Mean Velocity Gradient Research Articles

Turbulence Structure and Mixing in Strongly Stable Couette Flows over Thermally Heterogeneous Surfaces: Effect of Heterogeneity Orientation

AbstractDirect numerical simulations (DNS) of plane Couette flows over thermally heterogeneous surfaces at bulk Reynolds number $$Re=10^4$$ R e = 10 4 and bulk Richardson number $$Ri=0.25$$ R i = 0.25 are performed. The focus of the present study (that extends previous work by the authors) is the effect of surface heterogeneity orientation on boundary-layer structure. The temperature of the upper and lower walls is either homogeneous or varies sinusoidally, where the temperature-wave crests are either normal or parallel to the mean flow (HETx and HETy cases, respectively). Importantly, the horizontal-mean surface temperature is the same in all simulations. The stratification is strong enough to quench turbulence over a homogeneous surface, but turbulence survives over heterogeneous surfaces. In all heterogeneous cases, both molecular diffusion and turbulence transfer momentum down the gradient of mean velocity. The total (turbulent plus diffusive) heat flux is down-gradient, but quasi-organized eddy motions generated by the surface thermal heterogeneity induce heat transfer up the gradient of the mean temperature. Comparative analysis of HETx and HETy cases shows that the configuration with the spanwise heterogeneity is more turbulent and more efficient in transporting momentum and heat vertically than its counterpart with the streamwise heterogeneity. Vertical profiles of mean fields and turbulence moments differ considerably between the HETx and HETy cases, e.g., the streamwise heat flux differs not only in magnitude but also in sign. A close examination of the second-order turbulence moments, vertical-velocity and temperature skewness, and the flow eddy structure helps explain the observed differences between the HETx and HETy cases. The implications of our DNS findings for modelling turbulence in stably-stratified environmental and industrial flows with surface heterogeneity are discussed.

On the isotropy of temperature fluctuations in passive scalar turbulence

We use direct numerical simulation to investigate the scalar gradient skewness downstream of a square grid element. The passive scalar is generated by applying a constant heat flux on the grid element. We primarily focus on the far-downstream grid-element centerline, where the scalar turbulence is homogeneous, and there are no mean velocity or scalar gradients. In this region, some discrepancy exists in the literature concerning the isotropy of the scalar. To the best of our knowledge, this is the first study that measures scalar gradients in all three directions. We detect nonzero skewness for the lateral scalar gradients, while in the streamwise direction, the skewness is zero. We show, through statistical analysis, that the nonzero values are solely due to steep gradients called cliffs. The cliffs originate from the bars of the grid-element that generate sharp mean scalar gradients along the lateral directions in the near wake. These mean gradients decay as the flow develops downstream, but the convected cliffs remember the generating upstream conditions and, in particular, the direction of the mean scalar gradient. Due to this memory effect, the cliffs align preferentially along a specific direction despite the absence of a local mean scalar gradient, thus making the homogeneous scalar field anisotropic. We also report some hitherto undocumented properties of cliffs and ramps through conditional statistical analysis. Finally, we corroborate our conclusions with two additional simulations, one involving grid-element turbulence in the presence of a transverse mean scalar gradient and the other scalar turbulence due to a heated cylinder.

Inertial particles in a turbulent/turbulent interface

Turbulent interfaces are ubiquitous in the nature and in many important canonical flows (wakes, jets, mixing layers, boundary layers). In nature, the sharp edges of atmospheric clouds are defined by a turbulent/non-turbulent interface, where the droplet-laden turbulent cloud interior mixes with the unladen outer air. This study presents statistics of sub-Kolmogorov-scale inertial particles, in a parameter range representative of cloud droplets, in a sheared turbulent–turbulent interface. The study focuses on the effect of the inhomogeneous turbulent field on the particles’ clustering properties and settling velocity modification. Wind tunnel experiments were carried out in a well-characterised facility where a grid containing 81 independent gas/liquid injectors generates both high intensity turbulence and a field of small inertial droplets. These atomisers, located at the entrance of the test section, contribute significantly to the carrier phase turbulence and are used to create the sheared turbulent/turbulent interface. Selecting which atomisers are on or off enables us to control the mean velocity profile and the gradient of turbulent intensity through the tunnel cross-section. The resulting carrier flow is characterised by a gradient of mean velocity, turbulent velocity rms, and a sharp interface separating two regions with different turbulent scales. Particles’ velocities and diameters were measured with a Phase Doppler Particle Analyser, at closely-spaced positions across the turbulent interface. In agreement with previous experimental studies on the topic, particles are shown to be transported from the turbulent side, with higher turbulence intensity, to the low-intensity side by large-scale-energetic eddies. Newly observed in our results is an enhancement of particle preferential concentration and settling velocity in the sheared interface region, caused by the interaction between particle trajectories and turbulent structures of different sizes.

Large-scale semi-organized rolls in a sheared convective turbulence: Mean-field simulations

Based on a mean-field theory of a non-rotating turbulent convection [T. Elperin et al., Phys. Rev. E 66, 066305, (2002)], we perform mean-field simulations (MFS) of sheared convection that takes into account an effect of modification of the turbulent heat flux by the non-uniform large-scale motions. This effect is caused by the production of additional essentially anisotropic velocity fluctuations generated by tangling of the mean-velocity gradients by small-scale turbulent motions due to the influence of the inertial forces during the lifetime of turbulent eddies. These anisotropic velocity fluctuations contribute to the turbulent heat flux. As the result of this effect, there is an excitation of large-scale convective-shear instability, which causes the formation of large-scale semi-organized structures in the form of rolls. The lifetimes and spatial scales of these structures are much larger compared to the turbulent scales. By means of MFS performed for stress-free and no-slip vertical boundary conditions, we determine the spatial and temporal characteristics of these structures. Our study demonstrates that the modification of the turbulent heat flux by non-uniform flows leads to a strong reduction of the critical effective Rayleigh number (based on the eddy viscosity and turbulent temperature diffusivity) required for the formation of the large-scale rolls. During the nonlinear stage of the convective-shear instability, there is a transition from a two-layer vertical structure with two rolls in the vertical direction before the system reaches steady-state to a one-layer vertical structure with one roll after the system reaches steady state. This effect is observed for all effective Rayleigh numbers. We find that inside the convective rolls, the spatial distribution of the mean potential temperature includes regions with a positive vertical gradient of the potential temperature caused by the mean heat flux of the convective rolls. This study might be useful for understanding the origin of large-scale rolls observed in atmospheric convective boundary layers, as well as in numerical simulations and laboratory experiments.

Wake steering of wind turbine in the presence of a two-dimensional hill

Wake interference between turbines in wind farms can lead to significant losses in the overall power output from farms. Wake steering is a strategy in which yaw is introduced in the upstream turbines with respect to the incoming flow field to reduce wake interference with downstream turbines. To characterize the effectiveness of wake steering for turbines located on a hilly terrain, an open source simulator for wind farm applications has been used to perform large eddy simulations (LESs) of a 5 megawatt (MW) wind turbine located at the base of a sinusoidal hill. The height and length of the hill, as well as the turbine yaw angle, are systematically varied over a series of 10 simulations in which inflow corresponds to the neutral atmospheric boundary layer. Results from the LES statistics show that, for a given yaw angle, the power output from the turbine is determined primarily by the height of the hill, rather than the length of the hill. The magnitude of the centerline wake deficit and equivalent wake radius are reduced due to the presence of hills and are not very sensitive to the yaw angle. The theoretical prediction of the wake recovery appears to qualitatively agree with the LES statistics. The yaw-induced spanwise wake deflection is not affected by the hill height significantly. Streamwise vorticity distribution within the lower half of the wake intensifies due to the presence of strong mean velocity gradients present near the surface of the hill, which, in turn, leads to a reduction in the distortion of the shape of a wake deficit cross section.

Characterization of the mixing layer self-similarity with multiple parameters

In the paper, results from direct numerical simulation of a planar incompressible mixing layer spatially developing incompressible between two co-flowing laminar boundary layers are used to analyze a possibility for multiple flow parameters to achieve self-similarity within the same flow region. The Reynolds numbers for the boundary layers are 3930 and 2412 based on the free-stream velocities far above and below the splitter plate and the boundary layer thicknesses at the splitter plate trailing edge. The three-dimensional computational domain is sufficiently large for the mixing layer transition to fully turbulent far upstream the domain exit. The mixing layer growth is characterized using various definitions of the mixing layer thickness. It is shown that the proposed mixing layer thickness based on the gradient of the streamwise mean velocity in the transverse direction defines more accurately the area of turbulent mixing. Three regions of the flow linear growth are discovered using a rigorous approach, with only one of them being located within the fully turbulent mixing layer. Other parameters included in the flow self-similarity analysis are the streamwise and transverse mean velocities along with the Reynolds stresses. New normalization is proposed to observe self-similarity of the transverse mean velocity. The flow region where all considered parameters exhibit self-similarity is determined. It is shown that this region is limited by the “pulsating” streamwise distribution of the transverse mean velocity. The computational domain dimension along with the boundary conditions in the transverse direction for all considered parameters are suggested for the Reynolds-averaged Navier–Stokes simulations.

Direct numerical simulation of turbulence amplification in a strong shock-wave/turbulent boundary layer interaction

In this study, the turbulence amplification mechanism within the strong shock-wave/turbulent boundary layer interaction is investigated using direct numerical simulation (DNS) over a 24° compression ramp with Mach 2.9 flow. A new in-house solver based on the compact finite difference scheme is introduced, and its accuracy is validated by comparing the flow statistics with existing DNS and experimental data. Within the DNS findings, two distinct turbulence kinetic energy (TKE) hotspots are identified. In contrast to previous studies, this study sheds light on shocklets, characterized by mid-frequency features, as a key factor contributing to the second TKE amplification, which occurs near the reattachment point. Streamline coordinate analysis reveals that shear effects dominate TKE production over the flow deceleration effect in the shock-wave/turbulent boundary layer interaction. The shear effect induced by the rolling up of the boundary layer initiates the first TKE amplification near the wall region in proximity to the separation point, followed by flow deceleration due to the main shock wave contributing to TKE generation. The initial detachment of the shear layer enhances the shear contribution. While TKE decreases above the separation bubble due to the positive mean velocity gradient, TKE amplifies again due to the flow deceleration caused by the secondary shock wave. In addition, the intermittently spawning shocklets above the bulge structures enhance the shear effect on the TKE production. Moreover, the generated TKE subsequently transfers to the local pressure minimum line, created by the bulges effect, thereby establishing a spatially converged maximum TKE line.

Acoustic attenuation analysis of expansion chamber mufflers with non-uniform cold and hot flow

In the presence of flow, the acoustic field and the flow field inside mufflers will interact with each other. In order to capture this phenomenon, the frequency-domain linearized Navier–Stokes equations (LNSEs) are employed to investigate the vortex-sound interaction inside expansion chamber mufflers. The calculations are performed in three steps: (1) to obtain the background mean flow variables by using the steady-state CFD simulation, (2) to map CFD results to acoustic meshes, and (3) to calculate the acoustic perturbation by using the finite element method based on LNSEs. Primarily, the transmission loss of single expansion chamber with inlet/outlet extensions is predicted in the presence of cold flow and the numerical predictions of LNSEs showed consistent agreements with measurements published in the literature. With the increase of inlet flow velocity, transmission loss in the low frequency range is obviously influenced by the vortex-sound interaction, which is attributed to the energy transfer between the fluidic and acoustic scales inside the muffler. Further, the acoustic attenuation performance of dual-chamber mufflers with flow is investigated numerically and experimentally, and the LNSEs predictions agree well with measurements. In the presence of cold flow, the transmission loss curves of the mufflers in the low frequency range is disturbed by the acoustic dissipation and amplification, while the effect of hot flow on the acoustic attenuation behavior of the mufflers is almost the same as that of cold flow, except that the non-coaxial mufflers with side-inlet is remarkably influenced by temperature. The studies demonstrated that the background mean velocity gradient is the most important impact factor for acoustic attenuation performance of the dual-chamber mufflers in low frequency range, whether in the presence of cold or hot flow.

Numerical investigation of the linear evolution of Tollmien–Schlichting waves over longitudinal riblet surface

The effect of longitudinal riblets on the spatially developing Tollmien–Schlichting (T–S) waves within the boundary layer is numerically investigated by direct numerical simulation. The riblets, designed to reduce turbulent drag and featuring a blade-like shape with zero thickness, are the primary focus. Part of the flat plate is replaced by riblet surface, and T–S waves with varying frequencies are introduced prior to the onset of the riblets. Moreover, the influence of riblet size is further discussed, and the underlying mechanism by which riblets affect T–S waves is identified based on the analysis of disturbance energy equation. The results demonstrate that the presence of riblets significantly enhances the growth of T–S waves. The modulation of base flow by riblets results in the emergence of an inflection point in the velocity profile within the boundary layer, thereby enhancing the flow instability. The growth rate of T–S waves and the unstable region on the riblet surface are observed to be considerably amplified, and an increase in riblet's lateral spacing and height to spacing ratio intensifies this amplification. From the perspective of disturbance energy, it is shown that although riblets cause additional energy dissipation in their vicinity, their modification of the mean velocity gradient and the phase difference between streamwise and wall-normal velocity fluctuations contribute to a significant increase in the production term, which consequently accelerates the growth of T–S waves.

Decomposition of skin-friction and wall heat flux of temporal transition in compressible channel flows with direct numerical and constrained large-eddy simulations

The twofold integral-based decompositions of skin-friction and wall heat flux coefficients are implemented in compressible temporal transitional channel flows with direct numerical simulation and constrained large eddy simulation (CLES) to explore (i) the generations of the skin-friction and wall heat flux coefficients and their overshoot during the transition and (ii) why CLES under-predicts the overshoot phenomenon. The Reynolds shear stress, the mean velocity gradient with respect to time, and the mean velocity convection are dominating terms during the transition process of skin friction coefficient Cf, and the effect of the mean velocity convection becomes stronger as the Mach number (Ma) increases. For the wall heat flux coefficient Bq, the turbulent heat transfer, the mean energy gradients in time, and the viscous stress are significant contributors. The effects of molecular heat transfer and the mean convection on transition are increasingly important to Bq as Ma increases. The overshoot of Cf and Bq at Ma = 1.5 is mainly caused by the significant changes of mean velocity profiles and mean energy profiles with respect to time respectively. At Ma = 3.0, the overshoot of Cf is due to the significant change of mean velocity profiles in time and the mean velocity convection, while the overshoot of Bq is due to the mean energy changes in time and mean energy convection. It is found that the underestimation of the overshoots of Cf and Bq in CLES is primarily caused by the variances of the mean velocity gradient and mean energy gradient, respectively.

An Alternative Reynolds Shear Stress Model and Wake Model for a Flat Plate Boundary Layer Flow

The well-known closure problem has led to many models for the Reynolds shear stress. But many of these models are based on the Boussinesq approximation involving the mean velocity gradient and an eddy viscosity, which, however, requires to be modeled. Here, for a steady, incompressible and constant-pressure boundary layer, the Reynolds shear stress is expressed as a product of the mean velocity and the local momentum-deficit. This closure model is then incorporated in the boundary layer equation for the outer layer to predict the streamwise velocity in the wake region.

Effect of flow–thermodynamics interactions on the stability of compressible boundary layers: insights from Helmholtz decomposition

Helmholtz decomposition of velocity perturbations is performed in conjunction with linear stability analysis to examine the effects of flow-thermodynamics interactions on the stability of high-speed boundary layers. A corresponding decomposition of the pressure field is also proposed. The contributions of perturbation solenoidal kinetic, dilatational kinetic and internal energy to the various instability modes are examined as a function of Mach number ( $M$ ). As expected, dilatational and pressure field effects play an insignificant part in the first-mode behaviour at all Mach numbers. The second (Mack) mode, however, is dominantly dilatational in nature, and perturbation internal energy is significant compared to perturbation kinetic energy. The observed behaviour is explicated by examining the key processes of production and pressure-dilatation. Production of the second-mode dilatational kinetic energy is mostly due to the solenoidal-dilatational covariance stress tensor interacting with the mean (background) velocity gradient. This cross production component also inhibits the first mode. The dilatational pressure facilitates energy transfer from the kinetic to the internal field in the near‐wall region, whereas the energy transfer away from the wall is mostly due to the solenoidal pressure work. The dilatational characters of the fast and slow modes are also examined. The fast mode is dominantly dilatational at both $M=4$ and $M=6$ , while the nature of the slow mode is dependent on $M$ . Finally, Helmholtz decomposition of the perturbation momentum vector is performed. Interestingly, both first and second modes are dominated by solenoidal components of momentum.

Uniform momentum and temperature zones in unstably stratified turbulent flows

Wall-bounded turbulent flows exhibit a zonal arrangement, in which streamwise velocity organizes into uniform momentum zones (UMZs), separated by thin layers of elevated interfacial shear. While significant research efforts have focused on these structural features in neutrally stratified flows, the effects of unstable thermal stratification on UMZs and on analogous uniform temperature zones (UTZs) have not been considered previously. In this article, statistical properties of UMZs and UTZs are investigated using a suite of large eddy simulations of unstably stratified turbulent channel flow spanning weakly to highly convective conditions. When normalized by the friction velocity and stability-dependent mixing length, the mean velocity gradient based on UMZ interfacial velocity jumps and the vorticity thickness exhibits good collapse for all stabilities, establishing a link between UMZ properties and scaling predictions from Monin–Obukhov similarity theory. A similar relationship is found between UTZ properties and surface-layer scaling of the mean temperature gradient. In the mixed layer, mean UMZ depth is quasi-constant with wall-normal distance, while the deepest UTZs are found in the centre of the boundary layer. These instantaneous structures are found to be linked to the well-mixed velocity and temperature profiles in the convective mixed layer. Conditional averaging indicates that both UMZ and UTZ interfaces are associated with ejections of momentum and warm updrafts below the interface and sweeps of momentum and cool downdrafts above the interface. These results demonstrate a tangible connection between instantaneous structural features, mean properties and scaling laws in unstably stratified flows.

Approach towards local isotropy in statistically stationary turbulent shear flows

We analyse the approach towards local isotropy in statistically stationary turbulent shear flows using the transport equations for the fourth-order moments of the velocity derivative. It is found that terms of these equations representing the large-scale contribution associated with the uniform mean velocity gradient gradually decrease as the Taylor microscale Reynolds number $Re_\lambda$ increases, and finally disappear when $Re_\lambda$ is sufficiently large. This gradual weakening of the large-scale effect is accompanied by a gradual approach towards local isotropy of the small-scale motion. The rate at which local isotropy is approached depends on the weakening of the large-scale forcing, which is controlled by the magnitude of the non-dimensional velocity shear parameter $S^*$ ( $\equiv \overline {u_1^2}({{\partial {{\bar U}_1}}}/{{\partial {x_2}}})/{\bar {\varepsilon }_{iso}}$ , where $\bar {\varepsilon }_{iso}$ is the isotropic mean turbulent energy dissipation rate, $\overline {u_1^2}$ is the streamwise velocity variance, and ${\partial {{\bar U}_1}/\partial {x_2}}$ is the uniform mean velocity gradient in the transverse direction). In particular, we show that the approach towards local isotropy can be recast in the form $C\, Re_\lambda ^{-1}$ , where $C$ is the product of $S^*$ and a ratio of transverse-to-streamwise velocity derivative variances. This is consistent with the behaviour of the normalized third-order moments of transverse velocity derivatives. With the further use of the transport equations for the eighth- and twelfth-order velocity derivative moments, it is found that the even moments of transverse velocity derivatives can significantly affect the rate at which local isotropy is approached, especially for higher orders.

Turbulent kinetic energy evolution in turbulent boundary layers during head-on interaction of premixed flames with inert walls for different thermal boundary conditions

The statistical behaviour of turbulent kinetic energy, and its transport in turbulent boundary layers during premixed flame-wall interaction for isothermal and adiabatic chemically inert walls have been analysed using a Direct Numerical Simulation (DNS) database. The terms due to the mean velocity gradient (commonly known as the production term) and viscous dissipation remain leading order contributors to the turbulent kinetic energy transport when the flame is away from the wall, similar to that in the corresponding non-reacting turbulent boundary layer, but in addition to these terms, the pressure dilatation and pressure transport contributions play leading order roles when the flame interacts with the wall. It has been found that the gradient hypothesis-based Reynolds stress closures in the context of the k−ε model may yield an inaccurate prediction of the mean velocity gradient term due to the counter-gradient behaviour of Reynolds stresses in the premixed flame cases considered in this analysis. The thermal boundary condition at the wall does not have a major influence apart from a higher wall friction velocity for adiabatic boundary condition than in the case of isothermal boundary condition. The assumption of local equilibrium of production and dissipation of turbulent kinetic energy has been found to be rendered invalid when the flame is either near to the wall or interacting with the wall. This invalidates the conventional log-law for mean streamwise velocity variation, and the wall functions derived based on production-dissipation balance equipped by the usual gradient hypothesis in the context of the standard k−ε model for premixed flame-wall interaction in turbulent boundary layers. Therefore, improved wall functions are necessary for Reynolds averaged Navier-Stokes simulations of premixed flame-wall interaction in turbulent boundary layers.

Probing eddy size and its effective mixing length in stably stratified roughness sublayer flows

Stably stratified roughness sublayer flows are ubiquitous yet remain difficult to represent in models and to interpret using field experiments. Here, continuous high‐frequency potential temperature profiles from the forest floor up to 6.5 times the canopy height observed with distributed temperature sensing (DTS) are used to link eddy topology to roughness sublayer stability correction functions and coupling between air layers within and above the canopy. The experiments are conducted at two forest stands classified as hydrodynamically sparse and dense. Near‐continuous profiles of eddy sizes (length scales) and effective mixing lengths for heat are derived from the observed profiles using a novel conditional sampling approach. The approach utilizes potential temperature isoline fluctuations from a statically stable background state. The transport of potential temperature by an observed eddy is assumed to be conserved (adiabatic movement) and we assume that irreversible heat exchange between the eddy and the surrounding background occurs along the (vertical) periphery of the eddy. This assumption is analogous to Prandtl's mixing‐length concept, where momentum is transported rapidly vertically and then equilibrated with the local mean velocity gradient. A distinct dependence of the derived length scales on background stratification, height above ground, and canopy characteristics emerges from the observed profiles. Implications of these findings for (1) the failure of Monin–Obukhov similarity in the roughness sublayer and (2) above‐canopy flow coupling to the forest floor are examined. The findings have practical applications in terms of analysing similar DTS data sets with the proposed approach, modelling roughness sublayer flows, and interpreting nocturnal eddy covariance measurements above tall forested canopies.

Two-Dimensional Turbulent Thermal Free Jet: Conservation Laws, Associated Lie Symmetry and Invariant Solutions

The two-dimensional turbulent thermal free jet is formulated in the boundary layer approximation using the Reynolds averaged momentum balance equation and the averaged energy balance equation. The turbulence is described by Prandtl’s mixing length model for the eddy viscosity νT with mixing length l and eddy thermal conductivity κT with mixing length lθ. Since νT and κT are proportional to the mean velocity gradient the momentum and thermal boundaries of the flow coincide. The conservation laws for the system of two partial differential equations for the stream function of the mean flow and the mean temperature difference are derived using the multiplier method. Two conserved vectors are obtained. The conserved quantities for the mean momentum and mean heat fluxes are derived. The Lie point symmetry associated with the two conserved vectors is derived and used to perform the reduction of the partial differential equations to a system of ordinary differential equations. It is found that the mixing lengths l and lθ are proportional. A turbulent thermal jet with νT≠0 and κT≠0 but vanishing kinematic viscosity ν and thermal conductivity κ is studied. Prandtl’s hypothesis that the mixing length is proportional to the width of the jet is made to complete the system of equations. An analytical solution is derived. The boundary of the jet is determined with the aid of a conserved quantity and found to be finite. Analytical solutions are derived and plotted for the streamlines of the mean flow and the lines of constant mean thermal difference. The solution differs from the analytical solution obtained in the limit ν→0 and κ→0 without making the Prandtl’s hypothesis. For ν≠0 and κ≠0 a numerical solution is derived using a shooting method with the two conserved quantities as targets instead of boundary conditions. The numerical solution is verified by comparing it to the analytical solution when ν→0 and κ→0. Because of the limitations imposed by the accuracy of any numerical method the numerical solution could not reliably determine if the jet is unbounded when ν≠0 and κ≠0 but for large distance from the centre line, ν>νT and κ>κT and the jet behaves increasingly like a laminar jet which is unbounded. The streamlines of the mean flow and the lines of constant mean temperature difference are plotted for ν=0 and κ=0.

Investigation of turbulent entropy production rate with SWCNT/H2O nanofluid flowing in various inwardly corrugated pipes

AbstractThis paper presents turbulent heat transfer performance and entropy production rate in different inwardly corrugated pipes with single‐walled carbon nanotube (SWCNT)/H2O nanofluid as a working fluid using the finite volume method approach. The configurations considered were circular, triangular, and trapezoidal. The SWCNT/H2O nanofluid was modeled using a single‐phase approach and the model was used to simulate the turbulent flow. A parametric study was carried out on the effect of Reynolds number (5 × 103 ≤ Re ≤ 3 × 104) and nanoparticle volume ratio (0% ≤ φ ≤ 0.25%) on hydrodynamic, heat transfer performance, thermal entropy production rates (TEPRs; due to mean and turbulent temperature gradients), and viscous entropy production rates (VEPRs; due to mean and turbulent velocity gradients). The results showed that the mean temperature gradient contributes most to the TEPR, compared with the turbulent temperature gradient. However, the opposite was the case for the VEPR. Furthermore, the presence of corrugation decreases the TEPR but enhanced friction factor, Nusselt number, and VEPR. For example, at a Reynolds number of 2.5 × 104, the normalized friction factor, average Nusselt number, TEPR, and VEPR (referencing a smooth pipe) in circularly, triangularly, and trapezoidal corrugated pipes are {3.86, 1.39, 0.80, 3.88}, {3.80, 1.41, 0.72, 3.98}, and {4.34, 1.55, 0.69, 4.19}, respectively.

ATOMS: ALMA Three-millimeter Observations of Massive Star-forming regions – XI. From inflow to infall in hub-filament systems

ABSTRACT We investigate the presence of hub-filament systems in a large sample of 146 active proto-clusters, using H13CO+ J = 1-0 molecular line data obtained from the ATOMS survey. We find that filaments are ubiquitous in proto-clusters, and hub-filament systems are very common from dense core scales (∼0.1 pc) to clump/cloud scales (∼1–10 pc). The proportion of proto-clusters containing hub-filament systems decreases with increasing dust temperature (Td) and luminosity-to-mass ratios (L/M) of clumps, indicating that stellar feedback from H ii regions gradually destroys the hub-filament systems as proto-clusters evolve. Clear velocity gradients are seen along the longest filaments with a mean velocity gradient of 8.71 km s−1 pc−1 and a median velocity gradient of 5.54 km s−1 pc−1. We find that velocity gradients are small for filament lengths larger than ∼1 pc, probably hinting at the existence of inertial inflows, although we cannot determine whether the latter are driven by large-scale turbulence or large-scale gravitational contraction. In contrast, velocity gradients below ∼1 pc dramatically increase as filament lengths decrease, indicating that the gravity of the hubs or cores starts to dominate gas infall at small scales. We suggest that self-similar hub-filament systems and filamentary accretion at all scales may play a key role in high-mass star formation.

Investigation of the entropy production rate of ferrosoferric oxide/water nanofluid in outward corrugated pipes using a two-phase mixture model

This study investigates the turbulent entropy production rate of ferrosoferric oxide/water (Fe3O4/H2O) nanofluid flowing through outward corrugated pipes of different profiles (circular, triangular, and trapezoidal). Both the multi-phase mixture model and the k−ω turbulent model were adopted for simulating the turbulent ferrofluid flow. The effects of Reynolds number (between 5.0 × 103 and 3.0 × 104) and nanoparticle concentration (0.0–3.0%) on viscous entropy production rates (due to mean and turbulent velocity gradients) and thermal entropy production rates (due to mean and turbulent temperature gradient) were examined parametrically. The results show that trapezoidally corrugated pipes tend to have the best heat transfer performance, but also the worst hydraulic performance, where they increase the pressure drop and the average Nusselt number by 2.92 and 1.66 folds, respectively, for a 2.0% nanoparticles’ concentration at Reynolds number of 3.0 × 104. Increasing the concentration of nanoparticles from 0.0 to 3.0% has the same effect, where the two quantities increase by 1.31 and 1.07, respectively, for a triangularly corrugated pipe at a Reynolds number of 1.5×104. The mean temperature gradient contributes most to the thermal entropy production rate, compared to the turbulent temperature gradient. However, the opposite is the case for the viscous entropy production rate. Furthermore, the presence of corrugation was found to increase the viscous entropy production rate but reduce the thermal entropy production rate. The normalized thermal and viscous entropy production rates (referencing a smooth pipe) in circularly, triangularly, and trapezoidally corrugated pipes are {0.81, 0.75}, {0.56,3.38}, and {3.29,3.45}, respectively. It is also noticed that the Bejan number decreases as the Reynolds number increases by 51.4, 81.4, 82.2, and 87.6% for smooth, circularly corrugated, triangularly corrugated, and trapezoidally corrugated pipes, respectively.