A Parametric Numerical Study of Radiative Transfer in Thermotropic Materials

2013 ◽  
Author(s):  
Adam C. Gladen ◽  
Susan C. Mantell ◽  
Jane H. Davidson
Keyword(s):  
Particle Size ◽  
Radiative Transfer ◽  
Optical Thickness ◽  
Parametric Study ◽  
Volume Fraction ◽  
Numerical Study ◽  
Anisotropic Scattering ◽  
Index Of Refraction ◽  
Spherical Particles ◽  
Size Parameter

A thermotropic material is modeled as an absorbing, thin slab containing anisotropic scattering, monodisperse, spherical particles. Monte Carlo ray tracing is used to solve the governing equation of radiative transfer. Predicted results are validated by comparison to the measured normal-hemispherical reflectance and transmittance of samples with various volume fraction and relative index of refraction. A parametric study elucidates the effects of particle size parameter, scattering albedo, and optical thickness on the normal-hemispherical transmittance, reflectance, and absorptance. The results are interpreted for a thermotropic material used for overheat protection of a polymer solar absorber. For the preferred particle size parameter of 2, the optical thickness should be less than 0.3 to ensure high transmittance in the clear state. To significantly reduce the transmittance and increase the reflectance in the translucent state, the optical thickness should be greater than 2.5 and the scattering albedo should be greater than 0.995. For optical thickness greater than 5, the reflectance is asymptotic and any further reduction in transmittance is through increased absorptance. A case study is used to illustrate how the parametric study can be used to guide the design of thermotropic materials. Low molecular weighted polyethylene in poly(methyl methacrylate) is identified as a potential thermotropic material. For this material and a particle radius of 200 nm, it is determined that the volume fraction and thickness should equal 10% and 1 mm, respectively.

A Parametric Numerical Study of Optical Behavior of Thermotropic Materials for Solar Thermal Collectors

2014 ◽  
Vol 136 (7) ◽  
Author(s):  
Adam C. Gladen ◽  
Susan C. Mantell ◽  
Jane H. Davidson
Keyword(s):  
Particle Size ◽  
Optical Thickness ◽  
Numerical Study ◽  
Monte Carlo Model ◽  
Size Parameter ◽  
Solar Absorbers ◽  
Different Temperatures ◽  
Solar Thermal Collectors ◽  
Optical Behavior

A Monte Carlo model is applied to determinate the steady state, solar-weighted optical properties of potential thermotropic composite materials for overheat protection of polymer solar absorbers. The key results are dimensionless plots of normal-hemispherical transmittance, reflectance and absorptance as a function of particle size parameter, scattering albedo, and overall optical thickness. The optical behavior of thermotropic materials at different temperatures is represented by a change in the relative refractive index which affects the scattering albedo and optical thickness. At low temperatures where overheat protection is not required, referred to as the clear state, the overall optical thickness should be less than 0.3 to ensure high transmittance for the preferred particle size parameter of 2. At higher temperatures where overheat protection is required, referred to as the translucent state, the overall optical thickness should be greater than 10 and the scattering albedo should be greater than 0.995 to achieve 50% reflectance. A case study of low molecular weighted polyethylene in poly(methyl methacrylate) is presented to illustrate use of the results to guide the design of thermotropic materials.

Suspensions with a tunable effective viscosity: a numerical study

2012 ◽  
Vol 693 ◽  
pp. 345-366 ◽  
Author(s):  
L. Jibuti ◽  
S. Rafaï ◽  
P. Peyla
Keyword(s):  
Effective Viscosity ◽  
Volume Fraction ◽  
Numerical Study ◽  
Spherical Particles ◽  
Dimensionless Number ◽  
Particle Rotation ◽  
Concentrated Suspensions ◽  
Sheared Suspensions ◽  
Neutrally Buoyant ◽  
Universal Behaviour

AbstractIn this paper, we conduct a numerical investigation of sheared suspensions of non-colloidal spherical particles on which a torque is applied. Particles are mono-dispersed and neutrally buoyant. Since the torque modifies particle rotation, we show that it can indeed strongly change the effective viscosity of semi-dilute or even more concentrated suspensions. We perform our calculations up to a volume fraction of 28 %. And we compare our results to data obtained at 40 % by Yeo and Maxey (Phys. Rev. E, vol. 81, 2010, p. 62501) with a totally different numerical method. Depending on the torque orientation, one can increase (decrease) the rotation of the particles. This results in a strong enhancement (reduction) of the effective shear viscosity of the suspension. We construct a dimensionless number $\Theta $ which represents the average relative angular velocity of the particles divided by the vorticity of the fluid generated by the shear flow. We show that the contribution of the particles to the effective viscosity can be suppressed for a given and unique value of $\Theta $ independently of the volume fraction. In addition, we obtain a universal behaviour (i.e. independent of the volume fraction) when we plot the relative effective viscosity divided by the relative effective viscosity without torque as a function of $\Theta $. Finally, we show that a modified Faxén law can be equivalently established for large concentrations.

Effect of Stress Wave Scattering at the Liquid-Particle Interface on Viscosity Calculation of Nanocolloidal Dispersions

2008 ◽  
Author(s):  
Tao Wang ◽  
Xinwei Wang ◽  
Haiping Hong ◽  
Zhongyang Luo ◽  
Kefa Cen
Keyword(s):  
Particle Size ◽  
Autocorrelation Function ◽  
Stress Wave ◽  
Wave Scattering ◽  
Volume Fraction ◽  
Solid Particles ◽  
Spherical Particles ◽  
Computational Domain ◽  
Liquid Particle ◽  
Pressure Tensor

In this work, extensive equilibrium molecular dynamics simulations are conducted to study the shear viscosity of nanocolloidal dispersion. Strong oscillation of the pressure tensor autocorrelation function is observed. The computational domain contains solvent of liquid argon at 143.4 K and spherical particles with volume fraction of 3%. By studying the effect of the particle size, particle density, and acoustic impedance, it is found for the first time that the stress wave scattering/reflecting at the liquid-particle interface due to acoustic mismatch plays a critical important role in the oscillation of pressure tensor autocorrelation function. The Brownian motion/vibration of solid particles is considered to have little effect on the oscillation of pressure tensor autocorrelation function curve except the frequency. And when the particle size is comparable with the wavelength of stress wave, the diffraction of stress wave happens at the interface that will also weaken the oscillation of pressure tensor autocorrelation function.

Radiative Transfer With Dependent Scattering by Particles: Part 1—Theoretical Investigation

1986 ◽  
Vol 108 (3) ◽  
pp. 608-613 ◽  
Author(s):  
J. D. Cartigny ◽  
Y. Yamada ◽  
C. L. Tien
Keyword(s):  
Radiative Transfer ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Spherical Particles ◽  
Sphere Model ◽  
Radiation Scattering ◽  
Particle Volume ◽  
Scattering Approximation ◽  
Regime Map ◽  
Packed Sphere

Dependent radiation scattering for which the independent scattering theory fails to predict the scattering properties is important in analyzing radiative transfer in packed and fluidized beds. In this paper the dependent scattering properties have been derived assuming the Rayleigh–Debye scattering approximation for two cases: two identical spheres and a cloud of spherical particles. The two-sphere calculated results compare well with the exact solutions in the literature, giving confidence in the present analytical approach. The gas model and packed-sphere model have been employed to calculate dependent scattering properties for a cloud of particles of small and large particle volume fraction, respectively. The calculated dependent scattering efficiencies for a cloud of particles are smaller than the independent scattering efficiencies and decrease with increasing particle volume fraction. A regime map for independent and dependent scattering has been constructed and compared with existing empirical criteria.

scholarly journals Testing remote sensing on artificial observations: impact of drizzle and 3-D cloud structure on effective radius retrievals

2010 ◽  
Vol 10 (19) ◽  
pp. 9535-9549 ◽  
Author(s):  
T. Zinner ◽  
G. Wind ◽  
S. Platnick ◽  
A. S. Ackerman
Keyword(s):  
Remote Sensing ◽  
Particle Size ◽  
Radiative Transfer ◽  
Droplet Size ◽  
Optical Thickness ◽  
Marine Boundary Layer ◽  
Effective Radius ◽  
Retrieval Algorithm ◽  
Moderate Resolution Imaging Spectroradiometer ◽  
The Impact

Abstract. Remote sensing of cloud effective particle size with passive sensors like the Moderate Resolution Imaging Spectroradiometer (MODIS) is an important tool for cloud microphysical studies. As a measure of the radiatively relevant droplet size, effective radius can be retrieved with different combinations of visible through shortwave and midwave infrared channels. In practice, retrieved effective radii from these combinations can be quite different. This difference is perhaps indicative of different penetration depths and path lengths for the spectral reflectances used. In addition, operational liquid water cloud retrievals are based on the assumption of a relatively narrow distribution of droplet sizes; the role of larger precipitation particles in these distributions is neglected. Therefore, possible explanations for the discrepancy in some MODIS spectral size retrievals could include 3-D radiative transport effects, including sub-pixel cloud inhomogeneity, and/or the impact of drizzle formation. For three cloud cases the possible factors of influence are isolated and investigated in detail by the use of simulated cloud scenes and synthetic satellite data: marine boundary layer cloud scenes from large eddy simulations (LES) with detailed microphysics are combined with Monte Carlo radiative transfer calculations that explicitly account for the detailed droplet size distributions as well as 3-D radiative transfer to simulate MODIS observations. The operational MODIS optical thickness and effective radius retrieval algorithm is applied to these and the results are compared to the given LES microphysics. We investigate two types of marine cloud situations each with and without drizzle from LES simulations: (1) a typical daytime stratocumulus deck at two times in the diurnal cycle and (2) one scene with scattered cumulus. Only small impact of drizzle formation on the retrieved domain average and on the differences between the three effective radius retrievals is noticed for both cloud scene types for different reasons. For our, presumably typical, overcast stratocumulus scenes with an optical thickness of 8 to 9 and rain rates at cloud bottom up to 0.05 mm/h clear drizzle impact on the retrievals can be excluded. The cumulus scene does not show much drizzle sensitivity either despite extended drizzle areas being directly visible from above (locally >1 mm/h), which is mainly due to technical characteristics of the standard retrieval approach. 3-D effects, on the other hand, produce large discrepancies between the 1.6 and 2.1 μm channel observations compared to 3.7 μm retrievals in the latter case. A general sensitivity of MODIS particle size data to drizzle formation is not corroborated by our case studies.

Numerical study of GFRP joints bearing strength reduction due to drilling-induced delamination

2019 ◽  
Vol 54 (16) ◽  
pp. 2185-2194 ◽  
Author(s):  
M Safarabadi ◽  
M Sardar
Keyword(s):  
Parametric Study ◽  
Cohesive Zone ◽  
Volume Fraction ◽  
Numerical Study ◽  
Load Carrying Capacity ◽  
Zone Method ◽  
Bearing Strength ◽  
Load Carrying ◽  
Negative Effect ◽  
Good Agreement

Delamination is one of the most common defects caused by drilling, which can have negative effect on the joint performance. This study investigates the effect of delamination on the bearing strength of [0/90]2s, [15/−75]2s, [30/−60]2s and [45/−45]2s GFRP layers numerically. Cohesive zone method and virtual crack closure technique have been used for delamination modeling and the results of these two methods have been compared. FEM results show good agreement with available experimental data. Results demonstrated that delamination reduces the bearing strength. Among four different stacking sequences, delamination has the most effect on the laminate with the stacking sequence of [0/90]2s. In both delaminated and non-delaminated models, [0/90]2s and [45/−45]2s stacking sequences have the most and the least bearing strength, respectively. By increasing the radius of delaminated zone from 3 mm to 15 mm, bearing strength does not change a lot. As the delaminated zone reaches the edge of the specimen, bearing strength reduces strongly because the layers separate completely and the load-carrying capacity reduces. A parametric study was also conducted to examine the effects of different factors. The results of parametric study showed that by increasing the volume fraction of the fiber as well as the use of carbon fiber instead of glass fiber, the bearing strength increases.

scholarly journals Experimental investigation of turbulent suspensions of spherical particles in a square duct

2018 ◽  
Vol 857 ◽  
pp. 748-783 ◽  
Author(s):  
Sagar Zade ◽  
Pedro Costa ◽  
Walter Fornari ◽  
Fredrik Lundell ◽  
Luca Brandt
Keyword(s):  
Particle Size ◽  
Reynolds Number ◽  
Pressure Drop ◽  
Single Phase ◽  
Volume Fraction ◽  
Particle Diameter ◽  
Spherical Particles ◽  
Particle Sizes ◽  
Duct Flow ◽  
Square Duct

We report experimental observations of turbulent flow with spherical particles in a square duct. Three particle sizes, namely $2H/d_{p}=40$ , 16 and 9 ( $2H$ being the duct full height and $d_{p}$ being the particle diameter), are investigated. The particles are nearly neutrally buoyant with a density ratio of 1.0035 and 1.01 with respect to the suspending fluid. Refractive index matched–particle image velocimetry (RIM–PIV) is used for fluid velocity measurement even at the highest particle volume fraction (20 %) and particle tracking velocimetry (PTV) for the particle velocity statistics for the flows seeded with particles of the two largest sizes, whereas only pressure measurements are reported for the smallest particles. Settling effects are seen at the lowest bulk Reynolds number $Re_{2H}\approx$ 10 000, whereas, at the highest $Re_{2H}\approx 27\,000$ , particles are in almost full suspension. The friction factor of the suspensions is found to be significantly larger than that of single-phase duct flow at the lower $Re_{2H}$ investigated; however, the difference decreases when increasing the flow rate and the total drag approaches the values of the single-phase flow at the higher Reynolds number considered, $Re_{2H}=27\,000$ . The pressure drop is found to decrease with the particle diameter for volume fractions lower than $\unicode[STIX]{x1D719}=10\,\%$ for nearly all $Re_{2H}$ investigated. However, at the highest volume fraction $\unicode[STIX]{x1D719}=20\,\%$ , we report a peculiar non-monotonic behaviour: the pressure drop first decreases and then increases with increasing particle size. The decrease of the turbulent drag with particle size at the lowest volume fractions is related to an attenuation of the turbulence. The drag increase for the two largest particle sizes at $\unicode[STIX]{x1D719}=20\,\%$ , however, occurs despite this large reduction of the turbulent stresses, and it is therefore due to significant particle-induced stresses. At the lowest Reynolds number, the particles reside mostly in the bottom half of the duct, where the mean velocity significantly decreases; the flow is similar to that in a moving porous bed near the bottom wall and to turbulent duct flow with low particle concentration near the top wall.

Effective thermal conductivity of silicone/phosphor composites

2011 ◽  
Vol 45 (23) ◽  
pp. 2465-2473 ◽  
Author(s):  
Qin Zhang ◽  
Zhihua Pi ◽  
Mingxiang Chen ◽  
Xiaobing Luo ◽  
Ling Xu ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Particle Size ◽  
Effective Thermal Conductivity ◽  
Volume Fraction ◽  
Numerical Study ◽  
Element Model ◽  
Interfacial Thermal Resistance ◽  
Conductivity Measurements ◽  
The Monte Carlo Method ◽  
Random Particle

The effective thermal conductivity of silicone/phosphor composites is studied experimentally and numerically. Thermal conductivity measurements are conducted from 30°C to 150°C for the composites with phosphor volume fraction up to 40%. In the numerical study, a finite element model with empirical particle size distribution and random particle position is constructed using a probability density function and the Monte Carlo method, and the interfacial thermal resistance layer between phases also introduced in the model. The results indicate that when phosphor concentration is below 25 vol.%, the conductivity of the composite increases slightly with either phosphor volume fraction or temperature, and the Kapitza radius of the composite is 0.8 µm. When phosphor concentration is above 25 vol.%, the increase of conductivity correlates positively with phosphor volume fraction significantly but negatively with the temperature, and the Kapitza radius is 0.032 µm.

Infrared Radiative Properties of Thin Polyethylene Coating Pigmented With Titanium Dioxide Particles

2009 ◽  
Vol 132 (2) ◽  
Author(s):  
Mehdi Baneshi ◽  
Shigenao Maruyama ◽  
Atsuki Komiya
Keyword(s):  
Particle Size ◽  
Volume Fraction ◽  
Near Field ◽  
Field Approximation ◽  
Anisotropic Scattering ◽  
Radiative Properties ◽  
Emission Model ◽  
Tio2 Pigment ◽  
Pigmented Coatings ◽  
Thin Polyethylene

The infrared (IR) radiative properties of TiO2 pigment particles must be known to perform thermal analysis of a TiO2 pigmented coating. Resins generally used in making pigmented coatings are absorbing at IR wavelengths, which means that the conventional Mie solution (MS) may not be adequate in this domain. There are two approaches to evaluating radiative properties in an absorbing medium: far field approximation (FFA) and near field approximation (NFA). In this study, after reviewing these two approaches, we evaluated the radiative properties of TiO2 particles in polyethylene resin as an absorbing matrix in the wavelength range of 1.7–15 μm based on the MS, FFA, and NFA. We then calculated the effective scattering and absorption coefficients for different models. To investigate the effect of the particle size and volume concentration on the transmittance of IR wavelengths, we made a nongray radiative heat transfer in an anisotropic scattering monodisperse pigmented layer, with independent scattering using the radiation element method by the ray emission model. The results showed that all three approaches predicted similar results in the particle size domain and volume fraction range utilized in pigmented coatings.

Radiation Properties for Polydispersions: Application to Coal

1980 ◽  
Vol 102 (1) ◽  
pp. 99-103 ◽  
Author(s):  
R. O. Buckius ◽  
D. C. Hwang
Keyword(s):  
Particle Size ◽  
Index Of Refraction ◽  
Spherical Particles ◽  
Asymmetry Factor ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Absorption Coefficients ◽  
Spectral Radiation ◽  
Radiation Properties ◽  
Practical Temperature

The extinction and absorption coefficients and the asymmetry factor for polydispersions of absorbing spherical particles are analyzed. The results are based upon Mie’s theory for single spherical particles and particle size distributions found in practical systems. Dimensinnless spectral radiation properties are shown to be independent of the explicit size distribution and functions only of the average radii and the index of refraction. The Planck and Rosseland mean coefficients are also presented and the dependence on temperature is explicitly denoted for a large practical temperature range. The results for coal with optical properties which are wavelength dependent indicate the usefulness of the dimensionless and mean properties.

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