December 2005 / L. MichaudAGU NG23A-0090 Unrestrained Expansion1 Unrestrained Expansion a Source of Entropy by Louis M. Michaud Vortex Engine

December 2005 / L. MichaudAGU NG23A-0090 Unrestrained Expansion2 Earth Overall Entropy Budget Balancing the earth’s entropy budget requires that entropy be produced internally within the earth system. Entropy produced: 892 mW K -1 m -2 –Absorbtion in Upper atmosphere: 255 mW K -1 m -2 –Absorbtion at Surface: 580 mW K -1 m -2 –Atmospheric Convection: 77 mW K -1 m -2 Entropy received: 41 mW K -1 m -2 Entropy given up: 933 mW K -1 m -2

December 2005 / L. MichaudAGU NG23A-0090 Unrestrained Expansion3 Fig. 1

December 2005 / L. MichaudAGU NG23A-0090 Unrestrained Expansion4 Entropy budget of the Atmosphere Entropy production when solar radiation is absorbed by the upper atmosphere or by the earth’s surface results from thermal unequilibrium. Entropy production is immediate and occurs when the radiation is absorbed. – Fig 1 Entropy production when heat is transported upward by convection in the atmospheres results from mechanical unequilibrium. Entropy production is delayed and occurs when the heat is transported upward. - Fig. 2 Entropy production during upward heat transported could be avoided if the heat were transported by a Carnot engine. Dissipating the energy produced by the Carnot engine would restore entropy production. – Fig 3

December 2005 / L. MichaudAGU NG23A-0090 Unrestrained Expansion5 Fig. 2

December 2005 / L. MichaudAGU NG23A-0090 Unrestrained Expansion6 Fig. 3

December 2005 / L. MichaudAGU NG23A-0090 Unrestrained Expansion7 Gravity Power Cycle The differential pressure across the turbine results from the difference in density between the warmed rising air and the cooled descending air. – Fig. 4 Very high vertical conduits are required to achieve significant efficiency. There must be a turbine or expander to capture the work. - without the expander the work reverts to heat. The gravity cycle is equivalent to the ideal gas turbine power cycle. There is no entropy production in an ideal gas- turbine cycle. The efficiency of the gravity cycle is the same as that of a Carnot engine with the same average effective hot and cold source temperatures.

December 2005 / L. MichaudAGU NG23A-0090 Unrestrained Expansion8 Fig. 4

December 2005 / L. MichaudAGU NG23A-0090 Unrestrained Expansion9 Entropy Production In ideal cycles entropy production is eliminated by: 1.Keeping temperature differences small to eliminate thermal unequilibrium 2.Keeping velocites low to eliminate friction losses 3.Eliminating mixing by postulating that the water does not separate from the air 4.Restraining the expansion in an expander - either a turbine or piston expander Entropy production during upward heat convection can be due to: 1.Temperature differences (thermal unequilibrium) 2.Friction (mechanical unequilibrium) 3.Mixing of fluid of different temperature or composition (non-mechanical unequilibrium) 4.Unrestrained expansion. (mechanical unequilibrium)

December 2005 / L. MichaudAGU NG23A-0090 Unrestrained Expansion10 Unrestrained Expansion Van Ness Expander The Automat of the Van Ness expander illustrates the fact the work reverts to heat unless there is a force to restrain the expansion. – Fig. 5 Releasing the latch only produces useful work when the Automat restrains the piston. Unrestrained expansion in an ascending air parcel reduces net work to zero while producing the 77 mW K -1 m -2 of entropy necessary to balance the atmospheric entropy budget. Unrestrained expansion, which is usually ignored, is responsible for the largest part of the entropy produced during atmospheric upward heat convection.

December 2005 / L. MichaudAGU NG23A-0090 Unrestrained Expansion11 Fig. 5

December 2005 / L. MichaudAGU NG23A-0090 Unrestrained Expansion12 Atmospheric Engine Since atmospheric entropy production is mainly the result of unrestrained expansion, it might be possible to capture the work that would be produced if the heat were transported with a Carnot engine by simply providing an expander. There have been two proposals for capturing the energy produced during atmospheric upward heat convection: 1. The Solar Chimney – Fig. 6 2.The Atmospheric Vortex Engine – Fig. 7 - where the physical tube is replaced by centripetal force See web site: for additional information including text of the AGU presentation.

December 2005 / L. MichaudAGU NG23A-0090 Unrestrained Expansion13 Fig. 6 Manzanares solar chimney 200 m high, 10 m diameter, 50 kW

December 2005 / L. MichaudAGU NG23A-0090 Unrestrained Expansion14 Fig. 7 Vortex Solar chimney 100 m high, 200 m diameter, 200 MW

December 2005 / L. MichaudAGU NG23A-0090 Unrestrained Expansion15 Unrestrained Expansion – A Source of Entropy Louis Michaud, Vortex Engine AGU Poster Session paper: NG23A-0090 Paper sponsored and posted by: Dr. Ralph Lorenz Author Louis Michaud is unable to attend the AGU Fall 2005 Meeting. He can be reached by at: or by phone at: (519) Additional information including the text of this presentation is available at website: Summar y