Turbulent Eddy Viscosity Research Articles

Alteration of estuarine circulation pattern due to channel modification in the North Passage of the Changjiang River Estuary

The exchange flow structure was examined in the North Passage of Changjiang River Estuary, where a deep waterway project (DWP) was carried out to improve the navigability. Before the construction of the DWP, the friction effect played a significant role in shaping the transverse structure of the exchange flow. The turbulent eddy viscosity generated near the seabed can be transferred to the upper water column, which facilitated vertical momentum exchange. As a result, the landward inflow extended to −2 m below the water surface and the seaward outflow was concentrated on the shallow shoal on the southern side of the cross section. After the construction of the DWP, the turbulent mixing was suppressed as a result of density stratification. The friction felt by the water was constrained in the lower half of the water column and the vertical momentum exchange was reduced. Meanwhile, the channel became dynamically narrowed with a Kelvin number of 0.52. Therefore, the Coriolis played a minor role in shaping the transverse structure of the exchange flow. As a consequence, the exchange flow featured a vertically-sheared pattern, with outflow at the surface and inflow underneath. Additionally, the gravitational circulation was enhanced due to increase in along-channel density gradient and stratification. The exchange flow components associated with the lateral processes (residual currents induced by eddy viscosity-shear covariance and lateral advective acceleration) were reduced, which suggests that lateral processes played a minor role in modifying the along-channel dynamics when the estuary becomes dynamically-narrowed.

Reduced order modelling for a rotor-stator cavity using proper orthogonal decomposition

The paper describes the Reduced Order Modelling (ROM) for the turbulent flow in a rotor-stator cavity, a configurations commonly encountered in secondary air system of aircraft engines. The proper orthogonal decomposition (POD) that uses data from Large Eddy Simulations (LES) is here considered in order to identify a set of orthonormal basis functions for the Galerkin projection of the Navier-Stokes equations. The POD-Galerkin procedure has been validated for the relative simple turbulent shear flow of a plane Couette flow. LES statistics and experimental measurements have been used as a benchmark and overall we may claim that the models studied reasonably well predict the turbulence phenomenon for the rotor-stator flow. Two novelty are introduced in this work: (i) the extension of the estimation of the turbulent eddy viscosity proposed by Aubry et al. [1] to problems with high Reynolds numbers and rotating flows; (ii) the derivation of a nonintrusive reduced order model for turbulent rotor-stator cavity flows.

The O’KEYPS Equation and 60 Years Beyond

Some 60 years ago, six researchers obtained a semi-empirical equation that describes how the stability correction function for the mean velocity profile ( $$\phi _\mathrm{m}$$ ) in the atmospheric surface layer varies with the stability parameter—the famous O’KEYPS equation. Their derivations are essentially based on interpolation of the turbulent eddy viscosity between neutral and convective conditions. Comparing the O’KEYPS equation with new theoretical developments—such as phenomenological and cospectral budget models—suggests that Heisenberg’s eddy viscosity provides a unifying framework for interpreting the behaviour of $$\phi _\mathrm{m}$$ . The empirical coefficient in the O’KEYPS equation, which is on the order of 10 based on data fitting to observations, is found to be primarily linked to the increase of the size of turbulent eddies as instability increases. The ratio of the sizes of turbulent eddies under convective and neutral conditions is on the order of $$1{/}\kappa $$ , where $$\kappa $$ is the von Karman constant, and is modulated by the turbulent Prandtl number.

A turbulent eddy-viscosity surrogate modeling framework for Reynolds-averaged Navier-Stokes simulations

The Reynolds-averaged Navier-Stokes (RANS) equations for steady-state assessment of incompressible turbulent flows remain the workhorse for practical computational fluid dynamics (CFD) applications. Consequently, improvements in speed or accuracy have the potential to affect a diverse range of applications. We introduce a machine learning framework for the surrogate modeling of steady-state turbulent eddy viscosities for RANS simulations, given the initial conditions. This modeling strategy is assessed for parametric interpolation, while numerically solving for the pressure and velocity equations to steady state, thus representing a framework that is hybridized with machine learning. We achieve competitive steady-state results with a significant reduction in solution time when compared to those obtained by the Spalart–Allmaras one-equation model. This is because the proposed methodology allows for considerably larger relaxation factors for the steady-state velocity and pressure solvers. Our assessments are made for a backward-facing step with considerable mesh anisotropy and separation to represent a practical CFD application. For test experiments with either varying inlet velocity conditions or step heights we see time-to-solution reductions around a factor of 5. The results represent an opportunity for the rapid exploration of parameter spaces that prove prohibitive when utilizing turbulence closure models with multiple coupled partial differential equations.

Comparison of Reduced-Basis techniques for the model order reduction of parametric incompressible fluid flows

The applicability of two Reduced-Basis techniques to parametric laminar and turbulent incompressible fluid-flow problems in nuclear engineering is studied in this work. The Reduced-Basis methods are used to generate Reduced-Order Models (ROMs) that can accelerate multi-query problems often encountered in design optimization and uncertainty quantification. Both approaches are intrusive and utilize Proper Orthogonal Decomposition (POD) for data compression. The accuracy of the two methods for reconstructing the velocity, pressure, and turbulent eddy viscosity fields is assessed. The methods are classified based on how many reduced equations are involved. The first approach, often referred to as POD-FV-ROM, only solves one equation with additional physics-based approximations to relate the reduced pressure, velocity, and eddy viscosity fields. The second approach solves two equations and relies on a supremizer stabilization technique. Both methods are reviewed in the finite volume setting and are tested using transient problems: a backward facing step case with an inlet and outlet and a molten-salt closed-loop case. Extension of the methods to parametric reduced-order problems for uncertainty quantification purposes is presented. Conclusions, summarizing the advantages and disadvantages of these two approaches, and recommendations are provided.

Numerical Modeling of Formation and Rise of Gas and Dust Cloud from Large Scale Commercial Blasting

The emission of dust particles into the atmosphere during rock mass breaking by blasting in ore mining open-pits is one of the factors that determine the ground-level air pollution in the vicinity of pits. The data on dust concentration in the cloud, which is extremely difficult to obtain experimentally for large-scale explosions, is required to calculate the dust dispersion in the wind stream. We have elaborated a Eulerian model to simulate the initial stage of dust cloud formation and rising, and a Navier–Stokes model to simulate thermal rising and mixing with the ambient air. The first model is used to describe the dust cloud formation after a 500 t TNT (Trinitrotoluene equivalent) explosion. The second model based on the Large Eddy Simulation (LES) method is used to predict the height of cloud rising, its mass, and the evolution of dust particles size distribution for explosions of 1–1000 t TNT. It was found that the value of the turbulent eddy viscosity coefficient (Smagorinsky coefficient) depends on both the charge mass and the spatial resolution (grid cell size). The values of the Smagorinsky coefficient were found for charges with a mass of 1–1000 t using a specific grid.

On the Nature of the Turbulent Energy Dissipation Beneath Nonbreaking Waves

AbstractHere we have determined the nature of turbulent flow associated with oceanic nonbreaking waves, which are on average much more prevalent than breaking waves in most wind conditions. We found this flow to be characterized by a low turbulence microscale Reynolds number of 30 < Reλ < 100. We observed that the turbulent kinetic energy dissipation rate associated with nonbreaking waves ϵ, ranged to 3 · 10−4 W/kg for a wave amplitude 50 cm. The ϵ, under nonbreaking waves, was consistent with ; Sij is the large‐scale (energy‐containing scales) wave‐induced mean flow stress tensor. The turbulent Reynolds stress associated with nonbreaking waves was consistent with experimental data when parameterized by an amplitude independent constant turbulent eddy viscosity, 10 times larger than the molecular value. Given that nonbreaking waves typically cover a much larger fraction of the ocean surface (90–100%) than breaking waves, this result shows that their contribution to wave dissipation can be significant.

Erozyon Korozyonunda Tasarım Etkisinin Sonlu Elemanlar Analizi İle Araştırılması

The aim of this study is to minimize the corrosion effect of moving fluids in a pipe by design variable. The pipes used for fluid transport in the petrochemical industry have different designs. SolidWorks program is used for 3D studies considering two different pipe designs. Intra-pipe flow analyses are performed based on the finite volume method by using computational fluids dynamics program-Ansys Fluent. 90 ° sharp elbow pipe and rounded elbow pipe are used for analyses. Flow velocity, pressure, the turbulence kinetic energy, turbulence eddy dissipation, eddy viscosity, and erosion rate for each model have been obtained in the results of the analysis for two different pipes. The geometrical structure of the rounded elbow pipe model allows turbulence and hence eddy formation less than the 90 ° sharp elbow pipe.

Large-eddy simulation of gas–liquid two-phase flow in a bubble column reactor using a modified sub-grid scale model with the consideration of bubble-eddy interaction

The Eulerian–Eulerian Large-eddy simulations (LES) of gas–liquid two-phase flow in a cylindrical bubble column reactor have been conducted. When considering the turbulent eddy viscosity in LES, apart from the well-accepted contributions from shear turbulence and bubble induced turbulence (BIT), the effect of the interaction between entrained bubbles and eddies with a similar turbulence length scale to the sub-grid scale (SGS) cannot be neglected. With the consideration of the bubble response to the eddies on the induced sub-grid stresses, a modified SGS model, which incorporates the Stokes number, St, was proposed. The results of LES clearly indicate that the use of the modified SGS model can effectively capture the transient bubbly flow in the cylindrical bubble column. The power turbulent kinetic energy spectrum obtained in LES indicates that a slope similar to Komogorov -5/3 scaling law and the -3 scaling law can still be identified for a critical frequency f=10.70 Hz.

Fully-turbulent adjoint method for the unsteady shape optimization of multi-row turbomachinery

The possibility of taking into account unsteady flow effects if performing turbomachinery shape optimization is attractive to accurately address inherently time dependent design problems. The harmonic balance method is an efficient solution for computational fluid dynamics problems of turbomachinery characterized by quasi-periodic flows. If applied in combination with adjoint methods, it enables the possibility to deal with unsteady fluid-dynamic design in a cost effective manner, opening the way towards multi-disciplinary applications. This paper presents the development of a novel fully-turbulent discrete adjoint based on the time domain harmonic balance method and its application to the constrained fluid dynamic optimization of an axial turbine stage. As opposed to previous works, the proposed method does not require any assumption on the turbulent eddy viscosity and on the set of input frequencies. The results show that the method provides accurate gradients, if compared with second order finite differences, and significant deviation with respect to the sensitivity computed with the constant eddy viscosity approximation. The application of the method to the fluid-dynamic shape optimization of the exemplary stage leads to improve the total-to-static efficiency of 0.8%. The efficiency increase is found to be higher than that obtained by means of a steady state optimization method.

Sediment‐Induced Stratification in an Estuarine Bottom Boundary Layer

AbstractWe took field observations on the shallow shoals of South San Francisco Bay to examine how sediment‐induced stratification affects the mean flow and mixing of momentum and sediment throughout the water column. A Vectrino Profiler measured near‐bed velocity and suspended sediment concentration profiles, which we used to calculate profiles of turbulent sediment and momentum fluxes. Additional turbulence statistics were calculated using data from acoustic Doppler velocimeters placed throughout the water column. Results showed that sediment‐induced stratification, which was set up by strong near‐bed wave shear, can reduce the frictional bottom drag felt by the mean flow. Measured turbulence statistics suggest that this drag reduction is caused by stratification suppressing near‐bed turbulent fluxes and reducing turbulent kinetic energy dissipation. Turbulent sediment fluxes, however, were not shown to be limited by sediment‐induced stratification. Finally, we compared our results to a common model parameterization which characterizes stratification through a stability parameter modification to the turbulent eddy viscosity and suggest a new nondimensional parameter that may be better suited to represent stratification when modeling oscillatory boundary layer flows.

Improved Law-of-the-Wall Model for Turbulent Boundary Layer in Engineering

Accurate prediction of mean velocity in turbulent boundary layer is an important topic from the standpoints of both physics and engineering. In the current study, a unified form of law of the wall is proposed for the mean streamwise velocity in the turbulent boundary layer with zero pressure gradient. From the physical perspective, the improved form of the law is capable of reflecting the actual weight variations between the molecular viscosity and the turbulence-eddy viscosity in the viscous, transition, and logarithmic sublayers. In the viscous sublayer, a variety of direct numerical simulation (DNS) data, including 19 groups, are used to examine the proposed law. In the transition and logarithmic sublayers, 19 groups of canonical DNS velocity profiles and 14 groups of reliable experimental data are used to confirm the applicability and accuracy of the present formula under a wider ranges of Reynolds numbers. The local and maximum relative errors are given and analyzed in detail. The results show that the improved form of the law is sufficiently accurate to represent the mean streamwise velocities in the viscous, transition, and logarithmic sublayers. The present work is helpful for prediction of mean velocity behaviors in engineering.

Morphodynamic Modelling of Flash Rip Current Driven Coastal Sediment Transport

Park, S.; Kim, D.-H., Yoo, H., 2020. Morphodynamic modelling of flash rip current driven coastal sediment transport. In: Malvárez, G. and Navas, F. (eds.), Global Coastal Issues of 2020. Journal of Coastal Research, Special Issue No. 95, pp. 1229–1234. Coconut Creek (Florida), ISSN 0749-0208.The characteristics of the sediment transport driven by flash rip currents at nearshore areas was investigated using a morphodynamic model coupled with a fully nonlinear Boussinesq-type model and a sediment transport model. Wave transform processes in surfzone such as shoaling, refraction, breaking, runup, and rundown processes were included in the numerical model. The vorticity and turbulent eddy viscosity were considered to account for rotational and turbulent flow characteristics. In addition, the horizontal density variation and bottom evolution caused by sediment transport were integrated into the fully nonlinear Boussinesq-type model. A fourth-order finite volume method, based on the MUSCL scheme with an approximate Riemann solver, was used to solve the governing equations. Uniform and parallel wave fields were simulated on a plain beach with a uniform sandbar with very small disturbance on the bathymetry. Because the wave generator was parallel to the beach, no significant longshore current and longshore sediment transport were generated. From the tested case, transient offshore-directed strong rip currents (the wave-averaged flow velocity 0.5 m/s) appeared in various locations. Turbid suspended sediment currents were also randomly generated by the waves and currents. The modelling results and analysis showed that the offshore direction sediment transport was strongly associated with the flash rip current generated within the surfzone.

Computational Fluid Dynamics Model of Various Types of Rocket Engine Nozzles

The nozzle is an element of the rocket engine in which the potential energy of gases generated during combustion is converted into the kinetic energy of the gas flow. The design parameters of the nozzle have a decisive influence on the ballistic characteristics of the engine. Designing a nozzle assembly is therefore one of the most responsible stages in developing a rocket engine design. The paper presents the results of the simulation of three types of rocket propulsion nozzles. Calculations were made using CFD (Computational Fluid Dynamics) in ANSYS Fluent software. The analyzed types of nozzles differ in shape. The analysis referred to conical nozzle, a bell type nozzle with a conical supersonic part and a bell type nozzle. Calculation results are presented as pressure, velocity, turbulence kinetic energy and eddy viscosity distributions in the longitudinal section. The results show that the cone nozzle generates strong turbulence in the critical section, which negatively affects the flow of the working gas. In the case of a bell nozzle, the transformation of the wall caused the elimination of flow disturbances in the critical section, which reduced the probability of waves that can form before or after the trailing edge. The most sophisticated construction, the bell-type nozzle, allows for maximizing performance without adding extra weight. The bell type nozzle can be used as a starter and auxiliary engine nozzle due to its advantages.

Assessment of Shear Stress Transport Model with Its Variant for Heat Transfer Problems

Merits of shear-stress transport and its wall-distance-free variant are evaluated by accommodating comparisons with direct numerical simulation and experimental data for heat and fluid flow problems. To improve the temperature field predictions in turbulent boundary layers and around the stagnation region accompanied by flow separation and reattachment, the thermal eddy diffusivity is approximated via the turbulent eddy viscosity using a variable turbulent Prandtl number . A new eddy-viscosity bound that responds to both rotational and irrotational strains to better predict nonequilibrium flows is incorporated. Results show substantial improvement by both models (shear-stress-transport and wall-distance-free shear-stress transport) and demonstrate the efficacy to predict heat transfer problems with consistency and commendable accuracy. Unlike the original shear-stress-transport model, the wall-distance-free version of the shear-stress-transport model requires no wall function/distance parameter to bridge the near-wall integration. Both models produce almost identical results and are applicable to flows with an anisotropic , having much higher generality than the traditional constant Prandtl number models. The current approach serves as a guidance to improve heat transfer characteristics of an isotropic or simple gradient-type heat flux model in the wall vicinity and boundary layers.

Extended compressible thermal cavitation model for the numerical simulation of cryogenic cavitating flow

The compressibility of the vapour–liquid phase is indispensable in simulating liquid hydrogen or liquid nitrogen cavitating flow. In this paper, a numerical simulation method considering compressibility and combining the thermal effects of cryogenic fluids was developed. The method consisted of the compressible thermal cavitation model and RNG k–ε turbulence model with modified turbulent eddy viscosity. The cavitation model was based on the Zwart–Gerber–Belamri (ZGB) model and coupled the heat transfer and vapour–liquid two-phase state equations. The model was validated on cavitating hydrofoil and ogive, and the results agreed well with the experimental data of Hord in NASA. The compressibility and thermal effects were correlated during the phase change process and compressibility improved the accuracy of the numerical simulation of cryogenic cavitating flow based on thermal effects. Moreover, the thermal effects delayed or suppressed the occurrence and development of cavitation behaviour. The proposed modified compressible ZGB (MCZGB) model can predict compressible cryogenic cavitating flow at various conditions.

Open channel flow within and above a layered vegetation: Experiments and first-order closure modeling

Flow within vegetation characterized by non-uniform roughness density is drawing significant research attention given its relevance to a plethora of applications in eco-hydraulics including river restoration, and flow in wetland and marshes. The focus here is on flume experiments and modeling of the mean longitudinal velocity profile in a two layered cylindrical vegetation system. Layer 1 represents the region close to the channel bottom where the flow experiences maximum drag due to the densely placed vegetation, while layer 2 represents the flow region above the short vegetation characterized by a smaller vegetation density. Considering the aforementioned arrangements, a new analytical model based on Reynolds-averaged closure principles is proposed to describe the vertical distribution of mean streamwise velocity in an open channel with two different vegetation densities. In the proposed model, the one-dimensional steady and planar-homogeneous momentum equation is used where the turbulent eddy viscosity is assumed to be linearly related to the local mean velocity. The proposed analytical model has been calibrated using experiments reported here in which vegetation is represented by using circular plastic cylinders of two different heights. The proposed model is further tested against published experiments with similar arrangements. In total, 22 different experimental conditions with distinct densities, rigidity, and flow depths have been analyzed. The Root Mean Square Error (RMSE) of the velocity comparisons is found to be less than 0.0342 m/s, which is acceptable.

Experimental study of surface buoyant jets in crossflow

The dispersion of surface jets in crossflows such as rivers or channels can cause critical environmental problems in the form of chemical or thermal pollution of these water bodies. The turbulent flow structures occurring in such crossflows play an important role in the mixing of surface jets with the surrounding water bodies. In this study, experimental measurements of the time history of the 3-D velocity field were conducted to better understand the flow structure of surface jets in crossflow conditions. Stereoscopic Particle Image Velocimetry was used to measure the instantaneous spatial and temporal velocity distribution downstream of the jet’s discharge point. In addition to the mean velocity distribution, turbulent flow characteristics such as the turbulent kinetic energy ( $$k$$ ), turbulent kinetic energy dissipation rate ( $$\epsilon$$ ), and turbulent eddy viscosity ( $$\nu_{t}$$ ) were calculated. The formation and evolution of a vortex in the surface jet’s flow structure was detected over the measurement zone. The vortex in the surface jets in crossflow resembled to half of the vortices in a counter-rotating vortex pair (CVP) of submerged jets in crossflows. It can be inferred that the water surface performed like a plane of symmetry.

High-order natural transition simulation method based on deep residual network

Turbulence model combined with machine learning is one of the research hotspots in fluid mechanics. The existing approaches reconstruct or modify the turbulence eddy viscosity or Reynolds stress based on the experimental/numerical data. In this paper, we reconstruct the mapping function between intermittency and the mean flow variables by deep neural network (ResNet), developing an quasi-algebraic transition model coupled with the Spallart-Allmaras (SA) model. We mainly concentrate on the natural transition flows and take the results calculated by the computational fluid dynamics solver with the SST-<i>γ-Re<sub>θ</sub></i> model as the training data. Seventeen local mean flow quantities satisfying the Galilean invariants are selected as the input features. Five-time cross validation is performed to avoid overfitting. Combining with the high-precision weighted compact nonlinear format, S&K, T3a- transition plate and S809 airfoil are used to test the performance of the model. The results are compared with those from the SST-<i>γ-Re<sub>θ</sub></i> transition model, showing that the pure data-driven ResNet model can predict the intermittent field accurately, which greatly improves the ability of SA model to simulate the natural transition flow. For the example of S&K and T3a- transition plate, the comparison of wall friction shows that the SA-ResNet model is in good agreement with the experimental result, but the BC model, which is also an algebraic model, predicts the transition position of the T3a- transition plate model prematurely. The training data do not contain any numerical solution about airfoil, but the model can still be applied to the case of S809 airfoil with different attack angles. The predicted results of lift resistance characteristics, frictional coefficient distribution and transition position are close to the results from the SST-<i>γ-Re<sub>θ</sub></i> transition model. On this basis, another advantage of the model is the solution efficiency. The efficiency is improved more significantly in the case with larger mesh quantity. With the same convergence accuracy, the CPU time required by the SA-ResNet model for the S&K plate case is 85.6% that of the SST-<i>γ-Re<sub>θ</sub></i> transition model, while the CPU time required by the S809 airfoil with a larger mesh volume is only 67.2% that of the later model. This study demonstrates the great potential of machine learning in the construction of transition models.

A computational study on the influence of aortic valve disease on hemodynamics in dilated aorta.

A computational hemodynamics method was employed to investigate how the morphotype and functional state of aortic valve would affect the characteristics of blood flow in aortas with pathological dilation, especially the intensity and distribution of flow turbulence. Two patient-specific aortas diagnosed to have pathological dilation of the ascending segment while differential aortic valve conditions (i.e., one with a stenotic and regurgitant RL bicuspid aortic valve (RL-BAV), whereas the other with a quasi-normal tricuspid aortic valve (TAV)) were studied. When building the computational models, in addition to in vivo data-based reconstruction of geometrical model and boundary condition setting, the large eddy simulation method was adopted to quantify potential flow turbulence in the aortas. Obtained results revealed the presence of complex flow patterns (denoted by time-varying changes in vortex structure), flow turbulence (indicated by high turbulent eddy viscosity (TEV)), and regional high wall shear stress (WSS) in the ascending segment of both aortas. Such hemodynamic characteristics were significantly augmented in the aorta with RL-BAV. For instance, the space-averaged TEV in late systole and the wall area exposed to high time-averaged WSS (judged by WSS> two times of the mean WSS in the entire aorta) in the ascending aortic segment were increased by 176% and 465%, respectively. Relatively, flow patterns in the descending aortic segment were less influenced by the aortic valve disease. These results indicate that aortic valve disease has profound impacts on flow characteristics in the ascending aorta, especially the distribution and degree of high WSS and flow turbulence.