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We evaluate differences in clear-sky upwelling shortwave radiation reaching the top of the atmosphere in response to increasing the albedo of roof surfaces in an area of India with moderately high aerosol loading. Treated (painted white) and untreated (unpainted) roofs on two buildings in northeast India were analyzed on five cloudless days using radiometric imagery from the IKONOS satellite. Comparison of a radiative transfer model (RRTMG) and radiometric satellite observations shows good agreement (R2 = 0.927). Results show a mean increase of ∼50 W m−2 outgoing at the top of the atmosphere for each 0.1 increase of the albedo at the time of the observations and a strong dependence on atmospheric transmissivity.

Pressure vessels mounted on four-leg type supports form a non-isotopic support system with respect to lateral loads or overturning moments. Several loadings—for example, horizontal earthquake motions and wind loads—do not have a predefined direction of action. Structural safety analysis requires the determination of the most vulnerable direction of loading for the structure. Closed-form expressions for these loadings under certain conditions are derived in this paper. The importance of ‘optimality’ with respect to the developed stress in the support is illustrated via a numerical example.

Some basic relationships to characterize tubular heat exchanger thermal performance are derived in terms of the well-known state variables. It is shown that the knowledge of η (NTU), R (heat capacity rate ratio), and partial derivatives of the temperature efficiency P with respect to η and R enables complete characterization of the exchanger performance around an operating point. Thus, the exchanger performance can be readily predicted for the so-called “subdesign” conditions. Likewise, additional criteria to compare various exchanger styles for a given range of operating conditions can be developed. Two such criteria are developed in this paper.

Functional relations are derived to determine the reduction in the heat duty of a multipass heat exchanger due to tube-side fluid bypass. A simplified structural model of the channel cover is constructed to determine the interpass leakage due to cover deflection under pressurized (operating) conditions. A numerical example shows that design rules based on stress limits are adequate to keep interpass leakage within tolerable limits.

The mathematical problem of minimizing gross solids entrainment in an n-stage evaporator is formulated and solved using the method of Lagrange multipliers. The solution procedure enables direct comparison of the decontamination efficiencies of multistage evaporators as the number of stages (n) is varied. A numerical example is utilized to illustrate the method of solution. Equivalent expressions for batch distillation are also derived.

An expansion joint is normally employed to alleviate the tube axial load in fixed tubesheet heat exchangers. Incorporation of an expansion joint usually results in increased tubesheet thickness and hence increased cost of hardware. A design strategy to simultaneously reduce both tubejoint load and tubesheet stress in the heat exchanger (without the usual recourse of expansion joints) is presented in this paper. The range of application and practical feasibility of this concept is also discussed.

The formulation for “Three Element Bolted Joints” pertinent to removable bundle U-tube Heat Exchangers developed in an earlier work is herein extended to compute inter-tube-pass leakage rates. Design concepts aimed to reduce the leakage flows are proposed and their impact on the stress fields in the structural elements (tubesheet and flanges) is studied. Evaluation of stresses in the tubesheet and mating flanges in a typical example problem reveals potentially severe inadequacies in the existing design codes and standards. Practically feasible remedial design measures are proposed and examined as to their merits and limitations. In particular, the concept of “controlled” metal-to-metal contact beyond the bolt circle, introduced in an earlier work, is explored in depth. Effective use of this concept is shown to significantly alleviate stresses in the elements of the joints.

Governing equations for heat transfer in a split flow heat exchanger with two tube passes are developed and solved. The expressions for the “temperature efficiency” P and “LMTD temperature correction factor”, F are derived. F and P values for two tube pass and four tube pass are compared over the practical range of values of thermal flow rate ratio R and reduced thermal flux, η (NTU).

An analytical method is herein developed to evaluate the stress field in the critical regions of a U-tube subject to differential thermal expansion. The solution is intended to be used as a design tool to conveniently study the variation of geometric parameters on the U-tube stress distribution. Those design variables which have significant effects on the structural characteristics of the U-tube are identified by an in-depth study of a typical example problem. Some effective design remedies are also discussed.

Obround cross sections find extensive industrial use in pressure vessels and pipings. Yet guidelines for their design are not available in the published literature. The obround shape is inherently unsuitable to withstand internal pressure. Support gussets must be added to such pressure vessels to render their use economical. This paper gives a method to efficiently design a pressurised obround cross section by determining the appropriate gusset plate locations, and the associated bending stresses. Formulae to design the obround flanged end closures are also given.

Seismic analysis of free standing submerged racks is complicated by the presence of water and structural non-linearities such as fuel assembly cell impact and floor interface friction. A direct time integration technique has been proposed to analyze this class of structures. Application of the time integration technique on a fourteen degree of freedom lumped mass model of the rack reveals some heretofore unpublished quirks in the structure's behavior. The method of analysis is utilized to compare the seismic response of some representative rack designs. Results show wide differences in the structural response, depending on the fabrication details of racks.

The basic criteria are derived in determining whether the heat transfer relationship for a given heat exchanger geometry is invariant to the interchanging of shell-side and tube-side fluids. It is shown that the total heat duty, LMTD correction factor, and other indices of exchanger performance remain unchanged for a stream-symmetric exchanger when the two flow streams are switched, provided the overall heat transfer coefficient is not changed.

A simplified design procedure is presented to determine tubesheet thickness in U-tube, floating-head, and fixed-tubesheet shell-and-tube exchangers. The procedure is based on classical plate-and-shell theory and permits a design code-oriented manual solution procedure. The configuration analyzed includes an unperforated rim, three different tubesheet head-shell-joint configurations, and arbitrary material properties for each component. Thermal loading due to differential radial expansion and the effect of local pressures acting on the head and shell walls are included.

A method for computing the thickness of a tubesheet extension (rim) used as a flange is proposed. The method treats both fixed and floating-head stationary tubesheets and U-tube tubesheets. Numerical examples illustrate the calculation method.

From the standpoint of flow induced vibrations, U-bends of tubular heat exchangers constitute structurally one of the most vulnerable regions. The U-bends possess relatively low out-of-plane frequency enabling them to extract energy from the shell stream at low flow velocities. All published correlations in the literature imply the existence of a direct relationship between the flow velocities and the incidence of large ampitude tube vibrations. Hence it is important to determine the velocity profile in the U-bend region accurately. A method to obtain an engineering solution is proposed herein which may be utilized in conjunction with the available correlations to reliably predict the possibility of vibration. Determination of the flow profile may be further utilized to improve the estimates of shellside heat transfer coefficients.

Saddle supports of horizontally mounted pressure vessels, when subject to seismic and mechanical loads, interact with the foundation in a highly non-linear manner. The maximum foundation concrete pressure, and hold-down bolt stresses are important design considerations which often govern the vessel support geometry. A method is given herein to determine the foundation stresses due to arbitrary imposed loadings. The solution procedure lends itself easily to automated computation—a highly desirable feature—since most nuclear equipment has to be analyzed for a large number of loading conditions.

In many heat exchange applications, intermingling of shellside and tubeside fluids may cause undesirable results, not the least of which may be safety related. Therefore, prevention of any fluid leakage between shell side and tube side of shell and tube heat exchangers becomes a prime design consideration. One method to inhibit mixing of component fluids is to employ double tubesheet construction. Double tubesheet construction has been used in submarine systems primarily for safety reasons. In commercial applications, double tubesheet designs in standard heat exchangers have been used for a variety of reasons, such as the case where mixing of shell and tube side streams could lead to an explosive mixture. In recent years, double tubesheet construction has also been found in large power plant condensers. In the condenser application to large rectangular tubesheets, the primary concern has been prevention of contamination of treated and demineralized water due to the leakage of circulating water (raw water) into the condenser steam space.

Supports for heat exchangers and pressure vessels have remained largely beyond the pale of any governing codes. Whereas detailed rules for the design of the pressure parts have been available in the ASME Boiler and Pressure Vessel Codes for several decades [17.1.1–2], support design has received scant attention. Until recently, sizing of supports was generally left to the empirical judgement of the vessel designer. Since stresses due to dead weight, in most situations, amount to only a fraction of pressure-induced stress in the vessel, the effect of dead weight stress was deemed not critical. This situation changed radically with the advent of the commercial nuclear power industry. Equipment supports designed for use in nuclear power plants had to be checked for seismic loads, mechanical loads from attached piping, etc. Increased concerns about equipment reliability have resulted in the spillover of some of the nuclear power industry analysis requirements [17.1.3] into other sectors viz. fossil power, chemical, petrochemical and pharmaceutical industries. This chapter presents some introductory material and design data on sizing pressure vessel supports. Detailed treatment of specific support styles are found in subsequent chapters.

A wide range of industries — pharmaceutical, chemical, petrochemical, dairy, food, refrigeration, bio-chemical, fossil and nuclear power, etc. — utilize tubular heat exchangers. Exchangers have been given a variety of names depending on their heat transfer functions; viz. kettle reboiler, condenser, thermosiphon reboiler, regenerator, recuperator, blow-down heat exchanger, heating element, and so on. These names serve to identify the heat transfer function of the hardware, and in many cases, also conjure up the image of the shape and appearance of the unit. In most instances, thermal design considerations dictate the external appearance of the unit. Rating engineers recognize that boiling, partial or total condensation, highly viscous flows, etc., are considerations which may profoundly affect the desirable shape of the heat exchanger. Books covering thermal design of heat exchangers must labor through the maze of heat transfer conditions which might exist in an operating unit. The picture from the mechanical design viewpoint, however, is far more unified.

Discussion of the detailed anatomy of the heat exchanger and the methods to devise analysis-aided designs have been the primary focus of the material presented up to this point in the book. The evolution of a high quality design, however, requires the interplay of practical considerations with mathematical analysis. The designer must give sufficient thought and consideration to practical matters such as integration of the equipment in the available plant space, equipment maintenance, in-service inspection, handling, and repair. While the equipment design specification prepared by the owner/user seeks to serve the function of familiarizing the designer with the overall plant needs, the breadth and depth of information found in the “specs” varies considerably. The material provided in this chapter is aimed to provide the designer with an overview of these “trans-design” topics. Engineers engaged in specification development, and plant personnel responsible for heat exchanger inspection and maintenance, will also find the information presented here useful in their work.

In the preceding two chapters, several topics concerned with flanges have been discussed. The previous analyses have considered the gasket as a lineal element located at a particular radial position. For the most part, the effect of non-linear gasket material behavior has been neglected in all previous analyses. This chapter focuses on development of an analysis method which can be applied to flanges with either full face gaskets or ring type gaskets. The proposed method also permits inclusion of non-linear gasket material behavior. The procedure assumes use of a computer to effect the solution; as such, the method may not be directly suitable for inclusion in any design code that is intended to supply simple formulas for the designer’s use. However, we will show that it certainly has value as a design tool.

Fixed and floating head heat exchanger constructions find widespread application in the power and process industries. Fig. 9.1.1 shows a typical vertically mounted unit. We have included on that figure the nomenclature to be used in subsequent derivations. The response of the two tubesheets to external mechanical and/or thermal loading is not independent; the tube bundle provides a load transfer mechanism between the two tubesheets. A rigorous analysis of the unit, to determine tubesheet thicknesses, must consider the effects of coupling between the tubesheets when determining the stress and deformation in the tubesheets, tubes, shell, and channels. Unfortunately, the analysis becomes significantly more difficult to carry out compared to the analysis for U-tube heat exchanger tubesheets discussed previously.

Pressure vessels require flanged joints to permit their disassembly, in-spection and cleaning. Bolted joints are also utilized to alleviate stresses at sections where sharp temperature changes occur, such as the joint between tubeside and shellside chambers in a heat exchanger (Fig. 3.1.1). From a conceptual standpoint, flanged joints may be subdivided into two major categories.

A central goal in the thermal design of tubular heat exchangers is to utilize the available shellside pressure loss to maximize the shellside film coefficient. The most effective means of accomplishing this objective is to arrange the shellside fluid to flow across the tube bank. Single segmental baffles (Fig. 1.4.5) provide the nearest practical alternative to a pure cross flow arrangement. Due to its ability to actuate maximum heat transfer rate for available pressure loss in a minimum amount of space, the single segmental baffle design has become a standard construction detail. Early texts on heat exchanger rating methods [16.1.l–2] acknowledged the dominance of the single segmental baffle design. It was not until the ’60’s, when widespread failure of tubes began to occur [16.1.3], that another consequence of shellside cross flow — flow induced vibration — came to the fore. In retrospect, relatively high fouling factors used in the petrochemical, chemical, and process industries had indirectly prevented uncovering of the vibration problem. High fouling factors specified by the user blunted the heat exchanger designer’s motivation to maximize the shellside coefficient by maximizing cross flow velocities. Lower fouling factors, coupled with greater flow rates used in the power industry, removed this disincentive. Moreover, the specified pressure loss in power plant heat exchangers also tended to be greater. Conventional wisdom held, correctly so, that higher cross flow velocity (in the absence of erosion related problems) produce better operating heat exchangers by reducing the deposition rate of crud and debris on tube surfaces. Designers have since learned that ignoring the effect of increased cross flow velocity on tube vibration failure can be an expensive mistake. It is indeed true that sporadic failure of tubes in operating heat exchangers occurred even before the ’60’s. However, the significance of flow induced vibration on heat exchanger reliability did not attract sufficient attention until tube failures became commonplace, particularly in the power industry. Finally, it should be added that parallel flow has also been reported to be responsible for some tube failures. However, even in ostensibly parallel flow induced failures, cross flow components of the turbulent stream have been held responsible by some investigators [16.1.4]. From a practical designer’s point of view, the design focus should rightfully rest on the cross flow component of the flow velocity.

Design data for preliminary sizing of saddles for heat exchangers and pressure vessels was presented in Chapter 17. Saddle mounting is particulary preferable for heat exchangers where frequent tube replacement, or bundle or shell removal, is necessary. Horizontal mounting of the unit, however, suffers from the drawback of requiring additional “tube pull out” space at one end of the heat exchanger. Some of this loss of the available equipment mounting space can be made by stacking the units as shown in Photograph 19.a.

In previous chapters dealing with tubesheet stress analysis, we have focused exclusively on circular units and we have assumed that tubesheet geometry, loading, and edge conditions did not vary around the periphery. These restrictions permitted us to develop considerably detailed analytical models, leading either to numerical solution procedures, or to simplified, almost closed form, analytical solutions. Since the large majority of tubesheets are of circular shape, these analyses and solution methods have wide applicability. Tubesheets of non-circular shapes, however, are also used, particularly in low pressure, large volume flow rate conditions. Specifically, in this chapter, we will focus on the class of rectangular tubesheets used in large power plant condensers. We will provide a detailed discussion of the loading conditions and the geometry to highlight the complexities that obstruct the effort to obtain a satisfactory simplified solution. In the next section, we will first fully describe the power condenser tubesheet environment and provide an overview of the tubesheet design problem. Following this introductory material, we will present a very approximate design method, based on the theory of a beam strip on an elastic foundation. This approximate analysis, although replete with assumptions, both substantiated and unsubstantiated, at least permits investigation of the effect of various tubesheet parameters. We will fully develop the approximate method and show an application of it to the condenser tubesheet design problem.

Heat exchangers and pressure vessels are frequently mounted vertically to economize plant floor space. In some cases, the process function of the hardware requires vertical installation. For example, gravity driven boiling in a thermosiphon reboiler, or fractionation in a distillation column, can proceed only if the equipment is vertically installed. As discussed in Chapter 17, the supports may consist of a skirt, a set of lugs, or a ring-type structure at (or near) the bottom and a lateral restraint near the top. Photograph 20.a shows a skirt mounted unit with a lateral support at the top. Figure 20.1.1 shows a skirt mounted unit without a top lug. Preliminary design data on sizing supports for vertical mounting is given in Chapter 17. However, it is subsequently necessary to determine the adequacy of the preliminary design for external loads. The external loadings on such equipment arise from various sources such as from wind load, from seismic motion, and from reactions due to attached piping. In its most simplified form, a seismic loading is specified as a set of static inertial accelerations in three orthogonal directions (two horizontal and one vertical). A precise specification of loads on the vessel nozzles from inter-connecting piping is more problematic, since piping design is usually not complete at the time of equipment procurement. This problem is usually circumvented by postulating a set of loads for each nozzle and by requiring that the plant designer route the piping to maintain the loads on the equipment-piping interface to within these limits. Thus the process of equipment and piping design can proceed concurrently. The piping load can be prescribed in terms of six vectorial components; three forces and three moments. The sense of action of these loads is not specified.

In the preceding three chapters we studied the characteristics of bolted joints where the axial separating force due to internal pressure is counteracted by preloading the bolts. The bolts must have sufficient “pull” to oppose the axial pressure load, and to provide sufficient residual pressure on the gasket to effect the seal. Such bolted joints find wide use in the pressure vessel industry from low pressure to medium pressure applications. Since the thickness of the flat cover increases directly in proportion to the product of the shell diameter and the square root of the pressure, bolted flange closures become quite heavy and unwieldy as the pressure and diameter of the vessel increase. The number and diameter of bolts required to provide the necessary preload (Section 3.7) may exceed what can be arranged on the minimum circumferential pitch (set to accommodate a box wrench) on the bolt circle. This may necessitate two bolt circles, increased moment arms, and therefore, even heavier designs. It may be advisable, therefore, to explore “boltless” flange design “whenever the pressure/diameter combination is such that the shell thickness exceeds 1.5”.

Three element bolted joints consisting of an unstayed tubesheet, sandwiched between two tapered hub flanges, find extensive use in the heat exchanger and pressure vessel industries. For example, removable bundle U-tube heat exchangers, denoted as “BEU” in the lexicon of the heat exchanger trade [4.1.1] utilize this joint detail (Fig. 4.1.1). Figure 3.1.1 shows another application of this joint in a “pull through externally packed” construction. In view of its widespread use, we focus our attention on this joint in some depth and present a technique for performing a detailed stress analysis. The need to evolve a comprehensive solution for this class of joints is particularly important, since a standard application of the code design methods may produce grossly erroneous results for the low pressure side flange. The 1983 issue of the ASME Code [4.1.2] recognizes the quirks in the structural behavior of such joints, but offers no detailed solution.

The tubesheet constitutes a structurally important and economically significant element in a tubular heat exchanger. The thickness of the tubesheet affects the hardware cost in a number of ways. The time spent to drill and to ream the tube holes is directly related to the tubesheet thickness. The portion of the tube length lying within the tubesheet is effectively lost for heat transfer and must be replaced by increasing the tube (and hence the unit) overall length. The depth of the tube roll is also dependent on the tubesheet thickness; typically, the depth of the roll is specified as the tubesheet thickness less 1/8 in. Although some industry standards provide for limiting the maximum roll depth to 2 in., many process conditions warrant complete elimination of the stagnant annulus between the tube and the tubesheet on the shellside which necessitates a full depth roll. All of these factors pertaining to the tubesheet have a bearing on equipment cost.

The tubular heat exchanger, being a device to transfer heat between two fluids at different temperatures, is a natural candidate for thermal expansion related problems. Indeed thermal stresses merit careful analysis in the design of all kinds of heat transfer apparatus. In shell-and-tube exchangers, the thermal stress problem usually stems from the differential expansion between the shell and the tubes. The tubes are in (turbulent) contact with both fluids undergoing the heat transfer process, whereas the shell is in contact with the shell-side fluid only. The resultant differential expansion between the shell and the tubes, sometimes abetted by the difference in the thermal expansion coefficients of the tube and the shell materials, is a major source of structural problems in fixed tubesheet heat exchangers. Chapter 9 deals with the methods to predict the stress field in fixed tubesheet exchangers. As stated in Chapter 1, this drawback of the fixed tubesheet design is eliminated by resorting to U-tube construction, wherein the longitudinal expansion of the shell is physically isolated from that of the tubes. This inherent feature of U-tube design has fostered the mistaken belief that U-tube designs are immune from axial thermal expansion problems. While the relative differential expansion between the shell and the tube bundle is certainly eliminated as a potential design problem in the U-tube construction, the thermal stress problem now manifests itself in the tube bundle. The straight tube segments in different tube passes are, in general, subject to different flow patterns and to different fluid temperatures. As a consequence, the two constituent legs of a U-tube expand or contract by unequal amounts. Since the U-tubes are clamped (“built-in”) at the tubesheet for all intents and purposes, the semicircular bends at the rear end of the bundle must absorb most of the differential expansion between the adjoining legs. Often, the attendant stresses are quite high.

A variety of methods are used for making the joint between the tubesheet and the tubes. The joining technique must lend itself to mass production and to uniformity of quality. The most common attachment techniques are: (i) Roller expansion (ii) Hydraulic expansion (iii) Impact welding (iv) Edge welding (v) Butt welding

Closures for heat exchangers and pressure vessels are either in the form of flat covers (Chapter 12) or formed heads. The latter is the subject of this chapter. TEMA [13.1.1] designations “B”and “M”,respectively, refer to formed head front and rear closures (Table 1.3.1). Figure 4.1.1 shows a TEMA “BEU” heat exchanger where the shell closure is in the shape of a formed head. In contrast to a flat cover which resists pressure only by bending, a formed head resists pressure primarily by developing membrane (in-plane) stresses. Therefore, the thickness of a formed head can be considerably less than that of a flat cover. From the heat transfer perspective, a welded head design is superior to the bolted flat cover variety because any concern of interpass leakage between tubeside passes, through the closure-pass partition interface, is eliminated in the former construction. On the other hand, welding pass partition plates to the inside contour of the head can be a laborious operation, specially in small size units. Where quantities so warrant, heads can be cast with integral pass partition plates, thus eliminating the need for onerous welding.