A Tabular Taylor Series Expansion Method for Fast Calculation of Steam Properties

1997 ◽  
Vol 119 (2) ◽  
pp. 485-491 ◽  
Author(s):  
K. Miyagawa ◽  
P. G. Hill
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
International Association ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
The State ◽  
Steam Power ◽  
Direct Use ◽  
Derivatives Of ◽  
Plane Grid

A new method is proposed for rapid and accurate calculation of steam properties in the regions of the state plane of greatest importance to the steam power industry. The method makes direct use of the derivatives of that Helmholtz function that is the best available wide-ranging scientific formulation of the properties of steam. It is rapid because, with a six-term Taylor series expansion, it uses property values and derivatives evaluated once and for all from the Helmholtz function and stored in tables pertaining to an optimized state plane grid configuration. The method eliminates the need for iterative property calculations and is amenable to any region of the state plane. For properties in the ranges of temperature from 0 to 800°C and pressure from 0 to 100 MPa the core memory requirement for three functions of any given pair of independent properties is less than 1 Mb. With this memory allocation it is possible everywhere in the stated range to satisfy the specific volume and enthalpy tolerances specified by the International Association for the Properties of Water and Steam. An optimized formulation of the method is demonstrated in this paper for enthalpy, entropy, and volume functions of pressure and temperature in the superheat region.

Full-Scale Bounds Estimation for the Nonlinear Transient Heat Transfer Problems with Interval Uncertainties

2021 ◽  
pp. 2150026
Author(s):  
Ruifei Peng ◽  
Haitian Yang ◽  
Yanni Xue
Keyword(s):  
Heat Transfer ◽  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Transient Heat Transfer ◽  
High Fidelity ◽  
Interval Scale ◽  
Nonlinear Transient ◽  
Transfer Problems ◽  
Derivatives Of

A package solution is presented for the full-scale bounds estimation of temperature in the nonlinear transient heat transfer problems with small or large uncertainties. When the interval scale is relatively small, an efficient Taylor series expansion-based bounds estimation of temperature is stressed on the acquirement of first and second-order derivatives of temperature with high fidelity. When the interval scale is relatively large, an optimization-based approach in conjunction with a dimension-adaptive sparse grid (DSG) surrogate is developed for the bounds estimation of temperature, and the heavy computational burden of repeated deterministic solutions of nonlinear transient heat transfer problems can be efficiently alleviated by the DSG surrogate. A temporally piecewise adaptive algorithm with high fidelity is employed to gain the deterministic solution of temperature, and is further developed for recursive adaptive computing of the first and second-order derivatives of temperature. Therefore, the implementation of Taylor series expansion and the construction of DSG surrogate are underpinned by a reliable numerical platform. The parallelization is utilized for the construction of DSG surrogate for further acceleration. The accuracy and efficiency of the proposed approaches are demonstrated by two numerical examples.

scholarly journals Weighted Measurement Fusion Particle Filter for Nonlinear Systems with Correlated Noises

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3242 ◽  
Author(s):  
Ke Wei Zhang ◽  
Gang Hao ◽  
Shu Li Sun
Keyword(s):  
Nonlinear Systems ◽  
Particle Filter ◽  
Series Expansion ◽  
Taylor Series ◽  
Asymptotic Optimality ◽  
Taylor Series Expansion ◽  
Full Rank ◽  
Expansion Method ◽  
Least Square ◽  
Correlated Noises

The multi-sensor information fusion particle filter (PF) has been put forward for nonlinear systems with correlated noises. The proposed algorithm uses the Taylor series expansion method, which makes the nonlinear measurement functions have a linear relationship by the intermediary function. A weighted measurement fusion PF (WMF-PF) was put forward for systems with correlated noises by applying the full rank decomposition and the weighted least square theory. Compared with the augmented optimal centralized fusion particle filter (CF-PF), it could greatly reduce the amount of calculation. Moreover, it showed asymptotic optimality as the Taylor series expansion increased. The simulation examples illustrate the effectiveness and correctness of the proposed algorithm.

Rationalize the irrational and fractional expressions in nonlinear analysis

2016 ◽  
Vol 30 (04) ◽  
pp. 1650068 ◽  
Author(s):  
Yongfeng Yang ◽  
Tingdong Jiang ◽  
Zhong Ren ◽  
Junyao Zhao ◽  
Zheng Zhang
Keyword(s):  
Nonlinear Analysis ◽  
Series Expansion ◽  
Taylor Series ◽  
Impact Force ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Stochastic Bifurcation ◽  
Bifurcation And Chaos ◽  
Integral Process ◽  
Series Expansion Method

Chebyshev polynomial approximation is an effective method to study the stochastic bifurcation and chaos. However, due to irrational and fractional expressions existing in the denominator of some mechanical systems, the integral process is very complicated. The Taylor series expansion is proposed to expand the irrational and fractional expressions into a series of polynomials. Smooth and discontinuous oscillator was taken as an example, and the results show that the Taylor series expansion method is acceptable. The rub-impact force was taken as another example. Numerical results indicate that the method is suitable for the rub-impact rotor system.

scholarly journals An Alternative Approach to Energy Eigenvalue Problems of Anharmonic Potentials

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Okan Ozer ◽  
Halide Koklu
Keyword(s):  
Series Expansion ◽  
Excellent Agreement ◽  
Taylor Series ◽  
Taylor Expansion ◽  
Eigenvalue Problems ◽  
Energy Eigenvalue ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Energy Eigenvalues ◽  
Alternative Approach

Energy eigenvalues of quartic and sextic type anharmonic potentials are obtained by using an alternative method called asymptotic Taylor expansion method (ATEM) which is an approximate approach based on the asymptotic Taylor series expansion of a function. It is shown that the energy eigenvalues found by ATEM are in excellent agreement with the existing results.

Rapid and Accurate Calculation of Water and Steam Properties Using the Tabular Taylor Series Expansion Method

2001 ◽  
Vol 123 (3) ◽  
pp. 707-712 ◽  
Author(s):  
K. Miyagawa ◽  
P. G. Hill
Keyword(s):  
Taylor Series ◽  
High Speed ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Good Representation ◽  
Test Results ◽  
Helmholtz Equations ◽  
Industrial Use ◽  
Direct Use ◽  
Speed And Accuracy

In applications where both speed and accuracy of computation of thermodynamic properties are important and particularly where the independent variables are not those used in Helmholtz equations, direct use of such equations can be excessively time-consuming. This paper introduces the enthalpy-pressure version of the tabular Taylor series (TTSE) method, which has the accuracy and computing speed required for application in power industries. The IAPWS formulation for scientific use, IAPWS-95, was used as the basic Helmholtz equation. The speed and accuracy of the TTSE have been compared with the IAPWS formulation for industrial use, IAPWS-IF97, which has been developed to achieve high-speed calculation with good representation of IAPWS-95 values. Test results show that the TTSE accurately represents the basic equation and that the computation speed is higher than that of IF97.

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