Australas Phys Eng Sci Med (2013) 36:417–422 DOI 10.1007/s13246-013-0225-x
SCIENTIFIC PAPER
A new design and computational fluid dynamics study of an implantable axial blood pump Mojtaba Koochaki • Hanieh Niroomand-Oscuii
Received: 18 February 2013 / Accepted: 21 October 2013 / Published online: 8 November 2013 Ó Australasian College of Physical Scientists and Engineers in Medicine 2013
Abstract Considering small thoracic space, using implantable ventricular assist device requires reduction in a pump size. Among many available blood pumps, axial blood pumps have attracted greatly because of their small size. In this article, a new miniature axial blood pump has been designed and studied which can be easily implanted in the human body. In this design, the pump overall length decreased by a little increasing in the pump diameter, and new blade geometry is used to produce a streamlined, idealized, and nonobstructing blood flow path in the pump. By means of computational fluid dynamic, the flow pattern through the pump has been predicted and overall pump performance and efficiency has been computed. Also, to ensure a reliable VAD design, two methods for checking wall shear stress were used to confirm that this pump wouldn’t cause serious blood damage. Keywords Blood pump Ventricular assist device Axial pump Cardiac disease Heart pump
Introduction Nowadays cardiovascular diseases (CVDs) are one of the most important causes of death all over the world. ‘‘Since 1900 except 1918, in every year, CVD have accounted for more deaths than any other major causes of death in the United States’’ [1]. ‘‘An estimated 82,600,000 American adults ([1 in 3) have one or more types of CVD’’ [1]. One M. Koochaki H. Niroomand-Oscuii (&) Sahand University of Technology, Sahand, Iran e-mail: [email protected] M. Koochaki e-mail: [email protected]
of the most efficient equipment in treating the end stage heart failure is the ventricular assist device (VAD). They are clinically used as a bridge to transplantation and even as a long-term destination therapy. In a broad classification, VADs are subdivided into two major categories, rotary blood pump (RBP) and positive displacement blood pump (DBP), also they are known as continuous and pulsatile blood pump respectively. In general, DBPs are pulsatile flow devices which have flexible membranes, pusher plates and several valves. On the contrary, RBPs produce continuous blood flow with no membrane or valves. RBPs are mostly classified as radial flow, axial flow, and mixed flow rotary pumps [2]. The advantages and disadvantages of axial versus centrifugal VADs are still in dispute. Today, the authors believe that there are more advantages for the axial flow design, for example: it is much smaller [2], so it could easily be implanted in the body. In new designed axial blood pumps, mechanical bearings are replaced by magnetic ones, consequently, the red blood cells damages would greatly decrease by omitting mechanical contact parts. Unfortunately the main deficiency of these pumps is their high rotating speed needed to supply required flow rate [2]. Higher rotor speeds generate a higher magnitude of shear stress, which would result in hemolysis [3]. The destruction or dissolution of the red blood cells, along with the release of hemoglobin is called hemolysis. Since the shear stress imposed on the red blood cells and its exposure time are two important parameters which determine hemolysis, so many studies have been conducted in this field and the critical shear stress and exposure time have been defined completely [3, 4]. In designing a blood pump, these two parameters should be closely observed to avoid hemolysis. Also, blood pumps should be designed to
123
418
deliver streamlined, idealized blood flow with no stagnation point in its domain to avoid thrombosis. Today, anyone can ever deny the significance of the CFD as a powerful technique to simulate flow field in axial blood pumps and other VAD types [4–9]. For example Song et al. [10] were successful in applying this approach and predicted results were close to the observed data in the experimental tests. The authors of the present paper have attempted to design a new smaller axial blood pump with streamlined blood flow path that can deliver 100 mmHg pressure rise (head) at 6 L/min volume flow rate. The pump was totally suspended by magnetic bearings (MBs). These bearings have no moving parts so regions of stagnant and high shear flow reduced.
Materials and methods To conduct the study, both theoretical analysis and numerical simulation were applied. This is a common combination in most VAD designs. Turbomachinery theoretical analysis was applied to design the pump’s blades geometry and also to bring the basic idea for pump miniaturizing in practice. Numerical simulation was used not only to predict flow pattern but also to calculate pump performance. Pump design theory In order to achieve a compact pump design for the sake of less invasive implantation, the overall size of the device becomes the most important limitation during the design phase. For the same pressure and capacity requirements, the pump’s operational speed is inversely proportional to the size of the pump; thus, a smaller pump corresponds to a higher rotational speed of the impeller except that the impeller volume region remains constant. Impeller is the most important part of an axial pump mainly because it receives energy from motor and delivers it to the fluid. The fluid volume in this region is obtained by: 2 Vi ¼ p rsh rh2 Li In this formula, Vi denotes to fluid volume in the impeller region, rsh and rh are impeller shroud and hub radius, respectively and Li depicts the length of the impeller. According to this equation, the impeller volume depends on radius squared. Thus, the volume does not change, if the length of the impeller decreases greatly; however, its radius increases a little. Applying this method, the length of the impeller was reduced; subsequently, it caused great reduction in the pump overall size. It should be noted that small thoracic space is a limiting factor in
123
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changing pump diameter-length ratio that should be taken into account; therefore, the impeller blade height should be increased wisely. Obviously, in impeller designing procedure, the blade geometry is crucial. Basically, the blade geometry is defined by airfoil [11]. A slight change in the impeller blade curvature would significantly influence pump performance. In this project, after strict testing of many airfoil profiles, the best one was selected. Due to some characteristics, the NACA 44 series are used for the impeller blade design [12]. Pump geometrical parameters The pump designing principles is derived from other RBPs. Song and Untaroiu et.al [9, 10, 13] conducted a comprehensive study on axial blood pump structures. They determined the most adequate numbers of blades for impeller, diffuser and inducer. Generally, our pump has four sections: inducer, impeller, diffuser and straightener. Inducer blades remove swirling flows in the inflow fluid. Impeller blades receive energy from motor and deliver it to the fluid. The flow velocity is converted to pressure in the diffuser due to its blades and channel geometry. Straightener is used to improve pump performance by reducing flow swirling velocity. Figure 1 shows the pump overall geometry. Pump design considerations are presented in Table 1. Software and designing procedure All geometry designing, grid generation and fluid analysis were accomplished in ANSYS. The blade and pump geometry were designed via BladeGen. The TurboGrid module was used to generate suitable structure grids and finally the fluid domain was analyzed in CFX. Discretization of the governing equations was performed using a second order type and the residual target has been considered to be 10-4 for the sake of accuracy. Some researchers have discussed the important role of turbulence and its dominant effect on these pumps. Apel et al. [5] found that ‘‘the convergent solution could only be accomplished by the use of turbulence models’’. In this simulation, the turbulence blood flow was characterized by performing the standard k-e two-equation model. This model was successfully applied to the design of other numerous blood pumps [13–16]. Based on published data [17, 18], when the blood shear stress is high ([0.7 Pa) and its shear rate is more than 100 s-1, it will behave as Newtonian fluids. In this computational model, the above condition was satisfied, so the assumption of Newtonian fluid properties is completely reasonable hence a constant
Australas Phys Eng Sci Med (2013) 36:417–422
419
Fig. 1 Pump overall geometry right to left. 1 inducer 2 impeller 3 diffuser 4 straightener
Table 1 Pump design considerations Region
Blade number
Length (mm)
Blade height (mm)
Inducer
6
12
0.3–0.7
Table 3 Grid independency investigation according to important parameters in the simulation Number of mesh elements
Flow rate (L/min)
Maximum wall shear stress (Pa)
Impeller
4
35.5
3
Diffuser
5
7.5
3
1,392,405
2.94
381
3–4
2,148,472
3.88
370
2,551,481
4.31
375
2,928,612
4.73
368
3,051,215
4.81
367
Straightener
3
10
viscosity of 0.0035 kg/m*s and density of 1,050 kg/m3 was used for blood flow simulation, corresponding to hematocrit of approximately 33 %, which is reasonable for this condition [9]. The simulation was performed in parallel, on 8 core of a computer system. In this case, each single simulation takes about 8–10 h to converge. Mesh information and grid study To accomplish an acceptable computational accuracy 2,928,612 total mesh elements have been generated for pump modeling. The mesh element densities in different regions of the pump are listed in Table 2. One of the crucial aspects in CFD modeling is the number of mesh elements used in simulation. A correct simulation should be independent from the number of mesh elements in its domain called ‘‘grid independency’’. In this Table 2 Grid density in the pump individual components Region Inducer
Mesh element density 718,164
Impeller
1,272,560
Diffuser
599,080
Straightener
338,808
Overall pump
2,928,612
study, to address grid independency, five cases with different number of mesh elements were simulated and, their flow rate and maximum wall shear stress which are the most significant parameters in this study were examined and compared with each other. The obtained results are presented in Table 3. According to this table, it can be clearly found out that the best and sufficient mesh element number is 2,928,612.
Results and discussion In this study, hydraulic characteristics such as hydraulic efficiency and pressure-flow performance curves have been determined numerically for a range of pump operating conditions. The detailed results of the CFD analysis for new proposed miniature blood pump will be discussed in the following sections. Pressure performance curves The flow rate across the pump has been calculated for pressure rise of 70–135 mmHg and rotational speeds of 6,000–6,500 rpm. Figure 2 reveals the pressure performance
123
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Australas Phys Eng Sci Med (2013) 36:417–422
Fig. 2 Pump performance curve Fig. 4 Axial force exerted on the impeller
curves for this computational model. Each data point corresponds to a steady state simulation for a specific flow rate and rotational speed. The pump flow rate for a given rotational speed increased with decreasing pressure rise as expected according to theories. A flow rate range between 0 and 11 L/ min has been achieved under these operating conditions. The pressure performance curves demonstrate the pump’s ability to deliver adequate flow with the desired pressure rise. Fluid efficiency The hydraulic efficiency for each simulation was calculated according to following relation: m_ P2 P1 g¼ q Mx In this equation g is the power efficiency, m is the mass flow rate, q is the fluid density, M is the applied mechanical load and x signifies the rotational speed. Also P2 and P1 represent the total pressure at the pump outlet and inlet respectively [13]. Figure 3 depicts the efficiency performance curve for this pump. The best efficiency points for the given operating conditions obtained through CFD results are between 15 and 30 %, which are typical efficiencies for these types of blood pumps [5, 9, 20].
Fig. 5 Radial force exerted on impeller
Axial and radial fluid forces To design MBs, the axial and radial forces exerted on the impeller must be determined and remain in the reasonable range for various operating conditions. Figures 4 and 5 depict the computed axial and radial fluid forces on the pump impeller. These figures show that radial and axial forces exerted on the impeller region are in the reasonable range. Flow profile The fluid flow patterns throughout the VADs are extremely important. Any irregular flow pattern or reverse flow in any part of the pump can cause blood thrombosis. Figure 6 shows blood streamlines throughout the pump. As expected, these streamlines demonstrate no sign of separation, vortices or reverse flow except for a slight flow distortion in the interface region of stationary and rotating parts. Wall shear stress
Fig. 3 Hydraulic efficiency curves
123
The wall shear stress has been analyzed by two methods. First, maximum shear stress and the blood exposure time in this stress have been calculated. Then, the statistical analysis
Australas Phys Eng Sci Med (2013) 36:417–422
421
Fig. 6 Fluid stream lines in the pump at 6,250 rpm rotational speed and 100 mmHg pressure
Fig. 7 The wall shear stress along the pump at 6,250 rpm rotational speed and 100 mmHg pressure
70
shear stress (Pa)
was applied on numerical shear stress data in order to calculate the upper band of the shear stress through the pump. The results show the maximum shear stress within the range of 360–470 Pa at 6,250 rpm. Its exposure time was approximately 0.02 s. Figure 7 depicts wall shear stress throughout the pump. The maximum wall shear stress is observed only in a small region on the diffuser blade, since rotating fluid exiting the impeller region contacts the immobile diffuser blades. To make sure that the maximum shear stress occurs only in a small region of the pump, the average wall shear stress has been calculated in the axial cross section of the pump. Figure 8 depicts these average data at 6,250 rpm rotational
60 50 40 30 20 10 0 0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
The location of the pump cross section (m)
Fig. 8 The average wall axial cross section shear stress in the pump
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Australas Phys Eng Sci Med (2013) 36:417–422
Table 4 Flow rate, pressure head, rotational speed at design point and dimensions of various axial blood pumps Pump
Flow rate (lpm)
Pressure (mmHg)
Rotational speed (rpm)
Diameter (mm)
Length (mm)
NIVADIII
5
100
8,000
–
–
INCOR
5
70
7,500
30
120
LEV-VAD2
6
100
7,000
35
115
Present VAD
6
100
6,250
40
65
speed and 100 mmHg pressure head through the pump. The mean and upper bands of these data are 25 and 48 Pa, respectively. The upper band is calculated by summing the mean and standard deviation. In this case, the maximum exposure time calculated for the red blood cells in the pump was 0.2301 s. According to the literature reports, these measured shear stress and exposure times would not cause any serious damage on the red blood cells [17, 19]. Hence, our designed pump works at a completely safe domain. Comparison Table 3 compares the design point and dimensions of the present VAD and three other VADs [6, 9, 20]. They are several axial blood pumps which produce the same range of flow rates and pressure heads; however, their rotational speed is different. The present pump was designed to work at 6,250 rpm which is lower than that of others, so the risk of hemolysis occurrence is much lower, therefore the pump is more reliable. The overall length and diameter of the pump are 65 and 40 mm, respectively. Comparing these dimensions with those of other axial blood pumps [9], the length decreased 43.47 %; however, the diameter increased 14.28 %. These values indicate that how this design optimizes overall blood pump dimensions for implanting (Table 4). Conclusions Applying turbo-machinery theories and CFD, a new miniature axial blood flow pump was designed. In this design, the pump length was reduced by means of increasing the pump diameter, so that it could easily be implanted in the body. Moreover, in order to meet biological objectives for these new dimensions, novel blade geometry was designed. The pump performance and efficiency curves were calculated, also axial and radial forces exerted on the impeller were computed to design pump MBs. The analysis of blood flow paths and wall shear stress in the pump revealed that this pump would not cause any serious blood damages so it should operate as a safe VAD.
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References 1. Writing Group Members (2012) Heart disease and stroke statistics’’2012 update. Circulation 125(1):e2–e220 2. Timms D (2011) A review of clinical ventricular assist devices. Med Eng Phys 33(9):1041–1047 3. Arora D et al (2004) A Tensor-based measure for estimating blood damage. Artif Organs 28(11):1002–1015 4. Behbahani M et al (2009) A review of computational fluid dynamics analysis of blood pumps. Eur J Appl Math 20(04): 363–397 5. Apel Jr et al (2001) Computational fluid dynamics and experimental validation of a microaxial blood pump. ASAIO J 47(5):552–558 6. Fan H-M et al (2010) Applications of CFD technique in the design and flow analysis of implantable axial flow blood pump. J Hydrodynam Ser B 22(4):518–525 7. Swalen MJP (2012) Study of a bi-directional axial flow blood pump, in School of Engineering & Design. Brunel University, p 165 8. Timms DL (2005) Design, development and evaluation of centrifugal ventricular assist devices. Queensland University of Technology, School of Engineering Systems 9. Untaroiu A (2006) LEV-VAD2 axial flow blood pump: optimized flow path design by means of computational fluid dynamics. University of Virginia, Charlottesville 10. Song X et al (2004) Design and transient computational fluid dynamics study of a continuous axial flow ventricular assist device. ASAIO J 50(3):215–224 11. Turton RK (1984) Principles of turbomachinery. E & FN Spon 12. Shirani E (2000) Turbomachines. Isfahan University of Technology Publication 13. Untaroiu A et al (2005) Numerical and experimental analysis of an axial flow left ventricular assist device: the influence of the diffuser on overall pump performance. Artif Organs 29(7): 581–591 14. Anderson J et al (2000) Numerical analysis of blood flow in the clearance regions of a continuous flow artificial heart pump. Artif Organs 24(6):492–500 15. Curtas A et al (2000) CFD modeling of impeller designs for Heartquest Lvad. ASAIO J 46(2):188 16. Miyazoe Y et al (1998) Computational fluid dynamic analyses to establish design process of centrifugal blood pumps. Artif Organs 22(5):381–385 17. Paul R et al (2003) Shear stress related blood damage in laminar couette flow. Artif Organs 27(6):517–529 18. Wells RE, Merrill EW (1961) Shear rate dependence of the viscosity of whole blood and plasma. Science 133(3455): 763–764 19. Bacher RP, Williams MC (1970) Hemolysis in capillary flow. J Lab Clin Med 76(3):485–496 20. INCOR PUMP, industrial catalog, page 2
SCIENTIFIC PAPER
A new design and computational fluid dynamics study of an implantable axial blood pump Mojtaba Koochaki • Hanieh Niroomand-Oscuii
Received: 18 February 2013 / Accepted: 21 October 2013 / Published online: 8 November 2013 Ó Australasian College of Physical Scientists and Engineers in Medicine 2013
Abstract Considering small thoracic space, using implantable ventricular assist device requires reduction in a pump size. Among many available blood pumps, axial blood pumps have attracted greatly because of their small size. In this article, a new miniature axial blood pump has been designed and studied which can be easily implanted in the human body. In this design, the pump overall length decreased by a little increasing in the pump diameter, and new blade geometry is used to produce a streamlined, idealized, and nonobstructing blood flow path in the pump. By means of computational fluid dynamic, the flow pattern through the pump has been predicted and overall pump performance and efficiency has been computed. Also, to ensure a reliable VAD design, two methods for checking wall shear stress were used to confirm that this pump wouldn’t cause serious blood damage. Keywords Blood pump Ventricular assist device Axial pump Cardiac disease Heart pump
Introduction Nowadays cardiovascular diseases (CVDs) are one of the most important causes of death all over the world. ‘‘Since 1900 except 1918, in every year, CVD have accounted for more deaths than any other major causes of death in the United States’’ [1]. ‘‘An estimated 82,600,000 American adults ([1 in 3) have one or more types of CVD’’ [1]. One M. Koochaki H. Niroomand-Oscuii (&) Sahand University of Technology, Sahand, Iran e-mail: [email protected] M. Koochaki e-mail: [email protected]
of the most efficient equipment in treating the end stage heart failure is the ventricular assist device (VAD). They are clinically used as a bridge to transplantation and even as a long-term destination therapy. In a broad classification, VADs are subdivided into two major categories, rotary blood pump (RBP) and positive displacement blood pump (DBP), also they are known as continuous and pulsatile blood pump respectively. In general, DBPs are pulsatile flow devices which have flexible membranes, pusher plates and several valves. On the contrary, RBPs produce continuous blood flow with no membrane or valves. RBPs are mostly classified as radial flow, axial flow, and mixed flow rotary pumps [2]. The advantages and disadvantages of axial versus centrifugal VADs are still in dispute. Today, the authors believe that there are more advantages for the axial flow design, for example: it is much smaller [2], so it could easily be implanted in the body. In new designed axial blood pumps, mechanical bearings are replaced by magnetic ones, consequently, the red blood cells damages would greatly decrease by omitting mechanical contact parts. Unfortunately the main deficiency of these pumps is their high rotating speed needed to supply required flow rate [2]. Higher rotor speeds generate a higher magnitude of shear stress, which would result in hemolysis [3]. The destruction or dissolution of the red blood cells, along with the release of hemoglobin is called hemolysis. Since the shear stress imposed on the red blood cells and its exposure time are two important parameters which determine hemolysis, so many studies have been conducted in this field and the critical shear stress and exposure time have been defined completely [3, 4]. In designing a blood pump, these two parameters should be closely observed to avoid hemolysis. Also, blood pumps should be designed to
123
418
deliver streamlined, idealized blood flow with no stagnation point in its domain to avoid thrombosis. Today, anyone can ever deny the significance of the CFD as a powerful technique to simulate flow field in axial blood pumps and other VAD types [4–9]. For example Song et al. [10] were successful in applying this approach and predicted results were close to the observed data in the experimental tests. The authors of the present paper have attempted to design a new smaller axial blood pump with streamlined blood flow path that can deliver 100 mmHg pressure rise (head) at 6 L/min volume flow rate. The pump was totally suspended by magnetic bearings (MBs). These bearings have no moving parts so regions of stagnant and high shear flow reduced.
Materials and methods To conduct the study, both theoretical analysis and numerical simulation were applied. This is a common combination in most VAD designs. Turbomachinery theoretical analysis was applied to design the pump’s blades geometry and also to bring the basic idea for pump miniaturizing in practice. Numerical simulation was used not only to predict flow pattern but also to calculate pump performance. Pump design theory In order to achieve a compact pump design for the sake of less invasive implantation, the overall size of the device becomes the most important limitation during the design phase. For the same pressure and capacity requirements, the pump’s operational speed is inversely proportional to the size of the pump; thus, a smaller pump corresponds to a higher rotational speed of the impeller except that the impeller volume region remains constant. Impeller is the most important part of an axial pump mainly because it receives energy from motor and delivers it to the fluid. The fluid volume in this region is obtained by: 2 Vi ¼ p rsh rh2 Li In this formula, Vi denotes to fluid volume in the impeller region, rsh and rh are impeller shroud and hub radius, respectively and Li depicts the length of the impeller. According to this equation, the impeller volume depends on radius squared. Thus, the volume does not change, if the length of the impeller decreases greatly; however, its radius increases a little. Applying this method, the length of the impeller was reduced; subsequently, it caused great reduction in the pump overall size. It should be noted that small thoracic space is a limiting factor in
123
Australas Phys Eng Sci Med (2013) 36:417–422
changing pump diameter-length ratio that should be taken into account; therefore, the impeller blade height should be increased wisely. Obviously, in impeller designing procedure, the blade geometry is crucial. Basically, the blade geometry is defined by airfoil [11]. A slight change in the impeller blade curvature would significantly influence pump performance. In this project, after strict testing of many airfoil profiles, the best one was selected. Due to some characteristics, the NACA 44 series are used for the impeller blade design [12]. Pump geometrical parameters The pump designing principles is derived from other RBPs. Song and Untaroiu et.al [9, 10, 13] conducted a comprehensive study on axial blood pump structures. They determined the most adequate numbers of blades for impeller, diffuser and inducer. Generally, our pump has four sections: inducer, impeller, diffuser and straightener. Inducer blades remove swirling flows in the inflow fluid. Impeller blades receive energy from motor and deliver it to the fluid. The flow velocity is converted to pressure in the diffuser due to its blades and channel geometry. Straightener is used to improve pump performance by reducing flow swirling velocity. Figure 1 shows the pump overall geometry. Pump design considerations are presented in Table 1. Software and designing procedure All geometry designing, grid generation and fluid analysis were accomplished in ANSYS. The blade and pump geometry were designed via BladeGen. The TurboGrid module was used to generate suitable structure grids and finally the fluid domain was analyzed in CFX. Discretization of the governing equations was performed using a second order type and the residual target has been considered to be 10-4 for the sake of accuracy. Some researchers have discussed the important role of turbulence and its dominant effect on these pumps. Apel et al. [5] found that ‘‘the convergent solution could only be accomplished by the use of turbulence models’’. In this simulation, the turbulence blood flow was characterized by performing the standard k-e two-equation model. This model was successfully applied to the design of other numerous blood pumps [13–16]. Based on published data [17, 18], when the blood shear stress is high ([0.7 Pa) and its shear rate is more than 100 s-1, it will behave as Newtonian fluids. In this computational model, the above condition was satisfied, so the assumption of Newtonian fluid properties is completely reasonable hence a constant
Australas Phys Eng Sci Med (2013) 36:417–422
419
Fig. 1 Pump overall geometry right to left. 1 inducer 2 impeller 3 diffuser 4 straightener
Table 1 Pump design considerations Region
Blade number
Length (mm)
Blade height (mm)
Inducer
6
12
0.3–0.7
Table 3 Grid independency investigation according to important parameters in the simulation Number of mesh elements
Flow rate (L/min)
Maximum wall shear stress (Pa)
Impeller
4
35.5
3
Diffuser
5
7.5
3
1,392,405
2.94
381
3–4
2,148,472
3.88
370
2,551,481
4.31
375
2,928,612
4.73
368
3,051,215
4.81
367
Straightener
3
10
viscosity of 0.0035 kg/m*s and density of 1,050 kg/m3 was used for blood flow simulation, corresponding to hematocrit of approximately 33 %, which is reasonable for this condition [9]. The simulation was performed in parallel, on 8 core of a computer system. In this case, each single simulation takes about 8–10 h to converge. Mesh information and grid study To accomplish an acceptable computational accuracy 2,928,612 total mesh elements have been generated for pump modeling. The mesh element densities in different regions of the pump are listed in Table 2. One of the crucial aspects in CFD modeling is the number of mesh elements used in simulation. A correct simulation should be independent from the number of mesh elements in its domain called ‘‘grid independency’’. In this Table 2 Grid density in the pump individual components Region Inducer
Mesh element density 718,164
Impeller
1,272,560
Diffuser
599,080
Straightener
338,808
Overall pump
2,928,612
study, to address grid independency, five cases with different number of mesh elements were simulated and, their flow rate and maximum wall shear stress which are the most significant parameters in this study were examined and compared with each other. The obtained results are presented in Table 3. According to this table, it can be clearly found out that the best and sufficient mesh element number is 2,928,612.
Results and discussion In this study, hydraulic characteristics such as hydraulic efficiency and pressure-flow performance curves have been determined numerically for a range of pump operating conditions. The detailed results of the CFD analysis for new proposed miniature blood pump will be discussed in the following sections. Pressure performance curves The flow rate across the pump has been calculated for pressure rise of 70–135 mmHg and rotational speeds of 6,000–6,500 rpm. Figure 2 reveals the pressure performance
123
420
Australas Phys Eng Sci Med (2013) 36:417–422
Fig. 2 Pump performance curve Fig. 4 Axial force exerted on the impeller
curves for this computational model. Each data point corresponds to a steady state simulation for a specific flow rate and rotational speed. The pump flow rate for a given rotational speed increased with decreasing pressure rise as expected according to theories. A flow rate range between 0 and 11 L/ min has been achieved under these operating conditions. The pressure performance curves demonstrate the pump’s ability to deliver adequate flow with the desired pressure rise. Fluid efficiency The hydraulic efficiency for each simulation was calculated according to following relation: m_ P2 P1 g¼ q Mx In this equation g is the power efficiency, m is the mass flow rate, q is the fluid density, M is the applied mechanical load and x signifies the rotational speed. Also P2 and P1 represent the total pressure at the pump outlet and inlet respectively [13]. Figure 3 depicts the efficiency performance curve for this pump. The best efficiency points for the given operating conditions obtained through CFD results are between 15 and 30 %, which are typical efficiencies for these types of blood pumps [5, 9, 20].
Fig. 5 Radial force exerted on impeller
Axial and radial fluid forces To design MBs, the axial and radial forces exerted on the impeller must be determined and remain in the reasonable range for various operating conditions. Figures 4 and 5 depict the computed axial and radial fluid forces on the pump impeller. These figures show that radial and axial forces exerted on the impeller region are in the reasonable range. Flow profile The fluid flow patterns throughout the VADs are extremely important. Any irregular flow pattern or reverse flow in any part of the pump can cause blood thrombosis. Figure 6 shows blood streamlines throughout the pump. As expected, these streamlines demonstrate no sign of separation, vortices or reverse flow except for a slight flow distortion in the interface region of stationary and rotating parts. Wall shear stress
Fig. 3 Hydraulic efficiency curves
123
The wall shear stress has been analyzed by two methods. First, maximum shear stress and the blood exposure time in this stress have been calculated. Then, the statistical analysis
Australas Phys Eng Sci Med (2013) 36:417–422
421
Fig. 6 Fluid stream lines in the pump at 6,250 rpm rotational speed and 100 mmHg pressure
Fig. 7 The wall shear stress along the pump at 6,250 rpm rotational speed and 100 mmHg pressure
70
shear stress (Pa)
was applied on numerical shear stress data in order to calculate the upper band of the shear stress through the pump. The results show the maximum shear stress within the range of 360–470 Pa at 6,250 rpm. Its exposure time was approximately 0.02 s. Figure 7 depicts wall shear stress throughout the pump. The maximum wall shear stress is observed only in a small region on the diffuser blade, since rotating fluid exiting the impeller region contacts the immobile diffuser blades. To make sure that the maximum shear stress occurs only in a small region of the pump, the average wall shear stress has been calculated in the axial cross section of the pump. Figure 8 depicts these average data at 6,250 rpm rotational
60 50 40 30 20 10 0 0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
The location of the pump cross section (m)
Fig. 8 The average wall axial cross section shear stress in the pump
123
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Australas Phys Eng Sci Med (2013) 36:417–422
Table 4 Flow rate, pressure head, rotational speed at design point and dimensions of various axial blood pumps Pump
Flow rate (lpm)
Pressure (mmHg)
Rotational speed (rpm)
Diameter (mm)
Length (mm)
NIVADIII
5
100
8,000
–
–
INCOR
5
70
7,500
30
120
LEV-VAD2
6
100
7,000
35
115
Present VAD
6
100
6,250
40
65
speed and 100 mmHg pressure head through the pump. The mean and upper bands of these data are 25 and 48 Pa, respectively. The upper band is calculated by summing the mean and standard deviation. In this case, the maximum exposure time calculated for the red blood cells in the pump was 0.2301 s. According to the literature reports, these measured shear stress and exposure times would not cause any serious damage on the red blood cells [17, 19]. Hence, our designed pump works at a completely safe domain. Comparison Table 3 compares the design point and dimensions of the present VAD and three other VADs [6, 9, 20]. They are several axial blood pumps which produce the same range of flow rates and pressure heads; however, their rotational speed is different. The present pump was designed to work at 6,250 rpm which is lower than that of others, so the risk of hemolysis occurrence is much lower, therefore the pump is more reliable. The overall length and diameter of the pump are 65 and 40 mm, respectively. Comparing these dimensions with those of other axial blood pumps [9], the length decreased 43.47 %; however, the diameter increased 14.28 %. These values indicate that how this design optimizes overall blood pump dimensions for implanting (Table 4). Conclusions Applying turbo-machinery theories and CFD, a new miniature axial blood flow pump was designed. In this design, the pump length was reduced by means of increasing the pump diameter, so that it could easily be implanted in the body. Moreover, in order to meet biological objectives for these new dimensions, novel blade geometry was designed. The pump performance and efficiency curves were calculated, also axial and radial forces exerted on the impeller were computed to design pump MBs. The analysis of blood flow paths and wall shear stress in the pump revealed that this pump would not cause any serious blood damages so it should operate as a safe VAD.
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