# Thruster (38847)

### Micropyros Thruster (38847)

E. B. Rudnyi, rudnyi@imtek.uni-freiburg.de

The goal of the European project Micropyros (http://www.laas.fr/Micropyros/) was to develop a microthruster array shown in fig. 1. It is based on the co-integration of solid fuel with a silicon micromachined system [1]. In addition to space applications, the device can be also used for gas generation or as a highly-energetic actuator. When the production of a bit-impulse is required, the fuel is ignited by heating a resistor at the top of a particular microthruster. Design requirements and modeling alternatives are described in Ref [2]. The discussion of electro-thermal modeling related to the benchmark can be found in Ref [3].

The benchmark contains a simplified thermal model of a single microthruster to help with a design problem to reach the ignition temperature within the fuel and at the same time not to reach the critical temperature at neighboring microthrusters, that is, at the border of the computational domain. At the same time, the resistor temperature during the heating pulse should not become too high as this leads to the destruction of the membrane.

The benchmark suite has been made with the Micropyros software developed by IMTEK. There are four different test cases described in Table 1 with the goal to cover different cases of different computational complexity. Note that the results from different models cannot be compared directly with each other as the output nodes are located in slightly different geometrical positions and there is some difference in modeling for the 3D and 2D-axisymmetric cases.

Table 1. Microthruster benchmarks.

Code | comment | dimension | nnz(A) | nnz(E) |

T2DAL | 2D-axisymmetric, linear elements | 4257 | 20861 | 4257 |

T2DAH | 2D-axisymmetric, quadratic elements | 11445 | 93781 | 93781 |

T3DL | 3D, linear elements | 20360 | 265113 | 20360 |

T3DH | 3D, quadratic elements | 79171 | 2215638 | 2215638 |

The device solid model has been made and meshed in ANSYS. The material properties assumed to be constant. The system matrices have been converted to the Matrix Market format by means of mor4fem. Temperature is assumed to be in Celsius with the initial state of 0 C.

The output nodes are described in Table 2. Nodes 2 to 5 show the fuel temperature distribution and nodes 6 and 7 characterize temperature in the wafer, nodes 5 and 7 being the most faraway from the resistor.

Table 2. Outputs for the microthruster models.

# | Code | Comment |

1 | aHeater | within the heater |

2 | FuelTop | fuel just below the heater |

3 | FT-100 | fuel 0.1 mm below the heater |

4 | FT-200 | fuel 0.2 mm below the heater |

5 | FuelBot | fuel bottom |

6 | WafTop1 | wafer top (touching fuel) |

7 | WafTop2 | wafer top (end of computational domain) |

The benchmark files contain a constant load vector, corresponding to the constant power input of 150 mW. In order to insert a weak nonlinearity related to the dependence of the resistivity on temperature, one has to multiply the load vector by a function

1 + 0.0009 T + 3E-07 T^2

assuming the constant current. It is necessary to replace the temperature in the equation above by the temperature at the node 1.

The linear ordinary differential equations of the first order are written as

E dT/dt = A T + B

y = C T

where E and A are the system matrices (both are symmetric), B is the load vector, C is the output matrix, and T is the vector of unknown temperatures.

Download matrices in the Matrix Market format: (File 1); (File 2) 1700463 bytes; (File 3) 2222686 bytes; (File 4), 38519903 bytes. The matrix name is used as an extension of the matrix file. File *.C.names contains a list of ouput names written consecutively.

The ANSYS results for the original models as well as the reduced models obtained by mor4fem can be found at the micropyros page: choose EleThermo for T2DAL and T2DAH or EleThermo3D for T3DL and T3DH.

The model reduction of the microthruster model by means of mor4fem is described in Ref [4].

[1] C. Rossi, B. Larangot, T. Camps, M. Dumonteil, D. Lagrange, P. Q. Pham, D. Briand, N. F. de Rooij, M. Puig-Vidal, P. Miribel, E. Montane, E. Lopez, J. Samitier, E. B. Rudnyi, T. Bechtold, J. G. Korvink, Review of solid propellant microthrusters on silicon, Journal Propulsion and Power (2004), to be published.

[2] E. B. Rudnyi, T. Bechtold, J. G. Korvink, C. Rossi, Solid Propellant Microthruster: Theory of Operation and Modelling Strategy, Nanotech 2002 - At the Edge of Revolution, September 9-12, 2002, Houston, USA, AIAA Paper 2002-5755.

[3] G. Korvink, E. B. Rudnyi, Keynote: Computer-aided engineering of electro-thermal MST devices: moving from device to system simulation, EUROSIME'03, 4th international conference on thermal & mechanical simulation and experiments in micro-electronics and micro-systems Aix-en-Provence, France, March 30 - April 2, 2003.

[4] T. Bechtold, E. B. Rudnyi, J. G. Korvink and C. Rossi, Efficient Modelling and Simulation of 3D Electro-Thermal Model for a Pyrotechnical Microthruster. International Workshop on Micro and Nanotechnology for Power Generation and Energy Conversion Applications PowerMEMS 2003, Makuhari,Japan, 4-5 December 2003.