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Studying transitions from laminar to turbulence of non-Newtonian fluids can provide a theoretical basis to further mediate their dynamic properties. Compared with Newtonian fluids, transitions of non-Newtonian fluids turning are less focused, thus being lack of good predictions of the critical Reynolds number (Re) corresponding to the first Hopf bifurcation. In this study, we employ the lattice Boltzmann method as the core solver to simulate two-dimensional lid-driven flows of a typical non-Newtonian fluid modeled by the power rheology law. Results show that the critical Re of shear-thinning (5496) and shear-thickening fluids (11546) are distinct from that of Newtonian fluids (7835). Moreover, when Re is slightly larger than the critical one, temporal variations of velocity components at the monitor point all show a periodic trend. Before transition of the flow filed, the velocity components show a horizontal straight line, and after transition , the velocity components fluctuate greatly and irregularly. Through fast Fourier transform for the velocity components, it is noted that the velocity has a dominant frequency and a harmonic frequency when Re is marginally larger than the critical one. Besides, the velocity is steady before transition of flow filed, so it appears as a point on the frequency spectrum. As the flow filed turns to be turbulent, the frequency spectrum of the velocity component appears multispectral. Different from a single point in the velocity phase diagram before transition, the velocity phase diagram after transition forms a smooth and closed curve, whose area is also increasing as Re increases. The center point of the curve moves along a certain direction, while movement directions of different center points are different. Proper orthogonal decompositions for the velocity and vorticity field reveal that the first two modes, in all types of fluids, are the dominant modes when Re is close to the critical one, with energy, occupying more than 95% the whole energy. In addition, for one type of fluid, the dominant modes at different Re values have similar structures. Results of the first and second modes of velocity field show that the modal peak is mainly distributed in vicinity of the cavity wall.

The freezing of water droplet is a ubiquitous phenomenon in nature. Although the freezing process of water droplet impacting on cold surfaces is widely observed on a macroscopic scale, the study of freezing process on a micro-scale is still deficient, and it is definitely difficult to study micro-droplets and nano-droplets using experimental methods due to the obstacles in both generation and observation. For these reasons, simulation methods using molecular dynamics (MD) have been proposed to study micro-droplets and nano-droplets, as molecular dynamics can trace each atom, count up the collective behavior of a group of atoms and describe the detail interaction between atoms. In this paper, a three-dimensional model is established by molecular dynamics simulation to study the freezing process of water droplets impinging on a cold solid surface on a nanoscale. We select the micro-canonical ensemble (NVE) as a statistical system and the TIP4P/ice model as a potential energy function to simulate oxygen atoms, hydrogen atoms and water molecules. The LJ/126 model is used to simulate the interaction between water molecules and solid atoms. Different wettability walls are simulated by adjusting the potential energy parameters. For all the simulations, the velocity-rescale method is used to keep the temperature constant and the Verlet algorithm is adopted to solve the Newton equations. In the velocity-rescale method, the temperature is calculated by using the profile-unbiased thermostat. The freezing process inside the water droplet is determined by the temperature distribution of water molecules along the vertical direction, which is more concise than by the location coordinates of the microscopic atoms. Through the numerical experimentations, we find that when the surface temperature decreases, the completely freezing time of drops is reduced; meanwhile, the time required for water temperature to drop down to the wall temperature is increased. Moreover, the heat transfer inside the water droplet slows down with the decreasing of wall hydrophilicity while the total freezing time is prolonged.

When ultrasound propagates in a liquid alloy, nonlinear effect takes place such as cavitation effect and acoustic streaming, which accelerates the solute and thermal transportation during alloy solidification, and consequently, improves the solidification microstructures and mechanical properties of the metallic alloy. Therefore, it is significant to investigate the ultrasound propagation characteristics in liquid. Here, by choosing water as a model transparent material, the acoustic fields and flow fields induced by 20 and 490 kHz ultrasounds are investigated by numerical simulation, and the effects of frequency and ultrasonic horn radius are studied. Firstly, the simulation results demonstrate that the sound pressure under 20 kHz ultrasound decreases obviously along the ultrasonic propagation direction, and the maximum of sound pressure value is equal to the initial pressure. In this case, the cavitation effect only occurs in the region close to the ultrasonic horn. By contrast, when the ultrasonic frequency increases to 490 kHz, the sound pressure is higher than that of 20 kHz ultrasound, and displays periodical vibration characteristic along the wave propagation direction. The cavitation volume correspondingly expands to a large extent with a regular striped distribution. It can also be found that increasing the ultrasonic horn radius under 20 and 490 kHz ultrasounds can effectively promote the sound pressure level in water, and hence leads to the remarkable enlargement of cavitation volume. Secondly, the calculated results of flow field indicate that the streamlines in water are similar under the two ultrasounds with different frequencies. A jet produced by the center of horn spreads down and divergences to both sides after reaching the bottom. For both frequencies as the horn radius increases, the radius of jet increases and the average velocity in water first increases and then decreases, whose maximum value appears when the horn radius is 40 mm. Meanwhile, the average velocity under 20 kHz ultrasound is larger than that under 490 kHz ultrasound for each horn radius. Finally, particle image velocimetry method is employed to measure the velocity field in water. Both the positions of eddy and the velocity distribution are the same as the simulation results, which verifies the reliability of the present theoretical calculation model. The scenario in this work is analogous to the acoustic field and the flow field in liquid alloy, which is beneficial for the design of parameter optimization during ultrasonic processing in alloy solidification.

Exploring the freezing process and its potential mechanism of the droplets impacting on a solid surface is desperately desired, owing to its anti-icing applications in aircraft, cable, radar, etc. On the controllable low temperature test equipment, the freezing dynamic behaviors of droplets impacting on three cold plates, made of copper, aluminum and silicon, are recorded by a high-speed camera in this paper, and characterized by the droplet spreading diameter, oscillation and freezing time. Here, the freezing behavior of droplets is predicated by observing the color change of the droplet. Through the experimental exploration and theoretical analysis, we reveal the effects of the impacting speed, surface temperature and thermal conductivity of material on the freezing dynamics of the droplet. We demonstrate that a cold surface shrinks the maximum spreading diameter of droplet compared with the surface at ambient temperature; the lower the surface temperature, the shorter the freezing time would be and the smaller the maximum spreading diameter would be; the maximum spreading diameter increases with increasing Weber number, whereas the oscillation and freezing time decrease. Meanwhile, the higher the material thermal conductivity, the shorter the freezing time would be, and the bigger the rising slope of the maximum spreading diameter with increasing Weber number will be. A function to predict the freezing time is derived from thermodynamic condition. The calculated values are in good agreement with the experimental data, with the maximum relative error of less than 5.3%.

Superhydrophobic surfaces with micro- and nano-scale structures are conducible to maintaining a gas layer where prominent slippage effect exists. It has been demonstrated that the drag reduction of superhydrophobic surface increases with growing the fraction of the gas-water interface and the rising of the thickness of gas layer. Whereas a large thick gas layer on the superhydrophobic surface collapses easily under tangential water flow. Here, we present a new method to maintain large-scale gas layer by creating hydrophilic patterns at the superhydrophobic surface, on which the binding force of air on the solid surface can be caused by wettability difference. Through testing the states of gas layer trapped on surfaces with wettability differences equal to 54.8, 84.7, 103.6 and 144.0 in apparent contact angle, respectively, the conditions of maintaining gas layer are mainly considered. We demonstrate that the critical velocity, over which the gas layer begins to collapse under the tangential water flow, is positively correlated with the thickness of the gas layer and the wettability difference between the superhydrophobic area and hydrophilic area, however, this is negatively correlated with the width of the gas layer in the crosswise direction. It is noteworthy that even a centimeter-scale gas layer can be kept steady in ～0.9 m/s through this method. Furthermore, an obvious slip velocity up to ～25% of bulk velocity is observed at the gas-water interface, through measuring the velocity profile above the 0.6 cm-long, 0.5 cm-wide and 0.15 cm-thick gas layer by using the PIV technology. We anticipate that this novel method of gas entrapment under water will effectively widen the applications of superhydrophobic surfaces for drag reduction.

This article studies drag reduction rule and gas restoration and retention of hydrophobic surfaces numerically when taking into consideration the surface tension effect, the microstructure here is chessboard-like and the Reynolds number varies from 3,000 to 30,000. Results show that gas restoration and retention keep well, and a maximum drag reduction rate of approximately 30% has been gained at small Reynolds number(Re

According to the characteristics of coherent structures in near-wall turbulence, an accurate extraction and verification method is developed based on wavelet transform (WT) and correlation analysis in this paper. At first, the fluid field of a turbulent boundary layer is measured precisely in a gravitational low-speed water tunnel. On the basis of the distribution of the coherent structures, velocity data of three test points are selected and analyzed, whose dimensionless heights are 20.8, 33.5, and 42.6. According to the frequency range of power spectrum density (PSD), coherent and incoherent structures are both extracted from the original signals using continuous and orthogonal wavelet transforms. To confirm the validity of the extracted signals, the probability density function (PDF) of each extracted signal is calculated. The result demonstrates that the incoherent structures obey the Gaussian distribution, while the coherent structures deviate from the Gaussian distribution. The PDFs of the coherent structures and the original signals are similar, which shows that the coherent structures make most contributions to the turbulence. For further verification, a correlation parameter between coherent and incoherent structures is defined, which evidently proves the validity of the extraction method in this paper.