Gas Drag Research Articles

Global Modeling of Nebulae with Particle Growth, Drift, and Evaporation Fronts. III. Redistribution of Refractories and Volatiles

Formation of the first planetesimals remains an unsolved problem. Growth by sticking must initiate the process, but multiple studies have revealed a series of barriers that can slow or stall growth, most of them due to nebula turbulence. In a companion paper, we study the influence of these barriers on models of fractal aggregate and solid, compact particle growth in a viscously evolving solar-like nebula for a range of turbulent intensities α t = 10−5–10−2. Here, we examine how the disk composition in these same models changes with time. We find that advection and diffusion of small grains and vapor, and radial inward drift for larger compact particles and fractal aggregates, naturally lead to diverse outcomes for planetesimal composition. Larger particles can undergo substantial inward radial migration due to gas drag before being collisionally fragmented or partially evaporating at various temperatures. This leads to enhancement of the associated volatile in both vapor inside, and solids outside, their respective evaporation fronts, or snowlines. In cases of lower α t, we see narrow belts of volatile or supervolatile material develop in the outer nebula, which could be connected to the bands of pebbles seen by the Atacama Large Millimeter/submillimeter Array. Volatile bands, which migrate inwards as the disk cools, can persist over long timescales as their gas phase continues to advect or diffuse outward across its evaporation front. These belts could be sites where supervolatile-rich planetesimals form, such as the rare CO-rich and water-poor comets; giant planets formed just outside the H2O snowline may be enhanced in water.

Planetesimal Dynamics in the Presence of a Giant Planet. II. Dependence on Planet Mass and Eccentricity

The presence of an early-formed giant planet in the protoplanetary disk has mixed influence on the growth of other planetary embryos. Gravitational perturbation from the planet can increase the relative velocities of planetesimals at the mean motion resonances to very high values and impede accretion at those locations. However, gas drag can also align the orbital pericenters of equal-size planetesimals in certain disk locations and make them dynamically quiet and “accretion-friendly” locations for planetesimals of similar sizes. Following the previous paper, where we investigated the effect of a Jupiter-like planet on an external planetesimal disk, we generalize our findings to extrasolar planetary systems by varying the planet parameters. In particular, we focus on the dependence of the planetesimal relative velocities on the mass and eccentricity of the existing planet. We found that the velocity dispersion of identical-mass particles increases monotonically with increasing planet mass. Meanwhile, the dependence of the relative velocity between different-mass planetesimals on their mass ratio becomes weaker as the planet mass increases. While the relative velocities generally increase with increasing planet eccentricity, the velocity dispersion of lower-mass particles (m ≲ 1018 g) is almost independent of planet eccentricity owing to their strong coupling to gas. We find that the erosion limits are met for a wider range of parameters (planet mass/eccentricity, planetesimal mass ratio) when the planetesimal size decreases. Our results could provide some clues for the formation of Saturn’s core, as well as the architecture of some exoplanetary systems with multiple cold giant planets.

Unnecessary risks created by uncontrolled rocket reentries

Most space launches result in uncontrolled rocket body reentries, creating casualty risks for people on the ground, at sea and in aeroplanes. These risks have long been treated as negligible, but the number of rocket bodies abandoned in orbit is growing, while rocket bodies from past launches continue to reenter the atmosphere due to gas drag. Using publicly available reports of rocket launches and data on abandoned rocket bodies in orbit, we calculate approximate casualty expectations due to rocket body reentries as a function of latitude. The distribution of rocket body launches and reentries leads to the casualty expectation (that is, risk to human life) being disproportionately borne by populations in the Global South, with major launching states exporting risk to the rest of the world. We argue that recent improvements in technology and mission design make most of these uncontrolled reentries unnecessary, but that launching states and companies are reluctant to take on the increased costs involved. Those national governments whose populations are being put at risk should demand that major spacefaring states act, together, to mandate controlled rocket reentries, create meaningful consequences for non-compliance and thus eliminate the risks for everyone.

Monte Carlo Models of Comet Dust Tails Observed from the Ground

Dust particles leaving the comet nucleus surface are entrained by the gas within the first few nuclear radius distances and are subjected to a complex hydrodynamical environment. From distances of about 20 nuclear radii outwards, the particles decouple from the accelerating gas and are mainly affected by solar gravity and radiation pressure for small-sized nuclei. Their motion is then a function of their so-called β parameter, which is the ratio of the radiation pressure force to gravity force, and their velocity when the gas drag vanishes. At a given observation time, the position of those particles projected on the sky plane form the coma, tail and trail structures that can be observed from ground-based or space-borne instrumentation. Monte Carlo models, based on the computer simulation of the Keplerian trajectories of a large set of dust particles, provide the best possible approach to extract the dust environment parameters from the observed scattered solar light or thermal emission. In this paper, we describe the Monte Carlo code along with some successful applications of such technique to a number of targets.

Hydrodynamic behaviors of adiabatic and diabatic two-phase flow within various particle beds

In this paper, we comprehensively evaluate the hydrodynamic behaviors of fluid flow through porous particle beds using various types of experimental and numerical results including single-phase flows of both gas and liquid, and two-phase flows under both adiabatic and diabatic conditions. Moreover, the examined porous beds were constructed with both uniform and non-uniform sized particles (range of particle diameters: 0.5–10 mm). The experimental data clearly showed the featured trends of the two-phase pressure loss depending on relative intensity of the individual forces, such as gravitational, gas drag, liquid drag, and interfacial drag forces. Particularly, the numerical prediction results to the pressure loss indicate the importance of a proper model for the interfacial drag force considering the flow regime transition within the particle beds. From the two-phase experiments, the counter-current flooding limit (CCFL) and dryout heat flux (DHF) phenomena were observed for adiabatic and diabatic (boiling) cases, respectively. The existing models greatly overestimated the superficial gas velocity at which the CCFL occurs in the adiabatic experiments, and we modified the assumption of zero liquid flow into the gravitational liquid flow resisted by the viscous force. The modifications can properly predict the two-phase pressure loss and CCFL in the adiabatic experiments. The results of two-phase pressure loss and DHF in the boiling experiments indicates a relatively strong effect of the interfacial drag force due to the phase-change. We examined and analyzed quantitatively the physical relevance of existing models to simulate the hydrodynamics governing boiling phenomenon in porous beds. Additionally, the phenomenological descriptions associated with the numerical results on the local thermal and hydraulic behaviors can contribute to give a physical insight into the complicated two-phase flow phenomena involving the phase-change in porous particle beds.

LEGWORK: A Python Package for Computing the Evolution and Detectability of Stellar-origin Gravitational-wave Sources with Space-based Detectors

We present LEGWORK (LISA Evolution and Gravitational Wave Orbit Kit), an open-source Python package for making predictions about stellar-origin gravitational-wave sources and their detectability in LISA or other space-based gravitational-wave detectors. LEGWORK can be used to evolve the orbits of sources due to gravitational-wave emission, calculate gravitational-wave strains (using post-Newtonian approximations), compute signal-to-noise ratios, and visualize the results. It can be applied to a variety of potential sources, including binaries consisting of white dwarfs, neutron stars, and black holes. Although we focus on double compact objects, in principle LEGWORK can be used for any system with a user-specified orbital evolution, such as those affected by a third object or gas drag. We optimized the package to make it efficient for use in population studies, which can contain tens of millions of sources. This paper describes the package and presents several potential use cases. We explain in detail the derivations of the expressions behind the package as well as identify and clarify some discrepancies currently present in the literature. We hope that LEGWORK will enable and accelerate future studies triggered by the rapidly growing interest in gravitational-wave sources.

The dissipation of the solar nebula constrained by impacts and core cooling in planetesimals

Rapid cooling of planetesimal cores has been inferred for several iron meteorite parent bodies based on metallographic cooling rates, and linked to the loss of their insulating mantles during impacts. However, the timing of these disruptive events is poorly constrained. Here, we used the short-lived 107Pd / 107Ag decay system to date rapid core cooling by determining Pd-Ag ages for iron meteorites. We show closure times for the iron meteorites equate to cooling in the timeframe ~7.8 to 11.7 Myr after CAI, and indicate that an energetic inner Solar System persisted at this time. This likely results from the dissipation of gas in the protoplanetary disk, after which the damping effect of gas drag ceases. An early giant planet instability between 5 and 14 Myr after CAI could have reinforced this effect. This correlates well with the timing of impacts recorded by the Pd Ag system for iron meteorites.

A low accretion efficiency of planetesimals formed at planetary gap edges

Observations and models of giant planets indicate that such objects are enriched in heavy elements compared to solar abundances. The prevailing view is that giant planets accreted multiple Earth masses of heavy elements after the end of core formation. Such late solid enrichment is commonly explained by the accretion of planetesimals. Planetesimals are expected to form at the edges of planetary gaps, and here we address the question of whether these planetesimals can be accreted in large enough amounts to explain the inferred high heavy element contents of giant planets. We performed a series of N-body simulations of the dynamics of planetesimals and planets during the planetary growth phase, taking gas drag into account as well as the enhanced collision cross section caused by the extended envelopes. We considered the growth of Jupiter and Saturn via gas accretion after reaching the pebble isolation mass and we included their migration in an evolving disk. We find that the accretion efficiency of planetesimals formed at planetary gap edges is very low: less than 10% of the formed planetesimals are accreted even in the most favorable cases, which in our model corresponds to a few Earth masses. When planetesimals are assumed to form beyond the feeding zone of the planets, extending to a few Hill radii from a planet, accretion becomes negligible. Furthermore, we find that the accretion efficiency increases when the planetary migration distance is increased and that the efficiency does not increase when the planetesimal radii are decreased. Based on these results, we conclude that it is difficult to explain the large heavy element content of giant planets with planetesimal accretion during the gas accretion phase. Alternative processes most likely are required, such as accretion of vapor deposited by drifting pebbles.

Web of resonances and possible path of evolution of the small Uranian satellites

Satellite systems around giant planets are immersed in a region of complex resonant configurations. Understanding the role of satellite resonances contributes to comprehending the dynamical processes in planetary formation and posterior evolution. Our main goal is to analyse the resonant structure of small moons around Uranus and propose different scenarios able to describe the current configuration of these satellites. We focus our study on the external members of the regular satellites interior to Miranda, namely Rosalind, Cupid, Belinda, Perdita, Puck, and Mab, respectively. We use N-body integrations to perform dynamical maps to analyse their dynamics and proximity to two-body and three-body mean-motion resonances (MMR). We found a complicated web of low-order resonances amongst them. Employing analytical prescriptions, we analysed the evolution by gas drag and type-I migration in a circumplanetary disc (CPD) to explain different possible histories for these moons. We also model the tidal evolution of these satellites using some crude approximations and found possible paths that could lead to MMRs crossing between pairs of moons. Finally, our simulations show that each mechanism can generate significant satellite radial drift leading to possible resonant capture, depending on the distances and sizes.

A “no-drift” runaway pile-up of pebbles in protoplanetary disks

Context. Forming planetesimals from pebbles is a major challenge in our current understanding of planet formation. In a protoplanetary disk, pebbles drift inward near the disk midplane via gas drag and they may enter a zone of reduced turbulence (dead zone). In this context, we identified that the backreaction of the drag of pebbles onto the gas could lead to a runaway pile-up of pebbles, the so-called no-drift mechanism for the formation of planetesimals. Aims. We improve upon the previous study of planetesimal formation from accumulating pebbles via the no-drift mechanism by investigating the nature and characteristics of the resultant planetesimal belt. Methods. We performed 1D diffusion-advection simulations of drifting pebbles in the outer region of a modeled dead zone by including a pebble-gas backreaction to the radial drift of pebbles and including planetesimal formation via the streaming instability. We independently considered the parameters that regulate gas accretion (αacc) and vertical stirring of pebbles in the disk midplane (αmid). In this study, the pebble-to-gas mass flux (Fp/g) was fixed as a parameter. Results. We find that, for a constant Fp/g, after the criteria of the no-drift mechanism are satisfied, planetesimals initially form within a narrow ring whose width expands as accumulating pebbles radially diffuse over time. The system finally reaches a steady-state where the width of the planetesimal belt no longer changes, followed by a continuous formation of planetesimals. A non-negligible total mass of planetesimals (more than one Earth mass) is formed via the no-drift mechanism for a disk having Fp/g ≳ 0.1 for more than ~10–100 kyr with nominal parameters: a gas mass flux of ≳10−8 M⊙ yr−1, τs ≃ 0.01−0.1, αmid ≲ 10−4, and αacc ≃ 10−3−10−2 at r ≲ 10 au, where r, τs, αmid, and αacc are the heliocentric distance, the Stokes number, and the parameters in a dead zone controlling the efficiencies of vertical turbulent diffusion of pebbles (i.e., scale height of pebbles) and gas accretion of the α-disk (i.e., gas surface density), respectively.

Dust Dynamics in Transitional Disks: Clumping and Disk Recession

Abstract The role of radiation pressure in dust migration and the opening of inner cavities in transitional disks is revisited in this paper. Dust dynamics including radiation pressure is often studied in axisymmetric models, but in this work, we show that highly non-axisymmetric features can arise from an instability at the inner disk edge. Dust grains clump into high density features there, allowing radiation to leak around them and penetrate deeper into the disk, changing the course of dust migration. Our proof-of-concept, two-dimensional, vertically averaged simulations show that the combination of radiation pressure, shadowing, and gas drag can produce a net outward migration, or recession, of the dust component of the disk. The recession speed of the inner disk edge is on the order of 10−5 times Keplerian speed in our parameter space, which is faster than the background viscous flow, assuming a Shakura–Sunyaev viscosity α ≲ 10−3. This speed, if sustained over the lifetime of the disk, can result in a dust cavity as large as tens of astronomical units.

Studying the impacts of droplets depositing from the gas core onto a gas-sheared liquid film with stereoscopic BBLIF technique.

In annular gas-liquid flow, the droplets are torn from the liquid film surface by the turbulent gas stream, accelerate due to the gas drag force and eventually deposit back onto the wavy film surface, hitting it with a high speed at a shallow angle. Here we investigate individual impacts of droplets in annular flow in a horizontal rectangular duct, in a wide range of gas and liquid flow rates for three different working liquids. A stereoscopic modification of the Brightness-Based Laser-Induced Fluorescence technique is developed to reconstruct the spatiotemporal evolution of waves on the film surface in three-dimensional space, simultaneously with capturing instantaneous position, size, and three velocity components of the individual droplets and bubbles. Droplet impacts create furrows (with bubbles entrapment) and craters (with secondary droplets) on film surface. Propagation of the furrowing droplet may be facilitated by gliding on an air layer but hampered by the ripples on the film surface. The number of entrapped bubbles is mainly defined by the droplet diameter and by liquid properties. The saturation of the number of bubbles entrapped due to furrow impacts is confirmed experimentally. The secondary droplets are rarely created due to break-up of the crater crown. In most cases, the main role in secondary entrainment is played by longitudinal movement of the impacting droplet, which helps the droplet to escape the impact-created crater and detach from the film, creating various transient liquid structures, with different ways to create secondary droplets.

The vertical structure of debris discs and the impact of gas

ABSTRACT The vertical structure of debris discs provides clues about their dynamical evolution and the collision rate of the unseen planetesimals. Thanks to the ever-increasing angular resolution of contemporary instruments and facilities, we are beginning to constrain the scale height of a handful of debris discs, either at near-infrared or millimeter wavelengths. None the less, this is often done for individual targets only. We present here the geometric modeling of eight discs close to edge-on, all observed with the same instrument (SPHERE) and using the same mode (dual-beam polarimetric imaging). Motivated by the presence of CO gas in two out of the eight discs, we then investigate the impact that gas can have on the scale height by performing N-body simulations including gas drag and collisions. We show that gas can quickly alter the dynamics of particles (both in the radial and vertical directions), otherwise governed by gravity and radiation pressure. We find that, in the presence of gas, particles smaller than a few tens of microns can efficiently settle toward the midplane at the same time as they migrate outward beyond the birth ring. For second generation gas (Mgas ≤ 0.1 M⊕), the vertical settling should be best observed in scattered light images compared to observations at millimeter wavelengths. But if the gas has a primordial origin (Mgas ≥ 1 M⊕), the disc will appear very flat both at near-infrared and sub-mm wavelengths. Finally, far beyond the birth ring, our results suggest that the surface brightness profile can be as shallow as ∼−2.25.

Decoupling of chemical and isotope fractionation processes during atmospheric heating of micrometeorites

Micrometeorites experience varying degrees of evaporation and mixing with atmospheric oxygen during atmospheric entry. Evaporation due to gas drag heating alters the physicochemical properties of fully melted cosmic spherules (CSs), including the size, chemical and isotopic compositions and is thus expressed in its chemical and isotopic signatures. However, the extent of evaporation and atmospheric mixing in CSs often remains unclear, leading to uncertainties in precursor body identification and statistics. Several studies have previously estimated the extent of evaporation based on the contents of major refractory elements Ca and Al in combination with the determined Fe/Si atomic ratios. Similarly, attempts have been made to design classification schemes based on isotopic variations. However, a full integration of any previously defined chemical classification schemes with the observed isotopic variability has not yet been successful. As evaporation can lead to both chemical and isotope fractionation, it is important to verify whether the estimated degrees of evaporation based on chemical and isotopic proxies converge. Here, we have analysed the major and trace element compositions of 57 chondritic (mostly V-type) CSs, along with their Fe isotope ratios. The chemical (Zn, Na, K or CaO and Al2O3 concentrations) and δ56Fe isotope fractionation measured in these particles show no correlation. The interpretation of these results is twofold: (i) isotopic and chemical fractionation are governed by distinct processes or (ii) the proxies selected for chemical and isotope fractionation are inadequate. While the initial Fe isotopic ratios of chondrites are constrained within a relatively narrow range (0.005 ± 0.008‰ δ56Fe), the chemical compositions of CSs display larger variability. Cosmic spherules are thus often not chemically representative of their precursor bodies, due to their small size. As oxygen isotopes are commonly used to refine the precursor bodies of meteorites, triple oxygen isotope ratios were measured in thirty-seven of the characterized CSs. Based on the relationship between δ18O and δ57Fe, the evaporation effect on the O isotope system can be calculated, which allows for a more accurate parent body determination. Using this correction method, two ‘Group 4’ spherules with strongly variable degrees of isotope fractionation (δ56Fe of ∼1.0‰ and 29.1‰, respectively) could be distinguished. Furthermore, it was observed that all CSs that probably have a OC-like heritage underwent roughly the same degree of atmospheric mixing (∼8‰ δ18O). This highlights the potential of including Fe isotope measurements to the regular methodologies applied to CS studies.

Large planets may not form fractionally large moons

One of the unique aspects of Earth is that it has a fractionally large Moon, which is thought to have formed from a Moon-forming disk generated by a giant impact. The Moon stabilizes the Earth’s spin axis at least by several degrees and contributes to Earth’s stable climate. Given that impacts are common during planet formation, exomoons, which are moons around planets in extrasolar systems, should be common as well, but no exomoon has been confirmed. Here we propose that an initially vapor-rich moon-forming disk is not capable of forming a moon that is large with respect to the size of the planet because growing moonlets, which are building blocks of a moon, experience strong gas drag and quickly fall toward the planet. Our impact simulations show that terrestrial and icy planets that are larger than ~1.3−1.6R⊕ produce entirely vapor disks, which fail to form a fractionally large moon. This indicates that (1) our model supports the Moon-formation models that produce vapor-poor disks and (2) rocky and icy exoplanets whose radii are smaller than ~1.6R⊕ are ideal candidates for hosting fractionally large exomoons.

Experimental and computational study on thermal and fluid behaviours of powder layer during selective laser melting additive manufacturing

The movability of powder layer such as spattering and denudation is a major cause of defect formation and quality uncertainty in selective laser melting (SLM) additive manufacturing. Currently, the detailed thermal and fluid behaviours of the powder layer during laser scan process are still not fully understood. In this work, we employ a combination of high-speed imaging and multi-physics modelling to elucidate the thermal and fluid behaviours of the powder layer during the laser scanning process. The particle spattering speed, particle trajectory, and denudation zone of the powder layer are quantified. The sensitivity of particles’ thermo-fluid behaviours to the laser power intensity is also investigated. The multi-physics simulation is used to reproduce the scanning process of the powder layer with various laser power intensities. Detailed physics that result in the observed powder layer motion, such as hot metal vapour flow, ambient gas flow, drag force and heat flux on particles are investigated. This provides deeper insights into the thermal fluid dynamics of the powder layers. Potential ways to reduce the spattering and denudation of the powder layer during SLM process are discussed.

Interstellar Planetesimals: Potential Seeds for Planet Formation?

Abstract We investigate the trapping of interstellar objects during the early stages of star and planet formation. Our results show a very wide range of possible values that will be narrowed down as the population of interstellar objects becomes better characterized. When assuming a background number density of 2 · 1015 pc−3 (based on 1I’s detection), a velocity dispersion of 30 km s−1, and an equilibrium size distribution, the number of interstellar objects captured by a molecular cloud and expected to be incorporated to each protoplanetary disk during its formation is O(109) (50 cm–5 m), O(105) (5–50 m), O(102) (50–500 m), O(10−2) (500 m–5 km). After the disk has formed, the number of interstellar objects it can capture from the ISM during its lifetime is 6 · 1011 (50 cm–5 m), 2 · 108 (5–50 m), 6 · 104 (50–500 m), 20 (500 m–5 km); in an open cluster where 1% of stars have undergone planet formation, these values increase by a factor of O(102–103). These trapped interstellar objects might be large enough to rapidly grow into larger planetesimals via the direct accretion of the subcm-sized dust grains in the protoplanetary disk before they drift in due to gas drag, helping overcome the meter-size barrier, acting as “seeds” for planet formation. They should be considered in future star and planet formation models, as well as in the potential spread of biological material across the Galaxy.

Dynamics of irregularly shaped cometary particles subjected to outflowing gas and solar radiative forces and torques

ABSTRACTThe dynamics of irregularly shaped particles subjected to the combined effect of gas drag and radiative forces and torques in a cometary environment is investigated. The equations of motion are integrated over distances from the nucleus surface up to distances where the gas drag is negligible. The aerodynamic forces and torques are computed assuming a spherically symmetric expanding gas. The calculations are limited to particle sizes in the geometric optics limit, which is the range of validity of our radiative torque calculations. The dynamical behaviour of irregular particles is quite different to those exhibited by non-spherical but symmetric particles such as spheroids. An application of the dynamical model to comet 67P/Churyumov–Gerasimenko, the target of the Rosetta mission, is made. We found that, for particle sizes larger than ∼10 μm, the radiative torques are negligible in comparison with the gas-driven torques up to a distance of ∼100 km from the nucleus surface. The rotation frequencies of the particles depend on their size, shape, and the heliocentric distance, while the terminal velocities, being also dependent on size and heliocentric distance, show only a very weak dependence on particle shape. The ratio of the sum of the particles projected areas in the sun-to-comet direction to that of the sum of the particles projected areas in any direction perpendicular to it is nearly unity, indicating that the interpretation of the observed u-shaped scattering phase function by Rosetta/OSIRIS on comet 67P coma cannot be linked to mechanical alignment of the particles.

Theoretical and experimental insight into the homogeneous expansion of wet particles in a fluidized bed

The presence of liquid in a fluidized bed induces a homogeneous bed expansion at incipient fluidization, which improves the fluidization quality by enhancing the gas-holding capacity of emulsion phase. This paper made an insight into the expansion of wet bed through theoretical and experimental approaches. The bed expansion ratio increases with particle diameter and liquid surface tension, and hardly changes with liquid viscosity due to the absence of viscous term in liquid bridge force. The expansion ends up as the tensile strength of wet bed equals to the shear stress from gas drag force. The superficial gas velocity at this point is the complete fluidization velocity, Ucf. Theoretical calculation shows that Ucf sharply increases then gradually saturates with increasing liquid amount. The tensile strength of wet bed is most sensitive to the superficial gas velocity, followed by the particle diameter. The effect of liquid amount is the smallest. From an optimization perspective, increasing particle diameter and liquid surface tension can enhance the gas-holding capacity of a wet bed during fluidization.

Modeling of Melt Flow and Heat Transfer in Stationary Gas Tungsten Arc Welding with Vertical and Tilted Torches.

A 3D numerical simulation was conducted to study the transient development of temperature distribution in stationary gas tungsten arc welding with filler wire. Heat transfer to the filler wire and the workpiece was investigated with vertical (90°) and titled (70°) torches. Heat flux, current flux, and gas drag force were calculated from the steady-state simulation of the arc. The temperature in the filler wire was determined at three different time intervals: 0.12 s, 0.24 s, and 0.36 s. The filler wire was assumed not to deform during this short time, and was therefore simulated as solid. The temperature in the workpiece was calculated at the same intervals using heat flux, current flux, gas drag force, Marangoni convection, and buoyancy. It should be noted that heat transfer to the filler wire was faster with the titled torch compared to the vertical torch. Heat flux to the workpiece was asymmetrical with both the vertical and tilted torches when the filler wire was fully inserted into the arc. It was found that the overall trends of temperature contours for both the arc and the workpiece were in good agreement. It was also observed that more heat was transferred to the filler wire with the 70° torch compared with the 90° torch. The melted volume of the filler wire (volume above 1750 °K) was 12 mm3 with the 70° torch, compared to 9.2 mm3 with the 90° torch.