Revue des connaissances concernant les couches limites tridimensionnelles et autres couches de cisaillement ainsi que les ecoulements a tourbillons dans les turbomachines

Turbulent secondary flows

The mathematical modelling of turbulent flows

The turbulence models available for the prediction of complex turbulent shear layers are reviewed in this paper, concentrating mainly on three-dimensional flows, flows subjected to curvature and body rotation, separated flows, and vortex flows. A critical review of zero-equation, one-equation, two-equation, algebraic Reynolds stress, and full Reynolds stress models are carried out, with a specific emphasis on their applicability to complex flows. It is concluded that algebraic eddy viscosity models and kappa-epsilon/kappa-omega models, with a constant value of coefficients, are not adequate for complex flows. The models which include a description of stresses, either through an algebraic Reynolds stress model or a full Reynolds stress model, are essential for adequate prediction of these flows. It is recommended that systematic experimental investigations be carried out to isolate various complex interactions in order to understand and model the various effects and to carry out an extension of the present models to include complex flows.

Turbulence modeling for complex shear flows

The results are presented of turbulence measurements on an ‘infinite’ swept wing, simulated by a duct attached to a blower tunnel. The configuration is close to that used at the Netherlands NLR except that the boundary layer does not quite separate. The measurements include triple products, and a balance of the transport equation for turbulent energy is presented. The results confirm the NLR finding of a significant decrease in the magnitude of shear stress compared with an equivalent two-dimensional boundary layer: this is evidently the effect of crossflow on large eddies that have initially developed in a two-dimensional boundary layer. This unexpected effect of three-dimensionality is at least as important in prediction of real-life flows as the better-known lag between the direction of the shear stress and that of the mean-velocity gradient. Tentative suggestions for modelling the reduction in shear-stress magnitude are advanced.

Measurements in the turbulent boundary layer on an ‘infinite’ swept wing

The `law of the wall' for the inner part of a turbulent shear flow over a solid surface is one of the cornerstones of fluid dynamics, and one of the very few pieces of turbulence theory whose results include a simple analytic function for the mean velocity distribution, the logarithmic law Various aspects of the law have recently been questioned, and this paper is a summary of the present position Although the law of the wall for velocity has apparently been confirmed by experiment well outside its original range, the law of the wall for temperature seems to apply only to very simple flows Since the two laws are derived by closely analogous arguments this throws suspicion on the law of the wall for velocity Analysis of simulation data, for all the Reynolds stresses including the shear stress, shows that law-of-the-wall scaling fails spectacularly in the viscous wall region, even when the logarithmic law is relatively well behaved Virtually all turbulence models are calibrated to reproduce the law of the wall in simple flows, and we discuss whether, in practice or in principle, their range of validity is larger than that of the law of the wall itself: the present answer is that it is not; so that when the law of the wall (or the mixing-length formula) fails, current Reynolds-averaged turbulence models are likely to fail too

The law of the wall in turbulent flow

First a three-dimensional turbulent boundary-layer experiment is described. This has been carried out with the specific aim of providing a test-case for calculation methods. Much attention has been paid to the design of the test set-up. An infinite swept-wing flow has been simulated with good accuracy. The initially two-dimensional boundary layer on the test plate was subjected to an adverse pressure gradient, which led to three-dimensional separation near the trailing edge of the plate. Next, a calculation method for three-dimensional turbulent boundary layers is discussed. This solves the boundary-layer equations numerically by finite differences. The turbulent shear stress is obtained from a generalized version of Bradshaw's two-dimensional turbulent shear stress equation. The results of the calculations are compared with those of the experiment. Agreement is good over a considerable distance; but large discrepancies are apparent near the separation line.

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Measurements in an incompressible three-dimensional turbulent boundary layer, under infinite swept-wing conditions, and comparison with theory

First a three-dimensional turbulent boundary-layer experiment is described. This experiment has been carried out with the specific aim to provide a test-case for calculation methods. Much attention has been paid to the design of the test set-up. An infinite swept wing flow has been simulated with good accuracy. The initially two-dimensional boundary layer on the test plate is subjected to an adverse pressure gradient, which leads to a threedimensional separation near the trailing edge of the plate.
Furthermore, a calculation method for three-dimensional turbulent boundary layers is discussed. This calculation method solves the boundary layer equations numerically by finite differences. The turbulent shear stress is obtained from a generalized version of Bradshaw's two-dimensional turbulent shear stress equation. The results of the calculations are compared with those of the experiment. The agreement is good over a considerable distance, but large discrepancies are apparent near the separation line.

Measurements in an incompressible three-dimensional turbulent boundary layer under infinite swept wing conditions and a comparison with theory

An extended law of the wall is derived for three-dimensional flows. This law of the wall describes the variation of the magnitude and the direction of the velocity close to the wall. The effects of both the pressure gradient and the inertial forces have been taken into account. The derived wall law is valid only when the deviations from the simple law of the wall are not large. The most important feature of a three-dimenBional wall law is the prediction of the rotation of the velocity vector near the wall.
Comparisons of the flow angle variations predicted by the present wall law with the few available experimental data show good agreement

A three-dimensional law of the wall for turbulent shear flows

An extended law of the wall is derived for three-dimensional flows. It describes the variation of the magnitude and direction of velocity close to the wall. The effects of both the pressure gradient and the inertial forces have been taken into account. The derived wall law is valid only when the deviations from the simple law of the wall are not large. The most important feature of a three-dimensional wall law is the prediction of the rotation of the velocity vector near the wall. Comparison of the flow angle variations predicted by the present wall law with the few available experimental data shows good agreement.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112075001942

At the workshop nine participants presented the results of their calculations for a practical test case. The test case deals with the 3D turbulent boundary layer development, including separation, on the root section of a swept wing. The employed calculation methods comprise 3D integral methods as well as field methods. A short description of each method is given and the results are discussed. It is concluded that all participants are able to predict the flow globally correct. There is a large variation, however, in the details of the results.

B. Van den Berg

Papers

Measurements in an incompressible three-dimensional turbulent boundary layer, under infinite swept-wing conditions, and comparison with theory

Measurements in an incompressible three-dimensional turbulent boundary layer under infinite swept wing conditions and a comparison with theory

A three-dimensional law of the wall for turbulent shear flows

A three-dimensional law of the wall for turbulent shear flows

Comparison of boundary layer calculations for the root section of a wing