=Paper= {{Paper |id=Vol-3382/Short2 |storemode=property |title=Numerical Modeling of the Coronary Artery using ANSYS Fluent |pdfUrl=https://ceur-ws.org/Vol-3382/Short2.pdf |volume=Vol-3382 |authors=Bakhyt Alipova,Yevgeniya Daineko,Zhiger Bolatov |dblpUrl=https://dblp.org/rec/conf/dtesi/AlipovaDB22 }} ==Numerical Modeling of the Coronary Artery using ANSYS Fluent== https://ceur-ws.org/Vol-3382/Short2.pdf 
Numerical Modeling of the Coronary Artery using ANSYS Fluent
Bakhyt Alipova1,2, Yevgeniya Daineko2, and Zhiger Bolatov2
1
    University of Kentucky, Lexington, Kentucky, 40506, USA
2
    International Information Technology University, Manas St. 34/1, Almaty, 050040, Kazakhstan


                 Abstract
                 Cardiovascular disease (CVD) (Doost et al., 2016) are abnormalities that distort the effective
                 flow of blood to and away from the heart. To be able to fully understand how these things
                 happen, CFD tool (ANSYS Fluent) is used to model how blood flows into and away from the
                 coronary artery. Blood, air and aluminum was used as main materials in the simulation. The
                 present study aimed to establish a relationship between actual hemodynamic conditions and
                 the parameters that define with ANSYS Fluent. And, to obtain numerical solution to research
                 the best physical model to determine viscosity and pulsatile velocity in a healthy human.

                 Keywords 1
                 Cardiovascular disease, coronary artery, blood flow, Navier Stokes equation, ANSYS Fluent

1. Introduction
    Cardiovascular disease (CVD) [1] are abnormalities that distort the effective flow of blood to and
away from the heart. To be able to fully understand how these things happen, CFD tool (ANSYS Fluent)
is used to model how blood flows [2] into and away from the coronary artery.
    Governing Equation
    Continuity
                                              ẟ𝜌
                                              αΊŸπ‘‘
                                                 +𝛻.( πœŒπ‘£) = 0
    Navier Stokes equation
                                           𝑑𝑣
                                         𝜌( +v.𝛻v) =-𝛻p+¡𝛻 2 v+f
                                                                    𝑑𝑑

      Blood viscosity is modeled using the Carreau fluids model [3]
                                                                                π‘›βˆ’1
                               ¡𝑒𝑓𝑓 (𝛾̇ ) = Μ‡ ¡𝑖𝑛𝑓 + (Β΅π‘œ βˆ’ ¡𝑖𝑛𝑓 )(1 + ( πœ†π›ΎΜ‡ )2 ) 2

      With
                                                 π‘˜π‘”                                    π‘˜π‘”
                          Β΅π‘œ = 0.056 (π‘šπ‘ ), ¡𝑖𝑛𝑓 = 0.0035 (π‘šπ‘ ) , πœ† = 3.313𝑠 π‘Žπ‘›π‘‘ 𝑛 = 0.3568

      The Carreau model [4] for the velocity profile is given as

                             0.5 sin[4𝛱(𝑑 + 0.0160236)]        : 0.5𝑛 < 𝑑 ≀ 0.5𝑛 + 0.218
              v𝑖𝑛𝑙𝑒𝑑 (𝑑) = {
                            0.10                        : 0.5𝑛 + 0.218 < 𝑛 ≀ 0.5(𝑛 + 1)

      The power model [5]

                         𝑉𝑖𝑛𝑙𝑒𝑑 = 2 βˆ— 0.988[1 + 0.624 βˆ— 𝑠𝑖𝑛(7.854. 𝑑)]π‘š/𝑠 for the power law.

Proceedings of the 7th International Conference on Digital Technologies in Education, Science and Industry (DTESI 2022), October 20–21,
2022, Almaty, Kazakhstan
EMAIL: alipova.bakhyt@gmail.com (Bakhyt Alipova); y.daineko@iitu.edu.kz (Yevgeniya Daineko); zh.bolatov@iitu.edu.kz (Zhiger
Bolatov)
ORCID: 0000-0003-0915-2759 (Bakhyt Alipova); 0000-0001-6581-2622 (Yevgeniya Daineko); 0000-0002-1945-8156 (Zhiger Bolatov)
              ©️ 2022 Copyright for this paper by its authors.
              Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
              CEUR Workshop Proceedings (CEUR-WS.org)
   Another velocity model proposed by [6] is used in simulation. This model considers the duration of
a cycle to be 0.8s.

                                      0.8 sin[2.857𝛱𝑑]           : 0 < 𝑑 ≀ 0.35
                   𝑉𝑖𝑛𝑙𝑒𝑑 (𝑑) = {
                                 0.6 sin(2.22𝛱(𝑑 βˆ’ 0.35))            : 0.35 ≀ 𝑑 ≀ 0.8




Figure 1: Coronary artery physical model with boundary conditions

2. Physical model
  The first step in building physical models (figure 1) is the first step in running a CFD simulation [7].
The Ansys Design modeler is used in drawing the coronary artery [8, 9].

2.1.    Meshing and Grid independence study
   In the mesh workspace in Ansys, various surfaces corresponding to boundary conditions are named
to create these boundaries for simulation. The generated geometry is then meshed to obtain simpler
elements. Default settings are used. Grid independence analysis is conducted by running simulations
with grid cells numbers obtained as a result of varying element sizes.

2.2.    Numerical Setup in ANSYS Fluent
   Under general, pressure-based solver is selected and problem is solved in transient state. Energy
equation is selected and laminar is chosen for viscous model. K-epsilon model is chosen, and standard
wall functions is selected for Near Wall Treatment.

Table 1
Setting Parameters
            Setting Parameters                         Type                   Setting/Options
                Solver type                                                    Pressure-based
              Viscous model                                                       Laminar
  Pressure-velocity coupling scheme [10]                                    Phase Coupled Simple
                                                    Gradient              Least squares cell based
           Spatial discretization                   Pressure                   Second order
                                                  Momentum                 Second Order upwind
                                                   Continuity                      1e-04
                 Residuals
                                                 U,v,w- velocity                   1e-04




Figure 2: Residue graph showing convergence of continuity equation and velocity in the x, y and z
direction


2.3.    Material Properties
    The materials used for this simulation are blood and air (fluids) and aluminum (solid). Blood is
treated as an incompressible fluid in simulation and material properties are considered as constants.
Density of blood is assumed to be 1050kg/m3, cp=3513j/kg-K, thermal conductivity(K)=0.44W/mK,
viscosity(Β΅)=0.0035kg/ms. When blood is treated as compressible, a user defined function (udf) is
written and inserted into ANSYS Fluent to account for differences in properties. Properties of air are
written in ANSYS Fluent. Aluminum is material selected for aorta with properties already written in
ANSYS Fluent.

2.4.    Boundary Conditions
   All boundaries are considered to be in the mixture phase.
   Inlet_blood-is considered as a velocity inlet, with magnitude, normal to boundary chosen as velocity
specification method and an initial value of 0.3m/s. The initial temperature is 37̊C (310K).
   Mathematical description [4] for the velocity profile is given as

                           0.5 sin[4𝛱(𝑑 + 0.0160236)]         ∢ 0.5𝑛 < π‘₯ ≀ 0.5𝑛 + 0.218
          v𝑖𝑛𝑙𝑒𝑑 (𝑑) = {
                           0.10                         ∢ 0.5𝑛 + 0.218 < 𝑛 ≀ 0.5(𝑛 + 1)

    Interior_solid is the internal boundary and the interior wall boundary condition is applied.
    Outlet_blood is the outlet boundary, and the pressure outlet boundary condition is applied with a
gauge pressure of 13332Pa. Under momentum, Pressure profile multiplier of 1 is applied with a normal
to boundary backflow direction specification method.
    Outlet_small is the outlet boundary and the pressure outlet boundary condition is also applied here.
    Wall_artery- wall boundary conditions are applied.
2.5.    Solver Settings
   Hybrid initialization. Explicit method is used for discretization.




Figure 3: Pressure, velocity and wall shear stress distribution

   According to literature [11], the mean velocity of blood inside the artery ranges from 0.11-0.13m/s.
From the results above (figure 3), case A was closer with a value of 0.1399163m/s.
   The lowest pressure recorded was 13444.24Pa also in case A. The average shear stress that acts on
the artery wall is between 2.48-4.27Pa [12] depending on sex and age and it is observed that case A and
C had values in this range.




Figure 4: Plot of static pressure against diameter of blood inlet

3. Conclusion
   In this numerical investigation, ANSYS Fluent was used to investigate the best model to determine
viscosity and pulsatile velocity in a healthy human. The coronary artery was the main organ for study.
The numerical results showed that varying the viscosity of blood had a direct impact on viscosity and
wall shear stress.
   Models provided in ANSYS Fluent used for the simulation provided ranges that were above normal
for average pressure and velocity with values between 13564.89Pa and 13618.12Pa for case Carreau
and power law respectively. The highest shear stress was recorded for the Carreau model with a value
of 6.03 which was way above normal values. Generally, ANSYS Fluent works better when values of
viscosity and velocity are kept constant.

4. Acknowledgements
   The project was accomplished with the financial support of the Science Committee of the Ministry
of Science and Higher Education of the Republic of Kazakhstan according to the Program of grant
funding of scientific and (or) scientific-technical projects in 2022-2024 (Grant No.AP14871641).

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