Regenerator and Regenerator-Displacer Modeling

In Stirling cycle and Gifford-McMahon (GM) cycle engines, the displacer is the piston on the cold (heat input end) of the device. GM cycles also use regenerators, as do many Stirling cycles … at least those designs intent on achieving the highest possible thermodynamic efficiency. Regenerators are also key features in pulse-tube cryocoolers, a derivative of a Stirling cycle that lacks a displacer.

Regenerators are porous bodies, usually cylindrical in shape, through which fluid passes back and forth in a cyclic motion. They are often made either of packed (but not sintered) beads, or screens stacked perpendicular to the flow direction. Regenerators are hot on one end, and cold on the other. An ideal regenerator maintains that temperature gradient: heating fluid as it enters one direction, and cooling it when it flows in the opposite direction.

The following graphic from NIST illustrates both the regenerator and the displacer, as applied in a GM cycle:

Illustration of the regenerator and the displacer, as applied in a GM cycle

To quote Wikipedia:

“A regenerator is difficult to design. The ideal regenerator would be: a perfect insulator in one direction, a perfect conductor in another, have no internal volume yet infinite flow area and infinite surface area. As with the hot and cold exchangers, achieving a successful regenerator is a delicate balancing act between high heat transfer with low viscous pumping losses and low dead space. These inherent design conflicts are one of many factors which limit the efficiency of practical Stirling engines.”

Modeling a Single Stage Helium GM Cycle

In one variation of the GM cycle, the displacer is also the regenerator: the “regenerator-displacer” is a cylinder containing a porous material. This regenerator-displacer is driven back and forth between the cold end (say of a cryocooler, perhaps used in a vacuum pump or sensor cooling application) and the hot end where heat is rejected (by exhausting out the low pressure port).

In a paper by Kimo M. Welch, the action of a single-stage R-D is nicely summarized in the figure below:

The action of a single-stage R-D

A SINDA/FLUINT (Thermal Desktop® and FloCAD®) model has been developed corresponding to the above system.

The purpose of this model is two-fold:

  • Provide guidelines for regenerator modeling (the lessons learned being applicable to stationary regenerators as well)
  • Provide a template or starting point for modeling similar designs

Chart of Valve Flow Area versus Crank Angle

Chart of Temperature versus Crank Angle

Click here to fetch the Regenerator-Displacer Example from our User Forum


dispersed vs. coalesced front

Tuesday, June 26, 2018, 1-2pm PT, 4-5pm ET

This webinar describes flat-front modeling, including where it is useful and how it works. A flat-front assumption is a specialized two-phase flow method that is particularly useful in the priming (filling or re-filling with liquid) of gas-filled or evacuated lines. It also finds use in simulating the gas purging of liquid-filled lines, and in modeling vertical large-diameter piping.

Prerequisites: It is helpful to have a background in two-phase flow, and to have some previous experience with FloCAD Pipes.

Register here for this webinar

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 is designed to be attended in the order they were presented. 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.