Best Practice Advice AC7-03: Difference between revisions

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'''For LES:'''
'''For LES:'''


* In order to guarantee that most of turbulence within the VAD is directly resolved, a special treatment of the computational grid is necessary. This is especially the case for the near-wall resolution, since the energy-containing vortices, which need to be resolved by LES, scale linearly inverse with the wall distance. In order to resolve these vortices, a high grid resolution in all spatial directions is necessary. Therefore, we orient the grid characteristics on literature recommendations for wall-resolving LES, with a near-wall grid, which fitted the upper limits of <math> \Delta_x^+ \leq 50 </math> and <math> \Delta_z^+ \leq 20 </math> for the grid widths in the flow and spanwise direction. Furthermore, the first wall-normal node had a maximal dimensionless distance of <math> y_1^+  \leq  1 </math> and the grid growth factor was <math> r_g = 1.05 </math> near the wall. Additionally, further grid quality measures should be kept, to minimize discretization errors and obtain a proper convergence behavior. Grid angles should be larger than 20, aspect ratios smaller than 5 in the core flow region and the mesh expansion factor smaller than 20. Furthermore, the interfaces between the single domain are created as evenly as possible, in order to guarantee a smooth progression of the transported flow variables across the interfaces.
* In order to guarantee that most of the turbulence within the VAD is directly resolved, special consideration must be given to the computational grid. This is especially the case for the near-wall resolution, since the energy-containing eddies, which need to be resolved by LES, scale linearly with the wall distance. In order to resolve these eddies, a high grid resolution in all spatial directions is necessary. Therefore, the grid characteristics should follow the literature recommendations for wall-resolving LES, with a near-wall grid, which observes the upper limits of <math> \Delta_x^+ \leq 50 </math> and <math> \Delta_z^+ \leq 20 </math> for the grid sizes in the flow and spanwise direction. Furthermore, the first wall-normal node should have a maximum dimensionless distance of <math> y_1^+  \leq  1 </math> and the grid growth factor should not exceed <math> r_g = 1.05 </math> near the wall. Additionally, further grid quality measures should be kept to minimize discretization errors and obtain a proper convergence behavior. Grid angles should be larger than 20, aspect ratios smaller than 5 in the core flow region and the mesh expansion factor smaller than 20. Furthermore, the interfaces between the rotor-stator domains must be created as evenly as possible, in order to guarantee a smooth progression of the transported flow variables across the interfaces.


* An excellent overview about modeling (using frequency spectra) and resolution evaluation for general LES application is given in Ref. [12]. Some of these verification methods were applied in section [[CFD Simulations AC7-03|CFD Simulations]] to the LES in the VAD's flow.
* An excellent overview about modeling (using frequency spectra) and resolution evaluation for general LES application is given in Ref. [12]. Some of these verification methods were applied in section [[CFD Simulations AC7-03|CFD Simulations]] to the LES in the VAD's flow.

Revision as of 10:54, 24 October 2022

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Turbulent Blood Flow in a Ventricular Assist Device

Application Challenge AC7-03   © copyright ERCOFTAC 2021

Best Practice Advice

Key Fluid Physics

Flow Physics

The flow in a rotary blood pump is characterized by an interaction of the "idealized" primary flow (blade congruent, uniform, on circular-cylindrical paths) with secondary flows in the rotor and stator [27]. These secondary flows arise from rotational effects (Coriolis forces, centrifugal forces), from transient processes (e.g., rotor-stator intercation), in gaps, or in viscous boundary layers [35,36]. The processes lead to a three-dimensional, vortical and complex VAD flow with physiologically significant turbulent stresses in the pump blade channels (see sections Description and Evaluation)).


Fluid Physics

When calculating blood flow through complex medical devices, it should always be kept in mind that blood is a non-Newtonian, multiphase fluid. However, in simulations in rotary blood pumps, blood is always approximated as a Newtonian, single-phase fluid. The former is justified because the viscosity reached a asymptotic behaviour under high shear rates. In the latter, a blood-analogous fluid is assumed, which has density and viscosity comparable values to blood. This assumption is necessary because it is impossible with current computational technology to account for the multiphase character of blood in a VAD simulation. This is partly due to the fact that the dimensions of the blood components are much smaller than the vortex structures calculated by the simulation. Therefore, much larger computational grids than used in the current literature are needed to integrate the blood components (size order of erythrocytes of the order ) in the simulation.

Application Uncertainties

Experimental Uncertainties

There are some uncertainties that can explain the differences between experimental and numerical results:

  • It is important that the experimental validation uses a blood analogue fluid that adequately represents the simulated fluid properties. In this study, a mixture of glycerol-water is often used, which has a density 5% greater than that of the numerical fluid. Despite the same dynamic viscosity, this has an impact on the VAD flow field, since the density in the conservation equations is coupled to the pressure of the fluid. The deviation for the head is estimated to be ≈ 3 mmHg for the present case.
  • An additional deviation in the head is caused by the influence of the rotating shaft on the flow in the model. The shaft induces an additional swirl in the flow and also "blocks" part of the outflow cannula. From URANS calculations of the VAD with rotating shaft, deviations in in the head of ≤ 1 mmHg were determined.
  • Furthermore, geometric differences are inevitably present in the experimental model, such as axial gaps between the rotating and stationary regions, which do not exist in the numerical model. These geometric differences will alter the flow field in the experimental pump to some extent compared to the numerical flow, but are generally difficult to estimate.

Numerical Uncertainties

In this KB wiki entry, the VAD flow is considered at constant operating points (constant volume flow and constant speeds), which is typical for flow analysis in preclinical design of VADs. In reality, the VAD may be exposed to constantly varying inflow conditions if the diseased heart has residual activity [27]. Due to the constant acceleration and deceleration in the pulsatile flow, the flow and stress field in the VAD will also change in time [33]. In recent years, there has been a positive trend towards numerical investigations with pulsatile inflow. However, the boundary conditions for the VAD must be accurately defined here, since the VAD interacts in a reciprocal manner with the cardiovascular system.

The numerical uncertainties due to the grid with URANS in the calculation of fluid mechanical and hemodynamical parameters will be explained later.

Computational Domain and Boundary Conditions

Certain conditions have to be considered for domain size and boundary condition assignment:

  • For the analysis, straight inflow and outflow cannulas are included. These cannulas should extented sufficiently far (four and seven times the impeller diameter, respectively) from the guide vanes. Preliminary URANS studies in Ref. [37] have shown that the used distances are sufficient in order to prevent negative influences of the boundary conditions on the results.
  • It is reasonable that no turbulent perturbations are given at the inlet of the domain. This point is valid, since the Reynolds number was in the inflow cannula and any disturbances cannot be estimated upstream of the inflow cannula. Thus, no transitional flow structures in form of turbulent puffs should be present in the inflow region.
  • A constant flow rate should be defined at the outlet - and not at the inlet - of the domain, to guarantee that eddies with non-uniform pressure distribution can pass the outlet.

Discretisation and Grid Resolution

For LES:

  • In order to guarantee that most of the turbulence within the VAD is directly resolved, special consideration must be given to the computational grid. This is especially the case for the near-wall resolution, since the energy-containing eddies, which need to be resolved by LES, scale linearly with the wall distance. In order to resolve these eddies, a high grid resolution in all spatial directions is necessary. Therefore, the grid characteristics should follow the literature recommendations for wall-resolving LES, with a near-wall grid, which observes the upper limits of and for the grid sizes in the flow and spanwise direction. Furthermore, the first wall-normal node should have a maximum dimensionless distance of and the grid growth factor should not exceed near the wall. Additionally, further grid quality measures should be kept to minimize discretization errors and obtain a proper convergence behavior. Grid angles should be larger than 20, aspect ratios smaller than 5 in the core flow region and the mesh expansion factor smaller than 20. Furthermore, the interfaces between the rotor-stator domains must be created as evenly as possible, in order to guarantee a smooth progression of the transported flow variables across the interfaces.
  • An excellent overview about modeling (using frequency spectra) and resolution evaluation for general LES application is given in Ref. [12]. Some of these verification methods were applied in section CFD Simulations to the LES in the VAD's flow.

For URANS:

  • The extended grid convergence study shows that discretization errors are significant for blood damage prediction based on the effective stresses. Even when the similation indicates a small discretization error for the pump characteristics, the error can be significant for the blood damage prediction results.
  • The generally coarser grid resolution - especially in the near-wall region - leads to lower values for blood damage compared to the results computed with LES.

Physical Modelling

The fluid mechanical evaluation of the pump characteristics (head, efficiency) shows that the URANS can satisfactorily reproduce these quantities with the applied setup. However, for the hemodynamic evaluation, the similarity in stress progression depending on the operation point. At the partial load point, the equivalent stresses are similar to LES and the blood damage prediction results deviate less between both methods. At the nominal operation point, the deviations in equivalent stresses are larger, which also leads to larger differences in the blood damage prediction. Despite the quantitative differences between URANS and LES, a modeled turbulent parameter from the URANS turbulence model should always be included in the shear stress definition (Equation (6.2.)). Otherwise the difference to the reference will be even larger, which could massively bias the blood damage prediction (see stresses larger than 9 Pa in Table 5.3 and 5.4 in Evaluation).

Recommendations for Future Work

Two recommendations can be made on the experimental and numerical side:

  • On the one hand, it would be worthwhile to have more experimental validation data, e.g. of the turbulent kinetic energy, in order to perform a fluid mechanical investigation and validation of these quantities in the VAD as well.
  • On the other hand, hybrid URANS-LES models appear suitable to fill the trade-off between high accuracy (LES) and low computation time (URANS). It would be interesting to see how a hybrid LES model computes the hemodynamical parameters compared to the presented methods.

References

[1] Weiss, John (1991): The dynamics of enstrophy transfer in two-dimensional hydrodynamics. In: Physica D: Nonlinear Phenomena 48 (2-3), pp. 273–294. https://doi.org/10.1016/0167-2789(91)90088-Q.

[2] Torner, B.; Konnigk, L.; Abroug, N.; Wurm, F.-H. (2020): Turbulence and Turbulent Flow Structures in a Ventricular Assist Device. In: International Journal for Numerical Methods in Biomedical Engineering 37(3), e3431. https://doi.org/10.1002/cnm.3431

[3] Yu, Hai; Engel, Sebastian; Janiga, Gábor; Thévenin, Dominique (2017): A Review of Hemolysis Prediction Models for Computational Fluid Dynamics. In: Artificial Organs 41 (7), pp. 603–621. https://doi.org/10.1111/aor.12871.

[4] Thamsen, B.; Blumel, B.; Schaller, J.; Paschereit, C.O.; Affeld, K.; Goubergrits, L.; Kertzscher, U. (2015): Numerical Analysis of Blood Damage Potential of the HeartMate II and HeartWare HVAD Rotary Blood Pumps. In: Artificial Organs 39 (8), pp. 651–659. https://doi.org/10.1111/aor.12542.

[5] Wiegmann, L.; Boës, S.; Zélicourt, D. de; Thamsen, B.; Schmid Daners, M.; Meboldt, M.; Kurtcuoglu, V. (2018): Blood Pump Design Variations and Their Influence on Hydraulic Performance and Indicators of Hemocompatibility. In: Annals of biomedical engineering 46 (3), pp. 417–428. https://doi.org/10.1007/s10439-017-1951-0.

[6] Konnigk, L.; Torner, B.; Bruschewski, M.; Grundmann, S.; Wurm, F.-H. (2021): Equivalent Scalar Stress Formulation Taking into Account Non-Resolved Turbulent Scales. In: Cardiovascular Engineering and Technology 12(3), pp. 251-272 . https://doi.org/10.1007/s13239-021-00526-x

[7] Garon, A.; Farinas, M.-I. (2004): Fast three-dimensional numerical hemolysis approximation. In: Artificial Organs 28 (11), pp. 1016–1025. https://doi.org/10.1111/j.1525-1594.2004.00026.x.

[8] Hund, S.J.; Antaki, J. F.; Massoudi, M. (2010): On the Representation of Turbulent Stresses for Computing Blood Damage. In: International journal of engineering science 48 (11), pp. 1325–1331. https://doi.org/10.1016/j.ijengsci.2010.09.003.

[9] Wu, P.; Gao, Q.; Hsu, P-L (2019): On the representation of effective stress for computing hemolysis. In: Biomechanics and modeling in mechanobiology 18 (3), pp. 665–679. https://doi.org/10.1007/s10237-018-01108-y.

[10] Fraser, K. H.; Taskin, M. E.; Griffith, B. P.; Wu, Z. J. (2011): The use of computational fluid dynamics in the development of ventricular assist devices. In: Medical engineering & physics 33 (3), pp. 263–280. https://doi.org/10.1016/j.medengphy.2010.10.014.

[11] DIN EN ISO 9906, 2012: Kreiselpumpen - Hydraulische Abnahmeprüfung Klassen 1 und 2.

[12] Fröhlich, J.(2006): Large Eddy Simulation turbulenter Strömungen. 1st ed. Wiesbaden: Teubner.

[13] Menter, Florian R. (2015): Best Practice: Scale-Resolving Simulations in ANSYS CFD. 2nd ed.: ANSYS Germany GmbH, 2015.

[14] Eça, L. R. C.; Hoekstra, M. (2014): A procedure for the estimation of the numerical uncertainty of CFD calculations based on grid refinement studies. In: Journal of Computational Physics 262, pp. 104–130. https://doi.org/10.1016/j.jcp.2014.01.006.

[15] Smirnov, P. E.; Menter, F. R. (2009): Sensitization of the SST Turbulence Model to Rotation and Curvature by Applying the Spalart–Shur Correction Term. In: Journal of Turbomachinery 131 (4). https://doi.org/10.1115/1.3070573.

[16] Menter, F. R.; Langtry, R.; Völker, S. (2006): Transition Modelling for General Purpose CFD Codes. In: Flow Turbulence Combustion 77 (1-4), pp. 277–303. https://doi.org/10.1007/s10494-006-9047-1.

[17] Konnigk, L.; Torner, B.; Hallier, S.; Witte, M.; Wurm, F.H.: Grid-Induced Numerical Errors for Shear Stresses and Essential Flow Variables in a Ventricular Assist Device: Crucial for Blood Damage Prediction? In: Journal of Verification, Validation and Uncertainty Quantification 3(4). 2019. https://doi.org/10.1115/1.4042989.

[18] Eça, L. R. C.; Hoekstra, M.: A procedure for the estimation of the numerical uncertainty of CFD calculations based on grid refinement studies. In: Journal of Computational Physics 262, p. 104–130, 2014. https://doi.org/10.1016/j.jcp.2014.01.006.

[19] Errill, E. W.: Rheology of blood. In: Physiological reviews 49 (4), p. 863–888, 1969. https://doi.org/10.1152/physrev.1969.49.4.863

[20] ANSYS Inc., ANSYS CFX Reference Guide, 11.4.3. Transient Rotor-Stator, 2022.

[21] ANSYS Inc., ANSYS FLUENT User's Guide 12.0, 11.3 The Sliding Mesh Technique, 2022.

[22] Pope, S. B.: Turbulent Flows. Cambridge, New York: Cambridge University Press, 2000.

[23] Celik, I. B.; Klein, M.; Janicka, J.: Assessment Measures for Engineering LES Applications. Journal of Fluids Engineering 131(3), 2009. https://doi.org/10.1115/1.3059703

[24] Elsner, J. W.; Elsner, W.: On the measurement of turbulence energy dissipation. In: Meas. Sci. Technol. 7, p. 1334–1348, 1995.

[25] Torner, B.; Konnigk, L.; Hallier, S.; Kumar, J.; Witte, M.; Wurm, F.-H. LES in a Rotary Blood Pump: Viscous Shear Stress Computation and Comparison with URANS. International Journal of Artificial Organs (2018): https://doi.org/10.1177/0391398818777697.

[26] Wisniewski, A.; Medart, D.; Wurm, F.H., Torner, B.: Evaluation of Clinically Relevant Operating Conditions for Left Ventricular Assist Device Investigations. International Journal of Artificial Organs 2020. https://doi.org/10.1177/0391398820932925

[27] Torner, B.: Erforschung der Strömung in einem Herzunterstützungssystem unter Berücksichtigung des Turbulenzeinflusses auf die Blutschädigungsvorhersage. Shaker Verlag, 2021. https://doi.org/10.2370/9783844077506

[28] Escher, A.; Hubmann, E. J.; Karner, B.; Messner, B.; Laufer, G.; Kertzscher, U.; Zimpfer, D.; Granegger, M.: Linking Hydraulic Properties to Hemolytic Performance of Rotodynamic Blood Pumps. Advanced Theory and Simulations, p. 2200117, 2022. https://doi.org/10.1002/adts.202200117

[29] Torner, B.; Konnigk, L.; Wurm, F.H.: Influence of Turbulent Shear Stresses on the Numerical Blood Damage Prediction in a Ventricular Assist Device. International Journal of Artificial Organs 42(12). 2019. https://doi.org/10.1177/0391398819861395. 2021

[30] Zhang, T.; Taskin, M. E.; Fang, H.-B.; Pampori, A.; Jarvik, R.; Griffith, B. P.; Wu, Z. J.: Study of flow-induced hemolysis using novel Couette-type blood-shearing devices. Artificial Organs 35 (12), p. 1180–1186, 2011. https://doi.org/10.1111/j.1525-1594.2011.01243.x.

[31] Tobin, N.; Manning, K. B.: Large-Eddy Simulations of Flow in the FDA Benchmark Nozzle Geometry to Predict Hemolysis. Cardiovascular engineering and technology 11 (3), p. 254–267, 2020. https://doi.org/10.1007/s13239-020-00461-3.

[32] Thamsen, B.; Mevert, R.; Lommel, M.; Preikschat, P.; Gaebler, J.; Krabatsch, T. et al.: A two-stage rotary blood pump design with potentially lower blood trauma: a computational study. International journal of artificial organs 39 (4), p. 178–183, 2016. https://doi.org/10.5301/ijao.5000482.

[33] Chen, Z.; Jena, S. K.; Giridharan, G. A.; Sobieski, M. A.; Koenig, S. C.; Slaughter, M. S. et al.: Shear stress and blood trauma under constant and pulse-modulated speed CF-VAD operations: CFD analysis of the HVAD. Medical & biological engineering & computing, 2018. https://doi.org/10.1007/s11517-018-1922-0.

[34] Pauli, L.; Nam, J.; Pasquali, M.; Behr, M.: Transient Stress- and Strain-Based Hemolysis Estimation in a Simplified Blood Pump. In: Int. J. Numer. Meth. Fluids 29 (10), p. 1148–1160, 2013. https://doi.org/10.1002/cnm.2576

[35] Lakshminiarayana, B.: Fluid Dynamics and Heat Transfer of Turbomachinery. New York: Wiley, 2007.

[36] Dick, E.: Fundamentals of Turbomachinery (1st ed.). Drodrecht: Springer, 2015.

[37] Torner, B.; Hallier, S.; Witte, M.; Wurm, F.-H.: Large-Eddy and Unsteady Reynolds-Averaged Navier-Stokes Simulations of an Axial Flow Pump for Cardiac Support. In: ASME (Hg.): Proceedings of the ASME Turbo Expo 2017. Turbine Technical Conference and Exposition-2017. Turbo Expo. Charlotte, USA, 26.-30. June 2017. New York, N.Y.: ASME.





Contributed by: B. Torner — University of Rostock, Germany

Front Page

Description

Test Data

CFD Simulations

Evaluation

Best Practice Advice

© copyright ERCOFTAC 2022