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Medical Engineering & Physics 22 (2000) 381393

www.elsevier.com/locate/medengphy

The flow patterns within the impeller passages of a centrifugalblood pump model

S.C.M. Yu *, B.T.H. Ng, W.K. Chan, L.P. Chua

Nanyang Technological University, Thermal and Fluids Engineering Division, School of Mechanical and Production Engineering, Singapore

639798

Received 8 March 2000; received in revised form 5 July 2000; accepted 17 August 2000

Abstract

The effects of impeller geometry on the performance of a centrifugal blood pump model [the MSCBP design of Akamatsu andTsukiya (The Seventh Asian Congress of Fluid Mechanics (1997), 710) at a 1:1 scale] have been investigated both experimentallyand computationally. Four impeller designs were tested for pump hydraulic performance at the operating point (i.e. 2000 rpm),using blood analog as the working fluid. Each impeller has seven blades with different configurations including the radial straightblade and backward swept blade designs. The results show that both designs can achieve a stable head of about 100 mm Hg atthe operating point. Subsequent investigations involved the visualization of the relative flow field within the impeller passages viathe image de-rotation system coupled with a 2.5 W argon ion laser. Flow structures in all sectors of each impeller were examinedand discussed. To further quantify the possible effects of blade geometry to thrombus formation and hemolysis, computational fluiddynamics (CFD) was used to simulate a simplified two-dimensional blade-to-blade flow analysis so as to estimate the shear stresslevels. The results indicate that the stress levels found within the blade passages are generally below the threshold level of 150N/m2 for extensive erythrocyte damage to occur. There are some localized regions near the leading edge of the blades where thestress levels are 60% above the threshold level. However, given such a short residence time for the fluid particles to go through

these high shear stress regions, their effects appear to be insignificant. 2000 IPEM. Published by Elsevier Science Ltd. Allrights reserved.

1. Introduction

In general, all mechanical circulatory support devicesthat replace or assist the physiological function of theheart must exhibit a certain acceptable level of bio-com-patibility which is defined as the ability to pump bloodwith minimal hemolysis and thrombus formation. Inaddition, they must also exhibit the following features[1]. Such a device must:

generate a flow rate of approximately 56 l/min ofblood against the mean aortic pressure of about 100mm Hg for left ventricular assisting devices (VADs);

be inexpensive, small and compact to facilitate theimplantation of the device in adults and children;

Abbreviations: CFD, computational fluid dynamic; MSCBP, magneti-

cally suspended centrifugal blood pump; PS, pressure side; RBC, red

blood cell; SS, suction side; VAD, ventricular assisting device.

* Corresponding author. Tel.: +65-790-5595; fax: +65-791-1859.E-mail address: [email protected] (S.C.M. Yu).

1350-4533/00/$ - see front matter 2000 IPEM. Published by Elsevier Science Ltd. All rights reserved.

PII: S1 3 5 0 - 4 5 3 3 ( 0 0 ) 0 0 0 4 5 - X

be bio-chemically stable within the body; provide reliable and efficient long-term cardiac sup-

port (greater than 1 year); have minimal hemolysis and thromboembolic compli-

cations; have low heat generation so that damage to surround-

ing tissue is minimized; not cause any complications to other organs; and enable patients to lead a near normal lifestyle.

Although pumps operating on the pulsating principlesare, in general, preferable, they are usually very expens-ive, costing between US$16,000 and $200,000 [2]. Sur-gical problems relating to the use of pulsatile deviceshave often resulted in postponement of implantation.Clearly a less complex, less expensive and easy-to-usedevice is desired. Researchers such as Treichler et al.[3] and Nose et al. [4] recognized many inherent featuresof the centrifugal blood pumps that could have contrib-uted to an excellent implantable long-term device.Firstly, the reduced size of the non-pulsatile device,

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382 S.C.M. Yu et al. / Medical Engineering & Physics 22 (2000) 381393

Nomenclature

g gravitational acceleration (m/s2)H head rise (mm Hg)k turbulent kinetic energy

P pressure (Pa)Q flow rate (l/min)Re Reynolds numberSi source term due to internal energySx,y,z momentum source term in the x and y directions, respectivelyt time (s)u velocity vectoru,v,w velocity in the x, y, and z directions (m/s)(u)2,(v)2,(uv) Reynolds stressesx,y,z Cartesian coordinatesr density (kg/m3)m dynamic viscosity (kg/ms)n kinematic viscosity (m2/s)

q temperature (K)t shear stress (Pa)txx,tyy normal stresses (Pa) Laplacian operator dissipation functions1,s2 maximum and minimum normal stresses, respectively (N/m

2)w rotational speed (l/s)

which is due to the absence of heart valves and a largecompliance chamber, facilitates the ease of insertion intothe body without dissection of the patients diaphragm.

Secondly, the simplicity in design of the non-pulsatilepump simplifies the manufacturing process tremendouslyand hence greatly reduces the cost of a non-pulsatile cen-trifugal blood pump.

Although there are reports, for example by Nakata etal. [5] and Sezai et al. [6], that continuous blood flowprovided by the centrifugal pump will have several detri-mental physiological effects, Allen et al. [7] have indi-cated that these effects are only temporary. Despite thesecontroversies on the effect of non-pulsatile and pulsatileblood flow, it is certain that non-pulsatile flow is not alimiting factor to maintain life as reported by Yada etal. [8] and Minami et al. [9]. Thus, clinical centrifugalblood pumps have gained increasing roles in providingsupport for patients with a failing heart, due to their easeof application in the heartlung machine, relative lowcost, simplicity, small size and ability to generate highflow rates. These include management of patients withcardiogenic shock by Minami et al. [10], shock aftermyocardial infarction (MT) by Noda et al. [11] and asa bridge to transplantation by Deleuze et al. [12]. Usesof these pumps were estimated to replace the rollerpumps in 30% of the cardiac surgical procedures [13].

One of the ways to overcome the problems of throm-bus formation and heat generation at the shaft/seal inter-

face in a centrifugal blood pump would be to reduce thecomplications at the interface (or to eliminate the shaft)and develop a completely seal-less centrifugal pump.

Many research groups like Hart et al. [14] and Khanwil-kar et al. [15] are constantly working on a better andmore compact centrifugal blood pump system. Despitethese continual efforts, all centrifugal blood pumps stillhave high potential for blood trauma due to the highlevel of energy being transferred from the fast spinningrotor to the blood. Hemolysis occurs when blood is sub-

jected to high shear forces and sudden flow directionalchange in the pump housing. Thrombus formation occursin low velocity and re-circulating regions. Therefore todesign a good centrifugal blood pump with minimalhemolysis and thrombosis, high shear rate, flow re-circu-lation and stagnation regions have to be avoided or mini-mized.

Akamatsu et al. [16] reported that a magnetically sus-pended centrifugal blood pump (denoted as MSCBP) isproven to have a satisfactory pump performance. Theadvantage that the MSCBP has over the commercial cen-trifugal blood pump is the use of magnetic suspensionthat eliminates leakage and sealing problems. It also pre-vents blood clots on the shaft and heat generation by theshaft and bearings. Subsequent hemolytic tests perfor-med by Park et al. [17] and Nishimura et al. [18] onAkamatsu et al.s design showed that the index of hemo-lysis was significantly lower in the MSCBP than in other

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383S.C.M. Yu et al. / Medical Engineering & Physics 22 (2000) 381393

non-magnetically suspended centrifugal blood pumps. Infact, clinical application of the MSCBP for long-termventricular support (more than 200 days) has been achi-eved in a sheep as reported by Nishimura et al. [18].

However, the MSCBP is not exempted completelyfrom problems such as hemolysis and thrombosis, which

are common in all blood pumps. Thrombus formationappeared at the narrow gap between the impeller and thevolute as observed by Yamada et al. [19]. Though alarger gap would induce more regurgitant flow throughthe gap and thus reduce the thrombus formation, it willresult in lower pump efficiency. Too narrow a gap willinduce higher shear stress in the gap resulting in hemo-lysis. Park et al. [17] reported that maximum pumpefficiency occurs for a gap range between 0.15 and 0.25mm, but this does not guarantee minimum blood trauma.Other possible sites for blood trauma to occur includethe impeller passages where flow recirculation and stag-nation exist. Akamatsu and Tsukiya [20] attempted tostudy the flow patterns within the impeller passages inthe MSCBP at the off-design speeds of 300 and 600 rpm.To achieve Reynolds principle of similarity, the fluidviscosity was modified. Similar to the scaled-up model,the advantage of this technique is the reduction of pumprotational speed through the assumption of similarity.However, it should be noted that the results may not bethe true representation of the flows at higher rotatingspeed (usually at around 2000 rpm at the design point).

The objectives of the present investigation are twofold. Flow visualization was conducted first to examineany regions of flow stagnation and recirculation within

the impeller passages. The results were subsequentlycompared with the output from the computational fluiddynamics (CFD) analysis. After establishing the qualitat-ive agreements between the experiments and CFDresults, further investigations using CFD were carriedout to examine quantitatively the effects of flow stag-nation and recirculation to the thrombus formation andhemolysis. All impellers considered here have the sameblade numbers. The relative flow patterns within theimpeller passages were examined at the operating con-dition, i.e. at the design speed of 2000 rpm, with bloodanalog as the working fluid.

The following section describes the blood pumpmodel and the experimental set-ups including the imagede-rotating system for flow visualization. A briefdescription of the CFD code used (Fluent V4.3 [21]) willalso be provided. These sections will be followed bypresentation and discussion of the results. The paperends with a summary of the most important findings.

2. Pump configurations and instrumentation

2.1. Pump geometry and test rig

A transparent acrylic model of the centrifugal bloodpump (1:1 scale) was machined and tested in a closed

circuit loop. A schematic layout of the test rig ispresented in Fig. 1(a) and Fig. 1(b) shows the test rigtogether with the flow visualization set-up. The close-loop circuit shown in the figure consists of a fluid reser-voir, a throttle clamp, pressure transducers at the inletand outlet of the pump and a digital flowmeter. The

pump was connected to the reservoir with a 25.4 mmdiameter siliconplatinum cured tubing. The workingfluid was supplied to the centrifugal pump inlet from alarge reservoir.

A schematic view of the model blood pump is shownin Fig. 2(a) with detailed dimensions given and is similarto the MSCBP developed by Akamatsu et al. [16]. Themain difference between the present model pump andthe pump developed by Akamatsu et al. [16] is that thepresent model pump is not magnetically suspended. Themain drawback of the MSCBP was that optical accesswas not possible inside the impeller passages due to thepresence of gap sensors and electromagnets. The modelpump was therefore designed to be shaft-driven by aservomotor with one side of the volute optically access-ible. Furthermore, the shaft-driven design can eliminateany possible effects of impeller meandering so that amore stable condition can be obtained for the study offlow patterns between impeller passages.

The model blood pump consists of two main parts: animpeller and a volute. The pump had a double volutecasing, which comprised of two circular arc-shapedenclosures surrounding the impeller. The pump innerinlet and discharge pipe diameters were 12 and 16 mm,respectively. The volute was manufactured in two parts

via the CNC machine, i.e. lower and upper volutes asshown in Fig. 2(b). The impeller was sandwichedbetween the volutes and was allowed to rotate freelywithout rubbing the inner surfaces of the volutes.

Blood analog was used as the working fluid. Twoparts of pure glycerine were mixed with three parts ofdistilled water in order to achieve the required compo-sition which has a dynamic viscosity of 3.5 centipoise.

2.2. Geometry of the impellers

The impellers for the present investigation wereclosed-type shown in Fig. 3(a). Each impeller has aninner and outer diameter of 13 and 25 mm, respectively.It was formed by sandwiching the seven vanes betweenan upper and lower shroud. The blade profiles and thelower shroud of the impeller were machined from a solidaluminum block by the CNC machine. The impeller wasthen anodized (black) to eliminate optical interferenceduring flow visualization. The upper shroud, which wasmade of clear acrylic sheet, was polished and mountedonto the lower shroud by means of three M1 screws.The vanes of the impeller had a uniform height of 3.5mm. This impeller was then mounted onto the shaft,which was driven by a motor unit providing a constant

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Fig. 1. Schematic of the experimental set-up.

rotational speed of the centrifugal blood pump (to within0.5%). This motor unit, with a built-in feedback controlto regulate the speed, had maximum rated output, speedand torque of 100 W, 3000 rpm and 0.32 N m, respect-ively.

A total of four impellers with different blade profileswere studied using the same volute. As shown in Fig.3(b), the first impeller (R7) is a straight radial bladeimpeller design with inlet and exit blade angles of 90.The other three impellers are backward-facing impellers(denoted as A3, A4 and B2, respectively) with inlet andoutlet blade angles at 6.74 and 30, respectively. Theprofiles of the blade curvatures vary for all three cases.Further details of the blade profile design can beobtained from Li [22].

Measurement of the relative static pressure differencewas located at approximately two diameters upstream ofthe pump inlet and five diameters downstream of thepump outlet (by convention). Their difference is meas-ured by the pressure transducer (Druck DPI 260 seriesDigital Pressure Indicator) via silicon tubing. The press-ure transducer displays differential pressure from 0 to250 mm Hg with accuracy of 0.04% full scale.

2.3. Image de-rotating technique

Analysis of the relative flow patterns between theblades of an impeller is difficult when an observerremains stationary relative to the impeller. However,when the observer rotates with the impeller at the samespeed, the relative flow field can be observed. The de-rotator optically freezes the image of the rotatingimpeller, which is then analyzed by flow visualizationto provide flow patterns within the blades.

The principle of the rotating 459045 or the Porroprism is shown schematically in Fig. 4(a). When theupright object F is placed on the left side of the XXaxis of the prism, a laterally inverted image (mirrorimage) is formed on the right side of the XX of theprism axis (c.f. Fig. 1(b) for the locations of prisms).This can be better understood by studying the diagramin Fig. 4(b) which shows the path of light forming theinverted image. Regardless of the orientation of theobject F, a laterally inverted image of the object Fcan be obtained. However, when the object rotates by90, the prism needs to rotate only by 45 in the samedirection to obtain an inverted but upright image. Simi-

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Fig. 2. Schematic of the blood pump model.

larly, if the object rotates by 180 with the prism rotatingto 90, the image formed will continue to be invertedand upright. Therefore, for an object rotating at a certainangular velocity, the image of a rotating object willalways be upright but inverted and stationary in real timeif the image de-rotator rotates in the same direction butat half the speed of the object.

In order to render the flow pattern visible, polystyrenespheres of 50 m were used as tracers. A 2.5 W argon-ion laser operated in continuous mode was employed asa light source (c.f. Fig. 1(b)). Through a cylindrical lens,the laser beam was transformed into a light sheet of 1-mm thickness to illuminate the flow. The tracer particlesin the plane of the light sheet were then observed andphotographed in the direction normal to the illuminatedplane. The flow patterns within the illuminated regionof interest, i.e. the blades of the impeller, can be viewedby a CCD video camera via a beam-splitter. The cameraused has a frame rate of 25 per second with monochrome

high resolution of 768 by 576 pixels and a 2/3 CCDarray (JAI, CV-3000). It was capable of electronic shut-ter speeds up to l/10,000 s. An image acquisition board(MV-1000) was used to digitize the analog camera videooutput into 8 bits per pixel at rates up to 40 millionsamples per second. These digitized images were thenstored in a personal computer for further image analysis.

3. Numerical method

A commercial CFD code Fluent (V4.3) [21] was usedto perform the numerical investigation. The fundamentalgoverning equations in describing two-dimensional, ste-ady, compressible fluid flow can be written as below:

Continuity equation:

div(ru)0 (1)

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Fig. 3. Geometry of the impeller blades investigated.

Fig. 4. Optical principle of image de-rotator (taken from Ohki etal. [23]).

Momentum equations:

x(ruu)

p

xdiv(m u)Sx (2)

y(rvu)

p

ydiv(m v)Sy (3)

Internal energy equation:

div(riu)rdiv(u)div(k q)Si (4)

where is the Laplacian operator, p is the pressure, iis the internal energy, t is the time, u is the velocityvector, k is the thermal conductivity, r is the density, mis the dynamic viscosity, q is the temperature, u and v

are the velocities in the x and y directions respectively, is the dissipation function, Si is the source term dueto internal energy and Sx,y is the momentum source termin the x and y directions, respectively.

Fluent uses the Semi-Implicited Method for Pressure-Linked Equations (SIMPLE) algorithm and SIMPLE-Consistent (SIMPLEC) with convergence techniquessuch as block correction and multi-grid method, and pro-vides the velocity and pressure fields as solutions forthe discretized form of the above governing equations.Fluents ability to model flow in a rotating frame of ref-erence involving complex geometry with high robustnessand efficiency makes the code suitable for calculatingflow in rotating machinery. Further details can be foundin the Fluent V4.3 manual [21].

In this initial stage of numerical analysis, the focuswill be on the prediction of relative flow field betweentwo blades of an impeller without considering the influ-ence of the volute. As the flow through a real turbo-machine is three-dimensional, unsteady and viscous, itis necessary that all these characteristics be taken intoaccount during the design stage [24]. In spite of theavailability of powerful computer hardware, solutions tosuch complex equations are time consuming and expens-ive owing to limitations in CPU and memory. Therefore

approximations to simplify the problem are necessaryand are made by reducing the three-dimensional to two-dimensional problems, which are amendable to analysis.

It is a well-known fact that in centrifugal impellers,the axial velocity component can be neglected as com-pared to the radial and angular components. Hence, itwas reasonable to approximate the passage flow as atwo-dimensional problem. Only a segment of the impel-ler blades was modeled (see Fig. 3(a)).

The total number of nodes for each blade passage wasabout 6283. There were 21 nodes in both the inlet andoutlet extensions and 61 nodes on the blade surface, giv-ing a total of 103 grid points in the radial direction. Inthe circumferential direction, there were 61 grid points.The calculation was performed on a Pentium-II 400MHz processor and it required about 10,00015,000time-steps, which was approximately 67 h of centralprocessor unit (CPU) time. At the inlet of the compu-tational domain, an inlet relative velocity was prescribedwith the assumption of no pre-rotation. The inlet velocityconsisted of a normal velocity component, which was inthe radial direction and specified according to the flowrate of 5 l/min, and a tangential velocity componentbased on the design rotational speed. At the outlet, thenormal velocities were adjusted to satisfy the overall

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mass balance for the computation domain. At the bladesurface, the wall was defined with zero velocity. It wasassumed that the fluid was circumferentially periodic andinvariant with flow passages, thus CYCLIC boundaryconditions were specified at the two sides of the exten-sion areas. All velocity components, pressure, turbulence

kinetic energy (k) and dissipation rate (e) were the sameon the CYCLIC boundaries. This permitted the simul-ation of only one of the seven blade passages of animpeller.

The values of density (r) and dynamic viscosity (m)of the medium were taken to be 1050 kg/m3 and3.5103 kg/m s, respectively, to approximate bloodproperties under normal body temperature. The Reyn-olds number based on the angular velocity and the outerimpeller diameter was approximately 40,000. The flowinside the blade passage may be turbulent due to thegeometrical complexity and rotational effect. Therefore,a laminar flow model was not used to simulate the highlycomplex rotational flow in the impeller. The standarde turbulent model was therefore adopted.

4. Results and discussion

4.1. Pump performance

Fig. 5 shows the variation of the head rise (H) againstthe flow rate (Q) for respective impeller designs. Themeasured head produced by all these impellers are foundto be stable at each flow rate point measured (to within

1%). Also shown in the figure for comparison are thetheoretical head curves obtained from the Eulers equ-ation for outlet blade angle at 30 and 90, respectively.

As may have been expected, the head generated byeach of the four impeller designs gradually fell as theflow rate (Q) increased. The head at the design point (5l/min) for the radial blade was found to be the highest

Fig. 5. Pump performance curves for respective impeller blade

designs ( Eulers analysis: blade trailing edge angle at 90; Eulers analysis: blade trailing edge angle at 30).

at about 100 mm Hg. The performance curves for thestraight radial blade and backward swept blade showsome differences, to within 10%, with the former onebeing slightly higher. For the backward swept bladedesign, keeping the inlet and outlet blade angles con-stant, some further improvements on the head generated

across the pump can be obtained by varying the bladeprofiles. Maximum increase was around 12% at thedesign point; for example, compare impellers A3 andB2.

A few important observations can be extracted fromFig. 5. First, increasing the outlet blade angle would leadto higher head in the performance curves. The perform-ance curves estimated from the Eulers equation showthat the backward facing profile with an outlet bladeangle of 30 would produce a negative slope and thehead generated at the design point would be below thatof the straight radial blade. This is further supported bycomparing the performance curves of R7 and other back-ward swept blade designs (although there is small differ-ence in the inlet angle between the two designs). Theperformance of impeller R7 is expected to improvefurther if the inlet blade angle can match more closelywith the inlet flow angle.

Secondly, it can also be seen that the profile of impel-ler blade is an important factor in generating a higherhead. Comparing impellers A3, A4 and B2, despite hav-ing the same inlet and outlet blade angles, the achievablehead increased from 84 mm Hg for impeller A3 to 88mm Hg for impeller A4 and finally to 95 mm Hg forimpeller B2. There is about a 13% increase from impel-

ler A3 to impeller B2. Therefore changing the blade cur-vature while keeping both the inlet and outlet bladeangles constant can enhance the pump performance.

Thirdly, the pump characteristic is closely related tothe losses within the pump. Comparing the theoreticalhead and the head generated by impeller R7, a head lossof 105 mm Hg is noted. For impeller A3, the differenceis about 111 mm Hg. The head loss for impeller A4reduced to 107 mm Hg and to 100 mm Hg for impellerB2. The difference between the theoretical and measuredis a result of losses and of the flow from the blades. Thedeviation (referred to as slip in the pump literature) is aresult of the relative rotation, a finite number of bladesand viscous effects.

Head loss occurring in the MSCBP pump are sum-mation of several factors according to Akamatsu et al.[16]. They are firstly the mechanical losses caused bythe physical contact between the shaft/seal interface andthe shaft bearings. In addition, there are disk frictionlosses at the gap between the impeller and the volute.Losses in the form of fluid leakage that occurred whenpart of the fluids leaving the impeller exit returned backto the impeller inlet through the gap and the losses inthe volute also reduce the pump efficiency. Finally,hydraulic losses in the impeller passages as a result of

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flow separation are also an important factor. Akamatsuet al. [16] had estimated the losses contributed by eachof the three factors mentioned above in the MSCBP andhad identified that the hydraulic loss is comparable tothe disc friction loss at the design point, contributingabout 35% of the total losses. The leakage loss is the

lowest among the three losses (about 20%). The sub-sequent focus of the present investigation will be onhydraulic loss due to flow separations within the impel-ler passages.

4.2. Flow visualization results

The relative flow patterns of the seven passages of thefour impellers (R7, A3, A4 and B2) were obtained usingthe flow visualization set-up described earlier. The flowpatterns were taken at the mid-height of the vanes (c.f.Fig. 3(a)). Since the flow patterns for the three backwardswept designs are very similar, only the results for theA3 design will be presented here. Figs. 6 and 7 showthe relative flow patterns in every sector (S1, S2, S3, S4,S5, S6 and S7) between the blades of the R7 and A3designs. In each figure, the blade rotates in the clockwisedirection causing the side of the blade that leads therotation to be the pressure side (PS) while the side ofthe blade that follows the rotation is the suction side(SS). The diagram in the center of the figures shows theschematic of the pump and impeller, and position ofimpeller with respect to the volute. All flow visualiza-tions were conducted at the design point, i.e. at arotational speed of 2000 rpm and a flow rate of 5 l/mm.

Fig. 6. Flow visualization at different impeller passage of the blood pump model with impeller design R7.

The shutter speed of the camera was set to 1/500th ofa second.

4.2.1. Radial impeller (R7)

In every sector of the impeller R7 in Fig. 6, a pair oflarge-scale recirculating vortices near the suction side

was observed while the bulk flow went smoothly alongthe pressure side. In the case of radial blade impellerwhere the inlet blade angle is at 90, the direction of therelative velocity vectors at the inlet differ from that ofthe blade angle, thus giving rise to early flow separ-ations. Fig. 8a shows a sketch of the inlet velocity tri-angle and the flow patterns between any two blades.From the sketch it is noticed that regardless of therotational speed of the impeller, the relative velocitycomponents at the inlet of the blade passage will alwaysdiffer from the inlet blade angle. The vortex whichappeared near the leading edge of the suction side islargely due to the mismatch between the inlet flow andblade angles. The second vortex near the trailing edge ofthe suction side is due to the adverse pressure gradientsdeveloped along the blade. It should be mentioned thatthe two recirculating vortices do not represent deadwater regions. It was clearly shown during the visualiz-ation tests that tracer particles entering the blade pass-ages went smoothly through the recirculation regionsand left the passage.

The flow phenomena within the passages is not com-pletely two-dimensional as indicated by the criss-cross-ing of streaklines observed in the passages. At the impel-ler inlet region (c.f. Fig. 2(a), where the inlet center cone

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Fig. 7. Flow visualization at different impeller passage of the blood pump model with impeller design A3.

Fig. 8. Sketch of the inlet velocity triangles and flow patterns

between the blades of respective impeller designs (mirror image view).

changed the direction of flow from axial to radial), thefluids may not enter the passage with uniform velocitydistribution along the vane height and as a consequence,causing the criss-crossing of the streaklines.

The flow structures in all the sectors are qualitativelysimilar to one another. This implies that the interactionof the volute and the flow within the impeller passagesmay not be significant at the operating point. However,

some local effects of the volute on certain sectors of theimpellers exist. This can be observed in the spatial extentof the recirculation vortices formed. Although the vorti-ces appeared mainly on the suction side, the area occu-pied by the vortices varied at different sectors. Forexample, in sectors S4 and S5 it appeared that the sizeand strength of the vortices were larger than those in theother sectors due to the presence of the splitter plate.The splitter plate had restricted the flow from leavingthe passage causing flow reversal at the passage outlet.

In sector S1, the streaklines shown in the flow patternnear the impeller passage exit seem to be shorter indicat-ing a lower velocity. This is due to the blockage effectby the cut-water (or tongue region in Fig. 2(a)). Theirpresence restricted the amount of fluids leaving the pass-age. It should be noted that the fluid that departed fromthe passage had to squeeze through the space betweenthe tongue and the vanes, subjecting itself to higher velo-city gradients. For sectors S2, S3, S6 and S7, the fluidsleft the passage into the volute without any restrictions.

4.2.2. Backward facing impeller (A3)

The change in the blade shape from the straight radialtype to a backward facing blade altered the flow patterns.This caused a reduction in the number of vortices from

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two in impeller R7 to one in impeller A3. Similar obser-vations were also found in the other two backward sweptdesigns. Unlike impeller R7, where the vortices wereformed at both the leading and trailing edges of the suc-tion blade, there is no vortex formation at the leadingedge of impeller A3 due to the smaller difference

between the inlet flow and blade angles. From Fig. 7(a)and (e), it is evident that flow separation did not occurat the leading edge of the suction side because the flowwithin the impeller A3 at design condition seemed to bebetter aligned with the inlet blade angle. It is observedthat the flow patterns within the blade passages of impel-ler A3 are qualitatively similar to each other with thevortex being confined to the region near the trailing edgeof the suction blade while the main flow remainedattached along the pressure side in each sector. The for-mation of the vortex was likely to be the result ofadverse pressure gradients causing the flow to separate.A sketch of the flow pattern between the blades of impel-ler A3 is shown schematically in Fig. 8(b).

Along the pressure side, the streaklines in the bladepassage of impeller A3 are in general longer than thoseobserved in impeller R7 indicating higher velocities. Fora given blade number, though the circumferential bladepassage area is the same, the blade profile would cer-tainly affect the flow pattern. In the case of impeller A3,fluid particles have to accelerate through the curvedblade passage as compared to impeller R7. Higher velo-city gradients would appear on the pressure side and asa result incur higher levels of shear stresses. The longerblade length in impeller A3 may be a potential source

of blood trauma.The flow patterns in all sectors are qualitatively simi-

lar to one another. However, similar to those found inimpeller R7, some local effects on the flow passages dueto the volute/impeller interaction may exist. This isshown by the variation in the size of the vortices. Thevortices in sectors S1, S2, S3, S6, and S7 were aboutthe same size. In sector S4, the vortex seemed to be oflarger size compared to the rest of the sectors, blockingmost of the flow passage. The large vortex size couldbe attributed to the blockage of fluids from leaving thepassage by the presence of the splitter plate. There weretwo vortices present in sector S5. A pair of vortices,comprising of a large vortex and a smaller one, appearedat the trailing edge of the suction blade. The existenceof the smaller vortex might be due to induction by thebigger vortex.

Near the cut-water region at sector S1, the fluid didnot seem to be able to exit the passage into volute. Atthe passage outlet where the volute area was very lim-ited, the fluids got bounced off the volute wall andreversed back into the impeller passage. This can beobserved by the streaklines criss-crossing each other atthe corresponding region.

In general, for the other backward facing impeller

designs, i.e. impeller A4 and B2, the flow patterns werequalitatively similar to those observed in impeller A3.Vortex formation was found at the trailing edge of thesuction side while flow remained attached along thepressure side. The volute had some local effects on theflow patterns in several blade sectors. From the flow vis-

ualization studies of the four impellers, it is postulatedthat the number of vortices could be reduced if the rela-tive flow angle can be aligned better with the inlet bladeangle. However, vortex formation seemed to be unavoid-able at the suction side of the blade due to the build-upof the adverse pressure gradients.

4.3. Numerical simulation of flow within the impeller

passages

4.3.1. Velocity vectors

The computed velocity distributions in a single pass-age of impellers R7 and A3 are presented in Fig. 9. Thefigure shows the relative flow field of the blade passagesof the three impellers. The blades are rotating in thecounter-clockwise direction. This results in the suctionside (SS) on the upper surface and pressure side (PS) onthe lower surface.

In the case of impeller R7 and Fig. 9(a), a pair ofstrong re-circulating vortices indicated by the letters Aand B is observed within the blades. The flow isrestricted to the pressure side of the blade passage. Thesimulation clearly shows that the formation of vortex Ais mainly due to the difference in the relative flow angleand blade angle, while vortex B is due to the adverse

pressure gradients appearing on the suction side. Simi-larly, a dominating vortex B and a small vortex Aappearing near the impeller outlet are observed forimpellers A3, A4 and B2. Smooth flow is also restrictedto the pressure side. In general, the experimental flowvisualization is qualitatively similar to the predicted flowfield for all the impellers revealing the dominance ofvortex B. It should be mentioned that the smaller vortexA predicted by CFD is not obvious in the experimentalflow visualization of these impellers.

Numerical simulation and flow visualization haveshown the difference in flow patterns due to the differentvane profiles. The agreement between the numericalsimulation and experimental flow visualization results isreasonably good. Through observations of flow patterns,blood trauma can be anticipated by identifying the regionof re-circulation. However, this does not quantitativelyindicate the level of damage imposed onto the bloodcells. It is therefore desirable to establish quantitativelythe effects of shear stress on blood caused by differentblade profiles.

4.3.2. Shear stress analysis

The maximum shear stress tmax acting on the bloodcell in a two-dimensional analysis is the resultant of two

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Fig. 9. Computed velocity vectors at the mid-height of respective

impeller passage.

normal stresses txx, and tyy and the two shear stressesact on the faces of a control volume. Shear stress in vis-cous flow is divided into laminar and turbulent parts, andcan be calculated from the velocity vectors based on thefollowing equations:

txx2mu

x+

2

3m

u

x+v

y+r(u)2

laminar shear turbulent shear

(5)

tyy2mv

y

2

3m

u

xv

yr(v)2 (6)

txymu

yv

xruv (7)

tan 2a2txy

txytyy(8)

The resultant shear stress can be obtained by rearrang-ing Eqs. (5)(8) into Eqs. (9)(11).

s1txx+tyy

2txx+tyy

2cos 2atxy sin 2a (9)

s2txx+tyy

2txx+tyy

2cos 2atxy sin 2a (10)

tmax|s1s2|

2(11)

where r is the fluid density, m is the dynamic viscosity,(u)2,(v)2, and (uv) are the independent Reynoldsstresses, s1 and s2 are the maximum and minimum nor-mal stress values, respectively. Hence by discretizing theequations, the maximum shear stress tmax can be calcu-lated at every cell within the blade passage.

Fig. 10 shows the shear stress distribution for impel-

lers R7 and A3. From the shear stresses contours, it is

Fig. 10. Shear stress contours at the mid-height of respective impel-

ler passage.

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observed that the majority of the flow passage had shearstress magnitude below 40 N/m2. This is well below thethreshold level of about 1500 dynes/cm2 or 150 N/m2

for extensive erythrocyte damage to occure [25]. Theseresults are agreeable to low index of hemolysis found inthe MSCBP by Park et al. [17]. However, it should be

noted that there are actually a few small regions (lessthan 1/10 of the blade length) within the blade passagefor impeller R7 and A3 that are associated with highshear stresses. One particular high shear stress region isat the wall of the pressure side close to the blade leadingedge. It is the stagnation point where fluid particles firstcome into contact with the rotating blades. Anotherregion that induced high shear stress is along the press-ure side. The fluid near the wall of the pressure sideproduces a very high velocity gradient due to the viscouseffects. This results in a high shear stress region at cer-tain parts along the blade on the pressure side. The inter-face between the pair of re-circulating vortices is anothersite of high shear stress magnitude. The maximum shearstress that occurred within the blades for impellers R7,A3, A4 and B2 are approximately 230, 220, 273 and 267N/m2, respectively, and these are mostly found at theleading edge of the pressure side. Although these resultsare above the threshold level of 150 N/m2, it is unlikelythat they would cause irreversible damage to blood cells,as these happened only for a short period of time (thetransit time for a fluid particle to go through the pumpimpeller passage is estimated to be about 0.03 s).

The pump has an output of 5 l/min at the design pointand if we assume the blood pump patient also has a

blood volume of 5 l, all the blood will go through thepump once every minute. If we assume all RBC spend0.03 s inside the impeller passage for every minute inwhich 1/10 of their time (in proportion to the length ofthe blade) is in the high shear stress region near the lead-ing edge, i.e. 0.003 s, for every 24 h, the RBC wouldexperience a total of 4.32 s of shear stress greater than250 N/m2. It will take approximately 833 days beforeany possible rupture of the RBC could occur (when 250N/m2 for 60 min is required for cell rupture, [26]). Itshould be mentioned that the above analysis is verycrude and in blood pumps the blood is exposed tosubhemolytic shear stresses may times over a long per-iod of time. Their effects cannot be quantified easily bythe present analysis.

5. Concluding remarks

The present investigation focuses on the flow patternswithin the impeller passages of a centrifugal bloodpump. Four different types of blade geometry have beentested including the radial straight blade and backwardswept blade designs. Both designs can achieve a headof about 100 mm Hg at the design point. Modifying the

curvature of the blade may improve the backward sweptblade design performance but the effects appear to bemarginal. Subsequent investigations focused on visualiz-ing the relative flow patterns in all the seven sectors ineach impeller design. Recirculation vortices were foundin all the designs and they appeared mainly at regions

close to the suction side. Moreover, the recirculationregions did not seem to give rise to any flow stagnant(dead water) regions whereby thrombus is likely toaccumulate. The flow patterns in all the seven sectorswere similar but localized effects from the voluteexisted. For example, near the cutwater region, the out-ward flow from the impeller passages was restricted andbounds back inside into the passage. This blockageeffect however is considered transitory and smooth out-ward flow will resume when that passage continues torotate to the other sector of the volute.

Although the flow patterns inside the impeller pass-

ages appeared to be three-dimensional, as shown by thecriss-crossing of the streaklines, the two-dimensionalnumerical approach shows good qualitative agreementswith flow visualization results. The results indicate thatthe stress levels found within the blade passages are gen-erally below the threshold level of 150 N/m2 for exten-sive erythrocyte damage to occur. There are somelocalized regions near to the leading edge of the bladeswhere the stress levels are some 60% above the thresholdlevel. However, given such a short residence time(estimated to be less than 0.03 s) for the fluid particlesto go through the blade passage, their effects seemed tobe insignificant. It should be mentioned that the simula-tions were conducted using a simplified two-dimensionalanalysis and that the flow could be three-dimensional.Furthermore, the effects of the volute and splitter platewere not accounted for.

Although the pump prototype investigated here wasnot magnetically suspended and the efficiency amongdifferent designs cannot be compared directly, the resultsgenerally suggest that other differences between the twodesigns investigated are very little. Both can achieve thehead required and the shear stress levels are found to beacceptable for both cases. It should be noted that thepresent experiments were conducted using a shaft wher-

eby any possible meandering effects of the impellerstructure were not accounted for. It can be expected thatas the flow went around each impeller blade, an aerody-

namics lift would be generated, as shown in Fig. 8(c).While the lift generated by the radial blade would beacting tangentially with respect to the blade center, thelift generated by the backward swept blade would beacting at an angle in the outward direction. This may bethe likely cause of the impeller meandering effectobserved by some of the curved blade designs ([27] priv-

ate communications). On-going works include the exam-ination of the disk friction loss and gap loss to the overall

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pump performances and their effects on the thrombusformation and hemolysis.

It should be mentioned that the centrifugal pump mayhave several advances over the other pump designs suchas the axial (or diagonal) pump. Although the size of theaxial pump may be kept smaller than the centrifugal

pump investigated here, to achieve the same flow rate at5 l/min the working speed for the axial pump has toincrease. Multi-stage design may have to be consideredto achieve an acceptable head. This may inevitably leadto higher shear stresses (or hemolysis level) for the bloodtransiting the pump. It should be pointed out that theinvestigations on the simulated interaction of pump withthe heart on our centrifugal pump have not yet been car-ried out although this may be improvised by adjustingthe opening of the throttle clamp and elevation of thefluid reservoir shown in Fig. 1(a). Furthermore, thepump is basically designed for the left ventricle andfuture work will include its possible applications withthe right ventricle.

Acknowledgements

The authors are grateful to Professor T. Akamatsu inproviding much useful information with regards to theMSCBP design. Financial support to this project fromthe Academic Research Grant Committee and a researchstudentship to Mr Bernard T.H. Ng from the School ofMechanical and Production Engineering are gratefully

acknowledged.

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