The vorticity versus the scalar criterion for the detection of the turbulent/non-turbulent interface

2014 ◽  
Vol 750 ◽  
pp. 578-596 ◽  
Author(s):  
Markus Gampert ◽  
Jonas Boschung ◽  
Fabian Hennig ◽  
Michael Gauding ◽  
Norbert Peters
Keyword(s):  
Mixing Layer ◽  
Detailed Comparison ◽  
Passive Scalar ◽  
Normal Vector ◽  
Interface Position ◽  
Conditional Mean ◽  
Vortex Lines ◽  
The Mean ◽  
Conditional Statistics ◽  
Good Agreement

AbstractBased on a direct numerical simulation (DNS) of a temporally evolving mixing layer, we present a detailed study of the turbulent/non-turbulent (T/NT) interface that is defined using the two most common procedures in the literature, namely either a vorticity or a scalar criterion. The different detection approaches are examined qualitatively and quantitatively in terms of the interface position, conditional statistics and orientation of streamlines and vortex lines at the interface. Computing the probability density function (p.d.f.) of the mean location of the T/NT interface from vorticity and scalar allows a detailed comparison of the two methods, where we observe a very good agreement. Furthermore, conditional mean profiles of various quantities are evaluated. In particular, the position p.d.f.s for both criteria coincide and are found to follow a Gaussian distribution. The terms of the governing equations for vorticity and passive scalar are conditioned on the distance to the interface and analysed. At the interface, vortex stretching is negligible and the displacement of the vorticity interface is found to be determined by diffusion, analogous to the scalar interface. In addition, the orientation of vortex lines at the vorticity and the scalar based T/NT interface are analyzed. For both interfaces, vorticity lines are perpendicular to the normal vector of the interface, i.e. parallel to the interface isosurface.

Conditional Statistics for Passive-Scalar Mixing in Confined Turbulent Shear Flows

2006 ◽  
Author(s):  
Hua Feng ◽  
Michael G. Olsen ◽  
Rodney O. Fox ◽  
James C. Hill
Keyword(s):  
Linear Model ◽  
Mixture Fraction ◽  
Passive Scalar ◽  
Turbulent Shear ◽  
Mean Velocity ◽  
Conditional Mean ◽  
Image Velocimetry ◽  
Planar Laser ◽  
Conditional Statistics ◽  
Pdf Model

A combined particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) system was employed to investigate turbulent mixing in a confined rectangular jet. The Reynolds number based on bulk velocity and hydraulic diameter was 50,000. The Schmidt number for the passive scalar was 1,250. Velocities conditioned on the scalar were evaluated. Since the joint PDF was not jointly Gaussian in this flow, the conditional mean velocity agreed with a linear model only when the mixture fraction is close to the local mean mixture fraction. A gradient PDF model for the conditional velocity was also tested against the experimental data. The model predicted the crossstream conditional velocity very well, but gave poor predictions for the streamwise conditional velocity. Finally, the scalar fluctuations conditioned on velocity were presented and analyzed against a linear model.

The turbulent mixing layer with an asymmetrical distribution of temperature

1978 ◽  
Vol 89 (3) ◽  
pp. 561-587 ◽  
Author(s):  
Claude Béguier ◽  
Louis Fulachier ◽  
James F. Keffer
Keyword(s):  
Mixing Layer ◽  
Low Frequency ◽  
Passive Scalar ◽  
Frequency Component ◽  
Temperature Fields ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Turbulent Mixing Layer ◽  
The Mean ◽  
Large Eddies

An experimental programme has been carried out to examine the spread of heat as a passive scalar contaminant in a turbulent shear flow. The situation involves a slightly heated two-dimensional jet expanding into a quiescent medium on one side and a uniform stream with velocity equal to that of the warm jet on the other. Thus the developed flow is a typical mixing layer with an asymmetric mean temperature profile superimposed on it. Measurements of the mean and fluctuating velocity and temperature fields show the existence of a region where the production of temperature fluctuations is negative. Spectral analysis in this zone indicates a separation of large and small wavenumber components of the cospectrum into two regimes. The sign of the high-frequency portion is consistent with gradient-transport concepts while the low-frequency component is of opposite sign. From this it is inferred that the large eddies are mainly responsible for the negative production. A mathematical model has been developed to describe the transport within this region.

Computational Investigation of Different Turbulent Models When Predicting Airflow in an Enclosure

2008 ◽  
Author(s):  
Xi Wang ◽  
Hassan Naji ◽  
Ahmed Mezrhab
Keyword(s):  
Numerical Investigation ◽  
Turbulence Models ◽  
Turbulent Stress ◽  
Computational Investigation ◽  
Isothermal Case ◽  
The Mean ◽  
Turbulent Models ◽  
Rsm Model ◽  
Cold Case ◽  
Good Agreement

In the present study, a numerical investigation is carried out for an isothermal case, a hot case and a cold case with FLUENT code. Three turbulence models are considered: the k-ε realisable model, the RNG k-ε model and the RSM linear model. The obtained results are compared to experiments and show generally a good agreement for the mean velocities and temperatures, but less satisfactory for the turbulent stress. The performance of the RSM model is remarkable. Even if none of the models is able to give the exact experimental pattern on the map of turbulence, the RSM model seems able to predict such configuration.

The mixing layer over a deep cavity at high-subsonic speed

2003 ◽  
Vol 475 ◽  
pp. 101-145 ◽  
Author(s):  
NICOLAS FORESTIER ◽  
LAURENT JACQUIN ◽  
PHILIPPE GEFFROY
Keyword(s):  
High Speed ◽  
Mixing Layer ◽  
Interaction Mechanism ◽  
Boundary Layer Separation ◽  
Mixing Layers ◽  
Deep Cavity ◽  
Collective Interaction ◽  
Flow Over A Cavity ◽  
Conditional Statistics ◽  
Forced Mixing

The flow over a cavity at a Mach number 0.8 is considered. The cavity is deep with an aspect ratio (length over depth) L/D = 0.42. This deep cavity flow exhibits several features that makes it different from shallower cavities. It is subjected to very regular self-sustained oscillations with a highly two-dimensional and periodic organization of the mixing layer over the cavity. This is revealed by means of a high-speed schlieren technique. Analysis of pressure signals shows that the first tone mode is the strongest, the others being close to harmonics. This departs from shallower cavity flows where the tones are usually predicted well by the standard Rossiter’s model. A two-component laser-Doppler velocimetry system is also used to characterize the phase-averaged properties of the flow. It is shown that the formation of coherent vortices in the region close to the boundary layer separation has some resemblance to the ‘collective interaction mechanism’ introduced by Ho & Huang (1982) to describe mixing layers subjected to strong sub-harmonic forcing. Otherwise, the conditional statistics show close similarities with those found in classical forced mixing layers except for the production of random perturbations, which reaches a maximum in the structure centres, not in the hyperbolic regions with which turbulence production is usually associated. An attempt is made to relate this difference to the elliptic instability that may be observed here thanks to the particularly well-organized nature of the flow.

Respiratory Exchange and Body Size in the Aldabra Giant Tortoise

1971 ◽  
Vol 55 (3) ◽  
pp. 651-665 ◽  
Author(s):  
G. M. HUGHES ◽  
R. GAYMER ◽  
MARGARET MOORE ◽  
A. J. WOAKES
Keyword(s):  
Body Weight ◽  
Body Size ◽  
Metabolic Rate ◽  
Relative Proportion ◽  
The Body ◽  
O2 Consumption ◽  
Weight Range ◽  
Testudo Hermanni ◽  
The Mean ◽  
Good Agreement

1. The O2 consumption and CO2 release of nine giant tortoises Testudo gigantea (weight range 118 g-35·5 kg) were measured at a temperature of about 25·5°C. Four European tortoises Testudo hermanni (weight range 640 g-2·16 kg) were also used. The mean RQ values obtained were 1·01 for T. gigantea and 0·97 for T. hermanni. These values were not influenced by activity or size. 2. The data was analysed by plotting log/log regression lines relating body weight to O2 consumption. Both maximum and minimum metabolic rates recorded for each individual T. gigantea showed a negative correlation with body weight. For active rates the relation was O2 consumption = 140·8W0·97, whereas for inactive animals O2 consumption = 45·47W0·82. 3. The maximum rates were obtained from animals that were observed to be active in the respirometer and the minimum rates from animals that remained quiet throughout. The scope for activity increased with body size, being 82 ml/kg/h for animals of 100 g and 103 ml/kg/h for 100 kg animals. The corresponding ratio between maximum and minimum rates increases from about 2 to 6 for the same weight range. 4. Values for metabolic rate in T. hermanni seem to be rather lower than in T. gigantea. Analysis of the relative proportion of the shell and other organs indicates that the shell forms about 31% of the body weight in adult T. hermanni but only about 18% in T. gigantea of similar size. The shell is not appreciably heavier in adult T. gigantea (about 20%). 5. Data obtained for inactive animals is in good agreement with results of other workers using lizards and snakes. Previous evidence suggesting that chelonians show no reduction in metabolic rate with increasing size is not considered to conflict with data obtained in the present work.

Reaction in a scalar mixing layer

1991 ◽  
Vol 233 ◽  
pp. 211-242 ◽  
Author(s):  
R. W. Bilger ◽  
L. R. Saetran ◽  
L. V. Krishnamoorthy
Keyword(s):  
Chemical Reaction ◽  
Mixing Layer ◽  
Reacting Flow ◽  
Scalar Mixing ◽  
Scalar Theory ◽  
Thermal Mixing ◽  
Fast Chemistry ◽  
The Mean ◽  
Reactive Scalars ◽  
Made In

Reaction in a scalar mixing layer in grid-generated turbulence is studied experimentally by doping half of the flow with nitric oxide and the other half with ozone. The flow conditions and concentrations are such that the chemical reaction is passive and the flow and chemical timescales are of the same order. Conserved scalar theory for such flows is outlined and further developed; it is used as a basis for presentation of the experimental results. Continuous measurements of concentration are limited in their spatial and temporal resolution but capture sufficient of their spectra for adequate second-order correlations to be made. Two components of velocity have been measured simultaneously with hot-wire anemometry. Conserved scalar mixing results, deduced from reacting and non-reacting measurements of concentration, show the independence of concentration level and concentration ratio expected for passive reacting flow. The results are subject to several limitations due to the necessary experimental compromises, but they agree generally with measurements made in thermal mixing layers. Reactive scalar statistics are consistent with the realizability constraints obtainable from conserved scalar theory where such constraints apply, and otherwise are generally found to lie between the conserved scalar theory limits for frozen and very fast chemistry. It is suggested that Toor's (1969) closure for the mean chemical reaction rate could be improved by interpolating between the frozen and equilibrium values for the covariance. The turbulent fluxes of the reactive scalars are found to approximately obey the gradient model but the value of the diffusivity is found to depend on the Damköhler number.

Correlation between the sea level muon spectrum and the primary nucleon spectrum using the Cocconi–Koester–Perkins model

1979 ◽  
Vol 57 (7) ◽  
pp. 921-925 ◽  
Author(s):  
A. K. Chakrabarti ◽  
A. K. Das ◽  
A. K. De
Keyword(s):  
Sea Level ◽  
Pion Production ◽  
Spectral Shape ◽  
Muon Spectrum ◽  
Proton Proton ◽  
Absolute Value ◽  
Nucleon Spectrum ◽  
Scaling Models ◽  
The Mean ◽  
Good Agreement

Using the recent ISR data of proton–proton interactions on the inclusive production of pions and nucleons, realistic values of the mean pion inelasticity Kπ and the mean nucleon inelasticity KT have been estimated. These values have been used for the derivation of the sea level differential muon spectrum from the primary nucleon spectrum and vice versa using the CKP model as an extension of the work presented in an earlier article. It is found that none of the measured primary nucleon spectra of Ryan, Ormes, and Balasubrahmanyan and Grigorov, Rapoport, and Shestoperov fit any of the precisely measured muon spectra of Ayre, Baxendale, Hume, Nandi, Thompson, and Whalley and Allkofer, Carstensen, and Dau in spectral shape or the absolute value. On the other hand good agreement between the derived muon spectra and the spectra of Allkofer et al. and Ayre et al. is found if the primary nucleon spectra of the forms, N(Ep) = (1.38 ± 0.08)Ep−2.59 and N(Ep) = (1.00 ± 0.10)Ep−2.55, respectively, are assumed. The first form is comparable with that obtained by Brooke, Hayman, Kamiya, and Wolfendale following more approximate but similar procedure. It is also not unjustified when compared with the measured primary all nuclei spectrum of Grigorov et al. in the light of suggestions made by Ellsworth, Ito, Macfall, Siohan, Streitmatter, Tonwar, Vishwanath, Yodh, and Balasubrahmanyan. By comparing the pion production spectra derived from the same primary nucleon spectrum but using the CKP and the scaling models, it is concluded that the results are sensitive to the model assumed for the collisions.

Extraction Techniques and Analysis of Turbulence Quantities From In-Cylinder Velocity Data

1989 ◽  
Vol 111 (3) ◽  
pp. 466-478 ◽  
Author(s):  
A. E. Catania ◽  
A. Mittica
Keyword(s):  
Direct Injection ◽  
Detailed Comparison ◽  
Ensemble Average ◽  
Small Scale ◽  
Velocity Data ◽  
Mean Flow ◽  
Reciprocating Engine ◽  
Reduction Methods ◽  
The Mean ◽  
Correlation And Spectral Analysis

In addition to the frequently used statistical ensemble-average, non-Reynolds filtering operators have long been proposed for nonstationary turbulent quantities. Several techniques for the reduction of velocity data acquired in the cylinder of internal combustion reciprocating engines have been developed by various researchers in order to separate the “mean flow” from the “fluctuating motion,” cycle by cycle, and to analyze small-scale engine turbulence by statistical methods. Therefore a thorough examination of these techniques and a detailed comparison between them would seem to be a preliminary step in attempting a general study of unconventional averaging procedures for reciprocating engine flow application. To that end, in the present work, five different cycle-resolved data reduction methods and the conventional ensemble-average were applied to the same in-cylinder velocity data, so as to review and compare them. One of the methods was developed by the authors. The data were acquired in the cylinder of a direct-injection automotive diesel engine, during induction and compression strokes, using an advanced hot-wire anemometry technique. Correlation and spectral analysis of the engine turbulence, as determined from the data with the different procedures, were also performed.

scholarly journals In-Depth Verification of a Numerical Model for an Axisymmetric RC Dome

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2152
Author(s):  
Przemysław Czumaj ◽  
Sławomir Dudziak ◽  
Zbigniew Kacprzyk
Keyword(s):  
Three Dimensional ◽  
Spatial Models ◽  
Detailed Comparison ◽  
The Finite Element Method ◽  
Robot System ◽  
Engineering Structures ◽  
Computational Analyses ◽  
Computational Systems ◽  
Good Agreement ◽  
Made In

The designers of civil engineering structures often have to face the problem of the reliability of complex computational analyses performed most often with the Finite Element Method (FEM). Any assessment of reliability of such analyses is difficult and can only be approximate. The present paper puts forward a new method of verification and validation of the structural analyses upon an illustrative example of a dome strengthened by circumferential ribs along the upper and lower edges. Four computational systems were used, namely Abaqus, Autodesk Robot, Dlubal RFEM, and FEAS. Different models were also analyzed—two-dimensional (2D) and three-dimensional (3D) ones using continuum, bar, and shell finite elements. The results of the static (with two kinds of load—self-weight and load distributed along the upper ring) and modal analyses are presented. A detailed comparison between the systems’ and models’ predictions was made. In general, the spatial models predicted a less stiff behavior of the analyzed dome than the planar models. The good agreement between different models and systems was obtained for the first natural frequency with axisymmetric eigenmodes (except from the Autodesk Robot system). The presented approach to the verification of complex shell–bar models can be effectively applied by structural designers.

scholarly journals Universal dependence of the total number albedo of photons on the mean number of photon scatterings

2011 ◽  
Vol 26 (3) ◽  
pp. 249-253 ◽  
Author(s):  
Vladan Ljubenov ◽  
Rodoljub Simovic
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Analytic Functions ◽  
Least Squares Method ◽  
Mcnp Code ◽  
Initial Photon ◽  
Aluminum Iron ◽  
Universal Dependence ◽  
The Mean ◽  
Good Agreement

This paper presents the results of research on photon reflection from plane targets based on Monte Carlo simulations performed by the MCNP code. Five materials (water, concrete, aluminum, iron, and copper) are examined in the area of initial photon energies of up to 200 keV. The values of the total number albedo for photons dependent on the initial photon energy or the mean number of photon scatterings are calculated and graphically presented. We have shown that the values of the total number albedo for different target materials, expressed as a function of the mean number of photon scatterings, are in good agreement with each other and can be approximated by simple, universal analytic functions obtained by the least squares method. The accuracy of these analytic appoximations is confirmed by their comparison with the results of PENELOPE and FOTELP Monte Carlo codes.

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