Accurate prediction of solar radiation using Energy3D: Part II

Wednesday, July 16th, 2014 by Charles Xie
About a week ago, I reported our progress in modeling worldwide solar radiation with our Energy3D software. While our calculated insolation data for a horizontal surface agreed quite well with the data provided by the National Solar Radiation Data Base, those for a south-facing vertical surface did not work out as well. I suspected that the discrepancy was partly caused by missing the reflection of short-wave radiation: not all sunlight is absorbed by the Earth. A certain portion is reflected. The ability of a material to reflect sunlight is known as albedo. For example, fresh snow can reflect up to 90% of solar energy. People who live in the northern part of the country often experience strong reflection from snow or ice in the winter.

Figure 1. Calculated and measured insolation on a south-facing surface.
In the summer, the Sun is high in the sky. A south-facing plate doesn't get as much energy as in other seasons, especially near the Equator where the Sun is just above your head (such as Honolulu as included in the figures above). However, the ambient reflection can be significant. After incorporating this component into our equations following the convention in the ASHRAE solar radiation model, the agreement between the calculated and measured results significantly improves -- you can see this big improvement by comparing Figure 1 (new algorithm) with Figure 2 (old algorithm).

Figure 2. Results without considering reflected short-wave radiation.
This degree of accuracy is critically important to supporting meaningful engineering design projects on renewable energy sources that might be conducted by students across the country. We are working to refine our computational algorithms further based on 50 years' research on solar science. This work will lend Energy3D the scientific integrity needed for rational design, be it about sustainable architecture, urban planning, or solar parks.

Revisit Part I.

Accurate prediction of solar radiation using Energy3D: Part I

Tuesday, July 8th, 2014 by Charles Xie
Solar engineering and building design rely on accurate prediction of solar radiation at any given location. This is a core functionality of our Energy3D CAD software. We are proud to announce that, through continuous improvements of our mathematical model, Energy3D is now capable of modeling solar radiation with an impressive precision.

Figure 1. Comparison of measured and calculated solar radiation on a horizontal plate at 10 US locations.
Figure 1 shows that Energy3D's calculated results of solar energy density on a horizontal plate agree remarkably well with, the National Solar Radiation Database that houses 30 years of data measured by the National Renewable Energy Laboratory of the U.S. Department of Energy -- for 10 cities across the US. One striking success is the prediction of a dip of solar radiation in June for Miami, FL (see the second image of the first row). Overall, the predicted results are slightly smaller than the measured ones. 

Note that these results are theoretical calculations, not numerical fits (such as using an artificial neural network to predict based on previous data). It is pretty amazing if you think about this: Through some complex calculations the number for each month and each city come very close to the data measured for three decades at those weather stations scattered around the country! This is the holy grail of computer simulation. This success lays a solid foundation for our Energy3D software to be scientifically and engineeringly relevant.

Figure 2. Comparison of measured and calculated solar radiation on a south-facing plate at 10 US locations.
The National Renewable Energy Laboratory also measured the solar radiation on surfaces that tilt at different angles. The predicted trends for the solar energy density on an upright south-facing plate agree reasonably well (Figure 2) with the measured data. For example, both measured and calculated data show that solar radiation on a south-facing plate peaks in the spring and fall for most northern locations and in the winter for tropical locations. It is amazing that Energy3D also correctly predicts the exception --  Anchorage in Alaska, where the solar data peak only in the spring!

Quantitatively, Energy3D seems to underestimate the solar radiation more than in the horizontal case shown in Figure 1, especially for the summer months. We suspect that this is because a vertical plate has a larger contribution from the ambient radiation and reflection than a horizontal plate (which faces the sky). We are now working towards a better model to correct this problem.

For Energy3D to serve a global audience, we have collected geographical and climate data of more than 150 domestic and foreign locations and integrated them into the software (Version 3.2). If you live in the US, you are guaranteed to find at least one location in your state.

Go to Part II.

Multiphysics simulations of inelastic collisions with Energy2D

Friday, July 4th, 2014 by Charles Xie
Figure 1. Mechano-thermal simulation of inelastic collision.
Many existing simulations of inelastic collisions show the changes of speeds and energy of the colliding objects without showing what happens to the lost energy, which is often converted into thermal energy that spreads out through heat transfer. With the new multiphysics modeling capabilities, the Energy2D software can show the complete picture of energy transfer from the mechanical form to the thermal form in a single simulation.

Figure 2. Thermal marks left by collisions.
Figure 1 shows the collisions of three identical balls (mass = 10 kg, speed = 1 m/s) with three fixed objects that have different elasticities (0, 0.5, and 1). The results show that, in the case of the completely inelastic collision, all the kinetic energy of the ball (5 J) is converted into thermal energy of the rectangular hit object (at this point, the particles in Energy2D do not hold thermal energy, but this will be changed in a future version), whereas in the case of completely elastic collision, the ball B1 does not lose any kinetic energy to the hit object. In the cases of inelastic collisions, you can see the thermal marks created by the collisions. The thermometers placed in the objects also register a rise of temperatures. This view resembles infrared images of floors taken immediately after being hit by tennis balls.

Figure 3. Collisions in Energy2D.
Energy2D supports particle collisions with all the 2D shapes that it provides: rectangles, ellipses, polygons, and blobs. Figure 2 shows the thermal marks on two blobs created by a few bouncing particles. And Figure 3 shows another simulation of collision dynamics with a lot of particles bouncing off complex shapes (boy, it took me quite a while in this July 4 weekend to hunt down most of the bugs in the collision code).

The multiphysics functionality of Energy2D is an exciting new feature as it allows more realistic modeling of natural phenomena. Even in science classrooms, realism of simulations is not just something that is nice to have. If computer simulations are to rival real experiments, it must produce not only the expected effects but also the unexpected side effects. Capable of achieving just that, a multiphysics simulation can create a deep and wide learning space just like real experiments. For engineering design, this depth and breadth are not options -- there is no open-endedness without this depth and breadth and there is no engineering without open-endedness.

Simulating thermal radiation with Energy2D

Friday, June 27th, 2014 by Charles Xie
Figure 1: Stefan's Law in action.
The original ray-tracing radiation solver in our Energy2D software suffers from performance problems as well as inaccuracies (no, light particles do not travel that slowly as shown in it). After some sleepless nights, I finally implemented a real radiation solver, coupled it with the heat and fluid solvers, and supported both the convex and concave shapes (see this short paper for the mathematics and the algorithms). At last, Energy2D is capable of simulating all three heat transfer mechanisms in a decent way.

Figure 2: Radiation in a box.
Able to simulate heat, fluid, radiation, particles, and any combination of them, Energy2D is now one step closer towards a full multiphysics capacity. Despite the fact that all these complex calculations are done in real time on a single computer, the software still runs at a pretty amazing speed on an average Windows tablet (such as the Surface Pro). I guess this is why our industry friends love it (although Energy2D is mostly designed for K-12 students, to my surprise, quite a number of engineers are using it to do conceptual product design). Who doesn't like a CFD tool for dummies that can save time from the long preprocessor-solver-postprocessor cycle?

Figure 1 shows a simulation that illustrates radiation heat transfer. As you can see, energy can "jump" from a high-temperature object (a radiator) to a low-temperature one without heating the medium between them (unlike the cases of conduction and convection). Users
Figure 3. Radiation in a circle.
can adjust the temperature of the radiator on the left and investigate how the radiation heat transfer increases with respect to the temperature, as per Stefan-Boltzmann's Law. The image also shows the view factor field used in the computation. The simulation provides many subtleties. For example, if you observe carefully, you can find that the radiation barrier used to separate the left compartment from the right one increases the heating on the right side of the upper left object and the left side of the upper right object -- because it reflects the radiation from the two radiators at the lower part of the box to the two sides!

Figures 2 and 3 show radiation among different shapes in an enclosed space. They show how accurate the radiation solver may be. The radiation heating on the side walls seems to make sense. In Figure 2, the upper one gets the most radiation energy because it is the closest to the radiator. The right one gets the least because part of it is blocked from the radiator by the other object in a box. A further test case using a symmetric setup shows its accuracy.

Global pattern of insolation predicted by Energy3D

Saturday, May 31st, 2014 by Charles Xie
Figure 1. Global insolation pattern from Pole to Pole
The Sun's power drives the climate of the Earth. Accurately modeling the incident solar radiation, namely, insolation, at a given location is important to the design of high-performance buildings. As I have blogged last week, the insolation calculation in our Energy3D software considers the incident angle of the Sun to the surface, the duration of the day, and the air mass. And we have recently incorporated the effect of altitude and the ambient inputs.

Figure 2. Real data for the three locations (source)
In Energy3D, we can easily investigate the global pattern of insolation by horizontally placing a sensor module on the ground and then collecting the sensor data throughout the year. We can easily change the latitude and collect a new set of data. Figure 1 shows the global insolation pattern from the North Pole to the South Pole. The time integral of each curve represents the total solar energy a location at the corresponding latitude receives. There is an interesting observation from Figure 1: The Equator doesn't actually have the highest peak value and its peak values are not in the summer but in the spring and fall. However, because the insolation does not differ very much from season to season in the Equator, its time integral is much larger, which is the Equator is hot all year round.
Figure 3. Energy3D's prediction


How accurate are the predictions of Energy3D? Let's pick three locations that someone has collected real data, as shown in Figure 2. More insolation data can be found on this website. (Surprisingly, the peak solar energy at the South Pole is higher than the peak solar energy at the Equator.)

Figure 3 shows that the insolation values predicted by Energy3D. As you can see, the predicted trend agrees reasonably well with the trend in the real data. Overall, Energy3D tends to underestimate the insolation by about 50% (after unit conversion), however.

The effect of air mass on building solar performance

Monday, May 26th, 2014 by Charles Xie
Figure 1
As it travels through the atmosphere of the Earth, the light from the Sun interacts with the molecules in the air and are scattered or absorbed, causing the radiation energy that ultimately reaches the ground to weaken. This effect is more significant in early morning or late afternoon than at noon because sunlight has to travel a longer distance in the atmosphere before reaching the ground (Figure 1) and, therefore, has a higher chance of being scattered or absorbed in the atmosphere. This is also why stars appear to be less bright at the horizon than above head.

In solar energy engineering, this effect is called the air mass, which defines the length of the sunlight’s path through the atmosphere (not to be confused with air mass in meteorology, which defines a volume of air that can be as large as thousands of square miles).

Why is the air mass important to predicting solar energy performance of a building?

Figure 2
Let's consider a high latitude location like Boston. For a south-facing window, the Sun is lower in the sky in the winter, causing more solar energy to shine into the house, compared with the case in the summer. This is known as the projection effect (Figure 2). Does this mean that we get a lot more solar energy from the window in the winter like the cross-sections of the solar beams in Figure 2 seem to indicate? Not so fast.

In Boston, the day in the winter can be as short as 9 hours and the day in the summer can be as long as 15 hours. So even if the projection effect favors the winter condition, the duration of the day doesn't. Our calculation must consider these two competing factors. After these considerations, the solar energy the window gains in 12 months is shown in Figure 3: It turns out that the window still gets more energy in the winter -- the projection effect wins big!

For now.

OK, let's now include the effect of the air mass in the calculation. Big surprise (at least to me when I first saw the results)!

Figure 3
Figure 4 shows that a south-facing window no longer picks up the highest amount of solar energy in the winter. Its solar gain peaks in the spring and fall and the difference between the summer value and the winter value decreases dramatically.

As comparisons, Figures 3 and 4 also show the results for a west-facing and a north-facing window, both peaking in the summer (for different reasons that we will not elaborate here).

Figure 4
Is this finding the universal truth? Not at all! It turns out that the peak solar gain of a south-facing window depends on the latitude. Figure 5 shows the comparison of four locations from Miami to the North Pole. In Miami, the energy gain peaks in the winter and declines almost to zero in the summer. In contrast, at the North Pole (to which anywhere else is south), the energy gain peaks in the summer and is nearly zero for almost six months. The situation of Moscow is between Boston and the North Pole, with the peaks moving more towards the summer and are less distinguishable.
Figure 5

Given Figure 5, the fact that a south-facing window in Boston receives peak solar energy in the spring and fall becomes comprehensible now -- by the law of mathematics, the transition from the Equator to the North Pole must be smooth and the energy peak of any latitude in-between must be somewhere between winter (the season of peak energy in the Equator) and summer (the season of peak energy in the North Pole).

Interestingly enough, the peak energy at the North Pole is comparable to that at any other location in Figure 5. Considering that the Arctic has 24 hours of sun in the summer and the projection effect reaches maximum, this result is in fact a good demonstration of the air mass effect. Without the air mass, the North Pole would have gotten three times of solar energy as it does now, making the Arctic a tropical resort in the summer. Our planet would have been quite different.

All these analytic capabilities are freely available in our Energy3D software and all you need to do are some mouse clicks and some thinking. For the air mass calculation, you can choose to use the Homogeneous Sphere Model (default) or Kasten-Young Model. You can also turn the air mass off temporarily to evaluate its effect, just like what I showed in this article -- this is a piece of cake in Energy3D but is impossible to do in reality because you cannot turn the atmosphere off!

Iranian studies show the effectiveness of Molecular Workbench

Wednesday, May 7th, 2014 by Charles Xie
A Molecular Workbench virtual experiment used in the Iranian study.
In the May Issue of Journal of Educational and Social Research, published by MCSER (Mediterranean Center of Social and Educational Research) in Rome, researchers from Iran and Malaysia reported that "students who were taught using the Molecular Workbench software performed better in post-tests on five chemistry topics as compared with those who received conventional instruction." This study was conducted in Iranian secondary schools with 70 students. The researchers also reported that "students using the software also found this software useful in the learning of chemistry." Their paper, titled with "Molecular Workbench Software as Computer Assisted Instruction to Aid the Learning of Chemistry", is freely available in this open-access journal. The authors are Elaheh Khoshouie, Ahmad Fauzi Mohd Ayub, and Farhad Mesrinejad, from two universities in Iran and Malaysia, respectively.

This example, once again, demonstrates the power of visualization in science education. Regardless of the culture or religion children may have grown up with, scientific visualization transcends all the man-made barriers to convey science messages to the young minds. In the case of Molecular Workbench, the effect is even more profound because the heart of it has actually been written in the universal language of humanity -- mathematics.

More analytic capabilities added to Energy3D

Sunday, April 27th, 2014 by Charles Xie

Add any number of sensors to a house.
According to Wikipedia, computer-aided engineering (CAE) is typically done through the following steps:
  1. Pre-processing: This step defines the 3D geometry, the initial conditions, and the boundary conditions of the model.
  2. Analysis solver: This step predicts the properties of the model and, sometimes, their time evolution.
  3. Post-processing: This step visualizes the results of the analysis using maps and graphs.
Sensor graphs.
In real engineering practices, these three steps are often done using different computer programs, run on different computers, or even carried out by different people. This time-consuming and complicated process often prevents CAE tools from being productive in the classroom, as many students cannot overcome the long learning curve in a very short time permitted by their schedules.

One of the critical features that distinguish our Energy3D software from other CAD tools is that it eliminates all these gaps and delays. From day one of the Energy3D project, we have envisioned a CAD tool that supports concurrent inquiry and design, thus allowing students to explore many design options with scientific inquiry and rapidly get feedback to help them make design decisions. This is an essential innovation that makes a CAD tool broadly useful for teaching engineering design skills rather than just computer drawing skills.
Construction cost.

To move closer to our goal, we have recently added many new, exciting features to Energy3D Version 3.0 to greatly advance its analytic capacity. These features include:

1) Virtual sensors. Students can add any number of sensor modules to any surface of the buildings under design to measure insolation density and heat transfer at the building envelope. This is analogous to using sensor-based data loggers in building diagnostics. Virtual sensors will allow Energy3D to eventually support systems design, creating opportunities for students to practice systems thinking in the context of building intelligence. For example, students will be able to simulate Google's NEST Learning Thermostat and explore how much energy can be saved using these smart house technologies.

Energy vs. orientation
2) Construction cost analysis. Any real engineering project is subject to a budgetary limit. While students are designing, Energy3D predicts the construction cost and breaks it down into categories. They will get a warning when a design goes over a budget, creating a financial constraint for a design project.

3) Building orientation optimization. Students can rotate a building and explore how energy can be saved by simply choosing an optimal orientation.

Together with the features of seasonal analyses announced before, Energy3D provides an increasingly comprehensive simulation environment for learning engineering design in the context of sustainable housing.

Green building design with Energy3D: How big should south-facing windows be?

Thursday, April 17th, 2014 by Charles Xie
Many people know that south-facing windows can help to heat a house in the winter because they let a lot of sunlight in. Exactly how much of the south-facing wall should we allocate to windows? What are the downsides? How can we avoid them? Our Energy3D software allows students to explore the problems and find the solutions.

Figure 1


Suppose we have a simple house like the one shown in Figure 1 and we are in the Boston area. Energy3D supports students to try a design choice, run a simulation, collect the data, analyze the result, and evaluate the solution -- all in real time as is shown in the video in this post. Energy3D's powerful simulation and analysis tools provide instantaneous feedback to students so that their design processes can be guided and informed by the scientific and engineering principles built in the software. Let's use the investigation of south-facing windows described above as an example.


Figure 2 (Excel graph)
Suppose a student follows the design trajectory as shown in Figure 1. A challenge is to keep the yearly energy cost needed to maintain the temperature of the house at 20℃ to be as low as possible. The student begins with adding a small window to the south side of the house. By running the seasonal energy analysis tool in Energy3D, she immediately discovers that, by adding a small window, she can cut the energy cost a bit. Then she enlarges the window and finds that more energy can be saved. So she goes on to increase the size of the window. However, she finds that, at some point, larger windows on the south side start to cost more energy. After she adds two large windows, the energy cost increases over 15%, compared with the case of no window at all. Figure 2 shows the energy cost, broken down to heater and AC, as a function of the window area. That doesn't quite make sense to her. So she has to stop and think about why.
Figure 3 (Energy3D graph)


The trend in Figure 2 suggests that, with the enlargement of windows on the south side, the cooling cost continues to rise while the heating cost levels off. A monthly breakdown in Figure 3 reveals this trend more clearly. As shown by the golden dashed line in Figure 2, the solar heating through the windows increases rapidly when their total area gets enlarged.

Figure 4 (Energy3D graph)
Figure 5 (Energy3D graph)
If she wants to keep the large window area in the south side (for natural lighting and sanity of the occupants!), she has to reduce the solar heating effect through the windows in the summer. One way to do this is to plant tall deciduous trees in front of the windows as shown in Figure 1. The trees provide shading for the windows in the summer but let sunlight shine through to the windows in the winter (in Energy3D, deciduous trees have leaves from May 1st to November 30th). Figure 4 shows the effect of the two deciduous trees on the solar gain through the two south-facing windows. From the graph, she can see that the trees cut down the solar heating in the summer. As a result, the AC cost is reduced, as shown in Figure 5, whereas the heating cost is almost unchanged.

She concludes that, with the trees planted to the south of the house, the net energy cost over a year can be decreased to lower than the case of no window at all, providing an acceptable solution that takes care of view, lighting, and landscaping.

The Energy3D graphs in this blog post show that students can keep the results of previous runs (the curve of each run is labeled by a number) and superimpose new data on top of them. As the data view can get quite complex, Energy3D provides options to turn on/off data types and runs. The embedded video shows how those features work for visualizing and analyzing the simulation results.

PS: Some readers may notice that our calculations predict higher AC cost in September than in August or July. This is because when those calculations were done, the house had no window on the east or west side. Adding windows to those sides, the AC cost will peak around July or August -- even when the trees are not present.

The first paper on learning analytics for assessing engineering design?

Thursday, January 30th, 2014 by Charles Xie
Figure 1
The International Journal of Engineering Education published our paper ("A Time Series Analysis Method for Assessing Engineering Design Processes Using a CAD Tool") on learning analytics and educational data mining for assessing student performance in complex engineering design projects. I believe this is the first time learning analytics was applied to the study of engineering design -- an extremely complicated process that is very difficult to assess using traditional methodologies because of its open-ended and practical nature.

Figure 2
This paper proposes a novel computational approach based on time series analysis to assess engineering design processes using our Energy3D CAD tool. To collect research data without disrupting a design learning process, design actions and artifacts are continuously logged as time series by the CAD tool behind the scenes, while students are working on an engineering design project such as a solar urban design challenge. These "atomically" fine-grained data can be used to reconstruct, visualize, and analyze the entire design process of a student with extremely high resolution. Results of a pilot study in a high school engineering class suggest that these data can be used to measure the level of student engagement, reveal the gender differences in design behaviors, and distinguish the iterative (Figure 1) and non-iterative (Figure 2) cycles in a design process.

From the perspective of engineering education, this paper contributes to the emerging fields of educational data mining and learning analytics that aim to expand evidence approaches for learning in a digital world. We are working on a series of papers to advance this research direction and expect to help with the "landscaping" of  those fields.