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**THE SIMPLEST EXPLANATION CAME FIRST**

In 1824, Sadi Carnot wrote: to the flow of heat is due all movement including wind and precipitation. He simply considered how much mechanical energy can be produced when the heat is carried upward with Carnot engines. There is a potential for producing mechanical energy whenever heat flows from a hot source to a cold sink. The heat carried upward by convection in the atmosphere averages 102 W/m2 of which 24 W/m2 is sensible heat and 78 W/m2 is latent heat. Ideal conversion efficiency averages 12% because the heat is received and given up at average temperatures of 290 K and 255 K. There is a potential of converting approximately 12% of the heat carried upward by convection to mechanical energy. 12% is an average efficiency. For heat carried up to the upper troposphere where the temperature is 200 K, the conversion efficiency can be 30%. The heating of the atmosphere from the bottom by solar radiation and the cooling of the upper troposphere by infrared radiation to space require upward heat convection. Producing mechanical energy requires a mechanism for capturing the work; there must an expander with a shaft to take the work out of the system. Without a capture mechanism, conservation of energy requires the production of heat instead of mechanical energy. In the atmosphere there is no mechanism for capturing the work and therefore most of the work production potential is not realized. Upward convection is occurring naturally; capturing work requires the invention of a mechanism for doing so.

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DO THE MATH The figure shows the energy production potential of the Atmospheric Vortex Engine. The yellow arrow on the left shows that the total solar energy received by the Earth is 174,000 TW, The panel on the right shows that global total energy production and electrical energy production are 15 TW and 2 TW respectively, The heat carried upward by convection in the atmosphere is 52,000 TW (102 W/m2 times the earth surface of 510 x 1012 m2). Converting 12% of the heat carried upward by convection to mechanical would produce 6,000 TW. The mechanical energy production potential of atmospheric convection is 400 the world total thermal energy production of 15 TW(t). The mechanical energy production potential of atmospheric convection is 3000 the world total electrical energy production of 2 TW(e) . 7 of the 15 TW of primary thermal energy are used produce electricity. The remaining 8 TW are used for transportation and for industrial and residential heating. Electricity production primary energy source are 40% coal, 25% natural gas, 20% nuclear, 10% hydraulic, 1% wind and 0.01% solar. One large (1000 MW) AVE can produce TW of power continuously. One large wind turbine (3 MW) can produce TW of peak power very intermitently. A single large hurricane can produce 300 TW for a week. A single large hurricane can produce as much power as the electrical energy produced in the whole world in a year. A large tornado can produce more power than is produced by large thermal power station. Wind energy is currently responsible for approximately 1% (0.02 TW) of the world total electrical energy of 2 TW. The maximum wind energy that could possibly be captured is approximately 1 TW. The total wind energy actually produced in the atmosphere is estimated to be approximately 10 TW which is only 0.2% of the 6000 TW that could be produced in an ideal convection process. The wind energy actually produced is far less than could be produced when the heat were carried upward reversibly. MW peak capacity wind farms can produce an average of 10 GW, a mere 0.01 TW. World electricity need of 2 TW could be meet by: MW AVE’s 2000 – 1000 MW fossil fuel thermal power plants MW nuclear power plants 2,000,000 – 3 MW wind turbines (provided energy storage is available) USA energy consumption is approximately 20% of world energy production. Canadian energy production is approximately 2% of world energy production. World nuclear electricity production: 0.1 TW. Canadian nuclear electricity is 0.02 TW(e). Canadian oil sand is 0.05 TW(t).

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**THE SIMPLEST EXPLANTION ALWAYS COMES LAST**

In 1905 Austrian thermodynamist Max Margules used a piston covered closed insulated thermodynamic system to investigate how wind energy is produced. Margules used air masses of uniform potential temperature because rearranging the air masses isentropically does not change their potential temperature. Potential temperature (theta) is defined as the temperature that an air mass would reach if brought isentropically to a pressure of 100 kPa. The figure shows that work of 3703 J/kg shown on the right can be calculated in four ways all giving the same result: From the difference between the heat received and the heat given up. From the heat received multiplied by the Carnot efficiency. From the total energy equation commonly used by engineers to calculate the maximum work that can be produced when a fluid flows in a tube. .From the upward acceleration of the buoyant air mass (CAPE). The agreement between work calculated from net heat and work calculated from Carnot efficiency provides unquestionable verification of the validity of Margules’results. Work production depends on thermodymamics and is independent of fluid dynamics. The three states batch process shows that the mechanical energy is produced during lifting process 2-3. The work is not produced during heating process 1-2 or cooling process 3-1. The re-arrangement process can occur well after the heating process therefore mechanical energy production can occur some time after the heat is received. Margules used large air masses (as shown in the next slide ) which made it difficult to see the relationship better work production and temperatures. With a bottom layer of unit mass, it is easy to see that the work is equal to the heat required to re-establish the initial condition multiplied by the Carnot efficiency. One dimensional models are simple, in order to understand how energy is produce in the atmosphere it is necessary to simplify the model further by: Using air masses of uniform entropy, and by using a bottom layer consisting of a unit mass of air. Margules did not explain how the isentropic process could be carried out, he did not provide a mechanism for capturing the work. The air column can be considered to have a unit area of 1 m2, but work per unit mass is independent of column area The above calculations are based on a column of dry air with uniform entropy. It will be shown that the main results are valid for: Air columns that do not have uniform entropy. Moist air containing water in any phase. The closed system consisting of a piston covered column can fully explain atmospheric energy production. The essential points of this presentation have now been covered.

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**USING AIR MASSES OF REALISTIC SIZE MAKES THE ENERGY CONVERSION PROCESS MORE DIFFICULT TO UNDERSTAND**

In 1905, Max Margules used a piston covered closed system consisting of two large air masses of unit area (1 m2) and of uniform potential temperature. He showed that the total energy of the system is equal to the total enthalpy (H) of the system and developed equations for the total enthalpy of large air masses by integrating the equation for unit air masses. He calculated the mechanical energy produced when the air masses exchange position by dividing the reduction in total enthalpy by the total mass of air in the system. Margules used large air masses to be realistic since atmospheric air masses are large. The above work of 872 J/kg is approximately one quarter of the work produced in the unit air mass system (3703 J/kg) of slide 3 because the lower air mass is raised half as high and because the work is shared between the two air masses, which have twice as much mass as the raised air mass. Using large air masses hides the relationship between heat and work. Work production is equal to the heat required to restore the initial condition multiplied by the Carnot efficiency based on the average temperature at which the heat must be received and given up to restore the initial condition in both the previous unit air mass system and in the above large air mass system. Margules wrote: A researcher with persistence and imagination will eventually come to a full understanding of the process; the simplest answer always comes last. The energy conversion process can be understood by simply going back to the unit mass system which Margules started with. Margules also showed that work can be produced by rearranging air masses of uniform potential temperature initially side by side so that in the final condition the higher potential temperature air mass is on top of the lower potential temperature air mass. The work per unit mass (436 J/kg) is half as much as in the air mass initially on top of one another (872 J/kg) because only one quarter of the air in the system is raised.

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**THE ENGINEERING APPROACH**

Atmospheric work production process Energy conservation in an open system THE ENGINEERING APPROACH Ideal work production calculations can be based on either closed or open thermodynamic system. Open thermodynamics system such as the one shown here are used by engineers to calculate the minimum work required or the maximum work that can be produced when a fluid is moved form one place to another. Maximum work can be calculated by imagining that the flow takes place in an ideal tube. In the ideal system there are: no heat transfer, no friction loss, and exit velocity is negligible. When there is no change in elevation like in a gas turbine the work is the reduction in enthalpy; When there is change in elevation and no change in enthalpy, like in a hydraulic turbine, the work is the reduction in potential energy. In the AVE both terms are I important; ideal work is the decrease in the enthalpy of the fluid minus the increase in its potential energy. Actual work is ideal work times expander efficiency. When expander efficiency is less than 100%, conservation of energy requires that there be in increase in the enthalpy of the air leaving the expander corresponding to the difference between ideal work and the actual work. No work is produced if the expander is replaced by a restriction which corresponds to an expander efficiency of 0%. Reducing expander efficiency from 100% to 0% changes the expander process from a constant entropy process to a constant enthalpy process..

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**MECHANICAL ENERGY REVERTS TO HEAT UNLESS CAPTURED**

The piston covered column system can be reversible or irreversible. In the previous reversible process: the total energy of the system in state 3 was less than the total energy of the system in state 2 by the work produced of 3703 J/kg. In the irreversible process: No energy leaves the system during process 2-3, conservation of energy requires that the total energy of the system in state 3 be the same as in state 2. Conservation of energy requires that there be an increase potential temperature. Dissipating the work in the unit mass of air would increase its potential temperature from 300 K to 306 K corresponding the an increased in the temperature of the raised air from K to K, the temperature increase that would be produced by dissipating 3703 J of work. Alternatively dissipating the work could increase the average potential temperature of the whole column from 290 K to approximately K.

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**HURRICANE EFFICIENCY – CARNOT AGAIN**

A hurricane viewed as a Carnot cycle HURRICANE EFFICIENCY – CARNOT AGAIN Kerry Emanuel (2005) of MIT estimated hurricane efficiency at 33% by comparing a hurricane to a Carnot Engine receiving heat from the surface at a temperature of 300 K and giving up heat in the upper troposphere at a temperature of of 200 K. The air is heated by the sea surface at a temperature of 300 K and cooled at high elevation at lower temperatures. . Emanuel was named one of the most influential scientist of 2005 by Times magazine. He had predicted increased hurricane intensity as a result of global warming before hurricane Katrina. Nilton Renno (2008) of the University of Michigan estimated the average efficiency of convective vortices at 20% based on Carnot efficiency and average cold source temperature of 255 K. James Price 1981, upwelling of cold water from below is the primary mechanism that lowers sea surface temperature beneath a hurricane. Michaud 2012, Hurricane sea cooling is almost entirely due to heat removal from above and not to cold water from below. A large hurricane can produce more energy than all the energy produced by humans in a year. A medium size tornado can produce as much energy as a large thermal power plant. Efficiency n = 1 – Tc / Th = 1 – 200/300 = 33% Source Divine Wind by Kerry Emanuel

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**MECHANISM FOR CAPTURING MECHANICAL ENERGY**

Realizing the energy production potential requires that the rearrangement process be carried out reversibly. Early thermodynamists imagined that the work was captured by an automat. An automat is a device full of mechanism capable of capturing and giving back mechanical energy reversibly. The automat captures the work produces during process ‘ab’ when the air is pushed in the cylinder at constant pressure P1 and the work produced in process ‘bc” when the air in the cylinder expands from pressure P1 to P2. The automat uses some of the work of expansion to lift the cylinder from level 1 to level 2, some of the work to push the raised air back in the column at level 2, and is left with the net work (3703 J/kg in slide 1). Reversible process analysis calls for unrealistic assumptions; all that matter is what happens to the working fluid. The column is insulated. The cylinder is weightless and insulated. The automat is weightless. The raised layer is very thin. The automat could capture just enough energy to raise the cylinder and push the air back in the column by only restraining part of the expansion. The process would become fully irreversible and there would be no net work.

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**To the flow of heat is due all movement including wind and precipitation – Sadi Carnot 1824**

Carnot did not calculate the movement resulting heating; he simply looked at how much mechanical energy would be produced If the heat were transported reversibly with his imaginary Carnot engine.

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**SYSTEM FOR CONTINUOUS CAPTURE OF ALL, PART OR NONE OF THE IDEAL WORK**

Reversible and Irreversible Expansion SYSTEM FOR CONTINUOUS CAPTURE OF ALL, PART OR NONE OF THE IDEAL WORK The pressure at the base of a column of warm air is less than the surrounding pressure. This difference in pressure can be used to drive a continuous upward flow process. This slide shows that the continuous process can be reversible or irreversible. The net work is captured when the automat restrains the piston and otherwise lost. The net work is lost if there is no means of capturing the work. Capturing the work produced when a gas expands requires a means for doing so, usually a shaft thus shaft horsepower. Whether the work is captured or dissipated is dependent on whether the expansion is restrained or not. Work dissipation can be studied by examining the cylinder piston system only; the two air columns are irrelevant. Ideal cylinder and piston system and turbines are both constant entropy expanders. Process simulators permit adjusting expander efficiency from 100 (fully reversible constant entropy process) to 0% (fully irreversible constant enthalpy process). A turbine is essentially a nozzle where kinetic energy is produced followed by a blade where this kinetic energy is captured. A nozzle without a blade is a fully irreversible process. The work is dissipated whenever the gas flows through the nozzle or restriction not followed by a turbine blade. Work is dissipated when gas flows through a restriction such as valve #2. Unrestrained expansion in a cylinder and dissipation in a restriction are both constant enthalpy process but the two dissipation process are different and should be treated differently. Dissipation in a restriction involves velocity and viscosity; in unrestrained expansion work is dissipated irrespective of viscosity. In unrestrained expansion there is no way for the work to leave the system therefore it remains in the system as heat. In a way work lost in unrestrained expansion is never produced and does not have to dissipated through viscosity. The work of expansion can be reduced by only capturing part of the work of expansion; in process simulators this is done by simply reducing the expander efficiency. As shown in slide 2 there is a potential for producing 6000 TW of mechanical energy during upward heat convection. It is estimated that the wind energy actually produced is less than 10 TW. The wind energy actually produced is approximately 0.2% of the work production potential. Therefore loss work potential due to unrestrained expansion is 5990 TW. Atmospheric models have to use turbulent viscosity 105 times actual air viscosity to prevent getting unreasonably high wind velocity (Lorenz). Atmospheric models based on reversible expansion can have energy deficits of 20 W/m2. (Fiedler)

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NO RESTRAINT / NO WORK This figure shows that expansion must be constrained to realize the work production potential. If the piston is restrained the work is the isentropic expansion work. If the latch is let go without restraining the piston, the maximum work that can be produced is the work required to push the 95 kPa surrounding air out of the way. Any additional potential for doing work remains in the cylinder air in the form of heat. The work lost as a result of unrestrained expansion is approximately 22% of the isentropic expansion work. 22% of the work is lost irrespective of how small the pressure difference. Since the net cycle work is typically less that 22% of the total expansion work, loss work as a result of unconstrained expansion can easily consume all the net cycle work. Consider a rising bag loosely filled with buoyant air. As the bag rises the surrounding pressure decreases, the pressure inside the bag becomes higher the pressure outside the bag; the pressure are not balanced. There is insufficient resistance for the air inside the bag to push against therefore part of the work (about 22%) of expansion work is lost. It is difficult to achieve the ideal work production potential unless the expansion is constrained to take place in one direction. These ideal processes of slides 8, 9 and 10 all use different processes for capturing the work potential but they all use cylinder and piston system to constrain the expansion to take place in a single direction.

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**SENSIBLE AND LATENT HEAT ADDITION CAN BOTH INCREASE WORK PRODUCTION**

This slide shows that the total energy equation is valid for moist as well as for dry air. The work is 2240 J/kg In base Case 1. In Case 2 increasing the temperature of the bottom kilogram by 2°C with 2080 J of sensible heat increases work by 3140 J/kg. The work increase of 701 J/kg is equal to 33.7% of the heat addition of 2080 J/kg. The work increase is equal to the heat addition multiplied by the Carnot efficiency. In Case 3 increasing the mixing ration of the bottom kilogram by 1 g-water /kg-air with 2450 J of latent sensible heat increases work by 3230 J/kg. The work increase of 791 J/kg is equal to 33.1% of the heat addition of 2450 J/kg. The work increase is almost equal to the heat addition multiplied by the Carnot efficiency 32.2%. In Cases 2 and 3, the work calculated from the total energy equation is again equal to the work calculated from heat received multiplied by Carnot efficiency.

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**WORK PRODUCTION DEPENDS ON THE DEGREE OF RESTRAINT**

This slide shows capturing 1% of the ideal work is sufficient to produce a specific work of 24 J/kg which corresponds to a velocity of 7 m/s which is close to the average wind velocity in the atmosphere. Making the process irreversible increases the temperature (T4) of the raised air from °C tp °C.

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**REVERSIBLE CLOSED ATMOSPHERIC CYCLE**

Gravity Power Cycle REVERSIBLE CLOSED ATMOSPHERIC CYCLE Here is the ideal cycle for the AVE. The cycle is the same as the gas-turbine ideal cycle shown in the next slide except that the expansion takes place in stationary tall conduits instead of in mechanical turbines and compressor. The operating conditions are the same in the two cases. In both ideal cycles, the air is heated from 290 K to 300 K at a pressure of 100 kPa and cooled from 189.4 K to 183.1 K at the 20 kPa level. The gas is heated a constant pressure, expanded in the turbine, cooled at constant pressure, and compressed back to its original pressure. The work produced by the expansion of the warm gas is more than required to compress the cooled gas and the excess is available to drive a load. Once an ideal cycle is understood it is easy analyze irreversible cycles by taking into account the effect of turbine efficiency, friction losses, and kinetic energy.

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**REVERSIBLE CLOSED GAS TURBINE CYCLE**

Brayton gas-turbine power cycle REVERSIBLE CLOSED GAS TURBINE CYCLE Here is the standard Brayton gas-turbine ideal cycle. The work of compression appears explicitly in the gas-turbine case but is not as evident in the gravity cycle. In the gravity cycle the gas expands as it rise and is compressed as it descends. The efficiency of an ideal Brayton cycle is strictly a function of its pressure ratio. The ideal cycle efficiency for a compression ratio of 5:1 is 36.9%. The key to understanding thermodynamics is simplification. Ideal cycles are reversible; there is no entropy production in the ideal bas-turbine power cycle. Engineers use ideal processes: with no friction loss, negligible velocity, and without temperature difference during the heat transfer. Real processes are difficult to analyze, but it is usually possible to conceive of ideal process that can be analyzed. In reversible cycle analysis the size of the conduits and the fluid velocity is of no importance; the downflow conduit can be much larger in cross sectional area than the upflow conduit.

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**IRREVERSIBLE CLOSED GAS TURBINE**

Effect of losses on gas turbine power cycle efficiency. Ideal cycle efficiency based on average temperature at which heat is received and given up is 37%. Efficiency based on highest temperature at which heat is received and the lowest temperature at which heat is given up would be 70%. Actual overall cycle efficiency when the efficiency of the turbines and compressor are 85% is 25%.

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**IRREVERSIBLE CLOSE ATMOSPHERIC CYCLE**

Irreversible Gravity Cycle IRREVERSIBLE CLOSE ATMOSPHERIC CYCLE The efficiency of the AVE cycle can be reduce to zero by simply replacing the turbine with a restriction. There cannot be any work produced unless there is a shaft to take the work out of the system. In an irreversible cycle entropy, also called: “Internally Generated Entropy”, is produced. Note the increase in entropy.

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**ATMOSPHERIC VORTEX ENGINE (AVE)**

The lower half of the drawing shows a side view of an AVE. The upper half of the drawing shows a plan view of an AVE. The vortex is formed by admitting warm air in a circular arena via tangential entry ducts thereby causing the air to spin about the vertical axis and a vortex to form over the center of the arena. A roof with a circular opening at its center causes a vortex to form. The air is heated or humidified in heat exchangers located upstream of the tangential entries. The mechanical energy is produced in peripheral turbines. The reduced pressure at the base of the vortex is the driving force for the flow. The vortex would look like a small tornado at the centre of a large arena. There is no equipment near the vortex base because anything near the vortex could interfere with vortex formation.

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**SOLAR CHIMNEY VERSUS VORTEX ENGINE**

The AVE replaces the physical chimney with centrifugal force in a vortex. The AVE eliminates the solar collector by using waste heat or natural low temperature heat sources. SOLAR CHIMNEY VERSUS VORTEX ENGINE The Manzanares solar chimney at the upper left built in Spain with support from the German government had a 200 m high chimney and a peak power output of 50 kW. It demonstrated that upward heat convection can produce work and that the work can be transported to the base of the chimney and harnessed. The air was warmed up by 20 °C in a circular green house; the turbine and generator were located at the bottom of the chimney. The power production increases exponentially with size. The proposed EnviroMission solar chimney at the lower left would have had a peak output of 200 MW. times more than the Manzanares one. Efficiency increases exponentially with height. The ideal efficiency of the Manzanares solar chimney where the vertical temperature difference was 2 K is 0.6% (2/300). The ideal efficiency of the EnviroMission chimney where the vertical temperature difference would be 10 K would be 3.3% (10/300). The ideal efficiency of the AVE where the vertical temperature difference could be 90 K would be 30% (90/300). Actual efficiencies are somewhat smaller because of exit and friction losses. The central panel illustrates the height difference. A vortex can extend much higher than a physical chimney. The AVE simply replaces the physical chimney with centrifugal force in a vortex. The AVE eliminates the need for the green house since the required initial air temperature decreases with chimney height. Low temperature heat source such as warm sea water of just warm humid air would be sufficient. Waste heat from power plants could be a free heat source. An AVE could extend to a height of 10 km. A 30 m diameter vortex could produce 200 MW. The economics of solar chimneys is marginal because of the huge cost of the collector and chimney and because of their low efficiency. The AVE eliminates the cost the collector and the chimney and the fuel and could could produce clean power for less than $0.03/kw-hr.

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**Work 41 kW Ideal Work 75 kW Exit vel. k.e. 22 kW Friction losses 4 kW**

Conditions: Collector Efficiency 31 % Turbine Efficiency 80 % Insolation 1000 W/m2 Dia. Chimney 10 m Dia. Collector 244 m Conditions: Pb 100 kPa Tb ambient 30 °C Tt ambient 28 °C Tb chimney 47 °C z m Velocity 8 m/s Flow 680 kg/s Resulting efficiency: Ideal % (Carnot) Actual % Overall % Ideal Work kW Exit vel. k.e kW Friction losses 4 kW Efficiency: Ideal efficiency is 0.64%. (0.64% of the heat absorbed by the air). Carnot efficiency is 0.64% (2/303). Actual efficiency is 0.34% because of: exit kinetic energy losses, friction losses, and turbine losses. Overall efficiency is 0.11% because of the low collector efficiency of 31%. Energy budget for actual operating conditions: Ideal work 75 kW Turbine work 41 kW Turbine losses 8 kW Exit kinetic energy losses 22 kW Friction losses 4 kW If the turbine were removed or flared the upward velocity in the chimney would go up from 8 to 13.7 m/s (assuming the same temperature difference of 17°C): The ideal work would go up from 75 to 128 KW because of the increased flow. The exit losses would go up from 22 to 110 kW because of the higher exit velocity. The friction losses would go up from 4 to 18 kW because of higher velocity. The turbine work and turbine losses would go down from 49 to 0 kW. If the physical chimney were replaced with a Vortex: The exit losses would decrease from 22 to 2 kW because a vortex diameter increases with height. Friction losses would decrease from 4 to 0.1 kW because the flow changes from turbulent to laminar. The turbine work increases from 41 to 60 kW because there are less exit and friction losses. The turbine losses reamains ar 20% of the turbine work and therefore increases from 8 to 12 kW. Total Insolation 37,700 kW Turbine Loses kW Work 41 kW Heat input 11,680 kW Manzanares Solar Chimney – Base Case - Energy budget (Based on actual operating conditions)

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**MANZANARES SOLAR CHIMNEY WORK CALCULATIONS**

Case 1 - Conditions when operating at maximum output of 41 kW. Case 2 – Conditions when operating at maximum velocity (turbine blades flared). Case 3 – Conditions when turbine efficiency is 0% or when turbine is replaced by a restriction. Case 4 – Conditions for vortex flow - low exit velocity as a result of increasing diameter and low friction loss as a result of laminar flow Without friction loss kinetic energy can persist a long time or distance. The velocity can be present in a horizontal tube several thousand kilometers long. The quantity of kinetic energy in the system is not a good indication of how much kinetic is produced because kinetic energy can dissipate in very short or very long periods.

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**PETROLIA PROTOTYPE VORTEX**

4 m prototype vortex PETROLIA PROTOTYPE VORTEX

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**EARTH’S STORED ENERGY RESOURCES – DO THE MATH AGAIN**

Comparison of the Earth’s stored energy resources. The latent heat content of the water vapor in the bottom kilometer of the atmosphere is twice the heat content of all the Earth’s petroleum reserves. The sensible heat available by cooling the top 100 m of tropical water by 3°C is 20 times as much as the heat content of the oil reserves. The heat released in an average hurricane is 5 x 1019 Joules/day. Enough to cool a strip of ocean 500 km long by 100 km wide and 100 m deep by 3°C. At the present consumption rate the remaining world’s oil reserve will be used up in approximately 30 years. The cooling effect of hurricanes on sea water and its replenishment time are clearly visible on infrared satellite photos.

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EGR 334 Thermodynamics Chapter 4: Section 4-5

EGR 334 Thermodynamics Chapter 4: Section 4-5

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