E.F. Matthys

Fluid flow, heat transfer, and solidification of molten metal droplets impinging on substrates: Comparison of numerical and experimental results

A mathematical representation has been developed, and computed results are presented describing the spreading and solidification of droplets impacting onto a solid substrate. This impingement is of major practical interest in plasma spraying and spray forming operations. Experiments in which molten metal drops were made to impinge onto a substrate were used to test the model. High-speed videography was used to record the spreading process, which typically took a few milliseconds for the experimental conditions employed. A comparison was made of the theoretical predictions with the experimental measurements; these were found to be in very good agreement, suggesting that the theoretical treatment of the model is sound. These calculations permit the prediction of the time and extent of the spreading process, the solidification rate, and the effect of process parameters, such as droplet size, droplet velocity, superheat, and material properties, provided that a value of the thermal contact coefficient is known. The most important finding of the modeling work is that for large droplets (∼5-mm diameter) with low impinging velocities (∼2 m/s), spreading and solidification appear to take place at comparable rates; in contrast, for small (∼100−µm diameter) particles impacting at a high velocity (∼100 m/s), the time scale for spreading appears to be shorter than the time scale for solidification (within the range of parameters of this study.)

Shear thickening in low-concentration solutions of wormlike micelles. II. Slip, fracture, and stability of the shear-induced phase

The rheology of the shear-thickened state is investigated in low-concentration solutions of wormlike micellar solutions using mechanical, optical, and velocity profile measurements. The zero-shear-rate viscosity of the solutions increases by more than a factor of 1000 as the concentration of surfactant is increased from 1 to 10 mM. By contrast, the apparent viscosity of the shear-thickened state of these same solutions is observed to be remarkably independent of concentration over a wide range of shear rates. This is shown to be a consequence of the development of slip layers between the very viscous gellike shear-induced structures (SISs) which form in the bulk of the surfactant solution and on the walls of the Couette devices in which the measurements are made. As the applied shear stress is increased even further, there is evidence that the SIS fractures give rise to a shear-rate-independent stress and an apparent viscosity, which decreases with increasing shear rate. After the SIS fractures, large flu...

THERMAL-ANALYSIS AND MEASUREMENTS FOR A MOLTEN-METAL DROP IMPACTING ON A SUBSTRATE - COOLING, SOLIDIFICATION AND HEAT-TRANSFER COEFFICIENT

Abstract The behavior of a molten metal droplet impinging, spreading and solidifying on a solid substrate is relevant to manufacturing processes such as splat cooling and spray deposition. In this study, we have conducted experiments aimed at the investigation of the solidification and cooling of a metal droplet after impact. Temperature measurements were conducted during and after solidification. Some results are presented to illustrate the effect of superheat and substrate material on the cooling rate. We have also estimated the thermal contact coefficient between splat and substrate by matching for a number of conditions the experimental data to predictions of a heat transfer and phase change model. The results suggest that this coefficient can decrease by an order of magnitude during solidification for the case of a splat on metal substrates. For splats on quartz, where there is good bonding, the thermal contact coefficient appears to stay the same before and after solidification.

Numerical modelling of phase change and heat transfer during rapid solidification processes: use of control volume integrals with element subdivision

Abstract An effective interface-tracking scheme has been developed for the numerical modelling of heat transfer and phase change during rapid solidification. This technique is based on Control Volume Integrals, and achieves high-resolution tracking of the solid/liquid interface by element subdivision. It is particularly well-suited for rapid solidification with undercooling, for which the accurate prediction of the interface temperature during recalescence is very important. This approach has been used to model the Planar Flow Casting and Splat Cooling processes. Some results on temperature profiles and on interface velocity, location, undercooling, and cooling rate are shown for both processes.

Characterization of micellar structure dynamics for a drag-reducing surfactant solution under shear: normal stress studies and flow geometry effects

Some surfactant solutions have been observed to exhibit a strong drag reduction behavior in turbulent flow. This effect is generally believed to result from the formation of large cylindrical micelles or micellar structures. To characterize and understand better these fluids, we have studied the transient rheological properties of an efficient drag-reducing aqueous solution: tris (2-hydroxyethyl) tallowalkyl ammonium acetate (TTAA) with added sodium salicylate (NaSal) as counter ion. For a 5/5 mM equimolar TTAA/NaSal solution, there is no measurable first normal stress difference (N1) immediately after the inception of shear, but N1 begins to increase after a well-defined induction time — presumably as shear-induced structures (SIS) are formed — and it finally reaches a fluctuating plateau region where its average value is two orders of magnitude larger than that of the shear stress. The SIS buildup times obtained by first normal stress measurements were approximately inversely proportional to the shear rate, which is consistent with a kinetic process during which individual micelles are incorporated through shear into large micellar structures. The SIS buildup after a strong preshear and the relaxation processes after flow cessation were also studied and quantified with first normal stress difference measurements. The SIS buildup times and final state were also found to be highly dependent on flow geometry. With an increase in gap between parallel plates, for example, the SIS buildup times decreased, whereas the plateau viscosity increased.

On two distinct types of drag-reducing fluids, diameter scaling, and turbulent profiles

Two distinct scaling procedures were found to predict the diameter effect for different types of drag-reducing fluids. The first one, which correlates the relative drag reduction (DR) with flow bulk velocity ( V), appears applicable to fluids that comply with the 3-layers velocity profile model. This model has been applied to many polymer solutions; but the drag reduction versus V scaling procedure was successfully tested here for some surfactant solutions as well. This feature, together with our temperature profile measurements, suggest that these surfactant solutions may also show this type of 3-layers velocity profiles (3L-type fluids). The second scaling procedure is based on a correlation of w versus V, which is found to be applicable to some surfactant solutions but appears to be applicable to some polymer solutions as well. The distinction between the two procedures is therefore not simply one between polymer and surfactants. It was also seen that the w versus V correlation applies to fluids which show a stronger diameter effect than those scaling with the other procedure. Moreover, for fluids that scale according to the w versus V procedure, the drag-reducing effects extend throughout the whole pipe cross section even at conditions close to the onset of drag reduction, in contrast to the behavior of 3L fluids. This was shown by our measurements of temperature profiles which exhibit a fan-type pattern for the w versus V fluids (F-type), unlike the 3-layers profile for the fluids well correlated by drag reduction versus V. Finally, mechanically-degraded polymer solutions appeared to behave in a manner intermediate between the 3L and F fluids. Furthermore, we also showed that a given fluid in a given pipe may transition from a Type A drag reduction at low Reynolds number to a Type B at high Reynolds number, the two types apparently being more representative of different levels of fluid/flow interactions than of fundamentally different phenomena of drag reduction. After transition to the non-asymptotic Type B regime, our results suggest that, without degradation, the friction becomes independent of pipe diameter and that the drag reduction level becomes also approximately independent of the Reynolds number, in a strong analogy to Newtonian flow.

Asymptotes of maximum friction and heat transfer reductions for drag-reducing surfactant solutions

Abstract A new maximum drag reduction asymptote (MDRA) for surfactant solutions is presented. Various concentrations including cationic and non-ionic surfactant solutions were used to experimentally determine this asymptote. It is shown that if solvent viscosity is used to compute Reynolds and Prandtl numbers for viscous solutions, it leads to underestimations of the friction coefficient. To avoid uncertainties in the selection of the fluids viscosity, most solutions used were intentionally conditioned so their shear viscosity was water-like in the ranges covered. Using the same solutions, a maximum heat transfer reduction asymptote (MHTRA) was also determined – a correlation that did not exist for surfactants until now. Finally, by using slightly modified definitions to quantify the heat transfer and drag reductions (TRH and TRD), it is possible to express the ratio between the MHTRA and MDRA with a constant value of 1.06, independent of Reynolds number. This relationship can be used as an auxiliary criterion to determine whether or not a solution is asymptotic when there is an uncertainty about the shear viscosity.

Heat transfer, drag reduction, and fluid characterization for turbulent flow of polymer solutions: recent results and research needs

Abstract Some results of investigations on the heat transfer and friction reduction for viscoelastic polymer solutions flowing in circular tubes are presented. The effects of concentration and mechanical degradation on the drag and heat transfer are discussed. Measurements of heat transfer in the thermal entrance region are also reported and indicate a very long entrance region for asymptotic conditions and a shorter one for the non-asymptotic regime. Both these and fully-developed results suggest a departure from the friction/heat transfer analogies, both at the macroscopic coefficient level and at the turbulent diffusivity level. In particular, our computations showed that the turbulent Prandtl number may reach values of up to 15 for asymptotic drag-reducing solutions. In addition to the presentation of these results, the current understanding in this research area is discussed, with a review of some of the most important recent results and of the current research needs in terms of modeling, correlations, experiments, and fluid characterization.

Experimental Investigation of Thermal and Hydrodynamic Development Regions for Drag-Reducing Surfactant Solutions

The reductions in friction and heat transfer exhibited by a surfactant solution in the entry region of a circular pipe were measured and analyzed, with special attention paid to the relationship between the local heat transfer and friction. Two entrance configurations were used, a cone contraction and wire mesh plugs used as a device for velocity profile flattening. Both the simultaneous development of temperature and velocity profiles and the development of temperature profile with hydrodynamically predeveloped flow were studied. Interestingly, the local heat transfer measurements for surfactant solutions matched very well a correlation developed for polymer solutions, but for surfactants the development of the heat transfer and velocity profiles appear coupled, unlike what is thought to happen for polymer solutions. The development patterns appear to be independent of velocity and entrance type at low disturbance levels. At high disturbance levels, however, some striking changes in the fluid itself, likely due to temporary micellar structure degradation by high local shear stress in the inlet region, were observed as well, and quantified.

Experimental Investigation of Interfacial Thermal Conductance for Molten Metal Solidification on a Substrate

Experiments have been conducted to quantify the interfacial thermal conductance between molten copper and a cold metallic substrate, and in particular to investigate the heat transfer variation as the initial liquid/solid contact becomes a solid/solid contact after nucleation. A high heat transfer coefficient during the earlier liquid cooling phase and a lower heat transfer coefficient during the subsequent solid splat cooling phase were estimated through matching of model calculations and measured temperature history of the sample. The dynamic variations in the interfacial heat transfer resulting from the solidification process were quantified for splat cooling and were found to be affected by the melt superheat, the substrate material, and the substrate surface finish.