HEATING DEPTH OF GAS SUSPENSION FLOW BY COUNTER RADIATION

2021 ◽  
pp. 32-38
Author(s):  
Н.Л. Полетаев ◽  
Д.В. Ушаков ◽  
А.А. Абашкин
Keyword(s):  
Distribution Function ◽  
Temperature Distribution ◽  
Coordinate System ◽  
Gas Phase ◽  
Free Path ◽  
Surface Radiation ◽  
Gas Suspension ◽  
Analytical Estimate ◽  
Air Suspension ◽  
Inert Particles

Выполнена аналитическая оценка отношения глубины прогрева газовзвеси излучением продуктов горения S к длине свободного пробега излучения в газовзвеси L. Использована одномерная модель стационарного распределения температуры в потоке взвешенных в воздухе монодисперсных инертных частиц, движущихся на равномерно нагретую абсолютно черную поверхность, имитирующую фронт пламени. Учитывается отражение и переизлучение тепловой энергии частицами. S / L >> 1 при низкой степени черноты и/или высокой конечной температуре частиц. It is accepted that the depth of heating of the gas suspension by the radiation of combustion products SR is equal to the length LR of the free path of radiation in the gas suspension: SR ≈ LR. Numerical simulation of gas-air mixture combustion with the addition of inert particles, taking into account the re-emission of heat by heated particles of fresh suspension, shows the possibility of realizing the ratio SR >> LR (Ivanov M.F. et al, 2015). In this work, an analytical estimate of the SR/LR ratio is carried out within the framework of one-dimensional modeling of the temperature distribution in the flow of initially cold monodisperse inert particles suspended in air, moving to a uniformly heated absolutely black surface, permeable to air suspension and simulating a flame front. The following assumptions are used. The solution is stationary in the coordinate system associated with the emitting surface; radiation consists of two oppositely directed streams of electromagnetic energy; the interaction of particles and radiation is described in the approximation of geometric optics and takes into account both the processes of absorption and emission of thermal energy, and the process of reflection of radiation; the temperature inside the particle is the same. In contrast to the previously considered (Poletaev N.L., 2021) the simplified problem of the motion of particles in a vacuum or in the presence of a gas phase heated by particles but not experiencing thermal expansion, this work took into account both the presence of a gas phase heated by particles and expansion of the gas phase. The latter causes the acceleration and expansion of the air suspension as it approaches the radiating surface. The difference in the local values of temperatures and phase motion velocities of the air suspension was neglected. It is shown that the quasi-linear (in the above-mentioned coordinate system) temperature distribution function in the air suspension obtained in this work is qualitatively different from the quasi-exponential temperature distribution function obtained earlier by solving a simplified problem. At the same time, the ratio of the heating depth of the air suspension by thermal radiation and the free path of radiation in the layer of air suspension adjacent to the radiating plane turned out to be similar to that obtained for the simplified solution. Namely, SR/LR >> 1 at a low integral degree of emissivity of the particle material and / or at a high final temperature of the particles, comparable to the temperature of the emitting surface.

A Note on Modeling of Nano-Scale Thermal Flow via the Lattice Boltzmann Method

2012 ◽  
Author(s):  
P. Lopez ◽  
Y. Bayazitoglu
Keyword(s):  
Distribution Function ◽  
Free Path ◽  
Knudsen Number ◽  
Reference Data ◽  
Mean Free Path ◽  
Knudsen Layer ◽  
High Order ◽  
Distance Functions ◽  
Transition Flow ◽  
Wall Distance

Lattice Boltzmann (LB) method models have been demonstrated to provide an accurate representation of the flow characteristics in rarefied flows. Conditions in such flows are characterized by the Knudsen number (Kn), defined as the ratio between the gas molecular Mean Free Path ( MFP, λ) and the device characteristic length (L). As the Knudsen number increases, the behavior of the flow near the walls is increasingly dominated by interactions between the gas molecules and the solid surface. Due to this, linear constitutive relations for shear stress and heat flux, which are assumed in the Navier-Stokes-Fourier (NSF) system of equations, are not valid within the Knudsen Layer (KL). Fig. 1 illustrates the characteristics of the velocity field within the Knudsen layer in a shear-driven flow. It is easily observed that although the NSF equations with slip flow boundary conditions (represented by dashed line) can predict the velocity profile in the bulk flow region, they fail to capture the flow characteristics inside the Knudsen layer. Slip flow boundary conditions have also been derived using the integral transform technique [1]. Various methods have been explored to extend the applicability of LB models to higher Knudsen number flows, including using higher order velocity sets, and using wall-distance functions to capture the effect of the walls on the mean free path by incorporating such functions on the determination of the local relaxation parameters. In this study, a high order velocity model which contains a two-dimensional, thirteen velocity direction set (e.g., D2Q13), as shown in Fig. 2, is used as the basis of the current LB model. The LB model consists of two independent distribution functions to simulate the density and temperature fields, while the Diffuse Scattering Boundary Condition (DSBC) method is used to simulate the fluid interaction with the walls. To further improve the characterization of transition flow conditions expected in nano-scale heat transfer, we explored the implementation of two wall-distance functions, derived recently based on an integrated form of a probability distribution function, to the high-order LB model. These functions are used to determine the effective mean free path values throughout the height of the micro/nano-channel, and the resulting effect is first normalized and then used to determine local relaxation times for both momentum and energy using a relationship based on the local Knudsen number. The two wall-distance functions are based on integral forms of 1) the classical probability distribution function, ψ(r) = λ0−1e−r/λ0, derived by Arlemark et al [2], in which λ0represents the reference gas mean free path, and 2) a Power-Law probability distribution function, derived by Dongari et al [3]. Thus, the probability that a molecule travels a distance between r and r+dr between two successive collisions is equal to ψ(r)dr. The general form of the integral of the two functions used can be described by ψ(r) = C − f(r), where f(r) represents the base function (exponential or Power Law), and C is set to 1 so that the probability that a molecule will travel a distance r+dr without a collision ranges from zero to 1. The performance of the present LB model coupled with the implementation of the two wall-distance functions is tested using two classical flow cases. The first case considered is that of isothermal, shear-driven Couette flow between two parallel, horizontal plates separated by a distance H, moving in opposite directions at a speed of U0. Fig. 3 shows the normalized velocity profiles across the micro-channel height for various Knudsen numbers in the transition flow regime based on our LB models as compared to data based on the Linearized Boltzmann equation [4]. The results show that our two LB models provide results that are in excellent agreement with the reference data up to the high end of the transition flow regime, with Knudsen numbers greater than 1. The second case is rarefied Fourier flow within horizontal, parallel plates, with the plates being stationary and set to a constant temperature (TTop > TBottom), and the Prandtl number is set to 0.67 to match the reference data based on the Direct Simulation Monte Carlo (DSMC) method [5]. Fig. 4 shows the normalized temperature profiles across the microchannel height for various Knudsen numbers in the slip/transition How regime. For the entire Knudsen number range studied, our two LB models provide temperature profiles that are in excellent agreement with the non-linear profile seen in the reference data. The results obtained show that the effective MFP relationship based on the exponential function improves the results obtained with the high order LB model for both shear-driven and Fourier flows up to Kn∼1. The results also show that the effective MFP relationship based on the Power Law distribution function greatly enhances the results obtained with the high order LB model for the two cases addressed, up to Kn∼3. In conclusion, the resulting LB models represent an effective tool in modeling non-equilibrium gas flows expected within micro/nano-scale devices.

Numerical Simulation of Temperature Distribution in a Containment Vessel of an Operating PWR Plant

2015 ◽  
Vol 1 (1) ◽  
Author(s):  
Yoichi Utanohara ◽  
Michio Murase ◽  
Akihiro Masui ◽  
Ryo Inomata ◽  
Yuji Kamiya
Keyword(s):  
Numerical Simulation ◽  
Temperature Distribution ◽  
Temperature Gradient ◽  
Heat Release ◽  
Gas Phase ◽  
Large Temperature ◽  
Measured Temperature ◽  
Average Temperature ◽  
Containment Vessel ◽  
Large Temperature Gradient

The structural integrity of the containment vessel (CV) for a pressurized water reactor (PWR) plant under a loss-of-coolant accident is evaluated by a safety analysis code that uses the average temperature of gas phase in the CV during reactor operation as an initial condition. Since the estimation of the average temperature by measurement is difficult, this paper addressed the numerical simulation for the temperature distribution in the CV of an operating PWR plant. The simulation considered heat generation of the equipment, the ventilation and air conditioning systems (VAC), heat transfer to the structure, and heat release to the CV exterior based on the design values of the PWR plant. The temperature increased with a rise in height within the CV and the flow field transformed from forced convection to natural convection. Compared with the measured temperature data in the actual PWR plant, predicted temperatures in the lower regions agreed well with the measured values. The temperature differences became larger above the fourth floor, and the temperature inside the steam generator (SG) loop chamber on the fourth floor was most strongly underestimated, −16.2  K due to the large temperature gradient around the heat release equipment. Nevertheless, the predicted temperature distribution represented a qualitative tendency, low at the bottom of the CV and increases with a rise in height within the CV. The total volume-averaged temperature was nearly equal to the average gas phase temperature. To improve the predictive performance, parameter studies regarding heat from the equipment and the reconsideration of the numerical model that can be applicable to large temperature gradient around the equipment are needed.

scholarly journals The Effective Temperature Distribution Function of Cataclysmic Variable White Dwarfs

1987 ◽  
Vol 93 ◽  
pp. 47-51
Author(s):  
E.M. Sion
Keyword(s):  
Distribution Function ◽  
Temperature Distribution ◽  
Orbital Period ◽  
White Dwarf ◽  
White Dwarfs ◽  
Cataclysmic Variables ◽  
Cataclysmic Variable ◽  
Term Evolution ◽  
Effective Temperatures

AbstractWith the recent detection of direct white dwarf photospheric radiation from certain cataclysmic variables in quiescent (low accretion) states, important implications and clues about the nature and long-term evolution of cataclysmic variables can emerge from an analysis of their physical properties. Detection of the underlying white dwarfs has led to a preliminary empirical CV white dwarf temperature distribution function and, in a few cases, the first detailed look at a freshly accreted while dwarf photosphere. The effective temperatures of CV white dwarfs plotted versus orbital period for each type of CV appears to reveal a tendency for the cooler white dwarf primaries to reside in the shorter period systems. Possible implications are briefly discussed.

scholarly journals Lyman continuum escape fraction and mean free path of hydrogen ionizing photons for bright z ∼ 4 QSOs from SDSS DR14

2019 ◽  
Vol 632 ◽  
pp. A45 ◽  
Author(s):  
M. Romano ◽  
A. Grazian ◽  
E. Giallongo ◽  
S. Cristiani ◽  
F. Fontanot ◽  
...  
Keyword(s):  
Distribution Function ◽  
Free Path ◽  
Rest Frame ◽  
Rapid Evolution ◽  
Cosmic Time ◽  
Flux Ratio ◽  
Mean Free Path ◽  
Skewed Distribution ◽  
Observational Cosmology ◽  
Lyman Continuum

Context. One of the main challenges in observational cosmology is related to the redshift evolution of the average hydrogen (HI) ionization in the Universe, as evidenced by the changing in ionization level of the intergalactic medium (IGM) through cosmic time. Starting from the first cosmic reionization, the rapid evolution of the IGM physical properties in particular poses severe constraints for the identification of the sources responsible for maintaining its high level of ionization up to lower redshifts. Aims. In order to probe the ionization level of the IGM and the ionization capabilities of bright quasi-stellar objects (QSOs) at z = 4, we selected a sample of 2508 QSOs drawn from the Sloan Digital Sky Survey (SDSS, DR14) in the redshift interval 3.6 ≤ z ≤ 4.6 and absolute magnitude range −29.0 ≲ M1450 ≲ −26.0. Particularly, we focus on the estimate of the escape fraction of HI-ionizing photons and their mean free path (MFP), which are fundamental for characterizing the surrounding IGM. Methods. Starting from UV/optical rest-frame spectra of the whole QSO sample from the SDSS survey, we estimated the escape fraction and free path individually for each of the QSOs. We calculated the Lyman continuum (LyC) escape fraction as the flux ratio blueward (∼900 Å rest frame) and redward (∼930 Å rest frame) of the Lyman limit. We then obtained the probability distribution function (PDF) of the individual free paths of the QSOs in the sample and studied its evolution in luminosity and redshift, comparing our results with those in literature. Results. We find a lower limit to the mean LyC escape fraction of 0.49, in agreement with the values obtained for both brighter and fainter sources at the same redshift. We show that the free paths of ionizing photons are characterized by a skewed distribution function that peaks at low values, with an average of ∼49 − 59 proper Mpc at z ∼ 4, after possible associated absorbers (AAs) were excluded. This value is higher than the one obtained at the same redshift by many authors in the literature using different techniques. Moreover, the PDF of free path gives information that is complementary to the MFP derived through the stacking technique. Finally, we also find that the redshift evolution of this parameter might be milder than previously thought. Conclusions. Our new determination of the MFP at z ∼ 4 implies that previous estimates of the HI photoionization rate ΓHI available in the literature should be corrected by a factor of 1.2−1.7. These results have important implications when they are extrapolated at the epoch of reionization.

Study of Temperature Distribution Function of Star Sensor

2010 ◽  
Vol 47 (7) ◽  
pp. 070801
Author(s):  
谭威 Tan Wei ◽  
杨建坤 Yang Jiankun ◽  
朱梦真 Zhu Mengzhen ◽  
盛定仪 Shen Dingyi ◽  
王小兵 Wang Xiaobing ◽  
...  
Keyword(s):  
Distribution Function ◽  
Temperature Distribution ◽  
Star Sensor
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