## Modeling of Drift Effects on Solar Tower Concentrated Flux Distributions

*Lara-Cerecedo L.O., Moreno-Cruz I., Pitalúa-Diaz, N., Arancibia-Bulnes, C.A.*

### Abstract

A novel modeling tool for calculation of central receiver concentrated flux distributions is presented, which takes into account drift effects. This tool is based on a drift model that includes different geometrical error sources in a rigorous manner and on a simple analytic approximation for the individual flux distribution of a heliostat. The model is applied to a group of heliostats of a real field to obtain the resulting flux distribution and its variation along the day. The distributions differ strongly from those obtained assuming the ideal case without drift or a case with a Gaussian tracking error function. The time evolution of peak flux is also calculated to demonstrate the capabilities of the model. The evolution of this parameter also shows strong differences in comparison to the case without drift

Modeling of Drift Effects on Solar Tower Concentrated Flux Distributions

## Developing a Mini-heliostat Array for a Solar Central Tower Plant: A Practical Experience

*Victor H. Benitez, Jesús Pacheco-Ramirez, Nun Pitalua-Diaz*

### Abstract

This paper presents the modeling and control of an array of mini-heliostats developed for a solar central tower plant facility located outside of Hermosillo, Mexico. In order to deal with the real time implementation, an algorithm to significantly reduce the error that emerges in the solar tracking requirements is presented. Heliostats are oriented to reflect solar beam to a central receiver located in top of a tower. The heliostat tracks the apparent sun position with determined periodicity. A digital controller perform the tasks of calculate the control action to drive the actuators. The real time implementation of the control action introduces numerical issues that deviates the solar ray of the desired position. Results show that the proposed control strategy is able to track the solar sun position. The controller is implemented in real time via LabVIEW computational environment and is applied in a solar tower plant facility.

Developing a Mini-heliostat Array for a Solar Central Tower Plant: A Practical Experience

## Numerical study of the Boussinesq approach validity for natural convection and surface thermal radiation in an open cavity

*M. Montiel Gonzalez, J. Hinojosa Palafox, C. Estrada Gasca.*

### Abstract

A comparison was made between six turbulence models and experimental temperature profiles for the turbulent natural convection in a tilted open cubic cavity. The experimental setup consists of a cubic cavity of 1 m by side with one vertical wall receiving a constant and uniform heat flux, whereas the remaining walls are thermally insulated. The thermal fluid is air and the aperture is facing the heated wall. The temperature profiles were obtained at different heights and depths and each one consists of 10 positions inside the cavity. A commercial computational fluid dynamic software was used for the simulation and different turbulence models of k-εt and k-ω families were evaluated against experimental data. The lowest absolute average percentage difference for the experimental and numerical temperature profiles was for the rk-εt model and the highest was for the sk-ω model.

## Test of turbulence models for natural convection in an open cubic tilted cavity

*V. H. Benítez Baltazar, J. H. Pacheco Ramírez, N. Pitalúa Díaz.*

### Abstract

A comparison was made between six turbulence models and experimental temperature profiles for the turbulent natural convection in a tilted open cubic cavity. The experimental setup consists of a cubic cavity of 1 m by side with one vertical wall receiving a constant and uniform heat flux, whereas the remaining walls are thermally insulated. The thermal fluid is air and the aperture is facing the heated wall. The temperature profiles were obtained at different heights and depths and each one consists of 10 positions inside the cavity. A commercial computational fluid dynamic software was used for the simulation and different turbulence models of k-εt and k-ω families were evaluated against experimental data. The lowest absolute average percentage difference for the experimental and numerical temperature profiles was for the rk-εt model and the highest was for the sk-ω model.

Test of turbulence models for natural convection in an open cubic tilted cavity

## Theoretical and experimental study of natural convection with surface thermal radiation in a side open cavity

*M. Montiel-González, J.F. Hinojosa, H.I. Villafán-Vidales, A. Bautista-Orozco, C.A. Estrada.*

### Abstract

In this work a theoretical and experimental study of heat transfer by natural convection and thermal radiation on a solar open cubic cavity-type receiver is presented. The theoretical study consists on solving the laminar natural convection and the surface thermal radiation on a square open cavity at one end. The overall continuity, momentum, and energy equations in primitive variables are solved numerically by using the finite-volume method and the SIMPLEC algorithm. The thermophysical properties of the fluid are considered, for the first case, as temperature dependent in all the governing equations, and for the second case, constant, except for the density at the buoyancy term (Boussinesq approximation), with the purpose of comparing the results of both theoretical models with experimentally obtained results. Numerical calculations are conducted for Rayleigh number (Ra) values in the range of 104–106. The temperature difference between the hot wall and the bulk fluid (ΔT) is varied between 10 and 400 K, and is represented as a dimensionless temperature difference (φ) for the purpose of generalization of the trends observed. Experimental results include air temperature measurements inside the receiver. These results are compared with theoretically obtained air temperatures, and the average deviation between both results is around 3.0%, when using the model with variable thermophysical properties, and is around 5.4% when using the Boussinesq approximation.

## Heliostat image drift behavior for different error sources

*Martha Escobar-Toledo, Camilo A. Arancibia-Bulnes, Cuitlahuac Iriarte-Cornejo, Julio Waissman, David Riveros-Rosas , Rafael E. Cabanillas and Claudio A. Estrada.*

### Abstract

Drift is ubiquitous in heliostat fields, and may be caused by diverse geometrical inaccuracies during heliostat installation and operation. This phenomenon is studied for three important primary errors in the present paper: Angular offset in the drive mechanism, pedestal tilt, and canting error. Each error produces characteristic signatures, but there is a diversity of behavior depending on the error parameters and location of the heliostat. The variation of the extent of drift curves is studied as a function of distance, for fixed error parameters. It is found that, in general, this extent is not proportional to distance, except for far heliostats, and depends on a complicated manner on the different parameters involved. Moreover, even though the extent of drift curves becomes proportional to distance for far heliostats, the convergence is very slow, and very variable with the error parameters.

## Compensation of heliostat drift by seasonal sampling

*C. Iriarte-Cornejo, C.A. Arancibia-Bulnes, I. Salgado-Transito, J. Waissman, R.E. Cabanillas, C.A. Estrada.*

### Abstract

Heliostat image drift is a common phenomenon in central receiver solar power plants. Several geometrical errors produce drift of the heliostat solar spot at receiver surface, increasing radiation spillage. A heuristic drift compensation method is proposed, based on a polynomial approximation to the drift trajectories. Results of the practical implementation of the proposed method for the control of 10 heliostats in a solar tower facility are presented. A substantial improvement of heliostat tracking is observed on the experimental tests. Because heliostat drift experimental monitoring is a time consuming task, a numerical analysis of the yearly behavior of the compensation method, based on simulations of heliostat drift, was carried out. In these simulations, the behavior of the daily RMS deviation of the concentrated solar spot centroid is evaluated for a whole year, as the polynomial correction is applied. The simulations serve also to test the effectiveness of the proposal polynomial method in a wider range of conditions. Thus, heliostats with a variety of primary error values are simulated. Random wind induced vibrations are introduced in the simulation to evaluate the effectiveness of the calibration method under noise conditions. It is found that a very effective calibration can be achieved with a few sampling events of the heliostat behavior during the year, taking only a few minutes. The RMS deviation can be reduced to values of the order of the wind induced noise level. The proposed polynomial compensation looks like a promising alternative to be implemented in heliostat fields.## Improving parabolic trough mirror module qualification by FOCuS tool

*Manuel I. Peña-Cruz, Camilo A. Arancibia-Bulnes, Ana Monreal Vidal, and Marcelino Sánchez González.*

### Abstract

An improved tool for the shape qualification of parabolic trough mirror modules used in concentrated solar power plants was developed. The tool is based on the fringe reflection theory, in which sinusoidal fringe patterns are projected on a screen and their reflection over a specular surface is recorded by a camera. The observed distortions in the image are related directly to surface deviations from ideal geometry. Relevant aspects of the technique are its high spatial resolution (more than 1 × 106 points per mirror facet), short measurement time and easy setup. The developed tool (called FOCuS) is capable of calculating the local mirror slope deviations from its ideal design and the RMS value as a quality factor. Furthermore, the tool generates a file which can be loaded into CENER's TONATIUH ray tracing software, through a specially developed plug-in, for mirror modeling and intercept factor calculation with several tube absorber geometries.

Improving parabolic trough mirror module qualification by FOCuS tool