Inception Length Research Articles

Dynamics of falling films on the outside of a vertical rotating cylinder: waves, rivulets and dripping transitions

Falling liquid films on the underside of a plate or on the outside of a rotating cylinder are subject to a destabilizing body force. The evolution of the film topology is determined by interactions between the Kapitza and the Rayleigh–Taylor instability, leading to complex patterning of the film surface and eventually fluid detachment from the substrate. This study experimentally investigates the evolution of the surface topology for a film on the outside of a vertical rotating cylinder of large radius. Shear at the liquid/air interface is suppressed through an outer, co-rotating cylinder. The film evolution is captured through high speed visualization in dependence of the control parameters, namely Reynolds number and rotation frequency. An increasing influence of the Rayleigh–Taylor instability for an increasing destabilizing body force (increasing rotational speed of the cylinder) is most notably observed in the form of a decreasing inception length of rivulet structures dominating the film topology. Wavelength as well as inception length of rivulets match the predictions from linear stability analysis of the classical Rayleigh–Taylor problem. In this context, experimental and supporting numerical results suggest that the emergence of rivulets occurs for any non-zero value of the destabilizing body force after a given evolution length that decreases with increasing body force. Fluid detachment from the substrate is found to be intimately related to the existence of rivulet structures. In dependence of the control parameters, detaching droplets are either observed as a result of interactions of solitary pulses of varying phase speed on rivulets, directly after destabilization of two-dimensional waves into rivulets or immediately at the fluid inlet. By comparison to the convective/absolute instability transition predicted by linear stability analysis of an integral boundary layer formulation of the problem in question, it is shown that the prediction of a predominant dripping mechanism lies beyond the scope of linear analysis.

Wave Characteristics of Falling Film on Inclination Plate at Moderate Reynolds Number

Falling water film on an inclined plane is studied by shadowgraphy. The ranges of inclination angle and the film Reynolds number are, respectively, up to 21° and 60. Water is used as working fluid. The scenario of wave regime evolution is identified as three distinctive regimes, namely, initial quiescent smooth film flow, two-dimensional regular solitary wave pattern riding on film flow, and three-dimensional irregular wave pattern. Three characteristic parameters of two-dimensional solitary wave pattern, namely, inception length, primary pulse spacing, and propagation velocity, are examined, which are significant in engineering applications for estimation of heat and mass transfer on film flow. The present experimental data are well in agreement with the Koizumi correlations, the deviation from which is limited to 20% and 15%, respectively, for primary pulse spacing and propagation velocity. Through the scrutiny of the present experimental observation, it is concluded that wave evolution on film flow at the moderate Reynolds number is controlled by gravity and drag and the Rayleigh-Taylor instability that occurred on the steep front of primary pulse triggers the disintegration of continuous two-dimensional regular solitary wave pattern into three-dimensional irregular wave pattern.

Prediction of Inception Length of Flow over Different Stepped Chute Geometry

This research was performed to develop an inception model to be used over three different chute geometries which was not done by earlier researchers. The inception parameters (roughness Froude number and sine of the chute angles) were determined from the inception data of Munta and Otun. These parameters were analysed using a regression model to form the inception length equation in this study. The results showed that the inception length to the roughness height increases with increase in both roughness Froude number and slope of the chute angle. The results also indicated that for every unit discharge, inclined stepped chute type has the least length of inception compared to the plain and the end-sill chute types; indicating that the point of inception has shifted optimally upstream of the chute in the inclined stepped chute. The developed inception model has insignificant error range values of 0.044-0.89% over the various step chutes under consideration. Inclined step chute is more suitable to be used to safely transmit flood flow downstream of a dam. http://dx.doi.org/10.4314/njt.v34i3.29

Study of the Inception Length of Flow over Stepped Spillway Models

This study is the modification of Bauer’s development length in order to determine the excess in his length which has not been investigated by earlier researchers. The observations were performed in the non-aerated flow region of wooden stepped spillway models fabricated and installed at the Hydraulics Laboratory of the Department of Water Resources and Environmental Engineering, Ahmadu Bello University, Zaria-Nigeria. A total of 40 experiments were conducted over three different chute geometry to determine Bauer’s development length which were plotted on a drawing paper to a scale of 1:1 to obtained the development length in this study. The results showed that the inception (development) length increases as the unit discharge increases and it decreases with an increase in both stepped roughness height and chute angle. The ratio of the development length, in this study, to that of Bauer’s was found to be 4:5. Finally, SMM-5 produced the least velocity of flow and the highest depth of inception; indicating that it could be employed optimally, considering this study, in curbing or preventing cavitation as a flood controls structure. http://dx.doi.org/10.4314/njt.v33i2.6

Effect of buoyancy on the wakes of circular and square cylinders: a schlieren-interferometric study

Wakes behind heated cylinders, circular, and square have been experimentally investigated at low-Reynolds numbers. The electrically heated cylinder is mounted in a vertical airflow facility such that buoyancy aids the inertia of main flow. The operating parameters, i.e., Reynolds number and Richardson number are varied to examine flow behavior over a range of experimental conditions from forced to mixed convection regime. Laser schlieren-interferometry has been used for visualization and analysis of flow structures. Complete vortex shedding sequence has been recorded using a high-speed camera. The results on detailed dynamical characteristics of vortical structures, i.e., their size, shape and phase, Strouhal number, power spectra, convection velocity, phase shift, vortex inception length, and fluctuations are reported. On heating, alteration of organized (coherent) structures with respect to shape, size and their movement is readily perceived from instantaneous Schlieren images before they reduce to a steady plume. For both cylinders, Strouhal number shows a slow increase with an increase in Richardson number. At a critical value, there is complete disappearance of vortex shedding and a drop in Strouhal number to zero. The corresponding spectra evolve from being highly peaked at the vortex shedding frequency to a broadband appearance when vortex shedding is suppressed. The geometry of vortex structures transforms to a slender shape before shedding is suppressed. At this heating level, absence of multiple peaks in power spectra at cylinder centerline indicates absence of interaction between opposite shear layers. The convection velocity of vortices increases in stream wise direction to an asymptotic value and its variation is a function of Richardson number. The convection speed abruptly falls to zero at critical Richardson number. The phase difference of shed vortices between upstream and downstream location increases with an increase in Richardson number. Velocity profiles show an increase in fluid speed and beyond the critical point, buoyancy forces add enough momentum to cancel momentum deficit due to the cylinder. Overall, the combined effect of temperature gradient on the separating shear layer velocity profile in near field and vortical structures interaction in far field influences wake instability of a heated cylinder.

Influence of subcooled boiling on out-of-phase oscillations in boiling water reactors

In this paper, we develop a reduced order model with modal kinetics for the study of the dynamic behavior of boiling water reactors. This model includes the subcooled boiling in the lower part of the reactor channels. New additional equations have been obtained for the following dynamics magnitudes: the effective inception length for subcooled boiling, the average void fraction in the subcooled boiling region, the average void fraction in the bulk-boiling region, the mass fluxes at the boiling boundary and the channel exit, respectively, and so on. Each channel has three nodes, one of liquid, one with subcooled boiling, and one with bulk boiling. The reduced order model includes also a modal kinetics with the fundamental mode and the first subcritical one, and two channels representing both halves of the reactor core. Also, in this paper, we perform a detailed study of the way to calculate the feedback reactivity parameters. The model displays out-of-phase oscillations when enough feedback gain is provided. The feedback gain that is necessary to self-sustain these oscillations is approximately one-half the gain that is needed when the subcooled boiling node is not included.

A reduced order model of BWR dynamics with subcooled boiling and modal kinetics: application to out of phase oscillations

In this paper we develop a reduced order model that includes the sub-cooled boiling. New additional equations have been obtained for the following dynamics magnitudes: the effective inception length, the average void fraction in the sub-cooled boiling region, the average void fraction in the bulk boiling region, the mass fluxes at the boiling boundary and the channel exit, and so on. Each channel has three nodes, one of liquid, one with sub-cooled boiling, and one with bulk boiling. The reduced order model includes also a modal kinetics with the fundamental mode and the first sub-critical one, and two channels representing both halves of the reactor core. The model displays out of phase oscillations when enough feedback gain is provided. The feedback gain that is necessary to self sustain these oscillations is approximately one half the gain that is needed when the sub-cooled boiling node is not included.

Reynolds number effects in swept-shock-wave/turbulent-boundary-layer interaction

The interaction between a turbulent boundary layer and a glancing shock wave produced by a wedge is studied numerically and experimentally. The flows correspond to a nominal Mach number 2.5, two widely different Reynolds numbers, and a range of incidence angles giving both attached and separated flows. The Reynolds number effects on several flow features, including upstream influence, incipient separation, and inception length, are discussed. The computations are compared with the low-Reynolds-number experiments of Kubota and Stollery and also to some newly performed high-Reynolds-number experiments, and good agreement is achieved.

Inception length to a fully developed, fin-generated, shock-wave, boundary-layer interaction

An experimental study of fin-generated shock wave turbulent boundary-layer interactions confirmed previous observations that, sufficiently far from the fin apex, such interactions become conical. The inception length to conical symmetry was found to increase weakly with Mach number for Mach numbers from 2.5 to 4 and fin angles from 4 to 22 deg. For the range of interactions examined, the inception length was found to depend primarily upon the inviscid shock angle, this angle ranging from 21 to 40 deg. The behavior of the inception length with shock angle can be broadly divided into two categories. For 'weak' interactions with shock angles less than about 35 deg, the inception length decreased as the shock angle increased. For 'strong' interactions with shock angles greater than about 35 deg, the inception region was small and was approximately constant at three boundary-layer thicknesses in length. In the latter, strong interaction case, the inception length was an order of magnitude smaller than that found in the weakest interactions examined, to the extent that strong interactions were practically fully-developed from the apex.

Spanwise propagation of upstream influence in conical swept shock/boundary-layer interactions

It is shown that the motion within any boundary layer underlying an exactly conical inviscid flow with a swept shock cannot be conical at an arbitrary radial distance r from the origin, and that the resulting viscous-inviscid interaction from the displacement effect of this layer would violate the inviscid conicity. However, the far-field behavior at large radial distances beyond a certain inception length is shown to approach a quasi-twodimensional state in conical arc length coordinates, a state compatible with the corresponding far-field conical behavior of the overlying inviscid flow including viscous-inviscid interaction effects. Based on an analysis of the governing flow equations for large r, we establish that this inception length is proportional to the product of the interaction zone width (normal to the shock line) and the tangent of the shock sweep angle. These conclusions apply to a wide range of attached shock inviscid flow conditions and boundary-layer states independently of the turbulence modeling, heat transfer, or separation.

Reply by Authors to S.M. Bogdonoff and S. Wang

W thank Prof. Bogdonoff and Mr. Wang for their comments on our work, although we disagree with them. We did not use selected test results, but based our conclusions on the data set obtained by F.K. Lu during his Master's thesis research. Subsequent work by Good win using fins at larger angles of attack also substantiated our conclusions. If conflicting data have been obtained at Princeton in the interim, we are unaware of them. We are willing to consider conflicting data if any exist. Bogdonoff and Wang question our assertion that conical flow symmetry exists in the outboard region of swept shock/boundary-layer interactions generated by fins. This assertion is supported not only by our data, but by a number of experimental and computational studies conducted in several countries. To our knowledge no form of far-field symmetry other than conical has ever been observed in fingenerated interactions. The matter of the spanwise growth of incoming boundarylayer thickness is admittedly not completely understood. The preponderance of known experiments has used rectangular flat plates that naturally generate boundary layers which grow in the spanwise direction at the upstream limit of a swept interaction. However, in one experiment, the flat-plate leading edge was intentionally swept back 45 deg in order to check such boundary-layer growth effects. The results showed the surface pressure footprints of 4and 10-deg fin interactions at Mach 3 to be invariant to leading-edge sweepback of the flat plate. We find this to be a plausible result; the scale of the incoming boundary layer apparently having exerted its influence only in the establishment of the inception zone, according to dimensional arguments. In further support of conical symmetry, note that the outer inviscid flow is naturally conical. The interaction requires an equilibrium between an outer conical flow and an inner viscous layer. This layer is extremely thin at high Reynolds numbers compared to the dimensions of the fin (as was the case in Ref. 1). Therefore, if the viscous layer refuses to respond to the symmetry of the outer flow, enormous gradients would have to be supported by this thin wall layer. Thus, it seems clear that swept shock/boundary-layer interactions must rapidly adopt the symmetry imposed by the outer flow. The length required for this to occur is the inception length referred to in our paper. This argument has been quantified in an order-of-magnitude analysis by Inger. As for the inception length itself, our description in Ref. 1 was admittedly preliminary. This was not the primary subject of our work, and at that time no one had studied inception lengths per se. More recent work clarifies this issue. It is clear that the inception zone merges gradually into the out-

針対平板ギャップの正コロナストリーマの発生電圧とその長さの検討

針対平板ギャップの正コロナストリーマの発生電圧とその長さの検討