Geometry-coupled pitch system for passive laminar flow

Abstract

Passive fluid system (e.g. gravity driven) flow channel having hydraulic diameter and inclined at pitch angle θ calculated by arcsin((Re_max * 32 * μ^2) / (ρ^2 * g * Dh^3)) to maintain laminar flow. R

Description

1. Field of the Invention The present invention relates to a fluid management system for maintaining passive laminar transport. Specifically, the invention relates to a system that functionally couples channel pitch angle to hydraulic diameter to achieve sustained, energy-efficient fluid movement in civilian infrastructure, medical, and industrial applications. 2. Background of the Invention Conventional fluid transport relies on active pumping to overcome frictional head loss. This process is energy-intensive and often results in turbulent flow regimes, which further increase parasitic energy losses. While gravity-fed systems exist (e.g., sewers), they generally do not regulate the laminar-to-turbulent transition threshold via geometric coupling, leading to unpredictable flow velocities and higher maintenance requirements. There is a need for a scale-invariant, passive system that preserves the laminar state to reduce carbon emissions and mechanical wear. 3. Summary of the Invention The present invention achieves passive laminar transport by converting gravitational potential energy into kinetic energy in a precisely controlled manner. By applying the geometry-coupled pitch relationship, the system ensures that the gravitational driving force substantially balances viscous resistance. This allows for sustained fluid momentum without active mechanical pumping, applicable across all scales from micro-fluidics to industrial manifolds. 4. Detailed Description The core principle of the invention is the functional coupling of the pitch angle (theta) of a flow path to its hydraulic diameter (Dh). To ensure the Reynolds number (Re) remains below the critical transition threshold (Re_max), the system must satisfy the following inequality: theta <= arcsin((Re_max * 32 * muA2) I (rhoA2 * g * DhA3)) Where: Re_max = critical Reynolds number for the laminar-to-turbulent transition for the specific flow path geometry mu = dynamic viscosity of the fluid (Pa-s) rho = density of the fluid (kg / m3) g = gravitational acceleration (approx. 9.81 m / s2) Dh = hydraulic diameter (m) The geometry-coupled pitch relationship defines an upper bound on allowable channel inclination such that the Reynolds number remains below the laminar-to-turbulent transition threshold for the working fluid. 4.1 Gravitational Equilibrium Unlike perpetual motion claims, the present system operates on the principle of potential energy dissipation. The pitch angle (theta) is calculated such that the work performed by gravity on the fluid mass substantially balances the energy lost to internal fluid friction (viscosity). By maintaining the flow at or below Re_max, the system avoids the high-energy dissipation associated with turbulent eddies. 4.2 Definition of Re_max For the purpose of this invention, Re_max is defined as the critical Reynolds number where the flow transitions from laminar to turbulent. For smooth-walled rigid conduits, this value is typically between 2,000 and 2,300. The system is designed to operate in a safety buffer zone, ideally maintaining a Re of 1,500 to 1,800 to ensure stability against external vibrations or temperature-induced viscosity changes. 4.3 Scale-Invariant Embodiments (Civilian Applications) The system is intended for civilian and commercial use-cases to maximise energy efficiency and decarbonisation: Embodiment 1 - HVAC and Heat Exchangers: in industrial heat exchangers, a series of helical conduits (Claim 3) are arranged with a constant pitch theta. Because laminar flow has a predictable velocity profile, heat transfer coefficients can be optimised with significantly less energy than forced-air or pumped-liquid systems. Embodiment 2 - Sustainable Water Infrastructure: for greywater or treated water distribution, the system utilises vertically offset trays forming a laminar cascade (Claim 4). Multi-directional transition gates (Claim 5) use the Coanda effect to maintain a continuous laminar bridge between levels, preventing air entrainment and splashing. Embodiment 3 - Medical Fluid Delivery: in micro-fluidic applications where Dh is less than 1.0 mm, the high surface-area-to-volume ratio makes viscous forces dominant. The geometry-coupled pitch relationship allows for precise, pump-free delivery of medications or multi-phase biological suspensions without shear-induced damage to cells. 4.4 Dynamic Adjustment In advanced implementations, the pitch angle (theta) may be mechanically adjusted via feedback-controlled actuators. If sensors detect a change in fluid temperature (altering mu) or density (rho), the actuator adjusts the incline of the flow path to maintain the system within the calculated laminar limit. 5. Hydraulic Diameter for All Channel Geometries The hydraulic diameter Dh = 4A / P applies universally to all channel cross-sections as shown in Figure A and Figure B: Circular channel: Dh = D (diameter) Semi-circular channel: Dh = piD / (pi + 2) Rectangular channel (width w, depth d): Dh = 2wd / (w + d) Annular channel (outer Do, inner Di): Dh = Do - Di Irregular channel: Dh = 4A / P from actual cross-sectional geometry 6. System Configurations The geometry-coupled pitch relationship may be implemented in any configuration: Helical channels: channels following a helical path, pitch angle theta selected for channel Dh, as shown in Figure A. Straight inclined channels: linear channels inclined at pitch angle theta relative to horizontal. Stacked tray manifolds: vertically stacked trays each defining a flow channel with geometry-coupled pitch, as shown in Figure B. Parallel channel arrays: multiple channels in parallel, each with geometry-coupled pitch, enabling industrial-scale flow volumes. Spiral, serpentine, and three-dimensional channel networks. 7. Working Mediums The geometry-coupled pitch relationship applies to any working medium with known fluid properties rho and mu. This includes, but is not limited to: aqueous solutions, agricultural nutrients, biodegradable heat transfer fluids, glycol-based mixtures, dielectric insulating oils, high-density brines, liquefied gases for civilian refrigeration, and atmospheric air. The system is compatible with both Newtonian and non-Newtonian fluids, including shear-thinning and thixotropic fluids, subject to the substitution of the effective physical constants into the geometry-coupled pitch relationship. 8. Passive Operation When the pitch angle theta is selected according to the geometry-coupled pitch relationship, the working medium flows passively under gravitational equilibrium without continuous external mechanical pumping: Initialisation: a brief initial momentum pulse introduces the working medium to the inlet. The pulse may be electrical, mechanical, fluidic (gravity head pressure from a reservoir), or any other transient input sufficient to establish initial flow. Passive cascade: once flow is established, the gravitational driving force substantially balances viscous resistance at the laminar limit. The working medium continues to flow without continuous external mechanical pumping for as long as the inlet maintains head pressure or the system operates in a continuous loop. Sustained laminar conditions: the geometry-coupled pitch relationship ensures Re remains below the laminar-to-turbulent transition threshold throughout, maintaining continuous fluid-wall contact and efficient heat transfer. Optional maintenance: one or more ultrasonic transducers may be integrated within the system to remove minor deposits from channel surfaces on an intermittent basis without disrupting the passive laminar cascade. 9. Industrial and Civilian Applications The invention is designed for civilian and commercial applications requiring sustainable fluid transport or thermal management. The following carbon-displacement features are integrated: Carbon Displacement: the system is configured to minimise the carbon intensity of infrastructure by replacing active, electricity-dependent pumping with passive momentum control. Passive Energy Reduction: by utilising ambient gravitational potential as the primary motive force, the system achieves very low operational energy consumption during steady-state operation. Parasitic Load Elimination: maintaining a laminar regime eliminates boundary layer insulation and turbulent friction, significantly reducing the energy losses inherent in traditional transport manifolds. Life-Cycle Sustainability: the geometric precision allows for the use of recyclable bio-polymers and sustainable elastomers, as reduced pressure requirements decrease the necessity for high-carbon-intensity metal alloys. Targeted Infrastructure: specific applications include residential and commercial HVAC, renewable energy heat exchangers, sustainable power generation, and civilian water reclamation. 10. Description of the Drawings Description of Figure A Figure A illustrates the primary embodiment of the fluid management system, configured as a continuous helical flow channel

[10] arranged around a central longitudinal axis. Geometric Regulation of Helical Flow In this embodiment, the flow channel

[10] possesses a circular cross-section where the hydraulic diameter (Dh) is equal to the channel diameter. Unlike conventional helical coils used in heat exchangers that require high-pressure pumping to overcome centrifugal and viscous losses, the helical path in Figure A is precision-engineered with a pitch angle (theta) functionally coupled to the Dh via the geometry-coupled pitch relationship. This functional coupling ensures that the gravitational component acting along the helical path is substantially balanced by the viscous resistance of the channel walls. Consequently, the fluid maintains a stable, laminar profile without transitioning to turbulence, regardless of the total vertical height of the assembly. Constant Velocity Gradient The helical geometry provides a continuous, uninterrupted flow path from the inlet [A] to the outlet [B]. By maintaining a constant pitch angle (theta) relative to the horizontal plane throughout the winding, the system ensures a uniform velocity gradient. This prevents localised acceleration that typically occurs in vertical or steeply inclined tubing, allowing the medium to descend at a controlled terminal laminar velocity determined by the geometry-coupled pitch relationship. Passive Operational Stability The helical system remains in a state of passive equilibrium following a brief initial momentum pulse. This pulse overcomes the initial static inertia and surface tension within the circular channel

[10] . Once the flow is established, the system operates as a gravity-equilibrated cascade, using the potential energy of the fluid head to maintain motion. The circular geometry of Figure A is particularly effective for civilian infrastructure applications where structural integrity and continuous wall contact are required. Description of Figure B Figure B illustrates a stacked manifold embodiment of the fluid management system, specifically configured as a sequential laminar cascade. In this arrangement, the flow path is defined by a plurality of vertically offset rectangular trays [2]. Geometric Regulation of Flow Unlike standard gravity-fed systems that accelerate fluid to turbulent velocities, each tray [2] in Figure B is precision-engineered with a pitch angle (theta) functionally coupled to the tray hydraulic diameter (Dh) via the geometry-coupled pitch relationship, where Dh = (2wd) / (w+d). This functional coupling ensures that the gravitational acceleration of the working medium is substantially balanced by the viscous resistance of the channel walls. Consequently, the fluid maintains a stable, parabolic velocity profile throughout the length of each tray, preventing the Reynolds number (Re) from reaching the turbulent transition threshold. Passive Directional Transitions (Laminar Damping) The system incorporates multi-directional gates or spillways

[12] that facilitate the transfer of the working medium between vertically adjacent trays. These transition zones are designed as Passive Laminar Damping Zones. At each directional change, the effective pitch angle is shallow enough to reorganise the fluid momentum without triggering flow separation or vortex shedding. The spillways utilise a streamlined profile to ensure that the working medium transitions between levels via surface adhesion (the Coanda effect), maintaining a continuous laminar bridge rather than breaking into turbulent droplets. Operational Equilibrium The system remains in a state of passive equilibrium following a brief initial momentum pulse. This pulse overcomes the initial static inertia and surface tension. Once the flow is established, the system operates without continuous external mechanical pumping, as the potential energy of the fluid head is dissipated at a constant, laminar rate through the engineered resistance of the tray geometry. Description of Figure C Figure C illustrates the universal scaling curve for the fluid management system, providing the mathematical boundary for maintaining passive laminar flow across varying scales. Laminar Zone and Boundary Conditions The graph in Figure C establishes the functional relationship between the hydraulic diameter (Dh) and the maximum allowable pitch angle (theta). The central curve represents the critical transition point where the Reynolds number (Re) reaches the transition threshold at Re = 2,300. The region on or below this curve is defined as the Laminar Zone. Within this zone, the geometry-coupled pitch relationship ensures that gravitational acceleration is substantially balanced by viscous drag, maintaining a stable parabolic velocity profile. Calibration for Multi-Directional Gates Figure C serves as the primary calibration tool for the multi-directional gates and transitions described in Figure B. For any change in direction or cross-sectional geometry within a gate, the local pitch is adjusted based on this curve to ensure the fluid remains in the Laminar Zone. This prevents momentum spikes during directional shifts, allowing the system to function as a self-damping manifold. The scale-invariance of this curve enables implementation from micro-scale medical channels (Dh = 0.5 mm) to industrial-scale manifolds (Dh = 50.0 mm). 11. Broad Scope Interpretations The following interpretations apply to ensure the protection is comprehensive and focuses on sustainable outcomes: Passive Preference: while compatible with hybrid architectures to reduce parasitic losses, the preferred embodiment is a strictly passive system that functions without continuous external pressure or auxiliary pumping. Sustainable Fluids: fluid encompasses any substance in a liquid, gaseous, or multiphase state, with a specific focus on biodegradable heat transfer fluids, agricultural nutrients, and atmospheric air. Scale-Invariant Decarbonisation: the geometry-coupled pitch relationship remains protective across all scales, from micro-fluidics to large-scale industrial water infrastructure, ensuring uniform energy savings regardless of geometric volume. 12. Statement of Novelty The invention is novel over the prior art in the following respects: Universal Geometry-Coupled Pitch Relationship: existing systems do not disclose the functional coupling of pitch angle to hydraulic diameter as a universal design principle for passive laminar flow across all scales. Significant Decarbonisation Potential: existing systems do not provide a unified principle for industrial-scale fluid transport that achieves significant decarbonisation through geometric design alone, without continuous external pumping.

Claims

1. A passive fluid transport system for maintaining laminar flow using gravitational potential energy as the primary motive force, comprising:at least one flow path defined by a boundary surface and having a hydraulic diameter (Dh);the flow path being inclined at a pitch angle (theta) relative to a horizontal plane;characterised in that the pitch angle (theta) is constrained by the physical properties of the fluid and the geometry of the flow path in accordance with the following relationship:theta <= arcsin((Re_max * 32 * muA2) I (rhoA2 * g * DhA3))wherein:Re_max is a critical Reynolds number corresponding to the transition from laminar flow to turbulent flow for the geometry of the flow path, mu is the dynamic viscosity of the fluid (Pa-s), rho is the density of the fluid (kg / m3), g is gravitational acceleration (m / s2), and Dh is the hydraulic diameter of the flow path,such that the Reynolds number of the fluid within the flow path remains at or below the laminar transition threshold.

2. The system of claim 1, wherein Re_max is a predefined constant for a specific geometry, having a value between 2,000 and 2,400 for Newtonian fluids in smooth-walled rigid conduits, preferably maintained with a safety margin such that the operational Reynolds number remains at or below 1,800.

3. The system of claim 1, wherein the flow path is configured as a helical conduit arranged around a longitudinal axis, and the pitch angle (theta) is constant along the helical path.

4. The system of claim 1, wherein the flow path comprises a plurality of vertically offset trays forming a sequential laminar cascade.

5. The system of claim 4, further comprising at least one multi-directional transition gate positioned between adjacent trays, the transition gate having a streamlined profile configured to maintain a continuous laminar bridge via surface adhesion leveraging the Coanda effect.

6. The system of claim 1, wherein the boundary surface is selected from the group consisting of: rigid conduits, semi-rigid conduits, flexible membranes, porous structures, and open-surface films.

7. The system of claim 1, wherein the fluid is a non-Newtonian fluid selected from the group consisting of: shear-thinning fluids, thixotropic fluids, and multi-phase suspensions, where mu represents the effective viscosity of the medium.

8. The system of claim 1, wherein the system operates in a state ofgravitational equilibrium following an initial momentum pulse - said pulse being a transient pressure surge from a fluid head or reservoir discharge - such that the gravitational driving force substantially balances viscous dissipation to sustain fluid transport without continuous active mechanical pumping.

9. A method for designing a laminar flow transport system, comprising:determining a hydraulic diameter (Dh) of a flow path;determining fluid properties including density (rho) and dynamic viscosity (mu);calculating a maximum pitch angle (theta_max) according to:theta_max <= arcsin((Re_max * 32 * muA2) / (rhoA2 * g * DhA3));and configuring the flow path such that its pitch angle (theta) does not exceed theta_max,whereby the Reynolds number of the flowing medium is maintained below the laminar-to-turbulent transition threshold.

10. The system of claim 1, wherein the boundary surface comprises a flexible elastomer configured to expand or contract based on fluid volume while maintaining the geometry-coupled pitch relationship.

11. The system of claim 1, wherein the flow path is an external surface configured for laminar film flow, wherein the fluid adheres to the surface via surface tension and the Coanda effect.

12. The system of claim 1, wherein the hydraulic diameter (Dh) is non-uniform along the length of the flow path, and the pitch angle (theta) is adjusted at localised points along the path via a sensor-actuator feedback loop to maintain the geometry-coupled pitch relationship.

13. The system of claim 1, integrated into a civilian fluid infrastructure as a passive momentum regulator configured to suppress turbulent kinetic energy without continuous external mechanical work.

14. The system of claim 1, wherein the fluid transport is achieved through a multi-phase medium comprising a primary liquid and secondary dispersed particles, where the effective viscosity (mu) of the mixture determines the pitch angle (theta).

15. The system of claim 1, wherein the flow path is formed within a 3D-printed lattice or porous matrix, where the effective Dh of the interstitial spaces is functionally coupled to the matrix inclination.

16. The system of claim 5, wherein the multi-directional transition gate includes a laminar damping zone configured to reorganise fluid momentum during a change in flow direction to prevent vortex shedding.

17. The system of claim 1, configured for micro-fluidic scales where Dh is less than 1.0 mm.

18. The system of claim 1, configured for industrial-scale civilian infrastructure where Dh is greater than 20.0 mm.

19. The system of claim 1, further comprising a feedback-controlled actuator and at least one sensor measuring fluid density, viscosity, or temperature, wherein the actuator mechanically modifies the pitch angle (theta) in real-time within a predefined range to maintain the geometry-coupled pitch relationship as fluid properties fluctuate.

20. The system of claim 1, wherein the system is integrated into a civilian infrastructure component selected from the group consisting of: heat exchangers, HVAC manifolds, water distribution networks, and medical fluid delivery devices.

21. The system of claim 7, wherein for non-Newtonian fluids, mu represents the apparent viscosity calculated at the wall shear rate dictated by the geometry-coupled pitch relationship.

22. The system of claim 15, wherein the 3D-printed lattice comprises an isotropic or anisotropic porous matrix where the effective Dh is defined by the mean pore hydraulic diameter.

23. The system of claim 21, wherein the wall shear rate (gamma) is determined by the relationship gamma = (8V) / Dh, where V is the average fluid velocity, to determine the local effective viscosity.

24. The system of claim 1, comprising a plurality of parallel flow paths, each flow path having a hydraulic diameter (Dh) and being inclined at a pitch angle (theta) satisfying the geometry-coupled pitch relationship such that laminar flow is maintained within each flow path during operation.

25. The system of claim 19, wherein the feedback-controlled actuator adjusts the pitch angle (theta) within a mechanical range of 0.1 to 15.0 degrees.Amendments to the claims has been filed as follows:21 04 26CLAIMSCLAIM 1A passive fluid transport system configured to convey a working fluid under gravitational driving forces, comprising:a plurality of discrete flow path segments arranged in a vertically stepped cascade, each flow path segment defining a channel having a hydraulic diameter (Dh) and a fixed geometric inclination relative to a horizontal reference plane defined by a pitch angle (0);wherein each flow path segment is separated from an adjacent flow path segment by a transition structure defining a curved, contoured flow surface configured to redirect the working fluid between non-collinear flow path segments while maintaining continuous fluid-wall contact along the transition surface;wherein each flow path segment is dimensioned such that, in use under gravitational head, the Reynolds number of the working fluid remains below a laminar-to-turbulent transition threshold (Re_max) for the hydraulic diameter (Dh) of that segment;wherein each transition structure defines a flow reconditioning region having a continuously curved profile configured to suppress flow separation and redistribute the velocity profile of the working fluid prior to entry into the next flow path segment;and wherein the pitch angle (0) of each flow path segment is selected in dependence on the hydraulic diameter (Dh) and fluid viscosity (p) such that gravitational driving force along each segment is constrained to a level that maintains laminar flow within that segment under steady-state operation.CLAIM 2The system of claim 1, wherein each transition structure is configured to promote re-establishment of a substantially fully developed laminar velocity profile downstream of the transition prior to entry into a subsequent flow path segment.CLAIM 3The system of claim 1 or 2, wherein the transition structures maintain continuous flow between vertically offset segments via surface-guided attachment of the working fluid along the contoured flow surface.CLAIM 4The system of any preceding claim, wherein each transition structure defines a flow conditioning zone having a length and surface curvature configured to permit recovery of a substantially fully developed laminar velocity profile prior to entry of the fluid into a subsequent flow path segment.21 04 26CLAIM 5The system of any preceding claim, wherein the pitch angle (0) is selected such that flow within each flow path segment is maintained below a laminar-to-turbulent transition threshold determined in dependence on hydraulic diameter (Dh), fluid density (p), and dynamic viscosity (p).CLAIM 6The system of claim 5, wherein the pitch angle (0) satisfies the relationship: 0 <arcsin((Re_max • 32 • p2) I (p2 • g • Dh3)) where Re_max defines a laminar-to-turbulent transition limit and g is gravitational acceleration.CLAIM 7The system of any preceding claim, wherein each flow path segment has a length selected such that a substantially fully developed laminar velocity profile is established before the fluid reaches the corresponding downstream transition structure.CLAIM 8The system of any preceding claim, wherein the transition structures are configured to reduce flow separation during directional redirection between flow path segments.CLAIM 9The system of any preceding claim, wherein at least one transition structure is configured to reduce vortex formation during directional change of the working fluid.CLAIM 10The system of any preceding claim, wherein the flow path segments comprise at least one of vertically offset trays or helical conduits.CLAIM 11The system of any preceding claim, configured for operation under gravitational driving forces following initiation of fluid movement by a transient input.CLAIM 12The system of any preceding claim, further comprising at least one sensor and at least one actuator configured to adjust the pitch angle (0) in response to measured fluid properties including temperature, density, or viscosity.CLAIM 13A transition structure for a passive fluid transport system, the transition structure comprising a contoured flow surface configured to redirect a working fluid between flow path segments of differing orientation while maintaining continuous fluid-wall contact and reducing flow separation during directional change; wherein the contoured flow surface is shaped such that fluid passing over the transition structure undergoes a redistribution of velocity profile as it moves between adjacent flow path segments, thereby re-establishing laminar development conditions prior to entry into a downstream flow path segment.CLAIM 14A method of configuring a passive fluid transport system, comprising: (a) providing a plurality of flow path segments; (b) selecting pitch angles (0) in dependence on hydraulic diameter (Dh) and fluid properties to maintain gravitationally driven flow conditions below a Reynolds number transition threshold within each flow path segment, by functionally coupling pitch angle to hydraulic diameter and viscous properties such that gravitational driving force is balanced against viscous resistance; (c) providing transition structures between adjacent segments configured to redirect and condition fluid flow and to re-establish laminar development conditions prior to entry into each subsequent flow path segment; and (d) arranging the flow path segments in a gravitationally stepped configuration.21 04 26A

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