## The most important results from 2001

**2012**

1. For the first time, an experimental and theoretical investigation of the formation of horizontal convective rolls over the non-uniformly heated surface of a close-ended rectangular cuvette in a wide range of Prandtl and Rayleigh numbers was carried out. It has been found that the structure of secondary flows is defined by the supercriticality level in the temperature boundary layer and the intensity of the main (advective) flow. The regimes with longitudinal and transverse rolls and a combination of these rolls are found to exist. The numerical analysis shows that heat transfer over the heated surface increases significantly due to the presence of secondary flows.

#### Summary

Direct numerical simulation and experimental investigation have been carried out to study the flow in a rectangular cuvette, whose bottom consists of two heat exchangers causing a temperature rise in the vicinity of their interface. In the cuvette, an advective flow occurs, and secondary flows in the form of longitudinal and transverse rolls develop.

The objective of the paper is to investigate the generation and evolution of secondary convective flows in the boundary layer and to evaluate their influence on heat transfer in this layer. Studies have been carried in a wide range of Prandtl (7 ≤ Pr ≤ 1020) and Rayleigh (300 ≤ Ra ≤ 2.8•10^7) numbers.

It has been found that the longitudinal convective rolls appear at some distance from the interface between the two heat exchangers, and the depth of the boundary layer increases as it moves away from the temperature rise. The vertical size of rolls increases mostly due to stretching of their upper parts. The increase in the temperature difference leads to reducing the roll height and increasing the roll rotation rate. A variety of regimes with transverse and longitudinal orientation of secondary convective rolls has been observed. Both the longitudinal and transverse rolls lead to remarkable heat transfer enhancement.

All the regimes which display longitudinal rolls lie in the phase diagram in the Ra-Re plane above the line Re ≈ 2•10–4Ra0.7. Transverse rolls appear in the flow under the conditions of the simultaneous existence of a large temperature drop and a weak large-scale flow (this is possible at large values of the Prandtl number only). The obtained results are of importance in estimating the influence of secondary flows on the heat transfer in boundary layers.

Sukhanovsky A., Frick P., Teimurasov A., Batalov V. Horizontal rolls in convective flow above a partially heated surface // Eur.Phys.J. B, 2012. V.85: 9.

**Prime investigator prof. Frick P.G.**

2. Direct simultaneous measurements of turbulent viscosity and turbulent diffusivity of the magnetic field in the turbulent flow of a conducting fluid at moderate magnetic Reynolds numbers have been made for the first time. Measurements were taken in the non-stationary turbulent flow of liquid sodium in a toroidal channel. The behavior of turbulent magnetic diffusivity is defined by the magnetic Reynolds number, Rm, defined in terms of the root-mean-square velocity pulsations. At Rm1, turbulent magnetic diffusivity is proportional to turbulent viscosity.

#### Summary

Laboratory measurements of two transport coefficients, i.e. the effective (turbulent) magnetic diffusivity and turbulent viscosity, were taken in the impulse turbulent flows of liquid sodium. One of the coefficients was obtained from integral conductivity measurements, and the other – from local velocity measurements. The flow in a rapidly rotating toroidal channel was generated by means of sharp braking. The kinematic viscosity was defined as a ratio of the root-mean-square turbulent pulsation energy density to energy dissipation rate. In order to determine these quantities, two components of the velocity vector of liquid sodium flow were measured using a two-axis conduction transducer. Variations in the inductance of the coil embracing the channel filled with liquid sodium were also measured. The laws of decaying mean flow energy, pulsation energy, anisotropy coefficient and turbulent viscosity were obtained. It is shown that the behavior of turbulent magnetic diffusivity depends significantly on the magnetic Reynolds number, Rm, defined in terms of the root-mean-square amplitude of velocity pulsations and the radius of the channel cross-section. At Rm<1, the turbulent magnetic diffusivity grows in proportion to the root-mean-square magnetic Reynolds number, and at Rm > 1 it becomes proportional to the turbulent viscosity.

Noskov V., Denisov S., Stepanov R., Frick P. Turbulent viscosity and turbulent magnetic diffusivity in decaying spin-down flow of liquid sodium // Physical Review E, 2012. V.85. 016303.

**Prime investigator prof. Frick P.G.**