Indirect Heat Exchanger Pressure Vessel with Controlled Wrinkle Bends

This application claims the benefit of U.S. Provisional Patent Application No. 63/138,655, filed Jan. 18, 2021, and U.S. Provisional Patent Application No. 63/270,953 filed, Oct. 22, 2021, which are hereby incorporated herein by reference in their entireties.

This disclosure relates to indirect heat exchangers and, more particularly, to indirect heat exchangers having serpentine circuit tubes with multiple formed bends that convey a pressurized working fluid through the serpentine circuit tube and permit heat transfer between the working fluid inside of the serpentine circuit tube and a fluid external to the serpentine circuit tube. The working fluid and the external fluid may each be gas, liquid or a mixture of gas and liquid.

Heat exchangers are known that include direct heat exchangers and indirect heat exchangers. A direct heat exchanger transfers heat between a working fluid and another fluid via contact between the fluids. An indirect heat exchanger transfers heat between a working fluid and another fluid indirectly through a medium separating the fluids.

Various types of heat exchange apparatuses are known that include direct heat exchangers, indirect heat exchangers, or both. Known heat exchange apparatuses include open circuit heat exchange apparatuses such as open circuit cooling towers and closed circuit heat exchange apparatuses such as closed circuit cooling towers. Open circuit cooling towers may exchange heat between a working fluid, such as water, and an external fluid such as ambient air by distributing the working fluid onto fill. The working fluid is directly cooled by ambient air as the working fluid travels along the fill. Closed circuit cooling towers, by contrast, keep the working fluid separated from the external fluid.

Closed circuit heat exchanger apparatuses include closed circuit cooling towers for fluids, evaporative condensers for refrigerants, dry coolers, air cooled condensers, and ice thermal storage systems. These heat exchange apparatuses utilize one or more heat exchangers to transfer heat between a pressurized working fluid and an external fluid such as ambient air, an evaporative liquid, or a combination thereof.

For example, a heat exchanger apparatus may include a closed circuit cooling tower having an indirect heat exchanger pressure vessel including an inlet header that receives a pressurized working fluid, an outlet header, and an indirect heat exchange coil connecting the inlet and outlet headers. The indirect heat exchange coil may include one or more serpentine circuit tubes configured to transfer heat between the pressurized working fluid inside the indirect heat exchange coil and a fluid, such as an evaporative liquid, external to the indirect heat exchange coil. The inlet header receives the internal working fluid from an upstream component of the heat exchange apparatus and the outlet header collects the pressurized working fluid before the working fluid is directed to a downstream component of the heat exchange apparatus.

Indirect heat exchanger pressure vessels, which includes the inlet header, outlet header, and one or more serpentine circuit tubes, are required to withstand high pressures appropriate for the specific application and satisfy domestic and international engineering standards such as ASME Standard B31.5. For example, an indirect heat exchanger pressure vessel of a closed circuit cooling tower may be rated to withstand an internal pressure of 150 psig for fluids such as water, glycols and brines. As another example, the indirect heat exchanger pressure vessel of an evaporative condenser may be able to withstand an internal pressure of up to 410 psig or higher for typical refrigerants such as ammonia or R-407C. As yet another example, some evaporative condensers have indirect heat exchanger pressure vessels with internal pressure ratings of 1200 psig or greater for refrigerants such as CO.

Serpentine circuit tubes of indirect heat exchanger pressure vessels typically include straight lengths and bends connecting the straight lengths. The straight lengths of the serpentine circuit tubes are typically joined with bends of approximately 180 degrees or by compound bends having multiple bends, such as two 90 degree bends joined by a tube length. The serpentine circuit tubes may be stacked together during assembly of the heat exchange apparatus with the serpentine circuit tubes contacting one another, typically in the area of the return bends, and with the serpentine circuit tubes having a vertically staggered positioning.

Serpentine circuit tubes are often made by first forming an elongated tube from a long, flat strip of metal such as mild steel or stainless steel. The flat strip of metal is roll formed into a generally circular cross section and the longitudinal edges are welded together with a continuous, longitudinal weld to form a straight tube. In another approach, a seamless tube forming process is used to form the straight tube. The resulting straight tube may then be bent at spaced locations along the tube to form the tube into a serpentine shape with straight runs connected by bends. Tube bending is a complicated process and often utilizes a hydraulically, electrically, or manually-powered tube bender having a bend die, a clamp die, a pressure die, and optionally a mandrel and wiper die. The tube bender may be setup to form bends with any desired angle up to and including 180 degree bends, such as 80 degrees, 90 degrees, 100 degrees, or 180 degrees. As noted above, the return bends of a serpentine circuit tube may include compound bends each having two or more bends, such as an 80 degree bend and a 100 degree bend, connected by a length of straight tube.

To form a bend in a tube, the tube is fed into the tube bender and a portion of the tube is nestled in a recess of the bend die. The pressure die and clamp die, with recesses for the tube, are moved against the opposite side of the tube such that the pressure die is positioned to support the tube and the clamp die clamps the tube portion between the clamp die and the bend die. The tube bender then rotates or pivots the bend die and the clamp die through the desired bend angle. The pressure die moves forward as the bend die and clamp die pivot to support the tube and ensure the tube follows the profile of the bend die. Once the bend has been formed in the tube, the clamp die and pressure die retract from their clamped positions, the tube is fed forward until the next bend location of the tube is positioned in the tube bender, and the bend die, clamp die, and pressure die all move back to their initial positions. The bending process is repeated for each bend to be formed in the serpentine circuit tube. Some tubes are bent only once to form single-bend tubes, which commonly are referred to as hairpin or candy-cane tubes, that can be subsequently butt welded together.

The bending of a tube that is to receive a pressurized working fluid is a process that balances various considerations including performance, safety, and packaging criteria for a particular application. Further, unintended deformations in the tube wall during the bending process may lead to tube failures due to the pressure of the working fluid within the tube, corrosion of the tube, and/or a higher pressure drop of the working fluid through the tube. In some tube bending processes, an internal mandrel is advanced into the interior of the tube to support the tube wall during bending and a wiper die may be used to stiffen the tube wall at a trailing end of the inside of the bend to prevent unintended deformations in the tube. The internal mandrel may be a plug mandrel or may have one or more balls or rings, in which case the internal mandrel is referred to as a ball mandrel.

Tube bending generally involves the following parameters:

The dimensions are measured using a common measurement scale, such as inches or millimeters. These parameters are used to calculate the following two characteristic ratios:

Two other parameters that are featured in the bending process are the Outside Radius (OSR) of the bend, usually referred to as the extrados, and the Inside Radius (ISR) of the bend, usually referred to as the intrados.

The W and D ratios are further consolidated into a single factor that is indicative of the complexity of the bend. This factor is calculated as:

The values of W, D, and/or Cmay be used to determine whether a bend can be formed without an internal mandrel, called empty bending, or if an internal mandrel will be required, in which case the process is called mandrel bending. For mandrel bending, these ratios help determine whether the internal mandrel required should be a multiple ball, single ball or a simpler plug mandrel. Finally, these ratios help determine whether a wiper die will be required in combination with the internal mandrel. As an example, process recommendations for various bend complexities are shown in the table below:

It is typical to look up the W, D, and/or Cratios on industry standard tube bending charts to decide the type of bending process required. For example, to determine the process parameters to bend a tube with outside diameter of 1″ and a wall thickness of 0.05″ with a centerline radius of 2″, then the ratios W and D are:

An industry standard tube bending chart may recommend, in view of the W ratio of 20 and the D ratio of 2, that a regular pitch internal mandrel with 1 ball, supplemented with a wiper die, should be used.

Alternately, the Cfor the example bend above is:

Referring to the table above, this Cvalue also indicates that an internal mandrel is recommended, although a wiper die could be optional. The small differences in recommendations on mandrels and wipers are indicative of a certain amount of flexibility in bend configurations where tool design and tube material choices can sometimes compensate for the absence of an internal mandrel and/or wiper die.

The conventional bending charts used in industry and the bend complexity value (C) ranges discussed above are based on the assumption that the profile of the tooling groove formed by the bending and clamp dies, where the tube is seated during the bending process, is circular, complementing the shape of the round tube. However, bending tool design has made several advances in recent years and it is possible to design bend tooling with a composite radius in the tooling groove to compress and support the tube during the bending process and extend the range of empty bending up from a Cvalue of approximately 5 to approximately 12.

Beyond this, especially as Capproaches and exceeds 20, it becomes progressively more necessary to use internal mandrels and wiper dies to successfully bend the tube. The internal mandrel bending process has several disadvantages including that using a mandrel requires additional tooling which adds cost, may increase scrap if mandrels are not used correctly, may add to cycle time, and requires the use of lubricants which adds time and cost for the lubricant and subsequent environmental mitigation.

One issue as Capproaches and exceeds 20 is that the associated mandrel bending imposes a limit on the continuous length of the tube. Serpentine circuit tubes can be very long, up to 400 feet long for some applications. The physical limits on the length of the mandrel rod and setup mean that internal mandrels cannot be used to bend long, continuous serpentine circuit tubes with several bends. This forces a manufacturer to form one or two bends in short segments of tube, sometimes called candy canes, and then butt weld the tube segments together to create larger circuits. Not only does this involve additional labor and cost, but additional butt welds increase the possibility of leaks and may not be permitted in many applications due to the high operating pressure the serpentine circuit tube will experience.

Another issue that may arise as Capproaches and exceeds 20 is that the associated internal mandrel bending moves the neutral axis of the bend closer to the inside of the bend and may cause excessive thinning of the outside wall portion of the bend. Thinning of the outside wall portion of the bend may weaken the serpentine circuit tube such that the serpentine circuit tube cannot withstand the pressure of the working fluid for a particular application. Excessive thinning of the outside bend wall also creates variability in the process when forming the bends causing reduced quality in the bend areas.

The above issues make it desirable for a manufacturer to avoid the use of internal mandrels for tube bending. One way to avoid using internal mandrels for a tube with a given OD is to increase WT or increase CLR to a suitable value to bring the bend within the range of empty bending. Increasing the wall thickness (WT) may not be an option for manufacturers whose products do not require such relatively thick walls from an operational perspective. In certain cases, the thicker walls may increase the fluid side pressure drop, may make the products less thermally efficient, increase the weight of the assembly, and may increase the material cost of the serpentine circuit tube. Further, increasing CLR may not be an option where the serpentine circuit tube needs to fit in a given space for other operational considerations. Increasing CLR can also have negative impact on overall coil thermal and hydraulic efficiency in some cases.

In one aspect of the present disclosure, an indirect heat exchanger pressure vessel is provided that includes an inlet header to receive a pressurized working fluid, an outlet header to collect the pressurized working fluid, and a serpentine circuit tube connecting the inlet and outlet headers and permitting the pressurized working fluid to flow from the inlet header to the outlet header. The pressurized fluid may be, for example, water, glycol, a glycol mixture, ammonia, or COas some examples. The pressurized fluid may be a liquid such as water or a liquid/gas combination such as refrigerant liquid and refrigerant vapor. The serpentine circuit tube includes runs and a return bend connecting the runs. The return bend includes a controlled wrinkled portion including alternating ridges and grooves. The controlled wrinkled portion of the return bend provides a rigid structure that resists internal pressure during operation of the indirect heat exchanger pressure vessel. Further, the controlled wrinkled portion provides a constructive bend centerline radius that is larger than an actual bend centerline radius of the return bend. The larger constructive bend centerline radius reduces the bend complexity factor for the return bend compared to a return bend of a conventional serpentine circuit tube having the same outer diameter and wall thickness. Due to the reduced bend complexity factor, the return bend having controlled wrinkled portions may be bent without the use of an internal mandrel which simplifies the manufacturing process of the serpentine circuit tube.

The present disclosure also provides an indirect heat exchanger pressure vessel including an inlet header to receive a pressurized working fluid, an outlet header to collect the pressurized working fluid, and a serpentine circuit tube connecting the inlet and outlet headers to permit flow of pressurized working fluid from the inlet header to the outlet header. The serpentine circuit tube includes runs, a return bend connecting the runs, and tangent points at junctures between the return bend and the runs. The return bend includes a bend angle and a controlled wrinkled portion. The controlled wrinkled portion is spaced from the tangent points along the serpentine circuit tube and has an angular extent about an inside of the return bend that is less than the bend angle. In this manner, the controlled wrinkled portion may be formed using a bend die having corresponding controlled wrinkle-forming features for less than the entire intrados of the return bend to permit the serpentine circuit tube to be slid out lengthwise from the bend die and increases the rapidity at which return bends may be formed in the serpentine circuit tube. In one embodiment, the controlled wrinkled portion includes ridges having amplitudes that are smaller adjacent the tangents points and increase as the wrinkled portion extends away from the tangent points to reduce resistance to fluid flow through the return bend and reduce the internal fluid pressure drop at the return bend relative to a non-tapered or non-eased configuration of the wrinkle ridges.

In another aspect, an indirect heat exchanger pressure vessel is provided that includes an inlet header to receive a pressurized working fluid, an outlet header, and a serpentine circuit tube connecting the inlet header and the outlet header to facilitate flow of the pressurized working fluid from the inlet header to the outlet header. The serpentine circuit tube includes a pair of runs and a return bend connecting the runs. The return bend includes an inner portion having a sinusoidal wave pattern at an intrados of the return bend, the sinusoidal wave pattern including peaks and valleys. The inner portion of the bend includes an arc pattern intersecting the sinusoidal wave pattern, the arc pattern comprising peak arcs intersecting the peaks and valley arcs intersecting the valleys. The intersecting sinusoidal wave pattern and arc pattern provide a smooth, continuously curving side wall of the serpentine circuit tube which strengthens the return bend against internal pressure. In one embodiment, the sinusoidal wave pattern has one or more end portions with shallower peaks and valleys and an intermediate portion with deeper peaks and valleys to reduce the internal fluid pressure drop across the return bend compared to a sinusoidal wave pattern having a constant peak and valley size.

The present disclosure also provides a closed circuit cooling tower including an indirect heat exchanger comprising a plurality of serpentine circuit tubes having runs and return bends connecting the runs. The return bends include wrinkled bends having controlled wrinkled portions. The closed circuit cooling tower comprises a fan operable to generate airflow relative to the serpentine circuit tubes and an evaporative liquid distribution assembly configured to distribute evaporative liquid onto the serpentine circuit tubes. The closed circuit cooling tower further comprises a sump to receive falling evaporative liquid from the serpentine circuit tubes and a pump operable to pump evaporative fluid from the sump back to the evaporative liquid distribution assembly. The controlled wrinkled bends strengthen the serpentine circuit tubes to withstand internal pressure from the working fluid within the serpentine circuit tubes during operation of the cooling tower. The controlled wrinkled bends also provide a constructive centerline radius of the wrinkled bends that is larger than the actual centerline radius of the controlled wrinkled bends and provides a reduced bend complexity factor compared to a return bend of a conventional serpentine circuit tube having the same outer diameter and wall thickness. The reduced bend complexity factor permits the controlled wrinkled bend to be bent without the use of an internal mandrel which simplifies the manufacturing process of the serpentine circuit tube.

Regarding, an indirect heat exchanger pressure vessel such as a coil assemblyis provided that may be used in a heat exchange apparatus, such as an evaporative condenser, closed circuit fluid cooler, or an ice thermal storage system. The coil assemblyincludes an inlet header, outlet header, and serpentine circuit tubes. The serpentine circuit tubeseach include runsthat are connected with 180 degree bendsor compound bendsincluding two 90 degree bends,separated by a straight length. The serpentine circuit tubespermit working fluid to flow from the inlet header, through the serpentine circuit tubes, and to the outlet header.

Regarding, a heat exchange apparatus such as a cooling toweris provided that includes an outer structure, one or more fansincluding fan bladesand motor(s), a direct heat exchanger such as fill, and an indirect heat exchanger pressure vessel. The cooling towermay be an evaporative condenser, closed circuit cooing tower, or dry cooler heat exchanger as some examples. The indirect heat exchanger pressure vesselincludes inlet header, one or more serpentine circuit tubeswith circuit runsand bendsand outlet header. The inlet and outlet headers,may be reversed depending on the application. In some embodiments, the fillis above the indirect heat exchanger pressure vesseland/or the fillis located between runs of the serpentine circuit tubes.

Regarding, the cooling towerincludes an evaporative liquid distribution systemincluding a spray assemblyhaving spray nozzles or orificesthat distribute an evaporative fluid, such as water, onto the serpentine circuit tubesand the fill. The evaporative liquid distribution systemincludes a sumpfor collecting evaporative fluid from the filland the coiland a pumpthat pumps the collected evaporative fluid through a pipeto the spray assembly. The cooling towerfurther includes one or more air inlets, inlet louverswhich keep the evaporative liquid from leaving cooling tower, an air outlet, and an eliminatorto collect water mist from the air before the air leaves the air outlet. The fanis operable to generate or induce air flow upwards relative to the serpentine circuit tubesand the fill. In other embodiments, the cooling towermay have one or more fans configured to induce airflow in upflow, downflow, or crossflow directions relative to the indirect heat exchanger and/or direct heat exchanger of the cooling tower.

Regarding, a serpentine circuit tubeis provided that may be utilized with a heat exchange apparatus, such as the coil assemblyin, or the cooling towerdiscussed above with respect to. The serpentine circuit tubeincludes an internal passagewayand a tubular side wallextending thereabout. The serpentine circuit tube includes an end portionthat may be connected to an inlet header and an end portionthat may be connected to an outlet header. Depending on the application, the end portionmay alternatively be connected to an outlet header and the end portionmay be connected to an inlet header. The serpentine circuit tubeincludes runs, such as runs,, and bends. In one embodiment, the runsmay be parallel. In other embodiments, one or more of the runsextend transversely, e.g., sloped, relative to one another to allow for internal fluid draining. The serpentine circuit tubemay be self-draining such that any liquid in the internal passagewaytravels down toward the end portionunder the effect of gravity. The material of the serpentine circuit tube, outer diameter of the serpentine circuit tube, wall thickness of the side wall, number of runs, length of runs, number of bends, angular extent of bends, centerline radius of the bends, and intrados/extrados of the bendsmay be selected for a particular heat exchange apparatus. As another example in this regard, instead of a single angle bendconnecting a pair of runs, the serpentine circuit tube may have one or more bendsthat each include a pair of bends, such as 90 degrees, connected by a straight segment similar to the compound bendshown in. The runsmay have circular cross-sections throughout the runs. In other embodiments, the serpentine circuit tubeincludes one or more runswith non-circular cross-sections such as cross sections that are elliptical or obround.

The serpentine circuit tubemay be formed from a single straight tube that is bent at spaced locations along the tube to form the bends. The serpentine circuit tubemay be formed by progressively roll forming an elongated strip of material into a tubular shape and welding longitudinal edges of the elongate strip together to form a single weld running along the length of the serpentine circuit tube. In another approach, the serpentine circuit tubemay be made from a plurality of separately formed components. For example, the runsmay be separate components that are welded to the bends. Alternately the serpentine circuit tubemay be formed by welding separate lengths of tube together and then bending the longer welded tube. The serpentine circuit tubemay be made of a metallic material, such as carbon steel or stainless steel.

Regarding, each bendincludes an intrados, an extrados, and a controlled wrinkled portionof an insideof the bendand a smooth outer surfaceat an outsideof the bend. The controlled wrinkled portionincludes a continuously curving and controlled wrinkled surfaceof the ridgesand the grooves. The continuously curving controlled wrinkled surfaceis uninterrupted by edges, corners, or flats to avoid localized areas of stress. The continuously curving and controlled wrinkled surfaceis shaped by ridgesand groovesof the bendthat are, in turn, defined at least in part by an intersecting sinusoidal wave patternand an arc patternas discussed in greater detail below with respect to. The bendshown inhas a 180 degree bend angle. When the subject disclosure refers to a particular bend angle of a bend, it is intended that the bend angle is an approximate value, such as +/−5 degrees. In some embodiments, all of the bendsof the serpentine circuit tubehave controlled wrinkled portions. In other embodiments, fewer than all of the bendshave controlled wrinkled portions.

The serpentine circuit tubehas a tube center lineextending through the runs,and in the bend. The controlled wrinkled portionis radially inward from the tube center lineand separated therefrom by a side surface portion. The smooth outer surface portionand the side surface portionpermits the bendto be stacked with bends of other serpentine circuit tubes in conventional arrangements as would a prior art tube having a smooth inner bend.

Referring toat the intradosof the bend, the controlled wrinkled portionhas a sinusoidal wave patternat the intradosof the bendas discussed below with respect to. The wrinkled portionincludes an alternating series of ridgesand grooves. In one embodiment, the bendhas relief portions,intermediate the sinusoidal wave patternand tangent points,between the runs,and the bend. The relief portions,facilitate provision of a controlled wrinkled portion anglethat is less than a bend angleas discussed in greater detail below. The relief portions,extend from the tangent points,to points,. The wrinkled portionfurther includes tapered lead-in portions,extending between points,and points(see) wherein the sinusoidal wave patternbegins and ends. In one embodiment, the relief portions,each have a first radius and the tapered lead-in portions,each have a smaller, second radius. The sinusoidal wave patternstarts at one point, extends through a peakof the end ridge, undulates through the ridgesand grooves, extends through a peakof the end ridge, until reaching the other point.

The ridgesinclude end ridges,that optionally have tapered lead-in portions,. The tapered lead-in portions,provide a smooth transition between the relief portions,and the sinusoidal wave pattern. The tapered lead-in portions,smooth flow of the working fluid through the bendand assists the material of the bendto flow during bending. The tapered lead-in portions,, ridges, and groovesreduce the internal fluid pressure drop caused by the working fluid flowing through the bend. Further, the tapered lead-end portionfacilitates better draining of the serpentine circuit tube. The bendmay have both tapered lead-in portions,if the working fluid may flow through the bendin either direction,. If the working fluid will only be flowing through the bendin one direction,, the bendmay have only one tapered lead-in portion,.

Regarding, a cross-sectional view of a bend′ is provided that is similar to the bendand has a sinusoidal wave pattern′ at a midline of the bend′. The bend′ has ridges′ and grooves′ that vary in amplitude around the bend′. Specifically, the ridges′ and grooves′ closer to runs′,′ have small amplitudes and the ridges′ and grooves′ near a middle of the bend′ have larger amplitudes. For example, ridgesA′,B′ have larger amplitudes than ridgesC′,D′. The more gradual increase in the amplitude of the ridges′ and grooves′ provide a reduced resistance to fluid flow through the bend′ such that the bend′ has a reduced pressure drop across the bend′ compared to the bendin some applications. The more gradual increase in the amplitude of ridges′ and grooves′ may also reduce stress in the material of the bend′ during the bending operation compared to the bendin some applications. In other embodiments, the amplitude of the sinusoidal wave pattern of the bend′ may increase from adjacent one run connected to the bend′ to adjacent the other run connected to the bend′.

Regarding, a cross-sectional view of a bend″ is provided that is similar to the bendand has a controlled wrinkled portion″ with a sinusoidal wave pattern″ at an intrados of the bend″. The controlled wrinkled portion″ includes ridges″ and grooves″. The controlled wrinkled portion″ includes a first portion″ having ridges″A, B and grooves″A, B with a first amplitude and a first period″. The controlled wrinkled portion″ includes a second portion″ having ridges″C, D and grooves″C, D with a second amplitude greater than the first amplitude. The ridges″C, D and grooves″ C, D have a second period″ that is less than the first period″. The controlled wrinkled portion″ further includes a third portion″ having ridges″E, F and grooves″E, F with a third amplitude that is substantially the same as the second amplitude of the second portion″ and a third period″ that is less than the second period″. The bend″ receives fluid in direction″ and the ridge″A includes a tapered lead-in portion″ to smooth fluid flow through the bend″. The tapered lead-in portion″ reduces pressure drop across the bend″ and improves draining of fluid in the bend″.

The characteristics of the sinusoidal wave patternutilized for a given return bend may be selected for a particular application. For example, the number of ridges/grooves, amplitude, period, and/or one or more tapered lead-in portions may be selected for a particular application. The characteristics of the return bend may vary throughout the return bend, such as the amplitude and period varying throughout the return bend. The shape of the controlled wrinkled portionas formed at least in part by two different intersecting cross-sectional profiles. Regarding, the controlled wrinkled portionincludes a sinusoidal wave portionat the intradosof the bend. The other pattern is an arc patternthat includes alternating peak arcsand valley arcs. Referencing, the peak archas a peak arc radius′ and a centerand the valley archas a valley arc radiusand a center. In this embodiment, the peak arcand valley arcare substantially the same. As used herein, the term substantially the same refers to dimensions that are effectively the same when taking manufacturing variation into account, such as within +/−10% of one another. The peak arcextends through an anglethat is greater than an anglethrough which the valley arcextends.

Returning to, the valley arcforms a valley semicircular inner wall portionhaving the valley arc radiusand the center. Opposite the valley semicircular inner wall portion, the bendincludes an outer wall portionthat may be semicircular. In some embodiments, the outer wall portionmay be curved with a flattened portion due to extrados(see) of the bendbeing tensioned during the bending process. The bendincludes connecting wall portions,that connect the valley semicircular inner wall portionto the outer wall portion. The connecting wall portions,have a curvature that may be dissimilar from the inner and outer wall portions,. The connecting wall portions,provide a smooth transition between the geometries of the inner and outer wall portions,to minimize stress concentration at the junctures between the geometries of the inner and outer wall portions,. By reducing stress concentration at the juncture between the geometries of the inner and outer wall portions,, the connecting wall portions,assist in the bendbeing able to withstand high internal operating pressure.

Regarding, the peak arcdefines a peak semicircular inner wall portionhaving the peak arc radiuswith the center. The bendhas an outer wall portionopposite the peak semicircular inner wall portion. Like the outer wall portion(see), the outer wall portion may be semicircular. In some embodiments, the outer wall portionmay be curved with a flattened portion due to the extrados(see) of the bendbeing tensioned during the bending process. The bendfurther includes connecting wall portions,connecting the peak semicircular inner wall portionand the outer wall portion. Like the outer wall portion, the outer wall portionmay have a semicircular shape or generally curved shape in some embodiments. Further, the connecting wall portions,provide a smooth transition between the geometries of the inner and outer wall portions,to minimize stress concentration at the junctures between the geometries of the inner and outer wall portions,. The connecting wall portions,contribute to the ability of the bendto withstand high internal operating pressure. The peak arcand valley arcmay each have a respective single radius as shown in. In another embodiment, the peak arcand/or the valley archas a compound or composite radius. For example, and with reference to, the peak arc′ has different radiiA′,B′. Each radius of the peak arc′ is tangent at the point where the radius joins an adjacent radius. Likewise in, the valley arc′ has different radiiA′,B′.

In another embodiment, the peak arcand/or the valley archas a shape that is a portion of an ellipse. For example, the peak arc″ ofis an arc defined by an angle of″, such as 160 degrees, between points″,″ of an ellipsehaving a major dimensionand a minor dimension. Similarly, the valley arc″ inhas a shape that is defined by an angle″, such as 142 degrees, between points,of an ellipsehaving a major axisand a minor axis.

Regarding, the runis shown with the side wallhaving a circular cross-section with a center at the tube center line. Side wallmay also have a non-circular cross section such as elliptical or oblong cross-section. The side wallof the serpentine circuit tubehas a wall thicknessthat extends about the inner passageway.