Field of invention

This invention concerns solar powered devices by which a fluid can be heated by concentrating the energy from the sun incident on the earth's surface so as to produce an intense local heating effect.

Background to the invention

Various systems have been proposed for collecting energy from the sun using mirrors to focus the heat energy so as to elevate the temperature of an object placed at the focal point.

Since the sun is distant from the earth the rays of energy from the sun can be considered to be substantially parallel at the surface of the earth and with rotation of the earth relative to the sun the angle of incidence of the "parallel" rays will vary for any point on the surface of the earth during the daylight hours.

In order to harness the energy incident at that point, it is therefore necessary to rotate the reflecting surface so as to concentrate the reflected energy through a fixed position relative to the surface of the earth or to provide a fixed reflecting surface and move the object which is to be heated relative thereto so as to correspond with the movement of the locus of the focal point of the rays from the reflected surface.

In some arrangements it has been proposed to use a large number of plane mirrors arranged in an array, each mounted separately and spaced from adjoining mirrors in the array and each driven separately by drive means which is controlled so as to alter the position of each mirror as required so as to reflect the rays of

the sun incident on the surface of the mirrors through a predetermined point in space above the array. By positioning a heat exchanger at that point so the heat energy incident on all of the mirrors is concentrated onto the surface of the heat exchanger.

The complexity and cost of such an arrangement and the energy absorbed in moving and tracking the mirrors has proved to be non commercial.

French Patent Specification No. 635283 describes an arrangement in which a generally hemispherical reflecting surface is fixed relative to the surface of the earth and a heat exchanger is located above the hemispherical surface, drive means being provided to move the heat exchanger as the angle at which energy from the sun varies during the daylight hours and during the year. The hemispherical reflecting surface is itself inclined depending on the latitude at which the reflector is located on the surface of the earth.

The radiation incident on the heat exchanger heats either water or oil which is pumped through the heat exchanger so as to provide a mechanism for transferring heat from the exchanger to heating coil so as to heat air to drive a turbine H which itself can then rotate another machine such as an altenator.

The heat exchanger shown in the French Patent Specification No. 635283 suffers from a significant disadvantage in that much of the reflected energy from the sun impinges on the surf ce of the heat exchanger with only grazing incidence.

It is thus an object of the present invention to provide an improved form of heat exchanger for use in conjunction with a spherical reflector.

The heat exchange system described in French Patent Specification No. 635283 also suffers from the disadvantge in that the air

supply to the turbine H cannot be raised to a temperature greater than the temperature of the fluid medium circulating in the heat exchanger. The fluids described are liquids such as water or oil. It is now known that the temperature of the air supplied to the driven turbine H should be considerably higher than is achievable using water or oil as the heat transfer medium.

It is therefore a subsidiary object of the invention to provide an improved heat exchange system which does not suffer from the temperature limitation of the system shown in French Patent Specification No. 635283.

Summary of the invention

According to the present invention a device for use in a solar energy collecting device adapted to concentrate solar energy to heat fluid medium therein comprises an upright stem and an upper member having a concavely curved downwardly facing underside arranged symmetrically above the stem, each of said stem and said upper member having fluid passage means associated therewith through which fluid can pass, the outer surface of the stem and the underside of the upper member serving as heat energy collecting surfaces which are thermally coupled to the fluid passage means so as to comprise heat exchange means, in which the heat exchange means of the upper member forms the main heat energy collecting part of the device.

The downwardly facing upper member is typically supported by two or more generally radially directed spokes having minimal thickness so as to cast minimal shadow on the underside of the said upper member.

The upright ste may extend upwardly to the centre of the concavely curved surface, but in a preferred arrangement, the stem only extends up to the point where the spokes radiate outwardly, so that there is minimal obstruction to cast a shadow.

Fluid flow is typically via a first passage to the upper end of the central strut, a co-axial downfeed from the top of the strut to the bottom thereof internally of the strut, an annular return passage between the co-axial downfeed and the wall of the strut through which fluid can rise, one or more passages through the spokes between the upper end of the strut and the lower outer edge of the downwardly facing upper member through which fluid can pass to the outermost and lowermost regions of the concavely curved surface thereof, and one or more fluid paths within the said member thermally coupled to the said surface to enable the fluid to flow to one or more upper outlets from which heated fluid can pass.

In accordance with a preferred aspect of the invention, the fluid is a gas, a mixture of gases, or air.

In a preferred embodiment, the fluid passage through the downwardly facing member follows a generally tortuous path so as to increase the dwell time of the fluid therewithin, so as to increase the time that the fluid is exposed to solar energy reflected from the reflector onto the concavely curved surface.

The tortuous path may for example comprise one or more spiral passages.

Where fluid passages extend from the upper end of the strut through two or more of the spokes, a separate spiral path may be started from the outermost end of each of the said spokes and the different spiral paths may be intertwined in the form of a multistart thread.

A device as aforesaid is preferably used with a part- spherical reflector for heating air to drive a turbine.

Preferably means is provided to move the device relative to the reflector to compensate for the movement of the sun during the day and the position of the sun in the sky at different times of

the year.

The curved surface on the underside of the upper member is preferably positioned so as to be post focal to the reflector surface.

The curved surface must have sufficient depth and its profile or shape can be predicted using equations which use as their starting point the condition of perpendicularity of all rays reflected off the reflector surface to the heat exchanger at any point.

The equation for the profile of the curved heat exchange surface in parametric form is: x=Cos# - A.Cos20 - Sinf?.ctg2 ^* , and y=A Sin20 where A = 2-1-Cosf? - Sin θ

Sin 20 (1)

The above will be referred to as equation (1).

In equation (1) when I is less than or equal to 0.5 a post focal surface exists.

In equation (1) if 1 is greater than 0.5, the surface is pre- focal.

The geometrical surface containing all the possible local focal points is sometimes referred to as the caustic surface.

Various values of 2 can be used depending on circumstances and overriding requirements. Preferably the caustic curve must not be crossed by the heat exchanger because the edge of the heat exchanger will then create a shadow on part of the surface of revolution of the caustic curve.

The heat exchange means within the stem and the heat exchange

means within the upper member may be connected in series so as to heat the same fluid or they may operate quite independently, the one heating one fluid and the other heating another fluid.

The effective aperture of the part-spherical reflecting surface is increased if the first elongate heat exchanger in the stem is used to preheat the fluid before it passes to the upper member.

The surface of the elongate unit may be profiled so as to provide trunkated conical surfaces having different inclined angles at different positions along the length of the stem so that energy reflected by the reflector towards the stem will be incident more or less normally on the various regions of the surface thereof. This is of distinct advantage since the reflectivity from a surface is usually least when the angle of incidence is near normal to the surface.

Where either heat exchange means requires reinforcing ribs to increase rigidity or fins to increase the surface area, these ribs and/or fins should be inside the unit.

The invention also lies in a method of heating a fluid to drive a rotary machine such as a turbine comprising the steps of mounting a solar energy reflecting surface so as to collect and reflect energy from the sun towards a heat exchanger comprising a first elongate heat exchange means below a second heat exchange means which latter has a downwardly facing concavely curved surface, and passing fluid to be heated through both of said heat exchange means in succession before suppying the heated fluid to the rotary machine.

The fluid may pass first through the elongate unit and then through the second unit.

The fluid may be gas, a mixture of gases, or air.

The method advantageously comprises the step of compressing the

fluid before it is supplied to at least the second heat exchange means and typically before it is supplied to the first heat exchange means.

Where the fluid leaving the rotary machine retains some of the heat imparted to it by one or other of the two heat exchange means, a further heat exchange means may be located in the fluid output of the machine to enable some of the heat in the said output fluid to be recovered.

In a preferred arrangement the further heat exchange means may be used to heat fluid before the latter passes to the said first heat exchange means.

Where a compressor is located ahead of the first heat exchange means, the fluid which is to be compressed is preferably first heated by the said further heat exchange means.

The invention will now be described by way of example with reference to the accompanying drawings, in which:

Figure 1 illustrates how parallel rays of energy incident on a part spherical surface will be reflected;

Figure 2 illustrates the coordinates of the point of crossing of the main heat exchanger with caustic curves;

Figure 3 further illustrates the reflection of energy from a spherical surface;

Figure 4 shows a basic form of construction of a composite heat exchanger to collect more energy than would be collected by a single heat exchanger;

Figure 5 illustrates the parameters associated with the design of Figure 4;

Figure 6 illustrates a ^' preferred form of construction for the outside surface of the lower linear heat exchange element of Figure 4;

Figure 7 shows the fluid flow through the elongate supplementary heat exchanger;

Figure 8 shows how the exit pipe can leave the upper end of the heat exchanger of Figure 7;

Figure 9 is a diagrammatic representation of a composite heat exchanger in accordance with the invention for use with a spherical surface mirror;

Figure 10 is a plan view from below of the exchanger unit of Figure 9;

Figure 11 shows an alternative form of construction of the tortuous path through the main heat exchanger between the inner and outer surfaces;

Figure 12 shows how the outside diameter of the main unit of Figure 9 can be reduced;

Figures 13, 14 and 15 illustrate the theory behind the development of the main exchanger;

Figures 16 and 17 illustrate the theory behind the development of the supplementary or additional heat exchanger;

Figure 18 is a theoretical illustration of a part spherical reflector surface set to receive radiation from the sun for heating a heat exchanger (not shown) in accordance with the invention;

Figure 19 is a diagrammatic constructional drawing showing one embodiment of reflector and heat exchanger and mounting assembly;

Figure 20 illustrates alternative detail of the upper end of the tower and illustrates how the swinging heat exchanger assembly can be mounted for movement about two axes; and

Figure 21 illustrates a further embodiment of a heat exchanger according to the invention.

Detailed description of the drawings

The solar energy station shown in the drawings has a fixed spherical concentrator (mirror) 10 using air as the agent of energy transfer.

The unit is intended to have low capital and operating costs for the widest usage. Production of models producing electricity of a few kW to multiples of 10MW is envisaged.

The following Technical Requirements relate to a first experimental prototype with anticipated electrical output of 50- 100 k .

The Main Heat Exchanger 12 heat exchanger selected is of the post-focal type, concave to the mirror. The profile (shape) of the working-surface of the heat exchanger (12) is dictated by equations, worked out using the condition of perpendicularity of all rays reflected off the spherical mirror surface to the heat exchanger (12) at any point.

In Figure 2, the results of calculations for the post-focal heat exchanger working surface (with 1=0.49 and 1=0.45) are tabulated. Here also the caustic curve is shown and the points where it crosses the heat exchanger heat exchanger. The caustic curve must not intersect the heat exchanger curve because the edge of the heat exchanger will then create a shadow.

In order to increase the area of active surface of the mirror (of the coefficient of the used surface of the mirror : CUS = R2 =

Sin20) an additional heat exchanger 14 of cylindrical design is employed, displaced along the axis of symmetry (see Figure 4). Exchanger 14 plays the role of economiser or preliminary heater. It can, however, also be used separately.

Gases heated by the two heat exchangers 12 and 14 can be used to drive a high temperature air turbine with integral preliminary compressor, gas turbine engine used in helicopters and aircraft. In fact, it is only necessary to remove the combustion chamber and introduce air ducts, in order to modify such an engine.

A preferred gas turbine engine this project, comprises the type GTE-350 as used in the M12 helicopter. Such an engine will work at half-power in the present system, which will extend its life and result in considerable noise reduction. Unfortunately it also decreases the turbine's efficiency. All low-power GTEs have low efficiency (approx 10%). It is, however, possibe to double the efficiency by use of a 'regenerative' heat exchanger. Powerful GTEs (1 to 20 MW) have an efficiency of up to 40%.

The main parameters of GTE-350 to be taken into account in this instance are: power at output shaft (P _mec ) = 110 kW (150 hp); length : «1.2m; volume of air required : 1.5kg/sec; speed of rotation : 3,000 rpm; efficiency : 0.22 (using a regenerative heat exchanger to be described) ; air temperature : a. after compressor 133°C b. after regenerative heat 430°C; exchanger c. at turbine input 810°C; d. at turbine output/input regen. heat exchanger 533°C.

Selection of variant

The main heat exchanger has been selected as a post-focal with 1=0.49.

For P _mec = HOkW, and an assumed efficiency of electrical energy conversion of 93%, then the output electrical power (P _el ) will be equal to: P.e.l = 0.93 x P _m iπ„e _p c = 103kW.

Assuming the solar constant at the site, K _s = lkW/m ² and: e ficiency of mirror (reflection, absorption, shadow)= 0.85(K _|nr ), heat exchangers (heat exchangers) efficiency

(main and additional) = 0.86(K _e ), efficiency of turbine with compressor and regen. heat exchanger = 0.22(K _t ), efficiency of electro=generator = 0.93(K );

the overall efficiency of the unit is equal to:

0.85 X 0.86 X 0.22 X 0.93 = 0.15.

Therefore the energy required from the sun (P _s ) (when K ₅ = lkW/m ² ) is equal to (P _s - 103/0.15) = 685kW and the surface of the (used) aperture of the mirror is equal to (S _u - 685)m ² .

If the system produces only heat energy, then it is given by:

P _h = 0.85 X 0.86 X 685 (= 500kW) .

When S = 685m ² , then the radius of the used aperture is equal to R _u = VS _U / 3.14159' (= 14.76m); and its diameter = 2R _U (=29.5m)

The CUΞ of the mirror is equal to (Ru/Ro) ² , where R ₀ is the radius of the spherical mirror. Below we will divide all values to the R ₀ = 1.

It will be assumed that the full CUS of the mirror (with main and

additional heat exchangers) is equal to 0.777 ² , (= 0.6). We have R _u = 0.777 = Sin0 _πχ (see Figure 1) and 0-^ = 51° and 20 _πχ = 102° which is the aperture angle of the used part of the spherical mirror (looking from the centre of the sphere). On the assumpion that R _U =R, then the radius of the sphere R ₀ =14.76/0.777 (= 19m).

Main heat exchanger

The edge of the main heat exchanger must not reach the caustic curves. We therefore assume for the edge R = 0.6225 (= Sinø); θ = 38°30'; 20 = 77° which is the aperture angle of the area used by the main heat exchanger.

Then the coordinates of the edge of the main heat exchanger will be equal to

X = 0.619 = 0.619 x 19 (= 11.76m) and

Y = 0.0862 (= 1.638m) (see Equation (1)).

This is the radius of the aperture of the main heat exchanger.

The diameter of the aperture of the main heat exchanger is equal to 2R = 0.1724 (= 3.276m). The top of the main heat exchanger is displaced by the distance from the centre 1 = 0.49 (= 9.31m) and the depth of main heat exchanger is given by:

(X-l) = (0.619 - 0.49) = 0.129 (= 2.451m).

The working surface of the main heat exchanger is given by S _Hm =π{9(2-1)Cos0 _e -[2(2-2) ² +3]Cos20e+5/3(2-1)Cos30e-3/8Cos40 _e - 32/3(2-l)+2(2-l) ² + 27/8}=0.0543 (=19.6m ² )

Additional heat exchanger (economiser)

R = 0.777 is selected to ensure the optimal length of the additional heat exchanger. Its length can extend to the mirror surface (in which case the entire hemisphere will be used). But this is not optimal either in regard to construction or cost.

Having such a length, there would be problems of movement, requirement for major construction and rotation mechanisms - resulting in high costs and creating large shadows on the mirror. At the same time, in order to make use of the edges of the hemisphere, it would be necessary to construct a mirror having almost ten times the surface area.

The selected value of R = 0.777 ensures reception of the required power and relatively reduced length of the additional heat exchanger. The upper edge of this heat exchanger must make contact with the ray which is directed to the edge of the main heat exchanger (that is R = 0.6225).

The value of the diameter of the additional heat exchanger is very important. We assume it equal 2r = 0.025 (= 0.475m) or the radius r=0.0125 (= 0.237m). Then its leneth can be calculated by the formula:

(I _β = _1 = r/tg20) [2]

2COS0 The main parameters of the additional heat exchanger are shown in Table I.

The degree of solar energy concentration on the surface and the surface temperature of the additional heat exchanger depends greatly on its diameter 2r.

The working surface of the additional heat exchanger equals: S _ua = 2πr (1^ -2 _a1 ) = 2ττx0.0 125x0.15 = 0.0118 = (4.25m ² )

The additional heat exchanger does not cast a shadow on the mirror (because it is positioned in the shadow of the main heat exchanger), nor on the main heat exchanger. It is important that the latter is achieved.

It can also be shown that the additional heat exchanger does not cast a shadow with its upper edge for ray 0.1 directed to the top of the main heat exchanger (See Figure 5).

Here we have : R = 0.1; 0 = 5°44'; 1 _{0 Λ} = 0.505, and we find : g = 0.028 >r since r = 0.0125.

There is no shadow. The ray 0.1 goes from the upper edge of the additional heat exchanger for a distance (horizontal) equal to (g - r) = 0.0155, which is more than enough.

The additional heat exchanger is not optimal because it extends upwardly and downwardly from its centre along its axis. We are, however, using the optimal section close to its centre (R = 0.707 = 2 ₀₇ ) . Obviously the condition of perpendicularity of the rays on the additional heat exchanger surface is satisfied only in its central section. Due to the extensions, there is no point in using special round ribs etc. These ribs, however, can be useful to increase efficiency for another reason. The coefficient of reflection from the surface depends greatly on the angle of impingement by the rays - and has a minimum when impingement is perpendicular. In Figure 6, a variant of the additional heat exchanger 14 is shown at 16 with ribbed construction.

The simplest form of construction (tube-in-tube) is shown in Figure 7.

It is necessary that all the ribs giving solidity and increasing the surface areas of the heat exchanger 14, 16 and 18 (carrying the structure etc) must be constructed inside the respective heat exchanger. The working surface of the additional heat exchanger should be cylindrical in shape.

The cylindrical heat exchanger requires in fact the highest degree of accuracy in design of the mirror surface.

Concentration coefficient and heat temperature

The heat exchangers have to ensure the heating of the 1.5kg/sec air flow up to the required temperature required for at the input

15 to the selected turbine. Typically this temperature should be not less than 810°C. At the same time, there must not be any substantial loss of pressure due to friction within the heat exchangers. The required pressure at the turbine input is approximately 3 atmospheres.

Changing 1 for the main heat exchanger and r for the additional heat exchanger, it is possibe to change the surfaces and sizes of these heat exchangers and to achieve different concentration coefficients and heat temperatures.

The following options/requirements relate to and affect the design of the heat exchangers.

A The main heat exchanger

Equation (1) describes the profile of the main heat exchanger.

It is pssible to give two definitions of the concentration coefficient [K _m ] for the main heat exchanger.

Version 1

K is the ratio between the surface (<--S _o ) of the elementary ring in the aperture plane of the mirror and the surface (oS _m ) of the corresponding elementary ring on the surface of the main Heat exchanger.

Km = lim OS^ = δS^ (3) αS→O oS_m δS„

If the solar constant is taken as K _s = 1 kW/m ² then the value of K is equal to the power density P _m on the working surface of the main heat exchanger in units of kW/m ²

To obtain the distribution of K (and P over the surface of the heat exchanger it is necessary to discover QS ₀ and QS _m

It is obvious that oS ₀ = (Sin ² 0 _n - Sin^.^,) (4)

At the same time (see equation (1)), we have;

m τr{9(2-2)(Cos0 _n _ ₁ - Cos0 _n )-[2(2-2) ² =3]x

(Cos20 _n _- - Cos20 _n + 5/3(2-2) (Cos30 _n _- - Cos30 _n )-

3/8(Cos40 _n _- - Cos40 _n ) } (5)

Then

K _m = lim ^ = {(δώS ₀ /δ0 _n _ ₁ ).(δoS ₀ /50 _n _ ₁ )} _θn _ →θ _n n-1 n m

and with equations (4) and (5) we have:

K _ra =Sin20{9(2-1)Sin0-2[2(2-2) ² +3]Sin20+5(2-2)Sin30-3/2Sin40} ^"1 .. (6)

When 0=0 (top of main heat exchanger), formula (6) becomes:

K _m = 1/(1-21) ²

and K _π approaches infinity when 2=0.5 (top of caustic curve).

Figure 10 shows graphically the dependence of K _m (and P _m ) on R = Sinø, ie on R, 0, and the distance d from the top of the heat exchanger to the current point x, y along the curve of the line of the profile. The x-axis is limited on the left side by the border of the shadow made on the mirror by the heat exchanger. This border is given by Y = 0.082 = R _min .

Assuming R _rain = 0.1 (0 _mi = 5°44' and d _mi = 0.002),

the border on the right side corresponds to the edge of the heat exchanger and

R = 0-6225 (0 _mx = 38°30' and d _mx = 0.162).

The shadow surface made by the heat exchanger is equal to 2.6% of the surface of the mirror aperture as used by the main heat exchanger, ie (0.1 / 0.6225) ² , and 1.6% of the surface used by both heat exchangers together ie (0.1 / 0.777) ² . This value of the shadow (less than 2%) is incorporated in the efficiency which was assumed for the mirror (K = 0.85).

The relationship between the distance d and the angle is defined as: d = ^V(δx60) ² - (δy/δø) ² ' . δø where:

x = 3/2 Cos0- ( 2-l ) Cos20+l/2Cos30} y = -3/2Sin0+ ( 2-2 ) Sin20-l/2Sin30}

This is another version of equation (1)

So we have d = {2. (2-2) - 3Sin0} (7)

Figure 10 also shows the theoretical curve of temperature distribution along the shape of the main heat exchanger, supposing that there is no flow of air and that it achieves a heat balance between absorption and transmission of energy (ie that the material of the heat exchanger surface is absolute black body). The temperature of heating (t _m °C) can be calculated by the formula:

t = 10 ³ .VP _m /56.7'- 273 (8)

Version 2

K _ra (here K _ms ) is the ratio between the surface of mirror aperture (less the shadow surface from the main heat exchanger) and the corresponding surface of cross section of the main heat exchanger.

So K over the cross sections (denoted as K _ms ) is given by: ^κ πs = < ^R2 ~ ° ^{• l2 )} /y ² / < ^{9 )}

(for each corresponding angle 0)

In Figure 10 the broken curve indicates the distribution of K along the shape of the main heat exchanger . The same curve also shows the distribution of power density P along the shape of the main heat exchanger in this given case. Since the calculation has been made including the shadow of the main heat exchanger, the curve represents "zero" at the distance d = 0.002 (= 3.8cm) from the top of the heat exchanger and rapidly increases to the maximum (592) at a distance d = 8cm from the top.

Figure 10 also shows the (broken) curve t-. _s °C of temperature distribution along the hypothetical discs in the cross sections of the main heat exchanger which are in heat balance (absorption- transmission) without flow of air. This curve is only theoretical, just giving an impression of the physics of the main heat exchanger. Obviously the curve has the same character as the curve K _ras , P _ms . It is calculated by formula (8).

Without taking account of the shadow, the curve K _ms , P _ms , rises to 1620 when R = 0.1 and the curve ms to 2040°C when R = 0.1.

These, theoretically, are the maximum possible temperatures on the working surface of the main heat exchanger.

The additional heat exchanger

The surface of the mirror aperture, used by the main heat exchanger, is 1.1854 (= 428m ² ).

The surface of the mirror aperture, used by the additional heat exchanger, is: S = (0.777 ² - 0.6225 ² ) = 0.679 (= 245m ² ).

The total used surface is therefore equal to 673m ² .

In reality, however, it is 685m ² because the surface of the shadow from the main heat exchanger (approx 12m ² or 1.6%) was used in the calculation of the coefficient of used surface (CUS)

of the mirror.

Therefore the additional heat exchanger receives energy from about 56% of additional surface to the surface used by the main heat exchanger and 36% of the total used surface of the mirror aperture. This is a major increase.

The coefficient of concentration K _a on the surface of the additional heat exchanger is the ratio between the surface of the elementary ring in the plane of the mirror aperture (o.S ₀ ) - and the surface of the corresponding elementary cylinder on the surface of the additional heat exchanger (αS _a ).

K _a = li QS^ = dS^ (10)

QS→O ΩS _a dS _a

If the solar constant is assumed K _s = lkW/m ² , so the value of K _a (non-dimensional) is numerically equal to the power density P _a on the working surface of the additional heat exchanger (in kW/m ² ) .

For the elementary surfaces in formula (10) , we have

DS ₀ = τr ( R ² _n - R ² ^ ) = Tr ( Sin ² 0 _n - Sin ² ^ = π ( Sin ² 0 ₂ - Sin ² ^ ) aS _a = 2ττZ ( l _a2 - l _al ) = 2rrZ . ώl _an .

( see Figure 12 )

After substitution and simplification, it can be shown that:

K _a = Sin ³ 20 (11)

4Z(Sin ³ 0-Z)

Figure 13 shows the graph of distribution of K _a (and P _a ) dependant on the distance 2 _a along the axis of the additional heat exchanger for two different diameters (2r) of the cylinder. The curve K _a1 (P _a1 ) is for the radius r, = 0.0125 (2r., = 0.474m) and the curve K _a2 (P _a2 ) is for r ₂ =0.018 (2r ₂ =0.684m) .

c

Figure 13 also shows the curves of distribution of temperatures (t °C) along the length of the additional heat exchanger, which is calculated by formula (8) on the supposition that there is no air flow in the heat exchanger and, on its surface (considered to be absolute black body), there is a balance between absorbed and transmitted energy. The curve t _a1 corresponds to r-=0.0125 and curve t _a2 corresponding to r ₂ =0.018.

These are the maximum possible theoretical temperatures on the surface of the additional heat exchanger. Obviously, with the air flow, they will decrease, which is essential in order to achieve a high value of efficiency.

The mirror

The parameters of a mirror-concentrator to be located on a South facing slope of Mount Aragtz, Armenia are as follows:

(latitude : +40°, altitude 1,800m, soklar constant K _s lkW/m ² , number of sunshine days per year, 300).

Type: spherical, completely unmoveable (fixed) Radius of sphere curvature: = 19m

R ₀ ⁼¹ )

Diameter of used aperture: (2R) 29.52m Radius of used aperture: (R) = 14.76m

(=0.777)

Coefficient of diameter in use: (R/R ₀ ) = 0.777

Coefficient of surface in use: (R ² /Ro ² = 0.604

Coefficient of diameter in use for main Heat exchanger: (Rm) = 0.6225

Used surface of aperture: (S _u ) = 685m ²

Aperture surface used by main Heat exchanger: (S _um ) = 440m ²

(64%)

Aperture surface used by addit. Heat exchanger: (S _ua ) = 245m ² Aperture angle (from centre of sphere): (0 _m ) = 51°

21

Efficiency (absorption, reflection/shadow): 85%

Heat output power: (P _h ) = 500kW

Electrical output power: (P _eL ) = 103kW

At the chosen location for the unit, the main axis of the mirror has to decline from the vertical by 40° to the South, so as to lie in the equator plane. During the year, the sun changes position from this direction by ±23°30'.

Figure 14 illustrates the mirror in the local meridian plane. Here the full aperture is given by {102°+(2x23°) } = 148°. This is sufficient so that the full used aperture is in operation during the entire year (except 30').

It is not necessary to build an entire hemisphere. It is possible to omit part of hemisphere in the direction along the main axis for the distance dictated by Sin 16° = 0.2756, (ie 5.24m). So the depth of the actual built mirror equals 0.7244 (=13.76m) .

Figure 15 illustrates the cross section of the mirror in the equator plane. If, in this plane, we make the same reduction based on the Sin 16° factor, then with the full aperture angle (used) the mirror will work for (±24°) ie lh hours each side of midday.

Outside this period, the used surface slowly decreases and, for angles of ±51° (±3hr 24 min each side of midday), we will have half the value of the used aperture.

For angles of ±75° (giving 5 hrs each side of midday, ie 10 hours per day), the used surface decreases by approximately a further 10% since some of the rays beyond ±51° will be screened by the edge of the mirror.

The surface of the full aperture of the built mirror with the given reduction is equal to

7T(Cosl6°) ² = 2.9 = 1048m ² .

The full surface of the built mirror area (curved) is equal to: = 2πRo ² ( ^N 1 - Sinl6°)' = 4.55Ro ² = 1643m ² .

Since the surface of the used aperture is equal to 685m ² , the CUS _o of aperture is equal to 685/1048 = 0.6536.

The surface of the mirror area (curved) inside the used aperture

S.u,-m,-r = 2πRo ² x 0.3705 = 845m ² .

So the total coefficient in use of the built mirror surface (curved) is equal S _umr /S _fmr = 845/1643 = 0.5143.

This means that, at any given moment of time, more than half of the surface of the built mirror is used (CUS = 0.5143). The remainder of the surface is used at other times.

However, as compensation for that, it must be recalled that the mirror is completely stationary which reduces the cost more than tenfold compared with moveable mirror systems having the same collecting area.

The dimensions of the mirror in the meridian plane are illustrated in Figure 16 and the total configuration of the proposed mirror is seen in Figure 17.

Figure 18 illustrates the geodesic map of the chosen site.

The average coefficient of concentration for the main heat exchanger K _aa is given by: ^κ _a a _m m = ^s „u _m m/' ^s u _m rn ^• = 440/'19.6 = 22.45

Thus P _am = 22.45kW/m ² The average coefficient of concentration for the additional heat exchanger K _aa , is:

^K aa - = 245 / 4 . 25

23

The mirror may be constructed from a large number of separate pieces with dimensions of 0.3m x 0.3m. Nine or twelve such pieces can be considered to make up one standard panel. The panels are set on the supporting structure with provision to adjust their inclination.

In the prototype mirror there will be more than 18,000 separate pieces making up about 2,000 panels. The reflecting pieces are made from polished metal (aluminium) or glass (typically of 5mm thickness) with the reverse side made reflective by a film of aluminium or silver together with a protective coating. The coeficient of reflection should be close to 0.9.

It is proposed that the supporting structure, tower and swinging arm are made from welded steel frames. Typically the control equipment is housed within this structure.

Figure 17 illustrates the arm in two extreme positions. The down position permits direct access from the tower to the heat exchangers, turbine and other equipment housed inside the arm.

The mounting system is of "azimuth - elevation" type (see Figure 17).

An automatic control system is included to target and track the sun. (Tracking is also achieved by photo-guide). The control equipment is preferably programmed to rapidly removel the heat exchanger from the focal point of the mirror in the event that the incoming flow of air to the heat exchanger fails.

The control system desks may be housed in one area and electrical transformers and high voltage equipment may be housed in a separate area.

In order to clean and wash the surface of the mirror, a pipework system conveys water around the upper perimeter of the mirror. Using warm water, it is also possible to clean away snow. Snow-

removal is not a major problem because, during winter, it tends to be the more vertical parts of the mirror which .are used to reflect the solar energy onto the heat exchangers.

A further embodiment of a heat exchanger in accordance with the invention is shown in Figure 21. In this embodiment the main surface 20 is similar to that previously decribed in connection with the embodiment of Figure 9 with an additional extension 22 to the upper part of the main surface which acts as a 'black body'. The extension 22 is preferably spherical although it may be cylindrical, conical or any other suitable shape. In such an embodiment the shape of the main working surface 20 may be described by the following equations:

x = Cos0 + wCos20 y = -Sinø - wSin20

W = 0.5 (2-2 +f-Cosfl, ² -l-f ² +2f+Cosfl 2 Cos0-f Cos20-(2-2:e+f)

The main surface is non-perpendicular to the rays coming from the mirror as it was in version described in connection with Figure 9. There will be further reflections from the main surface. But the reflected rays will go into the 'black body' and be absorbed there after further reflection.

For an extension 22 in the shape of a cylindrical tube, the power of the paraxial rays coming into the tube is about 40kw for a diameter of about 30cm (R = 0.2).

The paraxial rays will go directly to the 'black body'.

The main surface can be mirrored. But then the temperature in the 'black body' will be too high. So the solution is to make the surface absorbant ('black'). Then the reflected rays will be scattered but the main part of the energy will go into the 'black body'. The rest of the rays will be absorbed (secondary) by the main surface.

The temperature of the surface (and of the air flux) will increase from input to output.