High Reynolds Number Experiments Research Articles

Direct numerical simulation of deformable rising bubbles at low Reynolds numbers

We investigate numerically the dynamics of freely rising gas bubbles driven by buoyancy at low Reynolds numbers, focusing on two distinct characteristics: the clustering morphology and the probability density functions (p.d.f.) of the velocity fluctuations for bubbles. A modified Volume-of-fluid (VOF) method is implemented in our direct numerical simulations to circumvent the nonphysical coalescence between bubbles. Four values of the gas fraction are studied: 5%, 10%, 15%, and 20%. The Eötvös number and the Galileo number are fixed at Eo = 2 and Ga = 855, respectively. For a single rising bubble, the Reynolds number according to the terminal velocity and the bubble diameter is around 27, displaying an ellipsoidal shape. For a swarm of bubbles, both irregular and regular clustering configurations are observed in our numerical simulations as we vary the gas fraction, which can only be realized at high Reynolds numbers in the previous experiments due to the low gas fraction limit. Moreover, we find that the p.d.f.s for bubble velocity fluctuations exhibit distinctly different behavior from the high Reynolds number experiments. The horizontal components for these p.d.f.s approach Gaussian distributions only when the gas fraction is high, i.e., α=15% and 20%. It suggests that the strong bubble–bubble interaction through their flow wakes is an efficient way to trigger the flow into turbulent states.

Some observations on Reynolds number scaling in wall-bounded flows

Wall-bounded turbulence is sometimes described as consisting of hierarchies of similar structures. This is embodied in the Attached Eddy Model, and at high Reynolds numbers this model predicts a logarithmic variation of the turbulence intensity with distance from the wall. The high Reynolds number experiments described here confirm this behavior, but they also reveal new aspects such as the slower than expected rise in the near-wall peak, and the unexpected appearance of an outer layer peak. Turbulence remains an elusive phenomenon.

Insights into the growth rate of spatially evolving plane turbulent free-shear layers from 2D vortex-gas simulations

Although the free-shear or mixing layer has been a subject of extensive research over nearly a century, there are certain fundamental issues that remain controversial. These include the influence of initial and downstream conditions on the flow, the effect of velocity ratio across the layer, and the nature of any possible coupling between small scale dynamics and the large scale evolution of layer thickness. In the spirit of the temporal vortex-gas simulations of Suryanarayanan et al. [“Free turbulent shear layer in a point vortex gas as a problem in nonequilibrium statistical mechanics,” Phys. Rev. E 89, 013009 (2014)], we revisit the simple 2D inviscid vortex-gas model with extensive computations and detailed analysis, in order to gain insights into some of the above issues. Simulations of the spatially evolving vortex-gas shear layer are carried out at different velocity ratios using a computational model based on the work of Basu et al. [“Vortex sheet simulation of a plane canonical mixing layer,” Comput. Fluids 21, 1–30 (1992) and “Modelling plane mixing layers using vortex points and sheets,” Appl. Math. Modell. 19, 66–75 (1995)], but with a crucial improvement that ensures conservation of global circulation. The simulations show that the conditions imposed at the origin of the free shear layer and at the exit to the computational domain can affect flow evolution in their respective downstream and upstream neighbourhoods, the latter being particularly strong in the single stream limit. In between these neighbourhoods at the ends is a regime of universal self-preserving growth rate given by a universal function of velocity ratio. The computed growth rates are generally located within the scatter of experimental data on plane mixing layers and closely agree with recent high Reynolds number experiments and 3D large eddy simulation studies. These findings support the view that observed free-shear layer growth can be largely explained by the 2D vortex dynamics of the quasi-2D large-scale structures known to be a characteristic of plane mixing layers.

A turbulence model for large interfaces in high Reynolds two-phase CFD

A model for two-phase (six-equation) CFD modelling of turbulence is presented, for the regions of the flow where the liquid–gas interface takes place on length scales which are much larger than the typical computational cell size. In the other regions of the flow, the liquid or gas volume fractions range from 0 to 1. Heat and mass transfer, compressibility of the fluids, are included in the system, which is used at high Reynolds numbers in large scale industrial calculations. In this context, a model based on k and ɛ transport equations in each phase was chosen. The paper describes the model, with a focus on the large interfaces, which require special treatments and transfer terms between the phases, including some approaches inspired from wall functions. The validation of the model is based on high Reynolds number experiments with turbulent quantities measurements of a liquid jet impinging a free surface and an air water stratified flow. A steam–water stratified condensing flow experiment is also used for an indirect validation in the case of heat and mass transfer.

A new formulation for the streamwise turbulence intensity distribution

Numerical and experimental data from zero pressure-gradient turbulent boundary layers over smooth walls have been analyzed by means of the so called diagnostic plot introduced by Alfredsson & Örlü [Eur. J. Fluid Mech. B/Fluids, 42, 403 (2010)]. In the diagnostic plot the local turbulence intensity is shown as a function of the local mean velocity normalized with a reference velocity scale. In the outer region of the boundary layer a universal linear decay of the turbulence intensity is observed independent of Reynolds number. The deviation from this linear region appears in the buffer region and seems to be universal when normalized with the friction velocity. Therefore, a new empirical fit for the streamwise velocity turbulence intensity distribution is proposed and the results are compared with up to date reliable high-Reynolds number experiments and extrapolated towards Reynolds numbers relevant to atmospherical boundary layers.

Effects of large-scale free stream turbulence on a turbulent boundary layer

Results of a wind tunnel experiment in which there are systematic variations of free stream turbulence above a flat-plate boundary layer are presented. Upstream of the plate, an active grid generates free stream turbulence varying in intensity from 0.25% to 10.5%. The momentum thickness Reynolds number of the boundary layer varies from 550 to nearly 3000. In all cases, the ratio of the free stream turbulence length scale to the boundary layer depth is greater than unity. Hotwire measurements show that, at high turbulence intensities, the effects of the free stream turbulence extend deep into the boundary layer, affecting the wall stress as well as the small-scale (derivative) statistics. Premultiplied energy spectra show a double peak. At very low free stream turbulence intensities these peaks are associated with the inner and outer scales of the turbulent boundary layer, but at high turbulence intensities the free stream energy peak dominates over the boundary layer’s outer scale. The implications of the effect of the large free stream turbulence scales on the small, near-wall scales is discussed with reference to recent high Reynolds number experiments in a turbulent boundary layer without free stream turbulence [Hutchins and Marusic, Philos. Trans. R. Soc. London, Ser. A 365, 647 (2007)].

CICLoPE—a response to the need for high Reynolds number experiments

Although the equations governing turbulent flow of fluids are well known, understanding the overwhelming richness of flow phenomena, especially in high Reynolds number turbulent flows, remains one of the grand challenges in physics and engineering. High Reynolds number turbulence is ubiquitous in aerospace engineering, ground transportation systems, flow machinery, energy production (from gas turbines to wind and water turbines), as well as in nature, e.g. various processes occurring in the planetary boundary layer. High Reynolds number turbulence is not easily obtained in the laboratory, since in order to have good spatial resolution for measurements, the size of the facility itself has to be large. In this paper, we discuss limitations of various existing facilities and propose a new facility that will allow good spatial resolution even at high Reynolds number. The work is carried out in the framework of the Center for International Cooperation in Long Pipe Experiments (CICLoPE), an international collaboration that many in the turbulence community have shown an interest to participate in.

Relation between shear parameter and Reynolds number in statistically stationary turbulent shear flows

Studies of the relation between the shear parameter S* and the Reynolds number Re are presented for a nearly homogeneous and statistically stationary turbulent shear flow. The parametric investigations are in line with a generalized perspective on the return to local isotropy in shear flows that was outlined recently [J. Schumacher, K. R. Sreenivasan, and P. K. Yeung, Phys. Fluids 15, 84 (2003)]. Therefore, two parameters, the constant shear rate S and the level of initial turbulent fluctuations as prescribed by an energy injection rate εin, are varied systematically. The investigations suggest that the shear parameter levels off for larger Reynolds numbers which is supported by dimensional arguments. It is found that the skewness of the transverse derivative shows a different decay behavior with respect to Reynolds number when the sequence of simulation runs follows different pathways across the two-parameter plane. The study can shed new light on different interpretations of the decay of odd order moments in high-Reynolds number experiments.

Lagrangian velocity statistics in turbulent flows: effects of dissipation.

We use the multifractal formalism to describe the effects of dissipation on Lagrangian velocity statistics in turbulent flows. We analyze high Reynolds number experiments and direct numerical simulation data. We show that this approach reproduces the shape evolution of velocity increment probability density functions from Gaussian to stretched exponentials as the time lag decreases from integral to dissipative time scales. A quantitative understanding of the departure from scaling exhibited by the magnitude cumulants, early in the inertial range, is obtained with a free parameter function D(h) which plays the role of the singularity spectrum in the asymptotic limit of infinite Reynolds number. We observe that numerical and experimental data are accurately described by a unique quadratic D(h) spectrum which is found to extend from h(min) approximately 0.18 to h(max) approximately 1.

Large eddy simulation of a plane jet

Large eddy simulations of spatially evolving planar jets have been performed using the standard Smagorinsky, the dynamic Smagorinsky, and the dynamic mixed models and model performance evaluated. Computations have been performed both at a low Reynolds number, Red=3000, in order to make comparisons with a previous DNS at the same Reynolds number, and at a higher value, Red=30 000, to compare with high Reynolds number experiments. Model predictions with respect to the evolution of jet half-width, centerline velocity decay, mean velocity profiles, and profiles of turbulence intensity are evaluated. Some key properties of the SGS models such as the eddy-viscosity constant and the subgrid dissipation are also compared. It is found that the standard Smagorsinsky model is much too dissipative and severely underpredicts the evolution of the jet half-width and centerline velocity decay. The dynamic versions of the Smagorinsky model and the mixed model allow for streamwise and transverse variation of the constant in the eddy-viscosity expression which results in much better performance and good agreement with experimental and DNS data. The mixed model has an additional scale-similarity part which, in a priori tests against filtered jet DNS data, is found to predict the subgrid shear stress profile. Although the subgrid shear stress obtained by the dynamic Smagorinsky model is substantially smaller than that obtained in the a priori tests using the jet DNS data, surprisingly, in the a posteriori computations, the dynamic Smagorinsky model performs as well as the dynamic mixed model. Analysis of the mean momentum equation gives the reason for such behavior: the resolved stress in computations with the dynamic Smagorinsky model is larger than it should be and compensates for the underprediction of the subgrid shear stress by the Smagorinsky model. The numerical discretization errors have been quantified. The error due to noncommutativity of spatial differentiation and physical space filtering on nonuniform grids is found to be small because of the relatively mild stretching used in the present LES. The modeling error is found to be generally smaller than the discretization error with the standard Smagorinsky model having the largest modeling error.

Structures and transition in a high Reynolds number experiment

We present a brief review of experimental results obtained in high Reynolds number flows using Helium gas as the working fluid. We focus on measurements of the skewness and the flatness of the velocity derivative, and in particular their evolution with the Reynolds number. A transition, observed at R λ ≈ 700, is discussed. In the second part, we analyze the structures associated with high velocity gradients, which we identify as “worms”; we finally present a detailed analysis of the evolution of their mean size, their number and their velocity increment with Reynolds number.

Stern Flows at Full-Scale Reynolds Numbers

A numerical method for the solution of the Reynolds-averaged Navier-Stokes equations for three-dimensional flow of an incompressible fluid, used previously for calculations at model-scale Reynolds numbers, has been applied to the flow over the stern of an axisymmetric body and a representative ship over a range of Reynolds numbers up to five billion. High Reynolds number experiments on axi-symmetric bodies strongly support the use of wall functions in the turbulence model. Comparisons with traditional ship wake scaling laws suggest that such laws do not properly describe the scale effects on the flow in the propeller plane.

Low-Reynolds number flow over a rotatable cylinder–splitter plate body

Uniform flow around a body consisting of a cylinder with a splitter plate attached to it is considered. The body is free to rotate about the axis of the cylinder. Numerical results show that on increasing the Reynolds number above a critical value a symmetry-breaking bifurcation appears and the splitter plate migrates to an asymmetric equilibrium position, confirming previous high-Reynolds number experiments. The present results reveal that this phenomenon is due to the flow in the separation bubble behind the cylindrical part of the body.