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Scientific Essay, 2017
18 Pages
1 Introduction
2 Classical Form of Fin Tube Characteristics
3 New Form of Fin Tube Characteristics
4 Base Evaluation
5 General Evaluation
6 Optimization Examples
7 Summary
Nomenclature
Bibliography
Fin tubes are core elements of air cooled heat exchangers in industrial cooling applications. Thermohydraulic performance of the cooling system defines the overall size of the equipment. Fin tube characteristics vary over a large range resulting from geometry, material or manufacturing process. As a general rule - the better the performance the smaller and more competitive the design will be. Consequently, manufacturers strive for thermohydraulic optimization of their product line. A key factor is the ability to properly compare different cooling devices.
Comparison methods have been a topic in the academic field over a long period of time. Methods proposed so far have been based on classical dimensionless parameters, especially Reynolds number. Apart from transport properties Reynolds numbers include a geometric parameter pertinent to the individual heat exchanger system. If geometry is varied Reynolds changes as well. This is one of the reasons why Reynolds based comparison methods – although theoretically sound – lack practical applicability.
The following report attempts to make up for the deficiencies of theoretical Reynolds comparison by using an approach based on redefined parameter groups – specifically meant for cross-flow air coolers and/or air-cooled condensers. It will allow to directly evaluate different fin tube systems based on their performance characteristics alone.
Atmospheric cooling systems are generally arranged in cross-flow with different number of rows and passes. The cooling medium is ambient air flowing at the external (fin) side by either forced or natural draft. Basically, inlet/outlet planes of air and process sides are oriented perpendicularly whatever the internal row-pass arrangement may be. All types of dry air coolers have this feature in common – irrespective of process medium, tube geometry, single or two-phase heat transfer.
Manufacturers all over the world have developed a multitude of fin tube variations with the focus on cooling effectiveness, low cost manufacturing and material availability. Core tube geometry is one of the noticeable features of different fin tube systems – see fig. 1 with examples of (a) channel type, (b) circular or (c) elliptical core tubes. Other variations are in the form of the finning with single fins or fin sheets covering the bundle. Plain fins are used as well as turbulence promoted surfaces to augment heat transfer. There is also an abundance of fin or tube pitches. Apart from classical multi-row arrangements the bulk of cooling bundles for air-cooled condensers consists nowadays of single-row fin tube bundles with an elongated channel type core tube and only one tube row (fig. 1a). These examples show that the variety of geometry is extreme. Not surprisingly, general correlations covering all these variants are not available. Therefore, it is impossible to define a common Reynolds with only one hydraulic diameter as a comprehensive flow number.
The size of the air side inlet/outlet plane defines the total plot area in each form of bundle arrangement. Apart from that auxiliary power consumption and total surface requirement to fulfil the heat duty define total system cost. The similarity of atmospheric cooling systems with respect to inlet/outlet plane may therefore be used by a general approach.
To ease the optimization the classical form of fin tube characteristics will be modified considering the face area concept. Basically, the alternative form of fin tube correlations has been used by Kroeger [1] and others.
Fin tube characteristics are commonly summarized by correlations based on dimensionless numbers of heat transfer and pressure drop coefficient. The typical form is
illustration not visible in this excerpt
As for pressure drop, it is convenient to include the ratio of hydraulic flow length to diameter into the correlation factor. Theoretically, the heat transfer coefficient - based on total fin side surface - must be corrected by a fin efficiency factor. However, in standard atmospheric cooling the change of fin efficiency is small over the typical range of air temperatures. Following general practice this effect may be implemented into the heat transfer coefficient.
The main critical issue of general fin tube correlations is the definition of hydraulic diameter. As mentioned already the complexity of fin tube geometries cannot be covered by one geometric parameter alone. Researchers have circumvented the problem of varying air cross-flow velocity within the structure by using the maximum air velocity within the narrowest flow gap for definition of Reynolds number – so that details such as inter-fin gap, fin height or fin structure are taken into account to at least some extent. On the other hand, the narrowest inter fin gap is normally not used for the definition of hydraulic diameter. The core tube diameter is used in most correlations. So, practically there is a large variation of Reynolds numbers caused by different hydraulic diameter definitions at similar air velocity which makes Reynolds unfit as general operation variable. Therefore, in the proposed alternative classical dimensionless parameters will be modified.
The proposed form of correlations uses a black box principle (fig. 2). For definition of parameters and variables see the attachment. Face area velocity which is independent from the type of fin tube system is used as defining air speed. The area concentration ratio combines face velocity directly to maximum air speed in the narrowest gap. By switching to face velocity the tube bundle internal geometry is made part of the correlation constant. Also, the hydraulic diameter may be defined with reference to face area and in this way is identical for all fin tube variations. Consequently, the hydraulic diameter can be made part of the correlation constant as well.
Thus, the new pseudo Reynolds flow number is defined as
illustration not visible in this excerpt
For convenience, the relation to the classical number is given. Heat transfer is also referred to face area. This gives a new heat transfer (pseudo Nusselt) number as
illustration not visible in this excerpt
The resistance factor correlation takes the following form:
illustration not visible in this excerpt
For comparison purposes however the absolute pressure drop is of interest. Leaving out the length to diameter ratio the new pressure drop (pseudo Euler) number is defined as
illustration not visible in this excerpt
In the new form the fin tube characteristics may be correlated as
illustration not visible in this excerpt
illustration not visible in this excerpt
Constants of classical and new form are connected in the following way:
illustration not visible in this excerpt
It is easy to see how fin geometry transforms into correlation constants. Characteristics of different tube types are now a function of the same flow number, Ry.
The new heat transfer and pressure drop numbers are directly correlated:
Abbildung in dieser Leseprobe nicht enthalten, or Abbildung in dieser Leseprobe nicht enthalten.
For turbulent pipe flow Abbildung in dieser Leseprobe nicht enthalten. This ratio varies from 3 to 5 for a wide range of geometries. As a general rule - the more turbulent the flow the lower the exponent ratio. Typically, a single row system with a channel type core tube and basically laminar air flow will be in the range of 5.
If the ratio of Abbildung in dieser Leseprobe nicht enthalten is approximately identical for two systems a first simple comparison may be made by using the direct correlation form. Note that any test point of the two systems may be used. It is not even necessary to know the effective air velocity. The basic procedure is to find out if the extension of the operation point along the performance curves of system “1” matches system ”2”. For pressure drop we find
illustration not visible in this excerpt
The system with the lower pressure drop number is in tendency the better one. However, it must be considered that the correlation constants imply different hydraulic length factors (included in the correlation constants) which may shift the evaluation. Also the comparison considers only the core correlations and excludes external arrangement effects. No consideration is made for total fan power. Last not least the effect of different air temperature rise which defines the exchanger mean temperature difference and thus, total heat duty is not considered.
A meaningful evaluation must be based on an effective design case. Therefore, we take the design of a large air-cooled steam condensing system (ACC) as benchmark. A logical candidate for optimum is the fin tube system requiring the lowest face (plot) area. In that case we find small bundle and secondary cost such as fan size, steelwork or connection piping. In the following we shall use the approach as outlined in [2] and used in standards [3] and [4].
The comparison is made at same design conditions for identical heat duty and pumping power. Two systems must be known using the new form of correlations:
System 1: Abbildung in dieser Leseprobe nicht enthalten; Abbildung in dieser Leseprobe nicht enthalten
System 2: Abbildung in dieser Leseprobe nicht enthalten; Abbildung in dieser Leseprobe nicht enthalten
Note that in the following procedure average air side properties are assumed to be constant so that Abbildung in dieser Leseprobe nicht enthalten, Abbildung in dieser Leseprobe nicht enthaltenand Abbildung in dieser Leseprobe nicht enthalten.
In a first step the pumping power will be calculated.
illustration not visible in this excerpt
Possible variation of fan efficiency will not be considered. At this point keep in mind that in both designs air speed and total face area are not identical.
Total air side pressure drop is a combination of bundle pressure drop and parasitic loss which depends only on external arrangement and is generally taken as quadratic function of air speed. Assuming fraction Abbildung in dieser Leseprobe nicht enthaltenof system „1“ bundle pressure drop as parasitic loss the relative total pressure drop ratio will be
illustration not visible in this excerpt
With the abbreviations defined in the annex we find
illustration not visible in this excerpt
illustration not visible in this excerpt
For same fan power this leads to an implicit equation of flow number ratio.
illustration not visible in this excerpt
Face area and air speed are connected via heat duty balance:
illustration not visible in this excerpt
with Abbildung in dieser Leseprobe nicht enthalten
The fin side coefficient governs overall heat transfer with ACC’s. So, simplifying we avoid complexities of internal heat transfer calculation and take Abbildung in dieser Leseprobe nicht enthalten approximately constant so that
illustration not visible in this excerpt
For same heat duty we find the relative face area ratio as
illustration not visible in this excerpt
or, by re-arrangement of (4) and (5)
illustration not visible in this excerpt
Simplifying, face area ratio Abbildung in dieser Leseprobe nicht enthalten may be interpreted as inverse cost ratio of the two systems. This is because face area is directly related to plot area which on its part defines overall cost. And of course, cost minimum (i.e. face area minimum) will be the optimum in practical applications. In this form the comparison needs only one operation point at the same air speed apart from flow number exponents.
To evaluate equations (5) and (6) apart from the correlation constants we need reference design data. Apart from air speed the NTU number is relevant for design – see [5]. For the following general discussion data from practical experience will suffice. Typical values are
- Multi row systems: Abbildung in dieser Leseprobe nicht enthalten; Abbildung in dieser Leseprobe nicht enthalten; Abbildung in dieser Leseprobe nicht enthalten; Abbildung in dieser Leseprobe nicht enthalten
- Single row systems: Abbildung in dieser Leseprobe nicht enthalten; Abbildung in dieser Leseprobe nicht enthalten; Abbildung in dieser Leseprobe nicht enthalten; Abbildung in dieser Leseprobe nicht enthalten
The constants have been selected to match the pre-dominantly turbulent flow regime of multi-row fin tube systems (m ≈ 0.4-0.5) while single row systems tend to be laminar (m ≈ 0.2-0.3) as a consequence of the elongated air flow path between the fins. The corresponding pressure drop exponents will be estimated by exponent ratio Abbildung in dieser Leseprobe nicht enthalten.
We shall consider the system with less face area as thermo-hydraulically superior.
As a first example see fig. 3 showing the dependency of face area from relative pressure drop and heat transfer coefficient of pre-dominantly turbulent (i.e. multi-row) flow systems. Operation points above face area factor “1” indicate poorer thermohydraulic performance. All points crossing face area factor “1” will be equivalent.
This means that a system producing 60% higher pressure drop at same face area must be at least 27% better in heat transfer to be equivalent. At 160% pressure drop and only 110% heat transfer the required face area increases by 10%. Economically, this may only be made up for by reducing face area system cost by at least 10%. The main reason for face area enlargement is the reduction of air speed forced by fixed fan power consumption (fig. 4).
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