Engineers used heat-transfer capabilities in an FEA program to find the right depth and shape of a heating system that will warm the grass of a football field. The right amount of heat can keep the grass growing and healthy during the cold playing season.

The turf-conditioning system has 11.65 miles of plumbing and more than 40 miles of what's called Raupex pipe. It lies beneath a 75 3 115-yard playing field of natural, fully irrigated turf in the recently opened football stadium in Cleveland. The turf-conditioning system was designed and installed by Virginia-based Rehau Inc., North America.


Installing pipe(right) Workers installed more than 40 miles of a cross-linked polyethylene pipe developed by Rehau. Their engineers used steady-state heat-transfer analysis software from Algor Inc., Pittsburgh, to find the spacing needed between the pipes as well as the fluid temperature required to warm the grass roots.

Rehau engineers used heat-transfer software from Pittsburgh-based Algor Inc. to determine the amount of energy needed to run the system and optimize overall performance for differing environmental conditions. "The piping is made of a high-density cross-linked polyethylene," says Patrick Sauer, product manager. "Individual polyethylene molecular chains link into 3D connections under high temperature and pressure to provide high strength and flexibility."

System designers used Algor's steady-state heat-transfer-analysis software to optimize the pipe spacing for uniform heating. Pipes placed too far apart might let strips of grass turn brown.

The pipe network lies on a bed of gravel under a sandy-soil mixture. The soil composition and moisture level affects the conductivity of heat from the pipes through the soil to the root zone above. Sauer says the gravel-drainage system beneath the pipe helps to prevent downward heat loss, optimizing the heat that reaches the root zone.

Rehau engineers also considered wind speed, ambient temperature, and grass length in the Algor heat-transfer analyses. The wind speed, for instance, helps determine the heat-transfer coefficient and ambient temperature affects the rate of heat loss from the surface. In addition, longer grass retains more energy than shorter grass.

"The heat-transfer analyses let us better understand how external environmental conditions can affect thermal conductivity," says Scott Posey, project analyst with Rehau.

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

Rehau needed to demonstrate installation and operating costs, including the amount of pipe needed, energy required to operate the system (number of boilers), and the temperature at which a tarp would be required to protect the field. The system fluid temperature was key to determining these factors.

Posey first created a 2D isotropic model of a typical cross section with two parallel pipes in layers of gravel, soil, and turf. He used hand-meshing techniques to make a uniform mesh across the model and then refined the mesh around the pipes.

In about five iterations, Posey varied the fluid temperature and pipe spacing to verify the best spacing and fluid temperature needed to properly heat the field surface area. The FEA software's total-flow option automatically calculates heat flow over a surface. The feature determined the conditioning system's heating requirements. "In the past, I had to manually calculate total heat flow by averaging heat flux values at individual nodes. This is a linear approach to an often nonlinear problem," says Posey.


(left) Replays of Algor's transient heat-transfer analysis show the temperature distribution throughout several cross sections. The left temperature plot shows a steady-state condition in which the fluid temperature is at 105, the temperature to keep the root zone at 72 when ambient is 35. The center plot shows the fluid-system temperature increasing as the ambient drops. The right plot indicates a fluid temperature of 128 with an ambient of 5.
He examined the temperature distribution and heat flux results using built-in visualization capabilities and determined that a fluid temperature of 128 would sustain the minimum root zone temperature. Sauer and Posey calculated the energy required to operate the system in Btus/hr/sq ft. The calculation indicated that Cleveland's system would require nine boilers for severe conditions and half their capacity for normal conditions.

For the transient heat-transfer analysis Posey specified 384 time steps, every 15 min for four days. He also redefined the applied temperature boundaries at the inside pipe circumference to correspond with a first load curve, which describes changes in the system fluid temperature. Then he placed temperature boundaries at the top of the model (at the turf surface) to correspond with a second load curve, which describes changes in ambient temperature.

The first load curve let the system fluid temperature ramp up and hold 105. Then he increased the fluid temperature to 128 to correspond with the second load curve, which simulates a drop in ambient temperature from 35 to 5 over about 3 hr. "The load curve plots in data-entry screens let me visualize load curve data and ensure that it was correct before running the analysis," says Posey.