Towards a Fast, Open-Path Laser Hygrometer for Airborne Eddy Covariance Measurements

Water vapor fluxes play a key role in the energy budget of the atmosphere, and better flux measurements are needed to improve our understanding of the formation of clouds and storms. Large-scale measurements of these fluxes are possible by employing the eddy correlation (EC) method from an aircraft. A hygrometer used for such measurements needs to deliver a temporal resolution of at least 10 Hz while reliably operating in the harsh conditions on the exterior of an aircraft. Here, we present a design concept for a calibration-free, first-principles, open-path dTDLAS hygrometer with a planar, circular and rotationally symmetric multipass cell with new, angled coupling optics. From our measurements, the uncertainty of the instrument is estimated to be below 4.5% (coverage factor k = 1). A static intercomparison between a dTDLAS prototype of the new optics setup and a traceable dew point mirror hygrometer was conducted and showed a systematic relative deviation of 2.6% with a maximal relative error of 2.2%. Combined with a precision of around 1 ppm H2O at tropospheric conditions, the newly designed setup fulfills the static precision and accuracy requirements of the proposed airborne EC hygrometer.

Design of Multi-function Power Factor Instrument with STM32

Background: A multifunctional power factor device based on the FFT algorithm has been designed. The digital panel can display power factor, voltage, current, frequency, phase angle, active power and reactive power. Objective: To solve the influence of the harmonic interference and the aperiodic component on the accuracy of power factor measurement. Methods: In this paper, by combining a fixed-point 256-point FFT algorithm and taking STM32 as the core microcontroller, the hardware circuit and the software program are designed respectively. The hardware circuit is tested and analyzed in practice. Among them, the hardware circuit mainly includes the main circuit design, STM32 control circuit design, EMI and second-order RC filter circuit design, sampling circuit design, and signal conditioning circuit design. The software program mainly includes the main program, AD conversion subroutine, voltage and current acquisition subroutine, LCD display subroutine and twirl factor array. FFT algorithm is achieved by the table look-up method. Results: Finally, the hardware circuit is built and the software program is debugged to test the designed device. The experimental results show that the designed power factor instrument meets the task requirements under the different types of loads. Conclusion: After processing and analyzing the measurement results, it can be concluded that: under the pure resistive load, the maximal relative error of electrical parameters is 4.49%; and under the resistive inductive load, the maximal relative error of electrical parameters is 2.86%. Both results meet the design requirements.

Review of New Flow Friction Equations: Constructing Colebrook’s Explicit Correlations Accurately

Using only a limited number of computationally expensive functions, we show a way how to construct accurate and computationally efficient approximations of the Colebrook equation for flow friction. The presented approximations are based on the asymptotic series expansion of the Wright ω-function and symbolic regression. The results are verified with 8 million of Quasi-Monte Carlo points covering the domain of interest for engineers. In comparison with the built-in “wrightOmega” feature of Matlab R2016a, the herein introduced related approximations of the Wright ω-function significantly accelerate the computation. With only two logarithms and several basic arithmetic operations used, the presented approximations are not only computationally efficient but also extremely accurate. The maximal relative error of the most promising approximation which is given in the form suitable for engineers’ use is limited to 0.0012%, while for a little bit more complex variant is limited to 0.000024%.

Modelling Population Growth with Difference Equation Method

In this paper, we present a new method of the econometric model construction: the difference equation method. We illustrate the proposed approach using an application example from human population dynamic study. We find out that proposed method is very useful to find one of the three forms of proposed models of human population satisfying the small maximal relative errors. The maximal relative error is a measure to verify the model of human population. The proposed method is tested for all available data referring to the human population in the OECD countries as well as in selected non-OECD countries.

Very accurate explicit approximations for calculation of the Colebrook friction factor

To date, the Colebrook equation is mostly accepted as an unofficial standard for calculation of the friction factor in turbulent flow through pipes. Unfortunately, the unknown friction factor in the Colebrook equation is given implicitly. Therefore, the implicit Colebrook equation has to be solved in an iterative procedure or using some of the appropriate explicit correlations proposed by many authors. Although the iterative solution is simple and very accurate, it can cause some problems during the calculation of looped network of pipes or similar systems of pipes. Therefore, explicit approximations are favorable in these cases. Up to date, the most accurate approximations have maximal relative error of no more than 0.14% compared to the very accurate iterative solution. Here two explicit approximations are presented, based on already existing models which are improved using genetic algorithms optimization. They are with the maximal relative error of no more than 0.0083% and 0.0026%.

Discussion of “Gene expression programming analysis of implicit Colebrook–White equation in turbulent flow friction factor calculation” by Saeed Samadianfard [J. Pet. Sci. Eng. 92-93 (2012), 48-55]

Maximal relative error of the explicit approximation to the Colebrook equation for flow friction presented in the discussed paper by Saeed Samadianfard [J. Pet. Sci. Eng. 92-93 (2012), 48-55; doi. 10.1016/j.petrol.2012.06.005] is investigated. Samadianfard claims that his approximation is very accurate with the maximal relative error of no more than 0.08152%. Here is shown that this error is about 7%. Related comments about the paper are also enclosed. ; JRC.F.3-Energy Security, Systems and Market

Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

This paper presents evolutionary optimization of explicit approximations of the empirical Colebrook’s equation that is used for the calculation of the turbulent friction factor (λ), i.e., for the calculation of turbulent hydraulic resistance in hydraulically smooth and rough pipes including the transient zone between them. The empirical Colebrook’s equation relates the unknown flow friction factor (λ) with the known Reynolds number (R) and the known relative roughness of the inner pipe surface (ε/D). It is implicit in the unknown friction factor (λ). The implicit Colebrook’s equation cannot be rearranged to derive the friction factor (λ) directly, and therefore, it can be solved only iteratively [λ = f(λ, R, ε/D)] or using its explicit approximations [λ ≈ f(R, ε/D)], which introduce certain error compared with the iterative solution. The optimization of explicit approximations of Colebrook’s equation is performed with the aim to improve their accuracy, and the proposed optimization strategy is demonstrated on a large number of explicit approximations published up to date where numerical values of the parameters in various existing approximations are changed (optimized) using genetic algorithms to reduce maximal relative error. After that improvement, the computational burden stays unchanged while the accuracy of approximations increases in some of the cases very significantly.

Evolutionary Optimization of Colebrook’s Turbulent Flow Friction Approximations

Today, Colebrook’s equation is mostly accepted as an informal standard for modeling of turbulent flow in hydraulically smooth and rough pipes including transient zone in between. The empirical Colebrook’s equation relates the unknown flow friction factor (λ) with the known Reynolds number (R) and the known relative roughness of inner pipe surface (ε/D). It is implicit in unknown friction factor (λ). Implicit Colebrook’s equation cannot be rearranged to derive friction factor (λ) directly and therefore it can be solved only iteratively [λ=f(λ, R, ε/D)] or using its explicit approximations [λ≈f(R, ε/D)]. Of course, approximations carry in certain error compared with the iterative solution where the highest level of accuracy can be reached after enough number of iterations. The explicit approximations give a relatively good prediction of the friction factor (λ) and can reproduce accurately Colebrook’s equation and its Moody’s plot. Usually, more complex models of approximations are more accurate and vice versa. In this paper, numerical values of parameters in various existing approximations are changed (optimized) using genetic algorithms to reduce maximal relative error. After this improvement computational burden stays unchanged while accuracy of approximations increases in some of the cases very significantly.

An analytical thermal model for three-dimensional integrated circuits with integrated micro-channel cooling

An analytical thermal model is developed for N-die stacked chips with integrated micro-channels cooling. The model is implemented with some mathematical software. Comparison of the temperature predicted by the proposed model with some computer fluid dynamics software numerical results show excellent agreement, and the maximal relative error is less than 4.0%.

Analysis of a quasi-three-point bending test for fabrics with friction and extensibility effect

This paper presents a theoretical bending model to investigate the quasi-three-point bending step of the comprehensive handle evaluation system for fabrics and yarns (CHES-FY). The effect of the friction and extensibility of fabrics on the bending step of the CHES-FY is discussed based on the theoretical bending model in three cases, and bending parameters, including maximum bending force, linear fitting slope and bending work, are featured from the bending force–displacement curves of each case. Comparisons of the theoretical and experimental results were also conducted to validate the model. The results revealed that the friction effect tended to enhance the bending parameters of the bending force–displacement curve of the bending step, and the effect of the friction could be remarkable at low bending rigidity of samples. However, the effect of the extensibility of samples was almost negligible for the bending test of wear fabrics, as the maximal relative error was less than 11.7% for fabrics where the tensile elastic constant was higher than 0.1 N/cm·%. This work can also provide a theoretical guidance for improving the measurement accuracy of the three-point bending test.