Temperature Distributions in Microscale Fractal-Like Branching Channel Networks

2003 ◽  
Author(s):  
Ali Y. Alharbi ◽  
Deborah V. Pence ◽  
Rebecca N. Cullion
Keyword(s):  
Surface Temperature ◽  
Boundary Layers ◽  
Heat Sinks ◽  
Dimensional Model ◽  
One Dimensional ◽  
Temperature Distributions ◽  
Fluid Properties ◽  
Minor Losses ◽  
Branching Flow ◽  
The One

Heat transfer to liquid flow through fractal-like branching flow networks is investigated using a three-dimensional computational fluid dynamics approach. Results are used to assess the validity of, and provide insight for improving, assumptions imposed in a previously developed one-dimensional model to predict wall temperature distributions along a fractal-like flow network. Assumptions in the one-dimensional model include (1) reinitiating thermal and hydrodynamic boundary layers following each bifurcation, (2) negligible minor losses at the bifurcations, and (3) constant thermo-physical fluid properties. It is concluded that temperature varying fluid properties and minor losses should be incorporated in the one-dimensional model to improve its predictive capabilities. No changes to the redevelopment of the boundary layers at each wall following a bifurcation are recommended. Surface temperature distributions along heat sinks with parallel and fractal-like branching flow networks are also investigated and compared. For the same observed maximum surface temperature between the two heat sinks, considerably lower temperature variations and pressure drops, greater than 50 percent, are noted for the fractal-like heat sink.

Fluid Flow Through Microscale Fractal-Like Branching Channel Networks

2003 ◽  
Author(s):  
Ali Y. Alharbi ◽  
Deborah V. Pence ◽  
Rebecca N. Cullion
Keyword(s):  
Three Dimensional ◽  
Dimensional Model ◽  
Flow Networks ◽  
Channel Networks ◽  
One Dimensional ◽  
Fluid Properties ◽  
Flow Through ◽  
Minor Losses ◽  
Branching Flow ◽  
The One

Flow through fractal-like branching flow networks is investigated using a three-dimensional computational fluid dynamics approach. Results are used to assess the validity of, and provide insight for improving, assumptions imposed in a one-dimensional model previously developed. Assumptions in the one-dimensional model include (1) reinitiating boundary layers following each bifurcation, (2) negligible minor losses at the bifurcations, and (3) constant thermophysical fluid properties. It is concluded that the temperature dependence of fluid properties, boundary layer development, and minor losses following a bifurcation are not negligible in analyses of branching flow networks.

Thermal Characteristics of Microscale Fractal-Like Branching Channels

2004 ◽  
Vol 126 (5) ◽  
pp. 744-752 ◽  
Author(s):  
Ali Y. Alharbi ◽  
Deborah V. Pence ◽  
Rebecca N. Cullion
Keyword(s):  
Surface Temperature ◽  
Wall Temperature ◽  
Heat Sink ◽  
Three Dimensional ◽  
Dimensional Model ◽  
Channel Network ◽  
Flow Network ◽  
One Dimensional ◽  
Temperature Distributions ◽  
Branching Flow

Heat transfer through a fractal-like branching flow network is investigated using a three-dimensional computational fluid dynamics approach. Results are used for the purpose of assessing the validity of, and providing insight for improving, assumptions imposed in a previously developed one-dimensional model for predicting wall temperature distributions through fractal-like flow networks. As currently modeled, the one-dimensional code fairly well predicts the general wall temperature trend simulated by the three-dimensional model; hence, demonstrating its suitability as a tool for design of fractal-like flow networks. Due to the asymmetry in the branching flow network, wall temperature distributions for the proposed branching flow network are found to vary with flow path and between the various walls forming the channel network. Three-dimensional temperature distributions along the various walls in the branching channel network are compared to those along a straight channel. Surface temperature distributions on a heat sink with a branching flow network and a heat sink with a series of straight, parallel channels are also analyzed and compared. For the same observed maximum surface temperature on these two heat sinks, a lower temperature variation is noted for the fractal-like heat sink.

Fluid Flow Through Microscale Fractal-Like Branching Channel Networks

2003 ◽  
Vol 125 (6) ◽  
pp. 1051-1057 ◽  
Author(s):  
Ali Y. Alharbi ◽  
Deborah V. Pence ◽  
Rebecca N. Cullion
Keyword(s):  
Boundary Layers ◽  
Three Dimensional ◽  
Heat Fluxes ◽  
Dimensional Model ◽  
Local Pressure ◽  
Flow Area ◽  
One Dimensional ◽  
Fluid Properties ◽  
Flow Through ◽  
The One

Flow through fractal-like branching networks is investigated using a three-dimensional computational fluid dynamics approach. Results are used to assess the validity of, and provide insight for improving, assumptions imposed in a previously developed one-dimensional model. Assumptions in the one-dimensional model include (1) reinitiating boundary layers following each bifurcation, (2) constant thermophysical fluid properties, and (3) negligible minor losses at the bifurcations. No changes to the redevelopment of hydrodynamic boundary layers following a bifurcation are recommended. It is concluded that temperature varying fluid properties should be incorporated in the one-dimensional model to improve its predictive capabilities, especially at higher imposed heat fluxes. Finally, a local pressure recovery at each bifurcation results from an increase in flow area. Ultimately, this results in a lower total pressure drop and should be incorporated in the one-dimensional model.

Modelling Techniques in Applied Glaciology: Numerical Modelling of Avalanches

1983 ◽  
Vol 4 ◽  
pp. 297-297
Author(s):  
G. Brugnot
Keyword(s):  
Finite Difference Method ◽  
Transverse Velocity ◽  
Longitudinal Velocity ◽  
Momentum Conservation ◽  
Dimensional Model ◽  
One Dimensional ◽  
Modelling Techniques ◽  
Reference Grid ◽  
The One ◽  
Near Future

We consider the paper by Brugnot and Pochat (1981), which describes a one-dimensional model applied to a snow avalanche. The main advance made here is the introduction of the second dimension in the runout zone. Indeed, in the channelled course, we still use the one-dimensional model, but, when the avalanche spreads before stopping, we apply a (x, y) grid on the ground and six equations have to be solved: (1) for the avalanche body, one equation for continuity and two equations for momentum conservation, and (2) at the front, one equation for continuity and two equations for momentum conservation. We suppose the front to be a mobile jump, with longitudinal velocity varying more rapidly than transverse velocity.We solve these equations by a finite difference method. This involves many topological problems, due to the actual position of the front, which is defined by its intersection with the reference grid (SI, YJ). In the near future our two directions of research will be testing the code on actual avalanches and improving it by trying to make it cheaper without impairing its accuracy.

A Stefan problem in a Bridgman crystal grower

1995 ◽  
Vol 6 (3) ◽  
pp. 191-199
Author(s):  
P. den Decker ◽  
R. van der Hout ◽  
C. J. Van Duijn ◽  
L. A. Peletier
Keyword(s):  
Critical Speed ◽  
Internal Heat ◽  
Mushy Region ◽  
Dimensional Model ◽  
Real Situation ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
The One ◽  
Strong Curvature ◽  
Bridgman Crystal Grower

We discuss a one-dimensional model for a Bridgman crystal grower, where the removal of heat is described by an internal heat sink. A consequence is the apparent existence of mushy regions for relatively large velocities of the cooling machine; these mushy regions are an artefact of the one-dimensional approximation. We show that for some types of cooling profiles there exists a critical speed for the existence of mushy regions, whereas for different cooling profiles no such critical speed exists. The presence of a mushy region may indicate a strong curvature of the liquid/solid interface in the real situation.

On the numerical study of thermohydrodynamics and biochemistry of inland water bodies

2021 ◽  
Author(s):  
Daria Gladskikh ◽  
Evgeny Mortikov ◽  
Victor Stepanenko
Keyword(s):  
Mixed Layer ◽  
Numerical Study ◽  
Three Dimensional ◽  
Water Bodies ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
One Dimensional ◽  
Lake Model ◽  
Upper Mixed Layer ◽  
The One

<p>The study of thermodynamic and biochemical processes of inland water objects using one- and three-dimensional RANS numerical models was carried out both for idealized water bodies and using measurements data. The need to take into account seiche oscillations to correctly reproduce the deepening of the upper mixed layer in one-dimensional (vertical) models is demonstrated. We considered the one-dimensional LAKE model [1] and the three-dimensional model [2, 3, 4] developed at the Research Computing Center of Moscow State University on the basis of a hydrodynamic code combining DNS/LES/RANS approaches for calculating geophysical turbulent flows. The three-dimensional model was supplemented by the equations for calculating biochemical substances by analogy with the one-dimensional biochemistry equations used in the LAKE model. The effect of mixing processes on the distribution of concentration of greenhouse gases, in particular, methane and oxygen, was studied.</p><p>The work was supported by grants of the RF President’s Grant for Young Scientists (MK-1867.2020.5, MD-1850.2020.5) and by the RFBR (19-05-00249, 20-05-00776). </p><p>1. Stepanenko V., Mammarella I., Ojala A., Miettinen H., Lykosov V., Timo V. LAKE 2.0: a model for temperature, methane, carbon dioxide and oxygen dynamics in lakes // Geoscientific Model Development. 2016. V. 9(5). P. 1977–2006.<br>2. Mortikov E.V., Glazunov A.V., Lykosov V.N. Numerical study of plane Couette flow: turbulence statistics and the structure of pressure-strain correlations // Russian Journal of Numerical Analysis and Mathematical Modelling. 2019. 34(2). P. 119-132.<br>3. Mortikov, E.V. Numerical simulation of the motion of an ice keel in stratified flow // Izv. Atmos. Ocean. Phys. 2016. V. 52. P. 108-115.<br>4. Gladskikh D.S., Stepanenko V.M., Mortikov E.V. On the influence of the horizontal dimensions of inland waters on the thickness of the upper mixed layer // Water Resourses. 2021.V. 45, 9 pages. (in press) </p>

scholarly journals Hydraulic modeling of combined sewers overflow integrating the results of the SWMM and CFX models.

2021 ◽  
Vol 37 (1) ◽  
Author(s):  
D. Pulgarín ◽  
J. Plaza ◽  
J. Ruge ◽  
J. Rojas
Keyword(s):  
Three Dimensional ◽  
Hydraulic Modeling ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
One Dimensional ◽  
Ansys Cfx ◽  
Combined Sewer ◽  
The One ◽  
Swmm Model

This study proposes a methodology for the calibration of combined sewer overflow (CSO), incorporating the results of the three-dimensional ANSYS CFX model in the SWMM one-dimensional model. The procedure consists of constructing calibration curves in ANSYS CFX that relate the input flow to the CSO with the overflow, to then incorporate them into the SWMM model. The results obtained show that the behavior of the flow over the crest of the overflow weir varies in space and time. Therefore, the flow of entry to the CSO and the flow of excesses maintain a non-linear relationship, contrary to the results obtained in the one-dimensional model. However, the uncertainty associated with the idealization of flow methodologies in one dimension is reduced under the SWMM model with kinematic wave conditions and simulating CSO from curves obtained in ANSYS CFX. The result obtained facilitates the calibration of combined sewer networks for permanent or non-permanent flow conditions, by means of the construction of curves in a three-dimensional model, especially when the information collected in situ is limited.

Quantum entanglement in some topological insulator models

2019 ◽  
Vol 33 (24) ◽  
pp. 1950284 ◽  
Author(s):  
L. S. Lima
Keyword(s):  
Quantum Entanglement ◽  
Topological Insulator ◽  
Topological Charge ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Model Case ◽  
Topological Transition ◽  
One Dimensional ◽  
Zhang Model ◽  
The One

Quantum entanglement is studied in the neighborhood of a topological transition in some topological insulator models such as the two-dimensional Qi–Wu–Zhang model or Chern insulator. The system describes electrons hopping in two-dimensional chains. For the one-dimensional model case, there exist staggered hopping amplitudes. Our results show a strong effect of sudden variation of the topological charge Q in the neighborhood of phase transition on quantum entanglement for all the cases analyzed.

scholarly journals Quantitative Spectroscopy of Wolf-Rayet Stars

1988 ◽  
Vol 108 ◽  
pp. 133-140
Author(s):  
W. Schmutz
Keyword(s):  
Representative Point ◽  
Dimensional Model ◽  
Model Calculations ◽  
One Dimensional ◽  
The Past ◽  
First Results ◽  
The One ◽  
Expanding Atmospheres ◽  
New Generation ◽  
The Continuum

Advances in theoretical modeling of rapidly expanding atmospheres in the past few years made it possible to determine the stellar parameters of the Wolf-Rayet stars. This progress is mainly due to the improvement of the models with respect to their spatial extension: The new generation of models treat spherically-symmetric expanding atmospheres, i.e. the models are one-dimensional. Older models describe the wind by only one representative point. The older models are in fact ‘core-halo’ approximations. They have been introduced by Castor and van Blerkom (1970), and were extensively employed in the past (cf. e.g. Willis and Wilson, 1978; Smith and Willis, 1982). First results from new one-dimensional model calculations are published by Hillier (1984), Schmutz (1984), Hamann (1985), Hillier (1986), and Schmutz et al. (1987a); more detailed results are presented by Schmutz and Hamann (1986), Hamann and Schmutz (1987), Hillier (1987a,b), Wessolowski et al. (1987), Hillier (1987c) and Hamann et al. (1987). These results demonstrate that the step from zero- to one-dimensional calculations is essential. The important point is that the complicated interrelation between NLTE-level populations and radiation field is treated adequately (Schmutz and Hamann, 1986; Hillier, 1987). For this interrelation it is crucial to model consistently not only the line-formation region, but also the layers where the continuum is emitted. In fact, it is the core-halo approximation that causes the one-point models to fail in certain aspects.

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