An Analytically Derived Shear Stress and Kinetic Energy Equation for One-Equation Modelling of Complex Turbulent Flows

The Reynolds stress equations for two-dimensional and axisymmetric turbulent shear flows are simplified by invoking local equilibrium and boundary layer approximations in the near-wall region. These equations are made determinate by appropriately modelling the pressure–velocity correlation and dissipation rate terms and solved analytically to give a relation between the turbulent shear stress τρ and the kinetic energy of turbulence (k =q22). This is derived without external body force present. The result is identical to that proposed by Nevzgljadov in A Phenomenological Theory of Turbulence, who formulated it through phenomenological arguments based on atmospheric boundary layer measurements. The analytical approach is extended to treat turbulent flows with external body forces. A general relation τρ = a11 - AFRiFq22 is obtained for these flows, where FRiF is a function of the gradient Richardson number RiF, and a1 is found to depend on turbulence models and their assumed constants. One set of constants yields a1= 0.378, while another gives a1= 0.328. With no body force, F ≡ 1 and the relation reduces to the Nevzgljadov equation with a1 determined to be either 0.378 or 0.328, depending on model constants set assumed. The present study suggests that 0.328 is in line with Nevzgljadov's proposal. Thus, the present approach provides a theoretical base to evaluate the turbulent shear stress for flows with external body forces. The result is used to reduce the k–e model to a one-equation model that solves the k-equation, the shear stress and kinetic energy equation, and an e evaluated by assuming isotropic eddy viscosity behavior.

Numerical studies on drag reduction of an axisymmetric body of revolution with antiturbulence surface

This article presents numerical studies on the drag evolution of an axisymmetric body of revolution with microgrooves using Reynolds stress model-based computational fluid dynamics simulations. Experimental data of drag evolution along the non-grooved body was used to validate the numerical model predictions. After validation of the model predictions, a series of numerical simulations were performed to study the effect of toroidal grooving of the axisymmetric body on the drag evolution by varying the depth to the surface radius of the grooves at different Reynolds numbers. A maximum drag reduction of more than 43 percent was achieved with such effort. This was possible because of the drastic reduction of turbulent shear stress in the boundary layer, which has a direct relationship with the skin friction drag evolution along the body.

Analogies in stochastic behaviour from the microscale of turbulence to the large-scale hydrometeorological processes under the Hurst-Kolmogorov dynamics

<p>The turbulent shear stress and momentum regimes dominate and drive the energy exchange mechanisms among the hydrometeorological processes in the atmospheric boundary layer. To seek for stochastic analogies among the latter, Dimitriadis (2017) studied the observed variability of key hydrometeorological processes in local and global scale under the stochastic framework of the Hurst-Kolmogorov dynamics. It is found that several stochastic similarities exist in both the marginal and dependence structures of the examined processes. This conclusion permits the development of an integrated stochastic view of the atmospheric dynamics in the boundary layer as compared to traditional deterministic approaches. Finally, a robust algorithm for the explicit stochastic synthesis of the above processes from fine to large scales is presented and the merits and limitations compared to other existing methods are discussed.</p><p>Dimitriadis, P., Hurst-Kolmogorov dynamics in hydrometeorological processes and in the microscale of turbulence, Ph.D. thesis, Department of Water Resources and Environmental Engineering, School of Civil Engineer, National Technical University of Athens, 2017.</p>

A Meshless WCSPH Boundary Treatment for Open-Channel Flow over Small-Scale Rough Bed

A weakly compressible smoothed particle hydrodynamics (WCSPH) method was developed to model open-channel flow over rough bed. An improved boundary treatment is proposed to quantitatively characterize bed roughness based on the ghost boundary particles (GBPs). In this model, the velocities of GBPs are explicitly calculated by using evolutionary polynomial regression with a multiobjective genetic algorithm. The simulation results show that the proposed boundary treatment can well reflect the influence of wall roughness on the vertical flow structure. A fully developed open channel is established, and its flume length, processing time, and turbulent model are discussed. The mixed-length-based subparticle scale (SPS) turbulence model is adopted to simulate uniform flow in open channel, and this model is compared with the Smagorinsky-based one. For the modified WCSPH model, the results show that the calculated vertical velocity and turbulent shear stress distribution are in good agreement with experimental data and fit better than the calculations obtained from the traditional Smagorinsky-based model.

Compressible mixing layer in shock-induced separation

Unsteadiness in separated shock–boundary layer interactions have been previously analysed in order to propose a scenario of entrainment–discharge as the origin of unsteadiness. It was assumed that the fluid in the separated zone is entrained by the free shear layer formed at its edge, and that this layer follows the properties of the canonical mixing layer. This last point is addressed by reanalysing the velocity measurements in an oblique shock reflection at a nominal Mach number of 2.3 and for two cases of flow deviation ($8^{\circ }$ and $9.5^{\circ }$). The rate of spatial growth of this layer is evaluated from the spatial growth of the turbulent stress profiles. Moreover, the entrainment velocity at the edge of the layer is determined from the mean velocity profiles. It is shown that the values of turbulent shear stress, spreading rate and entrainment velocity are consistent, and that they follow the classical laws for turbulent transport in compressible shear layers. Moreover, the measurements suggest that the vertical normal stress is sensitive to compressibility, so that the anisotropy of turbulence is affected by high Mach numbers. Dimensional considerations proposed by Brown & Roshko (J. Fluid Mech., vol. 64, 1974, 775–781) are reformulated to explain this observed trend.

Compressibility effects in the shear layer over a rectangular cavity

The influence of compressibility on the shear layer over a rectangular cavity of variable width has been studied in a free stream Mach number range of 0.6–2.5 using particle image velocimetry data in the streamwise centre plane. As the Mach number increases, the vertical component of the turbulence intensity diminishes modestly in the widest cavity, but the two narrower cavities show a more substantial drop in all three components as well as the turbulent shear stress. This contrasts with canonical free shear layers, which show significant reductions in only the vertical component and the turbulent shear stress due to compressibility. The vorticity thickness of the cavity shear layer grows rapidly as it initially develops, then transitions to a slower growth rate once its instability saturates. When normalized by their estimated incompressible values, the growth rates prior to saturation display the classic compressibility effect of suppression as the convective Mach number rises, in excellent agreement with comparable free shear layer data. The specific trend of the reduction in growth rate due to compressibility is modified by the cavity width.

Abstract 329: The Role of TIE1 in Flow Mediated Lymphatic Vessel Remodeling and Valvulogenesis

Recently, it has been shown that the mechanical stimulus of turbulent shear stress caused by onset of lymph flow is required for lymphatic remodeling, maturation, and lymphatic valve (LV) development. Homeostasis of the adult lymphatic vasculature also relies on flow-mediated signal transduction. However, the cellular machinery responsible for transducing mechanosensory signals required for lymphatic network formation and maintenance is unknown. Our laboratory has previously shown that TIE1 is at least partially responsible for mechanotransduction of turbulent flow required for initiation and maintenance of atherosclerotic plaque formation at the branch points of systemic vasculature in the adult animal. Moreover, TIE1 is expressed throughout lymphatic vasculature during mouse embryogenesis into adulthood, with enrichment in LVs. To circumvent the embryonic lethality caused by global Tie1 disruption, we conditionally deleted Tie1 using Nfatc1Cre. Nfatc1Cre drives recombination in lymphatic endothelial cells, with strong expression in the LVs. Nfatc1Cre:Tie1fl/fl mutants survive to birth but accumulate chyle in the peritoneal and pleural cavities by postnatal day 2. The lymphatic vessels in the mutants are dilated and tortuous, and do not undergo normal hierarchical remodeling. The constrictions that normally indicate intraluminal valve development are lacking in the mutant lymphatic vessels. Underlying these defects in the Nfatc1Cre:Tie1fl/fl mutants is loss of the normal molecular landscape associated with lymphatic patterning and valvulogenesis. Therefore, we hypothesize that Tie1 orchestrates the mechanotransduction necessary for intraluminal LV development and postnatal maintenance.

Unusual Heat Transfer Characteristics of Supercritical Carbon Dioxide

Heat transfer mechanisms in supercritical fluids is quite different due to the fact that the thermophysical properties vary drastically within a span of few degrees Celsius near the critical point. A series of integral experiments were performed to investigate the unusual turbulent heat transfer characteristics of supercritical carbon dioxide flow in round tubes under heating conditions. Wall temperatures were measured over a range of experimental parameters that varied fluid inlet temperature from 20° C to 60° C, operating pressure from 7.5 to 10.2 MPa, mass flux from 100 to 1000 kg/m2-sec and a maximum heat flux of 100 KW/m2. Measurements were made for horizontal, upward, and downward flow to study the effects of buoyancy and flow acceleration caused by large variation in density. Existing criteria to predict the influence of buoyancy suggested that the experimental data can be classified into three regimes, namely normal, deteriorated, and enhanced heat transfer. Localized deterioration in heat transfer was characterized by a sharp increase in wall temperature and observed mainly in the case of upward flow due to reduction in the turbulent shear stress. Enhanced heat transfer regime was characterized by smooth variation in wall temperature and observed in the case of downward flow due to increase in the turbulent shear stress. Flow stratification occurred in horizontal flow resulting in a circumferential variation in wall temperature. Thermocouples mounted 180° apart on the tube revealed that wall temperatures on the top side are significantly higher than the bottom side of the tube. When the bulk temperature is much higher than the pseudocritical temperature, normal heat transfer was observed for all three tube orientations indicating that the buoyancy effects were negligible. Deterioration and enhancement in heat transfer were also observed in downward and upward cases respectively due to the flow acceleration effects. This occurred in the cases where outlet fluid density was much lower than the inlet fluid density causing the flow to accelerate. In the case of upward flow, this acceleration enhanced the turbulent shear stress and heat transfer. The large experimental database was used to evaluate the existing popular heat transfer correlations for supercritical fluids.