System designers used ALGOR’s steady-state heat transfer analysis software to optimize the pipe spacing to ensure uniform heating. If pipes are placed too far apart, brown strips of grass may appear on the field surface where the grass root zone is not heated adequately.

The flow of fluid through RAUPEX pipe causes it to expand. The molecular structure of RAUPEX piping enables it to compress to its original shape after expansion, causing significant loading on fittings that connect individual piping segments. According to Sauer, the EVERLOC fitting system takes advantage of the pipe’s compressive properties.

"The pipe is expanded over an EVERLOC insert to provide maximum strength without reducing the inside diameter of the pipe," says Sauer. "Then a sleeve is pressed onto the fitting to ensure the integrity of the connection. This fitting system enabled us to design the conditioning system without worrying about the accessibility of the joints after installation."

The pipe network lies on a bed of gravel, as shown in this cross section, to enable drainage away from the pipe. High levels of moisture in the soil can cause increased thermal conductivity, which results in the rapid loss of heat. Soil composition affects how well soil retains moisture. REHAU engineers considered both composition and moisture level when specifying material properties for the ALGOR steady-state and transient heat transfer analyses.

The pipe network lies on a bed of gravel beneath a sandy soil mixture. The composition and moisture level of the soil can affect the conductivity of heat from the pipes through the soil to the root zone inches above. Sandy loam releases fluid at a faster rate than dense clay soil, while wet soil releases more energy in the form of heat into the air than dry soil does, causing faster decreases in field temperature. On the other hand, drier soil releases less heat from the field, but requires longer periods of time to heat the root zone. According to Sauer, the herringbone construction of the gravel drainage system beneath the pipe network helps to prevent downward heat loss, optimizing the amount of heat that reaches the root zone above.

REHAU engineers also needed to consider external variables, including weather conditions and the length of the grass, in the ALGOR heat transfer analyses. The wind speed, which helps to determine the heat transfer coefficient in the analysis calculations, and the ambient temperature will affect the rate of heat loss from the surface. In addition, longer grass will retain more energy than will shorter grass. According to Project Analyst Scott Posey, these varying factors required new considerations when performing the heat transfer analyses.

"This application was different from other heat transfer analyses I’ve performed. In this case, the heat is transferred to another substance entirely, not just across a uniform surface having one material type," says Posey. "The heat transfer analyses also helped us to better understand how external environmental conditions can affect thermal conductivity."

Based on the steady-state results, Posey also developed transient heat transfer analyses to determine how the system would respond to changes in external environmental conditions over time.

Steady-State Analyses Help Determine Energy Requirements

To be awarded the Cleveland turf conditioning system contract, REHAU needed to demonstrate both installation and operational costs, including the quantities of pipe needed, energy required to operate the system (which determines the number of boilers needed) and the temperature at which a tarp would be required to protect the field. The required fluid temperature within the system was the key to determining all of these factors.

Posey started with a steady-state heat transfer analysis to find the optimal fluid temperature needed to keep the root zone at 72?/font> F when the ambient temperature is 5?/font> F, the criteria specified by the stadium developers. He created a 2-D isotropic model of a typical cross section, which consisted of two parallel pipes within layers of gravel, soil and turf, using Superdraw III, ALGOR’s single user interface for FEA and precision finite element model-building tool. Posey used hand-meshing techniques to make a uniform mesh across the model and then refined the mesh around the pipes.

Once he had built the model, Posey used individual groups with representative colors (i.e., group 8, identified as gray, was used for gravel) to specify the different material properties for gravel, turf, soil and polyethylene. The 1993 Ashrae Fundamentals Handbook provided material properties for gravel and turf, including convection coefficients for turf under varying wind speeds and at no wind speed, which Posey used in this case. In addition, Posey used the Ashrae handbook to find the appropriate material properties for the soil.

"We consulted with the field contractor to determine the approximate soil composition and moisture level to use in the analysis and then sourced the handbook to get the properties," says Posey. "We assumed a conservative moisture level of 42 percent to ensure the system would be effective through highly conductive soil."

The material properties for polyethylene were taken from REHAU’s past extensive materials research and testing. Using Algor’s Material Library Manager, Posey added the material properties to a customized library so the properties will be available for future analyses.

Finally, Posey added a temperature boundary of 58?/font> F, the ground temperature at that depth, to the bottom edge of the model and a temperature boundary of 128?/font> F at the internal circumference of the pipes. According to Posey, he chose a temperature of 128?/font> F based on Sauer’s extensive design experience with previous conditioning systems. In addition, the maximum allowable temperature for RAUPEX piping is 140?/font> F.

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The steady-state heat transfer analysis results showed that an optimal fluid temperature of 128?F is needed to maintain a root zone temperature of 72?F when the ambient temperature is 5?F with no wind. REHAU engineers used these results to determine how much energy would be required to operate the turf conditioning system.

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With Sauer’s knowledge of the systems as a guide, Posey conducted about five analysis iterations, in which he varied the fluid temperature and pipe spacing, to verify the optimal pipe spacing and fluid temperature needed to properly heat the field surface area. Posey found ALGOR’s total flow option, which automatically calculates heat flow over a surface, to be especially useful in determining the conditioning system’s heating requirements.

"In the past, I have manually calculated the total heat flow by averaging heat flux values at individual nodes. This is a linear approach to an often nonlinear problem," says Posey. "With the total flow calculation, the software saves me time by automatically calculating these values and it provides a more accurate result."

Posey examined the temperature distribution and heat flux results using ALGOR’s built-in visualization capabilities and determined that a fluid temperature of 128?/font> F would sustain the minimum root zone temperature. Factoring in this temperature value, Sauer and Posey calculated the energy required to operate the system in BTUs per hour per square foot. The calculation indicated that the Cleveland turf conditioning system would require a maximum of nine boilers under severe conditions; however, the engineers estimated that half that number would be needed under normal conditions.

The need to regulate the number of boilers in use and to adjust the fluid temperature to accommodate environmental changes led Posey to explore how quickly the system could respond to falling air temperatures. He was able to do this using ALGOR’s transient heat transfer analysis software.

Transient Analyses Yield More Than Just Results

Using the same model geometry and material properties, Posey set up the transient heat transfer analysis to simulate a drop in ambient temperature, similar to what would occur over the course of a sunset, and a corresponding rise in fluid temperature to keep the root zone at a constant 72?/font> F. He adjusted the temperature boundary conditions, defined load curves and specified the duration of the event for the transient analysis.

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ALGOR’s transient heat transfer analysis software was used to simulate a drop in ambient temperature, similar to what would occur over the course of a sunset, and a corresponding rise in fluid temperature to keep the root zone at a constant 72?F. REHAU engineers specified two load curves in Superdraw III, ALGOR’s single interface for FEA and precision finite-element model building tool. The plots helped the engineers to ensure their data was correct before performing the analysis.

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Posey first ran a steady-state heat transfer analysis to determine the fluid temperature needed (105?/font> F) to maintain the root zone temperature with an ambient temperature of 35?/font> F. Then for the transient heat transfer analysis, he set the duration of the event. Posey specified 384 timesteps (or every 15 minutes for four days) and then defined a capture rate of one, so that he could review the results for each timestep. Posey also redefined the applied temperature boundaries at the inside pipe circumference to correspond with the first load curve, which described changes in the system fluid temperature. Then he placed temperature boundaries at the top of the model (at the turf surface) to correspond with the second load curve, which described the changes in ambient temperatures.

The first load curve caused the system fluid temperature to ramp up to the previously analyzed temperature of 105?/font> F and then establish a steady-state situation. Then Posey increased the temperature again to 128?/font> F to correspond with the second load curve, which simulates a drop in ambient temperature from 35?/font> F to 5?/font> F over a period of about three hours. Posey ran several analysis iterations to determine when and how much to increase the fluid temperature as the ambient temperature drops.

"The load curve plots displayed in Superdraw’s data entry screens let me visualize load curve data and ensure that it was correct before running the analysis," says Posey. "Conducting the transient analyses required a lot of trial and error on my part," continues Posey, who had no prior experience with this analysis type. "I was able to successfully perform the analyses with the help of the documentation provided through ALGOR’s DocuTech system."

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Using ALGOR’s Monitor utility, the engineers superimposed temperature changes vs. time plots for the fluid, soil, root zone and turf, which were determined in the transient heat transfer analysis. The engineers concluded that the system fluid temperature should be increased slightly before the anticipated drop in ambient temperature to keep the root zone temperature constant.

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The REHAU engineers used ALGOR’s Monitor utility to superimpose temperature changes vs. time plots for the fluid, soil, root zone and turf. Having all of the data on one screen, Posey was able to conclude that the system fluid temperature should be increased slightly before the anticipated drop in ambient temperature to keep the root zone temperature constant. Posey also generated analysis replays in AVI format to animate the changes in temperature distribution over time.

"ALGOR’s bitmap to AVI converter enabled me to add in text at important points throughout the event. This helped to explain what happens in the analysis to others who may not be familiar with our turf conditioning systems or finite element analysis," Posey says.

ALGOR’s transient heat transfer analysis software illustrated system performance under falling environmental temperatures, showing that the system is capable of adjusting to changing conditions without dramatic temperature changes at the root zone. The transient heat transfer analysis also verified the performance capabilities for an automatically controlled heating system. In addition, replays of the transient results provided an invaluable visual tool that aided REHAU in earning the Cleveland turf conditioning system contract, according to Sauer.

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Analysis replays of the ALGOR transient heat transfer analysis show the temperature distribution throughout the cross section of the system. The first temperature plot (left) shows a steady-state situation, in which the fluid temperature is at 105?F, the temperature needed for a constant root zone of 72?F with an ambient temperature of 35?F. The second plot (center) shows the fluid system temperature increasing as the ambient temperature decreases. The third plot (right) indicates a fluid temperature of 128?F with an ambient temperature of 5?F.

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"While the technology used in the Cleveland system is not new for REHAU, the use of ALGOR heat transfer analysis software was new," Sauer said. "Being able to illustrate how the system works using analysis replays was an important factor in the contract discussions for the Cleveland project. The analysis replays also have been an integral part in securing additional contracts with other NFL stadiums."

REHAU is already planning future transient heat transfer analyses using ALGOR. The engineers plan to study how the turf conditioning systems can be used as cooling mechanisms to keep turf from scorching during the humid summer months or in year-round hot climates. REHAU is currently developing turf conditioning systems for other NFL teams.