Analytical estimation of mixing coefficient induced by surface wave-generated turbulence based on the equilibrium solution of the second-order turbulence closure model

Based on the equations of motion and the assumption that ocean turbulence is of isotropy or quasi-isotropy, we derived the closure equations of the second-order moments and the variation equations for characteristic quantities, which describe the mechanisms of advection transport and shear instability by the sum of wave-like and eddy-like motions and circulation. Given that ocean turbulence generated by wave breaking is dominant at the ocean surface, we presented the boundary conditions of the turbulence kinetic energy and its dissipation rate, which are determined by energy loss from wave breaking and entrainment depth respectively. According to the equilibrium solution of the variation equations and available data of the dissipation rate, we obtained an analytical estimation of the characteristic quantities of surface-wave-generated turbulence in the upper ocean and its related mixing coefficient. The derived kinetic dissipation rate was validated by field measurements qualitatively and quantitatively, and the mixing coefficient had fairly good consistency with previous results based on the Prandtl mixing length theory.

Comparison of a Full Second-Order Moment Model and an Algebraic Stress Two-Phase Turbulence Model for Simulating Bubble-Liquid Flows in a Bubble Column

A full second-order moment (FSM) model and an algebraic stress (ASM) two-phase turbulence modelare proposed and applied to predict turbulent bubble-liquid flows in a 2D rectangular bubble column. Predictiongives the bubble and liquid velocities, bubble volume fraction, bubble and liquid Reynolds stresses and bubble-liquidvelocity correlation. For predicted two-phase velocities and bubble volume fraction there is only slight differencebetween these two models, and the simulation results using both two models are in good agreement with the particleimage velocimetry (PIV) measurements. Although the predicted two-phase Reynolds stresses using the FSM are insomewhat better agreement with the PIV measurements than those predicted using the ASM, the Reynolds stressespredicted using both two models are in general agreement with the experiments. Therefore, it is suggested to usethe ASM two-phase turbulence model in engineering application for saving the computation time.

Modelling of Turbulent Nonpremixed CH4/H2 Flame Using Second-Moment Turbulence Closure Models

Turbulent nonpremixed CH4/H2 flame has been simulated using several typical differential secondmoment turbulence closure (SMTC) models. To clarify the applicability of the various models, the LRR-IP model,JM model, SSG model as well as two modified LRR-IP models were tested. Some of above-mentioned SMTC models cannot provide the overall satisfactory predictions of this challenging case. It is confirmed again that the standard LRR-IP model considerably overpredict the centerline velocity decay rate, and therefore performs not well. Also it is interesting to observe that the JM model does not perform well in this challenging test case, although it has already been proved successful in other cases. The SSG model produces quite satisfactory prediction and performs equally well or better than the two modified LRR-IP models in the reacting case. It can be concluded that the modified LRR-IP models as well as the SSG model are superior to the other SMTC models in the turbulent nonpremixed CH4/H2 flame.

A closure model on velocity structure functions in homogeneous isotropic turbulence

Closure models started from Chou＇s work have been developed for more than 70 years, aiming at providing analytical tools to describe turbulent flows in the spectral space. In this study, a preliminary attempt is presented to introduce a closure model in the physical space, using the velocity structure functions as key parameters. The present closure model appears to qualitatively reproduce the asymptotic scaling behav- iors at small and large scales, despite some inappropriate behaviors such as oscillations. Therefore, further improvements of the present model are expected to provide appropriate descriptions of turbulent flows in the physical space.

SECOND-MOMENT CLOSURE FOR MODELLING THE NEAR-WALL TURBULENCE IN 3D MEAN FLOWS

A second-moment closure for the near-wall turbulence is proposed. The limiting behaviour of this closure near a wall is consistent with that of the exact Reynolds-stress transport equations, and it converts asymptotically into a high- Reynolds-number closure remote from the wall. The closure is applied to a pressure- driven 3D transient channel flow. The predicted results are in fair agreement with the DNS data.

ON THE CLOSURE PROBLEM OF TURBULENCE MODEL THEORY

It is a wrong viewpoint that the turbulence closure problem is due to thenon-linearity, of N-S equation, because if we omit the non-linear terms in N-Sequation,many, physical quantities can not be obtained other than the mean-values. Inthis paper, we proof that the closure problem of turbulence be induced by lack ofstatistical disiribution in present turbulence theory. And the restriction of turbulencemodel theory and shortcoming of direct numerical simulation of N-S to solve theturbulence have been pointed out.

A Closure for Isotropic Turbulence Based on Extended Scale Similarity Theory in Physical Space

The closure of a turbulence field is a longstanding fundamental problem, while most closure models are introduced in spectral space. Inspired by Chou＇s quasi-normal closure method in spectral space, we propose an analytical closure model for isotropic turbulence based on the extended scale similarity theory of the velocity structure function in physical space. The assumptions and certain approximations are justified with direct numerical simulation. The asymptotic scaling properties are reproduced by this new closure method, in comparison to the classical Batchelor model.

Structural ensemble dynamics based closure model for wall-bounded turbulent flow

Wall-bounded turbulent flow involves the development of multi-scale turbulent eddies, as well as a sharply varying boundary layer. Its theoretical descriptions are yet phenomenological. We present here a new framework called structural ensemble dynamics （SED）, which aims at using systematically all relevant statistical properties of turbulent structures for a quantitative description of ensemble means. A new set of closure equations based on the SED approach for a turbulent channel flow is presented. SED order functions are defined, and numerically determined from data of direct numerical simulations （DNS）. Computational results show that the new closure model reproduces accurately the solution of the original Navier-Stokes simulation, including the mean velocity profile, the kinetic energy of the streamwise velocity component, and every term in the energy budget equation. It is suggested that the SED-based studies of turbulent structure builds a bridge between the studies of physical mechanisms of turbulence and the development of accurate model equations for engineering predictions.

NUMERICAL SIMULATION OF METHANE-AIR TURBULENT JET FLAME USING A NEW SECOND-ORDER MOMENT MODEL

A new second-order moment model for turbulent combustion is applied in the simulation of methane-air turbulent jet flame. The predicted results are compared with the experimental results and with those predicted using the well-known EBU-Arrhenius model and the original second-order moment model. The comparison shows the advantage of the new model that it requires almost the same computational storage and time as that of the original second-order moment model, but its modeling results are in better agreement with experiments than those using other models. Hence, the new second-order moment model is promising in modeling turbulent combustion with NOx formation with finite reaction rate for engineering application.

A Numerical Study of Second-Order Turbulent Moments in the Stably Stratified Nocturnal Boundary Layer

The structures and the vertical profiles of turbulent variance and covariance of the stably stratified boundary layer (SBL) are simulated with a second-order closure turbulence model. The results confirm that the vertical profiles of the dimensionless turbulence variance and covariance can be well represented by the form F = A(1 - Z / h)x. Here h is the height of SBL. and both exponent a and coefficient A are the functions of terrain, baroclinicity, radiation cooling and the state of temporal development of SBL. Comparing with Minnesota and Cabauw experiment data, we have analysed the value of a and expounded the main reasons that great difference in a exists among different literatures.

Second-order modeling of non-premixed turbulent methane-air combustion

The main purpose of this research is the second-order modeling of flow and turbulent heat flux in nonpremixed methane-air combustion.A turbulent stream of non-premixed combustion in a stoichiometric condition,is numerically analyzed through the Reynolds averaged Navier-Stokes(RANS) equations.For modeling radiation and combustion,the discrete ordinates(DO) and eddy dissipation concept model have been applied.The Reynolds stress transport model(RSM) also was used for turbulence modeling.For THF in the energy equation,the GGDH model and high order algebraic model of HOGGDH with simple eddy diffusivity model have been applied.Comparing the numerical results of the SED model(with the turbulent Prandtl 0.85) and the second-order heat flux models with available experimental data follows that applying the second-order models significantly led to the modification of predicting temperature distribution and species mass fraction distribution in the combustion chamber.Calculation of turbulent Prandtl number in the combustion chamber shows that the assumption of Pr_(t) of 0.85 is far from reality and Pr_(t) in different areas varies from 0.4 to 1.2.

Solid Boundary as Energy Source and Sink in a Dry Granular Dense Flow: A Comparison between Two Turbulent Closure Models

Solid boundary as energy source and sink of the turbulent kinetic energy of the grains, and its influence on the mean and turbulent features of a dry granular dense flow, are investigated by using the proposed zero- and first-order turbulent closure models. The first and second laws of thermodynamics are used to derive the equilibrium closure relations, with the dynamic responses postulated by a quasi-static theory for weak turbulent intensity. Two closure models are applied to analyses of a gravity-driven flow down an inclined moving plane. While the calculated mean porosity and velocity correspond to the experimental outcomes, the influence of the turbulent eddy evolution can be taken into account in the first-order model. Increasing velocity slip on the inclined plane tends to enhance the turbulent dissipation nearby, and the turbulent kinetic energy near the free surface. The turbulent dissipation demonstrates a similarity with that of Newtonian fluids in turbulent boundary layer flows. While two-fold roles of the solid boundary are apparent in the first-order model, its role as an energy sink is more obvious in the zero-order model.

Numerical simulation of the effect of void fraction and inlet velocity on two-phase turbulence in bubble-liquid flows

There are contradicted opinions on whether bubbles enhance or reduce the liquid turbulence. In this paper, the effect of void fraction and inlet velocity on the bubble-liquid two-phase turbulence of the multiple bubble-liquid jets in a two-dimensional channel is studied by using the two-phase second-order moment turbulence model. The results confirm the phenomena observed in experiments and reported in references that at a low void fraction and low inlet velocities the bubbles enhance the liquid turbulence, whereas at a high void fraction and high inlet velocities the bubbles reduce the liquid turbulence.

Numerical research on flow and thermal transport in cooling pool of electrical power station using three depth-averaged turbulence models

This paper describes a numerical simulation of thermal discharge in the cooling pool of an electrical power station, aiming to develop general-purpose computational programs for grid generation and flow/pollutant transport in the complex domains of natural and artificial waterways. Three depth-averaged two-equation closure turbulence models, k-ε, k- w, and k- w, were used to close the quasi three-dimensional hydrodynamic model. The k- w model was recently established by the authors and is still in the testing process. The general-purpose computational programs and turbulence models will be involved in a software that is under development. The SIMPLE （Semi-Implicit Method for Pressure-Linked Equation） algorithm and multi-grid iterative method are used to solve the hydrodynamic fundamental governing equations, which are discretized on non-orthogonal boundary-fitted grids with a variable collocated arrangement. The results calculated with the three turbulence models were compared with one another. In addition to the steady flow and thermal transport simulation, the unsteady process of waste heat inpouring and development in the cooling pool was also investigated.

Aero-Hydrodynamic Coupled Dynamic Characteristics of Semi-Submersible Floating Offshore Wind Turbines Under Inflow Turbulence

In this study,the frequency characteristics of the turbulent wind and the effects of wind-wave coupling on the low-and high-frequency responses of semi-submersible floating offshore wind turbines(FOWT)are investigated.Various wave load components,such as first-order wave loads,combined first-and second-order difference-frequency wave loads,combined first-and second-order sum-frequency wave loads,and first-and complete second-order wave loads are taken into consideration,while different turbulent environments are considered in aerodynamic loads.The com-parison is based on time histories and frequency spectra of platform motions and structural load responses and statistical values.The findings indicate that the second-order difference-frequency wave loads will significantly increase the natural frequency of low-frequency motion in the responses of the platform motion and structure load of the semi-submersible platform,which will cause structural fatigue damage.Under the action of turbulent wind,the influences of second-order wave loads on the platform motion and structural load response cannot be ignored,especially under extreme sea conditions.Therefore,in order to evaluate the dynamic responses of semi-submersible FOWT more accurately,the actual environment should be simulated more realistically.

On the thixotropic effect of turbulence

As a follow-up research of the work on the natural viscosity of turbulence of Huang et al. [Journal of Turbulence(2003)], here we investigate the thixotropic effect of a turbulent Newtonian fluid on the basis of the ensemble-averaged Navier–Stokes equation. In view of the natural viscosity, we show that in homogeneous isotropic turbulence the turbulent Newtonian fluid behaves like a thixotropic fluid, exhibiting the thixotropic effect with its natural viscosity decreasing with time.

Scaling of energy spectra in weakly compressible turbulence

We find an asymptotic expression for the characteristic timescales of decorrelation processes in weakly compressible and isothermal turbulence. This result is used in the Eddy-Damped Quasi-Normal Markovian equation to derive the scalings of compressible energy spectra: (1) if the acoustic waves are dominant, the compressible energy spectra exhibit \(-7/3\) scaling; (2) if local eddy straining is dominant, the compressible energy spectra are scaled as \(-3\). Meanwhile, the energy spectra of incompressible components display the same scaling of \(-5/3\) as those in incompressible turbulence. The direct numerical simulations of weakly compressible turbulence are used to examine the scaling.

SOME ISSUES OF TURBULENCE STATISTICS

The issue of dropping the random force f(i) and the arbitrariness of choosing the basic variable in the variational approach to turbulence closure problem, pointed out recently by the Russian scientists Bazdenkov and Kukharkin, are discussed. According to the mean-square estimation method, the random force f(i) should be dropped in the error expression of the LFP (Langevin-Fokker-Planck) model. However, f(i) is not neglected, its effect has been taken into account by the variational approach. In order to optimize the perturbation solution of the Liouville equation, the LFP model requires that the basic variable is as near to Gaussian as possible. Hence, the velocity, instead of the vorticity, should be chosen as the basic variable in the three-dimensional turbulence. Although the LFP model and the zero-order Gaussian term of PDF (probability density function) imply whiteness assumption (zero correlation time of f(i)), the higher-order non-Gaussian terms of PDF correspond to the nonwhiteness of turbulence dynamics, the variational approach does calculate the nonwhiteness effect properly.

TURBULENCE IN BROKEN LEE WAVES

In this paper, the waves' breaking in the lee waves is successfully simulated by the atmospheric mesoscale numerical model with a second-order tur- bulent closure. It is further proved that the turbulence in the wave-breaking region plays the role of intense mixing for the average field, which leads to the trapping of upward propagating waves and thus promotes the development of the downslope wind. The turbulent structure in the wave-breaking region is discussed and the fol- lowing conclusions are obtained: (1) In the wave-breaking region, the turbulent heat fluxes transfer from inside to outside and the turbulent momentum fluxes transfer from outside to inside. (2) In the wave-breaking region, the turbulent energy mainly comes from the wind shear and the buoyancy promotes the turbulent development only in part of the region. (3) In the upper part of the wave-breaking region, the turbulent momentum fluxes behave as a counter-gradient transfer. (4) The turbulent mixing in the wave-breaking region is non-local.

Derivation of a second-order model for Reynolds stress using renormalization group analysis and the two-scale expansion technique

With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Yakhot-Orszag renormalization group method to analyze the fluctuating field,the Reynolds-average terms in the Reynolds stress transport equation,such as the convective term,the pressure-gradient-velocity correlation term and the dissipation term,are modeled.Two numerical examples：turbulent flow past a backward-facing step and the fully developed flow in a rotating channel,are presented for testing the efficiency of the proposed second-order model.For these two numerical examples,the proposed model performs as well as the Gibson-Launder （GL） model,giving better prediction than the standard k-ε model,especially in the abilities to calculate the secondary flow in the backward-facing step flow and to capture the asymmetric turbulent structure caused by frame rotation.