Zoned Analytical Model for Airflow Temperature Rise in Spray- Insulated Three-Centered Arch Roadways with an Exposed Floor

Deep beneath the earth's surface, where metal mines carve tunnels into the planet's crust, a silent battle against heat is constantly waged. As miners dig deeper, the natural temperature of the surrounding rock rises, creating an environment that can become dangerously hot and humid. This geothermal warmth, combined with the heat generated by heavy machinery and the workers themselves, turns these underground passages into ovens. To keep the air breathable and the workers safe, engineers must constantly cool the air flowing through these tunnels. One common strategy involves spraying a layer of insulating material onto the tunnel walls, acting like a thermal blanket to stop the rock's heat from leaking into the air. However, in the real world of mining, there is a practical constraint: the floor of the tunnel must remain bare to support the weight of vehicles and equipment, meaning the insulating blanket covers the roof and sides but leaves the ground exposed.

For years, engineers have relied on mathematical models to predict how well these cooling systems work, but many of these models assumed that the entire tunnel, including the floor, was perfectly insulated. This assumption created a gap between theory and reality, often leading to overly optimistic predictions about how cool the air would stay. A team of researchers from China set out to close this gap by developing a new way to calculate airflow temperature that acknowledges the exposed floor. They focused on a specific tunnel shape common in deep mines, known as a three-centered arch, and created a model that treats the insulated roof and walls differently from the uninsulated floor. Their work reveals that the exposed ground is not just a minor detail; it is a major pathway for heat, fundamentally changing how engineers should design cooling systems for the future.

The researchers began by building a mathematical representation of a typical deep mine tunnel, one hundred meters long, four and a half meters wide, and four meters high. Instead of trying to model every curve of the actual rock, they simplified the shape into a form that preserved the essential areas where air flows and heat moves. They then divided the tunnel's boundary into two distinct zones: the sprayed roof and walls, and the bare floor. In the sprayed zone, heat must pass through the rock, then through the insulating layer, and finally into the air. In the floor zone, heat skips the insulation step entirely, moving directly from the rock to the air. By treating these two paths separately, the team could calculate exactly how much heat each section contributed to the rising air temperature. They also accounted for the heat generated by equipment and the cooling effect of water evaporating from damp walls, weaving all these factors into a single, clear equation that predicts the temperature of the air as it travels from the tunnel entrance to the exit.

When the team ran their calculations, they discovered a striking reality about the exposed floor. In a scenario where only the roof and walls were sprayed with insulation, the floor was responsible for nearly two-thirds of the total heat flowing from the rock into the air. This means that even with a thick layer of insulation on the sides, the bare ground acts as a massive thermal shortcut, allowing heat to bypass the protective barrier. The model showed that if the floor were also insulated, the cooling benefit would increase, but the improvement would be relatively small compared to the effort and cost required to protect the floor from heavy machinery. In fact, the researchers found that insulating just the roof and walls captures about seventy percent of the total cooling benefit that would be achieved by insulating the entire tunnel perimeter. This suggests that while the floor is a significant source of heat, the most efficient engineering solution often lies in focusing on the walls and roof, rather than attempting the difficult and expensive task of insulating the floor.

To ensure their new model was accurate, the researchers took their theory into a real mine. They selected a section of a tunnel and measured the air temperature at various points along its length under three different conditions: first with no insulation at all, second with insulation on the roof and walls but an exposed floor, and third with insulation covering the entire tunnel. They used precise instruments to track the air temperature, the speed of the airflow, and the heat radiating from the rock. The results matched their predictions with remarkable precision. The model correctly forecasted how the air temperature would rise as it moved down the tunnel, with errors so small they were within the margin of error for the measuring instruments themselves. Crucially, the field data confirmed that the exposed floor was indeed the dominant source of heat after the walls were insulated, validating the core idea that the floor acts as a bottleneck for cooling efforts.

The study also explored how other factors influence the tunnel's temperature, revealing that the speed of the airflow is the most powerful tool for cooling. When the researchers increased the speed of the air moving through the tunnel from a slow half-meter per second to a brisk three meters per second, the temperature at the exit dropped by more than four degrees Celsius. This change was far more significant than the effects of changing the thickness of the insulation or the type of material used. While better insulation helps, its benefits diminish quickly once the floor is left exposed, because the heat from the ground overwhelms the improvements made to the walls. Similarly, making the insulation layer thicker or using a material that blocks heat even better provided only marginal gains. The researchers concluded that for deep mines, the most effective approach is a coordinated strategy: use insulation to reduce the heat load from the rock, but rely on strong airflow to carry that remaining heat away.

This work provides a clear, practical guide for engineers designing cooling systems for deep mines. It moves beyond the idealized assumptions of the past to offer a model that reflects the messy reality of construction, where floors must remain bare. By understanding that the exposed floor is the primary source of residual heat, mine operators can make better decisions about where to spend their resources. They can see that while insulating the floor might seem like the perfect solution, the cost and difficulty often outweigh the small additional cooling it provides. Instead, the focus should be on optimizing the airflow and ensuring the roof and walls are well-insulated, a strategy that the new model confirms delivers the vast majority of the possible cooling benefit. The study stands as a testament to the value of looking closely at the specific conditions of the real world, showing that sometimes the most effective solutions come from understanding exactly where the heat is coming from, rather than trying to block it everywhere at once.