Cross-stream Plane Research Articles

Developing turbulent boundary layers with system rotation

Measurements are presented for low-Reynolds-number turbulent boundary layers developing in a zero pressure gradient on the sidewall of a duct. The effect of rotation on these layers is examined. The mean-velocity profiles affected by rotation are described in terms of a common universal sublayer and modified logarithmic and wake regions.The turbulence quantities follow an inner and outer scaling independent of rotation. The effect appears to be similar to that, of increased or decreased layer development. Streamwise-energy spectra indicate that, for a given non-dimensional wall distance, it is the low-wavenumber spectral components alone that are affected by rotation.Large spatially periodic spanwise variations of skin friction are observed in the destabilized layers. Mean-velocity vectors in the cross-stream plane clearly show an array of vortex-like structures which correlate strongly with the skin-friction pattern. Interesting properties of these mean-flow structures are shown and their effect on Reynolds stresses is revealed. Near the duct centreline, where we have measured detailed profiles, the variations are small and there is a reasonable momentum balance.Large-scale secondary circulations are also observed but the strength of the pattern is weak and it appears to be confined to the top and bottom regions of the duct. The evidence suggests that it has minimally affected the flow near the duct centreline where detailed profiles were measured.

Streamwise computation of three-dimensional parabolic flows

A new approach to calculate three-dimensional parabolic flows is presented. The flow field is computed by calculating velocity along a set of streamlines. The dependent variables commonly used in the computation of three-dimensional flows are the three velocity components. In contrast, the dependent variables in the present approach are the streamwise velocity and the two coordinates, in the cross-stream plane, of the chosen streamlines. The streamwise velocity is calculated from the finite difference equations obtained by applying Euler's momentum theorem to streamtubes constructed around the chosen streamlines; the streamline coordinates are calculated from the conservation of mass. Results of the calculations, based on the present approach, are compared with the experimental data for flow through rectangular ducts; the agreement is satisfactory.

Laser-Doppler measurements of laminar and turbulent flow in a pipe bend

Laser-Doppler measurements are reported for laminar and turbulent flow through a 90° bend of circular cross-section with mean radius of curvature equal to 2.8 times the diameter. The measurements were made in cross-stream planes 0.58 diameters upstream of the bend inlet plane, in 30, 60 and 75° planes in the bend and in planes one and six diameters downstream of the exit plane. Three sets of data were obtained: for laminar flow at Reynolds numbers of 500 and 1093 and for turbulent flow at the maximum obtainable Reynolds number of 43 000. The results show the development of strong pressure-driven secondary flows in the form of a pair of counter-rotating vortices in the streamwise direction. The strength and character of the secondary flows were found to depend on the thickness and nature of the inlet boundary layers, inlet conditions which could not be varied independently of Reynolds number. The quantitative anemometer measurements are supported by flow visualization studies. Refractive index matching at the fluid-wall interface was not used; the measurements consist, therefore, of streamwise components of mean and fluctuating velocities only, supplemented by wall pressure measurements for the turbulent flow. The displacement of the laser measurement volume due to refraction is allowed for in simple geometrical calculations. The results are intenden for use as benchmark data for calibrating flow calculation methods.

Measurements of turbulent developing flow in a moderately curved square duct

Laser-Doppler measurements in the turbulent flow in a right-angled bend of square cross-section, radius/duct-width ratio 7.0, are presented and show the development of secondary circulation in cross-stream planes. Distribution of the streamwise and radial components of the mean velocity and turbulence intensity, and the corresponding Reynolds shear stress, are presented as contour plots and are intended for use in the further development of numerical flow prediction methods.

Turbulent flow in a square duct with strong curvature

The steady, incompressible, isothermal, developing flow in a square-section curved duct with smooth walls has been investigated. The 40 × 40 mm duct had a radius ratio of 2·3 with long upstream and downstream straight ducts attached. Measurements of the longitudinal and radial components of mean velocity, and corresponding components of the Reynolds-stress tensor, were obtained with a laser-Doppler anemometer at a Reynolds number of 4 × 104 and in various cross-stream planes. The secondary mean velocities, driven mainly by the pressure field, attain values up to 28% of the bulk velocity and are largely responsible for the convection of Reynolds stresses in the cross-stream plane. Production of turbulent kinetic energy predominates close to the outer-radius wall and regions with negative contributions to the production exist. Thus, at a bend angle of 90° and near the inner-radius wall, is positive and represents a negative contribution to the generation of turbulent kinetic energy.In spite of the complex mean flow and Reynolds stress distributions, the cross-stream flow is controlled mainly by the centrifugal force, radial pressure gradient imbalance. As a consequence, calculated mean velocity results obtained from the solution of elliptic differential equations in finite difference form and incorporating a two-equation turbulence model are not strongly dependent on the model; numerical errors are of greater importance.

The Flow Characteristics of a Piston-Cylinder Assembly with an Off-Centre, Open Port

Laser-Doppler anemometry has been used to measure the mean and r.m.s. values of the velocity components of the flow in a reciprocating assembly containing an off-centre, open port in the cylinder head and a flat piston. The port was inclined at an angle of 60° to the head and gave rise to a three-dimensional flow with no significant compression. The rotational speed was 200 rev/min, ensuring fully turbulent flow. The measurements were restricted to the axial and circumferential velocity components and were made on three radial planes in order to describe the flow in sufficient detail. The results are presented in the form of radial profiles and vector diagrams in both the axial and cross-stream planes. The main flow pattern on the intake stroke is of the same general shape as that previously obtained with a symmetric port, a large vortex occupying the space bounded by the indrawn jet with a much smaller vortex in the corner between the cylinder head and wall. These vortices are however no longer symmetrical about the cylinder axis, but vary in both size and intensity with circumferential position. In the cross-stream plane, the primary vortex is characterized by the presence of a stress-induced swirling motion on either side of the plane of symmetry with velocities significantly greater than the circumferential velocity of the jet. At mid-stroke, these vortices rotate counter to the jet, but at 144° ATDC, the direction of rotation reverses over part of the length of the vortex and is in the same sense as the jet motion. On the exhaust stroke, the flow patterns are relatively simple with quasi-parallel axial flow and little swirl until the port is approached, when the outgoing jet accelerates and begins to rotate in a direction opposite to its motion on the intake stroke.

A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows

A general, numerical, marching procedure is presented for the calculation of the transport processes in three-dimensional flows characterised by the presence of one coordinate in which physical influences are exerted in only one direction. Such flows give rise to parabolic differential equations and so can be called three-dimensional parabolic flows. The procedure can be regarded as a boundary-layer method, provided it is recognised that, unlike earlier published methods with this name, it takes full account of the cross-stream diffusion of momentum, etc., and of the pressure variation in the cross-stream plane. The pressure field is determined by: first calculating an intermediate velocity field based on an estimated pressure field; and then obtaining appropriate correction so as to satisfy the continuity equation. To illustrate the procedure, calculations are presented for the developing laminar flow and heat transfer in a square duct with a laterally-moving wall.