scholarly journals Three-Dimensional Numerical Simulation and Performance Study of an Industrial Helical Static Mixer

2005 ◽  
Vol 127 (3) ◽  
pp. 467-483 ◽  
Author(s):  
Ramin K. Rahmani ◽  
Theo G. Keith ◽  
Anahita Ayasoufi
Keyword(s):  
Turbulent Flow ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Critical Role ◽  
Three Dimensional ◽  
Static Mixer ◽  
Performance Study ◽  
Mixing Processes ◽  
Viscous Liquids ◽  
Wide Range

In many branches of processing industries, viscous liquids need to be homogenized in continuous operations. Consequently, fluid mixing plays a critical role in the success or failure of these processes. Static mixers have been utilized over a wide range of applications such as continuous mixing, blending, heat and mass transfer processes, chemical reactions, etc. This paper describes how static mixing processes of single-phase viscous liquids can be simulated numerically, presents the flow pattern through a helical static mixer, and provides useful information that can be extracted from the simulation results. The three-dimensional finite volume computational fluid dynamics code used here solves the Navier-Stokes equations for both laminar and turbulent flow cases. The turbulent flow cases were solved using k-ω model and Reynolds stress model (RSM). The flow properties are calculated and the static mixer performance for different Reynolds numbers (from creeping flows to turbulent flows) is studied. A new parameter is introduced to measure the degree of mixing quantitatively. Furthermore, the results obtained by k-ω and RSM turbulence models and various numerical details of each model are compared. The calculated pressure drop is in good agreement with existing experimental data.

scholarly journals Three-Dimensional Numerical Simulation and Performance Study of an Industrial Helical Static Mixer

2003 ◽  
Author(s):  
Ramin K. Rahmani ◽  
Theo G. Keith ◽  
Anahita Ayasoufi
Keyword(s):  
Turbulent Flow ◽  
Single Phase ◽  
Stokes Equations ◽  
Critical Role ◽  
Three Dimensional ◽  
Static Mixer ◽  
Performance Study ◽  
Mixing Processes ◽  
Viscous Liquids ◽  
Wide Range

Viscous liquids have to be homogenized in continuous operations in many branches of processing industries. Consequently, fluid mixing plays a critical role in the success or failure of many industrial processes. The use of static mixers has been utilized over a wide range of applications such as continuous mixing, blending, heat and mass transfer processes, chemical reactions, etc. This paper illustrates how static mixing processes of single-phase viscous liquids can be simulated numerically, and presents the flow pattern of both Newtonian and non-Newtonian single-phase liquids through a helical static mixer, and provides useful information that can be extracted from the simulation results. Three-dimensional finite volume simulations are used to study the performance of the mixer. The CFD code used here solves the Navier-Stokes equations for both laminar and turbulent flow cases. The turbulent flow cases were solved using k–ω and Reynolds Stress models. The flow properties are calculated for both Newtonian and non-Newtonian fluids. The calculated pressure drop is in good agreement with existing experimental data.

A Study of the Accuracy, Global Performance, and Computational Expenses of k–ε, k–ω, and RSM Turbulent Models for Flow in an Industrial Static Mixer

2004 ◽  
Author(s):  
Ramin K. Rahmani ◽  
Theo G. Keith ◽  
Anahita Ayasoufi
Keyword(s):  
Single Phase ◽  
Critical Role ◽  
Three Dimensional ◽  
Static Mixer ◽  
Mixing Processes ◽  
Viscous Liquids ◽  
Pressure Drops ◽  
Wide Range ◽  
Global Performance ◽  
Turbulent Models

Viscous liquids have to be homogenized in continuous operations in many branches of processing industries; and therefore, fluid mixing plays a critical role in the success or failure of many industrial processes. The use of static mixers has been utilized over a wide range of applications such as continuous mixing, blending, heat and mass transfer processes, chemical reactions, etc. Consequences of improper mixing include non-reproducible processing conditions and lowered product quality, resulting in the need for more elaborate downstream purification processes and increased waste disposal costs. This paper extends previous studies by the authors on an industrial helical static mixer and illustrates how static mixing processes of single-phase viscous liquids can be simulated numerically. It also intends to present an improved understanding of the turbulent flow pattern for single-phase liquids through the mixer. Three-dimensional finite volume simulations are used to study the performance of the mixer for a range of practical Reynolds numbers, using three different turbulent models: k–ε model, k–ω model, and RSM model. The accuracy, global performance and costs of the different turbulent models have been examined. The flow velocities, pressure drops, etc. are calculated for each model. The calculated pressure drop of each case is compared with experimental results. Using different tools, the mixing results obtained from the different models are studied and compared.

A Numerical Study of Turbulent Flow in Helical Static Mixers

2006 ◽  
Author(s):  
Ramin K. Rahmani ◽  
Anahita Ayasoufi ◽  
Theo G. Keith
Keyword(s):  
Turbulent Flow ◽  
Molecular Diffusion ◽  
Stokes Equations ◽  
Numerical Study ◽  
Critical Role ◽  
Three Dimensional ◽  
Turbulent Dispersion ◽  
Working Fluid ◽  
Static Mixer ◽  
Static Mixers

Many processing applications call for the addition of small quantities of chemicals to working fluid. Hence, fluid mixing plays a critical role in the success or failure of these processes. An optimal combination of turbulent dispersion down to eddies of the Kolmogoroff scale and molecular diffusion would yield fast mixing on a molecular scale which in turn favors the desired reactions. Helical static mixers can be used for those applications. The range of practical flow Reynolds numbers for these mixers in industry is usually from very small (Re ∼ 0) to moderate values (Re ∼ 5000). In this study, a helical static mixer is investigated numerically using Lagrangian methods to characterize mixer performance under turbulent flow regime conditions. A numerical simulation of turbulent flows in helical static mixers is employed. The model solves the three-dimensional, Reynolds-averaged Navier-Stokes equations, closed with the Spalart-Allmaras turbulence model, using a second-order-accurate finite-volume numerical method. Numerical simulations are carried out for a six-element mixer, and the computed results are analyzed to elucidate the complex, three-dimensional features of the flow. Using a variety of predictive tools, mixing results are obtained and the performance of static mixer under turbulent flow condition is studied.

Three-Dimensional Numerical Simulation and Performance Study of an Industrial Static Mixer Using Pseudo-Plastic Fluids

2004 ◽  
Author(s):  
Ramin K. Rahmani ◽  
Theo G. Keith ◽  
Anahita Ayasoufi
Keyword(s):  
Numerical Simulation ◽  
Single Phase ◽  
Three Dimensional ◽  
Phase Reaction ◽  
Static Mixer ◽  
Performance Study ◽  
Mixing Processes ◽  
Numerical Predictions ◽  
Wide Range ◽  
Plastic Fluids

Mixing is an essential component of nearly all industrial chemical processes, ranging from simple blending to complex multi-phase reaction systems for which the reaction rate, the yield and the selectivity are highly dependent upon the mixing performance. Consequences of improper mixing include nonreproducible processing conditions and lowered product quality, resulting in the need for more elaborate downstream purification processes and increased waste disposal costs. A wide range of working fluids in industrial mixers are non-Newtonian. The non-Newtonian fluid studied here is a member of the pseudo-plastic fluids group, characterized by a progressively decreasing slope or shear stress versus shear rate. These fluids are termed shear thinning; the viscosity decreases with increasing velocity gradient. In this paper, a previous study by the authors on an industrial helical static mixer is extended to illustrate how static mixing processes of single-phase pseudo-plastic liquids can be simulated numerically. A further aim is to provide an improved understanding of the flow pattern of pseudo-plastic single-phase liquids through the mixer. A three-dimensional finite volume simulation is used to study the performance of the mixer. A commercial software, FLUENT, is used in a part of the numerical simulation. The flow velocities, pressure drops, etc. are calculated for various flow rates, using the Carreau and the power law models for non-Newtonian fluids. The numerical predictions by these two models are compared to existing experimental data. Also, a comparison of the mixer performance for both Newtonian and pseudo-plastic fluids is presented.

scholarly journals Finite Element Analysis of Turbulent Flows Using LES and Dynamic Subgrid-Scale Models in Complex Geometries

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Wang Wenquan ◽  
Zhang Lixiang ◽  
Yan Yan ◽  
Guo Yakun
Keyword(s):  
Finite Element ◽  
Turbulent Flow ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulent Channel Flow ◽  
Francis Turbine ◽  
Complex Geometries ◽  
Subgrid Scale ◽  
Element Analysis

An innovative computational model is presented for the large eddy simulation (LES) of multidimensional unsteady turbulent flow problems in complex geometries. The main objectives of this research are to know more about the structure of turbulent flows, to identify their three-dimensional characteristic, and to study physical effects due to complex fluid flow. The filtered Navier-Stokes equations are used to simulate large scales; however, they are supplemented by dynamic subgrid-scale (DSGS) models to simulate the energy transfer from large scales toward subgrid-scales, where this energy will be dissipated by molecular viscosity. Based on the Taylor-Galerkin schemes for the convection-diffusion problems, this model is implemented in a three-dimensional finite element code using a three-step finite element method (FEM). Turbulent channel flow and flow over a backward-facing step are considered as a benchmark for validating the methodology by comparing with the direct numerical simulation (DNS) results or experimental data. Also, qualitative and quantitative aspects of three-dimensional complex turbulent flow in a strong 3D blade passage of a Francis turbine are analyzed.

Large-Eddy Turbulent Flow Simulation of a KOMAX Static Mixer

2008 ◽  
Author(s):  
Ramin K. Rahmani ◽  
Theo G. Keith ◽  
Anahita Ayasoufi
Keyword(s):  
Turbulent Flow ◽  
Critical Role ◽  
Flow Simulation ◽  
Reynolds Numbers ◽  
Static Mixer ◽  
Viscous Liquids ◽  
Pressure Drops ◽  
Static Mixers ◽  
Eddy Simulation ◽  
Large Eddy

Viscous liquids have to be homogenized in continuous operations in many branches of processing industries; and therefore, fluid mixing plays a critical role in the success or failure of many industrial processes. Consequences of improper mixing include non-reproducible processing conditions and lowered product quality, resulting in the need for more elaborate downstream processes and increased costs. The range of practical flow Reynolds numbers for KOMAX static mixers in industry is usually from moderate values (Re ≈ 0) to very large values (e.g. Re ≈ 5,000,000). However, most of industrial applicants have a very small flow to moderate Reynolds numbers (e.g. Re ≈ 5,000). This paper presents an improved understanding of the turbulent flow pattern for single-phase liquids through the mixer. Large-Eddy Simulation (LES) model is applied to the flow in a KOMAX static mixer to calculate the flow velocities, pressure drops, etc. Using a variety of predictive tools, the mixing results are obtained.

scholarly journals Turbulent 2.5-dimensional dynamos

2016 ◽  
Vol 799 ◽  
pp. 246-264 ◽  
Author(s):  
K. Seshasayanan ◽  
A. Alexakis
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Two Dimensional Flow

We study the linear stage of the dynamo instability of a turbulent two-dimensional flow with three components $(u(x,y,t),v(x,y,t),w(x,y,t))$ that is sometimes referred to as a 2.5-dimensional (2.5-D) flow. The flow evolves based on the two-dimensional Navier–Stokes equations in the presence of a large-scale drag force that leads to the steady state of a turbulent inverse cascade. These flows provide an approximation to very fast rotating flows often observed in nature. The low dimensionality of the system allows for the realization of a large number of numerical simulations and thus the investigation of a wide range of fluid Reynolds numbers $Re$, magnetic Reynolds numbers $Rm$ and forcing length scales. This allows for the examination of dynamo properties at different limits that cannot be achieved with three-dimensional simulations. We examine dynamos for both large and small magnetic Prandtl-number turbulent flows $Pm=Rm/Re$, close to and away from the dynamo onset, as well as dynamos in the presence of scale separation. In particular, we determine the properties of the dynamo onset as a function of $Re$ and the asymptotic behaviour in the large $Rm$ limit. We are thus able to give a complete description of the dynamo properties of these turbulent 2.5-D flows.

Large-Eddy Turbulent Flow Simulation of an Industrial Helical Static Mixer

Volume 4 ◽  
2004 ◽  
Author(s):  
Ramin K. Rahmani ◽  
Theo G. Keith ◽  
Anahita Ayasoufi
Keyword(s):  
Turbulent Flow ◽  
Critical Role ◽  
Three Dimensional ◽  
Flow Simulation ◽  
Reynolds Numbers ◽  
Static Mixer ◽  
Static Mixers ◽  
Large Eddy ◽  
Turbulent Models ◽  
Les Model

Viscous liquids have to be homogenized in continuous operations in many branches of processing industries; and therefore, fluid mixing plays a critical role in the success or failure of many industrial processes. Consequences of improper mixing include non-reproducible processing conditions and lowered product quality, resulting in the need for more elaborate downstream purification processes and increased waste disposal costs. The range of practical flow Reynolds numbers for helical static mixers in industry is usually from very small (Re ≈ 0) to moderate values (e.g. Re = 5,000). However, it has been found that the flow regime within helical static mixers is turbulent for relatively low Reynolds numbers, compared to the flow inside a pipe with no mixing elements present. This paper extends previous studies by the authors on the industrial helical static mixer. Its purpose is to present an improved understanding of the turbulent flow pattern for single-phase liquids through the mixer. Three-dimensional finite volume simulations are used to study the performance of the mixer using different turbulent models. Large-Eddy Simulation (LES) model is applied to the flow in an industrial helical static mixer to calculate the flow velocities, pressure drops, etc. Using a variety of predictive tools, the mixing results are obtained. Also, the accuracy and global performance of several different turbulent models are compared against the LES model.

A Numerical Study of the Global Performance of Two Static Mixers

2005 ◽  
Author(s):  
Ramin K. Rahmani ◽  
Anahita Ayasoufi ◽  
Theo G. Keith
Keyword(s):  
Pressure Drop ◽  
Numerical Study ◽  
Critical Role ◽  
Design Procedure ◽  
Static Mixer ◽  
Flowing Fluid ◽  
Viscous Liquids ◽  
Static Mixers ◽  
Wide Range ◽  
Global Performance

Viscous liquids have to be homogenized in continuous operations in many branches of processing industries; and therefore, fluid mixing plays a critical role in the success or failure of many industrial processes. The use of static mixers has been utilized over a wide range of applications from simple blending to complex chemical reactions. Generally, a static mixer consists of a number of equal stationary units, placed on the inside of a pipe or channel in order to promote mixing of flowing fluid streams. These mixers have low maintenance and operating costs, low space requirements and no moving parts. A range of designs exists for a wide range of specific applications. The shape of the elements determines the character of the fluid motion and thus determines the effectiveness of the mixer. There are several key parameters in the design procedure of a static mixer. Some of the most important ones are: the degree of mixing of working fluids, pressure drop across the mixer, and residence time distribution of fluid elements. An ideal static mixer provides a highly mixed material with low pressure drop and similar traveling history for all fluid elements. To choose a static mixer for a given application or in order to design a new static mixer, besides experimentation, it is possible to use powerful computational fluid dynamics (CFD) tools to study the performance of static mixers. This paper extends previous studies by the authors on industrial static mixers and illustrates how static mixing processes of single-phase viscous liquids can be simulated numerically. Using different measuring tools, the global performance and costs of two static mixers are studied.

Parameter Extension Simulation of Turbulent Flows in a Compressor Cascade With a High Reynolds Number

2020 ◽  
Author(s):  
Yan Jin
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Simulation Method ◽  
Potential Method ◽  
Navier Stokes ◽  
Reference Solution ◽  
Compressor Cascade ◽  
High Reynolds

Abstract The turbulent flow in a compressor cascade is calculated by using a new simulation method, i.e., parameter extension simulation (PES). It is defined as the calculation of a turbulent flow with the help of a reference solution. A special large-eddy simulation (LES) method is developed to calculate the reference solution for PES. Then, the reference solution is extended to approximate the exact solution for the Navier-Stokes equations. The Richardson extrapolation is used to estimate the model error. The compressor cascade is made of NACA0065-009 airfoils. The Reynolds number 3.82 × 105 and the attack angles −2° to 7° are accounted for in the study. The effects of the end-walls, attack angle, and tripping bands on the flow are analyzed. The PES results are compared with the experimental data as well as the LES results using the Smagorinsky, k-equation and WALE subgrid models. The numerical results show that the PES requires a lower mesh resolution than the other LES methods. The details of the flow field including the laminar-turbulence transition can be directly captured from the PES results without introducing any additional model. These characteristics make the PES a potential method for simulating flows in turbomachinery with high Reynolds numbers.

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