gram is to model the flow of blood through the pump using computational fluid dynamics. An earlier study reported by Allaire et al. (1) was based on a simpli-.
Artificial Organs 24(5):377–385, Blackwell Science, Inc. © 2000 International Society for Artificial Organs
Computational Flow Study of the Continuous Flow Ventricular 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 †Medquest Products, Inc., Salt Lake City, Utah, U.S.A.
Abstract: A computational fluid dynamics study of blood flow in the continuous flow ventricular assist device, Prototype No. 3 (CFVAD3), which consists of a 4 blade shrouded impeller fully supported in magnetic bearings, was performed. This study focused on the regions within the pump where return flow occurs to the pump inlet, and where potentially damaging shear stresses and flow stagnation might occur: the impeller blade passages and the narrow gap clearance regions between the impeller-rotor and pump housing. Two separate geometry models define the spacing between the pump housing and the impeller’s hub and shroud, and a third geometry model defines the pump’s impeller and curved blades. The flow fields in these regions were calculated for various operating condi-
tions of the pump. Pump performance curves were calculated, which compare well with experimentally obtained data. For all pump operating conditions, the flow rates within the gap regions were predicted to be toward the inlet of the pump, thus recirculating a portion of the impeller flow. Two smaller gap clearance regions were numerically examined to reduce the recirculation and to improve pump efficiency. The computational and geometry models will be used in future studies of a smaller pump to determine increased pump efficiency and the risk of hemolysis due to shear stress, and to insure the washing of blood through the clearance regions to prevent thrombosis. Key Words: Computational fluid dynamics— Centrifugal pump—Hemolysis.
The development of a continuous flow ventricular assist device (CFVAD) is of considerable interest to the medical community. Current external use of centrifugal pumps during heart operations is limited to duration of only several hours. The Utah–Virginia CFVAD3 is the third prototype centrifugal pump to be tested incorporating an impeller levitated by magnetic bearings. The use of magnetic radial and axial thrust bearings allows the impeller to be isolated from the pump housing. It is desired to develop a pump with a working life of 15–20 years. One of the tasks in this research and design program is to model the flow of blood through the pump using computational fluid dynamics. An earlier study reported by Allaire et al. (1) was based on a simplified geometry model consisting of 2 circular plates, 1 rotating 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 narrow clearance regions of the pump. Extensive references to the literature are given in Allaire et al. (1). In the present study, we used the actual curving geometry of the CFVAD3 pump, and the flow has been calculated in three separate regions of the pump. Two of these regions consist of the spacing between the pump housing and the impeller’s hub and shroud, and the third region defines the pump’s impeller and curved blades. Computational grids of these regions were developed, and solutions of the flow fields were obtained for various operating conditions of the pump. The software Build, TurboGrid, and TascFlow used in this study are available from AEA Technology, U.K. In the results section, figures depicting the numerical grids and the velocity fields are presented. The flow is analyzed to determine pump performance, the flow rates, and regions of potentially high shear and stagnation. The velocity fields in the clearance regions show significant recirculation that leads to poor pump efficiency. The numerically predicted performance curves for the pump were determined
Received February 1999; revised October 1999. Presented in part at the 6th Congress of the International Society for Rotary Blood Pumps, July 25–27, 1998, in Park City, Utah, U.S.A. Address correspondence and reprint requests to Dr. Houston G. Wood, Department of Mechanical & Aerospace Engineering, University of Virginia, Charlottesville, VA 22903, U.S.A.
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FIG. 1. The schematic AutoCad drawing is of the CFVAD3.
FIG. 2. Shown is the computational grid for the clearance of the front gap region. Artif Organs, Vol. 24, No. 5, 2000
FIG. 3. Shown is the computational grid for the clearance of the back gap region.
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FIG. 4. Shown is the computational radial and azimuthal grid for the front gap region.
and compare reasonably well with performance curves based on experimental data, which provides validation that the numerical calculations are reasonably accurate. Next, a numerical study was performed to examine the effect of smaller clearances on the recirulation. The work reported here is a building block to be utilized in the development of computational and geometry models of the complete pump. These models are invaluable to the design of the next generation pump, the CFVAD4, which will be significantly smaller and operate at a higher rotational speed.
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FIG. 5. Shown is the computational radial and azimuthal grid for the back gap region.
gions between the impeller and housing also contain blood, although the net flow direction in these regions is dependent on two counteracting forces present in the flow. Radial cross-sections of the computational grids for the front and back gap regions are shown in Figs. 2 and 3. The pressure gradient imposed by the rotating impeller creates a high pressure region at the outer radius of the impeller, lo-
MATERIALS AND METHODS The geometry under study is shown in Fig. 1, and the three computational regions are shown: the impeller blade passage region, the back clearance region, and the front clearance region. The complete impeller assembly rotates without contacting the pump housing at any point, creating the two gap regions between the impeller and housing. For CFVAD3, 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 enters the impeller axially and is forced radially outward through the blade passages to the pump exit volute by impeller rotation. The two clearance re-
FIG. 6. Shown is the computational grid for the impeller blade passage region. Artif Organs, Vol. 24, No. 5, 2000
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J.B. ANDERSON ET AL. TABLE 1. Impeller flow summary 2,000 rpm
2,200 rpm
2,400 rpm
Volume flow rate (L/min)
Pressure rise (mm Hg)
Volume flow rate (L/min)
Pressure rise (mm Hg)
Volume flow rate (L/min)
Pressure rise (mm Hg)
8.0 10.0 12.0 14.0 16.0
131.2 125.4 119.7 114.0 106.9
8.0 10.0 12.0 14.0 16.0
162.0 155.4 149.2 143.1 136.5
8.0 10.0 12.0 14.0 16.0
195.6 188.5 181.7 175.1 168.4
only. The maximum Reynolds number, based on the length obtained from the cube root of the volume of the region, calculated for all the simulations completed was approximately 10,000, and the turbulent viscosity was found to be two orders of magnitude less than the user input dynamic viscosity at many points in the domain. These numerical predictions of low turbulent viscosity were expected and served as further confirmation of the solution. A comparison of solutions for flow in the gap regions with and without the turbulence model showed a negligible difference in flow field characteristics. The flow solver TascFlow uses the finite volume method to discretize the governing differential equations. Mass and momentum are conserved throughout the computational domain, which consists of volume mesh elements defined by either the TurboGrid or Build grid generators. In the case of the front and back gap regions, Build was used to define a volume mesh of approximately 15,000 elements for each geometry model. The computational meshes for the front and back gap regions in the radial and azimuthal directions are shown in Figs. 4 and 5. The front gap region has a concentration of smaller elements near the inlet face to model more accurately the tightly curved geometry in that region. Each gap region is defined by 10 elements across the width in the y-coordinate direction from the impeller to pump housing. TurboGrid was used to create a mesh of approximately 40,000 cells for the impeller blade passage geometry model. A computational section is shown in Fig. 6 that contains 1 blade meshed with periodic boundary conditions to account for the re-
cated at the outlet faces of both the front and back gap regions. The result of the imposed pressure gradient is a tendency for fluid in the two gap regions to flow radially inward from the high pressure outlet to the pump inlet region. Also present in the gap region flow is the thin Ekman layer adjacent to the rotating impeller casing, which creates a fluid force opposing the radial pressure gradient due to friction on the impeller rotating surface. The approximate thickness of the Ekman layer is calculated using the Ekman number (2): E=
a2
where µ is the fluid viscosity, is the fluid density, is the rotational speed, and a is the impeller radius. The dimensional boundary layer thickness is defined as: ␦ = aE1 Ⲑ 2 As the rotational speed is increased, the Ekman number decreases and so does the Ekman boundary layer thickness. For example, at 2,000 rpm, this thickness is on the order of 0.01 cm. For accurate numerical results, it is important that several grid points be placed “inside” the Ekman layer. Blood in these simulations was modeled as Newtonian, with constant density and viscosity. The fluid density was set to 1,050 kg/m3, and the viscosity was set to 0.0035 kg/m·s. A – turbulence model is available in TascFlow, and it was employed in simulations flagged by the solver as turbulent. These instances of turbulence were found to occur in the gap regions
TABLE 2. Back clearance region flow summary (0.03 inch clearance) 2,000 rpm
2,200 rpm
2,400 rpm
Impeller flow (L/min)
Back region flow (L/min)
Percent impeller flow
Back region flow (L/min)
Percent impeller flow
Back region flow (L/min)
Percent impeller flow
8.0 10.0 12.0 14.0 16.0
−0.62 −0.58 −0.53 −0.49 −0.46
7.8 5.8 4.4 3.5 2.9
−0.67 −0.62 −0.58 −0.55 −0.53
8.4 6.2 4.8 3.9 3.3
−0.73 −0.67 −0.64 −0.61 −0.59
9.1 6.7 5.3 4.4 3.7
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TABLE 3. Front clearance region flow summary (0.03 inch clearance) 2,000 rpm
2,200 rpm
2,400 rpm
Impeller flow (L/min)
Front region flow (L/min)
Percent impeller flow
Front region flow (L/min)
Percent impeller flow
Front region flow (L/min)
Percent impeller flow
8.0 10.0 12.0 14.0 16.0
−3.24 −2.84 −2.73 −2.36 −2.28
40.5 28.4 22.8 16.9 14.3
−3.41 −2.99 −2.88 −2.80 −2.64
42.6 29.9 24.0 20.0 16.5
−3.63 −3.24 −3.07 −2.96 −2.87
45.4 32.4 25.6 21.1 17.9
maining impeller flow domain. The gap region geometries were modeled as complete for ease of flow visualization during postprocessing. The boundary conditions for the impeller blade passage geometry model consisted of a mass flow specified condition at the inner radius and a static pressure specified opening at the outer radius as well as the periodic boundaries mentioned earlier. A pressure value of 30,000 Pa was applied at the outer radius of the impeller with impeller mass flow rates ranging between 0.035 kg/s and 0.07 kg/s. These mass flow values represent the flow through 1 blade passage; thus, the total impeller flow is four times the mass flow specified in TascFlow for this model geometry. The vector specifying mass flow direction at the inlet was set parallel to the machine rotation axis. Boundary conditions at the gap regions’ inlet and outlet faces were set as openings with a static pressure value set across the face of each boundary. A no-slip boundary condition was set at all solid boundaries. The simulation process was initiated by specifying a flow rate through the impeller and an impeller rotational speed. The resulting pressure rise across the impeller was then applied to each of the two gap regions, yielding the flow rates through each region at the impeller speed in question. In this way, the total flow rate through the pump at an operating point could be calculated by summing the flows through the impeller and gap regions. RESULTS The output from TascFlow consisted of nodal pressure and velocity component values as well as
flow rates across inlet and outlet boundaries. Table 1 shows impeller volume flow rates and pressure rise values from inlet to outlet for three rotational speeds. For these operating conditions, the net flow rates in the gap clearance regions were directed radially inward, as indicated by the minus signs in Tables 2 and 3. These tables show the total flow rates and the flow rates as a percentage of flow through the impeller for the gap clearance regions. With a flow rate of 0.71 L/min in the back region and 3.66 L/min in the front gap region at the 8 L/min impeller flow 2,400 rpm setting, the total flow rate through the gap regions toward the inlet is seen to reach 54% of the impeller flow. This large blood recirculation to the inlet via the gap clearance regions is detrimental to the pump operating efficiency. Table 4 gives a summary of the total flow through the pump, combining the three flow regions. Net volume flow rates were obtained by summing the flow rates of each of the three geometry regions modeled. Figure 7 shows the data presented in Table 4 graphically. These results are to be compared with the experimental results presented in Table 5 reported by Baloh et al. (3). Two experimental data sets gathered at impeller speeds close to those simulated are presented. A plot of these curves appears in Fig. 8. Considering the fact that the computational model is still somewhat idealized by not including the pump volute and interactions between the three flow regions, these numerical and experimental results agree rather well. In addition to these data, velocity profiles in the three regions were evaluated. Figures 9, 10, and 11
TABLE 4. Pump flow summary (0.03 inch clearances) 2,000 rpm
2,200 rpm
2,400 rpm
Volume flow rate (L/min)
Pressure rise (mm Hg)
Volume flow rate (L/min)
Pressure rise (mm Hg)
Volume flow rate (L/min)
Pressure rise (mm Hg)
4.14 6.58 8.74 11.15 13.26
131.2 125.4 119.7 114.0 106.9
3.92 6.39 8.54 10.65 12.83
162.0 155.4 149.2 143.1 136.5
3.64 6.09 8.29 10.43 12.54
195.6 188.5 181.7 175.1 168.4
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FIG. 7. The graph shows numerically predicted pump performance curves.
show velocity vector plots for the three regions at an impeller speed of 2,000 rpm and an impeller flow rate of 8 L/min. It is seen that the majority of the velocity vectors in the gap regions are directed radially inward toward the inlet faces. Based on these calculations and the reasonable agreement with the available experimental data, similar calculations were performed for two smaller gap sizes of 0.02 and 0.01 inches in an effort to reduce the recirculation. In the 0.02 inch clearance thickness cases, all net flow rates through the two clearance regions were directed radially inward as in the 0.03 inch cases. For a given impeller flow condition, the clearance flows for 0.02 inch clearances are lower than the corresponding 0.03 inch cases due to the constriction in volume of the region. The largest amount of blood recirculation was again found in the 2,400 rpm, 8 L/min case because the largest pressure gradient across the impeller is developed for this case. With a combined net flow of 3.82 L/min of flow from the outlet to inlet region, the total back flow is 47.7% of the impeller flow. Because these results do
FIG. 8. Experimentally determined pump performance curves are shown.
not provide much improvement, the details are not presented here but may be found in a report by Anderson (4). However, the calculations for the 0.01 inch clearance thickness show good promise of significantly reducing the unwanted recirculation. These results are given in Tables 6 and 7. By examining the 8 L/min impeller flow at 2,400 rpm, we see that the
TABLE 5. Experimental pump flow summary (0.03 inch clearance regions) 2,040 rpm
2,160 rpm
Volume flow rate (L/min)
Pressure rise (mm Hg)
Volume flow rate (L/min)
Pressure rise (mm Hg)
0.0 1.3 2.0 2.9 3.6 4.4 5.9 6.8 7.5 7.9 8.3
124.0 121.5 116.2 113.9 109.6 110.7 92.8 87.5 78.3 68.9 64.7
0.00 1.62 2.50 3.55 4.45 5.10 6.00 6.65 7.10 8.10
137.7 136.6 128.5 129.1 126.5 114.9 112.9 105.0 96.7 87.7
Artif Organs, Vol. 24, No. 5, 2000
FIG. 9. Shown are the velocity vectors for the flow in the front gap region for 2,000 rpm and 8 L/min impeller flow.
COMPUTATIONAL FLOW STUDY
FIG. 10. Shown are the velocity vectors for the flow in the back gap region for 2,000 rpm and 8 L/min impeller flow.
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FIG. 11. Velocity vectors for the flow in the impeller blade passage region for 2,000 rpm and 8 L/min impeller flow are depicted.
total back flow in this case is less than 16% of the impeller flow as compared to 54% in the 0.03 inch clearance. The calculations that produced Table 4 were performed for the 0.02 and 0.01 inch clearance regions. Experimental data have not been obtained for these clearances, but the trend for improving pump performance by reducing gap clearance is shown graphically for the case of 2,000 rpm in Fig. 12. As would be expected, the performance improves as the gap size is reduced. An analysis of the residence time of the blood in the gap regions was performed, and Fig. 13 displays streak-lines of fluid particles in the back gap region for the 2,000 rpm, 8 L/min impeller flow case. This
analysis was performed using a feature of the AEA software that calculates the Lagrangian paths of the particles from the Eulerian solutions. Each of these streak-lines represents particles entering the fluid domain at the outer radius and exiting the region at the inlet face. All the streak-lines were tracked back from the 9 nodes spanning the gap width at the inlet face to their entrance at the outlet face. In this way, it was confirmed that there was fluid flowing out of the domain at every nodal location on the inlet face. As seen in the plot, a fluid particle has a very brief residence time within the region, making only one or two 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
Impeller flow (L/min)
Back region flow (L/min)
Percent impeller flow
Back region flow (L/min)
Percent impeller flow
Back region flow (L/min)
Percent impeller flow
8.0 10.0 12.0 14.0 16.0
−0.19 −0.18 −0.17 −0.16 −0.15
2.4 1.8 1.4 1.1 0.9
−0.23 −0.22 −0.21 −0.20 −0.18
2.9 2.2 1.8 1.4 1.1
−0.27 −0.25 −0.24 −0.23 −0.22
3.4 2.5 2.0 1.6 1.4
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J.B. ANDERSON ET AL. TABLE 7. Front clearance region flow summary (0.01 inch clearance) 2,000 rpm
2,200 rpm
2,400 rpm
Impeller flow (L/min)
Front region flow (L/min)
Percent impeller flow
Front region flow (L/min)
Percent impeller flow
Front region flow (L/min)
Percent impeller flow
8.0 10.0 12.0 14.0 16.0
−0.72 −0.67 −0.63 −0.59 −0.53
9.0 6.7 5.3 4.2 3.3
−0.85 −0.81 −0.76 −0.72 −0.67
10.6 8.1 6.3 5.1 4.2
−0.99 −0.94 −0.89 −0.85 −0.80
12.4 9.4 7.4 6.1 5.0
posure to shear in the region is therefore limited. The streak-line terminating at the node closest to the rotating impeller (Fig. 14) on the inlet face is seen to take many revolutions through the region before exiting. This is likely because this particle path is within the bounds of the Ekman layer. The particle is held within the region for many circuits before exiting because the rotational forces closely match the counteracting radial pressure forces along its path. This is the area of concentration for future analysis because of the longer exposure time to shearing forces and the possibility of thrombosis.
CONCLUSIONS In the current configuration, CFVAD3 operates at a relatively low efficiency, partly due to the blood recirculation through the gap regions. The pump’s peak efficiency in the range of impeller speeds simulated was determined experimentally to be approximately 12% (3). At the higher operating speeds, the larger pressure gradient imposed by the impeller cre-
FIG. 12. The graph shows the predicted pump performance curves at 2,000 rpm impeller speed with clearance gap as a parameter. Artif Organs, Vol. 24, No. 5, 2000
ates a strong tendency for blood to flow to the inlet through the gap clearance regions. Lessening the gap region thickness would tend to restrict this flow, although the velocity gradients within the regions would likely increase, resulting in larger shear forces. The gap region thickness currently selected for CFVAD3 represents a balance between pump efficiency and providing a suitable environment for red blood cells. With the addition of shear stress data to the computational model, the thickness of the gap clearance region will be further optimized keeping the shear stresses at an allowable level while reducing or eliminating the recirculation of blood to the inlet. The computational flow curves were found to match closely the corresponding experimental curves at low pump flow rates. At a total flow rate of about 6 L/min, the experimental curves’ pressure rise
FIG. 13. Shown are the streak-lines for flow outside the Ekman layer in the back gap region at 2,000 rpm and 8 L/min impeller flow.
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with flow paths in close proximity to the impeller may be subjected to extended residence times due to the Ekman layer. The absence of this flow behavior near the impeller wall at higher speed settings suggests the Ekman effect is diminished to a point where the nearest node point is not within the boundary layer. A refinement of the computational grid across the gap region widths is needed to resolve the boundary layer and study this behavior further. Future studies also will focus on the shear forces experienced by blood cells in the gap regions, and whether red blood cells experiencing extended residence times within the regions are damaged. Studies have been completed that provide general threshold values for maximum shear before the onset of hemolysis (5–7).
FIG. 14. Shown are the streak-lines for flow inside the Ekman layer in the back gap region at 2,000 rpm and 8 L/min impeller flow.
values fall away quickly with increased flow rate while the computational curves exhibit nearly linear behavior for all operation points simulated. This is likely due to the fact that each flow region is simulated independently with no flow interaction between them. At the lower impeller speed settings, it was found that fluid particles in the back gap region near the rotating impeller wall could be entrapped for many revolutions of the impeller before exiting the flow domain. For an impeller speed of 2,000 rpm, the predicted Ekman layer thickness is approximately 0.005 inches, which would extend to the node closest to the impeller wall in the gap regions. The node spacing in the axial direction in the gap regions is approximately 0.003 inches. These results suggest particles
Acknowledgments: Research for this project has been supported in part by the Development Fund of the Artificial Heart Research Laboratory at the University of Utah, to which contributions have been made by the Minneapolis Heart Institute of Minneapolis, MN, U.S.A. and the Medforte Research Foundation, Inc., of Salt Lake City, UT, U.S.A. Also, this project has been supported by Medquest Products, Inc., Salt Lake City, UT, U.S.A., and the University of Virginia, Charlottesville, VA, U.S.A. The project described was supported by Grant 1R43HL55807 from the National Heart, Lung, and Blood Institute.
REFERENCES 1. Allaire PE, Wood HG, Awad RS, Olsen DB. Blood flow in a continuous flow ventricular assist device. Artif Organs 1999;23:769–73. 2. Greenspan HP. The theory of rotating fluids. Cambridge, England: Cambridge University Press, 1968. 3. Hilton EF, Allaire PE, Wei N, Baloh MJ, Bearnson G, Olsen DB, Khanwilker P. Test controller design, implementation and performance for a magnetic suspension continuous flow ventricular assist device. Artif Organs 1999;23:785–91. 4. Anderson JB. Computational flow analyses of a ventricular assist device. Unpublished master’s thesis, University of Virginia, Charlottesville, 1999. 5. Bludszuweit C. Model for general mechancial blood damage prediction. Artif Organs 1995;19(7):583–9. 6. Leverett LB, Hellums JD, Alfrey CP, Lynch EC. Red blood cell 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. New York: McGraw-Hill, 1987:15.1.
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