W.A. Beckman

Diffuse fraction correlations

The influence of climatic and geometric variables on the hourly diffuse fraction has been studied, based on a data set with 22,000 hourly measurements from five European and North American locations. The goal is to determine if other predictor variables, in addition to the clearness index, will significantly educe the standard error of Liu- and Jordan-type correlations (IdI = f(k1)). Stepwise regression is used to reduce a set of 28 potential predictor variables down to four significant predictors: the clearness index, solar altitude, ambient temperature, and relative humidity. A piecewise correlation over three ranges of clearness indices is developed to predict the diffuse fraction as a function of these four variables. A second piecewise correlation is developed for predicting the diffuse fraction as a function of the clearness index and solar altitude, for use when temperature and relative humidity are not available. A third piecewise correlation of the Liu- and Jordan-type is developed from the same data set. Comparing this correlation with the new correlations provides a direct measure of the value of added predictor variables. The full diffuse fraction correlation reduced the residual sum squares by 14% when compared to the correlation that is a function of the clearness index only. The correlation including the clearness index and solar altitude diminished the residual sum squares by 9%. The correlations exhibited some degree of location dependence. This is expected, as the climates are quite different. The correlations also showed some seasonal dependence; the errors are higher in the fall and winter than on an annual basis.

A design procedure for solar heating systems

This paper is concerned with the design of solar space and water heating systems for residences. A simulation model capable of estimating the long-term thermal performance of solar heating systems is described. The amount of meteorological data required by the simulation in order to estimate long-term performance is investigated. The information gained from many simulations is used to develop a general design procedure for solar heating systems. The result is a simple graphical method requiring monthly average meteorological data which architects and heating engineers can use to design economical solar heating systems. A method of estimating the monthly average radiation on tilted surfaces is given in the Appendix.

Behavioral implications of mechanistic ecology

SummaryMechanistic principles from engineering, meteorology, and soil physics are integrated with ecology and physiology to develop models for prediction of animal behavior. The Mojave Desert biome and the desert iguana are used to illustrate these principles.A transient energy balance model for animals in an outdoor environment is presented. The concepts and relationships have been tested in a wind tunnel, in a simulated desert, and in the field. The animal model requires anatomical information and knowledge of the thermoregulatory responses of the animal. The micrometeorological model requires only basic meteorological parameters and two soil physical properties as inputs. Tests of the model in the field show agreement between predicted and measured temperatures above and below the surface of about 2 to 3°C.The animal and micrometeorological models are combined to predict daily and seasonal activity patterns, available times for predator-prey interaction, and daily, seasonal and annual requirements for food and water. It is shown that food, water and the thermal environment can limit animal activity, and furthermore, the controlling limit changes with season. Actual observations of activity patterns and our predictions show close agreement, in many cases, and pose intriguing questions in those situations where agreement does not exist. This type of modeling can be used to further study predator-prey interactions, to study how changes in the environment might affect animal behavior, and to answer other important ecological and physiological questions.

Performance study of one-dimensional models for stratified thermal storage tanks

Two basic approaches are used to model the temperature distribution in thermal storage tanks for solar domestic hot water (SDHW) systems. In the multinode approach, the tank is divided into N nodes, with an energy balance written for each node. This approach results in a set of N differential equations that can be solved for the temperatures of the nodes as a function of time. In the plug flow approach, segments of liquid of different temperatures and sizes are assumed to move through the tank in a plug flow manner. The sizes of the fluid elements are determined mainly by the simulation time step and the flow rates. Whenever the incoming fluid from the heat source is colder than the fluid at the top of the tank, “plume entrainment” occurs. A model describing plume entrainment has been incorporated into both the multinode and the plug flow models in the TRNSYS program[1]. A performance study of the TRNSYS tank models has been carried out with experimental data from two different sources. Three performance numbers have been defined for quantifying the accuracy of the models compared with experimental data. Recommendations are given as to which tank model should be used under which conditions.

A method for estimating the long-term performance of direct-coupled PV pumping systems

Abstract A method is developed to predict the long-term performance of direct-coupled PV pumping systems. The method uses only information available from the PV module and pump-motor manufacturers. Weather data are “generated” from monthly averages of horizontal radiation and ambient temperatures using well-known weather data statistics. The method predicts monthly pumped water to within 6% of TRNSYS predictions based on hourly weather data. The use of a single monthly-average day is shown to underpredict monthly pumped water at low monthly average radiation levels and overpredict monthly pumped water at intermediate radiation levels. Only at high radiation levels does the use of a single monthly-average day provide a reasonable estimation of monthly pumped water.

Solar Heating and Cooling.

We have adequate theory and engineering capability to design, install, and use equipment for solar space and water heating. Energy can be delivered at costs that are competitive now with such high-cost energy sources as much fuel-generated, electrical resistance heating. The technology of heating is being improved through collector developments, improved materials, and studies of new ways to carry out the heating processes. Solar cooling is still in the experimental stage. Relatively few experiments have yielded information on solar operation of absorption coolers, on use of night sky radiation in locations with clear skies, on the combination of a solar-operated Rankine engine and a compression cooler, and on open cycle, humidification-dehumidification systems. Many more possibilities for exploration exist. Solar cooling may benefit from collector developments that permit energy delivery at higher temperatures and thus solar operation of additional kinds of cycles. Improved solar cooling capability can open up new applications of solar energy, particularly for larger buildings, and can result in markets for retrofitting existing buildings. Solar energy for buildings can, in the next decade, make a significant contribution to the national energy economy and to the pocketbooks of many individual users. very large-aggregate enterprises in manufacture, sale, and installation of solar energy equipment can result, which can involve a spectrum of large and small businesses. In our view, the technology is here or will soon be at hand; thus the basic decisions as to whether the United States uses this resource will be political in nature.

Transient Considerations of Flat-Plate Solar Collectors

A mathematical study showed that a quasi-steady-state model which assumes zero capacitance adequately represents the performance of a flat-plate solar collector if hourly meteorological data are the best available. The use of more complex models which account for capacitance is justified only if better data can be obtained.

A general design method for closed-loop solar energy systems

Abstract A general design method is presented for closed loop energy systems consisting of solar collectors, sensible energy storage and a closed-loop flow circuit in which thermal energy is supplied (through heat exchange) to a load above a specified minimum temperature. It is assumed that the energy supplied to the load is used at a constant thermal efficiency. Computer simulations were used to estimate the long-term thermal performance of these systems, and correlations between the system performance and the system design parameters, such as the collector characteristics, load size, climatic data, and the minimum useful temperature, are presented.

Loss-of-load probabilities for stand-alone photovoltaic systems

Abstract A general method is presented for estimating the loss-of-load probability (LLP) of stand-alone photovoltaic systems. The method was developed by correlating simulation results. The simulations were driven with synthetic radiation sequences having the same statistical significance as available historical data. The method assumes a constant nighttime load and accounts for the distribution and persistence in daily solar radiation data. It is shown that the 10-year average performance of systems having loss-of-load probabilities less than about .01 can vary greatly from one 10-year period to the next and thereby cannot be considered realistic performance estimates of a system during its lifetime.

A simplified method for estimating the monthly-average performance of photovoltaic systems

Abstract A method is presented for estimating the monthly-average conventional energy displaced by photovoltaic systems. Monthly-average array efficiency is estimated in terms of array parameters and monthly-average meteorological data. Monthly-average excess capacity is estimated for systems having a constant load during daylight hours. If the system does not have battery storage, excess capacity must be dissipated or fed back to the utility. With battery storage, a portion of the excess capacity can be stored for later use. A method is presented for estimating the monthly-average system performance for a constant 24 hr-per-day load with a battery of specified capacity.