Engines without dedicated heater and cooler space

( or DHT (Direct Heat Transfer) engines ) Many of these types of Stirling engine are known by the phrase LTD (Low Temperature Differential) engines as shown schematically to the right. It has to be pointed out though that there is no inherent feature in these engines which limits the temperatures on the hot and cold side other than those restrictions which apply to all other types of Stirling engines. The programs mentioned below can be used to to investigate power output as function of engine parameters. (Example of Power output versus RPM at different phase angles between power and displacer piston motion). It is important though to know a little bit about the various assumptions underlying each program as explained below.

Presently three web-based simulator programs are available of which the program DHT_GapHt is the most advanced and the one which will be updated as needed. The three programs have the following features in common :

1. Pressured drop across the displacer piston due to flow resistance in the gap surrounding the displacer piston is simulated such that the instantaneous pressure drop and flow velocity are related to each other as if the flow were steady (quasi-steady flow assumption).
2. Flow resistance between the cold and power space is neglected.
3. Leakage of gas between the engine and the environment is assumed to be zero.
4. The displacer piston is rigid neither changing its volume nor absorbing/releasing any working gas during an engine cycle.
5. The displacer and power piston move in sinusoidal fashion with adjustable phase lag.
6. Friction of the driving mechanism is neglected.
7. The displacer piston does not contain any built-in regenerator capabilities.

The three programs ( most recent and sophisticated first ) are :

1. DHT_GapHt.1.0

   This program provides the opportunity to study flow friction losses in the displacer gap as well as the influence of heat transfer rates in the compression and expansion space on engine performance. The newest version, DHT_GapHt.1.1 allows the user to choose between sinusoidal piston motion and a classical crank drive.

   It integrates directly a set of ordinary differential equations taking into account pressure differences between compression and expansion space as needed to overcome flow resistance in the displacer gap. Pressure drop and gas flow velocity are related to each other assuming steady, low Mach number flow. Additionally, the assumption of isothermal behavior in the compression and expansion space has been dropped and replaced by a simple heat transfer model for both spaces. The integration starts at some initial point and proceeds over as many engine cycles as necessary to achieve steady-state (same conditions at end of an engine cycle as at the beginning). For some more details on the involved physics and math background click here. This page contains also links to the details of the employed gap flow resistance model and the heat transfer model for the compression and expansion space.

   NOTE : For the purpose of comparison this program performs additionally the same calculations as those done by the two programs mentioned below, DHT-NoRegen and DHT-Schmidt-NoRegen. The latter two are still offered for legacy reasons but not developed any further.

2. DHT-Schmidt-NoRegen. This program performs a Schmidt-type analysis assuming isothermal conditions in the compression and expansion space. This provides among others the mass flow rate through the displacer gap at each crank angle which in turn allows us to determine the pressure drop across the displacer piston necessary to achieve these mass flow rates. It assumes that these pressure drops are so small that incorporating them would lead only to insignificant changes in the mass flow rates. Based on the thus determined pressure difference history across the displacer piston the loss in power ( which I would call the displacer shuttle losses ) is determined by the program.

   NOTE : This program will no longer be updated as its calculations are also performed by program DHT_GapHt, above, with almost identical input.

3. DHT-NoRegen. This program first repeats exactly the calculations as outlined for program DHT-Schmidt-NoRegen assuming again isothermal condition inside the compression and expansion space. Additionally, ( which makes this program somewhat slower ) a direct simulation is performed in which the flow resistance across the displacer gap is taking into account as mass flow rates are calculated. To my great surprise, for at least the few test case I have run, the results of both programs (DHT-NoRegen and DHT-Schmidt-NoRegen) differ only insignificantly but maybe somebody else finds an engine configuration where this is not the case. The benefit for myself is that this latter type of analysis is extensible to a more sophisticated analysis incorporating finiteness of heat transfer etc.
   Note that his program suffers from a mathematical perculiarity called "stiffness of a system of ordinary differential equations" which becomes more and more pronounced as the RPM of an engine is reduced. The user notices this in prolonged execution times as the RPM is reduced. If you wish to investigate at lower RPMs ( down to zero ) I suggest you use the program DHT-Schmidt-NoRegen.

   NOTE : This program will no longer be updated as its calculations are also performed by program DHT_GapHt, above, with almost identical input.