Simulation of particle concentration distribution in primary clarifiers

1985 ◽  
Vol 12 (3) ◽  
pp. 454-463 ◽  
Author(s):  
Sameh Abdel-Gawad ◽  
John A. McCorquodale
Keyword(s):  
Numerical Model ◽  
Differential Equations ◽  
Removal Efficiency ◽  
Transport Model ◽  
Concentration Profiles ◽  
Steady Flows ◽  
Integral Technique ◽  
Solids Concentration ◽  
Proposed Model ◽  
Fifth Order

A numerical model to simulate the performance of both rectangular and circular primary clarifiers is presented. The proposed model is restricted to those mean steady flows that are isothermal, of neutral density, low in solids concentration, and nearly two-dimensional.The strip integral technique is used to reduce the partial differential equations of continuity, momentum, and mass transport to a set of ordinary differential equations. The resulting set of equations is numerically integrated using a fifth-order, Runge–Kutta method.The full numerical model contains a hydrodynamic submodel and a transport submodel. The hydrodynamic submodel predicts the velocity field and dispersion characteristics within the clarifier, which are prerequisite for the transport submodel.The model, as presented here, was used to simulate the circular tanks used in the cities of Windsor, Ontario and Waterloo, Ontario. The predicted concentration profiles and removal efficiency were in good agreement with the measured values. Key words: numerical model, primary clarifiers, strip integral technique, transport model, concentration profiles, removal efficiency.

scholarly journals Development of a Condensation Model and a New Design of a Condensation Hood—Numerical and Experimental Study

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1344
Author(s):  
Mieszko Tokarski ◽  
Arkadiusz Ryfa ◽  
Piotr Buliński ◽  
Marek Rojczyk ◽  
Krzysztof Ziarko ◽  
...  
Keyword(s):  
Heat Exchanger ◽  
Numerical Model ◽  
Transport Model ◽  
Measurement Data ◽  
Computation Time ◽  
High Heat ◽  
Condensation Process ◽  
Proposed Model ◽  
Flow Heat ◽  
High Heat Load

The development of a numerical model and design for the innovative construction of a heat exchanger (HE) used in a condensation hood (being a part of the combi-steamer) are described in this work. The model covers an air-steam flow, heat transfer, and a steam condensation process. The last two processes were implemented with the use of an in-house model introduced via User Defined Functions (UDF). As the condensate volume is negligible compared to the steam, the proposed model removes the condensate from the domain. This approach enabled the usage of a single-phase flow for both air and steam using a species transport model. As a consequence, a significant mesh and computation time reduction were achieved. The new heat exchanger is characterised by reorganised fluid flow and by externally finned pipes (contrary to the original construction, where internally finned pipes were used). This allowed a reduction in the number of the pipes from 48 to 5, which significantly simplifies construction and manufacturing process of the HE. The redesigned HE was tested in two cases: one simulating normal working conditions with a combi-steamer, the other with extremely high heat load. Measurement data showed that the numerical model predicted condensate mass flow rate (3.67 g/s computed and 3.56 g/s measured) and that the condensation capability increased at least by 15% when compared to the original HE design.

scholarly journals MHD Mixed Convection Nanofluid Flow over Convectively Heated Nonlinear due to an Extending Surface with Soret Effect

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Jamel Bouslimi ◽  
M. A. Abdelhafez ◽  
A. M. Abd-Alla ◽  
S. M. Abo-Dahab ◽  
K. H. Mahmoud
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Mixed Convection ◽  
Physical Meaning ◽  
Soret Effect ◽  
Concentration Profiles ◽  
Nanofluid Flow ◽  
Thermal Buoyancy ◽  
Buoyancy Parameter ◽  
Fifth Order

The aim of this paper is to investigate the flow of MHD mixed convection nanofluid flow under nonlinear heated due to an extending surface. The transfer of heat in nanofluid subject to a magnetic field and boundary conditions of convective is studied to obtain the physical meaning of the convection phenomenon. The governing partial differential equations (PDEs) of the boundary layer are reduced to ordinary differential equations (ODEs) considering a technique of the transformation of similarity. The transformed equations are solved numerically considering the technique of an efficient numerical shooting applying the Runge–Kutta technique scheme from the fourth-fifth order. The results corresponding to the dimensionless speed, temperature, concentration profiles, and the Nusselt number reduced, and the Sherwood numbers are presented by figures to display the physical meaning of the phenomena. A comparison has been made between the obtained results with the previous results obtained by others and agrees with them if the new parameters vanish. The results obtained indicate the impacts of the nondimensional governing parameters, namely, magnetic field parameter M, Soret number Sr, heat source λ, thermal buoyancy parameter λ T , and solutal buoyancy parameter λ C on the flow, temperature, and concentration profiles being discussed and presented graphically.

scholarly journals Influence of Chemical Osmosis on Solute Transport and Fluid Velocity in Clay Soils

2020 ◽  
Vol 18 (1) ◽  
pp. 232-238
Author(s):  
Zhihong Zhang ◽  
Gailei Tian ◽  
Lin Han
Keyword(s):  
Solute Transport ◽  
Transport Model ◽  
Fluid Velocity ◽  
Diffusion Mechanism ◽  
Clay Material ◽  
Chemical Osmosis ◽  
Advection Diffusion Equation ◽  
Test Study ◽  
Proposed Model ◽  
Membrane Effect

AbstractSolute transport through the clay liner is a significant process in many waste landfills or unmanaged landfills. At present, researchers mainly focus on the test study about semi-membrane property of clay material, however, the influence of chemical osmosis caused by membrane effect on solute transport and fluid velocity is insufficient. In this investigation, based on the classical advection-diffusion equation, a one-dimensional solute transport model for low-permeable clay material has been proposed, in which the coupled fluid velocity related with hydraulic gradient and concentration gradient is introduced, and the semi-membrane effect is embodied in the diffusion mechanism. The influence of chemical osmosis on fluid velocity and solute transport has been analyzed using COMSOL Multiphysics software. The simulated results show that chemical osmosis has a significant retarded action on fluid velocity and pollutant transport. The proposed model can effectively reveal the change in process of coupled fluid velocity under dual gradient and solute transport, which can provide a theoretical guidance for similar fluid movement in engineering.

scholarly journals A Semi-Empirical Model for Predicting Frost Properties

Processes ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 412
Author(s):  
Shao-Ming Li ◽  
Kai-Shing Yang ◽  
Chi-Chuan Wang
Keyword(s):  
Thermal Conductivity ◽  
Linear Programming ◽  
Numerical Model ◽  
Empirical Model ◽  
Quantitative Method ◽  
Predictive Ability ◽  
Dimensionless Temperature ◽  
Crystal Shape ◽  
Proposed Model ◽  
Semi Empirical

In this study, a quantitative method for classifying the frost geometry is first proposed to substantiate a numerical model in predicting frost properties like density, thickness, and thermal conductivity. This method can recognize the crystal shape via linear programming of the existing map for frost morphology. By using this method, the frost conditions can be taken into account in a model to obtain the corresponding frost properties like thermal conductivity, frost thickness, and density for specific frost crystal. It is found that the developed model can predict the frost properties more accurately than the existing correlations. Specifically, the proposed model can identify the corresponding frost shape by a dimensionless temperature and the surface temperature. Moreover, by adopting the frost identification into the numerical model, the frost thickness can also be predicted satisfactorily. The proposed calculation method not only shows better predictive ability with thermal conductivities, but also gives good predictions for density and is especially accurate when the frost density is lower than 125 kg/m3. Yet, the predictive ability for frost density is improved by 24% when compared to the most accurate correlation available.

Analysis of a New Class of Impulsive Implicit Sequential Fractional Differential Equations

2020 ◽  
Vol 21 (6) ◽  
pp. 571-587 ◽  
Author(s):  
Akbar Zada ◽  
Sartaj Ali ◽  
Tongxing Li
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Integer Order ◽  
New Class ◽  
Proposed Model ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

AbstractIn this paper, we study an implicit sequential fractional order differential equation with non-instantaneous impulses and multi-point boundary conditions. The article comprehensively elaborate four different types of Ulam’s stability in the lights of generalized Diaz Margolis’s fixed point theorem. Moreover, some sufficient conditions are constructed to observe the existence and uniqueness of solutions for the proposed model. The proposed model contains both the integer order and fractional order derivatives. Thus, the exponential function appearers in the solution of the proposed model which will lead researchers to study fractional differential equations with well known methods of integer order differential equations. In the last, few examples are provided to show the applicability of our main results.

scholarly journals NUMERICAL MODEL INVESTIGATION OF SELECTED TIDAL INLET-BAY SYSTEM CHARACTERISTICS

1978 ◽  
Vol 1 (16) ◽  
pp. 76
Author(s):  
William N. Seelig ◽  
Robert M. Sorensen
Keyword(s):  
Sediment Transport ◽  
Numerical Model ◽  
Transport Model ◽  
Tidal Inlet ◽  
Inlet Channel ◽  
Astronomical Tide ◽  
Order Of Magnitude ◽  
Flow And Sediment Transport ◽  
Transport Factors ◽  
System Characteristics

A spatially integrated one-dimensional numerical model of inlet bay hydraulics has been combined with a simple sediment transport model to investigate selected tidal inlet-bay system characteristics. A parametric study has been performed using the models to determine the effect of various factors on the net direction and order of magnitude of inlet channel flow and sediment transport. Factors considered include astronomical tide type, storm surge height and duration, variation in bay surface area, time-dependent channel friction factor, and the addition of a second inlet connecting the bay and sea.

scholarly journals Joint Partial Optimal Transport for Open Set Domain Adaptation

2020 ◽  
Author(s):  
Renjun Xu ◽  
Pelen Liu ◽  
Yin Zhang ◽  
Fang Cai ◽  
Jindong Wang ◽  
...  
Keyword(s):  
Optimal Transport ◽  
Transport Model ◽  
Domain Adaptation ◽  
General Setting ◽  
Feature Space ◽  
Set Domain ◽  
Target Domain ◽  
Source Domain ◽  
Open Set ◽  
Proposed Model

Domain adaptation (DA) has achieved a resounding success to learn a good classifier by leveraging labeled data from a source domain to adapt to an unlabeled target domain. However, in a general setting when the target domain contains classes that are never observed in the source domain, namely in Open Set Domain Adaptation (OSDA), existing DA methods failed to work because of the interference of the extra unknown classes. This is a much more challenging problem, since it can easily result in negative transfer due to the mismatch between the unknown and known classes. Existing researches are susceptible to misclassification when target domain unknown samples in the feature space distributed near the decision boundary learned from the labeled source domain. To overcome this, we propose Joint Partial Optimal Transport (JPOT), fully utilizing information of not only the labeled source domain but also the discriminative representation of unknown class in the target domain. The proposed joint discriminative prototypical compactness loss can not only achieve intra-class compactness and inter-class separability, but also estimate the mean and variance of the unknown class through backpropagation, which remains intractable for previous methods due to the blindness about the structure of the unknown classes. To our best knowledge, this is the first optimal transport model for OSDA. Extensive experiments demonstrate that our proposed model can significantly boost the performance of open set domain adaptation on standard DA datasets.

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