|Abstract: ||This paper fits in the feasibility analysis of a Magneto-Hydrodynamic (MHD) inductive generator, coupled with a Thermo Acoustic (TA) energy conversion system. The MHD and TA processes have the great advantage to convert energy without mechanical moving components. In conventional MHD generator a plasma passes through an intense magnetic field, so, by closing the circuit on a load, the induced electromotive force determines in the fluid an electric current. Instead in the proposed generator the charge carriers are first created by means of an electrical discharge and then separated by an HVDC electrostatic field. Once the equilibrium is reached, if the gas inside the duct gets to vibrate, the charge carriers give rise to an alternating electric current; this induces an electromotive force in a toroidal coil wrapped around the duct and connected to the electrical load. In this work, first the design criteria are given; then the order of magnitude of the obtained parameters is used to model the system by using the FEM analysis. A thermo-acoustic analysis has been done in order to study the velocity profiles within the duct. As assumption we have an homogeneous fluid with no steady flow, and sinusoidal perturbations of small amplitude (no circulation and no turbulence). Furthermore the tube is long enough, so that end effects are negligible. Different velocity profiles were obtained by varying the radius of the duct and the frequency of the vibration. The numerical results confirm the theoretical ones retrieved from the literature. The axial velocity shows a parabolic profile for a low shear wave number (s = R*sqrt[ρ*ω/µ]); for higher values of said parameter the velocity becomes smaller in the center and the profile becomes more and more uniform. For very high values of shear wave number the profile is almost completely flat, with small peaks close to the tube wall. An electromagnetic analysis has been performed in a glass tube containing a ionized gas with two sleeve copper electrodes connected to an HVDC power supply. Near the sleeves a space charge density has been thickened. Applying the right voltage to the electrodes, we obtained an electrical potential profile that is null and flat in the zone between the electrodes where the electric field is thus equal to zero.
Starting from a homogeneous distribution, the third FEM model has been used to study the dynamics of separation and accumulation of charges. The fluid is considered macroscopically stationary, so we can neglect the convective phenomena. The electrons move under the action of a transverse external electric field and of diffusion phenomena linked to the electronic concentration gradient, tending to thicken near to the electrodes.
The results obtained make apparent that with appropriately frequency and radius, one can get a velocity profile with the best shape for ensure a sufficiently strong vibration of the particles thickened near the electrodes.|