Turbulent Velocity Fluctuations Research Articles

Numerical Study of Mitigating Cloud Cavitation Shedding Using Biomimetic Protuberant Stripes

Abstract Cloud cavitation usually appears on impeller blades of hydraulic machinery. When unsteady cloud cavitation travels downstream to a high-pressure region and collapses, performance drops and cavitation erosion appears. It is important to develop effective methods to mitigate the undesirable effects. By million years of natural selection, bird feather has presented excellent flow performance. As typical characteristic structure of bird feather, a number of barbs are supported by a central hollow shaft. Under inspiration of bird feathers, we presented a method of passive cavitation control. This method of passive cavitation control uses biomimetic protuberant stripes (PSs) mounted on a NACA66 hydrofoil. The effects of various biomimetic PS arrangements on the cavitation pattern, pressure fluctuation, and hydrodynamic load are numerically studied. Then, the cavitation control mechanism of the biomimetic PS is analyzed in detail. We observe that the biomimetic PSs not only inhibit the shedding of large-scale cloud cavitation but also reduce the cavitation size. Moreover, analysis shows that turbulence velocity fluctuation may be mitigated and boundary layer thickness is reduced with biomimetic PSs, which enhances the flow intensity in the main flow direction.

Predictive models for near-wall velocity and temperature fluctuations in supersonic wall-bounded turbulence

Predictive models for near-wall velocity and temperature fluctuations in compressible wall-bounded turbulence are developed in the present study based on the model proposed by Marusic et al. (Science, vol. 329 (5988), 2010, pp. 193–196), which incorporates the superposition and amplitude modulation effects of the large-scale motions in the outer region on near-wall turbulence. The density variation is involved in the predictive model for velocity fluctuations to achieve Mach number independence. The predictive model for temperature fluctuations is derived to keep its consistency with the strong Reynolds analogy, in which the modulation effect is supposed to be cast as the quadratic function of the large-scale velocity fluctuations. An algebraic method is proposed to directly determine the modulation coefficients and extract the universal signals. A direct numerical simulation (DNS) of turbulent channel flow at the friction Reynolds number of $1170$ and bulk Mach number of $2.88$ is carried out for parameter calibration and validations. The variances and joint probability density functions of the predicted velocity and temperature fluctuations agree well with the DNS results.

Scaling of rough-wall turbulence in a transitionally rough regime

In this Letter, we propose a roughness scaling method based on the direct numerical simulation of turbulent channel flow over three-dimensional sinusoidal rough walls in a transitionally rough regime. A new coupling scale Reτ/(k¯+S)n is defined by combining the Reynolds number Reτ and the roughness parameter k¯+S, where k¯+ is the mean roughness height, S is the roughness steepness, and n is the scaling exponent—which depends on the roughness type. The relationships between Reτ, k¯+S, the roughness function, the friction factor, and the peak of the streamwise turbulent velocity fluctuation are explored. This approach provides an effective way for collapsing rough-wall turbulence data with different Reτ and k¯+S.

Coherent structures in turbulent mixed convection flows through channels with differentially heated walls

The occurrence and shape of turbulent structures in mixed convection flows through a differently heated vertical channel are investigated in terms of thermally induced attenuation and amplification of turbulent velocity, pressure, and temperature fluctuations using direct numerical simulations. It is shown that the wall-normal momentum transport is decreased and increased near the heated and cooled wall, respectively, and that this leads to a reduced and elevated production of turbulent velocity fluctuations in the streamwise velocity component in the aiding and opposing flow, respectively. The corresponding flow structures are smoother, faster and warmer in the aiding flow and aligned along the main flow, while the colder structures in the opposing flow are more frayed and less directed. The warmer flow structures in the aiding flow are overall more stable than the colder structures in the opposing flow. Besides, the study reveals that the position of the maximum temperature fluctuations moves toward the heated wall, so that the sweeps produced at the two walls are affected differently by the former. As a consequence, the distance and time period over which the fluctuations develop in the aiding flow are shorter than in the opposing flow. It is further shown that vortex structures oriented in the streamwise direction usually arise with an offset to the right or left above a sweep or an ejection, whereby the decreasing values of the correlation coefficients with increasing Grashof number indicate a weakening of the vortex structures. Since none of the evaluated vortex criteria, that is, the distributions of the vorticity, λ 2 - value or Rortex-value correlate well with the evaluated minima of the pressure fluctuations, they do not allow a clear identification of the vortex structures. Finally, analyzing the budget of the turbulent kinetic energy it is confirmed that the velocity fluctuations are only indirectly influenced by the buoyancy force. Thus, the attenuation and amplification of the turbulent velocity fluctuations is reflected in the reduction and exaggeration of the Reynolds shear stresses in the aiding and opposing flow, respectively.

Cloud microphysical measurements at a mountain observatory: comparison between shadowgraph imaging and phase Doppler interferometry

Abstract. The microphysical properties of cloud droplets, such as droplet size distribution and droplet number concentration, were studied. A series of field experiments was performed in the summer of 2019 at the Umweltforschungsstation Schneefernerhaus (UFS), an environmental research station located just below the peak of the Zugspitze mountain in the German Alps. A VisiSize D30 manufactured by Oxford Laser Ltd., which is a shadowgraph imaging instrument, was utilized for the first time to measure the size and velocity of cloud droplets during this campaign. Furthermore, a phase Doppler interferometer (PDI) device, manufactured by Artium Tech. Inc., was simultaneously measuring cloud droplets. After applying modifications to the built-in software algorithms, the results from the two instruments show reasonable agreement regarding droplet sizing and velocimetry for droplet diameters larger than 13 µm. Moreover, discrepancies were observed concerning the droplet number concentration results, especially with smaller droplet sizes. Further investigation by applying appropriate filters to the data allowed the attribution of the discrepancies to two phenomena: the different optical performance of the sensors with regard to small droplets and high turbulent velocity fluctuations relative to the mean flow that result in an uncertain estimate of the volume of air passing through the PDI probe volume.

Exploring the relation between turbulent velocity and density fluctuations in the stratified intracluster medium

Context. The dynamics of the intracluster medium (ICM) is affected by turbulence driven by several processes, such as mergers, accretion and feedback from active galactic nuclei. Aims. X-ray surface brightness fluctuations have been used to constrain turbulence in galaxy clusters. Here, we use simulations to further investigate the relation between gas density and turbulent velocity fluctuations, with a focus on the effect of the stratification of the ICM. Methods. In this work, we studied the turbulence driven by hierarchical accretion by analysing a sample of galaxy clusters simulated with the cosmological code ENZO. We used a fixed scale filtering approach to disentangle laminar from turbulent flows. Results. In dynamically perturbed galaxy clusters, we found a relation between the root mean square of density and velocity fluctuations, albeit with a different slope than previously reported. The Richardson number is a parameter that represents the ratio between turbulence and buoyancy, and we found that this variable has a strong dependence on the filtering scale. However, we could not detect any strong relation between the Richardson number and the logarithmic density fluctuations, in contrast to results by recent and more idealised simulations. In particular, we find a strong effect from radial accretion, which appears to be the main driver for the gas fluctuations. The ubiquitous radial bias in the dynamics of the ICM suggests that homogeneity and isotropy are not always valid assumptions, even if the turbulent spectra follow Kolmogorov’s scaling. Finally, we find that the slope of the velocity and density spectra are independent of cluster-centric radii.

Coherence of Velocity Fluctuations in Turbulent Flows.

We investigate the spatiotemporal quantity of coherence for turbulent velocity fluctuations at spatial distances of the order or larger than the integral length scale l_{0}. Using controlled laboratory experiments, an exponential decay as a function of distance is observed with a decay rate that depends on the flow properties. The same law is observed in two different flows, indicating that it can be a generic property of turbulent flows.

Transient numerical simulations of a cold-flow bidirectional vortex chamber

Bidirectional chambers are well-studied in terms of the flow structure and influence of their input parameters. However, most of the available studies are based on steady-state or time-averaged research methods and do not allow to obtain data on bidirectional flow dynamics over time. The present paper reports on detailed numerical studies based on detached eddy simulations (DESs) and unsteady Reynolds-averaged Navier–Stokes methods applied for two vortex chambers with different aspect ratios. A comparison of the numerical results with the available experimental data shows that the DES method gives the most accurate results on bidirectional flow structure, turbulent fluctuations, and precessing vortex core (PVC) motion. A notable feature of the studied bidirectional flow is the central recirculation zone (CRZ) formation, which is correctly predicted by the DES method only. The presence of a CRZ in a bidirectional flow has a significant effect on turbulent velocity fluctuations and PVC behavior. It is found that CRZ formation leads to a significant decrease in radial and circumferential velocity fluctuations whereas the axial velocity fluctuations are slightly increased. Additionally, the paper reports new findings on CRZ and PVC interaction in bidirectional flows. PVC motion is almost completely nullified by the presence of a CRZ. This can prove useful in many industrial applications of bidirectional chambers, e.g., vortex thrusters and gas turbine combustors. The bidirectional swirling flow transient properties studied in this paper could assist in determining the most efficient operational modes and geometric configuration of industrial chambers as well as enabling control of turbulent fluctuations, which would allow for reliable ignition and stable combustion.

Influence of appendages on the wake field of surface combatant based on stereoscopic particle image velocimetry

As the supporting structure of a ship shafting, the shaft bracket has a significant impact on the hydrodynamic performance of the ship, especially the propulsion. To determine the influence of the shaft bracket and bilge keel on the wake field, we performed a surface combatant wake field experiment. The flow field of the model with/without appendages was measured in three different sections, and the wake field characteristics on the propeller disk with/without appendages were compared. The influence of the shaft bracket was investigated, revealing that the bilge keel exhibited a slight influence on the flow field, the shaft bracket can influence the wake field in the entire installation space, the influence of the outer bracket arm was more significant than the inner bracket arm, and flow separation occurred at the outer bracket arm. The shaft bracket exhibited a more significant influence on the area above the propeller disk, resulting in an uneven flow field. The vortices generated by the shaft bracket were paired in opposite directions, and the vortices generated by the outer support arm were dominant. The shaft bracket improved the turbulent kinetic energy and fluctuation velocity, increasing their local maxima. Simultaneously, the velocity boundary layer gradually thickened from front to back at different cross sections. The installation angle of the shaft bracket is critical for the uniformity of the propeller disk plane flow field. If the angle is excessively large, cavitation readily occurs, which has an adverse influence on the propeller.

Characterization of atmospheric coherent structures and their impact on a utility-scale wind turbine

Atmospheric turbulent velocity fluctuations are known to increase wind turbine structural loading and accelerate wake recovery, but the impact of vortical coherent structures in the atmosphere on wind turbines has not yet been evaluated. The current study uses flow imaging with natural snowfall with a field of view spanning the inflow and near wake. Vortical coherent structures with diameters of the order of 1 m are identified and characterized in the flow approaching a 2.5 MW wind turbine in the region spanning the bottom blade tip elevation to hub height. Their impact on turbine structural loading, power generation and wake behaviour are evaluated. Long coherent structure packets $(\mathrm{\ \mathbin{\lower.3ex\hbox{$\buildrel> \over {\smash{\scriptstyle\sim}\vphantom{_x}}$}}\ }200\;\textrm{m)}$ are shown to increase fluctuating stresses on the turbine support tower. Large inflow vortices interact with the turbine blades, leading to deviations from the expected power generation. The sign of these deviations is related to the rotation direction of the vortices, with rotation in the same direction as the circulation on the blades leading to periods of power surplus, and the opposite rotation causing power deficit. Periods of power deficit coincide with wake contraction events. These findings highlight the importance of considering coherent structure properties when making turbine design and siting decisions.

The Turbulent Lagrangian Dissipative Particle Velocity Statistics

A statistical description of turbulence comprising a probability distribution for stationary flows is the basis for determining the nature of turbulent velocity fluctuations. Away from the Eulerian spatial increments of the velocity field, the Lagrangian notion of temporal velocity increments along particle trajectories appears to be the hob of turbulent velocity statistics, ostensibly in the presence of inherent intermittencies observable in particle tracking. Such intermittencies were analyzed by using the well-known velocity structure functions, which defer to the Kolmogorov similarity theory (KST). Since particle trajectories, under normal circumstances, submit to Gaussian statistics, the deviations from Kolmogorov similarity theory are considered a culprit in the event of intermittency.

LES two-phase modelling of suspended sediment transport using a two-way coupled Euler–Lagrange approach

Sediment plume development was modelled using an Euler–Lagrangian two-way coupled large eddy simulation. Momentum exchange was calculated based on interaction forces in the Maxey–Riley equation. Validation showed good agreement with experimental data from literature. For analysis of interaction between sediment and fluid 6,859 particles were released into turbulent fluid flow. In order to ensure independence of the results from arbitrary turbulent velocity fluctuations in the initial fluid velocity field, 41 simulations of the test case starting from different initial flow fields were analysed. Results of these simulations are normally distributed. Mean values indicate three phases of the development of the sediment plume: (i) acceleration phase, (ii) transport phase and (iii) deposition phase. Significant slow down of fluid flow and particle sorting turned out to be relevant processes in the initial development of the sediment plume which are not accounted for in one-way coupled models.

난류생성기 판 형상에 의한 난류화염 특성 연구

The cross-shaped fractal grids which have RRBT(reduced ratio of bar thickness) and the hexagonal grid were used to generate various turbulent flow properties for low swirl flames. In the non-reacting flow field with the fixed bulk velocity at 10 m/s, decreasing RRBT induces the increasing turbulent intensity(ISUBU/SUB) with the delay in the location of lowest turbulent mean velocity(Ū) and highest turbulent fluctuation(ú) due to vortex shedding from the bar thickness. This phenomenon was well explained by a wake interaction theory using axial velocity profiles at the centerline. At various equivalence ratios for Hexa. and fractal grids, the characteristics of low swirl flames could be identified to a thin reaction zone regime in the Borghi – Peter regime diagram. Decreasing RRBT increases ISUBU/SUB in front of flame brush with increasing turbulent local displacement speeds (SSUBT,LD/SUB) via a linear correlation. The turbulent Reynolds number, ReSUBT/SUB composed of the ratio of length scale and velocity components induced the proportional trends in non linear relationship showing that the influence of the length scale ratio. The empirical correlation study of SSUBT,LD/SUB as a function of ReSUBT/SUB and ú/SSUP0/SUPSUBL/SUB was investigated to compare the influence of velocity and turbulent length scales ratio. The result of linear correlation equation with SSUBT,LD/SUB indicates the influence of velocity factors greater than ReSUBT/SUB through the exponential factor.

Turbulence modulation in thermally expanding and contracting flows

We present direct numerical simulations of developing turbulent channel flows subjected to thermal expansion or contraction downstream of a heated or cooled wall. Using different constitutive relations for viscosity we analyse the response of variable property flows to streamwise acceleration/deceleration by separating the effect of streamwise acceleration/deceleration from the effect of wall-normal property variations. We demonstrate that, beyond a certain streamwise location, the flow can be considered in a state of ‘quasi-equilibrium’ regarding semilocally scaled variables. As such, we claim that the development of turbulent quantities due to streamwise acceleration/deceleration is localized to the region of impulsive heating/cooling, while changes in turbulence occurring farther downstream can be attributed solely to property variations. This finding allows us to study turbulence modulation in accelerating/decelerating flows using the semilocal scaling framework. By investigating the energy redistribution among the turbulent velocity fluctuations, we conclude that a change in bulk streamwise velocity has a non-local effect which originates from the change in mean shear and modifies the energy pathways through velocity-pressure-gradient correlations. On the other hand, the wall-normal property gradients have a local effect and act through the modification of the viscous dissipation. We show that it is possible to superimpose and compare the two different effects when using the semilocal scaling framework.

Time-Accurate Evaluation of Film Cooling Jet Characteristics for Plenum and Crossflow Coolant Supplies

Abstract Gas turbine film cooling creates complicated and highly unsteady flow structures. This study seeks to examine the unsteady characteristics created by different cooling hole inlet geometries using a fast-response pressure-sensitive paint (PSP) technique able to capture time-accurate measurements at 2000 frames per second, resolving frequencies up to 1000 Hz. Time-accurate and time-averaged measurements are used to evaluate the performance of a plenum-style inlet and a crossflow-style inlet in varying turbulence environments over a flat plate. The results of this study are intended to begin the process of breaking down widely accepted time-averaged film effectiveness trends into the cumulative effects of freestream turbulence and momentum flux ratio, with emphasis on the cooling jet motions they cause. Jet behaviors observed in this study include a sweeping oscillation, unsteady attachment and separation from the plate, and time-accurate and time-averaged flow bias. Cooling hole inlet geometry and momentum flux ratio affect the core of the jet, and freestream turbulence affects the periphery of the jet. Crossflow-fed cooling holes show bias to the upstream side of the cooling hole with respect to the internal crossflow direction. Plenum-fed cooling holes outperform crossflow-fed cooling holes, and the difference grows with increasing momentum flux ratio. The frequency of both plenum- and crossflow-fed cooling jet motions is influenced by the freestream turbulent velocity fluctuations. The resulting mode shapes show dominant side-to-side sweeping for higher turbulence environments and a separation and reattachment motion for lower turbulence environments. At higher momentum flux ratio, the jets were seen to increasingly favor separation and reattachment motions. The results of this study are intended to better inform existing predictive tools. With a better understanding of the time-accurate behaviors responsible for creating the commonly accepted time-averaged coolant distributions, simple predictive tools may be better equipped to accurately model film cooling flows.

Effective method of predicting confined pressure behavior under isotropic turbulence

Explosion pressure prediction is indispensable to ensure process safety against accidental gas explosions. This work is aimed at establishing a theoretical method for predicting confined methane-air explosion pressure under isotropic turbulence. The results indicated that the pressure rise rate becomes significantly increased by the existence of isotropic turbulence, which effect on peak value of explosion pressure is negligible. Among various models of turbulent burning velocity, the calculated pressure rise rate using Chiu model, Williams model and Liu model is relatively closer to experimental value. With the increase of turbulent integral length and RMS turbulent fluctuation velocity, the pressure rise rate becomes increased continuously. The influence of adiabatic compression and isothermal compression on pressure rise rate could be ignored. To predict explosion pressure in a more accurate way, the dynamic variation of turbulent integral length and RMS turbulent fluctuation velocity should be considered in the future.

Analytical Solution of Heat Conduction from Turbulence with an Isotropic Example

Aerodynamic heating due to turbulence significantly affects the operation of high-speed vehicles and the entrainment of fluid by turbulent plumes. In this paper, the heat generated and convected by fluid turbulence is examined by rearranging the Navier-Stokes equations into a single equation for the fluctuating dependent variables external to unsteady chaotic motions. This equation is similar to the nonhomogeneous heat equation where sources are terms resulting from this rearrangement. Mean and fluctuating quantities are introduced, and under certain circumstances, a heat equation for the fluctuating density results with corresponding mean and fluctuating source terms. The resultant equation is similar to Lighthill’s acoustic analogy and is a “heat analogy.” A solution is obtained with the use of Green’s function as long as the observer is located outside the region of chaotic motion. Predictions for the power spectrum are shown for high Reynolds number isotropic turbulence. The power spectrum decays as the inverse of the wavenumber of the turbulent velocity fluctuations. The developed theory can easily be applied to other turbulent flows if the statistics of unsteady motion can be estimated.

Degradation of Armco iron caused by cavitation: Part I – Correlation with flow

Cavitation erosion resistance of Armco iron was studied using a tunnel equipped with a system of barricades at two flow conditions, inlet pressure of 1000 and 1200 kPa, and outlet pressure of 125 and 130 kPa, respectively. In order to analyse the mechanism of mass losses, numerical investigations concerning the flow behaviour in the vicinity of the samples were carried out. After 480 min of testing, the increase in inlet pressure from 1000 to 1200 kPa caused an approximately two-and-a-half-fold increase in the erosion rate of samples located closest to the upper barricade that served together with the lower barricade as a cavitation generator. The surface degradation depended on the test conditions: for the test at 1000 and 125 kPa, single pits were formed, while for the test at 1200 and 130 kPa, a large number of pits contributed to the formation of micro-undulation on the entire surface of the sample. Taking into account the time required for the water stream to reach samples’ surface from the low-pressure region and erosion rates, an exponential correlation with a determination coefficient R2 = 0.9247 was obtained. The erosion rate also increased exponentially with turbulence intensity and turbulent dissipation rate. The study of turbulence intensity showed that as the turbulent velocity fluctuations are larger than the mean velocity, the erosion rate increases more intensively, which indicates an increase in the aggressiveness of cavitation.

Compressibility effects on hypersonic turbulent channel flow with cold walls

Compressibility effects on velocity and temperature fluctuations in hypersonic turbulence over cold walls are investigated by exploiting a direct numerical simulation database. We found that the compressibility effects are enhanced by the decrease in wall temperature, which is directly reflected by the rapid increase in velocity divergence and turbulent Mach number. Helmholtz decomposition is adopted to evaluate the genuine compressibility effects by splitting the velocity fluctuation into a solenoidal component and a dilatational component. As the wall temperature decreases, the vertical motion is gradually dominated by the dilatational component, while the wall-parallel motions still by the solenoidal component. The dilatational components tend to decrease the skin friction by around 4%–6%. The instantaneous and conditionally averaged field around strong compressive motions further suggests that the dilatational structures behave as traveling-wave packets surrounded by vortex clusters. To improve the strong analogy between temperature and velocity fluctuations, their correlation in spectral space is studied. The results show that they are strongly correlated at the scales of energy-containing motions, but they are mutually independent at small scales.

Derivation of a macroscopic mixture model for two-phase turbulent flows

This article addresses the issue of reduced models to describe turbulent two-phase flows in industrial applications. A spatially-averaged mixture or drift-flux model is derived theoretically from the local instantaneous Navier-Stokes description. Reynolds-averaging and space-averaging are applied successively. Between these two steps, a model reduction is achieved to account for the non-equilibrium between phases via algebraic relations. Applications of this work are not limited to porous media but also include macroscopic descriptions to model high-shear regions developing near the walls for internal flows. Thermal effects, heat transfer at the wall and phase-change are also considered and briefly discussed. The final model describes the evolution of mixture variables, including effects of both sub-filter spatial variations, turbulence, and local non-equilibrium in velocity, pressure and enthalpy. This analysis provides bridges between different approaches to model two-phase flows (local instantaneous description, two-fluid model, local drift-flux model and spatially-averaged drift-flux model). It clarifies the content of each model involved by defining them in terms of local instantaneous quantities. Turbulent fluctuations and phase intermittency are crucial mechanisms. Important effects to model also include void fraction dispersion and turbulent diffusion; then, it is necessary to model the relative velocity, including the drift velocity orthogonal to gravity induced by the complex interactions between turbulent velocity fluctuations and the interfacial momentum transfer.The final macroscopic (spatially-averaged) mixture formulation is open, in the sense that expressions to model the various terms representing the physics of the small scales are not provided; instead, the physical sense and the origin of these models are discussed. The paper is meant as a basis on which analyses on local imbalance assumptions or relative velocity closures can be assessed. CFD simulations can provide information to complement experiments in technically challenging physical conditions or on processes essential to the models yet difficult to access experimentally (such as interfacial transfers for instance). Different kinds of two-fluid models can be tested to analyse their consequences on the macroscopic spatially-averaged model. In addition, a new path to calibrate closure laws or propose new models is opened based on finer-scale descriptions. Guidelines to use fine simulations along with the open expressions to derive closure relations either for the local drift-flux or for the spatially-averaged models are presented. They concern the modelling of the local relative velocity, the spatial average of the diffusion of void fraction and of the pressure drop.