Triple velocity correlations in isotropic turbulence

1951 ◽  
Vol 47 (1) ◽  
pp. 146-157 ◽  
Author(s):  
R. W. Stewart
Keyword(s):  
Reynolds Number ◽  
Kinematic Viscosity ◽  
Isotropic Turbulence ◽  
Initial Period ◽  
Reynolds Numbers ◽  
Velocity Correlation ◽  
Mean Wind Speed ◽  
The Mean ◽  
Mesh Grid ◽  
Working Section

AbstractThe triple velocity correlation, in turbulence produced by inserting a square-mesh grid near the beginning of the working section of a wind tunnel, has been measured for mesh Reynolds numbers of RM = 5300, 21,200 and 42,400 (RM = UM/ν, where U is the mean wind speed in the working section of the tunnel and M is the centre to centre spacing of the rods making up the grid; ν is the kinematic viscosity of air). At the lowest Reynolds number the correlation has been measured at distances downstream of the grid varying from 20 to 120M. This range covers practically all of the initial period of the decay of turbulence, where the turbulent intensity varies as t−1.

A comparison of heisenberg's spectrum of turbulence with experiment

1951 ◽  
Vol 47 (1) ◽  
pp. 158-176 ◽  
Author(s):  
Ian Proudman ◽  
G. K. Batchelor
Keyword(s):  
Reynolds Number ◽  
Correlation Functions ◽  
Isotropic Turbulence ◽  
Reynolds Numbers ◽  
Velocity Correlation ◽  
Approximate Form ◽  
Velocity Correlation Functions ◽  
Limiting Case

AbstractIn this paper, the theoretical double and triple velocity correlation functions, f(r), g(r) and h(r), which correspond to Heisenberg's spectrum of isotropic turbulence, are obtained numerically for two Reynolds numbers. One set of these correlations is for the limiting case of infinite Reynolds number. In addition, a method is developed for deriving the approximate form of the double correlations for any Reynolds number, which is not too small, from the corresponding correlations for infinite Reynolds number. These theoretical correlations are then compared with the results of experiment.

The diffusion behind a line source in homogeneous turbulence

1954 ◽  
Vol 224 (1159) ◽  
pp. 487-512 ◽  
Keyword(s):  
Turbulent Flow ◽  
Decay Time ◽  
Molecular Diffusion ◽  
Initial Period ◽  
Reynolds Numbers ◽  
Particle Diffusion ◽  
Velocity Correlation ◽  
Rate Of Spread ◽  
Heated Wire ◽  
The Mean

The theory of turbulent diffusion by continuous movements relates the mean particle diffusion from a fixed source to the Lagrangian velocity correlation function, and measure­ments of the diffusion of heat behind a thin heated wire in a uniform turbulent flow have been used to compute this correlation, assuming that the processes of diffusion by con­tinuous movements and molecular conduction are statistically independent. A series of measurements both of the mean temperatures and the temperature fluctuations in the wake of a thin heated wire has been made in the uniform turbulent flow behind bi-plane grids, for grid Reynolds numbers between 2700 and 21000 and within the initial period of decay of the turbulence. In these measurements, the rate of spread of the heat wake was determined in two ways, directly from measurements of the turbulent transport of heat and by numerical differentiation of widths computed from observations of mean temperature. The extent of the accelerated diffusion of heat, which is caused by intensification of the temperature gradients by the turbulent motion, can be computed from the measurements of lateral temperature correlations in the flow, and was found to be comparable with the total diffusion. Both the total diffusion process and the process of accelerated molecular dif­fusion are very nearly self-preserving during decay in the initial period, with a time scale that varies as the decay time and a velocity scale varying inversely as the square root of the decay time, which is consistent with the observed self-preservation of Eulerian correlations. The rate of spread of the heat wake is simply related to the particle diffusion only for short diffusion times at ordinary Reynolds numbers, and the mean-square particle accelera­tion can be computed. The results are significantly larger than those found by other workers who have neglected the additional spread of the wake by accelerated molecular diffusion.

A simple turbulence closure hypothesis for the triple-velocity correlation functions in homogeneous isotropic turbulence

1984 ◽  
Vol 140 ◽  
pp. 45-61 ◽  
Author(s):  
J. A. Domaradzki ◽  
G. L. Mellor
Keyword(s):  
Experimental Data ◽  
Correlation Functions ◽  
Eddy Viscosity ◽  
Isotropic Turbulence ◽  
Initial Period ◽  
Laboratory Data ◽  
Reynolds Numbers ◽  
Isotropic Case ◽  
Velocity Correlation ◽  
Viscosity Function

A simple two-point closure scheme for homogeneous axisymmetric turbulence is developed. For the isotropic case it is essentially an eddy-viscosity assumption in real space for the Kármán-Howarth equation. The eddy-viscosity function for large internal Reynolds numbers is derived from Kolmogoroff's 1941 theory. For moderate Reynold's numbers of order 102, approximately the same expression for the eddy-viscosity function is determined from experimental data. The resulting closed equation for the double-correlation function is solved numerically for both large and moderate Reynolds numbers, and the results are compared with experimental data. Self-similar solutions of the basic equation predict turbulent energy decay inversely proportional to time. It is shown that the departure from this ‘initial-period decay law’ observed in laboratory data is due to the behaviour of grid-produced correlation functions for large separation distances.

The flow of liquid in a stream from the standard turbine impeller

1979 ◽  
Vol 44 (3) ◽  
pp. 700-710 ◽  
Author(s):  
Ivan Fořt ◽  
Hans-Otto Möckel ◽  
Jan Drbohlav ◽  
Miroslav Hrach
Keyword(s):  
Reynolds Number ◽  
Kinematic Viscosity ◽  
Momentum Flux ◽  
Relative Size ◽  
Mean Velocity ◽  
Axial Profile ◽  
The Mean ◽  
Hot Film ◽  
Turbine Impeller

Profiles of the mean velocity have been analyzed in the stream streaking from the region of rotating standard six-blade disc turbine impeller. The profiles were obtained experimentally using a hot film thermoanemometer probe. The results of the analysis is the determination of the effect of relative size of the impeller and vessel and the kinematic viscosity of the charge on three parameters of the axial profile of the mean velocity in the examined stream. No significant change of the parameter of width of the examined stream and the momentum flux in the stream has been found in the range of parameters d/D ##m <0.25; 0.50> and the Reynolds number for mixing ReM ##m <2.90 . 101; 1 . 105>. However, a significant influence has been found of ReM (at negligible effect of d/D) on the size of the hypothetical source of motion - the radius of the tangential cylindrical jet - a. The proposed phenomenological model of the turbulent stream in region of turbine impeller has been found adequate for values of ReM exceeding 1.0 . 103.

scholarly journals Aerodynamics of smooth and rough square-section prisms at incidence in very high Reynolds-number cross-flows

2021 ◽  
Vol 62 (3) ◽  
Author(s):  
Nils Paul van Hinsberg
Keyword(s):  
Reynolds Number ◽  
Cross Sections ◽  
Reynolds Numbers ◽  
Circular Cylinders ◽  
Surface Boundary ◽  
Experimental Proof ◽  
Surface Boundary Layer ◽  
Pitch Moment ◽  
The Mean ◽  
High Reynolds

Abstract The aerodynamics of smooth and slightly rough prisms with square cross-sections and sharp edges is investigated through wind tunnel experiments. Mean and fluctuating forces, the mean pitch moment, Strouhal numbers, the mean surface pressures and the mean wake profiles in the mid-span cross-section of the prism are recorded simultaneously for Reynolds numbers between 1$$\times$$ × 10$$^{5}$$ 5 $$\le$$ ≤ Re$$_{D}$$ D $$\le$$ ≤ 1$$\times$$ × 10$$^{7}$$ 7 . For the smooth prism with $$k_s$$ k s /D = 4$$\times$$ × 10$$^{-5}$$ - 5 , tests were performed at three angles of incidence, i.e. $$\alpha$$ α = 0$$^{\circ }$$ ∘ , −22.5$$^{\circ }$$ ∘ and −45$$^{\circ }$$ ∘ , whereas only both “symmetric” angles were studied for its slightly rough counterpart with $$k_s$$ k s /D = 1$$\times$$ × 10$$^{-3}$$ - 3 . First-time experimental proof is given that, within the accuracy of the data, no significant variation with Reynolds number occurs for all mean and fluctuating aerodynamic coefficients of smooth square prisms up to Reynolds numbers as high as $$\mathcal {O}$$ O (10$$^{7}$$ 7 ). This Reynolds-number independent behaviour applies to the Strouhal number and the wake profile as well. In contrast to what is known from square prisms with rounded edges and circular cylinders, an increase in surface roughness height by a factor 25 on the current sharp-edged square prism does not lead to any notable effects on the surface boundary layer and thus on the prism’s aerodynamics. For both prisms, distinct changes in the aerostatics between the various angles of incidence are seen to take place though. Graphic abstract

scholarly journals Plunging Airfoil: Reynolds Number and Angle of Attack Effects

Aerospace ◽  
2021 ◽  
Vol 8 (8) ◽  
pp. 216
Author(s):  
Emanuel A. R. Camacho ◽  
Fernando M. S. P. Neves ◽  
André R. R. Silva ◽  
Jorge M. M. Barata
Keyword(s):  
Reynolds Number ◽  
High Performance ◽  
Angle Of Attack ◽  
Systems Design ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Low Reynolds Numbers ◽  
Operational Conditions ◽  
Naca0012 Airfoil ◽  
The Mean

Natural flight has consistently been the wellspring of many creative minds, yet recreating the propulsive systems of natural flyers is quite hard and challenging. Regarding propulsive systems design, biomimetics offers a wide variety of solutions that can be applied at low Reynolds numbers, achieving high performance and maneuverability systems. The main goal of the current work is to computationally investigate the thrust-power intricacies while operating at different Reynolds numbers, reduced frequencies, nondimensional amplitudes, and mean angles of attack of the oscillatory motion of a NACA0012 airfoil. Simulations are performed utilizing a RANS (Reynolds Averaged Navier-Stokes) approach for a Reynolds number between 8.5×103 and 3.4×104, reduced frequencies within 1 and 5, and Strouhal numbers from 0.1 to 0.4. The influence of the mean angle-of-attack is also studied in the range of 0∘ to 10∘. The outcomes show ideal operational conditions for the diverse Reynolds numbers, and results regarding thrust-power correlations and the influence of the mean angle-of-attack on the aerodynamic coefficients and the propulsive efficiency are widely explored.

Initial motion of a viscous vortex ring

1994 ◽  
Vol 446 (1928) ◽  
pp. 589-599 ◽  
Keyword(s):  
Reynolds Number ◽  
Asymptotic Analysis ◽  
Vortex Ring ◽  
Kinematic Viscosity ◽  
Reynolds Numbers ◽  
Initial Radius ◽  
Dimensionless Form ◽  
Ring Radius ◽  
Initial Motion ◽  
Matched Asymptotic Analysis

The behaviour of a viscous vortex ring is examined by a matched asymptotic analysis up to three orders. This study aims at investigating how much the location of maximum vorticity deviates from the centroid of the vortex ring, defined by P. G. Saffman (1970). All the results are presented in dimensionless form, as indicated in the following context. Let Γ be the initial circulation of the vortex ring, and R denote the ring radius normalized by its initial radius R i . For the asymptotic analysis, a small parameter ∊ = ( t / Re ) ½ is introduced, where t denotes time normalized by R 2 i / Γ , and Re = Γ/v is the Reynolds number defined with Γ and the kinematic viscosity v . Our analysis shows that the trajectory of maximum vorticity moves with the velocity (normalized by Γ/R i ) U m = – 1/4π R {ln 4 R /∊ + H m } + O (∊ ln ∊), where H m = H m ( Re, t ) depends on the Reynolds number Re and may change slightly with time t for the initial motion. For the centroid of the vortex ring, we obtain the velocity U c by merely replacing H m by H c , which is a constant –0.558 for all values of the Reynolds number. Only in the limit of Re → ∞, the values of H m and H c are found to coincide with each other, while the deviation of H m from the constant H c is getting significant with decreasing the Reynolds number. Also of interest is that the radial motion is shown to exist for the trajectory of maximum vorticity at finite Reynolds numbers. Furthermore, the present analysis clarifies the earlier discrepancy between Saffman’s result and that obtained by C. Tung and L. Ting (1967).

Heat Transfer and Flowfield Measurements in the Leading Edge Region of a Stator Vane Endwall

1999 ◽  
Vol 121 (3) ◽  
pp. 558-568 ◽  
Author(s):  
M. B. Kang ◽  
A. Kohli ◽  
K. A. Thole
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Secondary Flows ◽  
Edge Region ◽  
Leading Edge Vortex ◽  
Stator Vane ◽  
Edge Vortex ◽  
The Mean

The leading edge region of a first-stage stator vane experiences high heat transfer rates, especially near the endwall, making it very important to get a better understanding of the formation of the leading edge vortex. In order to improve numerical predictions of the complex endwall flow, benchmark quality experimental data are required. To this purpose, this study documents the endwall heat transfer and static pressure coefficient distribution of a modern stator vane for two different exit Reynolds numbers (Reex = 6 × 105 and 1.2 × 106). In addition, laser-Doppler velocimeter measurements of all three components of the mean and fluctuating velocities are presented for a plane in the leading edge region. Results indicate that the endwall heat transfer, pressure distribution, and flowfield characteristics change with Reynolds number. The endwall pressure distributions show that lower pressure coefficients occur at higher Reynolds numbers due to secondary flows. The stronger secondary flows cause enhanced heat transfer near the trailing edge of the vane at the higher Reynolds number. On the other hand, the mean velocity, turbulent kinetic energy, and vorticity results indicate that leading edge vortex is stronger and more turbulent at the lower Reynolds number. The Reynolds number also has an effect on the location of the separation point, which moves closer to the stator vane at lower Reynolds numbers.

Fully developed MHD turbulence near critical magnetic Reynolds number

1981 ◽  
Vol 104 ◽  
pp. 419-443 ◽  
Author(s):  
J. Léorat ◽  
A. Pouquet ◽  
U. Frisch
Keyword(s):  
Reynolds Number ◽  
Kinetic Energy ◽  
Isotropic Turbulence ◽  
Magnetic Energy ◽  
Reynolds Numbers ◽  
Magnetic Reynolds Number ◽  
Mhd Equations ◽  
Liquid Sodium ◽  
Turbulent Heat ◽  
Mhd Turbulence

Liquid-sodium-cooled breeder reactors may soon be operating at magnetic Reynolds numbers RM where magnetic fields can be self-excited by a dynamo mechanism (as first suggested by Bevir 1973). Such flows have kinetic Reynolds numbers RV of the order of 107 and are therefore highly turbulent.This leads us to investigate the behaviour of MHD turbulence with high RV and low magnetic Prandtl numbers. We use the eddy-damped quasi-normal Markovian closure applied to the MHD equations. For simplicity we restrict ourselves to homogeneous and isotropic turbulence, but we do include helicity.We obtain a critical magnetic Reynolds number RMc of the order of a few tens (non-helical case) above which magnetic energy is present. RMc is practically independent of RV (in the range 40 to 106). RMc can be considerably decreased by the presence of helicity: when the overall size of the flow L is much larger than the integral scale l0, RMc can drop below unity as suggested by an α-effect argument. When L ≈ l0 the drop can still be substantial (factor of 6) when helicity is a maximum. We examine how the turbulence is modified when RM crosses RMc: presence of magnetic energy, decreased kinetic energy, steepening of kinetic-energy spectrum, etc.We make no attempt to obtain quantitative estimates for a breeder reactor, but discuss some of the possible consequences of exceeding RMc, such as decreased turbulent heat transport. More precise information may be obtained from numerical simulations and experiments (including some in the subcritical regime).

scholarly journals Nonlinear amplification in hydrodynamic turbulence

2021 ◽  
Vol 930 ◽  
Author(s):  
Kartik P. Iyer ◽  
Katepalli R. Sreenivasan ◽  
P.K. Yeung
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Developed Turbulence ◽  
Advection Term ◽  
Nonlinear Amplification

Using direct numerical simulations performed on periodic cubes of various sizes, the largest being $8192^3$ , we examine the nonlinear advection term in the Navier–Stokes equations generating fully developed turbulence. We find significant dissipation even in flow regions where nonlinearity is locally absent. With increasing Reynolds number, the Navier–Stokes dynamics amplifies the nonlinearity in a global sense. This nonlinear amplification with increasing Reynolds number renders the vortex stretching mechanism more intermittent, with the global suppression of nonlinearity, reported previously, restricted to low Reynolds numbers. In regions where vortex stretching is absent, the angle and the ratio between the convective vorticity and solenoidal advection in three-dimensional isotropic turbulence are statistically similar to those in the two-dimensional case, despite the fundamental differences between them.

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