Improvements to Common Data Reduction and Calibration Methods for Seven Hole Probes

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
James Crawford ◽  
A. Michael Birk
Keyword(s):  
Calibration Data ◽  
Curve Fit ◽  
Polynomial Curve ◽  
Calibration Methods ◽  
Polynomial Extrapolation ◽  
Order Polynomial ◽  
Physical Response ◽  
Probe Response ◽  
Fourth Order Polynomial ◽  
Data Sorting

The influence of calibration data sorting procedures and the order of polynomial curve fit used to calibrate seven hole pressure probes in subsonic, incompressible flow are discussed. It is shown that the inclusion of fourth order polynomial terms is necessary to properly model the physical response of the probe. It is also shown that the uniformity of probe response error is significantly affected by polynomial extrapolation near sector boundaries, and that the uniformity can be improved by using some calibration points in multiple sectors.

Improvements to Common Data Reduction and Calibration Methods for Seven Hole Probes

2012 ◽  
Author(s):  
James Crawford ◽  
A. M. Birk
Keyword(s):  
Calibration Data ◽  
Curve Fit ◽  
Polynomial Curve ◽  
Calibration Methods ◽  
Polynomial Extrapolation ◽  
Order Polynomial ◽  
Physical Response ◽  
Probe Response ◽  
Fourth Order Polynomial ◽  
Data Sorting

The influence of calibration data sorting procedures and the order of polynomial curve fit used to calibrate seven hole pressure probes in subsonic, incompressible flow are discussed. It is shown that the inclusion of fourth order polynomial terms is necessary to properly model the physical response of the probe. It is also shown that the uniformity of probe response error is be significantly affected by polynomial extrapolation near sector boundaries, and that the uniformity can be improved by using some calibration points in multiple sectors.

Manufacturing Process for Circular-Arc Curvilinear Cylindrical Gears with Predesigned Fourth Order Transmission Error

2010 ◽  
Vol 37-38 ◽  
pp. 623-627 ◽  
Author(s):  
Jin Zhan Su ◽  
Zong De Fang
Keyword(s):  
Fourth Order ◽  
Gear Tooth ◽  
Transmission Error ◽  
Circular Arc ◽  
Cylindrical Gears ◽  
Polynomial Curve ◽  
Order Polynomial ◽  
Tooth Surfaces ◽  
The Stability ◽  
Fourth Order Polynomial

A fourth order transmission error was employed to improve the stability and tooth strength of circular-arc curvilinear cylindrical gears. The coefficient of fourth order polynomial curve was determined, the imaginary rack cutter which formed by the rotation of a head cutter and the imaginary pinion were introduced to determine the pinion and gear tooth surfaces, respectively. The numerical simulation of meshing shows: 1) the fourth order transmission error can be achieved by the proposed method; 2) the stability transmission can be performed by increasing the angle of the transfer point of the cycle of meshing; 3) the tooth fillet strength can be enhanced.

scholarly journals Statistically Generated Weighted Curve Fit of Residual Functions for Modal Analysis of Structures

1997 ◽  
Vol 4 (4) ◽  
pp. 211-222
Author(s):  
Paul Stanley Bookout
Keyword(s):  
Weighting Function ◽  
Second Order ◽  
Test Method ◽  
Mode Shapes ◽  
Modal Parameter ◽  
Residual Function ◽  
Curve Fit ◽  
Polynomial Curve ◽  
Residual Functions ◽  
Order Polynomial

A statistically generated weighting function for a second-order polynomial curve fit of residual functions has been developed. The residual flexibility test method, from which a residual function is generated, is a procedure to modal test large structures in a free-free environment to measure the effects of higher order modes and stiffness at distinct degree of freedom interfaces. Due to the present damping estimate limitations in the modal parameter evaluation (natural frequencies and mode shapes) of test data, the residual function has regions of irregular data, which should be a smooth curve in a second-order polynomial form. A weighting function of the data is generated by examining the variances between neighboring data points. From a weighted second-order polynomial curve fit, an accurate residual flexibility value can be obtained. The residual flexibility value and free-free modes from testing are used to improve a mathematical model of the structure, which is used to predict constrained mode shapes.

Development of a new combined heat source model for welding based on a polynomial curve fit of the experimental fusion line

2016 ◽  
Vol 87 (5-8) ◽  
pp. 1985-1997 ◽  
Author(s):  
Junqiang Wang ◽  
Jianmin Han ◽  
Joseph P. Domblesky ◽  
Zhiyong Yang ◽  
Yingxin Zhao ◽  
...  
Keyword(s):  
Heat Source ◽  
Source Model ◽  
Fusion Line ◽  
Heat Source Model ◽  
Curve Fit ◽  
Polynomial Curve ◽  
Experimental Fusion

Evaluation of Measurement Uncertainties for Pneumatic Multi-Hole Probes Using a Monte Carlo Method

2016 ◽  
Author(s):  
Magnus Hölle ◽  
Christian Bartsch ◽  
Peter Jeschke
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Compressible Flows ◽  
Uncertainty Evaluation ◽  
Calibration Data ◽  
Input Quantity ◽  
Parameter Evaluation ◽  
Polynomial Curve ◽  
Different Types ◽  
Measurement Uncertainties

The subject of this paper is a statistical method for the accurate evaluation of the uncertainties for pneumatic multi-hole probe measurements. The method can be applied to different types of evaluation algorithms and is suitable for steady flowfield measurements in compressible flows. The evaluation of uncertainties is performed by a Monte Carlo method (MCM), which is based on the statistical law of large numbers. Each input quantity, including calibration and measurement quantities, is randomly varied on the basis of its corresponding probability density function (PDF) and propagated through the deterministic parameter evaluation algorithm. Other than linear Taylor series based uncertainty evaluation methods, MCM features several advantages. On the one hand, MCM does not suffer from lower-order expansion errors and can therefore reproduce nonlinearity effects. On the other hand, different types of PDFs can be assumed for the input quantities and the corresponding coverage intervals can be calculated for any coverage probability. To demonstrate the uncertainty evaluation, a calibration and subsequent measurements in the wake of an airfoil with a 5-hole probe are performed. MCM is applied to different parameter evaluation algorithms. It is found that the MCM approach presented cannot be applied to polynomial curve fits, if the differences between the calibration data and the polynomial curve fits are of the same order of magnitude compared to the calibration uncertainty. Since this method has not yet been used for the evaluation of measurement uncertainties for pneumatic multi-hole probes, the aim of the paper is to present a highly accurate and easy-to-implement uncertainty evaluation method.

Explicit solutions to nonlinear Chen–Lee–Liu equation

2021 ◽  
pp. 2150438
Author(s):  
Lanre Akinyemi ◽  
Najib Ullah ◽  
Yasir Akbar ◽  
Mir Sajjad Hashemi ◽  
Arzu Akbulut ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Nonlinear Phenomena ◽  
Explicit Solutions ◽  
Mathematical Algorithm ◽  
New Exact Solutions ◽  
Order Polynomial ◽  
Fourth Order Polynomial

In this work, a generalized [Formula: see text]-expansion method has been used for solving the nonlinear Chen–Lee–Liu equation. This method is a more common, general, and powerful mathematical algorithm for finding the exact solutions of nonlinear partial differential equations (NPDEs), where [Formula: see text] follows the Jacobi elliptic equation [Formula: see text], and we let [Formula: see text] be a fourth-order polynomial. Many new exact solutions such as the hyperbolic, rational, and trigonometric solutions with different parameters in terms of the Jacobi elliptic functions are obtained. The distinct solutions obtained in this paper clearly explain the importance of some physical structures in the field of nonlinear phenomena. Also, this method deals very well with higher-order nonlinear equations in the field of science. The numerical results described in the plots were obtained by using Maple.

scholarly journals An Improved Analysis for the Harmonic Distortion of MOS Voltage-Controlled-Resistors

1997 ◽  
Vol 19 (4) ◽  
pp. 253-260
Author(s):  
Muhammad Taher Abuelma'atti
Keyword(s):  
Fourth Order ◽  
Harmonic Distortion ◽  
Voltage Characteristic ◽  
Current Voltage Characteristic ◽  
Mos Transistor ◽  
Current Voltage ◽  
Order Polynomial ◽  
Polynomial Expression ◽  
Analytical Expressions ◽  
Fourth Order Polynomial

In this paper, a fourth-order polynomial expression is obtained for the nonlinear current-voltage characteristic of a MOS transistor operating in the triode region. Using this expression, closed-form expressions are obtained for the second-, third- and fourth-harmonic distortion of a MOS voltage-controlled- resistors. The analytical expressions obtained in this paper can be used for a quantitative study of the effect of different parameters of the performance of MOS voltage-controlled-resistors.

ENERGY-LIKE FUNCTIONS FOR SOME DISSIPATIVE CHAOTIC SYSTEMS

2005 ◽  
Vol 15 (08) ◽  
pp. 2507-2521 ◽  
Author(s):  
C. SARASOLA ◽  
A. D'ANJOU ◽  
F. J. TORREALDEA ◽  
A. MOUJAHID
Keyword(s):  
Phase Space ◽  
Dynamic Behavior ◽  
Fourth Order ◽  
Chaotic Systems ◽  
Quantitative Measure ◽  
Energy Functions ◽  
Dissipation Of Energy ◽  
Rossler System ◽  
Order Polynomial ◽  
Fourth Order Polynomial

Functions of the phase space variables that can considered as possible energy functions for a given family of dissipative chaotic systems are discussed. This kind of functions are interesting due to their use as an energy-like quantitative measure to characterize different aspects of dynamic behavior of associated chaotic systems. We have calculated quadratic energy-like functions for the cases of Lorenz, Chen, Lü–Chen and Chua, and show the patterns of dissipation of energy on their respective attractors. We also show that in the case of the Rössler system at least a fourth-order polynomial is required to properly represent its energy.

scholarly journals World Records in Half-Marathon Running by Sex and Age

2018 ◽  
Vol 26 (4) ◽  
pp. 629-636 ◽  
Author(s):  
Pantelis T. Nikolaidis ◽  
Stefania Di Gangi ◽  
Beat Knechtle
Keyword(s):  
Sex Difference ◽  
Marathon Running ◽  
Nonlinear Regression Analysis ◽  
Race Time ◽  
Marathon Race ◽  
The World ◽  
Order Polynomial ◽  
The Relationship ◽  
World Records ◽  
Fourth Order Polynomial

The relationship between age and elite marathon race times is well investigated, but little is known for half-marathon running. This study investigated the relationship between half-marathon race times and age in 1-year intervals by using the world single age records in half-marathon running and the sex difference in performance from 5 to 91 years in men and 5 to 93 years in women. We found a fourth-order polynomial relationship between age and race time for both women and men. Women achieve their best half-marathon race time earlier in life than men, 23.89 years compared with 28.13 years, but when using a nonlinear regression analysis, the age of the fastest race time does not differ between men and women, with 26.62 years in women and 26.80 years in men. Moreover, the sex difference in half-marathon running performance increased with advancing age.

scholarly journals A Conceptual Model for Entrainment in Cumulus Clouds

2005 ◽  
Vol 62 (7) ◽  
pp. 2602-2606 ◽  
Author(s):  
Amit Agrawal
Keyword(s):  
Streamwise Velocity ◽  
Cloud Base ◽  
Cumulus Clouds ◽  
Proposed Model ◽  
Momentum Fluxes ◽  
Order Polynomial ◽  
Long Time ◽  
The Mean ◽  
Polynomial Factor ◽  
Fourth Order Polynomial

Abstract Cumulus clouds are generally modeled as a plume, and the model works well up until the cloud base is encountered, beyond which the continuously entraining model does not appear appropriate. Although it has been known for a long time that cumulus clouds have very little lateral entrainment, the reason for it is not evident. An expression for the mean streamwise velocity profile as a Gaussian multiplied by a fourth-order polynomial factor is hereby proposed such that the mass and momentum fluxes are decoupled. This model suggests that cumulus clouds differ from other shear flows in that the former need not interact with the ambient for some downstream distance. The proposed model replicates a number of characteristics of cumulus clouds like a conserved mass flux with varying momentum flux, and may therefore be employed to describe them, in a time-averaged sense, beyond the cloud base.

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