HumCooler: Critical Distances

HumCooler: Critical Distances

Back: Building the HumCooler - Up: Index - Forward: The Stack

There are several dimensions and distances that are central to the design and construction of a HumCooler. First, we will look at the values of the working fluid or gas itself. We want the HumCooler to be simple to build, so we don't want to use exotic fluids (like Freon or other chemicals dangerous to the environment). Second, we will look at the dimensions of the resonator.

The Working Fluid

There are two critical distances that are determined by the working fluid. First is the thermal penetration depth, which determines how far the thermal effect of the stack reaches into the fluid. Second is the viscous penetration depth, which determines how far the viscous effects of the stack reach into the fluid. Viscosity causes loss of efficiency, and we'd like to have as little as possible ... unfortunately, for most gases, the thermal and viscous depths are about the same, so we must carefully design the HumCooler to minimize viscous losses.

Of course, the easiest working fluid we can imagine is air. Air is mostly nitrogen, with oxygen, water vapor, and other stuff mixed in. The thermal and viscous depths will depend on temperature, pressure, and the frequency of the resonant sound wave.

Here is a table of thermal and viscous depths for air. All depth values are in millimeters. Temperature is 300 Kelvin, frequency is 500 Hz.
Atmospheres 1 2 3 5 10
Thermal Depth 0.119 0.084 0.069 0.053 0.038
Viscous Depth 0.101 0.071 0.058 0.045 0.032
These values are pretty small, compared to the gap size in a typical stack (it's hard to make gaps smaller than a millimeter or so). Although air will work, it's not the most effective working fluid for our purposes, and most serious thermoacoustic work is done with other gases.

It turns out that high pressure and high speed-of-sound are the most desirable characteristics for a gas to make a high power HumCooler. High sound speed means a light gas. Hydrogen would be ideal, but it has a distressing tendency to explode and destroy huge airships, making dramatic cover art for Led Zeppelin albums and so on. So most serious thermoacoustic work uses helium, which is safe, cheap, and readily available.

Here is a table of thermal and viscous depths for helium. All depth values are in millimeters. Temperature is 300 Kelvin, frequency is 500 Hz.
Atmospheres 1 2 3 5 10
Thermal Depth 0.439 0.311 0.254 0.196 0.139
Viscous Depth 0.362 0.256 0.209 0.162 0.114
Helium has much better characteristics for our HumCooler: bigger distances mean larger gaps for the stack, and its light weight allows high power transfer.

The Resonator

Once the working fluid is chosen (which determines the speed of sound: 345 m/s for air, 1019 m/s for helium), there are two dimensions that are controlled by the resonator itself. The first is the length of the resonator, which determines the operating frequency of the HumCooler. The frequency is the speed of sound divided by the wavelength (which is four times the tube length, for a quarter wave resonator). For example, a 16 cm long tube filled with air should resonate at about 540 Hz, and a 37 cm tube filled with helium should resonate at 688 Hz.

The second dimension is the gas displacement length: how far the packet of gas moves during one cycle of oscillation. This is determined by the intensity (amplitude of oscillation) as well as the location in the tube, since velocity values are different in different places. We will return to this value when we consider the heat exchangers.

This page maintained by Wil Howitt
Last updated 3 April 2003