Transient Lubricating Films With Inertia—Turbulent Flow

1984 ◽  
Vol 106 (1) ◽  
pp. 134-139 ◽  
Author(s):  
H. G. Elrod ◽  
I. Anwar ◽  
R. Colsher
Keyword(s):  
Steady State ◽  
Turbulent Flow ◽  
Stream Function ◽  
Velocity Gradient ◽  
Eddy Viscosity ◽  
Mean Velocity ◽  
Steady State Operation ◽  
Pressure Development ◽  
Transient And Steady State

This paper presents some new equations for the treatment of turbulent lubricating films when the effects of inertia cannot be neglected. The eddy-viscosity concept is used to represent the turbulent stresses in terms of mean-velocity gradient. Transient and steady-state operation are both considered by means of a generalized stream-function-pressure development.

scholarly journals Model-based design of transverse wall oscillations for turbulent drag reduction

2012 ◽  
Vol 707 ◽  
pp. 205-240 ◽  
Author(s):  
Rashad Moarref ◽  
Mihailo R. Jovanović
Keyword(s):  
Turbulent Flow ◽  
Numerical Simulations ◽  
Eddy Viscosity ◽  
Traditional Approach ◽  
Turbulent Viscosity ◽  
Transverse Wall ◽  
Mean Velocity ◽  
Model Based ◽  
Turbulent Drag ◽  
Linearized Model

AbstractOver the last two decades, both experiments and simulations have demonstrated that transverse wall oscillations with properly selected amplitude and frequency can reduce turbulent drag by as much as $40\hspace{0.167em} \% $. In this paper, we develop a model-based approach for designing oscillations that suppress turbulence in a channel flow. We utilize eddy-viscosity-enhanced linearization of the turbulent flow with control in conjunction with turbulence modelling to determine skin-friction drag in a simulation-free manner. The Boussinesq eddy viscosity hypothesis is used to quantify the effect of fluctuations on the mean velocity in flow subject to control. In contrast to the traditional approach that relies on numerical simulations, we determine the turbulent viscosity from the second-order statistics of the linearized model driven by white-in-time stochastic forcing. The spatial power spectrum of the forcing is selected to ensure that the linearized model for uncontrolled flow reproduces the turbulent energy spectrum. The resulting correction to the turbulent mean velocity induced by small-amplitude wall movements is then used to identify the optimal frequency of drag-reducing oscillations. In addition, the control net efficiency and the turbulent flow structures that we obtain agree well with the results of numerical simulations and experiments. This demonstrates the predictive power of our model-based approach to controlling turbulent flows and is expected to pave the way for successful flow control at higher Reynolds numbers than currently possible.

Added stresses because of the presence of FENE-P bead–spring chains in a random velocity field

1997 ◽  
Vol 337 ◽  
pp. 67-101 ◽  
Author(s):  
HESHMAT MASSAH ◽  
THOMAS J. HANRATTY
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Turbulent Flow ◽  
Drag Reduction ◽  
Velocity Gradient ◽  
Gradient Field ◽  
Shear Stresses ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Random Velocity

FENE-P bead–spring chains unravel in the presence of large enough velocity gradients. In a turbulent flow, this can result in intermittent added stresses and exchanges of energy between the chains and the fluid, whose magnitudes depend on the degree of unravelling and on the orientations of the bead–spring chains. These effects are studied by calculating the average behaviour at different times of an ensemble of chains, contained in a fluid particle that is moving around in a random velocity field obtained from direct numerical simulation of turbulent flow of a Newtonian fluid in a channel. The results are used to evaluate theoretical explanations of drag reduction observed in very dilute solutions of polymers.In regions of the flow in which the energy exchange with the fluid is positive, the possibility arises that turbulence can be produced by mechanisms other than the interaction of Reynolds stresses and the mean velocity gradient field. Of particular interest, from the viewpoint of understanding polymer drag reduction, is the finding that the exchange is negative in velocity fields representative of the wall vortices that are large producers of turbulence. One can, therefore, postulate that polymers cause drag reduction by selectively changing the structures of eddies that produce Reynolds stresses. The intermittent appearance of large added shear stresses is consistent with the experimental finding of a stress deficit, whereby the total local shear stress is greater than the sum of the Reynolds stress and the time-averaged shear stress calculated from the time-averaged velocity gradient and the viscosity of the solvent.

Measurement of a Recirculating, Two-Dimensional, Turbulent Flow and Comparison to Turbulence Model Predictions. I: Steady State Case

1983 ◽  
Vol 105 (4) ◽  
pp. 439-446 ◽  
Author(s):  
D. R. Boyle ◽  
M. W. Golay
Keyword(s):  
Steady State ◽  
Turbulent Flow ◽  
Turbulence Model ◽  
Turbulence Models ◽  
Scale Model ◽  
Test Facility ◽  
Two Dimensional ◽  
Mean Velocity ◽  
Flow Area ◽  
Flow Measurements

Turbulent flow measurements have been performed in a two-dimensional flow cell which is a 1/15-scale model of the Fast Flux Test Facility nuclear reactor outlet plenum. In a steady water flow, maps of the mean velocity field, turbulence kinetic energy, and Reynolds stress have been obtained using a laser doppler anemometer. The measurements are compared to numerical simulations using both the K–ε and K–σ two-equation turbulence models. A relationship between K–σ and K–ε turbulence models is derived, and the two models are found to be nearly equivalent. The steady-state mean velocity data are predicted well through-out most of the test cell. Calculated spatial distributions of the scalar turbulence quantities are qualitatively similar for both models; however, the predicted distributions do not match the data over major portions of the flow area. The K–σ model provides better estimates of the turbulence quantity magnitudes. The predicted results are highly sensitive to small changes in the turbulence model constants and depend heavily on the levels of inlet turbulence. However, important differences between prediction and measurement cannot be significantly reduced by simple changes to the model’s constants.

scholarly journals Transient and Steady-State Analysis of Single Switched Capacitor Converter

2018 ◽  
Vol 14 (1) ◽  
pp. 38-45
Author(s):  
Alexander Kushnerov
Keyword(s):  
Steady State ◽  
Switched Capacitor ◽  
Equivalent Resistance ◽  
Accurate Calculation ◽  
First Order ◽  
Voltage Ripple ◽  
Steady State Operation ◽  
Switched Capacitor Converter ◽  
Analytical Expressions ◽  
Transient And Steady State

The paper derives closed form expressions for transient and steady-state operation of a DC-DC converter with single switched capacitor. To this end, the result of each switching is considered as a point in the iterative process, and the function between the points is reconstructed. As opposed to the commonly accepted approach, when each of the topologies is approximated by a first order circuit, the proposed analysis is carried out for second order circuits. This allows obtaining the waveform of output voltage ripple and paves the way to more accurate calculation of equivalent resistance. The obtained analytical expressions were verified by simulations and an excellent agreement between the results was found.  

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