Computational Flow Study of the Continuous Flow Ventricular Assist Device, Prototype Number 3 Blood...

Computational Flow Study of the Continuous FlowVentricular Assist Device, Prototype Number 3

Blood Pump

*Jay B. Anderson, *Houston G. Wood, *Paul E. Allaire, †G. Bearnson, and†P. Khanwilkar

*Department of Mechanical & Aerospace Engineering, University of Virginia, Charlottesville, Virginia; and †MedquestProducts, Inc., Salt Lake City, Utah, U.S.A.

Abstract: A computational fluid dynamics study of bloodflow in the continuous flow ventricular assist device, Pro-totype No. 3 (CFVAD3), which consists of a 4 bladeshrouded impeller fully supported in magnetic bearings,was performed. This study focused on the regions withinthe pump where return flow occurs to the pump inlet, andwhere potentially damaging shear stresses and flow stag-nation might occur: the impeller blade passages and thenarrow gap clearance regions between the impeller-rotorand pump housing. Two separate geometry models definethe spacing between the pump housing and the impeller’shub and shroud, and a third geometry model defines thepump’s impeller and curved blades. The flow fields inthese regions were calculated for various operating condi-

tions of the pump. Pump performance curves were calcu-lated, which compare well with experimentally obtaineddata. For all pump operating conditions, the flow rateswithin the gap regions were predicted to be toward theinlet of the pump, thus recirculating a portion of the im-peller flow. Two smaller gap clearance regions were nu-merically examined to reduce the recirculation and to im-prove pump efficiency. The computational and geometrymodels will be used in future studies of a smaller pump todetermine increased pump efficiency and the risk of he-molysis due to shear stress, and to insure the washing ofblood through the clearance regions to prevent thrombo-sis. Key Words: Computational fluid dynamics—Centrifugal pump—Hemolysis.

The development of a continuous flow ventricularassist device (CFVAD) is of considerable interest tothe medical community. Current external use of cen-trifugal pumps during heart operations is limited toduration of only several hours. The Utah–VirginiaCFVAD3 is the third prototype centrifugal pump tobe tested incorporating an impeller levitated by mag-netic bearings. The use of magnetic radial and axialthrust bearings allows the impeller to be isolatedfrom the pump housing. It is desired to develop apump with a working life of 15–20 years.

One of the tasks in this research and design pro-gram is to model the flow of blood through the pumpusing computational fluid dynamics. An earlier studyreported by Allaire et al. (1) was based on a simpli-fied geometry model consisting of 2 circular plates, 1rotating and 1 stationary. With this simple geometry,preliminary analysis was performed to determine the

clearance flow rates, the clearance flow directions,and the level of shear to be expected in the narrowclearance regions of the pump. Extensive referencesto the literature are given in Allaire et al. (1).

In the present study, we used the actual curvinggeometry of the CFVAD3 pump, and the flow hasbeen calculated in three separate regions of thepump. Two of these regions consist of the spacingbetween the pump housing and the impeller’s huband shroud, and the third region defines the pump’simpeller and curved blades. Computational grids ofthese regions were developed, and solutions of theflow fields were obtained for various operating con-ditions of the pump. The software Build, TurboGrid,and TascFlow used in this study are available fromAEA Technology, U.K.

In the results section, figures depicting the numeri-cal grids and the velocity fields are presented. Theflow is analyzed to determine pump performance,the flow rates, and regions of potentially high shearand stagnation. The velocity fields in the clearanceregions show significant recirculation that leads topoor pump efficiency. The numerically predictedperformance curves for the pump were determined

Received February 1999; revised October 1999.Presented in part at the 6th Congress of the International So-

ciety for Rotary Blood Pumps, July 25–27, 1998, in Park City,Utah, U.S.A.

Address correspondence and reprint requests to Dr. HoustonG. Wood, Department of Mechanical & Aerospace Engineering,University of Virginia, Charlottesville, VA 22903, U.S.A.

Artificial Organs24(5):377–385, Blackwell Science, Inc.© 2000 International Society for Artificial Organs

377

FIG. 1. The schematic AutoCaddrawing is of the CFVAD3.

FIG. 2. Shown is the computational grid for the clearance of thefront gap region.

FIG. 3. Shown is the computational grid for the clearance of theback gap region.

J.B. ANDERSON ET AL.378

Artif Organs, Vol. 24, No. 5, 2000

and compare reasonably well with performancecurves based on experimental data, which providesvalidation that the numerical calculations are rea-sonably accurate. Next, a numerical study was per-formed to examine the effect of smaller clearanceson the recirulation.

The work reported here is a building block to beutilized in the development of computational andgeometry models of the complete pump. These mod-els are invaluable to the design of the next genera-tion pump, the CFVAD4, which will be significantlysmaller and operate at a higher rotational speed.

MATERIALS AND METHODS

The geometry under study is shown in Fig. 1, andthe three computational regions are shown: the im-peller blade passage region, the back clearance re-gion, and the front clearance region. The completeimpeller assembly rotates without contacting thepump housing at any point, creating the two gapregions between the impeller and housing. ForCFVAD3, the impeller radius is 3.05 cm (1.2 inches),and the front and back gap clearances are 0.0762 cm(0.03 inches).

The majority of the blood flow into the pump en-ters the impeller axially and is forced radially out-ward through the blade passages to the pump exitvolute by impeller rotation. The two clearance re-

gions between the impeller and housing also containblood, although the net flow direction in these re-gions is dependent on two counteracting forces pres-ent in the flow. Radial cross-sections of the compu-tational grids for the front and back gap regions areshown in Figs. 2 and 3. The pressure gradient im-posed by the rotating impeller creates a high pres-sure region at the outer radius of the impeller, lo-

FIG. 4. Shown is the computational radial and azimuthal grid forthe front gap region.

FIG. 5. Shown is the computational radial and azimuthal grid forthe back gap region.

FIG. 6. Shown is the computational grid for the impeller bladepassage region.

COMPUTATIONAL FLOW STUDY 379


cated at the outlet faces of both the front and backgap regions. The result of the imposed pressure gra-dient is a tendency for fluid in the two gap regions toflow radially inward from the high pressure outlet tothe pump inlet region. Also present in the gap regionflow is the thin Ekman layer adjacent to the rotatingimpeller casing, which creates a fluid force opposingthe radial pressure gradient due to friction on theimpeller rotating surface. The approximate thicknessof the Ekman layer is calculated using the Ekmannumber (2):

E =m

rva2

where µ is the fluid viscosity, r is the fluid density,v is the rotational speed, and a is the impeller ra-dius. The dimensional boundary layer thickness isdefined as:

d = aE1/2

As the rotational speed is increased, the Ekmannumber decreases and so does the Ekman boundarylayer thickness. For example, at 2,000 rpm, thisthickness is on the order of 0.01 cm. For accuratenumerical results, it is important that several gridpoints be placed “inside” the Ekman layer.

Blood in these simulations was modeled as New-tonian, with constant density and viscosity. The fluiddensity was set to 1,050 kg/m3, and the viscosity wasset to 0.0035 kg/m·s. A k–« turbulence model is avail-able in TascFlow, and it was employed in simulationsflagged by the solver as turbulent. These instances ofturbulence were found to occur in the gap regions

only. The maximum Reynolds number, based on thelength obtained from the cube root of the volume ofthe region, calculated for all the simulations com-pleted was approximately 10,000, and the turbulentviscosity was found to be two orders of magnitudeless than the user input dynamic viscosity at manypoints in the domain. These numerical predictions oflow turbulent viscosity were expected and served asfurther confirmation of the solution. A comparisonof solutions for flow in the gap regions with andwithout the turbulence model showed a negligibledifference in flow field characteristics.

The flow solver TascFlow uses the finite volumemethod to discretize the governing differential equa-tions. Mass and momentum are conserved through-out the computational domain, which consists of vol-ume mesh elements defined by either the TurboGridor Build grid generators. In the case of the front andback gap regions, Build was used to define a volumemesh of approximately 15,000 elements for each ge-ometry model. The computational meshes for thefront and back gap regions in the radial and azi-muthal directions are shown in Figs. 4 and 5. Thefront gap region has a concentration of smaller ele-ments near the inlet face to model more accuratelythe tightly curved geometry in that region. Each gapregion is defined by 10 elements across the width inthe y-coordinate direction from the impeller topump housing. TurboGrid was used to create a meshof approximately 40,000 cells for the impeller bladepassage geometry model. A computational section isshown in Fig. 6 that contains 1 blade meshed withperiodic boundary conditions to account for the re-

TABLE 1. Impeller flow summary

2,000 rpm 2,200 rpm 2,400 rpm

Volume flowrate (L/min)

Pressurerise (mm Hg)





8.0 131.2 8.0 162.0 8.0 195.610.0 125.4 10.0 155.4 10.0 188.512.0 119.7 12.0 149.2 12.0 181.714.0 114.0 14.0 143.1 14.0 175.116.0 106.9 16.0 136.5 16.0 168.4

TABLE 2. Back clearance region flow summary (0.03 inch clearance)

Impeller flow(L/min)

2,000 rpm 2,200 rpm 2,400 rpm

Back regionflow (L/min)

Percentimpeller flow





8.0 −0.62 7.8 −0.67 8.4 −0.73 9.110.0 −0.58 5.8 −0.62 6.2 −0.67 6.712.0 −0.53 4.4 −0.58 4.8 −0.64 5.314.0 −0.49 3.5 −0.55 3.9 −0.61 4.416.0 −0.46 2.9 −0.53 3.3 −0.59 3.7



maining impeller flow domain. The gap region ge-ometries were modeled as complete for ease of flowvisualization during postprocessing.

The boundary conditions for the impeller bladepassage geometry model consisted of a mass flowspecified condition at the inner radius and a staticpressure specified opening at the outer radius as wellas the periodic boundaries mentioned earlier. Apressure value of 30,000 Pa was applied at the outerradius of the impeller with impeller mass flow ratesranging between 0.035 kg/s and 0.07 kg/s. These massflow values represent the flow through 1 blade pas-sage; thus, the total impeller flow is four times themass flow specified in TascFlow for this model ge-ometry. The vector specifying mass flow direction atthe inlet was set parallel to the machine rotation axis.Boundary conditions at the gap regions’ inlet andoutlet faces were set as openings with a static pres-sure value set across the face of each boundary. Ano-slip boundary condition was set at all solidboundaries.

The simulation process was initiated by specifyinga flow rate through the impeller and an impellerrotational speed. The resulting pressure rise acrossthe impeller was then applied to each of the two gapregions, yielding the flow rates through each regionat the impeller speed in question. In this way, thetotal flow rate through the pump at an operatingpoint could be calculated by summing the flowsthrough the impeller and gap regions.

RESULTS

The output from TascFlow consisted of nodalpressure and velocity component values as well as

flow rates across inlet and outlet boundaries. Table 1shows impeller volume flow rates and pressure risevalues from inlet to outlet for three rotationalspeeds.

For these operating conditions, the net flow ratesin the gap clearance regions were directed radiallyinward, as indicated by the minus signs in Tables 2and 3. These tables show the total flow rates and theflow rates as a percentage of flow through the im-peller for the gap clearance regions. With a flow rateof 0.71 L/min in the back region and 3.66 L/minin the front gap region at the 8 L/min impeller flow2,400 rpm setting, the total flow rate through the gapregions toward the inlet is seen to reach 54% of theimpeller flow. This large blood recirculation to theinlet via the gap clearance regions is detrimental tothe pump operating efficiency.

Table 4 gives a summary of the total flow throughthe pump, combining the three flow regions. Net vol-ume flow rates were obtained by summing the flowrates of each of the three geometry regions modeled.Figure 7 shows the data presented in Table 4 graphi-cally. These results are to be compared with the ex-perimental results presented in Table 5 reported byBaloh et al. (3). Two experimental data sets gatheredat impeller speeds close to those simulated are pre-sented. A plot of these curves appears in Fig. 8. Con-sidering the fact that the computational model is stillsomewhat idealized by not including the pump vo-lute and interactions between the three flow regions,these numerical and experimental results agreerather well.

In addition to these data, velocity profiles in thethree regions were evaluated. Figures 9, 10, and 11

TABLE 3. Front clearance region flow summary (0.03 inch clearance)


2,000 rpm 2,200 rpm 2,400 rpm

Front regionflow (L/min)






8.0 −3.24 40.5 −3.41 42.6 −3.63 45.410.0 −2.84 28.4 −2.99 29.9 −3.24 32.412.0 −2.73 22.8 −2.88 24.0 −3.07 25.614.0 −2.36 16.9 −2.80 20.0 −2.96 21.116.0 −2.28 14.3 −2.64 16.5 −2.87 17.9

TABLE 4. Pump flow summary (0.03 inch clearances)

2,000 rpm 2,200 rpm 2,400 rpm







4.14 131.2 3.92 162.0 3.64 195.66.58 125.4 6.39 155.4 6.09 188.58.74 119.7 8.54 149.2 8.29 181.7

11.15 114.0 10.65 143.1 10.43 175.113.26 106.9 12.83 136.5 12.54 168.4



show velocity vector plots for the three regions at animpeller speed of 2,000 rpm and an impeller flowrate of 8 L/min. It is seen that the majority of thevelocity vectors in the gap regions are directed radi-ally inward toward the inlet faces.

Based on these calculations and the reasonableagreement with the available experimental data,similar calculations were performed for two smallergap sizes of 0.02 and 0.01 inches in an effort to re-duce the recirculation. In the 0.02 inch clearancethickness cases, all net flow rates through the twoclearance regions were directed radially inward as inthe 0.03 inch cases. For a given impeller flow condi-tion, the clearance flows for 0.02 inch clearances arelower than the corresponding 0.03 inch cases due tothe constriction in volume of the region. The largestamount of blood recirculation was again found in the2,400 rpm, 8 L/min case because the largest pressuregradient across the impeller is developed for thiscase. With a combined net flow of 3.82 L/min of flowfrom the outlet to inlet region, the total back flow is47.7% of the impeller flow. Because these results do

not provide much improvement, the details are notpresented here but may be found in a report byAnderson (4).

However, the calculations for the 0.01 inch clear-ance thickness show good promise of significantlyreducing the unwanted recirculation. These resultsare given in Tables 6 and 7. By examining the 8L/min impeller flow at 2,400 rpm, we see that the

TABLE 5. Experimental pump flow summary (0.03 inchclearance regions)

2,040 rpm 2,160 rpm





0.0 124.0 0.00 137.71.3 121.5 1.62 136.62.0 116.2 2.50 128.52.9 113.9 3.55 129.13.6 109.6 4.45 126.54.4 110.7 5.10 114.95.9 92.8 6.00 112.96.8 87.5 6.65 105.07.5 78.3 7.10 96.77.9 68.9 8.10 87.78.3 64.7

FIG. 7. The graph shows numerically predicted pump perfor-mance curves. FIG. 8. Experimentally determined pump performance curves

are shown.

FIG. 9. Shown are the velocity vectors for the flow in the frontgap region for 2,000 rpm and 8 L/min impeller flow.



total back flow in this case is less than 16% of theimpeller flow as compared to 54% in the 0.03 inchclearance. The calculations that produced Table 4were performed for the 0.02 and 0.01 inch clearanceregions. Experimental data have not been obtainedfor these clearances, but the trend for improvingpump performance by reducing gap clearance isshown graphically for the case of 2,000 rpm in Fig.12. As would be expected, the performance im-proves as the gap size is reduced.

An analysis of the residence time of the blood inthe gap regions was performed, and Fig. 13 displaysstreak-lines of fluid particles in the back gap regionfor the 2,000 rpm, 8 L/min impeller flow case. This

analysis was performed using a feature of the AEAsoftware that calculates the Lagrangian paths of theparticles from the Eulerian solutions. Each of thesestreak-lines represents particles entering the fluiddomain at the outer radius and exiting the region atthe inlet face. All the streak-lines were tracked backfrom the 9 nodes spanning the gap width at the inletface to their entrance at the outlet face. In this way,it was confirmed that there was fluid flowing out ofthe domain at every nodal location on the inlet face.As seen in the plot, a fluid particle has a very briefresidence time within the region, making only one ortwo revolutions before exiting. The fluid particle ex-

TABLE 6. Back clearance region flow summary (0.01 inch clearance)


2,000 rpm 2,200 rpm 2,400 rpm







8.0 −0.19 2.4 −0.23 2.9 −0.27 3.410.0 −0.18 1.8 −0.22 2.2 −0.25 2.512.0 −0.17 1.4 −0.21 1.8 −0.24 2.014.0 −0.16 1.1 −0.20 1.4 −0.23 1.616.0 −0.15 0.9 −0.18 1.1 −0.22 1.4

FIG. 10. Shown are the velocity vectors for the flow in the backgap region for 2,000 rpm and 8 L/min impeller flow. FIG. 11. Velocity vectors for the flow in the impeller blade pas-

sage region for 2,000 rpm and 8 L/min impeller flow are depicted.



posure to shear in the region is therefore limited.The streak-line terminating at the node closest to therotating impeller (Fig. 14) on the inlet face is seen totake many revolutions through the region before ex-iting. This is likely because this particle path is withinthe bounds of the Ekman layer. The particle is heldwithin the region for many circuits before exitingbecause the rotational forces closely match the coun-teracting radial pressure forces along its path. This isthe area of concentration for future analysis becauseof the longer exposure time to shearing forces andthe possibility of thrombosis.

CONCLUSIONS

In the current configuration, CFVAD3 operates ata relatively low efficiency, partly due to the bloodrecirculation through the gap regions. The pump’speak efficiency in the range of impeller speeds simu-lated was determined experimentally to be approxi-mately 12% (3). At the higher operating speeds, thelarger pressure gradient imposed by the impeller cre-

ates a strong tendency for blood to flow to the inletthrough the gap clearance regions. Lessening the gapregion thickness would tend to restrict this flow, al-though the velocity gradients within the regionswould likely increase, resulting in larger shear forces.The gap region thickness currently selected forCFVAD3 represents a balance between pump effi-ciency and providing a suitable environment for redblood cells. With the addition of shear stress data tothe computational model, the thickness of the gapclearance region will be further optimized keepingthe shear stresses at an allowable level while reduc-ing or eliminating the recirculation of blood to the inlet.

The computational flow curves were found tomatch closely the corresponding experimentalcurves at low pump flow rates. At a total flow rate ofabout 6 L/min, the experimental curves’ pressure rise

TABLE 7. Front clearance region flow summary (0.01 inch clearance)


2,000 rpm 2,200 rpm 2,400 rpm







8.0 −0.72 9.0 −0.85 10.6 −0.99 12.410.0 −0.67 6.7 −0.81 8.1 −0.94 9.412.0 −0.63 5.3 −0.76 6.3 −0.89 7.414.0 −0.59 4.2 −0.72 5.1 −0.85 6.116.0 −0.53 3.3 −0.67 4.2 −0.80 5.0

FIG. 12. The graph shows the predicted pump performancecurves at 2,000 rpm impeller speed with clearance gap as aparameter.

FIG. 13. Shown are the streak-lines for flow outside the Ekmanlayer in the back gap region at 2,000 rpm and 8 L/min impellerflow.



values fall away quickly with increased flow ratewhile the computational curves exhibit nearly linearbehavior for all operation points simulated. This islikely due to the fact that each flow region is simu-lated independently with no flow interaction be-tween them.

At the lower impeller speed settings, it was foundthat fluid particles in the back gap region near therotating impeller wall could be entrapped for manyrevolutions of the impeller before exiting the flowdomain. For an impeller speed of 2,000 rpm, the pre-dicted Ekman layer thickness is approximately 0.005inches, which would extend to the node closest to theimpeller wall in the gap regions. The node spacing inthe axial direction in the gap regions is approxi-mately 0.003 inches. These results suggest particles

with flow paths in close proximity to the impellermay be subjected to extended residence times due tothe Ekman layer. The absence of this flow behaviornear the impeller wall at higher speed settings sug-gests the Ekman effect is diminished to a pointwhere the nearest node point is not within theboundary layer. A refinement of the computationalgrid across the gap region widths is needed to resolvethe boundary layer and study this behavior further.Future studies also will focus on the shear forcesexperienced by blood cells in the gap regions, andwhether red blood cells experiencing extended resi-dence times within the regions are damaged. Studieshave been completed that provide general thresholdvalues for maximum shear before the onset of he-molysis (5–7).

Acknowledgments: Research for this project has beensupported in part by the Development Fund of the Arti-ficial Heart Research Laboratory at the University ofUtah, to which contributions have been made by the Min-neapolis Heart Institute of Minneapolis, MN, U.S.A. andthe Medforte Research Foundation, Inc., of Salt LakeCity, UT, U.S.A. Also, this project has been supported byMedquest Products, Inc., Salt Lake City, UT, U.S.A., andthe University of Virginia, Charlottesville, VA, U.S.A.The project described was supported by Grant1R43HL55807 from the National Heart, Lung, and BloodInstitute.

REFERENCES1. Allaire PE, Wood HG, Awad RS, Olsen DB. Blood flow in a

continuous flow ventricular assist device. Artif Organs1999;23:769–73.

2. Greenspan HP. The theory of rotating fluids. Cambridge, En-gland: Cambridge University Press, 1968.

3. Hilton EF, Allaire PE, Wei N, Baloh MJ, Bearnson G, OlsenDB, Khanwilker P. Test controller design, implementationand performance for a magnetic suspension continuous flowventricular assist device. Artif Organs 1999;23:785–91.

4. Anderson JB. Computational flow analyses of a ventricularassist device. Unpublished master’s thesis, University of Vir-ginia, Charlottesville, 1999.

5. Bludszuweit C. Model for general mechancial blood damageprediction. Artif Organs 1995;19(7):583–9.

6. Leverett LB, Hellums JD, Alfrey CP, Lynch EC. Red bloodcell damage by shear stress. Biophysical J 1972;12:257–73.

7. Blackshear PL, Blackshear GL. Mechanical hemolysis. In:Skalak R, Chien S, eds. Handbook of bioengineering. NewYork: McGraw-Hill, 1987:15.1.

FIG. 14. Shown are the streak-lines for flow inside the Ekmanlayer in the back gap region at 2,000 rpm and 8 L/min impellerflow.



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