A thermodynamic non-equilibrium model for the expansion of a real gas in a turbine cascade

The paper addresses the problem of the evolution of systems from a given initial state to a final one in the most general case in which the transformations include non-equilibrium states.The specific phenomenon addressed here is the expansion of a real gas (non-constant specific heats) in a turbine cascade (nozzle + rotor).The model is based on an equation of motion similar to the real Ginzburg-Landau equation but rephrased in terms of exergy, and it was described in previous publications.The fundamental assumption here is that the evolution of the fluid is driven by the specified temperature and pressure gaps between the up-and downstream boundaries, but that the details of the intermediate states are linked to the local deflection angle E.Thus, for a fixed initial pair (T0, p0) and an assigned degree of reaction, it is possible to explicitly express the local work, friction-and heat losses along the passage as functions of the (integral of the) head coefficient \.This paper may be considered as a corollary to the proof of the existence and quantification of a non-equilibrium exergy presented in previous articles by the present Authors.The model does not make use of the local equilibrium assumption, and for simplicity's sake in the example discussed here a quasi-1D approach is adopted, assuming that at each station along its path the fluid is homogeneous in the directions perpendicular to the main motion (radial velocity identically zero and tangential velocity constant in the circumferential direction).The model calculates the (transversally averaged) non-equilibrium exergy at each station along the chord, and the main result is that its value at rotor exit is substantially higher than its equilibrium counterpart.The evolution history depends strongly on the deflection angle, i.e.on both the head and flow coefficients, \ and [respectively.The solution to the mass-and energy balances leads to an analytical expression for the non-equilibrium exergy.The paradigm is theoretically simple and the resulting model of relative ease of implementation (the solution presented here was obtained on a I5 core using MATHEMATICA), and fully two-dimensional solutions may be obtained as well, provided a proper form of the heat equation is used to calculate the fluid-to-wall thermal diffusion.Applications of the proposed framework may help designers to gain a better insight into real non-equilibrium expansion processes and to more accurately tune the nozzle-and rotor efficiency.