Free Turbulence Research Articles

PIV studies on turbulence structure in air/water interface with wind-induced water waves

When wind appears over the free surface, water waves and turbulence are generated by an interfacial shear stress. In particular, turbulent diffusion promotes significantly mass and momentum transport beneath the interface between the water and air significantly in ocean and lakes, and thus it is very important for global environment problems to reveal such turbulence property and coherent structure. Simultaneous measurements of velocities and free-surface elevation allow us to conduct reasonably the phase analysis of the coherent structure in interfacial shear layer. Furthermore, multi-point measurements such as PIV are very powerful to detect the space-time structure of coherent motions. Therefore, in the present study, we developed a specially designed PIV system which can measure the velocity components and surface-elevation fluctuation simultaneously by using two sets of high-speed cameras to reveal the coherent structure in the interfacial shear layer.

Turbulent Film Boiling on A Non-Isothermal Horizontal Elliptical Tube with Steam Heating Surface

AbstractThe present theoretical study investigates turbulent film boiling on an elliptical tube with steam heating surface inside. The flow direction of the heating steam is opposite to the vapor film of the outer tube. Thus, the surface temperature is expressed by cosine function. The effect of temperature amplitude, eccentricity, nonlinear viscosity, nonlinear thermal conductivity, radiation and eddy diffusivity are all included in the present analysis. And the paper also discusses the vapor thickness, local Nusselt number and mean Nusselt number. The result shows, first, under the free convection turbulent film boiling with temperature variation, the bigger the temperature amplitude value is, the better the heat transfer efficiency is. Next, the increase of the eccentricity values will bring out the increase of the Nusselt number. Finally, a comparison between the results of the present study and those reported in a previous theoretical data is provided.

Hydrodynamic Cavitation for Food and Water Processing

Hydrodynamic cavitation, which was and is still looked upon as an unavoidable nuisance in the flow systems, can be a serious contender as an alternative to acoustic cavitation for intensification of different physical and chemical processing applications. Hydrodynamic cavitation results in the generation of hot spots, highly reactive free radicals and turbulence associated with liquid circulation currents, which can result in the intensification of various physical/chemical operations. The present work highlights the different aspects of hydrodynamic cavitation including the basic mechanism, bubble dynamics analysis with recommendations for optimum operating parameters, reactor designs and an overview of applications in different areas of food and water processing. The major applications discussed in the work include food sterilization, microbial cell disruption for the release or extraction of enzymes, water disinfection and wastewater treatment. It appears that hydrodynamic cavitation results in conditions similar to those generated using acoustic cavitation but at comparatively much larger scale of operation and with better energy efficiencies.

Experiments on turbulence beneath a free surface in a stationary field generated by a Crump weir: turbulence structure and correlation with the free surface

This paper is a companion paper to a study devoted to the analysis of experimental instantaneous fluid levels and three-component fluid velocity measurements in a stationary flow field generated by a Crump weir in a laboratory flume, using an ultrasonic distance sensor and a three-probe arrangement of an ultrasonic Doppler velocity profiler (UVP) (Longo in Exp Fluids, doi: 10.1007/s00348-010-0881-5, 2010). Whereas Longo (Exp Fluids, doi: 10.1007/s00348-010-0881-5, 2010) deals with a general overview of the problem, the description of the experiments and the analysis of the free surface statistics and relevant scales, the present manuscript is devoted to a detailed analysis of the turbulence and the correlation with the free surface. The data are elaborated by obtaining the macroturbulence Reynolds tensor, using conditional averages based on free surface–fluctuation statistics. We also compute the two-point correlations of fluid velocity, the micro-scale and the integral scale, the correlation between free surface and the turbulence beneath. A free surface–boundary layer was detected having a thickness proportional to the root mean square of the free surface–height series and with a velocity scale that correlates well with the free surface–elevation time gradient. Most of the relevant state variables, such as the mean velocity and Reynolds stress components, collapse to a single curve if scaled appropriately. There are many indicators that a specific regime occurs that has an optimal tuning between the free surface and turbulence. In this regime, the length scales are considered as an indicator.

Experiments on turbulence beneath a free surface in a stationary field generated by a Crump weir: free-surface characteristics and the relevant scales

This work concerns the analysis of experimental instantaneous fluid levels and three-component fluid velocity measurements in a stationary flow field generated by a Crump weir in a laboratory flume using an ultrasonic distance sensor and a three-probe arrangement of an ultrasonic Doppler velocity profiler. The tests are characterised by different and increasing Froude numbers (Fr = 0.10–0.38), with the free surface of the fluid ranging from flat (low Froude number) to almost aerated (high Froude number). The statistics of the free surface are computed, and the relevant length and velocity scales are measured. A free-surface boundary layer was detected having a thickness proportional to the root mean square of the free-surface height series and with a velocity scale that related well to the free-surface elevation time gradient. The mean velocity profiles are presented. There are many indicators that a specific regime occurs with an optimal tuning between free surface and turbulence. In this regime, the length scales are raised.

Head-wave parametric rolling of a surface combatant

Complementary CFD, towing tank EFD, and nonlinear dynamics approach study of parametric roll for the ONR Tumblehome surface combatant both with and without bilge keels is presented. The investigations without bilge keels include a wide range of conditions. CFD closely agrees with EFD for resistance, sinkage, and trim except for Fr>0.5 which may be due to free surface and/or turbulence modeling. CFD shows fairly close agreement with EFD for forward-speed roll decay in calm water, although damping is over/under predicted for largest/smaller GM. Most importantly CFD shows remarkably close agreement with EFD for forward-speed parametric roll in head waves for GM=0.038 and 0.033 m, although CFD predicts larger instability zones at high and low Fr, respectively. The CFD and EFD results are analyzed with consideration ship motion theory and compared with Mathieu equation and nonlinear dynamics approaches. Nonlinear dynamics approaches are in qualitative agreement with CFD and EFD. The CFD and nonlinear dynamics approach results were blind in that the actual EFD radius of gyration k xx was not known a priori.

Free Turbulence on R³ and T³

Free Turbulence on R³ and T³

Free Turbulent Reacting Jet Simulation Based on Combination of Transport Equations and PDF

In this paper, a method based on the combination of transport equations and PDF (Probability Density Function) calculations is tested through the study of a free axisymmetric turbulent jet and non-premixed flames. This method solves the difficulties related to the closure of the chemical source term. PDF calculations provide the statistical properties of the flow by which the mean values of physical quantities are calculated. In addition, Favre averaged quantities, i.e. temperature, species concentration and velocity fields, can be obtained by using PDF. A comparison has been made with previous experimental and numerical studies in the same field. The model is then applied to the investigation of a diffusive turbulent flame for which experimental data exist. The results obtained show good accuracy for velocities, main species and temperature and are very encouraging for use in combustion simulations.

Non-linear turbulence models for multiphase recirculating free-surface flow over stepped spillways

The flow over a stepped spillway is free surface, multiphase and turbulent. Moreover, a recirculation region occurs at each step of the spillway. The flow characteristic is hence complicated and difficult to predict. In previous work on stepped spillways (Chen et al. Journal of Hydraulic Engineering, ASCE, 128 (7), 683–688 and Xiangju et al. Science in China Series E: Technological Sciences, 49 (3), 674–684), only the linear turbulence model was applied which gave low accuracy. Furthermore, there are still no optimised model constants for this kind of flow. The present work therefore aims to apply the large eddy simulation (LES), the non-linear and the modified non-linear turbulence models to simulate the flow over the spillways with various slopes and step heights. It is found that the modified model is able to predict the flow close to the LES but requires less computational time by a factor of up to 4. Moreover, the modified model gives higher accuracy than the LES for the cases of the spillways with higher slopes and step heights.

Solution to diffusion equation of impurity propagation in a free turbulent flow

An analytical solution to a diffusion equation for calculating stationary field of impurity in a free turbulent flow, provided that the coefficient of turbulent diffusion is directly proportional to the distance of particles from the impurity sources, is proposed. It is shown that, at great distances from the source, the solution obtained has the same character as has the solution obtained on the basis of statistical hypotheses on distribution of the concentration in a gas plume.

Reynolds Stress Anisotropy in Open-Channel Flow

This paper reports the results of an experimental study characterizing turbulence and turbulence anisotropy in smooth and rough shallow open-channel flows. The rough bed consists of a train of two-dimensional transverse square ribs with a ratio of the roughness height (k) to the total depth of flow (d) equal to 0.10. Three rib separations (p/k) of 4.5, 9, and 18 were examined. Here, p is the pitch between consecutive roughness elements and was varied to reproduce the classical condition of d- and k-type roughness. For each case, two-component velocity measurements were obtained using a laser Doppler velocimetry system at two locations for p/k=4.5 and 9: on the top of the rib and above the cavity, and an additional location for p/k=18. The measurements allow examination of the local variations of the higher-order turbulent moments, stress ratios as well as turbulence anisotropy. Large variations of the turbulence intensities, Reynolds shear stress, turbulent kinetic energy and turbulence production are found for y1<3k. In this region, the flow is more directly influenced by the shear layers from the preceding ribs. The higher-order moments appear to be similar for all rough surfaces beyond y1≈7k. In the outer layer (y1>3k), all higher-order turbulent moments for the k-type roughness show a substantial increase due to the complex interactions between the roughness and the remnants overlying shear layers shed from succeeding ribs. Analysis of the components of the Reynolds stress anisotropy tensor shows that at p/k=18, the flow at y1<5k tends to be more isotropic which implies that for this particular case, the effect of the roughness density could also be important. On the smooth bed, at the shallower depths, the correlation coefficient near the free surface increases and turbulence tends to become less anisotropic.

Propagation of Gaussian Schell-model vortex beams through atmospheric turbulence and evolution of coherent vortices

Taking the Gaussian Schell-model (GSM) vortex beam as a typical example of partially coherent vortex beams, the analytical expressions for the cross-spectral density, average intensity and root mean square (rms) width of a GSM vortex beam with topological charge m = ± 1 propagating through atmospheric turbulence are derived, which enable us to study the propagation properties of GSM vortex beams through atmospheric turbulence and evolution behavior of their coherent vortices. The propagation of GSM vortex beams undergoes several stages of evolution of the intensity profile in both free space and turbulence, and is different from that of GSM non-vortex beams. An increase of the refraction index structure constant Cn2 and a decrease of the spatial correlation length σ0 speed up the evolution process. The beam-width spreading of GSM vortex beams is less than that of GSM non-vortex beams. The smaller the correlation length σ0 is, the less the beam-width spreading of GSM vortex beams is affected by turbulence. The position and number of coherent vortices depend on the structure constant Cn2, correlation length σ0 and topological charge m. The smaller Cn2 and larger σ0 result in a larger propagation distance for the conservation of the topological charge in turbulence.

Telegraph-Type versus Diffusion-Type Models of Turbulent Relative Dispersion

Properties of two equations describing the evolution of the probability density function of the relative dispersion in turbulent flow are compared by investigating their solutions: the self-similar telegraph equation derived by Ogasawara and Toh and the Richardson diffusion equation with the drift term. The solution of the self-similar telegraph equation vanishes at a finite point, while that of the Richardson equation extends infinitely just after the initial time. Each equation has a similarity solution, which is found to be an asymptotic solution of the initial value problem. The time lag has a dominant effect on the relaxation process into the similarity solution. The approaching time to the similarity solution can be reduced by advancing the time of the similarity solution appropriately. The Batchelor scaling is observed only for the telegraph case. The Richardson constant is estimated using the similarity solutions of both equations for our previous direct numerical simulation of two-dimensional free convection turbulence.

Effect of Sen Design on Surface Fluctuation and Solidifying Shell in Slab Mold and Its Optimization

Turbulent flow and heat transfer coupled with solidification in slab continuous casting mold was studied by numerical simulation method. Volume of fluid (VOF) model is used to solve steel-air two-phase flow problem and enthalpy-porosity scheme is introduced to solve the fluid flow problem involving solidification. Contributions of various nozzle port angles and port widths and heights on the free surface fluctuation and the thickness of solidifying shell in slab mold were particularly investigated, based on which the structure of submerged entry nozzle was optimized. Flow inside the common nozzle port cannot fill the entire outlet area, having a recirculation in the upper portion of the port, which is enlarged for the nozzle port with both larger height and width. Results show that the flow in mold cavity is mainly controlled by the nozzle port angle. The increase of the angle of upper face of the port to shape a roughly streamlined inner-wall improves the effective area fraction of the nozzle, resulting in less jet impingement, weaker free surface turbulence and thicker solidifying steel shell.

Numerical simulation of turbulent free surface flow over obstruction

A two-dimensional hybrid numerical model, FEM-LES-VOF, for free surface flows is proposed in this study, which is a combination of three-step Taylor-Galerkin finite element method, large eddy simulation with the Smagorinsky sub-grid model and Computational Lagrangian-Eulerian Advection Remap Volume of Fluid (CLEAR-VOF) method. The present FEM-LES-VOF model allows the fluid flows involving violent free surface and turbulence subject to complex boundary configuration to be simulated in a straightforward manner with unstructured grids in the context of finite element method. Numerical simulation of a benchmark problem of dam breaking is conducted to verify the present model. Comparisons with experimental data show that the proposed model works well and is capable of producing reliable predictions for free surface flows. Using the FEM-LES-VOF model, the free surface flow over a semi-circular obstruction is investigated. The simulation results are compared with available experimental and numerical results. Good performance of the FEM-LES-VOF model is demonstrated again. Moreover, the numerical studies show that the turbulence plays an important role in the evolution of free surface when the reflected wave propagates upstream during the fluid flow passing the submerged obstacle.

Double-averaging methodology and its application to turbulent flow in and above vegetation canopies

Double averaged equations for atmospheric boundary layer flows are introduced as natural extensions of single averaged Reynolds equations. We show that in circumstances where double averaged equations are needed, the two fundamental properties of Reynolds averaging are violated. First, we consider double-averaging in free air turbulence, where the aim is to separate coherent motions from background turbulence. We illustrate the different properties of the main operators that have been used and the physical meaning of the terms that result. Second, in canopy flows, the multiply connected nature of the canopy airspace leads to a different set of departures from the standard Reynolds equations. We establish the physical meaning of the extra terms that arise. Finally we briefly discuss the problems, both practical and theoretical, that arise when we use double averaged equations to interpret real data.

Systematic analysis of high Schmidt number turbulent mass transfer across clean, contaminated and solid interfaces

A series of numerical simulation is carried out for high Schmidt number turbulent mass transfer across interfaces of different dynamical conditions, i.e., a clean or contaminated free surface and also a solid surface. A distinct feature of free surface turbulence close to a contaminated interface is drastic damping of the surface divergence fluctuations at low frequencies, which play a critical role in the interfacial mass transfer. Various concentration statistics reveal that the transport mechanism at a highly contaminated interface becomes dynamically equivalent to that at a solid surface. Consequently, the interfacial mass transfer rate falls down to the value on a solid surface, so that the Schmidt number dependency of the mass transfer rate switches from Sc −0.5 to Sc −0.7. Based on a one-dimensional advection–diffusion equation, it is demonstrated that the ratio between typical intensity and frequency of the fluctuating surface divergence is a critical parameter for the transition of the turbulent mass transfer mode.

Numerical simulation for the collision between a vortex ring and solid particles

This study is concerned with the numerical simulation for the collision between a vortex ring and an ensemble of small glass particles. The vortex ring, convecting with its self-induced velocity in a quiescent air, collides with the particles. The Reynolds number for the vortex ring is 2600, and the particle diameters are 50 and 200 μm. The Stokes number St for the 50 μm particle is 0.74, while the St for the 200 μm particle is 11.4. Immediately after the collision with the vortex ring, the 50 μm particles surround the vortex ring, forming a dome. It is parallel with the preferential distribution for the particle with St ≃ 1 around large-scale eddies, which has been measured experimentally and simulated numerically in various free turbulent flows. The 200 μm particles disperse more due to the collision with the vortex ring. This is attributable to the centrifugal effect of large-scale eddy, which has been reported by the numerical simulation for the motion of the particle with St = 10 in a wake flow. The collision between the vortex ring and the particles induces an organized three-dimensional vortical structure. It also reduces the strength and convective velocity of the vortex ring.

Spectral changes of partially coherent flat topped beam in turbulent atmosphere

Spectral characteristics of partially coherent flat-topped (PCFT) beams propagated in a turbulent atmosphere are investigated and an analytical formula for the spectrum S(ω) is derived. It is shown that, if the scaling law is valid, the normalized spectrum S(ω) of PCFT beams propagating through turbulent atmosphere is the same as the normalized source spectrum S(0)(ω), this similarity is valid for any arbitrary order of the circular flat-topped “N”. It is proved that if the scaling law is not valid, S(ω) of PCFT is different from S(0)(ω). Also spectral behavior of PCFT beams in free space and turbulence media is investigated in detail.

A theoretical study of free convection in turbulent film boiling on a horizontal elliptical tube

The present theoretical study investigates turbulent film boiling on an isothermal elliptical tube under quiescent liquid. The effect of radiation is included in the present analysis. The results of the boiling heat transfer under the turbulent vapor show both the temperature and velocity present the non-linear distribution. Besides, under the free convection turbulent film boiling with higher Rayleigh values, the elliptical tube can get a better heat transfer efficiency than a circular tube. However, when Rayleigh values are low, the eccentricity of an elliptical tube seldom influences the heat transfer. Finally, a comparison between the results of the present study and those reported in a previous theoretical and experimental data is provided.