Radial Temperature Profiles Research Articles

FLOW AND HEAT TRANSFER IN ROTATING COMPRESSOR CAVITIES WITH INVERTED SHROUD-THROUGHFLOW TEMPERATURE DIFFERENCES

Abstract In an aero-engine compressor, co-rotating discs form cavities that interact with an axial throughflow of secondary air at low radius. In the high-pressure (HP) compressor the shroud is hotter than the throughflow (directed downstream to the turbine) and the radial temperature gradient creates buoyancy-induced flow at Grashof numbers ∼ 1013. Such flows can be unstable and typically take the form of counter-rotating vortex pairs separated by radial hot and cold plumes. However, in low pressure (LP) and intermediate pressure (IP) compressors the secondary air is directed upstream. In this inverse scenario the axial throughflow is hotter than the compressor discs, reversing the disc temperature gradient and eliminating the fundamental driver for buoyancy. Despite its practical application and importance, this inverse scenario has not been previously investigated. The University of Bath Compressor Cavity Rig has been uniquely designed to simulate such flows, measuring temperature and unsteady pressure in the frame of reference of the rotating discs. Bayesian and spectral analysis have determined the radial distribution of disc heat flux, as well as the asymmetry of the rotating vortex structures and their slip relative to the discs. Unexpectedly, the new data reveal the flow structure in cavities with positive and inverted temperature differences are fundamentally similar (albeit with reversed radial-temperature profiles). Isothermal cases identified a critical Rossby number (Ro), above which the flow structure in the cavity was dominated by a toroidal vortex. At sub-critical Ro, the flow structure for the inverted temperature gradient continued

Toward electron temperature profiles in hot-dense plasmas from x-ray spectral ensembles

High repetition rate laser systems enable new strategies for diagnosing plasma behavior with large datasets. Here, we define an ensemble technique that relies on randomized targeting of x-ray tracer micro-stripes. On each shot, a high-intensity laser pulse is focused on a solid target with Ti tracer stripes embedded in an Al foil, randomly targeting a micro-stripe, a portion of a stripe, or a gap between stripes. High-resolution, time-integrated x-ray spectrometers capture line emission from the portion of the micro-stripe that is heated to sufficiently high electron temperatures. Accumulation of many such cases is used to construct ensemble distributions of x-ray line intensities that encompass all relative offsets of the laser focus to the micro-stripe centers. Synthetic intensity distributions are likewise generated using collisional-radiative modeling. Bayesian fitting of modeled to measured intensity distributions establishes the most likely radial temperature profiles, enabling comparison to hydrodynamic models and calling into question the cylindrical symmetry of these micro-stripe-embedded systems. Ensemble techniques have significant potential for high-energy-density plasma diagnostics, especially with the advent of high repetition rate experiments.

Predicting smoke temperature distribution beneath ceiling for a large subway station fire

Fire accident seriously threatens the stable operation and personnel security in the subway station, and clarifying the smoke temperature distribution is conducive to arranging reasonably fire alarm. In this study, model experiments and numerical simulations are conducted to investigate the ceiling temperature profiles, mainly altering the heat release rate (HRR) and fire locations in a large subway station. The repeatability of the experimental data is confirmed, and the numerical model is validated by the measurement data. During a fire happening in a large-wide space, the smoke movement beneath the ceiling can be divided into radial and one-dimensional flow, whose prediction models are proposed under fire source located at the center. On this basis, it can be found that the radial temperature profile is independent of fire source location. While, the one-dimensional temperature distribution model is modified by introducing the effects of transvers and longitudinal fire locations respectively. This work could provide data support and theoretical reference for clarifying the smoke movement for large subway station fire.

Emergence of high-mass stars in complex fiber networks (EMERGE). IV. Environmental dependence of the fiber widths

Despite their variety of scales throughout the interstellar medium, filaments in nearby low-mass clouds appear to have a characteristic width of sim 0.1 pc from the analysis of Herschel observations. The validity and origin of this characteristic width, however, has been a matter of intense discussions during the last decade. We made use of the EMERGE Early ALMA Survey comprising seven targets among low- (OMC-4 South, NGC 2023), intermediate- (OMC-2, OMC-3, LDN 1641N), and high-mass (OMC-1, Flame Nebula) star-forming regions in Orion, which include different physical conditions, star formation histories, mass, and density regimes. All targets were homogeneously surveyed at high-spatial resolution (4.5 or sim 2000 au) in N$_2$H$^+$ (1$-$0) using a dedicated series of ALMA+IRAM-30m observations, and previous works identified a total of 152 fibers throughout this sample. Here, we aim to characterise the variation in the fiber widths under the different conditions explored by this survey. We characterised the column density and temperature radial profiles of fibers using the automatic fitting routine FilChap, and systematically quantified its main physical properties (i.e. peak column density, width, and temperature gradient). The Orion fibers show a departure from the isothermal condition with significant outward temperature gradients with $ T_ K > 30$ K pc$^ $. The presence of such temperature gradients suggests a change in the equation of state for fibers. By fitting their radial profiles, we report a median full width at half maximum ($FWHM$) of $ 0.05$ pc for the Orion fibers, with a corresponding median aspect ratio of $ Along with their median, the $FWHM$ values for individual cuts are consistently below the proposed characteristic width of 0.1 pc. More relevantly, we observe a systematic variation in these fiber $FWHM$ between different regions in our sample. We also find a direct inverse dependence of the fiber $FWHM$ on their central column density, $N_0$, above $ $ cm$^ $, which agrees with the expected $N_0-FWHM$ anti-correlation predicted in previous theoretical studies. Our homogeneous analysis returns the first observational evidence of an intrinsic and systematic variation in the fiber widths across different star-forming regions. While sharing comparable mass, length, and kinematic properties in all of our targets, fibers appear to adjust their $FWHM$ to their density and to the pressure in their host environment.

Numerical investigation of heat transfer characteristics of hydrogen flow in a randomly packed bed

In this study, two randomly packed beds with small tube-to-particle diameter (D/d) ratios of D/d = 4 (PB-4) and D/d = 5 (PB-5) are constructed using the discrete element method (DEM). The pore-scale heat transfer characteristics of hydrogen flow at low pore Reynolds numbers (Rep < 100) are investigated using a DEM-CFD simulation approach, with the temperature-dependent thermo-properties of hydrogen being considered. Distinct local channeling flow patterns are revealed by detailed analyses of the flow fields in PB-4 and PB-5. The overall friction factors for both beds are found to agree well with empirical correlations. Notably, a faster spatial temperature increase is exhibited by PB-5, with a larger D/d ratio, as evidenced by a shorter axial distance for fully-heated hydrogen flow compared to PB-4. For the pore-scale heat transfer in the packed beds, the radial temperature profiles are compared at various heights of the packed beds depending on the radial porosity oscillation, in which the wall effect should be especially considered in the near-wall region. Furthermore, the axial pore-scale Nusselt number (Nup,axial) exhibits an inverse fluctuation with the axial porosity oscillation. Finally, the global Nusselt numbers (Nu) in the packed beds are analyzed under different operating conditions, which are in good agreement with empirical correlations.

New correlations for focusing effect evaluation of the light metal layer in the lower head of a nuclear reactor in case of severe accident

In case of a severe accident (SA) in a nuclear reactor, the core heats up and materials melt and relocate to the lower head of the vessel. In such configuration, stratification occurs between the oxide and metal phases present in the melt. When the metal phase is lighter than the oxide phase, the maximum heat flux applied to the vessel wall is concentrated at the location of this top metal layer, creating the so-called “focusing effect”. The modelling of the focusing effect is essential for SA codes to properly evaluate the vessel failure time or to demonstrate the vessel integrity, when In Vessel Retention (IVR) strategy is implemented. However, existing correlations used in SA codes for focusing effect modelling have some limitations: if the thickness of the metal layer becomes very small, they predict an extremely high heat flux. Moreover, they were validated with tests using water, whereas the Prandtl number was found to play a significant role in this heat transfer.In this paper, the focusing effect is studied based on 3D Direct Numerical Simulations (DNS) of a cylindrical metal layer, covering all possible metal layer characteristics in terms of geometry and boundary conditions, especially for its top surface where the intensity of radiative heat transfer may vary. The analysis of the fluid behavior and the quantitative results obtained allow to derive new correlations and a new model based on the radial profile of the mean temperature of the system and on the radial profile at the top surface. Results at reactor scale confirm the overestimation of existing 0D model used in SA codes for a thin metal layer and highlight the relevance of the proposed model for focusing effect evaluation during transient situations.

On the Role of Radial Dispersion in the Behavior of a Cooled Fixed‐Bed Reactor: Numerical Investigation of Fischer–Tropsch Synthesis with a Cobalt‐Based Catalyst

AbstractThe impact of radial dispersion of both heat and mass on the behavior of cooled fixed‐bed reactors was explored using a two‐dimensional reactor model. This study accounted for dispersion through an effective radial thermal conductivity (λrad) and a radial dispersion coefficient of mass (Drad), with Fischer–Tropsch synthesis serving as an illustrative process example. Under moderate reaction conditions and hence still rather gentle radial temperature profiles, the effect of mass dispersion on reactor performance was found to be minimal, even if disregarded (Drad = 0), whereas dispersion of heat (λrad) always significantly impacts reactor behavior. Nevertheless, for precise thermal runaway predictions by a reactor model, incorporating mass dispersion by a realistic Drad value is essential.

Non-invasive temperature monitoring in fixed-bed reactors by electrical capacitance tomography

Abstract Knowledge of the temperature distribution in fixed-bed reactors is of great importance for process control and optimization in many processes of the chemical industry. The state of the art is defined by invasive measuring methods for temperature measurement in such reactors. However, all invasive methods influence both the structure of the fixed-bed and the flow conditions and thus falsify the measurement results compared to real undisturbed conditions in a fixed-bed, above all with regard to the radial temperature profile. In addition, the temperature distribution in the entire reactor is usually derived from a few discrete measuring points based on a model, which sometimes results in large deviations from reality. In this article, electrical capacitance tomography (ECT) is explored as an alternative, non-invasive measurement method to monitor the temperature distribution inside fixed-bed reactors. The method exploits the temperature dependence of the effective bulk permittivity of the reactor filling. By way of an example, this dependence has been investigated in this work for two different hydrogenation catalysts. A temperature-resistant ECT sensor has been designed to perform measurements under the influence of temperature. The investigations show that, with the aid of ECT, it is possible to detect relative temperature changes in the region of interest with the materials examined.

Design and simulation of a novel reactor for the H2 storage mechanism in methylcyclohexane

The present study addresses the modeling and simulation of an intensified dehydrogenation reactor-heat exchanger system designed for a H2-based 2.0 MW mobile power plant. The reactor consisted of a multiple triple-tube system where the catalyst was packed in the middle tube while hot exhaust gases passed through the innermost and outermost tubes. A basecase design was defined and the reactor was simulated using the rigorous kinetics developed elsewhere for the MCH dehydrogenation. The parabolic differential equations of mass and heat energy were solved and the axial and radial conversion and temperature profiles were computed. Moreover, the effects of the number of longitudinal fins on the reactor tubes as well as the flow direction were also studied. With 12 number of fins on the reactor tube, the MCH conversion increased from 70.8% to 81.8%, with a corresponding increase in the average bed temperature from 569.3 K to 577.6 K and hydrogen yield from 37.05 kmol h−1 to 42.79 kmol h−1.

A generalized curvilinear solver for spherical shell Rayleigh-Bénard convection

Summary A three-dimensional finite-difference solver has been developed and implemented for Boussinesq convection in a spherical shell. The solver transforms any complex curvilinear domain into an equivalent Cartesian domain using Jacobi transformation and solves the governing equations in the latter. This feature enables the solver to account for the effects of the non-spherical shape of the convective regions of planets and stars. Apart from parallelization using MPI, implicit treatment of the viscous terms using a pipeline alternating direction implicit scheme and HYPRE multigrid accelerator for pressure correction makes the solver efficient for high-fidelity direct numerical simulations. We have performed simulations of Rayleigh-Bénard convection at two Rayleigh numbers Ra = 105 and 107 while keeping the Prandtl number fixed at unity (Pr = 1). The average radial temperature profile and the Nusselt number match very well, both qualitatively and quantitatively, with the existing literature. Closure of the turbulent kinetic energy budget, apart from the relative magnitude of the grid spacing compared to the local Kolmogorov scales, ensures sufficient spatial resolution.

A Scaling Relation for Core Heating by Giant Impacts and Implications for Dynamo Onset

AbstractAccretional heating of Earth's interior during formation is pivotal to its subsequent thermal and chemical evolution. In particular, impact heating of Earth's core is expected, but its amplitude and radial distribution within the core is unknown and could influence the onset of the geodynamo. The uncertainty is due, in part, to the lack of constraints on the temperature of the interior following formation due to the difficulty of preserving a record of such a high energy environment, and the assertion that super‐heating during formation would be rapidly lost through magma ocean cooling. Here we systematically investigate core heating due to giant impacts using a Smoothed Particle Hydrodynamics (SPH) code with simulations spanning a range of impact angles, velocities, and masses. From these simulations we derive a scaling relation for core heating that depends on the impact parameters and predicts the radial core temperature profile following the impact. Our findings show that a significant amount of heat is deposited into the core, with a canonical impact scenario resulting in an average core temperature increase of about 3000 K, approximately 500 K higher than that of the overlying mantle. In this case the heat distribution within the core produces a strong thermal stratification. We use a parameterized cooling model to estimate that the core could have cooled to an adiabatic state ∼290 Myr after a canonical impact, which is consistent with the observed time span between the age of the Moon and evidence for an active geodynamo.

Mass and heat transfer in the boundary layer region of modified second-grade fluid flow over a linearly stretched sheet embedded in porous media

Here, we have improved a model to describe the flow variables, velocity, mass and heat transfer in the boundary layer region of modified second-grade fluid flow over a linearly stretched sheet in a porous media. The modified model is used to study the qualitative impact of buoyancy parameter, second-grade fluid parameter, magnetic parameters, porous parameter, power-law index, and chemical reaction parameter on the flow profiles, radial and axial velocities, temperature, and concentration. Starting with the steady-state governing equations of mass, momentum, heat, and concentration of the fluid flow, we obtained the boundary layer approximations of the flow near the linearly stretched sheet with the no-slip boundary condition. Similarity transformation has been used to convert the partial differential equations system into a nonlinear ordinary differential equations system. The radial velocities, temperature, and concentration profiles have been solved numerically, and the qualitative influence of the flow parameters on the flow variables has been simulated and graphically presented for comparison. We have observed that radial and axial velocities were increasing for the shear-thinning and shearthickening fluids with solutal Grashof number, thermal Grashof number and second-grade fluid parameters. In contrast, the porous and chemical reaction parameters slow down both fluids’ radial and axial velocities. The temperature and concentration increase with the porous and magnetic parameters. However, thermal and solutal Grashof and second-grade fluid parameters suppress temperature and concentration. In shear-thickening fluids, chemical reaction parameters enhance concentration but suppress in shear-thinning fluids.

Elevated Electron Temperature Coincident with Observed Fusion Reactions in a Sheared-Flow-Stabilized Z Pinch.

The sheared-flow-stabilized Z pinch concept has been studied extensively and is able to produce fusion-relevant plasma parameters along with neutron production over several microseconds. We present here elevated electron temperature results spatially and temporally coincident with the plasma neutron source. An optical Thomson scattering apparatus designed for the FuZE device measures temperatures in the range of 1-3keV on the axis of the device, 20cm downstream of the nose cone. The 17-fiber system measures the radial profiles of the electron temperature. Scanning the laser time with respect to the neutron pulse time over a series of discharges allows the reconstruction of the T_{e} temporal response, confirming that the electron temperature peaks simultaneously with the neutron output, as well as the pinch current and inductive voltage generated within the plasma. Comparison to spectroscopic ion temperature measurements suggests a plasma in thermal equilibrium. The elevated T_{e} confirms the presence of a plasma assembled on axis, and indicates limited radiative losses, demonstrating a basis for scaling this device toward net gain fusion conditions.

Thermalization of Mesh Reinforced Ultra-Thin Al-Coated Plastic Films: A Parametric Study Applied to the Athena X-IFU Instrument.

The X-ray Integral Field Unit (X-IFU) is one of the two focal plane detectors of Athena, a large-class high energy astrophysics space mission approved by ESA in the Cosmic Vision 2015-2025 Science Program. The X-IFU consists of a large array of transition edge sensor micro-calorimeters that operate at ~100 mK inside a sophisticated cryostat. To prevent molecular contamination and to minimize photon shot noise on the sensitive X-IFU cryogenic detector array, a set of thermal filters (THFs) operating at different temperatures are needed. Since contamination already occurs below 300 K, the outer and more exposed THF must be kept at a higher temperature. To meet the low energy effective area requirements, the THFs are to be made of a thin polyimide film (45 nm) coated in aluminum (30 nm) and supported by a metallic mesh. Due to the small thickness and the low thermal conductance of the material, the membranes are prone to developing a radial temperature gradient due to radiative coupling with the environment. Considering the fragility of the membrane and the high reflectivity in IR energy domain, temperature measurements are difficult. In this work, a parametric numerical study is performed to retrieve the radial temperature profile of the larger and outer THF of the Athena X-IFU using a Finite Element Model approach. The effects on the radial temperature profile of different design parameters and boundary conditions are considered: (i) the mesh design and material, (ii) the plating material, (iii) the addition of a thick Y-cross applied over the mesh, (iv) an active heating heat flux injected on the center and (v) a Joule heating of the mesh. The outcomes of this study have guided the choice of the baseline strategy for the heating of the Athena X-IFU THFs, fulfilling the stringent thermal specifications of the instrument.

Plasma profile reconstruction supported by kinetic modeling

Combining the analysis of multiple diagnostics and well-chosen prior information in the framework of Bayesian probability theory, the Integrated Data Analysis code (IDA Fischer et al 2010 Fusion Sci. Technol. 58 675–84) can provide density and temperature radial profiles of fusion plasmas. These IDA-fitted measurements are then used for further analysis, such as discharge simulations and other experimental data analysis. Since IDA considers measurement data, which is frequently fragmentary, with statistical and systematic uncertainties, which are often difficult to quantify, from a heterogeneous set of diagnostics, the fitted profiles and their gradients may be in contradiction to well-established expectations from transport theory. Using the modeling suite ASTRA coupled with the quasi-linear transport solver TGLF, we have created a loop in which simulated profiles and their uncertainties are fed back into IDA as an additional prior, thus providing constraints about the physically reasonable parameter space. We apply this physics-motivated prior to several different plasma scenarios and find improved heat flux match, while still matching the experimental data. This work feeds into a broader effort to make IDA more robust against measurement uncertainties or lack of measurements by combining multiple transport solvers with different levels of complexity and computing costs in a multi-fidelity approach.

Simulating X-Ray Reverberation in the Ultraviolet-emitting Regions of Active Galactic Nuclei Accretion Disks with Three-dimensional Multifrequency Radiation Magnetohydrodynamic Simulations

Active galactic nuclei (AGN) light curves observed with different wave bands show that the variability in longer wavelength bands lags the variability in shorter wavelength bands. Measuring these lags, or reverberation mapping, is used to measure the radial temperature profile and extent of AGN disks, typically with a reprocessing model that assumes X-rays are the main driver of the variability in other wavelength bands. To demonstrate how this reprocessing works with realistic accretion disk structures, we use 3D local shearing box multifrequency radiation magnetohydrodynamic simulations to model the UV-emitting region of an AGN disk, which is unstable to the magnetorotational instability and convection. At the same time, we inject hard X-rays (>1 keV) into the simulation box to study the effects of X-ray irradiation on the local properties of the turbulence and the resulting variability of the emitted UV light curve. We find that disk turbulence is sufficient to drive intrinsic variability in emitted UV light curves and that a damped random walk model is a good fit to this UV light curve for timescales >5 days. Meanwhile, X-ray irradiation has negligible impact on the power spectrum of the emitted UV light curve. Furthermore, the injected X-ray and emitted UV light curves are only correlated if there is X-ray variability on timescales >1 day, in which case we find a correlation coefficient r = 0.34. These results suggest that if the opacity for hard X-rays is scattering dominated as in the standard disk model, hard X-rays are not the main driver of reverberation signals.

Area averaging of packed bed in continua conservation equations in axial flow

AbstractA novel averaging of the conservation equations for axial flow in packed beds is presented to express the momentum, continuity, and energy equations in terms of the cross‐sectional averages of concentration, temperature, and superficial velocity. The model integrates the radial fluctuations of the intrinsic variables into the partial differential equations of the model and presents a method for the design and analysis of catalytic reactors at a broad range of Reynolds numbers without the necessity of adjusting the operating conditions to minimize the impact of the radial profiles of velocity, concentration, and temperature. Since the control of the industrial reactors is dependent on the average values of the concentration and temperature, the model can be directly employed for design, optimization, and control processes with the added advantage of time and cost savings for both the numerical resolution and laboratory testing expenses. The model is limited to reaction systems with Péclet numbers of less than 700 with an average void fraction of for which the ratio of the bed length‐to‐particle diameter to particle Péclet number exceeds . The model was applied to the simulation of steam methane reforming (SMR). The results indicate that the average equations predict the responses of the SMR properly and thus the model could be reliably utilized for process design, operation, and control.

Can radial temperature profiles be inferred using NH3 (1, 1) and (2, 2) observations?

ABSTRACT A number of works infer radial temperature profiles of envelopes surrounding young stellar objects using several rotational transitions in a pixel-by-pixel or azimuthally averaged basis. However, in many cases the assumption that the rotational temperature is constant along the line of sight is made, while this is not the case when a partially resolved envelope, assumed to be spherically symmetric, is used to obtain values of temperature for different projected radii. This kind of analysis (homogeneous analysis) is intrinsically inconsistent. By using a spherical envelope model to interpret NH3 (1,1) and (2,2) observations, we tested how robust it is to infer radial temperature profiles of an envelope. The temperature and density of the model envelope are power laws of radius, but the density can be flat for an inner central part. The homogeneous analysis was applied to obtain radial temperature profiles, and resulted that for small projected radii, where the optical depth of the lines is high, the homogeneous temperature can be much higher than the actual envelope temperature. In general, for larger projected radii, both the temperature and the temperature power-law index can be underestimated by as much as 40 per cent, and 0.15, respectively. We applied this study to the infrared dark cloud G14.225–0.506 for which the radial temperature profile was previously derived from the dust emission at submillimetre wavelengths and the spectral energy distribution. As expected, the homogeneous analysis underestimated both the temperature and the temperature power-law index.

Feasibility of Using Mixed-Oxide Fuel for a Pressurized Water Reactor Instead of Traditional UO2 Fuel Material

This study examines the feasibility of utilizing mixed-oxide fuel [(U0.9, rgPu0.1) O2] instead of traditional UO2 in nuclear reactors. The utilization of (U0.9, rgPu0.1) O2 is particularly significant as it represents an effective approach to nuclear fuel recycling by combining reactor-grade plutonium extracted from partially used nuclear fuel and depleted uranium obtained through the enrichment process. The fundamental neutronic characteristics, such as the radial power distribution, were investigated using the MCNPX 2.7 algorithm to identify the specific channel for subsequent thermal-hydraulic (TH) analysis. The TH analysis was conducted using COMSOL-Multiphysics, allowing for the estimation of the fuel rod’s axial and radial temperature profiles, as well as the determination of the departure from the nucleate boiling ratio. Furthermore, the coupling between heat transfer and solid structure (SS) was achieved using the Multiphysics tool in COMSOL-Multiphysics. This coupling facilitated the simulation of key SS parameters, including von Mises stress, volumetric strain, and displacement, while considering the influence of heat transfer. The results demonstrate significant improvements and enhanced safety margins when utilizing (U0.9, rgPu0.1) O2.

Interaction between forced and natural convection in a thin cylindrical fluid layer at low Prandtl number

Motivated by nuclear safety issues, we study the heat transfers in a thin cylindrical fluid layer with imposed fluxes at the bottom and top surfaces (not necessarily equal) and a fixed temperature on the sides. We combine direct numerical simulations and a theoretical approach to derive scaling laws for the mean temperature and for the temperature difference between the top and bottom of the system. We find two asymptotic scaling laws depending on the flux ratio between the upper and lower boundaries. The first one is controlled by heat transfer to the side, for which we recover scaling laws characteristic of natural convection (Batchelor, Q. Appl. Maths, vol. 12, 1954, pp. 209–233). The second one is driven by vertical heat transfers analogous to Rayleigh–Bénard convection (Grossmann &amp; Lohse, J. Fluid Mech., vol. 407, 2000, pp. 27–56). We show that the system is inherently inhomogeneous, and that the heat transfer results from a superposition of both asymptotic regimes. Keeping in mind nuclear safety models, we also derive a one-dimensional model of the radial temperature profile based on a detailed analysis of the flow structure, hence providing a way to relate this profile to the imposed boundary conditions.