configurations of solar bowls by a thesis in submitted …

OUTPUT AND COST PROJECTIONS FOR DIFFERENT

CONFIGURATIONS OF SOLAR BOWLS

by

ZEHAN ZEB, B.Sc. Engr.

A THESIS

IN

ELECTRICAL ENGINEERING

Submitted to the Graduate Faculty of Texas Tech University in

Partial Fulfillment of the Requirements for

the Degree of

MASTER OF SCIENCE

IN

ELECTRICAL ENGINEERING

Approved

Accepted

Au·gust, 1989

~[)j

13 lq <t q JJ, IDI

C.op·;;_ ACKNOWLEDGMENTS

I am thankful to God, the most merciful, the most beneficent. I would like

to express my deep indebtness and most sincere appreciation to Dr. Edgar A.

O'Hair for his invaluable help and support in every step of this work. I am

also profoundly grateful to Dr. John P. Craig and Dr. 11. A. K. Lodhi for

their thoughtful suggestions and sincere cooperation in helping me complete

this thesis.

I am also grateful to the Department of Electrical Engineering for providing

me financial support.

I \Yould like to express my deep gratefulness to my parents, 1ir. and :\Irs.

Arangzeb, and thanks to my husband, Rokon, for everything .

. . 11

TABLE OF CONTENTS

ACKNOWLEDGEMENTS .. 11

TABLE OF CONTENTS 111

LIST OF TABLES v

LIST OF FIGURES V111

CHAPTER

1. INTRODUCTION 1

1.1 FMDF Concept 1 1.2 Objectives 2

2. LITERATURE REVIE\Y 9

3. E~ERGY COI\IPUTATION 13

3.1 Theory 13 3.2 Energy Calculations 15

3.2.1 Weather Data Analysis 15 3.2.2 Concentrator Efficiency 16 3.2.3 Receiver Efficiency 17 3.2.4 Energy 18

3.3 Low Insolation Energy 19 3.3.1 Mode of Operation 19 3. 3. 2 Excess Energy 20

3.4 Energy with Short Receiver 21

4. COST ANALYSIS 37

4.1 Component Costs 37 4.1.1 Baseline Design 37 4.1.2 Alternate Shallow Bowls 39

4.2 Bowl Cost 40 4.3 Iris Cost Approach · 41

111

5. COMPARISON OF ENERGY PER UNIT COST 55

5.1 Effect of Truncated Receiver 55 5.2 Effect of Bowl Parameters 56

5.2.1 Rim Angle 56 5.2.2 Aperture Diameter 57

6. DEVELOPMENT OF EMPIRICAL EQUATIONS 64

6.1 Concentrator Efficiency 64 6.2 Receiver Efficiency 66 6.3 Bowl Cost 68 6.4 Energy 68 6.5 Energy Per Unit Cost 69

7. CONCLUSIONS AND RECOMMENDATIONS 91

BIBLIOGRAPHY 94

APPENDICES 96

A. E~ERGY CO~IPUTATIO~ DATA 97

B. COST1 CODE 113

. IV

LIST OF TABLES

Table Page

3. 1 Weather data sorted by inclination 24

3. 2 Data sorted in 10 deg. inclination steps 26

3. 3 Receiver and concentrator efficiencies: OR= 30° 27

3. 4 Receiver and concentrator efficiencies: OR= 60° 27

3. 5 Receiver and concentrator efficiencies: OR= 30°, 2¢o = 90°, OH = 15° 28

3. 6 Receiver and concentrator efficiencies: 0R=35°, 2¢0 = 110°, OH = 20° 28

3. 7 Calculated energies for different bowls 32

3. 8 Calculated energies for different bovvls with iris 32

3. 9 Annual increase in energy output from auxiliary mode operation 33

3.10 Energy increase by adding fossil energy 33

4. 1 Unit construction costs 46

4. 2 Subcomponent cost factors for bowls with same radius of curvature; normalized with respect to the baseline bowl 47

4. 3 Subcomponent cost factors for bowls with fixed aperture diameters; normalized with respect to the baseline bowl 48

4. 4 Normalized total cost factors (CF) with and without receiver truncation: scheme 1 50

v

4. 5 Normalized total cost factors (CF) with and without receiver truncation: scheme 2 50

4. 6 Normalized total cost factors (CF) with fixed aperture diameter and varying rim angles 52

4. 7 Normalized total cost cost factors ( CF) of all bowls with and without iris for scheme 1 and scheme 2 54

5. 1 Energy /unit cost (E/C) for scheme 1: fixed radius of curvature 60

5. 2 Energy/unit cost (E/C) for scheme 2: fixed radius of curvature 61

5. 3 Energy /unit cost for different aperture diameters: varying radius of curvature 62

6. 1 Concentrator efficiency curYe-fit results 71

6. 2 Receiver efficiency curve-fit results 79

6. 3 Cost factor curve-fit results 83

6. 4 Energy curve-fit results with and without iris 83

6. 5 Energy per unit cost curve-fit results 88

A. 1 ROSA input parameters 98

A. 2 RHTC input parameters (set 1) 99

A. 3 RHTC input parameters (set 2) 100

A. 4 Concentrator and receiver efficiencies: BR = 35° 102




VI

A. 8 Concentrator and receiver efficiencies: (}R = 55° 104

A. 9 Concentrator and receiver efficiencies: (}R = 35° 2c/>o = 100° , (}H = 20° 104

A.10 Enthalpy data for different rim angle bowls: (}R = 30° 105







.. Vll

LIST OF FIGURES

Figure

1. 1 Reflecting properties of a parabolic surface

1. 2 Reflecting characteristics of a spherical surface

1. 3 Geometry of a solar bowl

1. 4 Geometry of a bowl with an iris attached

3. 1 Projected aperture area and reflecting characteristics at 30 deg. inclination

3. 2 Concentrator efficiency vs. inclination

3. 3 Receiver efficiency vs. inclination

3. 4 Receiver efficiency for different temperature setpoints

3. 5 Annual energy increase from auxiliary mode energy

3. 6 Effect of bowl number on extra energy

3. 7 Percent energy loss for short receivers

4. 1 Sub-structure weight vs. surface area; data obtained from CSPP report vol. 1 [1]

4. 2 Super-structure weight vs. surface area; data obtained from CSPP report vol. 1 [1]

4. 3 Receiver and boom weight vs. dia. of curvature; data obtained

Page

5

6

7

8

23

29

30

31

3-!

35

36

42

43

from CSPP report vol. 1 [1] 44

4. 4 Receiver and boom weight reduction with receiver length truncation; after CSPP report vol. 1 [1] 45

Vlll

4. 5 Cost increase pattern for scheme 1 and scheme 2; fixed radius of curvature 51

4. 6 Cost increase with aperture diameter for a 30° bowl 53

5. 1 Effect of receiver length reduction on energy /unit cost 58

5. 2 Energy /unit cost for different rim angle bowls; both with full length receiver and receiver truncated to optimum length 59

5. 3 Effect of aperture diameter on energy /unit cost 63

6. 1 Parameter A1 vs. rim angle 72

6. 2 Parameter A2 vs. rim angle 73

6. 3 Predicted and computed values of concentrator efficiency: 30 deg. bo,vl: Tis = .92 74

6. 4 Predicted and computed values of concentrator efficiency: 45 deg. bowl: T/s = .92 (;)

6. 5 Predicted and computed values of concentrator efficiency: 60 deg. bowl: Tis = .92 76

6. 6 Predicted and computed values of concentrator efficiency: 30 deg. bowl: T/s = .86 77

6. 7 Predicted and computed values of concentrator efficiency: 60 deg. bowl: Tis = .86 78

6. 8 Predicted and computed values of receiver efficiency: 30 deg. bowl 80

6. 9 Predicted and computed values of receiver efficiency: 45 deg. bowl 81

6.10 Predicted and computed values of receiver efficiency: 60 deg. bowl 82

. lX

6.11 Predicted and computed values of cost factor: scheme 1 84

6.12 Predicted and computed values of cost factor: scheme 1 and scheme 2 85

6.13 Predicted and computed values of energy: 30, 35 and 40 deg. bowls with iris and 30 to 60 deg. bowls without iris 86

6.14 Parameters D 1 and D 2 of energy curve-fit: with iris 87

6.15 Predicted and computed values of energy per unit cost: scheme 1 89

6.16 Predicted and computed values of energy per unit cost: scheme 2 90

X

CHAPTER 1

INTRODUCTION

Solar energy is the most abundant and cleanest form of energy available to

mankind. Although the sunlight that reaches the earth's surface has a maximum

power density of roughly 1 kw per square meter, lenses and mirrors can be used

to focus the direct solar rays to intensities approaching 1 MW per square meter

which can produce working temperatures in the range of several hundred to

several thousand degrees Celsius, equal to that attainable from conventional

fuel systems. Heat in this thermal range can drive conventional steam rankine

or high temperature gas turbines. At high temperatures, solar heat can also

drive thermo-chemical processes.

~Iany different types of devices are used to collect and concentrate the solar

energy for the purpose of thermal energy conversion, e. g. , parabolic trough,

parabolic dish, heliostats using central receiver, spherical bowl, etc. As can be

deduced from their names, the major difference between them is their shape.

1.1 FJ\1DF Concept

This study is involved with spherical bowl concentrators, which are called

spherical even though the bowl surface is only a segment of a sphere. It can be

understood from the geometry of a sphere that, unlike the parabolic reflector

(Fig. 1. 1) ·which has a point focus, a sphere has a line focus (Fig. 1. 2), which

extends from the reflector surface to a point half way to the center of curvature

of the sphere. In an operational bowl, the receiver is placed along this line which

1

tracks the sun as it moves across the sky; the bowl remains fixed in position.

As the name implies, this concept is known as Fixed Mirror Distributed Focus

(FMDF) concept. A fluid (water, steam, oil, etc. ) is pumped through helical

coils, wrapped around the receiver and serves to convert the incident solar energy

into a useful form.

The geometry of the FMDF concept is shown in Fig. 1. 3. The aXIs of

symmetry of the bowl is A, the axis which points toward the sun is ZR. The

angle between the bowl axis of symmetry and the receiver axis is the inclination

angle I. Angle BR is the rim angle, i. e. , BR = 30° means the bowl is a 30°

conical section of a sphere. The aperture diameter is 2RA and R is the radius

of curvature.

Figure 1. --! shows the bowl geometry with an iris attached, where 81 is the

rim angle of the iris, 2¢0 is the width of the iris and 81- BR = BH is the height

of the iris. The iris is a tracking reflector, ,,-hich can be connected to a bowl

of relatively lower rim angle, to collect additional energy. This concept was

introduced by the French, with the speculation that it can provide more energy

for a cost that would be less than that necessary for increasing the rim angle.

1.2 Objectives

For a bowl of fixed spherical radius the highest annual energy capture would

be achieved for the largest aperture, i.e. , when BR = 90°. If a coordinate system

is selected (Fig. 1. 2), in which y is the distance from the center of curvature

along the ordinate and x is the distance from the center of the sphere along

the abscissa, and if the x axis is aligned with the direction of the sun, then

2

the outermost rays which intercept the y axis with one reflection, correspond

to those with x = 0 and y = 0.865, considering the unit radius of curvature

(y = R = 1). Rays falling on the mirror surface at y > .865 have to be reflected

more than once before reaching the receiver. In other words, rays falling on the

surface which belong to BR > 60°, would suffer power loss due to more than one

bounce. Also, due to the steep curvature of the surface, bowls with BR > 60°

are less cost-effective [1].

One of the main advantages of fixed spherical bowls is that only the receiver

moves to track the sun. This results in lower overall-production cost of the

bowl. But these savings are relative because the most expensive part of the

solar concentrator system is the reflective surface. It is also eYident that both ..

energy and cost increase with increasing rim angle and/or aperture diameters.

Bowls ,,·ith BR < 25° can produce quality steam only for a very short period of

time compared to the higher rim angle bowls. Again, it is technically difficult to

build a low-cost concentrator for a bowl having a high rim angle. Therefore, in

order to find the most cost-effective geometry, which is both theoretically and

technically feasible, one has to find the actual cost increase pattern of a bo\Yl.

The overall objectives of this investigation were to make a comparative study

of the energy produced per unit cost of different configurations of bowls haYing,

• different rim angles with fixed aperture diameter,

• fixed rim angle with varying aperture diameters,

• same radius of curvature with different rim angles.

3

Most of the previous studies [1, 2, 3] were performed considering the receiver

having a length equal to half the radius of curvature (R/2). The present study

also includes energy and cost benefit analysis for a number of low rim angle

bowls, having a receiver length less than 100 percent of R/2.

When the sun is relatively low in the sky, steam production with high tem

perature and pressure may not be possible. In this study an attempt was made

to compute the increased percentage of annual quality steam output, for each

bowl, by utilizing its low temperature steam production.

Energy computations, in this study, were addressed with the aid of com

puter simulation codes. Cost-estimating data were acquired from the engineer

ing analysis and various designs v;·hich had been done in the past. Costs 'vere

than estimated at the subcomponent level and aggregated to component totals.

V/eather data for Barstow, California (1976), was used in the simulation.

4

aola.r rays

F- focal point

I 1 Aperture plane

1./ ~ I I I I I

Figure 1.1: Reflecting properties of a parabolic surface

5

•

X

I

J•Jr:.xi:sl0 fo~us · \D

I

y

._:__-----r y :: i = 1G

~ ..::. .865

sc.lar rays

Figure 1.2: Reflecting properties of a spherical surface

6

I I

I

' L r,

Figure 1.3: Geometry of a solar bowl

7

D

Figure 1.4: Geometry of a bowl with an iris attached

8

CHAPTER 2

LITERATURE REVIEW

The FMDF system offers the only approach to produce turbine quality steam

utilizing fixed aperture optics. This concept is particularly likely to be competi

tive for medium size power plants (e. g. , 1 to 15 MW) and at medium required

temperatures [2]. The central receiver system utilizes a large number of he

liostats to reflect sunlight to a single receiver. In this system, concentrator and

receiver performance improve rapidly with increased plant size. The central re

ceiver system is likely to be competitive in large scale, high temperature range,

·whereas the parabolic trough can be competitive at low temperature, small scale

range [2]. 1\ at ural solar energy is a low intensity resource; thus, large areas are

needed to obtain enough energy for any useful purpose for a power station [5].

Steward and Kreith [4] developed optical characteristics of the F:0.IDF system

and the axial variation of its concentration ratio to provide information for the

engineering design and sizing of this solar collector system.

To investigate the merits of the FMDF or Solar Gridiron concept for produc

tion of electricity, a 65-foot diameter 60° bowl was built in Crosbyton, Texas [6].

This project was funded by the United States Department of Energy (USDOE).

Both theoretical and experimental studies were involved in this investigation.

A huge volume of operational and performance data was generated from more

than _five years of operation of this facility. The detailed theoretical and practi

cal accomplishments of the project are contained in eight volumes of Crosbyton

Solar Power Project reports [6]. Based on the verified design of this system, a 5

9

MW solar-fossil hybrid power plant design was proposed to USDOE [7, 8, 9, 10].

This design consists of ten 60° bowls each having a 200-foot aperture diameter.

The design for each of the ten bowls is called the baseline design. The base

line represents the standards against which other design, use or application can

be compared, since this design was based upon actual costs and a successfully

operated bowl.

The Ratio of Solid Angles (ROSA) code [11] was developed by Anderson

and Ford, to determine the optical power concentration ratio profiles at points

along the receiver surface. Anderson and Obeyesekere also developed a code [12]

which calculates the power loss due to spillage, but the ROSA code automatically

takes care of spillage losses. For optimum energy capture, the axis of the receiYer

should lie along the line which passes through the center of curvature of the bowl

and the sun (Fig. 1. 3). HoweYer: this code will also handle misalignment of the

receiYer due to tracking errors in terms of misalignment angle input parameters.

ROSA permits any convex surface of revolution as a receiver.

The ROSA program has been modified and named SOLAVG [13] which uses

Romberg's integration algorithm to ayerage the concentration around the re

ceiver. It gives an average concentration at any point along the receiYer. The

last version, ROSAIRIS [12], calculates the concentration when an iris is at

tached. The iris rim angle ( Bn + BH ) and the iris width ( 2¢0 ) (Fig. 1. 4) are

inputs to ROSAIRIS.

Trahan [14] showed that optical flux distributions along the receiver in morn

ings and afternoons were about 8 percent less than the predicted value of con

centration. He also found that these discrepencies were due to concentrator

10

focusing defects introduced during manufacturing processes and internal reflec

tions between the glass and air interfaces.

Hou [15] developed a model to calculate the azimuthal dependence of surface

efficiency of a spherical segment bowl. The results of this study can be used to

aid in determining where to place the better mirrors and which concentrator

surface areas to keep cleanest in order to increase the bowl output. Brock [16]

also performed a similar study with constant solar insolation. Agarwal [17]

developed a computational model for prediction of temperature in the mirror

panels of an FMD F system.

Not all of the power imparted to the receiver is absorbed by the working

:fluid; part of it is lost by radiation and convection. The actual mechanics of

the computation of this energy balance through helically wrapped tubes along

the receiver is quite involved. Subramanyam [18] developed the Receiver Heat

Transfer Code (RHTC) ,,-hich computes this energy balance and is the tool

for simulating the receiver performance. Receiver geometry, inlet temperature,

pressure, mass flow rate, solar insolation, windspeed and ROSA generated con

centration profile, are inputs to RHTC.

According to the application and end use of the steam produced, solar boiler

(receiver) operation modes are chosen. A mode is defined as the state of the

output :fluid of the boiler. A criterion for switching from one mode to another,

in order to improve plant performance, is referred to as a solar boiler oper

ating strategy [7]. Several strategies were investigated by \Vat son [7], to find

procedures which maximize annual solar penetration. Solar penetration can be

defined as the fraction of the annual output of a plant that is supplied by solar

11

energy. Again, choosing the most effective strategy depends on the ultimate

fluid state requirements and on some economic considerations.

The strategy of operation chosen to run RHTC, along with the inputs to

ROSA and RHTC selected for the present study, will be discussed in a later

chapter.

Jonish and O'Hair [19] proposed some other construction schemes as alter

natives to the baseline design scheme. These schemes with low rim angles have

the potential for significant cost savings in both concentrator and receiver.

Wright [20] studied the possibility of constructing bowls with membrane

reflectors, thus reducing the major cost of the reflector surface.

Gustafson and Craig [21] performed a detail analysis of the intrumentation

and control system for solar boiler operations.

Hedberg [3] performed a cost-benefit analysis for a number of iris-attached

bowls, having lower rim angles and the same radius of curvature. Since, there

may be a variety of construction schemes possible, cost was represented by a

scale factor for different scenarios. He assumed a 3.5 percent cost increase \i·ith

each degree of rim angle increase. He also performed a regression analysis for

receiver and concentrator efficiencies and for energy per unit cost, based on the

data computed by using the ROSA and RHTC codes.

The present investigation can be considered as a continuation of Hedberg's

study emphasizing the FMDF concept in its purest form, i. e., without iris, for

both higher and lower rim angles.

12

CHAPTER 3

ENERGY COMPUTATION

3.1 Theory

The size of the aperture area determines the amount of solar energy that is

available for collection. This fact is unique to the fixed aperture optics of the

bowl concept, and therefore it is the bowl aperture area rather than the surface

area, which is used in determining the incident flux.

Although the aperture area of the bowl (Fig. 1. 3) is fixed (AA), the effective

aperture area (AE ), as seen by the sun, varies with the time of the day. If

a reference plane were fixed (Fig. 3. 1) above the bowl with normal direction

pointing towards the sun, then the perpendicular projection of the rim onto the

reference plane would form an ellipse in the reference plane [4, 12]. All input

flux would pass through this area which depends on the inclination angle I. This

area would be the cosine component (Fig. 3. 2) of the actual aperture (AA),

. I. e. '

(3.1)

From Fig. 1. 3,

(3.2)

If the bowl tilt angle is i' solar elevation from the horizontal is ( e ) and solar

azimuth from the south is A, then the cosine of the inclination angle is given by

cos I = sin; cos e cos A + cos ; sin e. (3.3)

If the solar insolation (Idn) at a particular inclination (I) is known then solar

13

flux entering the aperture is

(3.4)

Anderson and Obeyesekere [12] showed that the effective aperture area of a

bowl with an iris is,

( 7r - <Po)) +sin I sin </>o(fh - BR - .5( sin 281 - sin 28R)) ). (3.5)

If the concentrator efficiency ( T/conc) and receiver efficiency ( T/rec) can be cal

culated (discussed in sec. 3. 2. 2 and sec. 3. 2. 3), then the output power for a

particular inclination (i), would be

(3.6)

and if the length of time the sun is at that particular inclination is H ri then,

the total energy at inclination i is

(3.7)

Annual energy would be the sum of the energies at all inclinations from 0 to 90

degrees. 90

Ean = L IdniAEiT/conciT/reciH ri. i=l

(3.8)

Equation 3. 8 can be used to calculate and compare energy of all bowls with

any radius of curvature, as long as the receiver length is the same (100 percent

of R/2) for all bowl configurations. If the radius of curvature is fixed but the

receiver length is varying (equal or less than R/2), then TJconc and TJrec might be

the same, but the mass flow rate (m),would change for the same bowl and same

14

elevation and hence the net heat received or the output would not be the same.

In that case, the enthalpy (H) and the mass flow rate can be used to calculate

and compare the outputs.

90

Ean = L mi( Hi(tout,Pout) - Hi(tin.Pin) )H ri. i=l

3.2 Energy Calculations

(3.9)

In this study, energy calculations were addressed with the use of computer

codes ROSA and RHTC. Barstow, California, weather data of 1976 was used in

the simulation.

3.2.1 Weather Data Analysis

There were more than 4000 hours of data for Barstow in 1976. For each hour

the solar insolation (kw I m 2), ambient temperature (0 0), solar altitude (degrees

from horizontal), solar azimuth (degrees from south) and winds peed (meter I sec)

were recorded. For this analysis each hour of data was read and sorted by

inclination, from 1 to 90 degrees using Eqn. 3.3. The corresponding hours,

and solar insolations were added separately. An average annual insolation ( Idn)

was found for each degree of inclination (i). It was computed, taking the ratio

of the total insolation and the number of hours the sun was at that particular

inclination. Insolation data less than 300 WI m 2 was discarded since solar bowls

if operating, lose energy instead of gaining at such levels of insolations. Table

3.1 shows the computed insolation and the corresponding inclination as obtained

from the above analysis of the Barstow data.

15

Simulation of the RHTC code showed that there was no significant difference

in 'f/.,.ec or mass flow rate corresponding to an inclination (or elevation) difference

of less than 10 degrees. Therefore, for further simplification, a weighted average

of insolation at an inclination step of 10 degrees was taken as Idni and the number

of hours for each inclination was added to be used as H ri. Table 3.2 lists the

final inclinations and the corresponding average insolations used for computing

the annual energy output. Since the RHTC code also requires the wind speed

data, the effective windspeed was considered as 5.5 miles per hour. Although

the wind speed at Barstow (1976) varied from 10.8 to 11.5 mph, the effective

wind speed inside the bowl would be much less.

3.2.2 Concentrator Efficiency

Each time a ray bounces off the concentrator, it does not transmit all the

power to the receiver, due to various factors, e. g. , absorbtion within the mirror,

shading, gaps between mirrors, etc. Considering a clean mirror and perfect

curvature, and an 8 percent loss accounted for those causes, a mirror efficiency

product "'• of .92 was considered for the present study (also for easy comparison

with the energy computed by Hedberg [3]). TJ• can be considered as the mirror

surface loss factor, i. e., if a one bounce ray would transmit 92 percent of its

power then a ray bouncing five times would transmit only TJ! or 66 percent of

its original power. Bowl tilt angle of 15 degrees and a cylindrical receiver were

considered. For this energy computation, inputs to the ROSA code used are

contained in Appendix A.

16

The code divides the receiver into 100 equal divisions and gives an average

concentration for each one of those 100 points in terms of number of suns. The

area of a single division would be 21rrh where r is the radius of the receiver and

h is the height of each division. For unit radius of curvature and according to

the original design dimensions of the Crosbyton receiver radius, r and h would

be .00667 and .005, respectively. If C(zh) is the concentration at any point (h),

then the power imparted to the receiver [3] is

100

Pr = 27r * .00667 * .005Idn L C( zh) (3.10) h=1

and if the input power is given by Eqn. 3. 4 then concentrator efficiency is

or, 100

"leone= .00021 L C(zh)/AE. (3.11) h=1

Inclination(!), normalized imparted power (Pr ), normalized effective aperture

area ( AE ), and concentrator efficiency ("leone) are contained in Tables 3.3 through

3.6 for a number of bowl configurations. Other tables are included in Appendix

A. Figure 3. 2 shows a plot of concentrator efficiency versus inclination angle for

different rim angles.

3.2.3 Receiver Efficiency

The Receiver Heat Transfer Code (RHTC) calculates the receiver efficiency

after taking care of the radiation and convection losses. Two sets of inputs were

used to run this code and are listed in Appendix A. One set considers the bowl

17

geometry which was designed originally for the 5 Mw plant at Crosbyton [6,

7, 10]. The other set contains the bowl geometry used by Hedberg [3). It was

observed that if an optimum mechanical design can be made, the bowl geometry

(i. e., length, diameter, wall thickness and number of tubes) of the receiver effect

the "'rec values to a very small extent. The receiver efficiency TJrec for several bowl

configurations is also included in Tables 3.3 through 3.6. Figure 3.3 is a plot for

receiver efficiency versus inclination obtained with the Barstow data used. The

efficiency of the boiler, when it cannot produce 1000° F steam, was not included

in these tables. A mode should be chosen to operate the boiler at this point.

This problem is discussed in sec. 3.3.

The receiver efficiency '1'/rec is a function of output temperature and pressure.

As the temperature and pressure requirement go up, the effective solar day

becomes shorter. This is because, when the sun is low in the sky, the effective

aperture of the bowl is smaller and less power is imparted to the receiver to

produce high temperature superheated vapour.

If the application of the steam is to produce electricity, then turbine quality

steam has to be produced. Watson [7) considered 850° F, 950 psia steam, while

Hedberg considered close to 1000° F, 1000 psia steam, to be produced at the

receiver end. For this study, 1000° F temperature and 1000 psia pressure output

requirements were considered. Of course, there were reduced mass flow rate and

lower efficiency [21] when these higher temperature set points were set. Figure

3.4 is a receiver efficiency plot for a 60° bowl for different temperature setpoints.

18

3.2 .4 Energy

Normalized annual energy outputs (considering unit radius of curvature),

for different bowl configurations were calculated (Tables 3. 7 and 3.8) using the

Barstow weather data. Actual energy can be found by multiplying these with

the square of the radius of curvature R 2 •

3.3 Low Insolation Energy

3.3.1 Mode of Operation

The reason behind switching from one mode of the boiler to another is to

maximize the solar penetration and to prolong the lifetime of the boiler. Operat

ing the boiler at each instant with the highest possible TJrec would not maximize

the solar penetration in terms of useful energy produced; because this strategy

would result in production of more low quality steam or hot water.

The mode for producing the expected 1000° F and 1000 psia steam is known

as the quality (Q) mode. If the boiler produces quality steam at the expense of

very high radiation losses, then high wall temperature reduces the boiler lifetime.

At this point the boiler should be switched to another auxiliary (A) mode where

it would still produce steam but of lower temperature. When the boiler cannot

produce steam, it is operated in the default (D) mode where it produces 500° F

feedwater.

Although, the strategies might be different [7], for a large multibowl plant,

the above strategy ( QAD) was chosen for the present study, because it was the

most practical approach for analyzing the performance of the receiver.

19

In running the RHTC, the auxiliary mode was chosen when the radiation loss

exceeded the net heat supplied to the working fluid (the wall temperature became

very high at this point). The auxiliary mode set point was 700° F temperature

and 900 psia pressure.

3.3.2 Excess Energy

This section includes the methodology adopted to find the usable excess

energy that can be added to the annual quality steam output of each bowl, by

utilizing the auxiliary mode 700° F and 900 psia energy. Two possibilities might

be investigated to extract more energy, although the choice would depend on

which is more cost-effective. This study did not include the cost prospective of

these two methods.

The first possibility would be to preheat feedwater which would provide

turbine quality steam in the auxiliary mode. Another choice would be to use

the output of some bowls in a plant, to provide pre-heated fluid to other bowls

which would then produce quality steam.

The theory and the computer program for calculating this extra energy are

developd in Appendix A. The RHTC code was run for the auxiliary mode re

ceiver efficiency and energy was calculated from Eqn. 3.8. The energy necessary

for each bowl to produce quality steam was found by considering the shortage

in enthalpy, i.e.,

Delbtu = (1.505- Hout)m (3.12)

where m is the mass flow rate (lbm/hr in thousands) and Hout is the output

enthalpy (Btu/lb in thousands). If fossil energy is added then this is the amount

20

of additional energy (MBtu) necessary for each bowl. It was considered that

some of the energy would be lost in the pipe lines in order to supply the output

of one bowl to some other bowls. A variable line loss factor (2.5, 5, 7.5 percent)

was taken into consideration.

Tables 3.9 and 3.10 show the original and the increased energy (MBtu) pro

duced by each bowl, having the dimensions of the baseline bowl, i.e., 112 feet

radius of curvature and 5 percent line loss. These tables also show the number of

bowls one bowl can support (N sup), additional energy (MBtu) necessary to ex

tract this energy (which is always zero for the preheating case), and the average

annual increase in output for each bowl of the plant "'iner . Of course the number

of bowls in the plant was a variable and the tables give a good indication of the

most suitable number of bowls, for a plant for different rim angles. For a 60°

bowl, energy increase from auxiliary mode is negative because it operates in the

quality mode (even with low insolation levels) where it needs a small amount

of additional energy to produce 1000° F steam. Figure 3.5 shows that more

energy would be available from low rim angle bowls. Figure 3.6 shows the effect

of number of bowls on the auxiliary mode energy collection. If fossil energy is

added then the number of bowls has no effect, whereas when energy of one bowl

is used to preheat other bowls, energy increase depends on the number of bowls

one bowl can support (N sup in Table 3.9).

3.4 Energy with Short Receiver

A bowl with low rim angle does not need a receiver having a length of half

the radius of curvature. A study was performed to compute energy for 30°, 35°

21

and 40° bowls with receiver lengths upto 60 percent shorter than R/2. A 25°

bowl was not considered because it produces 1000° F steam for only a very short

period of time.

A small correction was necessary for the RHTC code, because it considers

receiver length as 100 percent of R/2 and reads both receiver position (z) and

concentration (C) from the ROSA generated data. Since the receiver length is

being truncated, z would not be equal to R/2. Care should be taken that the

RHTC does not read z but calculates it according to the new receiver length.

Since the length is being reduced, the number of tubes had to be reduced ac

cordingly to maintain the output temperature and pressure requirements.

Figure 3. 7 shows the annual energy loss for bowls with shorter receivers.

It can be seen that for a 30° bowl the receiver length can be easily reduced

to half or even shorter depending on the cost per unit energy produced (more

discussions are included in chapter 5). It was observed (Fig. 3.7) that a 30° bowl

gained energy up to 40 percent of its original length reduction, whereas a 35°

bowl gained only up to 10 percent of its length reduction. This can be explained

by the fact that for low rim angle bowls, when the receiver length is R/2, heat

loss due to radiation from the lower part of the receiver is more than what it

gains in this region.

22

r----------- -· ··-· ------ -·· ·- -- ·- ----

--- FftotaTA ME.A ,.._~--

'

. ' \

Figure 3.1: Projected aperture area and reflecting characteristics at 30 deg. inclination

23

Table 3.1: \~leather data sorted by inclination

Idn > 300w/m2

NO OF SU111IED AVG NO OF SU1HdED AVG I HOURS ENERG\~ PO\VER I HOl"RS ENERGY PO\YER

I

de a hrs kw-hr/m 2 kw/ m 2 I deg hrs kw-hr/·m2 kw'j m 2 0 I 1 0 0.0 0.0 23 49 43.49 .887 2 0 0.0 0.0 2-! 48 42.64 .888 3 7 6.03 .862 ')-...... ,) -!8 4'J --....... ,J,J .886 4 20 18.20 .910 26 31 28.09 .906 ,J 14 12.36 .882 ')-_, 26 22.16 s-') . ,) ......

6 49 44.87 .915 28 21 17.53 .835 7 9 8.78 .975 29 26 23.16 .890 8 20 16.58 .829 30 21 19.73 .939 9 33 30.25 .916 31 21 18.35 .81-!

10 -!3 39.4 .916 32 -- 6-!. 71 .862 /,J

11 32 27.75 .867 33 52 -!-!.81 .861 12 16 14.57 .911 34 56 48.74 .870 13 13 11.93 .918 35 42 35.84 .853 14 14 12.07 .862 36 45 39.02 .867 15 9 7.83 .870 37 1-! 63.68 .860 16 10 9.27 .927 38 61 52.28 .857 17 16 13.42 .838 39 69 59.93 .868 18 46 40.59 .882 40 58 50.59 .872

19 39 36.32 .931 41 51 43.37 .850 20 51 44.67 .876 42 49 42.71 .871 21 25 20.61 .824 43 66 56.67 .858 22 27 22.95 .850 44 61 52.79 .865

24

Table 3.1: continued

Idn > 300w/m2

NO OF SU11MED AVG NO OF SU1111ED AVG I HOURS ENERGY PO"TER I HOURS ENERGY PO\VER

deg hrs k\v-hr/m 2 kv·:/ m 2 deg hrs kw-hr/m 2 kw/ m 2

45 53 44.81 .8456 68 45 28.69 .637 46 46 86 74.01 .8607 69 37 24.8 .670

47 83 70.08 .8444 70 50 30.80 .616 48 53 44.16 .8333 71 24 14.48 .603 49 56 -! 7.38 .846 72 20 11.23 .561 50 81 67.81 .837 73 53 35.07 .661 51 56 46.81 .836 74 44 26.-!5 .551 -') 51 41.81 .816

,..._ 37 20.41 .547 ,) ..... {,)

53 61 - 49.92 .818 76 44 24.10 .500 54 57 45.60 .800 77 64 32.00 .511 55 55 44.54 .809 78 59 30.14 .491 56 31 24.69 .796 79 40 19.64 .451 57 29 22.60 .779 80 31 14.00 .-!-±5 58 32 23.27 .727 81 23 10.24 .426 59 72 54.77 760 82 17 7.24 ...126 60 53 42.22 .796 83 11 4.04 .367 61 42 31.96 .761 84 3 1.038 .346 62 42 30.99 .737 85 1 .3428 .3-!2 63 51 38.24 .75 86 30 13.12 .-!37 64 75 53.02 .707 87 19 8.54 .449 65 86 61.11 .716 88 8 2.72 .340 66 41 28.87 .704 89 1 .3131 .313 67 44 29.28 .665 90 8 2.7239 .3405

25

Table 3.2: Data sorted in 10 deg. inclination steps

Inclination Insolation Hours . Idn· Hri 1

I

de a 0 kw/m2 Hrs.

5 .905 195

15 .888 246

? ... _.) .878 322

35 .864 553

45 .851 639

55 .797 497

65 .697 573

75 .547 416

26

Table 3.3: Receiver and concentrator efficiencies: ()R = 30°

I AE Pr 7Jconc 7Jrec de g. m2 kw/ m 2

5 .7824 .7212 .922 .779 15 .7586 .7 .922 .741 25 .7118 .655 .921 .662 35 .6433 .583 .906 .46 45 .555 .583 .83 55 .45 .321 .712 65 .331 .182 .55 75 .203 .083 .408

Table 3.4: Receiver and concentrator efficiencies: ()R = 60°

I AE Pr 7Jconc 7Jrec

de g. m2 kw/ m2

5 2.347 2.155 .918 .872 15 2.275 2.065 .907 .867 25 2.135 1.917 .897 .845 35 1.930 1.715 .888 .827 45 1.666 1.483 .890 .783 55 1.351 1.209 .894 .711 65 .996 .865 .868 75 .6098 .512 .838

27

Table 3.5: Receiver and concentrator efficiencies: BR = 30°, 2¢0 = 90°, BH = 15°

I AE Pr 7]conc 1Jrec

de g. m2 kw/ m 2

5 .9901 .9113 .920 .827 15 .9839 .9053 .920 .817 25 .9479 .8721 .919 .773 35 .8832 .6472 .732 .565 45 .7916 .5824 .735 55 .6759 .4776 .706 65 .5397 .3307 .613 75 .3871 .2103 .543

Table 3.6: Receiver and concentrator efficiencies:

8 R = 35°, 2cf>o = 110°, 8 H = 20°


de g. m2 kw/ m 2

5 1.381 1.271 .92 .854 15 1.389 1.278 .919 .856 25 1.355 1.246 .919 .834 35 1.279 1.143 .893 .779 45 1.165 .749 .643 .49 55 1.105 .648 .638 65 .834 .515 .617 75 .628 .356 .566

28

1

0.9

0.8

6 _,. 0.7 -LLJ

D ~ 0.8 w a: 0.5 ~ <{ 0! .._ 0.4 _,. -LLJ 0 z 0.3

8 0.2

0.1

0 5 15 25 35 45 55 85 75

RIM ANGLE. degree:. c 30 ~ 40 A 45 X 80

Figure 3.2: Concentrator efficiency vs. inclination

29

0.88

0.86

0.84

0.82

0.8

~ 0.78 i ~ 0.78 ... .,

0.74 c. G 0.7.2 > -., M 0.7 a::

0.88

0.66

0.84

0.82

O.B 0

0 35 deg.bowl 80 dag. bowl

Figure 3.3: Receiver efficiency vs. inclination

30

: .·· .

.. · . Ct. 95 ··--------·------------------·------·-----

0.9

0.65

~ 0.8 c C) ·-t) u. '5 ~

'to-., c. I) 0.7 > ·-tl ¥ 0.65 a::

0.6

0.55

o.s -·--· 0 20 40

Incsllna.tlon (d•g.) D 700 dag .,.

4- 85(1 diig fi r

Figure 3.4: Receiver efficiency for different temperature setpoints

31

Table 3. 7: Calculated energies for different bowls

Bowls without iris Rim angle Energy de g. kw-hr 30 462.03 35 703.34 40 1170.74 45 1527.0 50 2043.9 ....

2468.95 i)i)

60 2961.63

Table 3.8: Calculated energies for different bowls with iris

Bowls with iris Rim Iris Iris Energy angle height width

deg deg deg kw

30 15 90 695.23 30 20 90 730.19 30 20 100 756.56 30 20 110 779.45 35 10 80 756.89 35 15 90 1169.39 35 20 90 1270.99 35 20 110 1347.99 40 15 90 1065.58 40 20 90 1815.00

32

Table 3.9: Annual increase in energy output from auxiliary mode operation

No. of Bowls = 10 Bowl Steam New Nsup Add. I ncr . . nm steam energy energy de g. MBtu MBtu . MBtu 1Jina

30.0 17914.5 20418.5 7 0.0 14.0 35.0 27145.5 34856.9 9 0.0 28.4 40.0 45895.6 49000.3 7 0.0 6.8 45.0 59558.4 66184.3 9 0.0 11.1 50.0 78345.5 82304.4 8 0.0 5.1 55.0 94336.8 100896.5 9 0.0 7.0 60.0 113268.9 113133.5 0 0.0 -0.1

Table 3.10: Energy increase by adding fossil energy

No of Bowls = 10 Bowl Steam New Nsup Add. Incr. . steam energy nm de g. 11Btu 1t1Btu 1IBtu T]incr

30.0 17914.5 21491.7 0 44.0 20.0 35.0 27145.5 35577.9 0 66.3 31.1 40.0 45895.6 50330.9 0 49.6 9.7

45.0 59558.4 66920.5 0 66.3 12.4

50.0 78345.5 83294.1 0 49.6 6.3 55.0 94336.8 101533.5 0 58.7 7.6

60.0 113268.9 113133.5 0 -13.5 -0.1

33

32

30

28

26

~ 2+

z 22

~ 20 >-~ 18

z 16 LIJ

~ 1+

12 z -r -~ 10

8

6

+ 2

JO

0 RIM ANGLE, dogrooo

FooDil -+ Pr~hoot

• Figure 3.5: Annual energy increase from auxiliary mode energy

34

30 PRE: HEAT

28 t~ 26 -~

I

~

-; 20 ~ 18 >-~ 16 ..... 1+ L.

L1J

~ 12

10 ~"~ :;. .... z ~

~ ~. ~ J -~~~-{i( ... ~__-Q-- '~~ ..,

" • 0

30 3+ 38 +2 +6 50 5+ 58

- a 15 BOWLS RIM ..A.NG~ d09rccD + 7 BO S 0 10 BOWLS

"'

FOSSIL 3+ 32

'\ .

1/ \

~ \\ -;

~ 22

20 >-ffi 18

z 16 L1J

~ 1+

12 z z 10 -· -.. 8

6

+ 2

0 30 3 .... 38 +2 +6 50 5+ 58

0 15 BOYlLS RIM ANGL~ d09rccD + 7 80~ s 0 10 EK~NLS

Figure 3.6: Effect of bowl number on extra energy I

35

q

~+-----------~-----------r----------~----------~~--------~ 20.0

Figure 3. 7: Percent energy loss tor short receivers

36

CHAPTER 4

COST ANALYSIS

This chapter represents an effort to identify the cost increase pattern of a

solar bowl with increasing rim angle and/or aperture diameter. The objective

was to estimate the costs associated with principal bowl parts and then adding

those to find the total bowl cost for each bowl configuration. This investigation

is based on the structural study done during the construction of the 65-foot

bowl at Crosbyton [1]. This analysis used the same assumptions that were used

during the design of the baseline bowls (of the 5 Mw plant) [8, 9].

Cost estimates of a bowl and the resulting unit cost of energy produced, can

vary considerably between a prototype bowl and that of a commercialized one.

Obviously this study is of the former type.

4.1 Component Costs

4.1.1 Baseline Design

The principal cost components were the excavation cost, sub-structure cost,

super-structure cost, general concrete and reinforcing bars, mirror panel and

receiver cost. Excavation cost was estimated considering the bowl geometry and

the corresponding volume of excavation. Maximum (underground) depth of the

vertex of the bowl was considered as 20 feet, as suggested in Ref.[8].

The structural analysis data for calculating the sub-structure and super

structure cost for different configurations of bowls can be found in the Interim

Technical Report, volume 1, [1]. Figures 4.1 and 4.2 show how the sub-structure

37

and super-structure weight increases with increasing surface area. Concrete

volume and reinforcing bar weight were estimated by adding the sub-structure

and super-structure weight and using the baseline design estimation.

Receiver and boom weight with increasing diameter of curvature is shown

in Fig. 4.3 [1]. The corresponding weight of the receiver support structure

was found (from the baseline design) to be approximately eight times that of

the receiver and boom weight. Figure 4.4 [1] shows the decrease in structural

weight of a receiver, with the length of the receiver reduced to less than 100

percent of R/2.

All these structural analyses were done during or prior to the construction

of the 65-foot Crosbyton bowl. Several literatures [8, 9, 19] reported that the

structural support for the Crosbyton bowl was overdesigned; therefore, for the

baseline design of the 5 Mw plant, the bowl structural weights were decreased to

one-half (or one-third) of the values found from the curves (Figs. 4.1 to 4.3). The

present study also uses the same observation. For this analysis, the component

structural weights corresponding to surface area (or radius of curvature) of each

bowl configuration, were taken from these curves (Figs. 4.1 to 4.3).

Table 4.1 (items 1 to 10) lists the costs per unit weight (or volume), used

in this study which is based on the baseline design [8, 9] and also based on the

analysis of Jonish and O'Hair [19]. These unit costs also include the construction

or installation cost, management and profit. The costs given in terms of per unit

surface were multiplied by the bowl surface area which is given by,

( 4.1)

where R is the radius of curvature and BR is the rim angle of the bowl.

38

All the component costs were calculated in 1982 dollars (no inflation factor

was assumed) and then converted to normalized cost factors (CF), with respect

to the baseline bowl in order to make the study as general as possible. Tables

4.2 and 4.3 include the cost factors of principal bowl components for different

rim angle bowls.

Appendix B includes the cost analysis code ( COST1) developed for the

present study. The COST1 code computes the cost and the corresponding en

ergy per unit cost, for bowls with different rim angles but with the same radius

of curvature. The structural weight and the energy should be input to the code.

The weight and cost reduction factors, due to receiver truncation, for 30°, 35°

and 40° bowls are 'hard-wired' in the RECTRUN subroutine. Another program

similar to COST1 was used to estimate cost for varying rim angle and aper

ture diameters. The rim angles were varied from 30° to 60° and the aperture

diameters considered were 100, 150, 200 and 250 feet. Four distinct sets of var

ious structural weight data were used (from curves 4.1 to 4.3) for four different

aperture diameter values.

4.1.2 Alternate Shallow Bowls

Although there are several different options of constructing a bowl, two major

cost items which vary are the support structure cost and the reflector cost.

Since the variation in energy output for using other reflectors (i.e., membrane,

sheetmetal, etc.) is unknown, this study did not include those scenarios.

The Baseline design (scheme 1) represents the most expensive verified ap

proach for the bowl concept. One other less expensive scenario, as discussed by

39

Jonish and O'Hair [19], was also included in this analysis. This method consists

of forming an accurate spherical reinforced concrete slab directly on the soil, and

then gluing flat mirrors directly to the slab. This method (scheme 2) should ap

proximately represent the cheapest bowl construction possible, using mirrors as

the reflecting surface. Items 1 to 3 and 7 to 10 in Table 4.1 are common to

both of these scenarios; whereas items 11 through 13 are only applicable to this

method (scheme 2).

4.2 Bowl Cost

Table 4.4 shows the normalized costs (Total CF), with respect to the baseline

bowl, for different rim angle bowls with the radius of curvature being fixed.

Column 3 represents the same, but using a receiver length less than 100 percent

of R/2. The receiver length which produces maximum energy per unit cost

(E/C) was chosen. Discussion on the variation of E/C with receiver length is

included in chapter 5. Table 4.5 shows the variation in total CF for scheme 2.

Figure 4.5 shows the cost increase pattern for scheme 1 and scheme 2 . Table

4.6 includes the normalized costs (Total CF) for bowls with four different sets

of fixed apertures and varying rim angles. Figure 4.6 is a plot of CF for varying

aperture diameters (i.e., increasing radius of curvature) for a 30° bowl.

4.3 Iris Cost Approach

This section includes the methodology of defining a comparatively realistic

approach to estimate the cost of constructing an iris. Anderson and Obeyesekere

40

[12] have shown that the area of an iris (Fig. 1.3) is given by

sA - 7r </>I R2 ( (} (} ) IRIS -180

curv COS R- cos I ( 4.2)

where, <I> I is half the iris width, (}R is the rim angle of the bowl, and (}I is (}R + 8H,

i. e., bowl rim angle plus the iris height.

Mirror panel cost per unit surface area times the surface area of the iris give

the mirror cost of the iris. The super-structure cost of the bowl (rim angle 8R),

without the iris, was subtracted from the super-structure cost of a bowl having a

rim angle of 8I, (8I = 8R+8H)· Then this cost, multiplied by the iris width ratio

(iris-width 2</>0 /360°), was taken as the super-structure cost of the iris. The Sub-

structure cost was calculated following the same procedure. Both sub-structure

and super-structure costs were increased by 20 percent for the construction of

the tracking structure. Fifty percent of the original bowl excavation cost was

added for the excavation of the rail-road tracker.

The COST1 code also calculates the iris cost by applying the above approach.

For scheme 2, the iris cost was kept the same as scheme 1; since the iris has to be

movable, stable steel structure support for mirrors is essential. Table 4. 7 shows

the normalized costs (Total CF) obtained for all bowl configurations considered,

both for scheme 1 and scheme 2.

41

-~ ~ . ._.

t-:I: ~ --IJJVJ ~"'0

c ~s ::l:J .,_o Of-::l'-a: t-U1 I

m :::> Ui

4-50,--

I 400 I -.c-._h.JV

:300

250

200

150

100

50 _J I I

v I

0 20 40 80 (Thousands)

SURFACE ARE.A .. ~sqft)

80 100

Figure 4.1: Sub-structure weight vs. surface area; data obtained from CSPP report vol. 1 [1]

42

-... .B ..;::.. ·t-:z: (!J

!:U..-. :>n w-g ~R -J, t--oo -:::Jf: a:......, ~ I ~ UJ u. ::l ,,

~0

400

350

300 J I

250 l 200 _J

150 l 100

50

(j

0 20

"\..&..&•_.. ... _____ •

40 80 (Theus ends)

SURFACE AREA {sqft)

BO 100

Figure 4.2: Super-structure weight vs. surface area; data obtained from CSPP report vol. 1 [1]

43

,...._ .B -~' t-:a:: <!J

~~ ::1-'lJ ~c

S§ mo

~t ~

~ ~ !.!.! cr

16 .

15 / 1.:!. /

12 -i / /

11 -j 10

9

8

7

8

c: w

4

50 70 90 110 130 150 170 190 210 2~0

CURVATURE DIAMETER (ft)

Figure 4.3: Receiver and boom weight vs. dia. of curvature; data obtained from CSPP report vol. 1 [1]

44

z 0 -r- 16 ---u :J 0 lU 15 Q( ,...... CIJ

..0 14 .;::.

~ u [ij..,_ 13 3:VJ

"'0 ::;!C oo

12 oVJ m~ ~~ - 1 1

~ w 0 w 0::

10

9

8 ~--------~----·----.--------~---- --.-·--------~------~ 40 60 BO 100

RECEIVER LENGTH (PERCENT OF R/2)

Figure 4.4: Receiver and boom weight reduction with receiver length truncation; after CSP P report vol. 1 [1]

45

Table 4.1: Unit construction costs

Item Component Unit cost * nO. (dollar)

1. Excavation 2.57 jyd3

2. Concrete( gen.) 73.72/yd3

3. Reinforcing bars 925.13/ton

4. Sub-structure 3,254.95/ton

steel support, fa b. 5. Superpanel steel 4788./ton /

and fabrication 6. Iv1irror panel 13.5/ ft 2

7. Receiver support 6270.24/ton v 8. Solar receiver 84,436/ton

9. Hot spot .235/ ft 2

protection system 10. Painting, pump, 1.1111 ft 2

etc. 11. Special curved 6.70/ft2 /

forms /

12. Construction of 2.74/ ft 2

the ·concrete slab 13. Flat mirrors on 3.0/ ft 2

concrete slab

* The sources are Re£.[8] and Re£.[19] and current analysis.

46

Table 4.2: Subcomponent cost factors for bowls with same radius of curvature; normalized with respect to the baseline bowl

FIXED RADIUS OF CURVATURE RIM EXCA- SUB- SUPER- CON CR. REO- MIRROR ANG. VATION STRUC. STRUC. R. BAR CEIVER PANEL

30 .000358 .006057 .040097 .001083 .177437 .100614 0

35 .001114 .009086 .055691 .001526 .198673 .135816

40 .002659 .013326 .080195 .002204 .286290 .175700

45 .005362 .022412 .102918 .003002 .286290 .219962

50 .009611 .034831 .133659 .004085 .286290 .268266

55 .015783 .053003 .162618 .005315 .286290 .320244

60 .024209 .068147 .202716 .006641 .286290 .375-199

47

Table 4.3: Subcomponent cost factors for bowls with fixed aperture diameters; normalized with respect to the baseline bowl

APDIA RIM EXCA- SUB- SUPER-feet de g. VATION STRUC. STRUC. 100 30 0.0005 0.0048 0.0311 100 35 0.0006 0.0048 0.0325 100 40 0.0010 0.0051 0.033-1 100 45 0.0015 0.0054 0.0343 100 50 0.0022 0.0057 0.0356 100 55 0.0029 0.0060 0.0378 100 60 0.0038 0.0066 0.0400 150 30 0.0010 0.0145 0.0801 150 35 0.0020 0.0148 0.0824 150 40 0.0035 0.0163 0.0846 150 45 0.0053 0.0172 0.0891 150 50 0.0074 0.0187 0.0926 150 55 0.0088 0.0208 0.0980 150 60 0.0083 0.0227 0.1033 200 30 0.0023 0.0499 0.1657 200 35 0.0049 0.0530 0.1715 200 40 0.0083 0.0560 0.1804 200 45 0.0126 0.0590 0.1857 200 50 0.0128 0.0620 0.1951 200 55 0.0119 0.0681 0.2031 200 60 0.0113 0.0754 0.2138 250 30 0.0046 0.1114 0.2539 250 35 0.0095 0.1150 0.2606 250 40 0.0162 0.1196 0.2650 250 45 0.0176 0.1272 0.2704 250 50 . 0.0162 0.1350 0.2771 250 55 0.0151 0.1438 0.2851 250 60 0.0143 0.1559 0.2940

48

Table 4.3-continuel- .

APDIA RIM CON CR. RECEIVER J\1IRROR feet de g. R.BAR PANEL 100 30 0.0008 0.1634 0.0802 100 35 0.0008 0.0942 0.0822 100 40 0.0009 0.0754 0.0847 100 45 0.0009 0.0618 0.0876 100 50 0.0009 0.0555 0.0911 100 55 0.0010 0.0419 0.0951 lOO 60 0.0011 0.0335 0.0997 150 30 0.0022 0.2220 0.1804 150 35 0.0023 0.1885 0.1851 150 40 0.0024 0.1644 0.1906 150 45 0.0025 0.1414 0.1972 150 50 0.0026 0.1236 0.2049 150 - 55 0.0028 0.1047 0.2140 150 60 0.0030 0.0942 0.2245 200 30 0.0052 0.3037 0.3208 200 35 0.0055 0.2660 0.3291 200 40 0.0058 0.2325 0.3390 200 45 0.0060 0.2074 0.3507 200 50 0.0063 0.1885 0.3644 200 55 0.0067 0.1738 0.3804 200 60 0.0071 0.1634 0.3991 250 30 0.0092 0.3875 0.5013 250 35 0.0094 0.3310 0.5142 250 40 0.0097 0.2974 0.5296 250 45 0.0101 0.2681 0.5479 250 50 0.0105 0.2451 0.5694 250 55 0.0109 0.2283 0.5944 250 60 0.0115 0.2178 0.6236

49

Table 4.4: Normalized total cost factors ( CF) with and without receiver truncation: scheme 1

RIM CF CF

ANGLE (RECEIVER (RECEIVER LENGTH R/2) TRUNCATED)

30 0.442499 0.333672 35 0.502706 0.415091 40 0.577429 0.577429 45 0.661296 0.661296 50 0.762779 0.762779 55 0.874335 0.874335 60 1.0 1.0

Table 4.5: Normalized total cost factors (CF) with and without receiver truncation: scheme 2

RIM CF CF

ANGLE (RECEIVER (RECEIVER

LENGTH R/2) TRUNCATED)

30 0.379422 0.270595 35 0.415085 0.327470 40 0.454347 0.386514 45 0.498949 0.498949 50 0.549127 0.549127 55 0.604784 0.604784 60 0.665885 0.665885

50

E ·~ ~ 0 a. t)

8 ~ u - -~ ~ ~,

8

1

l ------

0.9 ~ I I

v.c i I I

r'\7j -- I I

O.B l 0.5 ··i

I

30 38 42 48 50 54 58

Rim engle deg. D S1 .._ SJ.

Figure 4.5: Cost increase pattern for scheme 1 and scheme 2; fixed radius of curvature

51

Table 4.6: Normalized total cost factors (CF) with fixed aperture diameter and varying rim angles

APERTURE RIM CF CF (receiver DIAMETER ANGLE truncated) 100 30 0.311678 0.232031 100 35 0.247900 0.210906 100 40 0.233409 0.228643 100 45 0.224761 0.224761 100 50 0.224566 0.224566 100 55 0.218695 0.218695 100 60 0.219225 0.219225 150 30 0.570880 0.462642 150 35 0.549287 0.475299 150 40 0.536582 0.526188 150 45 0.528057 0.528057 150 50 0.526108 0.526108 150 55 0.526126 0.526126 150 60 0.533993 0.533993 200 30 0.969182 0.849979 200 35 0.957748 0.853343 200 40 0.950733 0.936036 200 45 0.951307 0.951307 200 50 0.960477 0.960477 200 55 0.976969 0.976969 200 60 1.004714 1.004714 250 30 1.434056 1.281970 250 35 1.415981 1.315419 250 40 1.415335 1.396534 250 45 1.420780 1.420780 250 50 1.434819 1.434819 250 55 1.461701 1.461701 250 60 1.503973 1.503973

52

;:-- •• r!

~ tz :J

'1 .4

1.3

1.2

'1.1

1

0.9

o.e I 0.7 1 0.6 J 0.5

0.4

_,/ ,./

//

///-·

_/ _./

(

0.3 -r---.--~---.------.r---r---~--.---,---~---r---r--~--~--~~~ 100 '12.0 '140 '180 180 200 220 240

APERTURE DIAMETER (ft)

Figure 4.6: Cost increase with aperture diameter for a 30° bowl

53

Table 4.7: Normalized total cost factors (CF) of all bowls with and without iris for scheme 1 and scheme 2

RIM IRIS IRIS CF CF ANGLE HEIGHT \VIDTH SCHM 1 SCH~~I 2 30 0 0 0.442499 0.379422

35 0 0 0.502706 0.415085

40 0 0 0.577429 0.454347

45 0 0 0.661296 0.498949

50 0 0 0. 762779 0.549127

55 0 0 0.874335 0.604784

60 0 0 1.000000 0.665885

30 15 90 0.496268 0.433191

30 20 85 0.516924 0.4538-18

30 20 90 0.521292 0.458215

30 20 95 0.525659 0.462583

35 10 85 0.540288 0.452667

35 15 90 0.567490 0.479869

35 20 90 0.594624 0.507003

35 20 95 0.599700 0.512078

40 15 90 0.651525 0.528442

40 20 90 0.681912 0.558829

40 20 110 0.704835 0.581752

54

CHAPTER 5

COMPARISON OF ENERGY PER UNIT COST

5.1 Effect of Truncated Receiver

As discussed in sec. 3.4, energy loss was computed for receiver lengths re

duced by upto 40 percent of R/2 for 30°, 35° and 40° bowls. The corresponding

cost reduction method was also discussed in sec. 4.1.1. Energy per unit cost

(E/C) produced for these short receivers was computed by the COST1 com

puter code. Figure 5.1 shows the change in E/C with receiver length reduction.

It can be observed that for a 30° bowl, maximum E/C can be obtained with

a receiver length of 40 percent of R/2 (60 percent reduced); ,,·hereas for a 35°

bowl maximum E/C is attained with a receiver length reduced to 50 percent of

R/2. Since the cost reduces considerably, these receiver lengths can be used as

optimum lengths for the above two bowl configurations.

For a 40° bowl, E/C starts decreasing (Fig. 5.1) with the reduction of its

original length (R/2). Furthermore, the E/C curve for the 40° bowl is drawn

upto 40 percent length reduction point because it was found that if the receiver

length for a 40° bowl is reduced more than 40 percent then it cannot produce

1000° F temperature and 1000 psia pressure steam. That means, the 40° bowl

produces the maximum energy per unit cost with the receiver length being 100

percent of half the radius of curvature. This implies that, reducing the receiver

length of any higher rim angle ( > 40°) bowl would not be justified. Figure 5.2

is a plot of E/C versus different rim angle bowls using both optimum and 100

percent of R/2 receiver lengths.

55

5.2 Effect of Bowl Parameters

5.2.1 Rim Angle

Table 5.1lists the energy per unit costs for a number of bowl configurations

with different rim angles (radius of curvature (R) being fixed), both with and

without iris. The energy output for bowls with iris were used from Hedberg's

thesis [3], since he computed the output energy using 4000 hours of Barstow data

for a number of bowls with a variety of iris height and width combinations. The

iris cost approach, discussed in sec. 4.3, was used for these iris cost calculations.

This table (5.1) is for scheme 1, i. e., the expensive bowl and iris scenano.

The table gives some intuitive implications that for this expensive scenano,

\vithout iris, a 60° bowl would be the most cost-effectiYe bowl. But if all bowl

configurations ( v'lith and without iris) are considered, then a 40° bo-wl, with an

iris height of 20° and width goo would be a better choice. This is because, \vith

much less expense, it produces more energy than that of a 60° bowl 'vithout iris.

Energy produced per unit cost (E/C) for scheme 2, i. e., concrete bowl, with

flat, fitted mirrors, is included in Table 5.2. This is a cheaper bowl, with an

expensive iris, the engineering design of which may not be technically feasible

for higher rim angle bowls, because it would become very hard to achieve a

smooth, truly spherical concrete surface with the steep curvature of higher rim

angle bowls [1g]. Even though this exact boundery is unknown, for comparison

purposes and from a practical point of view, rim angles upto 40° with and

without iris are included in Table 5.2 . For this scheme, the most economic E/C

can be achieved with a 35° bowl having an iris of 15° height and goo width,

compared to the bowls without iris.

56

5.2.2 Aperture Diameter

It is assumed that the FMDF system considered here would be utilized as a

part of a large plant. Also it is assumed, from a practical point of view, that

economies of scale increases with larger sizes. Four different aperture diameters,

100, 150, 200 and 250 feet, were chosen to find out the effect of the aperture

diameter on maximum energy per unit cost.

Table 5.3 shows that for a fixed aperture diameter, the highest energy per

unit cost can be obtained with the highest rim angle, i. e., 60°. Table 5.3 also

gives an idea of choosing the most suitable aperture diameter (within the range

considered), for a particular rim angle. To get a more intuitive insight on this

matter, the effect of aperture diameter for 35°, 40°, 45° and 55° bowls is plotted

in Fig. 5.3. For example, from the results of this analysis, if a 55° bo·wl is to be

constructed, then a 100-foot aperture diameter should be chosen.

57

I ., .7 -I

I

I 1.6 ..,

I ., .5 _.

I

1.2 ~ I

1.1 -1·

1 ~ ll -----..a--

0.9 ~----------------~---------------------r-----------------~----------------~----------------~--------------~ 0 2.0 40 80

~ REDUCTION IN RECEIVER LENGTH [] 30 d~g.bowl + 3-S deg. bcwl ¢

Figure 5.1: Effect of receiver length reduction on energy /unit cost

58

~-: -,---------- I 2.4 l 2 .. 31 2.2 4

2.1 ~ 21

1.9 1

1.8

1.7

1.6-

1.5

1.4

1.3

1.2

1.1

1

0.9 ~-----r----r----~-----,-------r-----r-----~----~----,----~---~----r---~---~---~ 34 38 42 46 50 54 58

RIM ANGLE (deg.) CI RECL=100~ + SHORT RECEr./ER

Figure 5.2: Energy /unit cost for different rim angle bowls; both with full length receiver and receiver truncated to optimum length

59

Rl1-1

de g.

30

35

40

45

50

55

60

30

30

30

30

35

35

35

35

40

40

40

Table 5.1: Energy/unit cost (E/C) for scheme 1: fixed radius of curvature

IRIS IRIS ENERGY PER HEIGHT WIDTH UNIT COST de g. de g. watt/ dollar 0 0 907.5757

0 0 1213.753

0 0 1758.900

0 0 2003.192

0 0 2324.558

0 0 2449.707

0 0 2569.274

15 90 1635.477

20 85 1839.899

20 90 1900.736

20 95 1946.024

10 85 1745.387

15 90 2095.538

20 90 2283.97

20 95 2317.237

15 90 2359.550

20 90 2669.344

20 110 2790.096

60

Table 5.2: Energy /unit cost (E/C) for scheme 2: fixed radius of curvature

RI11 IRIS IRIS ENERGY PER ANGLE HEIGHT WIDTH UNIT COST de g. de g. de g. watt/ dollar 30 0 0 1058.453

35 0 0 1469.967

40 0 0 2235.386

30 15 90 1873.616

30 20 85 2095.610

30 20 90 2162.385

30 20 95 2211.378

35 10 85 2083.235

35 15 90 2478.171

35 20 90 2678.690

35 20 95 2713.737

40 15 90 2909.127

40 20 90 3257.270

40 20 110 3380.403

61

Table 5.3: Energy /unit cost (E/C) for different aperture diameters: varying radius of curvature

APERTURE Rl1v1 ENERGY PER ENERGY PER DIA11ETER ANGLE UNIT COST: UNIT COST:

REC. LENGTH REC. LENGTH = Rl2 TRUNCATED

feet de g. watt I dollar watt I dollar 100 30 1027.195 1301.638 100 35 1491.038 1663.822 100 40 2098.892 2098.892 100 45 2349.264 2349.264 100 50 2681.585 2681.585 100 55 2908.888 2908.888 100 60 3114.318 3114.318 150 30 1261.817 1468.837 150 35 1514.082 1661.164 150 40 2054.261 2054.261 150- 45 2249.852 2249.852 150 50 2575.391 2575.391 150 55 2720.568 2720.568 150 60 2876.736 2876.736 200 30 1321.338 1479.374 200 35 1543.743 1644.877 200 40 2061.155 2061.155 200 45 2220.200 2220.200 200 50 2507.888 2507.888 200 55 2604.632 2604.632 200 60 2718.132 2718.132 250 30 1395.317 1532.599 250 35 1631.507 1708.272 250 40 2163.366 2163.366 250 45 2322.769 2322.769 250 50 2623.121 2623.121 250 55 2720.122 2720.122 250 60 2837.220 2837.220

62

t(/1) b

z w

D

.3--------

2.9 .., R __ .... ..,...., --. 2.6 .., c --..J

., ... --..J 2.2

2.1

2~ 1.9 jl 1.8

1.7

i 1.8 1_ __ ---e-__ -a.-------l 1.5

1.4 ~------r-----~-----~-----~----------r------r------T------~-----~-----~--~---r--~-~--~ 100 120 140 180 180 200 220 240

APERTURE DIAMETER (ft) .35 deg 45 deg ~ 40 deg 55 deg

Figure 5.3: Effect of aperture diameter on energy /unit cost

63

CHAPTER 6

DEVELOPMENT OF EMPIRICAL EQUATIONS

The objective of this chapter is to develop a number of empirical equations

employing least-square curve-fit from the computed data. These equations may

provide a quick method of computing energy and cost for different solar bowl

configurations without using any computer code. Inclination and bowl rim an-

gle, radius of curvature and aperture diameter are the primary variables for

concentrator and receiver efficiencies, energy output and cost.

6.1 Concentrator Efficiency

As discussed in chapter 3, concentrator efficiency ("leone) was calculated using

the ROSA code results from Eqn. 3.11, which is

100

"leone= .00021 L C(hi)/AE (6.1) h=1

where C( zi) is the concentration in terms of number of suns at any point Zi along

the receiver and AE is the effective aperture area of the bowl. The equation

considered to fit the concentration efficiency data for any bowl is

A(1-cosl) A2 I "leone = "'• 1 COS (6.2)

where "'• is the solar efficiency product, and I is the inclination angle of the sun

from the symmetry axis of the bowl. The parameters to be estimated are A1

and A2. Equation 6.2 is non-linear, but it was transformed to a linear one by

taking logarithmic of both sides.

log "leone = ( 1 - cos I) log A1 + A2log cos I ,. 64

(6.3)

or,

Y = ( 1 - cos I) A + A2 log cos I, (6.4)

where log A1 = A. For the least-square curve fitting approach, the sum of

deviations from the true curve is

n n

S = L f~ = L [Yi- {(1 -cos Ii)A + A2 log cos Ji}] 2• (6.5)

i=l i=l

Here, n is the number of computed data. The least possible value of S in Eqn.

6.5 will produce the best-fit values of the parameters A and A2 • This can be

estimated by differentiating Eqn. 6.5 with respect to the unknown parameters '

A and A2 and setting the results equal to zero. After simplifications the final

equation to be solved would be

A (6.6)

where X 1 = 1-cosii and X 2 = logcosii. Fitted values of the parameters A1 and

A2 are included in Table 6.1 . Both of these parameters show definite patterns

with respect to the rim angle of the bowl. Variations of these parameters with

rim angle are shown in Figs. 6.1 and 6.2. Employing the same procedure, fitted

values for A2 , which are constant for each bowl configuration, were fitted with

the following equation

(6.7)

The final predicted equation for TJconc for all bowl configurations is

_ A(l-cos I)( /)39.45 exp( -7.02148R) T/conc - T/1 1 COS • (6.8)

Thus, only one variable, parameter A1 , corresponding to each bowl rim angle,

is required to compute the concentrator efficiency. In this curve-fit process the

65

range of rim angle ( BR) was taken from 25° to 60° and inclination (I) was in the

range of oo to 90°. For any bowl rim angle (within the used range), A1 can be

found from Fig. 6.1, and Eqn. 6.8 would give the efficiency at any particular

inclination. One other important aspect of this empirical equation is that it is

generalized for any "'a (a loss factor, which accounts for gaps between mirrors,

dirt, shading, etc.) value. This parameter, TJa, is also one of the input parameters

of the ROSA code.

Figures 6.3 to 6.5 show the predicted and computed concentrator efficiencies

for 30°, 45° and 60° bowls for "'a = .92. Also Fig. 6.6 and Fig. 6. 7 show the

predicted and computed concentrator efficiencies with "'a = .86 for a 30° and 60°

bowl, respectively.

6.2 Receiver Efficiency

The Receiver Heat Transfer Code (RHTC) calculates the receiver efficiency.

The receiver efficiency is a function of multiple parameters [18]. The ROSA

code generated heat flux profile along the receiver and is one of the inputs

to the RHTC. The receiver efficiency data obtained for the present study was

for a bottom-feed receiver. The value used for both the emmissivity and the

absorptivity of tubes was .9 and the value used for the thermal conductivity of

the tube walls was 10.6 Btu/hr ft ° F. Ambient temperature and wind velocity

were kept constant and were chosen according to the Barstow weather data.

The ldn was varied according to the weather data and the mass flow rate was

varied to meet the output requirements of 1000° F temperature and 1000 psia

pressure. The efficiency data obtained for each bowl, within all these constraints,

66

was fitted with the equation

(6.9)

by following the same approach described in sec. 6.1. The parameter values

are included in Table 6.2. Figures 6.7 to 6.10 show the predicted and computed

receiver efficiencies for 35°, 45° and 60° bowls, corresponding to varying Idn

(according to the Barstow data).

The receiver efficiency simulation analysis in this study used the measured

1976 insolation values for Barstow, California, in order to be comparable to a

number of studies [2, 3, 22, 23). It should be recognized that the actual climate

in a given year, in a given place, and the output steam-state requirements would

play a major role in the receiver efficiency data. Data that has been collected at

Barstow at 1976 can be considered good relative to the last few years experienced

at Barstow [2). Therefore, the receiver efficiency which can be obtained using

Eqn. 6.9 would only give reasonable values for places situated around 35° N

latitude and climates, which closely resemble the Barstow climate.

The receiver efficiency equation can be generalized by using the following

equation.

(6.10)

where ci 's are the input variables and operating variables used for calculating

the receiver efficiency (Table A.2; Appendix A) and F(Ci) is a non-dimensional

factor of all those variables.

67

6.3 Bowl Cost

The cost for the solar bowl concepts was calculated on component levels, and

the component costs were added to get the total bowl cost both for scheme 1

and scheme 2. All costs were then normalized with respect to the baseline bowl.

The normalized cost was fitted with the following equation.

(6.11)

The above equation is also non-linear with respect to C2 and was made linear

by taking logarithmic of both sides.

The estimated values of the parameters obtained from the least-square curve-

fit are included in Table 6.3 for scheme 1 and scheme 2. Figures 6.11 and

6.12 show the computed versus predicted values of the cost factor (CF) plotted

against the rim angle and aperture diameter. As may be seen in these figures,

the predicted values showed very good agreement with the computed values

within the entire range considered.

6.4 Energy

The following empirical equation was considered to fit the computed data of

energy, obtained in chapter 3.

(6.12)

where 4>1 is the iris width, BR is the bowl rim angle and BH is the iris height.

The estimated values for parameters obtained from the curve-fit (energy in Btu

and R in feet) are included in Table 6.4. Figure 6.13 shows the computed versus

predicted energy values for bowls without iris. Figure 6.14 shows the computed

68

versus predicted energy values for 30°, 35° and 40° bowls with iris and for 30° to

60° bowls without iris. The estimated values of the parameters for bowls with

iris are plotted in Fig. 6.15.

6.5 Energy Per Unit Cost

The empirical equation, which was chosen to fit the computed data obtained

in chapter 5, for energy per unit cost is

(6.13)

This is a non-linear three-parameter equation which was made linear by taking

logarithmic of both sides. Then for the least-square linear curve-fit procedure,

the final equation to be solved took the form,

n

(6.14)

where

Eo log E 1 R2

y log(E /C)

xl log sin iJR

x2 R 2(1 -cos iJR)

Table 6.5 includes the parameter values for both scheme 1 and scheme 2 with

full receiver length and truncated receiver length. Figures 6.16 and 6.17 show

69

the predicted and computed values of E/C for scheme 1 and scheme 2. As it

may be seen in this figure, Eqn. 6.13 gave very good predicted results.

The empirical equations developed in this chapter employ the bowl rim angle

BR, the inclination angle I and the radius of curvature R, to determine the de

pendent variables. The benefit of this is that these equations can have a versatile

use for preliminary screening, in any design system for any bowl configuration.

70

Table 6.1: Concentrator efficiency curve-fit results

RIM Al A2 ANGLE

25 6.518778 1.923266

30 2.257652 1.068405

35 1.400329 0.627043

40 1.032376 0.319966

45 .884411 0.122017

50 .854135 0.04490-1

55 .945259 .063455

60 .942296 0.032900

71

r.:c,,u:enlrcticn efficiency 7 ·-,------ ·-···----------· ·----------.,

35 45

RIM ANGLE (OE:G.)

Figure 6.1: Parameter A1 vs. rim angle

72

55

.. , ... w tUJ

~ ,·4

-0~ ·:!. u.

PARAfv1ETER A2 ~ -·--_______________ c:_u_n_c: cnt.rcti en cffi c::ie nc:y

1. •3 °

1 ~- I -~ 1

, .7 l , .e -f

1.51 1 .4- -1 , , I I • ..J j

1.2-i ,., -f

, i <).9 -1 0 .. 3 ~ 0.7 -1 0.6 -f

Ct.-5 i o.4 I (J •. 3 I " .., • .J - .... 1 0.1 --4

- ~'~------~------~--------~------~------~--------r-------~ '-' .....,

35 45

RIM .ANGLE (DEG.)

Figure 6.2: Parameter A 2 vs. rin1 angle

73

55

;~ _.) z UJ u fl. u. i •• ..... ~ 0 r-: -~J

a:: - t-

"'7" -ld 0 z (J ·:..)

PREDICTED VS COtv1PlJTEC) .:!0 OE:G. BOWL

, .00 .--------··--·------------------------,

0 0.90 "1

0

I

I --. 0 R,.-., i

I I I

0.71) i I I I o.eo ~ I I

0.50 -l I I

0.40

5 15 25 ~5 45 55 135 75

RIM ANGLE 0 cot ... 1P - PREO

Figure 6.3: Predicted and computed values of concentrator efficiency: 30 deg. bowl: 11.= .92

74

.,_ u z UJ u lJ.. LL.. w ~ (l !;;: a!

-~ w 0 z 8

PREDICTED VS CC)~v1PLJTEC) 45 DE:G. BOW'L

, .00 -.,---·-------·--------1

o. 90 -.r---J.L..----~[1!___

I I

o.~o I 0.70 ~

I 0.80 ~

0 .. 50

0.40 ~----------r------~----------,---------~r---------.--------r------~ 5 15 25 :55 45 55 es 75

RIM ANGLE 0 · COMP - PREO

Figure 6.4: Predicted and computed values of concentrator efficiency: 45 deg.

bowl: TJ,= .92

75

~ ..

i::i z w u J,1.. u.. w a= (l r-: ·=1 ~ ,_ -:r - w 0 z 8

PF~E[)I(~TED \/S COtv1F,LJTED 60 DE:G. BOWL

, .oo -1--------· ---------------------------

0.90 D c [] 0

o.eo ~

0.70

0.80

0.-50 ..

~:•.40 -r-----.-----,-----.-----r------r----r-----l 5 15 25 45 55 85

Rl~,-1 ANGLE 0 COMP -- PRED


bowl: T/4 = .92

76

75

,-.... :_.j •::C . i . ., ('I

t) ,..

:::J

..!.. ,_ {j .... ..:.. ... ~ ·~ ,..-u.. ~ w

c:;ot\i1PUTED VS. PREC)ICTED 1

30 OEG BOWL

0.9 I

-t I I 0 []

I 0.~ _J

I I I I

0.7 I , I I I I

0.8 I

-t I . I I

0.-5 J I I I

0.4 I 0 20 40 80

RIM ANGLE (DEG) 0 .8 B COMP .8 B Pf'i.ED


bowl: 7J 11 = .86

77

80

i

.... ... . . . ~

u u: •• w

80 DEG BOWL 1 ··r---------·-·-------------------

1 I

o.·;, ~

I I

0.8 ~ I

Ll 0 c

0 c----a.___ ---a---...._ ___

0

o.·? ~ 0.8

o.s

0.~~-----------.-----.------~----~------~----~----~ .20 40 80 BO

RIM ANGLE (DEG) 0 (.B6)CC,MP - (.BS)PRED

Figure 6. 7: Predicted and computed values of concentrator efficiency: 60 de g.

bowl: TJ.= .86

78

Table 6.2: Receiver efficiency curve-fit results

RIM B1 B2 ANGLE

30 .812547 2. 703311

35 .847224 1.618984

40 .873687 1.363239

45 .873232 .8687844

50 .907485 .9592331

55 .881617 .5067696

60 .911222 .6022401

79

COfv1PLJTED VS PREDIC~TED RECEJVER EFFICIENCY : 30 DEG BOWL

0.9 -~------

o_a J I I

07...J --. I I I

- ~ I O.o -f

I 0.5 ~

0

0_44-------------.-----------~----------.-----------~-------~---------~---------~ 0 20 40 BO

INCLINATION (DEGREE) 0 COMP -, PRED

Figure 6.8: Predicted and computed values of receiver efficiency: 30 deg. bowl

80

CO~v1PUTED VS PREDICTED RECEIVER EFFC. : 45 DEG BOWL

0.9 ,-----------------------------------------------------~

0.85

0.8

6 z

0.75 UJ u tt UJ 0.7 a:: ~

- .c.. w 0.85 u UJ a::

0.8

0.55

0.5~------~------~------~------~------~----~------~

0 20 40 80

INCIOE:NT ANGLE I, degree 0 t:orr,p - pred


81

COMPUTED VS PREDICTED 0 9

RECEIVER EFFC. : BO OEG BOWL . ~------------~~~~~~~~~~~-------------

0.85

0.8

'- "'S..... 0 ............. ~ z 0.75 w D tt w 0.7 ' a:

. ~ "~ .... w 0.85 0 w ~

O.B

0.55

0.5;-------.------.-------.------~------r-----~------~ 0 20 40 80

INCIDENT ANGLE I, degree 0 corr,p - pr~:d


82

Table 6.3: Cost factor curve-fit results

SCHEME Cl C2

1 .337627 1.77413E-04

2 .314368 1.21852E-04

Table 6.4: Energy curve-fit results with and without iris

without iris

RBv1 A~GLE D1 D2

de g. 30-60 1.3508476 3.419983

with iris

RI~vl

ANGLE D1 D2 de g.

30 18.4387 7.193785

35 14.7429 7.796407

40 6.0623 6.673668

83

•·

c:;c)~v1PLJTED VS. PREC)I(~:TECJ

1.: r------ SCHEME 1

1 I

- ·~ I v ... -1 '

110 130 150 170

RIM ANGLE {dcg.) 0 COtvtPUTED -- PREDICTED

190

Figure 6.11: Predicted and computed values of cost factor: scheme 1

84

,_, T 1 1

0.9 ~ c.a I

0.7

PREDI(:;TED VS. COMPLJTED

/

150 170 190

.APERTURE OIAN\ETER (ft) 0 COt,.•IPUTED - PREDIC'fED

Figure 6.12: Predicted and computed values of cost factor: scheme 1 and scheme 2

85

-~ ...

COMPUTED VS PREDICTED 11~--------------------~~~--------------------~

1 ~--r--,--~--~~~~--,---~~--~--P-~--~--~~ tO ,. 28 •• ~

IIOW .. :._~~.. M· ft. COPUTf.:D .unr~~~EDfCTEO

Figure 6.13: Predicted and computed values of energy: 30, 35 and 40 deg. bowls with iris and 30 to 60 deg. bowls without iris

86

E~~ERG'( -;, with iri:i . -· ·1-·---·------------------ ·----------1 --------

12 -4r-----------.--...a..._ I

11 ~ I

10 i I

9i 8 .

7~r,------------~--------__ _j B~~-----r----,----.----.----,-----.-----.----~----~--_j

34 38 38 40

RIM .ANGLE (DEG.) C A2 + A1.

Figure 6.14: Parameters D 1 and D 2 of energy curve-fit: with iris

87

Table 6.5: Energy per unit cost curve-fit results

Receiver Length = R/2

SCHEME E1 E2 E3

1 3.37914 3.375304 1.7481E-04

2 4.20663 3.557165 1.403491E-04

\Vith Optimum Receiver Length

SCHE1,IE E1 E2 E3

1 1.49388 2.122862 7.12276E-05

2 1.64413 2.073219 2.264527£-05

88

ENERGY PER UNIT COST PMDICIID VII. COUPliRD

·~------------------------~~--~~------------~

Figure 6.15: Predicted and computed values of energy per unit cost: scheme 1

89

ENERGY PER UNIT COST 14 PRIDICim VS. COMPUTED

13

12

.... 11 c-.

10

• •

g 7

e

8

4

3 30 ....

IUU ANGLE. degrae

Figure 6.16: Predicted and computed values of energy per unit cost: scheme 2

90

CHAPTER 7

CONCLUSIONS AND RECOMMENDATIONS

One of the objectives of this study was to explore several different possibilities

of extracting the maximum energy output per unit cost for a solar bowl, following

a realistic cost approach. The variable parameters were the bowl rim angle,

aperture diameter, receiver length and different iris sizes. Obviously the energy

output is limited by the incident solar flux at a particular location.

A bowl having a rim angle of less than 40 degrees, does not need a receiver

length of half the radius of curvature (R/2). The optimum receiver lengths on

the basis of energy per unit cost was obtained for low rim angle (shallow) bowls

with no iris. If high output temperature requirements are to be met, then for

any scenario (cheap or expensive) of constructing bowls utilizing the FMDF

concept, the receiver has to be constructed with expensive material. Therefore,

if these optimum receiver lengths are used, the cost savings are considerable.

A study was done to find out the percentage annual increase in energy from

an auxiliary energy collection mode and also the effect of number of bowls in

a plant on this energy. When the sun is relatively low in the sky, more extra

energy could be extracted from the low rim angle bowls. Two possibilities were

considered. One was to preheat the fluid by using solar energy during the

auxiliary mode operation and the other was to use fossil fuel to preheat. After

considering high losses in the pipe-lines, it was observed that in the order of 15

to 20 percent more energy could be extracted from the auxiliary mode operation

for low rim angle bowls.

91

The results of energy per unit cost indicate that with low rim angle, and

iris attached bowls, there is a potentiality of considerable cost savings, and

thereby obtaining very high energy per unit cost. Because of the wide diversity

of possible reflector material that can be used to concentrate the solar flux '

the maximum energy per unit cost results of this analysis are not necessarily

indicative of the best possible energy per unit cost for any scheme; but for the

scenarios which use mirror as the reflecting material.

Concentrator efficiency was calculated from the output of the powerful Ratio

of Solid Angles (ROSA) code for different inclinations. The computation time

this code takes depends on the computer used. On a TI, Business Pro. computer

it takes several hours, whereas if VAX is used, it takes about twenty to thirty

minutes for only one set of inclination. The output of ROSA is used as a

part of the input to the Receiver Heat Transfer Code (RHTC) to calculate the

receiver efficiency. The empirical equations developed in this study to find the

concentrator and receiver efficiencies would be useful as a preliminary screening

tool for rapid and easy estimation of energy output for any bowl.

Even though it is not exact, the concentrator efficiency equation would serve

the purpose of estimating the bowl concentrator performance at any place.

Barstow, California, weather data was used in the simulation analysis, in

order to be comparable to several other works reported in literature [2, 3,]. This

factor would not affect the relative performance of different configurations of this

study; but would have a significant impact on the absolute receiver performance

that could be achieved in other climatic conditions. Therefore, the receiver

efficiency equation would be applicable only to those places the climatic data

92

of which closely resembles the Barstow weather and if the output temperature

requirements remain the same as those used in this analysis. Equation 6.10

can be used to generalize the receiver efficiency equation using its operating

variables.

The empirical equation for the bowl cost should be reliable because it is

based on a verified cost and engineering design. The equation showed very good

agreement with the computed values for both scenarios, scheme 1 and scheme

2 of this study. Scheme 1 is an expensive verified scenario and scheme 2 is

the concrete bowl scenario using flat mirrors as the reflecting surface. Scheme 2

should approximately represent the least expensive scenario of constructing solar

bowls, using mirrors as the reflecting surface. The empirical equation developed

for energy and energy per unit cost also showed very good agreement with the

computed data.

An important initial assessment in solar energy applications is to evaluate

the performance from a proposed design point of view and thereby estimate

its economic competitiveness. Before going for any exhaustive and expensive

computer simulation, which may be required to design an efficient system, the

simple empirical equations developed in this study can be used for rapid and easy

comparison of efficiency, cost and energy for different configurations of bowls.

To generalize the global optimum bowl configurations, future studies on con

centration and survivability performance of other less expensive reflecting sur

faces are recommended.

93

BIBLIOGRAPHY

1. Reichert, J.D. and Liberty, S. R., "Crosbyton Solar Power Project Phase 1 Interim Tech:rllcal Report," The Crosbyton Solar Power Project, Vol. 1, Texas Tech University, Lubbock, Texas, 1977.

2. Williams, T. A., Dirks, J. A., Brown, D. R., Drost, M. K., Antoniak, Z. I., and Ross, B. A., "Characterization of Solar Thermal Concepts of Electricity Generation." A report prepared for U. S. Department of Energy by Pacific Northwest Laboratory, operated for the U. S. Department of Energy by Battelle Memorial Institute, 1987.

3. Hedberg, H., "Optimization of the Geometrical Configuration of a Solar Bowl with Iris," M. S. Thesis, Texas Tech University, Lubbock, Texas, 1987.

4. Steward, W. G. and Kreith, F., "Stationary Concentrating Reflector cum Tracking Absorber Solar Energy Collector : Optical Design Characteristics," Applied Optics, Vol. 14, No 7, 1975.

5. Lodhi, M. A. K., "Hydrogen City," International Journal of Hydrogen Energy, Vol. 12, No 11, 1987.

6. The Crosbyton Solar Power Project, Vol. I to Vol. VIII, Texas Tech U :rllversity, Lubbock, Texas, 1977 to 1982.

7. Watson, K. L., "Strategy of Operation and Theme for Control of a SolarFossil Hybrid Electric Plant," Ph.D. Dissertation, Texas Tech University, Lubbock, Texas, 1986.

8. Reichert, J. D., O'Hair, E. A., and Simpson, T. L., "Performance and Cost of Solar Gridiron Electric Power Plants," CSPP, Vol. VII, Texas Tech U:rllversity, Lubbock, Texas, 1981.

9. Reichert, J.D., O'Hair, E. A., and Simpson, T. A., "Preliminary Estimation of Cost and Performance of a 5 Mw Solar Power Plant," CSPP Vol. VIII, Texas Tech University, Lubbock, Texas, 1982.

10. Watson, K. L., "Performance Analysis of a Solar Gridiron Design Verification System," M. S. Thesis, Texas Tech University, Lubbock, Texas, 1981.

11. Anderson, R. M. and Ford, W. T.,"ROSA: A Computer Model for Optical Power Ratio Calculations," Technical Information Center, Office of Scientific and Technical Information, U. S. Department of Energy, 1984.

94

12. Anderson, R. M. and Obeyesekere, M., "Calculation of Optical Power Profile for a Solar Bowl with Iris," Texas Tech University, Lubbock, Texas, 1987.

13. Ford, W. T. and Anderson, R. M., "SOLAVG : Radially Averaged Optical Power Ratio Calculations," Texas Tech University, Lubbock, Texas, 1985.

14. Trahan, M. R., Jr., "Reflection Characteristics at Large Incident Angles with Reference to Solar Bowl," M. S. Thesis, Texas Tech University, Lubbock, Texas, 1988.

15. Hou, W. J ., "Surface Efficiency Assessment of the Spherical Segment Solar Collector," M. S. Thesis, Texas Tech University, Lubbock, Texas, 1987.

16. Brock, B. C., "Optical Analysis of Spherical Segment Solar Collectors," Ph.D. Dissertation, Texas Tech University, Lubbock, Texas, 1977.

17. Agarwal, V. K., "The Thermal Behaviour of Mirror Panels Exposed to Concentrated Solar Radiation," M. S. Thesis, Texas Tech University, Lubbock, Texas, 1980.

18. Subramanyam, S., "Simulation of the Crosbyton Receiver," Ph. D. Dissertation, Texas Tech University, Lubbock, Texas, 1986.

19. Jonish, J. E. and O'Hair, E. A., "Economic Analysis of Alternate Uses and Design," CSPP, Texas Tech University, Lubbock, Texas, 1986.

20. Wright, J. G., "Design of a Low Cost Solar Concentrator," M. S. Thesis, Texas Tech University, Lubbock, Texas, 1986.

21. Gustafson, D. L. and Craig, J. P., "Fluid Control and Instrumentation System for a Multi-Bowl/Multi-Load Solar System," A report submitted to the U.S. Department of Energy, Texas Tech University, Lubbock, Texas, 1986.

22. Apley, W. J ., "Analysis of Electric Power Generating Costs for Systems Larger than 10 MWe. Vol. I of Assessment of Generic Solar Thermal Systems for Large Power Applications," PNL-3533, Pacific Northwest Laboratory, Richland, Washington, 1980.

23. Laity, W. W., "Vol. II - Identification and Characterization of Concepts for Analysis; Assessment of Solar Options for Small P?wer System Applications." PNL-4000, Pacific Northwest Laboratory, Richland, Washington, 1980.

95

APPENDICES

A. ENERGY COMPUTATION DATA

B. COSTl CODE

96

APPENDIX A

ENERGY COMPUTATION DATA

A.l Concentrator and Receiver Efficiency

The concentrator efficiency ( 1Jconc) was computed using the concentration

data generated by the ROSA code. The inputs to the ROSA code used are

contained in Table A.l. RHTC code directly gives the receiver efficiency. Two

sets of inputs were used. The first set uses the bowl geometry originally designed

for the 5 M w plant (supposed to be constructed) at Crosbyton. The second set

uses the bowl geometry which was used by Hedberg [3]. Tables A. 2 and A. 3

contain the two sets of inputs used, respectively. Of course ROSA generated

concentrator data was also input to RHTC. The purpose of using two types of

bowl geometry was to observe the effect of bowl geometry. It was found that

the second set of input data resulted around 3 percent less efficiency than that

obtained with the baseline design geometry. Also it was observed that it was

an effect of wall thickness. If the wall thickness was reduced to 0.015 ft for the

second set then the two sets gave the same efficiency results. Tables A.4 through

A.9 contain the concentrator and receiver efficiency data for a number of bowl

configurations used.

A.2 Excess Energy

Extra energy produced during the operation of the boiler in the auxiliary

mode can be extracted by either preheating a number of bowls (case A) or by

adding fossil fuel (case B). The number of bowls in the plant plays an important

97

role in case A. If the number of bowls that one bowl can support is Nsup, then

the preheating process would be most efficient if the total number of bowls in

the plant is a multiple of (N sup+ 1 ); (definitely after considering the losses in

the pipelines).

In calculating this energy, the amount of quality steam (from Q mode), the

amount of auxiliary energy (from A mode) and the shortage in enthalpy for

each bowl to produce quality steam, are calculated. Assuming a certain line loss

factor, the number of bowls that can be supported by one bowl is computed. If

the number of bowls at the plant is not a multiple of (N sup+ 1) then a certain

number of bowls would remain unsupported. It was considered in this case that

if the number of unsupported bowls (Nrest) is not greater than Nsup/2, then

those bowls should not be preheated by other bowls. In a practical situation,

preheating of feedwater of those bowls by using fossil fuel could maximize the

solar penetration. The computer program (EXTRA) included in this appendix

calculates this energy, both for case A and case B. From actual data, upto 950

° F steam was considered as quality mode energy and upto 650° F steam was

considered as auxiliary mode energy. The data used is also included in Tables

A.lO through A.16. For lower inclinations the data is written as zero because

this default mode energy is not being considered here. Mdot is the mass flow

rate (lbm/hr; thousands), Tout is the output temperature (° F), and Hout is

the output enthalpy (Btu/lb; thousands).

98

Table A.1: ROSA input parameters

ROSA SYMBOL VALUE EXPLANATION PARAMETER USED

DPSID 1/Jd 0.0 Receiver elevation misalignment angle

DPHID cPd 0.0 Receiver azimuth misalignment angle

SIGMAD ud .267 Sun cone half-angle

ED £ oo- goo Elevation

AD A 0.0 Azimuth

THTARD BR 30°- 60° Bowl rim angle

GAl\11\lAD I 15° Bowl tilt angle

PHIDD cPd 0.0 Azimuth of bowl tilt from south

REFC 1]. .92 Solar efficiency diameter product

ZETAD ( 0.0 cone vertex ; 0.0 for cylinder

RTOP Rctop .00667 radius of receiver

TIRIS cPI or goo- 110° Iris width 2¢o

HIRIS 81 30°- 60° Iris height

99

Table A.2: RHTC input parameters (set 1)

-RHTC VALUE EXPLANATION PARAMETER USED RECL 56ft Receiver length DTREC 1.5 ft Receiver diameter at top DBREC 1.5 ft Receiver diameter at bottom NTUBES 20 No. of tubes DO .03125 ft Outside diameter of tubes DI .02583 ft Inside diameter of tubes TLFRT variable lbm /hr Mass flow rate TIN 200 oF Wind speed PI~ 1010 to 1050 psia Inlet pressure TA~1B 75° F Ambient temperature V\VIXD 5.5 miles/hr \Yind velocity SE~C variable from Solar insolation

Barstow data Btu/hr- ft 2

!FLUID 1 Fluid type 1 - for steam

I TYPE 1 Recei\·er type 1 - for cylindrical

SANG 10°to80° Solar elevation £ \VALLK 10.6 Btu/hr ft 2 Thermal conductivity FEX .9 Emissivity of tubing FEXS .9 Absorptivity of tubing LF 1 1 - for Bottom feed

2 - for top feed IBASE 1 : 1- for cylinder

2 - for cone IDYN 0 0 - for steady state

100

Table A.3: RHTC input parameters (set 2)

RHTC VALUE EXPLANATION PARAMETER USED RECL 101.5 ft Receiver length DTREC 2.75 ft Receiver diameter at top DBREC 2.75 ft Receiver diameter at bottom NTUBES 16 No. of tubes DO .09375 ft Outside diameter of tubes DI .0625 ft Inside diameter of tubes TLFRT variable lbm /hr Mass flow rate TIN 200 oF \\find speed PIN 1010 to 1050 psia Inlet pressure TA11IB 75° F Ambient temperature V\VIND 5.5 miles/hr \Vind Yelocity SINC variable from Solar insolation

Barstow data Btu/hr- ft 2

IFLUID 1 Fluid type 1 - for steam

IT.YPE 1 Receiver type 1 - for cylindrical

SANG 10°to80° Solar elevation £ \VALLK 10.6 Btu/hr ft 2 Thermal conductivity FEX .9 Emissivity of tubing FEXS .9 Absorptivity of tubing LF 1 1 - for Bottom feed

2 - for top feed !BASE 1 1- for cylinder

2 - for cone IDYN 0 0 - for steady state

101

Table A.4: Concentrator and receiver efficiencies: BR = 35°


deg m2 kw/ m 2

5 1.0296 .9485 .92 .834 15 .9983 .9196 .92 .801 25 .9367 .8627 .921 .737 35 .8466 .77 .909 .608 45 .7308 .6139 .839 55 .5928 .4382 .739 65 .4368 .2678 .613 75 .2675 .139 .519

Table A.5: Concentrator and receiver efficiencies: BR = 40°


deg m2 kw/ m 2

5 1.293 1.905 .92 .854 15 1.253 1.154 .92 .822 25 1.176 1.081 .919 .773 35 1.063 .9627 .905 .698 45 .917 .789 .859 .529 55 .744 .568 .764 65 .548 .372 .678 75 .336 .21 .625

102

Table A.6: Concentrator and receiver efficiencies: OR= 45°

I AE P.,. TJconc TJrec

deg m2 kw/ m 2

5 1.564 1.440 .92 .865 15 1.517 1.396 .92 .836 25 1.423 1.298 .912 .818 35 1.286 1.159 .901 .739 45 1.110 .981 .883 .641 55 .901 .724 .803 65 .663 .490 .738 75 .406 .295 .738

Table A. 7: Concentrator and receiver efficiencies: OR= 50°

I AE P.,. TJconc TJrec

deg m2 kw/ m 2

5 1.836 1.69 .92 .871 15 1.78 1.636 .919 .863 25 1.67 1.517 .908 .819 35 1.51 1.353 .896 .780 45 1.30 1.149 .881 .708 55 1.057 .894 .845 .498 65 .779 .606 .777 75 .477 .372 .7

103

Table A.8: Concentrator and receiver efficiencies: (}R = 55°

I AE Pr "'eone 'T/ree

deg m2 kw/ m 2

5 2.100 1.932 .92 .873 15 2.036 1.857 .912 .862 25 1.91 1.726 .903 .833 35 1.72 1.538 .890 .758 45 1.49 1.322 .887 .653 55 1.209 1.070 .885 65 .89 .739 .829 75 .54 .443 .812

Table A.9: Concentrator and receiver efficiencies: (}R = 35°, 2</Jo = 100°, (}H = 20°

I AE Pr "'eone 'T/ree

deg m2 kw/ m 2

5 1.094 1.006 .919 .837 15 1.09 1.012 .92 .821

25 1.07 .9862 .92 .809

35 1.01 .6949 .68 .615

45 .92 .5908 .64

55 .80 .515 .643

65 .657 .390 .594

75 .493 .257 .52

104

Table A.10: Enthalpy data for different rim angle bowls: (JR = 30°

Mass flow Output Output rate (Mdot) temp.(Tout) enthalpy(Hout) 1.3 1014.45 1.518 1.175 1015. 1.517 .975 999.0 1.508 .6 972. 1.491 .375 656. 1.309 0. 0. 0. 0. 0. 0. 0. 0. 0.

Table A.11: Enthalpy data for different rim angle bowls: (JR = 35o

Mass flow Output Output

rate (Mdot) temp.(Tout) enthalpy( Rout)

1.8 1034. 1.529 1.675 1010. 1.506 1.425 1007. 1.52 1.025 1019.0 1.517 .9 721. 1.351 0. 0.0 0.0 0.0 0. 0.

'

0. 0. 0.

105

Table A.12: Enthalpy data for different rim angle bowls: ()R = 40°

Mass flow Output Output rate (Mdot) temp.(Tout) enthalpy(Hout) 2.35 1008. 1.51 2.15 1011. 1.513 1.975 1004.0 1.509 1.475 1000.0 1.50 .95 999.0 1.506 .6 683.93 1.321 0.0 0. 0. 0.0 0. 0.

Table A.13: Enthalpy data for different rim angle bowls: ()R = 45o


rate (l\1dot) temp.(Tout) enthalpy(Hout)

2.875 1005. 1.511 2.65 1019. 1.509 2.6 1009. 1.504 1.875 1002. 1.511 1.35 996. 1.506 1.0 719. 1.348

0.0 0.0 0.0 0.0 0.0 0.0

106

Table A.14: Enthalpy data for different rim angle bowls: BR = 50°

Mass flow Output Output rate (Mdot) temp.(Tout) enthalpy( Rout) 3.425 1002. 1.501 3.25 1001.0 1.504 2.75 1028.0 1.521 2.3 1015.0 1.513 1.75 1003.0 1.507 .9 998.0 1.505 .6 638.35 1.295 0.0 0.0 0.0

Table A.15: Enthalpy data for different rim angle bowls: BR = 55°


rate (11dot) temp.(Tout) enthalpy( Rout)

3.9 1006.0 1.51 3.65 1008.0 1.498 3.2 1025.0 1.511 2.7 i012.0 1.511 2.15 1007.0 1.510 1.4 1001.0 1.513 .85 732.0 1.357 0.0 0.0 0.0

107

Table A.16: Enthalpy data for different rim angle bowls: ()R = 60°

i'/Iass flow Output Output -rate (l\Idot) temp.(Tout) enthalpy(Hout)

4.35 1005.0 1.505 4.05 1001.0 1.505 3.6 1004.0 1.51 3.1 1010.0 1.507 2.5 1012.79 1.507 1.725 1010. 1.514 . 6 968 . 1.488 0.0 0.0 0.0

108

A.3 EXTRA Code

C EXTRA: PROGRAM FOR CALCULATING LOW INSOLATION ENERGY c

DIMENSION HR(10) C REAL MDOT C OPEN(UNIT=1,FILE='TEXT.DAT' ,STATUS='OLD')

OPEN(UNIT=2,FILE='TEXT1.0UT',STATUS='NEW') OPEN(UNIT=3,FILE='TEXT2.0UT',STATUS='NEW')

C NC=NO OF RIM ANGLES,BN=NO OF BOWLS IN THE PLANT, C FLOSS=LINELOSS FACTOR

READ (1,5)NC,BN,FLOSS 3 FORMAT(25X) 5 FORMAT(I2,2F10.3)

10 FORMAT(F10.4) 15 FORMAT(5F10.4) 20 FORMAT(F10.1,2F12.1,3I5,F6.2,2F11.1)

DO 80 K=1,8 READ(1,10)HR(K)

80 CONTINUE C INITIALIZING PARAMETERS C NC IS THE NO. OF BOWLS C ST1 =QUALITY MODE ENERGY; ST2=AUXILLIARY MODE ENERGY; C DELBTU= NET SHORTAGE IN ENTHALPY

DO 200 N=1,NC STEAM1=0. STEAM2=0. ST1=0. ST2=0. BTUNET=O. DELBTU=O. STEAMNEW=O. STMINCR=O. PERCENT=O. FEXT=O. FNEWSTEAM=O. FPERCENT=O.

READ(1,10)BOWLTYPE E=70. DO 100 I=1,8

C NO OF ELEVATIONS = 8 STEAM1=0. STEAM2=0. DEL=O.

109

DEL1=0. C FDOT=MASS FLOW RATE; TOUT=OUTPUT TEMPERATURE; C HOUT=OUTPUT ENTHALPY

READ(1,15)FDOT,TOUT,HOUT IF(HOUT .LT. 1.44)GO TO 30 STEAM1=STEAM1+(FDOT*HOUT)*HR(I)

C DEL1=(1.5051-HOUT)*FDOT*HR(I) 30 IF(TOUT .LT. 650.0 .OR. BOUT .GE. 1.44)GO TO 40

C 30 IF(HOUT .LT. 1.196 .OR. BOUT .GE. 1.44)GO TO 40 STEAM1=0. STEAM2=STEAM2+(FDOT*HOUT)*HR(I) DEL=(1.5051*FDOT-FDOT*HOUT)*HR(I) DELBTU=DELBTU+DEL GO TO 45

40 STEAM2=0. 45 E=E-10.

IF(STEAM1 .EQ. 0 .. AND. STEAM2 .EQ. O.)GO TO 100 ST1=ST1+STEAM1 ST2=ST2+STEAM2 BTUNET=BTUNET+STEAM1+STEAM2

100 CONTINUE C CASE A C BNN IS THE PERCENTAGE NO. OF BOWLS 1 BOWL CAN SUPPORT

NBN=NINT(BN) IF(ST2 .EQ. O.)THEN BSUP=O. BNN=O. NBSUP=O NBNN=O EQN=BN NEQN=NBN NREST=O ELSE

C FLOSS=LINE LOSS FACTOR (VARIABLE INPUT); C NBSUP= NO OF BOWLS SUP. BY 1 BOWL

BSUP=(ST2/DELBTU)*FLOSS NBSUP=NINT(BSUP) IF (NBSUP .GE. NBN)THEN NBSUP=NBN-1 DELBTU=(ST2/NBSUP)*FLOSS END IF IF (NBSUP .GE. 1)NBNN=1 NBDIF=NBN-NBSUP-NBNN

C FINDING THE NO. OF SUPPORTING BOWLS (NBNN)

110

85 IF (NBDIF .GT. NBSUP)THEN NBNN=NBNN+1 NBDIF=NBN-(NBNN*NBSUP)-NBNN GO TO 85 ELSE END IF

C NREST= NO. OF UNSUPPORTED BOWLS NREST=NBN-(NBNN*NBSUP) END IF

C STEAMNEW=BTUNET+(DELBTU/(BSUP+1.)) C STMINCR=STEAMNEW-ST1 C PERCENT=((STMINCR*NEQN)/(ST1*NBN))*100. C ANNUAL INCREASE IN 1000 DEG.1000 PSIA STEAM

OA=ST1*NBN C IF THE NO OF UNSUPPORTED BOWLS IS > (BSUP/2) THEN C THOSE MAY BE SUPPORTED

X1=(BSUP/2.) KX1=NINT(X1) NBD=NBDF-1 IF(NBD .GE. KX1)THEN NBNN=NBNI~+1

AN=(NBN-NBNN)*(ST1+ST2+DELBTU)+(ST1*NBNN) ELSE AN=(NBN-NREST)*(ST1+ST2+DELBTU)+(ST1*NREST) END IF PCENT=((AN-OA)/OA)*100. EXT=O.

C NEQN IS EQUIVALENT NO. OF BOWLS EQN=(AN/(BTUNET*BN))*BN

C NEQN=NINT(X) WRITE(2,20)BOWLTYPE,OA,AN,NBN,NBSUP,NBNN,EQN,EXT,PCENT

c C CASE B: FOSSIL ENERGY NECESSARY

FNEWSTEAM=(BTUNET+DELBTU) FEXT=DELBTU FSTMINCR=FNEWSTEAM-ST1 FPERCENT=(FSTMINCR/ST1)*100. FBNN=O. FBSUP=O. MFBSUP=O MBNN=O MREST=O FOA=ST1*BN FNA=(ST1+ST2+DELBTU)*BN

111

-•

i

FEQN=(FNA/(BTUNET•BN))•BN FPCENT=((FNA-FOA)/FOA)•lOO.

199 WRITE(3,20)BOWLTYPE,FOA,FNA,NBN,MFBSUP,MBNN,FEQN,FEIT,FPCENT 200 CONTINUE

STOP ~D

. 112 . ~ .

APPENDIX B

COST1 CODE

C COST ANALYSIS PROGRAM FOR BOWLS WITH DIFFERENT RIM ANGLES AND C FIXED RADIUS OF CURVATURE c

c

c

c

COMMON/A1/EC,RECC,APDIA,RCURV,RCURVM,RADIAN,ENERGY,RIM,RST COMMON/B1/QEC,QTC100,QECMAX,QTCMIN

DIMENSION RANG(30),0UTPUT(30),TC(10,20),EPUC(10,20),RSWT(10) DIMENSION QTC(10,20),QEPUC(10,20) DIMENSION ECT(10,20),TCT(10,20),UTC(10,20),UEC(10,20) DIMENSION QECT(10,20),QTCT(10,20),QUTC(10,20),QUEC(10,20) DIMENSION UTCT(10,20),UECT(10,20),HEIGHT(30),WIDTH(30) DIMENSION EAC(20),SUBC(20),SUPC(20),CRC(20),REC(20),SMPC(20) DIMENSION QEAC(20),QSUBC(20),QSUPC(20),QCRC(20),QSMPC(20) DIMENSION HSPC(20),SMISC(20),HT(20),HT1(20)

OPEN(UNIT=1,FILE='BT.in',STATUS='OLD') OPEN(UNIT=2,FILE='WT1.IN' ,STATUS='DLD') OPEN(UNIT=18,FILE='EXCA.IN',STATUS='DLD') OPEN(UNIT=3,FILE='PCOST1.frc',STATUS='NEW') OPEN(UNIT=24,FILE='QTC1.FRC',STATUS='NEW') OPEN(UNIT=4,FILE='TC1.FRC' ,STATUS='NEW') OPEN(UNIT=25,FILE='QTCT1.FRC' ,STATUS='NEW') OPEN(UNIT=5,FILE='TCT1.FRC',STATUS='NEW') OPEN(UNIT=7,FILE='TC2.FRC',STATUS='NEW') DATA RSWT(1),RSWT(2),RSWT(3),RSWT(4)/

+ 5.25,12.0,20.5,27.0/

HALFPI=2.*ATAN(1.) PI=2.*HALFPI RADIAN=PI/180.

C READING RIM ANGLE & UNIT ENERGY DO 100 I=1,7 READ (1,10)RANG(I),HEIGHT(I),WIDTH(I),OUTPUT(I)

10 FORMAT(4F20.4) 100 CONTINUE

c C ECMAX IS MAX ENERGY/UNIT COST OF A TRUNCATED RECEIVER C AND TCMIN IS THE CORRESPONDING COST

TCMIN=O.

113

ECMAX=O. C TMAXEC IS MAX ENERGY/UNIT COST C CMAX IS THE MAXIMUM COST C TMAXEC AND CMAX MAY NOT NECESSARILY CORRESPOND

TMAXEC=O. CMAX=O.

C RECEIVER LENGTH IS IN FEET;SA IN FT-2

c c

RECL=56.0

IA=l DO 200 IR=1,7

C READING SUBSTRUCTURE WT(lb thousands),SUPERSTRUCTURE WT(lb thousands) C EXCAVATION COST C ALL COST ARE IN $ THOUSANDS c

RIM=RANG(IR) H=HEIGHT(IR) W=WIDTH(IR) ENERGY=OUTPUT(IR) RIMR=RIM*RADIAN DCURV=RECL*4.0 APDIA=DCURV*SIN(RIMR)

C DCURV=APDIA/SIN(RIMR) RCURV=DCURV/2.0 RCURVM=RCURV*.3048 SA=2.*PI*(RCURV**2)*(1-COS(RIMR))

c READ(2,20)SUBWT,SUPWT

20 FORMAT(2F10.2) C ECOST IS EXCAVATION VOLUME

READ(18,21)EXCAVOL 21 FORMAT(F15.2) C EXCAVATION COST (20 'l. MORE VOLUME FOR WORKING & INSTRUMENT MOVING)

EAC(IR)=EXCAVOL*2.57/1000.0 WRITE(*,999) SUBWT,SUPWT

999 FORMAT(4F10.2,F10.2) C SUBSTRUCTURE COST

SUBTON=SUBWT/(2.*2.) SUBC(IR)=SUBTON*3.25495

C FOR SCHEME 3 (SPECIAL CURVED FORMS) QSUBC(IR)=SA*.0067

C SUPERSTRUCTURE CQST SUPTON=SUPWT/(2.*2.)

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SUPC(IR)=SUPTON*4.788 C FOR SCHEME 3 (TROWEL,FINISH,GRINDING OF CONCRETE)

QSUPC(IR)=SA*0.00027 C CONCRETE & REINFORCING BAR

TWT=SUBTON+SUPTON CONVOL=TWT*.7448 CONC=CONVOL*.07372 RBARWT=TWT*.055 RBARC=RBARWT*.92513 CRC(IR)=CONC+RBARC

C FOR SCHEME 3 (CONCRETE BOWL) QCRC(IR)=(SA*.25/27)*.07372+(RBARC*2.0)

C RECEIVER COST RST=27.0

C (i) STRUCTURE COST RECST=RST/2*6.27

C RECEIVER AND BOOM WT OF A 56 FT RECEIVER IS 15.3 lbs(thousands) RECWT=15.3

C (ii) RECEIVER RECTON=RECWT/(2.0*3.) RECB=RECTON*84.43 RECC=RECB+RECST REC(IR)=RECST+RECC

C MIRROR PANEL COST SMPC(IR)=SA*.0128

C FOR SCHEME 3 (FLAT MIRROR ON CONCRETE BOWL) QSMPC(IR)=SA*0.003

C HOT SPOT PROTECTION SYSTEM IF(RIM .LE. 30.)THEN HSPC(I)=O.O ELSE HSPC(IR)=SA*.000225 END IF

C CLANING,PAINTING,PUMP,DRAIN ETC SMISC(IR)=SA*.0010172

C TOTAL COST TC100=EAC(IR)+SUBC(IR)+SUPC(IR)+CRC(IR)+REC(IR)

+ +SMPC(IR)+HSPC(IR)+SMISC(IR) C SCHEME 3

QTC100=EAC(IR)+QSUBC(IR)+QSUPC(IR)+QCRC(IR)+REC(IR) + +QSMPC(IR)+HSPC(IR)+SMISC(IR)

C ENERGY PER UNIT COST(RCURV IN METER SINCE ENERGY IN KW) EC=ENERGY*((RCURV*.3048)**2)/TC100 QEC=ENERGY*((RCURV*.3048)**2)/QTC100

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C IF RECEIVER LENGTH CAN BE REDUCED THEN RECTRUN SUBROUTINE IS CALLED IF(RIM .GT. 40.)GO TO 400

c CALL RECTRUN(RECWT,TC100,ECMAX,TCMIN)

c

WRITE(12,110)RIM,APDIA,TC100,EC,TCMIN,ECMAX,QTCMIN,QECMAX 110 FORMAT(2F6.1,6F10.3) 400 TC(IA,IR)=TC100

QTC(IA,IR)=QTC100 EPUC(IA,IR)=EC QEPUC(IA,IR)=QEC IF (RIM .GT. 40.)THEN ECT(IA,IR)=EC QECT(IA,IR)=QEC TCT(IA,IR)=TC100 QTCT(IA,IR)=QTC100 ELSE ECT(IA,IR)=ECMAX QECT(IA,IR)=QECMAX TCT(IA,IR)=TCMIN QTCT(IA,IR)=QTCMIN END IF WRITE(19,40)APDIA,RIM,EAC(IR),SUBC(IR),SUPC(IR),

+ SMPC(IR),TCT(IA,IR) WRITE(3,40)APDIA,RIM,EAC(IR),SUBC(IR),SUPC(IR),

+ CRC(IR),TCT(IA,IR) WRITE(17,40)APDIA,RIM,REC(IR),SMPC(IR),HSPC(IR)

+ ,SMISC(IR),TC100

40 FORMAT(F6.1,F5.1,5F12.3) WRITE(4,55)APDIA,RIM,H,W,TC100,EC WRITE(24,55)APDIA,RIM,H,W,QTC100,QEC

50 FORMAT(4F20.4) WRITE(5,55)APDIA,RIM,H,W,TCT(IA,IR),ECT(IA,IR) WRITE(25,55)APDIA,RIM,H,W,QTCT(IA,IR),QECT(IA,IR)

55 FORMAT(4F10.4,2F20.4) C CMAX IS MAX COST

IF(TC100 .GE. CMAX)CMAX=TC100 C MAXEC IS MAX ENERGY/UNIT COST WHICH MAY NOT CORRESPOND TO CMAX

IF(EC .GE. TMAXEC)TMAXEC=EC 200 CONTINUE

c C IRIS COST CALCULATIONS BEGIN c

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DO 300 IR=8,18

READ (1,10)RANG(IR),HEIGHT(IR),WIDTH(IR),OUTPUT(IR) ENERGY=OUTPUT(IR) RIM=RANG(IR) RIMR=RIM*RADIAN APDIA=DCURV*SIN(RIMR) H=HEIGHT(IR) HR=H*RADIAN W=WIDTH(IR) WR=W*RADIAN

C IRIS RIM (RH)= BOWL RIM+IRIS HEIGHT RH=RIM+H RHR=RH*RADIAN RR=(RIM/5.)-5. NRR=NINT(RR) R=(RH/5.)-5. NR=NINT(R)

C TCO IS ORIGINAL BOWL COST TCO=TC(IA,NRR) QTCO=QTC(IA,NRR)

C WRATIO IS IRIS WIDTH /360 WRATIO=W/360.0

C SUB AND SUPERSTRUCTURE COST ARE INCREASED BY 20'/. C BECAUSE THE REFLECTOR WOULD BE TRACKING

SUPI=(SUPC(NR)-SUPC(NRR))*WRATI0*1.2 SUBI=(SUBC(NR)-SUBC(NRR))*WRATI0*1.2

C SUBI=O. CEXCAI=.5*EAC(NRR) AEI=(RCURV**2)*W*RADIAN*(COS(RIMR)-COS(RHR)) SMPCI=AEI*0.0128 TCI=TCO+SUPI+SUBI+CEXCAI+SMPCI QTCI=QTCO+SUPI+SUBI+CEXCAI+SMPCI

C ANOTHER OPTION C 10'l. OF OVERALL BOWL COST MAY BE KEPT FOR CONSTRUCTION OF THE TRACKING C INSTRUMENT C NEW COST WITH IRIS = TC

TC(IA,IR)=TCI QTC(IA,IR)=QTCI ECI=ENERGY*(RCURVM**2)/TC(IA,IR) QECI=ENERGY*(RCURVM**2)/QTC(IA,IR) EPUC(IA,IR)=ECI QEPUC(IA,IR)=QECI WRITE(4,55)APDIA,RIM,H,W,TC(IA,IR),EPUC(IA,IR) WRITE(24,55)APDIA,RIM,H,W,QTC(IA,IR),QEPUC(IA,IR)

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c

300 c

700 c c

80 800

c

c

WRITE(19,40)RIM,CEXCAI,SUBI,SUPI,SMPCI,TCO,TCI

IF(CMAX .GT. TC(IA,IR)) CMAX=TC(IA,IR) IF(TMAXEC .GT. EPUC(IA,IR)) TMAXEC=EPUC(IA,IR) CONTINUE

CONTINUE APDIA=100.0 DO 800 NA=1,4

NA=1 FORMAT(8E10.4) CONTINUE STOP END

SUBROUTINE RECTRUN(RECWT,TC100,ECMAX,TCMIN)

C SENDS THE MAX ENERGY/UNIT COST AS ECMAX AND THE CORRESPONDING C COST AS TCMIN c

c

c

c

COMMON/Al/EC,RECC,APDIA,RCURV,RCURVM,RADIAN,ENERGY,RIM,RST COMMON/B1/QEC,QTC100,QECMAX,QTCMIN

DIMENSION EL(20),WTP(6),COST(6),ECOST(6),QCOST(6),QECOST(6) DIMENSION ENE(20),DOL(20),TCR(20),ECT(20),QTCR(20),QECT(20) OPEN(UNIT=15,FILE='SUBTC.PRN' ,STATUS='NEW') OPEN(UNIT=16,FILE='SUBEC.PRN' ,STATUS='NEW')

DATA WTP(1),WTP(2),WTP(3),WTP(4),WTP(5),WTP(6)/ + .9368,.8734,.7991,.6962,.6076,.5126/

DATA EL(1),EL(2),EL(3),EL(4),EL(5),EL(6)/ + -.273,-1.131,-.645,-.303,1.81,5.664/

DATA EL(7),EL(8),EL(9),EL(10),EL(11),EL(12)/ + -.13,.447,1.533,2.731,5.064,11.383/

DATA EL(13),EL(14),EL(15),EL(16),EL(17),EL(18)/ + 2.938,5.664,8.428,12.735,26.774,31.518/

RIMR=RIM*RADIAN UCOST=4.62487 IF(RIM .EQ. 30.)THEN !=1 ECMAX=EC TCMIN=TC100

118

c

QECMAX=QEC QTCMIN=QTC100

ELSE END IF IF(RIM .EQ. 35.)THEN I=7 ECMAX=EC TCMIN=TC100 QECMAX=QEC

QTCMIN=QTC100 ELSE

END IF IF(RIM .EQ. 40.)THEN I=13 ECMAX=EC TCMIN=TC100

QECMAX=QEC QTCMIN=QTC100

ELSE END IF

C ECMAX=O.O C QECMAX=O.O C TCMIN=O.O C QTCMIN=O.O

K=I+5 M=1

C ENE=ENERGY OF TRUNCATED RECEIVER C RECC=ORIGINAL RECEIVER COST(100% OF R/2) C WTP=WEIGHT LOSS (ALSO COST REDUCTION) FACTOR C EL=ENERGY LOSS DUE TO LENGTH REDUCTION(%) C DOL=TRUNCATED RECEIVER COST C TCR=COST=BOWL COST AFTER RECEIVER TRUNCATION C ECT=ECOST=ENERGY/UNIT COST C KK=NO OF % RECEIVER IS TRUNCATED (UPTO 40% OF ITS ORIGINAL LENGTH) C Q INDICATES THE SAME FOR SCHEME 3 c

DO 100 KK=I,K ENE(KK)=(ENERGY-((EL(KK)/100.0)*ENERGY))*(RCURVM**2) DOL(KK)=RECC*WTP(M) TCR(KK)=TC100-RECC+DOL(KK) QTCR(KK)=QTC100-RECC+DOL(KK) COST(M)=TCR(KK) QCOST(M)=QTCR(KK)

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ECT(KK)=ENE(KK)/TCR(KK) QECT(KK)=ENE(KK)/QTCR(KK) ECOST(M)=ECT(KK) QECOST(M)=QECT(KK) IF(ECMAX .LT. ECT(KK))THEN ECMAX=ECT(KK) TCMIN=TCR(KK) ELSE END IF IF(QECMAX .LT. QECT(KK))THEN QECMAX=QECT(KK) QTCMIN=QTCR(KK) ELSE END IF M=M+1

100 CONTINUE WRITE(15,200)RIM,TC100,(COST(M),M=1,6) WRITE(16,200)RIM,EC,(ECOST(M),M=1,6)

200 FORMAT(2X,F5.1,7F9.1) RETURN END

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configurations of solar bowls by a thesis in submitted …

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