Calculation of the momentum and heat transfer in turbulent gas-particle jet flows

The equations for the second moments of the dispersed-phase velocity and temperature fluctuations are used for calculating gas-suspension jet flows within the framework of the Euler approach. The advantages of introducing the equations for the second moments of the particle velocity fluctuations has previously been quite convincingly demonstrated with reference to the calculation of two-phase channel boundary flows [9–11]. The flows considered below have a low solid particle volume concentration, so that interparticle collisions can be neglected and, consequently, the stochastic motion of the particles is determined exclusively by their involvement in the fluctuating motion of the carrier flow. In addition to the equations for the turbulent energy of the gas and its dissipation, the calculation scheme includes the equations for the turbulent energy and turbulent heat transfer of the solid phase; however, the model constructed does not contain additional empirical constants associated with the presence of the particles in the flow.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 69–80, May–June, 1992.     

Use of the turbulence energy equation in the theory of jet flows

In this study some of the assumptions introduced in [1] in developing a closed system of equations for a turbulent boundary layer will be simplified. With the aid of the system of equations of [1], a theoretical solution is found for the problem of a jet in an accompanying flow, it being assumed that the structure of the jet turbulence depends solely on local conditions. Experiment has shown that the turbulence in such a jet does depend also on the prehistory of the flow. At large distances from the source, the theoretical characteristics of the jet agree well with the experimentally determined characteristics of the wake beyond a body. Also examined is the problem of the boundary layer between two homogeneous flows, flowing with different velocities.Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 75–81, March–April, 1973.     

Dynamics of swirling jet flows

Experimental investigations of near-field structure of coaxial flows are presented for four different configurations: coaxial jets without rotation (reference case), outer flow rotating only (OFRO), inner-jet rotating only (IJRO) and corotating jets (CRJ). The investigations are performed in a cylindrical water tunnel, with an independent rotation of two coaxial flows. Laser tomography is used to document the flow field, and photographs are shown for different configurations. Time mean velocity profiles obtained by PIV, with and without swirl, are also presented. The dynamics of the swirling jets in the initial region (i.e. near the exit of the jets) is described. The effects of azimuthal velocity and axial velocity ratio variations on flow dynamics are examined. The appearance and growth of the first instabilities are presented and compared with some theoretical results, as is the influence of the rotation (inner or outer) on the dominating structures.     

Stability of nonplane-parallel three-dimensional jet flows

The problem of the stability of nonplane-parallel flows is one of the most difficult and least studied problems in the theory of hydrodynamic stability [1]. In contrast to the Heisenberg approximation [1], the basic state whose stability is investigated depends on several variables, and the stability problem reduces to the solution of an eigenvalue problem for partial differential equations in which the coefficients depend on several variables [2–7]. In the case of a periodic dependence of these coefficients on the time [2] or the spatial coordinates [3, 4], the analog of Floquet theory for the partial differential equations is constructed. With rare exceptions, the case of a nonperiodic dependence has usually been considered under the assumption of weak nonplane-parallelism, i.e., a fairly small deviation from the plane-parallel case has been assumed and the corresponding asymptotic expansions in the linear [6] and nonlinear [7] stability analyses considered. The present paper considers the case of an arbitrary dependence of the velocity profile of the basic flow on two spatial variables. The deviation from the plane-parallel case is not assumed to be small, and the corresponding eigenvalue problem for the partial differential equations is solved by means of the direct methods of [5], which were introduced for the first time and justified in the theory of hydrodynamic stability by Petrov [8].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 21–28, May–June, 1987.     

Turbulent jet flows with buoyancy and swirl

Übersicht Das gleichzeitige Auftreten von Auftrieb und Drall in vertikalen, runden, turbulenten Freistrahlen wird mit einer Integralmethode untersucht. Durch Hinzunahme der Bewegungs- und Energiegleichung an der Strahlachse kann auf die Verwendung eines empirischen Entrainmentkoeffizienten verzichtet werden. Es zeigt sich, daß zwischen Druck- und Axialgeschwindigkeitsprofilen eine ganz bestimmte Beziehung bestehen muß, um unrealistische Singularitäten im Strömungsfeld zu vermeiden. Die Beziehung wird durch Meßergebnisse annähernd bestätigt. Der Einfluß des Dralls auf alle Strömungsgrößen ist in der Nähe des Ursprungs am stksten. Eine Zunahme der dimensionslosen Drallzahl bewirkt eine starke Aufwertung des Strahls mit 180° Öffnungswinkel im Ursprung und eine Abnahme der axialen Geschwindigkeit. Im Grenzfall sehr hoher Drallzahlen entsteht eine neue Strahlströmung, die als drallbehafteter, auftriebserzeugter Strahl bezeichnet wird. Stromabwärts klingen die Dralleffekte rasch ab und Auftriebseffekte nehmen an Bedeutung zu. Das asymptotische Verhalten entspricht einem auftriebserzeugten Strahl (plume).

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Turbulent jet flows with buoyancy and swirl

Summary Vertical, round, turbulent jets with combined effects of buoyancy and swirl are investigated by an integral method. The method avoids application of an empirical entrainment coefficient by including the differential equations of motion and energy at the jet axis. It is shown that pressure and velocity profiles have to be related to each other in order to avoid unrealistic singularities in the flow field. This relationship is approximately confirmed by measurements. With respect to all flow quantities, the influence of swirl is felt strongest near the origin. Increasing the dimensionless swirl number strongly increases the width of the jet (with infinite derivative at the origin) and decreases the axial velocity. In the limiting case of very high swirl numbers a new type of jet flow is found which can be called a swirling plume. Further, downstream swirl effects decay rapidly and buoyancy becomes relatively more important. The asymptotic behaviour resembles that of a plume.

     

Investigation of flows induced by subsonic turbulent jets and their relation with the effect of static pressure reduction in a jet

The interaction between turbulent jets, both swirling and nonswirling, and the ambient medium is studied on the basis of the results of measurements and numerical simulation. It is shown that the turbulent flow and the swirl give rise to induced ejection flow toward the jet. The mechanism of the jet action on the ambient medium is connected with a decrease in the static pressure in the jet, which, in turn, is due to either the flow swirl or the fluctuating flow in the mixing layer, when the static pressure reduces owing to the presence of velocity fluctuations. The former rarefaction mechanism is predominant in swirling jets and the latter predominates in jets without swirling. It is shown that the ambient medium inflow into the jet due to the rarefaction is independent in nature of the mechanism of the lowered pressure generation and that it is the kinetic energy of the jet that is the energy source for the induced flow.     

Stability of some shear flows for concentrated suspensions

In this paper we investigate the stability of some viscometric flows for a concentrated suspension model which allows for the effects of shear-induced migration, including plane and circular Couette and Poiseulle flows, and unbounded and bounded torsional flows. In the bounded torsional flow, where its radial outer boundary is assumed frictionless, an exact closeform solution is given. With the exception of torsional flows, we find that a limit point for all the steady-state solutions can exist for certain range in the parameter values. In all cases, disturbances can persist for a long time, O (H ²/a ²), where H is a dimension of the flow field, and a is the particles' radius.     

Numerical simulation of confined laminar jet flows

Two‐dimensional incompressible jet development inside a duct has been studied in the laminar flow regime, for cases with and without entrainment of ambient fluid. Results have been obtained for the flow structure and critical Reynolds number values for steady asymmetric jet development and for the onset of temporal oscillations, at various values of the duct‐to‐jet width ratio (aspect ratio). It is found that at low aspect ratios and Reynolds numbers, jet development inside the duct is symmetric. For larger aspect ratios and Reynolds numbers, the jet flow at steady state becomes asymmetric with respect to the midplane, and for still higher values, it becomes oscillatory with respect to time. When entrainment is present, the instabilities of asymmetric development and temporal oscillations occur at a much higher critical Reynolds number for a given aspect ratio, indicating that the stability of the jet flow is higher with entrainment. Copyright © 2000 John Wiley & Sons, Ltd.     

Visualization of fan-spreading in two-phase jet flows

Flow visualizations obtained in a two-phase jet flow with 80 m particles at a mass loading of 5% revealed the following.

Numerical investigations of radial jet reattachment flows

A finite volume computational scheme to solve the Navier-Stokes equations for the laminar flow fields of partially enclosed axial and radial jets impinging on a flat plate has been devised and tested. This scheme is based on the SIMPLEC technique. However, because of the backflow at the ‘outflow’ boundary, the SIMPLEC pressure correction technique has to be modified. The need for this modification, necessitated by the convergence failure, showed the ‘hidden’ pressure boundary condition of SIMPLE-type techniques. Test computations with the present scheme for flows in a channel with a built-in cylinder show that the location of the exit boundary affects very slightly the separated flow behind the cylinder. Computed Squire jet flows compare quite well with the available analytical solution. Finally, impinging radial jets have been computed for different Reynolds numbers. The results show the critical Reynolds number below which a steady solution is obtained and above which periodic and eventually chaotic flows result.     

Oscillatory behavior of supersonic impinging jet flows

Oscillatory flows of a choked underexpanded supersonic impinging jet issuing from a convergent nozzle have been computed using the axisymmetric unsteady Navier--Stokes system. This paper focuses on the oscillatory flow features associated with the variation of the nozzle-to-plate distance and nozzle pressure ratio. Frequencies of the surface pressure oscillation and flow structural changes from computational results have been analyzed. Staging behavior of the oscillation frequency has been observed for both cases of nozzle-to-plate distance variation and pressure ratio variation. However, the staging behavior for each case exhibits different features. These two distinct staging behaviors of the oscillation frequency are found to correlate well if the frequency and the distance are normalized by the length of the shock cell. It is further found that the staging behavior is strongly correlated with the change of the pressure wave pattern in the jet shear layer, but not with the shock cell structure. Communicated by K. Takayama PACS 02.60.Cb; 47.40.−x; 47.40.Nm; 47.35.+I; 47.15.−x     

Turbulence characteristics of radially-confined impinging jet flows

Radially confined, axisymmetric impinging jet flows are investigated by using the standard particle image velocimetry experimental technique. The confinement is achieved by placing a confinement block around a jet, co-axially. The inner diameter of the block is successively varied to nine different values. The inlet-based Reynolds number of the jet is kept constant at 5000. The nine diametric values yielded nine different flows of widely different characteristics. Among other usage, an insight into the flow characteristics can be helpful in designing compact impinging jet applications, as such a radially confined flow is equivalent to passing the pre-impingement jet through a hole perforated in a solid wall (i.e. the jet source can be placed behind a wall). The study has revealed that the flows, in general, form two circulation zones, three mixing layers, and two boundary layers. Based on turbulence characteristics of the five shear layers, overall characteristics of the flows are understood systematically. Mean velocity and various turbulence statistics are also presented, and mechanisms underlying behind their variations are explained. Finally, scaling laws are obtained for the mean velocity and for the turbulence statistics, both in the impingement and in the wall jet regions.     

Identification of concentrated structures in slightly compressible two-dimensional flows

In this paper, different vortex diagnostic methods are compared to obtain a better understanding of boundary layer influence on the transport of vortical structures involving a complete analysis of vorticity, the Vorticity Threshold Criterion (VTC), and the Weiss Criterion (WC). These three techniques are basically confronted to find a suitable understanding of all flow characteristics for a range of laminar to transitional Reynolds numbers. The computations on this dihedral plane are done using a 2D DNS method. The Weiss criterion, coming from the analysis of the incompressible Euler equations is validated and applied to low speed compressible flows (Mach number=0.2).     

A comparative study of sound generation by laminar,combusting and non-combusting jet flows

Sound production by two-dimensional, laminar jet flows with and without combustion is studied numerically and theoretically. The compressible Navier–Stokes, energy and progress variable equations are solved by resolving both the near field and the acoustics. The combusting jet flows are compared to non-combusting jets of the same jet Mach number, with the non-combusting, non-isothermal jets having the same steady temperature difference as the combusting jets. This infers that the magnitude of entropic and density disturbances is similar in some of the combusting and non-combusting cases. The flows are perturbed by a sinusoidal inlet velocity fluctuation at different Strouhal numbers. The computational domain is resolved to the far field in all cases, allowing direct examination of the sound radiated and its sources. Lighthill’s acoustic analogy is then solved numerically using Green’s functions. The radiated sound calculated using Lighthill’s equation is in good agreement with that from the simulations for all cases, validating the numerical solution of Lighthill’s equation. The contribution of the source terms in Dowling’s reformulation of Lighthill’s equation is then investigated. It is shown that the source term relating to changes in the momentum of density inhomogeneities is the dominant source term for all non-reacting, non-isothermal cases. Further, this source term has similar magnitude in the combusting cases and is one of the several source terms that have similar magnitude to the source term involving fluctuations in the heat release rate.     

Approximate solutions of heat and momentum transfer in laminar plane wall jet

In the present paper approximate solutions for the fluid and thermal boundary layers in an incompressible laminar plane wall jet with isothermal and adiabatic walls have been studied respectively, and comparisons with the known exact solutions have been made wherever possible. It is found that the present method is simple and straightforward, and gives results being in good agreement with the exact solutions. For moderate values of the Prandtl number the method may be used for calculating the heat transfer from an isothermal wall and temperature recovery factor for an adiabatic wall respectively.Nomenclature a* dimensionless temperature gradient at the wall - c _p specific heat at constant pressure - K momentum flux through a cross-section of the jet - Q volume flux through a cross-section of the jet - r* temperature recovery factor - T temperature of the fluid in the boundary layer - T _r adiabatic wall temperature - T temperature of the fluid at rest - u, v velocity components along and normal to the plane wall respectively - x, y rectangular coordinates along and normal to the plane wall respectively - z Greek symbols fluid boundary layer thickness - _t, _T thermal boundary layer thickness for an isothermal and an adiabatic wall respectively - dimensionless y-coordinate - dimensionless temperature difference (T–T )/T - coefficient of thermal conductivity - coefficient of viscosity - coefficient of kinematic viscosity - Prandtl number - _w shearing stress on the plane wall     

Modeling of jet flows of a viscous fluid by the discrete vortex method

Results obtained previously by the discrete vortex method with a “viscous” correction are generalized. The boundaries of applicability of this method are determined. Previous results obtained for a flow past a flat plate are supplemented with solution convergence estimates. Exhaustion of a plane jet of a viscous incompressible fluid into the ambient space is modeled. The geometric parameters of the jet (its half-width, shapes of the streamwise velocity profiles, and intensity of oscillations) are analyzed. The calculated results are found to agree well with experimental data and with results calculated by other methods.