Lloyd H. Back

Convective heat transfer in a convergent-divergent nozzle☆

Abstract The results of an experimental investigation of convective heat transfer from turbulent boundary layers accelerated under the influence of large pressure gradients in a cooled convergent-divergent nozzle are presented. The investigation covered a range of stagnation pressures from 30 to 250 psia, stagnation temperatures from 1030° to 2000°R, and nozzle-inlet boundary-layer thicknesses between 5 and 25 per cent of the inlet radius. The most significant unexpected trend in the results is the reduction in the heat-transfer coefficient, below that typical of a turbulent boundary layer, at stagnation pressures less than about 75 psia. As expected, the results include a maximum in the heat-transfer coefficient upstream of the throat where the mass flow rate per unit area is largest, and a substantial decrease of the heat-transfer coefficient downstream of the point of flow separation which occurred in the divergent section of the nozzle at the low stagnation pressures. A reduction of about 10 per cent in the heat-transfer coefficient resulted from an increase in the inlet boundary-layer thickness between the minimum and maximum thicknesses investigated. Heat-transfer predictions with which the data were compared either incorporate a prediction of the boundary-layer characteristics or are related to pipe flow. At the higher stagnation pressures, predicted values from a modification of Bartzs turbulent-boundary-layer analysis are in fair agreement with the data. As a possible explanation of the low heat transfer at the lower stagnation pressures, a parameter is found which is a measure of the importance of flow acceleration in reducing the turbulent transport below that typical of a fully turbulent boundary layer.

Flow Rate-Pressure Drop Relation in Coronary Angioplasty: Catheter Obstruction Effect

Quantitative methods to measure the hemodynamic consequences of various endovascular interventions including balloon angioplasty are limited. Catheters measuring translesional pressure drops during balloon angioplasty procedures can cause flow blockage and thus inaccurate estimates of pre- and post-intervention flow rates. The purpose of this investigation was to examine the influence of the presence and size of an angioplasty catheter on measured mean pressure gradients across human coronary artery stenoses. Analytical flow modeling and in vitro experimental evidence, coupled with angiographic data on the dimensions and shape of stenotic vessel segments before and after angioplasty, indicated significant flow blockage effects with the catheter present.

ESTIMATED MEAN FLOW RESISTANCE INCREASE DURING CORONARY ARTERY CATHETERIZATION

The purpose of this investigation is to examine the influence of the presence and size of the catheter on the measurement of mean pressure drop and, thus, flow resistance in coronary vessels. Relatively large mean translesional pressure gradients have been reported, but they may be due to obstruction effects. To evaluate this hypothesis, analytical flow modeling coupled with in vitro experimental evidence was used to estimate mean flow resistance increases due to the presence of a catheter in a proximal vessel for concentric and eccentric catheter configurations. For an angioplasty catheter, over the relative range of catheter size to coronary vessel size (di/d(o)) from 0.3 to 0.7 (which is currently being used clinically), the flow resistance increased by a large factor of 3-33 for the concentric configuration. For smaller infusion catheters, the flow resistance increase was less, although still appreciable. Very small angioplasty guidewire also leads to sizeable increases in flow resistance. Effects of catheter eccentricity also indicated substantial increases in flow resistance, although the magnitude was less. These initial results might be used by clinicians to obtain rough estimates of actual mean pressure gradients in vivo in relatively straight proximal segments of artery from values measured with catheters. Since catheters are used so widely clinically, these initial results may be useful also for other vessels in the vascular system where the mean flow is describable by the Poiseuille relation. Whereas there is reasonable confidence in the flow modeling methodology, hemodynamic data are needed to evaluate the actual magnitude of the effects of obstruction in vivo.

Effect of Mild Atherosclerosis on Flow Resistance in a Coronary Artery Casting of Man

An in-vitro flow study was conducted in a mildly atherosclerotic main coronary artery casting of man using sugar-water solutions simulating blood viscosity. Steady flow results indicated substantial increases in pressure drop, and thus flow resistance at the same Reynolds number, above those for Poiseuille flow by 30 to 100 percent in the physiological Reynolds number range from about 100 to 400. Time-averaged pulsatile flow data showed additional 5 percent increases in flow resistance above the steady flow results. Both pulsatile and steady flow data from the casting were found to be nearly equal to those from a straight, axisymmetric model of the casting up to a Reynolds number of about 200, above which the flow resistance of the casting became gradually larger than the corresponding values from the axisymmetric model.

Flow phenomena and convective heat transfer in a conical supersonic nozzle.

Turbulent boundary layer flow in conical supersonic nozzle, discussing convective heat transfer and adverse pressure gradient effect

Experimental Investigation of Branch Flow Ratio, Angle, and Reynolds Number Effects on the Pressure and Flow Fields in Arterial Branch Models

An experimental investigation was carried out to acquire an understanding of local pressure changes and flow along the main lumen of arterial branch models similar to the femoral artery of man with three different branch angles (30, 60, and 90 deg) and side branch to the main lumen diameter ratio of 0.4. Effects of branch to main lumen flow rate ratios and physiological Reynolds numbers were found to be significant on the local pressure changes, while that of branch angle was also found to be important. The flow visualization study revealed that the flow separated in the main lumen near the branch junction when the pressure rise coefficient along the main lumen was above a critical value (i.e., 0.35 - 0.46), which was observed to be a function of the Reynolds number. The critical value of the branch to main lumen flow rate ratio was found to be about 0.38 - 0.44 also depending on the Reynolds number. Time averaged pressure distributions for pulsatile flow were similar in trend to steady flow values although they differed somewhat in detail in the main lumen in the branch region.

Physiological flow simulation in residual human stenoses after coronary angioplasty.

To evaluate the local hemodynamic implications of coronary artery balloon angioplasty, computational fluid dynamics (CFD) was applied in a group of patients previously reported by [Wilson et al. (1988), 77, pp. 873-885] with representative stenosis geometry post-angioplasty and with measured values of coronary flow reserve returning to a normal range (3.6 +/- 0.3). During undisturbed flow in the absence of diagnostic catheter sensors within the lesions, the computed mean pressure drop delta p was only about 1 mmHg at basal flow, and increased moderately to about 8 mmHg for hyperemic flow. Corresponding elevated levels of mean wall shear stress in the midthroat region of the residual stenoses, which are common after angioplasty procedures, increased from about 60 to 290 dynes/cm2 during hyperemia. The computations (Ree approximately equal to 100-400; alpha e = 2.25) indicated that the pulsatile flow field was principally quasi-steady during the cardiac cycle, but there was phase lag in the pressure drop-mean velocity (delta p - u) relation. Time-averaged pressure drop values, delta p, were about 20 percent higher than calculated pressure drop values, delta ps, for steady flow, similar to previous in vitro measurements by Cho et al. (1983). In the throat region, viscous effects were confined to the near-wall region, and entrance effects were evident during the cardiac cycle. Proximal to the lesion, velocity profiles deviated from parabolic shape at lower velocities during the cardiac cycle. The flow field was very complex in the oscillatory separated flow reattachment region in the distal vessel where pressure recovery occurred. These results may also serve as a useful reference against catheter-measured pressure drops and velocity ratios (hemodynamic endpoints) and arteriographic (anatomic) endpoints post-angioplasty. Some comparisons to previous studies of flow through stenoses models are also shown for perspective purposes.

Hemodynamic diagnostics of epicardial coronary stenoses: in-vitro experimental and computational study

BackgroundThe severity of epicardial coronary stenosis can be assessed by invasive measurements of trans-stenotic pressure drop and flow. A pressure or flow sensor-tipped guidewire inserted across the coronary stenosis causes an overestimation in true trans-stenotic pressure drop and reduction in coronary flow. This may mask the true severity of coronary stenosis. In order to unmask the true severity of epicardial stenosis, we evaluate a diagnostic parameter, which is obtained from fundamental fluid dynamics principles. This experimental and numerical study focuses on the characterization of the diagnostic parameter, pressure drop coefficient, and also evaluates the pressure recovery downstream of stenoses.MethodsThree models of coronary stenosis namely, moderate, intermediate and severe stenosis, were manufactured and tested in the in-vitro set-up simulating the epicardial coronary network. The trans-stenotic pressure drop and flow distal to stenosis models were measured by non-invasive method, using external pressure and flow sensors, and by invasive method, following guidewire insertion across the stenosis. The viscous and momentum-change components of the pressure drop for various flow rates were evaluated from quadratic relation between pressure drop and flow. Finally, the pressure drop coefficient (CDPe) was calculated as the ratio of pressure drop and distal dynamic pressure. The pressure recovery factor (η) was calculated as the ratio of pressure recovery coefficient and the area blockage.ResultsThe mean pressure drop-flow characteristics before and during guidewire insertion indicated that increasing stenosis causes a shift in dominance from viscous pressure to momentum forces. However, for intermediate (~80%) area stenosis, which is between moderate (~65%) and severe (~90%) area stenoses, both losses were similar in magnitude. Therefore, guidewire insertion plays a critical role in evaluating the hemodynamic severity of coronary stenosis. More importantly, mean CDPe increased (17 ± 3.3 to 287 ± 52, n = 3, p < 0.01) and mean η decreased (0.54 ± 0.04 to 0.37 ± 0.05, p < 0.01) from moderate to severe stenosis during guidewire insertion.ConclusionThe wide range of CDPe is not affected that much by the presence of guidewire. CDPe can be used in clinical practice to evaluate the true severity of coronary stenosis due to its significant difference between values measured at moderate and severe stenoses.

Laminarization of a Turbulent Boundary Layer in Nozzle Flow—Boundary Layer and Heat Transfer Measurements With Wall Cooling

Boundary layer and heat transfer measurements for turbulent boundary layer laminarizing in conical nozzle flow with wall cooling

Influence of coronary collateral flow on coronary diagnostic parameters: An in vitro study

Functional severity of coronary stenosis is often assessed using diagnostic parameters. These parameters are evaluated from the combined pressure and/or flow measurements taken at the site of the stenosis. However, when there are functional collaterals operating downstream to the stenosis, the coronary flow-rate increases, and the pressure in the stenosed artery is altered. This effect of downstream collaterals on different diagnostic parameters is studied using a physiological representative in vitro coronary flow-loop. The three diagnostic parameters tested are fractional flow reserve (FFR), lesion flow coefficient (LFC), and pressure drop coefficient (CDP). The latter two were discussed in recent publications by our group (Banerjee et al., 2007, 2008, 2009). They are evaluated for three different severities of stenosis and tested for possible misinterpretation in the presence of variable collateral flows. Pressure and flow are measured with and without downstream collaterals. The diagnostic parameters are then calculated from these readings. In the case of intermediate stenosis (80% area blockage), FFR and LFC increased from 0.74 to 0.77 and 0.58 to 0.62, respectively, for no collateral to fully developed collateral flow. Also, CDP decreased from 47 to 42 for no collateral to fully developed collateral flow. These changes in diagnostic parameters might lead to erroneous postponement of coronary intervention. Thus, variability in diagnostic parameters for the same stenosis might lead to misinterpretation of stenosis severity in the presence of operating downstream collaterals.