A Length-Scale Model For Developing Turbulent Flow in a Rectangular Duct

1977 ◽  
Vol 99 (2) ◽  
pp. 347-356 ◽  
Author(s):  
F. B. Gessner ◽  
A. F. Emery
Keyword(s):  
Reynolds Stress ◽  
Three Dimensional ◽  
Scale Model ◽  
Length Scale ◽  
Pressure Gradients ◽  
Mixing Length ◽  
Two Dimensional ◽  
Rectangular Duct ◽  
Corner Flows ◽  
Theory And Experiment

A three-dimensional mixing length model is proposed for modeling local Reynolds stress behavior in rectangular ducts of arbitrary aspect ratio. The model is applicable to both developing and fully-developed flows, and can be applied to other 90-degree corner flows with mild streamwise pressure gradients. Comparisons between theory and experiment show that all components of the Reynolds stress tensor are modeled reasonably well, both in the vicinity of a corner and in two-dimensional regions away from the corner.

A Reynolds Stress Model for Turbulent Corner Flows—Part II: Comparisons Between Theory and Experiment

1976 ◽  
Vol 98 (2) ◽  
pp. 269-276 ◽  
Author(s):  
F. B. Gessner ◽  
J. K. Po
Keyword(s):  
Reynolds Stress ◽  
Reynolds Stress Model ◽  
Length Variation ◽  
Stress Model ◽  
Duct Flow ◽  
Rectangular Duct ◽  
Proposed Model ◽  
Alternate Model ◽  
Corner Flows ◽  
Good Agreement

The applicability of the Reynolds stress model developed in Part I to fully developed rectangular duct flow is investigated. Two sets of experimental data are analyzed in order to prescribe a representative mixing length variation and appropriate values for the constants in the model. Predicted Reynolds stress values are in good agreement with their experimental counterparts for both sets of data. These results are compared with predictions referred to an alternate model in order to explain discrepancies observed in a previous study. Possible extensions of the proposed model to increase its flexibility are discussed.

THREE‐DIMENSIONAL INDUCED POLARIZATION AND ELECTROMAGNETIC MODELING

Geophysics ◽  
1975 ◽  
Vol 40 (2) ◽  
pp. 309-324 ◽  
Author(s):  
Gerald W. Hohmann
Keyword(s):  
Integral Equation ◽  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Induced Polarization ◽  
The Body ◽  
Scale Model ◽  
Two Dimensional ◽  
Electromagnetic Modeling ◽  
The Earth

The induced polarization (IP) and electromagnetic (EM) responses of a three‐dimensional body in the earth can be calculated using an integral equation solution. The problem is formulated by replacing the body by a volume of polarization or scattering current. The integral equation is reduced to a matrix equation, which is solved numerically for the electric field in the body. Then the electric and magnetic fields outside the inhomogeneity can be found by integrating the appropriate dyadic Green’s functions over the scattering current. Because half‐space Green’s functions are used, it is only necessary to solve for scattering currents in the body—not throughout the earth. Numerical results for a number of practical cases show, for example, that for moderate conductivity contrasts the dipole‐dipole IP response of a body five units in strike length approximates that of a two‐dimensional body. Moving an IP line off the center of a body produces an effect similar to that of increasing the depth. IP response varies significantly with conductivity contrast; the peak response occurs at higher contrasts for two‐dimensional bodies than for bodies of limited length. Very conductive bodies can produce negative IP response due to EM induction. An electrically polarizable body produces a small magnetic field, so that it is possible to measure IP with a sensitive magnetometer. Calculations show that horizontal loop EM response is enhanced when the background resistivity in the earth is reduced, thus confirming scale model results.

Effect of Adverse Pressure Gradients on Turbulent Boundary Layers in Axisymmetric Conduits

1957 ◽  
Vol 24 (2) ◽  
pp. 191-196
Author(s):  
J. M. Robertson ◽  
J. W. Holl
Keyword(s):  
Boundary Layer ◽  
Flow Parameter ◽  
Three Dimensional ◽  
Turbulent Boundary Layers ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Flow Conditions ◽  
Straight Pipe ◽  
Outer Flow ◽  
Dimensional Boundary

Abstract The development of the three-dimensional boundary layer in a diffuser with several discharge arrangements has been studied for air flow, in continuation of the work of Uram (1). The flow conditions in a diffuser when followed by a straight pipe, an additional length of the diffuser, or a jet, are compared. Extension of the method of analysis developed by Ross for two-dimensional layers is presented. In some cases the use of three-dimensionally defined parameters leads to different results. Ross’s (2) unique outer-flow parameter is found to be no longer satisfactory. Other outer parameters are presented as possible substitutes.

A Reynolds Stress Model for Turbulent Corner Flows—Part I: Development of the Model

1976 ◽  
Vol 98 (2) ◽  
pp. 261-268 ◽  
Author(s):  
F. B. Gessner ◽  
A. F. Emery
Keyword(s):  
Reynolds Stress ◽  
Flow Behavior ◽  
Reynolds Stress Model ◽  
Turbulence Structure ◽  
Stress Model ◽  
Mixing Length ◽  
Corner Flow ◽  
Global Representation ◽  
Corner Flows ◽  
Algebraic Reynolds Stress Model

A Reynolds stress model is proposed for modeling the local turbulence structure in flow along a streamwise corner. Initial discussion centers on present methods of predicting internal and extenal corner flow behavior. An algebraic Reynolds stress model is then developed by operating on a modified form of the Reynolds stress transport equations. Application of the model involves specification of two empirical constants and a global representation for the mixing length. The paper concludes with a discussion of the features and limitations of the model.

Reynolds stress development in pressure-driven three-dimensional turbulent boundary layers

1989 ◽  
Vol 202 ◽  
pp. 263-294 ◽  
Author(s):  
Shawn D. Anderson ◽  
John K. Eaton
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Reynolds Stress ◽  
Free Stream ◽  
Three Dimensional ◽  
Radius Of Curvature ◽  
Two Dimensional ◽  
Stress Vector ◽  
Dimensional Boundary ◽  
Cross Wire

The development of the Reynolds stress field was studied for flows in which an initially two-dimensional boundary layer was skewed sideways by a spanwise pressure gradient ahead of an upstream-facing wedge. Two different wedges were used, providing a variation in the boundary-layer skewing. Measurements of all components of the Reynolds stress tensor and all ten triple products were measured using a rotatable cross-wire anemometer. The results show the expected lag of the shear stress vector behind the strain rate. Comparison of the two present experiments with previous data suggests that the lag can be estimated if the radius of curvature of the free-stream streamline is known. The magnitude of the shear stress vector in the plane of the wall is seen to decrease rapidly as the boundary-layer skewing increases. The amount of decrease is apparently related to the skewing angle between the wall and the free stream. The triple products evolve rapidly and profiles in the three-dimensional boundary layer are considerably different than two-dimensional profiles, leaving little hope for gradient transport models for the Reynolds stresses. The simplified model presented by Rotta (1979) performs reasonably well providing that an appropriate value of the T-parameter is chosen.

A length-scale formula for confined quasi-two-dimensional plasmas

2009 ◽  
Vol 75 (4) ◽  
pp. 437-454 ◽  
Author(s):  
TIMOTHY D. ANDERSEN ◽  
CHJAN C. LIM
Keyword(s):  
Angular Momentum ◽  
Fluid Model ◽  
Three Dimensional ◽  
Coulomb Gas ◽  
Mean Field Approximation ◽  
Length Scale ◽  
Two Dimensional ◽  
Electron Fluid ◽  
Euler’S Equations ◽  
Euler's Equations

AbstractTypically a magnetohydrodynamical model for neutral plasmas must take into account both the ionic and the electron fluids and their interaction. However, at short time scales, the ionic fluid appears to be stationary compared to the electron fluid. On these scales, we need consider only the electron motion and associated field dynamics, and a single fluid model called the electron magnetohydrodynamical model which treats the ionic fluid as a uniform neutralizing background applies. Using Maxwell's equations, the vorticity of the electron fluid and the magnetic field can be combined to give a generalized vorticity field, and one can show that Euler's equations govern its behavior. When the vorticity is concentrated into slender, periodic, and nearly parallel (but slightly three-dimensional) filaments, one can also show that Euler's equations simplify into a Hamiltonian system and treat the system in statistical equilibrium, where the filaments act as interacting particles. In this paper, we show that, under a mean-field approximation, as the number of filaments becomes infinite (with appropriate scaling to keep the vorticity constant) and given that angular momentum is conserved, the statistical length scale, R, of this system in the Gibbs canonical ensemble follows an explicit formula, which we derive. This formula shows how the most critical statistic of an electron plasma of this type, its size, varies with angular momentum, kinetic energy, and filament elasticity (a measure of the interior structure of each filament) and in particular it shows how three-dimensional effects cause significant increases in the system size from a perfectly parallel, two-dimensional, one-component Coulomb gas.

Paper 1: Centrifugal Compressors for Gas Turbines

1968 ◽  
Vol 183 (14) ◽  
pp. 1-10 ◽  
Author(s):  
T. B. Ferguson
Keyword(s):  
Boundary Layer ◽  
Gas Turbines ◽  
Three Dimensional ◽  
Boundary Layer Theory ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Centrifugal Compressors ◽  
Blade Loading ◽  
Actual Flow ◽  
High Mach

The trends in fluid mechanical development of centrifugal compressors are discussed. The main developments in the impeller are the application of quasi-three-dimensional isentropic methods together with some separation criteria based on two-dimensional turbulent boundary layer theory. Diffusers are sometimes designed on a simplified two-dimensional basis but channel diffusers still appear to be preferred especially at high Mach numbers. Recent visualization studies have shown how far the actual flow in impellers may depart from the actual model and there is a lack of systematic quantitative experimental work on limiting blade loading and pressure gradients both in impellers and diffusers. A summary of gas turbine centrifugal compressors is also made.

Use of the mixing length concept to correctly reproduce velocity profiles of turbulent flows

1998 ◽  
Vol 25 (2) ◽  
pp. 232-240 ◽  
Author(s):  
Jean-Loup Robert ◽  
Mohamed Khelifi ◽  
Ahmed Ghanmi
Keyword(s):  
Turbulent Flows ◽  
Turbulent Viscosity ◽  
Three Dimensional ◽  
Velocity Profiles ◽  
Point Of View ◽  
The Other ◽  
Mixing Length ◽  
Two Dimensional ◽  
Constant Viscosity ◽  
Good Agreement

Since the viscous analogy of turbulence was introduced by Reynolds, many formulations for turbulent viscosity have been proposed. One of them, based on the mixing length concept, is investigated here in a broader point of view. The mixing length concept was used to correctly model turbulent velocity profiles for irregular two-dimensional and three-dimensional domains. Two cases of study were investigated for this purpose: a simple two-dimensional aerodynamic problem and a more complicated three-dimensional hydraulic problem. Results showed that the use of a constant viscosity fails to correctly reproduce experimental observations. On the other hand, the use of the mixing length concept leads to a good agreement between the measured and predicted values.Key words: fluid flow, finite element method, mixing length flow theory, turbulent flow, velocity profiles.

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