DerivFit: a program for rate equation parameter fitting using derivatives

A C program for fitting parameters in enzymatic rate equations is presented. The DerivFit program employs the reaction scheme in the form of ordinary differential equations (ODEs). The kinetic parameters are fitted to the experimental data by minimizing the sum of squared deviations of experimental points from theoretically predicted progress curves. In the minimization process we use the Gradient, Newton, and Marquardt algorithms. The gradients are calculated explicitly by solving a set of additional ODEs that are automatically attached by the program, taking advantage of a general formulation of the basic ODEs that determine the reaction's time course. The program is applied to simple enzymatic systems including slow tight-binding inhibition.     

Turbulent recirculating flow in induction furnaces: A comparison of measurements with predictions over a range of operating conditions

Experimental measurements and theoretical predictions are presented concerning the velocity fields, the maps of the turbulent kinetic energy, and the turbulent kinetic energy dissipation in an inductively stirred mercury pool. A single coil arrangement was used, and the frequencies examined ranged from 50 to 5000 Hz. A hot film anemometer and a direction probe were employed for characterizing the velocity fields. The theoretical predictions were based on the numerical solution of the turbulent Navier-Stokes equations. The technique of mutual inductances was employed to compute the magnetic field, while thek-ε model was used for calculating the turbulent viscosity. Overall, the theoretical predictions were in reasonable agreement with the measurements both regarding the velocities and the turbulence parameters. By presenting the results in a normalized, dimensionless form these findings were given a rather broader applicability than the actual numerical range explored. Formerly of the Department of Materials Science and Engineering at MIT     

Sustainability–steel and the environment

Abstract

A two-dimensional heat and fluid flow model was used to simulate the plasma arc furnace, where the flow is governed by the steady state incompressible Navier–Stokes equations. The flow has been taken as turbulent and the standard k-epsilon model was used to simulate the turbulence in the flow. The coupled non-linear differential equations were solved with suitable boundary conditions and temperature dependent plasma properties at atmospheric pressure by employing an efficient finite volume method. The calculations and heat transfer to various parts of the furnace were calculated for argon, nitrogen and hydrogen plasmas. The voltage–current characteristic for the different types of plasma and the effect of other process parameters on heat transfer are discussed.     

Effect of interphase lift force on fluid flow in air stirred cylindrical vessel

Abstract

In the present paper, based on the two-phase model (Eulerian model), the two-dimensional fluid flow in air stirred water systems is simulated, and the effect of interphase lift force on the fluid flow is specially discussed. In the Eulerian two-phase model, the gas and liquid phases are considered to be two different continuous fluids interacting with each other through the finite interphase areas. The exchange between the phases is represented by source terms in conservation equations. Turbulence is assumed to be a property of the liquid phase. The k–? model is used to describe the behaviour of the liquid phase. The dispersion of phases due to turbulence is represented by introducing a diffusion term into the mass conservation equation. The contribution of bubble movement to the turbulent energy and its dissipation rate are taken into account by adding extra volumetric source terms to the equations of turbulent energy and its dissipation rate. Comparison between the mathematical simulation and experimental data indicates that the interphase lift force has a strong effect on flow behaviour, and considering both drag force and lift force as interphase forces is important to accurately simulate the gas–water two-phase fluid flow in air stirred systems. The interphase lift force makes bubbles move away from the centreline; the gas concentration decreases near the centreline, and increases near the wall. The lift force is smaller than the drag force at the same place, especially far away from the centreline.     

Aspects of Inlet Boundary Prescription for a Turbulent Flow Field

In the literature on turbulent flow various combinations of velocity, turbulence kinetic energy, and eddy viscosity models have been proposed for the inlet boundary to a flow field. There appears to be no rational criterion for specifying inlet boundary conditions. The present study proposes a criterion to select the inlet boundary conditions by treating the inlet boundary as a part of the flow field. Using this criterion, any prescribed variation of velocity, turbulence kinetic energy k, and rate of dissipation of kinetic energy ε, must satisfy the governing flow field equations at the inlet boundary. Analysis of previously used profiles of velocity, kinetic energy, and dissipation of kinetic energy in the literature indicates that most of these do not satisfy the flow field equations. To substantiate the importance of inlet boundary conditions, several reported numerical simulations using k-ε turbulence models are reconsidered to determine if there is any linkage between the residual errors at the inlet boundary and the errors in the flow field simulation. Based on such an analysis, it is both logical and practical to hypothesize the inlet boundary as a part of flow field.     

叶片形状对涡轮桨搅拌槽内尾涡特性的影响

Particle image velocimetry technique was used to analyze the trailing vortices and elucidate their relationship with turbulence properties in a stirred tank of 0.48 m diameter, agitated by four different disc turbines, including Rushton turbine, concaved blade disk turbine, half elliptical blade disk turbine, and parabofic blade diskturbine. Phase-averaged and phase-resolved flow fields near the impeller blades were measured and the structure of trailing vortices was studied in detail. The location, size and strength of vortices were determined by the simplified λ2-criterion and the results showed that the blade shape had great effect on the trailing vortex characteristics. The larger curvature resulted in longer residence time of the vortex at the impeller tip, bigger distance between the upper and lower vortices and longer vortex life, also leads to smaller and stronger vortices. In addition, the turbulent kinetic energy and turbulent energy dissipation in the discharge flow were determined and discussed. High turbulent kinetic energy and turbulent energy dissipation regions were located between the upper and lower vortices and moved along with them. Although restricted to single phase flow, the presented results are essential for reliable design and scale-up of stirred tank with disc turbines.     

Numerical Solution of Fully Developed Flow with Vegetative Resistance

This paper presents a numerical solution of the Reynolds averaged Navier-Stokes and the near-wall k- (turbulent kinetic energy) and ω- (specific dissipation or dissipation per unit kinetic energy) transport equations, which are modified to include vegetative drag terms. For similar treatment of the model coefficients, the use of the near-wall k-ω model produces similar results to previous models that employed the standard k-ε models with wall functions. The study shows that reasonable predictions of streamwise velocity and Reynolds stress profiles can be achieved by adopting universal values for all model coefficients, but the calculated energy gradient can have significant error. The study also indicates that predictions of streamwise turbulence intensity are significantly improved by adopting the universal values of Cfk = 0.05 and Cfω = 0.16 rather than the theoretically based values, Cfk = 1.0 and Cfω = β/αβ?Cfk.     

Three-Dimensional Numerical Simulation of Compound Channel Flows

A three-dimensional numerical study is presented for the calculation of turbulent flow in compound channels. The flow simulations are performed by solving the three-dimensional Reynolds-averaged continuity and Navier–Stokes equations with the k?ε turbulence model for steady-state flow. The flow equations are solved numerically with a general-purpose finite-volume code. The results are compared with the experimental data obtained from the UK Flood Channel Facility. The simulated distributions of primary velocity, bed shear stress, turbulent kinetic energy, and Reynolds stresses are used to investigate the accuracy of the model prediction. The results show that, using an estimated roughness height, the primary velocity distributions and the bed shear stress are predicted reasonably well for inbank flows in channels of high aspect ratio (width/depth ≥ 10) and for high overbank flows with values of the relative flow depth greater than 0.25.     

气体底吹搅拌液态伍德合金流场的预报

本文用数学模型法预报了中心底吹气体搅拌的液态伍德合金流场。用标准κ-ε模型的计算结果显示出与实测结果一致的流谱。对标准κ-ε模型经验参数的特定调整,使计算和测量得到的流场达到吻合。定性预报表明,偏心底吹气体搅拌流场的特征不仅包括典型的三维流谱,还包括强烈的湍流运动及特有的三维湍动能,湍动能耗散率及有效粘度分布图。     

Fluid Flow and Mechanisms of Momentum Transfer in a Six-Strand Tundish

Flow in a six-strand billet tundish, using turbulence inhibitors (TIs), was characterized using inputs of a pulsed tracer and mathematical simulations. It was found that to control turbulence attaining high fluid fractions under plug flow patterns, the key parameter for designing TIs is the dissipation rate of kinetic energy. TI designs that induce steep dissipation gradients are less efficient as flow controllers than those designs that yield more prolonged dissipation gradients from the inhibitor bottom to the bulk flow. A direct relationship between the dissipation of kinetic energy and the linear acceleration of the smallest turbulent eddies in the flow was established through dimensional analysis. The inhibitor with the highest linear accelerations of eddies in the viscous sublayer at the Kolmogorov scale, for a given liquid flow rate, yields the better flow control.     

Dissipation of Turbulent Kinetic Energy in a Tundish by Inhibitors with Different Designs

Turbulent flow of liquid steel and its control is studied using different geometries of turbulence inhibitors. Four designs of turbulence inhibitors were characterized through experiments of tracer injection in a water model and mathematical simulations using the Reynolds Stress Model (RSM) of turbulence. Inhibitor geometries included octagonal‐regular, octagonal‐irregular, pentagonal and squared. A layer of silicon oil was used to model the behaviour of tundish flux during steel flow. Fluid flows in a tundish using these geometries were compared with that in a bare tundish. Experimental and simulation results indicate that the flow in a bare tundish and a tundish using turbulence inhibitors open large areas of oil close to the ladle shroud due to strong shear stresses at the water‐oil interface with the exception of the squared inhibitor. Oil layer opening phenomena are explained by the high gradient of the dissipation rate of turbulent kinetic energy. Using the squared inhibitor the kinetic energy reports a high gradient from the tundish floor to the free bath surface as compared with other geometries.     

Turbulent Boundary Layer Flows Above a Porous Surface Subject to Flow Injection

A new analytical expression for velocity profile in a fully developed turbulent boundary layer above a porous surface subject to flow injection is derived by solving the coupled Reynolds equations and turbulent kinetic energy equation. The advection of turbulent kinetic energy is considered during the derivation, whereas the earlier studies have neglected it. The new solution reduces to the universal logarithmic law in the case of no flow injection. For the small injection, the solution can be expanded into a series form in terms of the normalized injection velocity. The leading order terms are found to be equivalent to those in the earlier works in which the advection of turbulent kinetic energy has been neglected in the derivation. The new solution can provide more accurate prediction of bed shear stress for a wide range of flow injection rate, fluid type (e.g., from air to water), and surface roughness. On the other hand, the earlier theories may significantly underestimate bed shear stress under high injection rates.     

Turbulent Fluid Flow Phenomena in a Water Model of an AOD System

Experimental measurements are reported regarding fluid flow and turbulence property measurements in a water model of an AOD vessel. Laser velocimetry was used to determine the time smoothed velocities, the turbulent kinetic energy, and the Reynolds stresses in the system; in addition, the rate of melting of immersed ice rods was also measured to determine the local heat transfer rates. The measurements have shown that for the model AOD studied both the velocity fields and the distribution of the turbulent kinetic energy were quite uniform; the absence of inactive or dead zones would render these systems ideal for mixing and for a range of ladle metallurgical operations. The rate at which immersed ice rods dissolved depended on both the local velocities and on the turbulence levels; a previously developed correlation could be employed to predict the appropriate heat transfer coefficients. Finally, the rate of turbulent energy dissipation per unit volume in real industrial AOD vessels was found to be much higher than in any other ladle metallurgy operations. This could raise interesting possibilities regarding the more widespread use of these systems for molten metals processing.     

基于固液两相流模拟的选矿循环水深度澄清装置优化

部分选矿循环水中含一定量的高分散性悬浮颗粒,仅依靠简单浓缩沉降难以澄清,无法达到回用要求。针对这一难题,提出了一种选矿循环水固体悬浮物澄清装置。为优化装置的结构参数与运行参数,建立了选矿循环水深度澄清装置的二维物理模型,基于计算流体力学（CFD）的方法,选用Mixture和RNG k?ε 模型对装置主要的结构参数与运行参数展开了数值模拟研究。研究发现适当降低水力循环区喷嘴长度,增加喉管与喷嘴管径比、颗粒沉降区开口尺寸、装置直径等结构,能够降低颗粒沉降区平均湍动能,由于湍动能为单位质量流体由于紊流脉动所具有的动能,故降低了颗粒沉降区流场的紊流程度,增加了水流的稳定性,提高了装置对悬浮颗粒的去除效果;同时发现降低入口流速、增加悬浮颗粒粒径有助于提高悬浮物的去除率,当进水流速为0.1 m·s?1、经过混凝的悬浮颗粒形成粒径大于100 μm时,装置对选矿循环水中的悬浮颗粒去除效果显著。      

Decay of Turbulence Downstream of a Stilling Basin

Turbulence must be modeled accurately to simulate river processes, particularly transport of aqueous oxygen and nitrogen. Spillway operations affect downstream turbulence, but there has been little research on turbulence intensities downstream of stilling basins. For this study, laboratory measurements were taken on a three-dimensional, physical model of McNary Dam, Columbia River, United States to determine how the turbulence, initially generated by spillway flow, decreases with distance downstream. The experiments also examined how flow rate, tailwater depth, and the presence of spillway deflectors affect turbulence. A mathematical analysis was used to predict turbulent kinetic energy with distance, and good agreement was found between laboratory measurements and numerical predictions. Turbulence production generated by channel bed roughness was found to be small compared to turbulent energy dissipation, and the effect of flow separation related to bed irregularities on turbulence production was found to be negligible.     

Effect of Ar/O2 gas mixtures on heat‐transfer and fluid‐flow characteristics in AOD nozzles

A model of fluid flow and heat transfer in a nozzle used for injection of argon and oxygen in AOD converters was developed earlier. In this study the model was used to determine the effect of changes in the ratio of argon to oxygen in argon‐oxygen gas mixtures injected through the nozzle on fluid flow and heat transfer. It was found, for the studied conditions, that the temperature and laminar kinematic viscosity at the nozzle outlet were not dependent on the gas composition. However, the velocity, density, turbulent kinetic energy and dissipation of kinetic energy varied with a change in the fraction of oxygen injected. It is therefore concluded that for use as boundary‐condition input data for an AOD converter model (under development), it is important to be able to calculate reliable velocity and turbulence parameter data for gas mixtures of different argon/oxygen ratios.     

Steady and Unsteady Simulations of Turbulent Flow and Transport in Ultraviolet Disinfection Channels

The effects of unsteadiness in the turbulent flow through a staggered array of circular cylinders, modeling an ultraviolet disinfection system, are studied by means of solutions of the two-dimensional Reynolds-averaged Navier–Stokes equations incorporating the standard k–? turbulence model. Time averaging is applied to the unsteady solution, and the time-averaged characteristics are compared with a solution where a steady flow is a priori assumed, as well as with time-averaged measurements. Differences between the predictions of time-averaged and the steady-flow models are found to be largest in the entrance region of the array, and to decline in importance in the downstream direction. Comparison with measurements indicate that, while the time-averaged unsteady model predictions exhibited better agreement in some respects, the turbulent kinetic energy remained substantially underpredicted. Predictions of head losses through the array are also discussed.     

Effect of Turbulence Modeling on the Melt Flow and Inclusions Transport in a Steel Filtration Experiment

The current article deals with the effect of turbulence modeling on inclusions transport and melt flow in an induction crucible furnace (ICF), which was employed in order to investigate the efficiency and the performance of a ceramic filter. Furthermore, the influence of the discrete random-walk dispersion model on the behavior of inclusions in the ICF was investigated. Different turbulence models were employed in order to predict the turbulent melt flow. The numerical results show that the flow field is affected by the turbulence modeling method. Moreover, the distribution of the turbulent kinetic energy depends considerably on the choice of the turbulence model. In addition, the turbulence model and dispersion model also affect the inclusion transport in the melt. The filtration rate is also affected by the choice of the turbulence model.     

Mean Flow and Turbulence Structure of Open-Channel Flow through Non-Emergent Vegetation

The ability of turbulence models, based on two equation closure schemes (the k-ε and the k-ω formulations) to compute the mean flow and turbulence structure in open channels with rigid, nonemergent vegetation is analyzed. The procedure, developed by Raupach and Shaw (1982), for atmospheric flows over plant canopies is used to transform the 3D problem into a more tractable 1D framework by averaging the conservation laws over space and time. With this methodology, form∕drag related terms arise as a consequence of the averaging procedure, and do not need to be introduced artificially in the governing equations. This approach resolves the apparent ambiguity in previously reported values of the drag-related weighting coefficients in the equations for the turbulent kinetic energy and dissipation rates. The working hypothesis for the numerical models is that the flux gradient approximation applies to spatial∕temporal averaged conservation laws, so that the eddy viscosity concept can be used. Numerical results are compared against experimental observations, including mean velocities, turbulence intensities, Reynolds stresses, and different terms in the turbulent kinetic energy budget. The models are used to further estimate vegetation-induced flow resistance. In agreement with field observations, Manning's coefficient is almost uniform for some critical plant density and then increases linearly.     

Estimating Bottom Stress in Tidal Boundary Layer from Acoustic Doppler Velocimeter Data

Bed stresses in the bottom boundary layer of the York River estuary, Va., were estimated from 3D near-bottom velocities measured by Acoustic Doppler Velocimeters (ADVs) and also by a profiling array of electromagnetic current meters. By assuming the measurements were made in a constant stress layer, four methods of stress estimation were evaluated using ADVs: (1) direct covariance (COV) measurement; (2) turbulent kinetic energy; (3) inertial dissipation utilizing the Kolmogorov spectrum; and (4) log profile. The four methods yielded similar estimates of frictional velocity U* based on ADV output from both 14 and 44 cm above bed. All eight estimates of average U* were consistent with the overall mean of 1.10 cm∕s to within the 95% confidence interval for individual burst estimates. The COV method worked slightly better nearer the bed, possibly because of the sensitivity of COV to the upper limit of the constant stress layer. The inertial dissipation method performed marginally well at 14 cm above bed, likely due to sediment induced stratification and insufficient separation of turbulent production and dissipation scales. The log profile method was the most variable and appeared most sensitive to stratification and to the thickness of the constant stress layer. The turbulent kinetic energy method was the most consistent at both heights and appears most promising for further development. Results encourage future use of the ADV in estuarine environments but also favor the simultaneous use of several methods to estimate bottom stress.