By D Brian Spalding
ABSTRACT
Traditional heat-exchanger design methods do not predict steady-state uniform-property performance well; and they are totally unable to predict the influences of time-dependence and varying properties or the consequent stresses in the shell and tubes.
On the other hand, conventional CFD (computational fluid dynamics ) techniques, with their emphasis on body-fitting grids and sophisticated turbulence models, can contribute only to small-scale phenomena such as the velocity and temperature distributions within the space occupied by a few-tube sub-section of a tube bank.
Nevertheless, the practical importance of heat exchangers, including those which involve chemical reaction and phase change, is so great that engineers must find design tools which are both economically-affordable and more realistic in prediction than either of the just-mentioned extremes.
Such tools discretize space and time with the fineness allowed by modern computers; but they still inevitably employ space intervals which are large compared with tube diameters. They have been used for research purposes for many years;
however, the difficulty of supplying them with all the relevant empirical input data has deterred designers from using them.
The lecture will describe a means of greatly reducing the difficulty; it accepts the formulae (for heat-transfer coefficients, viscosity-temperature relations, etc) in the form with which designers are familiar; and it also produces information, for example about local heat fluxes, hot-spots and stress concentrations, which otherwise escape attention.
Examples will be presented and explained.
Contents
- The Historical Background
- The Requirements of a Heat-Exchanger Design Method
- Three Ways of Satisfying the Requirements
- Practical Examples
- Concluding Remarks
- Acknowledgements
- References
- Figures
1 THE HISTORICAL BACKGROUND
The first publication describing the application of CFD techniques for the simulation of heat exchangers appears to have been made more than thirty years ago by Patankar and Spalding [1] who concluded: “It therefore seems that a tool of considerable practical utility is in embryonic existence”.
At first their expectations appeared to be fulfilled; for the same technique, generalized so as to be applicable to two-phase flows, played an important role in elucidating and resolving the practical difficulties which, in the mid-1970s, were being encountered by the nuclear-power industry.
Specifically, the shell-side steam-water mixture circulating in boilers, heated by pressurized water from the nuclear reactor, caused the tubes to vibrate and the baffles to corrode. Consequently, first Combustion Engineering Inc and Kraftwerk Union, then Babcock and Westinghouse, and finally the Electric Power Research Institute, sponsored the development of a family of flow-simulating computer programs.
The work was of a pioneering nature; and therefore did not proceed always as rapidly as desired. This prompted one wag to suggest that the name adopted for the EPRI-sponsored code, URSULA, was an acronym for Urgently Required Solution Unusually Late Arriving.
Despite the implied criticism, to which pioneers must become inured, the work was successful; and it was followed by the development of further computer codes for simulating steam condensers and cooling towers.
Nevertheless, the heat-exchanger-design community has not shown much enthusiasm for the use of CFD techniques; and the authors of a recent paper [2] on the subject concluded “very few applications can be found of using CFD technique as a tool for heat-exchanger design optimization”. Instead, designers still prefer to use methods, for example those of Tinker [3] or Bell [4], in which the flow patterns are deduced from (educated) guesses rather than calculated.
The reasons for the failure of CFD techniques to attract the heat-exchanger-design community are not entirely clear. However, that they are in part psychological is suggested by the remarks of J Taborek [5] in the Hemisphere Handbook of Heat Exchanger Design. He there opines: “Only if calculations are performed manually will the engineer develop a ‘feel’ for the design process as compared to the impersonal ‘black box’ calculations of a computer program”.
It is to be hoped that the approach recommended in the present paper will be found more congenial by heat-exchanger designers; for it enables them to insert the same formulae, including Tinker-Bell ‘correction factors’, which they would supply to the ‘hand-held calculators’ preferred by Taborek. Indeed, so great is the speed of advance of the computer-hardware and -software industries, that computers performing full CFD analyses may soon indeed be ‘hand-held’.
The method to be described can be applied to heat exchangers of all types, to any participating fluids, and to any conditions of operation. However, in order to focus on essentials, discussion will henceforth be limited to:
- baffled shell-and-tube heat-exchangers,
- single-phase non-reacting fluids,
- steady-state operation, and
- thermal and pressure-drop performance.
- THE REQUIREMENTS OF A HEAT-
EXCHANGER DESIGN METHOD
2.1 Geometrical Input Data
No prediction is possible until the apparatus in question has been described in geometrical terms, which include (for the simplest cases):
- inside shell diameter
- inside shell-nozzle diameter
- tube outside diameter
- tube-wall thickness
- tube-layout pitch
- tube-layout characteristic angle
- tube length
- baffle cut
- baffle spacing
- number of tubes
- number of tube passes
2.2 Material Property Data
Specification must be made of:
- the thermal conductivity of the tube material
- the thermal conductivities of the shell- and tube-side fluids
- the specific heats of both fluids
- the densities of both fluids, and
- the viscosities of both fluids.
However, for most materials, these properties are known to vary with temperature; and this knowledge is expressed by way of:
- formulae,
- tables of numbers, or
- graphs of various kinds.
If graphs are in question, their content must be converted into formulae or tables before it can be communicated to a computer program. However, even when this has been done, the problem of using the information remains; for the whole point of a heat exchanger is to change temperature; and it is not known in advance what temperatures will prevail at any chosen point within the tubes or shell.
Therefore some means must be found of communicating to the computer program the whole content of the formulae or tables, together with the instruction: “You work out which values of conductivity and density etc to use at each point.”
How this can be done is the main theme of the present paper.
- Thermal and Mass-Flow Boundary
Conditions
Also needed, of course, are the (known):
- mass-flow rate and temperature of the shell-side fluid in the inlet nozzle; and
- mass-flow rate and temperature of the tube-side fluid in its inlet header.
The task of performance prediction is to determine what will be the (mass-flow-weighted average) temperatures of the shell- and tube-side fluids at their outlets from the heat exchanger.
2.4 Empirical Correlations
If the geometry in question were extremely simple, as for example if there were only one tube and the shell had a length of many diameters and was free from baffles, and if the flow were laminar and of uniform temperature, it could be left to any well-constructed CFD program to work out the performance from the above data.
However, industrial heat exchangers have hundreds or thousands of tubes; and baffles are present and the flow is often turbulent. This entails that, if performance were to be predicted purely from computational fluid dynamics, a very fine grid would have to be employed. Even if a computer with sufficient memory could be found, the time taken for the performance prediction would be orders of magnitude longer than any designer could afford to wait.
Moreover, so rudimentary is still the scientific knowledge of turbulence in flow patterns such as are found in tube banks, the reliability of the predictions would still be far from one hundred per cent.
The only practical solution is therefore to introduce additional information, derived from such experimental data as can be found, concerning the rates of heat and momentum transfer per unit area of solid-fluid interface. This information, which is the major outcome of thousands of man-years of heat-transfer and fluid-flow research, is usually expressed in the form of mathematically-expressed relationships between well-known ‘dimensionless parameters’:
- Nusselt or Stanton number, for the heat-transfer coefficient;
- Reynolds number, to characterize the state of the flow, and
- Prandtl number, to characterize the relative ease of heat and mass transfer in the fluid.
All these parameters involve the material properties listed in section 2.1; so the use of empirical correlations provides no escape from the need expressed there, namely to enable the computer program to work out the property values from the given formulae and the temperatures which it finds at every point.
- Predicting the Flow Pattern and Temperature Distribution
The temperatures of the fluids leaving the heat exchanger are the main quantities which it is desired to predict; however, even if the flow pattern were as simple as that of the idealized one-dimensional counter-flow heat exchanger, these outlet temperatures depend on the temperature just upstream of the outlet. These just-upstream-of-outlet temperatures depend on the temperatures upstream of them; and so on. Therefore, the whole temperature distribution has to be computed.
When the flow pattern is not of the above simple kind, what point lies ‘just upstream of’ a given point is not obvious a priori; therefore ability to calculate the temperature distribution depends on ability to calculate the flow distribution giving rise to it. This therefore is what the computer program must additionally do, providing incidentally two other pieces of information needed by the designer: the pressure losses suffered by the two streams.
Fortunately, computer programs (the so-called CFD codes) do exist for computing both the flow fields and the temperature distributions simultaneously. Although their accuracy depends on the fineness of computational grid which is employed, and desirably fine grids do increase computer times and therefore costs, the requirements relating to shell-and-tube heat exchangers are usually affordable.
However, just as the heat-transfer and friction correlations require material properties which vary with temperature according to formulae which must be made known to the code, they also contain other quantities which can not be specified a priori, namely the three components of the shell-side velocity.
It follows that, even if the temperature variations were small enough not to affect material properties, the need for the code to evaluate formulae from values which varied from place to place would remain. Thus the Reynolds Number enters most pressure-drop and convective-heat-transfer formulae; and its value depends on the local velocity, which varies with position in ways that are not known at the start.
In summary, predicting the performance of shell-and-tube heat exchangers necessitates use of a program with formula-processing capability.
- THREE WAYS OF SATISFYING THE REQUIREMENTS
3.1 Method 1: ‘User-Supplied Sub-Routines’
Of course, many CFD codes already have built-in correlation-evaluation sequences, representing friction and heat-transfer processes; and they also contain computer-coding modules which express the variations with temperature and pressure of the relevant properties of frequently-encountered materials.
In principle, there is no limit to the extent to which these provisions can be extended. But in practice, however much is provided, some users of the code will require more; they will want it at once; and they will not want to pay the costs incurred by the code-developer in providing it.
From the earliest years of commercial CFD, therefore, developers have allowed users to add coding modules of their own, usually in the form of Fortran or C subroutines, which would supplement the built-in correlations in the desired direction.
Users of the 1981 PHOENICS code, for example, will remember what clever use some users made of the so-called ‘GROUND-coding’ facility, which indeed many old-stagers continue to use. Reference [1] is an excellent example of the use of this technique.
However, the proportion of CFD-code users with the necessary skills is constantly diminishing; and the proportion of heat-exchanger designers who possess (or have the time to acquire) them must be very small.
- Method 2: ‘Automated Sub-Routine
Writing’
In order to enable PHOENICS users to benefit from the features of ‘GROUND-coding’ without themselves having to be familiar with either Fortran or C, the so-called ‘PLANT’ feature was introduced in 1997.
This enabled the user to express his wishes by way of formulae, written in accordance with prescribed rules; whereupon PHOENICS itself:
- interpreted the formulae;
- created corresponding Fortran subroutines;
- compiled them;
- re-built the executable; and
- carried out the required flow-simulating calculation.
This was a big step forward; and it did, at least potentially, satisfy the ‘formula-processing’ requirement which has been pointed out above. However, perhaps because it was not adequately presented to them, it did not convert many heat-exchanger designers into CFD users. Perhaps also the ‘prescribed rules’ were shaped by those thinking too much of the Fortran to be written, and not sufficiently of the prospective user.
To view the entire heat exchangers writeup, click here.
Heat Exchangers and Chemical Cleaning for Marine Services 