Abstract:
A method of transferring heat from a warmer stream of gas to a cooler stream of gas comprises flowing the warmer stream of gas through a heat exchanger in a manner such that the warmer stream of gas converges as the warmer stream of gas flows through the heat exchanger. The method further comprises flowing the cooler stream of gas through the heat exchanger in a manner such that the cooler stream of gas diverges as the cooler stream of gas flows through the heat exchanger. Another method comprises forming a heat exchanger by solid state welding a plurality of laminate members to each other. The heat exchanger may be a heatsink. The heat exchanger may also condense gas into a liquid.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
       [0001]    None. 
       STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT  
       [0002]    Not Applicable. 
       APPENDIX  
       [0003]    Not Applicable. 
       BACKGROUND OF THE INVENTION 
       [0004]    1. Field of the Invention 
         [0005]    This invention pertains to heat exchangers. More particularly, the present invention pertains to heat exchangers that are ideally suited for transferring heat between two gaseous fluids. 
         [0006]    2. General Background 
         [0007]    Heat exchangers are used in numerous industries and devices for numerous purposes. Many types of heat exchangers rely on the transfer of heat between two fluids. For example, many internal-combustion engines are typically water cooled and typically utilize a heat exchanger (radiator) to transfer heat from the liquid water or coolant to air. Some heat exchangers are gas-to-gas heat exchangers, wherein heat is transferred between two separate streams of gaseous fluid. The steady-state efficiency of a gas-to-gas heat exchanger is typically dependent upon the amount of surface area of the heat exchanger that contacts each of the fluid streams and the thermal conductivity of the material that separates the two fluid streams. Thus, it is advantageous to maximize the surface area of the heat exchanger that separates the fluid streams, while also minimizing the amount of material that separates the fluid streams. However, increasing the surface area to volume ratio of a heat exchanger can greatly complicate the fabrication or the size of heat exchangers, and therefore the cost and/or space required. 
         [0008]    Another thing impacting the amount of heat transferred by a heat exchanger is the differences in the temperatures of the fluid streams as they pass through the heat exchanger. It is known that by flowing the streams of fluid in opposite directions through a heat exchanger, the temperature differential of the fluid streams can be kept more uniform throughout the heat exchanger. Such “counter-flow” heat exchangers typically operate with a higher efficiency than heat exchangers wherein the streams flow in the same direction along opposite surfaces of the walls of the heat exchanger and with a higher efficiency than cross-flow heat exchangers. 
         [0009]    Unlike liquid fluids, gaseous fluids are easily compressed. As such, the temperature of fluids in a gas state can be altered by expanding or compressing such fluids. Likewise, as heat is removed from a gaseous fluid under constant pressure, the volume occupied by the fluid decreases. Thus, as a gaseous fluid stream of constant cross-sectional area passes through a heat exchanger and loses heat, the flow velocity normally decreases as the gaseous fluid passes through the heat exchanger as a result of the volume decrease. 
       SUMMARY OF THE INVENTION 
       [0010]    The present invention provides several advantages over prior art heat exchangers. One such advantage is that the invention allows for a relatively simplistic method of fabricating a highly efficient heat exchanger. The preferred embodiment of the present invention is configured such that the cross-sectional area of the stream of fluid being cooled decreases as said stream passes through the heat exchanger and, conversely, the cross-sectional area of the stream of fluid being heated increases as said stream passes through the heat exchanger. Assuming the fluid stream being cooled is gaseous, the reduction of the cross-sectional area of said fluid stream has the effect of decreasing the volume of said fluid stream which minimizes the reduction of the temperature of said fluid stream as said fluid stream passes through the heat exchanger. Likewise, assuming the fluid stream being heated is gaseous, the increases of the cross-sectional area of said fluid stream has the effect of increasing the volume of said fluid stream which minimizes the increase of the temperature of said fluid stream as said fluid stream passes through the heat exchanger. This is advantageous in that it maximizes the temperature differential between the fluid streams as they pass through the heat exchanger and therefore increases the overall amount of heat exchanged between the fluid streams. 
         [0011]    In one aspect of the invention, a method of transferring heat from a warmer stream of gas to a cooler stream of gas comprises flowing the warmer stream of gas through a heat exchanger in a manner such that the warmer stream of gas converges as the warmer stream of gas flows through the heat exchanger and in a manner such that the warmer stream of gas is at least partially bound by a wall of the heat exchanger. The method further comprises flowing the cooler stream of gas through the heat exchanger in a manner such that the cooler stream of gas diverges as the cooler stream of gas flows through the heat exchanger and in a manner such that the cooler stream of gas is at least partially bound by the wall of the heat exchanger. Still further, the method comprises allowing heat to conduct through the wall from the warmer stream of gas to the cooler stream of gas. 
         [0012]    In another aspect of the invention, a heat exchanger extends at least partially around and along a central axis (the central axis defining axial and radial directions). The heat exchanger at least partially encircles an interior fluid containing region and is at least partial encircled by an exterior fluid containing region. The heat exchanger comprises a plurality of arcuate fluid passageways alternating in the axial direction with a plurality of arcuate fluid cavities. Each of the arcuate fluid passageways extends radially through the heat exchanger and creates a fluid connection between the interior and exterior fluid containing regions. The heat exchanger also comprises first and second axially extending fluid passageways that traverse each of the arcuate fluid passageways and that are in fluid communication with each of the arcuate fluid cavities in a manner connecting the arcuate fluid cavities in parallel. The first axially extending fluid passageway is a first radial distance from the central axis and the second axially extending fluid passageway is a second radial distance from the central axis. The second radial distance is greater than the first radial distance. 
         [0013]    In yet another aspect of the invention, a method of fabricating a heat exchanger comprises solid state welding a plurality of substantially identical first laminate members to a plurality of substantially identical second laminate members in a manner creating a bonded stack of the first and second laminate members comprised of alternating first and second laminate members. Each of the first laminate members comprises a bottom surface, a top surface, at least two pass-through passageways, and at least one recess. The recess of each of the plurality first laminate members extends down into such first laminate member from the top surface and extends from an edge of such first laminate member to an opposite edge of such first laminate member. Each of the pass-through passageways extends through such first laminate member from the top surface to the bottom surface of such first laminate member. Each of the second laminate members comprises a bottom surface, a top surface, at least two openings, and at least one recess. The recess of each of the second laminate members extends down into such second laminate member from the top surface of such second laminate member. Each of the openings of each of the second laminate members extends from the bottom surface and opens into the recess of such second laminate member in a manner such that said recess operatively joins said openings. Each of the pass-through passageways of each of the first laminate members operative connects at least one of the openings of an adjacent one of the second laminate members to the recess of another adjacent one of the second laminate members. 
         [0014]    Further features and advantages of the present invention, as well as the operation of various embodiments of the present invention, are described in detail below with reference to the accompanying drawings. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0015]      FIG. 1  is a perspective view of one embodiment of a heat exchanger in accordance with the invention. 
           [0016]      FIG. 2  is another perspective view of the heat exchanger shown in  FIG. 1 , showing the opposite axial end of the heat exchanger. 
           [0017]      FIG. 3  is a perspective view of the upper end plate of one of the subassemblies of the heat exchanger shown in  FIGS. 1 and 2 , as viewed from above. 
           [0018]      FIG. 4  is a perspective view of the lower end plate of the subassembly of the heat exchanger shown in  FIGS. 1 and 2 , as viewed from below. 
           [0019]      FIG. 5  is perspective view of one of a plurality of similar laminate members that forms part of the subassembly of the heat exchanger shown in  FIGS. 1 and 2 , as viewed from above. 
           [0020]      FIG. 6  is perspective view of one of another plurality of similar laminate members that form the subassembly of the heat exchanger shown in  FIGS. 1 and 2 , as viewed from above. 
           [0021]      FIG. 7  is a detail view of the laminate member shown in  FIG. 5 , as indicated in  FIG. 5 . 
           [0022]      FIG. 8  is a detail view of the laminate member shown in  FIG. 6 , as indicated in  FIG. 6 . 
           [0023]      FIG. 9  is a cross-sectional view of an assembly comprising the heat exchanger shown in  FIGS. 1-8 . 
           [0024]      FIG. 10  is a front elevation view of a heatsink in accordance with the invention. 
           [0025]      FIG. 11  is a side elevation view of the heatsink shown in  FIG. 10 . 
           [0026]      FIG. 12  is a perspective view of a laminate of the heatsink shown in  FIGS. 10 and 11 . 
           [0027]      FIG. 13  is a perspective view of a plurality of laminates formed together during part of the preferred method of assembling the heatsink shown in  FIGS. 10 and 11 . 
       
    
    
       [0028]    Reference numerals in the written specification and in the drawing figures indicate corresponding items. 
       DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0029]    A heat exchanger in accordance with the present invention is shown in  FIGS. 1 and 2 . The heat exchanger  10  preferably comprises three identical arcuate subassemblies  12  that together form and annular ring. Each of the subassemblies  12  is capable of operating as a heat exchanger independently of the other subassemblies, but preferably acts in concert with the other subassemblies. For purposes of describing the invention, it should be appreciated that the annular ring defines an axial direction (i.e., any direction parallel to the center axis of the ring), a radial direction (any direction away or toward the center axis), and a circumferential direction (any curvilinear direction that revolves about the center axis). Additionally, the heat exchanger  10  and its components are referred to as having upper/top and lower/bottom elements. It should be appreciated that such adjectives are used merely to explain the orientation of the various elements relative to each other and not relative to the direction of gravity. 
         [0030]    Each of the sub assemblies  12  preferably comprises an upper  14  end plate, a lower end plate  16 , and a stack  18  of alternating first laminate members  20  and second laminate members  22 . As discussed in greater detail below, these components are preferably formed of metal and are preferably diffusion bonded to each other (also referred to as diffusion welded). 
         [0031]    The upper end plate  14  preferably has a polygonal arcuate outer edge  24  and a smooth arcuate inner edge  26 . A plurality of mounting holes  28  are circumferential spaced along the inner edge  26  and the outer edge  24  and extend through the upper end plate  14 . A plurality of oval fluid passageway openings  30  also extend through the upper end plate  14  and are circumferentially spaced adjacent the mounting holes  28  nearest the inner edge  26 . A gasket groove  32  having a semicircular cross-section extends down into the upper end plate  14  from the top surface  34  of the upper end plate and encircles the fluid passageway openings  30 . The bottom surface  36  of the upper end plate  14  is preferably a contiguous planar surface. 
         [0032]    The lower end plate  16  is similar to the upper end plate and preferably comprises a polygonal arcuate outer edge  24 , a smooth arcuate inner edge  26 , a plurality of mounting holes  28  that are identical to those of the upper end plate  14 . However, the fluid passageway openings  30  that extend through the lower end plate  16  are circumferentially spaced adjacent the mounting holes  28  nearest the outer edge  26  of the lower end plate and are preferably circular rather than oval. The total cross-sectional area of all the fluid passageway openings  30  of the lower end plate  16  is preferably appreciably greater than the total cross-sectional area of all of the fluid passageway openings of the upper end plate  14 . Similar to the upper end plate  14 , a gasket groove  32  having a semicircular cross-section extends upward into the lower end plate  16  from the bottom surface  36  of the lower end plate and encircles the fluid passageway openings  30 . The top surface  34  of the lower end plate  16  is preferably a contiguous planar surface. 
         [0033]    As mentioned above, the stack  18  laminate members comprises alternating first laminate members  20  and second laminate members  22 . One of the first laminate members  20  is shown in  FIGS. 5 and 7  and is formed of a thin sheet of metal having a thickness preferably from 0.030″ to 0.004″ (0.70 mm to 0.10 mm). The first laminate member  20  is preferably arcuate in shape and preferably has a contiguous planar bottom surface  38 . A recess  40  is preferably chemical etched into the first laminate member  20  from its top surface  42 . The recess  40  has a depth that is preferably at least half, and more preferably 70%, the thickness of the first laminate member  20  and extends from the first laminate member&#39;s outer radial edge  44  to its inner radial edge  46 . A plurality of pass-through passageways  48  extend through the first laminate member  20  from the top surface  42  of the first laminate member to its bottom surface  38 . The recess  40  is spaced from the pass-through passageways  48  in a manner such that the pass-through passageways are completely bound by material from the top surface  42  to the bottom surface  38  of the first laminate member  20 . A first set  50  of the pass-through passageways  48  are circumferential spaced from each other adjacent the outer radial edge  44  of the first laminate member  20 . A second set  52  of the pass-through passageways  48  are circumferential spaced from each other adjacent the inner radial edge  46  of the first laminate member  20 . The total cross-sectional area of the first set  50  of the pass-through passageways  48  is preferably appreciably greater than the total cross-sectional area of second set  52  of the pass-through passageways. A plurality of diamond shaped protrusions  54  preferably extend vertically through the recess  40  to the top surface  42  of the first laminate member  20  and are spaced relatively uniformly throughout the recess. A plurality of tooling holes  56  also extend vertically through the first laminate member  20 . 
         [0034]    One of the second laminate members  22  is shown in  FIGS. 6 and 8 . The second laminate member  22  preferably has a thickness and overall dimensions equal to that of the first laminate member  20 . Like the first laminate member  20 , the bottom surface  58  of the second laminate member is preferably a contiguous planar surface. Additionally, a recess  60  is preferably chemical etched into the second laminate member  22  from its top surface  62 . Unlike the recess  40  of the first laminate member  20 , the recess  60  of the second laminate member  22  stops short of the outer radial edge  64  and the inner radial edge  66  in a manner such that the entire perimeter of the second laminate member extends from the bottom surface  58  to the top surface  62 . A plurality of openings  68  extend through the second laminate member  20  from the bottom surface  58  of the second laminate member and into the recess  60 . A first set  70  of the openings  68  are circumferential spaced from each other adjacent the outer radial edge  64  of the second laminate member  22 . A second set  72  of the openings  68  are circumferential spaced from each other adjacent the inner radial edge  66  of the second laminate member  22 . The total cross-sectional area of the first set  70  of the openings  48  is preferably appreciably greater than the total cross sectional area of second set  72  of the openings. The recess  60  extends from the first set  70  of the openings  68  to the second set of the openings. Like with the first laminate member  20 , a plurality of diamond shaped protrusions  74  preferably extend vertically through the recess  60  to the top surface  62  of the second laminate member  22  and are spaced relatively uniformly throughout the recess. A plurality of tooling holes  76  also extend vertically through the first laminate member  20 . 
         [0035]    As mentioned above, each of the subassemblies  12  of the heat exchanger  10  is preferably assembled using a diffusion bonding technique. Although diffusion bonding can be a complicated process, the use of diffusion bonding renders the subassemblies  12  suitable for high temperature materials such as Nickel based alloys and titanium alloys and reduces the number of steps required to fabricate the subassemblies. Moreover, the inter-metallic bonds formed by diffusion bonding are superior to conventional brazed or welded bonds, reducing fatigue failure. 
         [0036]    During the assembly process, the stack  18  of alternating first laminate members  20  and second laminate members  22  is created using one-hundred and sixty of each of the first laminate members and the second laminate members. To ensure that the laminate members are properly aligned with each other, alignment rods can be inserted through the tooling holes  56 ,  76  of the laminate members. The stack  18  is then sandwiched between the upper end plate  14  and the lower end plate  16  and the assembly is then diffusion bonded to secure the laminate members to each other and to the end plates. The diffusion bonding step bonds the top surface of each of the laminate members to the bottom surface of the laminate member directly above (except for the upper most laminate, which bonds to the bottom surface of the upper plate. The diamond shaped protrusions transfer the axial compressive load generated during the diffusion bonding process from each laminate member to the next, ensuring that the entire top surface of each laminate becomes bonded. 
         [0037]    As assembled, the pass-through passageways  48  of the first laminate members  20  and the openings  68  of the second laminate members  22  form axial fluid passageways that extend from the top of the stack  18  to the bottom of the stack. These axial fluid passageways connect the recesses  60  of the second laminate members  22  in parallel. The fluid passageway openings  30  of the upper end plate  14  are aligned with the axial fluid passageways that are adjacent the inner radial edges  46 ,  66  of the first and second laminate members  20 ,  22 . Similarly, the fluid passageway openings  30  of the lower end plate  16  are aligned with the axial fluid passageways that are adjacent the outer radial edges  44 ,  64  of the first and second laminate members  20 ,  22 . The recesses  40  of the first laminate members  20  allow fluid to pass radially through the stack  18  of laminate members, without directly communicating with fluid in the recesses  60  of the second laminate members  22  or the fluid in the pass-through passageways  48  of the first laminate members. 
         [0038]    It should be appreciated that the heat exchanger  10  is well suited for exchanging heat between two gaseous fluid streams. More particularly, the heat exchanger  10  is configured and adapted to serve as a recuperator for recovering heat energy from a stream of combustion exhaust gas and transferring such energy to a stream of combustion intake gas. In use, exhaust gas travels radially inward through the heat exchanger  10  from the region of space around the heat exchanger via the recesses  40  of the first laminate members  20  and is expelled into the region of space encircled by the heat exchanger. Simultaneously, intake gas is preferably drawn into the fluid passageway openings  30  of the upper end plate  14  and out the fluid passageway openings  30  of the lower end plate  16 . As it does this, the intake gas is channeled radially outward through the recesses  60  of the second laminate members  22  from the axial fluid passageways adjacent the inner radial edges  46 ,  66  of the first and second laminate members  20 ,  22  and to the axial fluid passageways that are adjacent the outer radial edges  44 ,  64  of the first and second laminate members. 
         [0039]    Due to the arcuate shape of the fluid passageways created by the recesses  40 ,  60  of the first and second laminate members  20 ,  22 , the fluid passageways through which the exhaust gas travels narrow in cross-sectional area and the fluid passageways through which the intake gas travels expand in cross-sectional area. The narrowing of the fluid passageways through which the exhaust gas passes prevents the temperature of the exhaust gas from dropping as much as it would if the passageways maintained a constant cross-sectional area. Similarly, the expansion of the fluid passageways through which the intake gas passes prevents the temperature of the intake gas from increasing as much as it would if the passageways maintained a constant cross-sectional area. This increases the temperature differential between the exhaust gas and the intake gas throughout the heat exchanger and therefore increases the heat conducted through the laminate members from the exhaust gas to the intake gas. As a result, the stagnation temperature of the exhaust gas is actually reduced more than it otherwise would have reduced and the stagnation temperature of intake gas is increased beyond what it otherwise would have increased. 
         [0040]    As the fluids pass through the heat exchanger, the diamond shaped protrusions provide tie the laminations to each other in a manner preventing appreciable material deformation that could otherwise result from pressure differences between the two fluids. The diamond shaped protrusions also improve the flow direction and mixing of each of fluid stream. Still further, the diamond shaped protrusions increase heat transfer coefficient by disrupting the laminar flow, which creates regions having undeveloped velocity profiles. 
         [0041]    In view of the forgoing, it should be appreciated that the heat exchanger of the present invention provides a large amount of surface area for heat conduction per unit volume of the heat exchanger. Moreover, it should be appreciated that the heat exchanger of the present invention is highly efficient at transferring heat between two gaseous (i.e., compressible) fluid streams. Still further is should be appreciated that the method of manufacturing the heat exchanger is relatively simplistic and strait forward. 
         [0042]      FIG. 9  depicts a assembly  80  comprising the above-described heat exchanger  10 . The assembly  80  comprises a housing  82  having an internal cavity  84  in which the heat exchanger  10  is positioned. As shown in  FIG. 9 , the heat exchanger  10  is inverted such that its lower end plate  16  is oriented beneath its upper end plate  14 . The housing  82  of the assembly  80  comprises a cooling fluid inlet  86 , a cooling fluid outlet  88 , a hot fluid inlet  90 , a hot fluid outlet  92 , and a condensed fluid outlet  94 . The cooling fluid inlet  86  is in direct fluid communication with a portion of the internal cavity  84  of the housing  82  that lies beneath the heat exchanger  10 . Similarly, the cooling fluid outlet  88  is in direct fluid communication with a portion of the internal cavity  84  that lies above the heat exchanger  10 . These portions of the internal cavity  84  are also in communication with each other through the heat exchanger  10  via the fluid passageway openings  30  of the heat exchanger&#39;s end plates  14 ,  16 . The hot fluid inlet  90  is in direct fluid communication with an annular portion of the internal cavity  84  that encircles the heat exchanger  10 . This anular portion of the internal cavity  84  is isolated from the above mentioned portions of the internal cavity. However, fluid can pass radially into the region of space encircled by the heat exchanger  10  by passing through the recesses  40  of the first laminate members  20 . The region of space encircled by the heat exchanger  10  is also in direct fluid communication with the hot fluid outlet  92  and the condensed fluid outlet  94 . 
         [0043]    The assembly  80  just described is particularly well suited for use in connection with fuel cells and more particularly for separating steam for hydrogen as a mix of the same is cooled via the heat exchanger  10 . This is done by passing vaporized steam and hydrogen mixture into the assembly  80  via the hot fluid inlet  90 , while simultaneously passing cooler air or another cooler fluid into the assembly via the cooling fluid inlet  86  and out of the cooling fluid outlet  88 . The vaporized steam and hydrogen mixture is thereby cooled as it passes through the heat exchanger  10  and into the region of space encircled by the heat exchanger. The cooling of the vaporized steam and hydrogen mixture causes the steam to condense and thereafter gravity causes the lighter hydrogen to move upward and out of the assembly via the hot fluid outlet  92 , and causes the heavier liquid water to travel downward and out of the assembly via the condensed fluid outlet  94 . 
         [0044]    Another embodiment of the invention is shown in  FIG. 10  and is configured as an internally cooled heatsink  100 . Unlike the heat exchanger  10  described above, the heatsink  100  is configured to absorb heat through conduction from other objects, such as insulated gate bipolar transistors or central processing units. As such, the heatsink needs only comprise a single fluid inlet  102  and single fluid outlet  104 . The main body  106  of the heatsink  100  preferably comprises a stack of identical laminates  108  that are sandwiched between an upper end plate  110  and lower end plate  112 . As shown in  FIG. 12 , each laminate  108  comprises two fluid channel through-holes  114  that extend through the thickness of the laminate. An etched region  116  extends down into the laminate  108  from the top surface  118  of the laminate. The etched region  116  preferably extends approximately half way through the thickness of the laminate  108  and provides a fluid connection between the two fluid channel through-holes  114 . A plurality of diamond shaped protrusions  120  protrude upward from the bottom half of the laminate  108  all the way to the top surface  118 . One or more tooling holes  122  may also optionally extend through the thickness of the laminate  108 . The diamond shape protrusions  120  and the tooling holes  122  serve the same purpose as those of the first heat exchanger  10  described above. When stacked and diffusion bonded together, the fluid channel through-holes  114  of the laminates  108  from two fluid channels that extend vertically through the stack of laminates and the etched regions  116  or the laminates operatively connect the said fluid channels in parallel. The lower end plate  112  caps the openings of the stack of laminates and the upper end plate operatively connects one of the two fluid channels to the fluid inlet  102  and the other to the fluid outlet  104 . 
         [0045]    During the assembly of the heatsink  100 , a plurality of identical heatsinks are preferably from together. As shown in  FIG. 13 , multiple lamentations  108  can be formed and etched as a single part. Likewise, multiple endplates  110 ,  112  can be formed as a single part. After diffusion bonding the laminates and endplates together, the opposite faces of the stack can be milled down to separate the heatsinks from each other. 
         [0046]    In use, cooling fluid is passed into the fluid inlet  102 . The cooling fluid then travels through the etched regions  116  of the laminates  108  and subsequently out of the fluid outlet  104 . As such, heat conducted into the main body  106  of the heat sink  100  from an object being cooled is conducted and/or radiated into the cooling fluid and out of the heat sink. 
         [0047]    As various modifications could be made in the constructions and methods herein described and illustrated without departing from the scope of the invention, it is intended that all matter contained in the foregoing description or shown in the accompanying drawings shall be interpreted as illustrative rather than limiting. Thus, the breadth and scope of the present invention should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the following claims appended hereto and their equivalents. 
         [0048]    It should also be understood that when introducing elements of the present invention in the claims or in the above description of the preferred embodiment of the invention, the terms “comprising,” “including,” and “having” are intended to be open-ended and mean that there may be additional elements other than the listed elements. Additionally, the term “portion” should be construed as meaning some or all of the item or element that it qualifies. Moreover, use of identifiers such as first, second, and third should not be construed in a manner imposing any relative position or time sequence between limitations. Still further, the order in which the steps of any method claim that follows are presented should not be construed in a manner limiting the order in which such steps must be performed.