Disappearing Wakes and Dispersion in Numerically Simulated Flows Through Tube Bundles

Flow through a staggered array or bundle of parallel rigid cylinders of diameter D is computed with the help of a three-dimensional direct numerical simulation (DNS) at various values of Reynolds number between 50 and 6000. Two different spacings L of the tubes, i.e. L/D= 2 and L/D= 3, have been considered. When Re 500 the flow is laminar. In that case the converging flow between a pair of adjacent cylinders brings the oppositely signed vorticity at the two edges of the wake closer together behind the upstream cylinder so that the vorticity decreases quickly due to cancellation by diffusion. At Re 6000, when the flow is highly turbulent, the wake vorticity disappears rather by turbulent diffusion. This disappearance of the wakes in the closely packed flows (i.e. L/D 2) causes the mean flow in a cell, which consists of the region around a single cylinder, to be effectively independent of that in other cells. Another consequence is that the mean velocity field can be very well approximated by potential flow except in a thin boundary layer along the cylinder and a short wake behind it. The results have been applied to the transport of scalars in closely packed arrays. As in other complex flows, the dispersion of the scalars is dominated by the divergence and convergence of the streamlines around the cylinder rather than by the wake turbulence. Approximate expressions are derived for this topologically influenced dispersion in terms of the geometry of the array. The fact when most of the flow in the array can be approximated by a potential flow, allows us to introduce a fast approximate calculation method to compute the dispersion.     

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.     

The reduction of skin friction by riblets under the influence of an adverse pressure gradient

In this paper we address the effectiveness of riblets on skin friction reduction under the influence of an adverse pressure gradient. The measurements were taken in a wind tunnel. Skin friction was observed with a drag balance which has a reproducibility of better than 1%. The accuracy of the balance is estimated to be less than 1% for the case of zero-pressure gradient and at most 3% for a pressure gradient. The data on skin friction reduction at zero pressure gradient were consistent with previous results and amount to 5% at dimensionless riblet width of s ⁺ = 13. We find that at all adverse pressure gradients the skin friction reduction by riblets persists. At moderate pressure gradients the reduction increases somewhat to 7%. The velocity profile which is also measured, exhibits the characteristic shape for a boundary layer with an adverse pressure gradient and agrees well with theory. From the velocity profiles measured at two stations we estimated with the help of a momentum balance the skin friction and skin friction reduction. The results differ from the drag-balance data. Due to the poor accuracy of the momentum balance method which we estimate in our case, we conclude that the results obtained with this method are less reliable than those obtained with the drag balance. This throws some doubt on previous results on drag reduction under the influence of a pressure gradient which were based on the momentum balance method.     

A solution of the E-ε model for nearly homogeneous turbulence with a mean shear

An analytical solution of the E-ε model for the downstream evolution of a stationary and nearly homogeneous turbulent shear flow is presented. In case that the turbulent time scale has adjusted itself to the time scale imposed by the shear, an asymptotic solution can be derived from the full solution, which shows that both E and ε increase downstream exponentially. By comparing this asymptotic solution with experimental data a value for the unknown constant c _lε , in the ε-equation, is derived. Moreover, we find an expression for the downstream development of the variance of a scalar, which is also compared with experimental data. The analytical solution shows that a homogeneous shear flow with a uniform velocity gradient can only be obtained if the shear is sufficiently small. In the experiments this condition is not always satisfied. A discussion is given on how a nearly homogeneous shear flow can be obtained over a limited downstream interval by changing the initial conditions in E and ε, and a comparison is made with experimental data. Finally it is shown that better transverse homogeneity can be obtained by taking an exponential velocity profile instead of a linear profile.     

Measurement of product concentration of two parallel reactive jets using digital image processing

The chemically sensitive LIF technique [9] is employed to study the mixing of two reactive axisymmetric jets, one of which carries fluorescein, in an ambient quiescent fluid. The degree of mixing depends on the jet spacing and the axial position downstream of the jets and power laws are found to hold for some concentration characteristics. Unlike the far velocity field of dual plane jets, self preservation laws are not found to hold in general for the concentration field.     

On the Electric Potential Induced by a Homogeneous Magnetic Field in a Turbulent Pipe Flow

In this paper we study a turbulent pipe flow of a weakly electrical conducting fluid subjected to a homogeneous magnetic field which is applied perpendicular to the flow. This configuration forms the basis of a so-called electromagnetic induction flow meter. When the Hartmann number is small so that modification of flow by the Lorenz force can be neglected, the influence of the magnetic field results only in a spatially and temporally varying electric potential. The magnitude of the potential difference across the pipe is then proportional to the flow rate and this constitutes the principle of the flow meter. In this study the flow and electric potential are computed with help of a numerical flow simulation called Large-Eddy Simulation (LES) to which we have added an equation for the electrical potential. The results of the LES have been compared with experiments in which the electric potential is measured as a function of time at several positions on the circumference of the pipe. Both the experimental and numerical results for the mean potential at the pipe wall agree very well with an exact solution that can be obtained in this particular case of a homogeneous magnetic field. Furthermore, it is found that fluctuations in the electric potential due to the turbulence, are small compared to the velocity fluctuations. Based on the results we conclude that electrical-magnetic effects in pipe flow can be accurately computed with LES.     

The vorton method

After a general introduction to the vorton method, which is a vortex method resembling the 2-D point-vortex method, a set of equations describing dynamics of 3-D vortex singularities (vortons) is derived, avoiding the inconsistency in the derivation of other vorton equations which have been applied. Though inviscid, numerical simulations show reconnection phenomena.