Evaluation AC7-03: Difference between revisions
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'''Hydraulic Efficiencies <math> \eta_h </math> ''' | '''Hydraulic Efficiencies <math> \eta_h </math> ''' | ||
The hydraulic efficiencies of the impeller (index: <math> i </math>) and the whole pump (index: <math> p </math>) are plotted in Tab. 5.1. The deviation between the URANS and the reference LES case are minor for both operation points with a maximal deviation of <math> +3.2~% </math>. It can be concluded that the turbulence-modelling URANS method can reflect the efficiencies, and hence the global losses, as accurately as the turbulence-resolving LES method. | |||
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''' Equivalent Shear Stresses <math> \tau_{eff} </math> ''' | ''' Equivalent Shear Stresses <math> \tau_{eff} </math> ''' | ||
The computed equivalent stresses <math> \tau_{eff} </math> are plotted for both operation points in Fig. 5.4. The stresses from the reference | The computed equivalent stresses <math> \tau_{eff} </math> are plotted for both operation points in Fig. 5.4. The stresses from the reference LES are compared to the URANS computations with stress formulations (Eq. 6.1 and 6.2 in the chapter) with and without the contribution of the modeled parameter <math> \epsilon_{dir} </math>. | ||
[[Image:Spannungen.png|1000px|center|thumb|Fig. 5.4. Equivalent stresses <math> \tau_{eff} </math> of LES and URANS. The equivalent stresses with and without the contribution from the turbulence model <math> \epsilon_{mod} </math> is included. The figure displays a cylindical cut through the rotor and outlet guide vane at a radius of 80% of the outer radius <math> R_2 </math>. Top row: partial load at <math> Q=2.5~l/min </math>. Bottom row: nominal load at <math> Q=4.5~l/min </math>.]] | [[Image:Spannungen.png|1000px|center|thumb|Fig. 5.4. Equivalent stresses <math> \tau_{eff} </math> of LES and URANS. The equivalent stresses with and without the contribution from the turbulence model <math> \epsilon_{mod} </math> is included. The figure displays a cylindical cut through the rotor and outlet guide vane at a radius of 80% of the outer radius <math> R_2 </math>. Top row: partial load at <math> Q=2.5~l/min </math>. Bottom row: nominal load at <math> Q=4.5~l/min </math>.]] |
Revision as of 09:36, 13 December 2021
Turbulent Blood Flow in a Ventricular Assist Device
Application Challenge AC7-03 © copyright ERCOFTAC 2021
Evaluation
Discretization Errors for Fluid Mechanical & Hemodynamical Parameters with URANS
Figure 5.1. shows the discretization error uncertainties of the pressure headvia the VADs impeller and the whole pump. The error intervals of total pressure heads were up to 4.8% for the finest grid. From an engineering point of view, these uncertainties are in an acceptable range for the VAD design. In addition, the uncertainty for the pressure head for the whole VAD (4.8%) is higher than for the impeller alone (1.7%). The reason for this is that turbulent phenomena, e.g. detachment in the outlet guide vane, affect the pressure increase via the whole pump. Those effects may have a significant mesh sensitivity and thus affect the uncertainty of the pressure head for the entire VAD. Furthermore, the relatively small uncertainties for the pressure heads suggest that the finest grid resolution is enough to guarantee a grid-independent solution and no further grid refinement seems to be required for these results.
The uncertainties for the stress-dependent MIH (Fig. 5.2, bottom right) indicates a higher but acceptable value for the finest grid with an 8% interval. In contrast, the coarsest grid has a two times higher uncertainty for MIH (15%) as the uncertainty for the pressure head (15%). On the other hand, the uncertainties of the volumes, which exceeds certain stress thresholds, indicate larger error intervals. These uncertainties are up to 4 times larger as the uncertainties for the pump characteristics, as can be seen in Fig. 5.2. In terms of a potential blood damage prediction with this shear stress field, these results indicate that the finest grid is still too coarse. Of course, the uncertainties of the different blood damage indicators will decrease with higher grid resolutions wherein the absolute values will converge to a final state, but even for grid UR-7 a decay of the slope of the fit in Fig. 5.2. is not obvious in the range of data obtained from the flow computations. Unless the grid size for the finest grid is already quite large for design and optimisation studies, it has still recognizable discretisation uncertainties for the shear-dependent variables, which are important for the blood damage evaluation.
Experimental Validation of URANS and LES
For simulations in turbopumps, hydraulic characteristics such as the head are among the most important result variables. Also in the field of CFD applications in VADs, it is common to use the head to validate the numerical calculation. In fact, the measurement of the head is the only experimental validation of the numerical calculation in a large number of literature studies. Since the pressure in the pump is coupled via the governing equations to the rest of the flow field, the comparison of the heads can be used as the first stage of flow field validation in VADs.
The experimental and numerical results are given in Figure 5.3. For the operating point at , a good agreement between numerics and experiment can be observed with a deviation of for LES and for URANS. For the smaller flow rate the deviation are slightly larger with for LES and for URANS.
In summary, the discrepancy between numerically and experimentally determined head is still within an acceptable range for both LES and URANS. From this, it can be concluded that the numerical model is valid to reproduce the real pressure buildup of the VAD.
Fluid Mechanical & Hemodynamical Evaluation of URANS
Hydraulic Efficiencies
The hydraulic efficiencies of the impeller (index: ) and the whole pump (index: ) are plotted in Tab. 5.1. The deviation between the URANS and the reference LES case are minor for both operation points with a maximal deviation of . It can be concluded that the turbulence-modelling URANS method can reflect the efficiencies, and hence the global losses, as accurately as the turbulence-resolving LES method.
Flow Rate | Parameter | LES | URANS | Relative deviation to LES [%] |
---|---|---|---|---|
Equivalent Shear Stresses
The computed equivalent stresses are plotted for both operation points in Fig. 5.4. The stresses from the reference LES are compared to the URANS computations with stress formulations (Eq. 6.1 and 6.2 in the chapter) with and without the contribution of the modeled parameter .
Contributed by: B. Torner — University of Rostock, Germany
© copyright ERCOFTAC 2021