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Generation of Clean Energy, Desalination of Sea Water and Global Cooling of Atmospheric Air by

By Sshalva Tzivion

Summary of the Proposal
A clean and renewable energy source that substitutes oil burn and generates fresh water is of major importance to many global factors such as air pollution, economy and climate. A “Super Power Energy Tower” is a gigantic vertical tower at the top of which a large amount of water (that can be sea water) is poured as small drops. The evaporation of the falling drops produces a strong downward flow. At the bottom of the tower, the kinetic energy of the air can be converted to electrical power by the use of turbines. The results of a state-of-the-art numerical model demonstrate the potential and limitations of such a “Super Power Energy Tower”. Based on numerous numerical experiments optimal geometric, physical and atmospheric parameters for such a tower are obtained. The results show that a tower of 800 m height may produce up to 4500 MW of electricity. The out flowing air at the tower’s bottom is 12.5 °C colder than the environmental air and its relative humidity is near 97%. By extracting the small salty drops that remain in the air and by further cooling this air by about 5 °C, it is possible to obtain relatively cheap, essentially fresh water at a rate of 15m3/sec. Moreover, taking into account that the out-flowing air at the bottom of the tower is cold and produced at a rate of 1.2×107 m3/sec suggests that an extensive use of such towers may compensate for the global warming of the atmosphere, induced by greenhouse gases. However, it is important to notice that these results are not based on realistic conditions of an energy tower with turbines and environmental factors incorporated. The present proposal suggests expanding the work that was carried out by us until now in order to eliminate some of these deficiencies. For this purpose, it is proposed to develop a three-dimensional model of Energy Tower that incorporates influence of turbine and external environmental conditions on the airflow in the tower and energy production efficiency.
Conceptional Figure of Research Proposal
The worldwide demand for energy increases very rapidly, while natural energy resources are continuously being depleted and may lead to severe shortages in the future. In addition, as noted in [1], 89% of the United States’ and 80% of the world’s energy sources presently come from fossil fuels. The combustion of such fuels leads to high pollution of air, land and water, ultimately affecting our health. The use of alternative safe and clean energy sources, such as solar energy or wind power, is still insignificant. It seems clear that in the light of the need to reduce the output of greenhouse gases due to global warning, alternative sources of energy not involving emissions of carbon dioxide have to be developed. One alternative source is the use of nuclear power, but the use of such systems is often resisted due to the fear of hazardous and undesirable environmental pollution. Therefore, the search for alternative energy sources is mandatory.
Downdrafts generated by the evaporation of raindrops falling below clouds in a relatively dry and hot air are common in the atmosphere and are known as “microbursts”. Measurements and numerical modeling of these phenomena [2, 3] reported downdrafts that may reach as much as 25 m/s. Based on this natural phenomenon, the idea of “Energy Tower” was suggested [4, 5, 6,7].
Using very simple calculations of flow and evaporation process inside the “Energy Tower”, similar estimations of the generated power were obtained by different authors. For a tower with a height of 1000 m and the diameter of 300 m, the net estimated power reaches about 300-400 MW. It should be emphasized that these studies have a number of basic limitations. The first one is related to the flow inside the “Energy Tower” that was calculated as a laminar homogeneous flow. For towers exceeding 100 m in radius, the flow will definitely be a non-homogeneous, extremely turbulent with Reynolds numbers larger than 108 and with very complex boundary conditions. Because of inherent limitations of one-dimensional models, calculations of the flow and energy output from an “Energy Tower” with such dimensions could lead to large errors of even hundreds of percents. The second limitation is related to the calculation of the evaporation process. Since the driving force of the “Energy Tower” is the evaporation of the drops, this process must be calculated with great accuracy. However, the methods used to calculate the evaporation process in the mentioned studies were very simple. They assumed that the size distribution of falling drops from the tower’s top is homogeneous. Consequently, their calculation of the total evaporated water mass were based on the evaporated mass of one drop multiplied by the number of drops. In reality, inside the tower the size distribution of the drops is heterogeneous and changes with height and radial distance. Therefore, the process of evaporation in an “Energy Tower” must be studied on the basis of a common solution to the diffusion equation with respect to the drop size distribution and an equation with respect to the saturation deficit. In addition, since drops with different sizes fall with different velocities, gravitational collision and collection of drops is expected to occur. This also influences the evaporation of the drops.
Model description
In order to calculate correctly and accurately the flow of the air and the drops in an “Energy Tower” of large dimensions, an axisymmetric numerical model was developed based on the solution of the Navier-Stokes differential equations for turbulent flow and integro-differential kinetic transfer equations for calculating the drops evaporation, collection/breakup and sedimentation processes. A detailed description of the set of equations, turbulence parameterization, microphysical processes and numerical methods used in the model can be found in previous publications [8-11].
Modeling was carried out using an axisymmetric numerical model of the “Energy Tower”. As boundary conditions, no-slip solid walls that are thermally isolated from the environment are assumed. At the walls the vertical and horizontal flows become zero. It is assumed that no exchange of heat, moisture or momentum between the tower and the environment exists. These assumptions imply that in the present model issues related to the interactions between the tower and the environment are not addressed.
From the model, the size distribution of the drops and the air speed, temperature, humidity and pressure are calculated at every grid point in the domain. Using these parameters, integral parameters are calculated, such as: the air masses that flow through the top of the tower Mair,in(t) and out of its bottom through the diffuser Mair,out(t); the water mass that flows into the tower at its top Win(t) and outflows through the diffuser Wout(t);
In order to evaluate the performance of an “Energy Tower”, the following parameters are defined:
A} The pumping energy: the energy needed to lift water from the bottom to the top of the tower:
where g is the acceleration of gravity, is the tower height;
B} The kinetic energy of the out-flowing air:
Here , and u, w are the radial and vertical velocities, respectively, and ρair is the air density, is the tower radius;
C} The net energy:
D}.The loss of internal energy of the air in the tower by the cooling of the air by evaporation of the drops:
where cv is the specific heat at a constant volume, and are the absolute temperatures at the top of the tower and at the diffuser, respectively. The first term represents the internal energy of the air entering the top of the tower, and the second term is the internal energy of the out-flowing air through the diffuser.

Basing on the above, one can define the efficiency coefficient of the “Energy Tower” as
Assuming that we can get over the problem of separating the small drops from the out-flowing humid air, then we can calculate the amount of fresh water, which can be obtained by cooling the out-flowing humid air. Finally we correct the temperature of the out-flowing cold air due to the heating as a result of the condensation process.
In order to maintain the accuracy of the numerical method, the same resolution in space and time was used throughout all the simulations. For towers with HT ≥ 800 m the radial grid size was Δr = 20 m, the vertical grid size was Δz = 30 m, and the time step was Δt = 0.1 s. For towers with HT < 800 m we used: Δr(HT) = (HT /800) • 20 m, Δz(HT) = (HT /800) • 30 m, and Δt(HT) = (HT /800) • [W(HT=800)max/W(HT)max] • 0.1 s. Tests were conducted in which the spatial and time resolutions were increased by a factor of two. The differences in the results were smaller than 5% while computation times increased by a factor of 10.

For the above-mentioned initial and boundary conditions and numerical model parameters, very stable numerical solutions were obtained. In all the cases the flow in the “Energy Tower” reached a stationary state. The time required reaching this stationary condition varied from 12 min to 30 min depending on the geometric, physical and atmospheric parameters of the “Energy Tower”. Although the model is time dependent, only the results that are obtained when the stationary flow is reached are presented here.
More than 200 numerical experiments were conducted in order to determine the optimal parameters of the “Energy Tower” needed to obtain the maximum net energy. It was found that the largest net energy is obtained for the following relationships of geometrical parameters: RT = HT/2 and ΔHdiff = HT/4. In general, total mass was conserved in all the numerical simulations, and mass losses were less than 0.5%. Total energy was also conserved, with losses less than 3%. The mixing ratio of the drops at the top of the tower is LW = 6 g kg-1, and the average radius of the sprayed
drops is rdr = 40 m. The temperature at the bottom of the tower is 30ºC, and the relative humidity at its top is 30%. With these optimal parameters it is possible to obtain a considerable amount of net energy – 560 MW – even at the height of only HT = 400 m. When HT increases, the net energy grows very rapidly, and for HT = 880 m it reaches the value of 11,500 MW. However, in this case the water amount that must be lifted to the top of the tower and then dispersed as drops reaches 120 m2s-1. This is a huge amount of water that may be difficult to realize technically. Therefore, in the subsequent numerical experiments a limit to the height of the tower was set to HT = 800 m. Under these conditions, the amount of water needed is only about 78 m3s-1.
It should be noted that a good agreement was found between the model simulations and experimental data obtained in a tower 21m high [16] with the account for the fact that geometrical parameters of this tower are far from optimum.
The calculations using an axisymmetric numerical model of the “Energy Tower” indicate:
1. The idea to produce energy from the evaporation of falling drops in relatively warm and dry climate could be realistic.
2. A set of optimal geometric and physical parameters was found, for which the net energy could be larger than 4000 MW and in some cases may reach up to 11,500 MW.
3. Good agreement was found between the model simulations and those of an experiment conducted in a tower 21 m high.
4. Much smaller towers could also produce some energy (e.g., a tower 80 m high can produce 2.0 MW of energy) and could be used as prototypes to test the accuracy of the numerical model and the feasibility of the Project without making major investments in full-size towers.

The present proposal suggests addressing 5 additional subjects that have not been considered by the numerical model thus far:
1. Development of a three-dimensional theoretical model of the energy tower.
2. Simulation of the turbine loading influence on the flow in the “Energy Tower”.
3. Study of interrelationship between the environment and flows in the “Energy Tower”.
4. Solution of the problem of separation of small salt drops from the out-flowing humid air.
5. Estimate the effect of possible global cooling of atmospheric air by the insertion of several dozen “Energy Towers” in the Global Atmospheric Model.
Three-dimensional model: In order to study the influence of atmospheric wind at the top of the tower on the airflow in the tower, it is necessary to apply a three-dimensional model (preferably in cylindrical coordinates). Besides, the three-dimensional character of the flow can be stipulated by the geometry of the tower.

Influence of turbines: Turbines should be located at the exit of the diffuser. Their effect would be a reduction of the flow inside the tower and, therefore, a reduction in the energy yield of the system. We will model the effects of such turbines on the flow in the tower and evaluate their effects on the net energy that could be obtained.

Interaction with the environment: All the simulations conducted thus far assumed that the external environmental conditions are constant during the operation of the tower. Changing conditions may influence the performance of the tower and it is important to quantify them. The first step will be to increase the domain of the model in which the tower itself is located at the center of the domain. This will permit us to investigate the influence of the tower on the temperature and relative humidity profiles. The second stage of the research will be to investigate the influence of the environmental wind on the performance of the tower. For this purpose, a three-dimensional dynamic model will be needed. At our disposal we have such a model that was developed in Colorado State University with our special input in the cloud processes. This model (RAMS) [12-16] can be used with high accuracy and efficiency to simulate the present problem. A parallel computer SP-2 will be used for this purpose.
Microphysical processes: The droplets evaporation, coagulation break-up and sedimentation processes in a turbulent host medium will be taken into account in the proposed model. Since the proposed model considers small droplets a significant effect of the turbulence on these processes should be expected.
Separation of small drops: This problem will be solved by using the method of whirlwind, developed at the university of Beer-Sheva [17-19].
Global cooling of the atmosphere: By inserting several dozens of “Energy Towers” in an existing Global Atmospheric Model we will estimate the extent of atmosphere air cooling by “Energy Towers” and their ability to compensate for global warming of the atmosphere generated by green house gases. In addition, extensive use of such towers may diminish the amount of fuel combustion and essentially diminish the release of greenhouse gases in to the atmosphere. Combined together, these factors will bring to considerable diminution of atmospheric air pollution and its global warming.
Objectives and expected significance of the research:
The research objective is to estimate the feasibility of power generation by means of Energy Tower with a more realistic approach to the flow in it. The first step of the research will by executed theoretically. For this purpose, we will develop a three-dimensional theoretical model for the numerical modeling of Energy Tower. We will develop a numerical method of solving a system of three-dimensional Navier-Stokes equations for a turbulent flow of air with suspended water drops in the Energy Tower. In order to account for the effects of interactive evaporation of droplet clusters we will employ the model developed in studies [20-22]. In calculating turbulent two-phase flow in Energy Tower we will include a number of effects that we found recently: turbulent thermal diffusion of small internal particles, self-excitation of small-scale unhomogeneitius in space distribution of droplets etc.
We intend to accomplish theoretical modeling of the introduction of an electric generator turbine into the Tower and study its impact on the airflow in Energy Tower. The simulation of a turbine in the Tower will give a possibility to evaluate the realistic part of useful mechanical energy that can be obtained by “Super Power Energy Tower”.
This research will also allow to estimate the extent of influence of external wind on the airflow in the Energy Tower.
On the basis of this study we expect to:
1. Carry out a more realistic optimization of geometrical, physical and atmospheric parameters of Energy Tower taking into account the four above-mentioned results.
2. Produce considerable amounts of ecologically clean energy using the internal energy of relatively dry air heated by sun.
3. Obtain relatively cheap essential water by desalination of seawater.
4. By cooling air compensate for global warming of the atmosphere.

Using “Super Power Energy Towers” for these purposes is rather novel and urgent.
The present proposal is based on studies at the Tel-Aviv University [11] on the flow in Energy Tower, using a turbulent axisymmetric model involving integro-differential kinetic-transfer equations for calculating drops evaporation, collection/break-up and sedimentation processes as correctly and exactly as possible.

Why its necessary to carry out this theoretical research:
By Israeli Ministry of Energy in 17.7.1994 created a special committee in order to evaluate the scientific validity, technical feasibility, cost and economical efficiency of the project – “Energy Towers”.
In this committee was included well known scientists and specialists in interdisciplinary field of fluid mechanics, atmospheric physics and engineering..
This Committee gave its conclusions in 17.3.1996. According to these conclusions :
1) The idea of producing clean energy by the use of Energy Towers could be realistic.
2) Taking into account the technical progress of today , the realization of such project is technically possible.
3) The building of the Energy Tower with high of 1000m and diameter of 500m will cost about one billion dollars.
4) Using Energy Towers as a clean energy source could be in future economically vary acceptable.
5) However, at the same time, the committee emphasized that before the beginning of any building , even a prototype it is necessary first of all to take detailed scientific research by three dimensional theoretical model of “Energy Tower”.

At the end it must be emphasized that the basic idea of the project , namely, a new (indirect) and very effective use of the solar energy through “Super Power Energy Towers”.
Proposed theoretical study is certainly a necessary step in the future possible realization of Energy Towers. It is of high importance and certainly might have important practical and engineering outcomes. The small amount of money spent on this theoretical study may save much effort and money in possible technological developments. By using three dimensional model we can find the realistic optimal geometric and physical parameters of the Energy Tower. But by building a real Tower before knowing these optimal parameters would be an extremely waste of money.
The realization of this project will stimulate scientists and engineers to look for new, non –standard sources of clean energy.

On the basis of the results of the theoretical study we will recommend: to build a prototype with a height of 80 m, a radius of 40 m and a diffuser height of 20 m which may generate about 2 MW net energy. This prototype will be used to test the reality of the original idea of “Energy Towers” and to estimate the extent of accuracy of our numerical model by a relatively moderate expense.
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Professor Shalva Tzivion

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