Predictions of the Structure of Turbulent, Moderately Underexpanded Jets

1994 ◽  
Vol 116 (4) ◽  
pp. 707-713 ◽  
Author(s):  
P. S. Cumber ◽  
M. Fairweather ◽  
S. A. E. G. Falle ◽  
J. R. Giddings
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Dissipation Rate ◽  
Integration Scheme ◽  
Rate Model ◽  
Flow Equations ◽  
Underexpanded Jets ◽  
Model Predictions ◽  
Volume Integration ◽  
Grid Algorithm

A mathematical model capable of predicting the structure of turbulent, underexpanded jets is described. The model is based on solutions of the fluid flow equations obtained using a second-order accurate, finite-volume integration scheme coupled to an adaptive grid algorithm. Turbulence within these jets is modelled using a k-ε approach coupled to the compressible dissipation rate model of Sarkar et al. (1991a). Comparison of model predictions and experimental data, reported in the literature, on a number of moderately underexpanded jets demonstrate significant improvements over results derived using the standard k-ε approach, and the adequacy of the compressibility corrected turbulence model for predicting such jets.

Predictions of the Structure of Turbulent, Highly Underexpanded Jets

1995 ◽  
Vol 117 (4) ◽  
pp. 599-604 ◽  
Author(s):  
P. S. Cumber ◽  
M. Fairweather ◽  
S. A. E. G. Falle ◽  
J. R. Giddings
Keyword(s):  
Turbulence Model ◽  
Near Field ◽  
Integration Scheme ◽  
Mean Flow ◽  
Flow Properties ◽  
Flow Equations ◽  
Underexpanded Jets ◽  
Model Predictions ◽  
Volume Integration ◽  
Grid Algorithm

A mathematical model capable of predicting the shock and flow structure of turbulent, underexpanded jets is described. The model is based on solutions of the fluid flow equations obtained using a second-order accurate, finite-volume integration scheme together with an adaptive grid algorithm. Closure of these equations is achieved using a k-ε turbulence model coupled to the compressible dissipation rate correction proposed by Sarkar et al. (1991a). Extending earlier work which demonstrated the ability of this model to predict the structure of moderately underexpanded jets, the present paper compares model predictions and experimental data, reported in the literature, on a number of highly underexpanded releases. The results obtained demonstrate that the model yields reliable predictions of shock structure in the near field, inviscid region of such jets, while in the far field results derived using the compressibility corrected turbulence model are adequate for predicting mean flow properties, and are superior to those obtained using a standard k-ε approach.

CH4 Direct Reduction of In-Flight Fe3O4 Concentrate Particles

2018 ◽  
Vol 14 (1) ◽  
Author(s):  
Bahador Abolpour ◽  
M. Mehdi Afsahi ◽  
Ataallah Soltani Goharrizi
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Fine Particles ◽  
Direct Reduction ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Dynamic Motion ◽  
Magnetite Ore ◽  
Model Predictions ◽  
Kinetics Of

Abstract In this study, reduction of in-flight fine particles of magnetite ore concentrate by methane at a constant heat flux has been investigated both experimentally and numerically. A 3D turbulent mathematical model was developed to simulate the dynamic motion of these particles in a methane content reactor and experiments were conducted to evaluate the model. The kinetics of the reaction were obtained using an optimizing method as: [-Ln(1-X)]1/2.91 = 1.02 × 10−2dP−2.07CCH40.16exp(−1.78 × 105/RT)t. The model predictions were compared with the experimental data and the data had an excellent agreement.

scholarly journals Modelling Macrophage Infiltration into Avascular Tumours

2002 ◽  
Vol 4 (1) ◽  
pp. 21-38 ◽  
Author(s):  
C. E. Kelly ◽  
R. D. Leek ◽  
H. M. Byrne ◽  
S. M. Cox ◽  
A. L. Harris ◽  
...  
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Spatial Structure ◽  
Random Motion ◽  
Numerical Results ◽  
Macrophage Infiltration ◽  
Numerical Techniques ◽  
Model Predictions ◽  
Independent Experimental Data

In this paper a mathematical model that describes macrophage infiltration into avascular tumours is presented. The qualitative accuracy of the model is assessed by comparing numerical results with independent experimental data that describe the infiltration of macrophages into two types of spheroids: chemoattractant-producing (hepa-1) and chemoattractant-deficient (or C4) spheroids. A combination of analytical and numerical techniques are used to show how the infiltration pattern depends on the motility mechanisms involved (i.e. random motion and chemotaxis) and to explain the observed differences in macrophage infiltration into the hepa-1 and C4 spheroids. Model predictions are generated to show how the spheroid's size and spatial structure and the ability of its constituent cells influence macrophage infiltration. For example, chemoattractant-producing spheroids are shown to recruit larger numbers of macrophages than chemoattractant-deficient spheroids of the same size and spatial structure. The biological implications of these results are also discussed briefly.

Pretreatment of Textile Industry Wastewaters with Ozone

1994 ◽  
Vol 29 (9) ◽  
pp. 151-160 ◽  
Author(s):  
M. Tzitzi ◽  
D. V. Vayenas ◽  
G. Lyberatos
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Textile Industry ◽  
Batch Studies ◽  
Cod Reduction ◽  
Industrial Wastewaters ◽  
Model Predictions ◽  
Textile Wastewaters

Ozonation of textile industrial wastewaters was examined in CSTR and batch studies. Experiments were done for various types of textile wastewaters and for different reaction and retention times. Much better results were obtained using ozonation after the coagulation-precipitation stage. Also a mathematical model was developed, able to describe wastewater decolonization and COD reduction. In all cases the comparison between the model predictions and the experimental data was satisfactory.

The Dynamics of Liquid Cooling in Half-Coil Jackets

2008 ◽  
Vol 3 (1) ◽  
Author(s):  
Jayakumar Natesan Subramanian ◽  
Farouq S. Mjalli
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Mathematical Model ◽  
Liquid Temperature ◽  
Liquid Cooling ◽  
Shell Side ◽  
Stirred Vessel ◽  
Model Predictions ◽  
Temperature Dynamics ◽  
The Heat Transfer Coefficient

The heat transfer cooling of a hot liquid in a stirred vessel has been studied experimentally with coolant flowing through a half-coil around the vessel. Correlations have been developed for the heat transfer coefficient of the half coil jacket. A mathematical model for the half coil jacket liquid temperature dynamics and its analytical solution is used to find the shell side temperature profile as a function of time. It is found that the model predictions are in satisfactory agreement with the experimental data and that the developed correlation is superior to previously published correlations for similar systems.

scholarly journals Mathematical Model of VOCs Emission in Three-layer Building Materials

2021 ◽  
Vol 257 ◽  
pp. 03047
Author(s):  
Zhehua Du ◽  
Xin Lin
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Mathematical Model ◽  
Building Materials ◽  
Present Model ◽  
Transfer Resistance ◽  
Model Predictions ◽  
Layer Resistance ◽  
Boundary Layer Resistance ◽  
Good Agreement

A simple mathematical model is proposed to account for emissions of Volatile Organic Compounds (VOCs) from three-layer building materials. The model considers both the diffusion within three layer building materials and the mass transfer resistance through the air boundary layer. A general solution method based on Laplace transform is presented. Compared to other models capable of accounting for emissions of VOCs from multi layer building materials, the present model is fully analytical instead of being numerical. The present model was validated by the experimental data from the specially designed test. The results indicated that there was a good agreement between the model predictions and the experimental data. It can also be seen from calculation that model ignoring the boundary layer resistance cannot fully reflect the real situation.

MATHEMATICAL MODEL FOR HEAT DEPOSITION IN TISSUE DURING PHOTODYNAMICAL THERAPY

1996 ◽  
Vol 04 (02) ◽  
pp. 261-276
Author(s):  
ALFRED ŠVARC ◽  
MISLAV JURIN ◽  
SUZANA BOROVIĆ ◽  
HRVOJE ZORC ◽  
MARKO DOKO
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Theoretical Model ◽  
Light Source ◽  
Normal Tissue ◽  
Treatment Time ◽  
Red Light ◽  
Heat Deposition ◽  
Model Predictions

A mathematical model for the heat deposition in tissue during the exposition to the red light, essential for the phototherapy, is presented. The comparison of model predictions with in vivo experimental data for the normal CBA/HZgr mice hind leg tissue is done in order to illustrate the domain of confidence of the theoretical model. The highest usable power of the light source, and consequently the lowest phototherapy treatment time with no influence upon normal tissue is determined.

The Impact of Light Polarisation on Light Field of Scenes with Multiple Reflections

2020 ◽  
pp. 108-115 ◽  
Author(s):  
Vladimir P. Budak ◽  
Anton V. Grimaylo
Keyword(s):  
Mathematical Model ◽  
Light Field ◽  
Global Illumination ◽  
Multiple Reflections ◽  
Software Environment ◽  
The Monte Carlo Method ◽  
Mueller Matrices ◽  
Volume Integration ◽  
The Impact

The article describes the role of polarisation in calculation of multiple reflections. A mathematical model of multiple reflections based on the Stokes vector for beam description and Mueller matrices for description of surface properties is presented. On the basis of this model, the global illumination equation is generalised for the polarisation case and is resolved into volume integration. This allows us to obtain an expression for the Monte Carlo method local estimates and to use them for evaluation of light distribution in the scene with consideration of polarisation. The obtained mathematical model was implemented in the software environment using the example of a scene with its surfaces having both diffuse and regular components of reflection. The results presented in the article show that the calculation difference may reach 30 % when polarisation is taken into consideration as compared to standard modelling.

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