Freestream Turbulence Length Scale Research Articles

Disturbance growth on a NACA0008 wing subjected to free stream turbulence

The stability of an incompressible boundary layer flow over a wing in the presence of free stream turbulence (FST) has been investigated by means of direct numerical simulations and compared with the linearised boundary layer equations. Four different FST conditions have been considered, which are characterised by their turbulence intensity levels and length scales. In all cases the perturbed flow develops into elongated disturbances of high and low streamwise velocity inside the boundary layer, where their spacing has been found to be strongly dependent on the scales of the incoming free stream vorticity. The breakdown of these streaks into turbulent spots from local secondary instabilities is also observed, presenting the same development as the ones reported in flat plate experiments. The disturbance growth, characterised by its root mean squares value, is found to depend not only on the turbulence level, but also on the FST length scales. Particularly, higher disturbance growth is observed for our cases with larger length scales. This behaviour is attributed to the preferred wavenumbers that can exhibit maximum transient growth. We study this boundary layer preference by projection of the flow fields at the leading edge onto optimal disturbances. Our results demonstrate that optimal disturbance growth is the main cause of growth of disturbances on the wing boundary layer.

On the effect of free-stream turbulence on boundary-layer transition

Abstract

Stochastic analysis of the impact of freestream conditions on the aerodynamics of a rectangular 5:1 cylinder

Uncertainty plays a significant role in the Benchmark on the Aerodynamics of a Rectangular Cylinder (BARC) with a chord-to-depth ratio of 5. In particular, besides modeling and numerical errors, in numerical simulations it is difficult to exactly reproduce the experimental conditions due to uncertainties in the set-up parameters, which sometimes cannot be exactly controlled or characterized. In this study, the impact of the uncertainties in the inflow conditions of the BARC configuration is investigated by using probabilistic methods and two-dimensional URANS simulations. The following uncertain set-up parameters are investigated: the angle of incidence, the freestream longitudinal turbulence intensity and the freestream turbulence length scale. The stochastic collocation method is employed to perform the probabilistic propagation of the uncertainty in the three set-up parameters. This results in 25 URANS simulations based on the Smolyak sparse grid extension of the level-2 Clenshaw-Curtis quadrature points. The discretization error is estimated by repeating the same analysis on different grid sizes. Similarly, the effect of turbulence modeling is appraised by carrying out the uncertainty quantification for the Reynolds stress and the SST k−ω models. Finally, the results obtained for different assumed probability density functions of the set-up parameters are compared. The propagation of the considered uncertainties does not explain alone the dispersion of the BARC experimental data. For certain quantities of interest, the effect of turbulence modeling is more important than the impact of the uncertainties in inflow conditions. The sensitivity to the considered uncertainties also varies with the turbulence model, with a larger variability of the results obtained with the Reynolds stress model. The inflow turbulence length scale is in all cases the least important parameter.

Effects of small-scale freestream turbulence on turbulent boundary layers with and without thermal convection

Effects of weak, small-scale freestream turbulence on turbulent boundary layers with and without thermal convection are experimentally investigated using a wind tunnel. Two experiments are carried out: the first is isothermal boundary layers with and without grid turbulence, and the second is non-isothermal boundary layers with and without grid turbulence. Both boundary layers develop under a small favorable pressure gradient. For the latter case, the bottom wall of the test section is heated at a constant wall temperature to investigate the effects of thermal convection under the effects of freestream turbulence. For both cases, the turbulence intensity in the freestream is Tu = 1.3% ∼ 2.4%, and the integral length scale of freestream turbulence, L∞, is much smaller than the boundary layer thickness δ, i.e., L∞/δ≪1. The Reynolds numbers Reθ based on the momentum thickness and freestream speed U∞ are Reθ = 560, 1100, 1310, and 2330 in isothermal boundary layers without grid turbulence. Instantaneous velocities, U and V, and instantaneous temperature T are simultaneously measured using a hot-wire anemometry and a constant-current resistance thermometer. The results show that the rms velocities and Reynolds shear stress normalized by the friction velocity are strongly suppressed by the freestream turbulence throughout the boundary layer in both isothermal and non-isothermal boundary layers. In the non-isothermal boundary layers, the normalized rms temperature and vertical turbulent heat flux are also strongly suppressed by the freestream turbulence. Turbulent momentum and heat transfer at the wall are enhanced by the freestream turbulence and the enhancement is notable in unstable stratification. The power spectra of u, v, and θ and their cospectra show that motions of almost all scales are suppressed by the freestream turbulence in both the isothermal and non-isothermal boundary layers.

Effects of large-scale free stream turbulence on a turbulent boundary layer

Results of a wind tunnel experiment in which there are systematic variations of free stream turbulence above a flat-plate boundary layer are presented. Upstream of the plate, an active grid generates free stream turbulence varying in intensity from 0.25% to 10.5%. The momentum thickness Reynolds number of the boundary layer varies from 550 to nearly 3000. In all cases, the ratio of the free stream turbulence length scale to the boundary layer depth is greater than unity. Hotwire measurements show that, at high turbulence intensities, the effects of the free stream turbulence extend deep into the boundary layer, affecting the wall stress as well as the small-scale (derivative) statistics. Premultiplied energy spectra show a double peak. At very low free stream turbulence intensities these peaks are associated with the inner and outer scales of the turbulent boundary layer, but at high turbulence intensities the free stream energy peak dominates over the boundary layer’s outer scale. The implications of the effect of the large free stream turbulence scales on the small, near-wall scales is discussed with reference to recent high Reynolds number experiments in a turbulent boundary layer without free stream turbulence [Hutchins and Marusic, Philos. Trans. R. Soc. London, Ser. A 365, 647 (2007)].

Further Development of a Dynamic Intermittency Model For Wake-Induced Transition

The transition model studied in this paper uses an equation for free-stream intermittency and one for near-wall intermittency, combined with the SST turbulence model. The model was already assessed in earlier work for wake-induced transition in boundary layers in separated state and in attached state. For separated state transition, the model predicts the start and growth of transition very well, except for the impossibility to describe the breakdown of the roll-up vortices in a 2D RANS simulation. In attached state transition, the model has the tendency to generate a delayed start of transition and a too slow growth rate in the initial phase of transition. We demonstrate that a delayed start of transition is inherent for a RANS simulation. We propose a repair for the too slow growth rate in the initial stage of the transition. Additionally, both for wake-induced transition in separated state and in attached state, the original model has the tendency to predict a state too near to laminar in between wakes at the trailing edge. We demonstrate that this is caused by the too rapid destruction of the near-wall intermittency during relaminarization and in the lack of activation of near-wall intermittency for low turbulence level in the free stream. We propose a repair for both deficiencies. The fourth improvement is that we take into account the influence of the free stream turbulence length scale in the criteria for onset of transition. We demonstrate the high quality of the improved model for wake-induced transition on a steam turbine stator blade for outlet Reynolds number 600,000 and two levels of turbulence in the background flow: 3% and 0.4%.

On the receptivity of the by-pass transition to the length scale of the outer stream turbulence

The effect of length scale on flat-plate by-pass boundary layer transition under free stream turbulence conditions has been investigated. Plane grids generated a constant value of 3 percent intensity turbulent fluctuations and five values of the dissipation length parameter in the range of 2.2 mm to 33.3 mm at 5 m/s flow velocity in the plane of the leading edge of the flat plate. The investigated boundary layer corresponds to the ERCOFTAC Test Case T3A+. Distributions of integral parameters as well as the statistical characteristics of the turbulent fluctuations were measured. They document a significant effect of turbulence length scale on the onset and the end of by-pass transition. It was found that the onset of the final stage of transition comes on later in `fine-grained' turbulence than in the case of large free stream turbulence length scale. At the same time, the extent of the transition region shortens with decreasing length scale. Nevertheless, the transition process terminates sooner in a flow with a large turbulence length scale than in a flow with a small one. An attempt has been made to describe these observations quantitatively.

Effects of the length scale of free-stream turbulence and cylinder size on heat transfer in laminar separated flows

An experimental study is conducted to investigate the combined influence of length scale of free-stream turbulence, Λ, and cylinder diameter, D, on heat transfer from slightly heated circular cylinders in cross flow. By using a hot-wire anemometer, spectrum analysis of its signal with a Fourier analyzer is employed to investigate the separated shear layer formed behind the circular cylinder. Furthermore, a resistance thermometer is used to measure the time-averaged temperature behind the cylinder and the power-spectral density of the temperature fluctuation in the thermal boundary layer. The Nusselt number at the rear stagnation point varies with the relative scale Λ/D, although the Reynolds number is the same. Correspondingly, the laminar-to-turbulence transition region in the separated shear layer moves in the streamwise direction due to the change in the length scale ratio, and at the same time its variation gives a substantial increase in the power spectrum of the temperature fluctuation. It is disclosed that flow and heat transfer behind cylinders are affected by Λ/D, and are closely related with the streamwise movement of the transition region in the separated shear layer. A correlation equation including Λ/D as the parameter is derived to predict the heat transfer coefficient at the rear stagnation point.

EFFECTS OF THE LENGTH SCALE OF FREE-STREAM TURBULENCE AND CYLINDER SIZE ON LOCAL HEAT TRANSFER IN LAMINAR SEPARATED FLOWS

An experimental study has been conducted to investigate the combined influence of length scale of free-stream turbulence, A, and cylinder diameter, D, on heal transfer from slightly heated circular cylinders in cross flow. By using a hot-wire anemometer, spectrum analysis of its signal with a Fourier analyzer is employed to investigate the separated shear layer formed behind the circular cylinder. A resistance thermometer is used to measure the time-averaged temperature behind the cylinder and the power-spectral density of the temperature fluctuation in the thermal boundary layer. It is found that (I) the Nusselt number at the rear stagnation point varies with the relative scale A / D, at the same Reynolds number, (2) the laminar-to-turbulence transition region in the separated shear layer moves in the streamwise direction with the change in the length-scale ratio, and (3) a streamwise shift of the transition region in the separated shear layer causes a substantial increase in the power spectrum of the temperature fluctuation. A correlation equation with A/ Das a parameter is derived to predict the heat transfer rate at the rear stagnation point.

Prediction of Turbulent Boundary Layers With a Second-Moment Closure: Part I—Effects of Periodic Pressure Gradient, Wall Transpiration, and Free-Stream Turbulence

The purpose of this two-part paper is to assess the performance of a second-moment closure applicable up to a wall. In the present part, the turbulence model is applied to the boundary layers with periodic pressure gradient, with wall transpiration and with free-stream turbulence. The predictions are shown to be in good agreement with experiments and a direct simulation. In particular, a tendency towards relaminarization and a subsequent retransition in the oscillating boundary layer are faithfully reproduced, and the effect of the length scale of free-stream turbulence is correctly captured.

Stretching of freestream turbulence in the stagnation region

Characteristics of stretched vortices in the stagnation region, due to the presence of freestream turbulence in the incident stream, were studied by means of spatial correlation. The spanwise length scale of the stretched vortices, lm, and the characteristic height corresponding to the distance between the averaged position of the centres of the stretched vortices and the plate, Hv, are successfully correlated with the integral length scale of freestream turbulence.

Prediction of the effect of free-stream turbulence on turbulent boundary layers.

The effect of free-stream turbulence on turbulent boundary layers is calculated using a second-moment closure which was previously shown to reproduce various turbulent flows. The numerical results are mainly compared with Hancock and Bradshaw's empirical correlation between the fractional increase in skin friction and a single parameter involving the intensity and length scale of free-stream turbulence. The model calculation well reproduces the empirical correlation unless the free-stream turbulence parameter is very large. In particular, the effect of the length scale is correctly captured in contrast to previous studies. Calculated profiles of the mean velocity and the Reynolds stress components are also in reasonable agreement with experiments. These improvements are traced to a particular generation term in the dissipation-rate transport model.

低レイノルズ数型κ‐ε乱流モデルを用いた境界層の遷多計算

Calculations of laminar-turbulent transition of boundary layers are presented with low-Reynolds number versions of k-ε model of turbulence developed for the near-wall low-Reynolds-number flows. The models are tested for the transitional boundary-layers at various levels of free-stream turbulence with and without the pressure gradient. The test calculations of flows without the pressure gradient show that the model by Launder-Sharma and that by Lam-Bremhorst to some extent are able to handle the transition phenomena within a reasonable range of initial conditions of dissipation. The former model can reproduce the observed effects of level and length scale of free-stream turbulence on the transition, though the latter fails at the lower turbulence level and for the effect of length scale. It is also noted that the applicable range of the low-Reynolds-number k-ε model is limited to a relatively small pressure-gradient condition, as the model shows an opposite trend to the experimental effect of pressure gradient on the transition.