Prediction of Nanofluid Temperature Inside the Cavity by Integration of Grid Partition Clustering Categorization of a Learning Structure with the Fuzzy System

Prediction of gas velocity in two-phase flow using developed fuzzy logic system with differential evolution algorithm

In this investigation, differential evolution (DE) algorithm with the fuzzy inference system (FIS) are combined and the DE algorithm is employed in FIS training process. Considered data in this study were extracted from simulation of a 2D two-phase reactor in which gas was sparged from bottom of reactor, and the injected gas velocities were between 0.05 to 0.11 m/s. After doing a couple of training by making some changes in DE parameters and FIS parameters, the greatest percentage of FIS capacity was achieved. By applying the optimized model, the gas phase velocity in x direction inside the reactor was predicted when the injected gas velocity was 0.08 m/s.

Influence of machine learning membership functions and degree of membership function on each input parameter for simulation of reactors

To understand impact of input and output parameters during optimization and degree of complexity, in the current study we numerically designed a bubble column reactor with a single sparger in the middle of the reactor. After that, some input and output parameters were selected in the post-processing of the numerical method, and then the machine learning observation started to investigate the level of complexity and impact of each input on output parameters. The adaptive neuro-fuzzy inference system (ANFIS) method was exploited as a machine learning approach to analyze the gas-liquid flow in the reactor. The ANFIS method was used as a machine learning approach to simulate the flow of a 3D (three-dimensional) bubble column reactor. This model was also used to analyze the influence of input and output parameters together. More specifically, by analyzing the degree of membership functions as a function of each input, the level of complexity of gas fraction was investigated as a function of computing nodes (X, Y, and Z directions). The results showed that a higher number of membership functions results in a better understanding of the process and higher model accuracy and prediction capability. X and Y computing nodes have a similar impact on the gas fraction, while Z computing points (height of reactor) have a uniform distribution of membership function across the column. Four membership functions (MFs) in each input parameter are insufficient to predict the gas fraction in the 3D bubble column reactor. However, by adding two membership functions, all features of gas fraction in the 3D reactor can be captured by the machine learning algorithm. Indeed, the degree of MFs was considered as a function of each input parameter and the effective parameter was found based on the impact of MFs on the output.

Liquid temperature prediction in bubbly flow using ant colony optimization algorithm in the fuzzy inference system as a trainer

In the current research paper a novel hybrid model combining first-principle and artificial intelligence (AI) was developed for simulation of a chemical reactor. We study a 2-dimensional reactor with heating sources inside it by using computational fluid dynamics (CFD). The type of considered reactor is bubble column reactor (BCR) in which a two-phase system is created. Results from CFD were analyzed in two different stages. The first stage, which is the learning stage, takes advantage of the swarm intelligence of the ant colony. The second stage results from the first stage, and in this stage, the predictions are according to the previous stage. This stage is related to the fuzzy logic system, and the ant colony optimization learning framework is build-up this part of the model. Ants movements or swarm intelligence of ants lead to the optimization of physical, chemical, or any kind of processes in nature. From point to point optimization, we can access a kind of group optimization, meaning that a group of data is studied and optimized. In the current study, the swarm intelligence of ants was used to learn the data from CFD in different parts of the BCR. The learning was also used to map the input and output data and find out the complex connection between the parameters. The results from mapping the input and output data show the full learning framework. By using the AI framework, the learning process was transferred into the fuzzy logic process through membership function specifications; therefore, the fuzzy logic system could predict a group of data. The results from the swarm intelligence of ants and fuzzy logic suitably adapt to CFD results. Also, the ant colony optimization fuzzy inference system (ACOFIS) model is employed to predict the temperature distribution in the reactor based on the CFD results. The results indicated that instead of solving Navier–Stokes equations and complex solving procedures, the swarm intelligence could be used to predict a process. For better comparisons and assessment of the ACOFIS model, this model is compared with the genetic algorithm fuzzy inference system (GAFIS) and Particle swarm optimization fuzzy inference system (PSOFIS) method with regards to model accuracy, pattern recognition, and prediction capability. All models are at a similar level of accuracy and prediction ability, and the prediction time for all models is less than one second. The results show that the model’s accuracy with low computational learning time can be achieved with the high number of CIR (0.5) when the number of inputs ≥ 4. However, this finding is vice versa, when the number of inputs < 4. In this case, the CIR number should be 0.2 to achieve the best accuracy of the model. This finding could also highlight the importance of sensitivity analysis of tuning parameters to achieve an accurate model with a cost-effective computational run.

Multidimensional machine learning algorithms to learn liquid velocity inside a cylindrical bubble column reactor

For understanding the complex behavior of fluids in a multiphase chemical bubble column reactor, a combination of the computational fluid dynamic (CFD) method and the adaptive network-based fuzzy inference system (ANFIS) method is used to predict bubble flow inside a reactor based on the function of column height. In this study, the Euler–Euler model is employed as a CFD method. In the Eulerian method, continuity and momentum governing equations are mathematically computed for each phase, while the equations are connected together by source terms. After calculating the flow pattern and turbulence flow in the reactor, all data sets are used to prepare a fully artificial method for further prediction. This algorithm contains different learning dimensions such as learning in different directions of reactor or large amount of input parameters and data set representing “big data”. The ANFIS method was evaluated in three steps by using one, two, and three inputs in each one to predict the liquid velocity in the x-direction (Ux). The x, y, and z coordinates of the location of the node of the liquid were considered as the inputs. Different percentages of data and various iterations and membership functions were used for training in the ANFIS method. The ANFIS method showed the best prediction using three inputs. This combination also shows the ability of computer science and computational methods in learning physical and chemical phenomena.

Computational Modeling of Transport in Porous Media Using an Adaptive Network-Based Fuzzy Inference System

This investigation is conducted to study the integration of the artificial intelligence (AI) method with computational fluid dynamics (CFD). The case study is hydrodynamic and heat-transfer analyses of water flow in a metal foam tube under a constant wall heat flux (i.e., 55 kW/m²). The adaptive network-based fuzzy inference system (ANFIS) is an AI method. A 3D CFD model is established in ANSYS-FLUENT software. The velocity of the fluid in the x-direction (Ux) is considered as an output of the ANFIS. The x, y, and z coordinates of the node's location are added to the ANFIS step-by-step to achieve the best intelligence. The number and type of membership functions (MFs) are changed in each step. The training process is done by the CFD results on the tube cross-sections at different lengths (i.e., z = 0.1, 0.2, 0.3, 0.4, 0.6, 0.7, 0.8, and 0.9), while all data (including z = 0.5) are selected for the testing process. The results showed that the ANFIS reaches the best intelligence with all three inputs, five MFs, and "gbellmf"-type MF. At this condition, the regression number is close to 1.

gbell Learning function along with Fuzzy Mechanism in Prediction of Two-Phase Flow

The integration of the computational fluid dynamics (CFD) and the adaptive network-based fuzzy inference system, known as ANFIS, is investigated for simulating the hydrodynamic in a bubble column reactor. The Eulerian-Eulerian two-phase model is employed as the CFD approach. For the ANFIS technique, a sensitivity analysis is done by varying the number of inputs and the number of membership functions (MFs). The x and z coordinates of the fluid location, the air velocity, and the pressure are considered as the inputs of the ANFIS, while the air vorticity is the output. The results revealed that the ANFIS with all four inputs and the MFs of five achieved the highest intelligence with the regression number close to 1. More specifically, gbell function in the learning framework is used to train all local computing nodes from solving Navier-Stokes equations. In the decision or prediction part, the fuzzy mechanism is used for the prediction of extra nodes that solve, which Navier-Stokes equations did not solve. The results show that the gbell function enables us to fully train all numerical points and also store data set in the frame of mathematical equations. Besides, this function responds well with the number of inputs and MFs for accurate prediction of reactor hydrodynamics. Additionally, a high number of MFs and input parameters influence the accuracy of the method during prediction. In the current study, gbell MF was studied to investigate its accuracy in the prediction of the two-phase flow. Also, different numbers of MFs were considered to investigate the level of accuracy and capability of prediction. ANFIS clustering methods, grid partition and fuzzy C-mean (FCM) clustering, are compared to see the ability of the method in prediction. To compare the accuracy of the ANFIS method with FCM clustering, the data were compared to the gaussmf function. The results showed that the method has high accuracy and that it could predict the flow pattern.

Simulation of liquid flow with a combination artificial intelligence flow field and Adams-Bashforth method

Direct numerical simulation (DNS) of particle hydrodynamics in the multiphase industrial process enables us to fully learn the process and optimize it on the industrial scale. However, using high-resolution computational calculations for particle movement and the interaction between the solid phase and other phases in fine timestep is limited to excellent computational resources. Solving the Eulerian flow field as a source of solid particle movement can be very time-consuming. However, by the revolution of the fast and accurate learning process, the Eulerian domain can be computed by smart modeling in a very short computational time. In this work, using the machine learning method, the flow field in the square shape cavity is trained, and then the Eulerian framework is replaced with a machine learning method to generate the artificial intelligence (AI) flow field. Then the Lagrangian framework is coupled with this AI flow field, and we simulate particle motion through the fully AI framework. The Adams–Bashforth finite element method is used as a conventional CFD method (Eulerian framework) to simulate the flow field in the cavity. After simulating fluid flow, the ANFIS method is used as an AI model to train the Eulerian data-set and represents AI fluid flow (framework). The Lagrangian framework is coupled with the AI method, and the particle freely migrates through this artificial framework. The results reveal that there is a great agreement between Euler-Lagrangian and AI- Lagrangian in the cavity. We also found that there is an excellent agreement between AI overview with the Adams–Bashforth approach, and the new combination of machine learning and CFD method can accelerate the calculation of the flow field in the square-shaped cavity. AI model can mimic the vortex structure in the cavity, where there is a zero-velocity structure in the center of the domain and maximum velocity near the moving walls.

Pattern recognition of the fluid flow in a 3D domain by combination of Lattice Boltzmann and ANFIS methods

Many numerical methods have been used to simulate the fluid flow pattern in different industrial devices. However, they are limited with modeling of complex geometries, numerical stability and expensive computational time for computing, and large hard drive. The evolution of artificial intelligence (AI) methods in learning large datasets with massive inputs and outputs of CFD results enables us to present completely artificial CFD results without existing numerical method problems. As AI methods can not feel barriers in numerical methods, they can be used as an assistance tool beside numerical methods to predict the process in complex geometries and unstable numerical regions within the short computational time. In this study, we use an adaptive neuro-fuzzy inference system (ANFIS) in the prediction of fluid flow pattern recognition in the 3D cavity. This prediction overview can reduce the computational time for visualization of fluid in the 3D domain. The method of ANFIS is used to predict the flow in the cavity and illustrates some artificial cavities for a different time. This method is also compared with the genetic algorithm fuzzy inference system (GAFIS) method for the assessment of numerical accuracy and prediction capability. The result shows that the ANFIS method is very successful in the estimation of flow compared with the GAFIS method. However, the GAFIS can provide faster training and prediction platform compared with the ANFIS method.

ANFIS grid partition framework with difference between two sigmoidal membership functions structure for validation of nanofluid flow

In this study, a square cavity is modeled using Computational Fluid Dynamics (CFD) as well as artificial intelligence (AI) approach. In the square cavity, copper (Cu) nanoparticle is the nanofluid and the flow velocity characteristics in the x-direction and y-direction, and the fluid temperature inside the cavity at different times are considered as CFD outputs. CFD outputs have been assessed using one of the artificial intelligence algorithms, such as a combination of neural network and fuzzy logic (ANFIS). As in the ANFIS method, we have a non-dimension procedure in the learning step, and there is no issue in combining other characteristics of the flow and thermal distribution beside the x and y coordinates, we combine two coordinate parameters and one flow parameter. This ability of method can be considered as a meshless learning step that there is no instability of the numerical method or limitation of boundary conditions. The data were classified using the grid partition method and the MF (membership function) type was dsigmf (difference between two sigmoidal membership functions). By achieving the appropriate intelligence in the ANFIS method, output prediction was performed at the points of cavity which were not included in the learning process and were compared to the existing data (the results of the CFD method) and were validated by them. This new combination of CFD and the ANFIS method enables us to learn flow and temperature distribution throughout the domain thoroughly, and eventually predict the flow characteristics in short computational time. The results from AI in the ANFIS method were compared to the ant colony and fuzzy logic methods. The data from CFD results were inserted into the ant colony system for the training process, and we predicted the data in the fuzzy logic system. Then, we compare the data with the ANFIS method. The results indicate that the ANFIS method has a high potentiality compared to the ant colony method because the amount of R in the ANIFS system is higher than R in the ant colony method. In the ANFIS method, R is equal to 0.99, and in the ant colony method, R is equal to 0.91. This shows that the ant colony needs more time for both the prediction and training of the system. Also, comparing the pattern recognition in the two systems, we can obviously see that by using the ANFIS method, the predictions completely match the target points. But the other method cannot match the flow pattern and velocity distribution with the CFD method.

Prediction of Nanofluid Characteristics and Flow Pattern on Artificial Differential Evolution Learning Nodes and Fuzzy Framework

A combination of a fuzzy inference system (FIS) and a differential evolution (DE) algorithm, known as the differential evolution-based fuzzy inference system (DEFIS), is developed for the prediction of natural heat transfer in Cu-water nanofluid within a cavity. In the development of the hybrid model, the DE algorithm is used for the training process of FIS. For this purpose, first, the case study is simulated using the computational fluid dynamic (CFD) method. The CFD outputs, including velocity in the y-direction, the temperature of the nanofluid, and the nanoparticle content (Ø), are employed for the learning process of the DEFIS model. By choosing the optimum number of inputs and the number of population, the underlying DEFIS variable parameters are studied. After reaching the high value of DEFIS intelligence, in the learning step, a variety of Ø values (e.g., 0.5, 1, and 2) are reviewed. For the full intelligence of DEFIS, the velocity of the nanofluid is predicted in further nodes of the cavity domain. Finally, the velocity of the nanofluid is predicted by using the data at Ø = 0.15, which are absent in the DEFIS process.

Developing Intelligent Algorithm as a Machine Learning Overview over the Big Data Generated by Euler-Euler Method To Simulate Bubble Column Reactor Hydrodynamics

A bubble column reactor is simulated by a combination of Euler-Euler and adaptive network-based fuzzy inference system (ANFIS) method to develop an understanding of the machine learning (ML) technique in describing complex behavior of multiphase flow in bubble column reactors and for deep learning of input and output connections. In the validation stage of simulations, an intelligent bubble column is created that uses artificial intelligence nodes or neural network nodes, and the results of prediction indicated excellent agreement with computational fluid dynamics (CFD) simulation results. The hydrodynamic characteristics of the air bubbles and the amount of stress inside the bubble column reactor are used as the output of the ANFIS method. This study showed that when a three-dimensional bubble column is trained by a ML method, a similar CFD simulation can be created, which is independent of CFD source data. This type of smart simulation also enables us to avoid repeating the simulations with CFD methods that are time-consuming and computationally expensive for process modeling and optimization.

Molecular investigation into the effect of carbon nanotubes interaction with CO2 in molecular separation using microporous polymeric membranes

The use of nanofluids has been recently of great interest to separate acidic contaminants such as CO₂. The main objective of this research is to assess the influence of carbon nanotubes (CNTs) addition to distilled water on enhancing the CO₂ molecular separation through a porous membrane contactor (PMC). For this aim, a comprehensive model is developed based on non-wetted and counter-current operational modes to evaluate the principal mass and momentum transport equations in tube, membrane and shell compartments of PMC. Consequently, a CFD-based axisymmetrical simulation is implemented according to finite element technique (FET) to prognosticate the results. It is found from the results that the addition of 0.1 wt% carbon nanotubes (CNTs) particles to water significantly enhances the mass transfer and consequently the CO₂ molecular separation efficiency from 38 to 63.3%. This considerable enhancement can be justified due to the existence of two momentous phenomena including Brownian motion and Grazing effect, which enhance the mass transport of CO₂ molecules in the PMC. Moreover, the effect of CNTs concentration, some membrane's parameters such as number of hollow fibers and porosity and also some module's design parameters including module radius and length on the CO₂ separation performance are investigated in this paper as another highlight of the current work.

Modification of polyethersulfone membrane using MWCNT-NH2 nanoparticles and its application in the separation of azeotropic solutions by means of pervaporation

In this study, functionalized multi-walled carbon nanotubes (MWCNT-NH₂) were synthesized as an additive for the preparation of mixed matrix membranes (MMMs) and then were investigated by FTIR and FE-SEM techniques. Polyether sulfone (PES) polymeric membrane modified with functionalized MWCNT-NH₂ carbon nanotubes was prepared by phase inversion method. The effect of MWCNT-NH₂ on the morphology and property of the PES membrane was evaluated using scanning electron microscopy. The flux, enrichment factor and swelling properties of modified membranes were also used to investigate the membranes performance. The results showed that the flux and enrichment factor in modified PES membrane containing 5 wt.% of functionalized MWCNT-NH₂ carbon nanotubes were obtained 1.2 L.m^-2h^-1 and 3.3, respectively. The influence of methanol concentration on the flux and enrichment factor was investigated. The results corroborated that the flux didn’t change significantly, while the enrichment factor was decreased.

Thermal and Flow Visualization of a Square Heat Source in a Nanofluid Material with a Cubic-Interpolated Pseudo-particle

Using thermal sources with nanoparticles can change the thermal and velocity distribution and the streamline around solid objects in mechanical devices. In the current study, square-shaped thermal structures are used in the cavity, while the fluid in the domain is fully contaminated with nanoparticles to enhance the heat- and mass-transfer distribution within the system. The connection of thermal elements is installed with equal distance in the domain, and then the nanoparticle is added in the container to improve the heat-transfer rate. The nanofluid is simulated using Cubic-Interpolated Pseudo-particle (CIP) model in the domain with different concentrations. The study shows that the sequence of hot wall structure can disturb the flow as well as thermal distribution. However, a very small streamline can be generated during heat transfer. As a result of thermal structure in the domain, the zero velocity zone in the domain can move to other parts of the cavity. This disturbance can change the heating mechanism in the system, which results in a better rate of heat-transfer characteristics in the system and process engineering. Also, the CIP computing method shows great ability in the modeling of sharp walls/structures with thermal sources.

Changes in the Number of Membership Functions for Predicting the Gas Volume Fraction in Two-Phase Flow Using Grid Partition Clustering of the ANFIS Method

A 2D-bubble column reactor (BCR) including gas and liquid phases is simulated, and fluid characteristics such as gas-phase volume fraction and gas-phase turbulence are extracted from the CFD simulations. A type of heuristic algorithm called adaptive network-based fuzzy inference system (ANFIS) is applied here to simulate the gas-phase volume fraction in a physical system. Indeed, the x direction, the y direction, and gas-phase turbulence are considered as the ANFIS inputs. Changes in the number of inputs as well as membership functions are evaluated and studied to obtain a high level of ANFIS intelligence. By implementing the highest ANFIS intelligence, a surface is predicted, which suggests that the gas-phase volume fraction is based on x and y directions. It provides capability to achieve the amount of gas-phase volume fraction in different points of a 2D-BCR.