Publication NumberUS 4003405
Assignees
  • Canadian Patents and Development Limited
StatusIssued Patent
Application Number05/662842
AvailabilityUnknown
Filing Date1976-03-01
Publication Date1977-01-18

Abstract

An apparatus for regulating the flow rate of a fluid, comprising a casing having an annular or cone-shaped fluid passage, for radial flow (inwardly or outwardly) between an inlet and outlet which are spaced radially and form unobstructed flow paths to the whole of the fluid passage. The geometry of the fluid passage is defined for a compressible and incompressible fluid so that laminar flow is achieved in the fluid passage. The apparatus further provides a very rapid dynamic response, essentially free of hysteresis, and substantially no internal generation of fluid flow turbulence resulting in a minimum of noise and freedom from cavitation. In an adjustable configuration the apparatus provides a proportional fluid valving function. In a nonadjustable configuration the apparatus provides a laminar flow restriction.

Claims

  • 1. Apparatus for regulating the flow rate of a fluid, comprising; a. a casing having, when the apparatus is regulating the flow rate of a fluid, a fluid passage which is symmetrical about an axis and is annular shaped when viewed in the direction of the said axis and has a geometry such that any sectional area of the fluid passage which is symmetrical about the said axis and is normal to the mean direction for the flow of fluid therein forms a curved surface within the range of the curved surface of a frustrum of a cone and the curved surface of a circular cyliner, a fluid inlet cavity in the casing, for connection to a source of pressurized fluid, the fluid inlet cavity being coaxial with the annular shaped fluid passage and forming a substantially unobstructed flow path for fluid to the whole of a peripheral inlet area to the annular shaped fluid passage, and fluid outlet means coaxial with the annular shaped fluid passsage and spaced radially from the fluid inlet cavity, the fluid outlet means being for the escape of fluid from the fluid passage and forming a substantially unobstructed flow path, from the whole of a peripheral outlet area of the annular shaped fluid passage, for fluid which has flown through the annular shaped fluid passage from the fluid inlet cavity, and wherein, b. when the apparatus is regulating the flow rate of a fluid, the flow of fluid along the whole length of the fluid passage, and in the mean direction of fluid flow therein, is laminar as evidenced by the fluid passage geometry conforming with the relationships in the following equations designated (1) to (8): i. for a fluuid, having the characteristics of a substantially incompressible, substantially Newtonian fluid, flowing through the fluid passage, if the fluid passage is divided into incremental portions for which the centerline of the fluid passage generally in the mean direction of the fluid flow may be assumed to be substantially straight, then the fluid static pressure drop (p.sub.2 - p.sub.1) in each incremental portion conforms with the following relationship in consistent units: ##EQU13##where A and B are geometric parameters of the incremental portion under consideration and are defined, in consistent units, by the reltionships: ##STR3##and where r.sub.1 = the radius, of that incremental portion at which p.sub.1 occurs and where the radius is measured from the said axis of symmetry of the fluid passage to a first limit of the centerline of that incremental portion of the fluid passage in the mean direction of flow therealong, r.sub.2 = the radius of that incremental portion at which p.sub.2 occurs and where the radius is measured from the said axis of symmetry of the fluid passage to a second limit of the centerline of that incremental portion of the fluid passage in the mean direction of fluid flow therealong and downstream of the first limit, h.sub.1 = the lesser dimension of that incremental portion, transverse to the mean direction of flow of fluid therethrough, at the radius r.sub.1, h.sub.2 = the lesser dimension of that incremental portion, transverse to the mean direction of flow of fluid therethrough, at the radius r.sub.2, θ = the slope of the centerline of that incremental portion in the mean direction of fluid flow relative to the said axis of symmetry of the fluid passage, and is in the range greater than 0° and less than 180°, k = mean slope of one boundary wall of that incremental portion relative to the opposite boundary wall thereto, x = equivalent height of that incremental portion at the said axis of symmetry of the fluid passage as indicated by projecting the mean slope of each of the fluid passage boundary walls of that incremental portion to the said axis of symmetry, G = mass flow rate of fluid flowing along the fluid passage, ρ = density of fluid flowing along the fluid passage, μ = absolute viscosity of fluid flowing along the fluid passage, and g = acceleration due to gravity, and ii. for a fluid, having the characteristics of a substantially compressible, substantially Newtonian fluid, flowing through the fluid passage, if the fluid passage is divided into incremental portions for which the centerline of the fluid passage generally in the mean direction of fluid flow may be assumed to be substantially straight, and where the fluid static pressure in each incremental portion, at any point on the said centerline of the fluid passage in the mean direction of flow of fluid therethrough, is a substantially linear function of the radial distance from the said axis of symmetry of the fluid passage to that point on the said centerline of the fluid passage, then the following relationship exists in consistent units for each incremental portion: ##EQU14##where C and D are geometric parameters of the inremental portion under consideration and are defined, in consistent units, by the relationships: ##EQU15##and where similar symbols in the relationships (6), (7) and (8) are as previously defined for the relationships (1), (2) (3), (4) and (5) and where 1n =hyperbolic or natural logarithm, T =the absolute temperature of fluid flowing along the fluid passage, which with the fluid passages according to the present invention has been found to remain substantially constant along the whole length of the fluid passage, and R =a constant for the substantially compressible fluid flowing along the fluid passage and is in accordance with the relationship p/p.sub.c = R.T. where p = the absolute static pressure of the fluid at any position along the fluid passage, ρ.sub.c = the density of the substantially compressible fluid at the position along the fluid passage where the absolute static pressure p is defined.
  • 2. Apparatus according to claim 1, wherein the fluid inlet passage forms a substantially unobstructed flow path to the whole of an outer, peripheral inlet area to the annular shape of the fluid passage.
  • 3. Apparatus according to claim 1, wherein the fluid inlet passage forms a substantially unobstructed flow path to the whole of an inner, peripheral inlet area to the annular shape of the fluid passage.
  • 4. Apparatus according to claim 1, further comprising a fluid closure means upstream of the annular shaped fluid passage.
  • 5. Apparatus acccording to claim 1, further comprising a fluid closure means downstream of the annular shaped fluid passage.
  • 6. Apparatus according to claim 1, further comprising a member in the casing moveable along the axis of symmetry and forming one moveable member in the casing for adjusting the fluid passage to the said fluid passage geometry.
  • 7. Apparatus according to claim 6, wherein the means for adjusting the moveable member is capable of moving the said member sufficiently to close the fluid passage in a fluidtight manner.
  • 8. Apparatus according to claim 1, further comprising a flexible disk in the casing sealed around the periphery thereof to the casing and forming one boundary wall of the fluid passage, and means for deflecting the flexible disk to obtain the said fluid passage geometry.
  • 9. Apparatus according to claim 8, wherein the means for deflecting the flexible disk is capable of deflecting the flexible disk sufficiently to close the fluid passage in a fluidtight manner.
  • 10. Apparatus according to claim 1, further comprising two flexible disks in the casing with the periphery of each flexible disk sealed to the casing, each flexible disk forming one of the boundary walls of the fluid passage, and means for deflecting the flexible disks to obtain the said fluid passage geometry.
  • 11. Apparatus according to claim 10, wherein the means for deflecting the flexible disks is capable of deflecting at least one of the flexible disks sufficiently to close the fluid passage in a fluidtight manner.
  • 12. Apparatus according to claim 1, further comprising a flexible disk in the casing and sealed around the periphery thereof to the casing, the flexible disk dividing the casing into two fluid passages, a first one of the fluid passages being the said annular shaped fluid passage and a second one of the fluid passages satisfying the fluid flow equations given for the first one of the fluid passages, and means for deflecting the flexible disk in either direction along the said axis of symmetry for the adjustment of the fluid passage geometries of each fluid passage, and wherein the fluid inlet cavity is one of two, similar fluid inlet cavities each forming an inlet to one of the fluid passages, and the fluid outlet means is one of two, similar fluid outlet means each forming a fluid outlet from one of the fluid passages.
  • 13. Apparatus according to claim 12, wherein the means for deflecting the flexible disk is capable of deflecting the said disk sufficiently to close at least one fluid passage in a fluidtight manner.
  • 14. Apparatus according to claim 12, further comprising means having a fluid outlet port and connecting the fluid outlet means from the said first annular shaped fluid passage to the fluid inlet cavity of the said second fluid passage.