The equation of polytropic process of real gases

This study designs extended rods with bearings for vanes and guider slots on covered plates to improve the performance of a sliding vane rotary compressor and determines the load acting on the bearings and vanes. A polytropic process with a polytropic exponent was assumed during the compression process to calculate the air pressure in the vane segments. The air pressure was used with Newton’s law to calculate loads acting on bearings and vanes. A compressor and experimental setup were also built to measure the radial load acting on the bearings. The measured load acting on the bearing was then compared with the calculated results. The exponent constant of 1.05 determined can be used for the further development of the compressor.

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

Volume 2: Mechatronics; Mechatronics and Controls in Advanced Manufacturing; Modeling and Control of Automotive Systems and Combustion Engines; Modeling and Validation; Motion and Vibration Control Applications; Multi-Agent and Networked Systems; Path Planning and Motion Control; Robot Manipulators; Sensors and Actuators; Tracking Control Systems; Uncertain Systems and Robustness; Unmanned, Ground and Surface Robotics; Vehicle Dynamic Controls; Vehicle Dynamics and Traffic Control ◽

10.1115/dscc2016-9856 ◽

2016 ◽

Author(s):

Kang Song ◽

Devesh Upadhyay ◽

Tao Zeng ◽

Harold Sun

Keyword(s):

Dimensionless Parameter ◽

Transmission Loss ◽

Empirical Relationship ◽

Variable Geometry ◽

Turbine Stage ◽

Turbo Charger ◽

Variable Geometry Turbine ◽

Polytropic Process ◽

Nozzle Orientation ◽

Bearing Friction

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.

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.841.286 ◽

2016 ◽

Vol 841 ◽

pp. 286-291

Author(s):

Andrei Dragomirescu

Keyword(s):

High Pressure ◽

Variable Exponent ◽

Air Flow ◽

Numerical Results ◽

Strong Variation ◽

Polytropic Process ◽

Two Stages ◽

Spiral Casing ◽

Polytropic Exponent

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.

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Effects of Thermal Damping on the Dynamic Response of a Hydraulic Motor-Accumulator System

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.3149658 ◽

1984 ◽

Vol 106 (1) ◽

pp. 21-26 ◽

Cited By ~ 12

Author(s):

A. Pourmovahed ◽

D. R. Otis

Keyword(s):

Heat Transfer ◽

Time Constant ◽

Thermal Time ◽

Load Force ◽

Hydraulic Motor ◽

Small Perturbations ◽

Dissipative Effects ◽

Thermal Time Constant ◽

Polytropic Process ◽

Hydraulic Accumulator

A hydraulic accumulator is often modeled as a gas spring following a polytropic process, but this fails to properly account for the dissipative effects of heat transfer which produce damping and phase shift in the dynamic behavior. A thermal time constant can properly characterize the heat transfer between the charge gas and the accumulator walls, and it is shown that for the linearized case the accumulator becomes equivalent to the Anelastic Model. The transfer function for the accumulator is derived, and the mathematical solution is presented for a hydraulic accumulator coupled to the inlet of a hydraulic motor where the load force is subject to a small, sinusoidal variation with time. Experimental data are presented to show that the accumulator can be accurately modeled using a thermal time constant, and the Anelastic Model would adequately describe the accumulator for the case of small perturbations.

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

Journal of Thermodynamics ◽

10.1155/2012/246914 ◽

2012 ◽

Vol 2012 ◽

pp. 1-7

Author(s):

Abhishek Khanna ◽

Ramandeep S. Johal

Keyword(s):

Heat Transfer ◽

Ideal Gas ◽

Heat Capacities ◽

Working Fluid ◽

Maximum Power Point ◽

Power Extraction ◽

Heat Engines ◽

Special Cases ◽

Polytropic Process ◽

Power Point

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.

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