parabolic trough concentrators—design, construction and evaluation

Energy Convers. Mgmt Vol. 34, No. 5, pp. 401-416, 1993 0196-8904/93 $6.00 + 0.00 Printed in Great Britain Pergamon Press Ltd

PARABOLIC TROUGH CONCENTRATORS---DESIGN, CONSTRUCTION AND EVALUATION

A. T H O M A S I and H. M. GUVEN 2 l Instrumentation and Services Unit, Indian Institute of Science, Bangalore-560 012, India and

2Department of Mechanical Engineering, San Diego State University, San Diego, CA 92182, U.S.A.

(Received 11 January 1992; received for publication 18 August 1992)

A~traet--A brief review on the design aspects of the structural, optical and thermal subsystems of parabolic trough concentrators is given. Existing methods of performance evaluation and techniques to improve their performance are also discussed.

Parabolic trough concentrators Optical efficiency Universal error parameters Non-uniform heat flux efficiency

Intercept factor Incidence angle modifier Flux line tracker Wind load Thermal

I N T R O D U C T I O N

In response to the energy crisis of 1973 and the subsequent 10-fold increase in oil prices, the awareness to use alternate energy sources, including solar energy, has gained momentum both in industrialized and developing countries. Intensified research and development on renewable energy sources, which followed the energy crisis, resulted in demonstration of the technical feasibility of many alternate energy options.

The industrial sector, in general, consumes 40% of its country's commercial energy. Of the total energy used by industry, a major portion, approx. 4 5 ~ 5 % is used for direct thermal applications--in the preparation and treatment of goods, known as industrial process heat (IPH) [1, 2].

The thermal energy demand for IPH, in general, is below the temperature of 300°C. As indicated in Ref. [3], 37.2% of the total IPH demand is utilized in the temperature range of 92-204°C. It may be noted that this temperature range can be met easily by using line focus concentrators [4]. IPH applications involve hot air, hot water, low and high pressure steam and high temperature thermic fluids. A variety of line focus concentrators, like parabolic trough concentrators (PTC), Fresnel lens and fixed mirror solar concentrators (FMSC), can be used in the temperature range of 100-300°C [5-7].

Parabolic trough concentrators (PTCs) are capable of supplying thermal energy over a wide range of temperatures (up to about 310°C), and therefore, they can be used for a variety of applications ranging from electrical generation to industrial hot water and steam production.

In this paper, a brief review of the various subsystems of PTC and their performance evaluations are discussed.

Description o f parabolic trough concentrator

A parabolic trough concentrator (Fig. 1) consists of a reflecting surface mounted on a reflector support structure having the profile of a parabola. A receiver assembly comprising a circular absorber tube with suitable selective coating and enclosed in a concentric glass envelope is centred along the reflector focal line. With suitable end supports, the PTC module is supported on two bearings mounted on two pylons. It is also provided with a precise driving system in order to track the sun and, thus, to maintain focussing of the solar radiation on the receiver assembly. The incident energy is absorbed by a working fluid circulating through the absorber tube.

The various subsystems of a PTC are reflector, reflector support structure, receiver and tracking devices, and these are shown in Fig. 2.

401

402 THOMAS and GUVEN: PARABOLIC TROUGH CONCENTRATORS

Fig. 1. Parabolic trough concentrator.

D E S I G N P A R A M E T E R S

The design parameter of a PTC can be classified as geometric and functional. The geometric parameters of a PTC are its aperture width and length, rim angle, focal length, diameter of the receiver, diameter of the glass envelope and the concentration ratio.

The functional parameters of a PTC are optical efficiency, instantaneous and all day thermal efficiency and receiver thermal losses. These parameters are largely influenced by the properties of the materials used and the optical errors associated with the system. The material properties are reflectivity of the mirror, transmissivity of the glass envelope and absorptivity of the absorber. The errors are due to the defects in the reflector material, support structure, location of the receiver

Reflector Receiver • Apertutre width (w) / - Shape of a b s o r b e r

• R i m a n g l e (O~) / . Size of absorber-D Reflective surface • ' / . Absorber-glazing gap characteristics O, etc. i / width (i)

I / ~ • Absorber surface ~ ] - - ~ - c h a r a c t e r i s t i c s ' ~

~ Reflector support s t r= tu re ~ - Tracking

• True profile • Tracking m o d e

• M i n i m u m s l o p e e r r o r (1-axis, N-S, E-W) • High stiffness/weight • Tracking equipment, etc.

Fig. 2. Subsystem of a parabolic trough concentrator.

THOMAS and GUVEN: PARABOLIC TROUGH CONCENTRATORS 403

with respect to the focal plane of PTC and misalignment of PTC with respect to the sun caused by tracking errors.

D E S I G N A N A L Y S I S

The instantaneous efficiency of a PTC (r/i) can be calculated from an energy balance on the receiver tube. The instantaneous efficiency is defined as the rate at which useful energy is delivered to the working fluid per unit of aperture area (qu) divided by the beam solar flux (Ib) at the collector aperture plane. For example, Ref. [8] presents the expression:

q~ F~aoUe(T, - T . ) ,t, = T~ = FR ,7o AIb ( l )

where

FR = heat removal factor r/o = optical efficiency Uc = heat loss coefficient Ac = absorber area A = aperture area Ti = inlet fluid temperature Ta = ambient temperature.

In equation (1), FR, Uc and r/o can be identified as the three major design parameters which can be used to construct a three-parameter collector model for the preliminary design of PTC.

If the optical characteristics of the materials used can be assumed to be temperature independent, the optical analysis of the collector can be decoupled from the thermal analysis. Hence, the optical efficiency r/o can be modelled and analysed independently without knowledge of the thermal design and vice versa.

Optical analysis The optical efficiency r/o can be expressed as:

r/o = p (T0t)efr?0cos 0 (2)

where

p = average specular reflectance of the reflective surface (z~)efr = effective transmittance-absorptance factor

0 = angle of incidence of the sun's rays on the collector aperture measured from the normal to the aperture

?0 = instantaneous intercept factor (defined as the fraction of rays incident upon the aperture that reach the receiver for a given incidence angle 0).

The optical efficiency, r/o, given by equation (2), varies with angle of incidence between the aperture surface normal and the incoming radiation. There are several factors besides cos 0 that contribute to the decrease of optical efficiency with increasing incidence angle. These factors include the incident angular dependence of glazing transmittance and absorber absorptance. Also, the instantaneous intercept factor decreases with incidence angle. This decrease is brought about in two ways. First, there is a beam spreading due to reflector longitudinal slope and nonspecularity errors. Second, the apparent sun image becomes wider due to the longer reflected path length. The incidence angle effects can be singled out by using the incidence angle modifier K(O) which defines how the optical efficiency decreases with incidence angle, relative to the trough's normal incidence optical efficiency. Taking all these factors into consideration, the optical efficiency of PTC can be expressed as

,lo = [K(o)] [ p ( ~ ) o ] ~ (3)


where

(~ ) , = effective transmittance-absorptance factor at normal incidence y = intercept factor at normal incidence,

This definition of the optical efficiency allows a clear distinction between the factors contributing to it. The first bracketed term is the incidence angle effect. The second bracketed term represents the material properties and the last term, the intercept factor, contains the effects of all optical errors. To determine the optical design of the trough, values for each one of these terms should be determined or estimated. Gaul and Rabl [9] present experimental data and an analytical expression for determination of the incidence angle modifier.

The optical analysis of a PTC is usually carried out by means of ray tracing techniques [10-13], which provides an enormous amount of detailed information on functional relationships.

Prediction of optical performance of a PTC demands knowledge of the reflectance properties of the mirror materials as a function of the incident angle. The data collected by Glidden and Pettit [14] are useful in determining whether changes in specular reflectances with incident angle are due to changes in the reflected beam intensity or width or both. Pettit et al. [15] have calculated broadened sunshapes for a variety of incident sunshapes and for a variety of scattering distributions and presented them as design data.

The potential errors (or imperfections) that may be encountered in a PTC are well presented in Ref. [16] and illustrated in Fig. 3. These are nonspecularity (diffusivity) of the reflector material, profile and slope errors of the reflector support structure, tracking errors and misalignment of the receiver with respect to the focal plane of the PTC.

The contour error of a PTC, comprising profile and slope errors, plays a very prominent part in the spectrum of optical errors. These errors, which also follow a normal distribution, can be measured by LVDT and laser techniques [17].

In a real PTC, the incident sunshape depends upon the time of day, geographical location of a PTC and its orientation on the ground. The reflected radiation that reaches the receiver surface is broadened by the effects caused by the above errors and is called effective sunshape which is illustrated in Fig. 4.

Several investigators have studied the errors affecting the optical performance of the trough, e.g. Refs [18-20]. In all of these studies, however, the investigators relied exclusively on statistics to account for the effect of error on the optics of the trough.

In the statistical error analysis, all the optical errors and imperfections were treated as independent random processes and their occurrences were represented by normal probability

[~ = Concentrator misal igned and tracking errors

Non-uniform incident / +Y,'~, - Effective focus beam intensity ~ / ~ - - + " / Receiver locat ion

/ -x .!. +x errors

T

/ Reflect ive / material / dif fus iv i ty Local s lope errors

~ j ~ ~ (surface waviness )

profi le errors -Y

Fig. 3. Description of optical errors in PTCs.


Sunsha_. p_¢ " ~ Normal intensity ~. distribution w i t h stand, dev=Osu n mean=O

Incident central ray ..~.

\

Con~

~ ' - .-- G l a z i n g

~ /Receiver tube

Actual central A {,,/~) ) ray " '~. / ~

_ . ~ ~ Normal distribution ~ - - ~ x ' x ~ 7 - ~ i with stand, dev =

" ~ ~ otot, " mean= 18

/ / i ~ Effective sunshape . / g / x . Idea!°, i (. Flatter distributi~on

~ - / / ; / , ~ central I i due to random errors " /~ , ~ r a y ! • Shift to central ray

/ /" "~ ~ ! due to non-random

8 = misali~,nment'n~, errors) '~xaPnd t~acT~n~g . . . . i ~ Normal distrbution

with stand, dev = Otot, n m e a n = 0

Fig. 4. Modelling of errors.

(Gaussian) distributions with zero mean. A normal distribution approximation for the optical errors has subsequently permitted the convolution calculations for the errors to be reduced to a simple addition of the standard deviations and allowed for the characterization of the errors with a single error parameter, atot [18,19], represented as follows:

2 2 2 2 2 O'to t x/a~un + O'mi r + (20"),,op~ + (4) ~--- O'trac k -3 I- O'displacement

where terms under the radical represent the standard deviations of the sun's energy distribution, the mirror nonspecularity distribution, the slope error distribution (averaged over an entire collector surface), the tracking error distribution (time-averaged over several oscillations of tracking error for an entire field of collections) and the receiver location error distribution (averaged over an entire field of collections and time).

The optical errors can be grouped as random errors and systematic errors. The random errors can be represented by normal (probability) distributions. They are treated statistically and give rise to spreading (widening) of the reflected energy distribution. These errors are identified as: apparent changes in sun width, scattering effects that are associated with the optical material used in the reflector and scattering effects caused by random slope errors. The systematic errors are deterministic in nature and can have a somewhat greater impact on degradation of trough performance. They account for the gross errors in manufacture/assembly and/or operation. The non-random errors are identified as: reflector profile errors, consistent misalign- meat of the trough with the sun and misalignment of the receiver with the effective focus of the trough.

As shown in equation (3), the decrease in optical efficiency due to errors can be determined by analysing the effect of errors on the intercept factor, the parameter that embodies the effect of errors. The value of the intercept factor is governed by random and systematic errors as well as the concentrator geometry (concentration ratio C and rim angle 0). Hence, the intercept factor a t

normal incidence 7, can be written as

r =f.[~b, C , D , a = atot,,,fl,(dr)y] (5)

where

D = absorber tube diameter p = reflector misalignment and tracking error angle

dr = distance between the actual focus and the centre of the absorber tube (dr)y = dr along the axis of the trough.

ECM 34/5---F


The intercept factor can be determined if the distribution of flux around the receiver is known. Numerical analysis of flux distribution around the receiver has been carried out by several investigators [21, 22]. However, only limited information is available on experimental aspects. Bendtl et al. [23] and Mullick and Nanda [24] have suggested an indirect method of computing the intercept factor which is based on the optical efficiency of a PTC and is determined by thermal tests. The difficulty in this method is to have a large flow rate of the heat transfer fluid and the measurement of flow and temperatures at high orders of accuracy. Pettit et al. [25] have suggested a simplified computational procedure to determine the intercept factor.

Intercept factor can be experimentally determined by measuring the flux around the absorber tube of PTC. Lr f et aL [26] have used a silicon photovoltaic cell fixed in a water cooled mounting and Semmens [27] has chosen a water cooled radiometer for direct measurement of flux around the receiver. In comparison with these direct methods, the one employed by Authier [28] and Balasubramanian et al. [29] using lunar flux is considerably easier to carry out. The measurements reported by Authier are on a spherical mirror, whereas Balasubramanian et al. have applied the same on a fixed mirror concentrator of Russell's type. The measurement of flux distribution around the absorber of the PTC and the computation of data to determine the intercept factor are described by Thomas et al. [30] which can be adopted even for a system installed in situ.

Universal error parame te r s

In Refs [11] and [31], it is shown that random and systematic errors can be combined with the collector geometric parameters C and D to yield error parameters universal to all collector geometries. These are called "universal error parameters", and they allow for comprehensive optical analysis of the trough by reducing the number of independent variables in equation (5). There are two systematic error parameters and one universal random error parameter, and the universal parameters transform equation (5) into

= fn(dp, t r* , f l * , d* )

where

(6)

tr*= ac = universal random error parameter (rad) fl* = ac = universal systematic error parameter due to angular errors (rad)

d * = ( d r ) r i D = universal systematic error parameter due to receiver mislocation and reflector profile errors (dimensionless).

A mathematical derivation of the universal error parameters is given in Ref. [11], together with a numerical model which was used to validate the existence of the universal error parameters.

The introduction of universal error parameters is a significant finding because it allows for generalization of results and meaningful optimization of the collector geometry. Determination of realistic error tolerances using the universal error parameters is presented in Ref. [10]. The procedure for optimizing the concentration ratio using universal error parameters is presented in Refs [16] and [31].

In reality, however, determination of the error-tolerances and the final optimization of the trough geometry (C, q~) will be much more involved. For example, when sizing the receiver tube for a given reflector aperture (or in other words when optimizing (C), if the receiver tube is sized to capture all the photons scattered by the random errors, then the optical value of the design angular aperture must be considered. Since thermal losses are proportional to receiver tube diameter, trade-offs should be made between the percentage of photons which is allowed to miss a smaller receiver tube and the corresponding savings in thermal losses through diameter reduction. Furthermore, since systematic error tolerances are proportional to receiver tube diameter and concentration ratio, trade-offs would also be made between the allowable level of systematic error (error tolerances) in the design and the concentration ratio of the trough. As a result, for a given set of specifications and requirements, the optimum value of the "design angular aperture", should be determined by compromising between thermal losses, systematic error parameter, random errors, rim angle and concentration ratio. As a result, this will require implementation of an iterative optimization procedure (due to implicitness of the independent variables).


The universal design curves presented in Re£ [16] enable a designer to incorporate information about the effect of potential errors on performance into the design process during the preliminary design phase and to determine cost to performance trade-offs and choose realistic values for error tolerances based on various design requirements and the techno-economical capabilities of the design environment.

With these added capabilities, designers can dimension and optimize the trough efficiently and can develop efficient "error tolerant" trough designs in any design environment for any given set of constraints and design requirements.

T H E R M A L A N A L Y S I S

The primary function of the receiver subsystem of a PTC is to absorb and transfer the concentrated energy to the fluid flowing through it. In this process, however, the absorbing surface of the receiver will be heated, and its temperature will become considerably higher than that of the surroundings. For example, depending on the temperature requirements of the application, operating temperatures, as high as 300°C can be attained at the absorbing surface of the receiver during operation. Subsequently, the temperature difference between the absorbing surface and the surroundings will cause some of the collected energy to be transferred back to the surroundings. The knowledge of heat loss from the receiver is important for predicting the performance and, hence, designing PTCs.

Proper qualification of the heat loss from the receiver is important for predicting the performance, and hence, designing PTCs.

The cross section of the receiver subsystem is shown in Fig. 5. As shown, three different heat exchanges exist between the components of the receiver. These are

(1) Heat transfer from the absorber tube to the working fluid (2) Heat exchange between the absorber tube and the glass jacket (glassing) (3) Heat exchange between the glass jacket and the surroundings.

Since PTC will be optimized based on instantaneous or all-day efficiency, a steady-state thermal analysis of the receiver will suffice for design studies. In Fig. 6, a two-dimensional, steady-state energy exchange to the working fluid is shown. The working fluid will be heated as it travels through the fluid duct. Therefore, the value of the output temperature (Tan), flow rate (m), working fluid properties, length of the collector module (L), thickness and conductivity of the absorber tube and the absorber tube temperature, which will be a function of x, i.e. Tab, = Tab~(X). For a known heat flux along the absorber tube axis and for the given inlet and ambient conditions and collector parameters (i.e. Tan, m, Ta, L, etc.), one can solve for Tfo.t and Tabs(X ) and T#~(x) by setting three energy balance equations [33]. Then, the total heat loss from the collector module can be calculated by:

qo-L = UIo,s(x)[T~a~(x)- Taldx (7) o

Turbulence generator

Absorber tube with selective c o a t i ~ / ~

Working ~ @ fluid

Surroundings

Glass jacket

Annular space

Fig. 5. Cross section of receiver subsystem

Absorber tube Glass jacket (Tab s) -~ ? (Tslas s) f Annular space

Working fluid -~1 ~ "/" "/" " /"/'/" "1

Turbu::mc i ,_ -I '''~TIo"I generator I - L v I

Fig. 6. Two-dimensional energy exchange to the working fluid.


where U~oss(x) is the heat transfer coefficient for combined convection and radiation heat losses from the outer surface of the glass jacket. However, this is a very cumbersome method which requires numerous iterations, and more importantly, it requires prior knowledge of the collector parameters, which are normally not known. Therefore, further assumptions are needed.

Since at the preliminary stage of design, all one needs for design studies is an average value of the heat loss per unit length of receiver, it will be appropriate to assume a known average absorber tube temperature (Tabs = constant) and relate heat loss to this average absorber tube temperature and determine the heat loss coefficients for different modes of heat transfer as a function of the average absorber tube temperature too [32]. As a result, this will eliminate the need to specify the fluid inlet and outlet temperatures, flow rate, fluid properties and collector parameters, and more importantly, it will allow for the use of a one-dimensional heat transfer model (radial) which is shown in Fig. 7.

The radiation heat loss rate across the annulus can be calculated by the usual radiation exchange equation between two concentric cylinders [33].

Natural convection heat loss in the annular space will be negligible as long as the Rayleigh number is less than 1000 [34]. Therefore, for Rayleigh numbers less than 1000, only thermal conduction heat loss will exist in the annular space.

For Rayleigh numbers greater than 1000, the combined conduction and convection heat loss rate can be evaluated from an effective conduction coefficient [34].

The convection heat loss rate from glazing to surroundings will be a function of wind velocity and the heat loss coefficient will be a function of the Reynold's number, and its value can be obtained using Hilpert's formulation for forced convection over cylinders [35]. At present, there are no existing studies for calculating the heat loss rate for cylinders in parallel flows (i.e. flow along the axis of the tube).

For example, Gee et al. [32] have calculated the heat-loss coefficient UL as a function of average absorber tube temperature and absorber tube diameter for a "reference" receiver and an evacuated receiver using such a procedure. They have found that, for an evacuated receiver, annular gap sizing is not thermally significant because no conduction or convection occurs in the annulus.

Annulus gap sizing

In a typical high temperature absorber tube design, the rate of energy loss by combined thermal conduction and natural convection in the annulus is of the same order of magnitude as that due to thermal radiation and can amount to approx. 6% of the total area at which energy is absorbed

Working fluid Qslass Annular space filled \ . / with air at atmospheric

Qc°nd3"4 ~ Qc°nv4"a

• / - " - ' - F - " ~ \ Carbon-steel Glass envelope -/ ~ "absorber tube

Qrad4.5 with black chrome selective surface

Fig. 7. Heat transfer process in the receiver assembly. Q~o~d j ----conduction heat transfer from surface i to j; Q~o~v, j = convection heat transfer from surface i t~ j; Q~_j = radiation heat transfer from surface i to j; Q ~ = solar radiation absorbed by glass; Qt~ = solar radiation absorbed by absorber tube.


by the collector [34]. Therefore, elimination or reduction of conduction and natural convection loss can significantly improve the performance of a collector field.

Three different techniques can be used for reducing or eliminating these losses. They are

--Evacuation --Back filling the annulus with a heavy gas (gas with low thermal conductivity) ---4)versizing the annular space (to minimize conduction losses).

Raztel et al. [37-39] have investigated these heat reduction techniques extensively. Some of their conclusions are

--Overall collector efficiency could be improved by 11-12% if annulur pressure can be maintained below 10 -2 Pa [36]. However, maintaining a vacuum in the annulus was found to be very difficult

- -Heavy gas utilization in the annulur space can reduce receiver heat loss by 50%. This corresponds to a 4-5% improvement in overall collector efficiency [37]

- -The gap should be made as large as possible in order to suppress convection in the annulus, i.e. the Rayleigh number should be less than 1000.

Nature o f heat f lux around the absorber tube

Ratzel [40] has developed a solar energy deposition model for PTC and has shown that the solar flux distribution around the periphery of the receiver tube is non-uniform. Semmens [27] has confirmed the above prediction by measuring the solar flux distribution using water-cooled flux sensors. Later, Thomas et al. [30] have also confirmed this by conducting experiments using lunar flUX.

The effect of non-uniform heat flux on heat transfer has been studied by various investigators. Reynolds [41] has studied the effect of heat transfer to fully developed laminar flow in a circular tube with arbitrary circumferential heat flux. Numerical examples given by him show that the peripheral variation of wall temperature is quite significant, even for small heat flux variations around the tube. Reynolds [42] later extended his study by including the effect of heat conduction in the peripheral direction with arbitrary peripheral heat flux and constant axial wall heat flux.

Bhattacharyya and Roy [43] have found a significant effect on wall temperature and Nusselt numbers compared with uniform heat flux conditions.

Patankar et al. [44] have presented an analytical study on the effect of circumferentially non-uniform heating on steady state laminar and combined and forced convection on a horizontal tube. The non-uniform heating was obtained by uniformly heating around one-half of the tube and insulating the other half and vice versa. It was found that only in the case of the bottom half heating and top half insulation gave rise to vigorous secondary flow with the result that the average Nusselt numbers are much higher than those for pure forced convection, while the local Nusselt numbers are nearly circumferentially uniform.

Schmidt and Sparrow [45] conducted experiments on a specially fabricated tube to study the effect of circumferentially non-uniform heating on the fully developed turbulent heat transfer characteristics for flow in a horizontal circular tube. Separate sets of experiments were conducted with the heated portion at the top and at the bottom for Reynolds numbers 3000-70,000 for Prandtl numbers 3.5-11.5. Significant buoyancy effects were present for bottom heating at the lower and higher Reynolds numbers. This evidence included augumented values of circumferential average Nusselt numbers, uniform local Nusselt numbers and temperatures on the heated wall and relatively high temperatures on the adiabatic wall. On the other hand, the top heated experiments were not affected by buoyancy. The theoretical investigation of De Menezes and Kubair [46] using actual peripheral heat flux distributions, indicated the augumented heat transfer rates.

The results of experimental study conducted by Rajaram Shetty [47] have demonstrated that the effects of buoyancy on laminar convection heat transfer on a tube depend markedly on the circumferential variation of thermal boundary conditions. He has observed augmentation of heat transfer coefficient even with the small circumferential variation of heat flux obtainable in his experimental set-up. His investigations have also demonstrated that the buoyancy effects and the heat transfer coefficient increase with increasing values of the modified Grashof number.


M I R R O R M A T E R I A L S

The optical efficiency of PTC modules is largely dictated by the reflectivity of the materials used. In solar energy applications, back silvered glass plates, anodized aluminium sheets and aluminized plastic flms serve as reflectors. Of the various commercially available reflector materials [48, 49], Coming 0317 glass 1.5 mm thick, having evaporated silver coating, is the best reflector, since its reflectivity is high at all acceptance angles. The composite glass mirror manufactured by M/s. Glaverbel, Belgium, having reflectivity of the order of 92% in the solar spectrum, has been used in several industrial process heat systems [50].

R E F L E C T O R S U P P O R T S T R U C T U R E S

The reflector support structure is the primary member of a PTC which provides the correct optical shape for the reflector surface, maintains the same to within acceptable tolerances during operation and offers protection during operating and non-operating periods from extreme weather conditions. Commercially available PTCs have a sandwich structure, a monocoque structure or a stiffened rib structure.

The choice of materials of these categories is considered on the basis of environmental stability, durability, mechanical and physical properties, suitability of the construction method, fitness for high production rates, low total weight and resulting cost.

The sandwich structure is a good design, but high precision moulds are required in order to successfully fabricate high quality PTC. In commercial PTCs, either aluminium or stainless-steel honeycomb are used as sandwich materials. These are expensive. Alternatively, paper honeycomb with stainless steel or aluminium skin can be used. In addition to light weight, it is also cost effective. Although the monocoque structure is quite stiff, its weight per unit area is somewhat high. Also, it is difficult to achieve the required surface accuracies unless careful quality control is exercised at every stage of its fabrication. The stiffened rib design is superior to the above three designs, since it yields high surface accuracy and these can be assembled in situ.

Banas[51], Reuter and Allred[52] and Duffle and Beckman[8] summarize the functional requirements of the shell and the supporting structure of a PTC. The performance requirements for the PTC structure, according to them, arc:

(1) To provide and maintain the correct optical shape to the reflective surfaces (2) To maintain the shape within the specified tolerances during operations (3) To protect the reflective surfaces under extreme weather conditions and (4) To withstand long term exposure to the environment.

In engineering terms, these requirements mean that the stresses and the deflections experienced by the trough and the reflector must remain below specified levels under gravity, wind and thermal loads, and at the same time, the physical properties of the structure, such as the size and weight, must be compatible with the overall design objectives.

Reuter [53] has suggested an important parameter for design consideration in order to decide whether a specific design concept is worth pursuing. The parameter is based on the chosen mechanical and structural properties of the material and is known as the figure of merit "F". For a structural concept to be successful, it must satisfy the following conditions:

where

E 12D p3(1 _ v2 ) I> F where F = --y-

E = Young's modulus of the material v = Poisson's ratio p = density

D = flexural rigidity commonly used in plate and sheet theory = the areal weight of the panel.


In addition to high specific stiffness (E/p) , other factors like light weight and low fabrication cost must also be taken into consideration.

Structural design requirements

In addition to geometric parameters, a significant design consideration can be the loads that act on the PTC structure:

• the weight of the mirror • the weight of the mirror supporting members and • the wind loads.

Of these, the wind load is very important, since it decides the rigidity and integrity of a PTC structure as well as its foundation requirements.

The Sandia Laboratory of the U.S.A. has specified the following design requirements for a PTC structure [54]:

• survive 120 km/h wind in any position • operate in 40 km/h average wind and • drive to stow in a wind increasing at a rate of 7.5 km/h.

W I N D L O A D ON R E F L E C T O R S U P P O R T S T R U C T U R E

In developing solar collectors, wind loading is one of the major structural design considerations. The shape of the collector, its height above the ground, the collector pitch angle, the number and arrangement of collectors in an array and the direction of the wind are several parameters which can modify the loads applied to the collector. Besides having to safely sustain maximum expected loads, a tracking collector must also be able to maintain its desired orientation within a certain accuracy band in typical environments and at minimum cost. In addition, wind load information in terms of forces and moments is needed from the standpoint of foundation and other structural design considerations, while the pressure distribution is a valuable tool to be used in the detailed design of a PTC itself. A procedure has been outlined by Randall [55] to enable designers to design peak wind loads which might be anticipated during the operational lifetime of a solar collector array.

Static and dynamic load studies have been carried out by Thomas [56] on full scale modules which give the deflection and moment characteristic of the PTC structure for various loads corresponding to various wind speeds. Extensive wind load studies carried out on scale models of PTCs having various geometries are reported in Refs [56-58]. Results obtained on the distribution of normal forces caused by the varying angles of the wind are valuable data for design engineers.

The experimental work of Randall et al. with PTCs is of great practical importance [59, 60]. They have studied the force and moment characteristics of both isolated, horizontally mounted, single module troughs and of trough modules with array configurations, in operational and stow attitudes under different flow field environments. Their data indicate that force and moment increase with mounting height and with trough aspect ratio. They varied flow conditions corresponding to Reynolds numbers from 0.065 million to 1 million, and they have observed no significant effects of Reynolds number on peak lateral force. They have studied the effect of rim angle on lift and lateral coefficient by conducting tests on models having rim angles of 40, 65, 90 and 120 ° . The results of the tests show that lift force coefficient increases from 40 to 65 ° , from 65 to 90 ° , it is constant up to a rim angle of 90 ° and rapidly decreased from 90 to 120 °. The lateral force coefficient is constant from 40 to 90 ° and increases from 90 to 120 ° .

In a collector field with arrays of PTCs, modules at the perimeter of the field suffer the largest wind loads. Appropriate fences can provide reductions of lateral and lift forces in perimeter rows. Similar experiments have been conducted by Peterka et al. [61] on such models having rim angles of 40, 65, 90 and 120 °. Their results agree with those of Randall et al. [59].

Murphy [62] has made an excellent assessment of the work done on wind loading of solar collectors, such as heliostat, parabolic trough, parabolic dish and photovoltaic array: the commonality in earlier work is brought out and recommendations for further work are also


indicated. He has also presented typical experimentally determined maximum force and moment coefficients for various individual solar collectors subjected to static wind loading. In addition, the report has an excellent reference on wind loading of solar concentrators.

Bhaduri and Murphy [63] have reviewed and assessed the present design methodology for wind loading on collectors for solar thermal applications and recommended areas of further investigation for developing realistic criteria to determine reliable and adequate wind loads. They have considered the feasibility of using innovative design considerations to reduce the magnitude of wind loads on solar collectors. In addition, their report contains valuable information regarding the comparative studies of various aspects of design methodology.

ORIENTATION AND TRACKING

PTC modules can be provided with two axis, polar axis, horizontal east-west or horizontal north-south mountings. Neville [64] and Thomas [65] have analysed the merits of these systems. The two axis system is ideal and will give maximum thermal efficiency. The change in efficiency of polar axis mounting will vary from 0 to 9% over a year. But, for large systems, the horizontal east-west or horizontal north-south mount is highly suitable. The analysis of several investigators [66, 67] shows that, for low latitudes, horizontal north-south orientation is much more suitable than the horizontal east-west.

To track, a large array of PTC systems for thermal applications, three types of trackers (Fig. 8) are commercially available. They are computer tracker, shadow band tracker and flux line tracker [68]. As shown in Fig. 8(a), a computer tracker uses a clock to compute the sun's position and initiate the collector rotation to the computer anvil. Shaft encoders mounted on the driving unit provide accurate accounting of the angular position. Figure 8(b) shows the shadow band sun tracking system. A shadow based sensor is mounted on the collector and rotated along with it. Two sensors are separated by a shadowing strip which shades one of the sensors if the tracker is not pointed directly at the sun. The sensors produce an error signal when they are not illuminated equally. This error signal is used to drive the PTC in a proper direction to reduce the signal to zero. Boultinghouse [69] has developed a flux line tracker. As shown in Fig. 8(c) the flux line tracker has two sensors, which are sensitive to concentrated flux, located near the receiver. As with shadow

(a)

(b)

- ~ - ~ s i g n a l l - I drive I

(c)

Collector drive ]

(d)

oTmr: Microprocessor controller

Motor -I controls

Fig. 8. Tracking systems. (a) Computer tracker; (b) shadow-based tracker; (c) flux-line tracker; (d) combined computer and flux-line tracker.


band trackers, if the collector is off-pointed, an error signal is nulled. Flux line trackers are the only tracker versions that orient the collector based on where the focal line actually is, rather than where it should be. Sandia Laboratories have developed an efficient computer/flux line tracking system as shown in Fig. 8(d) [68]. The tracking angle is calculated with a microprocessor, and the collector is positioned in this direction. A fine tuning of the tracking angle is accomplished with the flux line tracker. A pair of resistance wires, helically wrapped around the receiver, provides an error signal. The resistance wire spans the full length of the receiver and integrates the receiver's entire flux distribution to find the best tracking angle for the collector as a whole.

PERFORMANCE EVALUATION OF PTCs

Thermal performance tests on a PTC are normally conducted to determine its instantaneous efficiency at solar noon and all-day efficiency. In addition, the heat loss from the receiver and the pressure drop in the receiver are also determined.

A common method of testing the efficiency of a solar collector employs an oil circulating system in which the temperature rise across the collector is measured under steady-state conditions. Along with the inlet and outlet collector fluid temperatures, the fluid mass flow rate and the instantaneous irradiance are measured as well.

The two standards that are normally recommended in the determination of the thermal performance of solar collectors are the standards evolved by the National Bureau of Standards (NBS) [70] and the standard 93-77 of the American Society of Heating, Refrigeration and Air Conditioning Engineers (ASHRAE)[71]; however, these standards are for nonconcentrating collectors [72]. A test standard for concentrating collectors has been developed by the Solar Energy Research Institute (SERI), Colorado, U.S.A. (ASTM Document No. 27)[73].

The reports published by Harrison [74-78] contain information on test procedure, test facility and results of tests conducted on commercial PTCs. The errors associated with the measurements are also discussed by several investigators [79, 80], and a total measurement error of +2.56% is anticipated. In general, all the commercial PTCs using FEK-244 and other polyester films give an optical efficiency of the order of 66%, and with glass, these give about 70%. The thermal loss depends upon the receivers of these PTCs. The incident angle effects on the performance of the PTC have been studied by Ramsey et al. [81]. Gaul and Rabl [82] have presented empirical equations for several commercial PTCs in the U.S.A.

A yearly average performance of the solar concentrators is significant in understanding the seasonal behaviour of PTCs; this can be simulated or experimentally determined. Rabl [83] has developed a correlation by which one can obtain hour-by-hour computer calculations with an accuracy of 2.4% for concentrators. The method is useful for evaluating the effect of collector degradation and the gains from collector improvements lead to enhanced optical efficiency or decreased heat loss per absorber surface.

Test results on a string of collectors are very useful to study the behaviour of individual modules in a system under varying operating conditions [84]. The influence of end effects and intra-array shading have been studied by Jeter et al. [85] on the performance of PTC. These factors have the effect of reducing the effective aperture of the collector. They have analysed the extent of these reductions and presented formulae quantifying the effects that enhance performance

Cameron and Dudley [86] have presented data collected on a modular industrial solar retrofit system. The test series include function and safety tests to determine whether the system operates as per specification, an unattended operation test to allow prediction of system performance and life cycle test to evaluate component lifetimes and maintenance requirements.

The studies of Lee and Schimmel [87] on thermal aspects of a PTC have given very useful results. The results of these studies indicate that the best extraction of energy and the best temperature rise in the fluid occur in the turbulent flow regions of the collector fluid. The maximum, however, for any given flow rate, with a given inlet temperature, occurs just after transition from laminar to turbulent flow.

Gee and Murphy [88] have suggested several improvements of the subsystems of a PTC which can yield up to 50% annual energy delivery at low temperatures and double the annual energy output at higher temperatures. Improvements suggested by them are increased reflectivity of mirror


materials, evacuated receiver assembly, glass envelope provided with A R coatings, solar selective coat ing with low emittance and high con tour accuracy for the mir ror support structure. These improvements have been incorporated in commercial PTCs [89, 90], and the optical efficiency has been increased from 70 to 81%.

C O N C L U S I O N

A parabol ic t rough concentra tor is a complex system which demands thorough knowledge of structural , optical, thermal ins t rumenta t ion and controls engineering. A ra t ional design can result from the experience gained by construct ing different models to suit indigenous facilities with various structures, configurations, materials and methods of manufac ture and conduct ing detailed studies on them. Knowledge of optical and thermal performance of a PTC is useful in its choice for a specific applicat ion.

R E F E R E N C E S

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parabolic trough concentrators—design, construction and evaluation

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