Wall-normal Turbulence Intensities Research Articles

Characteristics of turbulent boundary layers generated by different tripping devices

In this study, we employ a high-fidelity flow visualisation technique to investigate the resemblance between a turbulent boundary layer generated in a lab environment with a limited development length by different tripping devices and a naturally developed canonical turbulent boundary layer. Furthermore, we aim to provide statistics of the wall-normal velocity fluctuation of the tripped boundary layers and analyse them compared with the canonical turbulent boundary layer. This is achieved by conducting two-dimensional particle image velocimetry measurements to acquire the velocity components in the stream-wise wall-normal plane downstream of the tripping location. Different criteria including integral parameters, diagnostic plot, stream-wise and wall-normal turbulence intensities, and mean velocity deficit profiles are employed to compare the boundary layer profiles generated by different trips with well-behaved turbulent boundary layers presented in the literature. The generation of Reynolds shear stress in tripped boundary layers is analysed using quadrant analysis, and suitably sized trips are shown to have contributions of sweeps and ejections in a similar manner to a well-behaved turbulent boundary layer. Furthermore, through the detection of uniform momentum zones, the presence of coherent structures in the logarithmic and outer layers of these well-behaved tripped boundary layers is shown. The findings of this study identify the blockage created by trips as the main factor affecting the turbulence statistics at a certain downstream distance. The results also suggest that the investigation of inner-scaled mean stream-wise velocity is recommended as a simple yet reliable and rapid assessment of the impact of a trip on the turbulent boundary layer development in short test sections.

Particle transport in a turbulent pipe flow: direct numerical simulations, phenomenological modelling and physical mechanisms

In particle-laden turbulent wall flows, transport of particles towards solid walls is phenomenologically thought to be governed by the wall-normal turbulence intensity supporting the underlying particle–eddy interactions that are usually modelled by a combination of turbophoresis and turbulent diffusion. We estimate the turbophoretic and turbulent diffusive coefficients as a function of wall-normal coordinate directly from a generated direct numerical simulation (DNS) database of low volume fraction point particles in a turbulent pipe flow. These coefficients are then used in an advection–diffusion equation to estimate the particle concentration as a function of wall-normal distance and time, with favourable comparison against DNS for smaller Stokes number ( $St^+$ ) particles suggesting a limitation of the common gradient diffusion hypothesis for larger $St^+$ particles. Using DNS we explore the non-trivial effects of $St^+$ , pipe wall condition (particle absorbing or elastic) as well as the influence of drag and lift force on the velocity and particle statistics giving rise to different particle concentrations. We then appraise various Eulerian-based models of turbophoretic and turbulent diffusive coefficients and, finally, use physical insights from Lagrangian correlation times, conditional quadrant analysis and flow topology to shed further light on the particle transport as a function of various parameters and the limits of gradient diffusion hypothesis.

An investigation of particles effects on wall-normal velocity fluctuations in sand-laden atmospheric surface layer flows

Based on the high-quality observational data in the Qingtu Lake Observation Array (QLOA), the difference in the energy distribution, the scale of the coherent structures, and the amplitude modulation effect of the wall-normal velocity fluctuations between particle-free and particle-laden flow in the atmospheric surface layer are analyzed. The results show that the presence of particles enhanced the wall-normal turbulence intensity, especially the increase at the top of the logarithmic region is more significant though the particle mass loading decreases with the wall-normal distance. A further insight indicates that the increase in the length scale of the wall-normal fluctuating velocity coherent structure by particles is more significant further from the wall, which is supported by the premultiplied energy spectra and the two-point correlation. This leads to a drastic increase in kinetic energy of the large-scale coherent structures by the particle away from the wall and thus results in increased amplitude modulation effects of large-scale wall-normal velocity fluctuations onto small-scales.

Exploring the relationship between particle deposition and near-wall turbulence quantities in the built environment

Particle deposition in the built environment can cause discoloration or damage to indoor surfaces. To better understand the deposition mechanisms, this study explored the relationship between particle deposition and near-wall turbulence quantities by means of experimental measurements and numerical simulations, taking a multi-slot supply air nozzle in a commercial airplane as an example. Chamber experiments were conducted in a cabin mockup to measure the particle deposition velocity distribution on the multi-slot nozzle and the near-wall 3D air velocity components. The large-eddy simulation (LES)-Lagrangian approach was used to calculate the turbulent flow in the cabin and particle deposition on the nozzle. Correlations between the particle deposition velocity (vd) and the wall-normal turbulence kinetic energy (kw), the wall-normal turbulence intensity (TIw), and a new turbulence quantity defined in this study (TIw,towards−wall) were examined in the near-wall buffer, logarithmic, and outer layers. According to the simulation results, the particle deposition velocity was significantly correlated with all three turbulence quantities (TIw, kw, TIw,towards−wall) in the logarithmic and outer layers. Furthermore, both the experimental and simulation results indicate that the new turbulence quantity defined in this study (TIw,towards−wall) was most closely correlated with the particle deposition velocity (vd) among the three near-wall quantities.

Spatial Variation of Statistical and Spectral Properties of the Stream Wise and Wall-Normal Velocity Fluctuations in the Near-Neutral Atmospheric Surface Layer

Based on high-quality near-neutral atmospheric-surface-layer (ASL) data obtained from an observational site located in flat desert and existing experimental results for a friction Reynolds number Reτ 106, the change of the second-order statistics of the streamwise velocity component with height is consistent with the experimental results for Reτ < 106, while the second-order statistics of the wall-normal velocity component increase linearly with height. In combination with the experimental results for Reτ < 106, the variation of the slope of streamwise turbulence intensity with height and the variation of the slope and intercept of the wall-normal turbulence intensity with height are quantified to reveal that both the streamwise and wall-normal velocity variances follow a generalized logarithmic law, with the distribution of the streamwise and wall-normal velocity components satisfying sub- and super-Gaussian distributions. Spectral analysis shows that the variation of the wavenumber corresponding to the pre-multiplied streamwise and wall-normal spectra peaks with the ratio z/δ obeys the form $$ k_{x} \delta = a(\delta /z)^{b} $$ , where z is the height, kx is the streamwise wavenumber, and δ is the ASL thickness. For the pre-multiplied streamwise spectra, $$ b = 0.5 \pm 0.1 $$ and the value of a may have a Reynolds-number dependence, while for the pre-multiplied wall-normal spectra, $$ a = 2.2 \pm 0.09 $$ and $$ b = 1.0 \pm 0.1 $$ . The von Karman constant, the Townsend–Perry constant and other parameters also display a weak Reynolds-number dependence.

The amplification of large-scale motion in a supersonic concave turbulent boundary layer and its impact on the mean and statistical properties

Direct numerical simulation is conducted to uncover the response of a supersonic turbulent boundary layer to streamwise concave curvature and the related physical mechanisms at a Mach number of 2.95. Streamwise variations of mean flow properties, turbulence statistics and turbulent structures are analysed. A method to define the boundary layer thickness based on the principal strain rate is proposed, which is applicable for boundary layers subjected to wall-normal pressure and velocity gradients. While the wall friction grows with the wall turning, the friction velocity decreases. A logarithmic region with constant slope exists in the concave boundary layer. However, with smaller slope, it is located lower than that of the flat boundary layer. Streamwise varying trends of the velocity and the principal strain rate within different wall-normal regions are different. The turbulence level is promoted by the concave curvature. Due to the increased turbulence generation in the outer layer, secondary bumps are noted in the profiles of streamwise and spanwise turbulence intensity. Peak positions in profiles of wall-normal turbulence intensity and Reynolds shear stress are pushed outward because of the same reason. Attributed to the Görtler instability, the streamwise extended vortices within the hairpin packets are intensified and more vortices are generated. Through accumulations of these vortices with a similar sense of rotation, large-scale streamwise roll cells are formed. Originated from the very large-scale motions and by promoting the ejection, sweep and spanwise events, the formation of large-scale streamwise roll cells is the physical cause of the alterations of the mean properties and turbulence statistics. The roll cells further give rise to the vortex generation. The large number of hairpin vortices formed in the near-wall region lead to the improved wall-normal correlation of turbulence in the concave boundary layer.

Particle image and tracking velocimetry of solid-liquid turbulence in a horizontal channel flow

The turbulence statistics of the solid and liquid phases in a horizontal turbulent channel flow are experimentally investigated to identify the effect of particle size, flow Reynolds number (Re) and the volumetric concentration of particles. Glass beads with diameters of 285, 340, 530 and 700 µm are used to produce suspensions at particle volumetric concentrations between 0.05 and 0.18%. Measurements are made at Re of 50,000, 75,000, 100,000, and 125,000 based on channel height and average velocity. The instantaneous velocity of the glass beads is obtained using a correlation-based particle tracking velocimetry (PTV) while particle image velocimetry (PIV) using smaller tracers is applied simultaneously to obtain the liquid phase velocity. It is observed that the solid phase velocity is larger than the liquid phase in the near-wall region for the larger particles and higher flow Re. The particle Re number, Rep, defined based on the particle diameter and the slip velocity (mean relative velocity between the liquid and solid phases), and the Stokes number (St) are used to evaluate the turbulence modulation of the liquid phase. Particle Re numbers as large as 225 are calculated for the 700 µm particles at Re = 125,000, which leads to vortex shedding and, consequently, increases turbulence intensity of the liquid phase relative to the unladen flow. The PTV results indicate that the turbulence intensity of the solid phase decreases with increase of St (i.e. larger particles and higher flow Re). The solid phase volumetric concentration has negligible effect on the solid phase turbulence, while the wall-normal turbulence intensity of the liquid phase increases with the volumetric concentration. This observation reveals the two-way coupling of the solid and liquid phases at the range of concentrations investigated in the current study.

Streamwise variations of turbulence statistics up to maximum drag reduction state in turbulent boundary layer flow due to surfactant injection

We investigate streamwise variations of turbulence statistics in the wide range of drag reduction (DR) up to the maximum drag reduction (MDR; DR ≥ 60%) state for the turbulent boundary layer flow due to surfactant injection. One-component laser-Doppler velocimetry (LDV) measurements show that the DR is drastically varied from the low drag reduction (LDR) to the high drag reduction (HDR) regions and is saturated in the MDR region, and such variation is sensitive to the free-stream velocity and dependent on the process of diffusion of injected surfactant solution. Both two-component LDV measurements and particle image velocimetry (PIV) measurements clarify that the mean velocity in wall units agrees with the so-called Virk’s ultimate profile in the MDR region, where both wall-normal turbulence intensity and the Reynolds shear stress with outer scaling are considerably suppressed compared to those in the LDR and HDR regions, while the maximum of streamwise turbulence intensity is comparable with that of water. Such behavior is independent of flow types such as internal and external flows and kinds of additives such as polymer and surfactant. The principal axis angle in joint probability density function of streamwise and wall-normal velocity fluctuations near the wall is the most promising index as the amount of DR based on the LDR, HDR, and MDR. The PIV measurements also show that the sheet-like structures in the HDR and MDR regions expand to around the maximum location of streamwise turbulence intensity, at which spanwise length scales are evaluated.

Scaling of Wall-Normal Turbulence Intensity and Vertical Eddy Structures in the Atmospheric Surface Layer

Adequate high-quality data on three-dimensional velocities in the atmospheric surface layer (height \(\delta \)) were acquired in the field at the Qingtu Lake Observation Array. The measurement range occupies nearly the entire logarithmic layer from approximately \(0.006\delta \)–\(0.2\delta \). The turbulence intensity and eddy structures of the velocity fluctuations in the logarithmic region were primarily analyzed, and their variations in the z (wall-normal) direction were revealed. The primary finding was that the turbulent intensity of wall-normal velocity fluctuations exhibits a sharp upswing in the logarithmic region, which differs from classic scaling law and laboratory results. The upswing of the wall-normal turbulence intensity in the logarithmic region is deemed to be linear based on an ensemble of 20 sets of data. In addition, the wall-normal extent of the correlated structures and wall-normal spectra were compared to low Reynolds number results in the laboratory.

Experimental study of the flow structures of 3D turbulent offset jets

ABSTRACTThree-dimensional turbulent offset jets were investigated using a particle image velocimetry technique. Detailed measurements were performed for offset height ratios of 0, 2 and 4. The presence of backflow influenced the distribution of the mean velocity and Reynolds stresses. A two-point correlation analysis was used to investigate the spatial distribution of large-scale structures within the inner shear layer of the flow domain. The results revealed that large-scale structures dominate the inner layer of the self-similarity region. Proper orthogonal decomposition was performed on the fluctuating velocity field within the symmetry and lateral planes using the snapshot approach. Results from the reconstructed field provided insight into the contributions of the most energetic structures to the turbulence statistics. The energetic structures contributed more to the Reynolds shear stress and streamwise turbulence intensity, while contributing less to the wall-normal turbulence intensity.

Comparison of large- and very-large-scale motions in turbulent pipe and channel flows

Statistical measures of turbulence intensities in turbulent pipe and channel flows at a friction Reynolds number of Reτ ≈ 930 were explored by a population of large-scale motions (LSMs) and very-large-scale motions (VLSMs). Although the statistical measures characterizing these internal turbulent flows were similar in the near-wall region, the extents of the mean streamwise velocities and cross-stream components of the turbulence intensities differed in the core region. The population density of VLSMs/LSMs decreased/increased significantly in the core region of the pipe flow. The survival time of VLSMs of the pipe flow was shorter than that of the channel flow. The area fractions of the VLSMs displayed similar trends to the population density. The wall-normal and spanwise turbulence intensities in the pipe flow increased in the core regions due to the high-speed large-scale structures and associated motions above the structures. The large-scale structures increased the streamwise intensity and the Reynolds shear stress in the pipe and channel flows, whereas the effective streamwise intensities and the Reynolds shear stress were equivalent in both flows.

Turbulent drag reduction of boundary layer flow with non-ionic surfactant injection

AbstractWe experimentally investigated streamwise variations of turbulent dynamics in drag-reducing turbulent boundary layer flows following the injection of non-ionic surfactant solutions, which mainly consisted of oleyldimethylamine oxide. We focus on the comparison of turbulence statistics between injected (i.e. heterogeneous) and premixed (i.e. homogeneous) surfactant solutions, in which the maximum drag reduction ratio of 50 % is the same at the most downstream position for both cases. The wall-normal profiles of turbulence statistics, such as streamwise and wall-normal turbulence intensities, seem to be noticeably different between heterogeneous and homogeneous surfactant solutions. However, streamwise variations in these maxima and the wall-normal locations are essentially similar to one another, except for the maximum of streamwise turbulence intensity, which is not arranged by the amount of drag reduction and is also dependent on the normalization due to outer and inner variables. Such complex behaviour of streamwise turbulence intensity would be caused by the formation of near-wall layered structures that are parallel to the wall. For both heterogeneous and homogeneous surfactant solutions, the streamwise variation in the drag reduction ratio corresponds well to those of the mean velocity in wall units and the wall-normal locations of maxima of streamwise and wall-normal turbulence intensities with both outer and inner scaling. Unlike the Reynolds shear stress, the correlation coefficient of the streamwise and wall-normal turbulent fluctuations is correlated well with the drag reduction ratio. We present plausible pictures of the development of turbulence structures such as hairpin vortices and low-speed streaks for the drag-reducing turbulent boundary layer in heterogeneous and homogeneous surfactant solutions, which are comprehensively derived from the present set of experimental measurements such as flow visualization, planar laser-induced fluorescence, two-component laser-Doppler velocimetry and particle image velocimetry on the streamwise and wall-normal plane and the streamwise and spanwise plane.

A Reynolds stress model for turbulent flows of viscoelastic fluids

A second-order closure is developed for predicting turbulent flows of viscoelastic fluids described by a modified generalised Newtonian fluid model incorporating a nonlinear viscosity that depends on a strain-hardening Trouton ratio as a means to handle some of the effects of viscoelasticity upon turbulent flows. Its performance is assessed by comparing its predictions for fully developed turbulent pipe flow with experimental data for four different dilute polymeric solutions and also with two sets of direct numerical simulation data for fluids theoretically described by the finitely extensible nonlinear elastic – Peterlin model. The model is based on a Newtonian Reynolds stress closure to predict Newtonian fluid flows, which incorporates low Reynolds number damping functions to properly deal with wall effects and to provide the capability to handle fluid viscoelasticity more effectively. This new turbulence model was able to capture well the drag reduction of various viscoelastic fluids over a wide range of Reynolds numbers and performed better than previously developed models for the same type of constitutive equation, even if the streamwise and wall-normal turbulence intensities were underpredicted.

Characteristics of Turbulent Three-Dimensional Wall Jets

Three-dimensional turbulent wall jet was investigated using a particle image velocimetry technique. Three Reynolds numbers based on the jet exit velocity and diameter of 5000, 10,000, and 20,000 were studied. Profiles of the mean velocities, turbulence intensities, and Reynolds shear stresses as well as two-point velocity correlations and proper orthogonal decomposition analyses were used to document the salient features of the wall jets. The decay and spread rates are independent of Reynolds numbers in the self-similar region. The estimated values of 1.15, 0.054, and 0.255 for the decay rate, wall-normal spread rate, and lateral spread rate, respectively, are within the range of values reported in the literature. The two-point correlation analysis showed that the inclination of the streamwise velocity correlation contours in the inner layer is 11±3 deg in the wall region, which is similar to those of canonical turbulent boundary layers. The results from the proper orthogonal decomposition indicate that low-order modes contribute more to the turbulence statistics in the self-similar region than in the developing region. The Reynolds shear stresses are the biggest benefactors of the low-order mode contribution while the wall-normal turbulence intensities are the least.

Turbulence structures over irregular rough surfaces

Turbulent flow in a channel with irregular two-dimensional rough surfaces is analysed through wall-resolving large eddy simulation (LES). Both walls of the channel are roughened through the superimposition of sinusoidal functions having random amplitude and four different wavelengths. The downward shift of the velocity profile in the log region due to the roughness, known as roughness function, is well captured in the simulations. The spanwise and wall-normal turbulence intensities are found to increase with the roughness height, while the streamwise component decreases. The analysis of the Reynolds stress anisotropy tensor highlights a tendency towards isotropisation, confirmed by the vorticity rms. The analysis of the statistics shows that the effects of the roughness on the turbulent flow are greatly related to the increase of the height of the maximum peaks of the corrugations. Although the inner layer is dramatically affected by the wall irregularities, the outer layer appears not affected by the specific wall shape and a collapse of the turbulence statistics in smooth- and rough-wall conditions is observed. Much of the present results are consistent with the observations made over regular roughness, nevertheless the turbulence structures and the turbulent kinetic energy production analysis shows that the turbulence dynamics are directly affected by the local shape of the irregularities. The spatial inhomogeneities of the height of the roughness peaks and of the cavity region locally modifies the structures introducing variable length-scales. Overall the irregular roughness destroys the coherent pattern of the flow selectively, depending on the spatial distribution of the higher roughness peaks.

Scaling of the wall-normal turbulence component in high-Reynolds-number pipe flow

Streamwise and wall-normal turbulence components are obtained in fully developed turbulent pipe over a Reynolds number range from 1.1 × 105to 9.8 × 106. The streamwise intensity data are consistent with previous measurements in the same facility. For the wall-normal turbulence intensity, a constant region inv'r.m.s.is found for the region 200 ≤ y+≤ 0.1R+for Reynolds numbers up to 1.0 × 106. An increase inv'r.m.s.is observed below abouty+∼ 100, although additional measurements will be required to establish its generality. The wall-normal spectra collapse in the energy-containing region with inner scaling, but for the low-wavenumber region ay/Rdependence is observed, which also indicates a continuing influence from the outer flow on the near-wall motions.

Study of the near-wall-turbulent region of the high-Reynolds-number boundary layer using an atmospheric flow

Data from the near-wall-turbulent region of the high-Reynolds-number atmospheric surface layer are used to analyse the attached-eddy model of wall turbulence. All data were acquired during near-neutral conditions at the Surface Layer Turbulence and Environmental Science Test (SLTEST) facility located in the western Utah Great Salt Lake Desert. Instantaneous streamwise and wall-normal components of velocity were collected with a wall-normal array of two-component hot wires within the first 2 m above the surface of the salt flats. Streamwise and wall-normal turbulence intensities and spectra are directly compared to corresponding laboratory data and similarity formulations hypothesized from the attached-eddy model of wall turbulence. This affords the opportunity to compare results with Reynolds numbers varying over three orders of magnitude. The wall-normal turbulence-intensity similarity formulation is extended. The results show good support for the similarity arguments forwarded by the attached-eddy model as well as Townsend's (1956) Reynolds-number similarity hypothesis and lack of the ‘inactive’ motion influence on the wall-normal velocity component. The effects of wall roughness and the spread in the convection velocity due to this roughness are also discussed.

Influence of local ultrasonic forcing on a turbulent boundary layer

An experimental study was carried out to investigate the effect of local ultrasonic forcing on a turbulent boundary layer. The ultrasonic forcing system was constructed by adhering six ultrasonic transducers to a flat plate over which water was flowed. In this system, the ultrasonic waves projected into the water by the transducers caused cavitation, giving rise to an enormous number of tiny water-vapor bubbles. Stereoscopic particle image velocimetry (SPIV) was used to probe the flow characteristics. The SPIV results showed that imposition of the ultrasonic forcing caused a substantial increase in the mean wall-normal velocity but a decrease in the mean streamwise velocity. The ultrasonic forcing reduced the skin friction coefficient by up to 60% immediately downstream of the transducers; this effect gradually dissipated with moving downstream. The streamwise turbulence intensity was reduced near the wall but increased away from the wall, whereas the wall-normal turbulence intensity was not much affected near the wall but increased away from the wall. The Reynolds shear stress and the production of turbulent kinetic energy were reduced near the wall. Imposition of the ultrasonic forcing shifted the streamwise vortical structures away from the wall, leading to a reduction in skin friction.

Direct numerical simulation of turbulent heat transfer in plane impinging jet

The objectives of this study are to investigate the structures and characteristics of flows and heat transfer for plane turbulent impinging jets in a confined space, where a wall-jet type of flow is influenced by both lower (impingement) and upper walls, and to obtain turbulent statistics for the construction of a turbulent heat transfer model. For these purposes, we have performed direct numerical simulations (DNS) of impinging flows with heat transfer. To obtain the effects of an impingement distance on heat transfer, the value of H is changed in calculations, where H is the distance between the impingement wall and the upper wall. It is found from the present DNS that the Nusselt number increases with a decrease in the distance H similar to the experimental results. In addition, the Nusselt number of the case with the highest distance decreases monotonously in the wall-jet development direction, while in shorter distance cases the second peak of the Nusselt number is clearly observed away from the stagnation point, due to the increase in wall-normal turbulence intensities in the region away from the stagnation point.

Direct numerical simulation of compressible turbulent channel flow between adiabatic and isothermal walls

In this paper, the effects of adiabatic and isothermal conditions on the statistics in compressible turbulent channel flow are investigated using direct numerical simulation (DNS). DNS of two compressible turbulent channel flows (Cases 1 and 2) are performed using a mixed Fourier Galerkin and B-spline collocation method. Case 1 is compressible turbulent channel flow between isothermal walls, which corresponds to DNS performed by Coleman et al. (1995). Case 2 is the flow between adiabatic and isothermal walls. The flow of Case 2 can be a very useful framework for the present objective, since it is the simplest turbulent channel flow with an adiabatic wall and provides ideal information for modelling the compressible turbulent flow near the adiabatic wall. Note that compressible turbulent channel flow between adiabatic walls is not stationary if there is no sink of heat. In Cases 1 and 2, the Mach number based on the bulk velocity and sound speed at the isothermal wall is 1.5, and the Reynolds number based on the bulk density, bulk velocity, channel half-width, and viscosity at the isothermal wall is 3000.To compare compressible and incompressible turbulent flows, DNS of two incompressible turbulent channel flows with passive scalar transport (Cases A and B) are performed using a mixed Fourier Galerkin and Chebyshev tau method. The wall boundary conditions of Cases A and B correspond to those of Cases 1 and 2, respectively. Case A corresponds to the DNS of Kim & Moin (1989). In Cases A and B, the Reynolds number based on the friction velocity, the channel half-width, and the kinematic viscosity is 150.The mean velocity and temperature near adiabatic and isothermal walls for compressible turbulent channel flow can be explained using the non-dimensional heat flux and the friction Mach number. It is found that Morkovin's hypothesis is not applicable to the near-wall asymptotic behaviour of the wall-normal turbulence intensity even if the variable property effect is taken into account. The mechanism of the energy transfers among the internal energy, mean and turbulent kinetic energiesis investigated, and the difference between the energy transfers near isothermal and adiabatic walls is revealed. Morkovin's hypothesis is not applicable to the correlation coeffcient between velocity and temperature fluctuations near the adiabatic wall.