Mixing by random stirring in confined mixtures

2008 ◽  
Vol 617 ◽  
pp. 51-86 ◽  
Author(s):  
J. DUPLAT ◽  
E. VILLERMAUX
Keyword(s):  
Scalar Field ◽  
Cross Section ◽  
Concentration Distribution ◽  
Average Concentration ◽  
Constant Cross Section ◽  
Dissipation Scale ◽  
Key Factor ◽  
Rate Of Dissipation ◽  
Concentration Space

We study the relaxation of initially segregated scalar mixtures in randomly stirred media, aiming to describe the overall concentration distribution of the mixture, its shape and rate of deformation as it evolves towards uniformity. A stirred scalar mixture can be viewed as a collection of stretched sheets, possibly interacting with each other. We consider a situation in which the interaction between the sheets is enforced by confinement and is the key factor ruling its evolution. It consists of following a mixture relaxing towards uniformity around a fixed average concentration while flowing along a constant cross-section channel. The interaction between the sheets is found to be of a random addition nature in concentration space, leading to concentration distributions that are stable by self-convolution. The resulting scalar field is naturally coarsened at a scale much larger than the dissipation scale. Consequences on the mixture entropy and scalar rate of dissipation are also examined.

Effects of openings on the seismic behavior and performance level of concrete shear walls

2019 ◽  
Author(s):  
Hossein Alimohammadi ◽  
Mostafa Dalvi Esfahani ◽  
Mohammadali Lotfollahi Yaghin
Keyword(s):  
Static Analysis ◽  
Cross Section ◽  
Seismic Behavior ◽  
Shear Walls ◽  
Shear Wall ◽  
Constant Cross Section ◽  
Added Resistance ◽  
Different Shapes ◽  
And Performance ◽  
Abaqus Software

In this study, the seismic behavior of the concrete shear wall considering the opening with different shapes and constant cross-section has been studied, and for this purpose, several shear walls are placed under the increasingly non-linear static analysis (Pushover). These case studies modeled in 3D Abaqus Software, and the results of the ductility coefficient, hardness, energy absorption, added resistance, the final shape, and the final resistance are compared to shear walls without opening.

Uniform Horizontal Groundwater Flow against Dispersion in a Shallow Aquifer: Two Analytical Models

1992 ◽  
Vol 23 (1) ◽  
pp. 1-12
Author(s):  
Ram Raj Vinda ◽  
Raja Ram Yadava ◽  
Naveen Kumar
Keyword(s):  
Point Source ◽  
Groundwater Flow ◽  
Cross Section ◽  
Analytical Solutions ◽  
Concentration Distribution ◽  
Analytical Models ◽  
Shallow Aquifer ◽  
Horizontal Cross Section ◽  
Flow Components ◽  
Reactive Pollutant

Analytical solutions converging rapidly at large and small values of times have been obtained for two mathematical models which describe the concentration distribution of a non reactive pollutant from a point source against the flow in a horizontal cross-section of a finite saturated shallow aquifer possessing uniform horizontal groundwater flow. Zero concentration or the conditions in which the flux across the extreme boundaries are proportional to the respective flow components are applied. The effects of flow and dispersion on concentration distribution are also discussed.

scholarly journals Box Experiment Study of Thermally Enhanced SVE for Benzene

2021 ◽  
Vol 18 (8) ◽  
pp. 4062
Author(s):  
Qixiang Zhang ◽  
Qiyan Feng ◽  
Xueqiang Zhu ◽  
Mei Zhang ◽  
Yanjun Wang ◽  
...  
Keyword(s):  
Temperature Distribution ◽  
Concentration Distribution ◽  
Average Concentration ◽  
Soil Gas ◽  
Vapor Extraction ◽  
Operation Process ◽  
Repair Efficiency ◽  
Benzene Concentration ◽  
Benzene Content ◽  
Peak Value

In order to describe the changes of soil temperature field, air flow field and remediation situation with time during the process of thermally enhanced SVE (soil vapor extraction), a remediation experiment of benzene contaminated soil with single extraction pipe was carried out in a box device. The results showed that the whole temperature of the system was raised to 80 °C in 4 h. 43% of benzene were removed in the first 2% of the extraction time. After 24 h, the repair efficiency was close to 100%. The device can efficiently remove benzene from soil. By continuously monitoring the parameters in the operation process of the system, the spatial distribution of temperature and soil gas pollutant concentration with time was plotted. It showed the benzene concentration distribution in the soil gas was more consistent with the temperature distribution before the start of ventilation, and the concentration of benzene in the soil gas dropped rapidly after ventilation, while the temperature distribution was almost unaffected. In the treatment of soil with a benzene content of 17.8 mg∙kg−1, when the soil gas benzene concentration is the highest at 180 min, the peak value is 11,200 mg∙m−3, and the average concentration is 7629.4 mg∙m−3.

Condensation in a Variable Acceleration Field and the Condensing Thermosyphon

1965 ◽  
Vol 87 (4) ◽  
pp. 355-360 ◽  
Author(s):  
J. C. Chato
Keyword(s):  
Heat Transfer ◽  
Cross Section ◽  
Radial Distance ◽  
Constant Cross Section ◽  
Linear Variation ◽  
Temperature Differential ◽  
Acceleration Field ◽  
Nusselt Numbers ◽  
Increasing Temperature ◽  
Limiting Values

The general problem of condensation in a variable acceleration field was investigated analytically. The case of the linear variation, which occurs in a constant cross section, rotating thermosyphon, was treated in detail. The results show that the condensate thickness and Nusselt numbers approach limiting values as the radial distance increases. The effects of the temperature differential and the Prandtl number are similar to those in other condensation problems; i.e., the heat transfer increases slightly with increasing temperature differential if Pr > 1, but it decreases with increasing temperature differential if Pr ≪ 1.

scholarly journals Small-Scale Spectrum of a Scalar Field in Water: The Batchelor and Kraichnan Models

2011 ◽  
Vol 41 (11) ◽  
pp. 2155-2167 ◽  
Author(s):  
Xavier Sanchez ◽  
Elena Roget ◽  
Jesus Planella ◽  
Francesc Forcat
Keyword(s):  
Scalar Field ◽  
Thermal Gradient ◽  
Theoretical Models ◽  
Measured Data ◽  
Small Scale ◽  
Temperature Profiles ◽  
One Dimensional ◽  
Kraichnan Model ◽  
The One ◽  
Rate Of Dissipation

Abstract The theoretical models of Batchelor and Kraichnan, which account for the smallest scales of a scalar field passively advected by a turbulent fluid (Prandtl > 1), have been validated using shear and temperature profiles measured with a microstructure profiler in a lake. The value of the rate of dissipation of turbulent kinetic energy ɛ has been computed by fitting the shear spectra to the Panchev and Kesich theoretical model and the one-dimensional spectra of the temperature gradient, once ɛ is known, to the Batchelor and Kraichnan models and from it determining the value of the turbulent parameter q. The goodness of the fit between the spectra corresponding to these models and the measured data shows a very clear dependence on the degree of isotropy, which is estimated by the Cox number. The Kraichnan model adjusts better to the measured data than the Batchelor model, and the values of the turbulent parameter that better fit the experimental data are qB = 4.4 ± 0.8 and qK = 7.9 ± 2.5 for Batchelor and Kraichnan, respectively, when Cox ≥ 50. Once the turbulent parameter is fixed, a comparison of the value of ɛ determined from fitting the thermal gradient spectra to the value obtained after fitting the shear spectra shows that the Kraichnan model gives a very good estimate of the dissipation, which the Batchelor model underestimates.

Turbulent buoyant convection from a source in a confined region

1969 ◽  
Vol 37 (1) ◽  
pp. 51-80 ◽  
Author(s):  
W. D. Baines ◽  
J. S. Turner
Keyword(s):  
Point Source ◽  
Cross Section ◽  
Laboratory Experiments ◽  
Region Of Interest ◽  
Constant Cross Section ◽  
General Shape ◽  
Turbulent Environment ◽  
Starting Conditions ◽  
Upward Velocity ◽  
Local Mean

This paper considers the effect of continuous convection from small sources of buoyancy on the properties of the environment when the region of interest is bounded. The main assumptions are that the entrainment into the turbulent buoyant region is at a rate proportional to the local mean upward velocity, and that the buoyant elements spread out at the top of the region and become part of the non-turbulent environment at that level. Asymptotic solutions, valid at large times, are obtained for the cases of plumes from point and line sources and also periodically released thermals. These all have the properties that the environment is stably stratified, with the density profile fixed in shape, changing at a uniform rate in time at all levels, and everywhere descending (with ascending buoyant elements).The analysis is carried out in detail for the point source in an environment of constant cross-section. Laboratory experiments have been conducted for this case, and these verify the major predictions of the theory. It is then shown how the method can be extended to include more realistic starting conditions for the convection, and a general shape of bounded environment. Finally, the model is applied quantitatively to a variety of problems in engineering, the atmosphere and the ocean, and the limitations on its use are discussed.

Migration of Anionic Species of Radioactive Cobalt through Soil

1989 ◽  
Vol 176 ◽  
Author(s):  
Toshihiko Ohnuki ◽  
David E. Robertson
Keyword(s):  
Concentration Distribution ◽  
Correlation Coefficients ◽  
Ionic Species ◽  
Average Concentration ◽  
Disposal Site ◽  
Retardation Factor ◽  
Laboratory Measurements ◽  
Waste Disposal Site ◽  
Anionic Species ◽  
Cross Correlations

ABSTRACTThe migration of an anionic species of 60Co through soil has been examined utilizing data on the migration of radionuclides leached from an aqueous waste disposal site. Correlation coefficients between concentrations of the anionic species of 60Co and those of the particulate, cationic and non-ionic species of 60Co reveal that the anionic species of 60Co was not interconverted from the other species during migration. The cross correlations of changes in the concentrations of the anionic species of 60Co with time between three different down gradient positions give a calculated retardation factor of the anionic species of 60Co of approximately 19, being 1200 times lower than the results of laboratory measurements. The average concentration distribution of the anionic species of 60Co suggests that the migration of the anionic species of 60Co consists of two migration fractions which were driven by different migration mechanisms.

Deflection of Beams of Varying Cross Section

1937 ◽  
Vol 4 (2) ◽  
pp. A49-A52
Author(s):  
Miklós Hetényi
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Original Problem ◽  
New Method ◽  
Constant Cross Section ◽  
Deflection Curve ◽  
Force System ◽  
Uniform Cross Section ◽  
The Cross

Abstract This paper calls attention to a new method of dealing with deflections of beams, the cross sections of which vary by steps. It is shown that the effect of this variation on the shape of the deflection curve can be represented by a properly chosen force system acting on a beam of uniform cross section. There is no approximation involved in this substitution, whereby the original problem is reduced to one of computing deflections of beams of constant cross section.

Nozzles for Supersonic Flow Without Shock Fronts

1944 ◽  
Vol 11 (2) ◽  
pp. A93-A100
Author(s):  
Ascher H. Shapiro
Keyword(s):  
Cross Section ◽  
Compressible Fluids ◽  
Three Dimensions ◽  
Infinite Length ◽  
Constant Cross Section ◽  
Nozzle Design ◽  
Wave Fronts ◽  
A Value ◽  
Parallel Stream ◽  
Shock Fronts

Abstract Flow patterns for compressible fluids at supersonic velocities are discussed, and it is shown that shock fronts form when neighboring Mach lines (envelopes of wave fronts originating from point disturbances) intersect. A criterion for divergence of Mach lines is developed for cases in which the passage is symmetrical in two or three dimensions and has a straight axis. This criterion is used as the basis for designing supersonic nozzles and diffusers. The analysis indicates that only a nozzle of infinite length can discharge a parallel stream into a tube of constant cross section without the formation of shock fronts. Methods are presented for designing nozzles of finite length, with the intensity of shock fronts reduced to as small a value as possible, and it is shown that nozzles of reasonable length may be designed so that shock fronts are insignificant. Experimental observations indicate that the proposed method of nozzle design is a practical one. With regard to supersonic diffusers having a straight axis, it is shown that shock fronts cannot be avoided, even though the diffuser is of infinite length. However, the methods of this paper may be used as an aid in determining the best diffuser design.

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