The role of active Navier–Stokes angular momentum in identifying small-scale turbulence behavior

The relation between the helicity and the rate of dissipation of turbulent kinetic energy in turbulent flows has been a matter of debate. Herein, direct numerical simulations of turbulent Poiseuille and Couette flow were used in combination with the tracking of helicity, helicity density, and dissipation along the trajectories of passive scalar markers to probe the correlation between helicity and dissipation in anisotropic turbulence. The Schmidt number of the scalar markers varied between 0.7, 6, and infinite (i.e., fluid particles), while the friction Reynolds number for both simulations was 300. The probing tools were the autocorrelation coefficients, the cross correlation coefficients between helicity and dissipation, and the joint probability density function calculated in the Lagrangian framework along the positions of the scalar markers. These markers were released at different locations within the flow field, including the viscous wall sublayer, the transition layer, the logarithmic region, and the outer flow. In addition, conditional statistics for scalar markers that dispersed most or least in the flow field were also calculated. It was found that helicity and dissipation changed along the trajectories of scalar markers; however, helicity and dissipation were not correlated in the Lagrangian framework. There was anticorrelation between helicity and dissipation in the near wall region, which was less obvious in the logarithmic region. More importantly, helicity could be used to characterize the alignment of the fluctuating velocity and vorticity vectors along the trajectories of scalar markers that disperse the farthest in the direction normal to the channel wall.

In this study, energy loss within a centrifugal pump is investigated by post-processing three-dimensional unsteady flow field through kinetic energy dissipation theory. The three-dimensional unsteady flow field is predicted by solving unsteady Reynolds-averaged Navier–Stokes equations. The kinetic energy dissipation consists of three parts: averaged kinetic energy dissipation, turbulent kinetic energy dissipation, and near-wall revised kinetic energy dissipation. The total value variations of three kinetic energy dissipations in the centrifugal pump with flowrate are investigated and compared. Results show that with the increase in flowrate, the total near-wall revised kinetic energy dissipation gradually increases, the total turbulent kinetic energy dissipation first gradually decreases and then gradually increases, and reaches the minimum value at the design flowrate. The total averaged kinetic energy dissipation is less than the total turbulent and the total near-wall revised kinetic energy dissipations, and the total near-wall revised kinetic energy dissipation is larger than the total turbulent kinetic energy dissipation when the flowrate is larger than 0.75 Qdes. The space variation of the near-wall revised kinetic energy dissipation with flowrate shows that large near-wall revised kinetic energy dissipation mainly occurs at the volute and transfers from the small cross-section casing to large cross-section casing and discharge pipe with the increase in flowrate. The space variations of the turbulent kinetic energy dissipation with time for three flowrates are also discussed. Results indicate that large turbulent kinetic energy dissipation near the volute tongue evidently changes with the rotation of the impeller, particularly in 0.5 Qdes. The large turbulent kinetic energy dissipation gradually expands to the pressure side of the blade when the volute tongue gradually approaches the middle of the impeller blade passage. The large turbulent kinetic energy dissipation transfers from the impeller inlet and outlet to the volute tongue and discharge pipe with the increase in flowrate. The findings of this study can serve as guide to improve the design of centrifugal pumps.

Turbulent finite element model applied for blood flow calculation in arterial bifurcation

We investigate the flow and turbulence structure in front of a cylinder mounted on a flat plate by a combined study using highly resolved large-eddy simulation and particle image velocimetry. The Reynolds number based on the bulk velocity and cylinder diameter is $Re_{D}=39\,000$. As the cylinder is placed in an open channel, we take special care to simulate open-channel flow as the inflow condition, including secondary flows that match the inflow in the experiment. Due to the high numerical resolution, subgrid contributions to the Reynolds stresses are negligible and the modelled dissipation plays a minor role in major parts of the flow field. The accordance of the experimental and numerical results is good. The shear in the approach flow creates a vertical pressure gradient, inducing a downflow in the cylinder front. This downflow, when deflected in the upstream direction at the bottom plate, gives rise to a so-called horseshoe vortex system. The most upstream point of flow reversal at the wall is found to be a stagnation point which appears as a sink instead of a separation point in the symmetry plane in front of the cylinder. The wall shear stress is largest between the main (horseshoe) vortex and the cylinder, and seems to be mainly governed by the strong downflow in front of the cylinder as turbulent stresses are small in this region. Due to a strong acceleration along the streamlines, a region of relatively small turbulent kinetic energy is found between the horseshoe vortex and the cylinder. When passing under the horseshoe vortex, the upstream-directed jet formed by the deflected downflow undergoes a deceleration which gives rise to a strong production of turbulent kinetic energy. We find that pressure transport of turbulent kinetic energy is important for the initiation of the large production rates by increasing the turbulence level in the upstream jet near the wall. The distribution of the dissipation of turbulent kinetic energy is similar to that of the turbulent kinetic energy. Large values of dissipation occur around the centre of the horseshoe vortex and near the wall in the region where the jet decelerates. While the small scales are nearly isotropic in the horseshoe vortex centre, they are anistotropic near the wall. This can be explained by a vertical flapping of the upstream-directed jet. The distribution and level of dissipation, turbulent and pressure transport of turbulent kinetic energy are of crucial interest to turbulence modelling in the Reynolds-averaged context. To the best of our knowledge, this is the first time that these terms have been documented in this kind of flow.

Abstract. A simultaneous deployment of Doppler, temperature, and water-vapor lidars is able to provide profiles of molecular destruction rates and turbulent kinetic energy (TKE) dissipation in the convective boundary layer (CBL). Horizontal wind profiles and profiles of vertical wind, temperature, and moisture fluctuations are combined, and transversal temporal autocovariance functions (ACFs) are determined for deriving the dissipation and molecular destruction rates. These are fundamental loss terms in the TKE as well as the potential temperature and mixing ratio variance equations. These ACFs are fitted to their theoretical shapes and coefficients in the inertial subrange. Error bars are estimated by a propagation of noise errors. Sophisticated analyses of the ACFs are performed in order to choose the correct range of lags of the fits for fitting their theoretical shapes in the inertial subrange as well as for minimizing systematic errors due to temporal and spatial averaging and micro- and mesoscale circulations. We demonstrate that we achieve very consistent results of the derived profiles of turbulent variables regardless of whether 1 or 10 s time resolutions are used. We also show that the temporal and spatial length scales of the fluctuations in vertical wind, moisture, and potential temperature are similar with a spatial integral scale of ≈160 m at least in the mixed layer (ML). The profiles of the molecular destruction rates show a maximum in the interfacial layer (IL) and reach values of ϵm≃7×10-4 g2 kg−2 s−1 for mixing ratio and ϵθ≃1.6×10-3 K2 s−1 for potential temperature. In contrast, the maximum of the TKE dissipation is reached in the ML and amounts to ≃10-2 m2 s−3. We also demonstrate that the vertical wind ACF coefficient kw∝w′2‾ and the TKE dissipation ϵ∝w′2‾3/2. For the molecular destruction rates, we show that ϵm∝m′2‾w′2‾1/2 and ϵθ∝θ′2‾w′2‾1/2. These equations can be used for parameterizations of ϵ, ϵm, and ϵθ. All noise error bars are derived by error propagation and are small enough to compare the results with previous observations and large-eddy simulations. The results agree well with previous observations but show more detailed structures in the IL. Consequently, the synergy resulting from this new combination of active remote sensors enables the profiling of turbulent variables such as integral scales, variances, TKE dissipation, and the molecular destruction rates as well as deriving relationships between them. The results can be used for the parameterization of turbulent variables, TKE budget analyses, and the verification of large-eddy simulations.

Measurements of the particle-fluid velocity correlation and the extra dissipation in a round jet

The ability to estimate the rate of dissipation (ε) of turbulent kinetic energy at middepth in a high-speed tidal channel using broadband acoustic Doppler current profilers (ADCPs) is assessed by making comparisons to direct measurements of ε obtained using shear probes mounted on a streamlined underwater buoy. The investigation was carried out in Grand Passage, Nova Scotia, Canada, where the depth-averaged flow speed reached 2 m s−1 and the Reynolds number was 8 × 107. The speed bin–averaged dissipation rates estimated from the ADCP data agree with the shear probe data to within a factor of 2. Both the ADCP and the shear probe measurements indicate a linear dependence of ε on the cube of the flow speed during flood and much lower dissipation rates during ebb. The ebb–flood asymmetry and the small-scale intermittency in ε are also apparent in the lognormal distributions of the shear probe data. Possible sources of bias and error in the ε estimates are investigated, and the most likely causes of the discrepancy between the ADCP and shear probe estimates are the cross-channel separation of the instruments and the high degree of spatial variability that exists in the channel.

Abstract

Finite analytic solution of a two-dimensional sea breeze on a regular grid

The orientation moments and stresses for a suspension of rigid fibers are calculated along Lagrangian pathlines in a drag-reduced turbulent channel flow. The turbulent flow fields are calculated using the methods developed by Paschkewitz et al. [“Numerical simulation of turbulent drag reduction using rigid fibers,” J. Fluid Mech. 518, 281 (2004)]. These authors investigated turbulent drag reduction using rigid fibers with the Eulerian frame of reference direct numerical simulations, and demonstrated a correlation of drag reduction with fluctuations or “bursts” of fiber stress in intervortex extensional flow regions. These bursts are defined as events where certain components of the fiber stress exceed a specified level. Using probability density functions (PDFs) of the fiber stress contribution to the dissipation of turbulent kinetic energy weighted by the probability of occurrence of a particular stress level, we demonstrate that less than 0.001% of the dissipation is created by stress fluctuations of magnitude ∣τ13∣>5 and ∣τ22∣>7. We therefore define a “small” burst or fluctuation as one of this magnitude or less and a “large” burst to be one having a magnitude greater than these thresholds. Using conditional statistics in the Lagrangian frame, the detailed dynamics responsible for the generation of these stress bursts are quantitatively characterized. As a precursor to the burst, the fibers move into extensional flow regions and align with the wall-normal or spanwise directional axis in a process that takes approximately two local strain units, where the strain rate is defined along the direction of the fiber orientation. After the stress increases past a chosen large value and the stress burst begins, the fibers continue to align and generate increasing stress until the burst is roughly half complete; at this time, the extensional character of the surrounding flow is reduced to a level such that the fibers begin to realign in the flow direction and the fiber stresses decrease. These stress bursts also have a total duration of approximately two local strain units. By considering the flow kinematics in regions near the particle, as well as the time autocorrelation of fiber stress and the second flow invariant Q, we demonstrate that the bursts end because the surrounding vortices are strongly weakened or destroyed by the gradients in fiber stresses. Both frequently observed small stress fluctuations and rare large stress fluctuations exhibit this behavior, with the primary difference being the strength of the nearby vortices and the resulting extensional flow region that the fiber resides in during the burst. However, the more commonly observed small stress fluctuations appear to make the largest contribution to fiber dissipation of turbulent kinetic energy and thus are responsible for the majority of the drag reduction effect. The largest contribution to fiber dissipation of turbulent kinetic energy is made by small fluctuations in the spanwise shear stress component τ13, which result from fibers primarily confined to the x-z plane weakly rotating towards the z axis.

Turbulent mechanisms in open channel sediment-laden flows

Simulation of blood flow in this paper is analyzed using two-equation turbulent finite element model that can calculate values in the viscous sublayer. Implicit integration of the equations is used for determining the fluid velocity, fluid pressure, turbulence, kinetic energy, and dissipation of turbulent kinetic energy. These values are calculated in the finite element nodes for each step of incremental- iterative procedure. Developed turbulent finite element model, with the customized generation of finite element meshes, is used for calculating complex blood flow problems. Analysis of results showed that a cardiologist can use proposed tools and methods for investigating the hemodynamic conditions inside bifurcation of arteries.

Calculation of turbulent fluid flow in this paper is performed using two-equation turbulent finite element model that can calculate values in the viscous sublayer. Implicit integration of the equations is used for determining the fluid velocity, pressure, turbulence, kinetic energy, and dissipation of turbulent kinetic energy. These values are calculated in the finite element nodes for each step of incremental-iterative procedure. Developed turbulent finite element model with the customized generation of finite element meshes is used for solving complex blood flow problems. FEM Analysis results for the artery geometry of the selected anonymous patient provides us with data about important hemodynamics parameters such are blood velocity field and wall shear stress. Cardiologists could use proposed tools and methods to supplement clinical investigation of the hemodynamic conditions inside bifurcation of arteries.

In this paper, turbulent fluid flow is analyzed using a two-equation turbulent finite element model that can calculate values in the viscous sublayer. Implicit integration of the equations is used for determining the fluid velocity, fluid pressure, turbulence, kinetic energy, and dissipation of turbulent kinetic energy. These values are calculated in the finite element nodes for each step of the incremental-iterative procedure. Developed turbulent finite element model, with the customized generation of finite element meshes, is used for calculating complex blood flow problems. Analysis of results shows that a cardiologist can use the proposed tools and methods for investigating the hemodynamic conditions inside the bifurcation of arteries.

Profiles of the rate of dissipation of turbulent kinetic energy were inferred from temperature microstructure measurements near a bubble plume at the center of a tank with diameter of 13.7 m and maximum depth of 8.3 m. Six sets of between 18 and 51 profiles were collected at airflow rates of 0.1–0.6 L/s, measured at atmospheric pressure, and ensemble-averaged dissipation profiles were calculated. The dissipation in all cases was between 10-8 and 10-6 m2/s3 in most of the profile, but it increased sharply near the water surface. Energy considerations are used to discuss the experimental results in terms of previous numerical models of bubble plume turbulence. Two previous numerical studies show that the turbulence dissipates between 15 and 30% of the available power. In the experiments, the fraction is less than 1% because some of the energy of the plume is used to generate waves on the water surface and the profiles used to compute the volume-averaged dissipation were relatively far from the bubble plume.