Convective Boundary Research Articles

Convective Overshooting in sdB Stars Using the k–ω Model

Abstract Mixing in the convective core is quite uncertain in core helium-burning stars. To explore the overshooting mixing beyond the convective core, we incorporated the k–ω proposed by Li into the Modules of Experiments in Stellar Astrophysics (MESA), and investigated the overshooting mixing in evolution of subdwarf B (sdB) models. We found that the development of the convective core can be divided into three stages. When the radiative temperature gradient, ∇ rad , monotonically decreases outwardly, the overshooting mixing presents exponential decay similar with Herwig, and the overshooting distance is to make ∇ rad ≃ ∇ ad at the boundary of the convective core, in agreement with the prediction of the self-driving mechanism Castellani et al. When the radiative temperature gradient, ∇ rad , shows a minimum value near the convective boundary, the convective core may be divided into two if the minimum value of ∇ rad is smaller than the adiabatic temperature gradient ∇ ad . For the single-zone case, the overshooting mixing shows exponential decay, but the overshooting distance is much smaller than in the initial stage. For the double-zone case, the overshooting mixing is similar to that of the single case beyond the convective core, while it almost stops on both sides of the above convective shell. Our overshooting mixing scheme is similar to the maximal overshoot scheme of Constantino et al. In the final stage, helium injections into the convective core by the overshooting mixing happens, similar to the “core breathing pulses.”

Mass Transfer of MHD Nanofluid in Presence of Chemical Reaction on A Permeable Rotating Disk with Convective Boundaries, Using Buongiorno's Model

Mass Transfer of MHD Nanofluid in Presence of Chemical Reaction on A Permeable Rotating Disk with Convective Boundaries, Using Buongiorno's Model

Effects of Convection and Fracture Boundary Conditions on Heat Transfer Shape Factor in Fractured Geothermal Reservoirs

Advection–conduction equation (ACE) used to explain the combined conduction and convection mechanisms of heat transfer thorough porous media has received considerable attention with a wide range of applications in various disciplines. The present study concentrates on developing a generalized analytical solution to ACE through incorporation of Fourier series and a new dependent variable for the problem of heat transfer through porous media in one-dimensional finite spatial region assuming transient boundary conditions. Then, assuming that a fracture acts as the time-dependent boundary condition, an analytical solution is obtained for a typical fractured porous medium. Based on the analytical solution, heat transfer shape factor is also obtained, on which the effects of governing parameters of matrix block such as Peclet number are investigated throughout transient and pseudo-steady-state (PSS) periods for the first time. Moreover, a correlation is generated to estimate the PSS heat transfer shape factor in terms of dimensionless time and Peclet number for constant concentration and linearly ascending temperature boundary conditions. Additionally, the numerical finite difference and finite element methods were utilized to validate the analytical solution results. The results demonstrated that the obtained generalized analytical solution can be regarded as a reliably excellent and accurate mathematical lever to describe the heat transfer phenomenon through porous media subject to determine transient boundary conditions and also to verify numerical results.

Novel thermal model of microchannel cooling system designed for fast simulation of liquid-cooled ICs

The research and design of liquid-cooled integrated circuits (IC) relies heavily on accurate simulation. Ideally, finite-element-method (FEM) based tools should be used for this purpose. However, in most cases a fully coupled thermo-fluidic simulation of complex ICs is very long, mostly due to the fact that the simulation of fluid dynamics is very time consuming. Therefore, in this paper we propose a novel model for thermal simulation of ICs cooled by integrated microchannels which significantly reduces the simulation time. The new approach is based on removing the fluid from the model and treating the solid-liquid boundary as a convective boundary, described by the convection equation. It is shown that the proposed model offers very good accuracy in steady-state, with errors below 3 °C in every chip point. In transient domain the results are equally good, with the maximum error around 3.3 °C (6% relative error). Moreover, the simulation times have been reduced by about two orders of magnitude with respect to fully coupled FEM simulation. However, the proposed model has also important limitations: currently ICs with only one layer of straight microchannels are supported and the model requires recalculation if some chip parameters are changed.

The Red-giant Branch Bump Revisited: Constraints on Envelope Overshooting in a Wide Range of Masses and Metallicities

Abstract The red-giant branch bump provides valuable information for the investigation of the internal structure of low-mass stars. Because current models are unable to accurately predict the occurrence and efficiency of mixing processes beyond convective boundaries, one can use the luminosity of the bump—a diagnostic of the maximum extension of the convective envelope during the first-dredge up—as a calibrator for such processes. By combining asteroseismic and spectroscopic constraints, we expand the analysis of the bump to masses and metallicities beyond those previously accessible using globular clusters. Our data set comprises nearly 3000 red-giant stars observed by Kepler and with APOGEE spectra. Using statistical mixture models, we are able to detect the bump in the average seismic parameters ν max and , and show that its observed position reveals general trends with mass and metallicity in line with expectations from models. Moreover, our analysis indicates that standard stellar models underestimate the depth of efficiently mixed envelopes. The inclusion of significant overshooting from the base of the convective envelope, with an efficiency that increases with decreasing metallicity, allows us to reproduce the observed location of the bump. Interestingly, this trend was also reported in previous studies of globular clusters.

Laminar Mixed Convection Flow from a Vertical Surface with Induced Magnetic Field and Convective Boundary

The objective of this investigation is to study the influence of thermal radiation and radiation absorption parameter on a mixed convection flow over a continuously moving porous vertical plate under the action of transverse applied magnetic field taking into account the induced magnetic field with convective boundary. Under certain assumptions, the solutions for the velocity field, temperature distribution and induced magnetic field are obtained. The influences of various parameters on the velocity, temperature fields and on induced magnetic fields are studied graphically. It is also found that the dimensionless Prandtl number, Grashof number, Schmidt number and magnetic parameter have an appreciable influence on the independent variables.

Modulation of the atmospheric turbulence coherent structures by mesoscale motions

The precise modeling of turbulence is indispensable for weather forecasting and environmental heat-removal and pollution-dispersion assessment. Models rely on correlations derived from field measurements. Unfortunately, the readings are usually contaminated with mesoscale motions which alter turbulence statistics and mislead the characterization of turbulence coherent structures, the drivers of the heat and mass transport process. This article depicts the interference of the mesoscales in turbulence statistics and coherent structure detection. Atmospheric measurements were taken at EKOMAR on the east coast of Malaysia. Two ultrasonic anemometers at heights of 1.7 and 12 m were utilized. Twelve samples from the convective atmospheric boundary layer were analyzed. Spectral and auto-correlation analysis were conducted to assess the weight of the mesoscales relative to the shear coherent structure scales. The structure inclination angle and timescale were calculated for the wind speed signal with and without the mesoscale scales filtered out. It was found that these interfering structures largely shifts the calculated length- and time-scales of the coherent structures. The improper filtration of the signal may delete part of the coherent structures and hence worsen the situation.

Assessing Weather Research and Forecasting (WRF) Model Parameterization Schemes Skill to Simulate Extreme Rainfall Events over Dar es Salaam on 21 December 2011

This paper evaluates the skills of physical Parameterization schemes in simulating extreme rainfall events over Dar es Salaam Region, Tanzania using the Weather Research and Forecasting (WRF) model. The model skill is determined during the 21 December 2011 flooding event. Ten sensitivity experiments have been conducted using Cumulus, Convective and Planetary boundary layer schemes to find the best combination and optimize the WRF model for the study area for heavy rainfall events. Model simulation results were verified against observed data using standard statistical tests. The model simulations show encouraging and better statistical results with the combination of Kain-Fritsch cumulus parameterization scheme, Lin microphysics scheme and Asymmetric Convection Model 2 (ACM2) planetary boundary scheme than any other combinations of physical parameterization schemes over Dar es Salaam region.

Unsteady MHD Free Convective Heat and Mass Transfer Flow Past a Vertical Porous Plate in the Presence of Radiation and Chemical Reaction

The objective of this paper is to analyze an unsteady MHD free convective heat and mass transfer boundary flow past a semi-infinite vertical porous plate immersed in a porous medium with radiation and chemical reaction. The governing equations of the flow field are solved numerical a two term perturbation method. The effects of the various parameters on the velocity, temperature and concentration profiles are presented graphically and values of skin-frication coefficient, Nusselt number and Sherwood number for various values of physical parameters are presented through tables.

Quantifying the Accuracy and Uncertainty of Diurnal Thermodynamic Profiles and Convection Indices Derived from the Atmospheric Emitted Radiance Interferometer

AbstractWhile radiosondes have provided atmospheric scientists an accurate high-vertical-resolution profile of the troposphere for decades, they are unable to provide high-temporal-resolution observations without significant recurring expenses. Remote sensing technology, however, has the ability to monitor the evolution of the atmosphere in unprecedented detail. One particularly promising tool is the Atmospheric Emitted Radiance Interferometer (AERI), a passive ground-based infrared radiometer. Through a physical retrieval, the AERI can retrieve the vertical profile of temperature and humidity at a temporal resolution on the order of minutes. The synthesis of these two instruments may provide an improved diagnosis of the processes occurring in the atmosphere. This study provides a better understanding of the capabilities of the AERI in environments supportive of deep, moist convection. Using 3-hourly radiosonde launches and thermodynamic profiles retrieved from collocated AERIs, this study evaluates the accuracy of AERI-derived profiles over the diurnal cycle by analyzing AERI profiles in both the convective and stable boundary layers. Monte Carlo sampling is used to calculate the distribution of convection indices and compare the impact of measurement errors from each instrument platform on indices. This study indicates that the nonintegrated indices (e.g., lifted index) derived from AERI retrievals are more accurate than integrated indices (e.g., CAPE). While the AERI retrieval’s vertical resolution can inhibit precise diagnoses of capping inversions, the high-temporal-resolution nature of the AERI profiles overall helps in detecting rapid temporal changes in stability.

The treatment of mixing in core helium-burning models – III. Suppressing core breathing pulses with a new constraint on overshoot

Theoretical predictions for the core helium burning phase of stellar evolution are highly sensitive to the uncertain treatment of mixing at convective boundaries. In the last few years, interest in constraining the uncertain structure of their deep interiors has been renewed by insights from asteroseismology. Recently, Spruit (2015) proposed a limit for the rate of growth of helium-burning convective cores based on the higher buoyancy of material ingested from outside the convective core. In this paper we test the implications of such a limit for stellar models with a range of initial mass and metallicity. We find that the constraint on mixing beyond the Schwarzschild boundary has a significant effect on the evolution late in core helium burning, when core breathing pulses occur and the ingestion rate of helium is fastest. Ordinarily, core breathing pulses prolong the core helium burning lifetime to such an extent that models are at odds with observations of globular cluster populations. Across a wide range of initial stellar masses ($0.83 \leq M/\text{M}_\odot \leq 5$), applying the Spruit constraint reduces the core helium burning lifetime because core breathing pulses are either avoided or their number and severity reduced. The constraint suggested by Spruit therefore helps to resolve significant discrepancies between observations and theoretical predictions. Specifically, we find improved agreement for $R_2$, the observed ratio of asymptotic giant branch to horizontal branch stars in globular clusters; the luminosity difference between these two groups; and in asteroseismology, the mixed-mode period spacing detected in red clump stars in the \textit{Kepler} field.

Lithium Depletion in Solar-like Stars: Effect of Overshooting Based on Realistic Multi-dimensional Simulations

Abstract We study lithium depletion in low-mass and solar-like stars as a function of time, using a new diffusion coefficient describing extra-mixing taking place at the bottom of a convective envelope. This new form is motivated by multi-dimensional fully compressible, time-implicit hydrodynamic simulations performed with the MUSIC code. Intermittent convective mixing at the convective boundary in a star can be modeled using extreme value theory, a statistical analysis frequently used for finance, meteorology, and environmental science. In this Letter, we implement this statistical diffusion coefficient in a one-dimensional stellar evolution code, using parameters calibrated from multi-dimensional hydrodynamic simulations of a young low-mass star. We propose a new scenario that can explain observations of the surface abundance of lithium in the Sun and in clusters covering a wide range of ages, from ∼50 Myr to ∼4 Gyr. Because it relies on our physical model of convective penetration, this scenario has a limited number of assumptions. It can explain the observed trend between rotation and depletion, based on a single additional assumption, namely, that rotation affects the mixing efficiency at the convective boundary. We suggest the existence of a threshold in stellar rotation rate above which rotation strongly prevents the vertical penetration of plumes and below which rotation has small effects. In addition to providing a possible explanation for the long-standing problem of lithium depletion in pre-main-sequence and main-sequence stars, the strength of our scenario is that its basic assumptions can be tested by future hydrodynamic simulations.

Modeling of the melting characteristics of commercial paraffin wax in an inverted equilateral triangular enclosure: Effect of convective heat transfer boundary conditions

ABSTRACTA horizontal double-pipe heat exchanger with an inverted outer equilateral triangular tube is modeled to numerically investigate the low-temperature thermal energy storage capability of an impure phase change material (PCM). The energy source fluid (hot water) flows through the inner tube and transfers heat to the PCM (heat sink) residing in the annular gap. The results show that the inlet temperature of the heat transfer fluid (HTF) has a significant effect on the melting process compared with the mass flow rate (MFR). The configuration, as well the concentricity/eccentricity of the inner tube has a great influence on the energy storage.

Numerical Simulation and Experimental Casting of Nickel-Based Single-Crystal Superalloys by HRS and LMC Directional Solidification Processes

AbstractMathematical models for dynamic heat radiation and convection boundary in directional solidification processes are established to simulate the temperature fields. Cellular automaton (CA) method and Kurz-Giovanola-Trivedi (KGT) growth model are used to describe nucleation and growth. Primary dendritic arm spacing (PDAS) and secondary dendritic arm spacing (SDAS) are calculated by the Ma-Sham (MS) and Furer-Wunderlin (FW) models respectively. The mushy zone shape is investigated based on the temperature fields, for both high-rate solidification (HRS) and liquid metal cooling (LMC) processes. The evolution of the microstructure and crystallographic orientation are analyzed by simulation and electron back-scattered diffraction (EBSD) technique, respectively. Comparison of the simulation results from PDAS and SDAS with experimental results reveals a good agreement with each other. The results show that LMC process can provide both dendritic refinement and superior performance for castings due to the increased cooling rate and thermal gradient.

Asteroseismic Constraints on the Models of Hot B Subdwarfs: Convective Helium-Burning Cores

Asteroseismology of non-radial pulsations in Hot B Subdwarfs (sdB stars) offers a unique view into the interior of core-helium-burning stars. Ground-based and space-borne high precision light curves allow for the analysis of pressure and gravity mode pulsations to probe the structure of sdB stars deep into the convective core. As such asteroseismological analysis provides an excellent opportunity to test our understanding of stellar evolution. In light of the newest constraints from asteroseismology of sdB and red clump stars, standard approaches of convective mixing in 1D stellar evolution models are called into question. The problem lies in the current treatment of overshooting and the entrainment at the convective boundary. Unfortunately no consistent algorithm of convective mixing exists to solve the problem, introducing uncertainties to the estimates of stellar ages. Three dimensional simulations of stellar convection show the natural development of an overshooting region and a boundary layer. In search for a consistent prescription of convection in one dimensional stellar evolution models, guidance from three dimensional simulations and asteroseismological results is indispensable.

Numerical Investigation on Boundary Layer Flow of a Nanofluid Towards an Inclined Plate with Convective Boundary: Boungiorno Nanofluid Model

Numerical Investigation on Boundary Layer Flow of a Nanofluid Towards an Inclined Plate with Convective Boundary: Boungiorno Nanofluid Model

Idealized hydrodynamic simulations of turbulent oxygen-burning shell convection in 4π geometry

This work investigates the properties of convection in stars with particular emphasis on entrainment across the upper convective boundary (CB). Idealized simulations of turbulent convection in the O-burning shell of a massive star are performed in 4π geometry on 7683 and 15363 grids, driven by a representative heating rate. A heating series is also performed on the 7683 grid. The 15363 simulation exhibits an entrainment rate at the upper CB of 1.33 × 10−6 M⊙ s−1. The 7683 simulation with the same heating rate agrees within 17 per cent. The entrainment rate at the upper CB is found to scale linearly with the driving luminosity and with the cube of the shear velocity at the upper boundary, while the radial rms fluid velocity scales with the cube root of the driving luminosity, as expected. The mixing is analysed in a 1D diffusion framework, resulting in a simple model for CB mixing. The analysis confirms that limiting the MLT mixing length to the distance to the CB in 1D simulations better represents the spherically averaged radial velocity profiles from the 3D simulations and provide an improved determination of the reference diffusion coefficient D0 for the exponential diffusion CB mixing model in 1D. From the 3D simulation data, we adopt as the CB the location of the maximum gradient in the horizontal velocity component which has 2σ spatial fluctuations of ≈0.17HP. The exponentially decaying diffusion CB mixing model with f = 0.03 reproduces the spherically averaged 3D abundance profiles.

Application of the modeling probability distribution functions for Lagrangian simulation of a passive tracer in the atmospheric boundary layer

The numerical stochastic Lagrangian modeling of the passive tracer in a convective atmospheric boundary layer (CABL) was performed based on the random walk and Langevinmodels of turbulent dispersion. The statistical structure of turbulence is modeled by the probability density function (PDF) of vertical velocity fluctuations, which is recovered by the calculated statistical moments of the vertical velocity fluctuations. Four models of the PDF reconstruction were tested and the results of simulations are compared with the experimental data in CABL. The superiority of Langevin model over the random-walk models is demonstrated.

English

English

Boundary-Layer Development and Low-level Baroclinicity during High-Latitude Cold-Air Outbreaks: A Simple Model

A new quasi-analytical mixed-layer model is formulated describing the evolution of the convective atmospheric boundary layer (ABL) during cold-air outbreaks (CAO) over polar oceans downstream of the marginal sea-ice zones. The new model is superior to previous ones since it predicts not only temperature and mixed-layer height but also the height-averaged horizontal wind components. Results of the mixed-layer model are compared with dropsonde and aircraft observations carried out during several CAOs over the Fram Strait and also with results of a 3D non-hydrostatic (NH3D) model. It is shown that the mixed-layer model reproduces well the observed ABL height, temperature, low-level baroclinicity and its influence on the ABL wind speed. The mixed-layer model underestimates the observed ABL temperature only by about 10 %, most likely due to the neglect of condensation and subsidence. The comparison of the mixed-layer and NH3D model results shows good agreement with respect to wind speed including the formation of wind-speed maxima close to the ice edge. It is concluded that baroclinicity within the ABL governs the structure of the wind field while the baroclinicity above the ABL is important in reproducing the wind speed. It is shown that the baroclinicity in the ABL is strongest close to the ice edge and slowly decays further downwind. Analytical solutions demonstrate that the \(\mathrm{e}\)-folding distance of this decay is the same as for the decay of the difference between the surface temperature of open water and of the mixed-layer temperature. This distance characterizing cold-air mass transformation ranges from 450 to 850 km for high-latitude CAOs.