The effects of turbulence on molten pool transport during melting and solidification processes in continuous conduction mode laser welding of copper–nickel dissimilar couple

The melting and solidification stages of a continuous copper–nickel dissimilar metal conduction mode laser welding have been simulated numerically in this study. The heat, mass and momentum transports in molten metal pool have been analysed using both laminar and turbulent flow models separately for the same process parameters. The phase change aspects related to solidification and melting are accounted for by a modified enthalpy–porosity technique while the turbulent transport is modelled by a high Reynolds number k–ε model. It has been observed that temperature fields obtained from both laminar and turbulent transport simulations are qualitatively similar to each other. The molecular thermal diffusivity of the molten metal mixture is found to be in the same order of magnitude as eddy thermal diffusivity, as a result of which the thermal field gets marginally affected by fluid turbulence. By contrast, eddy viscosity remains much greater than molecular viscosity, which leads to greater amount of momentum diffusion in the case of a turbulent molten metal pool, in comparison to that obtained from the corresponding laminar simulation. This is reflected in the reduction in maximum velocity magnitude in the turbulent simulation in comparison to the maximum velocity obtained from laminar simulation. In the case of species transport, the turbulent mass diffusivity is found to be about 10⁷–10⁸ times greater than molecular mass diffusivity. As a result, the species field in turbulent simulation shows characteristics of better mixing between two dissimilar molten metals than the species field obtained using the laminar transport model. The species distribution obtained from turbulent transport is shown to be in better agreement with experimental data reported in literature than the corresponding mass fraction distribution obtained from laminar simulation. It is also found that species distribution in the molten pool is principally determined by advective and diffusive transport during the melting stage and species transport by advection and eddy diffusion in turbulent pool increasingly weakens with decreasing temperature during the cooling following the laser melting stage.     

Large-eddy simulation of turbulent heat convection in a spanwise rotating channel flow

In this paper, we investigate the effects of the Coriolis force in a heated plane channel flow subjected to spanwise rotation using the method of large-eddy simulation. We present both the general and simplified transport equations for the resolved turbulent stresses, which are essential for understanding the unique pattern of turbulent kinetic energy production in a rotating system. Numerical simulations are performed using primarily two dynamic subgrid-scale stress models and one dynamic subgrid-scale heat flux model; namely, the conventional dynamic model (DM) and a novel dynamic nonlinear model (DNM) for closure of the filtered momentum equation, and an advanced dynamic full linear tensor thermal diffusivity model (DFLTDM) for closure of the filtered thermal energy equation. The turbulent flow field studied herein is characterized by a Reynolds number Re_τ = 150 and various rotation numbers Ro_τ ranging from 0 to 7.5. In order to validate the LES approach, turbulent statistics obtained from the simulations are thoroughly compared with the available experimental results and direct numerical simulation (DNS) data. A detailed comparative study has been conducted in order to evaluate the performance of the DM and DNM in terms of their prediction of characteristic features of the velocity and temperature fields and their capability of reflecting both forward and backward scatter of kinetic energy between the filtered and subgrid scales.     

Effects of preferential transport in turbulent bluff-body-stabilized lean premixed CH4/air flames

Preferential species diffusion is known to have important effects on local flame structure in turbulent premixed flames, and differential diffusion of heat and mass can have significant effects on both local flame structure and global flame parameters, such as turbulent flame speed. However, models for turbulent premixed combustion normally assume that atomic mass fractions are conserved from reactants to fully burnt products. Experiments reported here indicate that this basic assumption may be incorrect for an important class of turbulent flames. Measurements of major species and temperature in the near field of turbulent, bluff-body stabilized, lean premixed methane–air flames (Le = 0.98) reveal significant departures from expected conditional mean compositional structure in the combustion products as well as within the flame. Net increases exceeding 10% in the equivalence ratio and the carbon-to-hydrogen atom ratio are observed across the turbulent flame brush. Corresponding measurements across an unstrained laminar flame at similar equivalence ratio are in close agreement with calculations performed using Chemkin with the GRI 3.0 mechanism and multi-component transport, confirming accuracy of experimental techniques. Results suggest that the large effects observed in the turbulent bluff-body burner are cause by preferential transport of H₂ and H₂O through the preheat zone ahead of CO₂ and CO, followed by convective transport downstream and away from the local flame brush. This preferential transport effect increases with increasing velocity of reactants past the bluff body and is apparently amplified by the presence of a strong recirculation zone where excess CO₂ is accumulated.     

Effects of Turbulent Reynolds Number on Turbulent Scalar Flux Modeling in Premixed Flames Using Reynolds-Averaged Navier–Stokes Simulations

The influence of turbulent Reynolds number (Re _t ) on the statistical behavior and modeling of turbulent scalar flux (TSF) has been analyzed using a direct numerical simulation database of freely propagating turbulent premixed flames. A range of different values of Re _t is considered in which the Damköhler and Karlovitz numbers are modified independent of each other to bring about the variation of Re _t . It has been found that the qualitative behavior of the various terms of the TSF transport equation does not change by the variation of Re _t , but their relative contributions to the transport of TSF are affected to some extent. The effects of Re _t on the modeling of the TSF using both algebraic and transport equation-based closures are addressed in detail. It is demonstrated that model parameters for an existing algebraic model, and the models for turbulent transport, pressure gradient and the reaction rate terms in the TSF transport equation, all exhibit Re _t dependence for small values of Re _t but all assume asymptotic values for Re _t  ≥ 50. By contrast, the model parameters for the combined molecular diffusion term are found to be insensitive to the variation of turbulent Re _t . Existing models for algebraic and transport equation-based closures of TSF have been modified to account for the observed Re _t dependence.     

Direct numerical simulation of turbulent flow and combined convective heat transfer in a square duct with axial rotation

Direct numerical simulations (DNS) of turbulent flow and convective heat transfer in a square duct with axial rotation were carried out. The pressure-driven flow is assumed to be hydrodynamically and thermally fully developed, for which the Reynolds number based on the friction velocity and hydraulic diameter is kept at constant (Re_τ = 400). In the finite length duct, two opposite walls are perfectly insulated and another two opposite walls are kept at constant but different temperatures. Four thermal boundary conditions were chosen in combination with axial rotation to study the effects of rotation and Grashof number on mean flow, turbulent quantities and momentum budget. The results show that thermal boundary conditions have significant effects on the topology of secondary flows, profiles of streamwise velocity, distribution of temperature and other turbulent statistic quantities but have marginal effects on the bulk-averaged quantities; Coriolis force affects the statistical results very slightly because it exerts on the plane normal to main flow direction and the rotation rate is low; Buoyancy effects on the turbulent flow and heat transfer increase with the increase of Grashof number (Gr), and become the major mechanism of the development of secondary flow, turbulence increase, and momentum and energy transport at high Grashof number.     

Modelling of turbulent molten pool convection in laser welding of a copper–nickel dissimilar couple

The effects of turbulence on momentum, heat, and mass transfer during laser welding of a copper–nickel dissimilar couple are studied by carrying out three-dimensional unsteady Reynolds Averaged Navier Stokes (RANS) simulations. The turbulent transport is modelled by a suitably modified high Reynolds number k–ε model. The solid–liquid phase change is accounted for by a modified enthalpy porosity technique. In order to demonstrate the effects of turbulence, two sets of simulations are carried out for the same set of processing parameters: one with the turbulence model, and the other without activating the turbulence model. The enhanced diffusive transport associated with turbulence is shown to decrease the maximum values of temperature, velocity magnitude, and copper mass fraction in the molten pool. The effects of turbulence are found to be most prominent on the species transport in the molten pool. The composition distribution in turbulent simulation is found to be more uniform than that obtained in the simulation without turbulent transport. The nickel composition distribution predictions, as obtained from the present turbulence model based simulations, are also found to be in good agreement with the corresponding experimental results.     

Characterization of the effect of Froude number on surface waves and heat transfer in inclined turbulent open channel water flows

Interfacial heat transport in open channel turbulent flows is strongly dependent on surface waves that can appear as a result of the interaction of bulk turbulence with the free surface. The paper describes wave/heat transfer phenomena in inclined turbulent open surface water flows. The experiments were conducted in a regime of transition from “weak” to “strong” turbulence, in which the stabilizing influences of gravity and surface tension are relatively small against the disturbing effects of turbulence. A key role of the Froude number, Fr_⊥, built through the surface-normal component of g has been revealed. As Fr_⊥ grows, the wave amplitude grows, and the frequency spectrum shifts towards shorter waves. These changes lead to a heat transfer improvement, enough to double the heat transfer coefficient. The experimental data have been compared with calculations based on a “K-ε” model. As a result, the range of applicability of the standard model has been established as Fr_⊥<2000. The turbulent Prandtl number has been evaluated for Fr_⊥<700.     

Large eddy simulation of stably stratified turbulent open channel flows with low- to high-Prandtl number

Large eddy simulation of thermally stratified turbulent open channel flows with low- to high-Prandtl number is performed. The three-dimensional filtered Navier-Stokes and energy equations under the Boussinesq approximation are numerically solved using a fractional-step method. Dynamic subgrid-scale (SGS) models for the turbulent SGS stress and heat flux are employed to close the governing equations. The objective of this study is to reveal the effects of both the Prandtl number (Pr) and Richardson (Ri_τ) number on the characteristics of turbulent flow, heat transfer, and large-scale motions in weakly stratified turbulence. The stably stratified turbulent open channel flows are calculated for Pr from 0.1 up to 100, Ri_τ from 0 to 20, and the Reynolds number (Re_τ) 180 based on the wall friction velocity and the channel height. To elucidate the turbulent flow and heat transfer behaviors, some typical quantities, including the mean velocity, temperature and their fluctuations, turbulent heat fluxes, and the structures of the velocity and temperature fluctuations, are analyzed.     

Effects of density ratio and differential diffusion on flame accelerative propagation of H2/O2/N2 mixtures

The effects of density ratio and differential diffusion on premixed flame propagation of H₂/O₂/N₂ mixtures are investigated by constant volume combustion chamber. The density ratio and differential diffusion are controlled independently by adjusting the O₂/N₂ ratio and equivalence ratio. Results show that the density ratio has no effect on turbulent burning velocity while the differential diffusion has a promotion effect on turbulent burning velocity. The onsets of laminar flame acceleration are promoted by both density ratio and differential ratio. The turbulent flames perform a continuous acceleration propagation and the dependence between flame propagation speed and flame radius can be characterized as (dR/dt)/(σ·S_L) ～ R^0.33～0.37, which is lower than the 1/2 power law. The acceleration parameters of laminar flames and turbulent flames (u^’/S_L = 1) are around 0.17 and 0.36 respectively, and both of them are not affected by density ratio and differential diffusion. The empirical formula m = 0.19·(u^’/S_L)^0.4+0.17 is concluded to quantitatively describe the accelerative characteristics of laminar and turbulent flames. The current study indicates that the acceleration of laminar flames is mainly induced by flame intrinsic instability, and the latter can affect the acceleration onset but not affect the fractal excess. The acceleration of turbulent flames is dominated by turbulent stretch, while the effects of density ratio and differential diffusion can be ignored.     

An investigation of the influence of natural convection on tin solidification using a quasi two-dimensional experimental benchmark

A well validated, quasi two-dimensional, unsteady solidification experimental benchmark is proposed to study the critical role of thermally driven natural convection using commercial pure tin. The experiment consists of solidifying a parallelipedic sample from two vertical sidewalls using two heat exchangers in a rectangular cavity. The mean temperature gradient G_T, and the mean cooling rate C_R, are set to control the experimental process. An array of 50 thermocouples allows us to measure the instantaneous temperature field and its evolution. While in the liquid state, the isotherms exhibit a plausible convective heat flow and its intensity increases as the Rayleigh number increases. In the solidification process, a novel recalescence phenomenon is observed by tracing the solidifying front in a relatively slow cooling rate case. By setting different mean temperature gradients, different patterns of the natural convection and the temperature field evolutions are obtained. A discussion is also presented regarding the crystallography.     

Direct numerical simulation of wall-normal rotating turbulent channel flow with heat transfer

Direct numerical simulation of wall-normal rotating channel flow with heat transfer has been performed for the rotation number N_τ from 0 to 0.1, the Reynolds number 194 based on the friction velocity of non-rotating case and the half-height of the channel, and the Prandtl number 1. The objective of this study is to reveal the effects of rotation on the characteristics of turbulence and heat transfer. Some statistical turbulence and heat transfer quantities, including the mean velocity, temperature and their fluctuations, turbulent heat fluxes, and turbulence structures, are investigated. Based on the present calculated results, two typical rotation regimes are identified. When 0 < N_τ < 0.06, the turbulence statistics correlated with the spanwise velocity fluctuation are enhanced since the shear rate of spanwise mean flow induced by Coriolis force increases; however, the other statistics are suppressed. When N_τ > 0.06, all the turbulence statistics are suppressed significantly. To elucidate the effects of rotation on the turbulent heat transfer, the budget terms in the transport equation of turbulent heat fluxes are analyzed. Remarkable change of the direction of near-wall streak structures of the velocity and temperature fluctuations, nearly in alignment with the absolute mean flow direction, is revealed. An attempt to evaluate the mean spacing and the direction of streaky structures near the wall has been examined based on the two-point correlations of the velocity and temperature fluctuations.     

Matched asymptotic solution for the solute boundary layer in a converging axisymmetric stagnation point flow

A novel boundary-layer solution is obtained by the method of matched asymptotic expansions for the solute distribution at a solidification front represented by a disk of finite radius R₀ immersed in an axisymmetric converging stagnation point flow. The detailed analysis reveals a complex internal structure of the boundary layer consisting of eight subregions. The development of the boundary layer starts from the rim region where the concentration, according to the obtained similarity solution, varies with the radius r along the solidification front as ∼ln^1/3(R₀/r). At intermediate radii, where the corresponding concentration is found to vary as ∼ln(R₀/r), the boundary layer has an inner diffusion sublayer adjacent to the solidification front, an inner core region, and an outer diffusion sublayer which separates the former from the outer uniformly mixed region. The inner core, where the solute transport is dominated by convection, is characterized by a logarithmically decreasing axial concentration distribution. The logarithmic increase of concentration along the radius is limited by the radial diffusion becoming effective in the vicinity of the symmetry axis at distances comparable to the characteristic thickness of the solute boundary layer.     

The influence of furnace design on the NO formation in high temperature processes

High temperature processes produce high NO_x emissions due to their elevated working temperatures. Strong regulations for emissions of pollutants [1] from industrial plants lead the operators to optimize their furnaces. In this paper a three-dimensional mathematical model for turbulent flow and combustion on the basis of turbulence-chemistry interactions and radiative heat transfer taking into account spectral effects of surrounding walls and combustion gases is described. The transport equation for radiative intensity was split into different wavelength ranges. A block-structured finite volume grid with local refinements was used to solve the governing equations. The calculation domain is subdivided into a number of subdomains which are linked within the solver based on the message passing interface (MPI) library. Computed distributions of velocity, temperature, species distribution and heat fluxes are given. Results of a parametric study in a producing horseshoe furnace by increasing the height of the furnace with regard to NO_x concentration distributions are presented.     

Large eddy simulation of heat and mass transport in turbulent flows. Part 2: Scalar field

Several subgrid-scale (SGS) scalar flux (τ_iA) and unmixedness (λ_AB) models are presented for large eddy simulation (LES) of heat and mass transport in turbulent flows. The models are similar to those considered in [Int. J. Heat Mass Transfer, in press] for SGS stresses and are based on the information residing at filtered or resolved field. All closures are implemented “locally” and are assessed a priori and a posteriori via data generated by direct numerical simulations of several nonreacting and reacting turbulent flows. A priori assessment indicates that the local values of τ_iA and λ_AB obtained by new “serial decomposition” closures are closer to “true” values than those obtained by dynamic-diffusivity and two-parameter mixed models. A posteriori assessment also indicates that the statistics of the scalar field in nonreacting and reacting flows are better predicted by LES when new SGS models are used.     

The numerical computation of the evaporative cooling of falling water film in turbulent mixed convection inside a vertical tube

An analysis has been developed for studying the evaporative cooling of liquid film falling inside a vertical insulated tube in turbulent gas stream is presented. Heat and mass transfer characteristics in air–water system are mainly considered. A low Reynolds number turbulence model of Launder and Sharma is used to simulate the turbulent gas stream and a modified Van Driest model suggested by Yih and Liu is adopted to simulate the turbulent liquid film. The model predictions are first compared with available experimental data for the purpose of validating the model. Parametric computations were performed to investigate the effects of Reynolds number, inlet liquid temperature and inlet liquid mass flow rate on the liquid film cooling mechanism. Results show that significant liquid cooling results for the system with a higher gas flow Reynolds number Re, a lower liquid flow rate Γ₀ or a higher inlet liquid temperature T_L0.     

Direct numerical simulation of hydrogen addition in turbulent premixed Bunsen flames using flamelet-generated manifold reduction

Direct numerical simulations of a lean premixed turbulent Bunsen flame with hydrogen addition have been performed. We show the results for a case with equivalence ratio of 0.7 and a molar fractional distribution of 40% H₂ and 60% CH₄. The flamelet-generated manifold technique is used to reduce the chemistry; flamelets with different equivalence ratios and inflow temperature are used to account for stretch effects that are enhanced by preferential diffusion. The three-dimensional simulation clearly shows enhanced burning velocity in regions convex toward the reactants and reduced burning velocity with possible extinction in regions concave toward the reactants. To obtain these effects it was found to be necessary to include two three-dimensional transport equations with essentially different diffusivities. This point is illustrated by comparison of the results with cases in which either a single transport equation was used or two transport equations with minor differences in diffusivities were used. These latter cases incorporated preferential diffusion in the 1D flamelets (and thus in the manifold), but not in the three-dimensional transport. Thus the three-dimensional preferential diffusion effects are shown to enhance curvature and thereby to increase the turbulent burning velocity and reduce the mean flame height. In addition the turbulent burning velocity increases because hydrogen addition leads to a larger laminar flamelet consumption speed. To demonstrate this second effect, results of the cases mentioned above are compared to the results of simulations of the Bunsen flame with 0% hydrogen added to the fuel.     

Particle transport in turbulent flow using both Lagrangian and Eulerian formulations

Lagrangian and Eulerian models for particle transport by a turbulent fluid phase are presented. In both methods, particle distribution results from the action of applied forces (buoyancy, inertial, added mass and drag forces) and turbulent effects are shown. The carrier phase flow – which is solved by finite element method using a k–ε turbulence model – is assumed not to depend on the particles' motion. In the Lagrangian formulation the dynamic equation for the particles is solved. A discrete random walk model is used to account for the turbulent effects. In the Eulerian formulation, the particle concentration is calculated from a convection–diffusion equation using the terminal particles' velocity and turbulent diffusivity. Both models are compared to experimental measurements and analytical results; a good agreement is observed.     

Cocurrent turbulent mixed convection heat and mass transfer in falling film of water inside a vertical heated tube

A detailed numerical study has been conducted in order to analyse the combined buoyancy effects of thermal and mass diffusion on the turbulent mixed convection tube flows. Numerical results for air-water system are presented under different conditions. A low Reynolds number k-ε turbulent model is used with combined heat and mass transfer analysis in a vertical heated tube. The local heat fluxes, Nusselt and Sherwood numbers are reported to obtain an understanding of the physical phenomena. Predicted results show that a better heat transfer results for a higher gas flow Reynolds number Re, a higher heat flux q_w or a lower inlet water flow Γ₀. Additionally, the results indicate that the convection of heat by the flowing water film becomes the main mechanism for heat removal from the wall.     

Dimensional analysis and equation for axial heat flow of Gorter-Mellink convection (He II)

Dimensional analysis of the heat transport through He II-filled ducts is carried out on the basis of Landau's two fluid equations for the limit of normal fluid depletion. Resulting functional relations between relevant groups of variables for Newtonian fluid behavior are extended up to the lambda point (T_λ) using the temperature dependence of the effective “turbulent” viscosity. The resulting convection equation is in good agreement with data of many authors and our own results from about 1.2 K to T_λ and for diameters of the order 10^?2 to 1 cm.