Exact formula for the spreading width of jet flow velocity under the assumption of a radial adjusting coefficient

Recently, Lee et al. (Arch Appl Mech 81:397–402, 2011) proposed a new and very interesting formula to describe the velocity profile of a submerged jet flow by introducing a radial adjusting coefficient depending on the jet flow direction. Under some simplifying assumptions (granting convergence), the authors were able to express the spreading width of the jet flow analytically in terms of infinite series. In this short note, we show that such simplifying assumptions can be relaxed and exact solutions for the spreading width of the jet flow can be obtained: Such results are computationally more efficient and are able to better demonstrate the qualitative features of the solutions.     

An experimental study of nonrheometric flows of viscoelastic fluids: II. Flow in a liquid jet exiting from a vertical tube

A laser anemometer has been used to study the region of accelerating shear flow near the exit of a vertical tube. It is in this region that the transition between steady laminar shear flow in the upstream tube and elongational flow in the downstream liquid jet takes place.Downstream velocity profiles were measured for solutions of 0.9% polyacrylamide in 85% glycerol/water and 0.9% polyacrylamide in water. Reynolds numbers (based on wall conditions in the fully developed upstream flow) ranged from 45 to 310 and Froude numbers from 0.294 to 4.11. Tubes, having sharpedged and rounded exit corners, with diameters of 1.25 cm and 1.90 cm were usedUpstream velocity profiles were measured for a solution of 0.9% polyacrylamide in water. Reynolds numbers ranged from 16 to 670. Only tubes having sharp-edged exit corners were used.It was found that the transition region did not extend upstream into the tube but was confined to the downstream jet. The transition took place over a distance of about 3–5 tube diameters depending upon the value of the Froude number. The axial distance downstream from the tube exit plane at which the velocity profile first became flat increased with increasing Froude number. The magnitude of the jet velocity at this point decreased with increasing Froude number.The condition of the tube exit corner was found to influence the flow in the transition region. Downstream velocity profiles obtained using tubes having rounded exit corners initially develop more slowly than, but soon catch up with and eventually overtake, the corresponding profiles obtained using tubes with sharp-edged exit corners.Downstream velocity profiles obtained for the 0.9% polyacrylamide in 85% glycerol/water solution were found to develop smoothly. The transition from steady shear flow in the tube to elongational flow in the jet took place through the combined processes of acceleration of the outer layers of the jet due to radial transfer of momentum with adjacent inner layers, the process spreading steadily inwards with increasing axial distance from the tube exit plane, and acceleration of the whole due to gravity. However, the velocity profiles obtained for the 0.9% polyacrylamide in water solution did not always develop so smoothly. At a Reynolds number of 310 and Froude number of 2.06 the radial momentum transfer process was restricted to a narrow outer region of the jet until a downstream axial distance of about 2 tube diameters was reached. Thereafter, the transition to a flat profile took place smoothly.     

A study of the flow characteristics in micro-abrasive jets

An experimental study of particle velocities in micro-abrasive jets by using the particle image velocimetry (PIV) technique is presented. It has been found that the particle jet flow has a nearly linear expansion downstream. The particle velocities increase with air pressure, and the increasing rate increases with nozzle diameter within the range considered. The instantaneous velocity profile of the particle flow field in terms of the particle velocity distribution along the axial and radial directions of the jets is discussed. For the axial profile in the jet centerline downstream, there exists an extended acceleration stage, a transition stage, and a deceleration stage. For the radial velocity profiles, a relatively flat shape is observed at a jet cross-section near the nozzle exit. Mathematical models for the particle velocities in the air jet are then developed. It is shown that the results from the models agree well with experimental data in both the variation trend and magnitude.     

An experimental study of a radial wall jet formed by the normal impingement of a round synthetic jet

The flow field of a radial wall jet created by the impingement of a round synthetic jet normal to a flat surface was characterized using hot-wire anemometry. In the synthetic wall jets the width of the outer layer was observed to increase linearly with the radial distance along the wall, while the local maximum velocity varied inversely. The synthetic wall jet exhibits self-similar behavior as distinguished by the collapse of the mean and rms velocity profiles when normalized by the outer layer scaling variables. Increasing the actuator driving amplitude at a fixed frequency (i) increased the growth rate of the outer layer, and (ii) decreased the decay rate of the local velocity maximum. The flow field of the synthetic wall jet was dominated by vortical structures associated with the actuator driving frequency, and harmonics connected with the interaction of the produced vortex structures. For the actuator conditions investigated, neither the classical laminar nor fully turbulent analytical solutions for continuous wall jets were amenable to modeling the synthetic wall jet profile due to the transitional and unsteady nature of the synthetic wall jet.     

Investigation of the surface jet formed as a buoyant plume spreads over a horizontal surface

A surface buoyant jet formed as a vertically ascending buoyant plume spreads radially after contact with a free water surface is considered. In the case of a plume spreading in a water medium beneath the water-air interface the presence of three characteristic zones in the spreading jet has been experimentally shown: a zone of linear expansion of the lower jet boundary, a zone of constant jet width, and a jet compression zone. For these zones the dependence of the width and the buoyancy integrated over the vertical profile on the radial distance is established. On the basis of an integral method the fluid entrainment velocity is parametrized for each of the characteristic zones in the absence of heat transfer and wave formation on the free surface, and the dependence of the jet width, the values of the radial velocity averaged over vertical cross-sections, and the buoyancy on radial distance is found.St. Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 62–71, November–December, 1995.     

Calculation of the transition region of a turbulent jet

The presently known methods for calculating plane and axisymmetric turbulent jets in a wake flow are based on dividing the flow region into two segments, initial and basic [1–3], Here the matching of the parameters of the initial and basic segments is of an artificial nature, since it permits the existence of a physically impossible discontinuity of the curves of the velocity distribution and the jet width along the axis.The aerodynamic characteristics of the transition segment, extending from the point of convergence of the boundary layers at the end of the initial segment to the section corresponding to the point of inflection of the curve u_m(x), differ significantly from the characteristics of the initial and basic segments. This difference is due not only to the sharp increase of the velocity pulsations, but also the marked deformation of the average longitudinal velocity component profile. Consequently, the calculation of the transition segment, in contrast to the initial and basic segments, cannot be based on the single-parameter method.Generally speaking, the flow development in the transition segment may be calculated with the aid of the method [4], which reduces the solution of the problem to an equation of the heat conduction type and assumes the use of an experimental curve of the velocity distribution along the jet axis. Abramovich has carried out the calculation of the transition segment of a plane submerged jet on the basis of certain assumptions which are based on the results of experimental studies [1].Below is presented an approximate method of calculating the transition segment of plane and axisymmetric turbulent jets in a wake flow in which the velocity profiles obtained for the extreme sections of this segment are used for calculating the flow parameters in the initial and basic segments.     

Single-phase convection and boiling heat transfer: Confined single and array-circular impinging jets

In the present study, the effects of diverse situations of confinement on heat transfer from single and array-circular jet impingements are carefully investigated over various heat transfer regimes of single-phase convection and fully developed nucleate boiling. For the single, circular, unconfined free-surface jet, the transition to turbulence was observed to start around x/d = 5.5 and end around x/d = 9. For the array-circular jet, however, the wall jet structure yielded no transition to turbulence for all the tested cases, instead monotonically decreasing the convection coefficient. Conversely, the single-circular jet experienced the transition for V ? 6.1 m/s. For the confined submerged jet, the transition length was very short due to the vigorous mixing driven by lateral velocity components, and the locus of the secondary peak moved downstream as velocity increased. The temperature distributions of the confined array-circular jet were fairly uniform over the whole heated surface. The averaged single-phase convection coefficients indicated that the confined jet provided the most uniform convection in the lateral direction.     

Laminar swirling power law non-newtonian fluid jet impinging on a normal plane

An analysis is presented for a steady, laminar, incompressible, swirling, Ostwald—De Waele type non-Newtonian fluid jet impinging normally over a horizontal plane with a free surface. A similarity solution is obtained in a region of radial distance away from the central stagnation point. Numerical solutions for the radial and swirling velocities have been obtained for the flow behavior index, n, varying from 0.1 to 2.5. Expressions for the free surface radial velocity, growth of the free surface and skin friction coefficient are given.     

A plane turbulent wall jet on a fully rough surface

The mean velocity field and skin friction characteristics of a plane turbulent wall jet on a smooth and a fully rough surface were studied using Particle Image Velocimetry. The Reynolds number based on the slot height and the exit velocity of the jet was Re = 13,400 and the nominal size of the roughness was k = 0.44 mm. For this Reynolds number and size of roughness element, the flow was in the fully rough regime. The surface roughness results in a distinct change in the shape of the mean velocity profile when scaled in outer coordinates, i.e. using the maximum velocity and outer half-width as the relevant velocity and length scales, respectively. Using inner coordinates, the mean velocity in the lower region of the inner layer was consistent with a logarithmic profile which characterizes the overlap region of a turbulent boundary layer; for the rough wall case, the velocity profile was shifted downward due to the enhanced wall shear stress. For the fully rough flow, the decay rate of the maximum velocity of the wall jet is increased, and the skin friction coefficient is much larger than for the smooth wall case. The inner layer is also thicker for the rough wall case. The effects of surface roughness were observed to penetrate into the outer layer and slightly enhance the spread rate for the outer half-width, which was not observed in most other studies of transitionally rough wall jet flows.     

PIV measurements of a turbulent jet issuing from round sharp-edged plate

An experimental investigation is presented of a turbulent jet issuing from a round sharp-edged orifice plate (OP) into effectively unbounded surroundings. Planar measurements of velocity were conducted using Particle Image Velocimetry (PIV) in the near and transition regions. The Reynolds number, based on the jet initial diameter and velocity, is approximately 72,000. The instantaneous and mean velocities, Reynolds normal and shear stresses were obtained. The centerline velocity decay and the half-velocity radius were derived from the mean velocity. It is revealed that primary coherent structures occur in the near field of the OP jet and that they are typically distributed asymmetrically with respect to the nozzle axis. Comparison of the present PIV and previous hot-wire measurements for the OP jet suggests that high initial turbulence intensity leads to reduced rates of decay and spread of the mean flow field and moreover a lower rate of variation of the turbulence intensity. Results also show that self-similarity of the mean flow is well established from the transition region while the turbulent statistics are far from self-similar within the measured range to 16 diameters.     

Full-field measurements of self-excited oscillations in momentum-dominated helium jets

Flow structure of momentum-dominated helium jets discharged vertically into ambient air was investigated using a high-speed rainbow schlieren deflectometry (RSD) apparatus operated at up to 2,000 Hz. The operating parameters, i.e., Reynolds number and Richardson number were varied independently to examine the self-excited, flow oscillatory behavior over a range of experimental conditions. Measurements revealed highly periodic oscillations in the laminar region at a unique frequency as well as high regularity in the flow transition and initial turbulent regions. The buoyancy was shown to affect the oscillation frequency and the distance from the jet exit to the flow transition plane. Instantaneous helium concentration contours across the field of view revealed changes in the jet flow structure and the evolution of the vortical structures during an oscillation cycle. A cross-correlation technique was applied to track the vortices and to find their convection velocity. Time traces of helium concentration at different axial locations provided detailed information about the oscillating flow.     

Numerical simulation of turbulent impinging jet on a rotating disk

The calculations of quasi‐three‐dimensional momentum equations were carried out to study the influence of wall rotation on the characteristics of an impinging jet. The pressure coefficient, the mean velocity distributions and the components of Reynolds stress are calculated. The flow is assumed to be steady, incompressible and turbulent. The finite volume scheme is used to solve the continuity equation, momentum equations and k–ε model equations. The flow characteristics were studied by varying rotation speed ω for 0?ω?167.6 rad/s, the distance from nozzle to disk (H/d) was (3, 5, 8 and 10) and the Reynolds number Re base on V_J and d was 1.45 × 10⁴. The results showed that, the radial velocity and turbulence intensity increase by increasing the rotation speed and decrease in the impingement zone as nozzle to disk spacing increases. When the centrifugal force increases, the radial normal stresses and shear stresses increase. The location of maximum radial velocity decreases as the local velocity ratio (α) increases. The pressure coefficient depends on the centrifugal force and it decreases as the distance from nozzle to plate increases. In impingement zone and radial wall jet, the spread of flow increases as the angular velocity decreases The numerical results give good agreement with the experiment data of Minagawa and Obi (Int. J. of Heat and Fluid Flow 2004; 25 :759–766). Copyright © 2006 John Wiley & Sons, Ltd.     

Investigation on gas-solids hydrodynamics and matching enhancement in feedstock injection zone of double-level nozzle riser

With the development of current energy economy, it is necessary to improve the product distribution of fluid catalytic cracking process, which is achieved by a riser reactor with double-level of nozzles. The new riser is constructed by adding a level of secondary nozzle 0.5 m below the main nozzle of traditional riser. This paper investigates the gas-solids flow and oil-catalyst matching feature based on the optical fiber and tracer technologies. According to the distribution of solids holdup, particle velocity and dimensionless jet concentration, the feedstock injection zone can be divided into the upstream flow control region, the main flow control region, and the secondary flow control region in the radial direction. The size of the regions is changed by the jet gas velocity and axial height. There is a poor match of secondary nozzle jet to particles below the main nozzle. The jet gas from secondary nozzles can improve the matching effect of oil-catalyst near the wall and reduce the probability of coking above the main nozzle.     

Investigation of Submerged Jets with an Extended Initial Laminar Region

The method of producing laminar submerged jets using a device, whose length is comparable with the jet diameter, is described. A submerged air jet, 0.12 m in diameter, produced by means of this technique is experimentally investigated in the Reynolds number range from 2000 to 13 000. Hot-wire anemometer measurements of the flow parameters and laser visualization of the flow are performed. It is shown that the device developed makes it possible to produce submerged jets with the laminar regions as long as 5.5 jet diameters. The initial regions of such jets can be used to study the development of disturbances in submerged jets, as well as used in medicine and engineering in organizing various gasdynamic curtains which produce zones with given properties with respect to purity and composition inside another gas media.     

Experimental investigation of circular free-surface jet impingement quenching: Transient hydrodynamics and heat transfer

An experimental study of heat transfer during quenching of a cylindrical stainless steel test specimen has been performed. A subcooled water jet is directed onto the upward facing flat face of the cylinder. The test specimen is heated to an initial temperature slightly above 900 °C and then quenched. The resulting boiling curves and heat transfer distributions are presented for impingement velocities of 2.85 and 6.4 m/s (Re = 7900 and 18,900). High-speed imaging shows that three distinct regions on the quenched surface can be identified: an expanding circular wetted region surrounding the impinging point, annular transition zone just outside the wetting front, and a unwetted region outside this zone. The free-surface of the liquid in the wetted region is smooth in the nucleate and transition boiling regimes. The annular transition zone or the wetting front region outside the wetted region is characterized by a highly disturbed liquid-gas interface, which can be attributed to intense vapor generation. At the outer edge of the transition zone, the liquid is deflected away from the surface. The velocity of the wetting front significantly increases with the jet impact velocity, which indicates that the wetting front position is governed by the ability of the flowing liquid to transport the bubbles radially outwards from the wetted region.     

Radial jet in rotating outer flow

The rotating radial jet formed by fluid introduced radially outwards into a rotating environment is studied by the momentum integral method and by perturbation for weak swirl, assuming incompressible laminar flow. For non-swirling outer fluid, the results slightly extend previously published results. For swirling outer fluid, the jet is characterized by a finite radial penetration distance. Its development over that distance is divided into three regions: an initial adjustment, a central pseudo-similarity region, and a final decay.     

Visualization and structure of confined, milliscale, unsteady impinging slot jets and associated vortices

Flow characteristics of confined, laminar milliscale slot jets are investigated from visualizations, as they impinge upon a flat target plate, with a fully developed velocity profile at the nozzle exit. The effects of Reynolds number Re and normalized nozzle-to-plate distance H/B are considered for a nozzle width B of 1.0 mm. Transition from a stable symmetric jet to an unsteady oscillating jet is observed as the Reynolds number increases (with H/B constant), where the Reynolds number associated with this transition decreases as the normalized nozzle-to-plate distance H/B increases. Instantaneous visualizations show unsteady lateral distortions of jet columns at experimental conditions corresponding to the presence of continuous sinusoidal oscillations, intermittent oscillating motion of the jet column, and jet flow fluctuation/flapping motion. Also apparent in flow visualization sequences are smoke signatures associated with instantaneous vortex structures, which form as secondary flows develop in fluid which, initially, is just adjacent to and within the jet column. Associated jet and vortex structural changes are described as different modes of unsteadiness are present, including characterization of jet column unsteadiness using jet column oscillation frequency, and lateral and streamwise extents of jet distortion.     

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.     

Efficient approaches of determining the motion of a spherical particle in a swirling fluid flow using weighted residual methods

The motion of a spherical particle released in a swirling fluid flow is studied employing the least-squares method and method of moments. The governing equations are obtained and solved employing the two methods. The accuracy of the results is examined against the results of a fourth-order Runge–Kutta numerical method. The effects of various parameters, namely the initial radius, initial radial velocity, initial angular velocity, and drag-to-inertia ratio, on the non-dimensional velocity profiles and particle position distribution are considered. The results show that the radial velocity increases over time while the angular velocity decreases, and that an increase in the initial radial velocity increases the particle radial distance and angular velocity but decreases the radial velocity profile.