The links below provide an outline of the material for this lesson. Be sure to carefully read through the entire lesson befor returning to Canvas to submit your assignments.
Informed decision making via an integrative design process and iterative energy simulations (early and often) is crucial during the development of a building design.
— Witmer & Brownson, 2010
This lesson introduces the concept of load and demonstrates how the fundamental heat transfer computations are applied to simple practical scenarios. In the previous lessons we focused on how the solar raditaion is converted to heat and how much useful gain is acquired from different collectors. Now we are moving into the applications zone. Let us see what kind of work that heat does next. You will have an opportunity to run a SAM model for a small scale solar heating system and see how the performance depends on different initial parameters and how it varies over time. Chapter 10 in D&B contains a number of example problems, which explain the behind-the-scene math for such modeling.
This lesson will take us one week to complete. Specific directions for different assignments are given in the table below and within this lesson pages.
Tasks | Assignment Details | Access/Directions |
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Readings |
Required:
Supplementary:
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Assignment | SAM model of a water heating system (based on D&B example, pp. ) | Specific directions for the assignments are provided on the Assignment page of this lesson. |
Quiz | 10 multiple choice questions related to Lesson 6 readings | Registered students can access the quiz in the Lesson 6 module in Canvas. |
Course Project | In lieu of discussion, this week think about the topic or scenario you would like to analyze in your Design Proposal for this course. | Share your proposed topic on the Project Topic discussion board in Course Project module in Canvas. Note: it is not final - the main goal is to start thinking in this direction and collect peer feedback. |
If you have any questions, please post them to our Questions and Answers discussion forum in Canvas. I will check that discussion forum daily to respond. While you are there, feel free to post your own responses if you, too, are able to help out a classmate.
In each solar energy system, there are supply and demand of energy, which, ideally, should be matched. The supply of solar energy depends on the available solar resource, the technology to convert solar radiation to the usable heat, losses, properties of materials, and system design. The energy demand depends on applications connected to the collectors - let it be water stoarge tank to be heated for domestic or industrial use, a space, a swimming pool, etc. Both supply and demand are time dependent. It is understandable that the solar energy varies on the daily basis, usually peaking during the day and diminishing over the night. The use of available energy also varies over time based on human activities or technical processes involved in the system. Here we use the term "load" to define a time-dependent energy need. Load is the amount of energy obtained from the source to do the work.
In a certain system, we can have a solar collector and another system - the auxiliary - to meet energy demand requirements. The solar system alone is not sometimes sufficient and requires such a backup to make sure the application in use does not run out of energy. The auxiliary can be represented by an on-site natural gas combustion system or grid, for example. Then the system load can be represented as:
L = Ls + La
with subscripts s and a standing for solar and auxiliary, respectively.
It is also useful to define the load rates (e.i. demanded power). The load rate is
L' = dL/dt
Note L' (rate) is denoted in the D&B book as L with a dot. Load rates are useful because the load are highly variable, and we may see times when the demands are met by solar energy and times when theya are met by auxiliar energy. The one important purpose of system modeling is to determine the hour-by-hour energy performance of the system, match it with loads, and decide how much auxiliary energy must be secured or purchased.
Here we can also define heating and cooling loads. Those depend on system thermal requirements. For example, if a building is too cold and requires some heating to meet a certain standard, then we deal with a heating load. On the contrary, if the building is too warm, due to internal gains and losses, then we deal with a cooling load, in other words we need to remove energy from the space.
How can loads be estimated?
Please refer to the following reading to understand what heat gains and losses should be taken into account and what equations can be used.
Book chapter: Duffie, J.A. Beckman, W., Solar Engineering of Thermal Processes, Chapter 9.
This text explains more detail about the hot-water loads, space-heating and cooling loads. Also you will be introduced to such terms as degree-days, balance temperature, building loss coefficient, and building energy storage capacity.
One commonly used method for calculating the heating and cooling requirements of a building is to calculate degree days (DD) as discussed in Section 9.3 of the D&B textbook. The rate of energy transfer from the building to the exterior environment makes up a significant piece of the energy balance calculation. This rate of energy transfer is considered to be directly proportional to degree days. The following video (3:36) provides a brief explanation on the calculation of degree days, showing how the number of degree days is directly calculated by a difference in temperature over a period of time.
OK, so this is a much shorter video than the last one, based on it example 9.3.1, which focuses on heating degree days. I just want to chat a bit about heating degree days, do one simple calculation, and talk about some of meaning behind it. So in this example, we're given a base temperature of 18 degrees Celsius and we're in Madison, Wisconsin. The example goes into much more detail on calculating heating degree days for different months, but at the real basic level we're going to calculate just December's here. Heating degree days are calculated simply by the number of days in the month and the base temperature and the month's ambient average temperatures, so t ambient bar is t average for the month. So for December, there's 31 days in the month, the base temperature's 18, and this is given a negative 5. It's pretty cold in Wisconsin. So what we end up with is 31 times 23.3, which is 722 heating degree days. So it's pretty high number. And again, I just want to chat a bit about what this means and why it's important. And essentially this number gives you an idea for how often you are far away from the reasonable temperature for your indoor space. So if it's really cold, then you'll get a high number, and that means you need to be heating a lot. Whereas, if your ambient temperature is close in temperature, if t ambient was 18 degrees right here, if this was 18 you get zero. Once you'd have zero. You would end up with zero degree days. So that means you don't need any heating that month if your month's average temperature was 18 degrees Celsius. So that's really the essence of what heating degree days are. And then in the summer months when you need cooling it goes the other way around where then you would end up with some degree days. If you're in a location that required cooling and they would be cooling degree days. So if your t ambient was very hot, then you would end up with a different number there as well. So again, that these numbers are used essentially to calculate overall heating cooling loads and how much a specific location would need in light of the ambient temperature. All right, thanks for listening.
The real-life solar energy systems are composed of a number of different components and units. Each of those components has specifics that require certain theoretical background and consideration. Several previous lessons introduced some theory behind those component models - heat transfer from the Sun to the collector; heat transfer from the collector to thermal fluid; concentration of solar radiation on optical devices, etc. While the basic calculations performed for those components can answer questions about what energy parameters can be output and what efficiency can be expected from each part of the system, the question still remains how those component models can be combined into a system model, that would allow optimization of the performance for a target application.
Overview of those component models is given in the first part of Chapter 10 if the D&B book. In these sections we can also read about the role of the heat exchangers, which provide interface between different components and allowheat transfer from one part of the system to another. Figure 10.2.1 from the D&B textbook shows a typical solar water heating system, containing a collector, heat exchanger, storage tank, pipes, and pumps. Throughout the system diagram, temperatures are noted. It is by these temperatures that the system component efficiencies can be calculated and subsequently integrated to find overall efficiency.
Book chapter: Duffie, J.A. Beckman, W., Solar Engineering of Thermal Processes, Chapter 10, Sections 10.1-10.3.
These sections discuss the key parameters responsible for heat exchange between the system components. You can also quickly scan through Sections 10.4-10.8 to be aware of various conditional adjustments to component models.
"System models are assemblies of appropriate component models." When you put together the equations decribing each of the components into the system model, the simultaneous solving of all those equations may be a serious challenge. Sometimes it is advantageous to treat the systems of equations numerically, especially if some of them are non-linear. A number of computer simulation software have been developed to help with this task. Commonly, models cover annual cycle of system operation based on available meteorological data.
Thermal analysis performed for the whole system over significant period of time provide valuable information for assessing the economics of the project. There are a couple of useful parameters that we need to introduce here. The first one - solar fraction (f) is the ratio of the solar energy obtained by the system to the total load:
fi = LS,i /Li
where Ls is the amount of solar energy used in the load, and Li is the total load per unit of time.
Or in integrated form (over a year), the same concept will be expressed as annual solar fraction (F):
F = LS/L
The second parameter useful from economical standpoint is solar savings fraction (Fsav). It accounts for energy expenditures needed to run the solar system equipment (pumps, fans, controllers..) - so call "parasitic energy".
Fsav = F - (CefΔE)/L
where Cef is the ratio of cost of additional electricity for solar system operation to the cost of fuel; ΔE is the amount of required "parasitic" electric energy. Read more about these metrics in the following source:
Book chapter: Duffie, J.A. Beckman, W., Solar Engineering of Thermal Processes, Chapter 10, Sections 10.9-10.11.
In this lesson activity you will be asked to estimate these factors for an example solar water heating system using SAM modeling.
Equilibrium and steady state are two very different thermal states, but both provide a way to analyze the thermal status of a system. Recall that an object in outer space absorbing solar radiation could be analyzed at thermal equilibrium to calculate the temperature of the object in light of the radiative heat loss and solar gain. A steady state energy balance is a similar method that is used to analyze heat transfer in light of system dynamics. The Alleyne and Jain article from the Mechanical Engineering magazine gives an overview of basic transient system modeling for thermal systems in light of the application of steady state energy balance. This method is how TRNSYS works, under the hood. Note that to simulate a thermal system, at steady state, the energy balance is calculated iteratively across time, and results in a time dependent solution. By calculating and tracking the energy through the system at each interface or sub-system, we can obtain the overall energy balance of the whole system. Careful accounting is required to calculate an accurate energy balance. All energy gain (heat transfer into the system) must equal all energy loss (heat transfer out of the system). When all energy is accounted for, we find a series of energy balance equations and can solve them simultaneously to calculate unknown temperatures, heat flow, and thermal properties.
Journal article: Alleyne A. and Jain N., Transient Thermal System, Focus on Dynamic Systems and Control, 2014, pp. 4-12.
Computer energy modeling is often used to compare the performance and cost of system alternatives. While many software tools are available for various energy modeling applications, few offer a flexible suite of components for multiple energy system types, such as buildings, solar thermal, photovoltaics, etc. One such tool that is System Advisor Model (SAM), which helps create performance and financial model for a variety of solar systems and projects. This assignment provides you with another opportunity to apply SAM modeling to a solar heating system.
Use the the example from the Introduction section of D&B online textbook (pages xxi - xxvi) to create a SAM profile of the water heating system and run the simulation for your chosen location.
The goal is to generate an estimate for the annual utilization of a solar water heater. Extract performance information, expected energy gains, and expected costs savings for water heating (here consider only cost of energy, not equipment). The adjustable parameters you can use to optimize the system performance are: type of the collector, tilt of the collector, and size of the collector.
More detailed instruction for this assignment in posted in Lesson 6 Module in Canvas.
Based on your model output, prepare a brief report to present your data and discuss the system performance. Submit your report as a single PDF file to the Lesson 6 Assignment dropbox in Canvas by 11:55 pm Wednesday night. You can insert the SAM output diagrams to your report to facilitate your discussion, although make sure they are clearly readable.
Computer energy modeling is utilized heavily in decision making during the design and retrofit process for solar thermal systems. While rarely “dead on” when it comes to accuracy, the comparative value (as opposed to absolute value) of one benchmarked model against another is tangible. Simulated energetic and financial impact of design alternatives enables the best path forward while developing a solar project.
Please double-check the to-do list on the Lesson 6 Introduction page [5] to make sure you have completed all of the activities listed there before you begin Lesson 7.