Application of the DSMC Method for Design of a Coaxial Microthruster Nozzle
The Direct Simulation Monte Carlo (DSMC) method is used to numerically simulate and design a micronozzle with improved performance. Thrust calculations using the DSMC method demonstrate that the coaxial micronozzles can achieve milli-Newton thrust levels with specific impulses on the order of 45 s using argon in a cold gas expansion. Improved micronozzle designs of coaxial microthrusters are also proposed. Coaxial micronozzles utilizing center-body geometries to exploit pressure thrust show about 140% increase in specific impulse at low Reynolds numbers compared to a traditional converging nozzle.
Gas flow in miniaturized nozzles for micro-thrusters
A new satellite philosophy, developed during the last two decades, suggests to make satellites smaller and lighter rather than bigger and heavier. In other words, large (?m3), single system satellites are being replaced by ?eets of small (?dm3), so-called micro-satellites. Future developmentsmay result in swarms ofmicro satellites ?ying through space in formation. Together they would perform the same tasks as a single large satellite, but with great savings in costs, increased simplicity, less vulnerability, and better replicability. As part of this new generation of (micro-)satellites, in order to provide highly precise station keeping, altitude control or long duration low thrust acceleration, new propulsion systems with thrusts in the ¹N to mN range need to be developed. One of the simplest forms ofmicro propulsion systems is a cold gas thruster: here, the energy stored in a pressurized gas is converted into kinetic energy through an expansion. The ef?ciency of such devices is strongly geometry and size dependent. Moreover, due to their small dimensions, combined with the low exhaust pressures in space, these systems behave differently than conventional large scale nozzles. Whereas experimental studies of micro propulsion systems are time consuming, dif?cult to perform with suf?cient accuracy, and require expensive experimental setups, numerical computer simulations can be a powerful tool of investigation. This thesis deals with the use and, where needed, the optimum combination of different numerical simulation models for the computational design of micro-thrusters, aimed at optimizing their performance and understanding the physics of the ?ow in such systems. In the ?rst phase of this work, we developed and used models for the design and optimization of micro thrusters providing a thrust in the mN range, as being developed for the actual state-of-the-art in micro propulsion system design. It was shown that conventional continuum Computational Fluid Dynamics can be used to study the gas ?ow and pressure distribution in such these micro-nozzles. Computationally predicted thrusts were in good agreement with experimental data. For mN thruster micro nozzles, in deviation from conventional large (kN-MN) thruster nozzles, viscous effects cannot be neglected due to the largely increased surface-to-volume ratio. As a result, ef?ciency loss due to developing viscous boundary layers, as well as surface roughness, are two main areas of concern in micro nozzles. Viscous losses were found to lead to an ef?ciency decrease of about 10%. Wall roughness added an extra 10% in ef?ciency loss. The increased boundary layer thickness reduced the effective cross sectional area of the divergent part of the nozzle. As a consequence it was found that, for optimum performance, micro nozzles should have a larger divergent angle than common in large scale nozzles. When the dimensions of micro-nozzles are further reduced, towards thrusts in the order of ¹N’s, the gas in the nozzle, particularly in its divergent part, becomes rare?ed. Under these conditions continuum based Computational Fluid Dynamics no longer provides an accurate description of ?ows and pressures, and non-continuum models should be used instead. Direct Simulation Monte Carlo was selected as the simulation method of choice for these conditions, because of its favorable combination of accuracy, ?exibility and computational costs compared to other available methods. Nevertheless, DSMC simulations are extremely more expensive than CFD simulations, particularly for weakly rare?ed gases. A possible solution lies in the application of a hybrid CFD/DSMC approach, where CFD is applied in those regions where rarefaction is not important, and DSMC is used in those regions where rarefaction needs to be accounted for. One of the main challenges faced in the second phase of this project was therefore in the consistent and ef?cient coupling of DSMC and CFD, making use of an existing general purpose CFD code and an existing general purpose DSMC code. The general idea was to apply continuum CFD in the upstream, high pressure convergent part of the nozzle, and use the CFD results as boundary condition for DSMC simulations in the downstream, low pressure divergent part of the nozzle. A detailed analysis of the numerical accuracy and computational costs of such a hybrid approach was carried out by comparing the results to those of, extremely costly, full DSMC simulations. Both accuracy and computational costswere found to critically depend on the chosen location of the interface between the CFD and DSMC regions, at which data is transferred from the ?rst to the latter. Rather than locating this interface at the throat, as is common in literature, we provide a simple recipe for the a priori determination of the optimal interface location. In this way, we were able to ?nd an optimum combination between accuracy and costs, leading to results that deviate less than 2% from full DSMC simulations at typically 5-25% of the computational costs of full DSMC. Finally, combining the three computational approachesmentioned above,we were able to produce master curves for the performance of micro nozzles as a function of the gas-wall collision accommodation coef?cient, over a wide range of nominal thrusts from O(10N) down to O(0.1¹N). For thrusts larger than 1mN, ef?ciencies larger than 90% were found, independent of the accommodation coef?cient. For smaller thrusts, the ef?ciency becomes strongly dependent on the accommodation coef?cient, i.e. on the nature of gas-wall collisions, and drops to 50% for thrusters in the ¹Nrangewith accommodation coef?cients equal to one. By reducing this accommodation coef?cient to a value below 0.5, which may be achieved by a proper selection of nozzle wall material and nozzle fabrication technique in combination with the proper choice of gas, this ef?ciency may be increased up to 70-80%. This thesis has resulted in: (i) design rules for micro thruster nozzles, (ii) computation methods that can be used in their design and evaluation, and (iii) in master ef?ciency curves that relate their nominal thrust and material properties to their thruster ef?ciency.
A torsional balance for the characterization of microNewton thrusters
We describe the performance of a torsional balance suitable for the study of microNewton thrusters. A design based on flexural pivots and electrostatic forces (for calibration and active damping) makes it possible to test thrusters with a mass of a few kilograms, and measure submicroNewton level forces with high accuracy and a resolution better than 0.03 μN. The usefulness of the balance is proved by measuring the performance of two different electric propulsion accelerators: a colloid thruster generating thrust in the 2–13 μN range, and a micropulsed plasma thruster yielding single impulse bits of 19 μN s. The low noise figure of the balance (below 0.1 μN/Hz in the 7 mHz–1 Hz bandwidth) will make it possible to measure the thrust noise requirements imposed in colloid thrusters by missions such as the Space Technology 7 and the Laser Interferometer Space Antenna.