## Study of the radiation flux distribution in a parabolic dish concentrator

*Nidia Aracely Cisneros-Cárdenas, Rafael Cabanillas-López, Ricardo Pérez-Enciso, Guillermo Martínez-Rodríguez, Rafael García-Gutiérrez, Carlos Pérez-Rábago, Ramiro Calleja-Valdez, David Riveros-Rosas*

### Abstract

The radiation flux distributions produced by the concentrating solar systems used to produce thermal/electrical power are usually non-homogeneous. This results in non-uniform temperature distributions on the solar receivers, causing adverse effects on the system’s overall performance. An approach to better understand the problem is to study the surfaces around the focal zone where the radiation density is homogeneous (isosurfaces), generating them from experimental data. For this, it is necessary to superimpose built volumes of the different irradiance levels using parallel planes in different directions from the focal point of a concentrator. These volumes are known as effective volumes. This study presents the model used to generate effective volume produced by a point focus concentrator, comparing it with experimental results in a direction perpendicular to the focal axis. The effective volumes were developed considering a global optical error of the system of 2.8 mrad. The set of methods used to generate effective volumes has not been previously presented in the literature. The theoretical-experimental research consisted of the combination of the camera-target method and the simulations by the ray-tracing technique. The results showed effective volumes with the highest value of 10 MW/m2 and the lowest value of 4.5 MW/m2.

Study of the radiation flux distribution in a parabolic dish concentrator

## Effect of non-uniform concentrated solar flux on direct steam generation in vertical pipes of solar tower receivers

*V.M.Maytorena, J.F.Hinojosa*

### Abstract

The purpose of this work is to analyze the effect of non-uniform concentrated solar radiation on direct steam generation in a vertical tube of solar tower receiver. The modified RPI model was used for the conditions of critical heat flux coupled to a Eulerian two fluid model. The mathematical model was solved with CFD software. The results were validated with experimental data reported in the literature and a parametric study was carried out to determinate the effect of non-uniform concentrated solar radiation, on the steam quality, the volumetric fraction, enthalpies and temperatures of liquid and steam. Non-uniform concentrated solar fluxes favor generation of steam but produce conditions that may influence the structural durability of DSG receivers, like high axial temperature gradients and zones with temperatures above the melting temperature of stainless steel.

## Effect of spatial resolution of heliostat surface characterization on its concentrated heat flux distribution

*C. Iriarte-Cornejo, C.A. Arancibia-Bulnes, J.F. Hinojosa, Manuel I. Peña-Cruz*

### Abstract

The optical characteristics of solar concentrators are key factors influencing the overall efficiency of solar power plants. For instance, heliostats need to be evaluated prior to installation and during its operation lifetime. This guarantees that the optical and thermal performance of these systems is close to design. One methodology that has gained importance due to its potential capabilities has been the Fringe Reflection Technique. This technique uses the reflection of a series of regular stripes to obtain the local slope deviations from a specular surface. Coupled to a ray tracing analysis, these slopes can be used to identify the distortion in concentrated solar spots. The enormous amount of data needed to carry out this analysis difficult its implementation at large scale. In this work, a study for determining the optimal number of sample points for heliostat surface characterization is realized. It has been found that, depending on the level of errors, the number SPFS required to reach convergence in the flux distribution profiles and intercept factors is variable. However, for the wide range of parameters considered in all cases 48 SPFS where enough to reach convergences to 1%. This is equivalent to one point per every 2.5cm of facet side length. For values of slope and canting errors up to 2mrad, half this density is sufficient.

## Thermal analysis of a finned receiver for a central tower solar system

*A Piña-Ortiz, JF Hinojosa, RA Pérez-Enciso, VM Maytorena, RA Calleja, CA Estrada*

### Abstract

In this study, a thermal analysis of a finned receiver prototype for a thermosolar tower system is presented. The experimental system consists of parallelepiped aluminum enclosure of 1.2 m high, 1.23 m wide and 0.1 m depth. At the interior, 1232 cylindrical fins with a diameter of 0.0095 m (3/8”) and 0.09 m length increases the heat transfer area up to 225%. The vertical wall receives the incoming solar concentrated radiation from a group of heliostats whilst at the interior a constant flow of water removes the absorbed energy. Experimental temperature profiles were obtained at different heights and depths and a comparison was made with numerical results obtained with the use of commercial CFD software. It was found that the maximum thermal efficiency of the receiver was 94.4 %, decreasing as the radiative flux increases.

Thermal analysis of a finned receiver for a central tower solar system

## 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.