Hybrid turbulence models aim to unite the strengths of RANS and LES approaches. Recent developments include improved definitions of the hybrid length scale to better handle wall-bounded and massively separated flows. Further research focuses on more adaptable and aggressive formulations to generate faster transition from modeled to resolved turbulence. While hybrid models have been applied successfully in various cases, more comprehensive testing on diverse test cases is still needed to fully evaluate model performance and development.
This document provides an introduction to turbulence modeling methods for computational fluid dynamics simulations. It discusses direct numerical simulation (DNS), large eddy simulation (LES), and Reynolds-averaged Navier-Stokes (RANS) modeling. It explains that DNS resolves all scales of turbulence but is limited to low Reynolds numbers due to computational costs, while LES and RANS attempt to model turbulence to study higher Reynolds number flows. Key aspects of length scales, energy transfer, and the assumptions and limitations of each modeling approach are summarized.
Large Eddy Simulation of Turbulence Modeling for wind Flow past Wall Mounted ...IJERA Editor
This paper will present the large eddy simulation of turbulence modeling for wind flow over a wall mounted 3D cubical model. The LES Smagorinsky scheme is employed for the numerical simulation. The domain for this study is of the size of 60 cm x 30 cm x 30 cm. The 3D cube model is taken of the size of 6 cm x 6 cm x 4 cm. The Reynolds number for the flow in respect of the height of the cube i.e, 4 cm is 5.3x104. The hexahedral grids are used for the meshing of the flow domain. The results are discussed in terms of various parameters such as velocity profile around the cube and the computational domain, the pressure distribution over the cube, near wall velocity profile and the shear stress distribution and also the result of drag coefficient is verified by neural network time series analysis using MATLAB. In this present study we have used the OpenFoam platform for the computational and numerical analysis. The numerical scheme employed is the combination of the steady state incompressible Newtonian flow model using SIMPLE algorithm followed by the transient model of incompressible Newtonian flow using PISO algorithm. We have observed that there is a constant positive drag coefficient in case of steady state simulation where as there is a negative lift coefficient in the initial run and a very low lift coefficient at the end of the steady state simulation.
This document summarizes a study that used the Dynamic Relaxation method coupled with finite differences to analyze the deflection of laminated composite plates. The Dynamic Relaxation method was used to solve first-order shear deformation equations for the nonlinear bending response of rectangular plates. The accuracy and convergence of Dynamic Relaxation solutions for isotropic, orthotropic, and laminated plates were established by comparison to exact and approximate solutions, showing fairly good agreement. Factors like boundary conditions, mesh size, damping coefficients, and applied load were found to influence the accuracy and convergence of the Dynamic Relaxation solution.
CFD and Artificial Neural Networks Analysis of Plane Sudden Expansion FlowsCSCJournals
It has been clearly established that the reattachment length for laminar flow depends on two non-dimensional parameters, the Reynolds number and the expansion ratio, therefore in this work, an ANN model that predict reattachment positions for the expansion ratios of 2, 3 and 5 based on the above two parameters has been developed. The R2 values of the testing set output Xr1, Xr2, Xr3, and Xr4 were 0.9383, 0.8577, 0.997 and 0.999 respectively. These results indicate that the network model produced reattachment positions that were in close agreement with the actual values. When considering the reattachment length of plane sudden-expansions the judicious combination of CFD calculated solutions with ANN will result in a considerable saving in computing and turnaround time. Thus CFD can be used in the first instance to obtain reattachment lengths for a limited choice of Reynolds numbers and ANN will be used subsequently to predict the reattachment lengths for other intermediate Reynolds number values. The CFD calculations concern unsteady laminar flow through a plane sudden expansion and are performed using a commercial CFD code STAR-CD while the training process of the corresponding ANN model was performed using the NeuroShellTM simulator.
This document discusses using statistical learning techniques and direct numerical simulation (DNS) data to develop closure relationships for a simplified two-fluid model of bubbly two-phase flow in a vertical channel. DNS is used to simulate bubbly upflow in the channel, and the data is averaged and used to train a neural network model to relate unknown closure terms in the two-fluid model equations to resolved variables. The model predictions are then tested against additional DNS data. The presence of walls adds complexity compared to previous work on periodic domains by introducing new closure terms related to surface tension effects near walls.
This paper compares two methods for simulating separated flows at high Reynolds numbers using LES: a hybrid RANS-LES scheme and a zonal two-layer modeling approach. Both methods use RANS-type models near the wall to remove the need for wall-resolving grids while still capturing separation dynamics. The hybrid scheme dynamically couples a RANS solution and LES domain, while the zonal method solves RANS equations in the near-wall layer and feeds the wall shear stress to the LES region. These methods are applied to simulate flow over a hydrofoil trailing edge and around a three-dimensional hill, aiming to improve predictive capabilities for separated flows compared to standard LES or RANS alone.
Review and Assessment of Turbulence Transition ModelsIJERDJOURNAL
ABSTRACT: Turbulent boundary layer transition can greatly affect flow characteristics such as skin friction, heat transfer, pressure loads, and boundary layer separation point. Accurate computation of such effect is vital to the design of components and vehicles subjected to turbulent transition flows. In this paper we report our review of the existing boundary layer transition models, selection of the boundary layer transition models most appropriate for the existing Reynolds-averaged Navier-Stokes flow solvers, and implementation and evaluation of the selected transition models with some benchmark test cases, ranging from subsonic to hypersonic flows. The objective of this assessment study is not intended to pick the best transition model (in fact, there is no transition model accurately predict the boundary layer transition for all cases tested here). Rather it is to demonstrate that (1) the flow physics of turbulence transition is very complicated and not yet well understood, (2) the applicability of empirical transition models is limited and their use should be cautious due to different transition characteristics for different flow regimes/environments, and (3) further research on prediction of turbulence transition is warranted to improve the accuracy, efficiency and range of applicability.
This document provides an overview and summary of a book titled "Slurry Transport: Fundamentals, Historical Overview & The Delft Head Loss & Limit Deposit Velocity Framework". The book was written by Dr.ir. Sape A. Miedema and edited by Robert C. Ramsdell. It covers the fundamentals of horizontal transport of settling slurries in pipelines and develops theoretical models for different flow regimes based on constant volumetric spatial concentration. A new model is presented for the Limit Deposit Velocity and derivation of relationships for pressure loss, concentration distribution, and bed height as a function of line speed. The book is based on experimental data and aims to mathematically describe physical processes involved in slurry transportation.
This document provides an introduction to turbulence modeling methods for computational fluid dynamics simulations. It discusses direct numerical simulation (DNS), large eddy simulation (LES), and Reynolds-averaged Navier-Stokes (RANS) modeling. It explains that DNS resolves all scales of turbulence but is limited to low Reynolds numbers due to computational costs, while LES and RANS attempt to model turbulence to study higher Reynolds number flows. Key aspects of length scales, energy transfer, and the assumptions and limitations of each modeling approach are summarized.
Large Eddy Simulation of Turbulence Modeling for wind Flow past Wall Mounted ...IJERA Editor
This paper will present the large eddy simulation of turbulence modeling for wind flow over a wall mounted 3D cubical model. The LES Smagorinsky scheme is employed for the numerical simulation. The domain for this study is of the size of 60 cm x 30 cm x 30 cm. The 3D cube model is taken of the size of 6 cm x 6 cm x 4 cm. The Reynolds number for the flow in respect of the height of the cube i.e, 4 cm is 5.3x104. The hexahedral grids are used for the meshing of the flow domain. The results are discussed in terms of various parameters such as velocity profile around the cube and the computational domain, the pressure distribution over the cube, near wall velocity profile and the shear stress distribution and also the result of drag coefficient is verified by neural network time series analysis using MATLAB. In this present study we have used the OpenFoam platform for the computational and numerical analysis. The numerical scheme employed is the combination of the steady state incompressible Newtonian flow model using SIMPLE algorithm followed by the transient model of incompressible Newtonian flow using PISO algorithm. We have observed that there is a constant positive drag coefficient in case of steady state simulation where as there is a negative lift coefficient in the initial run and a very low lift coefficient at the end of the steady state simulation.
This document summarizes a study that used the Dynamic Relaxation method coupled with finite differences to analyze the deflection of laminated composite plates. The Dynamic Relaxation method was used to solve first-order shear deformation equations for the nonlinear bending response of rectangular plates. The accuracy and convergence of Dynamic Relaxation solutions for isotropic, orthotropic, and laminated plates were established by comparison to exact and approximate solutions, showing fairly good agreement. Factors like boundary conditions, mesh size, damping coefficients, and applied load were found to influence the accuracy and convergence of the Dynamic Relaxation solution.
CFD and Artificial Neural Networks Analysis of Plane Sudden Expansion FlowsCSCJournals
It has been clearly established that the reattachment length for laminar flow depends on two non-dimensional parameters, the Reynolds number and the expansion ratio, therefore in this work, an ANN model that predict reattachment positions for the expansion ratios of 2, 3 and 5 based on the above two parameters has been developed. The R2 values of the testing set output Xr1, Xr2, Xr3, and Xr4 were 0.9383, 0.8577, 0.997 and 0.999 respectively. These results indicate that the network model produced reattachment positions that were in close agreement with the actual values. When considering the reattachment length of plane sudden-expansions the judicious combination of CFD calculated solutions with ANN will result in a considerable saving in computing and turnaround time. Thus CFD can be used in the first instance to obtain reattachment lengths for a limited choice of Reynolds numbers and ANN will be used subsequently to predict the reattachment lengths for other intermediate Reynolds number values. The CFD calculations concern unsteady laminar flow through a plane sudden expansion and are performed using a commercial CFD code STAR-CD while the training process of the corresponding ANN model was performed using the NeuroShellTM simulator.
This document discusses using statistical learning techniques and direct numerical simulation (DNS) data to develop closure relationships for a simplified two-fluid model of bubbly two-phase flow in a vertical channel. DNS is used to simulate bubbly upflow in the channel, and the data is averaged and used to train a neural network model to relate unknown closure terms in the two-fluid model equations to resolved variables. The model predictions are then tested against additional DNS data. The presence of walls adds complexity compared to previous work on periodic domains by introducing new closure terms related to surface tension effects near walls.
This paper compares two methods for simulating separated flows at high Reynolds numbers using LES: a hybrid RANS-LES scheme and a zonal two-layer modeling approach. Both methods use RANS-type models near the wall to remove the need for wall-resolving grids while still capturing separation dynamics. The hybrid scheme dynamically couples a RANS solution and LES domain, while the zonal method solves RANS equations in the near-wall layer and feeds the wall shear stress to the LES region. These methods are applied to simulate flow over a hydrofoil trailing edge and around a three-dimensional hill, aiming to improve predictive capabilities for separated flows compared to standard LES or RANS alone.
Review and Assessment of Turbulence Transition ModelsIJERDJOURNAL
ABSTRACT: Turbulent boundary layer transition can greatly affect flow characteristics such as skin friction, heat transfer, pressure loads, and boundary layer separation point. Accurate computation of such effect is vital to the design of components and vehicles subjected to turbulent transition flows. In this paper we report our review of the existing boundary layer transition models, selection of the boundary layer transition models most appropriate for the existing Reynolds-averaged Navier-Stokes flow solvers, and implementation and evaluation of the selected transition models with some benchmark test cases, ranging from subsonic to hypersonic flows. The objective of this assessment study is not intended to pick the best transition model (in fact, there is no transition model accurately predict the boundary layer transition for all cases tested here). Rather it is to demonstrate that (1) the flow physics of turbulence transition is very complicated and not yet well understood, (2) the applicability of empirical transition models is limited and their use should be cautious due to different transition characteristics for different flow regimes/environments, and (3) further research on prediction of turbulence transition is warranted to improve the accuracy, efficiency and range of applicability.
This document provides an overview and summary of a book titled "Slurry Transport: Fundamentals, Historical Overview & The Delft Head Loss & Limit Deposit Velocity Framework". The book was written by Dr.ir. Sape A. Miedema and edited by Robert C. Ramsdell. It covers the fundamentals of horizontal transport of settling slurries in pipelines and develops theoretical models for different flow regimes based on constant volumetric spatial concentration. A new model is presented for the Limit Deposit Velocity and derivation of relationships for pressure loss, concentration distribution, and bed height as a function of line speed. The book is based on experimental data and aims to mathematically describe physical processes involved in slurry transportation.
An Adaptive Moving Mesh Method For Two-Dimensional Relativistic Magnetohydrod...Scott Faria
This document describes an adaptive moving mesh method for solving two-dimensional thin film flow equations that include surface tension. The method uses moving mesh partial differential equations (MMPDEs) and mesh density functions to adaptively move the computational mesh based on solution characteristics like curvature. Numerical results show this r-adaptive moving mesh technique accurately captures the moving contact line and associated fingering instability with reduced computational effort compared to a fixed uniform mesh.
An Algebraic Multigrid Solver For Transonic Flow ProblemsLisa Muthukumar
This document summarizes an article about developing an algebraic multigrid solver for transonic flow problems. The key points are:
- The solver is based on the full potential equation, which can model subsonic, transonic, and supersonic flows.
- Algebraic multigrid methods are used instead of geometric multigrid to avoid dependencies on grid geometry.
- The discretization approach handles the mixed elliptic-hyperbolic nature of the governing equations across flow regimes.
- Applications to complex geometries on structured grids are demonstrated, achieving an order of magnitude reduction in residual per cycle.
First order orthotropic shear deformation equations for the nonlinear elastic bending response of rectangular plates are introduced. Their solution using a computer program based on finite differences implementation of the Dynamic Relaxation (DR) method is outlined. The convergence and accuracy of the DR solutions for elastic large deflection response of isotropic, orthotropic, and laminated plates are established by comparison with various exact and approximate solutions. The present Dynamic Relaxation method (DR) coupled with finite differences method shows a fairly good agreement with other analytical and numerical methods used in the verification scheme.It was found that: The convergence and accuracy of the DR solution is dependent on several factors including boundary conditions, mesh size and type, fictitious densities, damping coefficients, time increment and applied load. Also, the DR large deflection program using uniform finite differences meshes can be employed in the analysis of different thicknesses for isotropic, orthotropic or laminated plates under uniform loads. All the comparison results for simply supported (SS4) edge conditions showed that deflection is almost dependent on the direction of the applied load or the arrangement of the layers
A Robust Topology Control Solution For The Sink Placement Problem In WSNsJim Webb
This document proposes a topology control solution using discrete particle swarm optimization (DPSO) with local search to solve the sink placement problem in wireless sensor networks (WSNs). The goal is to minimize the maximum worst case delay in the network by determining the optimal number and locations of sinks. Traffic flow analysis (TFA) is used to calculate delay, and the approach is extended to allow its use for multiple sink scenarios. Experiments show the DPSO approach outperforms genetic algorithm-based sink placement (GASP), the state-of-the-art solution, finding better sink locations up to 3 times faster.
Support Recovery with Sparsely Sampled Free Random Matrices for Wideband Cogn...IJMTST Journal
The main objective of this project is to design an eigenvalue-based compressive SOE technique using asymptotic random matrix theory. In this project, investigating blind sparsity order estimation (SOE) techniques is an open research issue. To address this, this project presents an eigenvalue-based compressive SOE technique using asymptotic random matrix theory. Finally, this project propose a technique to estimate the sparsity order of the wideband spectrum with compressive measurements using the maximum eigenvalue of the measured signal's covariance matrix. .
This document discusses the built-in filters of two eddy viscosity subgrid scale models used in large-eddy simulation (LES): the Smagorinsky model and the Schumann model. It presents the theoretical basis of LES filtering and equations. The study identifies the forms of the built-in filters associated with each model by varying a characteristic length scale in the models and analyzing the effective filter rendered by the simulations. The behavior of an equivalent Kolmogorov constant is also compared to theory. The results provide insight into how the modeling terms influence the filtering process and flow dynamics in LES without using explicit filtering.
The convergence and accuracy of the Dynamic
Relaxation (DR) solutions for elastic large deflection
response of isotropic, orthotropic, and laminated plates
are established by comparison with various exact and
approximate solutions. The present Dynamic
Relaxation method (DR) coupled with finite differences
method shows a fairly good agreement with other
analytical and numerical methods used in the verification
scheme.
It was found that: The convergence and accuracy of the
DR solution is dependent on several factors including
boundary conditions, mesh size and type, fictitious
densities, damping coefficients, time increment and
applied load. Also, the DR large deflection program
using uniform finite differences meshes can be
employed in the analysis of different thicknesses for
isotropic, orthotropic or laminated plates under uniform
loads. All the comparison results for simply supported
(SS4) edge conditions showed that deflection is almost
dependent on the direction of the applied load or the
arrangement of the layers.
This document summarizes a large eddy simulation of flow around a sharp-edged surface-mounted cube. The simulation was performed using the Petsc-Fem code developed at CIMEC. The flow conditions matched published benchmarks, with a Reynolds number of 40,000. An upstream channel flow was first simulated to provide turbulent inflow conditions. The simulation results are analyzed to validate the LES implementation and identify areas for improving turbulence modeling.
First – order orthotropic shear deformation equations
for the nonlinear elastic bending response of rectangular
plates are introduced. Their solution using a computer
program based on finite differences implementation of the
Dynamic Relaxation (DR) method is outlined. The
convergence and accuracy of the DR solutions for elastic
large deflection response of isotropic, orthotropic, and
laminated plates are established by comparison with various
exact and approximate solutions. The present Dynamic
Relaxation method (DR) coupled with finite differences
method shows a fairly good agreement with other analytical
and numerical methods used in the verification scheme.
It was found that: The convergence and accuracy of the
DR solution is dependent on several factors including
boundary conditions, mesh size and type, fictitious densities,
damping coefficients, time increment and applied load. Also,
the DR large deflection program using uniform finite
differences meshes can be employed in the analysis of
different thicknesses for isotropic, orthotropic or laminated
plates under uniform loads. All the comparison results for
simply supported (SS5) edge conditions showed that
deflection is almost dependent on the direction of the applied
load or the arrangement of the layers
This document discusses recent trends in computational fluid dynamics (CFD). It begins by defining CFD as using numerical analysis and algorithms to solve fluid flow problems described by partial differential equations. CFD offers advantages over physical experiments by enabling low-cost simulation-based design and analysis of fluid phenomena that are difficult to measure experimentally. The document outlines the basic CFD process of geometry description, model selection, grid generation, solution, and post-processing. It provides examples of CFD applications in aerospace, automotive, biomedical, and other industrial fields to analyze designs. The conclusion discusses iterative solution methods and potential future advances in multidisciplinary and on-demand CFD simulations.
Performance of the Maximum Stable Connected Dominating Sets in the Presence o...csandit
The topology of mobile ad hoc networks
(
MANETs
)
change dynamically with time. Connected
dominating sets
(
CDS
)
are considered to be an effective topology for net
work-wide broadcasts
in MANETs as only the nodes that are part of the CD
S need to broadcast the message and the
rest of the nodes merely receive the message. Howev
er, with node mobility, a CDS does not exist
for the entire duration of the network session and
has to be regularly refreshed
(
CDS
transition
)
. In an earlier work, we had proposed a benchmarkin
g algorithm to determine a
sequence of CDSs
(
Maximum Stable CDS
)
such that the number of transitions is the global
minimum. In this research, we study the performance
(
CDS Lifetime and CDS Node Size
)
of the
Maximum Stable CDS when a certain fraction of the n
odes in the network are static and
compare the performance with that of the degree-bas
ed CDSs. We observe the lifetime of the
Maximum Stable CDS to only moderately increase
(
by a factor of 2.3
)
as we increase the
percentage of the static nodes in the network; on t
he other hand, the lifetime of the degree-based
CDS increases significantly
(
as large as 13 times
)
as we increase the percentage of static nodes
from 0 to 80
.
This document summarizes research on using direct numerical simulation (DNS) to study bubbly flows in vertical channels and develop closure terms for two-fluid models of multiphase flows. It describes DNS of small laminar systems with several spherical bubbles that show a non-monotonic transient evolution as bubbles initially move toward walls then slowly return to the channel center. Larger turbulent simulations are also discussed. The goal is to use DNS data to provide values for unresolved terms in simplified averaged models through statistical learning, with prospects for filtering interface structures in large-eddy simulations discussed.
Effect of Geometry on Variation of Heat Flux and Drag for Launch Vehicle -- Z...Abhishek Jain
Above Research Paper can be downloaded from www.zeusnumerix.com
The research paper aims at studying the variation of the geometry of the launch vehicle nose and its effect on heat flux. CFDExpert software is first validated on NASA's hyperballistic model and then used on proposed geometries. Various nose radius and blending shapes are studied for effect on drag and heat flux. Cone ogive shape is found to decrease heat flux with an insignificant increase in drag. Authors Abhishek Jain (Zeus Numerix), Rohan Kedar and Prof V Kalamkar (SPCOE).
Flow Modeling Based Wall Element TechniqueCSCJournals
Two types of flow where examined, pressure and combination of pressure and Coquette flow of confined turbulent flow with a one equation model used to depict the turbulent viscosity of confined flow in a smooth straight channel when a finite element technique based on a zone close to a solid wall has been adopted for predicting the distribution of the pertinent variables in this zone and examined even with case when the near wall zone was extended away from the wall. The validation of imposed technique has been tested and well compared with other techniques.
2011 santiago marchi_souza_araki_cobem_2011CosmoSantiago
This document discusses the performance of the multigrid method for solving the Navier-Stokes equations using two alternative formulations: streamfunction-velocity and streamfunction-vorticity. The study examines the lid-driven cavity flow problem for different grid sizes, Reynolds numbers, numbers of grid levels, and inner iterations to determine optimal parameter values that minimize CPU time. Previous research has found that the multigrid method is less effective for the Navier-Stokes equations at higher Reynolds numbers. The document aims to investigate how formulation choice and multigrid parameters influence efficiency.
Researched improvements on increasing efficiency of organic solar cells by utilizing and modifying the Purdue University researchers NanoMOS MATLAB simulations
https://nanohub.org/resources/1305?rev=1
This document proposes a holistic approach to reconstruct data in ocean sensor networks using compression sensing. It involves two key aspects:
1) A node reordering scheme is developed to improve the sparsity of signals in the discrete cosine transform or Fourier transform domain, reducing the number of measurements needed for accurate reconstruction.
2) An improved sparse adaptive tracking algorithm is adopted to estimate the sparse degree and then reconstruct the signal in a step-by-step manner, gradually converging on an accurate reconstruction even with unknown sparsity.
Simulation results show the proposed method can effectively reduce signal sparsity and accurately reconstruct signals, especially in cases of unknown sparsity.
- The document summarizes responses to questions about wave and hydrodynamic modeling for the Gulf of Thailand Early Warning System.
- It describes that SWAN was used for wave modeling with a 300m resolution, and wave setup was estimated using an empirical equation rather than direct modeling. Delft3D Flexible Mesh was used for hydrodynamic modeling with a Courant-adaptive grid and horizontal viscosities of 1 m^2/s.
- The models were not online coupled, and wind forcing, boundaries, and water levels were handled separately rather than exchanged between the wave and hydrodynamic models.
Constructing Minimum Connected Dominating Set in Mobile Ad Hoc NetworksGiselleginaGloria
One of the most important challenges of a Mobile Ad Hoc Network (MANET) is to ensure efficient routing among its nodes. A Connected Dominating Set (CDS) is a widely used concept by many protocols for broadcasting and routing in MANETs. Those existing protocols require significant message overhead in construction of CDS. In this paper, we propose a simple, inexpensive and novel algorithm of computing a minimum CDS. The proposed algorithm saves time and message overhead in forming a CDS while supporting node mobility efficiently. Simulation results show that the proposed algorithm is efficient in terms of both message complexity and the size of the CDS.
This document summarizes a numerical study on free-surface flow conducted using a computational fluid dynamics (CFD) solver. The study examines the wave profile generated by a submerged hydrofoil through several test cases varying parameters like the turbulence model, grid resolution, and hydrofoil depth. The document provides background on the governing equations solved by the CFD solver and the interface capturing technique used to model the free surface. Five test cases are described that investigate grid convergence, the impact of laminar vs turbulent models, the relationship between hydrofoil depth and wave height, and the effect of discretization schemes.
Presentation of IEEE Slovenia CIS (Computational Intelligence Society) Chapte...University of Maribor
Slides from talk presenting:
Aleš Zamuda: Presentation of IEEE Slovenia CIS (Computational Intelligence Society) Chapter and Networking.
Presentation at IcETRAN 2024 session:
"Inter-Society Networking Panel GRSS/MTT-S/CIS
Panel Session: Promoting Connection and Cooperation"
IEEE Slovenia GRSS
IEEE Serbia and Montenegro MTT-S
IEEE Slovenia CIS
11TH INTERNATIONAL CONFERENCE ON ELECTRICAL, ELECTRONIC AND COMPUTING ENGINEERING
3-6 June 2024, Niš, Serbia
6th International Conference on Machine Learning & Applications (CMLA 2024)ClaraZara1
6th International Conference on Machine Learning & Applications (CMLA 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Machine Learning & Applications.
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An Adaptive Moving Mesh Method For Two-Dimensional Relativistic Magnetohydrod...Scott Faria
This document describes an adaptive moving mesh method for solving two-dimensional thin film flow equations that include surface tension. The method uses moving mesh partial differential equations (MMPDEs) and mesh density functions to adaptively move the computational mesh based on solution characteristics like curvature. Numerical results show this r-adaptive moving mesh technique accurately captures the moving contact line and associated fingering instability with reduced computational effort compared to a fixed uniform mesh.
An Algebraic Multigrid Solver For Transonic Flow ProblemsLisa Muthukumar
This document summarizes an article about developing an algebraic multigrid solver for transonic flow problems. The key points are:
- The solver is based on the full potential equation, which can model subsonic, transonic, and supersonic flows.
- Algebraic multigrid methods are used instead of geometric multigrid to avoid dependencies on grid geometry.
- The discretization approach handles the mixed elliptic-hyperbolic nature of the governing equations across flow regimes.
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First order orthotropic shear deformation equations for the nonlinear elastic bending response of rectangular plates are introduced. Their solution using a computer program based on finite differences implementation of the Dynamic Relaxation (DR) method is outlined. The convergence and accuracy of the DR solutions for elastic large deflection response of isotropic, orthotropic, and laminated plates are established by comparison with various exact and approximate solutions. The present Dynamic Relaxation method (DR) coupled with finite differences method shows a fairly good agreement with other analytical and numerical methods used in the verification scheme.It was found that: The convergence and accuracy of the DR solution is dependent on several factors including boundary conditions, mesh size and type, fictitious densities, damping coefficients, time increment and applied load. Also, the DR large deflection program using uniform finite differences meshes can be employed in the analysis of different thicknesses for isotropic, orthotropic or laminated plates under uniform loads. All the comparison results for simply supported (SS4) edge conditions showed that deflection is almost dependent on the direction of the applied load or the arrangement of the layers
A Robust Topology Control Solution For The Sink Placement Problem In WSNsJim Webb
This document proposes a topology control solution using discrete particle swarm optimization (DPSO) with local search to solve the sink placement problem in wireless sensor networks (WSNs). The goal is to minimize the maximum worst case delay in the network by determining the optimal number and locations of sinks. Traffic flow analysis (TFA) is used to calculate delay, and the approach is extended to allow its use for multiple sink scenarios. Experiments show the DPSO approach outperforms genetic algorithm-based sink placement (GASP), the state-of-the-art solution, finding better sink locations up to 3 times faster.
Support Recovery with Sparsely Sampled Free Random Matrices for Wideband Cogn...IJMTST Journal
The main objective of this project is to design an eigenvalue-based compressive SOE technique using asymptotic random matrix theory. In this project, investigating blind sparsity order estimation (SOE) techniques is an open research issue. To address this, this project presents an eigenvalue-based compressive SOE technique using asymptotic random matrix theory. Finally, this project propose a technique to estimate the sparsity order of the wideband spectrum with compressive measurements using the maximum eigenvalue of the measured signal's covariance matrix. .
This document discusses the built-in filters of two eddy viscosity subgrid scale models used in large-eddy simulation (LES): the Smagorinsky model and the Schumann model. It presents the theoretical basis of LES filtering and equations. The study identifies the forms of the built-in filters associated with each model by varying a characteristic length scale in the models and analyzing the effective filter rendered by the simulations. The behavior of an equivalent Kolmogorov constant is also compared to theory. The results provide insight into how the modeling terms influence the filtering process and flow dynamics in LES without using explicit filtering.
The convergence and accuracy of the Dynamic
Relaxation (DR) solutions for elastic large deflection
response of isotropic, orthotropic, and laminated plates
are established by comparison with various exact and
approximate solutions. The present Dynamic
Relaxation method (DR) coupled with finite differences
method shows a fairly good agreement with other
analytical and numerical methods used in the verification
scheme.
It was found that: The convergence and accuracy of the
DR solution is dependent on several factors including
boundary conditions, mesh size and type, fictitious
densities, damping coefficients, time increment and
applied load. Also, the DR large deflection program
using uniform finite differences meshes can be
employed in the analysis of different thicknesses for
isotropic, orthotropic or laminated plates under uniform
loads. All the comparison results for simply supported
(SS4) edge conditions showed that deflection is almost
dependent on the direction of the applied load or the
arrangement of the layers.
This document summarizes a large eddy simulation of flow around a sharp-edged surface-mounted cube. The simulation was performed using the Petsc-Fem code developed at CIMEC. The flow conditions matched published benchmarks, with a Reynolds number of 40,000. An upstream channel flow was first simulated to provide turbulent inflow conditions. The simulation results are analyzed to validate the LES implementation and identify areas for improving turbulence modeling.
First – order orthotropic shear deformation equations
for the nonlinear elastic bending response of rectangular
plates are introduced. Their solution using a computer
program based on finite differences implementation of the
Dynamic Relaxation (DR) method is outlined. The
convergence and accuracy of the DR solutions for elastic
large deflection response of isotropic, orthotropic, and
laminated plates are established by comparison with various
exact and approximate solutions. The present Dynamic
Relaxation method (DR) coupled with finite differences
method shows a fairly good agreement with other analytical
and numerical methods used in the verification scheme.
It was found that: The convergence and accuracy of the
DR solution is dependent on several factors including
boundary conditions, mesh size and type, fictitious densities,
damping coefficients, time increment and applied load. Also,
the DR large deflection program using uniform finite
differences meshes can be employed in the analysis of
different thicknesses for isotropic, orthotropic or laminated
plates under uniform loads. All the comparison results for
simply supported (SS5) edge conditions showed that
deflection is almost dependent on the direction of the applied
load or the arrangement of the layers
This document discusses recent trends in computational fluid dynamics (CFD). It begins by defining CFD as using numerical analysis and algorithms to solve fluid flow problems described by partial differential equations. CFD offers advantages over physical experiments by enabling low-cost simulation-based design and analysis of fluid phenomena that are difficult to measure experimentally. The document outlines the basic CFD process of geometry description, model selection, grid generation, solution, and post-processing. It provides examples of CFD applications in aerospace, automotive, biomedical, and other industrial fields to analyze designs. The conclusion discusses iterative solution methods and potential future advances in multidisciplinary and on-demand CFD simulations.
Performance of the Maximum Stable Connected Dominating Sets in the Presence o...csandit
The topology of mobile ad hoc networks
(
MANETs
)
change dynamically with time. Connected
dominating sets
(
CDS
)
are considered to be an effective topology for net
work-wide broadcasts
in MANETs as only the nodes that are part of the CD
S need to broadcast the message and the
rest of the nodes merely receive the message. Howev
er, with node mobility, a CDS does not exist
for the entire duration of the network session and
has to be regularly refreshed
(
CDS
transition
)
. In an earlier work, we had proposed a benchmarkin
g algorithm to determine a
sequence of CDSs
(
Maximum Stable CDS
)
such that the number of transitions is the global
minimum. In this research, we study the performance
(
CDS Lifetime and CDS Node Size
)
of the
Maximum Stable CDS when a certain fraction of the n
odes in the network are static and
compare the performance with that of the degree-bas
ed CDSs. We observe the lifetime of the
Maximum Stable CDS to only moderately increase
(
by a factor of 2.3
)
as we increase the
percentage of the static nodes in the network; on t
he other hand, the lifetime of the degree-based
CDS increases significantly
(
as large as 13 times
)
as we increase the percentage of static nodes
from 0 to 80
.
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2. To alleviate the drawback of the RANS modeling approaches, one can use Direct
Numerical Simulation (DNS) or Large Eddy Simulation (LES). Nevertheless, the
computational cost of the numerical methods is very high. For the computation of wall
bounded flows even for ones of simple geometries using DNS or LES, high resolution-
meshes, i.e. isotropic grids in the massive turbulence regions to directly resolve the strongly
anisotropic-largest turbulence structures in the near wall region which are in the order of
the boundary layer thickness are a must. Such situations even are aggravated when dealing
with high Reynolds number-wall bounded flows where the boundary layer thickness
becomes thinner at high Reynolds number, thus making the utilization of DNS and LES
persists to be more restricted for the high Reynolds number-flows. That is why the demand
for RANS modeling is never any lower in the future even though one is aware of the strong
misgivings on the conceptual grounds of RANS [1], and the most valid reason that brings
the relentless aspiration to the RANS modeling urgency is that the demise of RANS
closures has not happened until today [2]. The readers are referred to Durbin [2] for recent
developments of the RANS closures.
As an attempt to unite the supremacies of RANS modeling approach and DNS or LES
into a single solution strategy, nowadays we are fortunate with the advent of various hybrid
turbulence modeling schemes. Too few to mention are Detached Eddy Simulation (DES)
and Very Large Eddy Simulation (VLES). In this paper, recent progresses and potential
researches within a class of the hybrid scale resolving schemes are discussed. A failure of a
seamless hybrid formulation which is not explicitly dependent on the grid scale is also
presented.
2 Recent progresses and further studies in hybrid turbulence
models
Since the conception of Spalart-Allmaras Detached Eddy Simulation (S-A DES) of Spalart
et al. [3] around 20 yr ago, various hybrid RANS-LES models being capable of resolving
the turbulence scales and maintaining the more affordable computation at practical
Reynolds numbers than DNS and standard LES such as, SST-Delayed Detached Eddy
Simulation (DDES) [4], Extra Large Eddy Simulaton (X-LES) [5], Partially Averaged
Navier-Stokes (PANS) [6], DDES [7], Embedded Large Eddy Simulation (ELES) [8],
Zonal Large Eddy Simulation (ZLES) [9], SST-Scale Adaptive Simulation (SAS) [9], SST-
Improved Delayed Detached Eddy Simulation (IDDES) [10], Spalart-Allmaras Zonal
Detached Eddy Simulation (S-A ZDES) [11], RANS-Implicit Large Eddy Simulation
(ILES) [12], and Stress-Blended Eddy Simulation (SBES) of ANSYS [13], are now
available for unsteady simulations. It is important to note here that the names of the models
containing the capital letter DES explicitly are DES variants, although this is not
necessarily the case as in RANS-ILES, SBES, and X-LES. Furthermore, the capital letters
preceding the hybrid model names, e.g. SST-DES, indicate the names of RANS model used
as the baseline model in the hybrid formulations. Among the scale resolving schemes, SST-
SAS is the only method having an inherently different strategy in the modification of the
turbulence transport equation, as compared to the DES forms.
In the above-mentioned hybrid proposals, one can classify the schemes into zonal and
non-zonal techniques. All the models (except ELES, S-A ZDES, and ZLES that are flow
problem-dependent zonalization) are non-zonal or global approach in the sense that the
method itself chooses automatically the simulation mode during the run, and thus
predefinitions between RANS and LES regions are avoided prior to the simulation, as
explained by Breuer et al. [14]. An opposite way holds for the zonal procedure where the
predefinition of the LES and RANS regions prior to the execution of the simulation is
decided by the user through the grid design, the determination of an explicit border, or the
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3. selection of domains not especially related to wall regions [14]. In this regard, the non-
zonal technique is more straightforward and practical than the zonal counterpart with
respects to reduced efforts from the user side on conceiving different turbulence regions
manifested through the grid design. In this paper we focus the progress of the hybrid
turbulence models on the group of non-zonal approach.
Within the DES families, a new search for more physically rationalized definitions of
the hybrid length scale in addition to the standard model in DES and DDES, i.e. the
maximum of the cell sizes max, was pioneered by Shur et al. [15] and Deck [16] due to the
needs of formulating a more modular DDES for wall bounded- and massively separated
turbulent flows and a more agressive DDES being competent to generate fast break-up of
modelled turbulence into resolved turbulence length scales. In this respect, a versatile
definition of the hybrid length scale IDDES for massively separated- and wall bounded-
turbulent flows and a new formulation of the filter width of [17] to prevent a delayed
development of instabilities in shear layer have been established in IDDES of [15] and S-A
ZDES of [16], respectively. Before [15] and [16], the upgrade of DES was dedicated to
prevent an improper activation of resolved turbulence scales simulation in the very near-
wall region through the development of a new blending or shielding function, fp, i.e. to
shield the boundary layer region from the attack of grid-induced separation (GIS) when
mesh refinement is required, as in Menter and Kuntz [4], and Spalart et al. [7]. Later on,
improvements in the hybrid scale resolving schemes were proposed by Gritskevich et al.
[10] for IDDES with fine-tuning to the SST background model. The urgency of developing
a more adaptable and aggressive hybrid formalism was also addressed by Menter [18].
Following the advances in IDDES, SBES of ANSYS [13], and RANS-ILES of Islam and
Thornber [12] were developed recently. In SBES, a new hybrid filter width SBES is defined
as a maximum numerical function between the cubic root of the cell volume of Deardorff
[19] and a corrected maximum of the cell size. A new grid scale is also used in RANS-
ILES but this novel filter width RANS-ILES is based on the cell Jacobian as to maintain a
smoother, gradual variation over stretched, anisotropic grids [12]. Clearly, these new
subgrid length scales control the level of eddy viscosity and which wavelengths can be
directly captured; thus strongly influencing the performance of the advanced turbulence
models.
The hybrid turbulence modeling approaches have been widely used in various cases
with varying degrees of success. In the literature, depending on the nature of studies chosen
either model application or model development, several hybrid scale-resolving schemes
exercised on a set of test case to study their performance or single hybrid turbulence model
tested on various geometries to analyse the strength of its modelling strategy are not always
performed. In many studies where the focus is on product development, it is usually
sufficient to only utilize one hybrid scale-resolving scheme where the choice of the hybrid
model used can depend on its availability in a flow solver or relevant supporting evidences
to the strength of the model given in the literature. To such situations we can cite for
example the works of Wang et al. [20] and Xia et al. [21] who studied the performance of a
hybrid turbulence model only on a case, i.e. SST-DDES on a control valve [20] and SST-
IDDES on a high-speed train [21]. Despite these prevailing stages, there are a number of
studies that employed several hybrid scale-resolving schemes on a set of test case during
the last five years such as the work of Islam and Thornber [12] that studied the
performances of PANS, S-A DDES, SST-DDES, RANS-ILES on circular cylinder, flat
plate, NACA4412 airfoil. In the mentioned studies, the capabilities of SST-DDES, SST-
IDDES, and the other hybrid models to produce the turbulence scales were well-proven.
More importantly, RANS-ILES was found to be the most superior model over PANS, S-A
DDES, SST-DDES [12]. Adding more studies which investigated the performances of the
hybrid turbulence models, quite recently aggresive performance of SBES has also been
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4. corroborated by Ravelli and Barigozzi [22], Meraner et al. [23], Straka et al. [24], and
Ekman et al. [25] on turbine nozzle guide vane, burner, segmental orifice plate, and truck;
respectively. Comparative studies of the performances of SBES and other hybrid model
variants, including SST-DDES, SST-SAS, k- DDES on circular cylinder with splitter and
hatchback vehicle can be found in Pratomo and Schäfer [26], Buscariolo et al. [27] where
SBES was proven to be the most superior over the other hybrid variants. Among the SBES
investigations, the study of Straka et al. [24] is the only one that introduced a new blending
function, fp, solely based on the non dimensional wall distance y+
instead of the standard
blending function exploited by the rest. Even though all the mentioned studies contribute to
the valuable knowledge on how the hybrid models perform, they are limited in the sense of
the certain cases used. In fact, computational engineers are always faced with various
geometries involving the turbulence where the turbulence itself is case-dependent and more
importantly the hybrid modelling approaches have differently ingrained strategies for the
turbulence treatment. Compelling questions always come up: “how do the hybrid
turbulence models perform on various new cases or existing configurations such as
circular cylinder with splitter, wall-mounted hemisphere, tandem circular cylinders?” and
“which the hybrid models perform better?” Thus, the availability of hybrid scale resolving
schemes is not without difficulty. Computational engineers are faced with the formidable
task to choose prospective hybrid models which are suited for various cases. Anyway such
a situation leads to a positive impact for the computational engineering community. At least
in the context of the model application, studies into the performances of the hybrid
turbulence models have never ended up. “How do RANS-ILES, SBES perform on a wall-
mounted hemisphere?” and “how do RANS-ILES, SBES perform on tandem circular
cylinders?” for example can be good proposals for future studies as they are relatively
young and still not much investigated.
3 Failure of SST-SAS on a simple configuration
Reducing the turbulent eddy viscosity is the way to solve the weakness in RANS modeling
approaches in order to derive the hybrid or RANS-LES turbulence models. Within the two-
equation eddy viscosity RANS models, the formulation of the viscosity contains two
turbulence scales, i.e. turbulence kinetic energy k, turbulence frequency or dissipation
where the turbulence scales are solved by their transport equations, that is, the k-transport
equation, -transport equation or -transport equation. For the DES variants such as DDES,
IDDES, the eddy viscosity reduction is realized in the k-transport equation through a
multiplier to the dissipation term of the turbulence kinetic energy. The multiplier in the
dissipation term is a length scale limiter or hybrid function which contains the RANS and
subgrid-or LES-length scales. The filter width mentioned many times in this paper
resides in the subgrid-length scales where the LES-scale resolutions are strongly
determined by the local grid spacings in the filter width definition.
Unlike the DES variants, the strategy of SAS to lower the eddy viscosity is different. In
SST-SAS of Menter and Egorov [9], the turbulent eddy viscosity is lessened by revising the
-transport equation of SST with an introduction of an additional source term QSAS that is a
function of flow variables, i.e. shear strain rate tensor S, length scale L, von Karman length
scale LvK, turbulence kinetic energy k, and turbulence frequency . The corresponding
formulations of the SAS -transport equation, the additional source term QSAS, and the von
Karman length scale LvK are given in equations (1) to (3). Interestingly, there is no filter
width variable given in the formulation of the additional source term QSAS (see Equation
(2)). Accordingly, such a strategy is safer than one of the DES variants from the attack of
GIS, an important term (in the scale-resolving scheme simulation) coined by Spalart et al.
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5. [7], when the mesh refinement is urgent in certain regions. Nevertheless, as the turbulence
is case-dependent the functionality of the additional production term QSAS is strongly
affected by the flow parameters where the key variables in the QSAS definition are the von
Karman length scale LvK and the shear strain rate tensor S. For this reason, when the new
source term QSAS is zero (owing to the calculation of those two flow solutions) then the -
transport equation returns back to its original form of SST, meaning that the vortex scales
can not be resolved by SST-SAS.
j
x
j
x
k
F
j
x
t
j
x
SAS
Q
k
P
k
j
U
j
x
t
1
2
2
1
1
2 (1)
,0
2
k
1
,
2
1
max
2
2
2
2
max
j
x
k
j
x
k
j
x
j
x
k
C
V
L
L
S
SAS
Q
(2)
U
S
vK
L (3)
In the equations, 2 is the value for the k- regime of the SST model and U’’ is the
second velocity derivative. The readers are referred to the paper of Menter and Egorov [9]
for further details.
(a)
k
U
inflow
-2
tUinflow D-1
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E3S Web of Conferences 130, 01013 (2019) https://doi.org/10.1051/e3sconf/201913001013
IC-AMME 2018
6. (b)
Fig. 1. (a) Evolution in time of the turbulence kinetic energy k. (b) monitoring points for the
turbulence kinetic energy k.
Application of SST-SAS [9] on a benchmark configuration was performed by Pratomo
and Schäfer [26]. The configuration considered is a fluid-structure interaction test case of
De Nayer et al. [28] where the rubber was treated as a rigid splitter. This was to study the
performance of SAS before proceeding with a fluid-structure interaction simulation with a
prospective hybrid turbulence model. The Reynolds number of the turbulent flow over the
geometry was in a subcritical region in the mode of a transition in the shear layer as in De
Nayer et al. [28]. The boundary conditions used inlet, no-slip wall (for the cylinder and the
splitter), outlet, slip walls, periodicity for the lateral walls where low turbulence intensity
and eddy viscosity ratio were imposed at the inlet. An LES mesh of 14x106
control volumes
with a growth rate of 1.05, y+
< 5, x+
= 40, and z+
= 64 was crafted for the simulation
with a subset case-domain. The subset domain was used as two-point correlations dropped
towards zero value within the subset domain [29]. Following Garcia-Villalba et al. [30],
two monitoring points for the turbulence kinetic energy k were added in the wake region
behind the circular cylinder (illustrated in Figure 1b) to conclude the evolution in time of
the turbulence kinetic energy k for the requirement of non-dimensional advection time
t*
100
inflow
D
U
t and the start of transient statistics averaging period. The progress of the
turbulence kinetic energy k in time is depicted in Figure 1a for 125 non-dimensional
advection times. From the figure the distribution of the turbulence kinetic energy k in time
is already settled, indicating that the turbulent flow was fully developed and ready for the
averaging phase.
Figure 2a illustrates the turbulence scales (colored with CFL number) modeled by SST-
SAS of Menter and Egorov [9], captured at the non-dimensional advection time of 125. It is
demonstrated that SST-SAS [9] failed to sufficiently resolve the vorticity scales on the
geometry, even with the LES quality mesh and a very small timestep size t of 2.5x10-5
s
corresponding to the CFL number of less than 1 [26]. The scale-resolving simulation on the
test case just produced a RANS like-solution. Moreover, using different non-dissipative
advection schemes and eddy viscosity limiters under the fine temporal and grid resolutions
also did not offer any helps, as reported by Pratomo and Schäfer [26]. The fine mesh
resolutions simply produced the shear strain rate S and the von Karman length scale LvK
that eventually neglected the additional source term QSAS in the -transport equation of
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E3S Web of Conferences 130, 01013 (2019) https://doi.org/10.1051/e3sconf/201913001013
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7. SST-SAS, that is, QSAS 0. From Equation (2), it is clear that when the argument
j
x
k
j
x
k
k
j
x
j
x
k
C
V
L
L
S
2
1
,
2
1
max
2
2
2
2
is never bigger than 0, the numerical
function “max” in the QSAS definition will take 0 as the largest value thus making QSAS = 0.
(a)
(b)
Fig. 2. (a) Turbulence scales colored with CFL number from the Q-criterion. (b) Contour of the shear
strain rate tensor. (Reproduced from Pratomo and Schäfer [26]).
Figure 2b displays the contour of the shear strain rate tensor S which, in this case,
contributed to the removal of the additional source term QSAS from Equation (1). It is seen
that the existence of the splitter behind the cylinder significantly increased the shear strain
rate tensor S in the wake region (shown in the red color). This is the source of the
neglection of the argument
j
x
k
j
x
k
k
j
x
j
x
k
C
V
L
L
S
2
1
,
2
1
max
2
2
2
2
in Equation (2) as
the multiplier
2
v
L
L in the first term gives a small value for the first term as a result of
bigger value of the von Karman lengthscale LvK (due to the shear strain rate tensor S, see
Equation (3)).
4 Conclusion and outlook
Recent progresses and further applied researches within the non-zonal hybrid (RANS-LES)
turbulence modelling formulation have been addressed in this paper. The non-zonal RANS-
LES model family is easier to use and more efficient than the zonal hybrid turbulence
model group in the sense that RANS and LES modes are automatically activated by the
non-zonal technique during the run and much effort to predefine different turbulence
regions during the grid design is avoided. To this day, the improvements in the non-zonal
RANS-LES proposal embrace several crucial aspects which make the approach remain
attractive and advantageous with respect to the computational cost and accuracy. In
addition to the extension to various RANS models as the background model for the non-
zonal hybrid formulation, the numerical method has been equipped with strong shielding
functions and better definitions for the filter width, thus keeping the flexibility and
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8. aggressive performance of the non-zonal RANS-LES approaches for simulating turbulent
flows. From the recent works, two young non-zonal hybrid models appear to be superior
among their predecessors. They are SBES and RANS-ILES, as mentioned in this paper. It
therefore will be of a strong interest to study the effect and weakness of the differently
ingrained strategies in the young hybrid models for the turbulence treatment on various
configurations such as circular cylinder with splitter, wall-mounted hemisphere, 3D-
diffuser, tandem circular cylinder as the turbulence is case-dependent. In the long run, this
brings a constantly renewed impetus in turbulence research, particularly when the hybrid
formulations are married with other disciplines such as acoustics and fluid-structure
interaction.
SST-SAS technology is not always more advantageous than RANS models. Proper
functionality of the approach directly relies on the inherent nature of turbulence generated
by a geometry, not explicitly depends on the grid resolution. This means that a fine spatial
resolution carefully crafted for SST-SAS can, otherwise, hinder the production of the
turbulence scales by the model because of a certain flow behavior leading to the neglection
of the keypart in the additional source term QSAS in the -transport equation of SST-SAS.
This is not similar with the DES variants which are explicitly grid dependent-techniques.
However, SAS is safer than any DES forms from the GIS phenomena.
Lastly, to reduce volume of the daunting task of deciding prospective hybrid
formulations for the turbulence simulation, two important terms have been introduced, i.e.
“globally unstable flow” and “locally unstable flow” at least can help the computational
engineering community to intuitively choose the potential models suited for certain
problems. When a turbulent flow is considered to be globally unstable, the turbulence is
strongly unstable. Such a flow type potentially occurs in turbulent flow over any obstacles
or bluff bodies. Conversely, turbulent wall bounded-flows with backward-facing steps and
turbulent free-shear flows emanating from walls can be categorized as locally unstable
flow. As a best practice, those hybrid turbulence models can be recommended to handle
each of the flow types.
The first author is indebted to Prof. Dr.rer.nat Michael Schäfer who has introduced and trusted him
for doing research in turbulence and fluid-structure interaction at Fachgebiet Numerische
Berechnungsverfahren im Maschinenbau (FNB), Technische Universität (TU) Darmstadt and
gratefully acknowledges the scholarships of Kementerian Riset, Teknologi, dan Pendidikan Tinggi
Republik Indonesia and Universitas Kristen Petra. It is expressly stated that major parts of this
manuscript were prepared by the first author during his doctoral study at FNB, TU Darmstadt.
Finally, insightful comments from reviewers which have strengthened the manuscript as well as deep
discussions with: Mr. Martin Straka of Physikalisch-Technische Bundesanstalt (PTB) Berlin, Dr.-Ing.
Wolfgang Bauer of ANSYS Germany and Institut für Land- und Seeverkehr – Fachgebiet
Fahrzengantriebe of TU Berlin, and Abe H. Lee, PhD, graduate of the Pennsylvania State University,
are also gratefully acknowledged.
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