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NASA NTRS1991

A one-equation turbulence transport model for high Reynolds number wall-bounded flows

A one-equation turbulence model that avoids the need for an algebraic length scale is derived from a simplified form of the standard-k-epsilon model equations. After calibration based on well established properties of the flow over a flat plate, predictions of several other flows are compared with experiment. The preliminary results presented indicate that the model has predictive and numerical properties of sufficient interest to merit further investigation and refinement. The one-equation model is also analyzed numerically and robust solution methods are presented.

Baldwin, Barrett S.↗
NASA NTRS1981

Role of coherent structures in turbulent shear flows

A definition for the large-scale coherent structure is presented, and the nature and role of coherent structures in turbulent shear flows are examined. The equations governing the coherent motions and the experimental considerations as well as constraints in the investigations of coherent structures in wall-bounded and free turbulent shear flows are discussed. Results from a few of our recent and on-going studies of coherent structures in excited and unexcited free turbulent shear flows are reviewed. These results show that coherent structures are dominant in transport in the early stages of their formation, but not in the self-preserving regions of turbulent shear flows.

Fazle Hussain, A. K. M.↗
NASA NTRS1988

Turbulence characteristics inside a turbulent spot in plane Poiseuille flow

In wall-bounded shear flows the transition to turbulence through localized disturbances goes through a pattern starting with a development of shear layers. The localized normal velocity fluctuations induce normal vorticity through the lift-up effect. These shear layers become unstable to secondary disturbances, and if the amplitudes of the disturbances are large enough, a turbulent spot develops. Investigations of the spot in boundary layers has shown that the turbulent part of the spot is very similar to a fully developed boundary layer. Wygnanski et al. (1976) showed that the mean profile at the center-symmetry plane has a logarithmic region and Johansson et al. (1987) showed that both the higher-order statistics and flow structures in the spot were the same as in the corresponding fully developed flow. In what respects the turbulence inside the Poiseuille spot is similar to fully developed turbulent channel flow is studied. The numerically simulated spot is used, where the characteristics inside the spot are compared to those of the wave packet in the wingtip area. A recent experimental investigation of the velocity field associated with the Poiseuille spot by Klingmann et al. is used for comparison.

Henningson, D. S.↗
NASA NTRS1988

Theoretical model for VITA-educed coherent structures in the wall region of a turbulent boundary layer

Experiments on wall-bounded shear flows (channel flows and boundary layers) have indicated that the turbulence in the region close to the wall exhibits a characteristic intermittently formed pattern of coherent structures. For a quantitative study of coherent structures it is necessary to make use of conditional sampling. One particularly successful sampling technique is the Variable Integration Time Averaging technique (VITA) first explored by Blackwelder and Kaplan (1976). In this, an event is assumed to occur when the short time variance exceeds a certain threshold multiple of the mean square signal. The analysis presented removes some assumptions in the earlier models in that the effects of pressure and viscosity are taken into account in an approximation based on the assumption that the near-wall structures are highly elongated in the streamwise direction. The appropriateness of this is suggested by the observations but is also self consistent with the results of the model which show that the streamwise dimension of the structure grows with time, so that the approximation should improve with the age of the structure.

Landahl, Marten T.↗
NASA NTRS1991

Comments on Reynolds number effects in wall-bounded shear layers

The effect of Reynolds number on the structure of turbulent boundary layers and channel flows is discussed. Published data are reexamined in light of the following questions: (1) does the boundary layer turbulence structure change after the well known Reynolds number limit viz, when Re(theta) is greater than 6000?; (2) is it possible to disturb a high Reynolds number flat plate turbulent boundary layer near the wall such that the recovery length is O(100 delta)?; and (3) how close is the numerically simulated low Reynolds number flat plate turbulence structure to that observed experimentally? The turbulence structure appears to change continuously with Reynolds number virtually throughout the bounday layer and sometimes in unexpected manners at high Reynolds numbers.

Bandyopadhyay, Promode R.↗
NASA NTRS1987

Investigation of turbulent shear flows by numerical simulation

A data base (Kim et al., 1986) generated by direct numerical integration of the Navier-Stokes equations for unsteady three-dimensional turbulent channel flow at low Reynolds numbers is applied to investigate the physical processes acting in wall-bounded shear flows. The techniques used to construct the data base are outlined; the modeling of turbulence, streaks and streamwise vortices, horseshoe and inverted-horseshoe vortices, and vortex rings is described; the conditional sampling techniques employed are discussed; and typical results are presented graphically. An organized vorticity-field structure is revealed and found to be associated with the bursting process and a local peak in the wall pressure, indicating a possible approach to reducing viscous drag.

Kim, J.↗
NASA NTRS1991

Instabilities and large structures in reattaching boundary layers

The underlying premise in this work is that large structures in turbulent shear flows are not universal and similar large structures in different flows owe their origins to basically similar instabilities. The turbulent boundary-layer flow over a backward-facing step and also the reattaching transitional boundary layer behind a large spanwise rod have been studied experimentally in parallel primarily to understand the origin of the curious large structures observed in the far downstream region (after 39 step heights) of the former flowfield. Simultaneous flow visualization and hot-wire anemometry and also plain-flow visualization have been carried out. In the backward-facing step, the three-dimensional mixing layer developing after detachment persists even after reattachment. The flow does not recover fully back to a regular turbulent boundary layer even far downstream of reattachment. The turbulence-producing instability of a turbulent boundary layer continues to compete with the wall-bounded mixing layer instability, giving rise to the curious schismatic arrays of large structures.

Bandyopadhyay, Promode R.↗
NASA NTRS1987

Investigations of a circulation control airfoil flowfield using an advanced laser velocimeter

The flowfield of a Circulation Control Airfoil was examined in detail through the use of a specially designed wind tunnel model and test program. Surface pressures on the model were obtained and the velocity field was surveyed in the trailing edge region of the model airfoil using the nonintrusive Laser Velocimetry technique. In this region mean flow and turbulence measurements indicate that, while the flowfield is similar to other wall-bounded jet flows, the external freestream plays an important role in the overall mixing and structure of the wall bounded flow. Finally, the turbulence measurements were used to compute eddy viscosities for the purpose of aiding computational fluid dynamics model development.

Novak, Charles J.↗
NASA NTRS1989

Numerical investigation of an internal layer in turbulent flow over a curved hill

The development of an internal layer in a turbulent boundary layer flow over a curved hill is investigated numerically. The turbulence field of the boundary layer flow over the curved hill is compared with that of a turbulent flow over a symmetric airfoil (which has the same geometry as the curved hill except that the leading and trailing edge plates were removed) to study the influence of the strongly curved surface on the turbulence field. The turbulent flow equations are solved by a control-volume based finite difference method. The turbulence is described by a multiple-time-scale turbulence model supplemented with a near-wall turbulence model. Computational results for the mean flow field (pressure distributions on the walls, wall shearing stresses and mean velocity profiles), the turbulence structure (Reynolds stress and turbulent kinetic energy profiles), and the integral parameters (displacement and momentum thicknesses) compared favorably with the measured data. Computational results show that the internal layer is a strong turbulence field which is developed beneath the external boundary layer and is located very close to the wall. Development of the internal layer was more obviously observed in the Reynolds stress profiles and in the turbulent kinetic energy profiles than in the mean velocity profiles. In this regard, the internal layers is significantly different from wall-bounded simple shear layers in which the mean velocity profile characterizes the boundary layer most distinguishably. Development of such an internal layer, characterized by an intense turbulence field, is attributed to the enormous mean flow strain rate caused by the streamline curvature and the strong pressure gradient. In the turbulent flow over the curved hill, the internal layer begin to form near the forward corner of the hill, merges with the external boundary layer, and develops into a new fully turbulent boundary layer as the fluid flows in the downstream direction. For the flow over the symmetric airfoil, the boundary layer began to form from almost the same location as that of the curved hill, grew in its strength, and formed a fully turbulent boundary layer from mid-part of the airfoil and in the downstream region. Computational results also show that the detailed turbulence structure in the region very close to the wall of the curved hill is almost the same as that of the airfoil in most of the curved regions except near the leading edge. Thus the internal layer of the curved hill and the boundary layer of the airfoil were also almost the same. Development of the wall shearing stress and separation of the boundary layer at the rear end of the curved hill mostly depends on the internal layer and is only slightly influenced by the external boundary layer flow.

Kim, S-W.↗
NASA NTRS1989

An analysis of curvature effects for the control of wall-bounded shear flows

The Reynolds stress transport equations are used to predict the effects of simultaneous and sequential combinations of distortions on turbulent boundary layers. The equations are written in general orthogonal curvilinear coordinates, with the curvature terms expressed in terms of the principal radii of curvature of the respective coordinate surfaces. Results are obtained for the cases of two-dimensional and three-dimensional flows in the limit where production and pressure-strain redistribution dominate over diffusion effects.

Gatski, T. B.↗
NASA NTRS1990

A subgrid-scale model based on the second-order velocity structure function

A series of tests were performed to help extend the use of a subgrid-scale model to compressible and wall-bounded flows. A priori tests were done in the case of the incompressible turbulent channel flow. They showed that a 1-D formulation of the structure-function model is more appropriate, leading to a satisfactory behavior of the model at the walls without requiring any damping function. This model is consistent with the original formulation of Metais & Lesieur (1990). In large-eddy simulations of compressible isotropic turbulence, both models performed well up to an initial rms Mach number of 0.6.

Comte, P.↗
NASA NTRS1989

On the large-eddy simulation of transitional wall-bounded flows

The structure of the subgrid scale fields in plane channel flow has been studied at various stages of the transition process to turbulence. The residual stress and subgrid scale dissipation calculated using velocity fields generated by direct numerical simulations of the Navier-Stokes equations are significantly different from their counterparts in turbulent flows. The subgrid scale dissipation changes sign over extended areas of the channel, indicating energy flow from the small scales to the large scales. This reversed energy cascade becomes less pronounced at the later stages of transition. Standard residual stress models of the Smagorinsky type are excessively dissipative. Rescaling the model constant improves the prediction of the total (integrated) subgrid scale dissipation, but not that of the local one. Despite the somewhat excessive dissipation of the rescaled Smagorinsky model, the results of a large eddy simulation of transition on a flat-plate boundary layer compare quite well with those of a direct simulation, and require only a small fraction of the computational effort. The inclusion of non-dissipative models, which could lead to further improvements, is proposed.

Piomelli, Ugo↗
NASA NTRS1990

On the large-eddy simulation of transitional wall-bounded flows

The structure of the subgrid scale fields in plane channel flow has been studied at various stages of the transition process to turbulence. The residual stress and subgrid scale dissipation calculated using velocity fields generated by direct numerical simulations of the Navier-Stokes equations are significantly different from their counterparts in turbulent flows. The subgrid scale dissipation changes sign over extended areas of the channel, indicating energy flow from the small scales to the large scales. This reversed energy cascade becomes less pronounced at the later stages of transition. Standard residual stress models of the Smagorinsky type are excessively dissipative. Rescaling the model constant improves the prediction of the total (integrated) subgrid scale dissipation, but not that of the local one. Despite the somewhat excessive dissipation of the rescaled Smagorinsky model, the results of a large eddy simulation of transition on a flat-plate boundary layer compare quite well with those of a direct simulation, and require only a small fraction of the computational effort. The inclusion of non-dissipative models, which could lead to further improvements, is proposed.

Piomelli, Ugo↗
NASA NTRS1989

New approximate boundary conditions for large eddy simulations of wall-bounded flows

Two new approximate boundary conditions have been applied to the large eddy simulation of channel flow with and without transpiration. These new boundary conditions give more accurate results than those previously in use, and allow significant reduction of the required CPU time over simulations in which no-slip conditions are applied. Mean velocity profiles and turbulence intensities compare well both with experimental data and with the results of resolved simulations. The influence of the approximate boundary conditions remains confined near the point of application and does not affect the turbulence statistics in the core of the flow.

Piomelli, Ugo↗
NASA NTRS1990

Organized motions underlying turbulent shear flows

The objective of this project is to determine the nature and significance of the organized motions underlying turbulent shear flow. There is considerable experimental evidence for the existence of such motions. In particular, one consistently observes longitudinal streaks with a spacing of about 100 in wall units in the near-wall region of wall-bounded shear flows. Recently, an analysis based on the direct resonance mechanism has predicted the appearance of streaks with precisely such a spacing. Also, the minimum channel simulations of Jimenez and Moin have given a strong dynamical significance to that spanwise length scale. They have shown that turbulent-like flows can not be maintained when the spanwise wavelength of the motion is constrained to be less than about that critical number. A critical review of the direct resonance ideas and the non-linear theory of Benney and Gustavsson is presented first. It is shown how this leads to the later mean flow-first harmonic theory of Benney. Finally, we note that a different type of analysis has led to the prediction streaks with a similar spacing. This latter approach consists of looking for optimum fields and directly provides deep insights into why a particular structure or a particular scale should be preferred.

Waleffe, F.↗
NASA NTRS1984

The structure of the vorticity field in turbulent channel flow. Part 2: Study of ensemble-averaged fields

Several conditional sampling techniques are applied to a data base generated by large-eddy simulation of turbulent channel flow. It is shown that the bursting process is associated with well-organized horseshoe vortices inclined at about 45 deg. to the wall. These vortical structures are identified by examining the vortex lines of three-dimensional, ensemble averaged vorticity fields. Two distinct horseshoe-shaped vortices corresponding to the sweep and ejection events are detected. These vortices are associated with high Reynolds shear stress and hence make a significant contribution to turbulent energy production. The dependency of the ensemble averaged vortical structures on the detection criteria, and the question of whether this ensemble-averaged structure is an artifact of the ensemble averaging process are examined. The ensemble-averaged pattern of these vortical structures that emerge from the analysis could provide the basis for a hypothetical model of the organized structures of wall-bounded shear flows.

Kim, J.↗
NASA NTRS1986

The structure of the vorticity field in turbulent channel flow. II - Study of ensemble-averaged fields

Several conditional sampling techniques are applied to a data base generated by large-eddy simulation of turbulent channel flow. It is shown that the bursting process is associated with well-organized horseshoe vortices inclined at about 45 deg to the wall. These vortical structures are identified by examining the vortex lines of three-dimensional, ensemble averaged vorticity fields. Two distinct horseshoe-shaped vortices corresponding to the sweep and ejection events are detected. These vortices are associated with high Reynolds shear stress and hence make a significant contribution to turbulent energy production. The dependency of the ensemble averaged vortical structures on the detection criteria, and the question of whether this ensemble-averaged structure is an artifact of the ensemble averaging process are examined. The ensemble-averaged pattern of these vortical structures that emerge from the analysis could provide the basis for a hypothetical model of the organized structures of wall-bounded shear flows.

Kim, J.↗
NASA NTRS1981

Higher-level simulations of turbulent flows

The fundamentals of large eddy simulation are considered and the approaches to it are compared. Subgrid scale models and the development of models for the Reynolds-averaged equations are discussed as well as the use of full simulation in testing these models. Numerical methods used in simulating large eddies, the simulation of homogeneous flows, and results from full and large scale eddy simulations of such flows are examined. Free shear flows are considered with emphasis on the mixing layer and wake simulation. Wall-bounded flow (channel flow) and recent work on the boundary layer are also discussed. Applications of large eddy simulation and full simulation in meteorological and environmental contexts are included along with a look at the direction in which work is proceeding and what can be expected from higher-level simulation in the future.

Ferziger, J. H.↗