Fluid Network Studio

Hot air line, a worked cooling example

This worked example couples two effects that usually get treated separately, compressible gas flow and heat loss along the same pipe. It is a built-in network in Fluid Network Studio. It shows what a hot gas line does as it cools, which runs opposite to the intuition you build from isothermal lines, and why the solver marches a gas pipe segment by segment when heat transfer is on.

The scenario

Hot air enters a bare line and travels to a draw-off. The pipe is uninsulated, so the air loses heat to a cooler ambient all the way along, and by the outlet it has cooled close to ambient temperature. The interesting question is what that cooling does to the flow. On an isothermal line the gas expands and speeds up toward the outlet. Cool the gas and the story reverses, and this example is built to make that reversal visible.

The real setup

The example uses these parameters exactly as built:

  • An inlet boundary at 500 kPa absolute.
  • Inlet air supplied at 400 K, which is 126.85 degrees C, close enough to call it 127 degrees C air.
  • A single bare pipe, 300 m long, 50 mm internal diameter, roughness 4.6e-5 m.
  • A direct overall heat-transfer coefficient on the line of 3.0 W/m2.K to an ambient of 15 degrees C.
  • A draw-off pulling a fixed mass flow of 0.18 kg/s.
  • Working fluid set to the gas phase, air, with gas constant 287.05 J/kg.K, viscosity 2.3e-5 Pa.s and thermal conductivity 0.0257 W/m.K.

The physics and method

With heat transfer on, a gas pipe is solved by a steady one-dimensional segment march rather than a single closed relation. Each segment accounts for friction, the acceleration term and wall heat loss together, in total-energy form, so the temperature, pressure, density and velocity all move down the pipe in step. The wall heat path reuses the same film and composite-cylinder treatment used for liquid heat loss, now driven by the gas conductivity. The march is solved with a midpoint scheme and step doubling for accuracy, and an always-on energy residual is reported so the heat balance is shown, not assumed.

What the solver computes and what you learn

Solve it and the air arrives near the 15 degrees C ambient. The signature is in the density and velocity. As the gas cools, its density rises, and because the mass flow is fixed the velocity falls along the pipe, the opposite of a hot isothermal line that speeds up toward the outlet. Switch the view to Colour by, then Temperature, and you can watch the line cool from inlet to draw-off. The lesson is that cooling and compressibility pull in opposite directions, and only a coupled march captures which one wins where.

Gas and heat transfer are both part of the Advanced plan, so solving this example needs that plan.

Take it further

This example sits behind two application pages, pipe heat loss for the thermal side and compressed air system design for the gas side. The glossary explains the terms the solver uses. Fluid Network Studio supports your engineering work and does not replace a qualified engineer, and it makes no claim of compliance with any standard.

Open this example in FNS and add insulation to slow the cooling.