An air-sea interaction theory for tropical cyclones [presentation]

We develop an alternative thermodynamic cycle for the Stirling machine, where the polytropic process plays a central role. Analytical expressions for pressure and temperatures of the working gas are obtained as a function of the volume and the parameter that characterizes the polytropic process. This approach achieves closer agreement with the experimental pressure-volume diagram and can be adapted to any type of Stirling engine.

Alternative thermodynamic cycle for the Stirling machine

The Fluidyne is a two-part hot-air engine, which has the peculiarity that both its power piston and displacer are liquids. Both parts operate in tandem with the common working gas (air) transferring energy from the displacer to the piston side, from which work is extracted. We describe analytically the thermodynamics of the Fluidyne engine using the approach previously developed for the Stirling engine. We obtain explicit expressions for the amplitude of the power piston movement and for the working gas temperatures and pressure as functions of the engine parameters. We also study numerically the power and efficiency of the engine in terms of the phase shift between the motions of piston and displacer.

The Fluidyne engine

The purpose of this paper is to review and analyze several types of instabilities as condensation oscillations (CO), stable condensation oscillations (SC), and bubbling condensation oscillation (BCO). These instabilities are produced during the discharge of steam into subcooled pools through vents or spargers. The mechanism of direct contact condensation (DCC) plays an essential role in these instabilities justifying that we review first the fundamental basis of DCC and the jet penetration length for the discharges of pure steam in subcooled water. Then, special attention is devoted to developing correlations for the nondimensional penetration length for ellipsoidal or hemi-ellipsoidal prolate steam jets observed in many experiments, to the heat transfer coefficients of DCC and to the best way to correlate the penetration length. Next, it is analyzed the stability of the steam jets with hemi-ellipsoidal shape in the transition and condensation oscillation regimes and it is computed the subcooling temperature threshold for low and high oscillation frequencies. These results for the subcooling temperature thresholds for low and high frequencies with a hemi-ellipsoidal steam jet are then compared with the results for spherical and cylindrical jets and with the experimental data in an interval of mass fluxes ranging from 0 to 180 kg/m2s. In addition, a sensitivity analysis is performed to know the dependence of the low and high frequency liquid temperature thresholds on the vent diameter and the polytropic coefficient. The third part of the paper is devoted to the study of the instabilities produced in the stable condensation (SC) and the interfacial condensation oscillations (IOC) regions of the map. First Hong et al. model (2012) is extended to include the entrainment in the liquid dominated region (LDR), obtaining new expressions for the oscillations frequency that depend on the entrainment coefficient and the expansion of the jet in the liquid dominated region. Finally, the mechanical energy balance is extended to include the momentum transferred to the jet by the condensate steam, obtaining a new equation for the frequency that is compared with Hong et al.’s data for a set of pool temperatures ranging from 35 °C to 90 °C and discharge mass steam fluxes ranging from 200 to 900 kg/m2s. 

Review of instabilities produced by direct contact condensation of steam injected in water pools and tanks

/pdf/development-of-an-excel-rocket-simulator-for-application-in-6b8dz06mh7.pdf

Development of an Excel® Rocket Simulator for Application in Middle School, High-School, and University STEM Education

We study the thermodynamics of the water rocket in the thrust phase, taking into account the expansion of the air with water vapor, vapor condensation and the energy taken from the environment. We set up a simple experimental device with a stationary bottle and verified that the gas expansion in the bottle is well approximated by a polytropic process $PV^\beta$= constant, where the parameter $\beta$ depends on the initial conditions. We find an analytical expression for $\beta $ that only depends on the thermodynamic initial conditions and is in good agreement with the experimental results.

Air expansion in the water rocket

We show a parallelism between the expansion and compression of the atmosphere in the secondary cycle of a tropical cyclone with the fast expansion and compression of wet air in a bottle. We present a simple model in order to understand how the system (cyclone) draws energy from the air humidity. In particular we suggest that the upward (downward) expansion (compression) of the warm (cold) moist (dry) air follows a polytropic process, $PV^\beta$= constant. We show both experimentally and analytically that $\beta$ depends on the initial vapor pressure in the air. We propose that the adiabatic stages in the Carnot-cycle model for the tropical cyclone be replaced by two polytropic stages. These polytropic processes can explain how the wind wins energy and how the rain and the dry bands are produced inside the storm.

Alejandro Romanelli

Papers

Air expansion in the water rocket

Polytropic process and tropical Cyclones