Posts Tagged ‘Heat transfer’

Simulating cool roofs with Energy3D

August 20th, 2014 by Charles Xie
Fig. 1: Solar absorption of colors.
Cool roofs represent a simple solution that can save significant air-conditioning cost and help mitigate the urban heat island effect, especially in hot climates. Nobel Prize winner and former Secretary of Energy Steven Chu is a strong advocate of cool roofs. It was estimated that painting all the roofs and pavements around the world with reflective coatings would be "equivalent to getting 300 millions cars off the road!"

With Version 4.0 of Energy3D (BTW, this version supports 200+ worldwide locations -- with 150+ in the US), you can model cool roofs and evaluate how much energy you can save by switching from a dark-colored roof to a light-colored one. All you need to do is to set the colors of your roofs and other building blocks. Energy3D will automatically assign an albedo value to each building block according to the lightness of its color.

Figure 1 shows five rectangles in different gray colors (upper) and their thermal view (lower). In this thermal view, blue represents low energy absorption, red represents high energy absorption, and the colors in-between represents the energy absorption at the level in-between.

Now let's compare the thermal views of a black roof and a white roof of a cape code house, as shown in Figure 2. To produce Figure 2, the date was set to July 1st, the hottest time of the year in northern hemisphere, and the location was set to Boston.

Fig. 2: Compare dark and white roofs.
How much energy can we save if we switch from a perfectly black roof (100% absorption) to a perfectly white roof (0% absorption)? We can run the Annual Energy Analysis Tool of Energy3D to figure this out in a matter of seconds. The results are shown in Figure 3. Overall, the total yearly energy cost is cut from 6876 kWh to 6217 kWh for this small cape code house, about 10% of saving.

Figure 3 shows that the majority of savings comes from the reduction of AC cost. The reason that the color has no effect on heating in the winter is because the passive solar heat gains through the windows in this well-insulated house is enough to keep it warm during the sunshine hours. So the additional heat absorbed by the black roof in the same period doesn't offset the heating cost (it took me quite a while to figure out that this was not a bug in our code but actually the case in the simulation).

Fig. 3: Compare heating and AC costs (blue is white roof).
Of course, this result depends on other factors such as the U-value and thermal mass of the roof. In general, the better the roof is insulated, the less its color impacts the energy cost. With Energy3D, students can easily explore these design variables.

This new feature, along with others such as the heat flux visualization that we have introduced earlier, represents the increased capacity of Energy3D for performing function design using scientific simulations.

Here is a video that shows the heating effect on roofs of different colors.

Visualization of heat flux in Energy3D using vector fields

August 14th, 2014 by Charles Xie
Fig. 1: Winter in Boston
One of the strengths of our Energy3D CAD software is its 3D visualizations of energy transfer. These visualizations not only allow students to see science concepts in action in engineering design, but also provide informative feedback for students to make their design choices based on scientific analyses of their design artifacts.

Fig. 2: Summer in Boston
A new feature has been added to Energy3D to visualize heat transfer across the building envelope using arrays of arrows. Each arrow represents the heat flux at a point on the surface of the building envelope. Its direction represents the direction of the heat flux and its length represents the magnitude of the heat flux, calculated by using Fourier's Law of Heat Conduction. Quantitatively, the length is proportional to the difference between the temperatures inside and outside the building, as well as the U-value of the material.

Fig. 3: Winter in Miami
The figures in this post show the heat flux visualizations of the same house in the winter and summer in Boston and Miami, respectively. Like the solar radiation heat map shown in the figures, the heat flux is the daily average. The U-value of the windows is greater than those of the walls and roof. Hence, you can see that the heat flux vectors in the winter sticking out of the windows are much longer than those sticking out of the walls or roof. In the summer, the heat flux vectors point into the house but they are much shorter, agreeing with the fact that Boston's summer is not very hot.

Fig. 4: Summer in Miami
Now move the same house to Miami. You can see that even in the winter, the daily average heat flux points inside the house, agreeing with the fact that Miami doesn't really have a winter. In the summer, however, the heat flux into the house becomes significantly large.

These visualizations give students clear ideas about where a house loses or gains energy the most. They can then adjust the insulation values of those weak points and run simulations to check if they have been fixed or not. Compared with just giving students some formulas or numbers to figure out what they actually mean to science and engineering practices, experiential learning like this should help students develop a true understanding of thermal conduction and insulation in the context of building science and technology.

Here is a YouTube video of the heat flux view.

Multiphysics simulations of inelastic collisions with Energy2D

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

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.

Temperature change may not represent heat transfer; heat flux does.

May 4th, 2014 by Charles Xie
Figure 1 (go to simulation)
There has been some confusion lately about the heat transfer representations in Energy2D simulations. By default, Energy2D shows the temperature distribution and uses the change of the distribution to visualize heat flow. This is all good if we have only one type of medium or material. But in reality, different materials have different thermal conductivities and different volumetric heat capacities (i.e., the ability of a given volume of a substance to store thermal energy when the temperature increases by one degree; the volumetric heat capacity is in fact the specific heat multiplied by the density).

Figure 2 (go to simulation)
According to the Heat Equation, the change of temperature is affected by the thermal diffusivity, which is the thermal conductivity divided by the volumetric heat capacity (now that I have written the terminology down, I can see why these terms are so confusing). In general, a higher thermal conductivity and a lower volumetric heat capacity will both result in faster temperature change.

To illustrate my points, Figure 1 shows a comparison of temperature changes in two materials. The pieces that have the same texture are made of the same material. The upper ones have a lower thermal conductivity but a higher thermal diffusivity. The lower ones have a higher thermal conductivity but a lower thermal diffusivity. In both upper and lower setups, the piece on the left side maintains a higher temperature to provide the heat source. Everything else starts with a low temperature initially. The entire container is completely insulated -- no heat in, no heat out. Two thermometers are placed just at the right ends of the middle rods. Their results show that the temperature rises more quickly in the upper setup (Figure 1) -- because it has a higher diffusivity.

The fact that something diffuses faster doesn't mean it diffuses more. In order to see that, we can place two heat flux sensors somewhere in the rods to capture the heat flows. Figure 2 shows the results from the heat flux sensors. Obviously, there is a lot more heat flow in the lower setup in the same time period.

Figure 3 (go to simulation)
The conclusion is that it is the heat flux, not the temperature change, that ultimately measures heat transfer. If you want to know how fast heat transfer occurs, the thermal conductivity is a good measure. However, if you want to know how fast temperature changes, the thermal diffusivity is a good measure. This may be also important to remember for those who use infrared cameras: Infrared cameras only measure temperature distribution, so what we really see from infrared images is actually thermal diffusion and thermal diffusion alone could be deceiving.

Figure 4 (go to simulation)
To make this even more fun (or confusing), let's replace the pieces on the right of the container with two pieces that are made of the same material that has a volumetric heat capacity between those of the other upper and lower ones. You wouldn't think this change would affect the results, at least not qualitatively. But the truth is that, the temperature in the lower setup in this case rises more quickly than the temperature in the upper setup -- exactly opposite to the case shown in Figure 1! The surprising result indicates how unreliable temperature change may be as an indicator of heat transfer. In this case, the temperature field of the middle rod is affected by what it is connected with. If we look at the results from the heat flux sensors (Figure 4), the heat flux that goes through the rod is much higher in the lower setup. This once again shows that heat flux is a more reliable measure of heat transfer.

In Energy2D, we have implemented an Energy Field view to supplement the Temperature Field view to remedy this problem.

Getting sensor data out of Energy2D

February 9th, 2014 by Charles Xie
Figure 1: Copy data from Energy2D.
Since a few users asked if the simulation data in Energy2D can be exported to other applications such as Excel, I have added a feature to the app for extracting virtual sensor data as multi-column time series data. For the user's convenience, there are three different ways of getting these data:
  1. When right-clicking on a sensor, the "View Data..." from the popup menu returns the data that has been recorded by the selected sensor.
  2. When right-clicking on a spot not occupied by a sensor, the "View Data..." from the popup menu returns a tabbed pane that contains all the sensor data -- different types of sensor are organized in different tabs.
  3. When the translucent graph is open, clicking the View Data button on the graph window's control panel returns the data recorded by all the sensors of the selected type, in consistent with the current display of the data in the graph window.
Figure 2: Paste data into Excel.
Regardless of which way you use, use the "Copy Data" button at the bottom of the data window to copy the data (Figure 1) and paste it into Excel. Once you get the data into Excel, you can process and plot them in any way you want (Figure 2). This feature is very handy if you need to combine data from multiple simulations into a single graph.

Note: This feature only works for the app. For security reason, the embedded applet is not allowed to access the System Clipboard (this is understandable, because people often copy and paste important information!)

Season’s greetings from Energy2D

December 14th, 2013 by Charles Xie
I have been so swamped in fund raising these days that I haven't been able to update this blog for more than two months. Since it is the time of the year again, I thought I should just share a holiday video made by Matthew d'Alessio, a professor at California State University Northridge, using our signature software Energy2D.

The simulator currently attracts more than 5,000 unique visitors each month, a number that probably represents a sizable portion of engineering students studying the subject of heat transfer on the planet. Over the past year, I have received a lot of encouraging emails from Energy2D's worldwide users. Some of them even compared it with well-known engineering programs. Franco Landriscina at the University of Trieste has written Energy2D into his recent Springer book "Simulation and Learning: A Model-Centered Approach."

I am truly grateful for these positive reactions. I want to say "Thank You" for all your nice words. There is nothing more rewarding than hearing from you on this fascinating subject of fluid dynamics and heat transfer. Rest assured that the development of this program will resume irrespective of its funding. In 2014, I hope to come up with a better radiation solver, which I have been thinking for quite a long time. It turns out that simulating radiation is much more difficult than simulating convection!

Here is a tutorial video in Spanish made by Gabriel Concha.

Engineers use Energy2D to simulate rocket mass heaters

April 24th, 2013 by Charles Xie
Link to simulation
A rocket mass heater is an innovative and highly efficient space heating system, which is popular among natural building DIYers since its invention in 1970s. A number of engineers who are interested in rocket stove design have used our Energy2D software to visualize the thermal physics involved.
Link to simulation

Martin Karl Waldenburg from Germany has designed a series of simplified rocket stove simulations. With his permission, we have published his simulations on our Energy2D website. This blog post provides links to three of his simulations. Another one was created by Pinhead of the Rocket Stove Forum (who also gave us permission to publish his simulation).

Link to simulation
Link to simulation
Since Energy2D hasn't supported chemical reactions yet, in all these simulations, burning is simulated using a heater with a fan to approximate the driving pressure due to combustion.

We will continue to work on Energy2D's computational engine and improve its graphical user interface. Currently, we are plowing through the math needed to model thermal radiation, chemical reactions, and phase changes. Once these features are added, we hope more people will find it useful, educational, and entertaining.

Using Energy2D to simulate Trombe walls

February 26th, 2013 by Charles Xie

A Trombe wall is a sun-facing wall separated from the outdoors by glass and an air space. It consists a solar absorber (such as a dark surface) and two vents for air in the house to circulate through the space and carry the solar heat to warm the house up. In a way, a Trombe wall is like a machine that uses air as a convey belt of thermal energy harvested from the sun. Trombe walls are very simple and easy to make and are sometimes used in passive solar green buildings.

Hiding sophisticated power of computational fluid dynamics behind a simple graphical user interface, our Energy2D software can easily simulate how a Trombe wall works. The two images in this blog post show screenshots of a Trombe wall simulation and its closeup version. You can play the simulation on this page and download the models there. If you open the models using Energy2D, you should be able to see how easy it is to tweak the models and create realistic heat flow simulations.

Solar chimneys operate based on similar principles. Energy2D should be able to simulate solar chimneys as well. Perhaps this would be a good challenge to you. (I will post a solar chimney simulation later if I figure out how to do it.)

Energy2D to reach thousands of schools

August 17th, 2012 by Charles Xie
Project Lead The Way (PLTW) is the leading provider of rigorous and innovative Science, Technology, Engineering, and Mathematics (STEM) education curricular programs used in middle and high schools across the US. The PLTW Pathway To Engineering (PTE) program includes a foundational course called the Principles of Engineering (POE) designed for 10-11th grade students. PLTW curriculum currently reaches 4,780 schools.

According to Bennett Brown, Associate Director of Curriculum and Instruction of PLTW, our Energy2D software will be adopted in the POE curriculum to support a variety of core engineering concepts including power, energy, heat transfer, controls, and environmental factors.
Solar heating cycles

Since the release of the first alpha version in 2011, Energy2D has already been used by thousands of users worldwide, but the collaboration with PLTW will be a big step forward for Energy2D to reach more students. The timing of this collaboration is particularly important to engineering tools such as Energy2D, as--for the first time--engineering has been officially written into the US K-12 Science Education Standards. Once the Standards roll out, thousands of teachers will be looking for leading-edge tools that can help them teach engineering. This will be a great opportunity for Energy2D.

Why is Energy2D so special that people want to use it? Our website provides many self-explanatory examples. But there is one hidden gem I want to emphasize here: Its computational engine is based on good algorithms I devised specially for this simulator. Its heat solver can be so accurate that a simulation can maintain the total energy of an isolated system at a level as accurate as 99.99% for as long as it runs, regardless of the complexity of the structures in the system! The fact that the sum of energy from all the 10,000 grid cells remains a constant after billions of individual calculation steps reflects the holy grail of science and engineering. If anything, engineering is about accuracy. A good engineering tool should be able to give students a good engineering habit of mind and accuracy should be a paramount part of it.