Longitudinal and transverse structure functions in a turbulent round jet: effect of initial conditions and Reynolds number

2001 ◽  
Vol 436 ◽  
pp. 231-248 ◽  
Author(s):  
G. P. ROMANO ◽  
R. A. ANTONIA
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Velocity Structure ◽  
Initial Conditions ◽  
Transverse Velocity ◽  
Structure Functions ◽  
Small Scale ◽  
Round Jet ◽  
Jet Nozzle ◽  
The Difference

The difference between scaling exponents of longitudinal and transverse velocity structure functions in the far-field of a round jet is found to depend on the anisotropy of the flow. The effect of the large-scale anisotropy is assessed by considering different initial conditions at the jet nozzle, and hence different ratios of the longitudinal to transverse rms velocities. The effect of the Taylor microscale Reynolds number on the small scale anisotropy is also considered. Both effects account, to a large extent, for the observed difference between longitudinal and transverse exponents and the disagreement between previously published results of different authors. This disagreement also depends on the method used to determine the inertial range. An empirical description of the overall behaviour of the structure functions provides reasonable estimates for the longitudinal and transverse exponents, accounting reasonably well for the anisotropy of both large- and small-scale motions.

scholarly journals Self-similarity of time-evolving plane wakes

1998 ◽  
Vol 367 ◽  
pp. 255-289 ◽  
Author(s):  
ROBERT D. MOSER ◽  
MICHAEL M. ROGERS ◽  
DANIEL W. EWING
Keyword(s):  
Reynolds Number ◽  
Large Scale ◽  
Initial Conditions ◽  
Spreading Rate ◽  
Momentum Thickness ◽  
Two Dimensional ◽  
Self Similarity ◽  
Order Of Magnitude ◽  
The Difference ◽  
Velocity Spectra

Direct numerical simulations of three time-developing turbulent plane wakes have been performed. Initial conditions for the simulations were obtained using two realizations of a direct simulation from a turbulent boundary layer at momentum-thickness Reynolds number 670. In addition, extra two-dimensional disturbances were added in two of the cases to mimic two-dimensional forcing. The wakes are allowed to evolve long enough to attain approximate self-similarity, although in the strongly forced case this self-similarity is of short duration. For all three flows, the mass-flux Reynolds number (equivalent to the momentum-thickness Reynolds number in spatially developing wakes) is 2000, which is high enough for a short k−5/3 range to be evident in the streamwise one-dimensional velocity spectra.The spreading rate, turbulence Reynolds number, and turbulence intensities all increase with forcing (by nearly an order of magnitude for the strongly forced case), with experimental data falling between the unforced and weakly forced cases. The simulation results are used in conjunction with a self-similar analysis of the Reynolds stress equations to develop scalings that approximately collapse the profiles from different wakes. Factors containing the wake spreading rate are required to bring profiles from different wakes into agreement. Part of the difference between the various cases is due to the increased level of spanwise-coherent (roughly two-dimensional) energy in the forced cases. Forcing also has a significant impact on flow structure, with the forced flows exhibiting more organized large-scale structures similar to those observed in transitional wakes.

Reynolds number dependence of the small-scale structure of grid turbulence

2000 ◽  
Vol 406 ◽  
pp. 81-107 ◽  
Author(s):  
T. ZHOU ◽  
R. A. ANTONIA
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Fourth Order ◽  
Transverse Velocity ◽  
Scale Structure ◽  
Small Scale ◽  
Grid Turbulence ◽  
Small Scale Structure ◽  
Velocity Increments ◽  
The Difference

The small-scale structure of grid turbulence is studied primarily using data obtained with a transverse vorticity (ω3) probe for values of the Taylor-microscale Reynolds number Rλ in the range 27–100. The measured spectra of the transverse vorticity component agree within ±10% with those calculated using the isotropic relation over nearly all wavenumbers. Scaling-range exponents of transverse velocity increments are appreciably smaller than exponents of longitudinal velocity increments. Only a small fraction of this difference can be attributed to the difference in intermittency between the locally averaged energy dissipation rate and enstrophy fluctuations. The anisotropy of turbulence structures in the scaling range, which reflects the small values of Rλ, is more likely to account for most of the difference. All four fourth-order rotational invariants Iα (α = 1 to 4) proposed by Siggia (1981) were evaluated. For any particular value of α, the magnitude of the ratio Iα / I1 is approximately constant, independently of Rλ. The implication is that the invariants are interdependent, at least in isotropic and quasi-Gaussian turbulence, so that only one power-law exponent may be sufficient to describe the Rλ dependence of all fourth-order velocity derivative moments in this type of flow. This contrasts with previous suggestions that at least two power-law exponents are needed, one for the rate of strain and the other for vorticity.

Finite Reynolds number effect on the scaling range behaviour of turbulent longitudinal velocity structure functions

2017 ◽  
Vol 820 ◽  
pp. 341-369 ◽  
Author(s):  
S. L. Tang ◽  
R. A. Antonia ◽  
L. Djenidi ◽  
L. Danaila ◽  
Y. Zhou
Keyword(s):  
Reynolds Number ◽  
Structure Function ◽  
Large Scale ◽  
Velocity Structure ◽  
Longitudinal Velocity ◽  
Structure Functions ◽  
Third Order ◽  
Reynolds Number Effect ◽  
Rate Of Increase ◽  
Velocity Structure Function

The effect of large-scale forcing on the second- and third-order longitudinal velocity structure functions, evaluated at the Taylor microscale $r=\unicode[STIX]{x1D706}$, is assessed in various turbulent flows at small to moderate values of the Taylor microscale Reynolds number $R_{\unicode[STIX]{x1D706}}$. It is found that the contribution of the large-scale terms to the scale by scale energy budget differs from flow to flow. For a fixed $R_{\unicode[STIX]{x1D706}}$, this contribution is largest on the centreline of a fully developed channel flow but smallest for stationary forced periodic box turbulence. For decaying-type flows, the contribution lies between the previous two cases. Because of the difference in the large-scale term between flows, the third-order longitudinal velocity structure function at $r=\unicode[STIX]{x1D706}$ differs from flow to flow at small to moderate $R_{\unicode[STIX]{x1D706}}$. The effect on the second-order velocity structure functions appears to be negligible. More importantly, the effect of $R_{\unicode[STIX]{x1D706}}$ on the scaling range exponent of the longitudinal velocity structure function is assessed using measurements of the streamwise velocity fluctuation $u$, with $R_{\unicode[STIX]{x1D706}}$ in the range 500–1100, on the axis of a plane jet. It is found that the magnitude of the exponent increases as $R_{\unicode[STIX]{x1D706}}$ increases and the rate of increase depends on the order $n$. The trend of published structure function data on the axes of an axisymmetric jet and a two-dimensional wake confirms this dependence. For a fixed $R_{\unicode[STIX]{x1D706}}$, the exponent can vary from flow to flow and for a given flow, the larger $R_{\unicode[STIX]{x1D706}}$ is, the closer the exponent is to the value predicted by Kolmogorov (Dokl. Akad. Nauk SSSR, vol. 30, 1941a, pp. 299–303) (hereafter K41). The major conclusion is that the finite Reynolds number effect, which depends on the flow, needs to be properly accounted for before determining whether corrections to K41, arising from the intermittency of the energy dissipation rate, are needed. We further point out that it is imprudent, if not incorrect, to associate the finite Reynolds number effect with a consequence of the modified similarity hypothesis introduced by Kolmogorov (J. Fluid Mech., vol. 13, 1962, pp. 82–85) (K62); we contend that this association has misled the vast majority of post K62 investigations of the consequences of K62.

scholarly journals Scale Effects of Footings on Geocell Reinforced Sand Using Large-Scale Tests

2018 ◽  
Vol 4 (3) ◽  
pp. 497
Author(s):  
A. Shadmand ◽  
Mahmoud Ghazavi ◽  
Navid Ganjian
Keyword(s):  
Large Scale ◽  
Initial Conditions ◽  
Scale Effects ◽  
Friction Angle ◽  
Full Scale ◽  
Small Scale ◽  
Granular Soils ◽  
Initial State ◽  
The Difference ◽  
Mean Stresses

The scale effect on bearing capacity of shallow footings supported by unreinforced granular soils has been evaluated extensively. However, the subject has not been addressed for shallow footings on geocell-reinforced granular soils. In this study, load-settlement characteristic of large square footings is investigated by performing large-scale loading tests on unreinforced and geocell-reinforced granular soils. The effects of footing width (B), soil relative density of soil (Dr), and reinforcement depth (u) have been investigated. The test results show that the scale effects exist in geocell-reinforced soils, like unreinforced soils, and the behavior of small-scale models of footings cannot be directly related to the behavior of full-scale footings due to the difference between initial conditions of tests and the initial state of mean stresses in the soil beneath the footings having different dimensions. Large footings create higher mean stresses in the soil, resulting in low soil friction angle and initial conditions of the test approach to the critical state lines. The results of tests indicate that model experiments should be conducted on low-density soil for better prediction of the behavior of full-scale footings, otherwise, the predicted behavior of full-scale footings does not seem conservative.

A numerical study of the transition of jet diffusion flames

1990 ◽  
Vol 431 (1882) ◽  
pp. 301-314 ◽  
Keyword(s):  
Reynolds Number ◽  
Diffusion Coefficient ◽  
Large Scale ◽  
Numerical Study ◽  
Small Scale ◽  
Surface Model ◽  
Flame Surface ◽  
Transition Mechanism ◽  
Air Stream ◽  
Scale Fluctuation

A numerical study on the transition from laminar to turbulent of two-dimensional fuel jet flames developed in a co-flowing air stream was made by adopting the flame surface model of infinite chemical reaction rate and unit Lewis number. The time dependent compressible Navier–Stokes equation was solved numerically with the equation for coupling function by using a finite difference method. The temperature-dependence of viscosity and diffusion coefficient were taken into account so as to study effects of increases of these coefficients on the transition. The numerical calculation was done for the case when methane is injected into a co-flowing air stream with variable injection Reynolds number up to 2500. When the Reynolds number was smaller than 1000 the flame, as well as the flow, remained laminar in the calculated domain. As the Reynolds number was increased above this value, a transition point appeared along the flame, downstream of which the flame and flow began to fluctuate. Two kinds of fluctuations were observed, a small scale fluctuation near the jet axis and a large scale fluctuation outside the flame surface, both of the same origin, due to the Kelvin–Helmholtz instability. The radial distributions of density and transport coefficients were found to play dominant roles in this instability, and hence in the transition mechanism. The decreased density in the flame accelerated the instability, while the increase in viscosity had a stabilizing effect. However, the most important effect was the increase in diffusion coefficient. The increase shifted the flame surface, where the large density decrease occurs, outside the shear layer of the jet and produced a thick viscous layer surrounding the jet which effectively suppressed the instability.

Fluid Flow and Heat Transfer of Liquid Sodium in Small-Scale Heat Sinks With Different Geometries

2021 ◽  
Author(s):  
Mahyar Pourghasemi ◽  
Nima Fathi
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Cross Sections ◽  
Heat Sink ◽  
Volume Ratio ◽  
Heat Sinks ◽  
Liquid Sodium ◽  
Small Scale ◽  
Nusselt Numbers ◽  
The Difference

Abstract 3-D numerical simulations are performed to investigate liquid sodium (Na) flow and the heat transfer within miniature heat sinks with different geometries and hydraulic diameters of less than 5 mm. Two different straight small-scale heat sinks with rectangular and triangular cross-sections are studied in the laminar flow with the Reynolds number up to 1900. The local and average Nusselt numbers are obtained and compared against eachother. At the same surface area to volume ratio, rectangular minichannel heat sink leads to almost 280% higher convective heat transfer rate in comparison with triangular heat sink. It is observed that the difference between thermal efficiencies of rectangular and triangular minichannel heat sinks was independent of flow Reynolds number.

Pressure gradient effects on the large-scale structure of turbulent boundary layers

2013 ◽  
Vol 715 ◽  
pp. 477-498 ◽  
Author(s):  
Zambri Harun ◽  
Jason P. Monty ◽  
Romain Mathis ◽  
Ivan Marusic
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Amplitude Modulation ◽  
Large Scale ◽  
Outer Region ◽  
Adverse Pressure Gradient ◽  
Turbulent Boundary Layers ◽  
Small Scale

AbstractResearch into high-Reynolds-number turbulent boundary layers in recent years has brought about a renewed interest in the larger-scale structures. It is now known that these structures emerge more prominently in the outer region not only due to increased Reynolds number (Metzger & Klewicki, Phys. Fluids, vol. 13(3), 2001, pp. 692–701; Hutchins & Marusic, J. Fluid Mech., vol. 579, 2007, pp. 1–28), but also when a boundary layer is exposed to an adverse pressure gradient (Bradshaw, J. Fluid Mech., vol. 29, 1967, pp. 625–645; Lee & Sung, J. Fluid Mech., vol. 639, 2009, pp. 101–131). The latter case has not received as much attention in the literature. As such, this work investigates the modification of the large-scale features of boundary layers subjected to zero, adverse and favourable pressure gradients. It is first shown that the mean velocities, turbulence intensities and turbulence production are significantly different in the outer region across the three cases. Spectral and scale decomposition analyses confirm that the large scales are more energized throughout the entire adverse pressure gradient boundary layer, especially in the outer region. Although more energetic, there is a similar spectral distribution of energy in the wake region, implying the geometrical structure of the outer layer remains universal in all cases. Comparisons are also made of the amplitude modulation of small scales by the large-scale motions for the three pressure gradient cases. The wall-normal location of the zero-crossing of small-scale amplitude modulation is found to increase with increasing pressure gradient, yet this location continues to coincide with the large-scale energetic peak wall-normal location (as has been observed in zero pressure gradient boundary layers). The amplitude modulation effect is found to increase as pressure gradient is increased from favourable to adverse.

Will Different Scales Impact on Design Collaboration in 3D Virtual Environments?

2012 ◽  
pp. 185-198
Author(s):  
Jerry Jen-Hung Tsai ◽  
Jeff WT Kan ◽  
Xiangyu Wang ◽  
Yingsiu Huang
Keyword(s):  
Virtual Environments ◽  
Large Scale ◽  
Protocol Analysis ◽  
Small Scale ◽  
Design Collaboration ◽  
The Difference ◽  
Communication Control ◽  
The Impact ◽  
3D Virtual Environments ◽  
Electronic Circuit Design

This chapter presents a study on the impact of design scales on collaborations in 3D virtual environments. Different domains require designers to work on different scales; for instance, urban design and electronic circuit design operate at very different scales. However, the understanding of the effects of scales upon collaboration in virtual environment is limited. In this chapter, the authors propose to use protocol analysis method to examine the differences between two design collaboration projects in virtual environments: one large scale, and another small scale within a similar domain. It shows that the difference in scale impacted more on communication control and social communication.

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