A statistical model of turbulence in two-dimensional mixing layers

1979 ◽  
Vol 92 (2) ◽  
pp. 303-326 ◽  
Author(s):  
Christopher K. W. Tam ◽  
K. C. Chen
Keyword(s):  
Statistical Model ◽  
Root Mean Square ◽  
Flow Direction ◽  
Single Point ◽  
Mixing Layer ◽  
Normal Wave ◽  
Quasi Equilibrium ◽  
Mean Square ◽  
Two Dimensional ◽  
Large Structures

A statistical model based on the proposition that the turbulence of a fully developed two-dimensional incompressible mixing layer is in a state of quasi-equilibrium is developed. In this model the large structures observed by Brown & Roshko (1974) which will be assumed to persist into the fully developed turbulent region are represented by a superposition of the normal wave modes of the flow with arbitrary random amplitudes. The turbulence at a point in the flow is assumed to be dominated by the fluctuations associated with these large structures. These structures grow and amalgamate as they are convected in the flow direction. Because of the lack of intrinsic length and time scales the turbulence in question can, therefore, be regarded as created or initiated at an upstream point, the virtual origin of the mixing layer, by turbulence with a white noise spectrum and are subsequently convected downstream. The model is used to predict the second-order turbulence statistics of the flow including single point turbulent Reynolds stress distribution, intensity of turbulent velocity components, root-mean-square turbulent pressure fluctuations, power spectra and two-point space-time correlation functions. Numerical results based on the proposed model compare favourably with available experimental measurements. Predictions of physical quantities not yet measured by experiments, e.g. the root-mean-square pressure distribution across the mixing layer, are also made. This permits the present model to be further tested experimentally.

The Generating Mechanism of Surface Roughness by Random Cutting Edges

1978 ◽  
Vol 20 (4) ◽  
pp. 197-200
Author(s):  
M. Hasegawa ◽  
T. Tsukizoe
Keyword(s):  
Surface Roughness ◽  
Root Mean Square ◽  
Statistical Approach ◽  
Ground Surface ◽  
Root Mean Square Roughness ◽  
Mean Square ◽  
Two Dimensional ◽  
Dimensional Distribution

This paper describes a statistical approach for predicting the generating mechanism of the surface roughness produced by random cutting edges. The two-dimensional distribution of the generated surface roughness is derived by considering the distribution of the maxima of the cutting edges. The method is used to determine the root-mean-square roughness of the ground surface.

scholarly journals The Solution of the Inverse Problem of Identifying the Thermal Conductivity Tensor in Anisotropic Materials

2021 ◽  
Vol 24 (3) ◽  
pp. 6-13
Author(s):  
Yurii M. Matsevytyi ◽  
◽  
Valerii V. Hanchyn ◽  
Keyword(s):  
Thermal Conductivity ◽  
Root Mean Square ◽  
Iterative Process ◽  
Regularization Parameter ◽  
Orientation Angle ◽  
Conductivity Tensor ◽  
Mean Square ◽  
Two Dimensional ◽  
Thermal Conductivity Tensor ◽  
Principal Axes

On the basis of A. N. Tikhonov's regularization theory, a technique has been developed for solving inverse heat conduction problems of identifying the thermal conductivity tensor in a two-dimensional domain. Such problems are replaced by problems of identifying the principal heat conductivity coefficients and the orientation angle of the principal axes, with the principal coefficients being approximated by Schoenberg’s cubic splines. As a result, the problem is reduced to determining the unknown coefficients in these approximations and the orientation angle of the principal axes. With known boundary and initial conditions, the temperature in the domain will depend only on these coefficients and the orientation angle. If one expresses it by the Taylor formula for two terms of series and substitutes it into the Tikhonov functional, then the determination of the increments of the coefficients and the increment of the orientation angle can be reduced to solving a system of linear equations with respect to these increments. By choosing a certain regularization parameter as well as some functions for the principal thermal conductivity coefficients and the orientation angle as an initial approximation, one can implement an iterative process for determining these coefficients. After obtaining the vectors of the coefficients and the angle of orientation as a result of the converging iterative process, it is possible to determine the root-mean-square discrepancy between the temperature obtained and the temperature measured as a result of the experiment. It remains to choose the regularization parameter in such a way that this discrepancy is within the root-mean-square discrepancy of the measurement error. When checking the efficiency of using the proposed method, a number of two-dimensional test problems for bodies with known thermal conductivity tensors were solved. The influence of random measurement errors on the error in the identification of the thermal conductivity tensor was analyzed.

scholarly journals Light-based methods for predicting circadian phase in delayed sleep–wake phase disorder

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Jade M. Murray ◽  
Michelle Magee ◽  
Tracey L. Sletten ◽  
Christopher Gordon ◽  
Nicole Lovato ◽  
...  
Keyword(s):  
Root Mean Square Error ◽  
Statistical Model ◽  
Dynamic Model ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Light Exposure ◽  
Mean Square ◽  
Healthy Individuals ◽  
Circadian Phase ◽  
Delayed Sleep

AbstractMethods for predicting circadian phase have been developed for healthy individuals. It is unknown whether these methods generalize to clinical populations, such as delayed sleep–wake phase disorder (DSWPD), where circadian timing is associated with functional outcomes. This study evaluated two methods for predicting dim light melatonin onset (DLMO) in 154 DSWPD patients using ~ 7 days of sleep–wake and light data: a dynamic model and a statistical model. The dynamic model has been validated in healthy individuals under both laboratory and field conditions. The statistical model was developed for this dataset and used a multiple linear regression of light exposure during phase delay/advance portions of the phase response curve, as well as sleep timing and demographic variables. Both models performed comparably well in predicting DLMO. The dynamic model predicted DLMO with root mean square error of 68 min, with predictions accurate to within ± 1 h in 58% of participants and ± 2 h in 95%. The statistical model predicted DLMO with root mean square error of 57 min, with predictions accurate to within ± 1 h in 75% of participants and ± 2 h in 96%. We conclude that circadian phase prediction from light data is a viable technique for improving screening, diagnosis, and treatment of DSWPD.

scholarly journals Parametric Mid-Spatial Frequency Surface Error Synthesis

Photonics ◽  
2021 ◽  
Vol 8 (12) ◽  
pp. 584
Author(s):  
Timothy Hefferan ◽  
Logan Graves ◽  
Isaac Trumper ◽  
Soojong Pak ◽  
Daewook Kim
Keyword(s):  
Spatial Frequency ◽  
Root Mean Square ◽  
Rotation Angle ◽  
Single Point ◽  
Incident Beam ◽  
Surface Irregularity ◽  
Mean Square ◽  
Optical Surface ◽  
Surface Error ◽  
Characteristic Features

Standard mid-spatial frequency tooling mark errors were parameterized into a series of characteristic features and systematically investigated. Diffraction encircled and ensquared energy radii at the 90% levels from an unpowered optical surface were determined as a function of the root-mean-square surface irregularity, characteristic tooling mark parameters, fold mirror rotation angle, and incident beam f-number. Tooling mark frequencies on the order of 20 cycles per aperture or less were considered. This subset encompasses small footprints on single-point diamond turned optics or large footprints on sub-aperture tool polished optics. Of the characteristic features, off-axis fabrication distance held the highest impact to encircled and ensquared energy radii. The transverse oscillation of a tooling path was found to be the second highest contributor. Both impacts increased with radial tooling mark frequency.

scholarly journals Numerical Simulation of Unsaturated Soil Water Flow from a Trickle Point System, Considering Evaporation and Root Water Uptake

2018 ◽  
Vol 14 (4) ◽  
pp. 103-114
Author(s):  
Lina Ali Khalil ◽  
Maysoon Basheer Abid
Keyword(s):  
Soil Moisture ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Water Flow ◽  
Single Point ◽  
Maximum Error ◽  
Soil Types ◽  
Point System ◽  
Mean Square

This research was carried out to study the effect of plants on the wetted area for two soil types in Iraq and predict an equation to determine the wetted radius and depth for two different soil types cultivated with different types of plants, the wetting patterns for the soils were predicted at every thirty minute for a total irrigation time equal to 3 hr. Five defferent discharges of emitter and five initial volumetric soil moisture contents were used ranged between field capacity and wilting point were utilized to simulate the wetting patterns. The simulation of the water flow from a single point emitter was completed by utilized HYDRUS-2D/3D software, version 2.05. Two methods were used in developing equations to predict the domains of the wetting pattern. The principal strategy manages each soil independently and includes plotting, fitting, and communicating relevant connections for wetted zone and profundity, maximum error did not exceed 31.2%, modeling efficiency did not less 0.95, and root mean square error did not surpass 1.43 cm. The second strategy additionally treated each soil independently yet used electronic programming that uses different relapse methods for wetted territory and profundity, the maximum error did not exceed 15.64 %, modeling efficiency did not less 0.98, and root mean square error did not surpass 1.18 cm. a field test was directed to quantify the wetted radius to check the outcome acquired by the software HYDRUS-2D, contrast the estimation and the reproduced by the software. The after effects of the conditions to express the wetted radius and depth regarding the time of water system, producer release, and initial soil moisture content were general and can be utilized with great precision.

Do large structures control their own growth in a mixing layer? An assessment

1988 ◽  
Vol 190 ◽  
pp. 427-450 ◽  
Author(s):  
Upender K. Kaul
Keyword(s):  
Mixing Layer ◽  
Tangential Velocity ◽  
Shear Layers ◽  
Two Dimensional ◽  
Galilean Transformation ◽  
Vorticity Field ◽  
Tangential Contact ◽  
Large Structures ◽  
Free Shear Layers ◽  
Specific Comparison

This study makes a specific comparison between two different two-dimensional free shear layers: the T-layer which develops in time from an initial tangential velocity discontinuity separating the two half-spaces; and the S-layer which develops downstream of the origin where two uniform streams of unequal velocity are brought into tangential contact. The method of comparison is to assume that the vorticity of the S-layer is given parabolically by a Galilean mapping of that of the T-layer; to satisfy the appropriate boundary conditions in the S-layer and to compute the velocity induced at any point in the S-layer by its vorticity field; and to compare this velocity to that which can be derived from the velocity of the T-layer at corresponding points by a Galilean transformation of the velocity itself. The purpose of this calculation is to assess approximately how far the flow in the S-layer is from parabolic and, in particular, to what extent the perturbations induced upstream by large concentrations of vorticity found downstream are instrumental in hastening or retarding the subharmonic instability that leads to the formation of these large structures. The calculations suggest that this elliptic influence, or the feedback, in a mixing layer is relatively small, at least for small velocity ratios.

scholarly journals Two-dimensional spreading properties and sealing characteristics of fluorocarbon surfactants on several typical hydrocarbon fuels

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Xuhong Jia ◽  
Yuzhen Luo ◽  
Rui Huang ◽  
Xinhua Zhu ◽  
Yuqiang Zhang ◽  
...  
Keyword(s):  
Surface Tension ◽  
Root Mean Square ◽  
Root Mean Square Deviation ◽  
Surfactant Solution ◽  
Mean Square ◽  
Mean Square Deviation ◽  
Two Dimensional ◽  
Volume Percentage ◽  
First Time ◽  
Good Agreement

AbstractA new method for studying the two-dimensional spreading properties and sealing characteristics of surfactant solution on oil surface was provided. The actual spreading situation of the C4-Br/oil systems in axisymmetric geometry was observed directly using HD camera for the first time and the results showed that the aqueous film expanded outwards in a circle with the guiding device as the center. Meanwhile, the relation between spreading radius and time was investigated and evaluated using the model for surface-tension-viscous regime. The root-mean-square deviation (RMSD) values obtained from the correlation for all of the systems we studied below 1.64, indicating a good agreement between the experimental and theoretical values. The results of sealing experiments showed that the aqueous film could absolutely seal the oil surface for 27–65 s and the sealing effect would be lost after 216–742 s for different systems. The stronger the volatility was, the shorter the sealing time was. Additionally, the volume percentage of oil vapor with film was always lower than that without film even when the evaporation was saturated. These findings were of great significance to guide the preparation of efficient AFFF.

scholarly journals Analytical design of refractive optical elements generating a prescribed two-dimensional intensity distribution

2020 ◽  
Vol 44 (6) ◽  
pp. 883-892
Author(s):  
E.V. Byzov ◽  
L.L. Doskolovich ◽  
S.V. Kravchenko
Keyword(s):  
Differential Equations ◽  
Root Mean Square ◽  
Intensity Distribution ◽  
High Performance ◽  
Optical Element ◽  
Mean Square ◽  
Two Dimensional ◽  
Optical Elements ◽  
Analytical Design ◽  
Simulation Results

A new source-target mapping for the design of refractive optical elements generating prescribed 2D intensity distributions is proposed. The calculation of the optical element is reduced to the solution of ordinary explicit differential equations. The simulation results presented demonstrate high performance of the proposed method. While generating uniform rectangular intensity distributions with angular dimensions varying from 80°×1° to 40°×20°, the normalized root-mean-square deviations between the generated and required distributions do not exceed 15 %.

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