scholarly journals An entrainment model for lazy turbulent plumes

2016 ◽  
Vol 811 ◽  
pp. 682-700 ◽  
Author(s):  
P. Carlotti ◽  
G. R. Hunt
Keyword(s):  
Experimental Data ◽  
Specific Heat ◽  
Power Law ◽  
Richardson Number ◽  
Buoyancy Flux ◽  
Underlying Assumption ◽  
Conservation Equations ◽  
New Model ◽  
Entrainment Coefficient ◽  
Definition Of

An entrainment model for lazy turbulent plumes is proposed, the resulting solutions of the plume conservation equations are developed and the implications for plume behaviour are considered and compared with the available experimental data. Indeed, the applicability of the classic solutions of the conservation equations subject to source conditions that produce lazy plumes, i.e. those with suitably high source Richardson number, contains an essential weakness: the underlying assumption of a constant entrainment coefficient. While entrainment models prescribing the dependence of the entrainment coefficient on the local Richardson number have been proposed for forced plumes, corresponding formulations for lazy plumes have not until now been considered. In the context of saline plumes, the model is applied directly. For hot gaseous plumes, we use a modified definition of buoyancy flux to recover a constant buoyancy flux in a non-stratified environment, despite the specific heat varying with the temperature. After a brief review of existing forced-plume formulations of entrainment, a power-law variation is adopted for the lazy plume. The plume equations are solved for the parameter $0\leqslant \unicode[STIX]{x1D714}<1$, where $\unicode[STIX]{x1D714}$ denotes the exponent of the power law. The cases of pure plumes and lazy plumes are then analysed in more detail; to the best of our knowledge this represents the first modelling of variable entrainment for lazy plumes. Specifically, it is shown that classic plume theory is recovered for $\unicode[STIX]{x1D714}=0$, while for $\unicode[STIX]{x1D714}=1/5$ the plume equations may be solved using usual functions (notably polynomials) only. The results of the models for these cases are very similar, which advocates the idea of selecting systematically $\unicode[STIX]{x1D714}=1/5$, instead of $\unicode[STIX]{x1D714}=0$, for cases where the effect of variation of entrainment is weak, since the new model leads to simple calculations. In the case of very lazy plumes, it is shown that, provided that a relevant value of $\unicode[STIX]{x1D714}$ is chosen, the new model reproduces the available experimental results well.

Turbulent Transport to a Rotating Cylinder for Large Prandtl or Schmidt Numbers

1975 ◽  
Vol 97 (4) ◽  
pp. 594-597 ◽  
Author(s):  
R. N. Smith ◽  
R. Greif
Keyword(s):  
Experimental Data ◽  
Mass Transport ◽  
Richardson Number ◽  
Turbulent Transport ◽  
Rotating Cylinder ◽  
Mixing Length ◽  
Centrifugal Forces ◽  
Conservation Equations ◽  
Schmidt Numbers

The heat or mass transport to a rotating cylinder is obtained by solving the conservation equations for large Prandtl or Schmidt numbers. A modified mixing length, which includes the effect of centrifugal forces in terms of the Richardson number, is used. Explicit relations are presented for the heat or mass transport and a comparison is made with the experimental data over a range of Prandtl and Schmidt numbers from 190 to 11,000.

CRITICAL BEHAVIOR OF THE SPECIFIC HEAT IN THE VICINITY OF THE TRANSITION TEMPERATURE FOR S-TRIAZINE

2009 ◽  
Vol 23 (09) ◽  
pp. 2253-2259 ◽  
Author(s):  
M. KURT ◽  
H. YURTSEVEN
Keyword(s):  
Experimental Data ◽  
Phase Transition ◽  
Transition Temperature ◽  
Critical Exponent ◽  
Specific Heat ◽  
Power Law ◽  
Order Phase Transition ◽  
Critical Behavior ◽  
First Order ◽  
Second Order Phase Transition

The critical behavior of the specific heat is studied in s-triazine ( C 3 N 3 H 3). Using the experimental data for the CP, the temperature dependence of the specific heat is analyzed according to a power-law formula and the values of the critical exponent for CP are extracted in the vicinity of the transition temperature (TC=198.07 K ). It is indicated that s-triazine undergoes a weakly first order (quasi-continuous) or second order phase transition.

Prediction of Turbulent Jets in Coflowing and Quiescent Ambients

1975 ◽  
Vol 97 (4) ◽  
pp. 558-564 ◽  
Author(s):  
I. K. Madni ◽  
R. H. Pletcher
Keyword(s):  
Experimental Data ◽  
Difference Scheme ◽  
Differential Form ◽  
Turbulence Models ◽  
Turbulent Jets ◽  
Physical Plane ◽  
Explicit Difference Scheme ◽  
Conservation Equations ◽  
New Model ◽  
Wide Range

Some existing turbulence models for the round jet in coflowing and quiescent ambients are compared to experimental data, and some modifications are suggested and examined. A new model is proposed which results in consistently good predictions for a wide range of velocity ratios, including the important case of a jet discharging into an ambient at rest. The conservation equations of mass, momentum, and energy in differential form for the jet flow are solved numerically in the physical plane using an explicit difference scheme of the DuFort-Frankel type.

Simultaneous heat and mass transfer during evaporation from a film of liquid into the turbulent gas

1982 ◽  
Vol 47 (3) ◽  
pp. 766-775 ◽  
Author(s):  
Václav Kolář ◽  
Jan Červenka
Keyword(s):  
Experimental Data ◽  
Mass Transfer ◽  
Liquid Film ◽  
Heat And Mass Transfer ◽  
Driving Forces ◽  
Proper Definition ◽  
Definition Of ◽  
Simultaneous Heat ◽  
Theory And Experiment

The paper presents results obtained by processing a series of published experimental data on heat and mass transfer during evaporation of pure liquids from the free board of a liquid film into the turbulent gas phone. The data has been processed on the basis of the earlier theory of mechanism of heat and mass transfer. In spite of the fact that this process exhibits a strong Stefan's flow, the results indicate that with a proper definition of the driving forces the agreement between theory and experiment is very good.

scholarly journals Polyconvex hyperelastic modeling of rubberlike materials

2021 ◽  
Vol 43 (7) ◽  
Author(s):  
Cyprian Suchocki ◽  
Stanisław Jemioło
Keyword(s):  
Experimental Data ◽  
Power Law ◽  
Curve Fitting ◽  
Constitutive Relations ◽  
Data Sets ◽  
Power Law Model ◽  
Stored Energy ◽  
Data Approximation ◽  
Exponential Power ◽  
Hyperelastic Models

AbstractIn this work a number of selected, isotropic, invariant-based hyperelastic models are analyzed. The considered constitutive relations of hyperelasticity include the model by Gent (G) and its extension, the so-called generalized Gent model (GG), the exponential-power law model (Exp-PL) and the power law model (PL). The material parameters of the models under study have been identified for eight different experimental data sets. As it has been demonstrated, the much celebrated Gent’s model does not always allow to obtain an acceptable quality of the experimental data approximation. Furthermore, it is observed that the best curve fitting quality is usually achieved when the experimentally derived conditions that were proposed by Rivlin and Saunders are fulfilled. However, it is shown that the conditions by Rivlin and Saunders are in a contradiction with the mathematical requirements of stored energy polyconvexity. A polyconvex stored energy function is assumed in order to ensure the existence of solutions to a properly defined boundary value problem and to avoid non-physical material response. It is found that in the case of the analyzed hyperelastic models the application of polyconvexity conditions leads to only a slight decrease in the curve fitting quality. When the energy polyconvexity is assumed, the best experimental data approximation is usually obtained for the PL model. Among the non-polyconvex hyperelastic models, the best curve fitting results are most frequently achieved for the GG model. However, it is shown that both the G and the GG models are problematic due to the presence of the locking effect.

scholarly journals On the emergent system mass function: the contest between accretion and fragmentation

2020 ◽  
Vol 500 (2) ◽  
pp. 1697-1707
Author(s):  
Paul C Clark ◽  
Anthony P Whitworth
Keyword(s):  
Star Formation ◽  
Standard Deviation ◽  
Mass Distribution ◽  
Power Law ◽  
Accretion Rate ◽  
Mass Function ◽  
High Mass ◽  
New Model ◽  
System Formation ◽  
Low Mass

ABSTRACT We propose a new model for the evolution of a star cluster’s system mass function (SMF). The model involves both turbulent fragmentation and competitive accretion. Turbulent fragmentation creates low-mass seed proto-systems (i.e. single and multiple protostars). Some of these low-mass seed proto-systems then grow by competitive accretion to produce the high-mass power-law tail of the SMF. Turbulent fragmentation is relatively inefficient, in the sense that the creation of low-mass seed proto-systems only consumes a fraction, ${\sim }23{{\ \rm per\ cent}}$ (at most ${\sim }50{{\ \rm per\ cent}}$), of the mass available for star formation. The remaining mass is consumed by competitive accretion. Provided the accretion rate on to a proto-system is approximately proportional to its mass (dm/dt ∝ m), the SMF develops a power-law tail at high masses with the Salpeter slope (∼−2.3). If the rate of supply of mass accelerates, the rate of proto-system formation also accelerates, as appears to be observed in many clusters. However, even if the rate of supply of mass decreases, or ceases and then resumes, the SMF evolves homologously, retaining the same overall shape, and the high-mass power-law tail simply extends to ever higher masses until the supply of gas runs out completely. The Chabrier SMF can be reproduced very accurately if the seed proto-systems have an approximately lognormal mass distribution with median mass ${\sim } 0.11 \, {\rm M}_{\odot }$ and logarithmic standard deviation $\sigma _{\log _{10}({M/M}_\odot)}\sim 0.47$).

scholarly journals Reactivity in social scientific experiments: what is it and how is it different (and worse) than a Placebo effect?

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
María Jiménez-Buedo
Keyword(s):  
Experimental Data ◽  
Conceptual Framework ◽  
Placebo Effect ◽  
Placebo Effects ◽  
Causal Inferences ◽  
Scientific Experiments ◽  
Social Scientific ◽  
The Many ◽  
Definition Of ◽  
In Virtue Of

AbstractReactivity, or the phenomenon by which subjects tend to modify their behavior in virtue of their being studied upon, is often cited as one of the most important difficulties involved in social scientific experiments, and yet, there is to date a persistent conceptual muddle when dealing with the many dimensions of reactivity. This paper offers a conceptual framework for reactivity that draws on an interventionist approach to causality. The framework allows us to offer an unambiguous definition of reactivity and distinguishes it from placebo effects. Further, it allows us to distinguish between benign and malignant forms of the phenomenon, depending on whether reactivity constitutes a danger to the validity of the causal inferences drawn from experimental data.

Entrainment and mixing in stratified shear flows

2001 ◽  
Vol 428 ◽  
pp. 349-386 ◽  
Author(s):  
E. J. STRANG ◽  
H. J. S. FERNANDO
Keyword(s):  
Internal Waves ◽  
Richardson Number ◽  
Transition Period ◽  
Lower Layer ◽  
Buoyancy Flux ◽  
Shear Instability ◽  
Mixing Efficiency ◽  
Buoyancy Frequency ◽  
Entrainment Rate ◽  
Turbulent Eddies

The results of a laboratory experiment designed to study turbulent entrainment at sheared density interfaces are described. A stratified shear layer, across which a velocity difference ΔU and buoyancy difference Δb is imposed, separates a lighter upper turbulent layer of depth D from a quiescent, deep lower layer which is either homogeneous (two-layer case) or linearly stratified with a buoyancy frequency N (linearly stratified case). In the parameter ranges investigated the flow is mainly determined by two parameters: the bulk Richardson number RiB = ΔbD/ΔU2 and the frequency ratio fN = ND=ΔU.When RiB > 1.5, there is a growing significance of buoyancy effects upon the entrainment process; it is observed that interfacial instabilities locally mix heavy and light fluid layers, and thus facilitate the less energetic mixed-layer turbulent eddies in scouring the interface and lifting partially mixed fluid. The nature of the instability is dependent on RiB, or a related parameter, the local gradient Richardson number Rig = N2L/ (∂u/∂z)2, where NL is the local buoyancy frequency, u is the local streamwise velocity and z is the vertical coordinate. The transition from the Kelvin–Helmholtz (K-H) instability dominated regime to a second shear instability, namely growing Hölmböe waves, occurs through a transitional regime 3.2 < RiB < 5.8. The K-H activity completely subsided beyond RiB ∼ 5 or Rig ∼ 1. The transition period 3.2 < RiB < 5 was characterized by the presence of both K-H billows and wave-like features, interacting with each other while breaking and causing intense mixing. The flux Richardson number Rif or the mixing efficiency peaked during this transition period, with a maximum of Rif ∼ 0.4 at RiB ∼ 5 or Rig ∼ 1. The interface at 5 < RiB < 5.8 was dominated by ‘asymmetric’ interfacial waves, which gradually transitioned to (symmetric) Hölmböe waves at RiB > 5:8.Laser-induced fluorescence measurements of both the interfacial buoyancy flux and the entrainment rate showed a large disparity (as large as 50%) between the two-layer and the linearly stratified cases in the range 1.5 < RiB < 5. In particular, the buoyancy flux (and the entrainment rate) was higher when internal waves were not permitted to propagate into the deep layer, in which case more energy was available for interfacial mixing. When the lower layer was linearly stratified, the internal waves appeared to be excited by an ‘interfacial swelling’ phenomenon, characterized by the recurrence of groups or packets of K-H billows, their degeneration into turbulence and subsequent mixing, interfacial thickening and scouring of the thickened interface by turbulent eddies.Estimation of the turbulent kinetic energy (TKE) budget in the interfacial zone for the two-layer case based on the parameter α, where α = (−B + ε)/P, indicated an approximate balance (α ∼ 1) between the shear production P, buoyancy flux B and the dissipation rate ε, except in the range RiB < 5 where K-H driven mixing was active.

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