Turbulent Flow Friction Factor Calculation Using a Mathematically Exact Alternative to the Colebrook–White Equation

We present a novel, mathematically equivalent representation of the Colebrook–White equation to compute friction factor for turbulent flow in rough pipes. This new form is simple, no iterative calculations are necessary, and is well suited for accurate friction factor estimation. A limiting case of this equation provided friction factor estimates with a maximum absolute error of 0.029 and a maximum percentage error of 1% over a 20×500 grid of ε/D and R values (10?6 ? ε/D ? 5×10?2; 4×103相似文献   

Mathematical modeling of flows in large tundish systems in steelmaking

Numerical solutions of the three-dimensional turbulent Navier-Stokes equations, incorporating thek-ε turbulence model, are presented for the turbulent flow of liquid within a tundish of high aspect ratio. Experimental results, obtainedvia Laser-Doppler anemometry and flow visualization techniques, are also reported. Calculated flow fields were shown to be similar to corresponding experimental flow fields. Such results can provide useful technological information regarding the design of tundishes in the steel industry for optimization of steel cleanliness.     

Flow Depletion Induced by Pumping Well from Finite Length of Stream

A procedure for calculating the flow depletion from a finite length of a stream induced by a pumping well in an adjacent aquifer is developed. Four management cases of finite length of the stream including a basic case are considered. A “basic flow depletion factor” is defined, in terms of which the flow depletion factors for all cases are expressed. The basic flow depletion factor is twice the Hantush M function. A computationally simple and accurate practical approximation of the basic flow depletion factor is presented that encompasses the full practical range of the solutions. Using this approximation, an optimization method is proposed for the estimation of the aquifer hydraulic diffusivity and effective distance from the pumping well to the line of recharge from the measured temporal variation of stream flow depletion between two sections. During optimization, repeated computation of stream flow depletion is required; use of the proposed approximation simplifies the computation.     

Effects of tundish size,tundish design and casting flow rate on fluid flow phenomena of liquid steel

Fluid dynamics of liquid steel in continuous casting tundishes is closely related to tundish volume and geometry, existence of flow control devices and steel flow rate. To study this complex interaction physical and mathematical models were used in the present work. The first one was based in a 1/3 scale water model with injection of tracers and the second one on the solution to the steady state-turbulent Navier-Stokes equations using the K-ε [1] approximation for the turbulent viscosity. When the tundish size is increased from 30 t to 50 t the tracer indicates a strong bypassing in the second case. The mathematical predictions indicate very high fluid velocities along the tundish bottom in agreement with the experimental findings. The employment of turbulence inhibitors promotes a counter-flow that surrounds the incoming stream jet of liquid from the inlet nozzle with steel displacing itself, after leaving this zone, along the upper free surface of the liquid. The addition of well designed baffles complements the action of the turbulence inhibitor to obtain a higher volume fraction under a plug flow pattern giving a softer flow of liquid steel. Besides, the positioning of baffles inside a tundish should be performed according to the steel flow rate.     

Computation of Three-Dimensional Nonlinear Panel Flutter

A recently developed three-dimensional viscous aeroelastic solver is applied to the solution of nonlinear panel flutter. The solution scheme implicitly couples a well validated Navier-Stokes code with a finite-difference procedure for the Von Karman plate equations by employing a subiteration strategy. Both low supersonic, M∞ = 1.2, and subsonic, M∞ = 0.95, cases are computed. For the supersonic case, the presence of either a laminar or turbulent boundary layer delays the onset of flutter, with higher flutter dynamic pressures resulting for thicker boundary layers. This effect is much less pronounced when the boundary layers are turbulent. In the subsonic case multiple solutions are obtained. The downwardly divergent solution displays a very complex interaction between the laminar boundary layer and the flexible panel that results in significant acoustic radiation from the vibrating panel.     

Analytical Study of Turbulent Pollutant Dispersion near a Low Hill

An analytical methodology is developed to study the pollutant dispersion in a turbulent wind flow over a two-dimensional hill with a small slope. As in a typical boundary layer problem, the flow domain is divided into an inner and an outer region: the inviscid outer region is further subdivided into an upper and a middle layer while the viscous inner region is subdivided into a shear stress and an inner surface layer. Based on the Reynolds-averaged Navier–Stokes equations and the continuity equations, closed form analytical solutions of the stream functions and velocities are readily obtained for all regions in the domain. The velocity information is then imported into the diffusion equation, and the pollutant concentration distribution is readily solved. For reasons of turbulent shear, a variational method with adjustments to the streamline coordinate system is used to obtain an accurate solution of the pollutant concentration. Results show that when the source is located in the upper layer, the concentrations decrease with distance along the upwind side of the hill and tend to reach a constant value rapidly near the hilltop. Similar results are observed when the source is located in the middle layer. However, due to the reduction of wind speed in the middle layer, the concentrations become saturated at a later upslope position as compared to the source in the upper layer. This methodology is shown to be able to provide a quick and accurate estimate of local pollutant patterns and can be applied to any flow field provided that the streamlines can be specified through the velocities.     

Extension of the k-ε model for the numerical simulation of the melt flow in induction crucible furnaces

Checking the calculations of turbulent melt flow in induction crucible furnaces that were carried out with various modifications of the two-dimensional (2-D)k-ε model using experimental findings has shown basic differences in the distributions of the specific generation of the turbulent energy and the kinetic energy of the turbulence. The discrepancies are explained by the distinctive three-dimensional (3-D) character of the pulsations and the low-frequency fluctuations of the macroscopic toroidal eddy; these are not taken into account in the numerical methods mentioned. With the aid of this 3-D model, the additional component of turbulent kinetic energy involved is estimated, and an approximation formula for the low-frequency component of the specific generation of turbulence is given. This results in an extension of the 2-Dk-ε model for a recirculated flow with several toroidal eddies, leading to good qualitative agreement of the characteristics of turbulent flow with the experimental findings. Since the numerical simulation—in agreement with industrial practice and the experiments carried out—demonstrates good effective mixing of the entire flow region, there is thus a possibility for the simulation of aterial transport in the melt of induction crucible furnaces as part of the widespread 2-D computation methods.     

Two-Dimensional Numerical Simulation of Primary Settling Tanks by Hybrid Finite Analytic Method

In order to investigate the turbulent flow and mass transfer in primary settling tanks, numerical simulations are conducted by using a modified k?ε two-layer model based Boussinesq’s approximation to model the Reynolds stress in primary settling tanks, and solving the governing equations using a hybrid finite analytic method (HFAM). The simulation results obtained using the mathematical model are compared with the experimental data and simulation results available in the literature, and the results of comparison indicate that the profiles of the primary velocity field are in line with the experimental results and the flow-through curve obtained using the mathematical model are in good agreement with the curves based on experimental data. It is therefore concluded that the HFAM approach can be used to simulate the turbulent flow and mass transfer in a primary settling tank, and the modified k?ε two-layer model can be used to establish the velocity field distribution at the bottom of a primary settling tank.     

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.     

Experiments on Unsteady Turbulent Pipe Flow

The paper explores the time-wise evolution of selected turbulence parameters during gravity-driven flow establishment of incompressible fluids in rigid circular pipes. Two initial conditions are considered: flow starting from rest, passing through laminar-to-turbulent transition, and terminating in a turbulent steady state; and transient flow between two turbulent steady states. It is found that, in the second case, the properties considered, i.e., local temporal mean velocity and its transverse distribution, axial turbulence intensity, and wall shear stress, are monotonically increasing with time. However, for flow starting from rest, all properties are strongly affected by the development of turbulence. In particular, at the critical moment when laminar-to-turbulent transition is complete, the wall shear stress changes abruptly from one to the other, identifying wall shear stress as a very sensitive indicator of criticality.     

Large‐Eddy Simulations and Particle‐Image Velocimetry Measurements of Tundish Flow

Large‐eddy simulations (LES) and digital particle‐image velocimetry (DPIV) of a tundish flow are performed to investigate the turbulent flow structures and vortex dynamics. The LES is carried out using an implicit approach. In implicitly filtered LES, the computational grid and the discretization operators are considered as the filtering tools of the governing equations. The numerical computations are performed by solving the viscous conservation equations for compressible fluids. An implicit dual‐time stepping scheme combined with low Mach number pre‐conditioning and a multigrid accelerating technique is implemented for LES computations. The impact of jet spreading, jet impingement on the wall, and wall jets on the flow field and steel quality is investigated. The characteristics of the flow field in a one‐strand tundish such as the time‐dependent turbulent flow structure and vortex dynamics are analysed and compared with experimental results. To validate the numerical results, DPIV measurements are performed in a reduced 1:1.7 scaled water model. The investigations focus on steady‐state casting conditions for the flow in a tundish. The results evidence a good agreement between the LES and experimental data. The LES solutions provide an extremely detailed insight into the highly intricate turbulent flow structure. Even phenomena like funnel‐shaped vortices downward the shroud jet are well captured.     

Mean Flow and Turbulence Structure in Vertical Slot Fishways

This paper presents the results of an experimental study on the mean and turbulence structures of flow in a vertical slot fishway with slopes of 5.06 and 10.52%. Two flow patterns existed in the fishway and for each one, two flow regions were formed in the pools: a jet flow region and a recirculating flow region. The mean kinetic energy decays rapidly in the jet region and the dissipation rate in most of the areas in the pool is less than 200?W/m3. For the jet flow, the nondimensional mean velocity profile across the jet agrees very well with that of a plane turbulent jet in the central part of the jet with some scatter near its boundaries. Its maximum velocity decays faster compared to a plane turbulent jet in a large stagnant ambient. The jet presents different turbulence structure for the two flow patterns and for each pattern, the turbulence characteristics appear different between the left and right halves of the jet. However, the turbulence characteristics show some similarity for each case. The normalized energy dissipation rate shows some similarity and has a maximum value on the center of the jet. The results are believed to provide useful insight on the turbulence characteristics of flow in vertical slot fishways and can be used to verify numerical models and also for guidance in the design of fishways in the future.     

Steel flow and inclusion separation in continuous casting tundishes

A model for the calculation of flow patterns and inclusion separation in continuous casting tundishes is described. Velocity and turbulence fields for the liquid steel are calculated, assuming three-dimensional, turbulent steady-state flow. A transport equation for particles is solved, which takes into account buoyancy, convection und turbulent dispersion. Particle concentration fields and the percentage of removed particles are calculated as a function of particle rise velocity. The influence of increased tundish width and height and of dams and weirs on the rate of inclusion separation is investigated for a slab caster tundish. Non-dimensional representations and approximation expressions are discussed and used to compare the computed removal rates to measured values from literature.     

Effect of SEN Parameters on 3D Flow Field in Mould of Beam Blank Continuous Caster

Duringtheprocessofcontinuouscasting ,theflowfieldofmoltensteelinfluencesdirectlyonthetemperaturefield ,heattransfer ,slaginclusionfloatationandcomposi tionuniformityinthemould ,thusrelatesdirectlytothein ternalandsurfacequalityofcastblank .Soitisveryimpor…     

Three-Dimensional Mean Velocity Analysis of a 30 Degree Bend Flow

The 3D velocity profiles of the 30° bend flow of Flack and Johnston have been analyzed in terms of the existing 3D turbulent boundary layer theories. Various cross-flow and near-wall similarity models were tested. Coles's cross-flow model described the velocity profiles satisfactorily. The wall function matched the data well, and the experimentally determined wake functions collapsed into a narrow band, which was however different from the originally suggested wake function. A new form of wake function has been proposed. Among the near-wall models, Hornung and Joubert's and Prahlad's models matched the data very well and excellent near-wall similarity from the wall to the boundary layer edge was achieved. This is rather unexpected in a 3D turbulent boundary layer flow with large skewing. The excellent performance of these two near-wall models could not be attributed to any particular reason.     

Use of In Situ Air Flow Measurements to Study Permeability in Cracked Clay Soils

The work describes in situ measurements of crack induced permeability as a function of depth, (down to ～ 1.75?m), in clay soils at two field sites, using the gas flow technique described in an earlier study. The gas flow response to applied pressure was found to exhibit a significant nonlinearity at all depths indicating non-Darcian flow despite the fact that the flow was likely to be well within the laminar flow regime. Application of three-dimensional finite-element models to describe the gas flow revealed that the nonlinearity is likely to be an intrinsic behavior related to the soil-gas flow interaction. The Forchheimer compressible flow equation successfully simulated the behavior at all depths. The viscous and inertial permeability parameters obtained from this analysis showed a wide range of values which were closely correlated to the pore-water content of the soil medium, clearly showing the influence of ped swelling on the contraction of macrovoid channels in the structured clay soil.     

密相干塔烧结烟气脱硫系统仿真研究

应用Fluent软件对密相干塔模拟仿真,研究了烟气整流系统和链式搅拌器对烟气流场和湍流、循环灰轨迹及系统压力损失的影响,并在模拟工况下确定了烟气整流系统较优导流板布置形式.研究结果表明,链式搅拌器能够显著增大塔内附近区域的湍动能,提高转速不能明显提高整体烟气湍流强度,双层链式搅拌器可以增大高湍流强度区且减缓其衰减速度,该工况下安装双层链式搅拌器,转速为100 r·min-1较为理想,此时密相干塔能够实现烟气均布和气固充分接触,大部分颗粒参与内循环,少部分进入除尘器,系统压损约为200 Pa.      

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.     

A Study on the mathematical modeling of turbulent recirculating flows in gas-stirred ladles

Computed results are presented describing the velocity field and the map of the turbulent kinetic energy in a water model of an argon-stirred ladle. The theoretical predictions agree well with the measurements, when an experimentally determined void fraction distribution is used in computing the body force driving the flow. The agreement is somewhat less satisfactory, particularly regarding the maps of the turbulent kinetic energy, when the no-slip or the drift flux models are used to predict the void fraction of the gas.