Motion of a cloud of particles under gravity and its sedimentation on a flat horizontal surface

On the basis of the nonstationary two-dimensional equations of the mechanics of heterogeneous media a numerical investigation is made of the motion of a cloud of particles under the influence of gravity in an unbounded medium and the interaction of the descending cloud of particles with a flat horizontal surface. Depending on the degree of hydrodynamic interaction between the particles, there are different regimes of motion of the cloud during sedimentation; the change in its spatial configuration determined by the large-scale vortex motion of the carrier medium is determined. The concentration distributions of the particles on the sedimentation surface are obtained. A coefficient of dispersal is introduced for the cloud of particles on the flat horizontal surface, and its dependence on the concentration of the particles, their diameters, and other parameters is investigated.     

Modelling impingement of hollow metal droplets onto a flat surface

Despite many theoretical and experimental works dealing with the impact of dense melt droplets on the substrate during the process of thermal spray coating, the dynamics of the impingement of hollow melt droplet and the subsequent splat formation are not well addressed. In this paper a model study for the dynamic impingement of hollow droplet is presented. The hollow droplet is modelled such that it consists of a liquid shell enclosing a gas cavity. The impingement model considers the transient flow dynamics during impact, spreading and solidification of the droplet using the volume of fluid surface tracking method (VOF) coupled with a solidification model within a one-domain continuum formulation. The results for spreading, solidification and formation of splats clearly show that the impingement process of hollow droplet is distinctly different from the dense droplet. Study with different droplet void fractions and void distribution indicates that void fraction and void distribution have a significant influence on the flow dynamics during impact and on the final splat shape. The results are likely to provide insights for the less-explored behaviour of hollow melt droplets in thermal spray coating processes.     

Integral solution for Forchheimer free convection over a horizontal flat surface

The aim of the present paper is to study the non-Darcy free convection from a horizontal flat surface in a fluid saturated porous medium using integral method for the case when the heat flux from the surface remains constant. The thermal dispersion effects are taken into consideration. The linear relation between the dispersion thermal diffusivity and the streamwise velocity component has been adopted. Exponential profiles are choosen for the velocity and temperature distributions. The Nusselt number results are in good agreement with the existing similarity solution.     

Calculating hydrodynamics problems for a liquid film flowing radially on a flat horizontal surface

A mathematical hydrodynamic model of a thin liquid film flowing radially on a flat horizontal surface has been elaborated. The model consisted of continuity and momentum equations which were resolved by means of the integral method. In fact, several versions of the model were examined; they differed mainly in film velocity distribution. The predictions of the different versions were then compared with liquid film thicknesses obtained from experimental investigation. The best version was applied in further calculations.     

Mixed convection boundary-layer flow on a horizontal flat surface with a convective boundary condition

The steady mixed convection boundary-layer flow on an upward facing horizontal surface heated convectively is considered. The problem is reduced to similarity form, a necessary requirement for which is that the outer flow and surface heat transfer coefficient are spatially dependent. The resulting similarity equations involve, apart from the Prandtl number, two dimensionless parameters, a measure of the relative strength of the outer flow M and a heat transfer coefficient γ. The free convection, M=0, case is considered with the asymptotic limits of large and small γ being derived. Results for the general, M>0, case are presented and the asymptotic limit of large M being treated.     

Energy distribution from vertical impact of a three-dimensional solid body onto the flat free surface of an ideal fluid

Hydrodynamic impact phenomena are three dimensional in nature and naval architects need more advanced tools than a simple strip theory to calculate impact loads at the preliminary design stage. Three-dimensional analytical solutions have been obtained with the help of the so-called inverse Wagner problem as discussed by Scolan and Korobkin in 2001. The approach by Wagner provides a consistent way to evaluate the flow caused by a blunt body entering liquid through its free surface. However, this approach does not account for the spray jets and gives no idea regarding the energy evacuated from the main flow by the jets. Clear insight into the jet formation is required. Wagner provided certain elements of the answer for two-dimensional configurations. On the basis of those results, the energy distribution pattern is analysed for three-dimensional configurations in the present paper.     

Pressure measurements on the impingement surface of sonic and sub-sonic jets impinging onto a flat plate at inclined angles

The flow field associated with a jet impinging onto a surface at an inclined angle is investigated using pressure-sensitive paint (PSP) and particle image velocimetry. The PSP yields continuous measurements of pressure on the jet impingement surface. The jet footprint on the impingement surface is visualized using the half-maximum pressure contour. The results indicate that the impingement angle of the jet is the dominant parameter in determining the footprint of the jet on the impingement surface. This contour is similar in shape to an ellipse that is created by projecting the nozzle through the impingement surface. The ellipse is centered at the location of maximum pressure and the width of the minor axis is just over one jet diameter. The location of maximum pressure is found upstream of the geometric impingement point and this location is a strong function of the impingement angle. A curve fit for the location of maximum pressure can be constructed using an exact solution of the Navier–Stokes equations for a non-orthogonal stagnation flow. The maximum value of pressure is a function of impingement angle and varies as the sine of the impingement angle squared; the maximum pressure is also a function of jet impingement distance. Using these results, a simple procedure for predicting the overall structure of the jet on the impingement surface is presented.     

Hollow droplets impacting onto a solid surface

The impact process of spherical hollow droplets impinging onto a solid surface has been experimentally studied. Formation of a counter-jet in a wide range of Reynolds and Weber numbers was revealed, this jet being similar to a Worthington jet. For characterizing the regime of liquid flow in the hollow droplet, we propose using the Euler number. Theoretically, the problem was treated using a simple model of axisymmetric liquid flow. The obtained results proved to be consistent with experimental data.     

Computations for a jet impinging obliquely on a flat surface

A SIMPLE-C algorithm and Jones-Launder k-ε two-equation turbulence model are used to simulate a two-dimensional jet impinging obliquely on a flat surface. Both the continuity and momentum equations for the unsteady state are cast into suitable finite difference equations. The pressure, velocity, turbulent kinetic energy and turbulent energy dissipation rate distributions are solved and show good agreement with various experimental data. The calculations show that the flow field structure of the jet impinging obliquely on a flat surface is strongly affected by the oblique impingement angle. The maximum pressure zone of the obliquely impinging jet flow field moves towards the left as the oblique impingement angle is decreased.     

The cooling of a lava flow spreading over a flat surface

The cooling of a lava flow modeled by a viscous incompressible fluid spreading over a flat surface is considered. In order to model the free surface, a known analytical solution is used in the thin-layer approximation. The thermal boundary layer thickness is determined and the evolution of thermal fields in the lava profile is studied.     

The impingement of sonic and sub-sonic jets onto a flat plate at inclined angles

The flow field associated with a jet impinging onto a surface at an inclined angle is investigated using particle image velocimetry (PIV). The results indicate that as a free jet impinges on a flat surface at an inclined angle the jet is turned by and spread laterally onto the impingement surface. The impingement angle of the jet is the dominant parameter in determining the rate of turning/spreading for the jet. The stagnation point is located using the PIV data and is found upstream of the geometric impingement point and upstream of the location of maximum pressure. The location of the stagnation point is a strong function of impingement angle and a weak function of impingement distance and pressure ratio. The location of the stagnation point is compared with the location of maximum pressure and compared to a curve fit for the location of maximum pressure based an exact solution of the Navier–Stokes equations for a non-orthogonal stagnation flow.     

Effect of normal vibrations of a flat horizontal heater on the second boiling crisis

The effect of normal vibrations of a flat horizontal heater on the second boiling crisis is considered within the framework of the hydrodynamic theory of boiling crises. The critical heat flux is estimated by characteristics of growth of the most dangerous disturbances destroying the liquid-vapor interface. As the vibration intensity increases, the interface can be destroyed either owing to the Rayleigh-Taylor instability or by virtue of parametrically excited disturbances with wavelengths corresponding to resonance zones. In the domain of parameters where the parametric instability in the first resonance zone is the most dangerous factor, it is possible to significantly reduce the critical heat flux, as compared with the value corresponding to the case with no vibrations. With a further increase in vibration intensity, the critical heat flux increases as a whole. The nonmonotonic character of the critical heat flux as a function of vibration intensity allows an effective control of the critical heat flux whose value can be made higher or lower than the value in the case without vibrations. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 88–97, July–August, 2006.