USER MANUAL:
THERMOSIPHON MATHEMATICAL MODEL
CONTENTS
I.
General Purpose Description
II.
Creating a Set of Criteria
III.
Opening the Mathematical Model
IV.
Inputs
A. Parameters
B. Operating Conditions
C. Initial Status
V.
Running the Program
VI.
Running a Single Sub-Analysis Worksheet
VII.
Managing Results
VIII.
Optimization Process
I.
GENERAL PURPOSE DESCRIPTION
The Mathematical Model is an analysis tool that can be used to aid in the
optimization of the design of a thermosiphon solar hot water heater. This tool
analyzes a specific design under given operating conditions and provides
information on the system’s operation – mainly temperatures and fluid flow rates
throughout the system.
First, criterion for evaluating the suggested system should be formed. This
criterion may include desired minimum temperature, desired maximum
temperature, maximum system cost, etc.
Once the physical thermosiphon design, operating conditions, and initial status
have been chosen for analysis, the specific values can be inputted into the
Mathematical Model and the program can be run. The consequential outputs will
provide an initial set of results to compare further designs. By changing the
parameters, a variety of different acceptable systems may be formed.
After a thorough parameters search has been completed, a complete cost analysis
should be completed for each design using the available materials and costs. This
will be the final design factor.
This process may be accelerated after realizing general trends that relate material
properties to system outputs.
II.
CREATING A SET OF CRITERIA
Creating a set of criteria is a crucial part of design optimization. This step
requires thorough communication with the client.
Questions to ask:
- Will this be used as a pre-heater?
- What is the budget?
- What is the desired temperature?
- What is the minimum temperature?
- What temperature is too hot?
- What percent of the time can the temperature be below the minimum
temperature?
- What is the desired payback period?
- Are there any geometric/weight constraints?
- How much does electricity cost?
- What are the available materials and their respective costs?
Once the constraints and the desired output criteria are well understood, create
acceptable ranges in terms of the Mathematical Model’s parameters and outputs.
Some of these constraints may be dependent on numerous design choices, for
instance, if the client wants to use the thermosiphon system as a pre-heater, then
the minimum temperature does not come into play, but the cost of electricity and
the payback period might. The final set of criteria should be easy to compare to
output data. If the desired criteria is not represented by the Mathematical Model’s
outputs, a new output sheet may be added (refer to ___________ for instructions).
III. OPENING THE MATHEMATICAL MODEL
1. Open the “[Mathematical Model Excel Name]” (the computer must be
equipped with Microsoft Excel).
2. Verify that Visual Basic is installed by going to Tools, Macros, Macro.
Highlight IMPLICIT, if the edit button is available, then the computer is
equipped with Visual Basic. Otherwise, Visual Basic must be installed.
3. Verify that the iteration function is calibrated correctly. Go to Tools,
Options. Click on the folder Calculation. Make sure Manual and
Iteration are checked. Set Maximum Iterations to ‘1’ and Maximum
Change to ‘0.001’.
IV. INPUTS
A. Parameters
The parameters include the geometry and material properties of a given
thermosiphon system. For a complete parameters list refer to the Mathematical
Model: Parameters worksheet. Note that the inputs are all in metric units.
The parameters are broken up into the parametric inputs for each sub-analysis
worksheet. Some of these parameters are repeated. Do not input data into the
gray cells as they are references to or functions of previously inputted parameters.
Also do not change the cells with red lettering unless better data can be found
than the reference noted.
Next to the inputted values indicate references, explanations, and other notes.
NOTE: Under Parameters: Tank Analysis: System Time Step references another
sheet. Inter-sheet references are undesirable, because each sheet should be able to
be isolated.
B. Operating Conditions
The operating conditions include weather conditions and the hot water usage
operation. For a complete list of operating conditions refer to the Mathematical
Model: Operating Conditions worksheet. Again all of the inputs are in metric
units. The System Time Step is the only input that is not a function of time (for
obvious reasons). The other input variables are again split up into of their
respective sub-analysis worksheets. The different rows denote different time
steps. Do not input values into the gray-headed columns; they include reference
to other operating conditions. The black background cells are variables that have
not been measured in our tests, but can be estimated. The yellow cells have been
inputted from our test data, and such information can be obtained from weather
data, estimations, or other correlations.
Ambient Temperature, Volumetric Flow Rate - Tank Output, and Insolation in the
Plane of the Panel are variables that vary with time. The other operating
conditions can be seasonal averages or approximations and can remain constant.
C. Initial Status
The initial status defines the first reference for the sub-analyses to base their first
calculations on. While these values may not be correct, they initialize the system
for iteration. They will converge after the first time step, making the zero’th time
step useless information. As long as the calculated variables converge to a
reasonable value, these do not need to be changed (although making them close to
the actual values may decrease the calculation time slightly). The cells with the
black background (Tank Temperature #) need to be initialized to their correct
value because they do not converge in a single time step like the other variables
do. Again, the gray variables denote references or calculations, and should not be
edited.
NOTE: Volumetric Flow Rate - Array Pipe and distance refer to the Parameters
worksheet.
V.
RUNNING THE PROGRAM
1. First make sure all Inputs (Parameters, Operating Conditions, and
Initial Status) are completed and within their accepted constraints.
2. Go to the worksheet to be viewed during the computations
3. Click on Tools, Macro, Macros
4. Highlight the Macro named IMPLICIT
5. Click Run
6. Return to the worksheet to be viewed during computations
7. Wait, this may take a while depending on the variation in the inputs of
consecutive time steps and the number of time steps.
8. If you want to interrupt the calculation, press Esc. Click Debug. After
making the desired operations, if you want to continue the calculations go
to the Visual Basic window and press the triangle at the top of the screen.
If you wish to end the calculation, press the square.
9. If the program fails to work, refer to the Trouble-Shooting Manual.
VI. RUNNING A SINGLE SUB-ANALYSIS WORKSHEET
If you wish to obtain outputs based on a single worksheet, you need not edit the
Inputs (Parameters, Operating Conditions, and Initial Status). Rather, you must
input the Inputs and Parameters within the worksheet in question. Hold the F9
key until the outputs converge.
VII. MANAGING RESULTS
The Operation History worksheet provides a set of quantitative data for the
outputs of every sub-analysis worksheet for each time step. The use of graphs can
greatly help interpret this data through the visual comparison of the desired
outputs with their corresponding criteria. Place the most helpful graphs on
another worksheet. As such graphs are obtained from different system designs,
they can be easily compared.
VIII. OPTIMIZATION PROCESS
1. Before choosing an initial set of parameters, run preliminary calculations
assuming a reasonable efficiency (20-40%) and a daily hot water usage
volume to find overall panel and tank size (refer to ___________).
2. Choose materials based solely on the best material properties (for the first
design, do not consider expenses).
3. Estimate the parameters; the most important values include the Tank Inner
Diameter, Tank Inner Length, Number of Array Pipes, Number of Glass Cover
Plates, Pipe Length – Vertical Array, Pipe Spacing – Vertical Array, Pipe
Inner Diameter – Vertical Array, Absorber Plate Thickness, Thermal
Conductivity – Absorber Plate, Thermal Conductivity – Array Pipe, and all
Thermosiphon Pressure worksheet parameters.
4. Input a standard set of operating conditions that can be used to verify that the
system meets the criteria. This standard set of operating conditions should be
chosen to include a wide range of conditions that may be experienced by the
system.
5. After analyzing the design using the Mathematical Model, make the smallest
thermosiphon system that still meets the design criteria by only changing the
geometry. Do not spend too much time perfecting the system, but get a
variety of different geometric suggestions with the best materials.
6. Obtain cost estimates for each of these.
7. Experiment with a new set of materials that have less desirable properties, but
are less costly.
8. Obtain acceptable designs comparable to the outputs of previous designs
under the same conditions.
9. Obtain cost estimates for each of these.
10. Continue to cycle through steps 7 through 9 until a satisfactory system has
been achieved.
11. Make better estimations for the system parameters.
12. Run the system again, and edit the system accordingly (if the outputs have
fallen below the acceptable limit increase the system size, if the outputs have
risen decrease the system size).