In this paper, we propose a novel optical flow formulation for estimating two-dimensional velocity fields from an image sequence depicting the evolution of a passive scalar transported by a fluid flow. This motion estimator relies on a stochastic representation of the flow allowing to incorporate naturally a notion of uncertainty in the flow measurement. In this context, the Eulerian fluid flow velocity field is decomposed into two components: a large-scale motion field and a small-scale uncertainty component. We define the small-scale component as a random field. Subsequently, the data term of the optical flow formulation is based on a stochastic transport equation, derived from the formalism under location uncertainty proposed in Mémin (Geophys Astrophys Fluid Dyn 108(2):119–146, 2014) and Resseguier et al. (Geophys Astrophys Fluid Dyn 111(3):149–176, 2017a). In addition, a specific regularization term built from the assumption of constant kinetic energy involves the very same diffusion tensor as the one appearing in the data transport term. Opposite to the classical motion estimators, this enables us to devise an optical flow method dedicated to fluid flows in which the regularization parameter has now a clear physical interpretation and can be easily estimated. Experimental evaluations are presented on both synthetic and real world image sequences. Results and comparisons indicate very good performance of the proposed formulation for turbulent flow motion estimation.;In this paper, we propose a novel optical flow formulation for estimating two-dimensional velocity fields from an image sequence depicting the evolution of a passive scalar transported by a fluid flow. This motion estimator relies on a stochastic representation of the flow allowing to incorporate naturally a notion of uncertainty in the flow measurement. In this context, the Eulerian fluid flow velocity field is decomposed into two components: a large-scale motion field and a small-scale uncertainty component. We define the small-scale component as a random field. Subsequently, the data term of the optical flow formulation is based on a stochastic transport equation, derived from the formalism under location uncertainty proposed in Mémin (Geophys Astrophys Fluid Dyn 108(2):119–146, 2014) and Resseguier et al. (Geophys Astrophys Fluid Dyn 111(3):149–176, 2017a). In addition, a specific regularization term built from the assumption of constant kinetic energy involves the very same diffusion tensor as the one appearing in the data transport term. Opposite to the classical motion estimators, this enables us to devise an optical flow method dedicated to fluid flows in which the regularization parameter has now a clear physical interpretation and can be easily estimated. Experimental evaluations are presented on both synthetic and real world image sequences. Results and comparisons indicate very good performance of the proposed formulation for turbulent flow motion estimation.

The problem of simulation of heat and mass transfer in the gas phase of film devices in the regime of weak and strong phase interaction has been solved. The Deissler three-layer model of turbulent boundary layer was used. Expressions have been derived for calculating the average Nusselt and Sherwood numbers. Examples of calculations for various conditions of phase interaction and comparison with experimental data are shown.;The problem of simulation of heat and mass transfer in the gas phase of film devices in the regime of weak and strong phase interaction has been solved. The Deissler three-layer model of turbulent boundary layer was used. Expressions have been derived for calculating the average Nusselt and Sherwood numbers. Examples of calculations for various conditions of phase interaction and comparison with experimental data are shown.;The problem of simulation of heat and mass transfer in the gas phase of film devices in the regime of weak and strong phase interaction has been solved. The Deissler three-layer model of turbulent boundary layer was used. Expressions have been derived for calculating the average Nusselt and Sherwood numbers. Examples of calculations for various conditions of phase interaction and comparison with experimental data are shown.

The paper describes a problem of accumulation of irradiated graphite due to operation of uranium-graphite nuclear reactors. The main noncarbon contaminants that contribute to the overall activity of graphite elements are iso-topes 137Cs, 60Co, 90Sr, 36Cl, and 3H. A method was developed for processing of irradiated graphite ensuring the volu-metric decontamination of samples. The calculation results are presented for equilibrium composition of plasma-chemical reactions in systems “irradiated graphite?argon” and “irradiated graphite?helium” for a wide range of tem-peratures. The paper describes a developed mathematical model for the process of purification of a porous graphite surface treated by equilibrium low-temperature plasma. The simulation results are presented for the rate of sublimation of radioactive contaminants as a function of plasma temperature and plasma flow velocity when different plasma-forming gases are used. The extraction coefficient for the contaminant 137Cs from the outer side of graphite pores was calculated. The calculations demonstrated the advantages of using a lighter plasma forming gas, i.e., helium.;The paper describes a problem of accumulation of irradiated graphite due to operation of uranium-graphite nuclear reactors. The main noncarbon contaminants that contribute to the overall activity of graphite elements are iso-topes 137Cs, 60Co, 90Sr, 36Cl, and 3H. A method was developed for processing of irradiated graphite ensuring the volu-metric decontamination of samples. The calculation results are presented for equilibrium composition of plasma-chemical reactions in systems “irradiated graphite?argon” and “irradiated graphite?helium” for a wide range of tem-peratures. The paper describes a developed mathematical model for the process of purification of a porous graphite surface treated by equilibrium low-temperature plasma. The simulation results are presented for the rate of sublimation of radioactive contaminants as a function of plasma temperature and plasma flow velocity when different plasma-forming gases are used. The extraction coefficient for the contaminant 137Cs from the outer side of graphite pores was calculated. The calculations demonstrated the advantages of using a lighter plasma forming gas, i.e., helium.;The paper describes a problem of accumulation of irradiated graphite due to operation of uranium-graphite nuclear reactors. The main noncarbon contaminants that contribute to the overall activity of graphite elements are iso-topes 137Cs, 60Co, 90Sr, 36Cl, and 3H. A method was developed for processing of irradiated graphite ensuring the volu-metric decontamination of samples. The calculation results are presented for equilibrium composition of plasma-chemical reactions in systems “irradiated graphite?argon” and “irradiated graphite?helium” for a wide range of tem-peratures. The paper describes a developed mathematical model for the process of purification of a porous graphite surface treated by equilibrium low-temperature plasma. The simulation results are presented for the rate of sublimation of radioactive contaminants as a function of plasma temperature and plasma flow velocity when different plasma-forming gases are used. The extraction coefficient for the contaminant 137Cs from the outer side of graphite pores was calculated. The calculations demonstrated the advantages of using a lighter plasma forming gas, i.e., helium.

EXPERIMENTS IN FLUIDS
ISSN：0723-4864 volume：59 Issue：1 page：1-19
Burns, Ross A
;
Cadell, Seth R
;
Woods, Brian G
;
Bardet, Philippe M
;
André, Matthieu A

A molecular tagging velocity (MTV) technique is developed to non-intrusively measure velocity in an integral effect test (IET) facility simulating a high-temperature helium-cooled nuclear reactor in accident scenarios. In these scenarios, the velocities are expected to be low, on the order of 1 m/s or less, which forces special requirements on the MTV tracer selection. Nitrous oxide $$({\rm N}_2{\rm O})$$ ( N 2 O ) is identified as a suitable seed gas to generate NO tracers capable of probing the flow over a large range of pressure, temperature, and flow velocity. The performance of $${\rm N}_2{\rm O}$$ N 2 O -MTV is assessed in the laboratory at temperature and pressure ranging from 295 to 781 K and 1 to 3 atm. MTV signal improves with a temperature increase, but decreases with a pressure increase. Velocity precision down to 0.004 m/s is achieved with a probe time of 40 ms at ambient pressure and temperature. Measurement precision is limited by tracer diffusion, and absorption of the tag laser beam by the seed gas. Processing by cross-correlation of single-shot images with high signal-to-noise ratio reference images improves the precision by about 10% compared to traditional single-shot image correlations. The instrument is then deployed to the IET facility. Challenges associated with heat, vibrations, safety, beam delivery, and imaging are addressed in order to successfully operate this sensitive instrument in-situ. Data are presented for an isothermal depressurized conduction cooldown. Velocity profiles from MTV reveal a complex flow transient driven by buoyancy, diffusion, and instability taking place over short $$(<1\, {\rm s})$$ ( < 1 s ) and long ( $$>30$$ > 30 min) time scales at sub-meter per second speed. The precision of the in-situ results is estimated at 0.027, 0.0095, and 0.006 m/s for a probe time of 5, 15, and 35 ms, respectively.

Flow characteristics of a liquid film flowing over a smooth surface and structured surface with the Reynolds number range from 10 to 1121 are studied. The mixture of R21 and R114 refrigerants is used as the test liquid. The 3D transient simulations are taken to capture the liquid film’s dynamic characteristics and spatial distribution. Effects of the inlet dimension, inlet flow rates, surface tension, and surface structuring on the wettability, average velocity, and film thickness are studied systematically. The obtained results show that surface tension is essential for an accurate simulation, while inlet width has no effect on the liquid film parameters in the steady-state flow regime. For low flow rates, wetting area and film thickness both are small, and a suggested range of Reynolds number is chosen to simulate further heat transfer in order to balance the film thickness and dry spots generation. It is shown that a ripple surface structure hinders the liquid film movement, reflected in a lower velocity and a larger film thickness compared to the smooth surface. Lateral movement of a liquid film can also be observed at the structured surface.;Flow characteristics of a liquid film flowing over a smooth surface and structured surface with the Reynolds number range from 10 to 1121 are studied. The mixture of R21 and R114 refrigerants is used as the test liquid. The 3D transient simulations are taken to capture the liquid film’s dynamic characteristics and spatial distribution. Effects of the inlet dimension, inlet flow rates, surface tension, and surface structuring on the wettability, average velocity, and film thickness are studied systematically. The obtained results show that surface tension is essential for an accurate simulation, while inlet width has no effect on the liquid film parameters in the steady-state flow regime. For low flow rates, wetting area and film thickness both are small, and a suggested range of Reynolds number is chosen to simulate further heat transfer in order to balance the film thickness and dry spots generation. It is shown that a ripple surface structure hinders the liquid film movement, reflected in a lower velocity and a larger film thickness compared to the smooth surface. Lateral movement of a liquid film can also be observed at the structured surface.;Flow characteristics of a liquid film flowing over a smooth surface and structured surface with the Reynolds number range from 10 to 1121 are studied. The mixture of R21 and R114 refrigerants is used as the test liquid. The 3D transient simulations are taken to capture the liquid film’s dynamic characteristics and spatial distribution. Effects of the inlet dimension, inlet flow rates, surface tension, and surface structuring on the wettability, average velocity, and film thickness are studied systematically. The obtained results show that surface tension is essential for an accurate simulation, while inlet width has no effect on the liquid film parameters in the steady-state flow regime. For low flow rates, wetting area and film thickness both are small, and a suggested range of Reynolds number is chosen to simulate further heat transfer in order to balance the film thickness and dry spots generation. It is shown that a ripple surface structure hinders the liquid film movement, reflected in a lower velocity and a larger film thickness compared to the smooth surface. Lateral movement of a liquid film can also be observed at the structured surface.

Thermophysics and Aeromechanics
ISSN：0869-8643 volume：25 Issue：1 page：21-30
Minakov, A V
;
Platonov, D V
;
Abramov, A V
;
Maslennikova, A V
;
Dekterev, D A

In the present study, we report on the results of an experimental study of pressure pulsations in the flow duct of a medium-scale hydrodynamic bench with Francis turbine. In various regimes, integral and pulsation characteristics of the turbine were measured. With the help of high-speed filming, the structure of the flow behind the turbine runner was analyzed, and the influence of this structure on the intensity and frequency of pressure pulsations in the flow duct was demonstrated.;In the present study, we report on the results of an experimental study of pressure pulsations in the flow duct of a medium-scale hydrodynamic bench with Francis turbine. In various regimes, integral and pulsation characteristics of the turbine were measured. With the help of high-speed filming, the structure of the flow behind the turbine runner was analyzed, and the influence of this structure on the intensity and frequency of pressure pulsations in the flow duct was demonstrated.;In the present study, we report on the results of an experimental study of pressure pulsations in the flow duct of a medium-scale hydrodynamic bench with Francis turbine. In various regimes, integral and pulsation characteristics of the turbine were measured. With the help of high-speed filming, the structure of the flow behind the turbine runner was analyzed, and the influence of this structure on the intensity and frequency of pressure pulsations in the flow duct was demonstrated.

A tailor-made convective heat transfer test facility is constructed to study the single-phase convective heat transfer of deionized water and 30 vol% and 60 vol% aqua–ethylene glycol in a stainless steel tube of 4 mm in inner diameter and 1 m in length. The heat flux is varied between 1 and 4 kW·m?2 and for mass flux ranging from 160 to 475 kg·m?2 s?1. The experiments were predominantly conducted only for laminar flow regime. Finally, the heat transfer coefficient is recorded and compared with the conventional theories. It is observed that the presence of ethylene glycol in water decreases the heat transfer coefficient by more than 50%, due to the decreased Reynolds number and thermal conductivity of the mixture.;A tailor-made convective heat transfer test facility is constructed to study the single-phase convective heat transfer of deionized water and 30 vol% and 60 vol% aqua–ethylene glycol in a stainless steel tube of 4 mm in inner diameter and 1 m in length. The heat flux is varied between 1 and 4 kW·m?2 and for mass flux ranging from 160 to 475 kg·m?2 s?1. The experiments were predominantly conducted only for laminar flow regime. Finally, the heat transfer coefficient is recorded and compared with the conventional theories. It is observed that the presence of ethylene glycol in water decreases the heat transfer coefficient by more than 50%, due to the decreased Reynolds number and thermal conductivity of the mixture.;A tailor-made convective heat transfer test facility is constructed to study the single-phase convective heat transfer of deionized water and 30 vol% and 60 vol% aqua–ethylene glycol in a stainless steel tube of 4 mm in inner diameter and 1 m in length. The heat flux is varied between 1 and 4 kW·m?2 and for mass flux ranging from 160 to 475 kg·m?2 s?1. The experiments were predominantly conducted only for laminar flow regime. Finally, the heat transfer coefficient is recorded and compared with the conventional theories. It is observed that the presence of ethylene glycol in water decreases the heat transfer coefficient by more than 50%, due to the decreased Reynolds number and thermal conductivity of the mixture.

The expedience of using the ratio of inertial β and viscous α hydraulic coefficients of a fluid flow in porous structures as the characteristic linear scale, when generalizing the experimental data on internal heat transfer in porous media, is shown. It is demonstrated that the correlation Nu = A · Pe, with both criteria based on β/α ratio, most efficiently describes the experimental data for a wide set of ordered and disordered porous structures, including sintered spheres, network materials, sintered felt and cellular foams of high porosity. The coefficient A depends on porosity and is equal to 0.004 for spheres, networks and felts, and 0.0004 for foams. For any specific case the values of α and β coefficients can be readily obtained from testing materials under consideration, control samples, or full-scale articles.;The expedience of using the ratio of inertial β and viscous α hydraulic coefficients of a fluid flow in porous structures as the characteristic linear scale, when generalizing the experimental data on internal heat transfer in porous media, is shown. It is demonstrated that the correlation Nu = A · Pe, with both criteria based on β/α ratio, most efficiently describes the experimental data for a wide set of ordered and disordered porous structures, including sintered spheres, network materials, sintered felt and cellular foams of high porosity. The coefficient A depends on porosity and is equal to 0.004 for spheres, networks and felts, and 0.0004 for foams. For any specific case the values of α and β coefficients can be readily obtained from testing materials under consideration, control samples, or full-scale articles.;The expedience of using the ratio of inertial β and viscous α hydraulic coefficients of a fluid flow in porous structures as the characteristic linear scale, when generalizing the experimental data on internal heat transfer in porous media, is shown. It is demonstrated that the correlation Nu = A · Pe, with both criteria based on β/α ratio, most efficiently describes the experimental data for a wide set of ordered and disordered porous structures, including sintered spheres, network materials, sintered felt and cellular foams of high porosity. The coefficient A depends on porosity and is equal to 0.004 for spheres, networks and felts, and 0.0004 for foams. For any specific case the values of α and β coefficients can be readily obtained from testing materials under consideration, control samples, or full-scale articles.

We visualized experimentally the internal flow inside inkjet droplets of polystyrene–anisole solution during solid film formation on substrates at room temperature. The effects of contact angle and evaporation rate on the internal flow and film morphology were quantitatively investigated. The transport process during film formation was examined by measuring the relationship between internal flow and film morphology, which provided three remarkable findings. First, self-pinning and the strength of outward flow on the free surface under 2.3?Pa?s determined film morphology. The solute distribution, corresponding to rim areas in ring-like films and a convex trough in dot-like films, had already developed at self-pinning. Second, the mass fraction at self-pinning close to the contact line converged to one, regardless of the film morphology. This implies that self-pinning is independent of parameters such as the contact angle and evaporation rate. Third, at room temperature, the solutal Marangoni numbers were 20–30 times larger than the thermal ones. Thus, the outward flow on the free surface caused by the solutal Marangoni effect dominates in droplets before self-pinning. The solutal Marangoni number at self-pinning and thickness variation at the center of the film displayed a good relationship for droplets with different contact angles and evaporation rates. This suggests that film morphology can be technically controlled by solutal Marangoni number at room temperature.;We visualized experimentally the internal flow inside inkjet droplets of polystyrene–anisole solution during solid film formation on substrates at room temperature. The effects of contact angle and evaporation rate on the internal flow and film morphology were quantitatively investigated. The transport process during film formation was examined by measuring the relationship between internal flow and film morphology, which provided three remarkable findings. First, self-pinning and the strength of outward flow on the free surface under 2.3?Pa?s determined film morphology. The solute distribution, corresponding to rim areas in ring-like films and a convex trough in dot-like films, had already developed at self-pinning. Second, the mass fraction at self-pinning close to the contact line converged to one, regardless of the film morphology. This implies that self-pinning is independent of parameters such as the contact angle and evaporation rate. Third, at room temperature, the solutal Marangoni numbers were 20–30 times larger than the thermal ones. Thus, the outward flow on the free surface caused by the solutal Marangoni effect dominates in droplets before self-pinning. The solutal Marangoni number at self-pinning and thickness variation at the center of the film displayed a good relationship for droplets with different contact angles and evaporation rates. This suggests that film morphology can be technically controlled by solutal Marangoni number at room temperature.

Submerged jets propagating under stable hydrate conditions and flow environment are considered. An integral Lagrangian control volume method is developed for calculating the jet parameters: the trajectory, radius, temperature, density, and volumetric content of jet components. The impact of two extreme schemes of hydrate formation on the jet parameters is identified. The impact of the initial value of the gas flow rate on the jet temperature is investigated.;Submerged jets propagating under stable hydrate conditions and flow environment are considered. An integral Lagrangian control volume method is developed for calculating the jet parameters: the trajectory, radius, temperature, density, and volumetric content of jet components. The impact of two extreme schemes of hydrate formation on the jet parameters is identified. The impact of the initial value of the gas flow rate on the jet temperature is investigated.;Submerged jets propagating under stable hydrate conditions and flow environment are considered. An integral Lagrangian control volume method is developed for calculating the jet parameters: the trajectory, radius, temperature, density, and volumetric content of jet components. The impact of two extreme schemes of hydrate formation on the jet parameters is identified. The impact of the initial value of the gas flow rate on the jet temperature is investigated.