Variation of polytropic exponent along converging-diverging nozzle axis.

1967 ◽  
Vol 4 (10) ◽  
pp. 1391-1394 ◽  
Author(s):  
T. K. BOSE
Keyword(s):  
Nozzle Axis ◽  
Polytropic Exponent

Fundamental study on reduction of dross in fiber laser cutting of steel by shifting nozzle axis

2021 ◽  
Vol 33 (1) ◽  
pp. 012022
Author(s):  
Atsushi Yagi ◽  
Seigo Kadonaga ◽  
Yasuhiro Okamoto ◽  
Hiroaki Ishiguro ◽  
Ryohei Ito ◽  
...  
Keyword(s):  
Fiber Laser ◽  
Laser Cutting ◽  
Fundamental Study ◽  
Nozzle Axis

Acoustic energy radiated by nonlinear spherical oscillations of strongly driven bubbles

2010 ◽  
Vol 466 (2118) ◽  
pp. 1829-1847 ◽  
Author(s):  
Joachim Holzfuss
Keyword(s):  
Wave Model ◽  
High Amplitude ◽  
Compressible Liquid ◽  
Acoustic Energy ◽  
Compressible Medium ◽  
Relevant Parameter ◽  
Wafer Cleaning ◽  
Viscous Compressible Liquid ◽  
Shock Wave Model ◽  
Polytropic Exponent

Based on the theory of F. Gilmore ( Gilmore 1952 The growth or collapse of a spherical bubble in a viscous compressible liquid ) for radial oscillations of a bubble in a compressible medium, the sound emission of bubbles in water driven by high-amplitude ultrasound is calculated. The model is augmented to include expressions for a variable polytropic exponent, hardcore and water vapour. Radiated acoustic energies are calculated within a quasi-acoustic approximation and also a shock wave model. Isoenergy lines are shown for driving frequencies of 23.5 kHz and 1 MHz. Together with calculations of stability against surface wave oscillations leading to fragmentation, the physically relevant parameter space for the bubble radii is found. Its upper limit is around 6 μm for the lower frequency driving and 1–3 μm for the higher. The radiated acoustic energy of a single bubble driven in the kilohertz range is calculated to be of the order of 100 nJ per driving period; a bubble driven in the megahertz range reaches two orders of magnitude less. The results for the first have applications in sonoluminescence research. Megahertz frequencies are widely used in wafer cleaning, where radiated sound may be implicated as responsible for the damage of nanometre-sized structures.

The Polytropic Approach in Modelling Compressible Flows Through Constant Cross-Section Pipes

2021 ◽  
Author(s):  
Alessandro Ferrari ◽  
Oscar Vento ◽  
Tantan Zhang
Keyword(s):  
Steady State ◽  
Cross Section ◽  
Compressible Flows ◽  
Analytical Formula ◽  
Local Maximum ◽  
Wall Friction ◽  
Numerical Code ◽  
Maximum Temperature ◽  
Constant Cross Section ◽  
Polytropic Exponent

Abstract A compressible flow with wall friction has been predicted in a constant cross-section duct by means of a barotropic modelling approach, and new analytical formulas have been proposed that also allow any possible heat transfer to the walls to be taken into account. A comparison between the distributions of the steady-state flow properties, pertaining to the new formulas, and to those of a classic Fanno analysis has been performed. In order to better understand the limits of the polytropic approach in nearly chocked flow applications, a numerical code, which adopts a variable polytropic coefficient along the duct, has been developed. The steady-state numerical distributions along the pipe, obtained for either a viscous adiabatic or an inviscid diabatic flow by means of this approach, coincide with those of the Fanno and Rayleigh models for Mach numbers up to 1. A constant polytropic exponent can be adopted for a Fanno flow that is far from choking conditions, while it cannot be adopted for the simulation of a Rayleigh flow, even when the flow is not close to choking conditions. Finally, under the assumption of diabatic flows with wall friction, the polytropic approach, with a constant polytropic exponent, is shown to be able to accurately approximate cases in which no local maximum is present for the temperature along the duct. The Mach number value at the location where the local maximum temperature possibly occurs has been obtained by means of a new analytical formula.

Polytropic Change of State Calculations

2014 ◽  
Author(s):  
Hans E. Wettstein
Keyword(s):  
Gas Turbines ◽  
Dissipation Rate ◽  
Pressure Ratio ◽  
Thermodynamic Cycle ◽  
Ideal Gas ◽  
Test Results ◽  
Stage Of Development ◽  
Change Of State ◽  
Calculation Algorithms ◽  
Polytropic Exponent

Polytropic change of state calculations are used within many thermodynamic cycle analysis tasks for turbomachinery like gas turbines or compressors. The typical approach is using formulas, which are theoretically valid for ideal gas conditions only. But often gases are used, which do certainly not behave like ideal gases. This is motivation to check how and which polytropic change of state algorithms can be used for real gases or corresponding mixtures. There is a vast experience on polytropic efficiencies achievable with existing turbomachinery. Manufacturers calibrate their performance analysis with real test results for compensating potential deviations from their analysis approach. But they normally do not disclose their approaches for the thermodynamic calculation and the corrections made based on their test results. But for investigations of new thermodynamic cycles before the stage of development with an available demonstrator a best possible prediction of the performance is desired. In this paper the assumptions and formulas for calculating polytropic changes of state and polytropic efficiencies are gathered from literature. The most fundamental assumption is based on a constant dissipation rate during the polytropic change of state. It could be tracked back to Zeuner, Stodola and Dzung. A numerically convenient approximation is the “polytropic exponent approach”. It fulfills the first assumption for an ideal gas but it is only an approximation for real gases. The temperature after a polytropic change of state is defined by its initial condition, the pressure ratio and the polytropic efficiency. Three different calculation algorithms are compared here: The recursive “constant dissipation rate algorithm” suggested by the author, the most used “ideal gas formula” and the “polytropic exponent formula” as the most used approximation for real gases. Numeric results for compression from 1bar to up to 100bar are shown for dry air, Argon, Neon, Nitrogen, Oxygen and CO2. The deviations of the different calculation approaches are considerable.

Thermal Effects in the Free Oscillation of Gas Bubbles

1971 ◽  
Vol 93 (3) ◽  
pp. 373-376 ◽  
Author(s):  
R. B. Chapman ◽  
M. S. Plesset
Keyword(s):  
First Principles ◽  
Thermal Effects ◽  
Thermal Conduction ◽  
Free Oscillation ◽  
Acoustic Radiation ◽  
Numerical Results ◽  
Air Bubbles ◽  
Gas Bubble ◽  
Physical Processes ◽  
Polytropic Exponent

A theory is developed from first principles which includes all the important physical processes which affect the frequency of the free oscillations of a gas bubble. The components of the damping: viscosity, thermal conduction in the gas, and acoustic radiation are all determined. Numerical results for the damping are given for air bubbles in water. Since there is physical interest in the polytropic exponent, κ, (in pVκ = const.), the value of κ which gives the correct natural frequency is also determined. Numerical results for this κ for air bubbles in water are presented.

In-Cycle Closed Loop Control of the Fuel Injection on a 1-Cylinder Heavy Duty CI-Engine

2010 ◽  
Author(s):  
Claes-Go¨ran Zander ◽  
Per Tunesta˚l ◽  
Ola Stenla˚a˚s ◽  
Bengt Johansson
Keyword(s):  
Heat Release ◽  
Real Time ◽  
Fuel Injection ◽  
Real Time Control ◽  
Loop Control ◽  
Time Control ◽  
Ci Engine ◽  
The Difference ◽  
Proportional Controller ◽  
Polytropic Exponent

The focus of this article is on implementation of real time combustion control by using an FPGA. The feedback used for the controller is the heat release. Due to the desire to avoid using division on the FPGA an alternative way of calculating the polytropic exponent is investigated. When this method is compared against using a constant exponent it shows less fluctuations in regards to cycle to cycle variations when calculating the heat release. A dual injection strategy is used and real time control is implemented on the second fuel injection. The calculated heat release is continuously compared with a reference and then the difference is converted to a duration correction of the fuel injection. This is done by a proportional controller which is initiated after the start of the second injection. By adding a perturbation on the first fuel injection the controller is shown to compensate during the second and thereby decreasing the cycle to cycle variations.

The Load Acting on Bearings of Rotary Compressor Sliding Vanes

2003 ◽  
Author(s):  
Yuan Mao Huang ◽  
Chien Liang Li
Keyword(s):  
Air Pressure ◽  
Rotary Compressor ◽  
Experimental Setup ◽  
Radial Load ◽  
Compression Process ◽  
Measured Load ◽  
Polytropic Process ◽  
Study Designs ◽  
Further Development ◽  
Polytropic Exponent

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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