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All sourcesNASA NTRSDOE OSTI
NASA NTRS2016

NuSTAR Discovery of a Cyclotron Line in the Accreting X-Ray Pulsar IGR J16393-4643

The high-mass X-ray binary and accreting X-ray pulsar IGR J16393-4643 was observed by the Nuclear Spectroscope Telescope Array in the 3-79 keV energy band for a net exposure time of 50 ks. We present the results of this observation which enabled the discovery of a cyclotron resonant scattering feature with a centroid energy of -29.3(sup +1.1)(sub -1.3) keV. This allowed us to measure the magnetic field strength of the neutron star for the first time: B = (2.5 +/- 0.1) x 10(exp 12) G. The known pulsation period is now observed at 904.0+/- 0.1 s. Since 2006, the neutron star has undergone a long-term spin-up trend at a rate of P= -2 x 10(exp -8) s s(exp -1) (-0.6 s per year, or a frequency derivative of v = 3 x 10(exp -14) Hz s(exp -1)). In the power density spectrum, a break appears at the pulse frequency which separates the zero slope at low frequency from the steeper slope at high frequency. This addition of angular momentum to the neutron star could be due to the accretion of a quasi-spherical wind, or it could be caused by the transient appearance of a prograde accretion disk that is nearly in corotation with the neutron star whose magnetospheric radius is around 2 x 10(exp 8) cm.

accretion disks – gamma-ray burst: general – s↗
DOE OSTI2022

Self-interacting dark scalar spikes around black holes via relativistic Bondi accretion

For this work, we consider the spike mass density profile in a dark halo by self-consistently solving the relativistic Bondi accretion of dark matter onto a non-spining black hole of mass M. We assume that the dominant component of the dark matter in the halo is a Standard model gauge-singlet scalar. Its mass m ≃ 10 -5 eV and quartic self-coupling λ ≲ 10 19 are constrained to be compatible with the properties of galactic dark halos. In the hydrodynamic limit, we find that the accretion rate is bounded from below, M min = 96πG 2 M 2 m 4 /λ$\hbar$ 3 . Therefore, for M = 10 6 M ⊙ we have M min ≃ 1.41 x 10 -9 M ⊙ yr -1 , which is subdominant compared to the Eddington accretion of baryons. The spike density profile ρ0(r) within the self-gravitating regime cannot be fitted well by a single-power law but a double-power one. Despite that, we can fit ρ 0 (r) piecewise and find that ρ 0 (r) ∝ r -1.20 near the sound horizon, ρ 0 (r) ∝ r -1.00 towards the Bondi radius and ρ 0 (r) ∝ r -1.08 for the region in between. This contrasts with more cuspy ρ 0 (r) ∝ r -1.75 for dark matter with Coulomb-like self-interaction.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Relativistic gas accretion onto supermassive black hole binaries from inspiral through merger

Accreting supermassive black hole binaries are powerful multimessenger sources emitting both gravitational and electromagnetic (EM) radiation. Understanding the accretion dynamics of these systems and predicting their distinctive EM signals is crucial to informing and guiding upcoming efforts aimed at detecting gravitational waves produced by these binaries. To this end, accurate numerical modeling is required to describe both the spacetime and the magnetized gas around the black holes. In this paper, we present two key advances in this field of research. First, we have developed a novel 3D general relativistic magnetohydrodynamics (GRMHD) framework that combines multiple numerical codes to simulate the inspiral and merger of supermassive black hole binaries starting from realistic initial data and running all the way through merger. Throughout the evolution, we adopt a simple but functional prescription to account for gas cooling through photon emission. Next, we have applied our new computational method to follow the time evolution of a circular, equal-mass, nonspinning black hole binary for ∼200 orbits, starting from a separation of 20⁢𝑟 𝑔 and reaching the postmerger evolutionary stage of the system. We have shown how mass continues to flow toward the binary even after the binary “decouples” from its surrounding disk, but the accretion rate onto the black holes diminishes. We have identified how the minidisks orbiting each black hole are slowly drained and eventually dissolve as the binary compresses. We confirm previous findings that the system’s luminosity decreases by a factor of a few during inspiral; however, we observe an abrupt increase by ∼50% in this quantity at the time of merger, likely accompanied by an equally abrupt change in spectrum. Lastly, we have demonstrated that during the inspiral, fluid ram pressure regulates the fraction of the magnetic flux transported to the binary that attaches to the black holes’ horizons.

Accretion disk & black-hole plasma↗
DOE OSTI2022

Numerical Modeling of Atmospheric Rime Ice Accretion on an Airfoil Using an Eulerian Approach

This paper presents an approach to numerically simulate the inherently unsteady rime ice accretion problem on a two-dimensional airfoil and elucidate the associated variations under different icing conditions. The airflow field and the water impingement on the airfoil are obtained based on an Eulerian two-phase model. A dynamic mesh strategy is employed to unsteadily account for the changes in the ice profile and its impact on the air and droplet flow by continuously reconstructing the computational grid at each time-step through smoothing and layering mechanisms. All main icing modules including the airflow field, droplet trajectory, icing thickness profile, and mesh management are fully coupled within the same computational framework without resorting to any external tools. Classical icing theory is employed to model the rime ice roughness, and it is assumed that the ice accretes in a direction normal to the airfoil surface. The governing Reynolds-averaged Navier–Stokes (RANS) conservation equations along with the energy and continuity equations are solved to produce the velocity and temperature fields. A convective film heat transfer coefficient is computed based on the surface heat flux and a recovery temperature which takes into account the dissipative heat release in the boundary layer in the vicinity of the airfoil surface. With the implemented strategy and calculating the convective heat transfer coefficient, the water film thickness is also calculated along with the ice shape. Furthermore, the model is validated by comparing the local collection efficiency distribution and ice shape with experimental data, and the results show that the implemented approach provides acceptable predictions of ice accretion profiles and rates.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

The Separation and Hα Contrasts of Massive Accreting Planets in the Gaps of Transitional Disks: Predicted Hα Protoplanet Yields for Adaptive Optics Surveys

We present a massive accreting gap planet model that ensures large gaps in transitional disks are kept dust free by the scattering action of three coplanar quasi-circular planets in a 1:2:4 mean motion resonance (MMR). This model uses the constraint of the observed gap size, and the dust-free nature of the gap, to determine within ∼10% the possible orbits for three massive planets in an MMR. Calculated orbits are consistent with the observed orbits and Hα emission (the brightest line to observe these planets) for LkCa 15 b, PDS 70 b, and PDS 70 c within observational errors. Moreover, the model suggests that the scarcity of detected Hα planets is likely a selection effect of the current limitations of non-coronagraphic, low (<10%) Strehl, Hα imaging with adaptive optics (AO) systems used in past Hα surveys. We predict that as higher Strehl AO systems (with high-performance custom coronagraphs; like the 6.5 m Magellan Telescope MagAO-X system) are utilized at Hα, the number of detected gap planets will substantially increase by more than tenfold. For example, we show that >25 ± 5 new Hα “gap planets” are potentially discoverable by a survey of the best 19 transitional disks with MagAO-X. Detections of these accreting protoplanets will significantly improve our understanding of planet formation, planet growth and accretion, solar system architectures, and planet–disk interactions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Discriminating Accretion States via Rotational Symmetry in Simulated Polarimetric Images of M87

In 2017 April, the Event Horizon Telescope observed the shadow of the supermassive black hole at the core of the elliptical galaxy Messier 87. While the original image was constructed from measurements of the total intensity, full polarimetric data were also collected, and linear polarimetric images are expected in the near future. We propose a modal image decomposition of the linear polarization field into basis functions with varying azimuthal dependence of the electric vector position angle. We apply this decomposition to images of ray traced general relativistic magnetohydrodynamics simulations of the Messier 87 accretion disk. Furthermore, for simulated images that are physically consistent with previous observations, the magnitude of the coefficient associated with rotational symmetry, β2, is a useful discriminator between accretion states. We find that at 20 μas resolution, $| {\beta }_{2}| $ is greater than 0.2 only for models of disks with horizon-scale magnetic pressures large enough to disrupt steady accretion. We also find that images with a more radially directed electric vector position angle correspond to models with higher black hole spin. Our analysis demonstrates the utility of the proposed decomposition as a diagnostic framework to improve constraints on theoretical models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Accretion onto a Supermassive Black Hole Binary before Merger

While supermassive binary black holes (SMBBHs) inspiral toward merger they may also accrete matter from a surrounding disk. To study the dynamics of this system requires simultaneously describing the evolving spacetime and the magnetized plasma. We present the first relativistic calculation simulating two equal-mass, nonspinning black holes as they inspiral from a 20 M (G = c = 1) initial separation almost to merger. Our results imply important observational consequences: for instance, the accretion rate $\dot{M}$ onto the black holes first decreases and then plateaus, dropping by only a factor of ~3 despite the rapid inspiral. An estimated bolometric light curve follows the same profile, suggesting some merging SMBBHs may be significantly luminous past the predicted circumbinary disk decoupling. The minidisks are nonstandard: Reynolds, not Maxwell, stresses dominate, and they oscillate between two states. In one part of the cycle, "sloshing" streams transfer mass between minidisks, carrying kinetic energy at a rate sometimes as high as the peak minidisk bolometric luminosity. We also discover that episodic accretion drives time-varying minidisk tilts. These complex dynamics all contribute to unique cyclical behavior in the light curves of late-time inspiraling SMBBHs. The poloidal magnetic flux on the black holes is roughly constant at a dimensionless level $\phi$ ~ 2–3, but doubles just before merger; for significant black hole spin, this flux predicts powerful jets with variability driven by binary dynamics, another potentially unique electromagnetic signature. This simulation is the first to employ our multipatch infrastructure PATCHWORK MHD, decreasing the computational expense to ~3% of conventional single-grid methods' cost.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Young Stellar Objects, Accretion Disks, and Their Variability with Rubin Observatory LSST

Vera C. Rubin Observatory, through the Legacy Survey of Space and Time (LSST), will allow us to derive a panchromatic view of variability in young stellar objects (YSOs) across all relevant timescales. Indeed, both short-term variability (on timescales of hours to days) and long-term variability (months to years), predominantly driven by the dynamics of accretion processes in disk-hosting YSOs, can be explored by taking advantage of the multiband filters option available in Rubin LSST, in particular the u, g, r, i filters that enable us to discriminate between photospheric stellar properties and accretion signatures. The homogeneity and depth of sky coverage that will be achieved with LSST will provide us with a unique opportunity to characterize the time evolution of disk accretion as a function of age and varying environmental conditions (e.g., field crowdedness, massive neighbors, metallicity) by targeting different star-forming regions. In this contribution to the Rubin LSST Survey Strategy Optimization Focus Issue, we discuss how implementing a dense observing cadence to explore short-term variability in YSOs represents a key complementary effort to the Wide–Fast–Deep observing mode that will be used to survey the sky over the full duration of the main survey (≈10 yr). The combination of these two modes will be vital to investigate the connection between the inner-disk dynamics and longer-term eruptive variability behaviors, such as those observed on EX Lupi–type objects.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2005

Experimental Investigation of Ice Accretion Effects on a Swept Wing

An experimental investigation was conducted to study the effects of 2-, 5-, 10-, and 22.5-min ice accretions on the aerodynamic performance of a swept finite wing. The ice shapes tested included castings of ice accretions obtained from icing tests at the NASA Glenn Icing Research Tunnel (IRT) and simulated ice shapes obtained with the LEWICE 2.0 ice accretion code. The conditions used for the icing tests were selected to provide five glaze ice shapes with complete and incomplete scallop features and a small rime ice shape. The LEWICE ice shapes were defined for the same conditions as those used in the icing tests. All aerodynamic performance tests were conducted in the 7- x 10-ft Low-Speed Wind Tunnel Facility at Wichita State University. Six component force and moment measurements, aileron hinge moments, and surface pressures were obtained for a Reynolds number of 1.8 million based on mean aerodynamic chord and aileron deflections in the range of -15o to 20o. Tests were performed with the clean wing, six IRT ice shape castings, seven smooth LEWICE ice shapes, and seven rough LEWICE ice shapes. Roughness for the LEWICE ice shapes was simulated with 36-size grit. The experiments conducted showed that the glaze ice castings reduced the maximum lift coefficient of the clean wing by 11.5% to 93.6%, while the 5-min rime ice casting increased maximum lift by 3.4%. Minimum iced wing drag was 133% to 3533% greater with respect to the clean case. The drag of the iced wing near the clean wing stall angle of attack was 17% to 104% higher than that of the clean case. In general, the aileron remained effective in changing the lift of the clean and iced wings for all angles of attack and aileron deflections tested. Aileron hinge moments for the iced wing cases remained within the maximum and minimum limits defined by the clean wing hinge moments. Tests conducted with the LEWICE ice shapes showed that in general the trends in aerodynamic performance degradation of the wing with the simulated ice shapes were similar to those obtained with the IRT ice shape castings. However, in most cases, the ice castings resulted in greater aerodynamic performance losses than those obtained with the LEWICE ice shapes. For the majority of the LEWICE ice shapes, the addition of 36-size grit roughness to the smooth ice shapes increased aerodynamic performance losses.

Ice shape↗
NASA NTRS2013

Can the 62 Day X-ray Period of ULX M82 X-1 Be Due to a Precessing Accretion Disk?

We have analyzed all the archival RXTE/PCA monitoring observations of the ultraluminous X-ray source (ULX) M82 X-1 in order to study the properties of its previously discovered 62 day X-ray period (Kaaret & Feng 2007). Based on the high coherence of the modulation it has been argued that the observed period is the orbital period of the binary. Utilizing a much longer data set than in previous studies we find: (1) The phase-resolved X-ray (3-15 keV) energy spectra - modeled with a thermal accretion disk and a power-law corona - suggest that the accretion disk's contribution to the total flux is responsible for the overall periodic modulation while the power-law flux remains approximately constant with phase. (2) Suggestive evidence for a sudden phase shift-of approximately 0.3 in phase (20 days)-between the first and the second halves of the light curve separated by roughly 1000 days. If confirmed, the implied timescale to change the period is approx. = 10 yrs, which is exceptionally fast for an orbital phenomenon. These independent pieces of evidence are consistent with the 62 day period being due to a precessing accretion disk, similar to the so-called super-orbital periods observed in systems like Her X-1, LMC X-4, and SS433. However, the timing evidence for a change in the period needs to be confirmed with additional observations. This should be possible with further monitoring of M82 with instruments such as the X-ray telescope (XRT) on board Swift.

ULX M82↗
NASA NTRS2015

Ice Accretion Measurements on an Airfoil and Wedge in Mixed-Phase Conditions

This paper describes ice accretion measurements from experiments conducted at the National Research Council (NRC) of Canada's Research Altitude Test Facility during 2012. Due to numerous engine power loss events associated with high altitude convective weather, potential ice accretion within an engine due to ice crystal ingestion is being investigated collaboratively by NASA and NRC. These investigations examine the physical mechanisms of ice accretion on surfaces exposed to ice crystal and mixed phase conditions, similar to those believed to exist in core compressor regions of jet engines. A further objective of these tests is to examine scaling effects since altitude appears to play a key role in this icing process.

ice crystals↗
NASA NTRS2018

Evaluation of a Thermodynamic Ice Crystal Icing Model Using Experimental Ice Accretion Data

This paper presents the evaluation of a thermodynamic ice crystal icing model, previously presented to describe the possible mechanisms of icing within the core of a turbofan jet engine. It has been proposed that there are two types of distinct ice accretions based on a surface energy balance: freeze-dominated icing and melt-dominated icing. In the former, ice accretion occurs where a freeze fraction (0 to 1) of melted ice crystals freezes on a surface, along with the existing ice of the impinging water and ice mass. This freeze-dominated icing is characterized by having strong adhesion to the surface. In the latter, icing occurs from accumulated unmelted ice on a surface, where a melt fraction (0 to 1) dictates the amount of unmelted impinged ice. This melt-dominated icing is characterized by weakly bonded surface adhesion. The experimentally observed ice growth rates suggest that only a small fraction of the impinging ice remains on the surface, implying a mass loss mechanism such as splash, runback, bounce, or erosion. This mass loss parameter must be determined in conjunction with the fraction of freezing liquid water or fraction of melting ice on an icing surface. This loss parameter, however, along with the freeze and melt fraction, are the only experimental parameters that are currently not measured directly. Using reported icing growth rates from published ice crystal icing experiments, a methodology is proposed to determine these unknown parameters. This work takes reported ice accretion data from tests conducted by the National Aeronautics and Space Administration (NASA) in 2016 and tests NASA collaborated on with the National Research Council (NRC) of Canada in 2012 that examined the fundamental physics of ice crystal icing. Those research efforts sought to generate icing conditions representative of those that occur inside a jet engine when ingesting ice crystals. This paper presents the fundamental equations of the thermodynamic model, the methodology used to determine the aforementioned unknown icing parameters, and results from model evaluation using experimental data. In addition, this paper builds on the previously proposed model by adding a transient conduction term to explain ice growth behavior at the onset of experimental tests that was observed to be different from steady-state ice growth that occurred later in the test run.With the addition of this energy term, this becomes a quasi-steady model. A key finding from this work suggests that mass loss fractions can exceed 0.90 for steady ice growth periods. In addition, due to conductive heat fluxes when using a warmer-than-freezing airfoil, lower mass loss fraction values were calculated during the initial transient period.

Ice-Crystal Ice Accretion↗
DOE OSTI2025

The variety and origin of materials accreted by Bennu’s parent asteroid

The first bodies to form in the Solar System acquired their materials from stars, the presolar molecular cloud and the protoplanetary disk. Asteroids that have not undergone planetary differentiation retain evidence of these primary accreted materials. However, geologic processes such as hydrothermal alteration can dramatically change their bulk mineralogy, isotopic compositions and chemistry. Here we analyse the elemental and isotopic compositions of samples from asteroid Bennu to uncover the sources and types of material accreted by its parent body. We show that some primary accreted materials escaped the extensive aqueous alteration that occurred on the parent asteroid, including presolar grains from ancient stars, organic matter from the outer Solar System or molecular cloud, refractory solids that formed close to the Sun, and dust enriched in neutron-rich Ti isotopes. We find Bennu to be richer in isotopically anomalous organic matter, anhydrous silicates, and light isotopes of K and Zn than its closest compositional counterparts, asteroid Ryugu and Ivuna-type (CI) carbonaceous chondrite meteorites. We propose that the parent bodies of Bennu, Ryugu and CI chondrites formed from a common but spatially and/or temporally heterogeneous reservoir of materials in the outer protoplanetary disk.

Kuiper belt↗
DOE OSTI2020

Cataloging accreted stars within Gaia DR2 using deep learning

The goal of this study is to present the development of a machine learning based approach that utilizes phase space alone to separate the Gaia DR2 stars into two categories: those accreted onto the Milky Way from those that are in situ. Traditional selection methods that have been used to identify accreted stars typically rely on full 3D velocity, metallicity information, or both, which significantly reduces the number of classifiable stars. The approach advocated here is applicable to a much larger portion of Gaia DR2. Methods. A method known as “transfer learning” is shown to be effective through extensive testing on a set of mock Gaia catalogs that are based on the F IRE cosmological zoom-in hydrodynamic simulations of Milky Way-mass galaxies. The machine is first trained on simulated data using only 5D kinematics as inputs and is then further trained on a cross-matched Gaia /RAVE data set, which improves sensitivity to properties of the real Milky Way. Results. The result is a catalog that identifies ~767 000 accreted stars within Gaia DR2. This catalog can yield empirical insights into the merger history of the Milky Way and could be used to infer properties of the dark matter distribution.

Astronomy & Astrophysics↗
DOE OSTI2022

Accretion disc sizes from continuum reverberation mapping of AGN selected from the ZTF survey

ABSTRACT We present the accretion disc-size estimates for a sample of 19 active galactic nuclei (AGNs) using the optical g-, r-, and i-band light curves obtained from the Zwicky Transient Facility survey. All the AGNs have reliable supermassive black hole (SMBH) mass estimates based on previous reverberation mapping measurements. The multiband light curves are cross-correlated, and the reverberation lag is estimated using the Interpolated Cross-Correlation Function method and the Bayesian method using the javelin code. As expected from the disc-reprocessing arguments, the g − r band lags are shorter than the g − i band lags for this sample. The interband lags for all, but five sources, are larger than the sizes predicted from the standard Shakura Sunyaev (SS) analytical model. We fit the light curves directly using a thin disc model implemented through the javelin code to get the accretion disc sizes. The disc sizes obtained using this model are on an average 3.9 times larger than the prediction based on the SS disc model. We find a weak correlation between the disc sizes and the known physical parameters, namely the luminosity and the SMBH mass. In the near future, a large sample of AGNs covering broader ranges of luminosity and SMBH mass from large photometric surveys would be helpful in a better understanding of the structure and physics of the accretion disc.

Jha, Vivek Kumar (ORCID:0000000232776335)↗
DOE OSTI2024

The three-dimensional structure of black hole accretion flows within the plunging region

ABSTRACT We analyse, using new analytical models and numerical general relativistic magnetohydrodynamic simulations, the three-dimensional properties of accretion flows inside the plunging region of black hole spacetimes (i.e. at radii smaller than the innermost stable circular orbit). These simulations are of thick discs, with aspect ratios of order unity $h/r \sim 1$, and with a magnetic field geometry given by the standard low-magnetization ‘SANE’ configuration. This work represents the first step in a wider analysis of this highly relativistic region. We show that analytical expressions derived in the ‘thin disc’ limit describe the numerical results remarkably well, despite the large aspect ratio of the flow. We further demonstrate that accretion within this region is typically mediated via spiral arms, and that the geometric properties of these spiral structures can be understood with a simple analytical model. These results highlight how accretion within the plunging region is fundamentally two-dimensional in character, which may have a number of observational implications. We derive a modified theoretical description of the pressure within the plunging region which accounts for turbulent heating and may be of use to black hole image modelling.

Astronomy & Astrophysics↗
DOE OSTI2024

Geometric and thermodynamic characterization of binary neutron star accretion discs

Accretion disks formed in binary neutron star mergers play a central role in many astrophysical processes of interest, including the launching of relativistic jets or the ejection of neutron-rich matter hosting heavy element nucleosynthesis. In this work we analyze in detail the properties of accretion disks from 44 ab initio binary neutron star merger simulations for a large set of nuclear equations of state, binary mass ratios, and remnant fates, with the aim of furnishing reliable initial conditions for disk simulations and a comprehensive characterization of their properties. We find that the disks have a significant thermal support, with an aspect ratio decreasing with the mass ratio of the binary from ~0.7 to 0.3. Even if the disk sample spans a broad range in mass and angular momentum, their ratio is independent from the equation of state and from the mass ratio. This can be traced back to the rotational profile of the disk, characterized by a constant specific angular momentum (as opposed to a Keplerian one) of 3 – 5×10 16 cm 2 s –1 . The profiles of the entropy per baryon and of the electron fraction depend on the mass ratio of the binary. For more symmetric binaries, they follow a sigmoidal distribution as a function of the rest mass density, for which we provide a detailed description and a fit. Furthermore, the disk properties discussed in this work can be used as a robust set of initial conditions for future long-term simulations of accretion disks from binary neutron star mergers, posing the basis for progress in the quantitative study of the outflow properties.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Quasi-Steady Simulation of Glaze Ice Accretion and Heat Transfer in the Supercooled Large Droplet Regime in Atmospheric Turbulent Air Flow

Abstract To avoid the use of a computationally intensive full unsteady simulation while providing an accurate solution, a quasi-steady simulation has been performed to study glaze and mixed ice accretion in the supercooled large droplet (SLD) regime in turbulent flow of atmospheric air. We have attempted to find the minimum time-step necessary to adequately simulate the icing process on an airfoil surface. Based on node displacement, a mesh morphing scheme has been adopted in the computations to account for the moving boundaries that are caused by the continuous ice buildup. We have modeled ice accretion on an airfoil surface for a time period of 232 s using several time steps. At each time-step we solved the steady-state conservation equations for the air and droplet phases and then used the results as initial conditions for the next time position. The magnitude of the time-step ranged from a least accurate two-shot simulation (where the time-step is 116 s) to a most accurate 2320-shot simulation (where the time-step is 0.1 s). In-between these two extreme time steps, we have performed a three-shot simulation (where the time-step is 77.33 s), a four-shot simulation (where the time-step is 58 s), a six-shot simulation (where the time-step is 38.67 s), a 46-shot simulation (where the time-step is 5 s), and a 232-shot simulation (where the time-step is 1 s). We have done so to find out the degree of accuracy (or inaccuracy) of the multishot simulation approach and to find out the appropriate time-step needed for a successful and valid quasi-steady simulation. A valid quasi-steady simulation needs to use a time-step that is small enough to reproduce the full time-dependent solution within a very small error band. We have found that both the 1 s and the 0.1 s time steps produce virtually identical results. This is the primary litmus test that proves the validity of the quasi-steady-state assumption. The results adopted in this paper are thus all based on the more conservative 0.1 s time-step. In the process of performing the simulations, remeshing was required in order to maintain the grid density in zones of high curvature to be able to capture the full physics in those zones. After successfully modeling glaze ice accretion over the airfoil surface using the 0.1 s quasi-steady simulation approach, the effects of supercooled large droplets (SLDs) impacting the surface have been examined and presented in terms of the variation of the local collection efficiency, the water film thickness, and the heat transfer rate. Examination of the variation of the angle that the ice horn makes with the airfoil chord line demonstrated a 20% improvement in angle prediction when the time-step is reduced from 116 s to 0.1 s. The analysis also reveals a 12% or 8.5% increase in the maximum collection efficiency, βmax, depending on whether the value of the liquid water content (LWC) has been doubled from 0.5 g/m3 to 1 g/m3, or the value of the freestream velocity has been doubled from 75 m/s to 150 m/s, respectively. Because of the need to monitor the local collection efficiency and convective heat fluxes at each shot (regardless of the number of shots employed), the approach adopted here was found to be effective in successively and successfully reproducing the curvature of the glaze ice horn.

Engineering↗