Modeling an Inflatable Habitat - nasa/gunns GitHub Wiki

Inflatable habitats are becoming a thing. They are attractive because they offer less launch weight for the same habitable volume than traditional metal can habs. ISS already has an inflatable module installed, the BEAM, and it is very possible that the LOP-G will have an inflatable module.

This page suggests a way to model inflatable modules in GUNNS. These will be modeled differently than traditional rigid-shelled habitats. There are two main differences:

1. The flexible volume creates a different pressure response to mass flows and temperature.
2. Thermal control and ventilation is different.

We characterize an inflatable’s volume V as a function of the difference between the inside and outside pressures, which we call P. We also assume that the inflatability, which is the change in volume for a change in pressure, or dV/dP, can also be characterized as a function of pressure, so we call it V’. These functions are due to the inflatable’s construction and material properties. In the real world, V and V’ would also depend on things like temperature, plastic deformations, and so on, but we don’t consider those effects. We expect V for a real-world inflatable to be non-linear and we guess it will look something like below:

GUNNS has a link specifically designed to model inflatables, the GunnsFluidBalloon. However, it has a significant limitation that its inflatability V’ is constant, so it can only model V as linear, or directly proportional to P. We must design around this limitation, because it prevents us from being able to match both the real-world’s V and V’ at most points. The picture below shows a GunnsFluidBalloon tuned to match the real-world V at a design point, but as we can see, it doesn’t match the slope, or V’ at that point. By modeling the habitat volume with a single node controlled by a GunnsFluidBalloon link, the volume is proportional to pressure and must pass through the (0,0) point, and we can’t match both V and V’ at any point.

A mismatch in V means we have the wrong mass of gas to pressurize a given volume. A mismatch in V’ means that:

• All net molar flows in or out of the inflatable, such as leaks, crew metabolics, ECLSS processes, pressure control systems, etc. cause the wrong pressure and volume change for the given mass flow.
• Thermal expansion and contraction of the air due to temperature changes cause the wrong pressure and volume change.

We can match both V and V’ at a desired pressure by adding a few pieces to the network. We do this by setting the balloon link’s inflatability to match the real-world V’ at the desired pressure, and then using extra nodes and links in the network to bias the balloon minimum volume or pressure as needed to also match the total volume at that pressure. There are two methods; which one used depends on the slope V’.

We use this if the tangent line to the real-world V at the design point would intersect the volume axis at a positive value, like shown below. This has the advantage of being accurate at the design point, at the expense of being stuck with a non-zero volume at zero pressure:

We achieve the fixed minimum volume at P = 0 with a GunnsFluidTank link on a separate node, connected to the balloon’s node by a large conductance. This connection ties the node pressures together so they act in concert as the total habitat volume. This split-node volume also gives us more options for modeling the ventilation and thermal control, discussed below. The network drawing would look like this:

Another thing to note about this method is since it divides the total habitat volume into multiple nodes, this complicates the edit capabilities for editing the air quality. Since these two nodes are tightly coupled, editing them one at a time when they are coupled could cause instability, undamped oscillations and model blow-ups. So, when using the edit controls in either the GunnsFluidTank link on the volume bias node, or the GunnsFluidBalloon link on the flexible volume node, it will be best to block the conductor tie link(s) between them, and then edit both nodes to the same pressure before reconnecting them when the edits are done.

We use this if the tangent line to the real-world V at the design point would intersect the pressure axis at a positive value, like shown below. The drawback to this approach is the volume reaches zero at a positive pressure.

We achieve the fixed minimum pressure at V = 0 with a GunnsFluidPotential link controlling the balloon link’s external node to the pressure at V = 0. The network drawing looks like this:

In all of the above options, we can set the balloon link’s maximum volume to limit the maximum habitat volume as desired. This might be chosen as the real-world’s absolute burst pressure & volume, or the volume at which the real-world’s V’ approaches zero and the habitat essentially becomes rigid, etc.

By expanding the above two methods to more nodes and balloon links, one could create almost any piecewise-linear V profile, with multiple linear segments. This would match V and V’ at multiple points and increase model accuracy across a wider range of pressures. However, we recommend against this. It generally works, but becomes unstable and can ‘blow up’ if there are rapid pressure changes when one or more of the balloons switches between its rigid and dynamic volume ranges.

In habitats, the air ventilation is usually ducted to flow where the crew spend most of their time, to keep them alive. In traditional rigid habitats, the inner wall of the shell is typically covered with equipment racks, and the crew stay in the center of the habitat volume. The rigid exterior shell also provides the structural rigidity in a stack with other modules.

In an inflatable habitat however, the flexible shell can’t provide structural rigidity in a stack, so there is typically a rigid central column or truss running along the central axis. Most equipment is attached to this column, and the crew stay between this and the shell. There is very little attached to the inner shell wall, so the shell wall sees a lot of the ventilation air flow.

These differences are illustrated below.

There is a fundamental difference in how the air volume interacts with the outside thermal environment, and therefore how to best model it.

In the rigid hab, since most of the air flow travels near the central axis there is very little air flow along the inside wall of the shell, and thus little convective heat transfer. Most of the heat transferred between the inside and outside is conductive, from the shell to equipment racks attached to it. Shell heaters are typically used to control the shell temperature: these tend to be large area heating pads attached to the inside of the shell. In GUNNS, we typically model a small thermal conductance for what little heat transfer there is between the shell and the air.

In inflatable habs, there is a lot of forced convection directly between the inner shell wall and the main ventilation air flow. Thus the vehicle’s air ventilation system can be used to help control the shell temperature, and vice-versa. We will model the heat transfer with convection instead of conductance links, since that is the main heat transfer mechanism. We can combine these convection links (GunnsFluidHeatExchanger or GunnsFluidPipe) with the supply & return vent links to & from the ECLSS system to save nodes. Since links are computationally cheap, we can add many of these links in parallel to interact with separate shell surface section temperatures from the thermal aspect, with no impact to the run speed of the cabin air network. We can also model convection between the air and the inner truss structure & equipment in the same way.

Below is an example of what this would look like.

This is using the Volume Bias method described above. Air is flowing clockwise in this example, in the order of node #. Nodes 0 and 1 are the fixed (volume bias) and inflatable volumes, respectively, and nodes 2 and 3 are in the ECLSS duct containing the fan. We’ve divided the habitat thermal geometry into 3 sections axially (Forward, Mid & Aft), 2 sections radially (Port & Starboard), but we could use more or less sections as desired. Air flows from Forward to Aft through the ECLSS fan duct, and Aft to Forward through the cabin volume, completing the loop. So the thermal convection of the air with the shell and tunnel walls sees the Aft section first, then the Mid section, then the Forward section. We would have 12 thermal nodes in the passive thermal network representing these 12 wall temperatures that the air sees in this loop. The large conductance to tie nodes 0 and 1 together, as used in the Volume Bias method, is implemented with the convection links for the Mid section.