Turbulence measurements in a swirling pipe flow

This paper reports laser-Doppler measurements of the mean flow and turbulence stresses in a swirling pipe flow. Experiments were carried out under well-controlled laboratory conditions in a refractive index-matched pipe flow facility. The results show pronounced asymmetry in mean and fluctuating quantities during the downstream decay of the swirl. Experimental data reveal that the swirl significantly modifies the anisotropy of turbulence and that it can induce explosive growth of the turbulent kinetic energy during its decay. Anisotropy invariant mapping of the turbulent stresses shows that the additional flow deformation imposed by initially strong swirling motion forces turbulence in the core region to tend towards the isotropic two-component state. When turbulence reaches this limiting state it induces rapid production of turbulent kinetic energy during the swirl decay.

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Stability of a flow in a circular tube

Many studies, both theoretical and experimental, have been dedicated to the stability of flow in a circular tube (see, for example, review [1]). In every case mathematical investigation has not succeeded in obtaining an expression for hydrodynamic instability of such a flow for disturbances of sufficiently low amplitude. (An exception is [2].) Experiment also indicates the stability of such a flow [3], with a laminar mode being extended to Reynolds numbers of the order of tens of thousands. These facts are the basis for the assumption that the flow of a viscous incompressible liquid in a circular tube is stable for small perturbations. However, there is no analytical or even numerical proof of this hypothesis. Moreover, some studies, for example [2], indicate the instability of such a flow in relation to three-dimensional nonaxiosymmetric perturbations. The analysis of hydrodynamic stability with respect to three-dimensional disturbances of flow within a circular tube conducted in this study showed the stability of the flow over a wide range of wave numbers and Reynolds numbers.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 20–24, January–February, 1973.     

Axial flow of gelling materials through a circular pipe

Summary A set of constitutive equations for a group of incompressible materials of technological importance previously proposed by the authors is used to analyze the axial flow of a gelling Binghamlike material. Through five material parameters these constitutive equations account for the phenomena of breakdown in rigidity after deformation has occurred and of recovery in rigidity in the state of continued deformation or in the state of rest. Due to the complexity of predicting the flow of such nonlinear materials only the steady state behaviour in general seems to be tractable.The solution presented here describes the steady state axial flow of this type material through a circular pipe. It is shown that, depending on the choice of material parameters, two separate solutions may occur. As in the case of axial flow of a Bingham material or a retarded Bingham material a concentric core with rigid body motion is found. Analytically the radius of this core enters into the formulation of the requirements that must be fulfilled to establish a continuous flow field.It is further shown that volume flow rate dependence on the current pressure gradient may be a function of the loading history. For a specific case this dependence is shown in graphical form.     

Subsonic flow of a compressible gas around a semiinfinite flat plate in a pipe

The subsonic flow of an ideal compressible gas around the rear end of a semiinfinite flat plate in a pipe is considered. The flow pattern is similar to that assumed by Efros [1, 2] with a return stream for the cavitational flows. Fal'kovich's method [3] is used to solve the problem and this makes it possible to obtain the solution to the problems of the gas streams at several typical velocities. The method is a generalization of that of Chaplygin [4] for flow problems at one typical velocity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 101–108, July–August, 1970.     

Investigation of the stability for inviscid compressible swirling flow between concentric cylinders

The temporal stability on inviscid compressible swirling flow between two concentric cylinders is investigated. First, a linearized differential equation is derived. Two stability criteria are derived for compressible swirling flow by an analytic method analogous to Ludwieg ’s method. A finite-difference numerical method is then used to solve the eigenvalue problem of this differential equation, to get temporal growth rate and to check these stabilitv criteria derived. Finally.The effect of compressibility for stability is disscused.     

Numerical analysis of swirling turbulent droplet-laden flow and heat transfer in a sudden pipe expansion

The effect of swirling intensity on the structure and heat transfer of a turbulent gas–droplet flow after a sudden pipe expansion has been numerically simulated. Air is used as the carrier phase, and water, ethanol, and acetone are used as the dispersed phase. The Eulerian approach is applied to simulate the dynamics and heat transfer in the dispersed phase. The gas phase is described by a system of Reynolds-averaged Navier-Stokes (RANS) equations, taking into account the effect of droplets on mean transport and turbulent characteristics in the carrier phase. Gas phase turbulence is predicted using the second-moment closure. A swirling droplet-laden flow is characterized by an increase in the number of small particles on the pipe axis due to their accumulation in the zone of flow recirculation and the action of the turbulent migration (turbophoresis) force. A rapid dispersion of fine droplets over the pipe cross-section is observed without swirling. With an increase in swirling intensity, a significant reduction in the length of the separation region occurs. The swirling of a two-phase flow with liquid droplets leads to an increase in the level of turbulence for all three types of liquid droplets investigated in this work due to their intensive evaporation. It is shown that the addition of droplets leads to a significant increase in heat transfer in comparison with a single-phase swirling flow. The greatest effect of flow swirling on heat transfer intensification in a two-phase gas-droplet flow is obtained for the droplets of ethanol and water and smallest effect is for the acetone droplets.     

Numerical and experimental study of an axially induced swirling pipe flow

In-line flow segregators based on axial induction of swirling flow have important applications in chemical, process and petroleum production industries. In the later, the segregation of gas bubbles and/or water droplets dispersed into viscous oil by swirling pipe flow may be beneficial by either providing a pre-separation mechanism (bubble and/or drop coalescer) or, in the case of water-in-oil dispersions, by causing a water-lubricated flow pattern to establish in the pipe (friction reduction). Works addressing these applications are rare in the literature. In this paper, the features and capabilities of swirling pipe flow axially induced by a vane-type swirl generator were investigated both numerically and experimentally. The numerical analysis has been carried out using a commercial CFD package for axial Reynolds numbers less than 2000. Pressure drop, tangential and axial velocity components as well as swirl intensity along a 5 cm i.d. size and 3 m long pipe were computed. Single phase flow experiments have been performed using a water–glycerin solution of 54 mPa s viscosity and 1210 kg/m³ density as working fluid. The numerical predictions of the pressure drop were compared with the experimental data and agreement could be observed within the range of experimental conditions. The experiments confirmed that swirl flow leads to much higher friction factors compared with theoretical values for non-swirl (i.e. purely axial) flow. Furthermore, the addition of a conical trailing edge reduces vortex breakdown. Visualization of the two-phase swirling flow pattern was achieved by adding different amounts of air to the water–glycerin solution upstream the swirl generator.     

A variational approach to non-steady non-newtonian flow in a circular pipe

The transient response of a non-Newtonian power-law fluid to several assumed forms of pressure pulse in a circular tube is analysed by the semi-direct variational method of Kanntovorich. Velocity profiles are shown for several power-law indices, and by comparing the results for the Newtonian case with the exact solution given by Szymanski, it is observed that the results are good to 5%. More accurate solutions have been found for the case involving Newtonian fluid flow. New results are reported concerning the effect of a triangular pressure pulse on the development and transient response of the flow field of a non-Newtonian fluid.     

Stability of pipe flow with blowing

The stability of self-similar flows in a porous circular pipe [1–4] with respect to classical and self-similar perturbations of axisymmetric and nonaxisymmetric form is investigated. The case of blowing through the porous lateral surface is examined. Two formulations of the linear stability problem are considered and stability in the sense of self-similar evolution is also investigated. The limiting stability situations are analyzed. Relations for the critical values of the blowing rate parameters are presented for all the types of perturbations investigated. It is shown that nonaxisymmetric classical perturbations are the most dangerous.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 63–71, January–February, 1989.     

Heat transfer in laminar flow of Bingham material through a circular pipe

Summary The fully developed heat transfer in laminar flow of Bingham material through a straight circular pipe has been analysed when the effect of dissipation is taken into consideration. The temperature distribution, the mixed-mean temperature and the Nusselt number are calculated and found to depend on the Modified Reynolds number, the Brinkman number and the rate of heat transfer at the wall. The effect of dissipation is to increase the temperature and the mixed-mean temperature of the material while the Nusselt number is found to decrease with increasing dissipation.Nomenclature r, , z space coordinates - u, v, w velocity components - density of the fluid - modulus of rigidity (constant) - bulk modulus - e _kk, the dilation - ₁ coefficient of viscosity (constant) - e _ik strain tensor - d _ik rate of strain tensor - p _ik stress tensor primes denote deviatoric components of tensors, e.g. - p _ik p _ik p _ik, p=–1/3p _kk - yield value (constant) - D/Dt material derivative with regard to time following the particle - R radius of the pipe - r ₀ radius of the yield surface (cylindrical) - r=r ₀/R non-dimensional radius of the yield surface - T ₀ temperature of the pipe - K conductivity - Modified Reynolds number - Br Brinkman number     

Justification of the drift-flux model for two-phase flow in a circular pipe

A flow of a gas-liquid dispersed mixture in a circular pipe with a variable inclination to the horizon, as applied to oil and gas flows in wells, is considered. Within the framework of a multi- fluid approach, the equations of an asymptotic drift-flux model, which contains an algebraic relation between the phase velocities and one momentum equation for the volume-averaged velocity of the mixture, are derived. It is shown that the drift-flux model in this formulation strictly follows from the balance laws under assumption of inertialess velocity slip of the phases in case of validity of one of the following conditions: (i) the dispersed-phase volume fraction is small; (ii) the phase velocity slip may be neglected; or (iii) the flow regime is inertialess and the acceleration of the mixture can be neglected. A numerical algorithm based on the SIMPLE method is implemented for solving the obtained equations of the drift-flux model. The possibility of modeling the gravitational segregation and the pressure buildup in a shut-in well and transient slug flows is demonstrated.     

Unsteady compressible boundary layer flow over a circular cone near a plane of symmetry

An analysis has been performed to study the unsteady laminar compressible boundary layer governing the hypersonic flow over a circular cone at an angle of attack near a plane of symmetry with either inflow or outflow in the presence of suction. The flow is assumed to be steady at time t=0 and at t>0 it becomes unsteady due to the time-dependent free stream velocity which varies arbitrarily with time. The nonlinear coupled parabolic partial differential equations under boundary layer approximations have been solved by using an implicit finite-difference method. It is found that suction plays an important role in stabilising the fluid motion and in obtaining unique solution of the problem. The effect of the cross flow parameter is found to be more pronounced on the cross flow surface shear stress than on the streamwise surface shear stress and surface heat transfer. Beyond a certain value of the cross flow parameter overshoot in the cross flow velocity occurs and the magnitude of this overshoot increases with the cross flow parameter. The time variation of the streamwise surface shear stress is more significant than that of the cross flow surface shear stress and surface heat transfer. The suction and the total enthalpy at the wall exert strong influence on the streamwise and cross flow surface shear stresses and the surface heat transfer except that the effect of suction on the cross flow surface shear stress is small.     

Hydrodynamics of swirling flow in a circular tube with sudden increase in cross-section and of the flow through a borda mouthpiece

By applying the mass, momentum, and angular momentum conservation laws and the maximum flow rate principle to swirling, effectively inviscid, incompressible flows in a circular tube with a sudden expansion and in direct-flow and reversed-flow Borda mouthpieces the dependence of the flow rate coefficient and mechanical energy losses on the radius ratio and nondimensional circulation is obtained. Several calculating approaches with potential and helical motion are introduced and investigated. In the case of helical motion, as the swirl decreases the axial core of the flow is found to close with a sudden change of the flow parameters.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.3, pp. 51–66, May–June, 1994.     

Steady natural convection flow of a particulate suspension through a circular pipe

A continuum model for two-phase (fluid/particle) flow induced by natural convection is developed and applied to the problem of steady natural convention flow of a particulate suspension through an infinitely long pipe. The wall of the pipe is maintained at a constant temperature. The particle phase is endowed by an artificial viscosity which may be used to model particle-particle interaction in dension suspensions. Boundary conditions borrowed from rarefied gas dynamics are employed for the particle-phase wall conditions. Closed-form solutions for the velocity and temperature profiles are obtained. For the assumptions employed in the problem, the temperatures of both phases in the pipe are predicted to be uniform. A parametric study of some physical parameters involved in the problem is performed to illustrate the influence of these parameters on the velocity profiles of both the fluid and particle phases.     

3D numerical simulation of compressible swirling flow induced by means of tangential inlets

The objective of the present work is to predict compressible swirl flow in the nozzle of air‐jet spinning using the realizable k–ε turbulence model and discuss the effect of the nozzle pressure. The periodic change of flow patterns can be observed. The recirculation zone near the wall of the injectors upstream increases in size and moves gradually upstream, whereas the vortex breakdown in the injector downstream shifts slowly towards the nozzle outlet during the whole period. A low axial velocity in the core region moves gradually away from the centerline, and the magnitude of the center reverse flow and the area occupied by it increase with axial distance due to the vortex breakdown. From the tangential velocity profile, there is a very small free‐vortex zone. With increasing nozzle pressure, the velocity increases and the location of vortex breakdown is moved slightly downward. However, the increase in the velocity tends to decline at nozzle pressure up to a high level. Copyright © 2008 John Wiley & Sons, Ltd.