Influence of a non-condensable gas on mixing of a melt with water in a stratified configuration

The influence of bubbles of hot non-condensable gas formed at the interface between the melt and water on the formation of a mixture of melt with water capable of producing steam explosions is considered. The dynamics of such a bubble in subcooled water is analyzed numerically in a one-dimensional spherically symmetric approximation. It is shown that with significant initial superheat of the bubble relative to the water, a rapid drop in pressure in the bubble occurs due to strong heat removal into the water. This leads to the collapse of the bubble and the appearance of an accompanying flow of water. The results obtained made it possible to approximately describe the stage of collapse of the bubble as the polytropic process and to determine its index. The axisymmetric problem of the impact of the water jet on the surface of a melt during collapse of a gas bubble near the interface between the melt and water is numerically investigated. In this case, the obtained polytropic process equation is used to determine the pressure in the bubble. It is found that the resulting impact on the melt is capable of knocking out melt droplets into the water to a height of several centimeters, which leads to the formation of a layer of water mixed with the melt droplets, which is capable of producing strong steam explosions.

Mathematical Modeling of the Polytropic Process Using the Sequential Cubic Polynomial Approximation

The polytropic process is used to signify the effect of “energy degradation” associated with the equipment losses, which is as an inherent irreversibility in a compression process. The polytropic process is path dependent, which entails the irreversibility associated with the system. The change of gas composition and operating conditions affect the energy degradation. In this paper the polytropic process of real gas is explained and thermodynamics and mathematical model used in Taher-Evans Cubic Polynomial Method [1], [2] is presented. The elegance of Taher-Evans Cubic Polynomial Method is its rapid solution technique and high precision for calculating polytropic efficiency as required for compressor performance testing by the ASME PTC-10 [3].

On Exact and Local Polytropic Processes: Etymology, Modeling, and Requisites

This preprint concerns polytropic processes, a fundamental process type in engineering thermodynamics. An etymology is presented for the term, and the ties to its usefulness are identified. The seemingly new support concept of ‘logical’ thermodynamic process, as well as the seemingly new working concept of ‘exact’ polytropic process, and a statement for ‘local’ polytropic process, are herein provided. The proposition of employing local polytropic processes as computational discrete elements for generic engineering thermodynamics process modeling is made. Finally, theoretical requisites for a process to be an exact polytropic one, including the deduction of the most general equation of state of the underlying substance, are discussed beyond a reference.

A Physics-Based Control-Oriented Model for the Turbine Power of a Variable-Geometry Turbo-Charger

In this paper, we discuss the development of a control-oriented model for the power developed by a Variable Geometry Turbine (VGT). The turbine exit flow velocity, Cex, is obtained based on a polytropic process assumption for the full turbine stage. The rotor inlet velocity, Cin, is estimated, through an empirical relationship between Cex and Cin as a function of a dimensionless parameter ψ. The turbine power is developed based on Euler’s equations of Turbomachinery under the assumptions of zero exit swirl and alignment between the nozzle orientation and the Cin velocity vector. A power loss sub-model is also designed to account for the transmission loss associated with the power transfer between the turbine and compressor. The loss model is an empirical model and accounts for bearing friction and windage losses. Model validation results, for both steady state and transient operation, are shown.

Simulation on polytropic process of air springs

Purpose The purpose of this paper is to propose a method to simulate the polytropic process of air springs. Design/methodology/approach An iterative finite element method (FEM) is proposed. Findings The proposed method is reliable and effective in solving the polytropic process of air springs. Originality/value This work would be helpful for understanding the simulation of pneumatic structures, and the proposed modified FEM would be useful for improving the simulation of the mechanical behavior of an air spring.

On the Variation of the Polytropic Exponent in a High Pressure Fan Impeller

Fan impellers are usually designed considering that the pumped air is incompressible and homogeneous, i.e. its density remains constant. When the incompressibility hypothesis can lead to significant errors, as in the case of high pressure fans, the analysis of the air flow can be made by considering that the air undergoes a polytropic process of constant polytropic exponent. In this paper, the concept of polytropic process of variable exponent depending on impeller radius is introduced, in order to better approximate the phenomena that take place inside blade passages. Numerical results obtained for an impeller of a high pressure fan without spiral casing suggest that the pumped air undergoes two different processes: an expansion in the first part of the impeller and the usual compression in the second part. The two processes are reflected in the strong variation of the polytropic exponent, which shows a vertical asymptote where the change of the process takes place. The results also suggest that high pressure fan impellers could consist of two stages, each stage being designed according to the process that takes place inside it: expansion or compression.

Maximum Power Point Characteristics of Generalized Heat Engines with Finite Time and Finite Heat Capacities

We revisit the problem of optimal power extraction in four-step cycles (two adiabatic and two heat-transfer branches) when the finite-rate heat transfer obeys a linear law and the heat reservoirs have finite heat capacities. The heat-transfer branch follows a polytropic process in which the heat capacity of the working fluid stays constant. For the case of ideal gas as working fluid and a given switching time, it is shown that maximum work is obtained at Curzon-Ahlborn efficiency. Our expressions clearly show the dependence on the relative magnitudes of heat capacities of the fluid and the reservoirs. Many previous formulae, including infinite reservoirs, infinite-time cycles, and Carnot-like and non-Carnot-like cycles, are recovered as special cases of our model.