Irrotational Fluctuations Research Articles

Acceleration, pressure and related quantities in the proximity of the turbulent/non-turbulent interface

This paper presents an analysis of flow properties in the proximity of the turbulent/non-turbulent interface (TNTI), with particular focus on the acceleration of fluid particles, pressure and related small scale quantities such as enstrophy,ω2=ωiωi, and strain,s2=sijsij. The emphasis is on the qualitative differences between turbulent, intermediate and non-turbulent flow regions, emanating from the solenoidal nature of the turbulent region, the irrotational character of the non-turbulent region and the mixed nature of the intermediate region in between. The results are obtained from a particle tracking experiment and direct numerical simulations (DNS) of a temporally developing flow without mean shear. The analysis reveals that turbulence influences its neighbouring ambient flow in three different ways depending on the distance to the TNTI: (i) pressure has the longest range of influence into the ambient region and in the far region non-local effects dominate. This is felt on the level of velocity as irrotational fluctuations, on the level of acceleration as local change of velocity due to pressure gradients, Du/Dt≃ ∂u/∂t≃ −∇p/ρ, and, finally, on the level of strain due to pressure-Hessian/strain interaction, (D/Dt)(s2/2) ≃ (∂/∂t)(s2/2) ≃ −sijp,ij> 0; (ii) at intermediate distances convective terms (both for acceleration and strain) as well as strain production −sijsjkski> 0 start to set in. Comparison of the results at Taylor-based Reynolds numbersReλ= 50 andReλ= 110 suggests that the distances to the far or intermediate regions scale with the Taylor microscale λ or the Kolmogorov length scale η of the flow, rather than with an integral length scale; (iii) in the close proximity of the TNTI the velocity field loses its purely irrotational character as viscous effects lead to a sharp increase of enstrophy and enstrophy-related terms. Convective terms show a positive peak reflecting previous findings that in the laboratory frame of reference the interface moves locally with a velocity comparable to the fluid velocity fluctuations.

A New Technique for Analysis of Unsteady Aerodynamic Responses of Cascade Airfoils with Blunt Leading Edge. Unsteady Aerodynamic Responses of the Cascade in Incompressible Flow.

Unsteady aerodynamic responses of cascade airfoils with a blunt leading edge, which are subjected to incident rotational and irrotational fluctuations, are analyzed by use of the method developed in the previous paper of Funazaki and Kakudate. Since some difficulties in the imposition of the boundary condition have been pointed out in that paper, most of the efforts in this study are devoted to refinement of the method of the boundary condition imposition on the inlet/outlet and periodic boundaries by employing the analytical solutions in the upstream/downstream far-fields. Although the method presented in this paper could be applied to compressible flow problems, numerical examples employed this time are limited to incompressible flow cases. Obtained results then show the usefulness of the method, and also reveal some of the notable features of the unsteady flow field induced within the blade-to-blade passage vividly.

Vorticity form of turbulence transport equations

The exact transport equations describing the turbulent kinetic energy, Reynolds stresses, and the dissipation rate of the turbulent kinetic energy are written in their vorticity form. The limiting behavior of the transport equations describing the irrotational fluctuations at the free-stream edges of shear flows is directly deduced from the exact transport equations. Additional relations of pure kinematic origin are also indicated. It is suggested that the formulation developed may be useful in improving the turbulence transport models.

The production of turbulent stress in a shear flow by irrotational fluctuations

This paper is a study of how external turbulence affects an initially turbulence-free region in which there is a mean-velocity gradient dU/dz. Rapid-distortion theory shows how external turbulence induces irrotational fluctuations in the sheared region, which interact with the shear to produce rotational velocity fluctuations and mean Reynolds stresses. These stresses extend into the sheared region over a distance of the order of the integral scale L∞. Since the actual front between the initial external turbulence and the shear flow is a randomly contorted surface, the turbulence of a fixed point near the front is intermittent. Intermittency is included in the present analysis by a simple statistical model.Experiments were done in a wind tunnel with the flow divided by a plate extending from upstream to x = 0. Above the plate, turbulence was produced by a grid. Below the plate a low turbulence shear was produced by wire screens. The wake of the plate (x > 0) decayed downstream.Turbulent shear stress was observed to grow from zero to significant values in the interaction region. The magnitude and extent of the observed stress agrees reasonably well with predictions. We conclude that turbulent stresses can be produced by irrotational fluctuations in a region of mean shear, and that this effect can be estimated using rapid-distortion theory.

A comparison of the wake structure of a stationary and oscillating bluff body, using a conditional averaging technique

A conditional averaging technique to extract the underlying vortex pattern from a turbulent bluff body wake is described. Ensemble averages of wake velocities are developed on the basis of a reference phase position, determined from the outer flow irrotational fluctuations. The method is applied to the wakes of a stationary and oscillating D-shape cylinder, where, in the latter case, the vortex shedding is locked to the frequency of body movement. Direct comparisons of average circulation and vortex street spacings are obtained and these demonstrate the significant change in wake structure that accompanies and sustains vortex-induced vibrations. It is observed in both conditions that only 25% of the estimated shed vorticity is found in the fully developed wake. In addition the analysis produces profiles of vorticity and velocity in an ‘average vortex cycle’. A model, developed to help interpret these results, suggests that a good representation of an average wake situation is obtained by the addition of considerable mean shear to a street of finite area axisymmetric vortices.

High-order moments of Reynolds shear stress fluctuations in a turbulent boundary layer

The cumulant-discard approach is used to predict the third- and fourth-order moments and the probability density of turbulent Reynolds shear stress fluctuations uv, the streamwise and normal velocity fluctuations being represented by u and v respectively. Measurements of these quantities in a turbulent boundary layer are presented, with the required statistics of uv obtained by the use of a high-speed digital data-acquisition system. Including correlations between u and u up to the fourth order, the cumulant-discard predictions are in close agreement with the measurements in the inner region of the layer but only qualitatively follow the experimental results in the outer intermittent region. In this latter region, predictions for the third- and fourth-order moments of uv are also obtained by assuming that the properties of both turbulent and irrotational fluctuations are Gaussian and by using some of the available conditional averages of u, v and uv.

Irrotational fluctuations near a turbulent boundary layer

A verification of some of the predictions of the theory of Phillips (1955) is presented, and the relation between one-dimensional and two-dimensional wavenumber spectra is discussed. The convection velocity of the irrotational field deduced from measurements of the frequency spectrum alone appears to be about 0.9U1in the frequency range carrying most of the energy. It follows that the pressure-fluctuation spectrum is proportional to the velocity-fluctuation spectrum and varies as ω2at low frequency. The discrepancy between this result and measurements of wall-pressure spectra is plausibly attributed to extraneous sound.

Turbulence in the noise-producing region of a circular jet

The flow in the noise-producing region of a circular jet is found to be dominated by a group of large eddies, containing nearly a quarter of the turbulent shear stress in the quasi-plane region of the shear layer: their contribution to the shear stress decreases as the effects of axisymmetry become noticeable at more than about two diameters downstream of the nozzle. These large eddies appear to be almost entirely responsible for the irrotational fluctuations near the nozzle, which, for this and other reasons, are larger relative to the reference dynamic pressure than in other shear flows. As a consequence of this, the convection velocity near the high- and low-velocity edges of the flow is biased towards the mean velocity in the high-intensity region. The dominance of the large eddies therefore explains the measurements of near-field pressure fluctuations by Franklin & Foxwell (1958), and of convection velocity by Davies, Barratt & Fisher (1963) and the present authors. The strength of these large eddies, compared with those in the boundary layer or wake, is remarkable.The large eddies appear to be mixing-jets similar to those found by Grant (1958) in the wake, but with their projection in the (y, z)-plane inclined at about 45° to the y (radial) axis instead of lying along the y-axis as in the wake.It is suggested that the augmentation of these large eddies by artificial means could be used to increase the mixing rate and permit the reduction of jet noise by means of acceptably short ejector shrouds.The medium-scale motion is found to be far from isotropic in scales, although the two scales associated with a given vorticity component are more nearly equal. This phenomenon is also noticeable in the wake.It is found that the departure from self-preservation, which starts when the shear layer thickness is no longer small compared with the nozzle radius, does not grossly affect the region of high turbulence intensity and maximum noise production until this region itself is no longer small compared with the radius. The maximum shear stress seven diameters downstream of the exit is still 70% of its value near the exit, and the non-dimensional mean velocity gradient is practically unchanged.