Arlificiirl Oryiins 20(6):JZY-533, Blackwell Science, Inc., Boston 0 1996 International Society for Artificial Organs

Application of Computational Fluid Dynamics Techniques to Blood Pumps

Ramakrishnan Sukumar, Mahesh M. Athavale, Vinod B. Makhijani, and Andrezj J. Przekwas

CFD Research Corporation, Huntsville, Alabama, U.S .A.

Abstract: Present-day computational fluid dynamics (CFD) techniques can be used to analyze the behavior of fluid flow in a variety of pumps. CFD can be a powerful tool during the design stage for rapid virtual prototyping of different designs, analyzing performance parameters, and making design improvements. Computational flow solutions provide information such as the location and size of stagnation zones and the local shear rate. These parameters can be correlated to the extent of hemolysis and thrombus formation and are critical to the success of a blood pump. CFD-ACE, an advanced commercial CFD code developed by CFD Research Corporation, has been applied to fluid flows in rotary machines, such as axial

Implantable cardiovascular assist devices are gaining acceptance among cardiac surgeons as a means of maintaining the cardiac output of a failing natural heart. This acceptance has led to the devel- opment of many blood pumps of widely varying de- signs, both pulsatile and nonpulsatile. Continuous flow pumps generally provide short-term cardiac support, ranging from a few days to 1 month, whereas pulsatile pumps are capable of providing support for much longer periods ( 1 ) . Currently available pulsatile flow support devices are too large and expensive to be used for the general pop- ulation (2). Continuous flow devices such as axial and centrifugal blood pumps are small and inexpen- sive. However, present pump designs can be used only for a limited duration because of problems such as hemolysis and thrombus formation (3).

The fluid dynamics of a blood pump play an im- portant role in the applicability of the device for

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Received January 1996. Address correspondence to Mr. R. Sukumar, CFD Research

Corporation, 3325 Triana Boulevard, Huntsville, AL 35805, U.S.A

flow pumps and inducers. Preprocessing and postpro- cessing tools for efficient grid generation and advanced graphical flow visualization are integrated seamlessly with CFD-ACE. The code has structured multiblock grid capability, non-Newtonian fluid treatment, a variety of turbulence models, and an Eulerian-Lagrangian particle tracking model. CFD-ACE has been used successfully to study the flow characteristics in an axial flow blood pump. An unstructured flow solver that greatly auto- mates the process of grid generation and speeds up the flow simulation is under development. Key Words: Computational fluid dynamics-Blood pump-Design- Virtual prototyping.

cardiac assist. Areas of flow separation, recircula- tion, and flow stagnation, which can lead to throm- bus formation, are undesirable. The pump should propel blood gently and not generate high fluid shear rates, thus minimizing damage to red blood cells (RBCs). One of the primary requirements of such a pump is that it should be able to generate approximately 5 L/min of blood flow against 100 mm Hg of pressure. Also, for the pump to be im- plantable, it should be compact (have a small dis- placement volume) and have high hydraulic and me- chanical efficiency so that a small power source can be used. These criteria have been discussed else- where (1) .

Experimental flow visualization techniques have been used in previous in vitro studies (1,4) to eval- uate pump flow dynamics. These techniques, how- ever, did not adequately resolve all of the flow field complexities, such as development of secondary flows between the rotor and stator (4). Also, they enabled only a two-dimensional (2D) evaluation of flow in the plane of the laser sheet (1,4). In addition, experimental techniques involve long lead times for

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setup, measurement, and processing of data, and they can be prohibitively costly.

The use of advanced numerical techniques for characterizing the performance of a blood pump is a cost-effective and viable alternative to experimental evaluation. A numerical model of the pump geom- etry can be created using computer-aided design (CAD) software. With the help of computational fluid dynamics (CFD), the entire flow field in the pump can be simulated and analyzed under physi- ologically relevant conditions. With the use of this methodology, the flow region is divided (dis- cretized) into small computational cells with the help of a grid (mesh). The equations of mass, mo- mentum, and energy conservation that govern fluid motion are expressed in an algebraic form. These take into account the physical conditions specified at the flow domain boundaries. The solution to these equations is obtained numerically in each cell (5) . Based on the results of the analysis, different design modifications, such as changes in the impel- ler blade configurations, can be implemented on the numerical prototype. The effect of these modifica- tions on the pump fluid dynamics can be studied further with the CFD model. Subsequently, such parametric analyses can be performed on multiple designs to evaluate the merits of each design. This concept is called virtual prototyping.

CFD Research Corporation has developed a vir- tual prototyping environment based on its CFD- ACE Package (CFD Research Corporation, Hunts- ville, Alabama, U.S.A.) that is suitable for analyzing fluid flows in rotary machines, such as axial flow pumps and inducers. This article de- scribes the application of the package for a prelim- inary study of the flow characteristics in an axial flow blood pump supplied by the University of Pittsburgh Medical Center. It also describes the computational flow analyses performed on other similar types of axial-flow pumps used in aerospace applications.

VIRTUAL PROTOTYPING ENVIRONMENT

CFD-ACE is a multiblock, structured grid, finite- volume CFD code that solves the three-dimensional (3D) Navier-Stokes equations governing fluid flow and heat transfer in a general curvilinear coordinate system (6,7). The default algorithm used in CFD- ACE is the SIMPLE-C algorithm, which is a fully implicit, pressure-based iterative technique (6). The multiblock grid capability (8) allows the user to break up a complicated flow geometry into multiple smaller domains (blocks) that would otherwise be

difficult to mesh in a single block. CFD-ACE also incorporates an Eulerian-Lagrangian particlei droplet tracking model (6) which allows for fully coupled modeling of dispersed “particulates,” such as RBCs or platelets along with the main fluid flow. This capability can be used to study the aggregation tendency of these particulates in any part of the flow domain and to estimate their residence times in areas of high fluid shear stress. These data can be used to predict hemolysis and thrombus formation in the pump (1 ) .

CFD-CEOM (CFD Research Corporation, Hunts- ville, Alabama, U.S.A.) is a front-end program for interactive 3D geometry modeling and grid genera- tion (9). The program offers interactive CAD-type nonuniform rational B-splines (N URBS)-based tools for generating complex geometries. Geometry information can also be imported/exported from/to almost any industrial CAD program. Toolkits for generating structured or unstructured grids or a hy- brid combination of both facilitate fast grid genera- tion on complex geometries. CFD-GEOM offers a tightly coupled link between the geometry and grid topology. Thus, with any change in the underlying geometry, the grid is updated automatically. This unique feature facilitates quick changes to design geometries for performing parametric studies, with- out the cumbersome task of regenerating the grids on the new geometry. Other advanced features in- clude a virtual parts library (VPL), whereby differ- ent components of a design system can be built in multiple “layers” and then assembled in a final layer, similar to a fabrication process. Alternative designs of components also can be stored in differ- ent layers to facilitate changing the design. All of these layers are stored in one VPL library, enabling quick parametric design changes and mix-and- match assembly capability.

Postprocessing of the results is performed using CFD-VIEW (CFD Research Corporation, Hunts- ville, Alabama, U.S.A.), a 3D interactive graphics, animation, and flow visualization program (10). The numerically computed results from CFD-ACE can be visualized in CFD-VIEW using velocity vectors, streamlines, particle traces, flow ribbons, surfaces, grids, contours, cutting planes, and iso-value sur- faces in an interactive, object-oriented, 3D graphics environment. Advanced features include a function calculator to calculate new variables as a user- defined function of the raw variables, point and line data probes, transient display of particulate motion, and animation.

CFD-CEOM, CFD-ACE, and CFD-VIEW are in- tegrated seamlessly into a single solution environ-

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CFD TECHNIQUES FOR ANALYZING BLOOD PUMPS 53 I

Blood Pump Design Concepts

Iterative Loops

CAD Systems

Optimize Design Process

\Pump - Final Prototype Product

FIG. 1. The concept of virtual prototyping using computa- tional fluid dynamics is shown.

ment, the “CFD-ACE package.” The package is totally self contained and interfaces smoothly into any existing computer-aided engineering (CAE) system. It is designed to be a virtual prototyping environment (Fig. 1) whereby a product can pro- ceed from concept to final design in the shortest possible time. Geometries designed using a CAD program or CFD-GEOM can be gridded and ana- lyzed in CFD-ACE with the results visualized us- ing CFD-VIEW. Based on the quality of results, the baseline geometry can be modified in CFD-GEOM for further simulations, or a new geometry can be created for analysis. Over many such iterations, the relative merits and demerits of each design can be evaluated to arrive at an optimum design for actual testing.

CFD ANALYSIS OF AN AXIAL FLOW BLOOD PUMP

Grid generation The geometry of the impeller for the axial flow

blood pump was provided in the form of an IGES file that was meshed in the CAD package, ICEM- CFD (Control Data Systems, Inc., U.S.A.). The im- peller was assumed to be flush with the cylindrical pump casing that enclosed it. A body fitted coordi- nate (BFC) multiblock grid with seven blocks was created in CFD-GEOM. Figure 2 shows the com- putational grid for the blood pump.

FIG. 3. Velocity vectors along the surface of the axial flow blood pump impeller are illustrated.

Problem setup The generated grid was read into CFD-ACE for

the model set-up. The flow was assumed to be in- compressible (density of 1.17 g/cm3) and Newtonian (dynamic) viscosity of 3.6 X lo-’ Ns/m2. A total (dynamic plus static) pressure boundary condition of 10 mm Hg was assumed at the inlet. Extrapola- tion conditions were used at the pump exit. Rotat- ing wall boundary conditions were specified at the hub and blade surfaces. The flow was assumed to be turbulent because the Taylor number was >7,000. The standard k-c turbulence model in the CFD-ACE code was used to model the effects of turbulence (6).

Results A converged steady-state solution was obtained

with a central processing unit (CPU) time of ap- proximately 10 minutes on an IBM RS 6000 work- station. The cumulative absolute residuals dropped more than 5 orders of magnitude. The residual is defined as the difference between the right- and left- hand sides of the Navier-Stokes equations being solved. The CFD code iterates from an initial guess to a final solution by trying to reduce these errors or residuals. The cumulative absolute residual is the sum of the absolute residual values in every com- putational cell.

The flow characteristics conform to the forcing of the fluid through the impeller passages by the blades as they rotate. As shown in Fig. 3, the ve- locity is highest in the inlet region corresponding to the low-pressure area. Because of a sharp pressure decrease in the flow negotiating the bend in the inlet

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FIG. 2. The geometry and computational grid of the axial flow blood pump impeller are shown.

FIG. 4. Particle flow traces along the surface of the axial flow blood pump impeller are shown.

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532 R . SUKUMAR ET AL.

FIG. 5. Pressure field and particle traces on an SSME impel- ler are displayed in the CFD-VIEW window. The line probe shows the variation in pressure along a line in the exit plane of the inducer.

area, there is a recirculation zone that can be seen clearly in the vector plot (Fig. 3) and particle traces (Fig. 4). As the flow is forced along the impeller, there is a pressure increase toward the exit (to al- most 200 mm Hg, compared with 10 mm Hg as- sumed at the inlet) with an accompanying decrease in the velocity profile.

CFD ANALYSES OF OTHER AXIAL FLOW PUMPS

CFD simulations have been carried out success- fully on complex turbomachinery problems similar to those of the blood pump analyzed above. Figure 5 shows the pressure field and particle traces in a space shuttle main engine (SSME) impeller dis- played in CFD-VIEW. Also shown in Fig. 5 is the line probe displaying the variation in pressure along a line at the exit plane of the impeller. Figure 6 shows the validation of the numerical data against experimentally available data for the same impeller. The two variables compared are the normalized me- ridional velocities and the exit flow angle in the cir- cumferential direction at a given radius in the exit cavity. The data are presented at several positions (B2 stations) from the hub (0%) to the shroud (100%). The numerical predictions showed good agreement with the experimental observations (1 I ) .

Similar analyses have been performed for a variety of turbomachinery applications (12) in the aero- space, automotive, gas turbine, and power genera- tion industries. CFD-ACE also incorporates an iso- enthalpic cavitation model, free of empiricism (13), to predict the onset of cavitation in turbomachinery

applications. Because cavitation is a complex phys- ical phenomenon, the present model is an initial ef- fort to characterize cavitation in such flows. Figure 7 shows the predicted cavitation bubble in an axial flow Pratt & Whitney alternative turbopump design inducer. This capability can be of great importance to the blood pump designer as a means of avoiding cavitation and the resulting pump and RBC damage.

FUTURE DIRECTIONS

The present simulations can be extended to ac- count for any leakage flow between the blade tip and the pump casing. Currently available non- Newtonian models in CFD-ACE, such as a Power- Law formulation, can be used to reproduce blood rheology more accurately based on the Walburn- Schneck model (14). Alternative non-Newtonian fluid flow models such as the generalized Old- royd-B model (IS) can be incorporated in the future.

CFD-ACE has the capability of incorporating user-defined subroutines to change existing models in the code or to input new boundary conditions.

FIG. 6. Numerical predictions (solid line) are compared with experimental data (symbols) for the SSME impeller along with normalized meridional velocities (left column) and flow angles (right column) at a given radius in the exit cavity.

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CFD TECHNIQUES FOR ANALYZING BLOOD PUMPS 533

Cavltation Bubble ’ FIG. 7. The predicted region of cavitation in the Pratt & Whit- ney alternative turbopump design inducer is shown.

Once relevant geometric and performance parame- ters are identified, a closed loop optimization pro- cess can be designed with the user subroutine sys- tem to automate parameter changes. Specialized postprocessing modules can be designed to trans- late the fluid flow results into parameters directly relevant to the blood pump designer. These include the extent of hemolysis indicated by the normalized index of hemolysis (NIH), percentage of lactate de- hydrogenate, and percentage of hemoglobin liber- ated, which can be calculated as functions of critical shear stress and erythrocyte residence times in these regions (1).

A next generation CFD code currently under de- velopment uses mixed element unstructured grids. This technique automates the process of grid gen- eration to a great extent. Automated, solution- adaptive meshes that automatically cluster in areas of high pressure or velocity gradients for a higher level of accuracy, convergence acceleration, and parallelization are some of the main features of this code. These innovations will further speed up the flow evaluation and design optimization process.

CONCLUSIONS

CFD can be a very efficient vehicle for the rapid virtual prototyping of blood pump designs. It pro- vides a physical insight into the complex flow of

physics of different designs and facilitates quick parametric analyses of geometric design changes and performance criteria. This process is a faster way of evaluating the performance of various can- didate designs and avoids the need to actually fab- ricate and test each design, which can be prohibi- tively expensive and time consuming. Ultimately, CFD analyses can replace the current “trial and error engineering” approach with a more stream- lined design process that stems from a detailed un- derstanding of the flow physics.

Acknowledgments: The authors wish to acknowledge the University of Pittsburgh Medical Center for providing the axial flow blood pump geometry, Dr. James Lee of CFD Research Corporation for his invaluable assistance in grid generation, and Dr. Ashok Singhal of CFD Re- search Corporation for his encouragement and guidance.

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