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A high-order computational fluid dynamics code was developed to simulate the compressible Taylor–Green vortex problem by means of large-eddy (LES) and direct numerical simulations. The code, BASIC, uses explicit central-differencing to compute the spatial derivatives and explicit low storage Runge–Kutta methods for the temporal discretization. Central-differencing schemes were combined with relaxation filtering or with splitting formulas to discretize convective derivative operators. The application of split forms to convective derivatives generally guarantees good stability properties with marginal dissipation. However, these types of schemes were found to be unsuited to perform implicit large-eddy simulations (ILES). The minimally dissipative schemes showed acceptance performance, only when combined with a sub-grid scale model. The relaxation-filtering strategy, on the other hand, although more dissipative, was proven to be more adequate to perform ILES. We showed that reducing the filter dissipation, by optimizing its damping function, has a positive impact in the flow solution. When performing ILES, the utilization of split formulas in conjunction with relaxation filtering has equally yielded promising results. This combined approach enhances numerical stability while preserving low levels of numerical dissipation. [ABSTRACT FROM AUTHOR]

The present study proposes a sub-grid scale model for the one-dimensional Burgers turbulence based on the neural network and deep learning method. The filtered data of the direct numerical simulation is used to establish the training data set, the validation data set, and the test data set. The artificial neural network (ANN) method and Back Propagation method are employed to train parameters in the ANN. The developed ANN is applied to construct the sub-grid scale model for the large eddy simulation of the Burgers turbulence in the one-dimensional space. The proposed model well predicts the time correlation and the space correlation of the Burgers turbulence.

This paper investigates the characteristics of turbine wake which is the major factor determining the turbulence in wind farm and overall wind farm performance. Using the lattice Boltzmann method (LBM) and the large eddy simulation (LES) approach, dynamic simulations of detailed fluid flow and wake trajectory induced by the MEXICO wind turbine were carried out. Moreover, with the help of adaptive mesh refinement (AMR) method, the lattice units were allowed to be automatically refined to allocate more grid points on the solid walls and in the wake region. The simulation results were firstly compared with the experimental data for validation of the numerical model, as well as for investigation of the impact of sub‐grid scale (SGS) turbulence models. Within the present modeling framework, the characteristics of transient wake propagation, detailed flow field, and rotor‐tower interaction were investigated, and the effect of tip‐speed ratio was also analyzed. The present work indicates that, with a suitable SGS turbulence model, the LBM‐LES method is an effective way for dynamic simulations of wake structures induced by a wind turbine with a rotating rotor. [ABSTRACT FROM AUTHOR]

In this present study, three-dimensional lattice Boltzmann method is implemented with the popular turbulence modeling method large-eddy simulation incorporating three different non-dynamic sub-grid scale models Smagorinsky, Vreman, and wall-adapting local eddy-viscosity for finding the inhomogeneous turbulent airflow patterns inside a model room with a partition. The large eddy simulation-lattice Boltzmann method code is validated with the experimental results of Posner's model, where the model room having one partition at the bottom, one inlet, an outlet placed at top wall considered for the comparisons. The lattice Boltzmann method code is also validated without any sub-grid scale model with the results of lid-driven flow in a cubic cavity. The present numerical simulations are performed by the graphics process unit accelerated parallel programs using compute unified device architecture C platform. Double precession capable a Tesla k40 with 2880 compute unified device architecture cores NVIDIA graphics process unit card has been used for these simulations. Graphics processor units have gained popularity in recent years as a propitious platform for numerical simulation of fluid dynamics. In fact, faster computational task performance in graphics process units is one of the key factors for researchers to choose graphics process unit over conventional central processing units for the implementation of data-intensive numerical methods like lattice Boltzmann method. The effects of the sub-grid scale model have been evaluated in terms of the mean velocity profiles, streamlines as well as turbulence characteristics and found that there are significant differences in the results due to the different sub-grid scale models. [ABSTRACT FROM AUTHOR]

In this work, the reconstruction of sub-grid scales in large eddy simulation (LES) of turbulent flows in stratocumulus clouds is addressed. The approach is based on the fractality assumption of turbulent velocity field. The fractal model reconstructs sub-grid velocity field from known filtered values on LES grid, by means of fractal interpolation, proposed by Scotti and Meneveau (Physica D 127, 198–232 1999). The characteristics of the reconstructed signal depend on the stretching parameter d, which is related to the fractal dimension of the signal. In many previous studies, the stretching parameter values were assumed to be constant in space and time. To improve the fractal interpolation approach, we account for the stretching parameter variability. The local stretching parameter is calculated from direct numerical simulation (DNS) data with an algorithm proposed by Mazel and Hayes (IEEE Trans. Signal Process 40(7), 1724–1734, 1992), and its probability density function (PDF) is determined. It is found that the PDFs of d have a universal form when the velocity field is filtered to wave-numbers within the inertial range. In order to investigate Reynolds number (Re) dependence, we compare the inertial-range PDFs of d in DNS and large eddy simulation (LES) of stratocumulus cloud-top and experimental airborne data from Physics of Stratocumulus Top (POST) research campaign. Next, fractal reconstruction of the subgrid velocity is performed and energy spectra and statistics of velocity increments are compared with DNS data. It is assumed that the stretching parameter d is a random variable with the prescribed PDF. We show that the agreement with the DNS is in such case better and the error in mass conservation is smaller compared to the use of constant values of d. The motivation of this study is to reproduce effect of sub-grid scales on a motion of Lagrangian particles (e.g. droplets) in clouds. [ABSTRACT FROM AUTHOR]

Abrasive flow machining technology is a new type of precision machining technology. Due to its unique rheological properties, it can process any complex structure and size parts to meet the requirements that conventional machining cannot meet. Combined with the turbulent flow characteristics of the abrasive flow, the large eddy simulation numerical method is used to simulate the machining process of the abrasive flow. The influence of different sub-grid scale models on the simulation results is discussed. Taking curved tube as the research object, the static pressure, dynamic pressure and velocity of different sub-grid models are analyzed to find the best sub-grid scale model. Large eddy simulation method is used to simulate the complex flow channel parts, and the best sub-grid scale model suitable for complex flow channels is determined, which reveals the grinding and polishing rule of abrasive flow and provides academic support for future research. Therefore, it has frontier and important research value. [ABSTRACT FROM AUTHOR]

This research work is aimed at proposing models for the hydrodynamic force and torque experienced by a spherical particle moving near a solid wall in a viscous fluid at finite particle Reynolds numbers. Conventional lubrication theory was developed based on the theory of Stokes flow around the particle at vanishing particle Reynolds number. In order to account for the effects of finite particle Reynolds number on the models for hydrodynamic force and torque near a wall, we use four types of simple motions at different particle Reynolds numbers. Using the lattice Boltzmann method and considering the moving boundary conditions, we fully resolve the flow field near the particle and obtain the models for hydrodynamic force and torque as functions of particle Reynolds number and the dimensionless gap between the particle and the wall. The resolution is up to 50 grids per particle diameter. After comparing numerical results of the coefficients with conventional results based on Stokes flow, we propose new models for hydrodynamic force and torque at different particle Reynolds numbers. It is shown that the particle Reynolds number has a significant impact on the models for hydrodynamic force and torque. Furthermore, the models are validated against general motions of a particle and available modeling results from literature. The proposed models could be used as sub-grid scale models where the flows between particle and wall can not be fully resolved, or be used in Lagrangian simulations of particle-laden flows when particles are close to a wall instead of the currently used models for an isolated particle. [ABSTRACT FROM AUTHOR]

The exploration on the microscale transport phenomena is of great significance to understand the mechanism of microscale mixing and chemical reaction in a rotating packed bed (RPB). In this paper, numerical investigation is carried out and compared with the experimental results. Two different scale reaction models are applied to simulate and the numerical result is in reasonable agreement with the experimental results. The fluid flow and the species transfer with a competitive and consecutive reaction are studied to obtain the evolution of the segregation index and flow field. Each environment changes and is updated continuously with the liquid film flowing outward, and the micromixing and reaction are influenced by the fractions p 1 and p 2 of different environments. It is evidenced that different factors such as rotational speeds, volume ratios and initial mixing concentration impose considerable influences on the micromixing and reaction processes. The micromixing time ranges about 5.2 × 10 −2 –1 × 10 −3 ms showing that micromixing performance in RPB is much better. The main product and by-product appear different evolution pattern along the package wires, which provide guideline for the optimization of RPB structure. The optimization on the RPB structure is provided and the simulation results clarify a deeper understanding on the micromixing and reaction features in RPB. [ABSTRACT FROM AUTHOR]

Flow over a circular cylinder is a significant phenomenon encountered in a wide range of engineering and industrial applications. It is a challenging case associated with a complicated flow regime having laminar separation, transition to turbulence, reattachment and vortical motions in the vicinity of cylinder. The current work assesses the performance of RAST (Rahman–Agarwal–Siikonen–Taghinia) model, a zero-equation sub-grid scale (SGS) model in predicting the flow features around a circular cylinder at R e D = 3900 . This SGS model is sensitized to non-equilibrium flows, preserving the anisotropic characteristics of turbulence; this aspect makes it a subtle means to simulate the flow with strong recirculating and separation. Results are compared with available experimental data in the literature as well as with those obtained by the dynamic Smagorinsky model (DSM). The comparisons dictate that the RAST model can accurately produce the mean flow characteristics that are in good agreement with existing experimental data, especially at the near wake of cylinder. Compared with the DSM, the RAST model needs a single-filtering operation that recovers the numerical stability and computational effort to a greater extent. In other words, the RAST model can be considered as a good compromise between accuracy and manageability; particularly, as simple as the original Smagorinsky model and as accurate as the DSM. [ABSTRACT FROM AUTHOR]

Computational fluid dynamics (CFD) provides a suitable means to predict the air distribution characteristics in indoor spaces. This paper evaluates the performance of two turbulence models in predicting an indoor airflow: the RAST (Rahman-Agarwal-Siikonen-Taghinia) sub-grid scale model (SGS) and SST-SAS (Shear Stress Transport with Scale-Adaptive Simulation) k- ω model of hybrid RANS-LES type. These two models are applied to investigate the airflows for three ventilation scenarios: (a) forced convection, (b) mixed (natural+forced) convection and (c) isothermal impinging jet in a room. The predictions are compared with the available experimental data in the literature. However, both models produce good results but comparisons show that RAST model predictions are in better agreement with experiments due to its sensitivity toward both the resolved strain rate and vorticity parameters. [ABSTRACT FROM AUTHOR]

Abstract: Large-eddy simulations (LES) of two plane impinging jets have been conducted. Predictions were first conducted for a natural impinging jet and found to be in good agreement with the experimental data of Yoshida et al. The validated code was then used to study the vortical structures of a forced impinging jet which had been experimentally investigated by Sakakibara et al. The numerical results show that the predictions have clearly captured the spanwise rollers, successive ribs, cross ribs and wall ribs observed by Sakakibara et al. They also show the predicted average convection velocity to be in good agreement with the measured value. Overall, the present study demonstrates the potential of LES simulations as a reliable tool to optimize the performance of engineering systems involving the use of forced impinging jets by regulating cross ribs through the inlet perturbations. [Copyright &y& Elsevier]

Using combined method of large-eddy simulations with lattice Boltzmann (LES-LBM), an eddy-viscosity sub-grid scale (SGS) model has been developed, which is suitable for the LES-LBM framework to study space-time correlation of homogeneous isotropic turbulence. The lattice Boltzmann algorithm of 19-velocity D3Q19 lattice mode was implemented to calculate time evolution of the kinetic energy, the decay exponents of the dissipation rate, the instantaneous energy spectra and the high-order statistical quantities. Comparing with the evaluations of the model coefficients as a function of sub-grid activity obtained from direct numerical simulation (DNS) and other experiments, the obtained results from LES-LBM based new SGS model exhibit more satisfactory behavior than that of the classical one. Further, the abilities of several SGS models to predict the frequency-wave number energy spectra in turbulent flows were examined. It is found that the temporal de-correlation of smaller scales is determined by random sweeping motion of larger scales, the normalized frequency energy spectra of different wave number exhibit a common similarity to a certain extent and the sweeping velocity dominates the frequency-wave number energy spectra. [ABSTRACT FROM AUTHOR]

Dynamo simulations require sub-grid scale (SGS) models for the momentum and heat flux, the Lorentz force, and the magnetic induction. Previous large eddy simulations (LES) using the scale similarity model have represented many aspects of the SGS motion. However, discrepancies are observed due to interchanging the order of filtering operation and spatial differentiation. In this study, we implement a correction term for this commutation error specifically for the scale-similarity model. Furthermore, we implement a dynamic scheme to evaluate time-dependent coefficients for the SGS models. We perform dynamo simulations in a rotating plane layer with different spatial resolutions, and compare results for the time dependence of the large-scale magnetic field. Simulations are performed at two different Rayleigh numbers, using constant values for the other dimensionless numbers (Ekman, Prandtl, and magnetic Prandtl numbers). Both cases show that the dynamic LES can accurately represent the large-scale magnetic field, whereas the dynamo failed in the direct simulations without the SGS terms at the same spatial resolutions. We conclude that the dynamic versions of the SGS and commutation error correction are essential for successful dynamos on coarser grids. [ABSTRACT FROM PUBLISHER]

Abstract: Although great progress has been made in modeling the bubbling fluidization of Geldart B and D particles using standard Eulerian approach, recent studies have shown that suitable sub-grid scale models should be introduced to improve the simulation on the hydrodynamics of Geldart A particles. In this study, the flow structures inside a bubbling fluidized bed of FCC particles are simulated in an Eulerian approach employing the energy minimization multi-scale (EMMS) model (Chemical Engineering Science, 2008, 63: 1553–1571) as the sub-grid scale model for effective inter-phase drag force, using an implicit cluster diameter expression. It was shown that the experimentally found axial and radial solid concentration profiles and radial particle velocity profiles can be well reproduced. [Copyright &y& Elsevier]

Abstract: Considering wrinkling as an analogue to perfect plasticity, this study employs the projection method from inelasticity model to take into account wrinkling of thin membranes. Along the additive strain decomposition, the total strains within the wrinkled membranes are divided into an elastic part and a wrinkling part. The projection method removes the wrinkling strain part, which has zero strain energy, from the total strains. As a consequence, the outcome is a modified constitutive tensor which represents only energy of the elastic strain part. Due to its simplicity, this method is advantageous for implementation and combines a good rate of convergence and low computational costs. Within this work, the incremental constitutive equation is derived in a general form which is applicable both for isotropic and orthotropic materials. The potential of the proposed wrinkling model is verified via various numerical analyses of wrinkled membranes. Furthermore, the model is attractive to be implemented into commercial finite element programs. [Copyright &y& Elsevier]

Abstract: In this work, we have presented a one-equation model for sub-grid scale (SGS) kinetic energy and applied it for an Euler–Euler large eddy simulation (EELES) of a bubble column reactor. The one-equation model for SGS kinetic energy shows improved predictions over the state-of-the-art dynamic procedure. With grid refinement, the amount of modelled SGS turbulent kinetic energy diminishes, as one would expect. Bubble induced turbulence (BIT) at the SGS level was modelled with two approaches. In the first approach an algebraic model was used, while in the other approach extra source terms were added in the transport equation for SGS kinetic energy. It was found that the latter approach improved the quantitative prediction of the turbulent kinetic energy. To the best of authors knowledge, this is the first use of a transport equation for SGS kinetic energy in bubbly flows. [Copyright &y& Elsevier]

Abstract: High-resolution Eulerian simulations are carried out to explore the problem of length scale dependence or filter size dependence in heterogeneous gas–solid two-phase flows. It was found that, with the extension of the simulated domain, the average inter-phase slip velocity or inter-phase drag coefficient and the index of heterogeneity increased initially and then approached asymptotic values, which demonstrates the existence of a scale-independent or filter-size-independent plateau for these properties. [Copyright &y& Elsevier]

Abstract: Gas–solid two-phase flow in CFB risers is characterized by the clustering of solid particles producing dynamical multi-scale structures, and how to quantify such heterogeneity is a critical yet unsolved issue. Recently, incorporating the energy minimization multi-scale (EMMS) model with Eulerian approach has obtained encouraging results for simulating the hydrodynamics in CFB risers. However, owing to the cluster diameter correlation used, the present model is still limited to the simulation of Geldart A particles. In this study, a stochastic geometry approach named doubly stochastic Poisson processes is used to analyze the fluctuation characteristics of solid concentration in CFB risers, which provides a mean to define the solid concentration inside clusters. The predicted results are validated by experimental data available in literature, and a revised cluster diameter correlation is then proposed for EMMS model previously developed for cocurrent-up gas–solid flow. Following our previous studies, the EMMS model thus improved is incorporated into an Eulerian–Eulerian description of gas–solid flow as a sub-grid scale model for inter-phase drag force, with which the hydrodynamics of both Geldart A and Geldart B particles in CFB risers are simulated. It is shown that the experimentally found S-shaped axial voidage profiles and the choking phenomenon can be well predicted. The computed one-dimensional slip velocities decrease toward the top of the risers and increase with decreasing cross-sectional averaged voidages. The experimentally found dependence of the root mean square of the solid concentration on its mean value at a given position is also well predicted. [Copyright &y& Elsevier]

We test a dynamic version of the scale-similarity model in plane-layer dynamo simulations. Previous work has shown that the scale-similarity model reproduces the spatial pattern of the SGS heat flux, even near the boundaries, when a correction is added for the commutation error. However, the average amplitude of the SGS terms deviates from the estimate inferred from a fully resolved calculation. In this study, we attempt to improve the average amplitude of the SGS terms by applying the dynamic scheme of Germano et al. (1991) to the scale-similarity model. This procedure yields estimates for the coefficients in the SGS model, which we evaluate as a function of vertical position in the plane layer. The resulting SGS heat flux is compared with the value determined from a resolved dynamo solution on a finer grid. The results show that the dynamic scheme improves the amplitude of the SGS heat flux. Furthermore, the results show that the coefficients for each SGS term in the dynamo simulation (heat flux, momentum flux, Maxwell stress, and magnetic induction) should be evaluated independently because the predicted coefficients for each SGS term have different values. [ABSTRACT FROM AUTHOR]

An error arises in large eddy simulations when the order of spatial differentiation and filtering operations is commuted on a non-uniform grid. The magnitude of the commutation error is controlled by spatial variations in the width of the filter function, which is conventionally defined in terms of the local grid size. We have previously found large commutation errors in the sub-grid scale (SGS) terms of a numerical dynamo model, particularly near boundaries where the grid size changes most rapidly. In the present study, we propose a correction for the commutation error which is specifically designed for use with the nonlinear gradient SGS model. The commutation error correction for each SGS term can be expressed as the product of the spatial derivative of the second-order moment of the filter function and the second spatial derivative of the SGS term. We test the correction using output from a fully resolved convection-driven dynamo simulation in a rotating plane layer. As an example, we evaluate the SGS heat flux on a coarser grid with and without the commutation error correction. The result is tested using the resolved dynamo solution on a finer grid. We find that the commutation error correction is comparable in magnitude to the SGS heat flux near the boundary. Addition of the correction term significantly improves the modeled SGS heat flux near the boundaries. [ABSTRACT FROM AUTHOR]

Abstract: Numerical simulations of the bubbly flow in two square cross-sectioned bubble columns were conducted with the commercial CFD package CFX-4.4. The effect of the model constant used in the sub-grid scale (SGS) model, , as well as the interfacial closures for the drag, lift and virtual mass forces were investigated. Furthermore, the performance of three models [Pfleger, D., Becker, S., 2001. Modeling and simulation of the dynamic flow behavior in a bubble column. Chemical Engineering Science, 56, 1737–1747; Sato, Y., Sekoguchi, K.,1975. Liquid velocity distribution in two-phase bubble flow. International Journal of Multiphase Flow 2, 79–95; Troshko, A.A., Hassan, Y.A., 2001. A two-equation turbulence model of turbulent bubbly flows. International Journal of Multiphase Flow 27, 1965–2000] to account for the bubble-induced turbulence in the – model was assessed. All simulation results were compared with experimental data for the mean and fluctuating liquid and gas velocities. It is shown that the simulation results with and agree well with the measurements. When is increased, the effective viscosity increases and subsequently the bubble plume becomes less dynamic. All three bubble-induced turbulence models could produce good solutions for the time-averaged velocity. The models of Troshko and Hassan and Pfleger and Becker reproduce the dynamics of the bubbly flow in a more accurate way than the model of Sato and Sekoguchi. Based on the comparison of the results obtained for two columns with different aspect ratio ( and ), it was found that the model of Pfleger and Becker performs better than the model of Troshko and Hassan, while the model of Sato and Sekoguchi performs the worst. It was observed that the interfacial closure model proposed by Tomiyama [2004. Drag, lift and virtual mass forces acting on a single bubble. Third International Symposium on Two-Phase Flow Modeling and Experimentation, Pisa, Italy, 22–24 September] performs better for the taller column. With the drag coefficient proposed by Tomiyama, the predicted slip velocity agrees well with the experimental data in both columns. The virtual mass force has a small influence on the investigated bubbly flow characteristics. However, the lift force strongly influences the bubble plume dynamics and consequently determines the shape of the vertical velocity profile. In a taller column, the lift coefficient following from the model of Tomiyama produces the best results. [Copyright &y& Elsevier]

Abstract: We develop a sub-grid scale (SGS) model for convection-driven dynamos, based on the nonlinear gradient model of Leonard [Leonard, A., 1974. Energy cascade in large-eddy simulations of turbulent fluid flows. Adv. Geophys. 18, 237–248]. The predictions of the SGS model are tested using snapshots from a direct numerical simulation (DNS). Good agreement is obtained throughout most of the fluid, but discrepancies occur near the boundaries. We also implement the SGS model in a large-eddy simulation (LES) to assess the temporal behavior of the SGS model. Both the DNS and LES have large time variation in the kinetic and magnetic energies, so comparisons are made using time averages. The time-averaged energies in the LES are slightly larger than those in the resolved DNS, but not as high as those obtained in an unresolved DNS with the same grid resolutions as the LES. The source of dissipation in the LES is revealed by examining the energy balances. The work done by the SGS Lorentz term and the magnetic energy generated by the SGS induction term are both negative, indicating that these SGS terms transfer energy from the resolved scales into the unresolved scales. [Copyright &y& Elsevier]

Abstract: Turbulent flow over a two-dimensional steep hill was analyzed by large-eddy simulations (LES). Here, six LES computations were carried out using four different sub-grid scale (SGS) models and two different ground surface conditions. The accuracy of these computations was assessed by comparing the results with those from an experiment by Ishihara et al. (An experimental study of turbulent boundary layer over a steep hill, Proceedings of the 15th National Symposium on Wind Engineering, 1998, pp. 61–66; J. Wind Eng. 89 (2001) 573). The results of the dynamic SGS models were in very poor agreement with those of the experiment. The poor prediction accuracy was mainly caused by the inaccurate estimation of the model coefficient near the ground surface. In order to improve the prediction accuracy of the dynamic SGS models, a hybrid SGS model, i.e., a combination of the standard Smagorinsky model and the dynamic Smagorinsky model, was introduced. The hybrid model provided very accurate predictions and produced the best results of the four SGS models compared here. [Copyright &y& Elsevier]

The paper presents numerical calculations of turbulent wind flow conditions around two parallel buildings with different wind directions and building arrangements. The numerical simulations are carried out with the RNG sub-grid scale model following an initial test case for a single building configuration with the time averaged and filtered Navier–Stokes equations based turbulence models. A comparison with the experimental data indicates that the present RNG sub-grid scale model gives much better results than other turbulence models tested to predict the time-dependent atmospheric flow field. This model is further extended to analyse the wind effects between buildings by considering different building geometry, wind flow direction and passage width. All numerical simulations are carried out by using the finite volume method (FVM). The simulation results show that the present sub-grid scale model with the FVM is rather promising to study the wind effects on buildings and can overcome the disadvantages of conventional Reynolds averaged Navier–Stokes equations based turbulence models. [Copyright &y& Elsevier]

• Develop a sub-grid scale model developed for the hexahedral grid. • The sub-grid scale model can reduce the computational cost of bubble mass transfer simulation. • Simulation of bubble mass transfer at high Péclet number. The gas-liquid mass transfer is widely applied in many industrial applications. The mass boundary layer at the interface is usually much thinner than that of the momentum boundary. To numerical simulate the interfacial mass transfer, an ultra-fine grid is needed to resolve the thin mass boundary layer, while the computational cost is usually unacceptable. In this paper, a sub-grid scale model based on the geometric VOF method has been developed for the hexahedral grid, which can be used to calculate the mass transfer flux based on the mass boundary layer thickness. Furthermore, the convection flux near the interface is estimated by the mass boundary layer thickness and the geometric information rather than a numerical interpolation method which would induce significant numerical diffusion. The sub-grid scale model can reduce the demanding requirement of the mesh resolution and a coarse grid can be used to obtain a good result. [ABSTRACT FROM AUTHOR]

• A modified SGS model was proposed to account for the effect of bubble response to turbulent eddies • The modified SGS LES can effectively capture the transient bubbly flow in the bubble column • Both Kolmogorov -5/3 scaling law and -3 scaling law were recovered in LES turbulent kinetic energy spectrum • Strong spatial correlation between the cross-sectional averaged gas hold-up and local vorticity of turbulent eddies 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. Image, graphical abstract [ABSTRACT FROM AUTHOR]