INCIDENCE ANGLE MODIFIERS IN CYLINDRICAL SOLAR COLLECTOR DESXGN FINAL REPORT FOR THE PERIOD - June 1996 May 1997 Joseph P. Ryan Solar Energy Applications Laboratory Colorado State University Fort Collins, CO 80523 Date Published: May 1997 PREPARED FOR THE DEPARTMENT OF ENERGY U.S. CONSERVATION AND RENEWABLE ENERGY Under Grant DE-FG36-95GO10093 DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government Neither the United States Government nor any agency thereof, nor any of their employets, makes any warranty, express or implied, or any legal liability or responsibility the compietcney or assumes for accuracy, use- fulness of any information, apparatus, product, or process disciosed, or rrpre~ents that its use would not infringe privately owned rights. Rcfemcc herein to any spc- cific commercial product, process, or service by trade name, trademark, manufac- turer, or otherwise does not ncccssariiy constitute or impiy its endorsement, recom- mendation. or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not ncocsslrily state or reficct those of the United States Government or any agency thereof. DISCLAIM ER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. THESIS INCIDENCE ANGLE MODIFIERS IN CYLINDRICAL COLLECTOR SOLAR DESIGN Submitted by Joseph P. Ryan Department of Mechanical Engineering partial fulfiknent of the requirements In for the degree of Master of Science Colorado State University Fort Collins, Colorado Spring 1997 .L D ABSTRACT OF THESIS INCIDENCE ANGLE MODIFIERS IN CYLINDRICAL SOLAR COLLECTOR DESIGN This thesis presents an analysis of the thermal performance of cylindrical solar col- lectors. A major contributor to performance is optics, the principle focus of this work. A tool used to compute the incidence angle modifiers (IAM’s) for cylindrical solar collectors is presented. The Monte Carlo Method is employed in a computer code to Fortran 90 compute the hemispheric IAM’s of cylindrical solar collectors. Using concentric cylin- ders, the tubes are modeled with and without back plane reflectors of varying size. The computed IAM’s are verified both analytically and experimentally. Outdoor experiments on an array of cylindrical tubes with various back planes and two different tube spacings are described. Agreement with TRNSYS runs in daily energy gain is excellent. Over the 38 data sets, taken on different days, a maximum error of 11.2% is observed, with an aver- age of 3%. Heat loss tests, used to calculate an overall heat loss coefficient for the error collector, are also described. A parametric variation study is used to illustrate the effect of varying many of the collector parameters. This study provides insight into the signScant design parameters for cylindrical collectors. This insight is used to analyze the effect of these design solar parameters on the annual energy delivered by the collector. In addition, a simple cost analysis illustrates the benefits of varying the design parameters. The use of this new pro- gram and a detailed Life Cycle Cost analysis are the tools needed for optimizing the design of a cylindrical solar collector. ... Ill *. c The IAM code, executables, sample input and output files and instruction manual can be found on the world wide web: http://www.ColoState.EDU/Orgs/SEAL/resemh/ IAM/iam.html. Joseph F? Ryan Department of Mechanical Engineering Colorado State University Fort Collins, Colorado 80523 Spring 1997 TABLE OF CONTENTS ................................................................................................ ABSTRACT OF THESIS iii ACKNOWLEDGMENTS ................................................................................................. v ................................................................................................. TABLE OF CONTENTS vi ......................................................................................................... LIST OF ix FIGURES ............................................................................................................. LIST OF TABLES x ........................................................................................................ NOMENCLAW xi CHAmR1 . INTRODUCTION ...................................................................................................... 1.1 Introduction 1 ...................................................................................................... 1.2 Background 3 ......................................................................................... 1.3 Research Objectives 6 .......................................................................................................... 1.4 Approach 6 ..................................................................................... 1.5 of Thesis 7 Organization CHAPTER 2 . THEORETICAL FORMULATION ...................................................................................................... 2.1 Introduction 9 ............................................................................................... 2.2 Physical System 9 ............................................................................... 2.2.1 Geometry of Cylinders 9 ................................................................... 2.2.2 Geometry of Planar Surfaces 11 ......................................................................................... 2.3 Material Properties 13 ............................................... 2.3.1 Radiative Properties for Opaque Surfaces 14 ................................ 2.3.2 Radiative Properties for Semi-transparent Surfaces 17 ................................................................................... 2.4 Balance Model 21 Energy ........................................................................... 2.4.1 General Thermal Model 21 ........................................................................ 2.4.2 TRNSYS Thermal Model 23 .............................................................................. 2.5 Problem Parameterization 25 ........................................................................................................ 2.6 26 Summary vi CHAPTER3 . MONTECARLOMODEL .................................................................................................... 3.1 Introduction 27 .............................................................................................. 3.2 Implementation 28 ................................................................................... 3.2.1 Material Properties 29 ............................................................................ 3.2.2 Ray Tracing Procedure 31 ............................................................................................ 3.2.3 Convergence 35 ........................................................................................................ 3.3 Summary 36 CHAPTER4 . EXPERIMENTALAPPROACH .................................................................................................... 4.1 Introduction 38 ........................................................................................ 4.2 System Description 38 ...................................................................... 4.2.1 NEG Sun Family Collector 38 ................................................................................. 4.2.2 Collector Variations 40 ...................................................................................... 4.3 Heat Gain Procedure 41 ................................................................................................ 4.4 Heat Loss Test 43 .............................................................................................. 4.5 Data Collection 45 ......................................................................................... 4.6 Experimental Error 45 ........................................................................................................ 4.7 Summary 50 CHAPTER 5 . RESULTS AND DISCUSSION .................................................................................................... 5.1 Introduction 51 ..................................................................... 5.2 Analytical Validation of IAM’s 51 ..................................................................................... 5.3 Experimental Results 53 ............................................................................. 5.3.1 Heat Loss Test Results 55 ............................................................................. 5.3.2 Heat Gain Test Results 57 ......................................................................... 5.4 Parametric Variation Results 60 ................................................................................. 5.4.1 Effect of Tube Pitch 61 ............................................................ 5.4.2 Effect of Back Plane Reflectance 63 ..................................................................... 5.4.3 Effect of Back Plane Width 65 ..................................................... 5.4.4 Effect of Back Plane to Spacing 66 Tube ..................................................... 5.4.5 Effect of Collector Tube Absorptance 67 ........................................................................ 5.4.6 Effect of Glass Properties 67 ............................................................. 5.5 Cylindrical Solar Collector Analysis 70 ................................................................. 5.5.1 Annual TRNSYS Simulations 71 ........................................................................................... 5.5.2 Cost Analysis 74 ........................................................................................................ 5.6 Summary 76 vii CHAPTER 6 . CONCLUSIONS AND RECOMMENDATIONS 6.1 Summary ........................................................................................................ 78 ................................................................ 6.2 Sun Family Collector Design 80 NEG .......................................................................... 6.3 IAM Program Modifications 81 ................................................................................................................ REFERENCES 82 APPENDIX A . PROGRAM MANUAL ............................................................... 84 IAM . ....................................................................................... A 1 General Description 84 ............................................................................................................... A.2 Units 84 ...................................................................................................... A.3 Input Deck 84 ........................................................................... A.4 Execution of IAM Program 87 AS Output Files .................................................................................................... 88 ........................................................................... A.6 Access to the IAM 88 Program APPENDIX B . DECK ....................................................................... 89 TRNSYS INPUT . .................................................................................................... B Introduction 89 1 ...................................................................................................... B.2 Input Deck 89 viii