Robert J. Poole

On the reproducibility of the rheology of shear-thinning liquids

The independent analysis of flow measurements is frequently hampered by incomplete characterisation of the working fluid. This problem is particularly acute in situations which require working fluids with identical properties, such as the development of scaling laws for the turbulent flow of drag-reducing liquids. In this paper, we demonstrate that the viscometric viscosity, loss and storage moduli for two of the most common polymers used for flow experiments, carboxymethylcellulose (CMC) and xanthan gum (XG), are practically insensitive to the chemistry of the tap water used as a solvent, to the method of mixing, and to the biocide added. However, the properties of CMC from two different manufacturers were found to be significantly different, whereas there was no difference between XG solutions prepared from different batches from the same manufacturer. Our conclusion is that for a given concentration in water, the properties of certain non-Newtonian liquids, such as CMC and XG, are essentially fixed and reproducible. Although the situation is less than ideal, comparisons of fluid-flow data from entirely independent laboratories can thus be made even in the absence of direct rheological measurements.

Ascending aortic curvature as an independent risk factor for type a dissection, and ascending aortic aneurysm formation: a mathematical model

OBJECTIVE To develop a mathematical model to demonstrate that ascending aortic curvature is an independent risk factor for type A dissections, in addition to hypertension, bicuspid aortic valve, aneurysm of ascending aorta, and intrinsic aortic tissue abnormalities, like Marfans syndrome. METHODS A steady state one-dimensional flow analysis was performed, utilising Newtons third law of motion. Five different clinical scenarios were evaluated: (1) effect of aortic curvature; (2) effect of beta-blockers, (3) effect of patient size, (4) forces on a Marfans aorta, and (5) site of entry flap in aortic dissection. RESULTS Aortic curvature increases the forces exerted on the ascending aorta by a factor of over 10-fold. Aortic curvature can cause patients with a systolic blood pressure of 8 0mmHg to have greater forces exerted on their aorta despite smaller diameters and lower cardiac outputs, than patients with systolic blood pressures of 120 mmHg. In normal diameter aortas, beta-blockers have minimal effect compared with aortic curvature. Aortic curvature may help to explain why normal diameter aortas can dissect, and also that the point of the entry tear may be potentially predictable. Aortic curvature has major effects on the forces exerted on the aorta in patients with Marfans syndrome. CONCLUSIONS Aortic curvature is relatively more important that aortic diameter, blood pressure, cardiac output, beta-blocker use, and patient size with regard to the force acting on the aortic wall. This may explain why some patients with normal diameter ascending aortas with or without Marfans syndrome develop type A dissections and aneurysms. Aortic curvature may also help to explain the site of entry tear in acute type A dissection. Further clinical study is needed to validate this studys finding.

Turbulent flow through a plane sudden expansion of modest aspect ratio

The results are reported of an experimental investigation of turbulent flow through a plane sudden expansion of expansion ratio R=D/d=4 and aspect ratio A=w/h=5.33. It is well known that plane sudden expansions of high aspect ratio (A>10) with R greater than 1.5 produce asymmetric flows and this was again seen in this study. The literature for the asymmetric flow situation is surprisingly limited and only axial velocity and axial turbulence intensity results have been reported previously. A laser Doppler anemometer was used here to measure mean and rms axial velocities, U and u′, as well as the transverse mean and rms velocities, V and v′, and the Reynolds shear stress, uv¯. Not only was the mean flow found to be strongly asymmetric, but integration of the mean axial velocity profiles revealed significant departures from two dimensionality along the centerplane of the expansion duct. Results are reported at three spanwise locations to highlight this three dimensionality and qualitative arguments are made ...

Development Length Requirements for Fully Developed Laminar Pipe Flow of Yield Stress Fluids

In this technical brief, we report the results of a systematic numerical investigation of developing laminar pipe flow of yield stress fluids, obeying models of the Bingham-type. We are able to show that using a suitable choice of the Reynolds number allows, for high Reynolds number values at least, the development length to collapse to the Newtonian correlation. On the other hand, the development length remains a weak, nonmonotonic, function of the Bingham number at small values of the Reynolds number (Re≤40).

Turbulent flow of non-Newtonian liquids over a backward-facing step Part II. Viscoelastic and shear-thinning liquids

Abstract The results are reported of an extensive experimental investigation of turbulent flow of polymeric non-Newtonian liquids (0.01, 0.075, 0.125 and 0.175% polyacrylamide (PAA) solutions) through a plane sudden expansion of expansion ratio R=1.43 and aspect ratio A=13.3. Three water-flows are also reported for comparative purposes. A laser Doppler anemometer was used to measure mean and RMS streamwise velocities, U and u′, as well as the transverse mean and RMS velocities, V and v′, and the Reynolds shear stress uv . For the water-flows we highlight the important influence on the reattachment length of the maximum turbulence intensity at separation. The PAA flows exhibit an increased reattachment length compared with the Newtonian situation. The magnitudes of the recirculating velocities and recirculating flowrates are increased for the lowest concentration (0.01% PAA) but decreased for the more viscoelastic high concentration (0.075–0.175% PAA) flows. In all cases these changes are accompanied by large reductions in the transverse turbulent intensity. The correspondingly high degree of turbulence anisotropy is instrumental in generating increased reattachment lengths for the lower concentration flows. The increased levels of viscoelasticity for the higher concentration PAA solutions lead to a reduction of the turbulence intensity at separation and this effect, coupled with the high turbulence anisotropy, plays an important role in increasing the reattachment length.

Laminar Natural Convection of Bingham Fluids in a Square Enclosure with Vertical Walls Subjected to Constant Heat Flux

In this study, two-dimensional steady-state simulations of laminar natural convection in square enclosures with vertical sidewalls subjected to constant heat flux have been carried out, where the enclosures are considered to be completely filled with a yield-stress fluid obeying the Bingham model. Yield stress effects on heat and momentum transport are investigated for nominal values of Rayleigh number (Ra) in the range 103–106 and a Prandtl number (Pr) range of 0.1–100. It is found that the mean Nusselt number Nu increases with increasing values of Rayleigh number for both Newtonian and Bingham fluids. However, Nu values obtained for Bingham fluids are smaller than that obtained in the case of Newtonian fluids with the same nominal value of Rayleigh number Ra due to weakening of convective transport. The mean Nusselt number Nu in the case of Bingham fluids is found to decrease with increasing Bingham number, and for large values of Bingham number Bn, the value settles to unity (Nu = 1.0) as heat transfer takes place principally due to thermal conduction. The Nu values for the vertical walls subjected to constant heat flux are smaller than the corresponding values in the same configuration with constant vertical wall temperatures (for identical values of nominal Rayleigh, Prandtl, and Bingham numbers). However, the value of Bingham number at which Nu approaches to unity remains the same for both constant wall temperature and constant wall heat flux configurations. It is demonstrated that for small values of Bingham number Nu increases with increasing Prandtl number, but the opposite behavior occurs for large values of Bingham number. New correlations are proposed for the mean Nusselt number Nu for both Newtonian and Bingham fluids for square enclosures with vertical walls subjected to constant heat flux, which are shown to satisfactorily capture the correct qualitative and quantitative behavior of Nu in response to changes in Ra, Pr, and Bn.

Closure technique after carotid endarterectomy influences local hemodynamics

BACKGROUND Meta-analysis supports patch angioplasty after carotid endarterectomy (CEA); however, studies indicate considerable variation in practice. The hemodynamic effect of a patch is unclear and this study attempted to elucidate this and guide patch width selection. METHODS Four groups were selected: healthy volunteers and patients undergoing CEA with primary closure, trimmed patch (5 mm), or 8-mm patch angioplasty. Computer-generated three-dimensional models of carotid bifurcations were produced from transverse ultrasound images recorded at 1-mm intervals. Rapid prototyping generated models for flow visualization studies. Computational fluid dynamic studies were performed for each model and validated by flow visualization. Mean wall shear stress (WSS) and oscillatory shear index (OSI) maps were created for each model using pulsatile inflow at 300 mL/min. WSS of <0.4 Pa and OSI >0.3 were considered pathological, predisposing to accretion of intimal hyperplasia. The resultant WSS and OSI maps were compared. RESULTS The four groups comprised 8 normal carotid arteries, 6 primary closures, 6 trimmed patches, and seven 8-mm patches. Flow visualization identified flow separation and recirculation at the bifurcation increased with a patch and was related to the patch width. Computational fluid dynamic identified that primary closure had the fewest areas of low WSS or elevated OSI but did have mild common carotid artery stenoses at the proximal arteriotomy that caused turbulence. Trimmed patches had more regions of abnormal WSS and OSI at the bifurcation, but 8-mm patches had the largest areas of deleteriously low WSS and high OSI. Qualitative comparison among the four groups confirmed that incorporation of a patch increased areas of low WSS and high OSI at the bifurcation and that this was related to patch width. CONCLUSIONS Closure technique after CEA influences the hemodynamic profile. Patching does not appear to generate favorable flow dynamics. However, a trimmed 5-mm patch may offer hemodynamic benefits over an 8-mm patch and may be the preferred option.

Influence of outlet geometry on strongly swirling turbulent flow through a circular tube

The results are reported for an extensive series of measurements (using laser Doppler anemometry) of the mean and fluctuating flow fields for swirling turbulent flow downstream of an orifice in a tube. The influence of a concentric outlet contraction is found to be negligible for low “supercritical” swirl. For high “subcritical” swirl, the outlet geometry is found to have a significant influence throughout the flow field and, in the case of an eccentric (i.e., offset) outlet, to lead to an asymmetric flow with a distorted core. In no case was the core found to precess or the flow to be periodic.

Turbulent flow of a viscoelastic shear-thinning liquid through a plane sudden expansion of modest aspect ratio

An experimental investigation is reported of turbulent flow of a 0.125% polyacrylamide (PAA) solution, a shear-thinning and viscoelastic liquid, through a plane sudden expansion of expansion ratio R=D/d=4 and aspect ratio A=w/h=5.33. A Newtonian fluid flow through the same geometry has been reported previously [Phys. Fluids 14 (2002) 3641] and limited results from that study are included here for comparative purposes. It is well known, for Newtonian fluids at least, that plane sudden expansions with R greater than 1.5 produce asymmetric flows. For the viscoelastic fluid flow, this asymmetry was initially (x/d<6) reduced but not eliminated and the flow found to be highly three dimensional and complex. Results are reported at three spanwise locations to highlight this three dimensionality.

Laminar Natural Convection of Power-Law Fluids in a Square Enclosure With Differentially Heated Sidewalls Subjected to Constant Wall Heat Flux

Two-dimensional steady-state laminar natural convection of inelastic power-law nonNewtonian fluids in square enclosures with differentially heated sidewalls subjected to constant wall heat flux (CHWF) are studied numerically. To complement the simulations, a scaling analysis is also performed to elucidate the anticipated effects of Rayleigh number (Ra), Prandtl number (Pr) and power-law index (n) on the Nusselt number. The effects of n in the range 0.6 � n � 1.8 on heat and momentum transport are investigated for nominal values Ra in the range 10 3 ‐10 6 and a Pr range of 10‐10 5 . In addition the results are compared with the constant wall temperature (CWT) configuration. It is found that the mean Nusselt number Nu increases with increasing values of Ra for both Newtonian and power-law fluids in both configurations. However, the Nu values for the vertical walls subjected to CWHF are smaller than the corresponding values in the same configuration with CWT (for identical values of nominal Ra, Pr and n). The Nu values obtained for power-law fluids with n 1) are greater (smaller) than that obtained in the case of Newtonian fluids with the same nominal value of Ra due to strengthening (weakening) of convective transport. With increasing shear-thickening (i.e., n >1) the mean Nusselt number Nu settles to unity (Nu ¼ 1:0) as heat transfer takes place principally due to thermal conduction. The effects of Pr are shown to be essentially negligible in the range 10‐10 5 . New correlations are proposed for the mean Nusselt number Nu for both Newtonian and power-law fluids. [DOI: 10.1115/1.4007123]