An LDV system for turbulence length scale measurements

An LDV system for making spatial correlation measurements of velocity fluctuations in turbulent nonreacting and reacting flows is presented. The LDV system is the dual beam type and consists of an elongated probe volume and a two-point optical fiber detector. Results are presented of the integral length scale measured in a nonreacting grid generated turbulent flow.A version of this paper was presented at the ASME Winter Annual Meeting of 1984 and printed in AMD, Vol. 66     

Boundary layer receptivity to the nonlinearly developing freestream turbulence

The turbulent-freestream-generated disturbances in the flat-plate boundary layer are studied. As distinct from the conventional representation of turbulence as superposition of exponentially decaying vortex disturbances frozen in the flow and satisfying the linearized Navier-Stokes equations, a model used takes account for their nonlinear development. Its basic features are the deviation of the phase velocity of vortex disturbances from the flow velocity and their slower decay. The model makes it possible to adequately describe the experimentally observable dependences of the velocity fluctuations in the boundary layer and their spectra on the stream wise coordinate.     

Effects of free‐stream turbulence on large‐scale coherent structures of separated boundary layer transition

It has been well established that large‐scale structures, usually called coherent structures, exist in many transitional and turbulent flows. The topology and range of scales of those large‐scale structures vary from flow to flow such as counter‐rotating vortices in wake flows, streaks and hairpin vortices in turbulent boundary layer. There has been relatively little study of large‐scale structures in separated and reattached transitional flows. Large‐eddy simulation (LES) is employed in the current study to investigate a separated boundary layer transition under 2% free‐stream turbulence on a flat plate with a blunt leading edge. The Reynolds number based on the inlet free stream velocity and the plate thickness is 6500. A dynamic subgrid‐scale model is employed to compute the subgrid‐scale stresses more accurately in the current transitional flow case. Flow visualization has shown that the Kelvin–Helmholtz rolls, which have been so clearly visible under no free‐stream turbulence (NFST) are not as apparent in the present study. The Lambda‐shaped vortical structures which can be clearly seen in the NFST case can hardly be identified in the free‐stream turbulence (FST) case. Generally speaking, the effects of free‐stream turbulence have led to an early breakdown of the boundary layer, and hence increased the randomization in the vortical structures, degraded the spanwise coherence of those large‐scale structures. Copyright © 2005 John Wiley & Sons, Ltd.     

Leading-edge receptivity of boundary layer to three-dimensional free-stream turbulence

The laminar-turbulent transition has always been a hot topic of fluid mechanics. Receptivity is the initial stage and plays a crucial role in the entire transition process. The previous studies of receptivity focus on external disturbances such as sound waves and vortices in the free stream, whereas those on the leading-edge receptivity to the three-dimensional free-stream turbulence(FST), which is more general in the nature,are rarely reported. In consideration of this, this work is devoted to investigating the receptivity process of three-dimensional Tollmien-Schlichting(T-S) wave packets excited by the three-dimensional FST in a flat-plate boundary layer numerically. The relations between the leading-edge receptivity and the turbulence intensity are established, and the influence of the FST directions on the propagation directions and group velocities of the excited T-S wave packets is studied. Moreover, the leading-edge receptivity to the anisotropic FST is also studied. This parametric investigation can contribute to the prediction of laminar-turbulent transition.     

Coherent fine scale eddies in turbulence transition of spatially-developing mixing layer

To investigate the relationship between characteristics of the coherent fine scale eddy and a laminar–turbulent transition, a direct numerical simulation (DNS) of a spatially-developing turbulent mixing layer with Re_ω,0 = 700 was conducted. On the onset of the transition, strong coherent fine scale eddies appears in the mixing layer. The most expected value of maximum azimuthal velocity of the eddy is 2.0 times Kolmogorov velocity (u_k), and decreases to 1.2u_k, which is an asymptotic value in the fully-developed state, through the transition. The energy dissipation rate around the eddy is twice as high compared with that in the fully-developed state. However, the most expected diameter and eigenvalues ratio of strain rate acting on the coherent fine scale eddy are maintained to be 8 times Kolmogorov length (η) and :β:γ = −5:1:4 in the transition process. In addition to Kelvin–Helmholtz rollers, rib structures do not disappear in the transition process and are composed of lots of coherent fine scale eddies in the fully-developed state instead of a single eddy observed in early stage of the transition or in laminar flow.     

Effect of the freestream turbulence scale and the leading edge shape on boundary layer laminar-turbulent transition

The effect of the leading edge shape and the turbulence scale on laminar-turbulent transition in the flat-plate boundary layer due to grid turbulence is investigated. In the experiments, the turbulence scale was changed by a factor of three and the bluntness radius of the edge by a factor of four, all other factors being fixed. It is shown that on the plate with a sharp edge the fluctuation growth rate and the laminar-turbulent transition point depend nonmonotonically on the turbulence scale. On the blunt plate transition occurs considerably earlier than on the sharp plate.     

Subharmonic transition to turbulence in channel flow

A direct numerical simulation of subharmonic transition to turbulence in channel flow has been performed. The stages of primary and secondary instability have been identified in the results leading to a staggered pattern of A-shaped vortices. The associated staggered symmetry has been found to persist up to rather late stages of the breakdown process. This symmetry rapidly disappears in the final stage of transition and a developed turbulent flow is attained. A pronounced difference in the development between the two channel halves is observed which is consistent with the predictions of secondary instability theory.     

Mechanism of flow instability and transition to turbulence

In this paper, a new mechanism of flow instability and turbulence transition is proposed for wall bounded shear flows. It is stated that the total energy gradient in the transverse direction and that in the streamwise direction of the main flow dominate the disturbance amplification or decay. Thus, they determine the critical condition of instability initiation and flow transition under given initial disturbance. A new dimensionless parameter K for characterizing flow instability is proposed which is expressed as the ratio of the energy gradients in the two directions for the flow without energy input or output. It is suggested that flow instability should first occur at the position of K_max which may be the most dangerous position. This speculation is confirmed by Nishioka et al.'s experimental data. Comparison with experimental data for plane Poiseuille flow and pipe Poiseuille flow indicates that the proposed idea is really valid. It is found that the turbulence transition takes place at a critical value of K_max of about 385 for both plane Poiseuille flow and pipe Poiseuille flow, below which no turbulence will occur regardless the disturbance. More studies show that the theory is also valid for plane Couette flows which holds a critical value of K_max of about 370.     

On fractional non-local bodies with variable length scale

This paper discusses the application of the variable length scale concept in the framework of non-local fractional model. The considerations are motivated by the fact that real material characteristic dimension is never uniform and simultaneously the problem of existence of the virtual boundary layer in the boundary value problems, discussed in previous papers, is removed. The considerations are illustrated with a series of analyses of 1D elasticity problems. Nonetheless, the conclusions are applicable for an arbitrary configurations.     

Universal threshold of the transition to localized turbulence in shear flows

Experimental and numerical studies have shown similarities between localized turbulence in channel and pipe flows. By scaling analysis of a disturbed-flow model, this paper proposes a local Reynolds number Re_M to characterize the threshold of transition triggered by finite-amplitude disturbances. The Re_M represents the maximum contribution of the basic flow to the momentum ratio between the nonlinear convection and the viscous diffusion. The lower critical Re_M observed in experiments of plane Poiseuille flow, pipe Poiseuille flow and plane Couette flow are all close to 323, indicating the uniformity of mechanism governing the transition to localized turbulence.     

Boundary-layer receptivity under interaction of free-stream turbulence and localized wall roughness

The boundary-layer receptivity under the interaction of free-stream turbu- lence (FST) and localized wall roughness is studied by the direct numerical simulation (DNS) and the fast Fourier transform. The results show that the Tollmien-Schlichting (T-S) wave packets superposed by a group of stability, neutral, and instability T-S waves are generated in the boundary layer. The propagation speeds of the T-S wave packets are calculated. The relation among the boundary-layer receptivity response, the amplitude of the FST, the roughness height, and the roughness width is determined. The results agree well with Dietz’s experiments. The effect of the roughness geometries on the receptivity is also studied.     

Evaluating turbulence model predictions of transition

This paper presents initial results from a collaborative assessment of turbulence model predictions for transition under the influence of free-stream turbulence. Results are presented from a number of test cases and some recommendations are made as to the best present models for use in engineering design codes.     

Tertiary and quarternary states of fluid flow and the transition to turbulence

The sequence of bifurcations from simple to complex forms of fluid motion can be studied numerically in the case of systems with high degrees of external symmetries. The relevance of tertiary and quarternary states for the problem of turbulence is discussed and as an example asymmetric traveling wave convection in a fluid layer heated from below is described.     

Formation of three-dimensional structures on the transition to turbulence in boundary layers

Experiments have established that there are two main qualitatively different regimes of the transition from laminar to turbulent flow and an intermediate regime which possesses the characteristic features of both. These regimes reflect the different ways in which a two-dimensional wave pattern can be transformed into a three-dimensional one; they must be a consequence of the initial conditions. The aim of the investigation reported in the present work was to analyze these regimes by systematically varying the initial data, to demonstrate the possibility of controlling the nature of the transition, to obtain some data to test theoretical models of the development of three-dimensional wave patterns on transition, and to make further experimental investigations of the transition mechanisms.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 42–50, November–December, 1984.We are grateful to N. N. Yanenko (deceased), P. Torgersen, and D. Frederick for supporting the work, and T. Herbert for helpful discussions.The work was done while the first two authors were at the Virginia Polytechnic Institute and University during November and December 1982.