Unleashing Empirical Equations with “Nonlinear Fitting” and “GUM Tree Calculator” (original) (raw)
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Investigación e Innovación en Ingenierías
The goal of this paper is applied the Ordinary Least Squares (OLS) method as a strategy in order to reduce the uncertainty measurement associated to the relevant physical quantities. Methodology or method: This work was motivated due to the efforts made in the measurement sciences to investigate alternative methods that allow obtaining greater metrological reliability of the results, that is, reducing the uncertainty associated with the measurement. Thus, the applied methodology consisted of the development of a computational code using the MatLab tool, in which an algorithm was programmed that supports the application of the OLS method. Three of the most used physical magnitudes at an industrial level were evaluated: temperature, pressure and mass. These magnitudes were evaluated from the calibration of three measuring instruments: thermistor, manometer and digital scale. Results: The applied methodology allowed to: (i) obtain the matrix of the coefficients for polynomials of degre...
STEAMEST: A Software Tool for Estimation of Physical Properties of Water and Steam
Journal of Software, 2009
A software tool, STEAMEST, has been developed for estimation of properties of water and steam for industrial applications using IAPWS-IF97 industrial formulation and subsequent updates. STEAMEST meets the precision and consistency standards of the International Association for the Properties of Water and Steam (IAPWS) as verified by 8 byte real values for all variables. It achieves maximum conformity (a tolerance of 1 part per billion) with "Basic Equations" of IAPWS-IF97 through use of iterative procedures instead of approximate "Backward Equations", where recommended "Basic Equations" are not available. The code has been written in highly flexible Microsoft .NET framework using an object-oriented approach to ensure portability and modularity in software design without making any compromise on performance. Given valid input(s), STEAMEST can predict more than 15 properties of water/steam with a user-selected precision. It includes integrated software for unit conversion. Thermodynamic plots created by STEAMEST have the provision of zooming a specified portion. STEAMEST can compete with similar software both in terms of performance and reliability. Thus it has the potential to become a valuable tool for industry and academia. Index Terms-software tool, properties of water and steam, IAPWS-IF97, STEAMEST
Computer codes for the calculation of thermodynamic properties of water
2013
Linear interpolation algorithms are commonly used for the calculation of the thermodynamic properties of water in thermal-hydraulic analysis systems. However, these algorithms can use a substantial amount of computation time. An alternative for this approach is to use approximation formulas. On the other hand, the steam tables are created from empirical data, which can be represented by a set of points in a graph of certain property. There is no function that can integrally represent the curves formed by these points, some functions are adjusted to represent satisfactorily certain range. Together they compose the curves that relate the properties. It aims to introduce two computer codes (PARSTEAM and NBSNRCE) designed to perform the function of steam tables printed, with the purpose of speeding up the process of analysis and as support for other computer codes; and show that such codes have good accuracy, compared with steam tables.
An R-package for water and steam properties for scientific and general use
International Journal of Nuclear Energy Science and Technology, 2018
The International Association for the Properties of Water and Steam (IAPWS) develops formulations for the calculation of thermophysical properties of water as a function of different combinations of temperature, density, pressure, enthalpy, and entropy. These properties are useful for scientists and nuclear, chemical, and mechanical engineers who analyse experimental data or are involved with projects and equipment development, like heat exchangers, turbines, or nuclear power reactors. The IAPWS-95 formulation solves the fundamental equation of Helmholtz free energy as a function of temperature and density. This paper gives a description of how these equations are solved and exemplifies the use of a package developed for the free platform R. The IAPWS95 package was developed to help users to get access to the IAPWS-95 formulation in a free software environment which is growing exponentially. Transport properties were programmed using other IAPWS releases. The examples consider the uncertainty analysis of thermal parameters of a nuclear power reactor and the preparation of tables and graphs of water properties.
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Mains water temperature (T{sub mains}) has significant influence on the energy consumption of water heating equipment. It is dominantly influenced by ambient temperature (T{sub amb}). Since T{sub amb} is roughly an annual sinusoid, T{sub mains} is assumed to be a sinusoid whose mean value varies directly with annual average temperature T{sub amb},{sub ann}. Model parameters are based on water system physics and include: (i) a constant offset from T{sub amb},{sub ann}; and (ii) amplitude and phase which vary linearly with T{sub amb},{sub ann}. Available T{sub mains} data indicate that the offset is 6 oF, and that the amplitude is 0.4T{sub amb} Uncertainties include: (i) data quality issues, including bias of T{sub mains} data from heat exchange with house air; (ii) inherent spatial variations in mains networks, and (iii) limited data sets. Future work includes acquiring quality data sets, testing the model in northern climates, and refining parameter estimates.
Atmospheric Chemistry and Physics, 2008
The representation of data, whether geophysical observations, numerical model output or laboratory results, by a best fit straight line is a routine practice in the geosciences and other fields. While the literature is full of detailed analyses of procedures for fitting straight lines to values with uncertainties, a surprising number of scientists blindly use the standard least squares method, such as found on calculators and in spreadsheet programs, that assumes no uncertainties in the x values. Here, the available procedures for estimating the best fit straight line to data, including those applicable to situations for uncertainties present in both the x and y variables, are reviewed. Representative methods that are presented in the literature for bivariate weighted fits are compared using several sample data sets, and guidance is presented as to when the somewhat more involved iterative methods are required, or when the standard least-squares procedure would be expected to be satisfactory. A spreadsheet-based template is made available that employs one method for bivariate fitting.
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The SCOR/IAPSO 1 Working Group 127 on Thermodynamics and Equation of State of Seawater has prepared recommendations for new methods and algorithms for numerical estimation of the the thermophysical properties of seawater. As an outcome of this work, a new International Thermodynamic Equation of Seawater (TEOS-10) was endorsed by IOC/UNESCO 2 in June 2009 as the official replacement and extension of the 1980 International Equation of State, EOS-80. As part of this new standard a source code package has been prepared that is now made freely available to users via the World Wide Web. This package includes two libraries referred to as the SIA (Sea-Ice-Air) library and the GSW (Gibbs SeaWater) library. Information on the GSW library may be found on the TEOS-10 web site (http://www.TEOS-10.org). This publication provides an introduction to the SIA library which contains routines to calculate various thermodynamic properties as discussed
Industrial need for accurate thermophysical data and for reliable prediction methods
Journal of Thermal Analysis and Calorimetry, 2008
The intelligent design of industrial chemical processes requires accurate thermophysical data. These data include pure component and mixture values. Three of the authors are involved in maintaining the DIPPR 801 Database [1] that contains pure component data. In order to use the data over wide ranges of conditions, correlating equations are needed. These data can be put into two broad classes: those for pure components and mixtures, including solutions. These data can then be separated into types; those that are constant and those that are functions of temperature, T, pressure, P, and/or composition, x. Examples of thermophysical properties needed by engineers to design processes are shown in .