Flow rate regulator for fluid flow devices

Abstract

A flow restrictor is provided, comprising a first sheet including a flow passage and a second sheet laminated to the first sheet, the second sheet being perforated, the flow passage including a groove in a surface of the first sheet and communicating with an expansion zone in a peripheral area of ​​the first sheet, the peripheral edge of the second sheet contacting the first sheet in the expansion zone.

Description

[Background technology]

[0001] A flow restrictor is a device that restricts the flow of a fluid (i.e., gas or liquid). The reliability of the performance of a flow restrictor that restricts the flow of a fluid is important in various applications, including gas supply systems. For example, in the field of semiconductor manufacturing, high reliability is required that a flow restrictor in a mass flow controller of a gas supply system used in semiconductor manufacturing can achieve a predetermined flow rate of one gas or a flow ratio between two gases. Furthermore, restrictors in flow meters help to achieve high reliability of the flow rate indicated by the flow meter when measuring gas flow rates, which require high accuracy in semiconductor manufacturing. Therefore, reducing the performance uncertainty of flow restrictors in fluid flow devices such as mass flow controllers and flow meters is desirable in terms of improving the quality of fluid delivery in various industrial applications. However, technical challenges have so far stood as a barrier to progress in restrictor design. Summary of the Invention

[0002] To address the above-mentioned problems, a flow restrictor is provided. The flow restrictor according to one aspect of the present disclosure includes a first sheet including a flow path and a second sheet stacked on the first sheet. The second sheet is provided with a hole. The flow path includes a groove provided on a surface of the first sheet and communicating with an expansion zone in a peripheral area (peripheral region or peripheral region) of the first sheet. A peripheral edge of the second sheet contacts the first sheet in the expansion zone.

[0003] A flow restrictor according to another aspect of the present disclosure includes a first sheet forming a flow path, and a second sheet stacked on the first sheet. The second sheet is provided with a hole, and the flow path is a serpentine groove within the thickness of the first sheet, forming a serpentine shape along the surface of the first sheet when viewed from above.

[0004] A flow restrictor according to yet another aspect of the present disclosure includes a first sheet defining a flow passage and a second sheet stacked on the first sheet, the second sheet having a hole therein and including a slit through its entire thickness, the first sheet and the second sheet being stacked and aligned to form a continuous flow path through the slit in the second sheet and the flow passage in the first sheet.

[0005] This Summary is provided to introduce in a simplified form some of the concepts that are further described below in the Detailed Description. This Summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter. Moreover, the claimed subject matter is not limited to implementations that solve any or all disadvantages noted in any part of the present disclosure. [Brief description of the drawings]

[0006] [Figure 1] FIG. 1 is a schematic diagram illustrating a fluid flow device including a flow restrictor according to one embodiment of the present disclosure. [Figure 2A] FIG. 2A is a schematic plan view showing a conventional disk of a conventional flow restrictor. [Figure 2B] 2B is a schematic perspective view of a flow restrictor according to one embodiment of the gas delivery system of FIG. [Figure 2C] FIG. 2C is a schematic top view of the flow restrictor of FIG. 2B. [Figure 2D] FIG. 2D is a schematic plan view of a first sheet of the flow restrictor of FIGS. 2B-2C. [Figure 2E] FIG. 2E is a schematic plan view of the second sheet of the flow restrictor of FIGS. 2B-2C. [Figure 2F] FIG. 2F is a schematic exploded view of the flow restrictor of FIGS. 2B-2C. [Figure 2G] FIG. 2G is a bar graph comparing the performance uncertainty of the flow restrictors of FIGS. 2B-2F with a conventional flow restrictor. [Figure 2H] FIG. 2H is a chart illustrating the reduction in uncertainty of the flow restrictor performance shown in FIG. 2G. [Figure 3A] FIG. 3A is a schematic cross-sectional side view of a conventional flow restrictor. [Figure 3B] 3B is a schematic cross-sectional side view of a flow restrictor according to one embodiment of the gas supply system of FIG. [Figure 4A] FIG. 4A is a schematic exploded view of a flow restrictor according to one embodiment of the gas delivery system of FIG. [Figure 4B] FIG. 4B is a chart illustrating that the uncertainty in the performance of the flow restrictor decreases as the number of first sheets increases. [Figure 4C] FIG. 4C is a chart showing the uncertainty of flow restrictor performance as a function of average Mach number for a large number of flow path geometries and process gases. [Figure 5A] FIG. 5A is a schematic top view of a conventional disk of a conventional flow restrictor. [Figure 5B] 5B is a schematic exploded view of a flow restrictor according to one embodiment of the gas delivery system of FIG. 1. [Figure 5C] 5C is a schematic top view of a first sheet of the flow restrictor of FIG. 5B. [Figure 5D] FIG. 5D shows a data plot comparing the performance uncertainty of the flow restrictor of FIGS. 5B-5C with a conventional flow restrictor with a conventional disk. [Figure 6]FIG. 6 is a bar graph comparing the gas ratio distribution of a conventional flow restrictor having smooth first and second sheets to the gas ratio distribution of a flow restrictor of the present disclosure in which the second sheet has a rougher surface than the first sheet. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0007] FIG. 1 is a schematic diagram of a fluid flow device 5 according to one embodiment of the present disclosure, which may be in the form of a mass flow controller 10. The mass flow controller 10 includes a flow restrictor 12, an upstream pressure sensor 14, a downstream pressure sensor 16, a control valve 18, and a temperature sensor 20. In other embodiments, one or more of the components may be omitted. For example, either of the pressure sensors 14, 16 may be omitted in some configurations. In another configuration, the control valve 18 may be located downstream of the flow restrictor 12. In yet other configurations, the fluid flow device 5 may be configured as a mass flow meter and may not include the control valve 18. Additionally, it should be noted that other components may be present in the mass flow controller 10 that are not depicted in FIG. 1. For example, isolation valves (e.g., shut-off valves) may be provided in the flow paths on either side of the assembly of FIG. 1 to isolate the fluid flow device 5, and a purge line valve may be provided downstream of the restrictor to allow purge gas to flow through the fluid flow device 5 to the purge line.

[0008] As shown in FIG. 1, the flow restrictor 12 typically includes a collar 12A and a backing plate 12B that sandwich and secure a stack S of sheets 21. Although seven sheets 21 are depicted in FIG. 1, a different number of sheets may be provided, as described below. The sheets 21 include first sheets 22 and second sheets 24 that alternate throughout the stack S. An end-to-end restrictor flow path through the restrictor is depicted by the fluid flow arrows and extends from the upstream restrictor inlet 12C to the downstream restrictor outlet 12D, although the restrictor can be used for flow in either direction (i.e., bidirectional flow). Within the end-to-end restrictor flow path, each of the first sheets 22 defines an intra-sheet flow path 26a. The intra-sheet flow path 26a allows fluid to flow from an interior region of the restrictor radially outward to the peripheral edge of the first sheets 22. Once the fluid exits the flow passage 26a of the first sheet 22 in the stack S, it is directed by the external structure along an end-to-end flow passage to the restrictor outlet 12D, as shown.

[0009] 2A is a schematic plan view of a conventional disk 422 in a flow restrictor that includes a flow passage 426 that extends in a spiral fashion from a hole 434 in the disk 422. It will be appreciated that the flow passage 426 maintains its spiral shape in the peripheral areas of the disk 422. A problem has been discovered with the design of the restrictor depicted in FIG. 2A, namely, the uncertainty of the flow rate measured through the restrictor is too high under certain flow conditions. It is believed that geometric uncertainties at the ends of the flow passage due to manufacturing tolerances may contribute to this flow rate uncertainty.

[0010] FIG. 2B shows a schematic perspective view of the flow restrictor 12 of the exemplary embodiment of FIG. 1, including a first sheet 22 containing flow passages 26a and a second sheet 24 superimposed on the first sheet 22. The term sheet is used here to refer to a structure having a thickness that is substantially less than its lateral dimensions (e.g., lateral and longitudinal dimensions in FIG. 2C). Although a circular sheet 21 is shown, the periphery of the sheet 21 may be other shapes, such as a polygon. Although multiple sheets 21 are shown with a uniform thickness, the multiple sheets 21 may alternatively be of non-uniform thickness. Alternatively, the sheets 21 may be referred to as plates. FIG. 2C shows a schematic plan view of the flow restrictor 12. The first sheet 22 and the second sheet 24 may be manufactured as circular disks with openings. Although the openings are shown in the center of the first sheet 22 and the second sheet 24, the openings may alternatively be located elsewhere. The first sheet 22 and the second sheet 24 are made of a metal, including, but not limited to, stainless steel or a superalloy made of an oxidation-corrosion resistant material. To laminate the second sheet 24 onto the first sheet 22, the first sheet 22 and the second sheet 24 may be fused together, for example, by diffusion bonding. Other bonding techniques may alternatively be used. Alternatively, in some cases, additive manufacturing methods may be used to form the channels described herein within a monolithic block of material.

[0011] FIG. 2D is a schematic plan view of the first sheet 22 in a separated state. The first sheet 22 is provided with a circular hole 34 in the center. Alternatively, the hole 34 may be of a shape other than circular and may be provided elsewhere in the first sheet 22. The flow passage 26a includes a groove provided in the surface of the first sheet 22 and communicating with the outer expansion zone 28 in the peripheral area of ​​the first sheet 22. In this example, the flow passage 26a is one of a plurality of flow passages 26 uniformly distributed radially around the hole 34. Each flow passage 26a may include a corresponding groove, each groove may extend in a spiral from the hole 34 to the corresponding outer expansion zone 28 in the peripheral area of ​​the first sheet 22. The spiral groove has the technical effect of lengthening the flow passage in the restrictor. However, although a spiral groove is illustrated, the groove may have another shape, for example a non-helical straight or curved shape. The outer expansion zone 28 typically has a cross-sectional area perpendicular to the flow direction that is greater than the cross-sectional area perpendicular to the flow direction in the flow channel 26a. In Fig. 2D, when viewed from above, the width W1 of the outer expansion zone 28 is greater than the width W2 of the flow channel 26a. Typically, the width W1 of the outer expansion zone 28 can be 20%, 50%, 100% or 500% greater than the width W2 of the flow channel 26a.

[0012] The spiral shape of the groove in the illustrated embodiment terminates at the inner boundary 30 of the outer expansion zone 28. Inside the outer expansion zone 28, the shape of the flow channel 26 inside the outer expansion zone 28 may be straight, as shown, or may continue in a curved shape. The grooves may be formed by chemical etching, laser micromachining, or a combination of both. Alternatively, the grooves may be formed by other techniques in which the material of the first sheet 22 is not cut completely through the sheet (i.e., cut to form a bottomed groove).

[0013] It will be appreciated that the outer peripheral edge 27 (see FIG. 2E) of the second sheet 24 contacts the first sheet 22 in an outer expansion zone 28 between the inner boundary 30 and the outer boundary 32 of the expansion zone 28. Here, the outer expansion zone 28 is received by one end of the flow channel 26a. The thickness of the first sheet 22 may be 10 μm to 100 μm. The length of the flow channel 26a may be 100 to 1000 times the thickness of the first sheet 22. The width of the flow channel 26a may be about 5 to 100 times the thickness of the first sheet 22.

[0014] Providing an outer expansion zone 28 at the peripheral region of the first sheet 22 reduces the uncertainty of the flow restriction performance as compared to a conventional restrictor including the conventional disk 422 of FIG. 2A.

[0015] As shown in FIG. 2D, an inner expansion zone 28' may be provided in the inner peripheral region of the first sheet 22. The inner expansion zone 28' may be provided in the first sheet 22 in addition to or instead of the outer expansion zone 28. The channels 26a including grooves in the surface of the first sheet 22 may connect with the inner expansion zone 28' in the inner peripheral region of the first sheet 22. The corresponding groove of each channel 26a spirals from the outer expansion zone 28 in the outer peripheral region of the first sheet 22 to the inner expansion zone 28' adjacent to the hole 34. The inner peripheral edge 27' (see FIG. 2E) of the second sheet 24 contacts the first sheet 22 in the inner expansion zone 28' between the inner boundary 30' and the outer boundary 32' of the inner expansion zone 28'. By providing the inner expansion zone 28' in the inner peripheral region of the first sheet 22, the uncertainty of the flow restriction performance can be reduced compared to a conventional restrictor including the conventional disk 422 of FIG. 2A. Typically, like the outer expansion zone 28, the inner expansion zone 28' has a larger cross-sectional area perpendicular to the flow direction than that area in the flow channel 26a. When viewed from above in Fig. 2D, the width W3 of the inner expansion zone 28' is larger than the width W2 of the flow channel 26a. Typically, the width W3 of the inner expansion zone 28' may be 20%, 50%, 100%, or 500% larger than the width W2 of the flow channel 26a.

[0016] 2E is a schematic plan view showing the second sheet 24 in a separated state. The second sheet 24 is provided with a hole 25, and here the hole 25 is located in the center of the second sheet 24. In this example, the second sheet 24 does not have any flow channels formed therein.

[0017] FIG. 2F illustrates a schematic exploded view of flow restrictor 12 formed by first sheet 22, upper second sheet 24a, and lower second sheet 24b.

[0018] FIG. 2G is a predictive bar graph based on simulation data comparing the performance uncertainty of the flow restrictor 12 of the exemplary embodiment of FIGS. 2B-2F with a conventional flow restrictor for several combinations of upstream (P1) and downstream (P2) pressures, measured in kPa. The results in FIG. 2G were obtained in a computational fluid dynamics (CFD) simulation using a CFD model that matches the experimental data within the experimental uncertainty. The uncertainty depicted in FIG. 2G is the sensitivity of the sulfur hexafluoride to nitrogen molar flow ratio to restrictor-geometry variations for the worst-case scenario. As can be seen in FIG. 2G, the configuration of the outer expansion zone 28 at the peripheral area of ​​the first sheet 22 of the flow restrictor 12 reduces the uncertainty compared to a conventional flow restrictor including a conventional disk 422. It is believed that this technical effect is achieved by mitigating the geometric uncertainty and the end of the flow passage.

[0019] FIG. 2H is a prediction based on simulation data showing the reduction in the uncertainty in the performance of the flow restrictor shown in FIG. 2G. FIG. 2H plots the molar flow rate per flow path of sulfur hexafluoride against the molar flow rate of nitrogen for three cases. Ideally, the restrictor can be manufactured with infinite precision, as shown in the benchmark case of FIG. 2H. However, in reality, there are manufacturing tolerances that must be considered. In FIG. 2H, it can be seen that the deviation from the ideal in sccm (standard cubic centimeters per minute) is smaller for the configuration of the outer expansion zone 28 at the peripheral area of ​​the first sheet 22 of the flow restrictor 12 compared to the flow restrictor with the conventional disk 422. This achieves the potential advantage of reducing the uncertainty in the flow restrictor performance, as shown in FIG. 2G.

[0020] 3A is a cross-sectional side view of a conventional flow restrictor 512. The direction of fluid flow from the flow inlet 536 through the flow restrictor 512 to the flow outlet 538 is indicated by the arrows. The first sheets 522a, 522b, 522c and the second sheets 524a, 524b, 524c, 524d are stacked alternately. In the conventional flow restrictor 512, the fluid flows radially outward between the second sheets 524a, 524b and through the flow passages in the first sheets 522a, 522b. However, in other conventional flow restrictors, the fluid flow may flow radially inward between the second sheets 524a, 524b and through the flow passages in the first sheets 522a, 522b. In this example, the fluid does not flow through the second sheets 524a-d.

[0021] 3B shows a cross-sectional side view of the flow restrictor 112 in an exemplary embodiment of the present disclosure. The direction of fluid flow is indicated by the arrows and flows through the flow restrictor 112 from the restrictor flow inlet 12C, through the sheet flow inlet 136, out the sheet flow outlet 138, and finally directed out the restrictor flow outlet 12D. The first sheets 122a, 122b, 122c and the second sheets 124a, 124b, 124c, 124d are alternately stacked to form the restrictor stack S. The flow restrictor 112 includes an upstream flow passage 126a connected to the upstream end of the restrictor stack 112. The downstream flow passage 126c is connected to the downstream end of the restrictor stack.

[0022] In this example flow restrictor 112, two of the second sheets 124b, 124c each include a slit 140a, 140b that extends through their entire thickness. Slit 140a provides fluid communication between flow passage 126a in first sheet 122a and flow passage 126b in first sheet 122b. Slit 140b provides fluid communication between flow passage 126b in first sheet 122b and flow passage 126c in first sheet 122c.

[0023] Thus, the first sheets 122a, 122b, 122c and the second sheets 124a, 124b, 124c, 124d are stacked and aligned to form a continuous flow path from the sheet flow inlet 136 through the channels 126a, 126b, 126c and the slits 140a, 140b of the flow restrictors 112 to the sheet flow outlet 138, which, when viewed in a vertical cross section of the second sheets 124a-c, forms a serpentine shape extending along the thickness of the second sheets 124a-c. In this example, the fluid flow passes through the channels 126a, slits 140a, channels 126b, slits 140b, and channels 126c, in that order, from the sheet flow inlet 136 through the stack S of flow restrictors 112 to the sheet flow outlet 138. By increasing the effective length of the flow path within the flow restrictor 112 and forcing the fluid flow through multiple first sheets 122a, 122b, 122c, the uncertainty of the flow resistance performance can be reduced compared to conventional flow restrictors 512.

[0024] FIG. 4A shows a schematic exploded view of a stack S of flow restrictor 212 in an exemplary embodiment of the present disclosure, in which eight first sheets 222a-h and nine second sheets 224a-i are stacked in an alternating manner to form a restrictor stack. As with the exemplary embodiment of FIG. 3B, each of the first sheets 222a-h has flow passages 226a-h formed therein, and each of the second sheets 224a-i has slits 240a-i formed therein that extend through the entire thickness of the second sheets 224a-i. It will be appreciated that the number of alternating first and second sheets is not particularly limited to the number depicted in FIG. 4A, and may be more or less than this number depending on the application of the mass flow controller incorporating flow restrictor 212. A preferred range of the number of sheets in stack S is between 3 and 99, and more preferably between 5 and 15.

[0025] In the exemplary embodiment of Figures 3B and 4A, the consecutively measured fluid flow rates through the restrictor divided by the number of first sheets divided by the number of flow passages per first sheet can result in an average Mach number of less than 0.1, where the average Mach number is defined as the mass flow rate divided by the product of the average density in the restrictor, the flow passage cross-sectional area, the speed of sound in the gas, and the total number of flow passages. Based on this definition, for a constant mass flow rate, the Mach number can be reduced to less than 0.1 by increasing the average density in the restrictor, increasing the flow passage cross-sectional area, and / or increasing the total number of flow passages. In the embodiment of Figures 3B and 4A, the total number of flow passages can be increased by increasing the number of first and second sheets that are alternately stacked to form the restrictor stack, thereby resulting in an average Mach number of less than 0.1.

[0026] In the exemplary embodiment of FIG. 3B, which includes three first sheets 122a-c with one flow passage per first sheet, dividing the successively measured fluid flow rates through the restrictor 112 by three and dividing by one can produce an average Mach number less than 0.1. In the exemplary embodiment of FIG. 4A, which includes eight first sheets 222a-h with twelve flow passages per first sheet, dividing the successively measured fluid flow rates through the restrictor 212 by three and dividing by 12 can produce an average Mach number less than 0.1.

[0027] FIG. 4B shows a prediction chart based on simulation data, showing that the uncertainty in the performance of the flow restrictor decreases as the number of first sheets increases, which is due to the averaging process. As FIG. 4B shows, the uncertainty in the performance of the flow restrictor decreases as the number of first sheets increases, due to the averaging process. FIG. 4B shows theoretical results using a simplified physics-based model that matches well with the CFD and experimental data. For this chart, the measured uncertainty is the sensitivity of the molar flow ratio of sulfur hexafluoride to nitrogen to random variations in the width of the first sheet. A number of representative operating conditions were used to obtain the results of FIG. 4B.

[0028] FIG. 4C is a prediction chart based on simulation data showing the uncertainty of flow restrictor performance as a function of average Mach number for a large number of flow path geometries and process gases. The results were obtained with a simplified physics-based model that is in good agreement with the CFD results and experimental data. The uncertainty is defined as in FIG. 2G and is plotted as the sensitivity of the molar flow ratio of sulfur hexafluoride to nitrogen to the variation of the restrictor geometry in the worst case scenario. However, unlike FIG. 2G, the chart in FIG. 4C uses flow ratios using different gases other than sulfur hexafluoride. FIG. 4C shows that the uncertainty can be reduced by keeping the average Mach number below about 0.1, as indicated by '1e-1' in the chart in FIG. 4C.

[0029] 5A is a schematic top view of a conventional disk 622 of a flow restrictor, the disk 622 including channels 626 extending radially from holes 634. Note that channels 626 are rectangular in shape.

[0030] 5B is a schematic exploded view of a flow restrictor 312 according to an exemplary embodiment of the present disclosure. As shown in FIG. 5B, the flow restrictor 312 comprises a first sheet 322 including a flow passage 326 and a second sheet 324 stacked on top of the first sheet 322. The second sheet 324 has a hole 325 formed therein, where the hole 325 is located at the center of the second sheet 324. The flow passage 326 is a serpentine groove formed in a thickness of the first sheet 322, which forms a serpentine shape along the surface of the first sheet 322 when viewed from above.

[0031] 5C is a schematic plan view of the first sheet 322 in a separated state. The first sheet 322 is provided with a hole 334, where the hole 334 is provided in the center of the first sheet 322. The flow passage 326 includes a plurality of serpentine grooves passing through the surface or thickness of the first sheet 322. Each of the plurality of serpentine grooves included in the flow passage 326 includes a pair of radial portions 326a, 326b extending in the radial direction and a plurality of arc-shaped portions 326c-k that define a flow passage between the plurality of radial portions 326a, 326b. By increasing the effective length of the flow passage within the flow restrictor 312, the performance uncertainty of the flow restrictor 312 can be reduced compared to a conventional flow restrictor including a conventional disk 622.

[0032] FIG. 5D is a predicted data plot based on simulation data comparing the performance uncertainty of the flow restrictor 312 of the exemplary embodiment of FIGS. 5B-C to a conventional flow restrictor with a conventional disk 622 for several combinations of upstream pressure (P1) and downstream pressure (P2), pressures are measured in kPa. The experimental results of FIG. 5D were obtained in a CFD simulation using a CFD model that matches the experimental data within the experimental uncertainty. The uncertainty depicted in FIG. 5D is the sensitivity of the molar flow ratio of sulfur hexafluoride to nitrogen to variations in restrictor geometry for the worst case scenario. As seen in FIG. 5D, the configuration of the flow passage 326 including multiple serpentine grooves on the surface of the first sheet 322 reduces the uncertainty compared to a prior art flow restrictor including a conventional disk 622. The inventors have demonstrated through CFD simulation that the pressure loss at the corners of the serpentine grooves is minimal and contributes little to the uncertainty.

[0033] FIG. 6 is a predictive bar graph based on simulation data comparing the gas ratio variance of a conventional flow restrictor having smooth first and second sheets to the gas ratio variance of an exemplary embodiment of the flow restrictor in which the second sheet has a rougher surface than the first sheet. In the exemplary embodiment of FIG. 6, the ratio of the roughness parameter (Ra) to the flow channel thickness was 1-5%. In other words, for the exemplary embodiment described above, the second sheet may have a roughened surface relative to the surface of the first sheet. In other words, the roughness parameter of the second sheet may be greater than the roughness parameter of the first sheet. The roughness parameter may be a profile roughness parameter or an areal roughness parameter.

[0034] The gas ratio variance in Figure 6 is defined as the maximum variation in the helium to nitrogen flow ratio under a given condition. The larger this variance, the greater the uncertainty in the performance of the flow restrictor. The results in Figure 6 were obtained by CFD simulation using a CFD model that matches the experimental data within the experimental uncertainty.

[0035] In principle, it has been traditionally believed that roughening the wall of the second sheet increases the uncertainty of the flow restrictor performance because the parameters characterizing the roughness add to the uncertainty. As a result, the use of second sheets with smooth (even) walls has become the norm in the design of flow restrictors. For example, the ratio of the roughness parameter (Ra) to the channel thickness is typically less than about 1%.

[0036] However, the unexpected results in Figure 6 show that roughening the second sheet results in a reduction in uncertainty that is not proportional to the effect of simply changing the roughness parameters. Thus, the unexpected results in Figure 6 show that roughening the walls can significantly reduce the uncertainty of a flow restrictor, at least for the operating parameters considered above. Roughening the surfaces of the first and second sheets can be achieved in a variety of different ways. One is by mechanically abrading the metal sheet used to make the second sheet. Another is by cycling temperature and pressure during diffusion bonding of the first and second sheets to roughen the walls.

[0037] It will be understood that the configurations and / or approaches described herein are exemplary in nature and that numerous variations are possible, and therefore these specific embodiments or examples are not to be considered in a limiting sense.

[0038] For example, features of the exemplary embodiment of Figures 2B-F may be combined with features of the exemplary embodiment of Figure 4A to incorporate an expansion zone in a restrictor stack having a plurality of first and second sheets with an average Mach number less than 0.1. Features of the exemplary embodiment of Figures 2B-F may be combined with features of the exemplary embodiment of Figure 3B to incorporate an expansion zone in a flow restrictor having a serpentine flow path extending along the thickness of the second sheet.

[0039] Alternatively, features of the exemplary embodiment of Figures 5B-C may be combined with features of the exemplary embodiment of Figure 4A to incorporate a serpentine groove on the first sheet of a restrictor stack having a plurality of first and second sheets with an average Mach number less than 0.1. Features of the exemplary embodiment of Figures 5B-C may be combined with features of the exemplary embodiment of Figure 3B to incorporate a serpentine groove on the first sheet of a flow restrictor having a serpentine flow path extending along the thickness of the second sheet. Additionally, features of the exemplary embodiment of Figure 3B may be combined with features of the exemplary embodiment of Figure 4A to incorporate a serpentine flow path extending along the thickness of the second sheet into a restrictor stack having a plurality of first and second sheets with an average Mach number less than 0.1.

[0040] Furthermore, the disclosure of the present specification may include the following aspects 1 to 20.

[0041] (Aspect 1) A flow restrictor comprising a first sheet including a flow path and a second sheet stacked on top of the first sheet, the second sheet having a hole formed in the center, the flow path including a groove cut into the surface of the first sheet, the groove communicating with an expansion zone in a peripheral area of ​​the first sheet, the peripheral edge of the second sheet contacting the first sheet between its inner and outer boundaries in the expansion region.

[0042] (Aspect 2) 2. The flow restrictor of embodiment 1, wherein the flow passage is one of a plurality of flow passages uniformly distributed radially around the aperture.

[0043] (Aspect 3) 3. The flow restrictor of embodiment 2, wherein each flow passage includes a corresponding groove that extends spirally from the hole to a corresponding expansion zone in the peripheral area of ​​the first sheet.

[0044] (Aspect 4) The flow restrictor of embodiment 1, wherein the first sheet is one of a plurality of first sheets, the second sheet is one of a plurality of second sheets, and the plurality of first sheets and the plurality of second sheets are stacked alternately to form a restrictor stack.

[0045] (Aspect 5) 5. The flow restrictor of claim 4, further comprising an upstream flow passage connected to an upstream end of the restrictor stack and a downstream flow passage connected to a downstream end of the restrictor stack, wherein a plurality of continuously measured fluid flow rates through the flow restrictor divided by a number of first sheets divided by a number of flow passages per first sheet results in an average Mach number of less than 0.1.

[0046] (Aspect 6) A flow restrictor as described in embodiment 1, wherein the second sheet includes a slit passing through its entire thickness, and the first sheet and the second sheet are stacked and aligned to form a continuous flow path through the slit in the second sheet and the flow path in the first sheet.

[0047] (Aspect 7) 7. The flow restrictor according to aspect 6, wherein the continuous flow path forms a serpentine shape extending along a thickness direction of the second sheet when viewed in a vertical cross section of the second sheet.

[0048] (Aspect 8) 2. The flow restrictor of embodiment 1, wherein the second sheet has a roughened surface relative to a surface of the first sheet.

[0049] (Aspect 9) A flow restrictor comprising a first sheet including a flow path and a second sheet laminated to the first sheet, wherein a hole is provided in the center of the second sheet, and the flow path is a serpentine groove that cuts through a thickness of the first sheet and has a serpentine shape along the surface of the first sheet when viewed from above.

[0050] (Aspect 10) 10. The flow restrictor of embodiment 9, wherein the flow path comprises a plurality of serpentine grooves extending through a thickness of the first sheet.

[0051] (Aspect 11) 11. The flow restrictor of claim 10, wherein each of the plurality of serpentine grooves includes a pair of radial portions extending radially and a plurality of arcuate portions defining flow paths between the plurality of radial portions.

[0052] (Aspect 12) 10. The flow restrictor of claim 9, wherein the first sheet is one of a plurality of first sheets, the second sheet is one of a plurality of second sheets, and the plurality of first sheets and the plurality of second sheets are stacked alternately to form a restrictor stack.

[0053] (Aspect 13) 13. The flow restrictor of embodiment 12, further comprising an upstream flow passage connected to an upstream end of the restrictor stack and a downstream flow passage connected to a downstream end of the restrictor stack, wherein a plurality of continuously measured fluid flow rates through the flow restrictor divided by the number of the plurality of first sheets divided by the number of flow passages per first sheet has an average Mach number of less than 0.1.

[0054] (Aspect 14) A flow restrictor as described in embodiment 9, wherein the second sheet includes a slit passing through its entire thickness, and the first sheet and the second sheet are stacked and aligned to form a continuous flow path through the slit in the second sheet and the flow path in the first sheet.

[0055] (Aspect 15) 15. The flow restrictor of claim 14, wherein the continuous path forms a serpentine shape extending along a thickness direction of the second sheet when viewed in a vertical cross section of the second sheet.

[0056] (Aspect 16) 10. The flow restrictor of embodiment 9, wherein the second sheet has a roughened surface relative to a surface of the first sheet.

[0057] (Aspect 17) A flow restrictor comprising a first sheet defining a flow path and a second sheet stacked on the first sheet, the second sheet having a hole in the center and including a slit passing through its entire thickness, the first sheet and the second sheet being aligned in a stack to form a continuous flow path through the slit in the second sheet and the flow path in the first sheet.

[0058] (Aspect 18) 18. The flow restrictor of claim 17, wherein the continuous flow path has a serpentine shape extending along a thickness direction of the second sheet when viewed in a vertical cross section of the second sheet.

[0059] (Aspect 19) 18. The flow restrictor of claim 17, wherein the first sheet is one of a plurality of first sheets, the second sheet is one of a plurality of second sheets, and the plurality of first sheets and the plurality of second sheets are alternately stacked to form a restrictor stack.

[0060] (Aspect 20) 20. The flow restrictor of embodiment 19, further comprising an upstream flow passage connected to an upstream end of the restrictor stack and a downstream flow passage connected to a downstream end of the restrictor stack, wherein a plurality of continuously measured fluid flow rates through the flow restrictor divided by the number of the plurality of first sheets divided by the number of flow passages per first sheet has an average Mach number of less than 0.1.

[0061] The present disclosure reduces the uncertainty in the performance of flow restrictors in mass flow controllers, thereby improving the quality of fluid delivery in a variety of industrial applications.

[0062] The subject disclosure includes all novel and non-obvious combinations and subcombinations of the various features and techniques disclosed herein. The various features and techniques disclosed herein are not necessarily required for every embodiment of the subject disclosure. Moreover, the various features and techniques disclosed herein may define patentable subject matter apart from the disclosed embodiments and may find utility in other embodiments not expressly disclosed herein.

[0063] As used herein, "and / or" refers to a logical disjunction, and thus, it will be understood that A and / or B have the following truth table: TIFF2025501482000002.tif61138

[0064] As used herein, terms such as "includes," "including," "has," "contains," and the like are intended to be inclusive, without excluding additional or other elements, similar to the open transition term "comprises."

Claims

1. a first sheet including a flow path; a second sheet stacked on the first sheet; The second sheet has a hole formed therein, the flow path includes a groove in a surface of the first sheet, the groove communicating with an expansion zone in a peripheral area of ​​the first sheet; A flow restrictor where a peripheral edge of the second sheet contacts the first sheet in the expansion region.

2. The flow restrictor of claim 1 , wherein the passage is one of a plurality of passages distributed around the aperture.

3. The flow restrictor of claim 2 , wherein each flow passage includes a corresponding groove that extends spirally from the hole to a corresponding expansion zone in the peripheral area of ​​the first sheet.

4. the first sheet is one of a plurality of first sheets; the second sheet is one of a plurality of second sheets; The flow restrictor of claim 1 , wherein the plurality of first sheets and the plurality of second sheets are stacked alternately to form a restrictor stack.

5. an upstream flow passage connected to an upstream end of the restrictor stack; a downstream flow path connected to a downstream end of the restrictor stack, 5. The flow restrictor of claim 4, wherein a plurality of successively measured fluid flow rates through the flow restrictor divided by a number of first sheets divided by a number of flow passages per first sheet has an average Mach number of less than 0.

1.

6. the second sheet includes a slit extending through its entire thickness; 2. The flow restrictor of claim 1, wherein said first sheet and said second sheet are aligned in a stack to form a continuous flow passage through a slit in said second sheet and a flow passage in said first sheet.

7. The flow restrictor of claim 6 , wherein the continuous flow passage forms a serpentine shape extending along a thickness direction of the second sheet when viewed in a vertical cross section of the second sheet.

8. The flow restrictor of claim 1 , wherein the second sheet has a roughened surface compared to a surface of the first sheet.

9. a first sheet including a flow path; A second sheet laminated on the first sheet, The second sheet has a hole therein; The flow path is provided within the thickness of the first sheet, and is a serpentine groove that has a serpentine shape along the surface of the first sheet when viewed from above.

10. The flow restrictor of claim 9 , wherein the flow passage comprises a plurality of serpentine grooves disposed within a thickness of the first sheet.

11. The flow restrictor of claim 10 , wherein each of the plurality of serpentine grooves includes a pair of radial portions extending radially and a plurality of arcuate portions defining flow paths between the radial portions.

12. the first sheet is one of a plurality of first sheets; the second sheet is one of a plurality of second sheets; 10. The flow restrictor of claim 9, wherein the plurality of first sheets and the plurality of second sheets are stacked in an alternating fashion to form a restrictor stack.

13. an upstream flow passage connected to an upstream end of the restrictor stack; a downstream flow path connected to a downstream end of the restrictor stack, 13. The flow restrictor of claim 12, wherein a plurality of successively measured fluid flow rates through the flow restrictor divided by the number of the plurality of first sheets divided by the number of flow passages per first sheet has an average Mach number of less than 0.

1.

14. the second sheet includes a slit extending through its entire thickness; 10. The flow restrictor of claim 9, wherein the first sheet and the second sheet are aligned in a stack to form a continuous flow passage through the slits in the second sheet and the flow passages in the first sheet.

15. The flow restrictor of claim 14 , wherein the continuous path forms a serpentine shape extending along a thickness direction of the second sheet when viewed in a vertical cross section of the second sheet.

16. The flow restrictor of claim 9 , wherein the second sheet has a roughened surface compared to a surface of the first sheet.

17. A first sheet that forms a flow path; a second sheet stacked on the first sheet, The second sheet has a hole therein, the second sheet includes a slit extending through its entire thickness; A flow restrictor in which the first sheet and the second sheet are aligned in a stack to form a continuous flow passage through the slit in the second sheet and the flow passage in the first sheet.

18. 18. The flow restrictor of claim 17, wherein the continuous flow path has a serpentine shape extending along a thickness direction of the second sheet when viewed in a vertical cross section of the second sheet.

19. the first sheet is one of a plurality of first sheets; the second sheet is one of a plurality of second sheets; 20. The flow restrictor of claim 17, wherein the plurality of first sheets and the plurality of second sheets are interleaved to form a restrictor stack.

20. an upstream flow passage connected to an upstream end of the restrictor stack; a downstream flow path connected to a downstream end of the restrictor stack, 20. The flow restrictor of claim 19, wherein a plurality of successively measured fluid flow rates through the flow restrictor divided by the number of the plurality of first sheets divided by the number of flow passages per first sheet has an average Mach number of less than 0.1.

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