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DOI: http://dx.doi.org/10.20534/ESR-17-1.2-201-203
Kuchkarov Akmaljon Axmadaliyevich, senior scientist, Institute of materials science, Uzbekistan Academy of sciences E-mail: ims-79@mail.ru Holov Sharifboy Ruzimatovich, research assistant, Institute of materials science, Uzbekistan Academy of sciences E-mail: maqsadbek79@mail.ru Abdumuminov Abdumaruf, research assistant, Institute of materials science, Uzbekistan Academyof sciences E-mail: fayz@bk.ru Abdurakhmanov Abdujabbar, doctor tech. sciences, Institute of materials science, Uzbekistan Academy of sciences E-mail: aabdujabbar46@mail.ru
Calculation of optical-geometrical characteristics of parabolic-cylindrical mirror concentrating systems
Abstract: The paper identifies the main optical and geometric characteristics of parabolic-cylindrical mirror concentrating systems (MCSs) of energy purposes, taking into account the characteristics of attainable manufacturing modern MCS.
Keywords: mirror concentrating systems, parabolic-cylindrical, concentrator, focus, optical power parameters.
It is known that the solar concentrators are constructed on the basis of composite reflective elements — facets. The geometry of the concentrator to the spot of is a parabolic and for linear focus — parabolic -cylindrical. The geometry of the facets may differ from the estimated concentrator's geometry. Introduction to the geometric method of concentrator inaccuracies reduces the problem of calculating faceted concentrator to the calculation of solid MCS. In addition to the energy-power devices MCS provides the highest efficiency of solar energy conversion. Therefore, the calculation of optical-geometrical parameters parabolic-cylindrical concentrators, as well as to determine the optimal size of radial surface of the receiver is an actual problem [1-3].
The degree of concentration optimal MCS values for converting solar energy into other forms of energy used in practical computed as follows.
To calculate the energy distribution in the focal zone parabolic-cylindrical MCS trajectory of the incident and reflected rays of the Sun is seen as a set of countless individual elementary beams based on the vertices of the point system reflecting surface. These sunlight beams having an elliptical cone shape, called elementary mappings. The rays, which are on the outer surface of the cone, called marginal rays and the angle between the two — the angular size of the unit display. Thus, the elementary display size depends on the size of the solar disk, the actual distance to the sun, that is, the visible angular size (Earth 2y0= 32 'arc min.) As well as the reflectivity, manufacturing precision reflector geometry and in aggregate form Sun's image. Real image dimensions are different from Rc and determined based on Figure 1.
Dimensions ofreal spots scattering parabolic-cylindrical MCS.
Section 12. Technical sciences
Figure 1. Formation of size and spot scattering density of parabolic-cylindrical MCS. Table. - The sires of the real spot dissipation are defined as follows:
for accurate concentrator parabolic-cylindrical form
r0 = ftgYo, r2 = f (1 + tg2 U^)tgy0,
f 1+tg
U
tgYo
1 - tg2 U + 2tgU tgYo
f 1 + tg
U
tgYo
1 - tg2 U - 2tgU- tgYo'
where, f — focus distance, r0, r2, r3, r4 — single dimension obtained in the focal plane ofthe solar image cone, U0 — angle concentrator disclosure, f — focal length, M — outermost point ofthe elementary section concentrating mirror-surface, j0—half apparent angular size of the Sun (often in the literature indicate that the value of p0), rc — range forms an image in the focal plane around, Aa — the rms manufacturing errors.
The optimum size of the focal spot parabolic-cylindrical MCS (d = 2r ) is determined on the basis of expression r obtained
* opt 4opt' r 4opt
above.
- t 2 U t tgY(1 + tg2U t)
_ opt _ f/-, ,2 opt N 6/ y <S opt^
4opt J ^ g ~ ' , .tt.
2 2 1 - tgU optgY
(5)
where y = j0 + Aa = 16' +16' = 32', tgY = 0,0093, Aa — the standard deviation of the reflected beam from the optical surface of the Aa=4S and S — standard deviation of the normal optical surface.
Accordingly, the average of using concentration level of energy is defined as the ratio of the MCS to the midsection area obtained scattering spots, for example, a circular symmetric MCS is defined as follows [4]:
C = nRk / nr2 = R2k/ r2 (6)
where, Rk = y2 - determined from the ratio of said top (1-4) and a parabolic:
C0 = y2/r02, C2 = y2/r22, C3 = y2/r32, C4 = y2/r42. (7) For parabolic-cylindrical:
C0=y/r0, C2=y/r2i, C3=y/r3i, C4=y/r4i, (8)
to further define the energy distribution in the focal plane parabolic-
for inaccurate concentrator parabolic-cylindrical form
r = ftg (Yo + Aa), r2 = f (1 + tg2 U)tg (7o + Aa),
r =
f 1+tg
U
tg (r0 + Aa)
1 - tg2 U + 2tgUtg(y0 + Aa)
r =
f 1 + tg
U
tg (Yo + Aa)
1 - tg2 U - 2tgU tg (Yo + Aa)
(1) (2)
(3)
(4)
cylindrical MCS is necessary to determine the mean concentration for different values of r [5].
C„ =
C 3 =
C 4 =
2 ^T
(ftgYo)
U
, C 2 =
2 ^
2tg -
i+g 2 ^
1 - tg2 U + 2tgU
tgYo tgYo
1+tg1T
tgY0
1 - tg2 U0 - 2tgU
tgYo
1+«■ ^
tgYo
at U0 = 900, Cmax = 1/tgY0 for theoretically exact parabolic-cylindrical MCS Aa^C = 1/(0.00465) = 215.
" = (f-x)^^^, (9)
1 - tgUo ■tgY y = (f - x )tgU0, c = y = tgU o ■ (1 - tgU 0 -tgY)
(10) (11)
r (tgUo + tgY) The optimum value of the degree of concentration is determined by Copt equated to zero the derivative of C by U0
2
2
2
CdtgU0 =tgU0 •(1 -tgU'^dtgU
(12)
(tgU 0 + tgY)
After differenitialequation finally we obtain the following quadratic equation:
tg2U0 + 2tgU0 • tgY-1 = 0. The solution of this quadratic equation
tgu = -tgy+yl tg Y +1. (13)
Finally, after an analysis based on tg u<1 find an acceptable solution:
tgU 1>2 = -tgy + V tg 2Y +1 = -0.00465 W0.00465 +1. (14) We define value Uopt parabolic-cylindrical to initial conditions: y = 16 tgU0 = 0.41285p U0 = 44 052'.
Table 1 shows the dependence of the optimal angle of opening of precision manufacturing parabolic-cylindrical MCS
Aa 0 4' 8' 12' 16' 20' 24' 1 0
tg (un/2)„r 0.41285 0.41251 0.41217 0.41183 0.41149 0.4111 0.4108 0.4091
u t opt 44n52' 44n50' 44n47' 44n46' 44044' 44042' 4440' 44029'
To achieve maximum energy density of required parabolic-cylindrical concentrator an aperture angle approaching 90 0, which is the main condition for MCS technological purposes. For energy forced MCS is necessary to optimize the aperture angle to the precision manufacture.
For high — temperature solar energy MCS purpose the most important characteristic is the average value of the concentration of the Cav and the value of the optimal radius r4.
C =
2^
5 2
1 - tg2 U - 2tgU 22
tgYo
100-
80-
60-
40-
20-
1 + tg2 U 2
107
(16)
tgYo
1" ■ Aa=0
■ ■ ■
■ / • • 1 71 1 •• ^ ; *ч i / ► X Aa=8' /
" " / ( о/ /.и 53 i Vx-i \ Aa=16'
/ z / * / У » A л V L V : X \ " \
f ~ A Л ^ k
15
30
45
60
75
90
Un,angle
Figure 2a. Character change the maximum (C ) and second-
o O V max'
ary (C ) values respectively, the degree of concentration in the focal point on the focal plane of the MCS parabolic- cylindrical aperture angle U0.
Calculations parabolic-cylindrical MCS led to the maximum concentration Cmax = 215 at U0 values (fig.3.a b). The analysis shows that for large C inaccuracies appear stronger. Thus if A = 16 ' then C = 53.
av
Conclusions: Aa
1. The expression of optimal concentrations of values depend-
Figure 2b. The nature of changes in average Cav) values respectively, the degree of concentration in the focal point on the focal plane of the MCS parabolic- cylindrical aperture angle U0
ing on the aperture angle are determined and the accuracy of its production for energy purposes at MCS Aa=0 opening angle is the optimum value Uopt = 44°52 '.
2. The dependence of changes in the average and the maximum degree of concentration of the MCS on the size of the aperture angle and a manufacturing error Aa = 4S r are obtained.
References:
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