reynolds averaged navier–stokes simulations of the airflow

International Review on Modelling and Simulations (I.RE.MO.S.), Vol. 12, N. 4

ISSN 1974-9821 August 2019

Copyright © 2019 Praise Worthy Prize S.r.l. - All rights reserved https://doi.org/10.15866/iremos.v12i4.17802

230

Reynolds Averaged Navier–Stokes Simulations of the Airflow in a Centrifugal Fan Using OpenFOAM

José Sánchez De la Hoz, Guillermo Valencia, Jorge Duarte Forero

Abstract – The use of numerical models through computational tools allows studying the inner flow of centrifugal fans; this is a normal practice in engineering and scientific communities. When an experimental work is expensive, numerical methods may be used to obtain necessary data. Computational Fluid Dynamics is the name given to computer simulations that enable the visualization and the inspection of flow phenomena in zones that are not easily accessible or measurable, such as blades of the impeller in a turbomachine. Important progresses have been made in Computational Fluid Dynamics over the years: accurate mathematical equations of numerical models, software with more efficient algorithms, and flexible solver codes that reduce the computational effort through user modifications. OpenFOAM is an open-source software developed in C++ library that offers different advantages over commercial computational tools, for instance, over 80 solver applications that can simulate specific cases in fluid mechanics and thermal sciences and engineering. In order to solve the Navier–Stokes equations for incompressible, and turbulent flows in a centrifugal fan with backward inclined blades, the steady-state MRFSimpleFOAM solver has been used. This study has aimed to simulate the flow behavior in the centrifugal fan and to compare the results of three turbulence models (standard k- , RNG k-, and realizable k- ) with the air flow – pressure curve acquired from experimental measurements

using LabVIEW software. A good agreement has been reached between experimental and simulated data. An error rate of 1% between simulated and experimental data has been reached; it is shown that the standard k -epsilon is a semi-empirical model with reasonable accuracy for a wide range of practical applications of flow phenomena. Copyright © 2019 Praise Worthy Prize S.r.l. - All rights reserved.

Keywords: Computational Fluid Dynamics, Fan, Model, OpenFOAM, Turbulence

Nomenclature

CFD Computational Fluids Dynamics RANS Reynolds Averaged Navier–Stokes URANS Unsteady Reynolds Averaged Navier–Stokes DNS Direct Numerical Simulations DES Detached Eddy Simulations LES Large Eddy Simulations PIV Particle Imaging Velocimetry k Turbulent kinetic energy [m2/s2] Dissipation rate [m2/s3]

Airflow velocity in a rotating frame of reference [m/s]

Angular velocity of the frame of reference [rpm]

Position vector Density of the airflow [kg/m3] Pressure of the airflow [Pa] Kinematic viscosity [m2/s]

Turbulent viscosity [m2/s] Airflow velocity [m/s] Transfer of kinetic energy [J] Constant of realizable k- turbulence model

µ Constant of turbulence model Constant of turbulence model Constant of turbulence model

I. Introduction

CFD [1] is regarded as a software tool that supplements analytical and experimental methods widely used in troubleshooting, design, and optimization of internal combustion engines [2], and turbomachines [3]. Based on the above, Shah [4] has proposed a review of CFD for centrifugal pumps and has concluded that URANS equations and k– have been appropriate to get approximations of the general performance of the centrifugal pump, obtaining a 10 percent error between experimental and simulated data.

The CFD’s growth has allowed the development of investigations on numerical solutions of partial differential equations [5]-[7] that describe the conservation of mass, momentum, and energy in a diverse range of flow problems in science and engineering applications [8]. Through a numerical solution of the incompressible Navier-Stokes equations

J. Sánchez, G. Valencia, J. Duarte Forero

Copyright © 2019 Praise Worthy Prize S.r.l. - All rights reserved International Review on Modelling and Simulations, Vol. 12, N. 4

231

using computational tools [9] it is possible to get an insight into the flow behavior in the design of new equipment [10] and processes within a virtual environment. Cavitation is an unsteady phenomenon that presents flow instabilities, excessive vibrations, and damage to material surfaces of turbomachinery. Based on the Finite Volume Method, Zhang [11] has performed a numerical simulation using the k– SST turbulence model [12] in order to analyze the cavitating turbulent flow in a high head Francis turbine. The mesh of the domain has been generated using ICEM CFD and 8.3×106 elements have been used. Simulation results have showed that OpenFOAM PISO solver might deliver computational solutions in an efficient and cost-effective way. In order to study the dynamics of the cavitation phenomenon in dredging centrifugal pumps, Duarte [13] has developed a parametric study using a RNG k– model. The operating parameters applied in the model have been swing speed, dredging depth and inclination, impeller rpm, density, and slurry velocity. A Central Composite Design has been used. Lastly, the cavitation phenomenon has been mitigated by multiple linear regression analysis through computational tools.

Turbulence is a three-dimensional and unsteady phenomenon of the flow characterized by strong gradients of the instantaneous velocity field, random fluctuations of velocity and pressure, countless swirling eddies determined by viscous forces, and boundary conditions of the flow [14]. OpenFOAM implements numerical simulations of turbulence models [15] through open-source flow solvers [16], keeping reproducible some statistical properties of flow, mean values ,and spectral distributions. It is available to simulate steady and unsteady flows by using DNS, LES, DES, and RANS approaches. RANS solvers are characterized by robustness, economy, and reasonable numerical accuracy for a wide range of practical turbulent flow calculations at efficient computational cost; InterDyFOAM [17] implements the volume-of-fluid method in order to solve the conservation equations, this solver subdivides the solution domain into finite volumes using a mesh. RANS k– models study the Reynold stresses [18] through the Eddy Viscosity approach and simplify the problem to the solution of two separate transport equations: turbulence kinetic energy and its dissipation rate (k– ), which are determined by decomposing the dependent variables into mean and fluctuating terms.

The choice of turbulence model depends on the level of accuracy required, computational resources, and the amount of time available for the numerical simulation; Capurso [19] has improved a novel impeller used in the feedwater of nuclear power plants, the 3D URANS k– SST turbulence model has been solved by modifying the open-source code OpenFOAM. Liu [20] has studied the grid independence and simulated the steady-state inner flow in a double blades pump through a MRFSimpleFOAM solver applying the standard k–model. Relative positions in the rotor and stator are fixed with the frozen rotor method. The CFD analysis has been

validated with PIV experimental results. A good agreement with the experimental data has been reached.

This paper proposes to verify the influence of three RANS k– turbulence models [21] on the three-dimensional CFD analysis of a centrifugal fan with backward inclined blades. The obtained results have been compared and validated against experimental data. Lastly, the prediction of OpenFOAM as a computational tool is defined to promote further CFD studies applied to computational optimization methods [22] in science and engineering. In order to achieve the main goal of this research, the airflow of the industrial centrifugal fan has been modeled from its main components (Fig. 2). This computational domain has been discretized (Fig. 4) by means of Salome 8.3.0 and exported to OpenFOAM software. The Numerical model computed with MRFSimpleFOAM solver has been used to study dependent variables of the Navier – Stokes equations [23], [24] that describe the behavior of the airflow in the industrial centrifugal fan under real working conditions and verify the agreement between processed data of k- , RNG k- , and realizable k- turbulence models and experimental data of the model. The results of this CFD analysis demonstrate that RANS k- is the better turbulence model used to describe the behavior of the inner airflow in the industrial centrifugal fan studied.

II. Methodology

The analysis of the previous research focusing on the development of numerical models generates a clear vision of the way forward to develop the CFD analysis in industrial centrifugal fans through computational tools and what could be the benefit from using them in the academy, in the industry, and in the engine science research. Understanding the behavior of a centrifugal fan by computational tools entails examining the inner airflow behavior in operational conditions using numerical models. It is necessary to take into account the error rates [25] during the process because of the discretization of the system of partial differential equations used and the development of numerical iterations until reaching the convergence degree defined in a previous configuration. It is proposed to use the following methodology (Fig. 1) in order to analyze the approximation of RANS k– turbulence models concerning experimental values measured for the centrifugal fan operation.

Fig. 1. Methodology used in the study



232

The basis of this research has been the experimental model of the industrial centrifugal fan developed. The first experimental flow rate – pressure curve has been plotted with data generated by measuring the pressure and airflow speed of the fan under real working conditions. Ventilation system restrictions determine the level of pressure (a backdraft shutter within the outlet duct in this particular case). Industrial centrifugal fan with backward inclined Blades CAD is used to generate the 3D airflow model applied in computational numerical analysis. SolidWorks software is used to model the complex geometry of the volute and impeller; then, the airflow CAD is modeled with flow simulation application. Continuous variables of the system of differential equations should be approximate to discrete variables in order to obtain an iterative solution in the solver; based on the above, the continuous domain of the inner airflow is replaced by a discrete domain using a mesh configuration with Salome 8.3.0 software. A mesh independence study is developed in order to ensure that the approximate solution does not depend on the mesh configuration defined in the numerical model. The mesh independency study relates the computational effort and resources needed with the quality and density of the mesh in order to achieve the convergence of the solution.

The domain discretized through a mesh is exported to OpenFOAM software. The solver configuration suggested for each turbulence model would solve the system of partial differential equations in order to obtain a solution for each dependent variable of the system.

With OpenFOAM software, it is possible to view the flow behavior under real working conditions through its virtual environment. Finally yet importantly, the agreement between RANS k– turbulence models and the experimental model has been developed to define the numerical model, which offers the best representation of the inner airflow behavior in the industrial centrifugal fan.

III. Studied Centrifugal Fan

Centrifugal fans with backward inclined Blades are characterized by using centrifugal force generated by the impeller rotation to increase the amount of kinetic energy

of the airflow. The configuration of this impeller allows the centrifugal fans operation in corrosive and low dusting environments. The main geometric features of the impeller are shown in Table I. After the air particles may be displaced when the impeller is in motion, they get into the centrifugal fan casing or volute; the airflow kinetic energy is transformed into pressure due to the ventilation system restrictions. The main components of the fan are shown in Fig. 2, and the measures that make up the geometry of the volute are shown in Table II.

TABLE I IMPELLER SPECIFICATIONS

Parameter Value Number of blades 12

Blade angle 25° Blade width 3.5 mm Blade length 103 mm Inlet diameter 244.5 mm

Outlet diameter 355 mm

TABLE II

MEASURE OF THE SPIRAL Measure Grades Longitude (cm)

1 0 31 2 30 24 3 60 25 4 90 27 5 120 28.5 6 150 30 7 180 32.5 8 210 35 9 240 37

10 270 38

IV. Numerical Model

The development of CFD as a computational tool facilitates the analysis of the airflow behavior over complex geometries that make up the main parts of a turbomachine; the preceding ensures that the centrifugal fan performance can be defined as saving considerable resources in the design and optimization process under specific operating conditions. The accurate prediction of the airflow behavior in the industrial centrifugal fan through Computational Fluid Dynamics is based on the turbulence analysis that occurs in the fan operation.

Fig. 2. CAD Centrifugal fan with backward inclined blades

Inlet pipe

Volute

Pressure measurement

Backdraft shutter Outlet pipe

Copyright © 2019 Praise Worthy Prize S.r.l.

approach;the airflow described by

k–resources Stokesflow behaviorequations are the basis in CFD analysis of turbomachineryexact numerical solution for this system of partial differential equatiosystem of withthrough computational tools.study indto applyincompressible airflowthe laws of conservation of mass and momentumEqsaccount

state analysis of the airflowmomentum equation in the region of the computational domain where the impeller rotates at a constant speed (rpm) using a frame of reference in motion. Effect(2) in the rotation zone during the development of the numerical simulation.

can be modeled through a meshaccurate solution iof the centrifugal fan. Thus the system of differential equations might be approximated to the system of


RANS kapproach;the airflow described by

Compared to LES models

resources Stokesflow behaviorequations are the basis in CFD analysis of turbomachineryexact numerical solution for this system of partial differential equatiosystem of with through computational tools.study industrial centrifugal fano apply

incompressible airflowthe laws of conservation of mass and momentum

qs. (1) and (2), respectivelyaccount

MRFSimpleFOAM solver state analysis of the airflowmomentum equation in the region of the computational domain where the impeller rotates at a constant speed (rpm) using a frame of reference in motion. Effect(2) in order in the rotation zone during the development of the numerical simulation.

A discrete approximation of the computational domain can be modeled through a meshaccurate solution iof the centrifugal fan. Thus the system of differential equations might be approximated to the system of


RANS kapproach;the airflow described by


resources Stokes equationsflow behaviorequations are the basis in CFD analysis of turbomachineryexact numerical solution for this system of partial differential equatiosystem of

CFD solution methods through computational tools.

for CFD analysisustrial centrifugal fan

o applyincompressible airflowthe laws of conservation of mass and momentum

. (1) and (2), respectivelyaccount:

MRFSimpleFOAM solver state analysis of the airflowmomentum equation in the region of the computational domain where the impeller rotates at a constant speed (rpm) using a frame of reference in motion. Effect and centrifugal forces are terms added to the E

in order in the rotation zone during the development of the numerical simulation.



RANS k–approach; these models the airflow described by


resources that equations

flow behaviorequations are the basis in CFD analysis of turbomachineryexact numerical solution for this system of partial differential equatiosystem of partial


for CFD analysisustrial centrifugal fan

o apply a steadyincompressible airflowthe laws of conservation of mass and momentum

. (1) and (2), respectively

(

MRFSimpleFOAM solver state analysis of the airflowmomentum equation in the region of the computational domain where the impeller rotates at a constant speed (rpm) using a frame of reference in motion.

and centrifugal forces are terms added to the Ein order to ta

in the rotation zone during the development of the numerical simulation.



– these models

the airflow described byCompared to LES

reduce that this CFD study

equationsflow behavior in practical engineering applications; these equations are the basis in CFD analysis of turbomachineryexact numerical solution for this system of partial differential equatio

partial CFD solution methods

through computational tools.for CFD analysis

ustrial centrifugal fana steady




and centrifugal forces are terms added to the Eto ta




turbulence modelsthese models

the airflow described byCompared to LES

reduce this CFD study

equations offer analytic descriptionsin practical engineering applications; these

equations are the basis in CFD analysis of turbomachineryexact numerical solution for this system of partial differential equatio

partial differential equationsCFD solution methods


ustrial centrifugal fana steady




and centrifugal forces are terms added to the Eto take into account the airflow displacement


IV.1.

A discrete approximation of the computational domain can be modeled through a meshaccurate solution in CFD analysis applied in the airflow of the centrifugal fan. Thus the system of differential equations might be approximated to the system of


turbulence modelsthese models

the airflow described byCompared to LES or DES numerical models, RANS

reduce the this CFD study

offer analytic descriptionsin practical engineering applications; these

equations are the basis in CFD analysis of turbomachineryexact numerical solution for this system of partial differential equations.

differential equationsCFD solution methods


ustrial centrifugal fana steady-state



) +


and centrifugal forces are terms added to the Eke into account the airflow displacement


IV.1.

A discrete approximation of the computational domain can be modeled through a mesh

n CFD analysis applied in the airflow of the centrifugal fan. Thus the system of differential equations might be approximated to the system of


turbulence modelsthese models perform a statistical

the airflow described by turbulent fluctuationsor DES numerical models, RANS

the this CFD study

offer analytic descriptionsin practical engineering applications; these

equations are the basis ofin CFD analysis of turbomachineryexact numerical solution for this system of partial

It is possible to approximate the differential equations


for CFD analysisustrial centrifugal fan is presented in

state incompressible airflow in the industrial centrifugal fanthe laws of conservation of mass and momentum


+ 2

=



in the rotation zone during the development of the

Mesh




turbulence modelsperform a statistical turbulent fluctuations

or DES numerical models, RANS efforts and

this CFD study offer analytic descriptions

in practical engineering applications; these of the numerical models applied

in CFD analysis of turbomachineryexact numerical solution for this system of partial



of turbulent airflow in the is presented in

state analysisin the industrial centrifugal fan

the laws of conservation of mass and momentum. (1) and (2), respectively

=

×

=

MRFSimpleFOAM solver state analysis of the airflow applying themomentum equation in the region of the computational domain where the impeller rotates at a constant speed (rpm) using a frame of reference in motion.



Mesh




turbulence modelsperform a statistical turbulent fluctuations


this CFD study offer analytic descriptions

in practical engineering applications; these the numerical models applied



CFD solution methods andThe algorithm used


analysisin the industrial centrifugal fan

the laws of conservation of mass and momentum. (1) and (2), respectively, should

= 0

×

MRFSimpleFOAM solver [27]applying the

momentum equation in the region of the computational domain where the impeller rotates at a constant speed (rpm) using a frame of reference in motion.



Generation




turbulence models perform a statistical turbulent fluctuations


may require.offer analytic descriptions




and The algorithm used


analysisin the industrial centrifugal fan

the laws of conservation of mass and momentum, should

+

[27] implementapplying the




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A discrete approximation of the computational domain can be modeled through a mesh in order


J

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or DES numerical models, RANS efforts and the



in CFD analysis of turbomachinery although there is no exact numerical solution for this system of partial


specific algorithms The algorithm used


analysis in the industrial centrifugal fan


×

+

implementapplying the




eneration

A discrete approximation of the computational domain in order


J. Sánchez

All rights reserved

proposeperform a statistical turbulent fluctuations

or DES numerical models, RANS the



although there is no exact numerical solution for this system of partial

It is possible to approximate the differential equations to discrete data


of turbulent airflow in the is presented in Fig. 3

[26]in the industrial centrifugal fan


×

·

implementapplying the conservation of




eneration

A discrete approximation of the computational domain in order


Sánchez

rights reserved

propose perform a statistical turbulent fluctuations

or DES numerical models, RANS computational

may require.offer analytic descriptions of turbulent



It is possible to approximate the to discrete data


of turbulent airflow in the Fig. 3

[26] considering in the industrial centrifugal fan

the laws of conservation of mass and momentumbe taken into

×

implementconservation of

momentum equation in the region of the computational domain where the impeller rotates at a constant speed (rpm) using a frame of reference in motion. The Coriolis



A discrete approximation of the computational domain to achieve an


Sánchez

rights reserved

a practical analysis of.


may require. Navier of turbulent





of turbulent airflow in the Fig. 3. In order

considering in the industrial centrifugal fan

the laws of conservation of mass and momentumbe taken into

implements a steadyconservation of

momentum equation in the region of the computational domain where the impeller rotates at a constant speed

The Coriolis and centrifugal forces are terms added to the E

ke into account the airflow displacement in the rotation zone during the development of the



Sánchez, G.

rights reserved

a practical analysis of


Navier of turbulent




specific algorithms The algorithm used in this

of turbulent airflow in the In order


the laws of conservation of mass and momentum usingbe taken into

a steadyconservation of


The Coriolis and centrifugal forces are terms added to the E




Fig. 4. Unstructured mesh

G. Valencia,



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specific algorithms in this



usingbe taken into

(1)

(2)

a steadyconservation of


The Coriolis and centrifugal forces are terms added to the Eq





Valencia,

233



– of turbulent




specific algorithms in this


considering in the industrial centrifugal fan,

using be taken into

(1)

(2)

a steady-conservation of


The Coriolis q.





Valencia,

233

algebraic variables iterative process by the solver in OpenFOAMsoftware.can be discretized into structured and unstructured cells.

that allow the build of 2D mesh shaped like triangles and quadrilaterals, and 3D meshprisms, pyramids, tetrahedrons, and dodecahedrons.

been usedwhich represents the discrete computational domain of the airflow in the centrifugal fan. The unstructured mesh allows the irregular connection between cells closer to domain wall vertices, and it also means an adaptation of the complex geometries, such as the volute walls, and blades of the impeller.faces, and nodes generated [21] in the mesh of the computational domain has been defined with the maximum value of skewness: 0.835 andaspect ratio value: 16.318. The mean value obtained for aspect ratio and skewness was 0.227 and 1.841, respectively; this guarantees that the convergence has been reached using MRFSimpleFOAM solver in iterative calculations of the model.


Valencia, J. Duarte


The mesh geometry is built based on lines and nodes that allow the build of 2D mesh shaped like triangles and quadrilaterals, and 3D meshprisms, pyramids, tetrahedrons, and dodecahedrons.

SMESH module [29] of Salome 8.3.0 software has been usedwhich represents the discrete computational domain of the airflow in the centrifugal fan. The unstructured mesh allows the irregular connection between cells closer to domain wall vertices, and it also means an adaptation of the complex geometries, such as the volute walls, and blades of the impeller.faces, and nodes generated [21] in the mesh of the computational domain has been defined with the maximum value of skewness: 0.835 andaspect ratio value: 16.318. The mean value obtained for aspect ratio and skewness was 0.227 and 1.841, respectively; this guarantees that the convergence has been reached using MRFSimpleFOAM solver in iterative calculations of the model.


J. Duarte

International Review on Modelling and Simulations, Vol. 12, N. 4





J. Duarte


algebraic variables iterative process by the solver in OpenFOAMsoftware. In this CFD study, the computational domain can be discretized into structured and unstructured cells.




J. Duarte Forero


algebraic variables iterative process by the solver in OpenFOAM

In this CFD study, the computational domain can be discretized into structured and unstructured cells.


SMESH module [29] of Salome 8.3.0 software has been used to generate the unstructured mesh (Fig. 4), which represents the discrete computational domain of the airflow in the centrifugal fan. The unstructured mesh allows the irregular connection between cells closer to domain wall vertices, and it also means an adaptation of the complex geometries, such as the volute walls, and blades of the impeller.faces, and nodes generated [21] in the mesh of the computational domain has been defined with the maximum value of skewness: 0.835 andaspect ratio value: 16.318. The mean value obtained for aspect ratio and skewness was 0.227 and 1.841, respectively; this guarantees that the convergence has been reached using MRFSimpleFOAM solver in iterative calculations of the model.

Forero


algebraic variables iterative process by the solver in OpenFOAM



SMESH module [29] of Salome 8.3.0 software has to generate the unstructured mesh (Fig. 4),

which represents the discrete computational domain of the airflow in the centrifugal fan. The unstructured mesh allows the irregular connection between cells closer to domain wall vertices, and it also means an adaptation of the complex geometries, such as the volute walls, and blades of the impeller.faces, and nodes generated [21] in the mesh of the computational domain has been defined with the maximum value of skewness: 0.835 andaspect ratio value: 16.318. The mean value obtained for aspect ratio and skewness was 0.227 and 1.841, respectively; this guarantees that the convergence has been reached using MRFSimpleFOAM solver in iterative calculations of the model.

Forero


algebraic variables [28]iterative process by the solver in OpenFOAM





F


[28]. This system is solved through an iterative process by the solver in OpenFOAM





Fig. 3


. This system is solved through an iterative process by the solver in OpenFOAM





3. CFD Algorithm




The mesh geometry is built based on lines and nodes that allow the build of 2D mesh shaped like triangles and quadrilaterals, and 3D mesh prisms, pyramids, tetrahedrons, and dodecahedrons.


which represents the discrete computational domain of the airflow in the centrifugal fan. The unstructured mesh allows the irregular connection between cells closer to domain wall vertices, and it also means an adaptation of the complex geometries, such as the volute walls, and blades of the impeller.faces, and nodes generated [21] in the mesh of the computational domain has been defined with the maximum value of skewness: 0.835 andaspect ratio value: 16.318. The mean value obtained for aspect ratio and skewness was 0.227 and 1.841, respectively; this guarantees that the convergence has been reached using MRFSimpleFOAM solver in iterative

CFD Algorithm




The mesh geometry is built based on lines and nodes that allow the build of 2D mesh shaped like triangles and

shaped like hexahedrons, prisms, pyramids, tetrahedrons, and dodecahedrons.


which represents the discrete computational domain of the airflow in the centrifugal fan. The unstructured mesh allows the irregular connection between cells closer to domain wall vertices, and it also means an adaptation of the complex geometries, such as the volute walls, and blades of the impeller.faces, and nodes generated [21] in the mesh of the computational domain has been defined with the maximum value of skewness: 0.835 andaspect ratio value: 16.318. The mean value obtained for aspect ratio and skewness was 0.227 and 1.841, respectively; this guarantees that the convergence has been reached using MRFSimpleFOAM solver in iterative

CFD Algorithm







which represents the discrete computational domain of the airflow in the centrifugal fan. The unstructured mesh allows the irregular connection between cells closer to domain wall vertices, and it also means an adaptation of the complex geometries, such as the volute walls, and blades of the impeller. The quality of cells, faces, and nodes generated [21] in the mesh of the computational domain has been defined with the maximum value of skewness: 0.835 andaspect ratio value: 16.318. The mean value obtained for aspect ratio and skewness was 0.227 and 1.841, respectively; this guarantees that the convergence has been reached using MRFSimpleFOAM solver in iterative

CFD Algorithm







which represents the discrete computational domain of the airflow in the centrifugal fan. The unstructured mesh allows the irregular connection between cells closer to domain wall vertices, and it also means an adaptation of the complex geometries, such as the volute

The quality of cells, faces, and nodes generated [21] in the mesh of the computational domain has been defined with the maximum value of skewness: 0.835 andaspect ratio value: 16.318. The mean value obtained for aspect ratio and skewness was 0.227 and 1.841, respectively; this guarantees that the convergence has been reached using MRFSimpleFOAM solver in iterative

CFD Algorithm








The quality of cells, faces, and nodes generated [21] in the mesh of the computational domain has been defined with the maximum value of skewness: 0.835 and the maximum aspect ratio value: 16.318. The mean value obtained for aspect ratio and skewness was 0.227 and 1.841, respectively; this guarantees that the convergence has been reached using MRFSimpleFOAM solver in iterative








The quality of cells, faces, and nodes generated [21] in the mesh of the computational domain has been defined with the

the maximum aspect ratio value: 16.318. The mean value obtained for aspect ratio and skewness was 0.227 and 1.841, respectively; this guarantees that the convergence has been reached using MRFSimpleFOAM solver in iterative







which represents the discrete computational domain of the airflow in the centrifugal fan. The unstructured mesh allows the irregular connection between cells closer to domain wall vertices, and it also means an optimal adaptation of the complex geometries, such as the volute




. This system is solved through an GNU





which represents the discrete computational domain of the airflow in the centrifugal fan. The unstructured mesh allows the irregular connection between cells closer to

optimal adaptation of the complex geometries, such as the volute







shaped like hexahedrons,








In this CFD study, the computational domain


shaped like hexahedrons,








234

IV.2. Boundary Conditions

Each CFD study applied to laminar or turbulent flows is defined by its features related to the initial and boundary conditions of the computational domain. Input and output conditions are set and established in the computational domain; these conditions maintain accordance with the measure of the pressure and velocity of the airflow in the experimental measurement point placed in the industrial centrifugal fan with backward inclined blades (Fig. 2). The angular velocity of the impeller is computed in the solver with a value of 3400 rpm. Pressure and velocity values are computed in OpenFOAM solver [19], such as presented in Table III.

TABLE III

INLET AND OUTLED CONDITIONS IN OpenFOAM Value Inlet Outlet

P FixedValue ZeroGradient U ZeroGradient mass flow

IV.3. Turbulence Models

Turbulence may be defined as the disorderly movement of particles in the flow. In this flow phenomenon, swirling flow, vortex breakdown, and flow fluctuations may be generated at space and time.

OpenFOAM GNU software offers computational tools applied to CFD studies that allow analyzing and evaluating the prediction of turbulent transport phenomena through an iterative solution of the system of partial differential equations. Turbulence models applied in CFD analysis using OpenFOAM software may be classified by the computational cost required in the numerical solution of the flow until the convergence in the solution is achieved, and the appropriate numerical model computed in the solver offering the higher approximation to the experimental model of the centrifugal fan is validated. Various CFD analysis methods can describe the flow behavior in different applications: DNS, DES, LES, and RANS approach. RANS turbulence models disintegrate the dependent variables of the system of partial differential equations in terms of averaged and fluctuating values to add the Reynolds stress tensor to the model. The numerical approach of this CFD study presents an alternative solution with a lower computational requirement [30]; for this reason, RANS approach is a very commonly used method in order to develop practical flow simulations in science and engineering. As previously mentioned, RANS approach is applied in this CFD study in order to analyze the performance of three turbulence models in the computational airflow analysis of the industrial centrifugal fan. The main goal of this CFD study is to implement OpenFOAM software as a computational tool in order to verify the approximation of the actual airflow behavior through CFD code and the application of k- , RNG k- , and realizable k- turbulence models in the airflow CAD of the industrial centrifugal fan. In each turbulence model used, the following should be taken

into account. Considering the incompressible airflow in the centrifugal fan with OpenFOAM software, the equations of k- , turbulence model that define turbulent kinetic energy (k) and dissipation rate ( ), are determined as:

+ · · ( + ) = (3)

+ · · ( + ) = (4)

where = , = 0.009. k- turbulence model

resolves separately two transport equations assuming fully developed turbulent flow. It is also regarded as a turbulence model that reaches a reasonable accuracy in the prediction of the flow behavior for a wide range of turbulent flows in engineering. Constants values of the k- turbulence model have been determined by the

numerical simulation of engineering applications for a wide range of turbulent flows. RNG k- and realizable k- [31] are variations of the k- turbulence model

developed in the CFD code of OpenFOAM software. Eq. (2) of the dissipation rate should be modified to apply the numerical analysis of the airflow in the centrifugal fan using RNG k- turbulence model. Therefore, the following equations should be taken into account:

=1

1 +( ) (5)

=( )

(6)

RNG k- turbulence model improves its accuracy in

the prediction of the flow due to the term added in the dissipation rate equation; therefore, this turbulence model is used to analyze flows in zones of the computational domain where the airflow produces high viscous stresses on the boundaries and eddies in the flow. This model has been developed using Re-Normalization Group (RNG) statistical techniques. RNG k- quantifies the effects of flows with a low Re for a wide range of engineering applications. Constant values are empirically derived from this model, unlike k- model, whose constant values are experimentally determined. Finally, the model introduces the dissipation rate term in realizable k- turbulence model as follows [31]:

=( + )

(7)

Compared to earlier turbulence models, there is a relevant modification developed in the realizable k- model: constant value is computed as a function of airflow velocity gradients in OpenFOAM software. In



235

consequence, realizable k- turbulence model presents a physical limitation in the airflow analysis of the computational domain.

V. Result and Discussion

Production and dissipation of turbulent kinetic energy of the airflow can be described over a statistical analysis of the velocity and pressure fluctuations using numerical simulations with OpenFOAM CFD code.

Results of simulations developed for each turbulence model have been compared with the data of the experimental model. ParaView application is used in the post-process of data generated in the numerical simulation of the airflow in the industrial centrifugal fan.

This application allows viewing the turbulence in the centrifugal fan in order to study the turbulent boundary layer in the blades of the impeller and to analyze the kinetic energy transfer in the airflow during the industrial centrifugal fan operation.

V.1. MRFSimpleFOAM Validation

In this section, the results of this CFD study are analyzed in order to validate the data generated in the numerical simulation of the airflow using the CFD code used in OpenFOAM software. The computational mesh has been generated with SMESH module of Salome 8.3.0 GNU software. Tetrahedral cells adapted efficiently to the complex zones of the computational domain, such as the spiral of the volute and the square to round pipe of the centrifugal fan. Due to the above, the stability has been reached in the convergence of the numerical solution considering a residual variation in the order of 10 for each turbulence model setup. A mesh independency study has been performed in order to obtain an efficient numerical solution of the flow; the numerical solution results are compared with the mesh density (quantity of nodes used in the mesh) through the SMESH module of Salome 8.3.0 GNU software (Table IV). The results of the mesh independency study have been used to define the mesh density in the computational domain: 1.003×106 nodes (Fig. 5). This study has allowed developing a numerical solution similar to the airflow behavior with a low computational effort through OpenFOAM CFD code. OpenFOAM CFD computational tool has been used to model the airflow behavior in the centrifugal fan. This has been possible using the use of numerical simulations in steady-state with MRFSimpleFOAM solver, and the validation of turbulence models computed. Unsteady state CFD analysis of turbomachinery may be solved with OpenFOAM PIMPLE solver [19]. The dynamic mesh

model is used in the unsteady state approach in order to simulate the rotation of the impeller and analyze its interaction with the volute in the computational domain. Steady-state simulation has been computed with the OpenFOAM CFD code in the present study. A simulation of the airflow behavior in the centrifugal fan with less computational effort has been developed; this result has been made possible by the implementation of the steady-state approach, which drops the dynamic mesh analysis in the numerical model developed. The CFD code has been able to demonstrate a good agreement between numerical data and the experimental model through numerical simulations developed in OpenFOAM GNU software. k- and realizable k- turbulence models simulate the airflow behavior similarly; however, k- turbulence model has achieved a closer approximation to the experimental model [20] with an error rate of 1 and 5 percent. Numerical results of k- , RNG k- , and realizable k- turbulence models can be shown in Tables V to VII and Figures 6 to 8.

V.2. Qualitative Assessment

OpenFOAM software provides data visualization tools in each one of the stages of the numerical simulation performed in a virtual environment (preprocessing, processing, and Postprocessing). Once the convergence is reached by MRFSimpleFOAM solver, it is possible to visualize and analyze the airflow behavior in the centrifugal fan to understand the energy transfer effects on the turbulence of the airflow and also to define possible further improvements in the performance of this turbomachine through the implementation of parametric studies with computational tools.

TABLE IV

MESH INDEPENDENCY STUDY Nodes ×106 Static pressure [kPa]

0.839 1.0230 0.881 1.0252 0.931 1.0248 1.003 1.0250 1.065 1.0250

Fig. 5. Mesh independency

TABLE V

k- TURBULENCE MODEL Data Flow rate, m3/s Exp. Vel, m/s CFD Vel, m/s % Error Exp. Pressure, kPa CFD Pressure, kPa % Error

1 0.14 3.50 3.66428 4.69 2.43 2.31032 4.93 2 0.35 8.75 8.62812 1.39 2.39 2.29913 3.80 3 0.70 17.5 17.1516 1.99 2.27 2.24174 1.24



236

TABLE VI RNG k- TURBULENCE MODEL

Data Flow rate, m3/s Exp. Vel, m/s CFD Vel, m/s % Error Exp. Pressure, kPa CFD Pressure, kPa % Error 1 0.14 3.50 3.80314 8.66 2.43 1.95732 19.45 2 0.35 8.75 9.09642 3.96 2.39 2.20726 7.65 3 0.70 17.5 17.4397 0.34 2.27 2.43029 7.06

TABLE VII

REALIZABLE k- TURBULENCE MODEL Data Flow rate, m3/s Exp. Vel, m/s CFD Vel, m/s %Error Exp. Pressure, kPa CFD Pressure, kPa % Error

1 0.14 3.50 3.90634 11.61 2.43 2.12236 12.66 2 0.35 8.75 8.59543 1.77 2.39 2.224 6.95 3 0.70 17.5 17.4494 0.29 2.27 2.15694 4.98

Fig. 6. Turbulence model RNG k-

Fig. 7. Turbulence model realizable k-

Fig. 8. Turbulence model k-

The recirculating airflow has been developed in the centrifugal fan due to the size ratio between the impeller and the spiral of the volute.

The recirculation phenomenon has been detected in the centrifugal fan with ParaView application through the visualization of the airflow patch; this is shown in Fig. 9.

RANS k- turbulence models can be applied in the analysis and the prediction of the airflow effects due to the initial configuration of the centrifugal fan. RNG k- and k- turbulence models are compared in Fig. 9 and Fig. 10. RNG k- model excels in the analysis and visualization of the kinetic energy transfer in the inlet pipe of the centrifugal fan. ParaView application of the OpenFOAM CFD code has been used to visualize the turbulent boundary layer in the trailing edge of the blades

where pressure fluctuations are generated throughout the fan operation; turbulence kinetic energy dissipation rate of the airflow has been described in this zone of the computational domain. The qualitative analysis of the turbulent boundary layer depends on the discretization of the dynamic zone and the turbulence model selected to simulate the airflow behavior in the industrial centrifugal fan. Velocity contour plots and the wake of the airflow simulated with RANS k – turbulence models are shown in Figs. 11-13. Experimental and simulated flow rate – pressure curves (Figs. 6-8) have been compared with the velocity contour plots (Figs. 11-13) for each turbulence model. k- model offered a uniform distribution of the velocity contour associated with increased pressure due to the viscous stresses generated throughout the airflow path in the volute of the centrifugal fan; this model has developed the best performance of the wake flow related to the turbulence kinetic energy dissipation rate of the airflow.

The above demonstrates that k- turbulence model develops the best description of the airflow behavior during the industrial centrifugal fan operation in a virtual environment.

Fig. 9. Backflow detection in centrifugal fan – k- model

Fig. 10. Backflow detection in centrifugal fan – RNG k- model

Experimental curve

RNG k- model

Experimental curve

Realizable k- model

k- model

Experimental curve

Backflow

Eddie generation

Eddie generation

Backflow



237

Fig. 11. Velocity of the airflow – RNG k- turbulence model

Fig. 12. Velocity of the airflow – realizable k- turbulence model

Fig. 13. Velocity of the airflow – k- turbulence model

VI. Conclusion

In this CFD study, OpenFOAM software has been used as a computational tool in order to analyze the performance of the RANS k– turbulence models: k– , RNG k– , and realizable k– in a numerical simulation of the airflow behavior produced by an industrial centrifugal fan with backward inclined blades. The turbulence models used in OpenFOAM CFD code have been compared with an experimental model. The experimental model has been defined with the pressure and flow rate measurement in the outlet pipe (Fig. 2) of the centrifugal fan. k– turbulence model has developed the best approach to the centrifugal fan performance under real working conditions, and it has also reached a relative error rate of 1 and 5 percent. Qualitative results of the numerical model computed with k– turbulence model have been associated with the description of the physical phenomenon developed in the OpenFOAM CFD code. k– turbulence model excels in the graphic representation of the kinetic energy transfer and dissipation rate of the airflow in the centrifugal fan. k–

turbulence model is recommended in the analysis of the turbulent flows with a high Reynolds number. RNG k–turbulence model is the most effective one in the analysis of the energy transfer and formation of eddies in the airflow with a low Reynolds number in the computational domain of the centrifugal fan. RNG k–turbulence model is recommended in the study of flows in practical engineering applications with a low Reynolds number. SMESH module of Salome 8.3.0 GNU software has been used in the mesh independency study of the computational domain in order to increase the numerical simulation efficiency of the airflow in the industrial centrifugal fan. Convergence has been reached with 1.003×106 nodes; the use of tetrahedral cells has facilitated the mesh adaptation to the complex geometry of the computational domain. The diffusion of the results has been controlled with the type of mesh generated in the numerical simulation. In advanced CFD simulations, this diffusion can be mitigated with the type of mesh computed, and a computational domain discretization in the direction of the flow model. MRFSimpleFOAM solver has been used to model the interaction between the

Wake flow

Turbulent flow patch

Wake flow



Wake flow Turbulent flow patch



238

static computational domain and the computational domain in motion using multiple frames of reference in the numerical simulation of the airflow. This solver has modeled the effects of the impeller rotation over the airflow during the centrifugal fan operation in a virtual environment. ParaView application has been used to view the effects of the energy transfer over the turbulent airflow in the industrial centrifugal fan: eddies production, pronounced turbulent boundary layer, and the recirculating airflow can subsequently affect the centrifugal fan efficiency under real working conditions.

It is suggested to use the methodology applied in this study for future CFD research on turbulent flows in practical engineering applications, parametric studies with computational tools, and design optimization methods for turbomachinery in a virtual environment.

Acknowledgements

The authors would like to acknowledge the Universidad del Atlántico and Sphere Energy company for their support in the development of this research.

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Department of Mechanical Engineering, Universidad del Atlántico, Barranquilla, Colombia

Univeran assistant professor of the Mechanical Engineering Program at Universidad del Atlántico.



Universidad Pontificia Bolivariana, Medellin, Colombia in 2014. He is an assistant professor of the Mechanical Engineering Program at Universidad del Atlántico.



sidad Pontificia Bolivariana, Medellin, Colombia in 2014. He is an assistant professor of the Mechanical Engineering Program at Universidad del Atlántico.





Authors’ informationDepartment of Mechanical Engineering, Universidad del Atlántico, Barranquilla, Colombia



Authors’ informationDepartment of Mechanical Engineering, Universidad del Atlántico, Barranquilla, Colombia.

José Sánchez De la HozColombiamethodsturbomachinfrom Universidad del Atlántico, located in Barranquilla, Colombia in 2019.

Guillermo ValenciaColombia,Universidad delMechanical Engineering from Universidad del Norte, located in Barranquilla, Colombia in 2005. Master in Mechanical Engineering from Universidad del Norte, Barranquilla, Colombia in 2008. Ph. D in Engineering from the



Authors’ informationDepartment of Mechanical Engineering, Universidad del Atlántico,

José Sánchez De la HozColombiamethodsturbomachinfrom Universidad del Atlántico, located in Barranquilla, Colombia in 2019.





José Sánchez De la HozColombiamethods turbomachinfrom Universidad del Atlántico, located in Barranquilla, Colombia in 2019.


sidad Pontificia Bolivariana, Medellin, Colombia in 2014. He is an assistant professor of the Mechanical Engineering Program at



José Sánchez De la HozColombia, is a researcher of

applied to the optimization of turbomachineryfrom Universidad del Atlántico, located in Barranquilla, Colombia in 2019.

Guillermo ValenciaColombia, is a fullUniversidad delMechanical Engineering from Universidad del Norte, located in Barranquilla, Colombia in 2005. Master in Mechanical Engineering from Universidad del Norte, Barranquilla, Colombia in 2008. Ph. D in Engineering from the




José Sánchez De la Hozis a researcher of applied to the optimization of

ery. He received his BSME degree from Universidad del Atlántico, located in Barranquilla, Colombia in 2019.

Guillermo Valencias a full

Universidad del Atlántico. Received a degree in Mechanical Engineering from Universidad del Norte, located in Barranquilla, Colombia in 2005. Master in Mechanical Engineering from Universidad del Norte, Barranquilla, Colombia in 2008. Ph. D in Engineering from the





. He received his BSME degree from Universidad del Atlántico, located in Barranquilla, Colombia in 2019.

Guillermo Valencias a full

Atlántico. Received a degree in Mechanical Engineering from Universidad del Norte, located in Barranquilla, Colombia in 2005. Master in Mechanical Engineering from Universidad del Norte, Barranquilla, Colombia in 2008. Ph. D in Engineering from the


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All rights reserved

Authors’ information

Department of Mechanical Engineering, Universidad del Atlántico,

José Sánchez De la Hoz, Barranquilla native, is a researcher of applied to the optimization of


, born in Barranquilla, time professor at the



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rights reserved


Barranquilla native, is a researcher of FEA and CFD applied to the optimization of





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Barranquilla native, FEA and CFD

applied to the optimization of . He received his BSME degree

from Universidad del Atlántico, located in




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Jorge Duarte ForeroColombia, Mechanical Engdel Atlántico. He received his BSME from Universidad del Atlántico, located in Barranquilla, Colombia in 2007. Master in Mechanical Engineering from Universidad del Norte, Barranquilla, Colombia in 2013. Ph. D in

from Universidad del Norte, Colombia in 2017. He is a Senior



from Universidad del Norte, Colombia in 2017. He is a Researcher.





Jorge Duarte Forerois an associated professor of the

Mechanical Engdel Atlántico. He received his BSME from Universidad del Atlántico, located in Barranquilla, Colombia in 2007. Master in Mechanical Engineering from Universidad del Norte, Barranquilla, Colombia in 2013. Ph. D in




Mechanical Engineering Program at Universidad del Atlántico. He received his BSME from Universidad del Atlántico, located in Barranquilla, Colombia in 2007. Master in Mechanical Engineering from Universidad del Norte, Barranquilla, Colombia in 2013. Ph. D in

from Universidad del Norte, Colombia in 2017. He is a



ineering Program at Universidad del Atlántico. He received his BSME from Universidad del Atlántico, located in Barranquilla, Colombia in 2007. Master in Mechanical Engineering from Universidad del Norte, Barranquilla, Colombia in 2013. Ph. D in



Jorge Duarte Forero, Barranquilla natiis an associated professor of the




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reynolds averaged navier–stokes simulations of the airflow

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