Diabatic supersonic flows of dense gases

Abstract

By adopting the van der Waals gas model the behavior of n-octane with addition or removal of heat in inviscid, steady, one-dimensional, supersonic flow is investigated. First, the given heat distribution is added in a constant area flow. Second, the effects in variable cross-sectional flows (nozzles) are shown for the additional condition of constant values of the Mach number or the static pressure, and for a given heat addition. As known from the isentropic flow of real gases, several gas-dynamic effects are inverted depending on the fundamental derivative Γ. Heat addition in a constant area duct at conditions near the thermodynamical critical point may cause an increase of the Mach number in transonic/supersonic flow, or a decrease in subsonic flow, which is the opposite behavior of a perfect gas. For heat addition at M=const a singularity is possible for Γ<0 in transonic/supersonic flow and for Γ≲1 in subsonic flow. Considering constant Mach number flows, the static pressure goes up for high values of Γ. Isobaric heat addition increases the Mach number for densities below the thermodynamical critical point. Perfect gas flow exhibits the opposite reaction in both cases without any singularity. Compared with the flow of a perfect gas (γ=1.4), in the dense gas the influence of the same rate of heat addition becomes much stronger.