The Impact of Receiver Position Error on Parabolic Trough Collector Optical Performance

2012 ◽  
Author(s):  
Guangdong Zhu
Keyword(s):  
Position Error ◽  
Geometrical Parameters ◽  
First Principle ◽  
Optical Performance ◽  
Optical Analysis ◽  
Parabolic Trough ◽  
Actual Measurement ◽  
Position Errors ◽  
Effective Coefficients ◽  
The Impact

A newly developed analytical optical approach — First-principle OPTical Intercept Calculation (FirstOPTIC) — is employed to study the optical impact of receiver position error on parabolic trough collectors. The FirstOPTIC program performs first-principle treatment system optical error sources. By analyzing a large number of cases with varying system parameters such as the overall system optical error and the collector geometrical parameters, the paper quantitatively examines the difference between the first-principle treatment and probability approximation to receiver position error. In addition, a practical correlation between actual measurement data and its probability approximation for receiver position errors is established from parametric study; the correlation can be used to evaluate the relative importance of receiver position error to the collector’s optical performance. The effective coefficients defining the correlation of receiver position errors are also summarized for some existing trough collectors and make it convenient to conduct error-convolution-based optical analysis, which was not straightforward before. It is also shown that FirstOPTIC is a suitable tool for in-depth optical analysis and fast collector design optimization, which otherwise requires computationally intensive ray-tracing simulations.

Study of the Optical Impact of Receiver Position Error on Parabolic Trough Collectors

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
Guangdong Zhu
Keyword(s):  
Measurement Data ◽  
Position Error ◽  
Geometrical Parameters ◽  
Parabolic Trough ◽  
Error Sources ◽  
Actual Measurement ◽  
Effective Coefficients ◽  
Slope Error ◽  
Computationally Intensive ◽  
Optical Impact

A newly developed analytical optical approach—first-principle OPTical intercept calculation (FirstOPTIC)—is employed to study the optical impact of receiver position error on parabolic trough collectors. The FirstOPTIC method treats optical error sources the way they are typically characterized in laboratory measurements using a geometrical or optical interpretation. By analyzing a large number of cases with varying system parameters, such as overall system optical error and the collector's geometrical parameters, a practical correlation between actual measurement data and its corresponding error-convolution approximation for receiver position error is established from parametric study; the correlation enables a direct comparison of receiver position error to the sun shape and other optical error sources (such as mirror specularity and slope error) with respect to the collector optical performance. The effective coefficients that define the correlation of actual measurement data and its error-convolution approximation for receiver position error are also summarized for several existing trough collectors; these make it convenient to characterize the relative impact of receiver position error compared with other optical error sources, which was not straightforward in the past. It is shown that FirstOPTIC is a suitable tool for in-depth optical analysis and fast collector design optimization, which otherwise require computationally intensive ray-tracing simulations.

scholarly journals Finite Element Modeling and Ray Tracing of Parabolic Trough Collectors for Evaluation of Optical Intercept Factors With Gravity Loading

2011 ◽  
Author(s):  
Joshua M. Christian ◽  
Clifford K. Ho
Keyword(s):  
Finite Element ◽  
Ray Tracing ◽  
Finite Element Models ◽  
Optical Performance ◽  
Parabolic Trough ◽  
Parabolic Trough Collector ◽  
Error Distributions ◽  
Slope Error ◽  
The Impact ◽  
Reflective Surfaces

Predicting the structural and optical performance of concentrating solar power (CSP) collectors is critical to the design and performance of CSP systems. This paper presents a performance analysis which utilizes finite-element models and ray-tracing of a parabolic trough collector. The finite-element models were used to determine the impact of gravity loads on displacements and rotations of the facet surfaces, resulting in slope error distributions across the reflective surfaces. The geometry of the LUZ LS-2 parabolic trough collector was modeled in SolidWorks, and the effects of gravity on the reflective surfaces are analyzed using SolidWorks Simulation. The ideal mirror shape, along with the 90° and 0° positions (with gravity deformation) were evaluated for the LS-2. The ray-tracing programs APEX and ASAP are used to assess the impact of gravity deformations on optical performance. In the first part of the analysis, a comprehensive study is performed for the parabolic trough to evaluate a random slope error threshold (i.e., induced by manufacturing errors and assembly processes) above which additional slope errors caused by gravity sag decrease the intercept factor of the system. The optical performance of the deformed shape of the collector (in both positions) is analyzed with additional induced slope errors ranging from zero up to 1° (17.44 mrad). The intercept factor for different solar incident angles found from ray-tracing is then compared to empirical data to demonstrate if the simulations provide consistent answers with experimental data.

Optical Analysis of Solar Parabolic Trough Collector with Flat Concentrating Photovoltaic Receiver

2014 ◽  
Vol 592-594 ◽  
pp. 2396-2403 ◽  
Author(s):  
Nikhilesh R Kamnapure ◽  
K. Srinivas Reddy
Keyword(s):  
Concentration Ratio ◽  
Total Error ◽  
Analytical Data ◽  
Numerical Results ◽  
Distribution Model ◽  
Local Concentration ◽  
Optical Analysis ◽  
Parabolic Trough ◽  
Parabolic Trough Collector ◽  
The Impact

In this paper, an optical analysis of parabolic trough collector with flat concentrating photovoltaic receiver is carried out by utilizing non-uniform intensity distribution model of the solar disk. The optical system simulation tool ASAP is used to analyze the parabolic trough system with single axis tracking having a mirror aperture of 1m and length of 3m. The impact of random errors including slope error, apparent change in sun’s width, tracking errors on the optical performance of trough system is carried out. The errors are assumed to follow Gaussian (normal) distribution and analyzed statistically. It is found that intercept factor increases with rim angle for given total error of 5, 10 and 20 mrad. Geometrical concentration ratio is varied to see the effect on the intercept factor and compared for various error values. The numerical results show that for De-focused performance (L=0.1f) the local concentration ratio value is 23 for the 45° rim angle. Numerical results are compared with the analytical data available in the literature which show good agreement.

THEORETICAL STUDY OF THE EFFECT OF GEOMETRICAL PARAMETERS AND LOCATION OF ROTOR IMPACT ELEMENTS OF AN IMPACT-CENTRIFUGAL GRINDER ON SPEED AND ANGLES OF CRUSHED PARTICLES FLIGHT

2020 ◽  
Keyword(s):  
Granulometric Composition ◽  
Theoretical Study ◽  
Process Efficiency ◽  
Geometrical Parameters ◽  
Grinding Process ◽  
Main Work ◽  
Impact Element ◽  
The Impact ◽  
Positive Effect ◽  
Efficiency Indicators

One of efficiency indicators of grain grinders is grain granulometric composition. The basis of mixed fodder is crushed grain, the particles of which must have a leveled granulometric composition for subsequent mixing and obtaining a high-quality feed mixture. In agricultural production, hammer crushers are widely used, in which the destruction of grain occurs due to the impact of a hinged hammer. The main disadvantage of these crushers is that not the entire surface of the hammers is involved in grinding, thus reduces grinding process efficiency. A slightly different principle of material destruction is laid down in the basis of the proposed design of the shock-centrifugal grinder. Main work is performed by flat impact elements located on the rotor, which serve to accelerate crushed particles with subsequent impact of them on the bump elements. An important step in the design of new constructions of shock-centrifugal grinders is to determine size and location of the impact elements on the rotor, without which the grinding process is not possible. In the calculation method presented, the dependencies for determining the velocities and angles of a single particle flight from the surface of a flat impact element for its specified dimensions are proposed. Two variants of an impact element location on the rotor are considered and analyzed: radial and at an angle in the direction of rotor rotation. As a result of research carried out, it is noted that in the case of inclined position of an impact element on the rotor an increase in flight speed and flight angles change in crushed particles, which gives the opportunity to have a positive effect on grinding process.

scholarly journals Consistency of the Empirical Distributions of Navigation Positioning System Errors with Theoretical Distributions—Comparative Analysis of the DGPS and EGNOS Systems in the Years 2006 and 2014

Sensors ◽  
2020 ◽  
Vol 21 (1) ◽  
pp. 31
Author(s):  
Mariusz Specht
Keyword(s):  
Normal Distribution ◽  
Root Mean Square ◽  
Statistical Tests ◽  
Position Error ◽  
Positioning System ◽  
Navigation Systems ◽  
Mean Square ◽  
Positioning Systems ◽  
Position Errors ◽  
System Errors

Positioning systems are used to determine position coordinates in navigation (air, land and marine). The accuracy of an object’s position is described by the position error and a statistical analysis can determine its measures, which usually include: Root Mean Square (RMS), twice the Distance Root Mean Square (2DRMS), Circular Error Probable (CEP) and Spherical Probable Error (SEP). It is commonly assumed in navigation that position errors are random and that their distribution are consistent with the normal distribution. This assumption is based on the popularity of the Gauss distribution in science, the simplicity of calculating RMS values for 68% and 95% probabilities, as well as the intuitive perception of randomness in the statistics which this distribution reflects. It should be noted, however, that the necessary conditions for a random variable to be normally distributed include the independence of measurements and identical conditions of their realisation, which is not the case in the iterative method of determining successive positions, the filtration of coordinates or the dependence of the position error on meteorological conditions. In the preface to this publication, examples are provided which indicate that position errors in some navigation systems may not be consistent with the normal distribution. The subsequent section describes basic statistical tests for assessing the fit between the empirical and theoretical distributions (Anderson-Darling, chi-square and Kolmogorov-Smirnov). Next, statistical tests of the position error distributions of very long Differential Global Positioning System (DGPS) and European Geostationary Navigation Overlay Service (EGNOS) campaigns from different years (2006 and 2014) were performed with the number of measurements per session being 900’000 fixes. In addition, the paper discusses selected statistical distributions that fit the empirical measurement results better than the normal distribution. Research has shown that normal distribution is not the optimal statistical distribution to describe position errors of navigation systems. The distributions that describe navigation positioning system errors more accurately include: beta, gamma, logistic and lognormal distributions.

Influence of nozzle exit geometrical parameters on supersonic jet decay

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Prasanta Kumar Mohanta ◽  
B. T. N. Sridhar ◽  
R. K. Mishra
Keyword(s):  
Aspect Ratio ◽  
Nozzle Exit ◽  
Ambient Air ◽  
Schlieren Image ◽  
Geometrical Parameters ◽  
Image Study ◽  
Aspect Ratios ◽  
Core Length ◽  
Supersonic Core Length ◽  
The Impact

Abstract Experiments and simulations were carried on C-D nozzles with four different exit geometry aspect ratios to investigate the impact of supersonic decay characteristics. Rectangular and elliptical exit geometries were considered for the study with various aspect ratios. Numerical simulations and Schlieren image study were studied and found the agreeable logical physics of decay and spread characteristics. The supersonic core decay was found to be of different length for different exit geometry aspect ratio, though the throat to exit area ratio was kept constant to maintain the same exit Mach number. The impact of nozzle exit aspect ratio geometry was responsible to enhance the mixing of primary flow with ambient air, without requiring a secondary method to increase the mixing characteristics. The higher aspect ratio resulted in better mixing when compared to lower aspect ratio exit geometry, which led to reduction in supersonic core length. The behavior of core length reduction gives the identical signature for both under-expanded and over-expanded cases. The results revealed that higher aspect ratio of the exit geometry produced smaller supersonic core length. The aspect ratio of cross section in divergent section of the nozzle was maintained constant from throat to exit to reduce flow losses.

Thermal performance comparison of different sun tracking configurations

2019 ◽  
Vol 88 (2) ◽  
pp. 20902
Author(s):  
O. Achkari ◽  
A. El Fadar
Keyword(s):  
Thermal Performance ◽  
Electricity Generation ◽  
Arid Regions ◽  
Performance Comparison ◽  
Water Desalination ◽  
Parabolic Trough ◽  
Parabolic Trough Collector ◽  
The Impact ◽  
The Mathematical Model ◽  
Good Agreement

Parabolic trough collector (PTC) is one of the most widespread solar concentration technologies and represents the biggest share of the CSP market; it is currently used in various applications, such as electricity generation, heat production for industrial processes, water desalination in arid regions and industrial cooling. The current paper provides a synopsis of the commonly used sun trackers and investigates the impact of various sun tracking modes on thermal performance of a parabolic trough collector. Two sun-tracking configurations, full automatic and semi-automatic, and a stationary one have numerically been investigated. The simulation results have shown that, under the system conditions (design, operating and weather), the PTC's performance depends strongly on the kind of sun tracking technique and on how this technique is exploited. Furthermore, the current study has proven that there are some optimal semi-automatic configurations that are more efficient than one-axis sun tracking systems. The comparison of the mathematical model used in this paper with the thermal profile of some experimental data available in the literature has shown a good agreement with a remarkably low relative error (2.93%).

Consistency analysis of global positioning system position errors with typical statistical distributions

2021 ◽  
pp. 1-18
Author(s):  
Mariusz Specht
Keyword(s):  
Normal Distribution ◽  
Global Positioning System ◽  
Position Error ◽  
Statistical Distribution ◽  
Positioning System ◽  
Statistical Distributions ◽  
Position Errors ◽  
Global Positioning ◽  
Gps System ◽  
Best Fit

Abstract Research into statistical distributions of φ, λ and two-dimensional (2D) position errors of the global positioning system (GPS) enables the evaluation of its accuracy. Based on this, the navigation applications in which the positioning system can be used are determined. However, studies of GPS accuracy indicate that the empirical φ and λ errors deviate from the typical normal distribution, significantly affecting the statistical distribution of 2D position errors. Therefore, determining the actual statistical distributions of position errors (1D and 2D) is decisive for the precision of calculating the actual accuracy of the GPS system. In this paper, based on two measurement sessions (900,000 and 237,000 fixes), the distributions of GPS position error statistics in both 1D and 2D space are analysed. Statistical distribution measures are determined using statistical tests, the hypothesis on the normal distribution of φ and λ errors is verified, and the consistency of GPS position errors with commonly used statistical distributions is assessed together with finding the best fit. Research has shown that φ and λ errors for the GPS system are normally distributed. It is proven that φ and λ errors are more concentrated around the central value than in a typical normal distribution (positive kurtosis) with a low value of asymmetry. Moreover, φ errors are clearly more concentrated than λ errors. This results in larger standard deviation values for φ errors than λ errors. The differences in both values were 25–39%. Regarding the 2D position error, it should be noted that the value of twice the distance root mean square (2DRMS) is about 10–14% greater than the value of R95. In addition, studies show that statistical distributions such as beta, gamma, lognormal and Weibull are the best fit for 2D position errors in the GPS system.

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