Numerical treatment of the steady flow of a liquid compound jet

A numerical treatment of the outflow of a two-layer laminar jet into a non-viscous continuous phase is performed. The dispersed phases (i.e. the central core and the concentric layer) are immiscible, incompressible and Newtonian fluids. The method of solution allows for the simultaneous determination of the shape of both interfaces, as well as of the corresponding velocity profiles. The equations of motion of both phases are obtained in a boundary layer approximation. The pressure jump in the radial direction, owing to forces of interfacial tension, is taken into account. Also studied is how the initial velocity profiles at the nozzle exit and some dimensionless parameters affect the interaction between the primary and secondary flow. Numerical results agree qualitatively with some experimental evidence. The approach can also be employed to predict the flow within a viscous continuous phase.     

Numerical analysis of turbulent flow dynamics and heat transport in a round jet at supercritical conditions

Using a direct numerical simulation (DNS), a round jet of cryogenic nitrogen, which mimics the experiment by Mayer et. al. (2003) in terms of geometry, thermodynamics, and hydrodynamics, but at reduced Reynolds-Number (Re = 5300 based on the injection diameter), is investigated. The objectives of the present paper are: (1) to reliably predict the turbulence statistics in order to investigate the physical mechanisms, that dominate the flow dynamics, and to investigate the fuel disintegration and mixture formation, (2) to analyze the characteristics of heat transport phenomena of supercritical flows in order to determine parameter regimes advantageous to mixing, and (3) to provide a database for model development and validation that is difficult to obtain experimentally at such extreme thermodynamic conditions.The correctness of the results has been established at two levels. First, a grid-sensitivity study has been carried out to determine the resolution, which provides grid-independent turbulence statistics. This ensures, that the quantities of interest depend only on the physics and are not affected by the numerical methods. Secondly, numerical results have been compared to available experimental data of sub- and supercritical jets. Assuming self-similarity, several characteristics of the jet, like spreading rate, density variations and thermodynamic properties have been assessed.Finally, a comprehensive database including instantaneous flow and temperature fields, mean flow characteristics, turbulence properties along with turbulent kinetic energy budget, and heat flux has been made available. A link to heat flux transport modeling has been established to evaluate the suitability of some existing heat flux models as employed in such supercritical fluid flow.     

Experimental analysis of transverse intermittency in a turbulent jet flow

The statistical properties of the velocity differences are experimentally investigated in a turbulent jet-flow at moderate Re _λ by X-probe hot wire anemometry measurements. It is found that the traverse velocity components show a more intermittent behavior with respect to the longitudinal ones. This result is obtained by the analysis of the longitudinal and transverse intermittency exponents measured by the Extended Self-Similarity form of scaling, and by the comparison of the longitudinal and transverse velocity difference Probability Distribution Functions. Received: 25 March 1996/Accepted: 15 August 1996     

Numerical calculations of two-phase turbulent round jet

The investigation deals with the effect of suspended particles on the dissipation of turbulence energy.Additional dissipation is hypothesized as caused by the relative velocity between the particles and the fluid, and by structural changes of turbulence.An extended model for the turbulence energy equation is derived and applied to the case of an axially symmetrical free jet. The governing equations are solved numerically, and the results are compared with experimental data. Reasonably good agreement is obtained.     

Numerical analysis of turbulent flow in a rotating U-bend with roughened walls

A numerical analysis has been performed for a developing turbulent flow in a rotating U-bend of strong curvature with rib-roughened walls using an anisotropic turbulent model. In this calculation, an algebraic Reynolds stress model is used to precisely predict Reynolds stresses, and a boundary-fitted coordinate system is introduced as a method of coordinate transformation to set the exact boundary conditions along the complicated shape of U-bend with rib-roughened walls. Calculated results for mean velocity and Reynolds stresses are compared to the experimental data in order to validate the proposed numerical method and the algebraic Reynolds stress model. Although agreement is certainly not perfect in all details, the present method can predict characteristic velocity profiles and reproduce the separated flow generated near the outer wall, which is located just downstream of the curved duct. The Reynolds stresses predicted by the proposed turbulent model agree well with the experimental data, except in regions of flow separation.     

Velocity gradients in a turbulent jet flow

We present a selection of results from experiments on an air turbulent jet flow, which included measurements of all the three velocity components and their nine gradients with the emphasis on the properties of invariant quantities related to velocity gradients (enstrophy, dissipation, enstrophy generation, etc.). This has been achieved by a 21 hot wire probe (5 arrays x 4 wires and a cold wire), appropriate calibration unit and a 3-D calibration procedure [1]. A more detailed account on the results will be published elsewhere.     

Numerical prediction of turbulent flow structure generated by a synthetic cross‐jet into a turbulent boundary layer

A detailed numerical study using large‐eddy simulation (LES) and unsteady Reynolds‐averaged Navier–Stokes (URANS) was undertaken to investigate physical processes that are engendered in the injection of a circular synthetic (zero‐net mass flux) jet in a zero pressure gradient turbulent boundary layer. A complementary study was carried out and was verified by comparisons with the available experimental data that were obtained at corresponding conditions with the aim of achieving an improved understanding of fluid dynamics of the studied processes. The computations were conducted by OpenFOAM C++, and the physical realism of the incoming turbulent boundary layer was secured by employing random field generation algorithm. The cavity was computed with a sinusoidal transpiration boundary condition on its floor. The results from URANS computation and LES were compared and described qualitatively and quantitatively. There is a particular interest for acquiring the turbulent structures from the present numerical data. The numerical methods can capture vortical structures including a hairpin (primary) vortex and secondary structures. However, the present computations confirmed that URANS and LES are capable of predicting current flow field with a more detailed structure presented by LES data as expected. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical modeling of a two-dimensional vertical turbulent two-phase jet

The results of numerically modeling two-dimensional two-phase flow of the “gas-solid particles” type in a vertical turbulent jet are presented for three cases of its configuration, namely, descending, ascending, and without account of gravity. Both flow phases are modeled on the basis of the Navier-Stokes equations averaged within the framework of the Reynolds approximation and closed by an extended k-? turbulence model. The averaged two-phase flow parameters (particle and gas velocities, particle concentration, turbulent kinetic energy, and its dissipation) are described using the model of mutually-penetrating continua. The model developed allows for both the direct effect of turbulence on the motion of disperse-phase particles and the inverse effect of the particles on turbulence leading to either an increase or a decrease in the turbulent kinetic energy of the gas. The model takes account for gravity, viscous drag, and the Saffman lift. The system of equations is solved using a difference method. The calculated results are in good agreement with the corresponding experimental data which confirms the effect of solid particles on the mean and turbulent characteristics of gas jets.     

Mean flow characteristics of a turbulent plane jet with buoyancy induced curvature

An experimental investigation of heated vertical and inclined plane air jets discharged into quiescent surroundings is described. A unique feature of this data is that Pilot tube measurements were used to define the mean trajectory of the inclined jets so that subsequent hot-wire traverses could be made normal to the curved path. While the mean velocity and temperature profiles are self-similar for the range of exit conditions studied, other aspects of the mean jet development depend on the exit Reynolds and Froude numbers, or the discharge angle. It is noted that variations between this study and other published data suggest further measurements of this flow situation are needed, with particular attention to specific features of the jet apparatus and ambient surroundings, and to the exit Reynolds number. Presently with Dept. of Mechanical Engineering, University of Alexandria, Alexandria, Egypt     

Numerical finite difference model for steady state array growth

A control volume finite difference analysis has been used to calculate self-consistent cellular growth shapes. The results obtained are compared with the analytical models which have been proposed to describe array growth. It is concluded that the analytical models should be used with extreme caution in the cellular region. A preliminary examination of the stability of the steady state shapes has been made numerically. The results are compared with experiment and it is found that neither the minimum undercooling condition nor marginal stability analysis as applied, correctly predicts the growth conditions.     

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.     

Numerical analysis of three-dimensional flow past a high-speed electric train with turbulent boundary layer separation

An approach to the numerical study of three-dimensional flow past a high-speed electric train is considered, including the case of turbulent boundary layer separation. The method of viscous-inviscid interaction is used to compute the aerodynamic characteristics. The results of calculating the 3D flow past two configurations of a high-speed electric train, taking into account the close proximity of the ground surface, are presented for a train speedV =300 km/h and the per meter Reynolds number Re=5.6·10⁶ m^–1. One of these configurations is shown to have the advantage of separationless flow past a front locomotive and less intense diffuser separations on the afterbody of a rear locomotive. A local separation zone on the sides of the front locomotive's nose was detected in one of the cases considered.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 89–97, September–October, 1993.     

Interaction of a gas-droplet turbulent jet with a cocurrent high-velocity high-temperature gas flow

A mathematical model and a method for calculating a gas-droplet turbulent jet with allowance for velocity nonequilibrium and virtual mass of the condensed phase during turbulent fluctuations and also heat and mass transfer within the three-temperature scheme are developed. Methodical calculations are performed. The results of these calculations are in reasonable agreement with available experimental data. The structure of the gas-droplet jet in a cocurrent high-velocity high-temperature gas flow is studied by numerical methods. The ratio of intensities of heat and mass transfer between the phases and turbulent diffusion transfers of substances is found to be different at the initial, transitional, and basic segments of the jet. This difference is responsible for the nonmonotonic axial distribution of vapor density and the lines of the halved mass flow of the condensed phase. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 85–94, May–June, 2008.     

Investigation of the flow structure in a plane turbulent jet

Results of an experimental investigation of a plane, submerged air jet are elucidated. The distribution of the mean velocity, the longitudinal and transverse velocity component pulsations, the tangential friction stress, and the correlation coefficient in jet cross sections are presented. The results of measurements are compared with the data of other authors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 176–179, July–August, 1970.     

Control of low-speed turbulent separated flow using jet vortex generators

A parametric study has been performed with jet vortex generators to determine their effectiveness in controlling flow separation associated with low-speed turbulent flow over a two-dimensional rearward-facing ramp. Results indicate that flow-separation control can be accomplished, with the level of control achieved being a function of jet speed, jet orientation (with respect to the free-stream direction), and jet location (distance from the separation region in the free-stream direction). Compared to slot blowing, jet vortex generators can provide an equivalent level of flow control over a larger spanwise region (for constant jet flow area and speed).Nomenclature C _p pressure coefficient, 2(P-P_)/V ² - C _Q total flow coefficient, Q/ v - D ₀ jet orifice diameter - Q total volumetric flow rate - R Reynolds number based on momentum thickness - u fluctuating velocity component in the free-stream (x) direction - V free-stream flow speed - VR ratio of jet speed to free-stream flow speed - x coordinate along the wall in the free-stream direction - jet inclination angle (angle between the jet axis and the wall) - jet azimuthal angle (angle between the jet axis and the free-stream direction in a horizontal plane) - boundary-layer thickness - momentum thickness - lateral distance between jet orifices A version of this paper was presented at the 12th Symposium on Turbulence, University of Missouri-Rolla, 24–26 Sept. 1990     

Numerical investigation of corner angle and wing number effects on fluid flow characteristics of a turbulent stellar jet

In this research the fluid dynamics characteristics of a stellar turbulent jet flow is studied numerically and the results of three dimensional jet issued from a stellar nozzle are presented. A numerical method based on control volume approach with collocated grid arrangement is employed. The turbulent stresses are approximated using k–ε and k–ω models with four different inlet conditions. The velocity field is presented and the rate of decay at jet centerline is noted. Special attention is drawn on the influence of corner angle and number of wings on mixing in stellar cross section jets. Stellar jets with three; four and five wings and 15–65° corner angles are studied. Also the effect of Reynolds number (based on hydraulic diameter) as well as the inflow conditions on the evolution of the stellar jet is studied. The Numerical results show that the jet entrains more with corner angle 65° and five wings number. The jet is close to a converged state for high Reynolds numbers. Also the influence of the inflow conditions on the jet characteristics is so strong.