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Shaping of large scale metal membrane concentrator
Solar&WmdTechnologyVol 4, No 3, pp 281-289,1987
0741-983X/87 $ 3 0 0 + 0 0 Pergamon Journals Ltd
Pnnted m Great Britain
SHAPING OF LARGE SCALE METAL M E M B R A N E CONCENTRATOR BAKR H. KHOSHAIM Solar Program Director, King Abdulazqz City for Science and Technology, P O Box 6086, Riyadh 11442, Saudl Arabia
(Recewed 15 February 1986, accepted 15 July 1986) Abstract--Efficient large-scale mirror membrane concentrators can be constructed with simple shaping techniques Those concentrators which use low cost materials would result m low cost concentrators The concentrator is extremely stable and resistant to external loads Fabrication can be done on site with low skilled labour Non-hnear finite element technique can be used to predetermine the shaping procedure and expected geometry
1. INTRODUCTION Solar c o n c e n t r a t o r s with high c o n c e n t r a t i o n capabilities for h i g h - t e m p e r a t u r e energy conversion require a defined reflector c o n t o u r o f high precision. Since 1976 a new m e t h o d of fabricating large concentrators has been developed by Schlalch a n d coworkers [1, 2]. In this new m e t h o d a precise large reflector c o n t o u r is provided virtually w h e n appropriate materials are used The large reflector is suspended a n d s u p p o r t e d o n
rails in such a way t h a t it can track the sun The reflector has a n energy converter, which converts the c o n c e n t r a t e d solar heat into electricity The energy conversion system consists o f a Stlrhng engine with a receiver located at the focal point o f the reflector. There xs a generator coupled directly to the engine to produce power Figure 1 shows the schematic diagram o f the concentrator. Such power plants with large reflector m e m b r a n e s are capable o f a n overall efficiency (defined as the ratio o f the o u t p u t usable electricity to the solar irradiation
~mbrankonzentrator : Dunnglassp~egel ~mbrane Concentrator th Glass M~rror erg~ewandler ergy Converter dverspannter Stutzbogen ble Stayed Support Frame ,'uerstand Jster Control
Fig I Schematic of the solar membrane concentrator 281
282
BAKR H KHOSHAIM
over the reflector surface) of up to 27%. This has never been achieved with other types of solar plants [3] The output of the energy converter depends on the accuracy of the beam path. The reflector membrane satisfies this requirement, though only simple technology is needed for its fabrication Two units of 17 m diameter metal membrane solar collectors have been constructed and are under extensive testing in Rlyadh, Saudl Arabia, under the joint Saudl-German Solar Program. This paper presents the theoretical basis and the practical techniques that have been employed to construct the most ~mportant part of the collector system l e. the membranes. Detailed system description and prehmlnary operatmnal results have been published earlier in [4, 5].
2. S I M U L A T I O N OF MEMBRANE SHAPING
BY FINITE ELEMENT CALCULATION 2 1 Definttton Pressure is applied to a thin metal membrane fitted into a reflector ring This pressure is increased until the thin sheet metal plastlclzes and takes on the shape of a spherical dome suitable for a solar concentrator The membrane can be prestretched before shaping; this allows for stretching or relaxing of pressure on the membranes dunng or after shaping. A final ring, 17 m m diameter, lies on the membrane. The membrane ~s permanently fixed to this ring after shaping After securing the upper rear membrane to the reflector rang, the glass mirror is stablhzed for operation by partial vacuum Pressure is reduced considerably by contmuous operation. The membrane then behaves elastically The numerical calculation is used to investigate a dome shape suitable for the beam path of the solar concentrator To do so the various phases of the shaping process, pressure rehef and continuous operatton, the rotational symmetry of which can be lnitmlly assumed, are simulated m a non-linear fimte element program
2 2 0 p t t m t z a t i o n of the structure F o r the purpose of numerical shaping the metal membrane is divided into 64 three-dimensional elements tangentially and into 24 three-dimensional elements radially (Fig 2) The stiffness of the reflector ring Is simulated by means of springs. As rotatlonally symmetric deformation behavlour is assumed, the calculation is conducted under appropriate conditions on a 1/64 spherical section. Between the surface of the actual reflector nngs (Ao) and the equivalent surface of the radially arranged spring (AR) the following relationship exists"
AR-
Iox2rcxAo 2 x 64ro
where ro " = the diameter of the reflector ring and I o. = the length of the radial spring 2 3 Descrtptton o f the calculatton method The problem was calculated by using the geometrically non-hnear finite-element program M A S L for membranes under tensxon as developed by Haug [6] and expanded by Oelbermann [7] The shaping pressure is increased m approximately 40 increments to approx. 1.0 N / c m 2 ; before each load step increase m pressure the state of e q u l h b n u m is determined. F o r the sake of better evaluation of mirror geometry under various load conditions, the beam path for ideally parallel hght was calculated and plotted. 2 4 Parameter studtes conducted Study 1. For the first study xt was assumed that the membrane fixed in the concrete ring was not prestretched The shaping pressure was raised to 1 05 N / c m 2 in increments of 0 03 N / c m 2 A dome height of 132 4 cm was attained After completion of shaping the pressure was lowered again to 0 1 N / c m 2 While plastic expansion in the membrane is irreversible, the
Fig 2 Optimization of the metal membrane for the fimte element calculation
Shaping of metal membrane concentrator elastic stretching is not, a n d the d o m e height thus decreases to 129 4 cm The shape thus p r o d u c e d deviates from the compensative sphere by a m a x i m u m of 0.5 cm (approx. 0.4% o f the d o m e height) (Fig. 3). The b e a m p a t h c o r r e s p o n d i n g to this shaping state is s h o w n in Fig. 4. Study 2 The m e m b r a n e was prestretched within the reinforced concrete ring by 2 % in all directions to b e y o n d the yield hmlt before shaping. Shaping to Pf = 1.15 N / c m 2 produces a d o m e height o f 123.1 cm. Subsequent lowering o f pressure to P, = 0.1 N / c m 2 causes the d o m e height to decrease to 119.6 cm. A t this p o i n t the rigid radial s u p p o r t is released a n d the radial spring, which is to simulate the final ring, IS activated. Thus, the d o m e height increases again to 120.7 cm. In Fig. 5 the b e a m p a t h for the m e m b r a n e w h e n fixed in the rigid concrete ring is s h o w n ; due to the c o n t r a c t i o n o f the flexible reflector ring the rays striking the o u t e r areas o f the m i r r o r also tend to reflect o n t o the receiver surface. Study 3. This study is a c o n t i n u a t i o n o f Study 2. In order to achieve a d o m e height o f 135 cm the m e m b r a n e , prestretched by 2 % , is loaded with a shaping pressure o f Pf = 1.27 N / c m 2. T h e developm e n t o f the d o m e rise is hsted in T a b l e 1. F o r reloading in the flexible reflector ring the beams for c o n t i n u o u s operating pressures o f P, = 0.1 N / c m 2 to Pz = 0.4 N / c m 2 show t h a t good c o n c e n t r a t i o n o n the receiver surface can be expected if operating pressure is m a i n t a i n e d at P, = 0 2 N / c m 2 It was for this reason t h a t the distributions o f intensity o n the receiver surface were determined, for focal lengths o f between 13 5 m a n d 14.5 m for pressure levels P, = 0.15 N / c m 2 a n d 0.25 N / c m 2. Study 4. This study is also based o n Study 2 The shaping pressure is raised to Pf = 1.32 N / c m 2 ; at this level the m e m b r a n e is then stretched over the radially
'
Fig 4 Beam path at
283
P, = 0 1 N/cm 2 (Study l)
a r r a n g e d springs by 5 cm W h e n pressure is reduced to P, -- 0 4 N / c m 2 the flexible reflector ring is introduced a n d loaded again to P, = 0.4 N / c m 2. The d e v e l o p m e n t o f the d o m e rise is s h o w n in Table 1 The c o r r e s p o n d i n g b e a m p a t h s are excellent. Study 5. In this study a m e m b r a n e in the shape o f a spherical d o m e with a radius of approx. 22 m was investigated W i t h this shape a n d radius the d o m e rise would be approx. 170 cm. Since the changed stressstrain relationship applied, the m e m b r a n e was again prestretched by 2 % a n d loaded up to PI = 2.06 N / c m 2, to achieve a d o m e height o f 173.0 cm. W i t h o u t increasing tension at the rim, the pressure o n the m e m b r a n e is reduced to Pz = 0 1 N / c m 2 as in Study 3. The memb r a n e is then fixed in the steel reflector ring a n d again loaded with service pressures o f u p to P, = 0 5 N / c m 2. Table 1 shows the d e v e l o p m e n t o f the d o m e rise following shaping
o'I''''
Fig. 3 (R = 2862 cm) Deviation from 1deal spherical surface
Fig 5 Beam path at P, = 0 1 N/cm 2, reflector ring =/10 (Study 2)
BAKR H KHOSHAIM
284
Table 1 Results of the study cases 3, 4 and 5 Study 3 height (cm) Shaping to 2 0 N/cm 2 Shaping to 1 32 N/cm 2 Shaping to 1 27 N/cm z Lowermg to 0 1 N/cm 2 Release at 0 1 N/cm z Reloading to P, = 0 15 =020 =025 = 0 30 = 0 35 =040 = 0 45
-134 43 131 12 131 99 132 47 13293 13338 133 82 134.26 13469 --
= 0 60
--
Study4 height (cm)
Study 5 height (cm)
-139 08
173 02
134 22 135 11
169 59 170 07
135 57 13601 13644 136 86 137 27 13768
170 36 17063 17090 171 17 171 43 17170 171 95 1 7 2 22
--
of tensile forces arising from pretension a n d forces from wind load, in this case "survival w i n d " of 160 k m / h velocity, produces no effective compression stresses All compressive strains are c o m p e n s a t e d by prior tensile pretenslonlng Hence, assuming difficult collector positions practically unaffected operation is assured at wind velocities of up to 50 km/h.
3 2 Temperature changes F o r the m e m b r a n e , the loads resulting from temperature changes in the housing interior a n d the natural changes in a t m o s p h e r i c air pressure also have to be t a k e n Into consideration Since the air in the conc e n t r a t o r housing represents a confined q u a n t i t y o f gas, the general gas e q u a t i o n m a y be applied
P'V T
The aim of the investigation with a radius of 22 m was to establish whether a c o n c e n t r a t o r with a receiver which can be swung d o w n w a r d s is also feasible A t this short focal distance the b e a m p a t h was almost ideal for open receiver designs but it was unsuitable for closed-type receivers.
3. CHARACTERISTICS
OF
METAL
MEMBRANE
P = absolute pressure (bar) V = air volume ( m 3) T = absolute t e m p e r a t u r e (K) Since the shape o f the m e m b r a n e a n d the relative v a c u u m must n o t change, c o m p e n s a t i o n must be effected by m e a n s o f the volume This means t h a t given a change in t e m p e r a t u r e from, e.g. 273 K to 313 K, a q u a n t i t y o f air equal to
3.1 Wmd loadm9 With a p p r o p r i a t e pretenslonlng, only tensile forces occur in the m e m b r a n e , regardless of loading: The pretensloning is ensured by a partial operating vacu u m in the interior of the c o n c e n t r a t o r housing ; this v a c u u m is so great (200 k p / m 2) t h a t even at wind velocities of u p to 160 k m / h compressive strains are prevented Symmetrical loads, e g. changes in pressure caused by changes in t e m p e r a t u r e or air pressure, can on the one h a n d easily be t a k e n up ( " m e m b r a n e c o m p a t i b l e " loading), o n the other h a n d they c a n also be c o m p e n s a t e d easily by regulating the partial vacuum The tensions in the m e m b r a n e as a result o f constant loading vertically to the m e m b r a n e surface, are equal in all directions In this context they can be calculated very simply using the m e m b r a n e theory equation
nx
p'r 2
ny.
With asymmetrical loads, e g. o b h q u e wind loads, the m e m b r a n e is d e f o r m e d in such a way t h a t equilibrium is achieved with m e m b r a n e forces only. It was possible to d e m o n s t r a t e t h a t these d e f o r m a t i o n s are so small that they do n o t affect the b e a m p a t h Overlapping
= constant
V = V2 -- Vi -
Ti " Vi
T2
Vt
313 K " 250 m 3 273 K
250 m 3 = 36 6 m 3
must be introduced into the c o n c e n t r a t o r housing Conversely this m e a n s t h a t when temperatures d r o p air m u s t be p u m p e d out The same applies to changes in a t m o s p h e r i c air pressure.
3 3 Circular frame The size of the circular f r a m e w o r k was chosen to enable it to discharge forces arising from the memb r a n e as n o r m a l forces by h o o p effect a n d to a b s o r b local disturbances t h r o u g h bending. 3.4 Dynamtc studws The simplified d y n a m i c investigation o f the conc e n t r a t o r system showed t h a t vibration caused by wind or the drive system is negligible. 3.5 Amsotropy of the sheet metal and weldm9 seams It IS i m p o r t a n t to achieve the greatest possible homogeneity and surface flatness at the outside there is flat elongation o f the m e m b r a n e by 2%. Deviations
Shaping of metal membrane concentrator caused by 4% can be reduced. Therefore, welding shrinkage along the seam can be eliminated. 4. M O D E L E X P E R I M E N T W I T H A 5 m DIAMETER METAL-MEMBRANE C O N C E N T R A T O R
A model experiment was performed at the DFVLR s]te m Lampoldshausen m order to simulate the fabncatlon of the 17 m metal-membrane concentrator. A reflector membrane was fabricated in accordance with the planned method of producing the 17 m metalmembrane concentrator - - T h e metal membrane was made up of sheet-metal strips 1 25 mm wide The fiat membrane was shaped by means of a partial vacuum ; not by applying pressure. --While the sheet-metal membrane was still fiat, ~t was plastically prestretched by 1%. During shaping the periphery of the sheet metal is held by the clamping jaws The measunng equipment comprises : --60 force-measuring tubes which were built into each stretching rod, and which indicate the distribution of the stretching force.
285
radial shift measuring points, all 90 °, at which the peripheral shifts of the sheet-metal membrane are measured. --1 height measurement at the centre of the membrane --1 manual pressure gauge. --1 electromc pressure gauge for measuring shaping pressure. strain gauge strip rosettes for determining the elongat]on of the sheet metal both meridlonally and circumferentlally --23 inclination meters, which were placed on the membrane at various cross-sections and which indicate the inclination of the mirror shape with an accuracy of 0.01 ° (Fig 6). The electromcally measured values were gathered in a central data processing system and were processed by special evaluation programs in such a way that accurate information was obtained.
Results o f the 5 m model experiment The best criterion for judging the membrane geometry is a comparison of the existing shape with a fitted paraboloid
5 = 225 s=O
cm
r = 193 c m
a = 208 9 = 240
5
:ion gauges
4 crn 8 7 .5 ii I<6 = ~16 R 7 = 2~()
Fig 6 Arrangement of the lnchnatlon meters
cm cm cm cm cm cm
cm
cm
at
286
BAKR H KHOSHAIM
The p a r a b o l o l d has a fixed focus in which all the light rays converge It thus guarantees t h a t the form of the focal spot will be rotationally symmetric a n d that the distribution of intensity will be u n i f o r m Some results out of 150 load strips for evaluation of various stages of shaping are presented an Table 2 They represent the shape of the m e m b r a n e at different shaping pressures. The calculated focal length at the respective stage of shaping for a fitted p a r a b o l a is also shown in the table; this was calculated by a linear regression covering all inclination measuring points The coefficient of correlation indicates in each case the deviation o f the actual geometry from a p a r a b o l a ; the geometry is better the closer the correlation coefficient a p p r o x i m a t e s to 1.0 It is evident from the table t h a t a favourable m e m b r a n e shape results even for a long focal length. The diameter o f the focal spot, which is hmited by the calculated tracer rays, is 11 2 cm in the x direction a n d 7.1 cm in the y direction It is evident from the table a n d the radiation diagrams t h a t the plastically shaped m e m b r a n e has a good, optically suitable form The m e a s u r e m e n t s showed a very good conformity with the calculations The possiblhtles o f influencing the shaping o f the m e m b r a n e are confirmed. The slight deviations from a rotationally symmetrical shape which occur in the b e a m paths m the x a n d y directions are due to variations in the rigidity of the material in the
tWO principal directions a n d in particular to the influence o f the welding seams
5. S H A P I N G OF T H E 17 M M E M B R A N E
5 1 The reflector shape and the mare parameters mfluencm9 it The shape of the reflector is created by a process k n o w n as "free f o r m i n g . " There are a great m a n y p a r a m e t e r s influencing the geometry a n d thus the b e a m p a t h The m a i n influencing parameters are : - - t h e m e m b r a n e material - - s t r e t c h i n g of the flat m e m b r a n e - - t h e internal pressure p - - p e r i p h e r a l plastic a n d elastic displacement r as affected by varying Internal pressures.
5.2 Shapmg procedure o f the membranes The shaping o f b o t h front m e m b r a n e s took place u n d e r real site conditions without the electrical m e a s u r e m e n t a n d control e q u i p m e n t t h a t was used in L a m p o l d s h a u s e n . The experiences o f the shaping procedure in L a m p o l d s h a u s e n a n d the following data evaluation h a d s h o w n t h a t it is possible to find out the exact reflector geometry on the basis of theoretical calculations a n d this is later verified by controlling some significant geometrical values during construction
Table 2 The membrane geometry at a shaping pressure of 28 9 m bar Shaping pressure 28 9 m bar Calc focal length 5406.88 cm
Hoght 3 4 cm Corr coeff 0 99693
Inclination (degrees)
Diff from stored parabola (degrees)
Section with calc focal length/height (cm)
x-axis 124 87 148 91 167 96 186 11 202 11 217 15 231 30
0 699 0 785 0 894 0 997 1 083 1 129 1 226
0 0149 --0 0195 --0 0060 0 0063 0 0122 --0 0173 0 0093
- 7 047 0.776 --0.719 --2 032 --2 252 4 143 0 092
y-axis 125 04 148 93 168 01 186 09 202 13 217 17 231 32
0 642 0 773 0.905 1.003 1 060 1 157 1 214
--0 0110 --0 0087 0 0197 0 0191 --0 0105 0 0054 --0 0140
3 939 2 959 --2 832 --3 134 2 096 --1 248 2 092
Radius (cm)
S h a p i n g o f metal m e m b r a n e c o n c e n t r a t o r
287
160 140
× Shaping
E
KI
ShapingKII --CaLcuLated
120 .I0
~oo
J
~
,,.~ .~.~%
o.
8° ~
60
~_
40 2O
20
40
60
80
too
f20
140
Domeheightf[cm] Fig 7 D o m e height o f m e m b r a n e m relation to the air pressure.
The process of shaping took place according to these precalculated steps. For controlling the membrane geometry the following values were measured at the site : --air pressure ~ o m e height of membrane ~ l s p l a c e m e n t s of membrane edge --hydraulic pressure of the jacks. For every step the measured geometrical values were compared with the calculated figures
Figure 7 shows the dome height of the reflector in relation to the air pressure The specified final dome height is 1.32 m. Figure 8 shows the focal length of the reflector front membrane in relanon to the air pressure During the shaping procedure it was very ~mportant to know the focal length at every step to make sure that the final focal length at operation pressure would be in the range between 13.5 m and 14.5 m Some diagrams were prepared in order to find the desired focal length depending on the actual air pressure and dome height
\×~ \\\\~
17
?
_-~_CaLcuLated ---- Measured
16
\\ '~
flO 15 ¢:
g d 13
12
0
I 20
I 40
I
I
I
60
80
IO0
Airpressure
I r20
p rmbar'l
Fig 8 F o c a l length d e p e n d i n g o n the air pressure
I 140
288
BAKR H KHOSHAIM
which could b o t h be measured. Figure 8 shows t h a t the final focal length at a n o p e r a t i o n a l pressure of 20 m b a r is m the expected range. According to experiences with the shaping procedure In L a m p o l d s h a u s e n we decided to fix the memb r a n e to the c o n c e n t r a t o r rang immediately after prestretching the plane m e m b r a n e to avoid uncontrolled &splacements o f the m e m b r a n e edges. The evaluation of the results from L a m p o l d s h a u s e n as well as the calculations h a d s h o w n that even m i n o r displacements of the edge resulted in considerable changes o f the reflector shape With these m e a n s we tried to eliminate the negative influence of the non-
Fig 9 3-D plot of intensity &strlbut~on in the focal plane w~th partly covered concentrator
uniformity of the hydraulic jack pressure o n the reflector geometry
5 3 Stretchmyfront and rear membrane The m e m b r a n e was m a d e o f individual sheet strips 1 25 m wide a n d 0.5 m m thick welded together in the same place with a special welding machine F o r stretching the sheet different forces should be applied - - S t r e t c h i n g the welded sheet surface after connecting the clamping jaws by a pressure up to 30 b a r - - I n c r e a s e the pressure to 1 l0 b a r
- - F i n a l l y mcrease the pressure to 250 bar to assure 1% elongation W h e n m o u n t i n g rear a n d front m e m b r a n e on the housing the welding lines should be perpendicular to each other. 5.4 Steps o f shapin9 procedure are shown in Table 3. 5.5 Measurement o f the focal pomt Figure 9 shows the 3-D plots including the c o n t o u r lines for the covered concentrator. It goes w i t h o u t saying t h a t the focal point shows a splendid symmetry
Table 3 Steps of shaping procedure
No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Shapmg air pressure (m bar) 0 5 10 20 40 60 90 100 104 105 113 115 118 119 100 70 60 4 59 4 40 30 20 20 20
Dome height (cm)
Stretching hydrauhc pressure (bar)
18 10 8 20 8 40 6 50 7 74 4 104 1 114 7 117 8 119 3 125 6 128 3 130 9 133 0 131 9 130 3 129 7 119 5 129 7 129 0 128 3 128 4 130 2
245 248 249 257 258 260 267 268 270 270 270 270 270 270 241 212 189 173 150 131 120 100 0
6. CONCLUSIONS Large scale solar c o n c e n t r a t o r s with high concentratlon capabdity for higher t e m p e r a t u r e energy conversions can be o b t a i n e d using the geometrically non-linear finite-element techniques Using the results a n d applying the stretching/deforming techniques would result in a very favourable m e m b r a n e shape t h a t has a good focal p o i n t distribution a n d a better radiation distribution o n the receiver
Acknowledgements--The author would hke to thank the Sau&-German Program for Solar Apphcatlons for supporting this project Thanks are due to Professor J Schlalch Thanks are also due to the persons looking after the system operations vlz, Mr Benz, Mr A1-Ajaml and Dr Kalt
REFERENCES
1 J Schlalch and Partner, 50 kW Solar Concentrator with Stlrhng Engine, Proposal for the Joint Sau& ArabianGerman ProJect Solar Energy (1982) 2 J Schlalch and S Gremer, Vorgespannte Flachentragwerke aus Metallmembranen Baumgemeur 53 (1978) 3 Saudl-47Jerman Solar Energy Cooperahon, 50 kW solar
Shaping of metal membrane concentrator farm with a large scale concentrator Preliminary Design Report (September 1982) 4 B H Khoshatm, 50 kW Solar Membrane Concentrator, Proceedings of the First Arab International Solar Energy Conference, Kuwait, 2-8 December 1983 Pergamon Press, Oxford 5 B H. Khoshalm, Performance Characteristics of Solar Membrane Concentrators, Solar Energy Prospects m the
289
Arab World, Second Arab International Conference, Bahrain, 15-21 February 1986 Pergamon Press, Oxford 6 E Haug, Finite Element Analysis of Non-linear Structures, University of Cahforma, Berkeley, Report No UCSESM 72 7, Berkeley, U.S A (1972) 7 J Oelbermann, Trag- und Verformungsverhalten Plastlsch geformter Metallmembran-Konstruktlonen, Dissertation Unlversitht Essen-GH, Essen (1982)
0741-983X/87 $ 3 0 0 + 0 0 Pergamon Journals Ltd
Pnnted m Great Britain
SHAPING OF LARGE SCALE METAL M E M B R A N E CONCENTRATOR BAKR H. KHOSHAIM Solar Program Director, King Abdulazqz City for Science and Technology, P O Box 6086, Riyadh 11442, Saudl Arabia
(Recewed 15 February 1986, accepted 15 July 1986) Abstract--Efficient large-scale mirror membrane concentrators can be constructed with simple shaping techniques Those concentrators which use low cost materials would result m low cost concentrators The concentrator is extremely stable and resistant to external loads Fabrication can be done on site with low skilled labour Non-hnear finite element technique can be used to predetermine the shaping procedure and expected geometry
1. INTRODUCTION Solar c o n c e n t r a t o r s with high c o n c e n t r a t i o n capabilities for h i g h - t e m p e r a t u r e energy conversion require a defined reflector c o n t o u r o f high precision. Since 1976 a new m e t h o d of fabricating large concentrators has been developed by Schlalch a n d coworkers [1, 2]. In this new m e t h o d a precise large reflector c o n t o u r is provided virtually w h e n appropriate materials are used The large reflector is suspended a n d s u p p o r t e d o n
rails in such a way t h a t it can track the sun The reflector has a n energy converter, which converts the c o n c e n t r a t e d solar heat into electricity The energy conversion system consists o f a Stlrhng engine with a receiver located at the focal point o f the reflector. There xs a generator coupled directly to the engine to produce power Figure 1 shows the schematic diagram o f the concentrator. Such power plants with large reflector m e m b r a n e s are capable o f a n overall efficiency (defined as the ratio o f the o u t p u t usable electricity to the solar irradiation
~mbrankonzentrator : Dunnglassp~egel ~mbrane Concentrator th Glass M~rror erg~ewandler ergy Converter dverspannter Stutzbogen ble Stayed Support Frame ,'uerstand Jster Control
Fig I Schematic of the solar membrane concentrator 281
282
BAKR H KHOSHAIM
over the reflector surface) of up to 27%. This has never been achieved with other types of solar plants [3] The output of the energy converter depends on the accuracy of the beam path. The reflector membrane satisfies this requirement, though only simple technology is needed for its fabrication Two units of 17 m diameter metal membrane solar collectors have been constructed and are under extensive testing in Rlyadh, Saudl Arabia, under the joint Saudl-German Solar Program. This paper presents the theoretical basis and the practical techniques that have been employed to construct the most ~mportant part of the collector system l e. the membranes. Detailed system description and prehmlnary operatmnal results have been published earlier in [4, 5].
2. S I M U L A T I O N OF MEMBRANE SHAPING
BY FINITE ELEMENT CALCULATION 2 1 Definttton Pressure is applied to a thin metal membrane fitted into a reflector ring This pressure is increased until the thin sheet metal plastlclzes and takes on the shape of a spherical dome suitable for a solar concentrator The membrane can be prestretched before shaping; this allows for stretching or relaxing of pressure on the membranes dunng or after shaping. A final ring, 17 m m diameter, lies on the membrane. The membrane ~s permanently fixed to this ring after shaping After securing the upper rear membrane to the reflector rang, the glass mirror is stablhzed for operation by partial vacuum Pressure is reduced considerably by contmuous operation. The membrane then behaves elastically The numerical calculation is used to investigate a dome shape suitable for the beam path of the solar concentrator To do so the various phases of the shaping process, pressure rehef and continuous operatton, the rotational symmetry of which can be lnitmlly assumed, are simulated m a non-linear fimte element program
2 2 0 p t t m t z a t i o n of the structure F o r the purpose of numerical shaping the metal membrane is divided into 64 three-dimensional elements tangentially and into 24 three-dimensional elements radially (Fig 2) The stiffness of the reflector ring Is simulated by means of springs. As rotatlonally symmetric deformation behavlour is assumed, the calculation is conducted under appropriate conditions on a 1/64 spherical section. Between the surface of the actual reflector nngs (Ao) and the equivalent surface of the radially arranged spring (AR) the following relationship exists"
AR-
Iox2rcxAo 2 x 64ro
where ro " = the diameter of the reflector ring and I o. = the length of the radial spring 2 3 Descrtptton o f the calculatton method The problem was calculated by using the geometrically non-hnear finite-element program M A S L for membranes under tensxon as developed by Haug [6] and expanded by Oelbermann [7] The shaping pressure is increased m approximately 40 increments to approx. 1.0 N / c m 2 ; before each load step increase m pressure the state of e q u l h b n u m is determined. F o r the sake of better evaluation of mirror geometry under various load conditions, the beam path for ideally parallel hght was calculated and plotted. 2 4 Parameter studtes conducted Study 1. For the first study xt was assumed that the membrane fixed in the concrete ring was not prestretched The shaping pressure was raised to 1 05 N / c m 2 in increments of 0 03 N / c m 2 A dome height of 132 4 cm was attained After completion of shaping the pressure was lowered again to 0 1 N / c m 2 While plastic expansion in the membrane is irreversible, the
Fig 2 Optimization of the metal membrane for the fimte element calculation
Shaping of metal membrane concentrator elastic stretching is not, a n d the d o m e height thus decreases to 129 4 cm The shape thus p r o d u c e d deviates from the compensative sphere by a m a x i m u m of 0.5 cm (approx. 0.4% o f the d o m e height) (Fig. 3). The b e a m p a t h c o r r e s p o n d i n g to this shaping state is s h o w n in Fig. 4. Study 2 The m e m b r a n e was prestretched within the reinforced concrete ring by 2 % in all directions to b e y o n d the yield hmlt before shaping. Shaping to Pf = 1.15 N / c m 2 produces a d o m e height o f 123.1 cm. Subsequent lowering o f pressure to P, = 0.1 N / c m 2 causes the d o m e height to decrease to 119.6 cm. A t this p o i n t the rigid radial s u p p o r t is released a n d the radial spring, which is to simulate the final ring, IS activated. Thus, the d o m e height increases again to 120.7 cm. In Fig. 5 the b e a m p a t h for the m e m b r a n e w h e n fixed in the rigid concrete ring is s h o w n ; due to the c o n t r a c t i o n o f the flexible reflector ring the rays striking the o u t e r areas o f the m i r r o r also tend to reflect o n t o the receiver surface. Study 3. This study is a c o n t i n u a t i o n o f Study 2. In order to achieve a d o m e height o f 135 cm the m e m b r a n e , prestretched by 2 % , is loaded with a shaping pressure o f Pf = 1.27 N / c m 2. T h e developm e n t o f the d o m e rise is hsted in T a b l e 1. F o r reloading in the flexible reflector ring the beams for c o n t i n u o u s operating pressures o f P, = 0.1 N / c m 2 to Pz = 0.4 N / c m 2 show t h a t good c o n c e n t r a t i o n o n the receiver surface can be expected if operating pressure is m a i n t a i n e d at P, = 0 2 N / c m 2 It was for this reason t h a t the distributions o f intensity o n the receiver surface were determined, for focal lengths o f between 13 5 m a n d 14.5 m for pressure levels P, = 0.15 N / c m 2 a n d 0.25 N / c m 2. Study 4. This study is also based o n Study 2 The shaping pressure is raised to Pf = 1.32 N / c m 2 ; at this level the m e m b r a n e is then stretched over the radially
'
Fig 4 Beam path at
283
P, = 0 1 N/cm 2 (Study l)
a r r a n g e d springs by 5 cm W h e n pressure is reduced to P, -- 0 4 N / c m 2 the flexible reflector ring is introduced a n d loaded again to P, = 0.4 N / c m 2. The d e v e l o p m e n t o f the d o m e rise is s h o w n in Table 1 The c o r r e s p o n d i n g b e a m p a t h s are excellent. Study 5. In this study a m e m b r a n e in the shape o f a spherical d o m e with a radius of approx. 22 m was investigated W i t h this shape a n d radius the d o m e rise would be approx. 170 cm. Since the changed stressstrain relationship applied, the m e m b r a n e was again prestretched by 2 % a n d loaded up to PI = 2.06 N / c m 2, to achieve a d o m e height o f 173.0 cm. W i t h o u t increasing tension at the rim, the pressure o n the m e m b r a n e is reduced to Pz = 0 1 N / c m 2 as in Study 3. The memb r a n e is then fixed in the steel reflector ring a n d again loaded with service pressures o f u p to P, = 0 5 N / c m 2. Table 1 shows the d e v e l o p m e n t o f the d o m e rise following shaping
o'I''''
Fig. 3 (R = 2862 cm) Deviation from 1deal spherical surface
Fig 5 Beam path at P, = 0 1 N/cm 2, reflector ring =/10 (Study 2)
BAKR H KHOSHAIM
284
Table 1 Results of the study cases 3, 4 and 5 Study 3 height (cm) Shaping to 2 0 N/cm 2 Shaping to 1 32 N/cm 2 Shaping to 1 27 N/cm z Lowermg to 0 1 N/cm 2 Release at 0 1 N/cm z Reloading to P, = 0 15 =020 =025 = 0 30 = 0 35 =040 = 0 45
-134 43 131 12 131 99 132 47 13293 13338 133 82 134.26 13469 --
= 0 60
--
Study4 height (cm)
Study 5 height (cm)
-139 08
173 02
134 22 135 11
169 59 170 07
135 57 13601 13644 136 86 137 27 13768
170 36 17063 17090 171 17 171 43 17170 171 95 1 7 2 22
--
of tensile forces arising from pretension a n d forces from wind load, in this case "survival w i n d " of 160 k m / h velocity, produces no effective compression stresses All compressive strains are c o m p e n s a t e d by prior tensile pretenslonlng Hence, assuming difficult collector positions practically unaffected operation is assured at wind velocities of up to 50 km/h.
3 2 Temperature changes F o r the m e m b r a n e , the loads resulting from temperature changes in the housing interior a n d the natural changes in a t m o s p h e r i c air pressure also have to be t a k e n Into consideration Since the air in the conc e n t r a t o r housing represents a confined q u a n t i t y o f gas, the general gas e q u a t i o n m a y be applied
P'V T
The aim of the investigation with a radius of 22 m was to establish whether a c o n c e n t r a t o r with a receiver which can be swung d o w n w a r d s is also feasible A t this short focal distance the b e a m p a t h was almost ideal for open receiver designs but it was unsuitable for closed-type receivers.
3. CHARACTERISTICS
OF
METAL
MEMBRANE
P = absolute pressure (bar) V = air volume ( m 3) T = absolute t e m p e r a t u r e (K) Since the shape o f the m e m b r a n e a n d the relative v a c u u m must n o t change, c o m p e n s a t i o n must be effected by m e a n s o f the volume This means t h a t given a change in t e m p e r a t u r e from, e.g. 273 K to 313 K, a q u a n t i t y o f air equal to
3.1 Wmd loadm9 With a p p r o p r i a t e pretenslonlng, only tensile forces occur in the m e m b r a n e , regardless of loading: The pretensloning is ensured by a partial operating vacu u m in the interior of the c o n c e n t r a t o r housing ; this v a c u u m is so great (200 k p / m 2) t h a t even at wind velocities of u p to 160 k m / h compressive strains are prevented Symmetrical loads, e g. changes in pressure caused by changes in t e m p e r a t u r e or air pressure, can on the one h a n d easily be t a k e n up ( " m e m b r a n e c o m p a t i b l e " loading), o n the other h a n d they c a n also be c o m p e n s a t e d easily by regulating the partial vacuum The tensions in the m e m b r a n e as a result o f constant loading vertically to the m e m b r a n e surface, are equal in all directions In this context they can be calculated very simply using the m e m b r a n e theory equation
nx
p'r 2
ny.
With asymmetrical loads, e g. o b h q u e wind loads, the m e m b r a n e is d e f o r m e d in such a way t h a t equilibrium is achieved with m e m b r a n e forces only. It was possible to d e m o n s t r a t e t h a t these d e f o r m a t i o n s are so small that they do n o t affect the b e a m p a t h Overlapping
= constant
V = V2 -- Vi -
Ti " Vi
T2
Vt
313 K " 250 m 3 273 K
250 m 3 = 36 6 m 3
must be introduced into the c o n c e n t r a t o r housing Conversely this m e a n s t h a t when temperatures d r o p air m u s t be p u m p e d out The same applies to changes in a t m o s p h e r i c air pressure.
3 3 Circular frame The size of the circular f r a m e w o r k was chosen to enable it to discharge forces arising from the memb r a n e as n o r m a l forces by h o o p effect a n d to a b s o r b local disturbances t h r o u g h bending. 3.4 Dynamtc studws The simplified d y n a m i c investigation o f the conc e n t r a t o r system showed t h a t vibration caused by wind or the drive system is negligible. 3.5 Amsotropy of the sheet metal and weldm9 seams It IS i m p o r t a n t to achieve the greatest possible homogeneity and surface flatness at the outside there is flat elongation o f the m e m b r a n e by 2%. Deviations
Shaping of metal membrane concentrator caused by 4% can be reduced. Therefore, welding shrinkage along the seam can be eliminated. 4. M O D E L E X P E R I M E N T W I T H A 5 m DIAMETER METAL-MEMBRANE C O N C E N T R A T O R
A model experiment was performed at the DFVLR s]te m Lampoldshausen m order to simulate the fabncatlon of the 17 m metal-membrane concentrator. A reflector membrane was fabricated in accordance with the planned method of producing the 17 m metalmembrane concentrator - - T h e metal membrane was made up of sheet-metal strips 1 25 mm wide The fiat membrane was shaped by means of a partial vacuum ; not by applying pressure. --While the sheet-metal membrane was still fiat, ~t was plastically prestretched by 1%. During shaping the periphery of the sheet metal is held by the clamping jaws The measunng equipment comprises : --60 force-measuring tubes which were built into each stretching rod, and which indicate the distribution of the stretching force.
285
radial shift measuring points, all 90 °, at which the peripheral shifts of the sheet-metal membrane are measured. --1 height measurement at the centre of the membrane --1 manual pressure gauge. --1 electromc pressure gauge for measuring shaping pressure. strain gauge strip rosettes for determining the elongat]on of the sheet metal both meridlonally and circumferentlally --23 inclination meters, which were placed on the membrane at various cross-sections and which indicate the inclination of the mirror shape with an accuracy of 0.01 ° (Fig 6). The electromcally measured values were gathered in a central data processing system and were processed by special evaluation programs in such a way that accurate information was obtained.
Results o f the 5 m model experiment The best criterion for judging the membrane geometry is a comparison of the existing shape with a fitted paraboloid
5 = 225 s=O
cm
r = 193 c m
a = 208 9 = 240
5
:ion gauges
4 crn 8 7 .5 ii I<6 = ~16 R 7 = 2~()
Fig 6 Arrangement of the lnchnatlon meters
cm cm cm cm cm cm
cm
cm
at
286
BAKR H KHOSHAIM
The p a r a b o l o l d has a fixed focus in which all the light rays converge It thus guarantees t h a t the form of the focal spot will be rotationally symmetric a n d that the distribution of intensity will be u n i f o r m Some results out of 150 load strips for evaluation of various stages of shaping are presented an Table 2 They represent the shape of the m e m b r a n e at different shaping pressures. The calculated focal length at the respective stage of shaping for a fitted p a r a b o l a is also shown in the table; this was calculated by a linear regression covering all inclination measuring points The coefficient of correlation indicates in each case the deviation o f the actual geometry from a p a r a b o l a ; the geometry is better the closer the correlation coefficient a p p r o x i m a t e s to 1.0 It is evident from the table t h a t a favourable m e m b r a n e shape results even for a long focal length. The diameter o f the focal spot, which is hmited by the calculated tracer rays, is 11 2 cm in the x direction a n d 7.1 cm in the y direction It is evident from the table a n d the radiation diagrams t h a t the plastically shaped m e m b r a n e has a good, optically suitable form The m e a s u r e m e n t s showed a very good conformity with the calculations The possiblhtles o f influencing the shaping o f the m e m b r a n e are confirmed. The slight deviations from a rotationally symmetrical shape which occur in the b e a m paths m the x a n d y directions are due to variations in the rigidity of the material in the
tWO principal directions a n d in particular to the influence o f the welding seams
5. S H A P I N G OF T H E 17 M M E M B R A N E
5 1 The reflector shape and the mare parameters mfluencm9 it The shape of the reflector is created by a process k n o w n as "free f o r m i n g . " There are a great m a n y p a r a m e t e r s influencing the geometry a n d thus the b e a m p a t h The m a i n influencing parameters are : - - t h e m e m b r a n e material - - s t r e t c h i n g of the flat m e m b r a n e - - t h e internal pressure p - - p e r i p h e r a l plastic a n d elastic displacement r as affected by varying Internal pressures.
5.2 Shapmg procedure o f the membranes The shaping o f b o t h front m e m b r a n e s took place u n d e r real site conditions without the electrical m e a s u r e m e n t a n d control e q u i p m e n t t h a t was used in L a m p o l d s h a u s e n . The experiences o f the shaping procedure in L a m p o l d s h a u s e n a n d the following data evaluation h a d s h o w n t h a t it is possible to find out the exact reflector geometry on the basis of theoretical calculations a n d this is later verified by controlling some significant geometrical values during construction
Table 2 The membrane geometry at a shaping pressure of 28 9 m bar Shaping pressure 28 9 m bar Calc focal length 5406.88 cm
Hoght 3 4 cm Corr coeff 0 99693
Inclination (degrees)
Diff from stored parabola (degrees)
Section with calc focal length/height (cm)
x-axis 124 87 148 91 167 96 186 11 202 11 217 15 231 30
0 699 0 785 0 894 0 997 1 083 1 129 1 226
0 0149 --0 0195 --0 0060 0 0063 0 0122 --0 0173 0 0093
- 7 047 0.776 --0.719 --2 032 --2 252 4 143 0 092
y-axis 125 04 148 93 168 01 186 09 202 13 217 17 231 32
0 642 0 773 0.905 1.003 1 060 1 157 1 214
--0 0110 --0 0087 0 0197 0 0191 --0 0105 0 0054 --0 0140
3 939 2 959 --2 832 --3 134 2 096 --1 248 2 092
Radius (cm)
S h a p i n g o f metal m e m b r a n e c o n c e n t r a t o r
287
160 140
× Shaping
E
KI
ShapingKII --CaLcuLated
120 .I0
~oo
J
~
,,.~ .~.~%
o.
8° ~
60
~_
40 2O
20
40
60
80
too
f20
140
Domeheightf[cm] Fig 7 D o m e height o f m e m b r a n e m relation to the air pressure.
The process of shaping took place according to these precalculated steps. For controlling the membrane geometry the following values were measured at the site : --air pressure ~ o m e height of membrane ~ l s p l a c e m e n t s of membrane edge --hydraulic pressure of the jacks. For every step the measured geometrical values were compared with the calculated figures
Figure 7 shows the dome height of the reflector in relation to the air pressure The specified final dome height is 1.32 m. Figure 8 shows the focal length of the reflector front membrane in relanon to the air pressure During the shaping procedure it was very ~mportant to know the focal length at every step to make sure that the final focal length at operation pressure would be in the range between 13.5 m and 14.5 m Some diagrams were prepared in order to find the desired focal length depending on the actual air pressure and dome height
\×~ \\\\~
17
?
_-~_CaLcuLated ---- Measured
16
\\ '~
flO 15 ¢:
g d 13
12
0
I 20
I 40
I
I
I
60
80
IO0
Airpressure
I r20
p rmbar'l
Fig 8 F o c a l length d e p e n d i n g o n the air pressure
I 140
288
BAKR H KHOSHAIM
which could b o t h be measured. Figure 8 shows t h a t the final focal length at a n o p e r a t i o n a l pressure of 20 m b a r is m the expected range. According to experiences with the shaping procedure In L a m p o l d s h a u s e n we decided to fix the memb r a n e to the c o n c e n t r a t o r rang immediately after prestretching the plane m e m b r a n e to avoid uncontrolled &splacements o f the m e m b r a n e edges. The evaluation of the results from L a m p o l d s h a u s e n as well as the calculations h a d s h o w n that even m i n o r displacements of the edge resulted in considerable changes o f the reflector shape With these m e a n s we tried to eliminate the negative influence of the non-
Fig 9 3-D plot of intensity &strlbut~on in the focal plane w~th partly covered concentrator
uniformity of the hydraulic jack pressure o n the reflector geometry
5 3 Stretchmyfront and rear membrane The m e m b r a n e was m a d e o f individual sheet strips 1 25 m wide a n d 0.5 m m thick welded together in the same place with a special welding machine F o r stretching the sheet different forces should be applied - - S t r e t c h i n g the welded sheet surface after connecting the clamping jaws by a pressure up to 30 b a r - - I n c r e a s e the pressure to 1 l0 b a r
- - F i n a l l y mcrease the pressure to 250 bar to assure 1% elongation W h e n m o u n t i n g rear a n d front m e m b r a n e on the housing the welding lines should be perpendicular to each other. 5.4 Steps o f shapin9 procedure are shown in Table 3. 5.5 Measurement o f the focal pomt Figure 9 shows the 3-D plots including the c o n t o u r lines for the covered concentrator. It goes w i t h o u t saying t h a t the focal point shows a splendid symmetry
Table 3 Steps of shaping procedure
No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Shapmg air pressure (m bar) 0 5 10 20 40 60 90 100 104 105 113 115 118 119 100 70 60 4 59 4 40 30 20 20 20
Dome height (cm)
Stretching hydrauhc pressure (bar)
18 10 8 20 8 40 6 50 7 74 4 104 1 114 7 117 8 119 3 125 6 128 3 130 9 133 0 131 9 130 3 129 7 119 5 129 7 129 0 128 3 128 4 130 2
245 248 249 257 258 260 267 268 270 270 270 270 270 270 241 212 189 173 150 131 120 100 0
6. CONCLUSIONS Large scale solar c o n c e n t r a t o r s with high concentratlon capabdity for higher t e m p e r a t u r e energy conversions can be o b t a i n e d using the geometrically non-linear finite-element techniques Using the results a n d applying the stretching/deforming techniques would result in a very favourable m e m b r a n e shape t h a t has a good focal p o i n t distribution a n d a better radiation distribution o n the receiver
Acknowledgements--The author would hke to thank the Sau&-German Program for Solar Apphcatlons for supporting this project Thanks are due to Professor J Schlalch Thanks are also due to the persons looking after the system operations vlz, Mr Benz, Mr A1-Ajaml and Dr Kalt
REFERENCES
1 J Schlalch and Partner, 50 kW Solar Concentrator with Stlrhng Engine, Proposal for the Joint Sau& ArabianGerman ProJect Solar Energy (1982) 2 J Schlalch and S Gremer, Vorgespannte Flachentragwerke aus Metallmembranen Baumgemeur 53 (1978) 3 Saudl-47Jerman Solar Energy Cooperahon, 50 kW solar
Shaping of metal membrane concentrator farm with a large scale concentrator Preliminary Design Report (September 1982) 4 B H Khoshatm, 50 kW Solar Membrane Concentrator, Proceedings of the First Arab International Solar Energy Conference, Kuwait, 2-8 December 1983 Pergamon Press, Oxford 5 B H. Khoshalm, Performance Characteristics of Solar Membrane Concentrators, Solar Energy Prospects m the
289
Arab World, Second Arab International Conference, Bahrain, 15-21 February 1986 Pergamon Press, Oxford 6 E Haug, Finite Element Analysis of Non-linear Structures, University of Cahforma, Berkeley, Report No UCSESM 72 7, Berkeley, U.S A (1972) 7 J Oelbermann, Trag- und Verformungsverhalten Plastlsch geformter Metallmembran-Konstruktlonen, Dissertation Unlversitht Essen-GH, Essen (1982)