Flow along tubes is frequently encountered in engineering practice; and it is often desired to determine the rate of heat transfer and also the pressure difference necessary to maintain the flow.
Engineers commonly deduce these quantities from formulae which connect:
Of these dimensionless numbers, the symbols and definitions are:
|friction coefficient||2 Δp/(ρU2 ) (L/D)- 1|
wherein the meanings of the symbols are:
For example, commonly accepted formulae are:
|Fully-deveoped laminar flow|
|ditto, uniform heat flux|
|ditto, uniform wall temperature|
|Fully-developed turbulent flow |
Re > 2.e4
|ditto, uniform heat flux
uniform wall temperature
However the values so deduced are of uncertain reliability because of factors which the formulae cannot correctly represent, including:
Each simulation scenario (SimScene for short) opens with its 'top page' where information about each specific scenario and its interface is presented. The TubeFlow top page is displayed below.
on which access to the Menu structure is provided from the
near-the-top tab: 'Inspect or modify input data'.
2. Menu items
Clicking on this allows the display and editing of all adjustable parameters,
into ten groups, namely:
This is the first image which is displayed when the 'inspect or modify input data' box is clicked. It is the 'general' menu as the blue colour of of the label on the left makes plain. Its sole use is to allow the selection of what is here called the 'flow formulation', the three available choices of which are revealed by clicking on the 'down' arrow by the side of the menu box.
The next image shows what is then revealed.
This makes it possible to observe in detail how the profiles of velocity and temperature change from their steep-sided shape near the entrance to a more rounded one farther downstream. The corresponding diminutions of heat transfer and ot pressure gradient can likewise be quantitatively calculated.
Far downstream the profiles of velocity and temperaturs vary with distance scarcely at all. The flow is then called 'fully-developed'. The Tube-Flow SimScene assists users to simulate such flows directly, without calculations extending along the length of the tube.
Fuller explanations are supplied here, as follows.
Alternatively, if the user knows that the internal diameter is referred to internally by PHOENICS-Direct as diam, he or she could insert 0.5*diam.
Each parameter has a name used by the underlying software. The complete list of names can be seen by clicking here, to reveal the file named frommenu.htm.
This file is written into the working folder by PHOENICS-Direct, as soon as
the user has pressed the green-man 'run' button, in order to convey to the
PHOENICS Satellite module what parameters have finally been selected in the
2.3 Variables solved
Clicking on the 'variables solved' button on the left reveals the image
which contains a list of the solved-for variables. What these variables are is
indicated on the right of each box, namely: pressure,
p1; circumferential velocity u1;
radial velocity v1; axial velocity, w1; and temperature, Tem1.
A user who so wished could delete any variable from the given list, by clicking on the arrow and replacing the symbol "T" (meaning "true") by "F" (meaning "false"); but this might be unwise; for no meaningful velocities could be computed if pressure were not solved for.
The only use which users are likely to make of this menu is to switch off
solution for Tem1, for economy of computer time, when only the
pressure drop is of interest and temperature variations are small enough for
fluid density and viscosity to be uniform-valued throughout.
2.4 Material properties
When clicked on, the 'material properties' button reveals the following image:
This menu enables the physical and thermal properties of the fluid flowing inside the tube to be set, in two different ways:
When one of these has been selected, the fluid-property settings in the lower boxes are ignored; then, as the simulation proceeds, the properties prevailing at each point in the tube are evaluated, from formulae listed in the Input-Library file 089.htm For these, the just-mentioned four constant properties are not used.
Scrolling to the bottom of the window reveals the three lowest boxes which allow specification of the relevant thermal properties of the tube-wall material. They are presumed not to vary significantly with temperature. The next picture shows what is to be seen there.
The button corresponding to this group, when clicked on, elicits the image:
The first box enables the turbulence model to be selected. Thus:
The default, lvel, is a model which is known to represent tube-flow turbulence rather well.
Other possible choices are:
The next box wherein 'gravity' is set false (F), indicates that the effect of gravity on free convection is not to taken into account. This being the case, the next three boxes dealing with Cartesian components of the gravitational acceleration are of no importance.
When the effect of gravity is to be accounted for, i.e. when the gravity setting is true (T), then 9.81 m/s**2 is the gravitational acceleration acting in x-direction in cartesian co-ordinates. This was the case for the calculation leading to the shown-above velocity vectors and temperature contours.
Other choices can be made by the user if the tube is not placed horizontally.
2.6 Initial conditions
This group does not appear in the list because only steady (i.e. not
time-dependent) flow is being discussed.
2.7 Boundary conditions
The 'boundary conditions' button opens the screen shown by the following image:
where the values of fluid inlet velocity, inlet and external temperatures, outlet pressure, external heat-transfer coefficient and fouling resistance have been grouped.
Because it is sometimes convenient to set the inlet velocity by way of the Reynolds number, the pull-down menu of the top-right-hand box allows this, as the following image shows.
Only when the second choice has been made will values entered in the 'inlet velocity' box be acted upon.
The PHOENICS solver always produces an alphanumeric RESULT file; but this usually
contains too large an amount of data to interest the majority of users. Therefore the designers of SimScenes make
provision for a limited amount of information to be printed to the much smaller file
called INFOROUT. It is this which is displayed on the screen, by default, at the end of
a simulation run. A typical example can be seen by clicking
The output-related button when clicked reveals that it is possible for the user to control the amount of information printed in Inforout.
All except the first of the boxes invite 'yes' or ' no' answers, i.e. T or F, to the implied question: 'do you want to print the groups of items indicated on the right?'
The number in the first box indicates how many times in the course of the run the values are to be printed. If it is left at its unity default, they will be printed once only at the end of the run. If 2 is supplied there will also be a print-out halfway through the run; if 3 at one third and two thirds of the way, etcetera.
Although the SimScene TubeFlow contains no examples, the 'output' group is where, in other SimScenes, menu items may be provided which control graphical output displays; and even the nature and amount of what is printed in RESULT.
2.9 Computational grid
Pressing the 'computational grid' button elicits the following
This reveals that, understandably, the default grid is polar. The 36 intervals in the circumfererential direction are each of 5 degrees.
The radial-direction grid has two regions: an inner one with 20 intervals for the fluid space inside the tube and an outer one with two intervals for the metal wall. The outer region is shaded grey in the image below.
The longitudinal grid has 1 region containing 50 uniform intervals.
The settings which may be changed in the final menu, numerical, are shown below.
about which it perhaps sufices to say:
There are no parameter sets saved so far. Clicking on the 'Add current set of parameters' button will result in the screen with an empty box for a new parameter set, e.g. set1. Then click on the 'Save' button. These actions will result in the following.
The user can save as many sets of settings as he wishes, adding them in the aforesaid manner to the favorite.xml file in the input folder.
When the user wishes to use a saved set of parameters instead of the set with the default settings, in this window he will have only to select the set in question and then press the 'Use selected set' button .
In the end, do not forget to save all created sets, clicking on the 'Save all sets' button .
The other buttons in this window toolbar are as follows:
Evidence of what is in progress appears if the form of:
This too can be examined in more leisure by inspection of the gxmoni.gif file from the working folder.
or temperature curves
in (one half of) the tube.
Contours are presented only for developing flows, because for developed flows a single longitudinal location is considered. The variations in the radial direction are independent of angular position, when gravitational effects are neglected. Therefore curved-line plots present the behaviour of the solution more clearly.
The list on the left shows the files that can be saved in course of this run. There is also the 'File Prefix' box wherein the name of the multirun session is to be entered should a user wish to save separately the earlier chosen files for each concrete variant of the multirun session. The "Collect inforout" box in the bottom left corner should be selected by default. Otherwise the results of the multirun session will be lost.
Some users might wish to introduce another to-be-varied parameter from some other group. In this case, they may click the "Add Parameter" button again, choose another group from the list, choose the parameter in question from the "Selected Parameters" list and set its values in a new box on the right.
Users may add as many parameters as they wish. It should be noted, however, that computer time will be increased accordingly, as during the multiruns calculations only one parameter is changed at a time. What follows is a set of parameters chosen for the multirun, Reynolds number from the Boundary conditions group and Prandtl number - from the Properties group.
The results will be plotted only if a user has selected the box in question.
The sequence of actions is as follows.
It should be mentioned that only those parameters which have been thought to be of widest interest have been presented for possible variation via the menu panels; for the underlying parameterised Data-Input file, which may be seen by clicking here contains many more parameters which could be set.
These too could be made available, but only by those who have learned how to do so. This is a subject for discussion elsewhere.