# Exploration of the sizing of an air-water exchanger

Calculation of the exchange surface A

# Introduction

In this guided exploration (DTNN-1), we will see how the surface of a heat exchanger can be determined and how its behavior in off-design conditions can be calculated.

Note that a second guided exploration (DTNN-2) relates to the sizing and study in off-design mode of a piston compressor used to supply a compressed air storage tank.

## Typology of problems posed and associated difficulties

The problem arises because the NTU heat exchanger calculation method which is implemented in the Thermoptim core can only determine the product UA of the global heat exchange coefficient U by the surface A of the exchanger, without evaluating these two terms separately.

For further explanations, we suggest you refer to the page of the Thermoptim-UNIT portal which deals with heat exchangers: https://direns.mines-paristech.fr/Sites/Thopt/en/co/echangeurs.html.

To be able to go further and separate these two terms, it is necessary to carry out what we call a sizing of the exchanger.

This is a relatively complex problem that you should understand before you go further. It is presented in this page of the Thermoptim-UNIT portal, which we strongly recommend that you read before anything else:https://direns.mines-paristech.fr/Sites/Thopt/en/co/present-dim-techno-non-nominal.html.

To be able to size an exchanger, To size an exchanger (i.e., calculate its surface area) , it is necessary on the one hand to choose its geometric configuration, and on the other hand to calculate U, which depends on this configuration, on the thermophysical properties of fluids, and on the operating conditions.

## Implementation in Thermoptim

Versions 2.7 and 2.8 of Thermoptim support sizing and off-design studies. For this, they introduce screens complementary to those which allow the usual phenomenological modeling to be carried out.

They define the geometric characteristics representative of the different technologies used, as well as the parameters necessary for calculating their performance. For a given component, they obviously depend on the type of technology chosen.

The calculations are carried out in extensions of the core of the software package, and in particular in programs called controllers of Thermoptim.

They are so called because they take control of the software by driving it to perform specific operations not available in the core screens.

There are many types of controllers. Two categories of controllers make it possible to carry out sizing studies, generic controllers and specific controllers.

The former are by nature multipurpose but can only perform simple calculations, while the latter, defined specifically for a particular model, can perform much more complex operations.

In this guided exploration, we will only use a generic controller.

# Loading the air-water exchanger model

Consider a tube and fin exchanger intended to cool 0.66 kg/min (11.7 g/s) of air leaving a compressor at 5 bar and 275 °C thanks to a flow of 1.17 kg/min (20 g/s) of cold water passing through a coil made up of two tubes in parallel. The diameter of the tubes is 15 mm, and their thickness 1.5 mm. The spacing between the fins is 3 mm. In this example, the wall and fouling resistances are neglected. The effectiveness of the exchanger is assumed to be 0.84.

## Loading the model

Click on the following link: Open a file in Thermoptim

You can also:

- either open the "Project files/Example catalog" (CtrlE) and select model m4.2 in Chapter 4 model list.
- or directly open the diagram file (exampleAirExchanger25.dia) using the "File/Open" menu from the diagram editor menu, and the project file (exampleAirExchanger25.prj) using the "Project files/Load a project " menu from the simulator.

Open the exchanger screen and calculate it.

The heat transfer rate is 2.57 kW.

The setting of this model is completely classic and does not require any particular explanation.

The only remark at this stage is that the flows were entered in kg/s and not in g/s, whereas Thermoptim would allow you to do so.

This is necessary because Thermoptim performs sizing studies using SI units.

The only sizing result that we arrive at is the product UA of the heat exchange coefficient by the surface of the exchanger, making it impossible to separate the values ​​of each of these two factors. Here UA = 0.02386 kW/K, or 23.86 W/K.

## Procedure to be implemented

Using the Thermoptim sizing screens, it is possible to calculate the overall heat exchange coefficient and to deduce the area necessary to transmit the desired thermal power.

The concepts underlying these calculations being relatively complex, we recommend that you read the sections relating to exchangers in volume 4 of the Thermoptim reference manual, much more detailed than what it is possible to indicate in this guided exploration.

The procedure is as follows:

- open the generic sizing controller
- create the sizing screen of the exchanger
- open the window giving access to the sizing screens of the components
- set the sizing screen of the exchanger
- perform its sizing

# Using the generic controller

## Loading the generic controller

The generic sizing controller can be loaded from the simulator screen. To do this, activate the "Driver frame" line in the "Special" menu.

Then select the line "generic techno design controller" from the list of available controllers, and click "OK".

The controller screen opens. Click on "Set the sizing screens".

A row appears in the table, corresponding to the exchanger.

It indicates that it is a heat exchanger (HeatEx), and that it is considered to be a simple exchanger (TechnoHx).

It is possible to change this type by double-clicking on the table row. This is what should have been done if it was an evaporator, but this is not the case here.

The sizing screen is now created.

To access it, return to the simulator screen, and activate the line "Component sizing screens" in the "Component sizing" menu, or type Ctrl T.

The window allowing access to the existing sizing screens is displayed.

Double-clicking on the table row opens the sizing screen for the selected component.

## Sizing screen of an exchanger

Here is the sizing screen of an exchanger set by default.

Calculating the heat transfer coefficients and pressure drops shows that , in addition to the surface of the exchanger A, two geometrical quantities play a particularly important role: the flow cross-section assigned to the fluid Ac, and the hydraulic diameter dh. When the heat exchange coefficients of fluids are very different, various devices such as fins are used to compensate for the difference between their values. We then speak of enhanced surfaces, which can be characterized by a surface factor f and a fin effectiveness eta0.

These four parameters are those used in Thermoptim to characterize the heat exchanges for each fluid. We add the length of the exchanger for certain calculations such as pressure drop.

In the sizing screen of the exchangers, the following conventions are adopted:

- the type of configuration (here "air-coil") is selected from a drop-down list
- "free flow area" represents the flow section Ac
- "hydr. diameter" is the usual hydraulic diameter dh
- "length" is the length of the exchanger (used for the calculation of the boiling number Bo and for the calculation of the pressure drop, not yet implemented in the two-phase case)
- "surface factor" is the surface factor f for enhanced surfaces
- "fin effectiveness" is the effectiveness of fins eta0

In our case, there are fins on the outside of the tubes only. The last two parameters therefore have the value 1 for the cold fluid but not for the hot fluid.

However, the default correlation is not correct. By clicking on "air-coil | Morisot correlation ...", the list of possible choices is displayed.

For the hot fluid, the relevant correlation is "ext_tube Colburn correlation ...."

For the cold fluid, it is "int_tube Mac Adams correlation ....".

Colburn's default correlation setting is given below. You can access it by clicking on the sizing screen of the exchanger, on the "correlation settings" button located below the correlation type.

The values ​​of the coefficients C1, a, b and c are those of this classic formula giving Nusselt as a function of Reynolds, Prandtl and viscosity.

If the default values ​​do not suit you, you can modify and save them using the "Save settings" button.

### Thermal resistance of the wall

The e/lambda parameter located at the top slightly right of the screen represents the thermal resistance due to the fluid wall (this is the ratio of the thickness of the wall to its thermal conductivity lambda). We will neglect it here.

### Setting of the exchanger

Let us recall the constructive hypotheses that we assumed to be retained for the exchanger: cold water passes through a coil made up of two tubes in parallel. The diameter of the tubes is 15 mm, and their thickness 1.5 mm. The spacing between the fins is 3 mm. We further assume that the length of the exchanger is 0.9 m.

We must first determine the hydraulic diameters dh and the flow sections Ac of the two fluids.

Inside the tubes, dh is given, and the calculation of Ac is very simple: it is equal to the product of the number of tubes by the unit section.

Outside the tubes, the calculations are a little more complicated. We have used a correlation specific to tube and fin exchangers, that of (Wang, Chi & Chang, 2000). Its parameters are: spacings Fp = 3 mm between the fins, Pt = 20 mm between the tubes and Pl = 55 mm between the layers, outer diameter of the tubes Dc = 15 mm, and number of layers N = 3. dh is equal to 4 times the section divided by the wetted perimeter.

As for Ac, it is the transverse surface offered to the air flow.

Detailed explanations of the required calculations are provided in this page of the Thermoptim-UNIT portal:https://direns.mines-paristech.fr/Sites/Thopt/en/co/fil-echangeurs.html. A link will allow you to download a spreadsheet showing how these calculations are performed.

This document provides more information on this setting.

It only remains to enter these values ​​in the sizing screen of each of the two fluids.

To make your task easier, you can simply read these values ​​in the setting file corresponding to this exchanger.

To do this, go to the sizing screens frame, and click on the "Read settings" button located at the top left, and select the file "volumComprHxSettings.par".

All the parameters of the exchanger are then updated.

Once the sizing screen is set, return to the controller screen.

Then click on "Design the selected components" after selecting the table row.

The sizing screen is calculated. Here is the result.

For the exchanger, the surface determined is equal to 0.0614 m2, the overall exchange coefficient being equal to 389 kW/m2/K.

On the left of the screen are displayed the values ​​of the heat exchange coefficient h within each fluid and those of their Reynolds numbers.

In the case of a single phase fluid like here, only one line is indicated.

The hot fluid appears in red, the cold in blue, according to the usual conventions.

The pressure drop values ​​(in bar) and the friction factor are displayed on the right of the screen, in the setting of each fluid.

Refer to volume 4 of the Thermoptim reference manual for more details.

## Geometric configuration of the exchanger

Taking into account the sizing which has just been carried out, the exchanger will consist of two 90 cm tubes arranged in a coil on 3 layers and crossing metal sheet plates with a total surface of 0.31 m2 separated from each other by 3 mm.

If you want to be precise, you enter this length as the value of the "length" field on the water side, and 6 cm on the air side, which allows you to refine the estimate of pressure losses.

# Off-design behavior

Once the exchanger has been sized, its behavior in off-design conditions can be studied directly from its screen in the simulator.

The "off-design" calculation mode in fact makes it possible to calculate, by the NTU method, the exchanger in off-design mode considering that its two inlet temperatures and its two flow rates are set:https://direns.mines-paristech.fr/Sites/Thopt/en/co/echangeurs.html.

Thermoptim updates the upstream links of the exchanger from the processes, then calculates the downstream temperatures and balances the exchanger on the enthalpy level, the UA having the value entered in the field of the exchanger screen. The points and processes associated with the model are updated according to the results.

However, when using the generic controller that we loaded previously, no correction is automatically made on UA ​​to take into account the evolution of the exchange coefficients as a function of flow rates and temperatures.

It is therefore necessary to operate as follows:

- 1) modify the values ​​of the inlet temperatures and flow rates of the two processes
- 2) calculate the heat exchanger in off-design mode from its usual screen
- 3) perform a new design calculation of the exchanger to determine the new value of U
- 4) calculate the product UA of the area initially determined and the new value of U
- 5) modify UA accordingly in the exchanger screen
- 6) restart the calculation in off-design mode, repeating operations 2 to 6 until the values ​​stabilize.

As an example, let's examine how our exchanger would behave if the flow rate and the temperature of the incoming air were changed from 0.01174 to 0.01 kg/s and from 275 to 300 °C respectively.

Proceed as follows:

1. modify the inlet conditions of the exchanger in Thermoptim, choose the "off-design" option instead of "design" in the exchanger screen;
2. recalculate the exchanger several times, until the values ​​stabilize;
3. finally click on the "Design the selected component" button in the generic controller screen.
4. The new value of U is calculated: it is worth 629.05 kW/m2/K, while the exchange surface changes to 0.038 m2.
5. Multiplying this value by the initial area of ​​the exchanger, you get a new value of UA, equal to 0.022725, which you enter in the corresponding field of the exchanger screen.
6. Repeat operations 2 and 3: a more precise estimate of U is obtained, taking into account the new setting. It is worth 338.66 kW/m2/K, while the exchange surface increases to 0.0672 m2.
7. Change UA accordingly, which takes you to the exchanger screen below.

All the explanations on this example are provided in the learning path on the heat exchangers of the Thermoptim-UNIT portal

: https://direns.mines-paristech.fr/Sites/Thopt/en/co/fil-echangeurs.html.

In the above, we manually modified the value of UA in the exchanger, the sizing screen having been constructed by the generic controller. This way of doing things has the advantage that it does not require any programming, but it is a bit long to put into practice when several iterations must be carried out. It would therefore become tedious if you had to simulate the off-design behavior of the exchanger for a wide variation range of its operating conditions.

In this case, it is far better to automate these updates using a specific controller.

# Conclusion

This exploration showed you how to calculate the surface area of ​​a finned heat exchanger and the specific settings it requires, using the generic sizing controller.

This generic controller makes it possible to carry out sizing of relatively simple models and to study their behavior in off-design conditions when the different components are not too strongly coupled.

When the systems to be studied are more complex, it becomes necessary to use specially programmed controllers.

Many examples of such models are available in the Thermoptim model library: https://direns.mines-paristech.fr/Sites/Thopt/en/co/module_Logiciel_7.html.

Finally, note that the exchanger that we used here will be reused in the DTNN-2 guided exploration on cooled positive displacement compressors.