Turbulence modulation model for gas–particle flow based on probability density function approach

he paper focuses on the turbulence modulation problem in gas–particle flow with the use of probability density function（PDF） approach. By means of the PDF method, a general statistical moment turbulence modulation model without considering the trajectory difference between two phases is derived from the Navier–Stokes equations. A new turbulence production term induced by the dispersed-phase is analyzed and considered. Furthermore, the trajectory difference between two media is taken into account. Subsequently, a new k–ε turbulence modulation model in dilute particle-laden flow is successfully set up. Then, the changes to several terms, including the turbulence production, dissipation, and diffusion terms, are well described consequently. The promoted model provides a more probable explanation for the modification of particles on the turbulence. Finally, we applied the model to simulate a gas–particle turbulence flow case in a wall jet, and found that the simulation results agree well with the experimental data.

SECOND-ORDER MOMENT TWO-PHASE TURBULENCE MODEL ACCOUNTING FOR TURBULENCE MODULATION IN SWIRLING SUDDEN-EXPANSION CHAMBER

A semi-empirical turbulence enhancement model accounting for the particle-wake effect was incorporated into the second-order moment two-phase turbulence model and employed to simulate gas-particle flows in a swirling sudden-expansion chamber. The simulated results for two-phases mean velocities and fluctuation velocities coincide well with the experiment ones, which demonstrates that this model, in comparison with the turbulence model not accounting for the wake effect, leads to higher calculating accuracy.

CFD-DEM simulation of turbulence modulation in horizontal pneumatic conveying

A study is presented to evaluate the capabilities of the standard k–ε turbulence model and the k–ε turbulence model with added source terms in predicting the experimentally measured turbulence modulation due to the presence of particles in horizontal pneumatic conveying, in the context of a CFD–DEM Eulerian–Lagrangian simulation. Experiments were performed using a 6.5-m long, 0.075-m diameter horizontal pipe in conjunction with a laser Doppler anemometry （LDA） system. Spherical glass beads with two sizes, 1.5 and 2 mm, were used. Simulations were performed using the commercial discrete element method software EDEM, coupled with the computational fluid dynamics package FLUENT. Hybrid source terms were added to the conventional k–ε turbulence model to take into account the influence of the dispersed phase on the carrier phase turbulence intensity. The simulation results showed that the turbulence modulation depends strongly on the model parameter Cε3. Both the standard k–ε turbulence model and the k–ε turbulence model with the hybrid source terms could predict the gas phase turbulence intensity trend only generally. A noticeable discrepancy in all cases between simulation and experimental results was observed, particularly for the regions close to the pipe wall. It was also observed that in some cases the addition of the source terms to the k–ε turbulence model did not improve the simulation results when compared with those of the standard k–ε turbulence model. Nonetheless, in the lower part of the pipe where particle loading was greater due to gravitational effects, the model with added source terms performed somewhat better.

Investigation of turbulence and skin friction modification in particle-laden channel flow using lattice Boltzmann method

Interaction between turbulence and particles is investigated in a channel flow. The fluid motion is calculated using direct numerical simulation(DNS) with a lattice Boltzmann(LB) method, and particles are tracked in a Lagrangian framework through the action of force imposed by the fluid. The particle diameter is smaller than the Kolmogorov length scale, and the point force is used to represent the feedback force of particles on the turbulence. The effects of particles on the turbulence and skin friction coefficient are examined with different particle inertias and mass loadings. Inertial particles suppress intensities of the spanwise and wall-normal components of velocity, and the Reynolds shear stress. It is also found that, relative to the reference particle-free flow,the overall mean skin-friction coefficient is reduced by particles. Changes of near wall turbulent structures such as longer and more regular streamwise low-speed streaks and less ejections and sweeps are the manifestation of drag reduction.

Particles-induced turbulence: A critical review of physical concepts,numerical modelings and experimental investigations

The presence of solid particles or water droplets in continuous fluid flow can either induce turbulence attenuation or amplification. The modification of the state of the turbulence depends on the characteristics of the particles, such as volume fraction, mean diameter, mass density, or carrier phase flow properties. In this brief review, the main physical concepts related to the most important physical aspects of turbulence modulation are summarized. Different criteria used to distinguish the enhancement or the attenuation effects of the particles on the carrier phase flows are recalled. For the interest of large-scale industrial applications, several theoretical,experimental and empirical approaches are discussed, which provides an interesting framework for the study of the effect of particles on turbulence behavior modification.

Turbulent Modulation in Particulate Flow: A Review of Critical Variables

A review of the main mechanisms influencing turbulent modulation in the presence of spherical and non-spherical particles is presented. The review demonstrates the need for more numerical and experimental work with higher accuracy than obtained so far and the need to resolve the flow near the surface of particles with the aim to re-evaluate the quantitative effect of different parameters on turbulent modulation. The review reveals that non-spherical particles have more adverse effect on turbulence as compared to spherical ones, for the same ambient conditions.

Vector properties of a tunable random electromagnetic beam in non-Kolmogrov turbulence

Analytical formulas for a class of tunable random electromagnetic beams propagating in a turbulent atmosphere through a complex optical system are derived with the help of a tensor method. One finds that the far field intensity distribution is tunable by modulating the source correlation structure function. The on-axis spectral degree of polarization monotonically increases to the same value for different values of order M in free space while it returns to the initial value after propagating a sufficient distance in turbulence. Furthermore, it is revealed that the state of polarization is closely determined by the initial correlation structure rather than by the turbulence parameters.

An experimental study on the velocity fluctuations generated by the flow past fixed spheres

We perform a series of experiments to study the velocity fluctuations generated by the flow past fixed spheres.Planar particle image velocimetry(PIV)is carried out to characterize the properties of the liquid fluctuation.The fluctuation induced by the spheres can be decomposed into the temporal fluctuation and the spatial fluctuation,which represent the contribution of flow instability and spatial inhomogeneity,respectively.In particularly,we focus on the contributions of temporal fluctuations and spatial fluctuations between low and high Reynolds number.At low Reynolds number(20<Re≤200),the total fluctuation mostly comes from the spatial fluctuation and increases as the area of velocity deficit in the wake of the sphere increases.The temporal fluctuation cannot be neglected at larger Reynolds number(200<Re≤700),and the total velocity fluctuation is induced by both flow instability and spatial inhomogeneity.Furthermore,the energy distribution in the flow direction and the span direction also changes drastically as the Reynolds number increases.The wavenumber spectra of fluctuations show a−3 slope at large scale,−5/3 slope at small scale.The starting scale of the−3 slope decreases with the increase of the Reynolds number.Specifically,it is consistent with the integral length scaleΛfor Re>200,but not for Re<200.The ending scale is aroundλ=0.5d and decreases slightly as Re increases.