Theoretical analysis of the onset of gas entrainment from a stratified region through multiple branches

A theoretical analysis has been developed to predict the critical height of the onset of gas entrainment (OGE) during dual and triple discharge from a stratified two-phase region. The two and three discharge branches are mounted on a circular wall, resembling a circular reservoir of a CANDU header–feeder configuration. A point sink model has been developed to predict the critical height and to map the velocities and acceleration flow fields during OGE. The model was verified by comparing the theoretically predicted critical height with the available experimental results. The theoretically predicted critical height is found to be a function of the branch Froude number, the location of the secondary branch with respect to the primary branch, and the angle between the branches. The effect of these variables on the predicted OGE height was investigated and is presented in this paper. Predictions of the critical height were shown to be within 25% of experimental values in both dual and triple discharge.     

Construction of Arnold tongue structures for coupled periodic oscillators

Arnold tongue structures generated due to the mutual entrainment of two periodic oscillators are studied experimentally and numerically. This mutual entrainment is provoked due to the mutual (bidirectional) coupling between the two oscillators. In experiments, this bidirectional coupling is achieved by immersing a pair of anodes (oscillators) in a common electrolytic solution. A voltage mismatch between these anodes renders the time period of the uncoupled oscillators non-identical. Moreover, the coupling strength between the two oscillators is uniquely determined by the Euclidean distance separating them. Systematically varying the distance between these two anodes as a function of their voltage mismatch, phase locked domains were located. Subsequently, Arnold tongue structures were constructed in the experiments. Numerical simulations, using a model for electrochemical corrosion, corroborate our experimental findings.     

Direct numerical simulation of a turbulent axisymmetric jet with buoyancy induced acceleration

Direct numerical simulations of an axisymmetric jet with off-source volumetric heat addition are presented in this paper. The system solved here involves a three-way coupling between velocity, concentration and temperature. The computations are performed on a spherical coordinate system, and application of a traction free boundary condition at the lateral edges allows physical entrainment into the computational domain. The Reynolds and Richardson numbers based on local scales employed in the simulations are 1000 and 12 respectively. A strong effect of heat addition on the jet is apparent. Heating causes acceleration of the jet, and an increased dilution due to an increase in entrainment. Further, the streamwise velocity profile is distorted, and the cross-stream velocity is inward for all radial locations for the heated jet. Interestingly, the maximum temperature is realized off-axis and a short distance upstream of the exit of the heat injection zone (HIZ). The temperature width is intermediate between the scalar and velocity widths in the HIZ. Normalized rms of the concentration and temperature increases in the HIZ, whereas that of streamwise, cross-stream and tangential velocities increases rapidly after decreasing. Both mass flux and entrainment are larger for the heated jet as compared to their unheated counterparts. The buoyancy flux increases monotonically in the HIZ, and subsequently remains constant.     

Forced oscillations of a rotating shaft with nonlinear spring characteristics and internal damping (1/2 order subharmonic oscillations and entrainment)

Nonlinear forced oscillations of a rotating shaft with nonlinear spring characteristics and internal damping are studied. In particular, entrainment phenomena at the critical speeds of 1/2 order subharmonic oscillations of forward and backward whirling modes are investigated. A self-excited oscillation appears in the wide range above the major critical speed. The amplitude of this oscillation reaches a limit value and then a self-sustained oscillation occurs. In the vicinity of a 1/2 order subharmonic oscillation of a forward whirling mode, a self-excited oscillation is entrained by a subharmonic oscillation. In the vicinity of a 1/2 order subharmonic oscillation of a backward whirling mode, either a self-excited oscillation or a subharmonic oscillation occurs.Experiments were made by an elastic rotating shaft with a disc. Nonlinearity in its restoring force was due to an angular clearance of a bearing and internal damping was due to friction between the shaft and an inner ring of the bearing. A self-excited oscillation was observed in the range above the major critical speed and this self-excited oscillation was entrained by a 1/2 order subharmonic oscillation of a forward whirling mode.Nomenclature O–xyz rectangular coordinate system - , _x, _y inclination angle of a shaft and its projections on the xz- and yz-planes - _x, _y inclination angles in rotating coordinates - , polar coordinates - I _p polar moment of inertia of a rotor - I diametral moment of inertia of a rotor - i _p ratio of I _p to I - dynamic unbalance of a rotor - rotating speed (angular velocity) - F magnitude of a dynamic unbalance force, F = (1 – i _p )² - c external damping coefficient - h internal damping coefficient - t time - D _x , D _y internal damping terms in stationary coordinates - D _x , D _y internal damping terms in rotating coordinates - N _x , N _y nonlinear terms in restoring forces     

Prediction of the slug-to-churn flow transition in vertical two-phase flow

An assessment is made of the various viewpoints on the slug-to-churn flow transition in vertical upward flow in the light of recent experimental results obtained at Harwell Laboratory. It is found that the flooding model of McQuillan & Whalley and the bubble entrainment model of Barnea & Brauner give satisfactory results at low and high liquid flow rates, respectively. An improved model for flooding, which takes account of the effect of the falling film, has been proposed. It is shown that this new model is in good agreement with experimental results at both low and high liquid flow rates.     

Modeling of droplet entrainment phenomena at a quench front

The phenomena of droplet entrainment at a quench front is of practical importance as a clear understanding of the underlying mechanisms required to effectively calculate the interfacial mass, momentum, and energy transfer, which characterizes nuclear reactor safety, system design, analysis, and performance. The present study proposes a model for droplet entrainment at a quench front that is based on the best-understood physics related to the Lagrangian quenching phenomenon characteristic to light water reactor (LWR) safety analysis. The model is based on a film boundary layer and stability analysis that attempts to match the characteristic time and length scales of the entrainment phenomenon. This model has been developed such that direct implementation can be made into any two-phase flow simulation code with a three-field (continuous liquid, droplet, and vapor) flow model. Comparisons with integrated transient test data independent of those used for model development have been performed to verify the applicability of the proposed model for the prediction of the entrainment rate of liquid droplets at a quench front under typical reflood conditions envisioned in LWRs.     

Leading-Edge Reaction Zones in Lifted-Jet Gas and Spray Flames

An investigation of the leading edge characteristics in lifted turbulent methane-air (gaseous) and ethanol-air (spray) diffusion flames is presented. Both combustion systems consist of a central nonpremixed fuel jet surrounded by low-speed air co-flow. Non-intrusive laser-based diagnostic techniques have been applied to each system to provide information regarding the behavior of the combustion structures and turbulent flow field in the regions of flame stabilization. Simultaneous sequential CH-PLIF/particle image velocimetry and CH-PLIF/Rayleigh scattering measurements are presented for the lifted gaseous flame. The CH-PLIF data for the lifted gas flame reveals the role that ``leading-edge' combustion plays as the stabilization mechanism in gaseous diffusion flames. This phenomenon, characterized by a fuel-lean premixed flame branch protruding radially outward at the flame base, permits partially premixed flame propagation against the incoming flow field. In contrast, the leading edge of the ethanol spray flame, examined using single-shot OH-PLIF imaging and smoke-based flow visualization, does not exhibit the same variety of leading-edge combustion structure, but instead develops a dual reaction zone structure as the liftoff height increases. This dual structure is a result of the partial evaporation (hence partial premixing) of the polydisperse spray and the enhanced rate of air entrainment with increased liftoff height (due to co-flow). The flame stabilizes in a region of the spray, near the edge, occupied by small fuel droplets and characterized by intense mixing due to the presence of turbulent structures. This revised version was published online in July 2006 with corrections to the Cover Date.     

A model of stratified entrainment using vortex persistence

A new model is proposed for the entrainment rate by vortices across stratified interfaces. In the model, different entrainment regimes are distinguished by the conventional parameters Richardson, Reynolds, and Schmidt number as well as a new parameter, the “vortex persistence”. Vortex persistence is defined as the number of rotations a vortex makes during the time it moves its own diameter with respect to the interface. It is further proposed that the concept of vortex persistence is important whenever a vortex is near any kind of surface, either stratified or solid. The model is in accord with most field and laboratory observations in a variety of stratified and bounded flows, including measurements of wall heat transfer and vortex formation in starting jets.     

入口扰动频率对矩形射流影响的大涡模拟

为研究入口扰动对矩形射流的影响,对不同扰动频率下的三维矩形射流进行了大涡模拟,用分布投影法求解动量方程,对压力泊松方程采用FACR直接解法.计算结果预报的速度在横向的单峰分布和速度半宽沿流向的近似线性增长与实验结果吻合良好.计算结果表明扰动频率为射流的本征频率fe=0.22时射流的卷吸作用最强,而高频扰动则抑制卷吸作用;激励频率接近本征频率时射流提前出现速度在展向的马鞍型双峰分布,更早趋于圆射流形态.进一步的流场二维和三维瞬态涡结构图谱表明:上述现象与f=0.1和f=0.22时射流近场更频繁卷起、更丰富的大涡结构存在密切关系,正是这些大涡运动不断地在横向卷吸入外界流体,实现射流在横向的迅速扩展.     

Effects of the Length of a Cylindrical Solid Shield on the Entrainment of Ambient Air into Turbulent and Laminar Impinging Argon Plasma Jets

When materials processing is conducted in air surroundings by use of an impinging plasma jet, the ambient air will be entrained into the materials processing region, resulting in unfavorable oxidation of the feedstock metal particles injected into the plasma jet and of metallic substrate material. Using a cylindrical solid shield may avoid the air entrainment if the shield length is suitably selected and this approach has the merit that expensive vacuum chamber and its pumping system are not needed. Modeling study is thus conducted to reveal how the length of the cylindrical solid shield affects the ambient air entrainment when materials processing (spraying, remelting, hardening, etc.) is conducted by use of a turbulent or laminar argon plasma jet impinging normally upon a flat substrate in atmospheric air. It is shown that the mass flow rate of the ambient air entrained into the impinging plasma jet cannot be appreciably reduced unless the cylindrical shield is long enough. In order to completely avoid the air entrainment, the gap between the downstream-end section of the cylindrical solid shield and the substrate surface must be carefully selected, and the suitable size of the gap for the turbulent plasma jet is appreciably larger than that for the laminar one. The overheating of the solid shield or the substrate could become a problem for the turbulent case, and thus additional cooling measure may be needed when the entrainment of ambient air into the turbulent impinging plasma jet is to be completely avoided.