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.

The turbulent boundary layer on a rotating cylinder in an axial stream

1970 ◽  
Vol 42 (1) ◽  
pp. 1-15 ◽  
Author(s):  
T-S. Cham ◽  
M. R. Head
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Integral Method ◽  
Richardson Number ◽  
Rotating Cylinder ◽  
Turbulence Structure ◽  
Mixing Length ◽  
Mean Velocity ◽  
Method Of Solution ◽  
Instability Parameter

Calculations are presented of the development of the turbulent boundary layer on a rotating cylinder with its axis along the stream, and the results are compared with measurements made by Parr. With the choice of a suitable co-ordinate system, the boundary layer downstream of the nose of the cylinder approximates closely to a condition of two-dimensionality, and a simple integral method of solution can be applied. The only evidence of three-dimensionality lies in the destabilizing effect of rotation on the turbulence structure of the layer and an analysis of this instability has been made which relates changes in mixing length and entrainment to an instability parameter in the form of a Richardson number.In spite of the changes in shear stress distribution and entrainment brought about by rotation, mean velocity profiles and skin friction values are found to be related to H and Rθ in the same way as for the stationary flat plate.

Prediction of Momentum, Heat and Mass Transfer in Swirling, Turbulent Boundary Layers

1974 ◽  
Vol 96 (2) ◽  
pp. 204-209 ◽  
Author(s):  
M. L. Koosinlin ◽  
B. E. Launder ◽  
B. I. Sharma
Keyword(s):  
Experimental Data ◽  
Mass Transfer ◽  
Richardson Number ◽  
Effective Viscosity ◽  
Swirling Flow ◽  
Turbulent Boundary Layers ◽  
Mixing Length ◽  
Strain Fields ◽  
Number Agreement ◽  
Complex Strain

The paper presents the outcome of finite-difference calculations of turbulent flow near spinning cones, disks, and cylinders. The turbulence model used is a version of the mixing-length hypothesis in which the mixing length which would prevail in the absence of swirl is made a linear function of the local “swirling flow” Richardson number. Agreement with available experimental data for these geometries is generally good. At high swirl rates, however, a few systematic differences between experiment and calculation become evident which are probably attributable to the nonisotropic nature of the effective viscosity in such complex strain fields.

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.

Asynchronous whirl in a rotating cylinder partially filled with liquid

1985 ◽  
Vol 150 ◽  
pp. 311-327 ◽  
Author(s):  
A. S. Berman ◽  
T. S. Lundgren ◽  
A. Cheng
Keyword(s):  
Surface Waves ◽  
Shallow Water ◽  
Solitary Waves ◽  
Water Waves ◽  
Rotating Cylinder ◽  
The Self ◽  
Hydraulic Jumps ◽  
Centrifugal Forces ◽  
Shallow Water Waves ◽  
Analytical Results

Experimental and analytical results are presented for the self-excited oscillations that occur in a partially filled centrifuge when centrifugal forces interact with shallow-water waves. Periodic and aperiodic modulations of the basic whirl phenomena are both observed and calculated. The surface waves are found to be hydraulic jumps, undular bores or solitary waves.

The electro-deposition of silver on stationary and rotating glassy carbon discs

1977 ◽  
Vol 55 (23) ◽  
pp. 4037-4044 ◽  
Author(s):  
Remigio Germano Barradas ◽  
Stephen Fletcher ◽  
Sandor Szabo
Keyword(s):  
Experimental Data ◽  
Mass Transport ◽  
Glassy Carbon ◽  
Quantitative Model ◽  
Nucleation And Growth ◽  
Experimental Conditions ◽  
Electro Deposition ◽  
Transport Effects ◽  
Mass Transport Effects

The deposition of silver onto glassy carbon is described. The solution consisted of 10−2 M AgClO4 in 1.0 M HClO4. Experiments reveal the difficulties in trying to separate nucleation and growth phenomena from mass transport effects. A simple semi-quantitative model is proposed to explain the experimental data. It is also shown that the deposition reaction is not completely reversible under certain experimental conditions.

Effect of Size and Slip Coefficient of a Porous Manifold on Thermal Stratification in Storage Tanks

2009 ◽  
Author(s):  
N. M. Brown ◽  
F. C. Lai
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Numerical Simulations ◽  
Storage Tank ◽  
Richardson Number ◽  
Thermal Stratification ◽  
Temperature Fields ◽  
Storage Tanks ◽  
Slip Coefficient ◽  
Wide Range

Numerical simulations have been performed to study the effects of size and slip coefficient of a porous manifold on the thermal stratification in a storage tank. The model is used to predict the development of flow and temperature fields during a charging process. Computations have covered a wide range of the Grashof number (1.8 × 105 &lt; Gr &lt; 1.8 × 108) and Reynolds number (10 ≤ Re ≤ 104), or in terms of the Richardson number, 10−2 &lt; Ri &lt; 105. The results obtained compare favorably well with the experimental data. In addition, the present results have confirmed the effectiveness of porous manifold in the promotion of thermal stratification and provide useful information for the design of such system.

Equilibrium-Turbulent Boundary Layer Prediction for a Proposed Prandtl Mixing Length Distribution

1968 ◽  
Vol 10 (5) ◽  
pp. 426-433 ◽  
Author(s):  
F. C. Lockwood
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Boundary Layers ◽  
Length Distribution ◽  
Momentum Equation ◽  
Turbulent Boundary Layers ◽  
Mixing Length ◽  
Good Agreement

The momentum equation is solved numerically for a suggested ramp variation of the Prandtl mixing length across an equilibrium-turbulent boundary layer. The predictions of several important boundary-layer functions are compared with the equilibrium experimental data. Comparisons are also made with some recent universal recommendations for turbulent boundary layers since the equilibrium experimental data are limited. Good agreement is found between the predictions, the experimental data, and the recommendations.

Mixing of Compressible Fluids

1961 ◽  
Vol 28 (3) ◽  
pp. 335-338 ◽  
Author(s):  
E. D. Kennedy
Keyword(s):  
Experimental Data ◽  
Compressible Fluid ◽  
Second Law Of Thermodynamics ◽  
Stagnation Pressure ◽  
Compressible Fluids ◽  
The Other ◽  
Second Law ◽  
Conservation Equations ◽  
Dimensionless Parameters ◽  
Constant Area

The problem of the mixing of two streams of the same compressible fluid in a constant-area duct is solved by applying certain dimensionless parameters first used by Kiselev. The extension to dissimilar fluids or to more than two streams is straightforward. Although the analysis is unrestricted, detailed results are given only for the case where one stream is sonic or supersonic and the other sonic or subsonic at the origin of mixing. For this case, the second law of thermodynamics indicates that, of the two solutions of the conservation equations, the subsonic one is always permitted while some of the supersonic solutions are thermodynamically impossible. Upon examination of experimental data, it is further concluded that of the admissible supersonic solutions, only one may be expected to occur. The establishment of this supersonic solution with its relatively high stagnation pressure leads to the conclusion that when the initial temperatures are sufficiently different, there exist thermodynamically possible solutions with a stagnation pressure higher than that of either of the two initial streams.

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