Single-phase Turbulent Flow Research Articles

Investigation of the effect of rectangular winglet angles on turbulent flow and heat transfer of water/Cu nanofluid in a three-dimensional channel

This numerical simulation studies a homogenous and single-phase nanofluid's turbulent flow and heat transfer behavior in a three-dimensional rectangular microchannel. This study's main purpose is to investigate the use of rectangular winglet angles on flow path and its effect on turbulent flow regime and heat transfer parameters. In the current study, the Reynolds number, winglet attack angle (θ), and twisted angle range (α) (or Pitch angle) from 3000 to 12000, 30°≤ θ ≤ 60°, and 15°≤α ≤ 45°, respectively. Also, Cu nanoparticles with volume fractions of 0–4% are used in water as the base fluid. Results of this study show that heat transfer and flow physics of cooling fluid are affected by the variations of attack angle and winglet twist, and the creation of secondary flows leads to the mixture and deviation of flow. A decrease in the attack angle of the winglet causes the creation of strong vortexes and an increase in Nusselt number and heat transfer. In all investigated situations, with the angle of attack constant, increasing the twist angle can improve the Nusselt number between 11 and 18 percent. Also, increasing the angle of attack of the winglet from 30 to 60° can reduce the Nusselt number by 4–8 percent. The results indicate that changing the winglet angle increases the friction coefficient, and at higher Reynolds numbers, this parameter decreases. Also, by increasing Reynolds number, the ratio of friction coefficient to Nusselt number reduces, leading to the decrease of performance evaluation criterion (PEC).

Thermal Hydraulic Analysis of Turbulent Flow of Superheated Steam Through Multiple Configurations of 3D Angular Piping Bend in Power Plant Installations

Abstract One of the most vulnerable parts in high-pressure and temperature pipeline networks in steam turbine power plant installations is pipe bends, due to intense fluctuation of velocity and pressure of the superheated steam flowing through the piping bend. On the other hand, because of unique chemical and physical properties, the transportation of superheated steam can adversely effect on the integrity of the pipe bends in the piping network. Therefore, the potential risk of pipeline failure becomes more probable at bends. Therefore, to ensure the survivability of the piping network, thorough investigations of the superheated steam flowing through pipe bends are of great significance in better understanding its flow behavior. However, to predict flow behavior at piping bend, intensive research by direct experiment at high temperature and pressure might not be possible to some extent. In that case, computer codes and models can help us analyze flow behavior of superheated steam at pipe bends. The current work is a computational fluid dynamics investigation, where numerical examination is carried out by commercial code ansys fluent for thermal hydraulic analysis of flow behavior of superheated steam through multiple configurations of 3D angular piping bend: 90 deg, 120 deg, and 135 deg. Validation of credibility of the computational approach is done against Sudo et al.'s experiment. With relatively good agreement between the experiment and numerical result using air flowing through 90 deg elbow, single-phase turbulent flow of superheated steam is examined by the application of realizable turbulence model (k–ɛ). The final assessment of the computed results has been done using qualitative and quantitative analyses. The study reveals that unlike the pressure profiles, the radial velocity profiles at the bend exit are noticeably different from those at the bend inlet, since they exhibit more rounded peaks and gentler velocity gradients. The study also shows that the radial pressure and velocity profiles do not display any sign of the existence of a pair of vortices.

Wall shear stress measurement of turbulent bubbly flows using laser Doppler displacement sensor

A novel wall shear stress meter is developed to promote studies of frictional drag reduction by injecting air bubbles into a turbulent boundary layer. Such studies require a tool having a time resolution sufficiently high to capture the unsteady effect of turbulent characteristics due to various bubble passage patterns. The present study adopts the principle of the heterodyne interferometer to capture of time variation of wall shear stress in turbulent flow up to 500 Hz in sampling frequency. We demonstrate the performance of the tool by applying it to bubbly flows beneath a flat-bottom model ship running at 3 m/s in a towing water reservoir, where bubbles experience wavy passage around a few Hz in frequency. The data obtained by the proposed shear stress meter agree well with Dean's formula for single-phase turbulent channel flow. The scattering of the data across three trials is sufficiently small, at approximately 3 %. This high reproducibility is a great advantage over conventional direct measurements, which have low reproducibility and a large scatter of the data of approximately 15 %. The obtained results represent reasonable drag reductions by injecting bubbles with different void fractions. We also evaluate histogram of the wall shear stress fluctuation to characterize the effect of drag reduction by unsteady passage of bubbles.

Opposing Mixed Convection Heat Transfer for Turbulent Single-Phase Flows

Convection, wherein forced and natural convections are prominent, is known as mixed convection. Specifically, when a forced convection flow is downward, this flow is called opposing flow. The objectives of this study are to gain a comprehensive understanding of opposing flow mixed convection heat transfer and to establish the prediction methodology by evaluating existing correlations and models. Several heat transfer correlations have been reported related to single-phase opposing flow; however, these correlations are based on experiments conducted in various channel geometries, working fluids, and thermal flow parameter ranges. Because the definition of nondimensional parameters and their validated range confirmed by experiments differ for each correlation reported in previous studies, establishing a guideline for deciding which correlation should be selected based on its range of applicability and extrapolation performance is important. This study reviewed the existing heat transfer correlations for turbulent opposing flow mixed convection and the single-phase heat transfer correlations implemented in the thermal–hydraulic system codes. Furthermore, the authors evaluated the predictive performance of each correlation by comparing them with the experimental data obtained under various experimental conditions. The Jackson and Fewster, Churchill, and Swanson and Catton correlations can accurately predict all the experimental data. The effect of the difference in the thermal boundary conditions, i.e., uniform heat flux and uniform wall temperature, on the turbulent mixed convection heat transfer coefficient is not substantial. The authors confirmed that heat transfer correlations using the hydraulic-equivalent diameter as a characteristic length can be used for predictions regardless of channel-geometry differences. Furthermore, correlations described based on nondimensional dominant parameters can be used for predictions regardless of the differences in working fluids. The authors investigated the extrapolation performance of the mixed convection heat transfer correlations for a wide range of nondimensional parameters and observed that the Jackson and Fewster, Churchill, and Aicher and Martin correlations exhibit excellent extrapolation performance with respect to natural and forced convection flows, indicating that they can be applied beyond the parameter range validated experimentally.

Numerical investigation of mixed-phase turbulence induced by a plunging jet

In nature and engineering applications, water jet plunging acts as a key process causing interface breaking and generating mixed-phase turbulence. In this paper, high-resolution numerical simulations of the plunging of a water jet into a quiescent pool were performed to investigate the statistical properties of mixed-phase turbulence, with a special focus on the closure problem of the Reynolds-averaged equation. We conducted phase-resolved simulations, with the air–water interface captured using a coupled level-set and volume-of-fluid method. Various cases were performed to analyse the effects of the Froude number and Reynolds number. The simulation results showed that the turbulence statistics are insensitive to the Reynolds number under investigation, while the Froude number influences the flow properties significantly. To investigate the closure problem of the mean momentum equation, the turbulent kinetic energy (TKE) and turbulent mass flux (TMF) and their transport equations were analysed further. It was discovered that the balance relationship of the TKE budget terms remained similar to many single-phase turbulent flows. The TMF is an additional unclosed term in mixed-phase turbulence over the single-phase turbulence. Our simulation results showed that the production term in its transport equation was highly correlated to TKE. Based on this finding, a closure model for the production term of TMF was further proposed.

The influence of particle density and diameter on the interactions between the finite-size particles and the turbulent channel flow

Understanding the influence of different particle parameters on the two-way interactions between the particles and wall-bounded turbulence is important in many natural phenomena and engineering applications. In this work, particle-resolved direct simulation of particle-laden turbulent channel flow is performed based on the mesoscopic lattice Boltzmann method (LBM), and the particle–fluid interface is treated using the interpolated bounce back scheme. The friction Reynolds number (Reτ) of the single phase turbulent channel flow is 180, and the particle volume fraction is fixed at 1%. Three particle–fluid density ratios and three particle diameters are considered, and five particle-laden simulations are performed to investigate the influence of particle density and diameter on the interactions between the particles and the carrier turbulence. Results show that the streamwise velocity of the solid phase is larger than that of the fluid phase in the near-wall region, and the velocity difference between the two phases decreases with increasing particle density, but increases with increasing particle diameter. The probability density functions (PDFs) of particle velocity and angular velocity depend on the distance between the particles and the wall, but the PDFs of particle acceleration and angular acceleration are not spatially dependent. The distribution of particle Reynolds number follows the Gamma distribution within the buffer region and viscous sublayer. The solid phase concentration is high in the near-wall region, and the largest solid-phase concentration in this region occurs in the case with particles of intermediate density. Particles with different parameters would lead to different modulation to the carrier flow. Then, two aspects of the turbulence modulation are explored, i.e., the streamwise velocity and the turbulent kinetic energy (TKE). The presence of finite-size particles typically increases the streamwise velocity in the near-wall region and reduce the streamwise velocity outside this region. The trend is similar for TKE, but the TKE attenuation mainly occurs in the buffer region. The modulation to the streamwise velocity is analyzed using the streamwise momentum balance equation. It is found that the streamwise velocity modulation is dominated by the weighted Reynolds stress, but the different modulation in the near-wall region is due to the difference in weighted particle-induced stress, whereas the different modulation outside the near-wall region is due to the change in weighted Reynolds stress. Through TKE budget analysis, it is found that the enhancement of the total TKE source in the viscous sublayer increases with increasing particle density and diameter and the attenuation of total TKE source in the buffer region increases with increasing particle density and diameter, which is consistent with the TKE modulation for different cases.

Thermo-Hydraulic Performance of Pillow-Plate Heat Exchangers with Secondary Structuring: A Numerical Analysis

Pillow-plate heat exchangers (PPHEs) represent a suitable alternative to conventional shell-and-tube and plate heat exchangers. The inherent waviness of their channels promotes fluid mixing in the boundary layers and facilitates heat transfer. The overall thermo-hydraulic performance of PPHEs can further be enhanced by applying secondary surface structuring, thus increasing their competitiveness against conventional heat exchangers. In this work, various secondary structures applied on the PPHE surface were studied numerically to explore their potential to enhance near-wall mixing. Computational fluid dynamics (CFD) simulations of single-phase turbulent flow in the outer PPHE channel were performed and pressure drop, heat transfer coefficients, and overall thermo-hydraulic efficiency were determined. The simulation results clearly demonstrate a positive impact of secondary structuring on heat transfer in PPHEs.

Prediction of interfacial shear stress and pressure drop in vertical two-phase annular flow

The interfacial shear stress and pressure drop of an upward vertical annular flow of nitrogen–water, HFC134a–water, and nitrogen–95 % ethanol solution were comprehensively investigated considering the effect of the liquid–gas density ratio and surface tension. A direct link between the disturbance wave height and equivalent sand-grain roughness was noted through the analogy with the famous Moody chart for single-phase turbulent flows. A predictive model of the interfacial friction factor was developed based on this finding. To predict the pressure drop of the annular flow, a new model with good predictive performance for annular flows of various working fluids including steam–water under boiling water reactor operating condition (286 °C and 7 MPa) was proposed.

Thermohydraulic Analysis of Aqueous Dispersions Effectiveness with TiO<sub>2</sub> and Al<sub>2</sub>O<sub>3</sub> Nanoparticles in a U-Shaped Geothermal Probe

The paper deals with the influence of Al2O3 and TiO2 nanoparticle admixtures to the water coolant on the heat exchange and the pumping power of its single-phase flow in the U-shaped vertical collector of the heat pump geothermal probe. The heat carrier is aqueous dispersions with TiO2 and Al2O3 nanoparticles at volume concentrations of 0.1 %, 0.3 %, 0.6 %, 1.0 % and 1.3 %. Studies were performed for turbulent single-phase flow with a range of Reynolds numbers 11,500–67,000 and Euler numbers 48–75 and compared with similar results for a water coolant. The optimal volume fraction of nanoparticles in the coolant, at which nanofluids provide the lowest pumping capacity of the coolant compared to the base fluid, ensuring the required heat transfer coefficient at the level of 2230 W∙m-2∙K-1 is analyzed in the article.

Prediction of pressure gradient and hold-up in horizontal liquid-liquid pipe flow

This paper aims to propose correlations to predict pressure gradient, friction factor and fluid phase hold-up in liquid-liquid horizontal pipe flow. To develop the correlations, experiments are conducted using high viscous oils (202 and 630 mPa⋅s) in a steel pipe of length 11.25 m and length-to-diameter ratio of 708. In addition, the experimental data from the literature comprising wide range of flow and fluid properties is analyzed. For the analysis, the liquid-liquid pipe flow data is categorized into two as: stratified and dispersed. The existing friction factor correlations are modified to incorporate the effects of viscosity of the oil phase, interfacial curvature (contact/wetting angle-in lieu of material of the pipe) and fluid phase fraction. In the two-fluid model of stratified flow, the wall stress and interfacial stress correlations are substituted with superficial velocities of fluids and superficial Reynolds numbers of fluid phases replacing fluid phase velocities and fluid Reynolds numbers. Similarly, for dispersed flow, an effective Reynolds number is described as the sum of superficial Reynolds number of oil and water phases. Substituting the generally employed mean or mixture Reynolds number with the effective Reynolds number into the existing single-phase turbulent flow friction factor correlation, an effective friction factor for oil-water flow is proposed. Employing the proposed correlations, the pressure gradient across the oil-water flow and hold-up volume fraction are predicted with significant reduction in error compared with that of conventionally employed correlations. The average error and standard deviation values of −7.06%, 20.72% and 0.31%, 18.79% are found for stratified flow and dispersed flow respectively.

A comparison study of the behaviors of single-phase turbulent flow at low to moderate Reynolds numbers through a vertical pipe: 3D counters analysis

The study presented three-dimensional (3D) analysis of water's upward flowing through the vertical pipe under turbulent characteristic considerations. Both numerical constructed and improved the model of 3D for cylindrical coordinates of governing equations for incompressible turbulent flow with the Reynolds Average Navier-Stokes (RANS) model using the improved constants of the (k–ε) type. The present model is then compared with a previous study to give the feasibility of the present single-phase turbulent flow parameters. The pipe length is tested to measure how much it affected the turbulent parameters though one of the expected factors is the turbulent time scale. On the other hand, the model is numerically examined to determine the velocity profile, shear rate, and surface deformation of the water domain. While the pressure distribution, turbulent kinetic energy, and turbulent dissipation rate, these parameters are classified as the mechanic's system factors. The simulation is done with wide software used to simulate industrial is COMSOL 5.4 Multiphysics software. The results obtained increased the velocity of three inlet water velocities used ranging from (0.087, 0.105, and 0.123 m/sec) of upward flow. High fluctuation in the water flow moves along the entire pipe length and it can notice the sensitivity to any change in water properties or mechanical properties. The liquid upward flow in turbulent conditions is suffered from many characteristics such them related to liquid properties and others related to the mechanics of the application through the systems. The interaction between the fluid film (fluid boarded the pipe inner diameter) has been observed by the shear rate and liquid surface deformation

RANS-Based Modelling of Turbulent Flow in Submarine Pipe Bends: Effect of Computational Mesh and Turbulence Modelling

Pipe bend is a critical integral component, widely used in slurry pipeline systems involving various engineering applications, including natural gas hydrate production. The aim of this study is to assess the capability of RANS-based CFD models to capture the main features of the turbulent single-phase flow in pipe bends, in view of the future investigation of the hydrate slurry flow in the same geometry. This is different from the available literature in which only a few accounted for the effects of a combination of computational mesh, turbulence model, and near-wall treatment approach. In this study, three types of mesh configuration were adopted to carry out the computations, namely unstructured mesh and two structured meshes with a uniform and nonuniform inflation layer, respectively. To explore the influence of the turbulence model, standard k-ε, low-Reynolds k-ε, and nonlinear eddy viscosity turbulence model were selected to close RANS equations. Pressure coefficient, mean axial velocity, turbulence intensity, secondary flow velocity, and magnitude of secondary flow were regarded as the critical variables to make a comprehensive sensitivity analysis. Predicted results suggest that turbulent kinetic energy is the most sensitive variable to the computational mesh while others tend to stabilize. The largest difference of turbulence kinetic energy was around 26% between unstructured mesh and structured mesh with a nonuniform inflation layer. Additionally, a fully resolved boundary layer can reduce the sensitivity of mesh on turbulent kinetic energy, especially for a nonlinear turbulence model. However, the large gradient and peak value of turbulence intensity near the inner wall of the bend was not captured by the case with a fully resolved boundary layer, compared with that of the wall function used. Furthermore, it has been confirmed that the same rule was detected also for different curvature ratios, Reynolds numbers, and dimensionless wall distance y+.

Влияние внезапного сужения плоского канала на вынужденную конвекцию в турбулентном газокапельном течении

Numerical modeling of the flow structure and heat transfer in a gas-droplet turbulent flow in a duct with forward-facing step is carried out. The two-dimensional RANS equations are used in the numerical solution. The Eulerian two-fluid approach is used for describing the flow dynamics and heat transfer in the gaseous and dispersed phases. The turbulence of the carrier phase is described using an elliptical Reynolds stress model with taking the presence of dispersed phase. It is shown that finely-dispersed droplets are involved in the separation recirculation motion of the gas phase. The addition of evaporating droplets to a single-phase turbulent flow in the forward-facing step leads to a significant intensification of heat transfer (more than 2 times) compared to a single-phase air flow, all other things being equal. This effect is enhanced with an increase in the initial mass fraction of the water droplets.

Effect of sudden constriction of a flat duct on forced convection in a turbulent droplet-laden mist flow

Numerical modeling of the flow structure and heat transfer in a gas-droplet turbulent flow in a duct with forward-facing step is carried out. The two-dimensional RANS equations are used in the numerical solution. The Eulerian two-fluid approach is used for describing the flow dynamics and heat transfer in the gaseous and dispersed phases. The turbulence of the carrier phase is described using an elliptical Reynolds stress model with taking the presence of dispersed phase. It is shown that finely-dispersed droplets are involved in the separation recirculation motion of the gas phase. The addition of evaporating droplets to a single-phase turbulent flow in the forward-facing step leads to a significant intensification of heat transfer (more than 2 times) compared to a single-phase air flow, all other parameters being equal. This effect is enhanced with an increase in the initial mass fraction of the water droplets. Keywords: Numerical simulation, Reynolds stress transport model, forward-facing step, droplet evaporation, turbulence, heat transfer enhancement.

A Residual Thermodynamic Analysis of Turbulence – Part 2: Pipe Flow Computations and Further Development of Theory

Single-phase turbulent pipe flows are analysed utilizing a new theory presented in a parallel paper. Arguably this new theory implies improvements in matching modelling results with experimental observations: To illustrate, unique for these computations is that a 1st law balance agreement between simulations and corresponding experiments is achieved, while resolving the time-averaged fluid flow velocity (including the various inner turbulent zones) and accounting for the wall surface roughness. Testing this new approach, the computations of 20 cases of turbulent pipe flow arrives at a remarkably high amount of kinetic energy dissipation occurring at near-wall positions, where some 54-83% of the net kinetic energy dissipation occurs within the viscous sublayer-, and 17-39% within the buffer layer. Although turbulence incorporates time-varying phenomena, e.g. swirls, large eddies, and breakup of the latter, it is argued that simulating these would have practically no effect on the net kinetic energy dissipation – and the associated wall shear stress – for the present pipe flow cases. Another illustration of the improvements relate to transition computations: While a proposed nominal transition model arrives at fair values of transition Reynolds numbers, some improvements on this transition analysis can be made, e.g. allowing for the modelling of the turbulence onset/offset hysteresis behaviour. For scientists who wish to model time-varying phenomena, e.g. for the study of mixing, boundary layer thickness, or wall-pressure fluctuations, there should be possibilities to implement this new theory in computational flow solvers.

A kinetic energy–and entropy-preserving scheme for compressible two-phase flows

Accurate numerical modeling of compressible flows, particularly in the turbulent regime, requires a method that is non-dissipative and stable at high Reynolds (Re) numbers. For a compressible flow, it is known that discrete conservation of kinetic energy is not a sufficient condition for numerical stability, unlike in incompressible flows.In this study, we adopt the recently developed conservative diffuse-interface method (Jain et al., 2020 [30]) for the simulation of compressible two-phase flows. This method discretely conserves the mass of each phase, momentum, and total energy of the system and consistently reduces to the single-phase Navier-Stokes system when the properties of the two phases are identical. We here propose discrete consistency conditions between the numerical fluxes, such that any set of numerical fluxes that satisfy these conditions would not spuriously contribute to the kinetic energy and entropy of the system. We also present a set of numerical fluxes—which satisfies these consistency conditions—that results in an exact conservation of kinetic energy and approximate conservation of entropy in the absence of pressure work, viscosity, thermal diffusion effects, and time-discretization errors. Since the model consistently reduces to the single-phase Navier-Stokes system when the properties of the two phases are identical, the proposed consistency conditions and numerical fluxes are also applicable for a broader class of single-phase flows.To this end, we present coarse-grid numerical simulations of compressible single-phase and two-phase turbulent flows at infinite Re, to illustrate the stability of the proposed method in canonical test cases, such as an isotropic turbulence and Taylor-Green vortex flows. A higher-resolution simulation of a droplet-laden compressible decaying isotropic turbulence is also presented, and the effect of the presence of droplets on the flow is analyzed.

Measurement error of tracer-based velocimetry in single-phase turbulent flows with inhomogeneous refractive indices

Inhomogeneous refractive index fields lead to errors in optical flow velocity measurements. Former respective studies are mostly in quasi two-dimensional flows, and attribute the measurement errors to spatial gradients in the refractive index field, while less attention has been paid to flows with three-dimensional refractive index fields which usually change in space and in time. In this study, ray tracing simulations were carried out in a three-dimensional flow, which is from a direct numerical simulation of single-phase turbulent mixing of two fluids. Given the data of the numerical simulation as reference, the ray tracing simulation is used to quantify the measurement errors of the flow velocity and flow acceleration for tracer-based velocimetry, i.e. particle tracking velocimetry in this study. The errors of both flow velocity and flow acceleration are attributed to the spatial and the spatio-temporal gradients of the refractive indices, respectively, which are closely inherited from flow characteristics. While the dominant type of error depends on the studied flow, the main measurement error for the considered turbulent mixing flow is caused by the random error. When the maximum spatial difference of the refractive indices is about 10−6, the relative random measurement error is about 1 % in velocity and about 200 % in acceleration, respectively. When the maximum index difference is about 10−2 (water), the relative random measurement errors of velocity and acceleration are 2000 % and 105 %, respectively, for the flow considered in this study.

Numerical Study of Different Models for Turbulent Flow in 90° Pipe Bend

The investigation of the turbulence statistics for single-phase turbulent flow around pipe bends have mainly been experimental. Considering the cost-effectiveness of the numerical computational fluid dynamics (CFD) compared to experimental measurement, this work aims to study the accuracies of different CFD models, and establish their functionality and limitations. This paper investigates the capabilities of different numerical turbulence models and spatial discretization schemes for CFD analysis of a pipe bend. The pipe has a curvature radius which is seven times the inside diameter and a Reynolds number of 34132. The numerical modelling was developed on the commercial CFD software, ANSYS Fluent, evaluating the following viscous models:,, Spalart-Allmaras and Reynolds Stress Models. The streamwise velocities of the flow at cross-stream planes along the bend at 45º and 75º were computed for each of the turbulence models under different discretization schemes. The numerical results were compared against the existing experimental data for streamwise velocity, in order to investigate the accuracies of the different models. The results showed that the realizable K-E and Spalart-Allmaras models exhibited the best agreements with the experimental measurements, with respective average errors of 3.83% and 3.27% under the first-order spatial discretization scheme. It was also observed that the velocity profiles obtained through the K-W models (Standard and BSL), Transition SST and Reynolds Stress models exhibited better correlation with the experimental velocity profiles within the velocity transition region.

Modulation of turbulent Couette flow with vortex cavitation in a minimal flow unit

Modulation of turbulent flow by cavitation in fluid machinery can cause vibrations, noise, and erosion. In this study, we confirm the cavitation phenomenon and observe its characteristics to predict the flow and control it accordingly. We perform a direct numerical simulation of the turbulent Couette flow of water with vortex cavitation using a cavitation model to predict phase change based on pressure distribution. In this simulation, we investigate the characteristics of the local interaction between turbulence vortices and cavitation and the global modulation of the turbulent flow, i.e. mean velocity and wall friction coefficient. We observe that a cavity is generated where a low-pressure region is created in the centre of the turbulence vortex; the growth of the cavity weakens the vortex and reduces the intensity of the turbulence. Further, the vortex becomes stronger as the cavity contracts; this phenomenon occurs repeatedly in a turbulent flow field with vortex cavitation. In a turbulent flow field with vortex cavitation, mechanical oscillations can occur spontaneously. In addition, we found that the turbulence vortex weakened by cavitation regenerates around the cavity. The unsteady phenomenon of the turbulence vortex cavitation repeatedly grows and decays monotonically; however, it does not necessarily repeat these spatially in the same manner. The spatial characteristics of the turbulence structure are different from those observed in single-phase turbulent flow.

Near-wall Lamb vector and its temporal–spatial evolution in the viscous sublayer of wall-bounded flows

This paper gives the relation between the Lamb vector and fundamental surface quantities in the vicinity of a no-slip flat wall using the Taylor-series expansion solution of the Navier–Stokes equations for incompressible viscous flow. The wall-normal component of the Lamb vector is dominated by the boundary enstrophy at the first order and the boundary enstrophy flux at the second order. The tangential Lamb vector is contributed by the terms related to both the boundary vorticity divergence and the skin friction divergence. Then, the derived relation is validated in the three-dimensional nonorthogonal Hiemenz flow (an attachment line flow) and a single-phase turbulent channel flow simulated using the lattice Boltzmann method. For this Hiemenz flow where the boundary vorticity divergence vanishes, the skin friction divergence-related term dominates the distribution of the near-wall tangential Lamb vector. In the turbulent channel flow, both the skin friction divergence and boundary vorticity divergence-related terms have significant contributions to the streamwise component of the Lamb vector, which are associated with the strong wall-normal velocity events (SWNVEs) in the viscous sublayer. In contrast, the boundary vorticity divergence-related terms have the main contribution to the spanwise component of the Lamb vector. Furthermore, the temporal–spatial evolution of the kinetic energy of the Lamb vector (half of the inner product of the Lamb vector denoted by J) is studied. In the turbulent channel flow, the SWNVEs are the main contributors to the temporal–spatial evolution of J in the viscous sublayer. This evolution is dominated by the viscous dissipation effect due to the gradient of the Lamb vector and the coupling effect between a viscous source term and the Lamb vector. The relations presented in this paper could be useful in understanding the physical mechanisms of the initial formation and evolution of the Lamb vector in the viscous sublayer of wall-bounded turbulence.