CROSS-REFERENCE TO RELATED APPLICATIONS

[0001 ] This application claims the benefit of 35 USC 1 19 based on the priority of co-pending US Provisional Patent Application 62/239,349 filed October 9, 2015 and entitled Switched Inertance Converter, which is incorporated herein in its entirety by reference

FIELD

[0002] The present subject matter of the teachings described herein relates generally to a switched inertance converter.

BACKGROUND

US Patent No. 8,302,410 discloses an inertance tube and a surge volume for a pulse tube refrigerator system may be integrally coupled together, such as by the inertance tube being at least in part a channel in a wall of the surge volume. The surge volume may have a helical channel in an outer wall that forms part of the inertance tube. The surge volume tank may be surrounded by a cover that closes off the channel to form the inertance tube as an integral part of the surge volume. The inertance tube may have a non-circular cross section shape, such as a square shape or non-square rectangular shape. The channel may be tapered, perhaps changing aspect ratio. Alternatively, the inertance tube may be a separate tube having a non-circular shape, which may be wrapped around at least part of the surge volume.

SUMMARY

[0003] This summary is intended to introduce the reader to the more detailed description that follows and not to limit or define any claimed or as yet unclaimed invention. One or more inventions may reside in any combination or sub-combination of the elements or process steps disclosed in any part of this document including its claims and figures.

[0004] In accordance with one aspect of the teachings described herein, a switched inertance pressure converter may include a first fluid inlet connectable to a first fluid source and a switching valve provided downstream from the first fluid inlet and switchable between an open configuration, in which fluid can flow through switching valve, and a closed configuration, in which fluid flow cannot flow through the switching valve. An inertance conduit may extend between an inlet end having an inlet flow area and that is in fluid communication with first fluid inlet and an outlet end downstream from the inlet end and having an outlet flow area. The inertance conduit may include an expanding section in which the flow area increases from the inlet flow area to a transition flow area, and a contracting section in which the flow area decreases from the transition flow area to the outlet flow area, the expanding section being downstream from the contracting section so that when a fluid is provided within the switched inertance pressure converter a pressure wave induced in the fluid by closing the switching valve is reflected back toward the switching valve by the contracting section and arrives at the switching valve as a non-inverted reflected pressure wave the next time the switching valve is closed. A second fluid inlet may be fluidly connected between the switching valve and the outlet end of the inertance conduit and connectable to a second fluid source (e.g. a non-pressurized reservoir). A fluid outlet may be downstream from the outlet end of the inertance conduit and may be connectable to a downstream fluid conduit.

[0005] The contracting section may begin at a distance downstream from the inlet end of the inertance conduit that is between about 50% and about 150% of Δt _p c/2.

[0006] The distance where the contracting section begins may be about Δt _p c/2 downstream from the from the inlet end of the inertance conduit.

[0007] The outlet flow area of inertance tube may be between about 50% and about 150% of the inlet flow area of inertance conduit.

[0008] The outlet flow of the inertance conduit may be substantially equal to the inlet flow area of the inertance conduit.

[0009] The ratio between the transition flow area and the inlet flow area may be less than about 10: 1 , and may be between about 2: 1 and about 8: 1 . [0010] Optionally, the flow length can be at least 7m, and may be at least 14m, and the inlet flow area can be at least between about 15mm ² and about 100mm ^2, and may be between about 19mm ² and about 80mm ² .

[001 1 ] The expanding section may smoothly and gradually increases from the inlet flow area to the transition flow area.

[0012] The contracting section may have a length that is between about 1 % and about 25% of a length of the expanding section.

[0013] The expanding section may extend along between about 15% and about 90% of a length of the inertance conduit and the contracting section extends between about 2% and about 30% of the length of the inertance conduit.

[0014] A flow control device may be provided at the second fluid inlet to inhibit fluid from flowing from the switched inertance pressure converter into the second fluid source.

[0015] A fluid reservoir may provide the second fluid source. When the switched inertance pressure converter is in use fluid in the inertance conduit may be at a first pressure and the fluid reservoir may be maintained at second pressure that is less than the first pressure, and may be less than about 50% of the first pressure.

[0016] The inertance conduit may include a generally helical channel wound along a conduit axis.

[0017] The inertance conduit may extends an axial length along the conduit axis and wherein a flow length of the inertance conduit is between about 1500% and about 2500% the axial length.

[0018] The inertance conduit may include a conduit defined by a generally helical groove in the outer surface of a cylinder that is sealed by an inner surface of a sleeve surrounding the cylinder.

[0019] A controller may be used to actuate the switching valve at a switching frequency of between about 50 Hz and about 15000Hz. [0020] The second fluid inlet may be fluidly connected between the switching valve and the inlet end of the inertance conduit.

[0021 ] The second fluid inlet may be spaced downstream from the switching valve whereby the reflected wave arrives at the second fluid inlet at a different time than it arrives at the valve.

[0022] The second fluid inlet may be positioned at a distance downstream from the switching valve where a ratio of L _cv /L is between about 0.2 and about 0.6.

[0023] In accordance with another aspect of the teachings described herein that may be used alone or in combination with any other aspects, a switched inertance pressure converter may include a first fluid inlet connectable to a first fluid source (e.g. from the working circuit) and a switching valve provided downstream from the first fluid inlet and switchable between an open configuration, in which fluid can flow through switching valve, and a closed configuration, in which fluid flow cannot flow through the switching valve. An inertance conduit may extend between an inlet end in fluid communication with first fluid inlet and an outlet end downstream from the inlet end. A second fluid inlet may be fluidly connected between the inlet end of the inertance conduit and the outlet end of the inertance conduit and may be connectable to a second fluid source. A fluid outlet may be downstream from the outlet end of the inertance conduit and connectable to a downstream fluid conduit.

[0024] A third fluid inlet may be fluidly connected between the second fluid inlet and the outlet end of the inertance conduit and connectable to a third fluid source.

[0025] The inlet end of the inertance conduit may have an inlet flow area and the outlet end of the inertance conduit may have an outlet flow area. The inertance conduit may include an expanding section in which the flow area increases from the inlet flow area to a transition flow area, and a contracting section in which the flow area decreases from the transition flow area to the outlet flow area. The expanding section may be downstream from the contracting section so that when a fluid is provided within the switched inertance pressure converter a pressure wave induced in the fluid by closing the switching valve is reflected back toward the switching valve by the contracting section and arrives at the switching valve as a non-inverted reflected pressure wave the next time the switching valve is closed.

[0026] In accordance with another aspect of the teachings described herein that may be used alone or in combination with any other aspects, a method matching load and supply pressures in a hydraulic power system, may include the steps of:

a) receiving a supply liquid flow from a supply liquid source at a supply pressure and a supply mass flow rate;

b) conveying the supply liquid flow through a valve in an open configuration and through an inertance conduit downstream from the valve;

c) closing the valve whereby:

i) inertia of the supply fluid flow downstream from the valve draws a supplemental liquid flow into the system from a supplemental liquid source to provide a combined liquid flow having a combined flow mass flow rate that is greater than the supply mass flow rate and a combined flow pressure that is less than the supply pressure; and

ii) a pressure wave is induced in the combined liquid flow flowing through the inertance conduit;

d) conveying the pressure wave along a section of the inertance conduit having an expanding flow area;

e) inhibiting the flow of supply fluid through the valve the next time the valve is transitioning from the open configuration to the closed configuration by reflecting the pressure wave off a section of the inertance conduit having a contracting flow area so that a non-inverted reflected pressure wave arrives back at the valve the next time the valve is closing; and

f) conveying the combined liquid flow from an outlet of the inertance conduit to a downstream load.

DRAWINGS [0027] The drawings included herewith are for illustrating various examples of articles, methods, and apparatuses of the teaching of the present specification and are not intended to limit the scope of what is taught in any way.

[0028] In the drawings:

[0029] Figure 1 is a schematic representation of one example of a switched inertance converter;

[0030] Figure 2 is a schematic representation of another example of a switched inertance converter;

[0031 ] Figure 3 is a partially exploded perspective view of one example of an inertance conduit;

[0032] Figure 4 is a side view of a portion of the inertance conduit of Figure

3;

[0033] Figure 5 is an end view of one end of the portion of the inertance conduit of Figure 4;

[0034] Figure 6 is an end view of the other end of the portion of the inertance conduit of Figure 4;

[0035] Figure 7 is a schematic representation of another example of a switched inertance converter;

[0036] Figure 8 is a schematic representation of another example of a switched inertance converter;

[0037] Figure 9 is a schematic representation of another example of a switched inertance converter;

[0038] Figure 10 is a plot showing Effect of resonance on energy efficiency for one example of a switched inertance converter with a fast switching valve (top) with a switching time of 0.1 ms, and a slower valve (bottom) with a switching time of 3ms;

[0039] Figure 1 1 is a plot showing the effect of resonance on flow loss fraction for one example of a switched inertance converter with a fast switching valve (top) with a switching time of 0.1 ms, and a slower valve (bottom) with a switching time of 3ms;

[0040] Figure 12 is a plot showing the effect of valve switching time on load power and losses for one example of a switched inertance converter operating at its resonant frequency and a 50% duty cycle;

[0041 ] Figure 13 is a plot showing the effect of valve switching time on energy efficiency for one example of a switched inertance converter operating at its resonant frequency and a 50% duty cycle;

[0042] Figure 14 is a plot showing the effect of valve switching time on flow loss for one example of a switched inertance converter operating at its resonant frequency and a 50% duty cycle;

[0043] Figure 15 is a plot showing the effect of resonance on power loss across the switching valve in a switched inertance converter as it is opening and closing, for a valve with a switching time of 3 ms;

[0044] Figured 16 is a plot showing the effect of resonance and valve switching time on energy efficiency for one example of a switched inertance converter operating at a 50% duty cycle;

[0045]

[0046] Figure 17 is a plot showing the effect of resonance and valve switching time on flow loss for one example of a switched inertance converter operating at a 50% duty cycle.

[0047] Figure 18 is a plot showing the effect of resonance on energy efficiency for one example of a switched inertance converter with a non-constant flow area.

[0048] Figure 19 is a plot showing the effect of resonance on flow loss for one example of a switched inertance converter with a non-constant flow area.

[0049] Figure 20 is a plot showing the effect of resonance on valve losses while opening and closing for one example of a switched inertance converter with a non-constant flow area. [0050] Figure 21 is a plot showing the effect of the position of the second fluid inlet on energy efficiency for one example of a switched inertance converter;

[0051 ] Figure 22 is a plot showing the effect of the position of the second fluid inlet on flow loss for one example of a switched inertance converter;

[0052] Figure 23 is a plot showing the effect of resonance and second fluid inlet position on energy efficiency for one example of a switched inertance converter;

[0053] Figure 24 is a plot showing the effect of resonance and second fluid inlet position on volumetric efficiency for one example of a switched inertance converter. The line A-B denotes Pareto-optimal operating points trading off energy efficiency and volumetric efficiency (A and B are in the same position as in Figure 23);

[0054] Figure 25 is a plot showing the trade-off of energy and volumetric efficiency along the E-V and A-B line in Figures 23 and 24;

[0055] Figure 26 is a plot showing the minimum reservoir pressure required to prevent cavitation as one varies the area of the inertance conduit between switching valve and check valve, with parameters at the optimal 'B' position in Figures 23 and 24, for one example of a switched inertance converter;

[0056] Figure 27 is a plot showing energy and volumetric efficiencies as one varies the area of the inertance conduit between switching valve and check valve, under the same conditions as Figure 26;

[0057] Figure 28 is a plot showing check valve flows while varying the elevated reservoir pressure and while using two check valves in one example of a switched inertance converter; and

[0058] Figure 29 is a plot showing the energy and volumetric efficiency of one example of a switched inertance converter while using two check valves. DETAILED DESCRIPTION

[0059] Various apparatuses or processes will be described below to provide an example of an embodiment of each claimed invention. No embodiment described below limits any claimed invention and any claimed invention may cover processes or apparatuses that differ from those described below. The claimed inventions are not limited to apparatuses or processes having all of the features of any one apparatus or process described below or to features common to multiple or all of the apparatuses described below. It is possible that an apparatus or process described below is not an embodiment of any claimed invention. Any invention disclosed in an apparatus or process described below that is not claimed in this document may be the subject matter of another protective instrument, for example, a continuing patent application, and the applicants, inventors or owners do not intend to abandon, disclaim or dedicate to the public any such invention by its disclosure in this document.

[0060] A common problem in fluid power applications is matching of supply pressure to load pressure. Often, this is solved via the inefficient method of using a resistive valve to reduce the pressure. However, considerable recent research has been performed on an alternate method: the switched inertance converter. This is the hydraulic equivalent of the electrical switched-mode power supply, but relies on fluid inertia rather than electrical inductance to adjust pressures and flows, with theoretically no losses. Figure 1 is a schematic representation of one known example of a switched inertance converter 10, also referred to as a buck converter, which can increase flow while reducing outlet pressure (a similar arrangement can be used to boost pressure while reducing flow).

[0061 ] As shown in Figure 1 , the switched inertance converter 10 includes an inlet 12 that can be connected to a supply of pressurized hydraulic fluid, such as pump or the like. A valve 14 is provided toward the inlet 12 and can be opened and closed to control the flow of the hydraulic fluid into the rest of the switched inertance converter 10. An inertance conduit 16 is positioned downstream from the valve 14, and a second fluid inlet 18 is connected to the system between the valve 14 and the inertance conduit 16. The second fluid inlet 18 can be connected to a second source of hydraulic fluid (i.e. a different source than is supplying fluid to the valve). A downstream, outlet end of the switched inertance converter 20 (i.e. downstream from the inertance conduit 16) can be connected to a load, such as a hydraulic actuator or the like. In the schematic illustration, the load 22 is represented by a compressible volume and fixed orifice.

[0062] When the switched inertance converter 10 is in use, the valve 14 can be rapidly opened and closed, for example using an automated controller. When the valve 14 is opened, the fluid begins to flow through valve 14 and through the inertance conduit 16, building inertia. When the valve 14 is closed, the inertia of the moving fluid will tend to urge the fluid to continue flowing through the inertance conduit 16. This can create a region of relative low pressure toward the inlet end 24 of the inertance conduit 16. If the valve remains closed, this low pressure can be sufficient to cause the inertance conduit 16 to suck additional hydraulic fluid into the switched inertance converter 10, from the second fluid source 18. Optionally, a check valve 26 can be provided at the second fluid inlet 18 to help inhibit the flow of fluid from the switched inertance converter 10 back into the second source 18. This may be helpful if the second fluid source 18 is maintained at a lower pressure than the first fluid supply and/or the switched inertance converter 10. As additional fluid is drawn in through the check valve 26, the flow of hydraulic fluid conveyed downstream to the load 22 is greater than the flow rate of fluid that was provided by the supply 12, and the pressure of the flow exiting the switched inertance converter 10 is correspondingly reduced to a pressure that is less than the pressure upstream from the valve 14. While the switched inertance converter 10 is schematically illustrated using a two-way valve 14 and check valve 26, a switched inertance converter may also be configured to include a three-way valve, two two-way valves, or other suitable valving and flow control members.

[0063] When in use, the switched inertance converter 10 can suffer from a number of losses. Some examples of such losses can include frictional losses in the inertance conduit 16, leakage in the valves, back-flow of fluid through the check valve 26 before it can close and frictional losses in the valves 14 and/or 26 while they are partially closed and fluid is flowing through them. The fact that commonly used hydraulic valves do not open and close instantaneously can lead to a loss as the valve is closing. For example, when the valve 14 is partially open there can be both flow through the valve and also a pressure drop, which may lead to a loss of energy.

[0064] Referring to Figure 2, a switched inertance converter 100 that may, under some operating conditions, help reduce some of the losses experienced by the switched inertance converter 10 is schematically illustrated. In the illustrated example, the switched inertance converter 100 includes a first fluid inlet 102 that is connectable to a first fluid source 104, such as a pressurized hydraulic source, and a fluid outlet 106 that is downstream from the fluid inlet 102 and is connectable to a downstream fluid conduit 108, which can be connected to a load 1 10 to be powered by the fluid.

[0065] A switching valve 1 12 is positioned toward the first fluid inlet 102. The valve 1 12 can be switched between an open configuration (as illustrated), in which fluid can flow through switching valve 1 12, and a closed configuration, in which fluid flow cannot flow through the switching valve 1 12. In the illustrated schematic, the valve is a two position valve that can be actuated by any suitable actuator 1 14, such as a solenoid, and a suitable controller 1 16 to cycle between its fully open and fully closed positions. For the purposes of this description, one cycle of the valve 1 12 is understood to mean the time for the valve 1 12 to move from one position (i.e. closed), to the other position (i.e. open) and then return to the initial position (i.e. closed).

[0066] When the valve 1 12 is fully open, its impact on the fluid flowing through the system is relatively low, and when the valve is fully closed the flow of fluid through the valve is at least substantially stopped (and optionally can be completely stopped). The actuator 1 14 and controller 1 16 can be configured to cycle the valve 1 12 at any desired frequency (measures a cycles/ second), and optionally can cycle the valve 1 12 at frequencies between about 50Hz and about 15000Hz, and optionally between about 100Hz and about 300Hz, and the valve switching time may be between about 0.1 ms or less, and about 3ms or more. [0067] Upstream from the valve 1 12, the hydraulic fluid can be supplied to the switched inertance converter 100 at any suitable supply pressure and supply flow rate. These supply conditions can be based on the nature of the hydraulic source, such as the performance and output curves of a hydraulic pump.

[0068] Downstream from the valve 1 12, the switched inertance converter 100 includes an inertance conduit 120 that has a non-constant flow area (i.e. a non-constant cross-sectional area taken in a plane that is generally orthogonal to the direction the fluid flows through the inertance conduit). As described in more detail here, operation of the valve 1 12, such as moving the valve into the closed position, can induce a corresponding pressure wave in the fluid. Providing an inertance conduit 120 having a non-constant flow area may help generate a non- inverted, reflected pressure wave within the inertance conduit 120, and the reflected pressure wave may travel back toward the valve 1 12. The configuration of the inertance conduit 120 may be selected so that the reflected pressure wave will return to the valve 1 12 after a desired length of time, such that the reflected pressure wave may influence, and preferably may help inhibit, the flow of fluid through the valve 1 12 when the valve 1 12 is only partially open. For example, the inertance conduit 120 can be configured so that the time it takes the reflected pressure wave to reach the valve 1 12 is between about 50% of the valve cycle time and about 150% of the valve cycle time, and optionally can be configured so that the time it takes the reflected pressure wave to reach the valve 1 12 is between about 90% and about 1 10% of the valve cycle time, and may be generally equal to the valve cycle time. For example, the inertance conduit 120 may be configured such that a pressure wave generated by the closing (or opening of the valve) of the valve 1 12 may be reflected back and reach the valve 1 12 the next time the valve 1 12 is closing (or opening).

[0069] In the illustrated example, the inertance conduit 120 extends between an inlet end 122 and an outlet end 124 that is downstream from the inlet end 122. The inlet end 122 is connected in fluid communication downstream from the valve 1 12, and thereby with first fluid inlet 102. The outlet end 124 of the inertance conduit 120 is in fluid communication with the fluid outlet 106 of the switched inertance converter 100.

[0070] The inlet end 122 of the inertance conduit 120 defines an inlet flow area (e.g. a cross-sectional area taken in a plane orthogonal to the direction the fluid is flowing through the inlet end 122), and the outlet end 124 of the inertance conduit 120 has an outlet flow area. The inlet and outlet flow areas may be any suitable areas, and may be determined based on a number of factors, including the desired operating conditions of the switch inertance converter 100 (i.e. fluid pressure and fluid flow rate). Optionally, the inlet flow area and outlet flow area may be between about 1 mm ² and about 8000mm ² , and may be between about 50mm ² and about 1500mm ² . In the illustrated example, the inlet flow area is about 14 mm ² and about 15mm ² . Optionally, the inlet flow area may be equal to the outlet flow area. Alternatively, the outlet flow area may be between about 10% and about 500% of the inlet flow area, and may be between about 50% and about 150% of the inlet flow area.

[0071 ] The inertance conduit has a conduit flow length 126, which is understood to be the flow length of the conduit. The flow length 126 may be any suitable length, and may be, for example, between about 1 m and about 50m or more, may be between about 5m and about 30m, and may be about 20m. The flow length 126 can be selected based on a variety of factors for any given embodiment of the switched inertance converter (such as the valve switching frequency, the nature of the fluid used, the location of the valves, the operating pressures and flow rates, etc).

[0072] In the schematic example, the inertance conduit is illustrated as a generally linear passage, and the flow length is generally the same as the physical distance between the inlet end 122 and the outlet end 124. Alternatively, the inertance conduit need not be linear/ straight, and may be curved or coiled about an axis (much like winding a garden hose on a reel), such that the linear, physical distance between the inlet end 122 and the outlet end 124 is less than the flow length of the inertance conduit. One example of an inertance conduit having a coiled or helical type arrangement is illustrated in Figures 3-6 and is discussed in more detail herein. Configuring the conduit 120 in this manner may help accommodate a relatively long conduit in a relatively small physical space. This may help reduce the overall size of the switched inertance converter 100. Reducing the size of the switched inertance converter may help facilitate using the switched inertance converter on vehicles and other portable apparatuses.

[0073] In the illustrated example, changes in the flow area of the inertance conduit are provided by an expanding section 128, in which the flow area increases in the flow direction, and a contracting section 130, in which the flow area decreases in the flow direction (from left to right as illustrated in Figure 2). Referring to Figure 2, in the illustrated example the expanding section 128 extends from the inlet end 122 of the inertance conduit to a transition point 132 located part way along the length 126 of the inertance conduit 120. In this configuration, the flow area of the inertance conduit 120 generally increases from the inlet flow area at the upstream end 134 of the expanding section to a transition flow area at the downstream end 136 of the expanding section 128, lying in the transition plane 132 as illustrated in this example. In the illustrated example, the upstream end 134 of the expanding section 128 is coincident with the inlet end 122 of the inertance conduit 120, and the transition flow area is the maximum flow area within the inertance conduit 120. Alternatively, the upstream end 134 of the expanding section 128 may be positioned downstream from the inlet end 122.

[0074] The ratio between the maximum flow area and the inlet flow area may be any suitable ratio for a given application, and in some instances may be less than about 10: 1 , and may be between about 2: 1 and about 8: 1 .

[0075] In the illustrated example, the upstream end 138 of the contracting section 130 is positioned directly adjacent the downstream end 136 of the expanding section 128. In this configuration, the upstream end 138 of the contracting section 130 is also located at the transition point 132. From the transition point 132, the flow area in the inertance conduit 120 can decrease, and optionally can suddenly decrease, toward the downstream end 140 of the contracting section 130 until reaching the outlet flow area (which may be reached at the outlet end 124 of the inertance conduit 120, or, as illustrated, at a location upstream from the outlet end 124). In this configuration, the expanding section 128 has a length 142 and the contracting section 130 has a shorter length 144. The relative lengths 142 and 144 of the contracting and expanding sections may be selected based so that the length 144 of the contracting section 130 is between about 1 % and about 25% of the length 142 of the expanding section 128, and may be between about 3% and about 10% of the expanding section length 142. In some configurations, the contracting section may include a stepped-face (i.e. a surface that is generally orthogonal to the flow direction), in which case the length 144 of the contacting section 130 may be minimal, and may be less than 1 % of the length 142 of the expanding section 128.

[0076] Optionally, the expanding section 128 may be configured to form between about 15% and about 90% of the length 126 of the inertance conduit 120, and the contracting section 130 may form between about 2% and about 30% of the length of the inertance conduit 126. In the illustrated example, the length 142 is about 80% of the conduit flow length 126, and the Iength144 is about 5% of the conduit flow length 126.

[0077] In the illustrated example, pressure waves caused by the opening and closing of the valve 1 12 can travel downstream from the valve 1 12 and through the inertance conduit 120. When the wave reaches the sudden decrease in the flow area at the upstream end 138 of the contracting section 130, a reflected pressure wave is generated which travels upstream, toward the valve 1 12.

[0078] In the illustrated configuration, the location at which the reflected pressure wave is generated may influence the travel time of the reflected wave and may determine when the reflected wave returns to the valve 1 12. In the illustrated example, the location at which the pressure wave is generated corresponds to the beginning of the contracting section, and is illustrated as the contracting section offset distance 146. In the illustrated example, the upstream end 138 of the contracting section 130 lies in the same plane 132 as the downstream end 136 of the expanding section 128, and the offset distance 146 is equal to the length 142 of the expanding section 128. Alternatively, the upstream end 138 may be spaced downstream from the downstream end 136, such that the offset distance 146 is different than the length 142.

[0079] Referring to Figure 2, the switched inertance converter 120 also includes a second fluid inlet 150 that can supply additional fluid to the system. The second fluid inlet 150 can be connected in fluid communication at any suitable location downstream from the switching valve 1 12 and upstream from the outlet end 124 of the inertance conduit 120. Optionally, as illustrated in the current example, the second fluid inlet 150 may be positioned upstream from the inlet end 122 of the inertance conduit 120, and in the same physical area as the valve 1 12.

[0080] Optionally, the offset distance 146 can be selected so that the reflected waves generated at the contracting section will return to the valve 1 12 as a non-inverted pressure wave after approximately one full valve cycle. For example, in this configuration closing the valve 1 12 may cause a suction wave that arrives back at the valve 1 12 and second fluid inlet 150 (practically simultaneously) as the valve 1 12 is closing on the next cycle. This may help increase the flow of fluid sucked in via the second fluid inlet 150, but may tend to increase switching losses. Conversely, when the valve 1 12 opens, a positive pressure wave is created that is also reflected off of the contracting section 130. When this wave arrives back at the valve 1 12 on the next opening cycle, it reduces the flow through the partially open valve, reducing the switching loss. Small changes in timing of these reflected waves can reduce switching losses and/or increase the flow through valve 154.

[0081 ] In the illustrated example, the contacting section offset distance 146 is approximately Δt _p c/2 from the inlet end 122 of the inertance conduit, where Δt _p is the valve switching cycle period and c is the sonic speed in the inertance conduit. This parameter can be calculated for a given inertance conduit and fluid combination. Optionally, in other embodiments the offset distance may be between about 50% and about 150% of Δt _p c/2. [0082] Optionally, instead of including a single expanding section and a single contracting section, the inertance conduit 120 may contain two or more expanding sections and/or two or more contracting sections, which may help provide different and/or multiple pressure wave reflections. Optionally, the sections may be arranged so that the flow area of an inertance conduit has alternating regions of increasing and decreasing flow area. If the inertance conduit contains only a single expanding section, the maximum flow area at the end of the expanding section may be the overall maximum flow area within the inertance conduit, as illustrated in Figure 2 for example. Alternatively, if an inertance conduit includes two or more expanding sections each expanding section may have a corresponding, local maximum flow area (i.e. the largest flow area provided in a given expanding section). If the expanding sections have different configurations, the local maximum flow area for a given expanding section may be less than the overall maximum flow area within the inertance conduit.

[0083] Optionally, instead of positioning the upstream end 138 of the contracting section 130 immediately beside the downstream end 136 of the expanding section 128 as illustrated, the inertance conduit 120 may include a connecting section that extends between the expanding and contracting sections 128 and 130. The connection section may have a constant flow area.

[0084] Referring again to Figure 2, the second fluid inlet 150 may be connected to any suitable source 152 of hydraulic fluid, including, for example a reservoir, accumulator, tank, the same fluid source that is used to supply the first fluid inlet, or any other suitable source. Optionally, as illustrated, the second fluid source 152 can be a reservoir that is maintained at a pressure that is less than the pressure at the first fluid inlet 102, and may be at generally atmospheric pressure (i.e. not substantially pressurized). Providing the second fluid source 152 at a lower pressure than the fluid at the first fluid inlet 102 may help reduce likelihood that fluid will be forced into the switched inertance converter 100, while still allowing fluid to be drawn into the switched inertance converter 100. The pressure at the second fluid inlet 150 can be selected so that it is between about 0% and about 80% of the pressure at the first fluid inlet 102. This pressure may be elevated to avoid cavitation.

[0085] Optionally, the second fluid inlet 150 can be provided with a flow control device that can allow fluid to flow into the switched inertance converter via the second fluid inlet 150, while inhibiting, and optionally preventing fluid from flow out via the second fluid inlet 150. This may help ensure that the fluid entering via the first fluid inlet 102 is conveyed into the inertance conduit 120, and is not inadvertently diverted out of the switched inertance 100 converter via the second fluid inlet 150. In the illustrated example, the second fluid inlet 150 has a flow control device in the form of a one-way check valve 154.

[0086] Optionally, as illustrated, the expanding section 128 of the inertance conduit 120 can be configured to provide a gradual, generally continuous expansion along its length 142. Providing a smooth transition along the length of the expanding section may help reduce the magnitude of reflected pressure waves that are created as the fluid flows through the expanding section. Alternatively, instead of generally linear, diverging sidewalls as illustrated in Figure 2, the expanding section 128 may have a curved or flared-type configuration (i.e. a trumpet like configuration), and/or may include one or more discontinuities or step-changes along the sidewall, where the flow area increases substantially over a short flow length. The particular geometry of an expanding section for use in a given application may be determined based on a variety of factors, including the operating flow rates and pressures, the nature of the fluid, the nature of the load be powered, the type of valve used, the configuration of the associated contracting section (if any) and the like.

[0087] Like the expanding section 128, the contracting section130 can be of any configuration that suitable for a given application. In the example illustrated the contacting section 130 has a short length and provides a sharp contraction in the flow area (operating generally like a step change in the conduit area). However, in other embodiments the contracting section 130 may have gradually converging linear sidewalls or arcuate sidewalls that provide a non-linearly reducing flow area, or any other suitable arrangement. The particular geometry of a contracting section for use in a given application may be determined based on a variety of factors, including the operating flow rates and pressures, the nature of the fluid, the nature of the load be powered, the type of valve used, the configuration of the associated expanding section (if any) and the like.

[0088] Referring to Figure 3, one example of an inertance conduit 1 120 that may be suitable for use with the switch inertance converter 100 is illustrated. The conduit 1 120 may have analogous features to the conduit 120 schematically illustrated in Figure 2, and like features are identified using like reference characters indexed by 1000.

[0089] In the illustrated example, the inertance conduit 1 120 is provided by the combination of a groove 1200 formed in the outer surface 1202 of a cylindrical spindle 1204, and a sleeve 1206 that surrounds the spindle 1204. In this configuration, the inertance conduit 1 120 is has a generally helical configuration, such that its axial length 1218, measured along the conduit axis 1208 about which the inertance conduit 1 120 is coiled, is much less than its flow length. The relationship between the axial length 1218 and the flow length may be selected such that the flow length is between about 1500% and about 2500% of the axial length 1218.

[0090] Referring also to Figure 4, in the illustrated example the groove 1200 is generally rectangular groove, having a base surface 1210 and sidewalls 1212 which together define a generally U-shaped channel in the spindle 1204. When the sleeve 1206 is positioned around the spindle 1204, an inner surface 1214 of the sleeve 1206 overlies the open top of the groove 1200, thereby enclosing the groove 1200 to form the enclosed fluid flow path through the inertance conduit 1 120.

[0091 ] In the illustrated example, the groove 1200 has a generally constant width 1216 along its length 1208, and changes in the cross-sectional flow area of the groove 1200 are facilitated by varying the radial depth 1220 of the groove 1200. Alternatively, the flow area of the groove 1200 could be changed by varying the width of the groove, or by varying both the width and depth. While a generally U-shaped groove is illustrated, the inertance conduit may be of any suitable cross-sectional shape, including, for example, round, oval, polygonal, square and the like.

[0092] Referring also to Figures 5 and 6, the inlet end 1 122 of the inertance conduit 1 120 is provided as an aperture 1222 in one end face 1224 of the spindle, that is in fluid communication with the rest of the groove 1200, and the outlet end 1 124 of the inertance conduit is provided as a corresponding aperture 1226 in the other end face 1228 of the spindle.

[0093] In accordance with another aspect of the teachings described herein, which may be used alone or in combination with any other aspects disclosed herein, the relative location of the second fluid inlet, e.g. inlet 150, can be changed, so that a reflected pressure wave may reach the second fluid inlet 150 and the first fluid inlet 102/ valve 1 12 at different times/ and or at different portions of the valve switching cycle. This may allow a given pressure wave to effect the first and second fluid inlets 102 and 150 differently.

[0094] For example, referring to Figure 7, another example of a switched inertance converter 2100 is schematically illustrated. The switched inertance converter 2100 may have some features that are similar to the switched inertance converter 100, and like elements are identified using like reference characters indexed by 2000.

[0095] In the illustrated example, the second fluid inlet 2150 may be spaced apart downstream from the valve 21 12, and optionally may be positioned downstream from the inlet end 2122 of the inertance conduit 2120 by an offset distance 2158. The behavior of the inertance converter 2100 having the second fluid inlet 2150 at various locations was simulated using computer models. As explained in more detail below, modifying the location of the second fluid inlet 2150 appears to influence the energy efficiency of the switched inertance converter 2100, and positioning the second fluid inlet 2150 so that the ratio L _cv /L is between 0 and about 0.8 or is between about 0.3 and about 0.6(where L _cv is the location of the second fluid inlet 2150 and corresponds to length 2158 in Figure 7, and L is the overall length and corresponds to length 2126), appears to provide relatively high efficiencies as compared to other ranges that were modelled.

[0096] Optionally, the switched inertance converter can be configured so that the second fluid inlet 2150 is located in the expanding section 2128 of the inertance conduit. Alternatively, the second fluid inlet 2150 may be located in the converging section 2130, at the transition point 2132 or in a portion of the inertance conduit 2120 having a constant flow area.

[0097] Optionally, modifying the location of the second fluid input may be used in combination with a constant flow-area inertance conduit, such as inertance conduit, as well as the non-constant flow-area inertance conduit.

[0098] For example, referring to Figure 8, another example of a switched inertance converter 3100 is schematically illustrated. The switched inertance converter 3100 may have some features that are similar to the switched inertance converter 100, and like elements are identified using like reference characters indexed by 3000.

[0099] In this example, the inertance conduit 3120 has a constant flow area along its length 3126. Positioning the second fluid inlet 3150 at a distance 3158 so that the so that the ratio L _cv /L is between 0 and about 0.8 or is between about 0.3 and about 0.6 (where L _cv is the location of the second fluid inlet 3150 and corresponds to length 3158 in Figure 8, and L is the overall length and corresponds to length 3128), appears to provide relatively high efficiencies as compared to other ranges that were modelled.

[00100] In accordance with another aspect of the teachings described herein, which may be used alone or in combination with any other aspect(s) of the teachings, an example of a switched inertance converter 3100 is schematically illustrated in Figure 9. The switched inertance converter 4100 may have some features that are similar to the switched inertance converter 100, and like elements are identified using like reference characters indexed by 4000.

[00101 ] In the illustrated example, the switched inertance converter 4100 is illustrated including an inertance conduit 4120 of constant flow area, but may also be configured to use an inertance conduit of non-constant flow area (as indicated using dashed lines). In this example, the switched inertance converter 4100 includes a second fluid inlet 4150, connected to a second fluid source 2152, that is connected between the valve 41 12 and the inlet end 4122 of the inertance conduit 4120. In addition to the second fluid inlet 4150, the switched inertance converter 4100 also includes a third fluid inlet 4160 that is located between the inlet end 4122 and outlet ends 4124 of the inertance conduit 4120. The third fluid inlet 4160 is fluidly connected to a third fluid source 4162, and includes a check valve 4164.

[00102] The third fluid source 4162 may be any suitable source. Optionally, the third fluid source 4162 may be fluidly connected to second fluid source 4152 and supply fluid at the same conditions (e.g. the same pressure). Alternatively, or in addition to being linked to the second fluid source 2152, the third fluid source 4162 may be fluidly connected to the system downstream from the outlet 4106 switched inertance converter 4100. For example, the third fluid source 4162 may be fluidly connected to the load 41 10, and may be maintained at generally the same pressure as the load 41 10. In such a configuration, fluid supplied through the second and third fluid inlets 4152 and 4162 may be at different pressures, and the pressure at the third fluid inlet 4162 may be greater than the pressure at the second fluid inlet 4152 (or vice versa). By spacing the second and third fluid inlets 4150and 4160 apart, a given pressure wave may reach each inlet at a different time, and may have different effects on the fluid flowing through the inlets. Modifying the spacing distance 4158 may help modifying the effects of a pressure wave on the third fluid inlet 4160.

[00103] Optionally, a switched inertance converter can be configured using any combination of the features/ aspects described herein. For example, a switch inertance converter may configured with the second fluid inlet connected between the inlet end and outlet ends of the inertance conduit with an inertance conduit of either constant or non-constant flow area. Optionally, a switched inertance converter can be configured with both second and third fluid inlets with an inertance conduit of either constant or non-constant flow area. Similarly, a switched inertance converter having an inertance conduit of non-constant flow area may be utilized in combination with a variety of second fluid inlet and/or third locations.

[00104] To examine some of the properties and behaviours of the switched inertance converters described herein, some experimental, computer modeling was performed.

[00105] In one aspect of the modeling, the switched inertance converter 10 of Figure 1 was modelled. In this example, the inertance conduit 16 was generally modelled as an open-ended tube (with the open end approximated by the load 22 including an accumulator and an orifice) capable of creating an inverted reflection of pressure waves. Resonance in the inertance conduit can have an effect on both energy efficiency and flow boosting performance of the converter 10. The conduit length and switching period were selected so that the distance from the switching valve 14 to the end of the conduit 16 and back was approximately half a wavelength. This selection of inertance tube parameters may allow for the positive pressure wave created when the switching valve 14 is opened to be reflected and inverted at the end of the tube 16, and subsequently arrive back at the valve 14 as a suction wave just as the valve 14 is closing (for 50% duty cycle). This suction wave may increase the flow of fluid through a check valve 26. However, this suction wave may also increase the flow of fluid through the partially closed switching valve 14, thereby increasing switching losses. A compromise operating point may be reached as a tradeoff between these gains and losses through implementing small changes in the period or tube length, so that the resultant operating point resides somewhat higher or lower than the resonant point of the tube. For an infinitely fast switching valve 14, switching valve losses may be insignificant compared to the check valve flow effects. However, as the switching speed of the valve 14 decreases (i.e. the time required to shift the valve increases), the valve effects become larger. This compromise may become more significant and may lead to unacceptable operating points.

[00106] To model the converter 10, the supply pressure, PS, is assumed to be constant, and the elevated tank pressure, PT , is assumed to be sufficient to avoid cavitation. The flow through the switching valve, QPA is assumed to be fully turbulent:

[001 07] where Cd is the discharge coefficient, A _PA (t) is the time-varying orifice area, r is the fluid density, and P _s and P _A are the supply pressure (at first fluid inlet 1 02 for example) and the pressure downstream of the valve. In this model, the discharge coefficients for all orifices are assumed to be constant. The orifice area is a square wave of period Δ _tp , fractional duty cycle ω _ΡΑ and maximum area A _PA max, that has been rate limited so that transition time from fully open to fully closed is Δt _sw - The load is assumed to consist of an orifice and volume. The load orifice is assumed to be a turbulent, sharp-edged orifice with constant area A|_, with its flow, Q _L , given by

[001 08] The load volume is assumed to be an ideal compressible volume, VL , with constant bulk modulus, β :

[001 09] where Q _B is the flow out of the inertance conduit. The check valve is modeled as a instantaneously fast valve with flow given by

[001 10] where ΔΡ = P _T - P _A is the differential pressure, and the orifice area, Α _ΤΑ (ΔΡ), increases linearly between the cracking pressure and fully open pressure:

[001 1 1 ] where ATAmin is the leakage area, ATAmax is the fully open orifice area, Pcr is differential cracking pressure, and Por is the pressure override.

[001 12] A lumped element method (LEM) transmission line model is used to simulate wave propagation through the inertance tube. The tube is divided into N elements, each consisting of an ideal compressible volume, a fluid inertia, and a laminar tube resistance. For segment i, with upstream pressure Pi and flow Qi, and downstream pressure and flow Pi+i and Qi+i , the governing equations for each segment are:

[001 13] where μ is the fluid viscosity, Li is the length of the segment, and Pi+0:5 is a fictional intermediate pressure, di is the diameter of the tube as interpolated at the midpoint of each segment, based on a lookup table defined by vectors of diameters, d and lengths from the inlet, Xd. This model was selected as it allows for varying cross sectional areas and related reflection effects, at relatively fast computation time.

[001 14] The speed of a pressure wave traveling through the inertance tube is governed by the equation:

[001 15] A simulation study was run in order to evaluate the switching losses for the model described above. The model described in the previous section was implemented in Simscape Language in Matlab Simulink, using the following parameters:

[001 16] Although the model allows for a shaped inertance tube, a tube with uniform cross section is used for this first test. For each run, the simulation was started from an initial condition of zero flow and all pressures at tank pressure, and run for 10 valve switching periods to allow the system to reach a steady state. The mean load pressure, and flow, were calculated over the last period.

Similarly, the mean power loss across the switching valve, mean supply power, and mean load power, were calculated. The system efficiency was calculated as

[001 1 7] Flow loss was also calculated, defined as the difference between the ideal flow through the check valve and the actual flow (averaged over a cycle) [001 18] the fractional flow loss, φ, is defined as the ratio of the flow loss to the theoretical flow:

[001 19] Simulations were run for 101 values of valve switching period, Dtp, ranging from 8 to 25 ms and 21 values for duty cycle, ωPA, ranging from 10 to 90%. This was repeated for two switching time values: a "fast" valve with a switching time of 0.1 ms and a "slow" valve with a switching time of 3 ms. The resulting efficiency and flow loss are shown in Figures 10 and 1 1 .

[00120] The simulation was also run with the duty cycle held at 50% and the period and inertance tube length matched for resonance at Δt _p c=(2L) = 2 (where L is the flow length of the inertance conduit, such as length 126 in Figure 2), while varying the valve switching time. 20 runs were simulated with Dt _sw varying between 0.1 and 3 ms. Figure 12 shows how the various power losses compare to the useful power at the load. This includes the frictional loss in the inertance tube, as well as the valve losses while the valve is opening, closing and also while the valve is fully open. Although the valve switching losses are less than the line loss in the inertance tube, they become significant as the switching time increases. Figures 13 and 14 show how the flow loss and efficiency are affected by the switching time. Both efficiency and flow loss become worse as the valve slows, although the effect on the flow loss is more profound.

[00121 ] Some switched inertance converters, such as converter 10, are designed so that the length of the inertance tube is equal to Δt _p c /4 with an accumulator at the load end, so that a standing wave is set up in the tube (i.e. the round-trip length to the end of the tube and back is 1/2 of a wavelength). If the duty cycle is 50%, just as the switching valve 14 is closing and the check valve 26 is about to open, a suction wave reflected off the open end of the conduit 16 returns to the check valve 26. This may tend to pull more fluid through the check valve 26, which may increase volumetric efficiency. A positive pressure wave also arrives at the valve 14 as it is opening, which tends to reduce flow through the partially open valve 14 and may help reduce switching valve pressure loss. However, just as this effect tends to increase the desired check valve 26 flow, it can also increase the flow through the partially open switching valve 14 as it is closing. This may have a deleterious effect on valve loss. For an infinitely fast valve, these valve losses may be insignificant when compared to the check valve flow effects. However, as the time taken to shift the valve 14 increases, the valve effects become larger. By slight adjustment of the tube length near Δt _p c /4, these effects can be traded off against each other as shown in Figures 15 through 17. As shown in the figures, while the resonant value is optimal from both an efficiency and flow perspective for the fast valve, it becomes a local worst operating point, with two optimal frequencies on either side of the resonant value. Thus, the optimal operating point may be adjusted away from the resonant point in order to compensate for valve switching time. For a "slow" valve of 3 ms switching time, this corresponds to an increase in efficiency from 46% for resonant operation to 58% for off-resonant operation, and a decrease in flow loss from 62% to 49%. Note that this strategy may only work in this manner for a 50% duty cycle without adjusting the switching period.

[00122] The exploitation of reflected waves in the model of the converter 10 is based on an inverted wave being reflected from the open pipe end (approximated by an accumulator or compressible volume) and arriving back at the valve approximately half a cycle later. However, referring to example of Figure 2, the inventors have discovered that it is also possible to gain similar effects by causing a non-inverted reflection to return after approximately a full cycle. To help facilitate this, the inertance conduit is configured to have a non-uniform flow area, such as the inertance conduit 120, so that the flow area contracts at a distance of approximately Δt _p c/2 from the valve 1 12, as shown in Figure 2. This system may not require a large accumulator at the load (unless desired to limit pressure fluctuations) and may be useable with a variety of duty cycles without adjusting switching frequency. In this case, the closing valve 1 12 causes a suction wave that arrives back at the second fluid inlet 150/ check valve 154 as the valve 1 12 is closing on the next cycle, which may help increase the flow through the second fluid inlet 150 but may also increase the switching losses. Switching losses may be reduced as the valve 1 12 opens due to the reflected pressure wave reducing

[00123] Flow through the partially open valve 1 12. As in the model of the flow through the converter 10, these effects can be traded off against each other by small changes in the position of the location of the upstream end 138 of the contacting section 130, as shown in Figures 18 through 20. Note that for this model L _c represents the position where the contracting section 130 begins (e.g. the length 142 in Figure 2).

[00124] While the valve's 1 12 switching time may somewhat degrade performance of the valve, this degradation may be at least somewhat smaller in magnitude than what is seen for the converter 10. Also, the switching time appears to have a smaller effect on the optimal operating point of the converter 100. This arrangement may be expected to have a somewhat higher manufacturing cost than the converter 10, for example due to the longer inertance conduit and more complex geometry, but it may have some better efficiencies than the half-wave version convert 10, under some operating conditions. For example, the "slow" valve version has an estimated efficiency of 62% at its optimal flow loss operating point, while the half-wave converter had an efficiency of 55% at its optimal flow loss point. This can be partially explained by the lower frictional losses in the expanded section of the inertance tube.

[00125] In accordance with another aspect of the teachings described herein, a switched inertance converter was modelled with the second fluid inlet spaced downstream from the switching valve, such as shown in the switched inertance converter 2100 in Figure 7.

[00126] By locating the second fluid inlet 2150/ check valve 2154 remotely from the switching valve 21 12, it may be possible to improve the suction wave effect at the check valve 2154 separately from the wave effects on the switching losses at the valve 21 12. This was simulated by breaking the shaped inertance tube 2128 into two portions, one between the switching valve 21 12 and the check valve 2154, and the second between the check valve 2154 and the load 21 10. For the purposes of the model, fluid dynamic effects of the mixing flows were ignored. In this simulation the distance between the switching valve 21 1 2 and check valve 21 54 is denoted as L _cv which corresponds to length 21 58 in Figure 7.

[001 27] Simulations were run varying the position between 0 and halfway to the converging section 21 28. As shown in Figures 21 and 22, moving the check valve increases efficiency over the Lev = 0 case up to a 2Lcv/( Δt _p c) ratio of approximately 0. 1 5 without large effects on flow loss. There is a second peak in efficiency just beyond 2Lcv/(Δt _P c) = 0.2 , just on the edge of an increase in flow loss that may also indicate a suitable check valve location. For the case of the 3 ms "slow" valve, the remotely positioned check valve may somewhat increase energy efficiency, for example from about 61 .6% to about 63.0% under some conditions, with no relatively little increase in flow loss.

[001 28] In addition to the simulations described above, another simulation was performed to examine the effect of the location of the second fluid inlet on the performance and characteristics of a switched inertance converter 31 00 having a inertance conduit 31 20 of substantially constant flow area and with a constant orifice load, as shown in Figure 8.

[001 29] In this simulation, the high pressure source at the first fluid inlet 31 02 may be assumed to maintain a constant supply pressure P _s , while the elevated tank pressure, P _T , at the second fluid inlet 31 50 may be assumed to be sufficient to avoid cavitation. The flow through the switching valve 31 1 2, Q _PA , may be modelled as a fully turbulent orifice with a time varying orifice area described by:

[001 30] where Cd is the discharge coefficient, p is the fluid density, and PA is the pressure downstream of the switching valve 31 1 2. The time-varying orifice area, A _PA (t), may be a square wave alternating between zero area and maximum area APAmax, with period At _p and duty cycle fraction w _PA . The signal may be rate limited so that the time required to open or close the switching valve 21 1 2 is Δt _sw . [001 31 ] The flow at the second fluid inlet 3150, e.g. through the check valve 3154 may be modelled as an infinitely fast turbulent orifice:

[001 32] where ΔΡ = P _T — P _B is the pressure differential, and the orifice area may be:

[001 33] where A _TBmin is the leakage area, A _TBmax is the fully open orifice area, P _cr is the cracking pressure, and P _or is the pressure override.

[00134] The load 31 10 may be modelled as a compressible volume and fixed orifice. The fluid volume may be assumed to have a constant effective bulk modulus, β, such that the load pressure P _L is:

[001 35] where V _L is the compressive volume, Q _c is the flow from the inertance conduit 3120 and Q _L is the flow to the load. The load flow may governed by the turbulent orifice equation:

where A _L is the orifice area.

[00136] Optionally, the inertance conduit 3120 may be simulated using the Lumped Element Method (LEM) of transmission line modelling, which allows for modelling of wave propagation within the conduit 3120. Each conduit may be divided into N segments, wherein each segment may be composed of an ideal compressible volume, a fluid inertia and a laminar resistance. For the ith segment, the governing equations may be described as:

[00137] where d is the diameter of the inertance conduit 3120, L _; is the segment length, and μ is the fluid's viscosity. P _; and Q _; are the pressure and flow at the segment entrance, and P _i+1 and Q _i+1 are at the outlet. P _iA is a fictional internal pressure between the inertia and resistance. The length of the inertance conduit 3120 between the switching valve 31 12 and check valve 3154 is L _cv and corresponds to length 3158 in Figure 8. The overall length between the switching valve 31 12 and load is L, and corresponds to length 3126 in Figure 8.

[00138] Alternatively, the inertance conduit 3120 (and optionally the conduit 10) may be simulated using an enhanced transmission line method (as further explained in Johnston, N., 2012, "The Transmission Line Method for Modelling Laminar Flow of Liquid in Pipelines," Proc. Inst. Mech. Eng., Part I, 226(5), pp. 586-597, which is incorporated herein by reference). This method uses a number of transfer functions to model the frequency-dependent flowpressure relationships within the tube, and pure time delays representing the transit time of pressure waves. As this is a linear method, it cannot easily handle cavitation, although it does have relatively good accuracy for the highly transient dynamics involved in this analysis. The two sections of the conduit 3120 (separated by the check valve 3154) were modeled separately, with Lcv being the length of the conduit between the switching valve 31 12 and check valve 3154 (corresponding to length 3158 in Figure 8) and the overall length between the switching valve and load is L, and corresponds to length 3126 in Figure 8. In this model parameters for tube diameter, d, fluid density p, and viscosity μ as well as effective bulk modulus, β. [00139] The speed of a pressure wave travelling through the inertance conduit 3120 may be expressed as:

[00140] The performance of the converter 3100 may be measured using two metrics: energy efficiency and volumetric efficiency. The energy efficiency of the system may be calculated as:

[00141 ] where the bar accent indicates the average over the valve cycle period, calculated after the system has reached a steady state.

[00142] Flow loss may be defined as the difference between the ideal and actual check valve flows as

[00143] While either model of the inertance conduit 3120 may be used (or any of other suitable model) a simulation using the enhanced transmission line method was carried out with base parameters found listed below:

[00144] The system of differential equations given above may be implemented in using known simulation programming languages such as Matlab Simscape Language and solved using the stiff equation solver ode15s. Other simulation parameters may include the number of valve switching periods (e.g. 8 to 25 ms), duty cycle (e.g. 10% to 90%) and switching times. A switching time of 0.1 ms may be regarded as "fast", while a switching time of 3ms may be regarded as "slow".

[00145] The simulation was run, varying the check valve 3154 position (e.g. length 3158) and the cycle period with the results shown in Figures 23 and 24. Notice that the best efficiency (labelled TV) does not coincide with the best flow performance ('Β'). The optimal design can occur anywhere along the Pareto- Optimal line between A and B, depending on the relative importance of efficiency and flow performance.

[00146] Figure 25 shows how the energy and volumetric efficiency vary along this line. Note that the improvement in volumetric efficiency is larger than the change in energy efficiency. All points on this line are better than any point with L _cv =0, as in a conventional design (such as converter 10). [00147] The above analysis includes an assumption that the pressure at the second fluid inlet 3150 is sufficient to avoid cavitation. In a conventional switched- inertance converter, such as converter 10, when the switching valve 14 closes, the local low pressure caused by the rapid change in flow may be limited by the closely located check valve 26, avoiding cavitation. In the converter 3100 the check valve 3154 is not located at the valve 31 12 to help limit this pressure. Rather, the compressibility of the fluid between the switching valve 31 12 and the check valve 3154 may influence how much the pressure drops behind the closed valve 31 12. This can be influenced by modifying the flow area of the tube connecting the switching valve 31 12 to the check valve 3154, thereby affecting the compressible volume.

[00148] Figure 26 shows the effect of modifying this tube diameter on the minimum reservoir pressure (e.g. the pressure at the second fluid inlet 3150) required to avoid cavitation (cavitation is conservatively assumed to occur at zero gauge pressure), by simulating the system at the 'B' optimal point. Figure 27 shows the corresponding effects on energy and volumetric efficiency. As the tube is enlarged, the required reservoir pressure is reduced, but this occurs at a cost of volumetric efficiency, which is reduced. The energy efficiency initially improves, perhaps due to the reduced frictional losses of the larger tube, but this effect is overcome by the reduced flow as the tube diameter increases further.

[00149] Referring again to Figure 9, another approach to limiting cavitation is to install a third fluid inlet 4160 in the converter 4100, so that the second fluid inlet 4150 can be collocated with the switching valve 41 12 (as shown in the converter 4100 in Figure 9). This arrangement may help facilitate operation at a lower reservoir pressure (but perhaps at the cost of increased complexity and reduced performance). This was simulated by adding a positioning the second fluid inlet 4150 and the third fluid inlet 4160 as shown in Figure 9. The third fluid inlet 4160 can be connected to a pressurized reservoir 4162, and the second fluid inlet 4150 can be generally identical, but is connected to an atmospheric reservoir 4152. The converter 4100 was simulated at the 'B' optimal point while varying reservoir pressure. Figure 28 shows the resultant check valve flows; the check valve sees 4154 significant flows for low reservoir pressures 4152, which transitions to the check valve 4164 as the pressure increases. Increasing reservoir pressures improve both energy efficiency and volumetric efficiency (see Figure 29) as more flow is sourced from the elevated reservoir rather (source 4162) than the atmospheric reservoir (source 4152).

[00150] What has been described above has been intended to be illustrative of the invention and non-limiting and it will be understood by persons skilled in the art that other variants and modifications may be made without departing from the scope of the invention as defined in the claims appended hereto. The scope of the claims should not be limited by the preferred embodiments and examples, but should be given the broadest interpretation consistent with the description as a whole.