Nanofluid flow occurs in extensive applications, and hence has received widespread attention. The transition of nanofluids from laminar to turbulent flow is an important issue because of the differences in pressure drop and heat transfer between laminar and turbulent flow. Nanofluids will become unstable when they depart from the thermal equilibrium or dynamic equilibrium state. This paper conducts a brief review of research on the flow instability of nanofluids, including hydrodynamic instability and thermal instability. Some open questions on the subject are also identified.

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The Reynolds-averaged general dynamic equation (RAGDE) for the nanoparticle size distribution function is derived, including the contribution to particle coagulation resulting from the fluctuating concentration. The equation together with that of a turbulent gas flow is solved numerically in the turbulent flow of a ventilation chamber with a jet on the wall based on the proposed model relating the fluctuating coagulation to the gradient of mean concentration. Some results are compared with the experimental data. The results show that the proposed model relating the fluctuating coagulation to the gradient of mean concentration is reasonable, and it is necessary to consider the contribution to coagulation resulting from the fluctuating concentration in such a flow. The changes of the particle number concentration M0 and the geometric mean diameter dg are more obvious in the core area of the jet, but less obvious in other areas. With the increase in the initial particle number concentration m00, the values of M0 and the standard deviation of the particle size σ decrease, but the value of dg increases. The decrease in the initial particle diameter leads to the reduction of M0 and σ, and the increase in dg. With the increase in the Reynolds number, particles have few chances of collision, and hence the coagulation rate is reduced, leading to the increase in M0 and σ, and the decrease in dg.

The Reynolds averaged N-S equation and dynamic equation for nanoparticles are numerically solved in the two-phase flow around cylinders, and the distributions of the concentration M0 and geometric mean diameter dg of particles are given. Some of the results are validated by comparing with previous results. The effects of particle coagulation and breakage and the initial particle concentration m00 and size d0 on the particle distribution are analyzed. The results show that for the flow around a single cylinder, M0 is reduced along the flow direction. Placing a cylinder in a uniform flow will promote particle breakage. For the flow around multiple cylinders, the values of M0 behind the cylinders oscillate along the spanwise direction, and the wake region in the flow direction is shorter than that for the flow around a single cylinder. For the initial monodisperse particles, the values of dg increase along the flow direction and the effect of particle coagulation is larger than that of particle breakage. The values of dg fluctuate along the spanwise direction; the closer to the cylinders, the more frequent the fluctuations of dg values. For the initial polydisperse particles with d0 = 98 nm and geometric standard deviation σ = 1.65, the variations of dg values along the flow and spanwise directions show the same trend as for the initial monodisperse particles, although the differences are that the values of dg are almost the same for the cases with and without considering particle breakage, while the distribution of dg along the spanwise direction is flatter in the case with initial polydisperse particles.

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