Economical Air cooler design is important forcompetitiveness

Situation

Environmental requirements, reduction of operating costs and low price offers by the increasing number of world wide compeditors require new rigorous optimization tools for air cooler design.

Consequences

To offer a competetive air cooler, the design should just meet the specifications at minimum manufacturing costs. This requires:

• Proved theoretical fundamentals

and

• Rigorous optimization tools

Rigorous design generates "ideal exchangers".

This means, that each design reflects an unique exchanger which can not be manufactured according to a standard code with standard component dimensions.

For reasons of cost saving and availability many manufacturers use prefabricated standard finned tubes or even complete bundles. The hydraulic and thermal design calculations are based on those standard component dimensions.At first sight, this allows a comfortable and favourable design. But only a free optimization of the most important parameters will show the quality of the design compared to the "ideal" exchanger

A compromize between the optimized and standarized exchanger must be found, to avoid that the elevated manufacturing costs compensate the material savings.

Solution

The powerful LV-Software leads to a more compact, less material and costs consuming design

Which optimization tool fits?

With growing number of variables also the possible number of variation increase excessivly and therefore traditional mathematical algorithms are not able to solve such problems or it takes unreasonable computing time.

The genetic LV-Optimizer

The LV-Optimizer is based on the Genetic-Optimization-Method, a method to solve complex optimization problem with a large number of variable parameters. This method is close to the evolution technic of nature and not random based like the Monte-Carlo-method. The genetic code always keeps the latest generations to compares the quality of the present and past species while searching for the better one. It is the "survival of fittest", but not limited to the present generation. In this way the solution is found faster without ending in a relative optimum.

The genetic optimizer is a mathematical tool, which may be called by any LV-Program. The optimizer adjusts the parameters of the calling program so that a minimum or maximum target value will be reached. The target value may be one of the parameters or a function of arbitrary parameters, defined by the user.

In the later shown example the weight of a heat exchanger is the target value which will be minimized by adjusting the parameters tube pitch, fin thickness and fin pitch.

Types of air-coolers

Air cooled exchangers have a brought industrial application. This covers small sizes for the air-conditionig-Systems to hugh "Base ball grounds" for the chemical industry or power stations.

Air cooled heat exchangers operate with free or forced convection whereas the latter is more important for industrial applications.

There are three major functional components:

1. the exchanger bundle
2. the motor driven fan
3. the casing with air louvers and supporting structure

Considering the different arrangements (Fig.1) there are various designs whose advantages and disadvantages are described in Table 1.

Fig 1: Types of air coolers

Table 1: Types of air coolers

Fan types and noise emission

Two general classifications of air-cooler fans are available : forced draft type,where air is pushed across the tube bundle, and , where air is pulled through the bundle(Fig.2).The advantages of each type are listet in table.2.

Fig 2: Horizontal arangement, forced draft and induced-draft type

Table 2: Induced, forced draft comparison

Due to the required air volume flow one or more fans are required. At design conditions the static pressure generated by the fans must compensate the bundle pressure drop by keeping the sound level L_W below the maximum allowable L_W,max.

L_W,max ³ L_W

For a unit with n similar fans, the sound level results from a logarithmic function :

L_W,max ³ L_W(n) = L_W + 10lgn

A further sound factor is the sound pressure level. Increasing the distance (r) to the sound source the sound pressure level decreases compared to a reference quantity (L_W) by.

L_p,max ³ L_p(r) = L_W - 20lg r -10lg 2P

Tubes

Tubes for air-cooled heat exchangers may be finned or bare.

Bare tube bundles are generally used for gas/gas or liquid/liquid heat transfer whereas finned tube bundles are used if the tube side fluid has a high heat transfer coefficient compared to the air side.

Heat coefficient times surface should be the same for both sides

For water, the heat transfer coefficient for 2 m/s flow velocity is 3000-5000 W/m²K what is 50 up to 100 times the coefficient for air (30-50 W/m²K). Due to thermodynamic reasons the specific heat duty should be the same on both sides. This is accomplished by increasing the surface area for the air side to compensate the lower transfer coefficient.

The optimal specific heat duty U* A is reached if :

U_inside × A_inside = U_outside× A_outside . ( U =Heat transfer coeff. , A = area )

Though, the increase of the finned surface is limited.

Geometry of fins has to be optimized

If the fin pitch is too small, the the laminar boundary layers will meet and thus cause a loss in heat transfer rate. An excessive fin height leads to a high resistance of thermal conductivity and hence to a lower fin efficiency.

Optimizing is necessary

Minimizing the manufacturing costs of a finned tube air cooler for guaranteed heat duty and according to all requested specifications represents a multi-dimensional optimizing problem which cannot be solved only by experience and short-cut methods. Optimiziation is essential to judge to design against the "ideal exchanger".

Live test

Table 3 shows an exchanger offered by an manufacturer

Table 3: Air cooler specifications

Rigorous optimization by LV

The simple example in table 3 shows that the modification of only few variables may result in a considerable cost reduction. The objective is to reduce the material requirements. For high-grade steel tubes even a small reduction of weight is it worth.

For the optimizing step, plausible upper and lower limits are defined for variables ( i.e. component dimensions) and target values with the respective limits are entered (Fig. 4)

Fig. 4 : Parameter input

The target value of the optimization is defined as minimizing the cost function.

f_K = (costs_{high-grade steel tube-}+ costs_C-steel-fins)

Considerable reduction potential results

Table 4: Comparison between basic and optimized design for an actual case

By a small modification of the fin pitch, fin thickness and the tube pitch the number of tubes was reduced by 14 which represents 6,7 % of the initial area . As this example has only a small optimization range it is supposed that a simple parameter study could have shown the same result in a short time. But it should be considered that every available geometric dimension has been modified during optimization while searching the minimum area.

Literature:

• Verfahrenstechnische Berechnungsmethoden Teil 1
  VCH-Verlag / 1986
• Wärmeaustauscher Vulkan Verlag 2.Ausgabe / 1994
• Lauterbach Verfahrenstechnik / Software