High-Order Large Eddy Simulation of Flow in Idealized and Patient-Specific TotalCavopulmonary ConnectionsKameswararao Anupindi1, Steven Frankel1, Jun Chen1, Dinesh Shetty1, Jeffrey Kennington1, Jonathan DeGan1, Mark D. Rodefeld2

1School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907., 2Department of Surgery, Indiana University School of Medicine, Indianapolis, IN 46202

Introduction

I Previous experimental (PIV) and numerical (CFD) studies of flow fields intotal cavopulmonary connections (TCPC) have revealed irregular or chaoticflow patterns at the TCPC junction where the inferior vena cavae (IVC) andthe superior vena cavae (SVC) streams collide (Zelicourt et al. [2])

I Such transitional or potentially turbulent flows are hard to predict usingstandard low-order numerical methods and turbulence model (e.g. RANSwith k − ε) widely utilized in commercial CFD packages.

I Recent Studies have shown that mechanical cavopulomonary support canrestore normal circulation to TCPC hemodynamics (virtual impeller pump(VIP) of Kennington et al. [3]).

I Low-order CFD predictions of VIP performance in idealized TCPC flowshave been in reasonably good agreement with measured H-Q data butdiscrepancies are still present.

I High-order LES predictions of TCPC flows with or without VIP support canbe useful to explain some of these discrepancies and to provide additionalinsight into these complex hemodynamic flows.

I Comparisons of LES results to PIV data will also allow validation andfurther elucidation.

Numerical Methods

Governing Equations Filtered incompressible Navier-Stokes

∂ui∂xi

= 0;∂ui∂t

+ uj∂ui∂xj

= −∂p∂xi

+1

Re

∂2ui∂xj∂xj

− ∂τij∂xj

WenoHydro[4] Solver DetailsConvective terms: 5th order WENO Scheme.Diffusion terms: 4th order Summation By Parts (SBP) Scheme.Temporal terms: 3rd order Runge Kutta scheme.Turbulence model: LES with Vreman SGS modelComplex geometry: Immersed Boundary Method (IBM) [1]

Immersed Boundary Method (IBM) and Validation

(a) IBM treatment, a direct forcing method

as described in Chaudhuri et al. [1] is used

(b) Length of separation bubble at different

Reynolds number

(c) Re = 60 (d) Re = 80 (e) Re = 100

Figure: Contours of Vorticity magnitude together with streamlines showing the length of theseparation bubble, in flow past a spherical object

Results - Ideal TCPC

Figure: Streamlines are shown plotted together with velocity and pressure contours onvarious cross sectional planes on LPA and RPA for a flow rate of 3.3 L/min through each ofSVC and IVC.

Figure: Contours of velocity magnitude on the mid plane passing through LPA and RPA

Results - Ideal TCPC with VIP

Figure: Contours of velocity magnitude on the vertical plane for the case of VIP rotating at3000 RPM. Also shown are the velocity magnitude and static pressure contours at variouscross sectional planes along LPA and RPA sections.

Figure: Contours of velocity magnitude on the mid plane passing through LPA and RPA forthe case of VIP rotating at 3000 RPM.

Figure: Instantaneous vortical structures in the vicinity of the VIP visualized by plotting theiso-surfaces of λ2 colored by velocity magnitude.

Ideal TCPC - Comparison to experiments

(a) PIV (b) CFD

Figure: Comparison of instantaneous velocity vectors between PIV and present CFD results.The PIV results are for a flow rate of 4.4 L/min and the CFD results are for a flow rate of3.3 L/min. The PIV results are courtesy of Ms. Anna-Elodie Kerlo from her experiments.

Hydraulic Data

H-Q data for a flow rate of 3.3 L/min. Pressure rise(+)/drop(-) foreach case is shown in mm of Hg.

Case Experimental High order LES RANS results [3]No VIP - -0.89 -2.0

VIP at 2000 RPM +2.2 +2.05 +4.4VIP at 3000 RPM +4.5 +2.76 -

Conclusions & Future Work

I Developed a high order LES IBM method that is suitable forturbo-machinery applications and applied it to fluid flow simulation inTCPC with and without a viscous impeller pump.

I The developed solver is able to capture highly unstable three dimensionalflow structures within the connection, because of its higher order accuracy.

I Future work will focus on idealized and patient-specific geometries withhigher RPM of the VIP.

Acknowledgments

Financial support received from NIH grants HL080089 and HL098353is acknowledged.

References

A. Chaudhuri, A. Hadjadj, and A. Chinnayya.On the use of immersed boundary methods for shock/obstacle interactions.Journal of Computational Physics, 230:1731–1748, 2011.

Diane A. de Zelicourt, Kerem Pekkan, Lisa Wills, Kirk Kanter, Joseph Forbess, Shiva Sharma, Mark Foegl, and Ajit P. Yoganathan.In virto flow analysis of a patient-specific intraatrial total cavopulmonary connection.The Annals of Thoracic Surgery, 79:2094–2102, 2005.

Jeffrey Kennington, Steven Frankel, Jun Chen, Mark D. Rodefeld, and Guruprasad A. Giridharan.Design of a novel cavopulmonary assist device for Fontan procedures: CFD, PIV and hydraulic testing.Proceedings of the ASME 2010 Summer Bioengineering Conference, Naples, Florida, USA, June 16-19 2010.

Dinesh Shetty, Travis Fisher, Aditya Chunekar, and Steven Frankel.High-order incompressible large-eddy simulation of fully inhomogeneous turbulent flows.J. Comput. Physics, 229(23):8802–8822, 2010.

ASME 2011 Summer Bioengineering Conference, June 22 - 25, Pennsylvania, USA SBC2011 - 53549