This paper presents a numerical study analyzing the effect of pulsating flow in a variable geometry radial inflow turbine. The turbine behavior is analyzed under isentropic pulses, which are similar to those created by a rotating disk in a turbocharger test rig. Three different pulse frequencies (50, 90 and 130 Hz) and two pulse amplitudes (100 and 180 kPa) were considered. Turbine flow was studied throughout the pressure pulsation cycles in a wide range of off-design operating conditions, from low pressure ratio flow detachment to high pressure ratio choked flow. An overall analysis of the phasing of instantaneous mass flow and pressure ratio was first performed and the results show the non-quasi-steady behavior of the turbine as a whole as described in the literature. However, the analysis of the flow in the different turbine components independently gives a different picture. As the turbine volute has greater length and volume than the other components, it is the main source of non-quasi-steadiness of the turbine. The stator nozzles cause fewer accumulation effects than the volute, but present a small degree of hysteretic behavior due to flow separation and reattachment cycle around the vanes. Finally, the flow in the moving rotor behaves as quasi-steady, as far as flow capacity is concerned, although the momentum transfer between exhaust gas and blades (and thus work production and thermal efficiency) is Email address: galindo@mot.upv.es, pabfape@mot.upv.es, ronagar1@mot.upv.es, luiga12@mot.upv.es (J. Galindo, P. Fajardo ( * ) , R. Navarro and L.M. García-Cuevas) Preprint submitted to Applied Energy September 7, 2012 affected by a hysteretic cycle against pressure ratio, but not if blade speed ratio is considered instead. A simple model to simulate the turbine stator and rotor is proposed, based on the results obtained from the CFD computations.

A Helicon Plasma Thruster has been tested in the 500 -1000 W radio-frequency power range, at 13.56 MHz. In order to determine its propulsive performances, a parametric study of some operational parameters has been carried out, including the exploration of the magnetic field topology and strength, the mass flow rate, and different propellants. The plasma plume has been characterized by means of intrusive plasma diagnostics, which allow an indirect estimation of the thrust, 2 -6.6 mN, and thrust efficiency, about 2.9 %. The structure of the plasma expansion is compared against a theoretical model showing a good agreement.

This paper details a physical based methodology to perform an extrapolation of the radial turbine performance maps, both mass flow characteristics and the efficiency curve. This method takes into account a narrow range of experimental data, which is usually the data available when such turbines are part of a turbocharger. Therefore, the extrapolation methodology is especially useful when data from third parties are being used or when the compressor of a turbocharger is used as turbine brake in a gas stand. The nozzle equation is used to develop an interpolation and extrapolation of the mass flow rate trough the turbine. Then, specific information is extracted from this extrapolation and is fed into a total-to-static efficiency equation to carry out an extension of the efficiency curve. This equation is developed using the definition of the total-to-static efficiency, velocity triangles and thermodynamic and fluid fundamental equations.This procedure has been applied to five radial turbines of different sizes and types. Results are compared against experimental information available in the literature or provided by the turbine manufacturers and a good agreement has been found between theoretical and experimentally estimated data.Keywords: Turbochargers, radial turbines, efficiency and mass flow rate maps extrapolation, physical equations based extrapolation. ------------------------------- Greek --------------------------------- Subscripts INTRODUCTIONA way to characterize the performance of a radial inflow turbine widely used in a turbocharger is via a turbine map. Turbine maps usually are presented using two separate plots: one for the mass flow rate and one for the energy conversion efficiency, which usually is taken as the total-to-static efficiency. The former chart is presented as the corrected mass flow ( * m  ) as a function of the totalto-static expansion ratio (ER). The corrected mass flow ( * m  ) is defined as the mass flow rate multiplied by a ratio between the square root of the turbine stagnation inlet temperature and the turbine stagnation inlet pressure [1]. The other chart is the total-to-static efficiency ( ts ) as a function of the blade to jet speed ratio (), which is a ratio of the rotor tip linear velocity to the isentropic velocity through the turbine stage, for different turbine rotational speeds [1]. [5] used a radial compressor instead of a dynamometer to enable increased power of larger turbines to be absorbed. Szymko [6] developed an installation where an eddy current dynamometer was used in order to absorb the power of the turbine and for providing a low known inertia of the rotating assembly, which increases the measurement accuracy of the instantaneous torque.In the continuous flow test bench at Universidad Politécnica de Valencia, the approach is to use a compressor as a braking device [7]. In this last case, a collection of only a narrow range of data is possible, due to the surge and choke limits of the compressor, so a limited widespread of the data is availabl...

The expansion of a rarefied axisymmetric plume emitted by a plasma thruster is analyzed and compared with a 3D Cartesian-type and a 2D cylindrical-type simulation code, both based on a particle-in-cell formulation for the heavy species and a simple Boltzmann-type model for the electrons. The first part of the paper discusses the 2D code numerical challenges in the moving of particles, their generation within the cells, and the weighting to the nodes, caused by the radial non-uniformity and the singular and boundary character of the symmetry axis. The second part benchmarks the 2D code against the 3D one for a high-energy, unmagnetized plume with three major species populations (injected neutrals, singly-charged and doubly-charged ions) and three minor species populations (constituted by particles coming from collisional processes, such as the charge-exchange reactions). The excellent agreement found in the results proves that both plume codes are capable of simulating, with a reasonable noise level, heavy particle populations differing by several orders of magnitude in number density. For simulations with a comparable level of accuracy, the 2D code presents a ten-fold gain in computational cost, although the symmetry axis remains its weakest point, due to particle depletion there and the related weighting noise.

A radial particle-in-cell model of the weakly-collisional plasma discharge in a Hall thruster, provides the non-Maxwellian velocity distribution functions (VDF) of ions and electrons. The model considers a radial magnetic field, secondary electron emission from the two walls, and phenomenological models of anomalous electron scattering. The electron VDF is used to assess the different terms in the macroscopic momentum and energy equations, identifying those differing from the standard fluid model for a near-Maxwellian VDF. The pressure tensor consists of an anisotropic gyrotropic part and a small gyroviscous part. Nonetheless, the gradient of this last one affects the cross-field electron current density, generating radial undulations that resemble those reported for near-wall conductivity. A gyroviscous energy flux is identified too. The heat flux parallel to the magnetic lines does not follow a conductive-type law but a convective-type one, already found in other weakly-collisional plasmas. The tails of the electron velocity distribution function are partially depleted due to wall collection, leading to reduced electron fluxes of particles and energy, which are characterized with parameters useful for fluid models. Differences in the plasma response for annular and planar channel geometries are highlighted. The levels of replenishment of the electron VDF and of the asymmetries in radial profiles differ for isotropic and anisotropic anomalous scattering models.