Prediction of Annulus Pressure Gradients in Pumping Wells

1980 ◽  
Vol 102 (4) ◽  
pp. 181-183 ◽  
Author(s):  
Zˇ. Schmidt ◽  
J. P. Brill ◽  
H. D. Beggs
Keyword(s):  
Experimental Data ◽  
Pressure Gradient ◽  
Physical Model ◽  
Physical Property ◽  
Pressure Gradients ◽  
Concentric Annulus ◽  
Pumping Wells ◽  
Adequate Representation ◽  
Gas Bubbling ◽  
S Curve

Experimental data on pressure gradients were obtained for gas bubbling through static liquids in various concentric annulus configurations with eight different liquids. Although a definite liquid physical property effect exists, the Gilbert “S” curve gave an adequate representation of the data. A more accurate correlation was developed, together with a physical model that separates hydrostatic and friction components of the pressure gradient.

Velocity and Temperature Profiles in Turbulent Boundary Layer Flows Experiencing Streamwise Pressure Gradients

1997 ◽  
Vol 119 (3) ◽  
pp. 433-439 ◽  
Author(s):  
R. J. Volino ◽  
T. W. Simon
Keyword(s):  
Experimental Data ◽  
Pressure Gradient ◽  
Velocity Profiles ◽  
Temperature Profiles ◽  
Pressure Gradients ◽  
Mean Velocity ◽  
Law Of The Wall ◽  
Prandtl Numbers ◽  
Energy Equations ◽  
Near Wall

The standard turbulent law of the wall, devised for zero pressure gradient flows, has been previously shown to be inadequate for accelerating and decelerating turbulent boundary layers. In this paper, formulations for mean velocity profiles from the literature are applied and formulations for the temperature profiles are developed using a mixing length model. These formulations capture the effects of pressure gradients by including the convective and pressure gradient terms in the momentum and energy equations. The profiles which include these terms deviate considerably from the standard law of the wall; the temperature profiles more so than the velocity profiles. The new profiles agree well with experimental data. By looking at the various terms separately, it is shown why the velocity law of the wall is more robust to streamwise pressure gradients than is the thermal law of the wall. The modification to the velocity profile is useful for evaluation of more accurate skin friction coefficients from experimental data by the near-wall fitting technique. The temperature profile modification improves the accuracy with which one may extract turbulent Prandtl numbers from near-wall mean temperature data when they cannot be determined directly.

Pressure Drop During Condensation in Microchannels

2013 ◽  
Vol 135 (9) ◽  
Author(s):  
Hua Sheng Wang ◽  
Jie Sun ◽  
John W. Rose
Keyword(s):  
Experimental Data ◽  
Pressure Gradient ◽  
Void Fraction ◽  
Annular Flow ◽  
Gradient Methods ◽  
Pressure Gradients ◽  
High Quality ◽  
Friction Pressure ◽  
Flow Condensation ◽  
Approximate Equations

The paper reports calculations of friction pressure gradient for the special case of laminar annular flow condensation in microchannels. This is the only flow regime permitting theoretical solution without having recourse to experimental data. Comparisons are made with correlations based on experimental data for R134a. The correlations differ somewhat among themselves with the ratio of highest to lowest predicted friction pressure gradient typically around 1.4 and nearer to unity at high quality. The friction pressure gradients given by the laminar annular flow solutions are in fair agreement with the correlations at high quality and lower than the correlations at lower quality. Attention is drawn to the fact that the friction pressure gradient cannot be directly observed and its evaluation from measurements requires estimation of the nondissipative momentum or acceleration pressure gradient. Methods used to estimate the nondissipative pressure gradient require quality and void fraction together with equations which relate these and whose accuracy is difficult to quantify. Quality and void fraction can be readily found from the laminar annular flow solutions. Significant differences are found between these and values from approximate equations.

Modeling of Interfacial Component for Two-Phase Frictional Pressure Gradient in Microchannels and Minichannels

2011 ◽  
Author(s):  
M. M. Awad ◽  
Y. S. Muzychka
Keyword(s):  
Experimental Data ◽  
Pressure Gradient ◽  
Single Phase ◽  
Simple Approach ◽  
Phase Flow ◽  
Pressure Gradients ◽  
Two Phase ◽  
Interfacial Pressure ◽  
Proposed Model ◽  
Phase Liquid

A simple approach for calculating the interfacial component of frictional pressure gradient in two-phase flow in microchannels and minichannels is presented. This approach is developed using superposition of three pressure gradients: single-phase liquid, single-phase gas, and interfacial pressure gradient. The proposed model can be transformed in two different ways. First, two-phase interfacial multiplier for liquid flowing alone (φl,i2) as a function of two-phase frictional multiplier for liquid flowing alone (φl2) and the Lockhart-Martinelli parameter, X. Second, two-phase interfacial multiplier for gas flowing alone (φg,i2) as a function of two-phase frictional multiplier for gas flowing alone (φg2) and the Lockhart-Martinelli parameter, X. This proposed model allows for the interfacial pressure gradient to be easily modeled. Comparisons of the proposed model with experimental data for microchannels and minichannels and existing correlations for both φl and φg versus X are presented.

A Numerical Investigation on the Development of an Embedded Streamwise Vortex in a Turbulent Boundary Layer With Spanwise Pressure Gradient

2001 ◽  
Vol 123 (3) ◽  
pp. 551-558 ◽  
Author(s):  
InSub Lee ◽  
Hong Sun Ryou ◽  
Seong Hyuk Lee ◽  
Ki Bae Hong ◽  
Soo Chae
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Three Dimensional ◽  
Simple Algorithm ◽  
Streamwise Vortex ◽  
Pressure Gradients ◽  
Reynolds Stresses ◽  
Turbulent Structures

It is the aim of this article to investigate numerically the effects of spanwise pressure gradient on an embedded streamwise vortex in a turbulent boundary layer. The governing equations were discretized by the finite volume method and SIMPLE algorithm was used to couple between pressure and velocity. The LRR model for Reynolds stresses was utilized to predict the anisotropy of turbulence effectively. The validation was done for two cases: one is the development of a streamwise vortex embedded in a pressure-driven, three-dimensional turbulent boundary layer. The other involves streamwise vortex pairs embedded in a turbulent boundary layer without the spanwise pressure gradient. In the case of the former, the predicted results were compared with Shizawa and Eaton’s experimental data. In the latter case, the calculated results were compared against the experimental data of Pauley and Eaton. We performed numerical simulations for three cases with different values of spanwise pressure gradient. As a result, the primary streamwise vortex with spanwise pressure gradients decays more rapidly than the case with no pressure gradients, as the spanwise pressure gradient increases. This indicates that the spanwise pressure gradient may play an important role on mean and turbulent structures. In particular, it can be seen that the increase of pressure gradient enhances a level of turbulent normal stresses.

scholarly journals Determinants of valve gating in collecting lymphatic vessels from rat mesentery

2011 ◽  
Vol 301 (1) ◽  
pp. H48-H60 ◽  
Author(s):  
Michael J. Davis ◽  
Elaheh Rahbar ◽  
Anatoliy A. Gashev ◽  
David C. Zawieja ◽  
James E. Moore
Keyword(s):  
Pressure Gradient ◽  
Muscle Tone ◽  
Lymphatic Vessels ◽  
Vessel Diameter ◽  
Intraluminal Pressure ◽  
Pressure Gradients ◽  
Rat Mesentery ◽  
Temporal Relationships ◽  
Wide Range ◽  
Valve Opening

Secondary lymphatic valves are essential for minimizing backflow of lymph and are presumed to gate passively according to the instantaneous trans-valve pressure gradient. We hypothesized that valve gating is also modulated by vessel distention, which could alter leaflet stiffness and coaptation. To test this hypothesis, we devised protocols to measure the small pressure gradients required to open or close lymphatic valves and determine if the gradients varied as a function of vessel diameter. Lymphatic vessels were isolated from rat mesentery, cannulated, and pressurized using a servo-control system. Detection of valve leaflet position simultaneously with diameter and intraluminal pressure changes in two-valve segments revealed the detailed temporal relationships between these parameters during the lymphatic contraction cycle. The timing of valve movements was similar to that of cardiac valves, but only when lymphatic vessel afterload was elevated. The pressure gradients required to open or close a valve were determined in one-valve segments during slow, ramp-wise pressure elevation, either from the input or output side of the valve. Tests were conducted over a wide range of baseline pressures (and thus diameters) in passive vessels as well as in vessels with two levels of imposed tone. Surprisingly, the pressure gradient required for valve closure varied >20-fold (0.1–2.2 cmH2O) as a passive vessel progressively distended. Similarly, the pressure gradient required for valve opening varied sixfold with vessel distention. Finally, our functional evidence supports the concept that lymphatic muscle tone exerts an indirect effect on valve gating.

Protein osmotic pressure gradients and microvascular reflection coefficients

1997 ◽  
Vol 273 (2) ◽  
pp. H997-H1002 ◽  
Author(s):  
R. E. Drake ◽  
S. Dhother ◽  
R. A. Teague ◽  
J. C. Gabel
Keyword(s):  
Reflection Coefficient ◽  
Pressure Gradient ◽  
Osmotic Pressure ◽  
Reflection Coefficients ◽  
Pressure Gradients ◽  
Fluid Filtration ◽  
The Mean ◽  
Osmotic Reflection Coefficient ◽  
New Equation ◽  
Osmotic Pressure Gradient

Microvascular membranes are heteroporous, so the mean osmotic reflection coefficient for a microvascular membrane (sigma d) is a function of the reflection coefficient for each pore. Investigators have derived equations for sigma d based on the assumption that the protein osmotic pressure gradient across the membrane (delta II) does not vary from pore to pore. However, for most microvascular membranes, delta II probably does vary from pore to pore. In this study, we derived a new equation for sigma d. According to our equation, pore-to-pore differences in delta II increase the effect of small pores and decrease the effect of large pores on the overall membrane osmotic reflection coefficient. Thus sigma d for a heteroporous membrane may be much higher than previously derived equations indicate. Furthermore, pore-to-pore delta II differences increase the effect of plasma protein osmotic pressure to oppose microvascular fluid filtration.

scholarly journals Simulation Analysis on Water’s Micro Seepage Laws under Different Pressure Gradients Using Computed Tomography Method

2018 ◽  
Vol 2018 ◽  
pp. 1-26 ◽  
Author(s):  
Gang Zhou ◽  
Lei Qiu ◽  
Wenzheng Zhang ◽  
Jiao Xue
Keyword(s):  
Pressure Gradient ◽  
Mass Flow ◽  
Simulation Analysis ◽  
Effective Porosity ◽  
Pressure Gradients ◽  
Seepage Velocity ◽  
Average Mass ◽  
Depth Analysis ◽  
Tomography Method ◽  
Insight Into

The aim of this paper was to develop a model that can characterize the actual micropore structures in coal and gain an in-depth insight into water’s seepage rules in coal pores under different pressure gradients from a microscopic perspective. To achieve this goal, long-flame coals were first scanned by an X-ray 3D microscope; then, through a representative elementary volume (REV) analysis, the optimal side length was determined to be 60 μm; subsequently, by using Avizo software, the coal’s micropore structures were acquired. Considering that the porosity varies in the same coal sample, this study selected four regions in the sample for an in-depth analysis. Moreover, numerical simulations on water’s seepage behaviors in coal under 30 different pressure gradients were performed. The results show that (1) the variation of the simulated seepage velocity and pressure gradient accorded with Forchheimer’s high-velocity nonlinear seepage rules; (2) the permeability did not necessarily increase with the increase of the effective porosity; (3) in the same model, under different pressure gradients, the average seepage pressure decreased gradually, while the average seepage velocity and average mass flow varied greatly with the increase of the seepage length; and (4) under the same pressure gradient, the increase of the average mass flow from the inlet to the outlet became more significant under a higher inlet pressure.

Pressure, Frictional Resistance, and Flow Characteristics of the Partially Wetted Rotating Disk

1968 ◽  
Vol 90 (2) ◽  
pp. 395-404 ◽  
Author(s):  
H. N. Ketola ◽  
J. M. McGrew
Keyword(s):  
Experimental Data ◽  
Reynolds Number ◽  
Pressure Gradient ◽  
Flow Characteristics ◽  
Frictional Resistance ◽  
Rotating Disk ◽  
Practical Applications ◽  
Stationary Wall ◽  
Spacing Ratio ◽  
Analytical Expressions

A theory of the partially wetted rotating disk is described and experimental data presented which verify the application of this theory in practical applications. Four different flow regimes may be identified according to the value of the disk Reynolds number and the spacing ratio between the disk and stationary wall. The analytical expressions for prediction of the pressure gradient developed and the frictional resistance are uniquely determined by the disk Reynolds number, spacing ratio, and the degree of wetting of the disk.

Predicting Turbulent Boundary Layer Wall Pressure Fluctuations in Adverse Pressure Gradients

2005 ◽  
Author(s):  
Frank J. Aldrich
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Pressure Fluctuations ◽  
Adverse Pressure Gradient ◽  
Wall Pressure ◽  
Prediction Tool ◽  
Pressure Gradients ◽  
Wall Pressure Fluctuations ◽  
The Difference

A physics-based approach is employed and a new prediction tool is developed to predict the wavevector-frequency spectrum of the turbulent boundary layer wall pressure fluctuations for subsonic airfoils under the influence of adverse pressure gradients. The prediction tool uses an explicit relationship developed by D. M. Chase, which is based on a fit to zero pressure gradient data. The tool takes into account the boundary layer edge velocity distribution and geometry of the airfoil, including the blade chord and thickness. Comparison to experimental adverse pressure gradient data shows a need for an update to the modeling constants of the Chase model. To optimize the correlation between the predicted turbulent boundary layer wall pressure spectrum and the experimental data, an optimization code (iSIGHT) is employed. This optimization module is used to minimize the absolute value of the difference (in dB) between the predicted values and those measured across the analysis frequency range. An optimized set of modeling constants is derived that provides reasonable agreement with the measurements.

The Effect of Real Turbine Roughness With Pressure Gradient on Heat Transfer

2003 ◽  
Author(s):  
Jeffrey P. Bons ◽  
Stephen T. McClain
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Combined Effects ◽  
Pressure Gradients ◽  
Smooth Wall ◽  
Reynolds Analogy ◽  
Integral Boundary ◽  
Favorable Pressure Gradient

Experimental measurements of heat transfer (St) are reported for low speed flow over scaled turbine roughness models at three different freestream pressure gradients: adverse, zero (nominally), and favorable. The roughness models were scaled from surface measurements taken on actual, in-service land-based turbine hardware and include samples of fuel deposits, TBC spallation, erosion, and pitting as well as a smooth control surface. All St measurements were made in a developing turbulent boundary layer at the same value of Reynolds number (Rex≅900,000). An integral boundary layer method used to estimate cf for the smooth wall cases allowed the calculation of the Reynolds analogy (2St/cf). Results indicate that for a smooth wall, Reynolds analogy varies appreciably with pressure gradient. Smooth surface heat transfer is considerably less sensitive to pressure gradients than skin friction. For the rough surfaces with adverse pressure gradient, St is less sensitive to roughness than with zero or favorable pressure gradient. Roughness-induced Stanton number increases at zero pressure gradient range from 16–44% (depending on roughness type), while increases with adverse pressure gradient are 7% less on average for the same roughness type. Hot-wire measurements show a corresponding drop in roughness-induced momentum deficit and streamwise turbulent kinetic energy generation in the adverse pressure gradient boundary layer compared with the other pressure gradient conditions. The combined effects of roughness and pressure gradient are different than their individual effects added together. Specifically, for adverse pressure gradient the combined effect on heat transfer is 9% less than that estimated by adding their separate effects. For favorable pressure gradient, the additive estimate is 6% lower than the result with combined effects. Identical measurements on a “simulated” roughness surface composed of cones in an ordered array show a behavior unlike that of the scaled “real” roughness models. St calculations made using a discrete-element roughness model show promising agreement with the experimental data. Predictions and data combine to underline the importance of accounting for pressure gradient and surface roughness effects simultaneously rather than independently for accurate performance calculations in turbines.

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