Theoretical Analysis of CFD-DEM Mathematical Model Solution Change With Varying Computational Cell Size

2018 ◽  
Author(s):  
Annette Volk ◽  
Urmila Ghia
Keyword(s):  
Mathematical Model ◽  
Standard Deviation ◽  
Cell Size ◽  
Volume Fraction ◽  
Particle Diameter ◽  
Independent Solution ◽  
Model Verification ◽  
Computational Cell ◽  
Drag Laws ◽  
Fraction Method

Successful verification and validation is crucial to build confidence in the application of coupled Computational Fluid Dynamics - Discrete Element Method (CFD-DEM). Model verification includes ensuring a mesh-independent solution, which poses a major difficulty in CFD-DEM due to the complicated solution relationship with computational cell size. In this paper, we investigate the theoretical relationship between the solution and computational cell size by tracing the effects of a change in cell size through the mathematical model. The porosity profile for simulations of fixed-particle beds is determined to be Gaussian, and the average and standard deviation of the representative distribution are reported against cell size. We find the standard deviation of bed porosity increases exponentially as the cell size is reduced, and the drag calculations are very sensitive to changes in the porosity standard deviation, resulting in an exponential change in expected drag when the cell size is small relative to the particle diameter. The divided volume fraction method of porosity calculation is shown to be superior to the centred volume fraction method, as it reduces the porosity standard deviation. The sensitivity of five popular drag laws to changes in the porosity profile is presented, and the Ergun and Beetstra drag laws are shown to be the least sensitive to changes in the cell size.

Theoretical Analysis of Computational Fluid Dynamics–Discrete Element Method Mathematical Model Solution Change With Varying Computational Cell Size

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Annette Volk ◽  
Urmila Ghia
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Standard Deviation ◽  
Discrete Element Method ◽  
Cell Size ◽  
Volume Fraction ◽  
Discrete Element ◽  
Grid Refinement ◽  
Computational Cell ◽  
Porosity Distribution

Successful verification and validation is crucial to build confidence in the application of coupled computational fluid dynamics–discrete element method (CFD–DEM). Model verification includes ensuring a mesh-independent solution, which poses a major difficulty in CFD–DEM due to the complicated relationship between solution and computational cell size. In this paper, we investigate the production of numerical error in the CFD–DEM coupling procedure with computational grid refinement. The porosity distribution output from simulations of fixed-particle beds is determined to be Gaussian, and the average and standard deviation of the representative distribution are reported against cell size. We find that the standard deviation of bed porosity increases exponentially as the cell size is reduced. The average drag calculated from each drag law is very sensitive to changes in the porosity standard deviation. When combined together, these effects result in an exponential change in expected drag force when the cell size is small relative to the particle diameter. The divided volume fraction method of porosity calculation is shown to be superior to the centered volume fraction (CVF) method. The sensitivity of five popular drag laws to changes in the porosity distribution is presented, and the Ergun and Beetstra drag laws are shown to be the least sensitive to changes in the cell size. A cell size greater than three average particle diameters is recommended to prevent errors in the simulation results. A grid refinement study (GRS) is used to quantify numerical error.

scholarly journals Nanofluid flow containing carbon nanotubes with quartic autocatalytic chemical reaction and Thompson and Troian slip at the boundary

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Muhammad Ramzan ◽  
Jae Dong Chung ◽  
Seifedine Kadry ◽  
Yu-Ming Chu ◽  
Muhammad Akhtar
Keyword(s):  
Mathematical Model ◽  
Carbon Nanotubes ◽  
Drag Force ◽  
Chemical Reaction ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Surface Drag ◽  
Nanofluid Flow ◽  
Velocity Parameter ◽  
The Impact

Abstract A mathematical model is envisioned to discourse the impact of Thompson and Troian slip boundary in the carbon nanotubes suspended nanofluid flow near a stagnation point along an expanding/contracting surface. The water is considered as a base fluid and both types of carbon nanotubes i.e., single-wall (SWCNTs) and multi-wall (MWCNTs) are considered. The flow is taken in a Dacry-Forchheimer porous media amalgamated with quartic autocatalysis chemical reaction. Additional impacts added to the novelty of the mathematical model are the heat generation/absorption and buoyancy effect. The dimensionless variables led the envisaged mathematical model to a physical problem. The numerical solution is then found by engaging MATLAB built-in bvp4c function for non-dimensional velocity, temperature, and homogeneous-heterogeneous reactions. The validation of the proposed mathematical model is ascertained by comparing it with a published article in limiting case. An excellent consensus is accomplished in this regard. The behavior of numerous dimensionless flow variables including solid volume fraction, inertia coefficient, velocity ratio parameter, porosity parameter, slip velocity parameter, magnetic parameter, Schmidt number, and strength of homogeneous/heterogeneous reaction parameters are portrayed via graphical illustrations. Computational iterations for surface drag force are tabulated to analyze the impacts at the stretched surface. It is witnessed that the slip velocity parameter enhances the fluid stream velocity and diminishes the surface drag force. Furthermore, the concentration of the nanofluid flow is augmented for higher estimates of quartic autocatalysis chemical.

An Efficient Immersed Boundary Method Based on Penalized Direct Forcing for Simulating Flows Through Real Porous Media

2012 ◽  
Author(s):  
Wim-Paul Breugem ◽  
Vincent van Dijk ◽  
René Delfos
Keyword(s):  
Porous Medium ◽  
Ct Scan ◽  
Immersed Boundary Method ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Particle Diameter ◽  
Immersed Boundary ◽  
Average Particle ◽  
Boundary Method ◽  
Direct Forcing

A computationally efficient Immersed Boundary Method (IBM) based on penalized direct forcing was employed to determine the permeability of a real porous medium. The porous medium was composed of about 9000 glass beads with an average particle diameter of 1.93 mm and a porosity of 0.367. The forcing of the IBM depends on the local solid volume fraction within a computational grid cell. The latter could be obtained from a high-resolution X-ray Computed Tomography (CT) scan of the packing. An experimental facility was built to determine the permeability of the packing experimentally. Numerical simulations were performed for the same packing based on the data from the CT scan. For a scan resolution of 0.1 mm the numerical value for the permeability was nearly 70% larger than the experimental value. An error analysis indicated that the scan resolution of 0.1 mm was too coarse for this packing.

Estimation of Interlayer Thickness in Inorganic Particulate-Filled Polymer Composites

2011 ◽  
Vol 24 (6) ◽  
pp. 777-788 ◽  
Author(s):  
J.Z. Liang
Keyword(s):  
Polymer Composites ◽  
Volume Fraction ◽  
Particle Diameter ◽  
Interfacial Structure ◽  
Interlayer Thickness ◽  
Filled Polymer ◽  
Mechanical And Physical Properties ◽  
The Relationship ◽  
Good Agreement

The structure of the interlayer between matrix and inclusions affect directly the mechanical and physical properties of inorganic particulate-filled polymer composites. The interlayer thickness is an important parameter for characterization of the interfacial structure. The effects of the interlayer between the filler particles and matrix on the mechanical properties of polymer composites were analyzed in this article. On the basis of a simplified model of interlayer, an expression for estimating the interlayer thickness ([Formula: see text]) was proposed. In addition, the relationship between the [Formula: see text] and the particle size and its concentration was discussed. The results showed that the calculations of the [Formula: see text] and thickness/particle diameter ratio ([Formula: see text]) increased nonlinearly with an increase of the volume fraction of the inclusions. Moreover, the predictions of [Formula: see text] and the relevant data reported in literature were compared, and good agreement was found between them.

A COMPARATIVE STUDY OF MULTIPLE REGRESSION AND MACHINE LEARNING TECHNIQUES FOR PREDICTION OF NANOFLUID HEAT TRANSFER

2021 ◽  
pp. 1-22
Author(s):  
Eyup Kocak ◽  
Ulku Ece Ayli ◽  
Hasmet Turkoglu
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Multiple Regression ◽  
Volume Fraction ◽  
Particle Diameter ◽  
Machine Learning Techniques ◽  
Exponential Factor ◽  
Nano Fluid ◽  
Neuro Fuzzy ◽  
Interface System

Abstract The aim of this paper is to introduce and discuss prediction power of the multiple regression technique, Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Interface System (ANFIS) methods for predicting the forced convection heat transfer characteristics of a turbulent nano fluid flow a pipe. Water and Al2O3 mixture is used as the nano fluid. Utilizing FLUENT software, numerical computations were performed with volume fraction ranging between 0.3% and 5%, particle diameter ranging between 20 and 140 nm and Reynolds number ranging between 7000 and 21000. Based on the computationally obtained results, a correlation is developed for Nusselt number using the multiple regression method. Also, based on the CFD results different ANN architectures with different number of neurons in the hidden layers and several training algorithms (Levenberg-Marquardt, Bayesian Regularization, Scaled Conjugate Gradient) are tested to find the best ANN architecture. In addition, Adaptive Neuro-fuzzy Interface System (ANFIS) is also used to predict the Nusselt number. In the ANFIS, number of clusters, exponential factor and Membership Function (MF) type are optimized. The results obtained from multiple regression correlation, ANN and ANFIS were compared. According to the obtained results, ANFIS is a powerful tool with a R2 of 0.9987 for predictions.

Observations of Precipitation Size and Fall Speed Characteristics within Coexisting Rain and Wet Snow

2006 ◽  
Vol 45 (10) ◽  
pp. 1450-1464 ◽  
Author(s):  
Sandra E. Yuter ◽  
David E. Kingsmill ◽  
Louisa B. Nance ◽  
Martin Löffler-Mang
Keyword(s):  
Particle Size ◽  
Standard Deviation ◽  
Volume Fraction ◽  
Bimodal Distribution ◽  
Particle Sizes ◽  
Large Standard Deviation ◽  
Air Temperatures ◽  
Isothermal Layer ◽  
Wet Snow ◽  
Fall Speed

Abstract Ground-based measurements of particle size and fall speed distributions using a Particle Size and Velocity (PARSIVEL) disdrometer are compared among samples obtained in mixed precipitation (rain and wet snow) and rain in the Oregon Cascade Mountains and in dry snow in the Rocky Mountains of Colorado. Coexisting rain and snow particles are distinguished using a classification method based on their size and fall speed properties. The bimodal distribution of the particles’ joint fall speed–size characteristics at air temperatures from 0.5° to 0°C suggests that wet-snow particles quickly make a transition to rain once melting has progressed sufficiently. As air temperatures increase to 1.5°C, the reduction in the number of very large aggregates with a diameter > 10 mm coincides with the appearance of rain particles larger than 6 mm. In this setting, very large raindrops appear to be the result of aggregrates melting with minimal breakup rather than formation by coalescence. In contrast to dry snow and rain, the fall speed for wet snow has a much weaker correlation between increasing size and increasing fall speed. Wet snow has a larger standard deviation of fall speed (120%–230% relative to dry snow) for a given particle size. The average fall speed for observed wet-snow particles with a diameter ≥ 2.4 mm is 2 m s−1 with a standard deviation of 0.8 m s−1. The large standard deviation is likely related to the coexistence of particles of similar physical size with different percentages of melting. These results suggest that different particle sizes are not required for aggregation since wet-snow particles of the same size can have different fall speeds. Given the large standard deviation of fall speeds in wet snow, the collision efficiency for wet snow is likely larger than that of dry snow. For particle sizes between 1 and 10 mm in diameter within mixed precipitation, rain constituted 1% of the particles by volume within the isothermal layer at 0°C and 4% of the particles by volume for the region just below the isothermal layer where air temperatures rise from 0° to 0.5°C. As air temperatures increased above 0.5°C, the relative proportions of rain versus snow particles shift dramatically and raindrops become dominant. The value of 0.5°C for the sharp transition in volume fraction from snow to rain is slightly lower than the range from 1.1° to 1.7°C often used in hydrological models.

scholarly journals The volume fraction method for the evaluation of kidney: A stereological study

2009 ◽  
Vol 50 (1) ◽  
pp. 233-239 ◽  
Author(s):  
Gulsun PAZVANT ◽  
Bunyamin SAHIN ◽  
K.Oya KAHVECIOGLU ◽  
Halil GUNES ◽  
Nazan GEZER ◽  
...  
Keyword(s):  
Volume Fraction ◽  
Fraction Method

scholarly journals Effects of Microstructure, Mechanical and Physical Properties on Machinability of Graphite Cast Irons

Metals ◽  
2020 ◽  
Vol 10 (2) ◽  
pp. 285 ◽  
Author(s):  
Jiangzhuo Ren ◽  
Fengzhang Ren ◽  
Fengjun Li ◽  
Linkai Cui ◽  
Yi Xiong ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Surface Roughness ◽  
Standard Deviation ◽  
Cutting Force ◽  
Volume Fraction ◽  
Internal Surface ◽  
Drilling Process ◽  
Turning Process ◽  
Cast Irons ◽  
Mechanical And Physical Properties

Flake (FGI) and spheroidal (SGI) graphite cast irons are often used to produce workpieces, which often need to be machined. Machinability differences under various machining methods are the basis for choosing machining equipment and technology. In this work, FGI and SGI were used to produce tractor front brackets, and the machinability of both materials under turning and drilling processes was compared. The machinability (turning and drilling ability) has been evaluated in terms of machining load, chips shape, surface roughness, and tool temperature. The influence of materials microstructure and thermal conductivity on the machinability was analyzed. In the turning process, the cutting force and its standard deviation of the FGI were larger than the SGI due to the higher volume fraction of pearlite. The surface roughness was similar in both materials. In the drilling process, the even action of the friction and cutting force on the bit turned into similar drilling loads for both materials. Higher friction and lower thermal conductivity caused a higher bit temperature in SGI drilling compared to FGI. The chip breaking was worse in SGI drilling, where the longer chips scratched the internal surface of the holes, resulting in the higher surface roughness.

scholarly journals Numerical Simulation of the Distribution of In Situ Cigarette Combustion-Generated Particulate Matter

2020 ◽  
Vol 4 (4) ◽  
pp. 59
Author(s):  
Shi Chen ◽  
Hanqing Liu ◽  
Zhiguo Sun ◽  
Hongyong Xie
Keyword(s):  
Mathematical Model ◽  
Particulate Matter ◽  
Cigarette Smoke ◽  
Cross Section ◽  
Constant Pressure ◽  
Particle Diameter ◽  
Axial Position ◽  
Number Density ◽  
Total Particulate Matter

This paper has established a two-dimensional (2D) mathematical model for the generation, growth, and deposition of cigarette total particulate matter (TPM) in the smoldering state. The model has covered the chemical reactions and mass transfer as well as the mechanism of generation, flow, and condensation of particulate matter inside a burning cigarette. Cigarette smoke was generated by puffing under a constant pressure, and the pressure of the filter outlet was −274 Pa. The peak of the concentration of particulate matter was spatially overlapped with the peaks of pyrolysis and oxidation. Pertaining to the cross section of the cigarette at the same axial position, the peak of the diameter of particulate matter along the radial distribution first appeared in the zone near the edge of the cigarette cross section, and then gradually moved to the center of the cigarette with the cigarette smoke moving away from the combustion cone. The maximum number density of particulate matter calculated by the 2D mathematical model at the same axial position of the cigarette and the corresponding particle diameter, as well as the filtration efficiency of the filter rod, are in good accordance with the experimental data reported in previous studies.

scholarly journals Investigation of porosity effect on flexural analysis of doubly curved FGM conoids

2019 ◽  
Vol 26 (1) ◽  
pp. 435-448
Author(s):  
Md Irfan Ansari ◽  
Ajay Kumar ◽  
Danuta Barnat-Hunek ◽  
Zbigniew Suchorab ◽  
Bartłomiej Kwiatkowski
Keyword(s):  
Mathematical Model ◽  
Shear Strain ◽  
Transverse Shear ◽  
Volume Fraction ◽  
Current Model ◽  
Lower Surface ◽  
Functionally Graded ◽  
Transverse Shear Strain ◽  
Flexural Analysis ◽  
Doubly Curved

AbstractThe flexural analysis of doubly curved functionally graded porous conoids was performed in the present paper. The porosities inside functionally graded materials (FGMs) can occur during the fabrication and lead to the occurrence of micro-voids in the materials. The mathematical model includes expansion of Taylor’s series up to the third degree in thickness coordinate and normal curvatures in in-plane displacement fields. Since there is a parabolic variation in transverse shear strain deformation across the thickness coordinate, the shear correction factor is not necessary. The condition of zero-transverse shear strain at upper and lower surface of conoidal shell is implemented in the present model. The improvement in the 2D mathematical model enables to solve problems of moderately thick FGM porous conoids. The distinguishing feature of the present shell from the other shells is that maximum transverse deflection does not occur at its centre. The improved mathematical model was implemented in finite element code written in FORTRAN. The obtained numerical results were compared with the results available in the literature. Once validated, the current model was employed to study the effect of porosity, boundary condition, volume fraction index, loading pattern and others geometric parameters.

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