Preventing overstroke of free-piston stirling engine from loss of load

Abstract

A method for limiting the amplitude of reciprocation of a piston reciprocating in a cylinder of a free-piston Stirling engine. The method is the combination of both at least partially covering the heat rejecter cylinder port by the piston sidewall during a peak part of the inward reciprocation of the piston and at least partially covering the heat rejecter cylinder port by the displacer sidewall during a peak part of the outward reciprocation of the displacer. The piston and the displacer, at times during their reciprocation, fully cover the effective heat rejecter cylinder port when the piston amplitude of reciprocation is large and approaches the physical limit of the amplitude of reciprocation in order to avoid internal collisions by a reciprocating component.

Claims

1. A method for limiting the amplitude of reciprocation of a piston reciprocating in a cylinder of a free-piston Stirling engine, the piston having a sidewall interfacing the cylinder and the piston sidewall having a circumferentially continuous end part at an inward end, the engine also including a displacer reciprocating in the cylinder and having a circumferentially continuous end part of the displacer sidewall at a displacer outward end, the engine further including a compression space interposed between the piston and the displacer and a heat rejecter cylinder port through the engine cylinder and opening into the compression space, wherein the method comprises: (a) at least partially covering the heat rejecter cylinder port by the circumferentially continuous end part of the piston sidewall during a peak of the inward reciprocation of the piston; and (b) at least partially covering the heat rejecter cylinder port by the circumferentially continuous end part of the displacer sidewall during a peak of the outward reciprocation of the displacer.

2. The method according to claim 1 wherein both the piston sidewall and the displacer sidewall entirely and continuously cover the heat rejecter cylinder port during peaks of their reciprocation.

3. The method according to claim 1 wherein the engine has a selected maximum engine output power for which the engine was designed and the piston begins to partially cover the heat rejecter cylinder port at a piston amplitude of reciprocation (X.sub.P1) that is less than a piston amplitude of reciprocation at the selected maximum engine output power, progressively covers more of the heat rejecter cylinder port as piston amplitude of reciprocation increases further and entirely covers the heat rejecter cylinder port at a piston amplitude of reciprocation (X.sub.P2) that is greater than its amplitude of reciprocation (X.sub.Ppp) at the selected maximum engine output power.

4. The method according to claim 3 wherein the displacer begins to partially cover the heat rejecter cylinder port at a piston amplitude of reciprocation that is greater than the piston amplitude of reciprocation (X.sub.Ppp) at the selected maximum engine output power, the displacer progressively covers more of the heat rejecter cylinder port as piston amplitude of reciprocation increases further and the displacer entirely covers the heat rejecter cylinder port at a piston amplitude of reciprocation (X.sub.P3) that is less than a piston amplitude limit (X.sub.Pmax) and before engine output power has declined to zero output power.

5. The method according to claim 3 wherein the displacer begins to cover the heat rejecter port at a piston amplitude of reciprocation (X.sub.P3) that is less than the piston amplitude of reciprocation (X.sub.P2) at which the piston entirely covers the heat rejecter port.

6. The method according to claim 4 wherein the displacer begins to cover the heat rejecter cylinder port before engine output power has declined to an engine output power that is 60% of the selected maximum engine output power.

7. The method according to claim 4 wherein the displacer entirely covers the heat rejecter cylinder port before engine output power has declined to an engine output power that is greater than 20% of the selected maximum engine power.

8. The method according to claim 7 wherein the displacer entirely covers the heat rejecter cylinder port before engine output power has declined to a selected engine output power that is 50% of the selected maximum engine output power.

9. The method according to claim 4 wherein the free-piston Stirling engine includes a working gas flow path between an expansion space and the compression space, the gas flow path including, in series fluid connection, a heat acceptor, which transfers externally applied heat into the working gas, a heat rejecter, which transfers heat out of the working gas, and an interposed regenerator, the heat rejecter cylinder port has an inward edge, the rejecter has an effective (net) cross sectional area of the flow path through the rejecter, and the method further comprises (a) selecting a piston amplitude at which engine output power will begin to be reduced; (b) at said selected piston amplitude positioning the inward end of the piston sidewall at a distance outward from the inward edge that is equal to $0.8\frac{A_{\mathrm{rejecter}}}{D_{\mathrm{cylinder}}}$ in which D.sub.cylinder=the diameter of the cylinder; A.sub.rejecter=the effective (net) cross sectional area of the flow path through the rejecter.

10. The method according to claim 9 wherein the selected piston amplitude (X.sub.P1) is less than piston amplitude (X.sub.Ppp) at maximum engine output power (PP).

11. The method according to claim 4 wherein the free-piston Stirling engine includes a working gas flow path between an expansion space and the compression space, the gas flow path including, in series fluid connection, a heat acceptor, which transfers externally applied heat into the working gas, a heat rejecter, which transfers heat out of the working gas, and an interposed regenerator, the heat rejecter cylinder port has an inward edge and an outward edge, the rejecter has an effective (net) cross sectional area of the flow path through the rejecter, and the method further comprises (a) selecting a piston amplitude at which the displacer begins to become effective to further reduce engine output power; (b) at the selected piston amplitude positioning the outward end of the displacer sidewall at a distance inward from the outward edge that is equal to $0.8\frac{A_{\mathrm{rejecter}}}{D_{\mathrm{cylinder}}}$ in which D.sub.cylinder=the diameter of the cylinder; A.sub.rejecter=the effective (net) cross sectional area of the flow path through the rejecter.

12. The method according to claim 11 wherein the selected piston amplitude is greater than piston amplitude (X.sub.Ppp) at maximum engine output power (PP).

13. The method according to claim 12 wherein the selected piston amplitude is greater than piston amplitude (X.sub.P2) at which the piston fully covers the rejecter port.

Description

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

(1) FIG. 1 is a diagrammatic and symbolic view in axial cross section of a beta type free-piston Stirling engine that embodies the invention.

(2) FIG. 2 is a graph showing a typical output power curve for an engine of the type illustrated in FIG. 1, a modified power curve that is the result of implementation of the invention and also illustrating the variation of engine output power as piston amplitude increases in an engine that implements the invention.

(3) FIG. 3 is a diagrammatic and symbolic view in axial cross section showing the beta type free-piston Stirling engine of FIG. 1 with the displacer covering the heat rejecting port.

(4) FIG. 4 is a Lissajous diagram showing piston and displacer motion when the rejecter port is not being periodically covered by the piston or the displacer.

(5) FIG. 5 is a Lissajous diagram showing piston and displacer motion when the rejecter port is being periodically partially covered by the piston.

(6) FIG. 6 is a Lissajous diagram showing piston and displacer motion when the rejecter port is being periodically fully covered by both the displacer and the piston with resulting zero power output from the engine.

(7) In describing the preferred embodiment of the invention which is illustrated in the drawings, specific terminology will be resorted to for the sake of clarity. However, it is not intended that the invention be limited to the specific term so selected and it is to be understood that each specific term includes all technical equivalents which operate in a similar manner to accomplish a similar purpose.

DETAILED DESCRIPTION OF THE INVENTION

(8) The present invention improves upon the Berchowitz concept by combining it with the present invention in order to improve its practical effectiveness by causing the engine output power to be driven entirely to zero and limiting the piston to a maximum amplitude of reciprocation X.sub.Pmax before any damaging collisions occur. In applicant's prior application, applicant described the covering of the rejecter port by the piston in more detail. Applicant therefore incorporates herein by reference its application Ser. No. 15/494,836, Pub. No. US 2018/0112624 A1.

(9) Referring to FIGS. 1 and 3, the invention is at least partially covering the heat rejecter cylinder port 20 by the piston sidewall 32 during a peak part of the inward reciprocation of the piston and additionally at least partially covering the heat rejecter cylinder port 20 by the displacer 30 sidewall 33 during a peak part of the outward reciprocation of the displacer 30. However, for a complete loss of load, the method will comprise both the piston sidewall 32 and the displacer sidewall 33 entirely covering the heat rejecter cylinder port 20 during those respective peak parts of their reciprocation. FIG. 1 shows with dashed lines the piston sidewall 32 advanced to its position 34A at which the piston sidewall 32 entirely covers the heat rejecter port 20 during the peak inward motion of the piston 28. FIG. 3 shows the sidewall 33 of the displacer 30 advanced to a position at which the displacer sidewall 33 entirely covers the heat rejecter port 20 during the peak outward motion of the displacer 30.

(10) The graphs of FIG. 2 show test data from an operating prototype Stirling engine that implements the invention. The rectangle 64 represents the piston amplitude range during which the piston 28 covers progressively more of the heat rejecter port 20. The piston begins to cover the rejecter port 20 at piston amplitude X.sub.P1 and eventually entirely covers the rejecter port 20 at piston amplitude X.sub.P2. As the piston amplitude increases over the range from X.sub.P1 to X.sub.P2, engine output power initially increases at a reduced rate until it peaks at its peak power PP which occurs at piston amplitude X.sub.Ppp. As the piston amplitude continues to increase, engine output power then declines along the modified power curve MP. As the piston amplitude increases further and the piston covers more of the rejecter port 20 during the peak of the piston's inward motion, engine output power declines at an increased rate. Immediately after the rejecter port 20 is entirely blocked at X.sub.P2 engine output power continues to decline although at a reduced rate.

(11) An engineer who is designing a free-piston Stirling engine ordinarily has a selected maximum engine output power as a principal design parameter. In order to implement the invention, the engine is designed so that the piston 28 begins to partially cover the heat rejecter cylinder port 20 at a piston amplitude of reciprocation X.sub.P1 that is less than the piston amplitude of reciprocation X.sub.Ppp at the selected maximum engine output power PP. The piston 28 should progressively cover more of the heat rejecter cylinder port 20 as piston amplitude of reciprocation increases further. The piston 28 should entirely cover the heat rejecter cylinder port 20 at a piston amplitude of reciprocation X.sub.P2 that is greater than its amplitude of reciprocation X.sub.Ppp at the selected maximum engine output power PP.

(12) As previously described, in the event of a complete loss of load and in the absence of the invention, engine output power would turn upward along the line IP as piston amplitude increased thereby making the engine unstable. The rectangle 66 represents the piston amplitude range during which the displacer 30 covers progressively more of the heat rejecter port 20. In order to implement the invention and prevent the upturn, the engine is designed so that the displacer 30 begins to partially cover the heat rejecter cylinder port 20 at a piston amplitude of reciprocation X.sub.P3 that is greater than the piston amplitude of reciprocation X.sub.Ppp at the selected maximum engine output power PP. Preferably, however, the engine is designed so that the displacer 30 begins to cover the heat rejecter port 20 at a piston amplitude of reciprocation X.sub.P3 that is less than the piston amplitude of reciprocation X.sub.P2 at which the piston entirely covers the heat rejecter port. As piston amplitude continues to increase, the sidewall 33 of the displacer 30 progressively covers more of the heat rejecter cylinder port 20. As piston amplitude of reciprocation increases still further, the displacer is made to eventually entirely cover the heat rejecter cylinder port 20 at a piston amplitude of reciprocation X.sub.P4 that is less than the piston amplitude limit X.sub.Pmax and before engine output power has declined to zero output power.

(13) The engineer may design the engine so that the displacer begins to cover the heat rejecter cylinder port before the piston amplitude of reciprocation X.sub.P increases to the amplitude X.sub.P2 at which engine output power has declined to an engine output power that is 60% of the selected maximum engine output power. As seen in FIG. 2, engine output power has declined to approximately 60% at the X.sub.P data point that is coincident with the piston amplitude X.sub.P2. Similarly, the engine may be designed so that the displacer has just completed fully covering the heat rejecter cylinder port before engine output power has declined to an engine output power that is 50% of the selected maximum engine output power. As seen in FIG. 2 for example, at a piston amplitude of reciprocation of X.sub.P4 the output power has declined to approximately 50% of the selected maximum engine output power PP. In any event, the displacer should be made to entirely cover the heat rejecter port well before the engine output power has declined to zero because full coverage of the heat rejecter port by the displacer is believed to be needed to drive the engine output power completely to zero. It is desirable that the engine is designed so that the displacer has just completed fully covering the heat rejecter cylinder port before engine output power has declined to an engine output power that is greater than 20% of the selected maximum engine output power.

(14) FIG. 2 also shows a graph .sub.d of displacer 30 phase lead ahead of the piston 28. Following the beginning of piston coverage of the heat rejecter port 20 at X.sub.P1, the displacer phase gradually makes a transition to a higher rate of phase lead reduction which continues across the range from X.sub.P1 to X.sub.P2. That phase lead reduction continues after the displacer begins to close the heat rejecter port. So it can be seen in FIG. 2 that covering the heat rejecter port by both the piston and the displacer causes the reduction of displacer lead. In both cases power is reduced as a result of the sum of three components losses: (1) a reduction of displacer phase angle lead (2) pumping losses through the rejecter port as it becomes progressively more covered and therefore more restricted and (3) pumping losses past the displacer seal 35 after the rejecter port is completely covered resulting in more leakage past the displacer seal 35. However, the proportional division of power losses between these three components is different for the three types of port coverage.

(15) Referring to FIG. 3, the piston amplitudes at which the displacer and the piston respectively begin to cover the heat rejecter cylinder port 20 is in part determined by the position of the inward edge 58 and the position of the outward edge 60 of the heat rejecter cylinder port 20. The distance between those two edges determines the width, in the axial direction, of the heat rejecter cylinder port 20.

(16) The size of the rejecter port should not cause a reduction of engine power during normal engine operation when neither the piston nor the displacer has reached the rejecter port. Analysis has shown that, for most typical Stirling engines, power reduction begins when the cross sectional area of the rejecter port is about 80% (a factor of 0.8) of the effective (net) cross sectional area of the flow path through the rejecter. Although the factor of 0.8 is typical for most engines, that factor can be different for some Stirling engines. For example, analysis has shown that, for a large engine with a unique rejecter design, the factor is closer to 1.0. The cross sectional area of the rejecter ports is approximately the circumference of the cylinder 22 multiplied by the port width in the axial direction of the rejecter ports 20. It is approximate because of the existence of the ribs 27 which are narrow and therefore can be ignored for a first approximation. Therefore the minimum area of the rejecter ports 20 should not be less than 80% of the effective (net) cross sectional area of the flow path through the rejecter. Although not required, if we assume that the inward edge of the rejecter ports is positioned at its normally preferred position at the outward end of the rejecter 16, we can determine the minimum width W.sub.P0 of the rejecter ports. This minimum width W.sub.P0 is the smallest width in the axial direction that the rejecter port can be made without the size of the rejecter ports limiting the power output of the engine.

(17) The cross sectional area of the rejecter ports is approximately equal to 80% of the cross sectional area of the effective (net) cross sectional area of the flow path through the rejecter 16 when
W.sub.P0[D.sub.cylinder]=0.8[A.sub.rejecter]

(18) Where W.sub.P0=the minimum width of the rejecter ports; D.sub.cylinder=the diameter of the cylinder; A.sub.rejecter=the effective (net) cross sectional area of the flow path through the rejecter.

(19) Therefore

(20) $W_{P0}=0.8\frac{A_{\mathrm{rejecter}}}{D_{\mathrm{cylinder}}}$

(21) From that it follows that the axial width of the rejecter ports W.sub.P should be greater than or equal to (i.e. at least equal to) 0.8[the effective (net) cross sectional area of the flow path through the rejecter] divided by [(the diameter of the cylinder)]. That is

(22) $W_{P}0.8\frac{A_{\mathrm{rejecter}}}{D_{\mathrm{cylinder}}}$

(23) Although that is a minimum rejecter port width, the outward edge 60 of the rejecter port 20 can be farther away from the assumed and usual position of the inward edge 58 than the minimum width W.sub.P0. That results in a greater width and cross sectional area of the rejecter ports and will require a greater displacer amplitude before the output power is brought to zero by the action of displacer blockage of the ports.

(24) The preceding assumes that the rejecter port is in the form of a circumferentially long slot as previously described. If instead of slots many closely circumferentially spaced drilled holes are used, the equations will be different but follow the principles outlined above.

(25) The above analysis means that the rejecter port width in the axial direction should be at least the minimum rejecter port width W.sub.P0. That condition assures that the port size does not reduce engine power output at piston amplitudes X.sub.P that are less than piston amplitude X.sub.P at the desired and designed maximum engine output power PP. If the rejecter port width in the axial direction is equal to the minimum rejecter port width W.sub.P0, then the inward end 34 of the piston sidewall 32 should just begin to cover the heat rejecter cylinder port 20 (that is, reach the outer edge of the heat rejecter cylinder port 20) at a piston amplitude X.sub.P1 at which the designer wants to initiate the engine output power reduction. The reason is that the effectiveness of covering the rejecter port begins when the width of the uncovered part of the rejecter port begins to be reduced below W.sub.P0.

(26) However, the rejecter port width can be greater than W.sub.K. In that case, the inward end 34 of the piston sidewall 32 should be at a position that partially covers the heat rejecter cylinder port 20 and leaves the uncovered part of the cylinder port 20 with a width equal to W.sub.P0 when the piston amplitude is at X.sub.P1 (the amplitude at which the designer wants to initiate the engine output power reduction).

(27) Based upon the above observations, the engineer who is designing the Stirling engine can select a piston amplitude at which engine output power will begin to be reduced. The FPSE is then designed so that the inward end 34 of the piston sidewall 32 will be positioned at a distance from the inward edge 58 of the heat rejecter cylinder port 20 that is equal to

(28) $0.8\frac{A_{\mathrm{rejecter}}}{D_{\mathrm{cylinder}}}$

(29) at the selected piston amplitude X.sub.P1 at which engine output power will begin to be reduced. That distance is W.sub.P0.

(30) The principle that the effectiveness of covering the rejecter port 20 begins when the width of the uncovered part of the rejecter port 20 begins to be reduced below W.sub.P0 is also applicable when the displacer covers the rejecter port 20. Therefore, the outward end 31 of the displacer 30 should be positioned so that its running outward excursion is inward from the outward edge 60 of the rejecter port 20 by the distance W.sub.P0 when the designer wants the displacer 30 to begin to be effective in further reducing the engine output power. Referring to FIG. 2, the displacer should begin to be effective in further reducing the engine output power after the piston amplitude X.sub.P has exceeded the piston amplitude X.sub.Ppp at maximum engine output power PP. Preferably, as shown in FIG. 2, the displacer should begin to be effective in further reducing the engine output power before the piston amplitude X.sub.P increases to the piston amplitude X.sub.P2 at which engine output power has declined further and the piston has fully covered the rejecter port.

(31) Because covering the rejecter port with the displacer begins to become effective when the uncovered part of the rejecter port has an uncovered width of W.sub.P0, the outward end 31 of the displacer 30 should be positioned by the distance W.sub.P0 from the outward edge 60 of the rejecter port 20 at a piston amplitude that exceeds the piston amplitude X.sub.Ppp at maximum engine output power PP. And preferably, the outward end 31 of the displacer 30 should be positioned by the distance W.sub.P0 from the outward edge 60 of the rejecter port 20 at a piston amplitude X.sub.P3 that is less than the piston amplitude X.sub.P2 at which the piston fully covers the rejecter port 20.

(32) Lissajous Graphs. FIGS. 4-6 are Lissajous graphs that were obtained from experimentation and illustrate the effectiveness of the invention on engine output power. They plot displacer versus piston position and the trace runs in a counterclockwise direction. The piston amplitude is represented on the horizontal axis and the displacer amplitude is represented on the vertical axis. Piston amplitude X.sub.P(t) is referenced from the position where the centering ports are in registration. That occurs when the centering system piston passageway 52 is aligned with the centering system annular cylinder groove 56. Displacer amplitude X.sub.d(t) is referenced from the point of static spring force of the planar spring 40; that is, when the planar spring is at its illustrated central position.

(33) FIG. 4 shows operation of an engine when neither the piston nor the displacer covers any portion of the rejecter port during their cyclical excursions. In FIG. 5 the rejecter port is partially but not completely covered by the piston. In FIG. 6 the piston fully covers the rejecter port during a peak part the inward excursion of its reciprocation and the displacer fully covers the rejecter port during a peak part the outward excursion of its reciprocation. The regions on the graphs at which covering of the rejecter port occurs is illustrated by the dashed line boxes. The dashed line boxes 68 and 70 in FIGS. 5 and 6 represent the locations on the graphs at which the rejecter port is being covered. The boxes 68 show port coverage by the piston and the boxes 70 show port coverage by the displacer. More specifically, the vertical lines of the boxes 68 represent the piston position where the piston begins to cover the rejecter port and the piston position where the piston has completed fully covering the rejecter port. Consequently, the distance between the vertical lines of the boxes represents the range of piston positions over which the piston progressively covers the rejecter port with the vertical line closer to the vertical axis being the beginning of port coverage and the vertical line farther from the vertical axis being the completion of port coverage. Similarly, the horizontal lines of the boxes 70 represent the displacer position where the displacer begins to cover the rejecter port and the displacer position where the displacer has completed fully covering the rejecter port. Consequently, the distance between the horizontal lines of the boxes represents the range of displacer positions over which the displacer progressively covers the rejecter port with the horizontal line closer to the horizontal axis being the beginning of port coverage and the horizontal line farther from the horizontal axis being the completion of port coverage.

(34) The Lissajous graphs also indicate that covering of the rejecter ports 20 also have an influence on the mean position of the piston 28 and the displacer 30. This is most evident in FIG. 6 which shows that the displacer 30 mean position has been pulled outward when the displacer covers the rejecter port 20. That is because, with the displacer 30 covering the rejecter port 20, the working gas that is between the piston and the displacer is trapped or confined in a closed space between them so the piston pulls the displacer outward along with the piston.

(35) Those skilled in the art are capable of designing a free-piston Stirling engine to have a selected amplitude under the operating conditions of their choice. Of course engineering design is not perfected to the extent that a prototype always operates exactly according to its design parameters. So persons skilled in the art can build a prototype engine, test it and then modify its design to obtain the design parameters they want. Repetition of the design, build, test and modify procedure is a common iterative process that eventually leads to a desired operation.

REFERENCE NUMBER LIST

(36) working space 8 heat accepting expansion space 10 heat rejecting compression space 12 heat acceptor 14 heat rejecter 16 regenerator 18 heat rejecter cylinder port 20 engine cylinder 22 heat acceptor cylinder port 24 entire head end 26 ribs 27 separating the rejecter ports 20 piston 28 displacer 30 outward end 31 of displacer 30 piston sidewall 32 sidewall 33 of displacer 30 inward end 34 of piston sidewall 32 seal segment 35 of displacer 30 boss 36 non-seal segment 37 of displacer 30 displacer connecting rod 38 planar spring 40 casing 42 large volume back space 43 gas bearing cavity 44, 44A and 44B gas bearing pads 50 centering system piston passageway 52 centering system cylinder passageway 54 centering system annular cylinder groove 56 inward edge 58 of rejecter cylinder port 20 outward edge 60 of rejecter cylinder port 20 inward end 62 of piston 28 piston amplitude range 64 over which the rejecter port is progressively covered by the piston piston amplitude range 66 over which the rejecter port is progressively covered by the displacer part of the cycle 68 during which the piston at least partially covers the rejecter port part of the cycle 70 during which the displacer at least partially covers the rejecter port

(37) This detailed description in connection with the drawings is intended principally as a description of the presently preferred embodiments of the invention, and is not intended to represent the only form in which the present invention may be constructed or utilized. The description sets forth the designs, functions, means, and methods of implementing the invention in connection with the illustrated embodiments. It is to be understood, however, that the same or equivalent functions and features may be accomplished by different embodiments that are also intended to be encompassed within the spirit and scope of the invention and that various modifications may be adopted without departing from the invention or scope of the following claims.