MHD interaction parameter S

It defines the strength of the interaction between the magneto-hydro-dynamic energy and the airflow.

pu with a = flow electrical conductivity (mho/m), p = gas density (kg/m3), u = gas velocity along MHD device (m/s) and pu = mass flow per unit area (kg/m2/s).

The mass flow per unit area along a vehicle increases by 25 or more from the nose to the engine area as the flow is compressed. This means that the Russian installation of a nose MHD device and plasma generator, to drive the hydrocarbon fuel arc reforming process and alter the surrounding flow field to reduce drag, is using basic physics to advantage. Again the nose mass flow per unit area is about an order of magnitude less for a hypersonic cruise vehicle compared to an accelerating space launcher, favoring the application of MHD to cruise vehicles. For the cruise vehicle the pressure is less and the ionization potential to create a plasma much greater than for an accelerator (see Figure 4.7). Note that the magnetic field strength (B) is squared, so a doubling of the B field increases the interaction by a factor of 4. The mass flow per unit area inside the combustor is too large to have a significant interaction at moderate magnetic field strengths. That is why the MHD generator and accelerator are placed where the local Mach number is higher and the mass flow per unit area and pressure are less. The B field for the MHD generator and accelerator usually is greater than that required for the nose device, because of the larger mass flow per unit area.

Radiative losses

The plasma transport equations include energy transport. In terms of temperature, T, the radiative energy transport is the left side of equation (4.23):

where the two terms on the right hand side are the radiation heat transfer due to recombination of electrons and ions (Drec), and the brehmsstrahlung radiation contribution (DBrem). The number of ions (Ni) and the degree of ionization (a) multiply the radiation heat transfer terms. Again there needs to be a compromise on a and to consider scaling of this loss with temperature.

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