Journal of Fluids Engineering, Transactions of the ASME

The turbulent fluid motion established in the wake of two long, smooth circular cylinders arranged perpendicular to each other has been investigated in a steady, low-turbulence, uniform flow at Reynolds numbers of 2×104 and 2×103 (based on cylinder diameter and freestream velocity). A complex three-dimensional regime was found at the center of the configuration, the precise nature of which is dependent upon the spacing of the cylinders. If the distance between the axis of each cylinder is less than three diameters, the fluid motion in the central near wake is dominated by secondary flows associated with trailing vortices and horseshoe vortices, whereas at spacings beyond this critical value there is a considerable reduction in the influence of secondary flow. The paper examines these spacing related regimes in detail and considers the extent of the associated interference effects.

One aspect of the flow around two intersecting cylinders, which has attracted little attention so far, is the structure of a three-dimensional near-wake behind the intersection. Some preliminary measurements of pressure distributions along the span were complemented by oil-film surface flow visualization. A strong secondary flow was found in the near-wake which extended spanwise more than three diameters from the intersection. The main feature was the formation of four symmetrically positioned pairs of swirling vortices which originated from the surface of the cylinders. The secondary flow caused an increase in the local drag coefficient.

There are infinite numbers of possible arrangements of two parallel cylinders positioned at right angles to the approaching flow direction. Of the infinite arrangements, two distinct groups may be identified: in one group, the cylinders are in a tandem arrangement, one behind the other at any longitudinal spacing; and in the second group, the cylinders face the flow side by side at any transverse spacing. All other combinations of longitudinal and transverse spacings represent staggered arrangements. The tandem arrangement will be treated first. A critical survey of previous research revealed some “odd” features which had been observed and overlooked by various authors. The discontinuity of vortex shedding implies that a similar discontinuity should be expected for the drag force on both cylinders. The measurements of the front (gap) pressures of the downstream cylinder and the base pressures of both cylinders at various spacings reveal a discontinuous “jump” at some critical spacing. The discontinuity is caused by the abrupt change from one stable flow pattern to another at the critical spacing. A new interpretation is given for the existing data on the drag force for both cylinders. The effects of Reynolds number and surface roughness are treated in some detail. Following this, two cylinders arranged side by side to the approaching flow are considered. All the available data on measured forces are compiled together with additional measurements in the range of intermittent changes of drag and lift forces. The bistable nature of the asymmetric flow pattern around each cylinder produces two alternative values of the drag force coupled with two alternative values of the lift force. The introduction of the interference force coefficient exposes the physical origin of two different forces experienced by the cylinders when arranged side by side. Finally, the least reported arrangement of two staggered cylinders is reviewed. The various arrangements are grouped into classes according to the sign of the lift force, or whether the drag force is greater or less than that for a single cylinder. The measurements of drag and lift forces for various arrangements reveal two different regimes for the lift force. In one regime, the lift force directed toward the wake of the upstream cylinder is due to the entrainment of the flow into the fully developed wake of the upstream cylinder. The lift force in this regime reaches a maximum value when the downstream cylinder is near to the upstream wake boundary. In the second regime, at very small spacings, the lift force becomes very large due to an intense gap flow which displaces the wake of the upstream cylinder. The maximum lift force occurs with the downstream cylinder near to the horizontal axis of the upstream cylinder. A discontinuity in the lift force for some staggered arrangements is found and attributed to the bistable nature of the gap flow.

A turbulent-energy-dissipation model is proposed for flows with and without drag reduction. The model is based on an eddy diffusivity approximation in the momentum equation, and on transport equations for the turbulent energy and the turbulent energy dissipation. The model describes the mean velocity profile and the turbulent energy distribution as a function of the reduction in the friction coefficient. It also yields a turbulent length scale which is shown to grow with drag reduction. The predictions of the model are in good agreement with the available experimental data.

A simple turbulent energy model, based on an improved version of Wolfshtein’s model for Newtonian flows, with a variable damping parameter, is used to describe the effect of linear polymers on the velocity profile and the turbulent energy distribution in channel and pipe flows. Measured mean velocity profiles seem to be in good agreement with the model, which predicts as well the observed increase in turbulent energy near the wall in flows with drag reduction.

Inadequate transport of rock cuttings during drilling of oil and gas wells can cause major problems such as excessive torque, difficulty to maintain the desired orientation of the drill string, and stuck or broken pipe. The problem of cuttings transport is aggravated in highly inclined wellbores due to the eccentricity of the annulus which results in nonuniformity of the flowfield within the annulus. While optimum cleaning of the borehole can be achieved when the flow is turbulent, the added cost due to the increased frictional losses in the flow passages may be prohibitive. A way around this problem is to add drag-reducing agents to the drilling fluid. In this way, frictional losses can be reduced to an acceptable level. Unfortunately, no model is available which can be used to predict the flow dynamics of drag-reducing fluids in annular passages. In this paper, a numerical model is presented which can be used to predict the details of the flowfield for turbulent annular flow of Newtonian and non-Newtonian, drag-reducing fluids. A one-layer turbulent eddy-viscosity model is proposed for annular flow. The model is based on the mixing-length approach wherein a damping function is used to account for near wall effects. Drag reduction effects are simulated with a variable damping parameter in the eddy-viscosity expression. A procedure for determining the value of this parameter from pipe flow data is discussed. Numerical results including velocity profiles, turbulent stresses, and friction factors are compared to experimental data for several cases of concentric and eccentric annuli.

The partially averaged Navier–Stokes (PANS) approach is a bridging closure model intended for any level of resolution between the Reynolds averaged Navier–Stokes (RANS) method and direct numerical simulations. In this paper, the proposed closure model is validated in the flow past a square cylinder. The desired ratio of the modeled-to-resolved scales in the PANS closure is achieved by appropriately specifying two bridging parameters: the ratios of unresolved-to-total kinetic energy (fk) dissipation (fε). PANS calculations of different bridging parameter values are performed and the results are compared with experimental data and large-eddy simulations. The Strouhal number(St), mean/root-mean-square (RMS) drag coefficient (CD), RMS lift coefficient (CL), mean velocity profiles, and various turbulent stresses are investigated. The results gradually improve from the RANS level of accuracy to a close agreement with the experimental results with decreasing value of the bridging parameter fk. Overall, the results indicate that the PANS method clearly satisfies the basic tenets of a bridging model: (i) provides a meaningful turbulence closure at any modeled-to-resolved scale ratio and (ii) yields improved accuracy with increasing resolution (decreasing modeled-to-resolved ratio).

Fully developed compound shear and buoyancy driven mixing layers are predicted using a k-ε turbulence model. Such mixing layers present an exchange of equilibrium in mixing flows. The k-ε buoyancy constant Cε3 = 0.91, defined in this study for buoyancy unstable mixing layers, is based on an approximate self-similar analysis and an accurate numerical solution. One-dimensional transient and two-dimensional steady calculations are presented for buoyancy driven mixing in a uniform flow field. Two-dimensional steady calculations are presented for compound shear and buoyancy driven mixing. The computed results for buoyancy alone and compound shear and buoyancy mixing compare well with measured data. Adding shear to an unstable buoyancy mixing layer does not increase the mixing growth rate compared with that from buoyancy alone. The nonmechanistic k-ε model which balances energy generation and dissipation using constants from canonical shear and buoyancy studies predicts the suppression of the compound mixing width. Experimental observations suggest that a reduction in growth rate results from unequal stream velocities that skew and stretch the normally vertical buoyancy plumes producing a reduced mixing envelope width.

An analysis is carried out on the wave formed during the slow phase of die casting injection processes. Viscous effects are assumed to be negligible and the problem is treated two-dimensionally using finite amplitude wave theory. Two commonly used types of plunger movements are considered, for which all the possible wave profiles are analyzed in depth as a function of the parameters which characterize the law of acceleration applied to the plunger, the initial shot sleeve filling fraction, and the geometrical characteristics of the problem. Different relationships between the relevant dimensionless parameters of the system are proposed, which make it possible to optimize the injection process, and so reduce the entrapment of air which leads to porosity. The validity of such relationships is analyzed in detail for different ranges of parameters. Some of the results obtained for the optimum acceleration are compared with those of other authors and experimental measurements. Finally, a law of plunger acceleration which would completely eliminate the air from the shot sleeve at the end of the slow phase of injection and minimizes the filling time is derived. [S0098-2202(00)02002-2]