Gravitational power plant

[igor53]

Gravitational power plant


     Gravitational power plant (GRAPP) is the power plant of enclosed type that converts the gravitational field energy to electricity and heat. It consists of the lifting duct 1, the upper compartment 2 with compressor 5 and heat exchangers 4 the lateral side of which is covered by the thin layer of capillary structure 3, the falling duct 6 and lower compartment 7 with hydro turbine 8. The working liquid lifts from lower compartment to upper compartment through the lifting duct with the help of forces of capillary suction that are created by capillary structure. When the liquid penetrates into the capillaries on the lateral side of the heat exchangers, it evaporates by the heat that enters into the liquid from the heat exchanger side. The vapor comes out the capillaries, it is compressed by the compressor and enters into the heat exchangers. Since the vapor is saturated, the temperature of saturation rises during the compression and begins to be more than temperature of liquid within capillaries. Therefore the temperature difference between the vapor within heat exchangers and liquid within capillaries at the external sides appears: the vapor condenses and emanates the heat that comes through the metal sides of heat exchangers and evaporates the new portions of liquid from capillaries. The condensate falls within duct 6 with the absorption of the gravitational field energy and gives the energy to hydro turbine with electro generator out. The part of produced electricity energizes the compressor and other part comes to a load.

     It is known that the phase transition heat drops with the increasing pressure, therefore many people could think that the condensing vapor will evolve the heat less than we are need to evaporate the same quality of liquid. The real situation will be absolute contrary. On compressing the vapor grows so hot, that its temperature becomes higher than saturation temperature and vapor is already superheated. The total sum of condensation and overheating will be more than evaporation since the compressor operates as a heater which enters an additional energy into the vapor and compensates the heat leakages from the upper compartment to atmosphere. Consequently, we shall have a problem how to remove the excesses of heat. In order to solve the problem we shall need to direct a part of the vapor at special steam condensers and to convert the vapor into the liquid with the help of air cooling.

     The GRAPP operates partially as the natural processes: water lifts under influence of capillary forces within an arboreal trunk to leaf and evaporates, the vapor lifts to upper strata of atmosphere and condenses owing to negative temperatures. The condensate falls in form of raindrops, then it penetrates into soil and roots and lifts again within arboreal trunk. But, there are differences from the nature and open constructions. The processes of evaporation and condensation that take place in the nature are separated in space and occur in diverse points with diverse temperatures. Existence of temperature difference in the nature results the absence of necessary of compressor. On the other hand, processes of evaporation and condensation in constructions of enclosed type take place in the same point practically and are separated within space only with thin wall of heat exchangers. As a result, such constructions need the compressor that will create the necessary temperature difference.

     We have found that the only acceptable today for GRAPP working substance is a liquid metal and the best characteristics show the metals of alkaline group and eutectics. Such circumstance is the consequence of the fact that optimal temperature difference between condensing vapor and evaporating liquid is relative small (as a rule, less than one grad), therefore we need to use a substance with high coefficient of heat transfer at evaporation and condensation in order to achieve the great heat flows through the wall of heat exchangers and great flows of the working substance. Only liquid metals satisfy the condition. The using of water results the decreasing productivity several times less in comparison with liquid metal and such GRAPP becomes to be uncompetitive one. The using of ammonia decreases productivity still more. The mercury could be a good working substance, but mercury vapor is very toxic one and shows a very high corrosion activity at temperature of saturation (the mercury dissolves many constructional metals at such temperatures). Finally, we have chosen an eutectic Na+K with temperature of melting -11 grad and temperature of evaporation 784 grad Celsius.

     As regards Freon, this liquid shows the characteristic that is very good for the using in GRAPP: the low heat of evaporation. The lower heat of evaporation the more flow of liquid at the same temperature difference and the more power and productivity of GRAPP. Unfortunately, Freon shows two serious shortcomings that put obstacles in the way of the using at GRAPP. First, Freon has low thermal conductivity in comparison with metal. This shortcoming plays no important role for process of evaporation from capillaries, as the high thermal conductivity of metal compensates the low thermal conductivity of liquid. But, this disadvantage is the key factor for process of condensation. The condensate covers the surface of heat transfer as thin layer and reduces the common thermal flow thousands times compared with liquid metal owing to low thermal conductivity. In order to overcome this shortcoming, it is necessary to organize the trickling condensation instead of layer one: the condensate comes together at individual points on the surface of heat transfer and retains the surface to be free for contact with liquid. For the goal, we need to cover the surface of heat transfer with the very thin layer of a substance which will repel the Freon. But, such substances do not exist still.

     Second, the Freons that exist today have a low temperature of evaporation, the temperature that is less than maximal temperature of the hot summer days. For such temperatures, the removal of heat from the upper compartment to atmosphere becomes to be impossible in summer. Therefore we need to have a new form of Freon that would show the temperature of evaporation at level 60-70 grad Celsius. Theoretically the principles how to create such Freon are known. Practice shows that the increase of molecular mass of Freon shifts the temperature of evaporation to higher values.  Simultaneously the densities of liquid and vapor increase too. The increasing density of liquid results the increasing power of GRAPP at the same height of lifting and falling ducts due to the increasing hydrostatic head. On the other hand, the increasing density of vapor results the decreasing consumption of energy in process of compression (on compressing the consumption of energy is in inverse proportion to the vapor density at the same mass flow).  But, such Freon does not exist too.

     The capillary structure at lateral side of heat exchangers has two layers: internal layer with large-sized pores and external very thin layer with fine-sized pores. Such structure resolves a contradiction between two trends. On the one hand, in order to achieve the maximal productivity of GRAPP and minimal cost of produced electricity it is necessary to elevate the working liquid as high as possible. We could satisfy the condition using the capillaries with fine-sized pores. On the other hand, the decreasing pores lead to the increasing hydraulic resistance and, as a result, to the decreasing flow of working liquid. If we use the two-layer structure, the hydraulic resistance is no high as the working liquid flows within layer with large-sized pores. Its subsequent motion transverse to external layer with fine-sized pores does not lead to significant increase of common hydraulic resistance as the thickness of the layer is very small, less as one millimeter.  But, significant curvature of meniscus of liquid within fine pores creates the high capillary forces.

     My calculations show that the optimal height of heat exchangers is in interval 10-15 meters, the performance coefficient is about 52%, the heights of lifting and falling ducts are 500-600 meters and power of GRAPP is 600-1000 megawatt. When we converse the produced in upper compartment heat to electricity by eventual turbo-engine method, the performance coefficient rises to 68-70% with the corresponding increase of electric power. It was found that the temperature difference between condensed vapor and evaporated liquid shows the optimal value too: 0.42 grad. For such temperature difference, we achieve the maximal electric power with other equal conditions. Increasing the temperature difference over the optimal value, we obtain the decrease of common productivity, as the major part of generated electricity goes to compressor and transforms itself to heat finally.

     It should be noted the fact, that the term ,,performance coefficient" which is typical one for thermal power engineering loses its meaning for GRAPP. Regarding thermal power plants, this term shows the relationship between useful electric energy that goes to consumer and common thermal energy which is generated in process of combustion of fuel. The last value depends on mass and quality of fuel only and any technical improvement of power plant cannot change it. On the other hand, a technical improvement of GRAPP changes both common power of hydro turbine and electric power that goes to consumer. As a consequence, the term ,,performance coefficient" does not reflect the technical perfection of process regards to GRAPP already. Theoretically, we could have even such situation when the decrease of performance coefficient is more commercially profitable trend (such situation takes place when a technical improvement leads to significant increase of hydro turbine power).

     The cross dimensions of the lifting and falling ducts show optimal values too: about 1.5 meters in diameter. The decrease of diameter less than the optimal value leads to the significant increase of hydraulic resistance and, as a consequence, the decrease of the working liquid flow and productivity. The increasing diameter over the optimal level results such situation when the hydraulic resistance of ducts becomes to be very less than hydraulic resistance of capillary structure and does not have an influence on common hydraulic resistance already. But, total mass of working liquid and financial expenditures for its clearing rises.

     Concerning the capital expenditures for building of GRAPP, they are 1.5-2 times less compared to thermal power plant with the same productivity usually. But, operational costs are dozens times less since the GRAPP does not expend a fuel. And environmental pollution is negligible one due to the absence of any wastes: green-house gases, carbon and nitrogen dioxide, radionuclides and other.

     The skeptic could assert that the function of GRAPP is impossible due to so-called rule of zero-energy. The rule was be proved by German physics and mathematics Carl Gauss in the middle of 19th century. Here is its formulation: in moving by closed contour in potential field the common work equals zero. The gravitational field is a particular case of potential field and therefore this rule is valid for gravitational field too. But, Gauss had not noticed an additional force that appears in case of gravitational field and changes the final result cardinally: buoyant force of Arhimed. In order to solve the problem of extraction of energy from gravitational field we need to analyze the integral A = ∫(FP + FA)dx, rather than integral A = ∫FP dx (here FP and FA are forces of gravitation and buoyant), and integral is circular, i.e. we have to take the integral around closed contour. As an integral of sum is the sum of integrals, we could rewrite the last equation as A = ∫FP dx + ∫FA dx. The first term equals to zero after Gauss. The second term could be rewrite as sum of half-circular integrals: one integral is extended along up-going half of contour and other integral is extended along down-going half of contour A = ∫F1A dx + ∫F2A dx. When Arhimed's forces at up-going half of contour F1A and at down-going half of contour F2A equal one to other, integrals of these forces will be equal one to other in absolute value too but have difference signs (such situation occurs as the force F1A and differential dx at up-going half of contour have the same direction, but force F2A and differential dx at down-going half of contour have opposite direction). Therefore the total sum of such integrals equals to zero. On other hand, when Arhimed's forces have different values, the sum of integrals will be non-zero already. How could we make the Arhimed's forces to be different? Very simple, with the help of exchange of aggregate stage of the working substance: the substance has to be as a liquid at one half of contour and as a vapor at other part of contour. The present project of GRAPP satisfies this condition: the working substance moves as vapor at some part of the lifting duct (after evaporation from capillaries and before condensation within heat exchangers), but it moves as a liquid at whole height of the falling duct.


Resume.

     We propose a new source of energy for future generations: gravitational field. Energy could be extracted from gravitational field with the help of so-called Gravitational Power Plant (or GRAPP). The principle of the GRAPP function is following: 1) working liquid moves upwards within lifting duct under influence of capillary forces; 2) it evaporates by heat that enters in capillaries; 3) vapor goes from capillaries and is compressed by compressors; 4) this compressed vapor flows about other side of capillary structure and condenses with liberation of heat that evaporates new portions of the working liquid; 5) the condensate falls down and absorbs the energy from gravitational field, then it revolves hydro-turbine and gives the energy to hydro-turbine back.

[igor53]

Unfortunatelly, I cannot make scheme.