Scanning radiation flux with moving sensors in Energy2D

Figure 1: Moving sensors facing a rectangular radiator.

The heat flux sensor in Energy2D can be used to measure radiative heat flux, as well as conductive and convective heat fluxes. Radiative heat flux depends on not only the temperature of the object the sensor measures but also the angle at which it faces the object. The latter is known as the view factor.

In radiative heat transfer, a view factor between two surfaces A and B is the proportion of the radiation which leaves surface A that strikes surface B. If the two surfaces face each other directly, the view factor is greater than the case in which they do not. If the two surfaces are closer, the view factor is greater.

Figure 2: Rotating sensors inside and outside a ring radiator.

To conveniently visualize the effect of a view factor, Energy2D allows you to attach a heat flux sensor to a moving or rotating particle, with a settable linear or angular velocity. In this way, we can set up sensors to automatically "scan" the field of radiation heat flux like a radar.

Figure 1 shows a moving sensor and a rotating sensor, as well as the data they record. A third sensor is also placed to the right of an object that is being heated by the radiator. This object has an emissivity of one so it also radiates. Its radiation flux is recorded by the third sensor whose data shows a slowly increasing heat flux as the object slowly warms up.

As an interesting test case, Figure 2 shows two rotating sensors, one placed precisely at the center of a ring radiator and the other outside. The almost steady line recorded by the first sensor suggests that the view factor at the center does not change, which makes sense. The small sawtooth shape is due to the limitation of discretization in our numerical simulation.

Accurate prediction of solar radiation using Energy3D: Part I

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 and Part III.

Multiphysics simulations of inelastic collisions with Energy2D

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.

Visual analytics for uncovering complex learning: Part II

Figure 1. Most students performed well throughout.

In an early article, I have introduced the idea of using graph theory to visualize learning. In this follow-up article, I will give an example based on our recent classroom study with our mixed-reality technology that engaged 65 high school students in three chemistry classes to learn the kinetic molecular theory through exploring gas laws. The primary task of the study is to investigate how a novel kind of mixed-reality technology that combines actions in and across real and virtual worlds can help students develop molecular reasoning skills to explain macroscopic phenomena with microscopic theories.

Figure 2. Less successful than Figure 1.

The key is to study students' interactions with the technology in great details in order to shed light on how the mixed-reality experience may help students make micro-macro connections. For most students, there is a huge gap between their macro perception and their micro conception. We want to fill the gap using this powerful real-time technology to provide just-in-time, integrated instruction.

Figure 3. Performed well initially and then went astray.

The challenge is to find a way to describe both the interaction process and the reasoning process. Our software logs everything students are doing behind the scenes (i.e., we can track students' hands). Meanwhile, through our embedded assessment using causality maps (a type of concept map), we can track students' minds. Our objective is to find any conceptual changes from the "mind-tracking" data and attribute them to the "hand-tracking" data. Only after we establish this association can we evaluate the worth of the mixed-reality technology in fostering science learning.

Both the "hand-tracking" and "mind-tracking" data are being studied using graph theory. In this article, we will show the analysis of the "mind-tracking" data first. The data were generated by students connecting 6-7 provided molecular concepts between a cause and an effect to compose an explanation. Some of the concepts are irrelevant and used as distractors. For example, increasing the number of molecules has nothing to do with the molecular mass.

Given the fact that there are 65 students and four causality maps, we need a way to quickly visualize student learning. Our solution is to construct graphs based on these data. It becomes immediately obvious that this visual analytics can provide extremely informative graphics that shows student learning on a statistical basis. The three images in this article show that: 1) Most students in Class E performed well throughout Graph 3; 2) Students are less successful in Class B in Graph 1; and 3) Students in Class D performed well in Graph 4 at the beginning and then went astray -- largely because this is a more difficult challenge that involves multiple reasoning paths. (The gray bands in the three images represent the correct reasoning chains in each case. The thickness of an edge represents the number of students who drew the link in the concept map.) These graphs can potentially show the weaknesses of the students at the scale of the whole class. I could not help thinking how useful this would be to the teacher if such informative feedback is provided to her.

This graph-based analytics is NOT just visual -- It is also interactive. You can examine all the student data we have collected at this page, programmed in Dart -- the latest Web programming language from Google. The page provides filters for you to examine and compare any number of students' work. You can also drag the nodes around for clarity. This kind of feedback tool is what teachers would want to have and what we should create for them. The world has spent billions of dollars building visual business analytics to assist business executives to make investment decisions day to day. How about spending a bit money to build an infographics system to assist teachers to make instructional decisions day to day?