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A generalization of the dual, non‐frontier profit function approach to evaluating allocative efficiency is developed that allows for training (human capital) variables to influence the efficiency level directly. An application to Pennsylvania dairy indicates that education and experience are substitutes and play a significant role in the level of efficiency. While these operators are not allocating their variable inputs in an absolutely efficient manner, relative efficiency can be achieved for four of six possible input combinations for prescribed levels of education and experience. Furthermore, the estimates of the efficiency measures suggest that these operators are maximizing production rather than short‐run profits.

This paper is presented in two parts. Part I (Tabular fluid properties for real gas analysis) describes an approach to creating a tabular representation of the equation of state that is applicable to any fluid. This approach is applied to generating an accurate and robust tabular representation of the RefProp CO2 properties. Part II (this paper) presents numerical simulations of a low flow coefficient supercritical CO2 centrifugal compressor developed for a closed loop power cycle. The real gas tables presented in part I are used in these simulations. Three operating conditions are simulated near the CO2 critical point: normal day (85 bar, 35C), hot day (105 bar, 50 C) and cold day (70 bar, 20C) conditions. The compressor is a single stage overhung design with shrouded impeller, 155 mm impeller tip diameter and a vaneless diffuser. An axial variable inlet guide vane (IGV) is used to control the incoming swirl into the impeller. An in-house three-dimensional computational fluid dynamics (CFD) solver named TACOMA is used with real gas tables for the steady flow simulations. The equilibrium thermodynamic modeling is used in this study. The real gas effects are important in the desired impeller operating range. It is observed that both the operating range (minimum and maximum volumetric flow rate) and the pressure ratio across the impeller are dependent on the inlet conditions. The compressor has nearly 25% higher operating range on a hot day as compared to the normal day conditions. A condensation region is observed near the impeller leading edge which grows as the compressor operating point moves towards choke. The impeller chokes near the mid-chord due to lower speed of sound in the liquid-vapor region resulting in a sharp drop near the choke side of the speedline. This behavior is explained by analyzing the 3D flow field within the impeller and thermodynamic quantities along the streamline. The 3D flow analysis for the flow near the critical point provides useful insight for the designers to modify the current compressor design for higher efficiency.

Simulation of ice shed into a multistage axial compressor involves a coupled two phase flow of a continuous phase comprising of air and water vapor and a discrete phase with ice crystals and water droplets. A first principles based discrete phase model is formulated to capture the heat and mass transfer processes of ice flow in air. A quasi one-dimensional model is used to represent the continuous phase. An exchange of information at every time step between the two models leads to a coupled response that alters characteristics like temperature and pressure distributions across the compressor. However, an understanding of the impact of various assumptions used for modeling of the icing physics is imperative in order to establish the fidelity of the developed icing model, before its use in gas turbine engine ice ingestion studies. This paper describes the assumptions and semi-numerical models used in the coupled discrete-continuous phase flow numerical models. The input characteristics of the discrete phase related to the size and distribution of ice crystals, the assumed percentage of ice particles escaping through compressor bleed ports, simplifications associated with ice and droplet breakup on impact with compressor blades, moisture content affecting the dry air properties, are some of the factors that are variables in the icing study. The impact of these factors on the compressor flow dynamics is estimated through a parametric analysis.

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