Spherical Livestock

Doug Bell

If, like me, you are a fan of the sitcom The Big Bang Theory, you may have heard the Spherical Chicken joke in the episode “The Cooper-Hofstadter Polarization:”

There's this farmer, and he has these chickens, but they won't lay any eggs. So, he calls a physicist to help. The physicist then does some calculations, and he says, “I have a solution, but it only works with spherical chickens in a vacuum.”

When I saw the episode with my family, I laughed out loud at the joke (probably a little too much like the nerdy characters) and received strange, but not unfamiliar, looks from my wife and sons. The joke has existed for years starring a veritable barnyard of orb-like livestock such as a poorly performing race horse and low-yield dairy cattle. The punchline is always the same, though: the problem is solved with improbable assumptions.

Engineers (and physicists) understand the joke. We often apply simplifying assumptions to make a problem manageable. These assumptions take many forms: incompressible fluids, inviscid flow, lumped capacitance, to name a few. The very equations used by analysis software are based on simplifying assumptions.

While the trend has been for engineers to include details in the analysis software and let it mesh and run, there is much to be gained by using simplifying assumptions. I am not saying that detailed models don't have their place, but simplified models have their place and are often overlooked.

A simple model provides insight into the key physics of the problem. By stripping out all but the most basic physics and adding them back in one at a time, you understand what affects the solution. Also, your solution does not waste time on irrelevant physics that may require unnecessarily complicated calculations. For example, if you need to find out if albedo from the Moon and Earth are both significant during a transfer orbit, model a sphere (it can be a chicken or a horse) and have it traverse away from the Earth and toward the Moon without worrying about the geometry or trajectory. A quick review will determine if both reflected solar loads are worth including in the system model at all times.

A simple model makes validation easier. A simple model can make it easier to perform the necessary calculations by hand to ensure the model does not have errors before moving toward more complex calculations. I had a supervisor who would not allow anyone to present a thermal analysis without first presenting a sketch of the system's energy balance. A simple model allows evaluating each input and output.

A simple model solves quickly. A fast-solving model allows evaluating more design options while a detailed model will be more constrained. Investigating a wider possibility of designs can lead to an unexpected design. The ability to run many cases quickly also enables correlating the model to test data. This provides further validation of the model and strengthens the trust in the model when it is used to evaluate untestable conditions. Statistical treatment of uncertainties provides another reason for having a fast-running model.

A related note: you can always present the results of a simple model along with the assumptions, but you cannot present the results of a complex model if it is not complete.

So, while the spherical animals make for a good punchline, they have their place in analysis. Just be sure you don't stop at the simplest model so you don't become the joke.

FloCAD model of a loop heat pipe

Since a significant portion of LHPs consists of simple tubing, they are more flexible and easier to integrate into thermal structures than their traditional linear cousins: constant conductance and variable conductance heat pipes (CCHPs, VCHPs). LHPs are also less constrained by orientation and able to transport more power. LHPs have been used successfully in many applications, and have become a proven tool for spacecraft thermal control systems.

However, LHPs are not simple, neither in the details of their evaporator and compensation chamber (CC) structures nor in their surprising range of behaviors. Furthermore, there are uncertainties in their performance that must be treated with safety factors and bracketing methods for design verification.

Fortunately, some of the authors of CRTech fluid analysis tools also happened to have been involved in the early days of LHP technology development, so it is no accident that Thermal Desktop ("TD") and FloCAD have the unique capabilities necessary to model LHPs. Some features are useful at a system level analysis (including preliminary design), and others are necessary to achieve a detailed level of simulation (transients, off-design, condenser gradients).

CRTech is offering a four-part webinar series on LHPs and approaches to modeling them. Each webinar will last 60 minutes and are designed to be attended in the order they were presented. If you miss one in the series, please check out our video page for a recording, or contact us before the next webinar starts. While the first webinar presumes little knowledge of LHPs or their analysis, for the last three webinars you are presumed to have a basic knowledge TD/FloCAD two-phase modeling.

Part 1 provides an overview of LHP operation and unique characteristics
Part 2 introduces system-level modeling of LHPs using TD/FloCAD.
Part 3 covers an important aspect of getting the right answers: back-conduction and core state variability.
Part 4 covers detailed modeling of LHPs in TD/FloCAD such that transient operations such as start-up, gravity assist, and thermostatic control can be simulated.

May 31, 2018, 1-2pm (PT), 4-5pm (ET)

This webinar provides an overview of LHP design and operation, from a basic understand of components to a review of important performance considerations and limitations.

Many topics will be covered, from start-up issues to the purpose of the evaporator bayonet to capillary flow regulators to load balancing in parallel LHP units. However, we will cover these topics only in enough depth that you will be able to understand the reasons for various modeling approaches that will be covered in later webinars. In other words, this webinar will survey the various ways in which LHPs require a specialized approach to design analysis and simulation.

This webinar is one of a four-part webinar series on LHPs and approaches to modeling them. Each webinar will last 60 minutes and is designed to be attended in the order they were presented. If you miss one in the series, please check out our video page for a recording, or contact us before the next webinar starts.

Prerequisites: Basic understanding of two-phase thermodynamics and heat transfer.
Please register for Part 1 here

June 5, 2018, 8-9am (PT), 11am-noon (ET)

This webinar explains how the toolbox approach of Thermal Desktop and FloCAD can be used to design and simulate LHPs at a system level, where the focus is on predicting conductance of nominally operating LHP, including thermostatic control (variable conductance).

This webinar is one of a four-part webinar series on LHPs and approaches to modeling them. Each webinar will last 60 minutes and is designed to be attended in the order they were presented. If you miss one in the series, please check out our video page for a recording, or contact us before the next webinar starts.

Prerequisites: Basic understanding of Thermal Desktop and FloCAD operation as applied to two-phase systems. Basic familiarity with LHP components and operation (see Part 1).
Please register for Part 2 here

June 7, 2018, 8-9am (PT), 11am-noon (ET)

Modeling wick back-conduction in an LHP is critical to accurate prediction of the overall loop conductance and operating point. This prediction can't be separated from an understanding of what is happening in the wick core. This webinar presents time-honored methods of dealing with these complex topics in a relatively simple (if abstract) thermal/fluid network.Prerequisites:

This webinar is one of a four-part webinar series on LHPs and approaches to modeling them. Each webinar will last 60 minutes and is designed to be attended in the order they were presented. If you miss one in the series, please check out our video page for a recording, or contact us before the next webinar starts.

Basic understanding of Thermal Desktop and FloCAD operation as applied to LHP modeling (see Part 1 and Part 2).
Please register for Part 3 here

June 12, 2018, 1-2pm (PT), 4-5pm (ET)

This webinar explains how Thermal Desktop and FloCAD can be applied to simulate complex and transient phenomena in LHPs, including condenser design, start-up, thermostatic control, and gravity assist (evaporator below condenser). The design of an actual LHP will be used to demonstrate concepts; the implications of attaching large masses to the evaporators (cooled electronics and support structures) will become clear as a result.

This webinar is one of a four-part webinar series on LHPs and approaches to modeling them. Each webinar will last 60 minutes and is designed to be attended in the order they were presented. If you miss one in the series, please check out our video page for a recording, or contact us before the next webinar starts.

Prerequisites: Familiarity with LHP modeling approaches in TD/FloCAD (see Part 1Part 2 and Part 3).
Please register for Part 4 here