Laminar Transport Research Articles

Predicting the vertical density structure of oceanic gravity current intrusions

Understanding the dynamics and structures in the deep ocean is one of the remaining challenges in oceanography and climate sciences. We present results from large-scale laboratory experiments of rotating down-slope gravity currents intruding into a two-layer stratified ambient, performed in the largest rotating tank in the world, the Coriolis Rotating Platform in Grenoble. By means of velocity and density measurements, we show that no mixing occurs once the current has detached from the boundary. The shape of the vertical density profile in the stratified receiving ambient enables to identify two distinct regimes: the first issued by laminar transport through Ekman dynamics, the second by turbulent transport due to intermittent dense water cascading. Vertical density gradients reveal a piece-wise linear dependence on the density anomaly for the turbulent transport, suggesting an advection-diffusion process. For the turbulent regime, the scale height is deduced and an analytical model based on the critical Froude number is proposed to predict its value. Results show that the total thickness of the intruding current is on average 2.5 times the scale height. For laminar intrusions the scale height diverges whereas the thickness of the intrusion is a few times the Ekman layer thickness. Comparing the intrusion scale height with its measured vertical extension has led to a criteria to distinguish between laminar and turbulent regimes, which is corroborated by two additional independent criteria, one based on the sign of the local vorticity and the other based on the local maxima of the vertical density gradient. The model allows us to connect laboratory experiments to deep sea observations, gravity currents and Meddies and emphasizes the importance of laboratory experiments in understanding climate dynamics.

Lagrangian Transport and Chaotic Advection in Three-Dimensional Laminar Flows

AbstractTransport and mixing of scalar quantities in fluid flows is ubiquitous in industry and Nature. While the more familiar turbulent flows promote efficient transport and mixing by their inherent spatio-temporal disorder, laminar flows lack such a natural mixing mechanism and efficient transport is far more challenging. However, laminar flow is essential to many problems, and insight into its transport characteristics of great importance. Laminar transport, arguably, is best described by the Lagrangian fluid motion (“advection”) and the geometry, topology, and coherence of fluid trajectories. Efficient laminar transport being equivalent to “chaotic advection” is a key finding of this approach. The Lagrangian framework enables systematic analysis and design of laminar flows. However, the gap between scientific insights into Lagrangian transport and technological applications is formidable primarily for two reasons. First, many studies concern two-dimensional (2D) flows, yet the real world is three-dimensional (3D). Second, Lagrangian transport is typically investigated for idealized flows, yet practical relevance requires studies on realistic 3D flows. The present review aims to stimulate further development and utilization of know-how on 3D Lagrangian transport and its dissemination to practice. To this end, 3D practical flows are categorized into canonical problems. First, to expose the diversity of Lagrangian transport and create awareness of its broad relevance. Second, to enable knowledge transfer both within and between scientific disciplines. Third, to reconcile practical flows with fundamentals on Lagrangian transport and chaotic advection. This may be a first incentive to structurally integrate the “Lagrangian mindset” into the analysis and design of 3D practical flows.

Significance of Joule heating and viscous heating on heat transport of MoS2–Ag hybrid nanofluid past an isothermal wedge

The problem of flow and heat transport of magneto-composite nanofluid over an isothermal wedge has not been addressed in the literature up to yet. Thus, this article features the laminar transport of Newtonian composite nanomaterial (C2H6O2–H2O hybrid base liquid + MoS2–Ag hybrid nanoparticles) in the presence of exponential space- and temperature-dependent heat source past an isothermal wedge. An incompressible and electrically conducting fluid is assumed. The effects of Joule heating and viscous heating are also accounted. Single-phase nanofluid model and boundary layer approximation are utilized to govern the equations of flow and heat transport phenomena. The solution of the simplified coupled system of dimensionless constraints is obtained by using the Runge–Kutta–Fehlberg method based on the shooting technique. Detailed analysis of active quantities of interest has been presented and discussed. The interesting physical quantities (friction factors and Nusselt number) are estimated. Also, the slope of the data point is calculated in order to estimate the amount of decrease/increase in physical quantities.

Sensitivity Analysis of a Wall Boundary Condition for the Turbulent Pipe Flow of Herschel–Bulkley Fluids

This article follows from a previous study by the authors on the computational fluid dynamics-based analysis of Herschel–Bulkley fluids in a pipe-bounded turbulent flow. The study aims to propose a numerical method that could support engineering processes involving the design and implementation of a waste water transport system, for concentrated domestic slurry. Concentrated domestic slurry results from the reduction in the amount of water used in domestic activities (and also the separation of black and grey water). This primarily saves water and also increases the concentration of nutrients and biomass in the slurry, facilitating efficient recovery. Experiments revealed that upon concentration, domestic slurry flows as a non-Newtonian fluid of the Herschel–Bulkley type. An analytical solution for the laminar transport of such a fluid is available in literature. However, a similar solution for the turbulent transport of a Herschel–Bulkley fluid is unavailable, which prompted the development of an appropriate wall function to aid the analysis of such flows. The wall function (called ψ 1 hereafter) was developed using Launder and Spalding’s standard wall function as a guide and was validated against a range of experimental test-cases, with positive results. ψ 1 is assessed for its sensitivity to rheological parameters, namely the yield stress, the fluid consistency index and the behaviour index and their impact on the accuracy with which ψ 1 can correctly quantify the pressure loss through a pipe. This is done while simulating the flow of concentrated domestic slurry using the Reynolds-Averaged Navier–Stokes (RANS) approach for turbulent flows. This serves to establish an operational envelope in terms of the rheological parameters and the average flow velocity within which ψ 1 is a must for accuracy. One observes that, regardless of the fluid behaviour index, ψ 1 is necessary to ensure accuracy with RANS models only in flow regimes where the wall shear stress is comparable to the yield stress within an order of magnitude. This is also the regime within which the concentrated slurry analysed as part of this research flows, making ψ 1 a requirement. In addition, when the wall shear stress exceeds the yield stress by more than one order (either due to an inherent lower yield stress or a high flow velocity), the regular Newtonian wall function proposed by Launder and Spalding is sufficient for an accurate estimate of the pressure loss, owing to the relative reduction in non-Newtonian viscosity as compared to the turbulent viscosity.

Resolved simulations of single char particle combustion in a laminar flow field

The aim of this work is to study spatially and chemically resolved particle combustion cases to understand chemical and laminar transport processes and to support model development. In the present study, the combustion process of a single char particle located in air or oxy-fuel atmosphere composed of oxygen, carbon dioxide, and steam is investigated. Char burnout is represented in highly resolved numerical simulations including a detailed description of the surface and the gas phase chemistry. At the solid-gas interface, heat and mass fluxes due to the surface reactions involving carbon oxidation and gasification are considered. The model is validated based on experimental results for char burnout phase in a flat flame burner. We perform a comprehensive set of fully resolved reactive 2-D simulations by varying particle size, relative velocity, diluent, and oxygen composition in the surrounding gas. The simulation results are discussed regarding the CO2 and N2 content of the atmosphere highlighting the effects of oxy-fuel combustion. Furthermore, the impact of the particle flow motion on the flame that forms around the char particle is investigated by varying relative Reynolds number with particle size and relative slip velocity.

Convection at an isothermal wall in an enclosure and establishment of stratification

In this experimental–theoretical investigation, we consider a turbulent plume generated by an isothermal wall in a closed cavity and the formation of heat stratification in the interior. The buoyancy of the plume near the wall and the temperature stratification are measured across a vertical plane with the temperature laser induced fluorescence method, which is shown to be accurate and efficient (precision of $0.2\,^{\circ }$C) for experimental studies on convection. The simultaneous measurement of the velocity field with particle image velocimetry allows for the calculation of the flow characteristics such as the Richardson number and Reynolds stress. This enables us to give a refined description of the wall plume, as well as the circulation and evolution of the stratification in the interior. The wall plume is found to have an inner layer close to the heated boundary with a laminar transport of hardly mixed fluid which causes a relatively warm top layer and an outer layer with a transition from laminar to turbulent at a considerable height. The measured entrainment coefficient is found to be dramatically influenced by the increase in stratification of the ambient fluid. To model the flow, the entrainment model of Morton, Taylor & Turner (Proc. R. Soc. Lond. A, vol. 234 (1196), 1956, pp. 1–23) has first been adapted to the case of an isothermal wall. Differences due to their boundary condition of a constant buoyancy flux, modelled with salt by Cooper & Hunt (J. Fluid Mech., vol. 646, 2010, pp. 39–58), turn out to be small. Next, to include the laminar–turbulent transition of the boundary layer, a hybrid model is constructed which is based on the similarity solutions reported by Worster & Leitch (J. Fluid Mech., vol. 156, 1985, pp. 301–319) for the laminar part and the entrainment model for the turbulent part. Finally, the observed variation of the global entrainment coefficient, which is due to the increased presence of an upper stratified layer with a relatively low entrainment coefficient, is incorporated into both models. All models show reasonable agreement with experimental measurements for the volume, momentum and buoyancy fluxes as well as for the evolution of the stratification in the interior. In particular, the introduction of the variable entrainment coefficient improves all models significantly.

Transition modelling implications in the CFD analysis of a turbine nozzle vane cascade tested over a range of Mach and Reynolds numbers

The aerodynamic performance of a gas turbine nozzle vane cascade was investigated over a range of Mach and Reynolds numbers. The work is part of a vast research project aimed at the analysis of fluid dynamics and heat transfer phenomena in cooled blades. In this paper computed results on the “solid vane” (without cooling devices) are presented and discussed in comparison with experimental data. Detailed measurements were provided by the University of Bergamo where the experimental campaign was carried out by means of a subsonic wind tunnel. The impact of boundary layer transition is investigated by using a novel laminar kinetic energy transport model and the widely used Langtry-Menter γ-Reθ,t model. The comparison between calculations and measurements is presented in terms of blade loading distributions, total pressure loss coefficient contours downstream of the cascade, and velocity/turbulence-intensity profiles within the boundary layer at selected blade surface locations at mid-span. It will be shown how transitional calculations compare favorably with experiments.

Computational hydrodynamics and optical performance of inductively-coupled plasma adaptive lenses

This study addresses the optical performance of a plasma adaptive lens for aero-optical applications by using both axisymmetric and three-dimensional numerical simulations. Plasma adaptive lenses are based on the effects of free electrons on the phase velocity of incident light, which, in theory, can be used as a phase-conjugation mechanism. A closed cylindrical chamber filled with Argon plasma is used as a model lens into which a beam of light is launched. The plasma is sustained by applying a radio-frequency electric current through a coil that envelops the chamber. Four different operating conditions, ranging from low to high powers and induction frequencies, are employed in the simulations. The numerical simulations reveal complex hydrodynamic phenomena related to buoyant and electromagnetic laminar transport, which generate, respectively, large recirculating cells and wall-normal compression stresses in the form of local stagnation-point flows. In the axisymmetric simulations, the plasma motion is coupled with near-wall axial striations in the electron-density field, some of which propagate in the form of low-frequency traveling disturbances adjacent to vortical quadrupoles that are reminiscent of Taylor-Gortler flow structures in centrifugally unstable flows. Although the refractive-index fields obtained from axisymmetric simulations lead to smooth beam wavefronts, they are found to be unstable to azimuthal disturbances in three of the four three-dimensional cases considered. The azimuthal striations are optically detrimental, since they produce high-order angular aberrations that account for most of the beam wavefront error. A fourth case is computed at high input power and high induction frequency, which displays the best optical properties among all the three-dimensional simulations considered. In particular, the increase in induction frequency prevents local thermalization and leads to an axisymmetric distribution of electrons even after introduction of spatial disturbances. The results highlight the importance of accounting for spatial effects in the numerical computations when optical analyses of plasma lenses are pursued in this range of operating conditions.

Modelling laminar transport phenomena in a Casson rheological fluid from an isothermal sphere with partial slip

The laminar boundary layer flow and heat transfer of Casson non-Newtonian fluid from a permeable isothermal sphere in the presence of thermal and hydrodynamic slip conditions is analyzed. The surface of the sphere is maintained at a constant temperature. The boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller-box finite-difference scheme. Increasing velocity slip induces acceleration in the flow near the surface of the sphere and the reverse effect further from the surface. Increasing velocity slip consistently enhances temperatures throughout the boundary layer regime. An increase in thermal slip parameter strongly decelerates the flow and also reduces temperatures in the boundary layer regime. An increase in Casson rheological parameter acts to elevate considerably the skin friction (non-dimensional wall shear stress) and this effect is pronounced at higher values of tangential coordinate. Temperatures are however very slightly decreased with increasing values of Casson rheological parameter. Increasing mass flow injection (blowing) at the sphere surface causes a strong acceleration, whereas increasing suction is found to induce the opposite effect. The study finds applications in rheological chocolate food processing.

Design and construction of low shear laminar transport system for the production of nixtamal corn dough

The tortilla is obtained by the traditional process of nixtamalization. This process has two disadvantages: production of liquid waste and it is in batches. Extrusion has resolved the problem of liquid waste, however, extrusion as of yet, has not been able to replace the traditional process of nixtamalization. This is because corn dough is a pseudoplastic fluid, which changes its viscosity in the presence of high shear velocities that occur inside the extruder. With this in mind, the following investigation proposes the mechanical design and construction of a low shear laminar transport system (LSLTS) for the production of corn dough for tortillas. This system consists of two thermally isolated stages: transport and cooking stages. The results showed that the prototype obtained meets the characteristics of homogenous cooking, low shear, absence of liquid waste and the product meets the specifications for nixtamal dough.

Heavy-mineral analysis as a tool in tephrochronology, with an example from the La Sal Mountains, Utah, U.S.A.

Abstract An essentially pure tephra layer on a steep slope in the La Sal Mountains, Utah, U.S.A., is correlated with the 1.65 Ma old Guaje Tephra derived from the Jemez Mountains, New Mexico, U.S.A. The heavy-mineral contents and glass shards in sediments beneath the La Sal tephra layer indicate that tephra constituents are contained in deposits considerably older than the pure layer. This suggests that tephra material may become reworked while retaining its pure character, possibly due to laminar transport or to dislocation in a frozen condition. This raises the need to handle tephrochronological findings with great care.

Numerical Study the Performance of Microfluidic Fuel Cell with Porous Electrodes

Microfluidic fuel cell with flow-through porous electrodes is a new concept design which can significantly improve cell performance. In this paper, a three-dimensional numerical model which is based on mathematical formulations of laminar flow, species transport, and electrochemical reactions was developed to determine the effects of some important physical factors on cell performance. Moreover, this model also can be used to guide further optimization. The numerical simulation results obtained show that the cell performance is considered as functions of volumetric flow rate and porosity value. The peak power density increased almost linearly with the increase of flow rate when it less than 60µL min-1 .However, as the flow rate up to 60µL min-1, the cell performance becomes less sensitive to the increase of flow rate, and the corresponding maximum fuel utilization was achieved at the porosity value of 0.65.

Modelling laminar transport phenomena in a Casson rheological fluid from an isothermal sphere with partial slip in a non-Darcy porous medium

The flow and heat transfer of Casson fluid from a permeable isothermal sphere in the presence of slip condition in a non-Darcy porous medium is analyzed. The sphere surface is maintained at a constant temperature. The boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller-box finite-difference scheme. Increasing the velocity slip parameter is found to decrease the velocity and boundary layer thickness and increases the temperature and the boundary layer thickness. The velocity decreases with the increase the non-Darcy parameter and is found to increase the temperature. The velocity increases with the increase the Casson fluid parameter and is found to decrease the temperature. The Skin-friction coefficient and the local Nusselt number is found to decrease with the increase in velocity and thermal slip parameters respectively.

Modelling laminar transport phenomena in a Casson rheological fluid from a horizontal circular cylinder with partial slip

The laminar boundary layer flow and heat transfer of Casson non-Newtonian fluid from a permeable horizontal cylinder in the presence of thermal and hydrodynamic slip conditions is analysed. The cylinder surface is maintained at a constant temperature. The boundary layer conservation equations, which are parabolic in nature, are normalised into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller–Box finite-difference scheme. Increasing velocity slip induces acceleration in the flow near the cylinder surface and the reverse effect further from the surface. Increasing velocity slip consistently enhances temperatures throughout the boundary layer regime. An increase in thermal slip parameter strongly decelerates the flow and also reduces temperatures in the boundary layer regime. An increase in Casson rheological parameter acts to elevate considerably the skin friction (non-dimensional wall shear stress) and this effect is pronounced at higher values of tangential coordinate. Temperatures are however very slightly decreased with increasing values of Casson rheological parameter. Increasing mass flow injection (blowing) at the cylinder surface causes a strong acceleration, whereas increasing suction is found to induce the opposite effect. The study finds applications in rheological chocolate food processing.

Stirring, stretching and transport generated by a pair of like-signed vortices

We consider a pair of like-signed, initially elliptical vortices with uniform vorticity distribution embedded in an incompressible, inviscid fluid occupying a two-dimensional, infinite domain. We characterize this finite-time, aperiodic, dynamical system in terms of its fixed points and separatrices, which divide the flow into inner core, inner recirculation, outer recirculation regions and outer flow. We numerically simulate the time evolution of the vortex pair using a contour dynamics algorithm. The rotational and co-rotational motion of the vortices perturb the separatrices, which undergo to deformations, yielding a tangle whose complexity increases as the amplitude of the perturbation increases. We analyse the dynamics of the tangle and explain the transport of fluid between different regions. We use two diagnostics to quantify stirring: stretching of the interface and the mix-norm. These two diagnostics characterize stirring in contradicting ways and present different sensitivity to the parameters considered. We find that stretching is dominated by the chaotic advection induced within the inner core and inner recirculation regions, whereas the mix-norm is dominated by the laminar transport induced within the outer recirculation regions. For pairs of vortices of small aspect ratio, stretching is piecewise linear and the mix-norm does not decrease monotonically. We show that these two effects are strongly coupled and synchronized with the rotational motion of the vortices. Since the nominal domain is unbounded, we quantify stirring on three concentric, circular domains. One domain nearly encloses the outer separatrices of the vortex pair, one is smaller and one larger than the first one. We show that the mix-norm is very sensitive to the size of the domain, while stretching is not. To quantify the sensitivity of stirring to the geometry of the initial concentration field, we consider, as an initial scalar field, two concentrations delimited by a straight-line interface of adjustable orientation. We show that the interface passing through the centroids of the vortices is the one most efficiently stretched, while the initial concentration field with an orthogonal interface is the most efficiently stirred. Finally, we investigate the effects of the angular impulse on the stirring performance of the vortex pair. Stretching is very sensitive to the angular impulse, while the mix-norm is not. We show that there is a value of the angular impulse which maximizes stretching and argue that this is due to two competing mechanisms.

Physical atmospheric structure and tropospheric mixing information in vertical profiles of atmospheric CO2 mixing ratios

Vertical distribution of atmospheric CO2 mixing ratios, as well as CO2 vertical variance and gradient are related to the vertical stability at the time of measurement, to the transport of coherent upstream plumes studied through changes in the upstream surface influence or to the historic mixing processes and dispersive behavior. Three vertical profiles of CO2 mixing ratios measured from 900 to 4200 m above sea level (masl) in 2006 at La Muela, Spain (LMU, 41.60°N 1.10°W, 570 masl) are examined. Changes in CO2 mixing ratio are associated with changes of the atmospheric physical parameters on the day of the survey; and with the transport of coherent air masses. Its consistency is examined through changes of the historical horizontal dispersion and chaotic mixing dynamics of air masses during the four days prior to measurements. A climatology of Lagrangian backward simulations run once a week at four altitudes (600, 1200, 2500 and 4000 masl) at LMU for 2006 shows that dispersion in these altitudes is superdiffusive (exponent coefficient γ > 1/2) and mixing follows a chaotic dynamics (power law exponent λ > 0) at all altitudes and in all seasons. Furthermore, a Horizontal Mixing Discontinuity (HMD) at ∼2500 masl separates two layers with different constraints on vertical mixing. Above the HMD, more coherent air masses and laminar transport characterizes the dynamics of atmospheric horizontal mixing whereas below it, filamentation and chaotic mixing dominate horizontal mixing. In the lower part of the vertical profile, within the ABL, mixing takes place by convection. Chaotic mixing below the HMD induces the boundary layer entrainment. Results highlight that there are two main discontinuities in the air column which separates different atmospheric dynamics. The ABL is driven by local meteorological conditions of the site at the sampling time; the HMD is driven by the synoptic‐scale historical mixing conditions of air masses. The effect of horizontal transport in the free troposphere should be considered equally as important as the local vertical mixing processes in the atmospheric boundary layer when interpreting CO2 vertical gradients. The dispersive exponents can be used to identify the transport of coherent plumes from anthropogenic emissions with different carbon composition that the one‐single backtrajectories models do not detect.

Interannual variability of ozone in the winter lower stratosphere and the relationship to lamina and irreversible transport

We use the high‐resolution dynamic limb sounder (HIRDLS) high‐vertical resolution ozone profiles in the northern hemisphere lower stratosphere to examine the meridional transport out of the tropics. We focus on February 2005–2007 when there are differences in the dynamical background in the lower stratosphere due to the states of the quasi‐biennial oscillation and polar vortex. HIRDLS data reveal a large number of low ozone laminae that have the characteristics of tropical air at midlatitudes. More laminae are observed in February in 2006 than in 2005 or 2007. Because laminae can form, move out of the tropics, and return to the tropics without mixing into the midlatitude ozone field, the number of laminae is not directly related to the net transport. We use equivalent latitude coordinates to discriminate between reversible and irreversible laminar transport. The equivalent latitude analysis shows greater irreversible transport between the tropics and lower midlatitudes in both 2005 and 2007 compared to 2006 despite the higher number of laminae observed in 2006. Our conclusion that there was more irreversible transport of tropical air into the lower midlatitudes in 2005 and 2007 is supported by equivalent length analysis of mixing using microwave limb sounder N2O measurements. This study shows that reversibility must be considered in order to infer the importance of lamination to net transport.

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 10 7–10 8 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.

Thermal Transport Regimes and Effects of Prandtl Number in Molten Pool Transport in Laser Surface Melting Processes

The effects of Prandtl number of the molten metal in weld pool convection are studied based on a systematic scaling analysis. It is demonstrated that for a very small Prandtl number the weld pool morphology is predominantly determined by heat conduction whereas convection has a marginal effect on the molten pool morphology. By contrast, for relatively greater values of Prandtl number the convection pattern in the molten pool significantly affects the pool shape and size. The criteria, which demarcate these two regimes, are estimated by a detailed scaling argument. It is also shown from scaling analysis that turbulence in the molten pool affects momentum and thermal transport differently. Turbulence may also significantly affect the momentum transport of the pool whereas the thermal transport is marginally affected. A regime diagram is constructed based on scaling arguments where the above flow regimes are clearly indicated. In order to validate the scaling arguments on which the regime diagram is based, two three dimensional simulations are carried out for laser welding of iron (for Fe, Prandtl number in order of 0.1) and copper (for Cu, Prandtl number in the order of 0.01). It is found that in the case of Cu, the weld pool obtained from conduction solution is almost the same as the pool morphology obtained using laminar and turbulent transport models. By contrast, in the case of Fe, the weld pools obtained from laminar and turbulent transport models are significantly different from each other, and are also different from the pool obtained from the heat conduction solution.

CFD analyses of complex flows

Computational fluid dynamics (CFD) of complex processes and complicated geometries embraces the transport of momentum, heat, and mass including the description of reaction kinetics and thermodynamics. The paper outlines the numerical models available for analyzing these processes and presents examples of such methodology. The unprecedented growth in computer capability has resulted in efficient simulations of most transport phenomena. The aerospace's interest in high-pressure turbulent combustion has created efficient computational tools for analyzing run-away-reactions in the process industries. Practical turbulence models, generalized thermodynamic properties, and extensive chemical kinetics data bases are currently used in three-dimensional, steady-state simulations. However, industrial needs have challenged CFD modelers to improve their flow solvers in order to simulate flows with more complicated physics, such as spray combustion, acoustic waves, transient start-up and shut-down, and flow instabilities. In addition, the practicality and efficiency of numerical simulations are highly dependent on the submodels employed, such as reaction mechanisms and turbulence models. There has been some progress in generalizing CFD tools, but more development is needed. Most of all, more high-quality and critical test data are required to validate the CFD simulations of complex processes. The laminar transport equations have been averaged by various means to locally describe both turbulent and multi-phase flows. Spray combustion, stirred-tank reactors, fluidization of catalytic beds, and highly exothermic supercritical reactors are among the several validated examples, which illustrate today's technology. The designer's access to public-domain, open-source software offers powerful methodology for his use. Such software and the variety of available modeling techniques will be inventoried to demonstrate the scope of computational transport methodology. The current state of CFD models will be assessed to address the need for future research.