In this article the principles of the field operation and manipulation (FOAM) C++ class library for continuum mechanics are outlined. Our intention is to make it as easy as possible to develop reliable and efficient computational continuum-mechanics codes: this is achieved by making the top-level syntax of the code as close as possible to conventional mathematical notation for tensors and partial differential equations. Object-orientation techniques enable the creation of data types that closely mimic those of continuum mechanics, and the operator overloading possible in C++ allows normal mathematical symbols to be used for the basic operations. As an example, the implementation of various types of turbulence modeling in a FOAM computational-fluid-dynamics code is discussed, and calculations performed on a standard test case, that of flow around a square prism, are presented. To demonstrate the flexibility of the FOAM library, codes for solving structures and magnetohydrodynamics are also presented with appropriate test case results given. © 1998 American Institute of Physics.

A tensorial approach to computational continuum mechanics using object-oriented techniques

The structure of round jets in cross-flow was studied using flow visualization techniques and flying-hot-wire measurements. The study was restricted to jet to freestream velocity ratios ranging from 2.0 to 6.0 and Reynolds numbers based on the jet diameter and free-stream velocity in the range of 440 to 6200.Flow visualization studies, together with time-averaged flying-hot-wire measurements in both vertical and horizontal sectional planes, have allowed the mean topological features of the jet in cross-flow to be identified using critical point theory. These features include the horseshoe (or necklace) vortex system originating just upstream of the jet, a separation region inside the pipe upstream of the pipe exit, the roll-up of the jet shear layer which initiates the counter-rotating vortex pair and the separation of the flat-wall boundary layer leading to the formation of the wake vortex system beneath the downstream side of the jet.The topology of the vortex ring roll-up of the jet shear layer was studied in detail using phase-averaged flying-hot-wire measurements of the velocity field when the roll-up was forced. From these data it is possible to examine the evolution of the shear layer topology. These results are supported by the flow visualization studies which also aid in their interpretation.The study also shows that, for velocity ratios ranging from 4.0 to 6.0, the unsteady upright vortices in the wake may form by different mechanisms, depending on the Reynolds number. It is found that at high Reynolds numbers, the upright vortex orientation in the wake may change intermittently from one configuration of vortex street to another. Three mechanisms are proposed to explain these observations.

An experimental study of round jets in cross-flow

The mixing of the round jet normal to a uniform crossflow is studied for a range of jet-to-crossflow velocity ratios, r, from 5 to 25. Planar laser-induced fluorescence (PLIF) of acetone vapour seeded into the jet is used to acquire quantitative two-dimensional images of the scalar concentration field. Emphasis is placed on r=10 and r=20 and a few select images are acquired up to r=200. The Reynolds number based on the jet exit diameter, d, and the exit velocity varies from 8400 to 41 500. Images are acquired for conditions in which the product rd is held constant, requiring decreasing d for increasing r.Results from this experimental study concern structural events of the vortex interaction region, and mixing and mean centreline concentration decay in the near and far fields. The results cover all three regions of the transverse jet, and suggest that the jet scales with three length scales: d, rd and r2d.Events within the vortex interaction region display d-scaling, including the crossflow boundary layer separation and roll-up. Over the range of velocity ratios studied, the vortex interaction region shows r-dependent variations in the flow field, including the emergence of jet fluid in the wake structures for r>10 and a slower development of the counter-rotating vortex pair (CVP) in higher-r jets.The trajectory and physical dimension of the jet in both the near and far field display rd-scaling. The near field is characterized by a centreline concentration decay along the centreline coordinate s of s−1.3, different from the decay rate (s−1) of the free jet. When normalized by rd, the decay of each velocity-ratio jet branches away from the s−1.3 decay, approaching a decay of s−2/3, a rate predicted by modelling efforts. The branch points represent a transition in the flow field from enhanced mixing to reduced mixing compared to the free jet. When normalized by r2d, the branch points occur at a uniform jet position, s/r2d=0.3, which is viewed to be the division between the near and far fields. Self-similarity is not seen in the near field, but may be present in the far field.The view of the branch points as a place of transition in the flow is supported by the probability density function (p.d.f.) of concentration along the upper edge of the jet. Before the branch points, the p.d.f.s are non-marching in character, and after the branch points, they are tilted in character.Instantaneously, the CVP is asymmetric in shape and concentration. End views reveal extensive motion of the CVP and plan views show this motion can occur in both axisymmetric and sinusoidal motion. Ensemble-averaged images show the jet concentration is asymmetric about the centreline plane.

Mixing, structure and scaling of the jet in crossflow

Ensemble-averaged statistics at constant phase of the turbulent near-wake flow (Reynolds number ≈ 21400 around a square cylinder have been obtained from two-component laser-Doppler measurements. Phase was defined with reference to a signal taken from a pressure sensor located at the midpoint of a cylinder sidewall. The distinction is drawn between the near wake where the shed vortices are ‘mature’ and distinct and a base region where the vortices grow to maturity and are then shed. Differences in length and velocity scales and vortex celerities between the flow around a square cylinder and the more frequently studied flow around a circular cylinder are discussed. Scaling arguments based on the circulation discharged into the near wake are proposed to explain the differences. The relationship between flow topology and turbulence is also considered with vorticity saddles and streamline saddles being distinguished. While general agreement with previous studies of flow around a circular cylinder is found with regard to essential flow features in the near wake, some previously overlooked details are highlighted, e.g. the possibility of high Reynolds shear stresses in regions of peak vorticity, or asymmetries near the streamline saddle. The base region is examined in more detail than in previous studies, and vorticity saddles, zero-vorticity points, and streamline saddles are observed to differ in importance at different stages of the shedding process.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112095004435

A laser-Doppler velocimetry study of ensemble-averaged characteristics of the turbulent near wake of a square cylinder

The paper reports on measurements in the flow generated by a jet issuing from a circular outlet in a wall into a cross-stream along this wall. For the jet-to-crossflow velocity ratios R of 0.5, 1 and 2, the mean and fluctuating velocity components were measured with a three-sensor hot-wire probe. The hot-wire signals were evaluated to yield the three mean-velocity components, the turbulent kinetic energy, the three turbulent shear stresses and, in the case of R = 0.5, the terms in the turbulent-kinetic-energy equation. The results give a quantitative picture of the complex three-dimensional mean flow and turbulence field, and the various phenomena as well as their dependence on the velocity ratio R are discussed in detail.

Experimental investigation of jets in a crossflow

Laser-Doppler measurements of the velocity characteristics are presented for the turbulent flow around a square cross-section cylinder mounted in a water channel for Re=14000. The study involved spectral analysis and digital filtering of the LDV data obtained behind the cylinder. The purpose of the measurements is to separate and quantify the turbulent and the periodic, non-turbulent, motions of the wake flow, in order to improve knowledge of the nature of the fluctuations in the near-wake region of two-dimensional bodies. The results show, for example, that in the zone of highest velocity oscillations the energy associated with the turbulent fluctuations is about 40% of the total energy.

Measurements of turbulent and periodic flows around a square cross-section cylinder

A Round Jet Normal to a Crossflow

Wake flows behind two-dimensional model hills

This paper describes the application of three-dimensional finite-difference calculation procedures to the problem of a jet impinging on a flat plate through the influence of a confined crossflow One procedure uses the hybrid central/upwind difference scheme, and the other uses a quadratic upstream weighted difference scheme (QUICK) to calculate the convection terms The standard two-equation "& — c" turbulence model is used to calculate the distribution of the Reynolds stresses The difficulty of assessing turbulence model performance in these complex flows due to the intrusion of numerical diffusion errors is demonstrated by comparing the calculations on both coarse and fine meshes and by improving the accuracy of the convection terms discretization using the higher-order QUICK method The ability of the model calculations to simulate both the mean and the turbulence fields is examined, particularly in the vicinity of the stagnation point The results show the advantages of QUICK differencing scheme over the hybrid treatment, since the same level of numerical accuracy requires far less CPU time and computer memory when the QUICK scheme is used The calculations reveal the existence of large regions of low pressure, associated with an upstream recirculating flow region due to the interaction between the upstream wall jet and the crossflow, which may produce a substantial lift loss for a VSTOL aircraft

Numerical study of single impinging jets through a crossflow

Laser-Doppler measurements of velocity characteristics of the flowfield resulting from the impingement of single and twin jets against a wall through a low-velocity crossflow are presented and discussed together with visualization of the flow. The experiments have been carried out for a velocity ratio between the jet and the crossflow of 30, for a Reynolds number based on the jet exit between 60,000 and 105,000, and for the jet exit 5 jet diameters above the ground plate. In addition, calculations based on a two-equation turbulence model are presented for the three-dimensional flow characterized by the measurements, and comparison between experimental and numerical results show that the mean flowfield is well predicted. The calculation of the turbulent field requires, however, consideration of the individual stresses. 21 refs.

Diamantino Durão

Papers

Measurements of turbulent and periodic flows around a square cross-section cylinder

A Round Jet Normal to a Crossflow

Wake flows behind two-dimensional model hills

Numerical study of single impinging jets through a crossflow

Impingement of single and twin turbulent jets through a crossflow