Heat Transfer in Two-Dimensional Turbulent Confined Flows

1972 ◽  
Vol 186 (1) ◽  
pp. 625-633
Author(s):  
A. P. Hatton ◽  
N. H. Woolley
Keyword(s):  
Prediction Method ◽  
Eddy Diffusivity ◽  
Reynolds Numbers ◽  
Turbulence Energy ◽  
Two Dimensional ◽  
Narrow Angle ◽  
Before And After ◽  
Dimensional Equation ◽  
Confined Flows ◽  
Good Agreement

Measurements of displacement and momentum thickness, friction factor and Stanton number were made in a narrow angle diverging duct consisting of two plane walls, width 0·82 m. The height of the duct varied from 0·051 to 0·152 m over a length of 3·94 m. Reynolds numbers ranged from 8·7 × 104 to 20·7 × 104. The results are compared with a prediction method using a numerical solution of the two-dimensional equation of motion and energy. An eddy diffusivity hypothesis was used, based on the turbulence energy equation and an empirical length scale distribution. Good agreement was obtained between the theoretical and experimental results, both before and after the boundary layers interfered, and with previously reported experiments in a parallel duct. It was necessary to change the value of one of the constants in the analysis for each geometry.

A Continuous Prediction Method for Fully Developed Laminar, Transitional, and Turbulent Flows in Pipes

1975 ◽  
Vol 42 (1) ◽  
pp. 51-54 ◽  
Author(s):  
N. W. Wilson ◽  
R. S. Azad
Keyword(s):  
Turbulent Flows ◽  
Flow Characteristics ◽  
Prediction Method ◽  
Reynolds Numbers ◽  
Mean Flow ◽  
Number Range ◽  
Circular Pipes ◽  
The Mean ◽  
Single Set ◽  
Good Agreement

A single set of equations is developed to predict the mean flow characteristics in long circular pipes operating at laminar, transitional, and turbulent Reynolds numbers. Generally good agreement is obtained with available data in the Reynolds number range 100 < Re < 500,000.

Life prediction method of copper thin film repaired by laser irradiation based on healing variable

2016 ◽  
Vol 26 (7) ◽  
pp. 1028-1042 ◽  
Author(s):  
Chong-Gang Ren ◽  
De-Guang Shang
Keyword(s):  
Laser Irradiation ◽  
Life Prediction ◽  
Copper Film ◽  
Prediction Method ◽  
Cyclic Stress ◽  
Notched Specimens ◽  
Constitutive Relationships ◽  
Irradiation Treatment ◽  
Before And After ◽  
Good Agreement

The cyclic stress–strain constitutive relationships for copper film smooth specimens with different damage degrees before and after laser irradiation treatment were investigated. Compared with the changes of the constitutive relationships under different damage degrees, a healing variable for the repaired copper film by laser irradiation was defined. Based on the analysis of the healing variable, a fatigue life prediction method was proposed. The experimental lives of the damaged notched specimens after laser irradiation treatment were used to verify the proposed life prediction method. The results showed that the predicted lives are in good agreement with the experimental results.

scholarly journals Kazantsev model in non-helical 2.5-dimensional flows

2016 ◽  
Vol 806 ◽  
pp. 627-648 ◽  
Author(s):  
K. Seshasayanan ◽  
A. Alexakis
Keyword(s):  
Turbulent Flows ◽  
Three Dimensional ◽  
Analytical Calculation ◽  
Reynolds Numbers ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Control Parameters ◽  
Governing Equations ◽  
Field Correlation ◽  
Good Agreement

We study the dynamo instability for a Kazantsev–Kraichnan flow with three velocity components that depend only on two dimensions $\boldsymbol{u}=(u(x,y,t),v(x,y,t),w(x,y,t))$ often referred to as 2.5-dimensional (2.5-D) flow. Within the Kazantsev–Kraichnan framework we derive the governing equations for the second-order magnetic field correlation function and examine the growth rate of the dynamo instability as a function of the control parameters of the system. In particular we investigate the dynamo behaviour for large magnetic Reynolds numbers $Rm$ and flows close to being two-dimensional and show that these two limiting procedures do not commute. The energy spectra of the unstable modes are derived analytically and lead to power-law behaviour that differs from the three-dimensional and two-dimensional cases. The results of our analytical calculation are compared with the results of numerical simulations of dynamos driven by prescribed fluctuating flows as well as freely evolving turbulent flows, showing good agreement.

Steady two-dimensional flow through a row of normal flat plates

1990 ◽  
Vol 210 ◽  
pp. 281-302 ◽  
Author(s):  
D. B. Ingham ◽  
T. Tang ◽  
B. R. Morton
Keyword(s):  
Finite Difference ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Corner Singularities ◽  
Flat Plates ◽  
Navier Stokes Equations ◽  
Flow Through ◽  
Good Agreement

A numerical and experimental study is described for the two-dimensional steady flow through a uniform cascade of normal flat plates. The Navier–Stokes equations are written in terms of the stream function and vorticity and are solved using a second-order-accurate finite-difference scheme which is based on a modified procedure to preserve accuracy and iterative convergence at higher Reynolds numbers. The upstream and downstream boundary conditions are discussed and an asymptotic solution is employed both upstream and downstream. A frequently used method for dealing with corner singularities is shown to be inaccurate and a method for overcoming this problem is described. Numerical solutions have been obtained for blockage ratio of 50 % and Reynolds numbers in the range 0 [les ]R[les ] 500 and results for both the lengths of attached eddies and the drag coefficients are presented. The calculations indicate that the eddy length increases linearly withR, at least up toR= 500, and that the multiplicative constant is in very good agreement with the theoretical prediction of Smith (1985a), who considered a related problem. In the case ofR= 0 the Navier–Stokes equations are solved using the finite-difference scheme and a modification of the boundary-element method which treats the corner singularities. The solutions obtained by the two methods are compared and the results are shown to be in good agreement. An experimental investigation has been performed at small and moderate values of the Reynolds numbers and there is excellent agreement with the numerical results both for flow streamlines and eddy lengths.

The decay of a turbulent swirl in a pipe

1965 ◽  
Vol 22 (2) ◽  
pp. 257-271 ◽  
Author(s):  
Frank Kreith ◽  
O. K. Sonju
Keyword(s):  
Experimental Data ◽  
Eddy Diffusivity ◽  
Reynolds Numbers ◽  
Experimental Measurements ◽  
Number Range ◽  
Swirl Velocity ◽  
Linearized Theory ◽  
Flow Through ◽  
Initial Intensity ◽  
Good Agreement

This paper presents a linearized theory for the average decay of a tape-induced fully developed turbulent swirl in flow through a pipe. In the Reynolds number range between 104 and 105 the theoretical analysis was found to be in good agreement with experimental data obtained with water in a 1 in. pipe, provided the eddy diffusivity was chosen appropriately.It was observed that a turbulent swirl decays to about 10–20% of its initial intensity in a distance of about 50 pipe diameters, the decay being more rapid at smaller than at larger Reynolds numbers. The theoretical swirl velocity distribution agreed qualitatively with experimental measurements at distances less than 20 diameters downstream from the outlet of the swirl inducer, but deviated from the experimental results further downstream.

An experimental study of turbulent separating and reattaching flows at a high Mach number

1972 ◽  
Vol 52 (3) ◽  
pp. 425-435 ◽  
Author(s):  
J. P. Batham
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Shear Layers ◽  
Two Dimensional ◽  
Pressure Coefficients ◽  
High Mach ◽  
Incipient Separation ◽  
Good Agreement

Separating and reattaching flows in a two-dimensional compression corner were investigated experimentally at a Mach number of 7·0 and Reynolds numbers (based on the distance from the leading edge to the corner) of 4·75 × 106, 9·51 × 106 and 1·55 × 107. Heat-transfer measurements and Pitot traverses in the upstream boundary layer showed that the boundary layer had become fully turbulent at the start of the interactions. Increases in the Reynolds number gave increases in the length of separated shear layers and decreases in the corner angle required for incipient, separation. The reattachment pressure coefficients gave good agreement with the criterion of Batham (1969).

Axisymmetric turbulent mass transfer in a circular tube

1969 ◽  
Vol 38 (3) ◽  
pp. 433-455 ◽  
Author(s):  
Alan Quarmby ◽  
R. K. Anand
Keyword(s):  
Mass Transfer ◽  
Velocity Profile ◽  
Circular Tube ◽  
Eddy Diffusivity ◽  
Reynolds Numbers ◽  
Eddy Diffusivities ◽  
Direct Measurements ◽  
Fluid Properties ◽  
Fully Developed Turbulent Flow ◽  
Good Agreement

Solutions of the diffusion equation are obtained for mass transfer in a fully developed turbulent flow in a plain circular tube in two axisymmetric situations. The cases studied are a point source positioned at the centre of the tube and a ring source in the tube wall in which there is a uniform mass flux along a short length of the tube. The purpose of the work is to establish the correctness of the descriptions of the velocity profile and radial eddy diffusivities of mass and momentum in order to provide a firm base from which consideration of the non-axisymmetric situation could proceed.The turbulent velocity profile is deduced from a two-part model based on a sublayer profile and the Von Kármán similarity hypothesis. The radial eddy diffusivity of momentum is described by an expression due to Reichardt and Van Driest and from this the radial eddy diffusivity of mass as a function of radius is obtained by use of a ratio which takes account of fluid properties and the value of the radial eddy diffusivity.The analysis is substantiated by experiments carried out with nitrous oxide, Schmidt number = 0·77, for Reynolds numbers from 20,000 to 130,000. The concentration profiles measured at several axial positions downstream from the source are in good agreement with the analytical solutions in both cases. Direct measurements of the eddy diffusivity of mass and momentum were obtained as added confirmation and also gave good agreement with the theory.

scholarly journals Entropy and Turbulence Structure

Entropy ◽  
2021 ◽  
Vol 24 (1) ◽  
pp. 11
Author(s):  
T.-W. Lee ◽  
J. E. Park
Keyword(s):  
Turbulent Flows ◽  
Maximum Entropy Principle ◽  
Reynolds Numbers ◽  
Turbulence Energy ◽  
Turbulence Structure ◽  
Reynolds Stresses ◽  
Dissipation Structure ◽  
Stress Components ◽  
Entropy Principle ◽  
Good Agreement

Some new perspectives are offered on the spectral and spatial structure of turbulent flows, in the context of conservation principles and entropy. In recent works, we have shown that the turbulence energy spectra are derivable from the maximum entropy principle, with good agreement with experimental data across the entire wavenumber range. Dissipation can also be attributed to the Reynolds number effect in wall-bounded turbulent flows. Within the global energy and dissipation constraints, the gradients (d/dy+ or d2/dy+2) of the Reynolds stress components neatly fold onto respective curves, so that function prescriptions (dissipation structure functions) can serve as a template to expand to other Reynolds numbers. The Reynolds stresses are fairly well prescribed by the current scaling and dynamical formalism so that the origins of the turbulence structure can be understood and quantified from the entropy perspective.

scholarly journals Rotating Taylor–Green flow

2015 ◽  
Vol 769 ◽  
pp. 46-78 ◽  
Author(s):  
A. Alexakis
Keyword(s):  
Numerical Simulations ◽  
Reynolds Numbers ◽  
Energy Dissipation Rate ◽  
Dynamical Behaviour ◽  
Linear Stability Theory ◽  
Two Dimensional ◽  
Rotating Turbulence ◽  
Order Expansion ◽  
Higher Order Terms ◽  
Good Agreement

The steady state of a forced Taylor–Green flow is investigated in a rotating frame of reference. The investigation involves the results of 184 numerical simulations for different Reynolds numbers $\mathit{Re}_{F}$ and Rossby numbers $\mathit{Ro}_{F}$. The large number of examined runs allows a systematic study that enables the mapping of the different behaviours observed to the parameter space ($\mathit{Re}_{F},\mathit{Ro}_{F}$), and the examination of different limiting procedures for approaching the large $\mathit{Re}_{F}$ small $\mathit{Ro}_{F}$ limit. Four distinctly different states were identified: laminar, intermittent bursts, quasi-two-dimensional condensates and weakly rotating turbulence. These four different states are separated by power-law boundaries $\mathit{Ro}_{F}\propto \mathit{Re}_{F}^{-{\it\gamma}}$ in the small $\mathit{Ro}_{F}$ limit. In this limit, the predictions of asymptotic expansions can be directly compared with the results of the direct numerical simulations. While the first-order expansion is in good agreement with the results of the linear stability theory, it fails to reproduce the dynamical behaviour of the quasi-two-dimensional part of the flow in the nonlinear regime, indicating that higher-order terms in the expansion need to be taken into account. The large number of simulations allows also to investigate the scaling that relates the amplitude of the fluctuations with the energy dissipation rate and the control parameters of the system for the different states of the flow. Different scaling was observed for different states of the flow, that are discussed in detail. The present results clearly demonstrate that the limits of small Rossby and large Reynolds numbers do not commute and it is important to specify the order in which they are taken.

Selection of a leading edge noise prediction method for PNoise

2018 ◽  
pp. 214-223
Author(s):  
AM Faria ◽  
MM Pimenta ◽  
JY Saab Jr. ◽  
S Rodriguez
Keyword(s):  
Wind Turbine ◽  
Turbine Blades ◽  
Prediction Method ◽  
Leading Edge ◽  
Wind Farms ◽  
Broadband Noise ◽  
Turbulence Energy ◽  
Noise Prediction ◽  
Migration Routes ◽  
Turbulent Inflow

Wind energy expansion is worldwide followed by various limitations, i.e. land availability, the NIMBY (not in my backyard) attitude, interference on birds migration routes and so on. This undeniable expansion is pushing wind farms near populated areas throughout the years, where noise regulation is more stringent. That demands solutions for the wind turbine (WT) industry, in order to produce quieter WT units. Focusing in the subject of airfoil noise prediction, it can help the assessment and design of quieter wind turbine blades. Considering the airfoil noise as a composition of many sound sources, and in light of the fact that the main noise production mechanisms are the airfoil self-noise and the turbulent inflow (TI) noise, this work is concentrated on the latter. TI noise is classified as an interaction noise, produced by the turbulent inflow, incident on the airfoil leading edge (LE). Theoretical and semi-empirical methods for the TI noise prediction are already available, based on Amiet’s broadband noise theory. Analysis of many TI noise prediction methods is provided by this work in the literature review, as well as the turbulence energy spectrum modeling. This is then followed by comparison of the most reliable TI noise methodologies, qualitatively and quantitatively, with the error estimation, compared to the Ffowcs Williams-Hawkings solution for computational aeroacoustics. Basis for integration of airfoil inflow noise prediction into a wind turbine noise prediction code is the final goal of this work.

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