Screen Surface Air Vortex Diameter
Mechanical energy is produced when heat is carried upwards by convection in the atmosphere. The Manzanares solar chimney, shown in Fig. 1, was built in Spain in the 1980s and consisted of a vertical tube 200 m high and 10 m in diameter with a turbine installed inside its base. The chimney was surrounded by a solar collector, a transparent plastic roof 240 m in diameter supported 2 m above the ground. The air flowed through the open rim of the collector and up the chimney. The solar collector increased the air temperature by some 20°C; the upward velocity in the chimney was typically 10 m s?1. The total insolation on top of the collector was 45 MW and the turbine generated 48 kW of electrical power for an overall efficiency of 
0.1%. The operating conditions shown in Fig. 1 are based on those described in Ref. 2.
A power station using a controlled tornado-like vortex instead of a physical tube was proposed in Ref. 3. The centrifugal force in the annular vortex replaces the physical tube. There is also no need for a covered solar collector because the boundary layer acts as the solar collector. The vortex could extend from the earth’s surface up to the tropopause and the heat to work conversion efficiency could be 15%.
The proposed vortex power station is shown in Fig. 2. The vortex would be started by heating the air in a circular station with fuel while giving the air converging towards the centre of the station angular velocity by having the air pass through a rotating perforated screen. Once the vortex is established it would persist without fuel and its base would remain at the centre of the station. An optional vertical-axis turbine located in the centre of the station would generate electricity. The earlier proposal used fixed deflectors instead of a rotating screen. However, a rotating screen would provide more positive control during development.
A medium size vortex power-station could be 300 m in diameter, and the perforated rotating screen could be 50 m high. The vortex could be 80 m in diameter at its base. The turbine could produce 100 MW of electrical power from a vortex the size of a small tornado. The heat needed to sustain the vortex, after heating with the fuel has stopped, would be derived from the sensible and latent heat content of the air at the bottom of the atmosphere.
The process could be used to produce convective vortices ranging in size from dust devils to medium-size tornadoes. Tornadoes are dangerous, but the process could be developed safely by using physical models of increasing size, first indoors and then outdoors. Some dust devils are less than a metre in diameter. Under optimal conditions, it should be possible to start a self-sustaining vortex to demonstrate the concept with a station 30 m in diameter. Large stations could be tested safely by supplying heat continuously under stable atmospheric conditions.
Fire whirls have been produced by burning fuel in the centre of a rotating screen. The author has built a 30 cm diameter model—essentially a small-scale version of Fig. 2. The model consisted of a circular plate, with a 20 cm high vertical perforated-screen attached to its edge. The screen was an ordinary metallic bug-screen. The plate was placed on a turntable; there is no need to rotate the base, but on such a small model, it is simply easier to rotate both the screen and the base. The vortex was produced by burning liquid fuel on the base of the model while the screen was rotating. The fuel could be placed either in a circular cavity at the centre of the model or in an annular groove just inside the screen. The vortex stayed in the centre of the model. The vortex, which was 1–5 cm in diameter was stable and visible to a height of 1 m because of the colour of the flame and smoke. Some vortices extended to a height of up to 2 m. The model was only used indoors because small vortices are easily disturbed by stray air currents.
The air converging towards the base of the vortex is entrained sideways as it passes through the small openings of the screen and acquires a tangential component of velocity approaching the tangential velocity of the screen. The tangential velocity of the air just inside the screen was measured to be 87% of the screen tangential velocity by [4]. As the air converges from the rotating screen, its tangential component of velocity increases to conserve the angular momentum acquired at the screen, except in the layer adjacent to the surface, where tangential velocity is reduced by friction. As a result convergence is limited to the thin surface layer.
A very small turbine was installed in the centre of the model to test a method of extracting energy. The turbine was 4 cm in diameter and sat on the tip of a pin. For the turbine test, the fuel was burned in the annular groove located just inside the screen. The speed of rotation of the turbine was estimated at over 1000 rpm, i.e. much higher than the speed of rotation of the turntable, which ranged from 30 to 80 rpm. The flame would cling to the surface of the plate and impinge directly on the turbine. The turbine behaved like a cup anemometer caught in a rotating flow.
Fig. 3, where q is the heat received during processes 1–2, h is the enthalpy of the raised air including the enthalpy of its water content; g is the acceleration of gravity; z is the height of the tube, and v is the velocity. For an adiabatic process, (i.e. q=0), with negligible inlet and outlet velocities (v?0), the total energy equation reduces to
The work is equal to the decrease in enthalpy of the air minus the increase in potential energy of the air. The work is a maximum when the process is frictionless and reversible, when the expansion is isentropic. The maximum work is, therefore, equal to the reduction in enthalpy minus the increase in potential energy in an constant entropy process, (i.e. s=constant).
The work due to buoyancy (wb) is equivalent to the convective available potential energy (CAPE), which is widely used in meteorology, and which is the integral part of the force of buoyancy times the distance moved. During periods of insolation, CAPE is typically 1200–2200 J kg?1. The average CAPE during a recent month of observation in an oceanic tropical area was 1920 J kg?1. The maximum work of buoyancy is readily calculated from atmospheric soundings. The following oceanic tropical conditions will be used to demonstrate the technique by calculating the work produced when air is raised from the surface to the 20 kPa level. The conditions are: P1=101 kPa; T1=27°C; U1=80% corresponding to m1=18.18 g kg?1; P2=20 kPa and z2=12400. In tropical oceanic areas, the level of neutral buoyancy is usually above the 20 kPa level and the elevation of the 20 kPa level is typically 12400 m. The corresponding energy variables are: h1=73485 J kg?1, h2=?51954 J kg?1, s1=s2=256.7 J kg?1, ?h=125440 J kg?1 ?gz=123730 J kg?1. The work of expansion when the air is expanded from 101 to 20 kPa is 125440 J kg?1, but 123730 J kg?1 is required to lift a kilogramme of air including its water content to the 20 kPa level. The net work is therefore: wb=1710 J kg?1.
The effect of sounding properties is difficult to see from Eq. (2), but is readily appreciated by applying Eq. (2) to different conditions. Increasing the temperature of the surface air by 1°C at a constant mixing ratio increases wb by 250 J kg?1. Increasing the relative humidity of the surface air by 5% at a constant temperature increase wb by 585 J kg?1. Increasing the mixing ratio of the surface air by 1 g kg?1 at a constant temperature increase wb by 517 J kg?1. Increasing the temperature of the surface air by 1°C at a constant relative-humidity increases wb by 825 J kg?1 because both the temperature and the mixing-ratio increase. A small change in the air temperature has a large effect on the work of buoyancy. Decreasing the temperature of the surface air by 2°C at constant relative-humidity, would reduce wb to near zero. Decreasing the average temperature of the sounding by approximately 2°C, without changing the surface air conditions, decreases the level of the 20 kPa surface by 100 m and increases wb by 1000 J kg?1.
Tags: screen surface
