Early Drag Crisis Research Articles

Calculation of Interphase Mass Transfer in a Spray Flow Produced by a Nozzle with Account of Crisis

This paper describes the numerical model and the results of calculating the interphase mass transfer in a two-phase flow generated by atomizing a liquid in a gas using a nozzle. The proposed mathematical model is based on differential equations of unsteady flow in a compressible medium, complemented by the equation of mass transfer from gas to droplets. The popular explicit Lax–Wendroff scheme is used for transition to difference analogs of continuity and phase motion equations. Axial profiles of droplet and gas velocities and gas impurity concentrations in a free spray cone are calculated and presented together with radial profiles of impurity concentrations in a two-phase flow through a cylindrical apparatus, taking into account early drag crisis of droplets and crisis of interphase mass transfer, as well as the features of turbulent friction in gas, discovered in previous experiments. The calculation established the dependencies of the gas flow rate, the concentration of gas impurities at the outlet of the apparatus, and the amount of impurities absorbed by the liquid from the height and cross-sectional area of the apparatus.

Расчет межфазного массообмена в факеле распыла форсунки с учетом кризиса

A numerical model and the results of calculation of the interfacial mass transfer in a two-phase flow formed by spraying a liquid in a gas with a nozzle are described. The basis of the proposed mathematical model is the differential equations of the nonstationary flow of a compressible medium supplemented by the equation of mass transfer from a gas to droplets. Going over to the difference analogues of the equations of continuity and phase motion, we used the well-known explicit Lax-Vendroff scheme. Herein, the axial profiles of the velocities of droplets and gas, concentrations of gas impurity in a free spray flow, as well as radial profiles of impurity concentrations in a two-phase flow through a cylindrical apparatus are calculated and presented accounting the early drag crisis of droplets, the mass-transfer crisis and the turbulent friction characteristics in gas discovered in previous experiments. Calculations show dependences of the volumetric gas flow, concentration of the gas admixture at the apparatus output, and the amount of impurity absorbed by a liquid on the height and cross-section area of the apparatus.

On the origin of the drag force on dimpled spheres

It is well established that dimples accelerate the drag crisis on a sphere. The result of the early drag crisis is a reduction of the drag coefficient by more than a factor of two when compared to a smooth sphere at the same Reynolds number. However, when the drag coefficients for smooth and dimpled spheres in the post-critical regime are compared, the latter is higher by a factor of two to three. To understand the origin of this behaviour, we conducted direct numerical simulations of the flow around a dimpled sphere, which is similar to commercially available golf balls, in the post-critical regime. By comparing the results to those for a smooth sphere, it is found that dimples, although effective in accelerating the drag crisis, impose a local drag penalty, which contributes significantly to the overall drag force. This finding challenges the broadly accepted view that dimples only indirectly affect the drag force on a sphere by energizing the near-wall flow and delaying global separation.

Giant drag reduction on Leidenfrost spheres evaluated from extended free-fall trajectories

Vapor layer sustained on the surface of a heated sphere, by the means of the Leidenfrost effect, can dramatically reduce the hydrodynamic drag on a sphere due to an early drag crisis transition. Here we investigate the vapor layer effect on the free fall of heated metallic spheres in a fluorocarbon liquid, FC-72 (perfluorohexane), employing two tall liquid tanks: a 3 m tall 14 cm wide tank and a 2 m tall 20 × 20 cm cross-section tank with a heater device. These tanks are significantly larger than the tanks used in prior studies. We use high-speed video camera recordings to track extended fall trajectories and to compare the drag on room-temperature no-vapor-layer spheres to that of heated Leidenfrost vapor-layer spheres. Analysis of the extended free-fall trajectories and acceleration, based on the sphere dynamic equation of motion, enables the accurate evaluation of the vapor-layers-induced drag reduction, without the need for extrapolation. We demonstrate that the drag on the Leidenfrost sphere in FC-72, can be as low as CD = 0.04 ± 0.01, or an order of magnitude lower than the values for the no vapor layer spheres in the subcritical Reynolds number range. This drag reduction extends into the supercritical Reynolds number range. The analysis method developed herein, to describe the sphere trajectories, can be applied in other related studies. Results of this study are expected to stimulate the development on energy saving drag-reduction technologies based on lubricating gas layers.

Numerical simulation of the two-phase flow produced by spraying a liquid by a nozzle

A numerical experiment on the simulation of the two-phase flow formed during spraying of a liquid by a nozzle has been described. The radial and axial velocity profiles of the droplets and gas in the free spray and in the two-phase flow through a cylindrical apparatus have been calculated and represented taking into account the early drag crisis of droplets and peculiarities of turbulent friction in the gas, which was detected in previous experiments. The distinguishing feature of the numerical model of the two-phase flow is that it employs the differential equations describing the nonstationary flow of a compressible gas as the initial equations. In transition to their difference analog, the familiar Lax–Wendorff algorithm has been used. A comparison of the results of calculations based on this model with experimental data has demonstrated their concordance.

Calculations of the flow resistance and heat emission of a sphere in the laminar and high-turbulent gas flows

An early drag crisis can occur at high turbulence of incoming gas flow to a sphere. To study the influence of a crisis on heat transfer from a sphere to gas, a numerical experiment was carried out in which the free gas flow around a sphere with a temperature lower than the sphere temperature was simulated for two cases. The flow was laminar in the first case and highly turbulent in the second case. To take into account turbulence, the kinematic coefficient of turbulent viscosity with a value, which is much higher (up to 2000 times) than that for physical viscosity, was introduced. The results of calculations show that the early drag crisis occurs at Reynolds numbers of about 100 and results in considerable (by four to seven times) decrease in the hydrodynamic force and sphere drag coefficient C d . The early drag crisis is also accompanied by the crisis of heat transfer from a sphere to gas with a decrease in Nusselt numbers Nu by three to six times.

Calculation of the drag and heat transfer from a sphere in the gas flow in a cylindrical channel

A numerical experiment on the simulation of heat transfer from a sphere to a gas flow in a cylindrical channel in the Stokes and transient flow regimes has been described. Radial and axial profiles of the gas temperature and the dependences of drag coefficient Cd of the body and Nusselt number Nu on Reynolds number Re have been calculated and analyzed. The problem of the influence of the early drag crisis for a sphere on its heat transfer to the gas flow has been considered. The estimation of this phenomenon has shown that the early drag crisis of the sphere in a strongly turbulent flow causes a reduction in heat transfer from the sphere to the gas by three to six times (in approximately the same proportion as for its drag coefficient).

Effect of the gas flow geometry and turbulence on the hydrodynamic drag of a body in the flow

The effect of the incoming flow geometry on the hydrodynamic drag of a body is investigated in a numerical experiment simulating a free gas flow past a sphere as well as flows in cylindrical tubes of various radii, in a confuser, and a diffuser. The results of calculations lead to the conclusion that the confinement of the flow by the tube walls, its contraction and expansion may change the hydrodynamic force and the drag acting on the body insignificantly (not more than by 30%). This cannot explain the early drag crisis, in which the values of these quantities decrease by 4–7 times for Reynolds numbers on the order of 100. This phenomenon is explained theoretically by the effect of strong turbulence of the incoming flow to the body.

Polymer and surface roughness effects on the drag crisis for falling spheres

. We make time resolved velocity measurements of steel spheres in free fall through liquid using a continuous ultrasound technique. We explore two different ways to induce large changes in drag on the spheres: 1) a small quantity of viscoelastic polymer added to water and 2) altering the surface of the sphere. Low concentration polymer solutions and/or a pattern of grooves in the sphere surface induce an early drag crisis, which may reduce drag by more than 50% compared to smooth spheres in pure water. On the other hand, random surface roughness and/or high concentration polymer solutions reduce drag progressively and suppress the drag crisis. We also present a qualititative argument which ties the drag reduction observed in low concentration polymer solutions to the Weissenberg number and normal stress difference.