Shape optimized headers and methods of manufacture thereof

Disclosed herein is a shape optimized header comprising a shell that is operative for collecting a fluid; wherein an internal diameter and/or a wall thickness of the shell vary with a change in pressure and/or a change in a fluid flow rate in the shell; and tubes; wherein the tubes are in communication with the shell and are operative to transfer fluid into the shell. Disclosed herein is a method comprising fixedly attaching tubes to a shell; wherein the shell is operative for collecting a fluid; wherein an internal diameter and/or a wall thickness of the shell vary with a change in pressure and/or a change in a fluid flow rate in the shell; and wherein the tubes are in communication with the shell and are operative to transfer fluid into the shell.

BACKGROUND

This disclosure is related to shape optimized headers and to methods of manufacture thereof.

Industrial plants such as chemical plants and power generation facilities often employ headers to collect fluids (e.g., steam and/or other vapors). These headers and the associated distribution hardware are always possessed of circular cross-sectional geometries with uniform wall thicknesses. These geometrical attributes are selected because they can easily be manufactured from available pipe, or by rolling and seam welding plates, or by centrifugal casting. Ease of manufacturing dictates the shapes of the header geometry as well as the wall thicknesses.

TheFIGS. 1A and 1Bdepicts a front view and a side view, respectively, of a current commercially available header100(also referred to herein as a “comparative header”). As can be seen from theFIGS. 1A and 1B, the header100comprises a shell102of a uniform circular cross-sectional internal diameter “d” and a uniform wall thickness “t” that is in communication with an array of tubes104that enter the header along its length. The shell102is operative to collect a fluid that is discharged into the shell via the array of tubes104.

The shell102comprises a first end106and a second end108that is opposite to the first end106. The first end106is sealed to the outside, while the second end108is in communication with an outlet port (not shown) that permits the evacuation of the fluid that is collected in the header100to the outside.

In the depiction shown in theFIGS. 1A and 1B, the steam pressure and/or the fluid flow rate into the header100is lowest in the array of tubes104that are closest to the first end106while it is highest in the array of tubes104that are closest to the opposite end. The internal diameter “d” of the shell102is determined by considering the pressure drop within the shell102. This is done to ensure that the array of tubes104are controlling the resistance in the system. The diameter d of the shell102is also calculated in such a manner as to limit frictional losses in the header itself. This internal diameter d then defines the bore of the pipe used to fabricate the shell102. Since the entire internal diameter is based upon the cumulative flow of the fluid entering shell102, the header design shown in theFIGS. 1A and 1Bis larger than it needs to be, other than at the outlet plane, and consequently uses a larger amount of material than needed for an efficient design. This increases material costs and results in headers that are expensive and occupy more space in the plant than needed.

As more expensive materials are used to manufacture the headers, these old designs may become cost prohibitive. It is desirable to use geometries and wall thickness that enable cost savings, while at the same time reducing maintenance costs and component breakdowns. It is also desirable to produce headers and associated distribution systems that can operate under existing conditions in a plant for time periods that are as long or longer than the currently existing header designs.

SUMMARY

Disclosed herein is a shape optimized header comprising a shell that is operative for collecting a fluid; wherein an internal diameter and/or a wall thickness of the shell vary with a change in pressure and/or a change in a fluid flow rate in the shell; and tubes; wherein the tubes are in communication with the shell and are operative to transfer fluid into the shell.

Disclosed herein is a method comprising fixedly attaching tubes to a shell; wherein the shell is operative for collecting a fluid; wherein an internal diameter and/or a wall thickness of the shell vary with a change in pressure and/or a change in a fluid flow rate in the shell; and wherein the tubes are in communication with the shell and are operative to transfer fluid into the shell.

DETAILED DESCRIPTION

The transition term “comprising” encompasses the transition terms such as “consisting essentially of” and “consisting of”.

All numerical ranges disclosed herein are inclusive of the endpoints. In addition, all numbers and numerical values (including those not expressly stated herein) within a given range are understood to be inherently included within the invention. All numerical values included herein are interchangeable.

Disclosed herein are shaped optimized headers and associated conduits (hereinafter “shape optimized headers”) that have cross-sectional areas and wall thicknesses that are optimized for localized operational stress and velocities of fluids (e.g., water, steam and/or other vapors or fluids) encountered during the operation of the header. The shaped optimized headers have shells of variable cross-sectional areas and/or wall thicknesses. The cross-sectional area of a particular portion of the shell of the header and/or the wall thickness varies in proportion to the localized flow and localized stress due to the combination of cumulative flow in the header of the incoming fluid and of geometry of the connecting tubes, and to the velocity of the fluid and/or the chemical composition of the incoming fluid in that particular portion of the shell. The shaped optimized headers are designed in such a manner so as to have larger cross-sectional areas and possibly, larger wall thicknesses (than other cross-sectional areas and wall thicknesses of the same header) only in those localized portions where the header encounters higher stress (due to geometry of incoming tubes) and fluid velocities.

Those sections of the shell that experience lower fluid velocities than those in close proximity to the outlet(s) have smaller cross-sectional areas and smaller wall thicknesses than the corresponding cross-sectional areas and wall thicknesses of shell designed in the conventional manner as that depicted in theFIGS. 1A and 1B.

The resulting shaped optimized headers can have numerous cross-sectional areas and wall thicknesses depending upon the localized stress and fluid velocities encountered during operation. In one embodiment, shape optimized headers can also use different materials of construction depending upon the chemistry of fluids encountered in different sections. The shaped optimized headers can be made of specialized materials that are more expensive than those used in the headers depicted in theFIGS. 1A and 1B, but because of the optimized design can cost less than if the header of theFIGS. 1A and 1Bwere constructed from the same specialized materials.

These shaped optimized headers are also advantageous in that they use less floor space and volumetric space in a plant and can be used in operation for as long or for longer periods of time than headers designed in the manner depicted in theFIGS. 1A and 1B.

TheFIGS. 2A and 2Bdepicts a shape optimized version of the comparative header of theFIGS. 1A and 1B. In theFIGS. 2A and 2B, the shape optimized header200comprises a shell202(in the form of a conical section)202having a circular cross-sectional internal diameter that varies from a minimum diametric value of d1(at the end where the stress and/or fluid flow rate is lowest) to a maximum diametric value d2at the opposite end (where the stress and/or fluid flow rate is greatest). The wall thickness also varies from a minimum wall thickness of t1(at the end where the stress and/or fluid flow rate is lowest) to a maximum wall thickness of t2at the opposite end (where the stress and/or fluid flow rate is greatest).

The header200comprises a first end206and a second end208that is opposite the first end206. The first end206is sealed to the outside (i.e., fluid from the outside cannot enter or leave the shell202via the first end206), while the second end208is in communication with an outlet port (not shown) that permits the evacuation of the header200to the outside. While theFIGS. 2A and 2Bdepicts a smooth linear variation in the cross-sectional area of the header and a smooth linear variation in the wall thickness from the first end206to the second end208, other variations may also be used. For example, the variation in either the cross sectional area or the thickness may be non-linear (e.g., curvilinear, varied according to an exponential or spline function, varied randomly in a discontinuous manner, or combinations thereof) according to the localized stress and/or fluid flow rate into the header. The inner surface218or outer surface220of the header200may be a continuously varying surface or it may be a discontinuously varying surface (i.e., one with variations that are similar to a step function), or it may be a combination thereof.

In one embodiment, the increase in the diameter and/or in the wall thickness of the shell is proportional to the local increase in the pressure experienced in different sections of the header and can be expressed by the equation (1) as follows:

d2d1=t2t1=p2p1,(1)
where d2, d1, t2and t1are indicated in theFIG. 2and where p2is the highest pressure and p1is the lowest pressure encountered in the different sections of the header.

In another embodiment, the change in diameter and/or the change in the wall thickness of the shell is proportional to a change in local pressure experienced in the shell and determined by the equation (1a):

Δ⁢⁢d2Δ⁢⁢d1=Δ⁢⁢t2Δ⁢⁢t1=Δ⁢⁢p2Δ⁢⁢p1,(1⁢a)
where Δd2is the change in the internal diameter of a second section of the shell, Δd1is the change in the internal diameter of a first section of the shell, Δt2is the change in the wall thickness of a second section of the shell, Δt1is the change in the wall thickness of a first section of the shell, where Δp2is the change in pressure experienced in the second section of the shell and Δp1is the change in pressure encountered in the first section of the shell.

In yet another embodiment, the increase in the diameter and/or in the wall thickness of the shell is proportional to the increase in the fluid flow rate experienced in different sections of the header and can be expressed by the equation (2) as follows:

d2d1=t2t1=f2f1,(2)
where d2, d1, t2and t1are indicated in theFIGS. 2A and 2Band where f2is the maximum fluid flow rate and f1is the minimum fluid flow rate encountered in the different sections of the header.

In another embodiment, a change in diameter and/or a change in a wall thickness of the shell is proportional to a change in fluid flow rate experienced in the shell and determined by the equation (2a):

Δ⁢⁢d2Δ⁢⁢d1=Δ⁢⁢t2Δ⁢⁢t1=Δ⁢⁢f2Δ⁢⁢f1,(2⁢a)
where Δd2is the change in the internal diameter of a second section of the shell, Δd1is the change in the internal diameter of a first section of the shell, Δt2is the change in the wall thickness of a second section of the shell, Δt1is the wall thickness of a first section of the shell, where Δf2is the change in the fluid flow rate experienced in the second section of the shell and Δf1is the change in the fluid flow rate encountered in the first section of the shell.

In one embodiment, in one manner of designing the header, Page: 8 it is desirable to maintain a uniform velocity or fluid flow rate along the length of the header. The flow rate or velocity is proportional to the cross sectional area of the header, and is therefore proportional to the square of the internal diameter of the header as shown in the equation (3).

f1f2=A1A2=d12d22(3)
where f2is the fluid flow rate experienced in the second section of the shell and f1is fluid flow rate encountered in the first section of the shell, A1and A2are the cross-sectional areas of those portions of the shell that encounter the fluid flows f1and f2respectively, while d1and d2are the respective internal diameters of the header at those portions of the shell that encounter the fluid flows f1and f2respectively.

The thickness of the header is varied to maintain uniform stress due to the pressure in the header. The stress is equal to the product of pressure and diameter, divided by thickness. In other words, the stress is proportional to diameter but is inversely proportional to thickness as shown in the equations (4) and (5).

σ=p*dt(4)
where p is the pressure in a given portion of the header, d is the internal diameter of the header and t is the wall thickness of the header.

σ1σ2=p1*d1*t2p2*d2*t1(5)
where d2is the internal diameter of a second section of the shell, d1is the internal diameter of a first section of the shell, t2is the wall thickness of a second section of the shell, t1is the wall thickness of a first section of the shell, where p2is the pressure experienced in the second section of the shell and p1is pressure encountered in the first section of the shell and where σ2and σ1are the stresses encountered in the second section of the shell and in the first section of the shell respectively. From the equations (4) and (5), it may be seen that for a given pressure, the stress may be maintained constant by reducing the diameter and the wall thickness by the same amount.

TheFIG. 3is a front view of an exemplary embodiment that depicts the header200of theFIGS. 2A,2b and3with the exception that the cross-sectional area of the shell is increased from the first end206to the second end208in a step-wise manner. This increase in the cross-sectional area varies with the increase in the local pressure and/or the fluid flow rate as witnessed in the equations (1) and (2) above. As the cross-sectional area is increased, the wall thickness t is increased as well to compensate for the increases in the pressure and/or the fluid flow rate.

From theFIG. 3it may be seen that the cross-sectional area increases from d1to d2to d3and the wall thickness increases from t1to t2to t3as pressure increases from p1to p2to p3and/or the fluid flow rate increases from f1to f2to f3.

While the headers200in theFIGS. 2A,2B and3each have a single outlet at the second end208, there can be two or more outlets if desired. TheFIG. 5shows headers200that have the plurality of outlets. TheFIG. 4shows a comparative configuration for a header100having a plurality of outlets while theFIG. 5shows a shaped optimized configuration for the same header200having a plurality of outlets. In theFIG. 5, the cross-sectional area of the shell202is greatest near the outlets at the first end206and the second end208since these regions experience the highest pressures and/or fluid flow rates. The wall thickness at the outlet regions is greater than the wall thickness at other regions of the header. As noted above, the outlets located near the first end206and the second end208of the header are used to remove the fluid or vapor being conveyed by the header from the header200.

TheFIG. 6Ashows a comparative header along with a shape optimized header for a design having a central tee that serves as the outlet. TheFIG. 7Ashows a comparative configuration for a header100having the central tee while theFIG. 6Bshows a shaped optimized configuration for the same header200having a single outlet. The central tee212is used as an outlet in theFIG. 7Awhile it is listed as112in theFIG. 6A.

From theFIG. 7Ait may be seen that the cross-sectional area of the shell is greatest at the center of the header because this is the region where the pressure and/or the fluid flow rate is greatest. Similarly, the wall thickness is greatest at the center. The wall thickness of the shell is narrowest at the opposite ends206and208where the pressure and/or the fluid flow rate, is the lowest.

In the absence of tube (204) penetrations and/or any other penetrations into the wall of the header, the wall thickness is determined by the internal pressure that the header has to withstand during normal operation, or as defined by a fault case or other condition as defined by prevailing codes, standards or other design rules. This principle is generally applied to the wall thickness of regions where the tubes are affixed to the wall of the header as well. However, these regions can be weakened by the addition of the tubes to the wall. In addition, these regions see a greater amount of utility since all of the fluids that enter the header contact the tubes204. The fluids that enter the header also contact the region of the header around the tubes204because of the proximity of the region to the point of entry of the fluid. The regions where the fluid enters the header therefore gets weakened more rapidly than other regions of the header.

In one embodiment, the regions where the tubes204are affixed to the walls of the header200may be increased in thickness in order to provide additional reinforcement to a region that would normally be weakened due to the removal of material to provide paths for entry of fluid from the tubes to the shell. The reinforcement also provides a longer life cycle to a region that sees greater usage than other regions during the course of operation of the header. This increase in thickness is local and is undertaken only in an appropriate vicinity to those regions where the tubes204are fixedly attached to the header.

In one embodiment depicted in theFIG. 7B, the regions of the wall to which the tubes204are fixedly attached are thickened to locally compensate for material removed by forming penetrations for the tubes to communicate with the shell, or to overcome wear and degradation that occurs with increased usage. This increase in local thickness provides the header with increased life cycle performance while at the same time reducing the weight of the header and reducing material costs.

TheFIG. 6Bdepicts a cross section of a comparative header wall100at the point where the tube104contacts the wall of the shell102. The header wall100would normally have a thickness of t4if the tube104were not contacted to the header. In order to compensate for structural weaknesses because of the presence of the tube104, the thickness of the header wall100is increased to t5. This increase in thickness from t4to t5in a conventional header causes increases in material costs and in the weight of the finished header.

FIG. 7Bdepicts a cross sectional view of the wall of a shape optimized header200. In the shape optimized header200, the wall thickness for the header is t4except in an appropriate vicinity to those regions where the tube204is fixedly attached to the header, where it is increased to t5. This local increase in thickness ensures uniformity of stress in the header while actually decreasing the weight when compared with the weight of the comparative header of theFIG. 6B.

The shell of the header200may be manufactured from iron based alloys, nickel based alloys, tantalum based alloys, and titanium based alloys.

In one embodiment, in one method of manufacturing the shape optimized header, a shell in the form of a conical section having a smaller diameter d1(corresponding to the lower flow rate f1) and a larger diameter d2(corresponding to the higher flow rate f2) at an end opposed to the smaller diameter d1has its opposing ends sealed to prevent fluid from inside the shell from contacting the outside. An outlet (or an inlet—inlets can also serve as outlets) is then drilled or cut in a portion of the shell. The outlet is used to evacuate the shell of its contents. Holes are drilled in the shell to accommodate the tubes that discharge fluid into the shell.

In one embodiment, in one method of manufacturing a shape optimized header having a smooth increase in cross sectional area (from those portions of the header that experience lower pressure to those portions of the header that experience higher pressures), a roll of sheet metal (e.g., a scroll of metal) is held or fixed at one end while the opposite end is extended from the fixed end. The metal is extended radially outwardly from the center of the scroll in addition to being extended longitudinally so that with each turn of the sheet metal, the diameter of the header increases along with the length. When the length and the diameter have reached the desired limits, the overlapping sheets may be seam welded or riveted together to form the shell of the header. The ends of the header may be cut off to form two parallel ends. The ends of the header may be welded onto the shell. One end may be sealed against the outside, while the other end has an opening through which the contents of the header are removed for recycling or discharged to waste.

Since it is generally desirable to increase the wall thickness in the direction of increasing cross-sectional area, a scroll of sheet metal of gradually increasing thickness can be used to manufacture the header as described above. In producing a header (shell) from such a sheet, the thinnest section is held fixed while the thickest section of the scroll is extended outwardly away from the thinnest section to produce a shell of smoothly increasing cross-sectional area and increasing wall thickness as well.

Holes may be drilled in a surface of the shell in order to fixedly attach the tubes to the header. The tubes may be welded onto the shell as shown in theFIGS. 2-5above. In another embodiment, the tubes may be screwed into threads formed in the walls of the shell, or welded to the shell. In one embodiment, the shell may be optionally thickened in the local region surrounding the tubes by using techniques such as laser welding. Other techniques used for forming the header and for local reinforcing are conventional casting, spray casting, spray forming and powder metallurgy.

In another embodiment, in another manner of manufacturing a header where the cross-sectional areas increase in a step function manner as seen in theFIG. 3(from those portions of the header that experience lower pressure to those portions of the header that experience higher pressures), pipes (spools) of varying desired diameters and thicknesses are first cut and then welded or riveted together to form the header. The ends of the header and the tubes are then welded together to form the header.

In addition to achieving materials savings from shape optimization, the use of thinner walls and shells reduces thermal stresses and increase the life cycle and the durability of the header or other devices manufactured using these methods and principles. Another advantage is that the decreased diameter and wall thickness results in smaller weldments (fewer passes) to joins several spools to form a large header.