Zero-pressure Gradient Turbulent Boundary Research Articles

Turbulent drag reduction by spanwise traveling ribbed surface waves

The combination of passive and active drag reduction techniques is investigated by particle-image velocimetry (PIV) and micro-particle tracking velocimetry (μ-PTV) measurements. To be more precise, the impact of a riblet-structured surface, which represents the passive control technique, undergoing spanwise transversal wave motion, which defines the active flow control method, on the wall-shear stress distribution of a zero-pressure gradient turbulent boundary layer is analyzed. The experimental setup consists of a flat plate equipped with an insert to generate a spanwise traveling wave on a riblet-structured aluminum sheet. The PIV and μ-PTV measurements are conducted downstream of the actuated riblet surface at two momentum thickness based Reynolds numbers Reθ=1200 and 2080. The surface deformation is generated by an electromagnetic actuator system at three amplitudes A= 0.25, 0.30, and 0.375 mm with a wavelength of λ=160 mm and a frequency of f=81 Hz. The nondimensional quantities in inner wall units defined by the friction velocity of the non-actuated flat plate flow at Reθ=1200 are the amplitudes A+=6, 7, and 9, the wavelength λ+=3862, and the frequency T+=110 and the corresponding quantities for Reθ=2800 are A+=11, 14 and 17, λ+=7170, and T+=380. The results are twofold. On the one hand, the combination of the riblet surface with the transversal wave motion increases the local drag reduction (DR). That is, compared to a boundary layer flow over a non-actuated smooth surface a local drag reduction of up to DR =9.4 % is determined at the chosen measurement position whereas the drag reduction due to the riblet surface is DR =4.7%. On the other hand, the dependence of the local drag reducing efficiency of the riblets on their geometric dimensions with respect to the flow field could be decreased. That is, the transversal wave motion extends the positive drag reducing efficiency range of the riblets.

Subgrid-scale turbulence in shock–boundary layer flows

Data generated by direct numerical simulation (DNS) for a Mach 2.75 zero-pressure gradient turbulent boundary layer interacting with shocks of different intensities are used for a priori analysis of subgrid-scale (SGS) turbulence and various terms in the compressible filtered Navier–Stokes equations. The numerical method used for DNS is based on a hybrid scheme that uses a non-dissipative central scheme in the shock-free turbulent regions and a robust monotonicity-preserving scheme in the shock regions. The behavior of SGS stresses and their components, namely Leonard, Cross and Reynolds components, is examined in various regions of the flow for different shock intensities and filter widths. The backscatter in various regions of the flow is found to be significant only instantaneously, while the ensemble-averaged statistics indicate no significant backscatter. The budgets for the SGS kinetic energy equation are examined for a better understanding of shock–tubulence interactions at the subgrid level and also with the aim of providing useful information for one-equation LES models. A term-by-term analysis of SGS terms in the filtered total energy equation indicate that while each term in this equation is significant by itself, the net contribution by all of them is relatively small. This observation is consistent with our a posteriori analysis.

Inner-layer intensities for the flat-plate turbulent boundary layer combining a predictive wall-model with large-eddy simulations

Time series velocity signals obtained from large-eddy simulations (LES) within the logarithmic region of the zero-pressure gradient turbulent boundary layer over a smooth wall are used in combination with an empirical, predictive inner-outer wall model [I. Marusic, R. Mathis, and N. Hutchins, “Predictive model for wall-bounded turbulent flow,” Science 329, 193 (2010)10.1126/science.1188765] to calculate the statistics of the fluctuating streamwise velocity in the inner region. Results, including spectra and moments up to fourth order, are compared with equivalent predictions using experimental time series, as well as with direct experimental measurements at Reynolds numbers Reτ = 7300, 13 600, and 19 000. The LES combined with the wall model are then used to extend the inner-layer predictions to Reynolds numbers Reτ = 62 000, 100 000, and 200 000 that lie within a gap in log (Reτ) space between laboratory measurements and surface-layer, atmospheric experiments. The present results support a loglike increase in the near-wall peak of the streamwise turbulence intensities with Reτ and also provide a means of extending LES results at large Reynolds numbers to the near-wall region of wall-bounded turbulent flows.

Power-law velocity profile in turbulent boundary layers: An integral reynolds-number dependent solution

Geophysical flows of practical interest encompass turbulent boundary layer flows. The velocity profile in turbulent flows is generally described by a log- or a power-law applicable to certain zones of the boundary layer, or by wall-wake law for the entire zone of the boundary layer. In this study, a novel theory is proposed from which the power-law velocity profile is obtained for the turbulent boundary layer flow. The new power-law profile is based on the conservation of mass and the skin friction within the boundary layer. From the proposed theory, analytical expressions for the power-law velocity profile are presented, and their Reynolds-number dependency is highlighted. The velocity profile, skin friction coefficient and boundary layer thickness obtained from the proposed theory are validated by the reliable experimental data for zero-pressure gradient turbulent boundary layers. The expressions for Reynolds shear stress and eddy viscosity distributions across the boundary layer are also obtained and validated by the experimental data.

J056011 剥離を伴う乱流境界層における大規模構造([J05601]乱流における運動量,熱,物質の輸送現象(1))

A direct numerical simulation (DNS) of a separated flat-plate turbulent boundary layer has been performed with a large spanwise domain. The inlet data are prescribed by a DNS of a zero-pressure gradient turbulent boundary layer with the rescaling-recycling method. The Reynolds number at the inlet is set to be Re 0=600 where Re 0 is the Reynolds number based on the free stream velocity and the momentum thickness. It is shown that in the simulation involving large turbulent separation, a spanwise domain, which is large enough to capture large-scale turbulence structures downstream from the reattached point, is required for obtaining proper turbulence statistics and structures. It is also shown that when there is a large separated region, positive and negative regions of the streamwise velocity fluctuation, which appear alternatively in the spanwise direction, exist in both detached and reattached regions where the spanwise spacing in the latter region is about twice as large as that in the former region.

Turbulent Boundary-Layer Separation Control with Single Dielectric Barrier Discharge Plasma Actuators

An experimental study was conducted to determine the effect of single dielectric barrier discharge plasma actuators on turbulent boundary-layer separation control. Two-component particle image velocimetry and laser Doppler velocimetry measurements showed the effect of plasma actuators on ambient air, a canonical zero-pressure gradient turbulent boundary layer, and a two-dimensional turbulent boundary-layer separation from a convex ramp section. Different actuator configurations and control strategies were implemented. Spanwise actuators were operated in both steady and unsteady modes. Plasma streamwise vortex generators were also used to enhance boundary-layer mixing. Flow visualization using a high-speed camera captured the temporal aspects of the separation control process and helped discern the physical mechanisms associated with each actuation strategy. The steady spanwise actuation produced a wall jet effect that augmented near-wall momentum and reattached the separated boundary layer. The streamwise oriented actuators also showed effective control authority by creating counter-rotating vortices within the boundary layer that promote mixing of high and low momentum fluid.

Comparison of large-scale amplitude modulation in turbulent boundary layers, pipes, and channel flows

Recent investigations by Monty et al. [J. Fluid Mech. 632, 431 (2009)] showed that important modal differences exist between channels/pipes and boundary layers, mainly in the largest energetic scales. In addition, Mathis et al. [J. Fluid Mech. 628, 311 (2009)] recently reported and quantified a nonlinear scale interaction in zero-pressure gradient turbulent boundary layers, whereby the large-scale motion amplitude modulates the small-scale motions. In this study, a comparison of this modulation effect of the streamwise velocity component is undertaken for all three flows for matched Reynolds number and measurement conditions. Despite the different large-scale phenomena in these internal and external wall-bounded flows, the results show that their amplitude modulation influence remains invariant in the inner region with some differences appearing in the outer region.

Theoretical evaluation of the Reynolds shear stress and flow parameters in transitionally rough turbulent boundary Layers

The theory by W.K. George and L. Castillo (Zero-pressure gradient turbulent boundary layers, Appl. Mech. Rev. 50 (1997), pp. 689–729) is extended for rough surfaces and numerically implemented on zero pressure gradient turbulent boundary layers. The method is based on the similarity transformations of the Navier–Stokes equations. From these equations, a composite profile for the Reynolds shear stress-⟨ uv⟩ is obtained over the entire boundary layer. The solution is in good agreement with the experiments in the inner and outer regions, for hydraulically smooth (k+ < 5) and transitionally rough surfaces up to roughness parameter of k+ ≈ 55. Beyond this limit, the accuracy of the solutions decreases with k+, especially in the inner region of the mean velocity. However, the accuracy always increases with the Reynolds number, Re_θ. In addition, the eddy viscosity ⟨ ν_T⟩/ν and flow parameters, including the x-dependence, have also been computed and tested with experimental data. Furthermore, the friction power law for smooth/rough surfaces has been used for all calculations and comparisons with direct methods and velocity-based methods are shown to be in good agreement with the theory.

Measurement in a Zero-Pressure Gradient Turbulent Boundary Layer with Forced Thermal Convection

A subsonic zero-pressure gradient turbulent boundary layer developing on a uniformly heated surface at a Reynolds number in the range of 3, 560 ≤ Re θ ≤ 5,360 was investigated. Particle-image velocimetry measurements were performed at various positions in the streamwise direction for several wind-tunnel speeds and for different wall excess temperatures to show the thermal convection effects to expand the boundary-layer thickness δ 0.99 and to enlarge the turbulence intensities in the log-law and wake region. The mean velocity profiles are found to be self-preserving. The inclination of large-scale ramp-like vortex packets increases to higher characteristic angles, i.e., the mean angles are enlarged by approximately 5–10°. Hairpin-like vortex structures originating from the near-wall region seem to undergo higher climbing rates in the wall-normal direction causing the above mentioned significant changes in the boundary-layer thickness δ 0.99 and the strongly increased distributions of turbulence intensities in the wake region of the boundary layer. Changes in the distributions of the skewness and flatness of the probability density function (PDF) of the streamwise fluctuations corroborate these findings. The two-point correlation distribution of the streamwise velocity fluctuations R uu is increased for wall distances y/δ 0.99 = 0.1 to y/δ 0.99 = 0.75 indicating the existence of coherent structures in higher regions of the boundary layer.

Inner and outer scalings in rough surface zero pressure gradient turbulent boundary layers

A new set of experiments have been performed in order to study the effects of surface roughness and Reynolds number on a zero pressure gradient turbulent boundary layer. In order to properly capture the x dependence of the single point statistics, consecutive measurements of 11 streamwise locations were performed which enabled the use of the full boundary layer equations to calculate the skin friction. This quantity was obtained within 3% and 5% accuracy for smooth and rough surfaces, respectively. For the sand grain type roughnesses used, only the Zagarola and Smits scaling, U∞δ*∕δ, was able to remove the effects of roughness and Reynolds number from the velocity profiles in outer variables. However, each scaling used for the velocity deficit profiles resulted in self-similar solutions for fixed experimental conditions. When examining the Reynolds stresses in the inner region [i.e., 0&amp;lt;(y+ϵ)+&amp;lt;0.1δ+], the ⟨u2⟩ component showed the largest influence of roughness, where the high peak near the wall was decreased and became nearly flat for the fully rough regime profiles. In addition, the Reynolds stresses in outer variables showed self-similarity for fixed experimental conditions. However, as the roughness parameter, k+ increases, all Reynolds stress profiles became similar in shape indicating increased isotropy near the wall. Furthermore, the boundary layer parameters also showed a considerable increase due to roughness.

Particle image velocimetry study of turbulent flow over transverse square ribs in an asymmetric diffuser

The objective of this paper is to study the combined effects of rib roughness and adverse pressure gradient produced in an asymmetric diffuser on turbulent flows. The two-dimensional asymmetric diffuser was comprised of a straight flat floor and a curved roof. The diffuser section was preceded and followed by straight parallel walls. The complete test conditions were comprised of a reference smooth floor and repeated arrays of transverse square ribs glued onto the floor to produce three pitch-to-height ratios, p∕k=3, 6, and 8. The curved roof was kept smooth in all the experiments. For each of the four test conditions, a particle image velocimetry was used to conduct detailed velocity measurements within the diverging section and also at locations upstream and downstream of the diverging section. From these measurements, the mean streamlines, mean velocities, turbulent intensities, Reynolds shear stress, and production terms in the transport equations for the turbulent kinetic energy and Reynolds stresses were obtained. The results obtained in the diverging section showed that the boundary layers that developed on the ribs thickened considerably at the expense of those adjacent to the roof opposite to the ribs. The streamlines and mean velocity profiles over the ribs showed that adverse pressure gradient increased the roughness sublayer substantially. Adverse pressure gradient and rib roughness also increased the drag and levels of the turbulent intensities, Reynolds shear stress and production terms compared to smooth-wall zero pressure gradient turbulent boundary layer. It appears, however, that adverse pressure gradient enhanced turbulence more effectively than it increased drag.

Effect of surface roughness on the coefficients of a power law for the mean velocity in a turbulent boundary layer

Mean velocity profiles in a two-dimensional zero pressure gradient turbulent boundary layer were obtained for a hydraulically smooth surface and 10 different rough surfaces created from sand paper, steel perforated sheet, and steel woven wire mesh. The physical size and geometry of the roughness elements were chosen to achieve transitionally rough and fully rough flow regimes. The measurements were made in a subsonic wind tunnel, and the Reynolds number based on the momentum thickness ranged from 3730 to 13 550. The power law formulation of George and Castillo (1997, Applied Mechanics Review, 50, 689) was used to estimate the skin friction coefficients for transitionally rough and fully rough flows, as well as hydraulically smooth flow. The values of the friction velocity obtained for the rough surfaces using the defect law and the power law profile fitting techniques were within ±3%. Values of the power law coefficient C i and exponent γ were determined by fitting the power law formulation to the experimental data. The surface roughness was found to significantly affect the behaviour of the coefficient C i and exponent γ in the power law relations. Based on the experimental results, correlations are proposed for the coefficient C i and exponent γ as a function of the roughness shift Δ U + for transitionally rough flows.

Direct Numerical Simulation of Drag-Reducing Turbulent Boundary Layer of Viscoelastic Fluid (2nd Report, Energy Transfer and Coherent Structures)

Energy transfer and turbulence structures in a zero-pressure gradient turbulent boundary layer of a drag-reducing viscoelastic solution were investigated using the direct numerical simulation (DNS) data with the Oldroyd-B and Giesekus models. This work is an extension of the first report, in which mean velocity profiles and turbulence statistics have been investigated. It is found that the contribution to turbulent kinetic energy transfer due to the polymer stress work term is not negligible for the Oldroyd-B model, whereas it is negligible for the Giesekus model. The polymer diffusion term for both the Oldroyd-B and Giesekus models is negligible. For the Oldroyd-B model, we can see that quasi-streamwise vortices are weakened and become larger in the streamwise direction, compared to Newtonian fluids. On the other hand, quasi-streamwise vortices for the Giesekus model are similar to those for Newtonian fluid.

An orthogonal-plane PIV technique for the investigations of three-dimensional vortical structures in a turbulent boundary layer flow

An experimental investigation was carried out regarding a three-dimensional topology of a zero-pressure gradient turbulent boundary layer. In this study, the polarization separation technique has been applied to the PIV measurements. Two mutually perpendicular measurement planes have been employed in x–y and x–z planes, respectively. Synchronization between a stereoscopic PIV with another plane PIV system was made toward the detection of such salient features of the coherent structure as the legs and the head of the hairpin vortices. Polarization rotation via a half-waveplate and subsequent particle image separation using polarizer minimized the spurious particle images. The PIV results clearly demonstrate the presence of hairpin-like coherent vortical structures and coincidence between the near-wall quasi-streamwise vortex pair and the legs of the hairpin vortex.

Self-similar profile of probability density functions in zero-pressure gradient turbulent boundary layers

The probability density function (pdf) of a streamwise velocity component is studied in zero-pressure gradient boundary layers. From analyzing the data up to R θ ≃ 13 , 000 , it is found that pdfs have self-similar profiles ranging from y + ≃ 180 to 0.049 Δ + , where Δ is Rotta–Clauser boundary layer thickness. Pdf profiles asymptote to the universal shape very close to the Gaussian, but are positively skewed at the core region, indicating smaller values in the tail parts. Based on this experimental fact, the mean velocity profile is reconsidered from the standpoint of pdf equation. The log-law profile is expected as the mean velocity distribution. The Kármán constant is evaluated to be 0.38, and the log-region starts at y s + = 180 and ends at y r + = 0.021 Δ + + 96.5 for R θ > 4000 . The end point locates in 0.15 δ + ⩽ y r + ⩽ 0.2 δ + . The relation to the new scaling law derived from Lie-group theory is also discussed.

Velocity measurement in turbulent boundary layer of drag-reducing surfactant solution

The influence of a drag-reducing surfactant on a zero-pressure gradient turbulent boundary layer was investigated using a two-component laser-Doppler velocimetry system. It was discovered that the streamwise turbulence intensity has a maximum near the center of the boundary layer in addition to the near-wall maximum which appears in canonical wall-bounded turbulent flow. At the location of the additional maximum, the Reynolds shear stress has a slight maximum, the skewness factor of streamwise turbulent fluctuation is zero, and the flatness factor has a minimum.

Invariant Assumption of PDF Profile and Universsal Velocity Law in Turbulent Boundary Layer (3rd Report, Contribution from Coherent Structures to Log-law Profile)

In a zero-pressure gradient turbulent boundary layer, the multi-point measurement by 24 ch I-probes is performed. The relation between coherent structures and logarithmic velocity profile is studied by way of proper orthogonal decomposition technique and the stochastic estimation. It is found that the existence of coherent structures are necessary condition for the universal velocity profile, however it is not enough. Small-scale motions are also necessary to realize the log-law profile. The probability density profile in the overlap region is studied, and as a result, the invariant assumption of PDF in relation to the coherent structure is obtained. It was also evaluated how the velocity fluctuation in the log-region is affected by the coherent structures.

Flow structures in zero pressure-gradient turbulent boundary layers at high Reynolds numbers

The near-wall region of zero-pressure gradient turbulent boundary layers was studied through correlation- and other two-point measurements over a wide range of Reynolds numbers. The requirements of high spatial resolution were met by use of a MEMS-type of hot-film sensor array together with a small, in-house built hot-wire probe. Streak-spacing and characteristics of buffer region shear-layer events were studied. At high Reynolds numbers the motions that are of substantially larger scale than the streaks have a significant influence on the near-wall dynamics. By removing such scales through high-pass filtering a streak spacing was recovered that is close to that found in low Reynolds number flows. The frequency of occurrence of shear-layer events was found to scale with a mixed time scale, in analogy with earlier findings in channel flow, again indicating the increasing relative influence of large scales with increasing Reynolds number.

Power law or logarithmic law? — A data analysis for zero pressure gradient turbulent boundary layers with low Reδ2

The paper presents an analysis of two-dimensional zero pressure gradient (ZPG) turbulent boundary layers (TBL) with regard to the application of power laws. Only TBL with low Reynolds number 300 < Reδ2 < 6200 are taken into account. It is found that a certain region of the mean velocity profile can be described with a power law of the formu +=C Pow{*}y +a. This power law region is not a priori identical with the overlap region. An algorithm for the determination of the wall skin friction using the power law is proposed. The method was applied with good result to ZPG TBL and to adverse pressure gradient (APG) TBL. To bridge the gap between the wall and the power law region an approach for the turbulent viscosity is suggested.

A comparison study of conditional-sampling methods used to detect coherent structures in turbulent boundary layers

The present work describes the results of an experimental study of coherent structures in a two-dimensional zero pressure gradient turbulent boundary layer by conditional sampling. The main aim of the work is to compare coherent events detected by various conditional sampling methods on a one-to-one basis and to investigate the degree of correspondence between them. The conditional-sampling techniques used include some existing ones, such as the uv-quadrant, the VITA, the u-level, and the pattern recognition methods, but also some suggested ones which are based on modifications of existing methods or ideas. The results are presented in two forms. First, the conditional averages of the streamwise and normal velocity fluctuations, and those of the Reynolds stress, are grouped into four classes based on the similarity of the pattern and then compared. Next, the correspondence between events detected by various methods are presented on a scale of zero to one, the latter indicating complete correspondence. The conditional-averaged patterns show very differing results for different methods. Also, very poor correspondences have been obtained between some pairs of methods. It is concluded that these methods may detect events of a different nature or different phases of the same event, and thus cause such discrepancies. The results are also discussed by relating them to the physics of the flow and coherent motions known as ejection and sweep.