Numerical Investigation of the Effect of Blade Geometryon Blood Trauma in a Centrifugal Blood Pump

W.K. Chan, Y.W. Wong, Y. Ding, L.P. Chua, and S.C.M. Yu

School of Mechanical & Production Engineering, Nanyang Technological University, Singapore, Republic of Singapore

Abstract: Fluid dynamic forces in centrifugal blood pumpimpellers are of key importance in destruction of red bloodcells (RBCs) because high rotational speed leads to stronginteraction between the impeller and the RBCs. In thispaper, three-dimensional models of five different bladegeometries are investigated numerically using the com-mercial software CFX-TASCflow, and the streaklines ofRBCs are obtained using the Lagrangian particle trackingmethod. In reality, RBCs pass through the pump alongcomplicated paths resulting in a highly irregular loadingcondition for each RBC. In order to enable the predictionof blood damage under the action of these complex-

loading conditions, a cumulative damage model for RBCswas adopted in this paper. The numerically simulated per-cent hemoglobin (%HB) released as RBCs traversed theimpeller and volute was examined. It was observed thatthe residence time of particles in the blade passage is acritical factor in determining hemolytic effects. This, inturn, is a function of the blade geometry. In addition, it wasobserved that the volute profile is an important influenceon the computed HB% released. Key Words: Bloodtrauma—Centrifugal blood pump—Numerical simula-tion—Computational fluid dynamics.

INTRODUCTION

The prediction of hemolysis in cardiac assist de-vices is of great importance for successful and long-term implantation. Blackshear (1) studied the effectsof mechanical hemolysis. Subsequent studies byBacher and Williams (2), Leverett and colleagues(3), and Sallam and Hwang (4) have demonstratedthe need to link hemolysis, shear stresses on RBCs,and the prevalent flow conditions. Based on the ex-perimental data of Wurzinger and colleagues (5,6),Giersiepen and colleagues (7) proposed a set of cor-relations for the percentage of released cytoplasmenzyme (LDH) and hemoglobin (HB). As it is bothtime-consuming and expensive to conduct actual ex-perimental studies, attempts have been made re-cently to predict hemolysis numerically. Bloodtrauma may be described approximately as a func-tion of the exposure time of the blood cell and theshear stress exerted on it. Papantonis and Croba (8)solved the flow within a radial blood pump, and their

results agreed qualitatively with experimental data.Pinotti and Rosa (9) solved the full Navier-Stokesequation for flow in a vaneless centrifugal pump.The flow is assumed to be axisymmetric. Their re-sults indicated that regions of high shear stress con-tribute to a higher %HB released. However, in re-ality, in centrifugal blood pumps, the presence of thevolute renders the flow non-axisymmetric. The mo-tivation of the current study is to numerically inves-tigate the hemolytic effects of blade geometry andpump volute on blood trauma. Blade profiles aregenerated using an inviscid inverse design techniquethat maintains both the blade inlet and outlet anglesconstant. This provides an indication of the effect ofthe blade camberline on blood trauma. Inverse de-sign method (10) is directed toward finding a suit-able blade geometry for a given flow field. Usually,the mean swirl distribution is chosen as an initialinput for the design. One of the advantages is that itenables the design of blade rows with constant workalong the span. This leads to higher efficiency be-cause no spanwise vortices are generated. Three-dimensional computational fluid dynamics (CFD)investigation on a complete pump model will be con-ducted, and particle streaklines will be tracked. Tonumerically predict blood trauma of RBCs, both

Received October 2001; revised February 2002.Address correspondence and reprint requests to Dr. W.K.

Chan, c/o School of Mechanical & Production Engineering,Nanyang Technological University, Nanyang Avenue, Singapore639798, Republic of Singapore.

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shear stress and residence time as fluid particles tra-verse the pump will be computed. Based on this in-formation, an indication of the cumulative damageon each RBC can be predicted.

MATERIALS AND METHODS

Although blood is a non-Newtonian suspension ofcells in plasma, for centrifugal blood pumps it is rea-sonable to model it as a Newtonian fluid (11). Theimpeller of the pump is of the closed type; that is, thehub and shroud are covered. The distance betweenthe impeller cover and the pump casing is about 0.3mm. It has an inner diameter of 13 mm and an outerdiameter of 25 mm. A total of five impellers withdifferent blade geometries were studied. The firstimpeller has a radial straight blade with inlet andoutlet blade angles of 90 degrees. The impellers ofDesigns 1, 2, and 3 are backward facing impellerswith inlet and outlet blade angles of 6.74 degrees and30 degrees, respectively. In Design 4, the outletblade angle is set at 90 degrees and the inlet bladeangle is 6.74 degrees. The profiles of the five impel-

lers are shown in Fig. 1. Further details of the bladeprofile design can be obtained from Li (12). To avoidextreme skewness of each element, the passage be-tween two blades is divided into three parts, and themesh is generated separately. The three-dimensional(3-D) view of the whole pump is shown in Fig. 2. Fora given impeller, the number of nodes for each partare as follows: inlet cone, 40,000; impeller, 81,600;and volute, 16,750. The grid modeling of the com-plete x-y plane of the blood pump is shown in Fig. 3.Grid dependency and validation of the numericalsimulation were carried out, and good agreementwas obtained when the predicted pump performanceis compared with available experimental data. In thecurrent study, the physical properties of blood areassumed to have a viscosity of 3.5 × 10−3 Pa·s and adensity of 1,055 kg/m3. The pump is operating at arotational speed of 2,000 rpm and delivers a flow rateof 5 L/min. The k-� model is assumed in the currentstudy following the suggestions of other investigators(13–17). A commercial software, CFX-TASCflow(18), was employed to model the flow in the entirepump. It incorporates an element-based finite-volume method with a rotating frame of reference.This feature makes the code suitable for predictingthe flow pattern within centrifugal blood pumps. Topredict the steady-state flow of an impeller plus vo-lute, a stage interface is adopted at the interface be-tween the inlet tube and the impeller inlet. At a stageinterface, circumferential averaging occurs as theflow crosses the interface, and it is assumed thatthere is complete mixing of the upstream flow. Atthe interface between the impeller and the volute, afrozen rotor interface is adopted. At a frozen rotor

FIG. 1. Blade profiles for the impeller designs are shown. FIG. 2. Three-dimensional view of the whole pump is shown.

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interface, information such as velocities is passedfrom the impeller side to the volute as the flowcrosses the interface without imposing any circum-ferential averaging. The relative position of the twocomponents remains fixed for the entire simulation.

To investigate the trajectories of red blood cells incentrifugal pumps and to numerically predict thedamage to which they are subjected, 100 particleswere released at the inlet tube for each case. Thedensity of RBCs is 1,055 kg/ m3, and the shape of theRBC is assumed to be spherical and 4 �m in diam-eter. At the inlet, the turbulent kinetic energy k andits dissipation � are set according to the followingequations:

k =32

�Tu × v�2

� =k1.5

L

where Tu is the turbulence intensity, which is as-sumed to be 2%, and L is the eddy length scale,which is assumed to be 10% of the diameter of theinlet tube.

The instantaneous blood trauma is computed ac-cordingly to the equation proposed by Giersiepenand colleagues (7), and the total damage is assumedto be accumulated linearly as proposed by Bludszu-weit (19). The computed blood trauma for each par-ticle is as follows:

Computed %HB − Liberation

= �i=inlet

i=outlet

3.62 × 10−5 × t0.79 × �2.4

where i refers to the location of a particular particle,t is the time of residence of particle at location i inseconds (s), and � is the shear stress of the particle at

location i (in Pa). The summation sign is the sumtotal of the computed %HB released for a particularparticle that is traced from the inlet to the outlet ofthe pump. About 100 particles are released at thepump inlet, and their trajectories are tracked. Foreach particle, its trajectory is divided into nearly2,000 points. At each point on the trajectory, infor-mation such as spatial coordinates, three compo-nents of velocity, and residence time of particle arerecorded. Based on this information, the shear stressand %HB released at each location can be deter-mined. The total %HB for a particle traversing thepump can hence be summed because the damage isassumed to be a linear cumulative function. Typi-cally for each particle, it will take about a fraction ofa second to traverse the pump, and the average timeof residence at each location is observed to be afraction of a millisecond. Only 100 particles werereleased because the computer resources as well asthe time involved in tracking the particles and thepostprocessing of information such as spatial coor-dinates, velocities, and residence time required arequite substantial. The current approach is an attemptto illustrate the possibility of using CFD to numeri-cally simulate and predict the blood trauma induced.

RESULTS AND DISCUSSION

The successful use of centrifugal pumps as long-term cardiac assist devices strongly depends on howblood trauma can be minimized. Centrifugal bloodpumps must not only achieve a physiologically ad-equate pump output, but also the damage to RBCsin the pump must be of an acceptable level.

Flow patternThe flow patterns in the impellers are shown in

Figs. 4A–E, respectively. The radial straight blade isthe simplest and cheapest to manufacture. However,the flow pattern in the blade passage is far fromsatisfactory. From Fig. 4A, there are two distinct vor-tices in the blade passage; one at the leading edge ofthe suction side while the second is in the middle ofthe impeller passage. The bulk flow is confinedmainly to the pressure side. In centrifugal bloodpumps, the flow rate is relatively low (5 L/min) whilethe rotation speed is high (2,000 rpm), hence theradial velocity is much smaller than the tangentialvelocity. For the radial blade impeller, the relativevelocity vector at the inlet will always differ from theblade inlet angle due to the obvious difference in theinlet flow and inlet blade angle. As a result, flowseparates at the leading edge of the suction side aspredicted. Hence, radial straight blade design ishighly susceptible to thrombus formation, and high

FIG. 3. Meshing is shown of the pump (x-y plane).

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shear stress is expected at the pressure side due to ahigher velocity gradient between the high-velocityoutflow and the low-velocity recirculatory flow. Theflow pattern would have damaging effects on thehemocompatibility of the pump.

As shown in Figs. 4B and 4C, the flow patterns ofDesigns 1 and 2 are quite similar. A vortex existsnear the trailing edge of the suction surface becauseof the existence of adverse pressure gradient. Design1 has a larger overlap angle than Design 2, so thepassage of Design 1 is narrower and longer. This

results in a lower adverse pressure gradient, and flowseparates further downstream in Design 1 than inDesign 2.

As compared with Designs 1 and 2, Design 3 hasan S-shaped blade profile. The blade is shorter butwith the same inlet and outlet angles, so that theoverlap angle of Design 3 is much smaller than thatof Designs 1 and 2. The blade is also twisted and itspassage is relatively wider. The relative circulation ofliquid particles due to inertia effect affects the rela-tive velocity distribution through an impeller chan-

FIG. 4. Shown are velocity vectors in the radial blade (A); ve-locity vectors in Design 1 (B); velocity vectors in Design 2 (C);velocity vectors in Design 3 (D); and velocity vectors in Design4 (E).

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nel. Fluid particles, while following the impeller in itstranslatory movement around the axis, fail to followthe impeller blade profile. In practice, because thenumber of blades cannot be infinite, the relative cir-culation is larger with a smaller number of blades.The relative circulation is smaller in a narrower im-peller passage such as Design 1 than in a wide onesuch as Design 3. Thus, flow separation and vorticesare very distinct as shown in Fig. 4D where it isobserved that there are two large vortices near thesuction surface of Design 3. Again, the bulk flow ismainly confined to the pressure side.

Design 4 has the same problem with Design 3where a large vortex appears at the trailing edgenear to the suction surface as shown in Fig. 4E. Cer-tainly such a flow pattern with large-scale vorticesand flow separation is unfavorable to red blood cells.Vortices will prolong the residence time of bloodcells inside the passage, and flow separation is usu-ally accompanied by high shear stress that may causehemolysis.

As the flow pattern in Design 2 is qualitatively themost favorable, the shear stress contours in Design 2are shown in Fig. 5 to provide a general idea of thedistribution and magnitude of the shear stress con-tours. In general, regions of high shear stress (ofmagnitudes about 150 Pa) are found at the interfaceof the impeller and volute housing. In addition, atthe volute wall casings and at the impeller inlet, ashear stress of about 100 Pa is observed. The block-age effect at the impeller inlet may have contributedto the increase in shear stress.

Pressure generated across the pumpThe basic function of blood pumps is to increase

the pressure from the inlet to the outlet. The pres-sure distribution is less sensitive than the velocityfield to a change of geometry. However, for differentblade inlet angles, there are differences between thepressure distribution within the blade passage. Table1 tabulates the computed head generated across thepump. In general, the difference in the head gener-ated by the various pumps is due to the interactionbetween the impeller and the volute. In the currentstudy, the volute geometry is kept constant while theimpeller blade profile is changed for the various im-pellers. In Table 1, the head rise across the impellerand across the whole pump is tabulated. The differ-ence between these two numbers indicates the pres-sure recovery in the volute. From the table, it isnoted that the pressure recovery is different for dif-ferent designs because the flow exiting the impelleris a function of the blade profile.

As expected, Design 4 produces the greatest pres-sure head across the whole pump because the outletangle is 90 degrees and it has an appropriate inletangle. For the radial straight blade, flow separatesimmediately at the inlet resulting in two large vorti-ces in the blade passage. Hence, the pressure devel-oped across the blade passage is lower. This indicatesthat the loss in the radial blade design is large al-though it has a 90-degree outlet angle. The long andnarrow passage of Design 1 provides more guidancefor fluid particles, and this resulted in a higher headthan Designs 2 and 3. Flow separation is also mini-mized. However, a long passage may not be reallydesirable because RBCs will remain in the impellerpassage for a longer time and hence are exposed tohigher shear stress. Future impeller designs for cen-trifugal blood pump should consider the effect of thenumber of blades and blade thickness to optimizethe pressure head while limiting flow separation inthe blade passage.

Blood trauma predictionThe particle traces in the impellers are shown in

Figs. 6A–E. In general, the trajectories are 3-D innature, but for clarity and ease of presentation, a

FIG. 5. Shear stress contours are shown in Design 2.

TABLE 1. Computed pressure head generated

DesignPressure head across

impeller (Pa)Pressure head across

pump (Pa)

1 12,425 14,6002 11,909 14,2903 11,750 13,8504 12,373 15,800Radial 10,875 14,130

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two-dimensional (2-D) projection is presented. Asthe impeller is of the closed type, all the particlestend to enter the impeller and leave through thevolute. It can be observed that the traces of the par-ticles in Designs 1 and 2 are quite similar; their tra-jectories are confined mainly to the pressure sideafter smooth entry into the blade passage. Near tomid-chord, it is observed that flow separates and par-ticles move from the pressure side toward the suc-tion side at the trailing edge. This is mainly due toflow separation at the suction side that is likely to becaused by adverse pressure gradient at the trailingedge of the suction side. This is consistent with thevelocity flow pattern, and while particles are drawntoward the suction side, they do not stay in the bladepassage for a long time.

Compared with Designs 1 and 2, the traces of theparticles in Designs 3 and 4 are more complicated. Itis difficult for particles to traverse the impeller pas-sage following the blade profile, and this is a result offlow separation and vortices at the suction side. They

formed circular spirals in the blade passages, andparticles do not leave the blade passage within ashort time. Among the five cases, the radial straightblade design is the worst. Here, particles are drawninto two vortices and may not be able to escape intothe volute smoothly.

In order to compare numerically the hemocom-patibility of pumps, it is necessary to quantify thedamage that RBCs experience in centrifugal bloodpumps. One hundred particles randomly released atthe inlet were tracked. Information such as shearstresses and particle residence time within the pumpwere obtained. The distribution of the number ofparticles with different range of computed %HB re-leased is shown in Fig. 7, and the maximum andminimum values are tabulated in Table 2.

The data showed that the radial straight blade de-sign is the worst, and the computed blood trauma isthe highest. Compared with the other four cases, thenumber of particles with a higher computed %HBreleased in the radial straight blade design is about10 times higher. Thus, for hemolytic reasons, the ra-dial straight blade is not suitable as a cardiac assistdevice. The current method provides a means ofcomparing the impeller that has the largest numberof particles with the highest computed %HB re-leased.

For the other four cases, from Fig. 7 and Table 2,

TABLE 2. Minimum, maximum, and average %HBreleased for impellers computed

Design

%HB value

Minimum Maximum Average

1 0.00002 0.0261 0.00612 0.00002 0.0218 0.00523 0.00003 0.0343 0.00684 0.00004 0.071 0.0073Radial blade 0.000674 0.3687 0.0364

FIG. 7. Particle damage distribution is shown.

FIG. 6. Shown are traces of particles in the radial impeller (A);traces of particles of Design 1 (B); traces of particles of Design 2(C); traces of particles of Design 3 (D); and traces of particles ofDesign 4 (E).

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it is noted that the average %HB released as well asthe maximum %HB released is the lowest for De-sign 2. In addition, the number of particles having an%HB released of 0.01 is about 15 which is smallerthan the other three cases. The four cases have thesame geometry and the only difference lies in theblade shapes so the blade shape of Design 2 is he-modynamically the best. Although Design 1 is simi-lar to Design 2, its wrap angle is larger, thus resultingin RBCs residing in the impeller passage for a longertime, and hence causes a higher blood damage. ForDesigns 3 and 4, the relatively wider blade passageand twisted blade shapes could not control the mo-tion of particles, and flow separation occurs.

The trajectories of selected particles having thehighest and lowest blood trauma are shown in Figs.8A–D. Only the results of Design 2 and the radialblade are shown because they are the blade profileswith the lowest and highest blood trauma computed.In addition, five points on the trajectory of Particle92 were examined to further reveal the extent ofcomputed %HB released as the particle traversed

the pump. In general, it can be observed that par-ticles having a low blood trauma have similar trajec-tories. They enter and leave the blade passagesmoothly and their residence time in the pump isvery short as compared with particles having ahigher blood trauma. Particles that are trapped invortices have a longer residence time in the bladepassage and are susceptible to higher blood traumaas can be seen from Figs. 8A and 8D. Although theimpeller region does not cause the highest bloodtrauma, it is important to ensure that RBCs are nottrapped in the impeller passage. From Figs. 8A and8B and Table 3, it is noted that the ratio of the bloodtrauma between Particles 92 and 29 in the impellerregion is of the order of 1,000 times. For Particles 88and 10 for the radial blade design, the ratio in theimpeller region is about 10 times. Hence, whenRBCs are trapped in the impeller region, such as thecase for vortices, blood trauma in the blade passagecould be significant. This is the case of the radialstraight blade design where the %HB released valueof Particle 88 in the impeller region is 2.59 × 10−3.

TABLE 3. %HB release in blade passage and whole pump

Particle 92(Design 2)

Particle 29(Design 2)

Particle 88(Radial blade)

Particle 10(Radial blade)

%HB release in blade passage 1.596 × 10−3 2.83 × 10−6 2.59 × 10−3 1.87 × 10−4

Total %HB release 1.56 × 10−2 2.03 × 10−5 1.39 × 10−1 6.74 × 10−4

FIG. 8. Shown is trajectory of Particle 29 (Design 2) (A); trajectory of Particle 92 (Design 2) (B); trajectory of Particle 10 (radial blade)(C); and trajectory of Particle 88 (radial blade) (D).

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Hence, it is important that particles entering theblade should follow a smooth path and leave theimpeller without being trapped in vortices. Compari-son of the two designs also showed that, in general,the radial blade design has a higher blood trauma ascompared to other designs. From Table 3, it is alsonoted that blood trauma in the volute region mustalso be addressed because it is a significant factorand cannot be neglected.

A closer examination of the five points on thetrajectory of Particle 92 as shown in Fig. 9 and Table4 reveals that the shear stress is relatively low atpoint A and the %HB released in the blade passageis very small. At point B, where the particle entersthe volute, the shear stress is much higher and the%HB released is much higher. This is due to the factthat the fluid particle exits the impeller passage andenters the volute region. In the volute region, thereis no rotating motion as opposed to that induced bythe impeller. A higher %HB released was also ob-served in the volute region. In the volute region,higher shear stresses were observed as flow from theimpeller exits into the volute. In addition, the time ofresidence in the volute region is higher than that inthe impeller passage, thus resulting in a higher %HBreleased. These results demonstrated that the volutehas an important influence on the %HB releasedand this will be the subject of future studies.

CONCLUSIONS

In the design of rotary blood pumps, considerationmust be given not only to achieving a high efficiency,but also to the level of blood trauma generated. Inthis paper, five different blade designs of a centrifu-gal blood pump were compared computationally. Alinear accumulation damage model was adopted, andthe blood trauma was computed. In general, all five

designs satisfy the general head and flow require-ments. However, it was observed that the radialblade design is the most hemolytic. From particletracking and calculation of %HB released, Design 2has shown the greatest promise. Although flow sepa-ration is still present, fluid particles are subjected tothe least trauma as compared to other designs. Theaverage as well as the maximum %HB released inDesign 2 is the lowest among the five cases. Thisindicates that narrow but not too long blade passagecan guide fluid particles closely and can minimizeflow separation while shortening the transit time.Employing the advantages of Design 2 while varyingthe blade number and changing the blade thicknessmay be a direction in which to search for an opti-mum blade profile.

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TABLE 4. Cumulative %HB released on trajectory ofParticle 92

PointShear stress

(Pa)Total time ofresidence (s)

Cumulative%HB

A 6.57 0.0665 6.08 × 10−5

B 112 0.1 1.60 × 10−3

C 97.5 0.151 4.10 × 10−3

D 92.1 0.181 1.48 × 10−2

E 15.6 0.237 1.58 × 10−2

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