Certain features of similarity solutions for flows in viscous vortex cores

A class of steady similarity solutions of the equations for viscous vortex cores which correspond to external inviscid similarity solutions with a power-law variation of the circumferential velocityv-r ^−m near the rotation axis is considered. It is found that if the Bernoulli function in external flow is constant, then these solutions will exist only on a certain range of the indexm of the exponential. For eachm on this range there are two solutions. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 38–43, January–February, 1998. The work was financially supported by the Russian Foundation for Fundamental Research (project No. 95-01-00483).     

Similarity solutions for the evolution of polydisperse droplets in vortex flows

A new mathematical analysis of the dynamics of evaporating sprays in the vicinity of a vortex flow field is presented. The governing equations for a polydisperse spray evaporating in an unsteady viscous vortex flow are formulated using the sectional approach. First, new similarity solutions are found for the dynamics of the spray in a mono-sectional framework. It is shown that similarity for the droplets’ drag term exists, and an explicit model for the drag is found using perturbation theory. Numerical simulations are conducted to validate the main assumptions of the analytic approach adopted in this study. An extension of the mono-sectional solution of the spray equations to a polydisperse spray solution is then derived and the dynamics of polydisperse spray in an Oseen type vortex are presented. It is shown that for a given radial location, the droplets in each section reach a maximal radial velocity due to the effect of vorticity. A simple model is derived for the prediction of this maximal radial velocity of the droplets using perturbation theory, which agrees very well with the full similarity solution. The present study shows that spray dynamics is highly affected by the droplets’ size, but also by the spray initial size distribution, even when the same Sauter mean diameter is considered. This may have far reaching implications, especially in spray combustion applications.     

Effects of vortex pairing on particle dispersion in turbulent shear flows

Particle dispersion in large-scale dominated turbulent shear flow is investigated numerically with special emphasis on the effects of the vortex-pairing phenomenon. The particle dispersion is visualized numerically by following the particle trajectories in a flow consisting of large vortices which are undergoing pairing interaction. The flow field is generated by a discrete vortex method. Important global and local fiow quantities from the numerical simulation compare reasonably well with experimental measurements.

For both cases of point sources with continuous particle release and an initially distributed line source, the particle dispersion results demonstrate that the extent of particle dispersion depends strongly on the Stokes number, the ratio of the particle aerodynamic response time to the characteristic time of the vortex-pairing flow field. Particles with relatively small Stokes numbers disperse laterally at approximately the saine rate as that of the fluid particles and particles with large Stokes numbers disperse much less than the fluid particles. Particles with intermediate Stokes numbers (0.5-5) may be dispersed laterally farther than the fiuid particles and may actually be flung out of the vortex structures. Due to the strong particie entrainment power, the flow during the vortex-pairing process seems to produce higher particle lateral dispersion than the pre-pairing and post-pairing flows.     

Secondary flows in turbulent surfactant solutions at maximum drag reduction

Secondary flows are always present when a turbulent Newtonian fluid flows through a square duct. We show that they are suppressed in surfactant solutions at maximum drag reduction. This result confirms the one-dimensional behaviour of such flows, which is caused by the alignment of the micelles.     

Group theoretical analysis and similarity solutions for stress boundary layers in viscoelastic flows

Lie group theory is used to obtain point symmetries of the boundary layer equations derived in the literature for the high Weissenberg number flow of upper convected Maxwell (UCM) and Phan-Tien-Tanner (PTT) type of viscoelastic fluids. The equations are reduced to ordinary differential equation systems with the use of scaling and spiral transformation groups. Similarity solutions are obtained and discussed for different cases such as flow around corners, flow over moving and stretching walls, and exponential shear flows.     

Gas-dynamic analogy for vortex free-boundary flows

The classical shallow-water equations describing the propagation of long waves in flow without a shear of the horizontal velocity along the vertical coincide with the equations describing the isentropic motion of a polytropic gas for a polytropic exponent γ = 2 (in the theory of fluid wave motion, this fact is called the gas-dynamic analogy). A new mathematical model of long-wave theory is derived that describes shear free-boundary fluid flows. It is shown that in the case of one-dimensional motion, the equations of the new model coincide with the equations describing nonisentropic gas motion with a special choice of the equation of state, and in the multidimensional case, the new system of long-wave equations differs significantly from the gas motion model. In the general case, it is established that the system of equations derived is a hyperbolic system. The velocities of propagation of wave perturbations are found. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 8–15, May–June, 2007.     

Degradation effects of dilute polymer solutions on turbulent drag reduction in pipe flows

An important practical problem in the application and study of drag reduction by polymer additives is the degradation of the polymer, for instance due to intense shearing, especially in recirculatory flow systems. Such degradation leads to a marked loss of the drag-reducing capability of the polymer.Three different polymer types were tested on degradation effects in a closed pipe flow system. The polymers used were Polyox WSR-301, Separan AP-273 and Superfloc A-110, dissolved in water in concentrations of 20 wppm each. The flow system consisted of a 16.3 mm pipe of 4.25 m length. Two different pumps were used: a centrifugal pump and a disc pump. Different solution-preparation procedures were tried and the experiments were performed at different flow rates.Superfloc A-110 proved to be both the most effective drag reducer and most resistant to degradation. Because of very fast degradation, Polyox WSR-301 was found to be unsuitable for being used as a drag reducer in re-circulatory systems. The disc pump proved to be much better suited for pumping the polymer solutions than the centrifugal pump. The degradation curve of the combination Superfloc/disc pump showed a plateau-like region with reasonable drag reduction, which makes it possible to perform (laser Doppler) measurements under nearly constant circumstances during a sufficient time.     

Inflow conditions for inhomogeneous turbulent flows

A cost‐effective method to generate inflow conditions for direct numerical simulations of wall‐bounded flows is presented. The method recycles a finite‐length time series of instantaneous velocity planes extracted from a precursor simulation and has earlier proved efficient for free shear layers. Now a spatially developing plane channel flow is considered. Different durations t_s of the time series are tested and compared. Excellent agreement with fully developed channel flow statistics is observed when t_s equals or exceeds the large‐eddy turnover time scale. The present results are more realistic than those obtained with synthetic turbulence generation and at the same time substantially cheaper than running an auxiliary simulation in parallel. Copyright © 2008 John Wiley & Sons, Ltd.     

Transport in a turbulent vortex ring

Transport in a turbulent vortex ring is considered; the mass of a passive impurity transported by the vortex is found as a function of distance traveled via a formula that agrees closely with experiment. A method is indicated for filling the part of the vortex that transports the impurity without loss. The effects of the following factors on the transport have been examined: initial Reynolds number, roughness in walls of the exit hole, and density difference between the solution and the medium. The transport of aerosols and suspended particles by vortex rings is considered. Two methods of transport measurement are compared.     

A Lagrangian vortex method for unbounded flows

A technique is presented for velocity calculations on the highly distorted node distributions typical of those found in Lagrangian vortex methods. The method solves the partial differential equation for streamfunction directly on the nodes, via a sparse, symmetric system of equations that can be solved using standard iterative solvers. When implemented in a triangulated vortex method, the technique gives computation times which scale as N^1.23, where N is the number of nodes. The computation scheme is derived for two‐dimensional problems and applied to the prediction of the evolution of perturbed multipolar vortices. Due to the numerical performance of the method, it has been possible to examine such evolution at higher and lower Reynolds numbers than have been considered in published numerical studies. Copyright © 2008 John Wiley & Sons, Ltd.     

Molecular transfer in turbulent flows

For modeling the molecular transfer of a passive scalar in a known turbulent field, the equations for the average scalar value and the correlation function for the scalar field are written in a form which makes it possible to examine the effect of molecular transfer on turbulent transfer and scalar dissipation. For the closure of the equation for the correlation function, the Prandtl hypothesis is used. The statistical reliability of this closure is demonstrated. The system proposed makes it possible to predict the dynamics of a decaying uniform scalar field and to explain why the effect of the real value of the molecular-transfer coefficient on the decaying scalar field is weak. Specific features of the transport process in a plane layer with prescribed scalar values on the layer boundaries are considered.     

Simulation of leading-edge vortex flows

An implicit upwind-relaxation finite-difference algorithm solving the incompressible Navier-Stokes equations is employed to simulate low-speed, three-dimensional, laminar, leadingedge vortex flows over three round-edged low-aspect-ratio wings. The effects of grid density, angle of attack, Reynolds number, and wing planform on the flowfield structures and integral values are studied. Computed results are presented and compared with experimental data.The work of the first author was supported by the NASA Langley Research Center under Contract NAS1-18585.