Flow instability of nanofuilds in jet

Abstract

A linear hydrodynamic instability of nanofluids in a channel flow is investigated. The instability equations of nanofluids are derived and solved numerically. The validity of the numerical formulations and schemes is tested by comparing the present results with the available experimental data and theoretical results. The results show that the existence of particles suppresses the flow instability, but cannot completely eliminate it. As particle mass loading is increased, the region of unstable wavenumbers is reduced from that of the pure Newtonian flow and the largest growth rate that governs the flow instability is reduced. The Stokes number has an effect on the instability behavior of the nanofluids. As the Stokes number and Knudsen number decrease, the critical Reynolds numbers increase and the unstable regions of small perturbations decrease, along with a decrease in the largest growth rates that govern the flow instability, therefore reinforcing the flow stability. Larger particles reduce the peak value of the velocity disturbance and hence attenuate the flow instability.

Detailed measurements in a developed particle-laden horizontal channel flow (length 6 m, height 35 mm, the length is about 170 channel heights) are presented using phase-Doppler anemometry for simultaneous determination of air and particle velocity. The particles were spherical glass beads with mean diameters in the range of 60 µm–1 mm. The conveying velocity could be varied between about 10 m/s and 25 m/s, and the particle mass loading could reach values of about 2 (the mass loading is defined as the ratio of particle to gas phase mass flow rates), depending on particle size. For the first time, the degree of wall roughness could be modified by exchanging the wall plates. The influence of these parameters and the effect of inter-particle collisions on the profiles of particle mean and fluctuating velocities and the normalised concentration in the developed flow were examined. It was shown that wall roughness decreases the particle mean velocity and enhances fluctuating velocities due to irregular wall bouncing and an increase in wall collision frequency, i.e. reduction in mean free path. Thereby, the larger particles are mainly more uniformly distributed across the channel, and gravitational settling is reduced. Both components of the particle velocity fluctuation were reduced with increasing mass loading due to inter-particle collisions and the momentum loss involved. Moreover, the effect of the particles on the air flow and the turbulent fluctuations was studied on the basis of profiles in the developed flow and turbulence spectra determined for the streamwise velocity component. In addition to the effect of particle size and mass loading on turbulence modulation, the influence of wall roughness was analysed. It was clearly shown that increasing wall roughness also results in a stronger turbulence dissipation due to two-way coupling.

Heat transfer characteristics of mildly rarefied gaseous flows in the slip regime

Poiseuille number, the product of friction factor and Reynolds number (fRe) for quasi-fully-developed gas microchannel flow in the slip flow regime, was obtained numerically based on the arbitrary-Lagrangian-Eulerian method. Two-dimensional compressible momentum and energy equations were solved for a wide range of Reynolds and Mach numbers for constant wall temperatures that are lower or higher than the inlet temperature. The channel height ranges from 2 μm to 10 μm and the channel aspect ratio is 200. The stagnation pressure pstg is chosen such that the exit Mach number ranges from 0.1 to 1.0. The outlet pressure is fixed at atmospheric conditon. Mach and Knudsen numbers are systematically varied to determine their effects on fRe. The correlation for fRe for the slip flow is obtained from that of fRe of no-slip flow and incompressible theory as a function of Mach and Knudsen numbers. The results are in excellent agreement with the available experimental measurements. It was found that fRe is a function of Mach and Knudsen numbers and is different from the values by 96/(1+12Kn) obtained from the incompressible flow theory.

An analysis of particle concentrations formed in direct numerical simulations of forced three-dimensional (3-D) turbulence is described. Up to 48 million particles responding passively to the flow with response times ranging from 0.2 to 6 times the dissipation time of the fluid were evolved together until the concentration field reached a statistical stationary state. The Stokes number (St), defined at the dissipation time scale, was the sole parameter used to characterize the particle–fluid coupling in the regime where particles preferentially concentrate. Concentrations resulting from three simulations equilibrating at the Taylor microscale Reynolds numbers (Reλ) 40, 80, and 140 were studied. We present several new results for concentration measures utilized in previous studies as well as measures introduced in this paper. The measures are compared and contrasted on a finer St grid than presented in previous work and are analyzed as functions of Reλ and spatial binning scale. The measures are based on (a) deviations of the concentration PDF (probability density function) from the PDF of a uniform particle field, (b) the correlation dimension (D2) for both 3-D and two-dimensional concentrations, and (c) the relative St-dependent concentrations contained in a localized region of space. Measure (c) is motivated by the observation that the total and St-dependent concentrations are linearly correlated. The concentration measures reveal St dependencies that are insensitive to the Reynolds number of the flow with each measure having its own characteristic shape. The widths and maxima of St functions for measures explicitly constructed on a single spatial binning scale showed a very weak dependence on bin sizes ranging from 2 to 6 times the Kolmogorov length scale. We conclude that the measures studied in this paper reveal a universality that may persist to much higher Reynolds numbers.

Turbulent transition in impactor jets and its effects on impactor resolution

This paper aims to employ the Stokes number to mark aerodynamic penalties of airfoils caused by particles, which is crucial to implement their scaling experiments in a gas-solid flow. Each Stokes number is associated with a series of approximate aerodynamic penalties which are obtained at the same Reynolds number with different chord lengths. In the process, two phenomena which go against the mark are discussed and their mechanisms are revealed. The results show they occur at smaller and larger ranges of Stokes number, respectively. The effect of gravity is the leading cause and a larger chord length or diameter particle can strength its effect. The application scope of the mark, meanwhile, is ascertained. A chord length smaller than 1.5 m is advised at Re = 1.00 × 106 and those at other Reynolds numbers are also presented. As Stokes number decreases from 3, the aerodynamic penalty increases exponentially first at the advised chord length and reaches up to their peak values at the Stokes number of 0.050. In addition, the change of the aerodynamic penalty with Stokes number is dominated by the momentum exchange in the direction of gravity in the region between the particle injection plane and the airfoil.

Due to the existence of a velocity slip and temperature jump on the solid walls, the heat transfer in microchannels significantly differs from the one in the macroscale. In our research, we have focused on the pressure driven gas flows in a simple finite microchannel geometry, with an entrance and an outlet, for low Reynolds (Re<200) and low Knudsen (Kn<0.01) numbers. For such a regime, the slip induced phenomena are strongly connected with the viscous effects. As a result, heat transfer is also significantly altered. For the optimization of flow conditions, we have investigated various temperature gradient configurations, additionally changing Reynolds and Knudsen numbers. The entrance effects, slip flow, and temperature jump lead to complex relations between flow behavior and heat transfer. We have shown that slip effects are generally insignificant for flow behavior. However, two configuration setups (hot wall cold gas and cold wall hot gas) are affected by slip in distinguishably different ways. For the first one, which concerns turbomachinery, the mass flow rate can increase by about 1% in relation to the no-slip case, depending on the wall-gas temperature difference. Heat transfer is more significantly altered. The Nusselt number between slip and no-slip cases at the outlet of the microchannel is increased by about 10%.

Effect of Thermal Buoyancy on the Two-Dimensional Upward Flow and Heat Transfer Around a Square Cylinder

Particle-laden flows in a horizontal channel were investigated by means of a two-phase particle image velocimetry (PIV) technique. Experiments were performed at a Reynolds number of 6 826 and the flow is seeded with polythene beads of two sizes, 60 μm and 110 μm. One was slightly smaller than and the other was larger than the Kolmogorov length scale. The particle loadings were relatively low, with mass loading ratio ranging from 5×10−4 to 4×10−2 and volume fractions from 6×10−7 to 4.8×10−5, respectively. The results show that the presence of particles can dramatically modify the turbulence even under the lowest mass loading ratio of 5×10−4. The mean flow is attenuated and decreased with increasing particle size and mass loading. The turbulence intensities are enhanced in all the cases concerned. With the increase of the mass loading, the intensities vary in a complicated manner in the case of small particles, indicating complicated particle-turbulence interactions; whereas they increase monotonously in the case of large particles. The particle velocities and concentrations are also given. The particles lag behind the fluid in the center region but lead in the wall region, and this trend is more prominent for the large particles. The streamwise particle fluctuations are larger than the gas fluctuations for both sizes of particles, however their varying trend with the mass loadings is not so clear. The wall-normal fluctuations increase with increasing mass loadings. They are smaller in the 60 μm particle case but larger in the 110 μm particle case than those of the gas phase. It seems that the small particles follow the fluid motion to certain extent while the larger particles are more likely dominated by their own inertia. Finally, remarkable non-uniform distributions of particle concentration are observed, especially for the large particles. The inertia of particles is proved to be very important for the turbulence modification and particles behaviors and thus should be considered in horizontal channels.

Tsien summarized the similarity in hypersonic flows, and related Knudsen number to Mach number and Reynolds number. Recently, a path-based problem, aero-optical effect, arises in hypersonic flows, and it concerns about the compressibility and the Knudsen number of the gas flows, which differs from the Tsien’s focus to some extent. In this paper, the similarity of hypersonic aero optics is theoretically studied, and both flow fields and induced aero-optical effect after flows pass through a cylinder are predicted by a well-accepted particle-based method, direct simulation Monte-Carlo (DSMC) method. The results show that the optical distortions are inversely proportional to the Knudsen number, while the compressibility plays an important role in the optical degradations. Hence, it is confirmed that the effects of Mach number and Knudsen number on the aero-optical effect induced by hypersonic flows are of great significance. Besides, since the Knudsen number is defined straightforwardly based on the optically active region, the physics is clearer than any other similarity criteria.

In this paper, combined convective heat transfer and nanofluids flow characteristics in a vertical rectangular duct are numerically investigated. This investigation covers Rayleigh numbers in the range of 2 × 106 ≤ Ra ≤ 2 × 107 and Reynolds numbers in the range of 200 ≤ Re ≤ 1000. Pure water and five different types of nanofluids such as Ag, Au, CuO, diamond, and SiO2 with a volume fraction range of 0.5% ≤ φ ≤ 3% are used. The three‐dimensional steady, laminar flow, and heat transfer governing equations are solved using finite volume method (FVM). The effects of Rayleigh number, Reynolds number, nanofluids type, nanoparticle volume fraction of nano‐ fluids, and effect of radiation on the thermal and flow fields are examined. It is found that the heat transfer is enhanced using nanofluids by 47% when compared with water. The Nusselt number increases as the Reynolds number and Rayleigh number increase and aspect ratio decreases. A SiO2 nanofluid has the highest Nusselt number and highest wall shear stress while the Au nanofluid has the lowest Nusselt number and lowest wall shear stress. The results also revealed that the wall shear stress increases as Reynolds number increases, aspect ratio decreases, and nanoparticle volume fraction increases. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.20354

A numerical study of laminar convective heat transfer in microchannel with non-circular cross-section

This work aims to verify whether the continuum mechanics assumption holds for the numerical simulation of a typical sample delivery system in serial femtosecond crystallography (SFX). Knudsen numbers were calculated based on the numerical simulation results of helium flow through the gas-focused liquid sheet nozzle into the vacuum chamber, representing the upper limit of Knudsen number for such systems. The analysed flow is considered steady, compressible, and laminar. The numerical results are mesh-independent, with a Grid Convergence Index significantly lower than 1% for global and local analysis. This study is based on an improved definition of the numerical Knudsen number: a combination of the cell Knudsen number and the physical Knudsen number. In the analysis, no-slip boundary and low-pressure boundary slip conditions are compared. No significant differences are observed. This study justifies using computational fluid dynamics (CFD) analysis for SFX sample delivery systems based on the assumption of continuum mechanics.