## The PHOENICS-Direct Simulation Scenario, HeatEx.

#### 1.1 What HeatEx does

The role of HeatEx is to simulate the performance of idealised heat exchangers of parallel-flow, counter-flow, cross-flow and other presumed-flow configurations, both for:
1. the circumstances for which analytical solutions exist, i.e. those of uniform fluid properties and uniform overall heat-transfer coefficient, and
2. those for which there exist no such solutions, because the said quantities are not uniform, as for example in the shell-and-tube heat exchanger illustrated below.

HeatEx therefore illustrates the ability of numerical methods to provide more realistic simulations than analytical ones can do; it is not however itself a design tool, because it is not supplied with practically-shaped three-dimensional objects or realistic Nusselt-Reynolds-Prandtl-number relationships.

It has been used as the means of generating results shown in section 1.4 of the latest Heat-Exchanger Design Handbook [Ref. 1]

#### 1.2 Restriction to 2D

Since nothing of essential importance is lost thereby, the underlying parameterised Q1 file is restricted to two-dimensional representations of heat exchangers, as indicated below for the first three (idealised) flow configurations to be considered:

about which it can be remarked that even a one-dimensional representation would suffice for the first two cases.

#### 1.3 The doubled-grid approach

For ease of display, the attributes of the two fluids will be presented side-by- side, as shown below fornthe third case:

The separation of the two parts is exploited as a computational device also, with the advantage that it permits solution for only one temperature variable, tlr (standing for temperature left or right); but in the left-hand part tlr represents the temperature of fluid 1 and in the right-hand part that of fluid 2, as shown below for the number of transfer units and the mass_times_specific_heat ratio (see next paragraph for explanation) both equal to unity.

The temperature has been non-dimensionalised by reference to the maximum overall temperature difference.

#### 1.4 Dimensional and non-dimensional parameters

The dimensional parameters which characterise the performance of the single-phase idealised exchangers to be considered here are:
 symbol meaning units Tin1 inlet temperature of fluid 1 deg C Tin2 inlet temperature of fluid 2 deg C C1 constant-pressure specific heat of fluid 1 J/(kg deg C) C2 constant-pressure specific heat of fluid 2 J/(kg deg C) Min1 mass inflow rate of fluid 1 kg/s Min2 mass inflow rate of fluid 2 kg/s A heat-transfer area between fluids m**2 U overall heat-transfer coefficient J/(m**2 s deg C)

The thermal performance of a heat-exchanger can however be equally-well represented in terms of a smaller set of dimensionless quantities, namely:

 symbol meaning definition M~ mass*specific-heat ratio (M1*C1)/(M2*C2) Tj~ (where j = 1 or 2) non-dimensional temperature (Tj-Tin1)/(Tin2-Tin1) N~ number of transfer units (U*A)/(M*C)min E~ heat-exchanger effectiveness Q/{(Tin2-Tin1)*(U*A)}

wherein:

• (M*C)min is the smaller of M1*C1 and M2*C2, while
• Q is the heat transferred from fluid 2 to fluid 1, which may be expressed in the following alternative ways:
 symbol expression meaning Q = M1*C1*(Tout1-Tin1) mass flow rate1 * enthalpy rise Q = M2*C2*(Tin2-Tout2) mass flow rate2 * enthalpy fall

#### 1.5 The purpose of the calculations

The main task is to determine the effectiveness E~ for prescribed values of M~ and N~; and a secondary one is to predict the distributions within the exchanger of the dimensionless temperatures T~ of the two fluids.

Of course, analytical expressions exist for the simplest cases; but the purpose here is to show how the effectivness and distributions can be computed numerically for both simple and complex cases.

#### 1.6 The use of HeatEx for learning about what influences heat-exchanger performance

The present version of HeatEx is rather simple. However, it does allow study of the effects of time-dependence, grid-size variation and non-uniformities of specific heat and heat-transfer coefficient; and so it can be said to enable newcomers to the subject, and to computer simulation in general, easily to explore the effects of the most important parameters.

The PHOENICS-Direct menu system provides all that is needed (which is good), but no more (which is even better); for an excess of options often leads to none being chosen.

#### (a) Activating the HeatEx Simscene

In the folder \phoenics\d_sapps\HeatEx, there is a batch file named start.bat. Activating this causes the following image to appear

which reveals, as well as the top page of the present document, the following buttons and tabs along the top:

#### (b) Choosing the flow configuration

Clicking on the "Inspect or modify input data" tab elicits the following image:

The seven boxes on the left contain the names of the groups of data items which are available for alteration via menus. On the right is the first of these, named 'general'.

The first of the two boxes on the right contains a pull-down menu as shown below:

It allows selection of a flow configuration differing from the default cross-flow, the full list being:
• for parallel flow,
• for counter-flow,
• for oblique flow,
• baffled flow with two baffles,
• baffled flow with four baffles
• baffled flow with two but with leaky baffles.
What is meant by the last four of these is explained by the following four images.

By the default the flow rates are taken as being independent of time. If however the 0.0 in the second menu box is changed to 2.0, thus,

a transient heat-transfer process is simulated, lasting specifically for a time during which fluid 1 fills the volume available to it twice; for that is the meaning of the somewhat cryptic formula appearing on the screen.

Other parameters which may be set are accessed by clicking on one of the other boxes on the left of the screen.

#### (b) Geometry

Clicking on the 'geometry' box elicits the following menu

the significance of which is self-explanatory.

#### (c) Material properties

Clicking on the 'material properties' box, in its turn, elicits the following image:

• The second-from-top box on the right is a two-item pull-down menu which, when the non-default 'yes' choice is made, sets the properties to non-dimensional unity values for simplicity. Otherwise those from the lower boxes are used.

• The lowest four boxes on the right, shown above, allow the influences of varying properties to be investigated to some extent. Specifically, the enthalpy-versus-temperature relation of fluid 2 is supposed to have the three-part form shown below:

• The menu allows the co-ordinates of points B and C to be varied, corresponding to the differing specific heats of the liquid and vapour phases, and to their 'latent heat' of vaporisation, to be reflected.
• Were C to be placed vertically above B, the enthalpy~temperature relation would correspond to that of a pure substance. Mixtures on the other hand, for example water and alcohol, will have enthalpy~temperature relations of which the transitions between the three straight lines will be rounded rather than abrupt. But the HeatEx SimScene, even in its present simple form, enable the main effects of real mixttres to be investigated.

#### (d) Initial conditions

Clicking on the left-hand-side 'initial conditions' box reveals the following menu.

For steady-state simulations, 'initial conditions' are no more than initial guesses; they do not influence the final solution.

They do however have significance for, and therefore influence on, the solution of time-dependent simulations, as will be seen in section 2.2 below.

#### (e) Boundary conditions

Clicking on the 'boundary conditions' box, for example, elicits the following image:

Here are more parameters which may be set by typing over existing entries in the white boxes on the right-hand side.

The meanings of the items occupying the first four boxes are self-explanatory; and the fifth, the number of transfer units is the means by which the overall heat-transfer coefficient, U W/(m2degC), is specified. The two lower boxes require more explanation.

Analytical expressions for heat-exchanger effectiveness are based on the presumption that the overall heat-transfer coefficient is uniform, i.e. that its value is the same at all points in the heat exchanger. The presumption is often far from the truth because:

• thermophysical properties vary with temperature; and
• the relative velocity of fluid and wall, which strongly influences the convective component of the coefficient, varies greatly with position.
Therefore HeatEx has been supplied with means for demonstrating that its numerical methods are subject to no such restriction. Specifically, if either or both of the numbers in the lower boxes are set to a non-zero value, the overall heat-transfer coefficient will be computed from the formula indicated.

No particular physical process is implied thereby; but users can gain insight into the effects by varying the numbers.

Clicking on any of the three boxes on the left-hand side of the screen leads to other menus in which other groups of parameters may be set.

#### (f) Output

Clicking on the 'output' box elicits the following image, enabling miscellaneous output-related settings to be made.

#### (g) Numerical

Of the image elicited by clicking on the 'numerical' button, as shown below

there is little to say. The numerical settings concern grid size and relaxation factors, the nature of which is known to most users of numerical-simulation packages.

The third item, namely the number of time steps, has an influence only if the second menu box of the 'general' menu has been filled with a value in excess of zero.

#### (i) Concluding remarks regarding settings which can be made via menus

About the settings which can be made via menus, the user may reasonably ask: "Why this? and not that?" The answer is: "Because the SimScene creator guessed, perhaps wrongly, what you would like to be able to adjust."

It should therefore be recognised that it is easy to make any simulation-influencing setting menu-adjustable. This is not the place to explain how to do so; but some insight will be provided in section 3 below.

#### 2.2 Running the flow-simulating calculation

When the user has made his choices, clicking on the 'Run the simulation' button causes the PHOENICS Satellite and Earth modules to be run in sequence, in the directory \phoenics\d_sapps\HeatEx\working. No user-intervention is needed.

#### 2.3 Inspecting the results

Inspection of the results of the calculation is facilitated by the screen which appears after the computation is completed, thus:

This is the 'inforout' file which has been placed by EARTH in the working directory. The heat-exchanger effectiveness is among the items printed there.

Another file of interest is the 'result' file that can be loaded via the 'Open file' button .

The user may immediately explore its content, aided by the 'Find' button.

If graphical display is preferred, it may be elicited by clicking on the button, whereupon (in the present case) PHOTON is launched, which reacts automatically to the macro, u, which has been automatically written in the working directory. A typical image is the following:

wherein the left-hand contours represent the distribution of heat flux to the cooler fluid entering from the left, while the right-hand ones represent the equal flux leaving the hotter fluid entering from below on the right. The two-leaky-baffle case is the one in question.

A different picture will appear if the process is transient, as shown by the following image:

There fifteen pairs of contour diagrams are shown, corresponding to the fact that the total simulation time will have been divided, by way of the 'numerical' menu, into fifteen equal intervals. The earliest-time interval is top-left; the latest is bottom-right. The flow configuration in this case is crossflow; and the specific-heat-times-mass-flow-rate products are equal. The total time considered is that which enables each fluid just to fill the volume available to it.

Inspection of the contour colours shows that both fluids were given the lowest temperature at the start. Then the hotter fluid entering from below on the right-hand side, evidently imparts some of its heat content to the cooler fluid entering on the left.

#### 2.4 Performing multiruns

It is sometimes convenient to conduct a series of runs in which parameters are systematically changed. There now exists a convenient provision for doing so in PHOENICS-Direct itself. It is activated by clicking the button shown below.

However, a HeatEx-specific multi-run facility was created earlier. Since it still exists, and has some interesting features of its own, it will now be described.

In sub-directory HeatEx\multirun, there then resided a (no-longer-existing) batch file called multi-run.bat, the content of which can be seen here.

Its purpose was to explore the influences of the number of transfer units and of the flow configuration on the effectiveness of presumed-flow heat exchangers for fixed values of grid size and mass_flow_times_specific_heat ratio.

Thirty runs were performed without user intervention. The values of effectiveness (and a few other items) were placed for later inspection in a file called info.htm, of which a typical example can be seen here.

Such systematic parametric studies allow useful lessons to be learned. For example, from consideration of the first six runs, all for ntumin=1.0, it can be concluded:

• For counter flow (flotyp=2):
EFFECTIVENESS = 4.941176E-01
whereas the theoretically exact value is 0.5.
No doubt the grid is not fine enough for better accuracy.

• For cross-flow (flotyp=3), the effectiveness is lower, namely:
EFFECTIVENESS = 4.711603E-01
as is of course to be expected.

• For oblique flow (flotyp=4),
EFFECTIVENESS = 4.786468E-01
i.e. between the two previous values, because the flow pattern has elements of both counter- and cross-flow.

• When two baffles are introduced (flotyp=5),
EFFECTIVENESS = 4.919908E-01
i.e. it increases;

• but leakiness (flotyp=5), i.e. the ability of shell-side fluid to pass throught the small gaps between the outsides of the tubes and the insides of the holes in the baffles reduces the effectiveness again: EFFECTIVENESS = 4.842865E-01

• Finally, introducing four (not-leaky) baffles (flotyp=6) raises the performance to:
EFFECTIVENESS = 4.926866E-01
i.e. very nearly to the level of the counter-flow value.

Qualitatively, none of these results are surprising; but possibly the small sizes of the quantitative differences may not have been expected. However there are other factors, for example the influence of number of baffles on shell-side velocity, and so on heat-transfer coefficient, which HeatEx has not yet been asked to pronounce upon.

As already stated, modern users of HeatEx perform multiruns by means of the top-of-screen multirun button, the most up-to-date account of how to use it being in the document describing the Multirun facility of the PHOENICS-Direct Package.

#### 3. Behind the scenes

It is not necessary for users of SimScenes to know how they work; but this section provides some information for neverthless inquisitive users, with emphasis on three important files.

#### (a) The parameterised Q1 file

Underlying all SimScenes is a file, Q1.htm, written in the PHOENICS Input Language known as PIL. The file which underlies the HeatEx SimScene can be viewed by clicking here.

Such files have four functions, namely:

1. Declaration of parameters which do not form part of PIL.
2. Ascribing values to these parameters and to some of the PIL variables.
3. Provision of means by which the user can re-set these ascriptions interactively.
4. Provision of consequential PIL statements which use the above-set parameters so as to express the user's wishes in terms which PHOENICS can understand.

#### (b) The scene file

Corresponding to the Q1 file, and indeed derived automatically from it, is a file called scene.xml. It can be viewed by clicking here. It is the file which, when read by PHOENICS-Direct, presents the on-screen menus discussed above.

At the end of the interactive session, PHOENICS-Direct writes a file called frommenu.htm which contains the parameter settings which have resulted from that session. A typical example can be seen by clicking here.

These settings are read by the PHOENICS input module, Satellite, because they are, in effect, included in the pre-existing Q1 file by way of the top line of what is seen here.

#### (c) Output files

The automatically-written RESULT and INFOROUT files have been mentioned above; but many more will be found to have been created in the heatex\working directory by the Satellite (input), Earth (solver) and PHOTON (display) modules of PHOENICS. For example:

All these actions are consequences of instructions placed by the human creator of the parameterised Q1 file, based upon specialist knowledge too extensive to be elaborated in the present document.

#### 4. Concluding remarks

The present version of HeatEx has been deliberately kept simple, as has indeed the present document. It is now left to the reader to perform the calculations which will reveal the influences on the heat-transfer effectiveness, and on the temperature distributions, of the many combinations of input parameters which the menus allow.

Once these possibilities have been exhaustedi, it may be remarked, extending their scope is not difficult. All that is needed is some acquaintance with the PHOENCS Input Language, into which section 3 has given some insight. Expertise in Computational Fluid Dynamics is not required.

The authors of HeatEx will be glad to receive advice as to how it can be modified so as better to meet the needs of persons who use it for teaching students about heat exchangers.

#### 5. References

1. G F Hewitt (Ed) 'Heat-Exchanger Design Handbook", Begell House. 2013
2. W M Kays and A L London, "Compact Heat Exchangers" (second edition), McGraw Hill, 1964