DOI: 10.1097/MAT.0b013e3180377aef

,  

Issn Print: 1058-2916

Publication Date: 2007/03/01


Print

Letter to the Editor: A Possible Major Mistake in the Paper Entitled “Collected Nondimensional Performance of Rotary Dynamic Blood Pump”: Smith WA, Allaire P, Antaki J, Butler KC, Kerkhoffs W, Kink T, Loree H, Reul H. ASAIO Journal 50: 25–32, 2004

William A. Smith

    loading  Checking for direct PDF access through Ovid

Excerpt

I appreciate the care with which Dr. Wu has read our paper. It is correct that, in making the use of radius and diameter consistent in our paper and data, we missed the need to double the value of the transition Reynolds number from Sabersky et al. quoted in our paper.
The point being made in that particular paragraph was that the transition Reynolds number for tube flow learned during elementary fluids courses is not a universal constant; based on the “pump Reynolds number,” blood pumps are frequently in a grossly laminar or transitional regime. Correcting this “major” error makes this particular argument stronger. Later in the paper, when Reynolds number is actually used as part of an efficiency adjustment calculation, we correctly refer to the 2 × 106 used by Balje as a reference value.1 As shown, the Balje formula seems to properly adjust the efficiency of this sample of blood pumps for Reynolds number, as compared with other conventional turbulent flow pumps. Corrected, our earlier paragraph would show the same 106 order of magnitude. Japikse and Baines discuss the Reynolds number effect on pump efficiency, noting that the scaling is not precise and is situation dependent.2 They provide some compressor data that shows the critical Reynolds number is of the order of 106 for this very different situation. The Pump Handbook uses a completely different approach to the calculation, the “Head-Flow” Reynolds number, but still shows the transition from laminar to turbulent flow with respect to estimating efficiency to be of the order 106.3
Of course, the fluid flow in a pump is complex, and the transition from laminar to turbulent flow may occur at different times in the inlet system, the blade channels, the outlet system, and the various clearances. An appropriate value for the transition in each situation must be applied. The “entrance length” effect can also be significant if the flow does not have time to achieve the flow pattern theoretically indicated by the Reynolds number calculation.
Dr. Wu is entirely correct with respect to the error made by not correcting the Sabersky et al. Reynolds number for our use of diameter as the characteristic length, as opposed to their use of the radius. However, all of the published data available to the first author, and his experience, indicates that for a gross pump Reynolds number calculation, the laminar-turbulent transition will be of the order 106, not 103. The point of the paper concerning Reynolds number, that these blood pump performance results appear consistent with industrial pump performance data when a standard Reynolds number correction is used, is not compromised. Dr. Wu’s experience seems to be unique among engineers with pump experience if it justifies a many-orders-of-magnitude-smaller value for a transition pump Reynolds number, and the supporting data may be worthy of publication to provide further information in this area.
As a closing note, the author would again invite pump researchers, if they have suitable pump test data (recognizing that hydraulic input power is a hard parameter to isolate accurately), to publish their results or contribute them to the author for an update of this paper.
    loading  Loading Related Articles