hole [5] fitting for a shaft is optional. Collins et al. demonstrate how a disk assembly can be combined without the use of a traditional shaft. Said bridges [3] connecting the hub [4] and the working area of the disk [2] create one or more fluid flow chambers [6]. Said chambers are shown in FIG. 3 to be trapezoidal in shape in the cylindrical coordinate system with consideration for rounds at the corners permitting ease of manufacture in the prior art. Said chambers are bounded by a constant outer diameter, ROD, [7] and a constant inner diameter, RID, [8].

FIG. 4 demonstrates the prior art described above consisting of a disk [10] comprised of a working surface [11] one or more bridges [12] connecting the working surface to the hub [15]. The center hole [16] fitting for a shaft is optional. Collins et al. demonstrate how a disk assembly can be combined without the use of a traditional shaft. Said bridges [12] connecting the hub [15] and the working area of the disk [11] create one or more fluid flow chambers [17]. Said chambers are shown in FIG. 4 to be triangular in shape in the cylindrical coordinate system with consideration for rounds at the corners permitting ease of manufacture. Said chambers are bounded by a constant outer diameter, ROD, [13] and a constant inner diameter, RID, [14].

FIG. 5 deviates from the prior art to introduce part of the invention disclosed here by providing an improvement in bridge design and fluid flow chamber design. FIG. 5 consists of a disk [20] comprised of a working surface [21] one or more bridges [22] of varying geometry connecting the working surface to the hub [25]. The center hole [28] fitting for a shaft is optional. Collins et al. demonstrate how a disk assembly can be combined without the use of a traditional shaft. Said bridges [22] connecting the hub [25] and the working area of the disk [21] create one or more fluid flow chambers [29] of varying size. Said chambers are shown in FIG. 5 to be trapezoidal in shape in the cylindrical coordinate system with consideration for rounds at the corners permitting ease of manufacture. Said chambers are bounded by a constant outer diameter, ROD, [23], [26] unique to each and a constant inner diameter, RID, [24], [27] unique to each. FIG. 5 isolates the first option in fluid flow chamber variation not seen in prior art. That option is variation in the outer diameter, ROD, [23], [26] or inner diameter, RID, [24], [27] (variation not shown in the figure) of one or more fluid flow chambers whether in constant, linear, non-linear, grouped or random relation to each other.

FIG. 6 introduces another aspect of the invention by providing an improvement in bridge design and fluid flow chamber design. FIG. 6 consists of a disk [30] comprised of a working surface [31] one or more bridges [33] of varying geometry connecting the working surface to the hub [38]. The center hole [40] fitting for a shaft is optional. Collins et al. demonstrate how a disk assembly can be combined without the use of a traditional shaft. Said bridges [33] connecting the hub [38] and the working area of the disk [31] create one or more fluid flow chambers [41] possibly of but not constrained to varying size from one chamber to another. Said chambers are shown in FIG. 6 to be teardrop in shape in the cylindrical coordinate system with consideration, but in no way limiting the scope of the invention, for possible rounds at the corners permitting ease of manufacture. Said chambers are bounded by an outer diameter, ROD, [35], as a function of both angular, axial and radial distance unique to each or constant, linear or non-linear in relation to each other and an inner diameter, RID, [36] also a function of angular, axial and radial distance unique to each or constant, linear or non-linear in relation to each other. FIG. 6 isolates further options beyond that in FIG. 5 in fluid flow chamber variation not seen in prior art. Now viewing the outer diameter, ROD(x,r,θ), inner diameter, RID(x,r,θ), leading, δm-1+0.5w(℄)m-1, and trailing, δm−0.5w(℄)m, edges of the fluid flow chamber as well as the bridge centerline, ℄(x,r,θ), as three-dimensional functions, their values are no longer viewed as constants in one dimension as with prior art. This invention asserts these parameters can be constant, linear, non-linear, grouped or even random values in each dimension and yet described as functions laid out through the theory in this invention. Thus the following definitions from definition list 1 are revised to comprehend the improvements in this invention in geometrical versatility and hence performance of the disk. These improvements are given in definition list 2.

Definition List 2
TermDefinition
ROD(x, r, θ)Outer diameter of the fluid flow
chamber, a function of angular distance,
radial distance and axial distance, f(x, r, θ)
RID(x, r, θ)Inner diameter of the fluid flow chamber,
a function of angular distance, radial
distance and axial distance, f(x, r, θ)
℄(x, r, θ)Center line of any given bridge, a
function of angular distance, radial
distance and axial distance, f(x, r, θ)
w(℄)Bridge width, a function isolated from
cylindrical coordinates of the disk
through placement in centerline-axial space.

Variation from the tear-drop shaped fluid flow chamber in FIG. 6 is now possible based on the principles laid out above. FIGS. 7a, 7b, and 7c demonstrate linear and non-linear relationships in the fluid flow chamber possible resulting in three variations to the tear-drop shape given above. Each configuration demonstrates four sides with a large end [71], [75] and [79], sides to the chamber [74], [72], [78], [76], [82] and [80] followed by a smaller, more pointed end, which when enlarged could become a side, [73], [77] and [81]. The orientation of these shapes on a disk are intentionally not shown in the figure. Nor are FIG. 5 and FIG. 6 considered to be limiting in any fashion as to the orientation of fluid flow chambers on a disk as prescribed by this invention. Furthermore, the representations in these figures are not to be considered limiting as to the size, length, depth, thickness or breadth of the suggested improvements therein. They may be oriented with any of the given sides being placed as the leading or trailing edge, inner or outer diameter with any given length as well as constant, linear, non-linear, grouped or random shape for each of the components of the fluid flow chamber.

Whereas prior art has demonstrated three and four-sided fluid flow chambers and FIG. 6 demonstrates the ability to introduce new geometry without altering the number of sides on a chamber, it is further pointed out in this invention that more than one side can exist in a coordinate direction furthermore, more than three or four sides can be used to create a fluid flow chamber. This is demonstrated in FIGS. 8a, 8b, 8c and 8d. Variation from the tear-drop shaped fluid flow chamber in FIG. 6 or prior art in FIG. 3 and FIG. 4 is now possible based on the principles laid out above. FIGS. 8a, 8b, 8c and 8d demonstrate but are not limited to linear and non-linear relationships in the fluid flow chamber possible resulting in four variations to improve performances over the triangular and/or trapezoidal shapes given in prior art. Each configuration demonstrates four sides with a one end which may be chosen by the designer as, but is not limited to being, the leading edge [84], [89], and [97], sides to the chamber [83], [88], [92], [96], [85], [90], [94] and [98] followed by an end, which may be regarded as but limited to being the trailing end [86], [87], [91], [99], and [95]. As just demonstrated with the possible trailing edge any given side may consist of one or more components. The orientation of these shapes on a disk are intentionally not shown in the figure. Furthermore, the representations in these figures are not to be considered limiting as to the size, length, depth, thickness or breadth of the suggested improvements therein. They may be oriented with any of the given sides being placed as the leading or trailing edge, inner or outer diameter with any given length as well as constant, linear, non-linear, grouped or random shape for each of the components of the fluid flow chamber.

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 chamber geometries in a given disk of a bladeless compressor, pump or turbine. The geometry of the individual fluid flow chambers themselves is recommended in this invention, but does not limit as to the possible design or configuration of the fluid flow chambers, to be maximized for compression and energy extraction purposes. These designs may be oriented on the disk in any fashion to maximize the efficiency of energy addition or extraction to the compressible or incompressible working fluid.