NEW H2020 Project Kick-off November 3-4



UNDULANT-Next: UNsteaDy boUndary LAyer flow coNTrol using plasma actuators of Next generation

Coordinator: José Páscoa
HyperMHD: Magnetoplasmadynamic Flow Manipulation on Hypersonic and Reentry Vehicles
Coordinator: Carlos Xisto


Numerical MHD Numerical Modelling in nozzles of MPD thrusters for space propulsion PTDC/CTE-SPA/114163/2009

Magnetoplasmadynamic (MPD) thrusters are Lorentz force accelerators that can provide the high-specific impulse, and high-power propulsion, required to enable human and robotic exploration missions to the Moon, Mars, and outer planets. In the past mainly the very efficient ion and Hall thruster technologies were employed, but these are dimensionally impracticable for high powers. Herein we will focus on Applied-Field MPD thrusters who, albeit their current poor efficiencies, are strong candidates for high powers (>100kW to MW). Conversely to ionic thrusters, that have been used in space (ESA's SMART-1), or to Pulsed Plasma Thrusters (PPT) used in satellite attitude motion control, the high-power AF-MPD thrusters have still to be developed, both resorting to experimental and numerical approaches, in order to be used in flight.

In the present work we will concentrate on extend, and develop, an existing numerical tool to the analysis and design of AF-MPD thrusters, in particular the nozzle component.This nozzle accelerating device plays a central role in the thruster efficiency, by converting pressure and thermal energy into kinetic energy, and also must ensure that the plasma flow reaches a super-Alfvénic plasma speed to guarantee that it detaches from the spacecraft. The fluid conditions at these high powers allow that the plasma can be treated as a continuum, and thus it can be modelled using a magnetohydrodynamic (MHD) approach. The field of magnetohydrodynamics (MHD) has recently become an area of renewed intensive research, since high-performance computing (HPC) allow the simulation of MHD equations, for realistic 2D and 3D configurations, and computer system technological limitations are being reduced. Albeit this, code deficiencies related to the computation of this class of flows still pace the development of these propulsive devices, both in Europe and United States. Magnetohydrodynamic equations comprise the Navier-Stokes equations coupled to the induction equation for the magnetic field. A current state-of-the art problem, related to the numerical imposition of a divergence free constraint, in one of the equations, will be carefully tackled. Typical flux functions used in MHD codes were originally devised for gas dynamics. Herein, they will be rederived for MHD flows, to cope with the solenoidal condition and to deal with degeneracies in the MHD eigenstructure. Furthermore, the MHD equations will consider viscous and anisotropic resistive conditions. In order to being able to compute, in a reasonable time, this class of intensive computing problems a distributed memory, parallel processing framework, will be used. This will use the existing HPC Cluster at UBI. The code will thus extended an existing, in-house, RANS code to MHD turbulent flow computation. Problems associated with the implementation of viscous and turbulent numerical models will be tackled. MHD effects will be incorporated by adapting classical turbulence models. The applied magnetic field introduce relaminarization on the turbulent structures. The k-e, k-w and S-A turbulence models will be modified in order to correctly model the physics of MHD turbulent flows. Further, a tensorial anisotropic resistivity distribution will be incorporated for the, single fluid, ionized plasma flow computations. The application of the code will be implemented to analyse the flow inside AF-MPD thrusters, and in particularly their nozzle geometry. The study on the geometry of magnetic nozzles will be considered for the problem of plume detachment from the spacecraft. The performance of the thrusters will be further enhanced by modelling non-uniform transport properties. Besides the decay in efficiency due to viscous dissipation, MHD nozzles will also be studied in order to reduce turbulent instabilities detected on course of experimental testing. It is expected that this later can be mitigated by modulating the MHD nozzle geometry coupled to the imposed magnetic field. Some of the activities of present work are already integrated in the framework of the, recently created, FCT National Space Consortium.

Project supported by FCT (National Foundation for Science and Technology).








Fig: Unsteady simulation of a Magnetoplasmadynamic thruster. a) Velocity contours; b) Numerical grid and Boundary Conditions; c) Temperature contours computed with an ideal gas model; d) Temperature contours computed with a real gas model for Argon.



- Xisto C.M., Páscoa J. C., Oliveira P.J. (2014), "A pressure-based high resolution numerical method  for resistive MHD", Journal of Computational Physics, In press, DOI: 10.1016/

- Xisto C. M. (2014), "Métodos numéricos para a dinâmica de gases e escoamentos magnetohidrodinâmicos a números de Mach arbitrários", Doctoral Thesis, Universidade da Beira Interior, Portugal.

- Xisto C.M., Páscoa J. C., Oliveira P.J. (2013), "A pressure-based method with AUSM-type fluxes for MHD flows at arbitrary Mach numbers", International Journal for Numerical Methods in Fluids, Vol. 72(11) pp 1165-1182, DOI: 10.1002/fld.3781.

- Xisto C.M., Páscoa J.C. , Oliveira P.J. (2013), "Numerical Modelling of Electrode Geometry Effects on a 2D Self Field MPD Thruster", in Proc. International Mechanical Engineering Congress & Exposition, IMECE2013, November 15-21, San Diego, California USA.

- Machado T., Páscoa J.C., Brojo F., Xisto C.M., (2013), " Numerical Modeling of Turbulent Transitional MHD Flow for Boundary Layer Control", in Proc. SAE Aerotech  2013, Montreal, Quebec, Canada Nº 2013-01-2269 doi:10.4271/2013-01-2269.

- Xisto C.M., Páscoa J. C. , Oliveira P.J. (2013), "Modelling plasma flow on a self-field MPD thruster using a PISO based method", in Proc. 44th AIAA Plasmadynamics and Lasers Conference, San Diego USA Nº AIAA2013-2627 DOI:10.2514/6.2013-2627.

- Xisto C.M., Páscoa J. C. , Oliveira P.J. (2012), "Introduction of a new algorithm for the MHD equations at all Mach number regimes", in Proc. European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012, 18 pp.

- Xisto C.M., Páscoa J.C., Oliveira P.J., Nicolini D.A. (2010), "Implementation of a 3D compressible MHD Solver Able to Model Transonic Flows",  in Proc. V European Conference on Computational  Fluid Dynamics ECCOMAS CFD 2010, 14 pp.