A new model of turbulent fibre suspension and its application in the pipe flow

A new model of turbulent fibre suspension in pipe flow is developed by deriving the equations of Reynolds averaged Navier‐Stokes, turbulence kinetic energy and turbulence dissipation rate with the additional term of the fibres, and the equation of probability distribution function for mean fibre orientation. The equations are solved numerically. The numerical mean velocity is in agreement with the experimental data. The effects of Reynolds number, fibre concentration, and fibre aspect‐ratio on the mean velocity, turbulent kinetic energy and turbulent dissipation rate are analysed. The results show that the effect of Reynolds number on the flow behaviour is insignificant. The turbulent kinetic energy and turbulent dissipation rate increase with an increasing fibre concentration and fibre aspect‐ratio. © 2012 Canadian Society for Chemical Engineering     

方型多火嘴石油化工管式炉中辐射室三维流动及传热的数学模拟

提出方型石油化工管式炉中辐射室的三维流动和传热的数学模型.对某焦化炉计算的结果与实测数据进行了初步比较并作出讨论.     

RANS modeling of a particulate turbulent round jet

A complete and accurate model for the symmetric gas–solid turbulent round jet is accomplished using the Reynolds Averaged Navier–Stokes (RANS) equations. The two-fluid model was used to describe the averaged characteristics of the two phases, including the particle mass concentration, the turbulent kinetic energy and its dissipation in the mixture. Particle–turbulence interaction (turbulence modulation) is described by a two-way coupling model. The drag, lift and gravitation forces are incorporated into the system of equations using appropriate closure equations. A finite difference numerical scheme was used for the solution of the set of the governing equations and the results of the model were validated by comparison with data from several experiments. The influence of two types of particles, namely glass and electrocorundum, of different sizes and different loadings on the velocity and turbulence structure of the jet is examined. The computational results show the influence of the particulate phase on the velocity and turbulence structure of the jet.The significance of this study is that for the first time it presents explicitly the full RANS equations for a fluid jet with particles in an unabridged way and specifies the entire set of closure relations that are used for fluid–particle interactions including the equations for the extended k–ε model, the two-way particle–turbulence interactions and turbulence modulation as well as the inclusion of a lateral Saffman force.     

Detached eddy simulation on the turbulent flow in a stirred tank

A detached eddy simulation (DES), a large‐eddy simulation (LES), and a k‐ε‐based Reynolds averaged Navier‐Stokes (RANS) calculation on the single phase turbulent flow in a fully baffled stirred tank, agitated by a Rushton turbine is presented. The DES used here is based on the Spalart‐Allmaras turbulence model solved on a grid containing about a million control volumes. The standard k‐ε and LES were considered here for comparison purposes. Predictions of the impeller‐angle‐resolved and time‐averaged turbulent flow have been evaluated and compared with data from laser doppler anemometry measurements. The effects of the turbulence model on the predictions of the mean velocity components and the turbulent kinetic energy are most pronounced in the (highly anisotropic) trailing vortex core region, with specifically DES performing well. The LES—that was performed on the same grid as the DES—appears to lack resolution in the boundary layers on the surface of the impeller. The findings suggest that DES provides a more accurate prediction of the features of the turbulent flows in a stirred tank compared with RANS‐based models and at the same time alleviates resolution requirements of LES close to walls. © 2011 American Institute of Chemical Engineers AIChE J, 58: 3224–3241, 2012     

MODELING OF TURBULENT, NEUTRALLY BUOYANT DROPLET SUSPENSIONS IN LIQUIDS

The mixing of neutrally buoyant, immiscible droplets in suspension in a turbulent liquid is being studied. In a statistically homogeneous field, it is anticipated that the droplets will affect the turbulent eddies, and that the turbulence will cause the droplets to break-up and coalesce. A cascade model is constructed by extension of the Desnyansky and Novikov equation, accounting for the wavenumber dependence of the fluctuating energy, for the intermittency factor of the turbulence and for the droplet population. In the absence of breakage and coalescence, interactions between eddies and droplets are assumed to be of collision type, so that the exchange of energy and the modifications to the eddy and droplet populations can be described. The resulting equations are solved for a fixed droplet population, showing the effect of droplet size on the turbulent energy spectrum. Continuation of the work is discussed, including droplet breakage and coalescence, as well as the introduction of non-homogeneous distributions.     

The impacts of standard wall function and drag model on the turbulent modelling of gas–particle flow in a circulating fluidised bed riser

A transient turbulence model was applied to simulate the gas–particle system in a circulating fluidised bed riser. The k–epsilon turbulent equations coupled with the fluctuating energy equation were used to simulate the gas–particle system in a riser. The simulation results were validated by the experimental data of a CFB system. A grid study was implemented to examine the impact of grid discretisation. A comparison between the conventional drag models and the EMMS model was also conducted. Other factors, like the restitution coefficient particle to particle, was also found to have a significant impact on the turbulence model. © 2013 Canadian Society for Chemical Engineering     

Numerical simulation of turbulent gaseous combustion in axially symmetric combustion chambers

A mathematical model and numerical algorithm are developed for the combustion of gaseous fuels in two dimensional turbulent flows. The model includes a system of basic differential conservation equations for the gaseous phase, supplemented by equations for the energy and dissipation rate of turbulent fluctuations for calculating the turbulent diffusion coefficient, as well as a mixing function for initially unmixed flows and its dispersion for describing the effect of turbulence on the concentration of the components, on the temperature, and on chemical reaction rates in terms of a probabilistic approach with a probability density function whose first moment is the mixing function and whose second moment is its dispersion. The calculations are compared with experimental data. The model is found to be effective for thermodynamic equilibrium and for finite kinetics. The results are in satisfactory agreement with the experimental data. Translated fromFizika Goreniya i Vzryva, Vol. 34, No. 4, pp. 3–12, July-August 1998     

垂直圆管内湍流泡状流的数值研究

在经典Euler/Euler型水动力模型基础上,引入考虑不同直径气泡的种群平衡方程来描述气液两相泡状流,对液相和气相分别建立了基本方程,通过对气泡的受力分析并考虑气泡之间聚合和破碎效应后给出了本构方程,建立了封闭的双流体模型并用于垂直管道湍流泡状流的三维数值模拟.模型预测值与实验数据的比较结果表明该模型能较好地模拟垂直管道湍流泡状流中的相含率分布、速度分布、湍动能分布、气泡直径分布以及气泡直径分布的演变过程.     

Turbulence model predictions of the radial jet — A comparison of κ-ϵ models

The (κ-?) turbulence closure model has become a widely used means of predicting turbulent fluid flows. In this paper the turbulent radial jet, the round jet and the plane jet are calculated in their similarity regions using various versions of the (κ-?) model to determine which is the most satisfactory for both plane and axisymmetric flows. The most general predictions were obtained using a model which contained additional terms to account for the effect of irrotational strains on the production of turbulence energy. Additionally, detailed mean velocity profiles and turbulence kinetic energy profiles of the radial jet are compared to the available experimental data.     

HEAT TRANSFER IN TURBULENT RECIRCULATORY FLOWS AFFECTED BY BUOYANCY FORCES IN RECTANGULAR CAVITIES

An analysis is carried out to investigate the heat transfer in a turbulent recirculatory flow affected by buoyancy forces.

Transport equations for turbulence kinetic energy, energy dissipation Tate and mean square temperature fluctuations are derived and solved numerically together with the mass, momentum and energy conservation equations. The flow pattern and temperature distribution are shown for different Reynolds numbers. The buoyancy effect on flow pattern and temperature distribution is analyzed. Mean Nusselt numbers, with and without buoyancy effect are presented. Turbulence characteristics such as turbulence kinetic energy and effective viscosity arc discussed.     

The significance of the buffer zone of boundary layer on convective heat transfer to a vertical turbulent flow of a supercritical fluid

A two-dimensional model is developed to simultaneously solve the momentum and energy equations in order to predict convective heat transfer to an upward turbulent flow of supercritical carbon dioxide in a round tube. It is very important to choose a proper turbulence model. An appropriate turbulence model, based on the previous studies, has been selected. The main focus of the present study is on significance of the buffer zone in the boundary layer. The results of this study indicate that in enhanced regime of heat transfer, the peak of heat transfer coefficient occurs when the pseudo-critical temperature, or the situation of maximum heat capacity, lies within the buffer layer. In deteriorated regime of heat transfer, the extent of the laminar sub-layer appears to be changed so that the buffer zone is experienced at a farther distance from the wall. This causes a delay in the turbulent diffusion near the wall and leading to a jump in the wall temperatures.     

鼓泡床内气泡-液体两相湍流代数应力模型的数值模拟

现有的气泡 -液体两相流动的数值模拟中 ,或者不考虑湍流 ,或者仅仅考虑液体湍流 ,但是直接模拟和PIV测量结果都表明气泡由于尾迹的作用有强烈的湍流脉动 .本文首次推导和封闭了同时模拟气泡湍流脉动和液体湍流脉动的二阶矩输运方程两相湍流模型 ,并在此基础上建立了代数应力气泡 -液体两相湍流模型 .用代数应力模型模拟了二维矩形断面鼓泡床内气泡 -液体两相流动 .预报结果给出了气泡和液体两相速度场、两相Reynolds应力及湍动能分布和气泡体积分数分布 .模拟结果与PIV测量结果符合很好 ,表明了模型的合理性 .研究结果表明 ,原先静止的液体在气泡因浮力而产生的上升运动的作用下产生回流流动 ,而气泡则只有上升运动 .气泡速度始终大于液体速度 .在床内气泡湍流脉动确实始终很强烈 .液体则由于气泡的作用以及自身速度梯度产生的双重作用而发生湍流脉动 .气泡的脉动显著地大于液体的脉动 .两相湍流脉动都是各向异性的 ,而且气泡湍流脉动的各向异性比液体的更强烈     

Investigation of Energy Loss Mechanisms in Cyclone Separators

Based on the transient Navier‐Stokes equation of an incompressible Newtonian fluid, a vorticity form of the mean mechanical energy equation is derived which is suitable for strongly swirling flow or vortex flow, and reveals the mechanism of mean mechanical energy losses in cyclone separators. Results show that the mean mechanical energy losses in cyclone separators are mainly caused by mean viscous dissipation, turbulent diffusion, and turbulent energy production in a steady turbulent flow. Order‐of‐magnitude analysis indicates that the rate of local turbulent energy production and mean viscous dissipation is related to the local turbulent Reynolds number at each point in cyclone separators. A large local turbulent Reynolds number designates the turbulent energy production as the primary contributor to mean mechanical energy losses, whereas in the case of a small turbulent Reynolds number the order‐of‐magnitude quotient between the two quantities decreases, indicating the increased significance of the mean viscous dissipation contribution to mean mechanical energy losses. A combination of theoretical analysis and LDV experimental results indicates the mean viscous dissipation is larger in the quasi‐forced vortex region and the boundary layer than in other regions of cyclone separators. The energy losses are mainly caused by turbulent energy production in a majority of the regions (except in the laminar sublayer very close to the wall), especially the largest energy losses in the central quasi‐forced vortex region. Hence, decreasing turbulence is an effective approach for drag reduction in cyclone separators.     

Numerical simulation and validation of dilute turbulent gas-particle flow with inelastic collisions and turbulence modulation

This work describes a theoretical and numerical study of turbulent gas-particle flows in the Eulerian framework. The equations describing the flow are derived employing Favre averaging. The closures required for the equations describing the particulate phase are derived from the kinetic theory of granular flow. The kinetic theory proposed originally is extended to incorporate the effects of the continuous fluid on the particulate phase behavior. Models describing the coupling between the continuous phase kinetic energy and particulate phase granular temperature are derived, discussed, and their effect on the flow predictions is shown.The derived models are validated with benchmark experimental results of a fully developed turbulent gas-solid flow in a vertical pipe. The effect of the models describing the influence of turbulence on the particle motion as well as the turbulence modulation due to the presence of particles is analyzed and discussed.     

NUMERICAL SIMULATION OF TURBULENT FLOW OF AGITATED LIQUID WITH PITCHED BLADE IMPELLER

The turbulent flow field in an agitated system with baffles was solved numerically using the standard k-e model, an algebraic Reynolds stress model (ASM) and a differential Reynolds stress model (RSM). The commercial software FLOW3D (CFDS, Harwell Laboratories, 1991) was used for this purpose. The aim of the study was to investigate the influence of the impeller boundary conditions and turbulence models to the agreement with experimentally obtained laser-Doppler anemometry data. The boundary conditions for the impeller discharge used in the numerical calculations were obtained as whole-cycle-ensemble averages from experimental LDA-measurements (Fort et al., 1992). Since measurements of the rate of dissipation of turbulent kinetic energy ( ε) was not available the dissipation rate per unit mass in the impeller discharge was estimated from the expression:

where k is the turbulent kinetic energy per unit mass and L the macroscale of turbulence in the pitched blade impeller discharge. The macroscale of turbulence (L) in the impeller boundary condition for e was varied in order to optimize the fit of theoretically obtained profiles of turbulent kinetic energy with experimental data. The constant A was fixed to 0.85 according to Wu and Patterson (1989). The optimal values of L for the different turbulence models were compared with the projected height of the impeller blade (h). All three components of the mean velocity were compared with experimental data for the optimal ratio of L/h for six radial cross-sections in the tank.

The mean velocity field obtained from simulations showed good agreement with experimental data for all models, with somewhat better agreement for the k — e model. An optimal value of the ratio L/h was found to be equal to 2.0 for the k — ε model and 1.3 for the ASM. However, no such optimal value for the RSM could be determined in this study.     

Numerical simulation of turbulent gas–particle flow in a 90° bend: Eulerian–Eulerian approach

A numerical investigation into the physical characteristics of dilute gas–particle flows over a square-sectioned 90° bend is reported. The modified Eulerian two-fluid model is employed to predict the gas–particle flows. The computational results using both the methods are compared with the LDV results of Kliafas and Holt, wherein particles with corresponding diameter of 50 μm are simulated with a flow Reynolds number of 3.47 × 10⁵. RNG-based κ–? model is used as the turbulent closure, wherein additional transport equations are solved to account for the combined gas–particle interactions and turbulence kinetic energy of the particle phase turbulence. Moreover, using the current turbulence modelling formulation, a better understanding of the particle and the combined gas–particle turbulent interaction has been shown. The Eulerian–Eulerian model used in the current study was found to yield good agreement with the measured values.     

Energy dissipation and macro instabilities in a stirred square tank investigated using an LE PIV approach and LDA measurements

In this study, the hydrodynamics and turbulence in a square tank stirred with a hydrofoil impeller, a Lightnin A310, is investigated using a large eddy particle image velocimetry (LE PIV) approach. The particle image velocimetry data are used as the large scale part of a large eddy simulation and the small scales are modelled assuming that the turbulent kinetic energy production is limited to the large scale structures, the turbulent energy dissipation is confined to the small scale structures and the transfer of energy takes place in the inertial sub-range. The small scale turbulence was modelled by direct calculation of the turbulent stress tensor using filtered particle image velocimetry data. The spatial distribution of the calculated dissipation rate tensors showed good agreement with previous work.

The macro instabilities of the flow structure were investigated by means of spectral analysis. Low frequency phenomena separated from the mean flow were detected. The cause of these could partly be explained by the circulation time for the tank, which corresponded to the low frequency phenomena found at 0.03N Hz, where N is the rotational speed.     

Numerical simulation of dilute turbulent gas‐particle flow with turbulence modulation

A numerical study of a dilute turbulent gas‐particle flow with inelastic collisions and turbulence modulation in an Eulerian framework is described. A new interpretation is provided for the interaction/coupling terms, based on a fluctuating energy transfer mechanism. This interpretation provides for a new robust closure model for the interaction terms with the ability to predict the turbulence dampening as well as the turbulence enhancement phenomenon. Further, the model developed herein is investigated along with a variety of other published closure models used for the interaction/coupling terms, particle drag, and solid stress. The models are evaluated against several sets of benchmark experiments for fully‐developed, turbulent gas‐solid flow in a vertical pipe. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

水力旋流器能耗机制与节能原理研究 Ⅳ.湍动能分布与湍动能耗散率

采用代数应力模型对水力旋流器内的湍流场进行了数值模拟,并用实测结果验证了计算结果的可信性,获得了旋流器内湍动能及湍动能耗散率的分布规律。结果表明,在溢流管端以下轴向位置上湍动能分布具有相似性,呈两边高中间低的不对称鞍形;在溢流管与旋流器壁之间的环隙空间内湍动能沿径向方向变化不大;旋流器内湍动能较大的区域是溢流管端以下空气柱附近的内旋流区域;旋流器内湍动能耗散率分布与湍动能分布有十分相似的规律,溢流管端以下空气柱附近的内旋流区域亦是湍动能耗散损失较严重的区域。     

Modelling of turbulent flow and mass transfer with wall function and low-reynolds number closures

A recent laser doppler anemometer study, by other researchers, of turbulent flow through a sudden expansion has been simulated using a kinetic energy of turbulence-dissipation rate of turbulence (k - ?) model. The near wall region was modelled in two different ways; using wall functions (WF), and a low-Reynolds number (LRN) formulation. The reattachment length under particular flow conditions was obtained. Radial profiles for the mean axial and radial velocity, turbulence kinetic energy and Reynolds shear stress were determined for six locations downstream of the sudden expansion. Both models performed reasonably well in predicting the flow with the LRN approach performing slightly better than the WF approach near to the wall. The application of the LRN approach to the calculation of local mass transfer rates in wall bounded complex turbulent flows is demonstrated.