Showing papers on "Pressure gradient published in 1984"

Instability of the flow of two immiscible liquids with different viscosities in a pipe

Abstract: We study the flow of two immiscible fluids of different viscosities and equal density through a pipe under a pressure gradient. This problem has a continuum of solutions corresponding to arbitrarily prescribed interface shapes. The question therefore arises as to which of these solutions are stable and thus observable. Experiments have shown a tendency for the thinner fluid to encapsulate the thicker one. This has been ‘explained’ by the viscous-dissipation principle, which postulates that the amount of viscous dissipation is minimized for a given flow rate. For a circular pipe, this predicts a concentric configuration with the more viscous fluid located at the core. A linear stability analysis, which is carried out numerically, shows that while this configuration is stable when the more viscous fluid occupies most of the pipe, it is not stable when there is more of the thin fluid. Therefore the dissipation principle does not always hold, and the volume ratio is a crucial factor.

Reduction of Turbulent Skin Friction by Microbubbles

Abstract: Measurements of the effect of microbubbles on a zero pressure gradient turbulent boundary layer generated on the test section wall of a water tunnel are described Microbubbles are created by injecting air through a 05 μm sintered stainless steel plate immediately upstream of a floating element drag balance At the downstream edge of the balance the length Reynolds number is as high as ten million Integrated skin friction reduction of greater than 80% is observed The drag balance results are confirmed by measurements with a surface hot‐film probe For the case in which buoyancy tends to keep the bubbles in the boundary layer, the skin friction data are shown to collapse when plotted against the ratio of air to water volume flow rate The effects of buoyancy on skin friction reduction are also documented

Muscular subaortic stenosis: the quantitative relationship between systolic anterior motion and the pressure gradient.

Abstract: We performed simultaneous echocardiographic and hemodynamic studies in 11 patients with muscular subaortic stenosis to determine whether systolic anterior motion (SAM) of the anterior mitral leaflet and the pressure gradient are related quantitatively. SAM without septal contact was associated with either no gradient or a small impulse gradient of less than 10 mm Hg. SAM with septal contact was always associated with a pressure gradient of more than 10 mm Hg. The size of the pressure gradient correlated inversely with the time periods: (1) onset of SAM-septal contact (r = .79, p less than .001) and (2) onset of aortic ejection to onset of SAM-septal contact (r = -.89, p less than .001). Size also correlated directly with the time period: (3) duration of SAM-septal contact (r = .80, p less than .001). Thus when the time from the onset of SAM to the onset of SAM-septal contact was long, SAM-septal contact developed late in systole, the duration of SAM-septal contact was brief and the pressure gradient was low. When SAM-septal contact developed in early systole, the duration of SAM-septal contact was long and the pressure gradient was high. With the index of time period (3) divided by time period (1), a regression equation was devised to predict the size of the pressure gradient (pressure gradient [mm Hg] = 25 [ratio] + 25; r = .90, p less than .001; SE +/- 15 mm Hg). The echocardiographic time period index was validated prospectively in nine other patients and the significant correlation with the hemodynamically determined gradient persisted (r = .89, p less than .01). We conclude that SAM and the pressure gradient are related quantitatively in muscular subaortic stenosis. These observations have implications regarding the mechanism and significance of the pressure gradient in muscular subaortic stenosis.

Scale Analysis of Marine Winds in Straits and along Mountainous Coasts

Abstract: The complicated wind regimes in straits which develop in response to difFerent large-scale pressure fields are investigated by scale analysis of the equations of motion. Adjustment of the mass and motion fields in straits O(lOs km) in width is governed by four nondimensional numbers: separate along- and cross-strait Rossby numbers, a strait drag coefficient, and a stratification parameter, which relates the internal Rossby radius of deformation to the width of the strait. The wind field is in approximate geostrophic balance with an imposed cross-channel pressure gradient. An along-channel pressure gradient is primarily balanced by ageostrophic acceleration of the wind field down the axis of the strait (the gap wind). Vertical motion and the accompanying horizontal divergence in the near-surface wind field can be large even for moderately stable stratification; as a consequence, there may be particularly abrupt transitions of the surface wind field at the exits of straits, where there is a rapid c...

The Structure of Turbulence in a Supersonic Shock-Wave/Boundary-Layer Interaction

Abstract: This paper reports the experimental results from a detailed investigation of the turbulent flowfields in supersonic shock-wave/boundary-layer interactions at Af=2.25. The interactions were produced by twodimensional compression corners having angles of 8, 13, and 18 deg, the flows being respectively attached, incipiently separated, and separated. Turbulence data from a laser velocimeter and a constant-temperature, hotwire anemometer are presented along with a mean flow survey from wall and pitot-static pressures. Qualitative aspects of the turbulence deduced from spectral analysis and high-speed schlieren pictures are also discussed. It is shown that a large amount of the turbulent energy is contained in large-scale structures that are still observed downstream of the interacting region, despite the severe pressure gradient. The lateral extent of these structures is of the order of one boundary-layer thickness and is roughly half of their longitudinal scale. A low-frequency unsteadiness is associated with the existence of a separation bubble, but does not affect the rest of the flow. The Reynolds shear stress is reduced in the vicinity of the separation bubble where the spatial derivatives of the normal stresses become significant.

Description and prediction of transition in two-dimensional, incompressible flow

Abstract: : This paper deals with a survey of transition problems in two-dimensional, incompressible flows. The first chapter is devoted to a general description of phenomena leading to turbulence under the influence of various factors: free-stream turbulence, sound, pressure gradient, oscillations of the external flow, roughness, suction, wall curvature. Then, linear and non-linear stability theories are briefly discussed. This chapter ends with a review of results concerning the structure and growth of turbulent spots and the progressive disappearance of intermittency phenomenon when positive pressure gradients are applied. The second chapter describes practical methods for calculating the transition onset as well as the transition region itself. Methods based on linear stability theory, empirical criteria, intermittency methods and turbulence models are presented successively. Some applications of these techniques are also given. (Author)

Changes in earth stresses around a wellbore caused by radially symmetrical pressure and temperature gradients

Abstract: Pressure and temperature gradients are created around wellbores during waterflooding or when fluids are injected in connection with any other secondary or tertiary recovery process. These gradients result in changes in recovery process. These gradients result in changes in earth stresses, which in turn cause hydraulic fracturing pressures to change. In this paper, analytical solutions have been used to determine the stresses resulting from radially symmetrical temperature and pressure changes around a wellbore. These stresses are required to predict the change in fracture extension pressure that is caused by the injection process. Exact, closed-form solutions are given for the stresses. These have been evaluated with a computer, and more convenient empirical formulas have been fitted to the calculated results. Solutions for discrete cylindrical or disk-shaped regions of changed temperature and pressure are shown. Also, the solutions can be adapted to annular elements of finite thickness that are convenient for incorporation to an r-z-type computer program. Such a program could then be used to compute the stresses resulting from temperature and pressure fields that vary gradually in the radial direction. This paper gives examples to illustrate the effect of injecting a large volume of liquid that is cooler than the insitumore » reservoir, as is common when waterflooding. The cooling can have a large effect on lateral earth stresses, and for some conditions vertical hydraulic fracturing pressures can be significantly reduced.« less

The Fluctuating Longshore Pressure Gradient on the Pacific Northwest Shelf: A Dynamical Analysis

Abstract: The majority of papers on Pacific Northwest shelf dynamics have emphasized the relationship between longshore wind stress τ3, and longshore velocity v. However, attempts to illustrate a balance of momentum in the longshore direction have not been encouraging: τ3*sol;H (where H is water depth) has insufficient magnitude to balance the vertically averaged longshore acceleration Vt,, at least during summer. In this paper it is demonstrated that the missing momentum is provided by the longshore pressure gradient force −py,. The pressure gradient was estimated using tide gauge and atmospheric pressure data at stations separated by roughly 400 km. Seasonal and long-term means from Hickey and Pola and, in some cases, nonseasonal monthly anomalies from Enfield and Allen were added to the sum of the tide gauge and atmospheric pressure data to form time series of total subsurface pressure. The pressure data were multiplied by an offshore deny factor to simulate coastal trapping. The analysis was performed ...

Relationships Between Radar-Derived Thermodynamic Variables and Tornadogenesis

Abstract: A methodology for obtaining pressure perturbations and buoyancy in thunderstorms observed with Doppler radar is described and applied to two tornadic thunderstorms. Extracted thermodynamic information is combined with kinematic analyses to study observed severe storm processes. The intensification of tornado parental circulations (mesocyclones) during tornadogenesis is found to be associated with deepening pressure deficits in lower storm levels. Upward directed perturbation pressure forces in the vicinity of the mesocyclone are reduced and can be reversed as the low-level vorticity amplifies. The sudden formation of concentrated rear downdrafts, commonly observed in tornadic thunderstorms, apparently stems from the vertical pressure gradient reversal. Reduced upward pressure forces decrease the storm's ability to lift low-level negatively buoyant air at the base of the updraft. Further, the restructured pressure forces create a flux of air parcels into the mesocyclone from higher levels on the s...

In vitro verification of Doppler prediction of transvalve pressure gradient and orifice area in stenosis.

Abstract: This study was designed to analyze the validity of application of the modified Bernoulli equation (pressure gradient = 4.0 X velocity2) for estimating the pressure drop and valve orifice area from the jet velocity measured by Doppler ultrasound. We used an in vitro model which permitted interchangeable orifices, accurate measurement of the valve area and pressure drop across the valve. An in-line Doppler ultrasound transducer measured jet velocity (VEL D) at various water flow rates at an incident angle of 180 degrees beyond the various tested orifices. Jet velocity was also determined independently by application of a modified Bernoulli equation using the experimentally measured pressure drop (VEL P) and by a standard continuity equation (VEL Q). VEL P correlated very closely with VEL D (r = 0.981, standard error of the estimate [SEE] = 17.0 and slope of the regression = 0.988). VEL Q, corrected for vena contracta effects, correlated with VEL P (r = 0.986, SEE = 21.6), but had a slope of 0.673. To experimentally determine the exponent of velocity in the Bernoulli equation, we plotted pressure drop against VEL D and found a value of 2.11; theory predicts 2.0. Experimental coefficient of velocity was 3.36 torr/m (standard deviation = 0.52), whereas theory predicts 3.75 for water. Orifice area, calculated using VEL D and the continuity equation, was consistently overestimated by 3 to 12% for flows that produced laminar jets. The pressure gradient and orifice areas calculated from Doppler-derived data accurately predict actual pressure gradients and orifice areas.

Tip streaming from slender drops in a nonlinear extensional flow

Abstract: The deformation of inviscid and slightly viscous drops is studied using slender-body theory. The imposed axisymmetric flow is a combination of a linear extensional flow, with velocity uz = G1 z along the axis of symmetry, together with a cubic flow uz = G3z3. When G3/G1 is sufficiently small the viscous drop breaks in a manner similar to that described by Acrivos & Lo (1978). For larger G3 > 0 the drop breaks by a rapid growth at its end. Steady-state experiments in a 4-roll mill show the ejection of a column of liquid from the tip of the drop, though this is probably caused by a change in the pressure gradient rather than the mechanism described above. The ejected column then breaks into droplets via the Rayleigh instability. It is hypothesized that one or other of these mechanisms corresponds to tip streaming as observed by Taylor (1934).

Volume-cycled oscillatory flow in a tapered channel

Abstract: Oscillatory viscous flow in a tapered channel is analysed under conditions of fixed stroke volume. A lubrication theory is developed for small taper and the general result is steady bidirectional drift and an induced steady pressure gradient. The characteristics of the drift profiles change significantly as the Womersley parameter is increased. For large values difficulties arise in the matched asymptotics method which are resolved by introducing a steady drift layer that is much thicker than the Stokes layer. This double boundary layer does not arise in pressure-cycled oscillations. Both Eulerian and Lagrangian drift are examined. The results are compared qualitatively to experimental observations which primarily focus on the application to ventilation in the lung.

The evolution of a flat eddy near a wall in an inviscid shear flow

Abstract: A flat eddy is defined by the condition e=δ/l≪1, where l=(l−21+l−23)−1/2, and l1, l3, and δ are the streamwise, spanwise, and vertical scales of the eddy, respectively. An approximate solution of the initial value problem for the evolution of a flat eddy in an inviscid flow is obtained using a Lagrangian formulation together with an expansion of the Euler equations in a Taylor series in time. The effects of horizontal pressure gradients on the eddy evolution are found to be small for small times such that eU0t/l≪1, where U0 is a measure of the initial horizontal velocity. Nonuniformity of the spanwise stretching rate, together with the shearing of the eddy by the mean flow, is found to lead to the formation of internal shear layers, also when such layers were absent initially. The separate contributions to the streamwise fluctuation velocity due to redistribution of background momentum and direct driving by the pressure gradient are compared; the latter is found to be significantly smaller than the former...

Factors Affecting Accuracy of In Vitro Valvar Pressure Gradient Estimates by Doppler Ultrasound

Abstract: Doppler ultrasound is used successfully in clinical situations for noninvasive measurement of pressure changes across stenotic cardiac valves. However, situations that might lead to errors in measurement have not been identified. This study determines the effect of flow rate, viscosity, orifice shape and size on the calculation of Doppler transvalvar gradient. Pressure gradient is usually computed from the equation P 1 -P 2 = 4 × Vmax 2 , where P 1 -P 2 is the gradient and Vmax is the maximal jet velocity measured by Doppler ultrasound. An in vitro model was developed with interchangeable orifices that permitted the jet to be detected by an in-line Doppler transducer. The model allowed alteration of flow rates, viscosities and pressure gradients. When P 1 -P 2 as predicted by Doppler was compared with that measured by manometers (PM), excellent correlations were obtained for triangular orifices of areas as small as 78.5 mm 2 (r = 0.95) and for circular and elliptical orifices to as small as 50.2 mm 2 (r = 0.99). For smaller orifices, P 1 -P 2 correlated poorly with PM. Good correlation was found between P 1 -P 2 and PM, with flow rates ranging from 0.7 to 8.4 liters/min (r = 0.97) with a 10-mm diameter circular orifice (area = 78.5 mm 2 ). No observable differences were found in the accuracy of the equation between high and low flow rates. Viscosity had no effect on the accuracy of the P 1 -P 2 comparison with PM over the range evaluated (1 to 10 cp). It is concluded that the modified Bernoulli Doppler gradient equation provides accurate results in the usual clinical situation when an orifice permits true jet formation.

Continuous-wave doppler determination of the pressure gradient across pulmonary artery bands: hemodynamic correlation in 20 patients

Abstract: The feasibility and accuracy of continuous-wave Doppler echocardiography in measuring pressure gradients across the pulmonary artery band were assessed. Simultaneous continuous-wave Doppler and catheter pressure measurements were prospectively performed in 20 patients with complex congenital heart disease and prior pulmonary artery banding. In two other patients, adequate Doppler signals could not be obtained. Doppler velocity was converted to pressure gradient by using the modified Bernoulli equation. Simultaneous continuous-wave Doppler spectral envelopes and catheter pressure wave forms were digitized at 10-ms intervals to obtain maximal instantaneous, mean, and peak-to-peak pressure gradients. The maximal Doppler gradient ranged from 23 to 154 mm Hg, and the simultaneous maximal catheter pressure gradient ranged from 34 to 168 mm Hg. The correlation (r) between these two measurements had a coefficient of 0.98 and a standard error of the estimate (SEE) of 7 mm Hg. The peak-to-peak systolic gradient ranged from 17 to 156 mm Hg and correlated with the maximal Doppler gradient (r = 0.95; SEE = 11 mm Hg). The mean Doppler and mean catheter pressure gradients also were correlated (r = 0.93; SEE = 9 mm Hg). As Doppler echocardiography measures instantaneous velocity and therefore instantaneous pressure gradient, the more precise correlation was between Doppler gradient and maximal instantaneous catheter gradient rather than peak-to-peak systolic gradient. Continuous-wave Doppler echocardiography is an accurate noninvasive technique for measurement of pressure gradients across pulmonary artery bands. In combination with clinical evaluation and two-dimensional echocardiography, it should substantially aid clinical decision making.

Transitional intermittency in boundary layers subjected to pressure gradient

Abstract: Results are reported from an extensive series of experiments on boundary layers in which the location of pressure gradient and transition onset could be varied almost independently, by judicious use of tunnel wall liners and transition-fixing devices. The experiments show that the transition zone is sensitive to the pressure gradient especially near onset, and can be significantly asymmetric; no universal similarity appears valid in general. Observed intermittency distributions cannot be explained on the basis of the hypothesis, often made, that the spot propagates at speeds proportional to the local free-stream velocity but is otherwise unaffected by the pressure gradient.

Theory of Vorticity Generation by Shock Wave and Flame Interactions

Abstract: : We present detailed numerical and theoretical studies of vorticity generation by the interaction of a weak planar shock with an azimuthally symmetric flame. The calculations are two-dimensional and correspond to a cylindrical flame. To analyze the fluid-dynamic aspects of the problem, we exclude chemical reactions and model the flame as a region of reduced density and elevated temperature. We find that the rotational flows associated with the vorticity distribution are long-lived and can produce a significant distortion of the heated region. The results of our numerical simulations and the estimates of the nonlinear theory are quite consistent. We also compare the nonreactive numerical simulations with the experimental data of Markstein on shock wave and flame interactions in a stoichiometric mixture of n-butane and air. The numerical simulations reproduce most of the major experimental observations. We show that conventional Rayleigh-Taylor instability theory, which assumes a very small initial perturbation, does not provide a viable description of vorticity generation in Markstein's experiment. Instead, a nonlinear treatment based on the finite misalignment and finite interaction time of the pressure gradient associated with the shock and the density gradient of the flame is necessary. The effects of chemical reactions are also clarified through the comparison of numerical simulation and experiment.

Translation Effects on Simulated Tornadoes

Abstract: A simulation of tornadoes translating over the ground was carried out in a modified Ward simulator The purpose was to investigate the effects of translation on tornado dynamics The results are as follows: • Secondary vortexes were found to be generated by the relative motion between the main vortex and rough “ground” The secondary vortexes trail the primary vortex Apparently they feed off the energy of the primary vortex, and achieve a momentary transition state from a single vortex to multiple vortexes • The core radius increases with swirl ratio and decreases with surface roughness Translation causes a local increase in swirl ratio, increasing the core size over that of a stationary vortex • The central pressure drop increases with swirl ratio during translation Translation also causes a steeper pressure gradient on the trailing side of the vortex core A similar characteristic tilt on the trailing side of the pressure profile has been noted on barograms for real tornadoes

The vertical structure of the zonal pressure gradient in the eastern equatorial Pacific

Abstract: CTD data from the EPOCS and NORPAX experiments were used to construct a mean zonal pressure gradient profile between 110°W and 150°W for the 1979 to 1981 pre-El Nino time period. The mean zonal pressure gradient referenced to 100 dbar had a value of −4.5 × 10−7 m s−2 at the surface and decreased to within two standard errors of zero at 200 dbar. Below this depth the mean was not significantly different from zero. Deviations from this mean were not related to fluctuations of the zonally averaged zonal wind stress between 150°W and 110°W. Rather, the largest deviations, in the boreal springs of 1979 and 1980, appeared to be associated first with vertical-mode Kelvin wave pulses propagating eastward along the equator. The 1979–81 mean profile was also used as a reference to examine variations in zonal pressure gradient during the 1982/83 ENSO event. The sea surface was more sharply sloped upward from the east to west in April and September 1982 before arid near the beginning of the event. The surface slope was below normal in April and October 1983. Vertical profiles of the zonal pressure gradient deviations showed large high vertical-mode contributions during the vent than in the prevent samples.

The thermal structure of the inn valley atmosphere

Abstract: The thermal structure of the Inn valley atmosphere is being investigated, in comparison with that over the adjacent plains. A new method has been developed for computing “fictitious”, smoothed vertical temperature profiles from SYNOP data, which enables us to derive temperature statistics. In this procedure, pressure and temperature at the Zugspitze mountain observatory play a key role. The daily range of the barometric mean temperature of an air column in the Inn valley is more than twice that of an air column over Munich. The main reason for this is geometrical: the lesser volume of air in the valley. From a schematic plot of horizontal pressure gradient versus wind speed along the valley we obtain an estimate of typical reaction times for the valley wind system, which are of the order of 30 minutes only. Thus, equilibrium between pressure gradient and friction force is being established quickly.

Numerical calculations of coastal flow with turbulent dynamics

Abstract: A two-dimensional numerical model of coastal flow, in which the eddy fluxes are computed by a second-order turbulence model, has been developed. The behaviour of the inertial oscillations due to an impulsive start is in excellent agreement with the analytical solution of Kunduet al. (Deep-Sea Research, 30, 1059–1082, 1983). Much of the inertial energy gain in the deep ocean is due to the downward leakage from the coast-surface corner and is accompanied by an upward phase propagation. The low-frequency upwelling solutions develop gravitationally unstable regions in the surface layer, even in the presence of realistic surface heating. But the thickness of the surface layer without surface cooling is never very large, so the analytical models driven by a sink at the coast-surface corner give realistic subsurface solutions. The upwelling solutions generate flow reversal across a strong thermocline, but no ‘closed’ double cells. Frictional turning, as suggested by several workers, is responsible for the flow reversal. These open double cell persist in the presence of surface heating but not in the presence of an alongshore pressure gradient, pγ = τγ(maximum depth). The imposition of pγ creates a poleward undercurrent on a flat shelf but not on a sloping shelf. The alongshore jet moves offshore due to the nonlinear advection of the thermocline, so that the width of the jet is larger than the Rossby radius. An approximate expression has been derived for predicting the offshore frontal location; the numerical calculation is in fair agreement with it.

Partially Penetrating Fractures: Pressure Transient Analysis of an Infinite Conductivity Fracture

Abstract: The effect of the partial penetration of an infinite conductivity fracture on the transient pressure behavior of a vertically fractured well is investigated. Analysis of results shows that the pressure behavior of a well intersected by a partially-penetrating infinite conductivity vertical fracture can be divided into three flow periods: 1) the early time flow period which is characterized by a formation linear flow as in the case of a fully-penetrating infinite-conductivity vertical fracture, 2) the infinite-acting flow period and 3) the pseudoradial flow period which develops after the effects of the vertical boundaries of the reservoir are felt in the pressure behavior of the well. A log-log graph of log(h /SUB f/ /h)p /SUB wD/ versus log t /SUB Dxf/ shows a slope of one half during the early time flow period of a well with an infinite-conductivity partially penetrating fracture. The time for the end of the early time flow period is directly related to the square of the dimensionless height of the fracture, h /SUB fD/, which is defined as the ratio between the height of the fracture and its half length.

Stress and relaxation time in the viscoelastic lithosphere inferred from the outer topographic rise

Abstract: The deformation of a thin viscoelastic plate is usually analyzed by use of an equation that is derived with an artificial assumption of the Poisson's ratio equal to 1/2. It is shown in this paper that a simple treatment applicable to an arbitrary value of Poisson's ratio is possible by introducing a new variable that represents the pressure gradient between the top and bottom of the plate. In this treatment a one-dimensional stationary deformation of moving plate is given by a simple analytic equation. This equation is used to analyze the bathymetry of the outer topographic rise seaward of the deep-sea trenches. The analysis reveals that the lithosphere in the western Pacific trenches is subject to an extensional horizontal force of 100 MPa or greater. The horizontal force may be much less or even compressive in the eastern Pacific trenches. To prevent horizontal force and bending stress from being extraordinarily large, the Maxwell relaxation time of the plate must be 1 m.y. or shorter, and the effective viscosity must be 1024 Pa s or less.

A Wall Law for Turbulent Boundary Layers in Adverse Pressure Gradients

Abstract: A relation between mean velocity and turbulent shear stress has been derived for turbulent boundary layers developed under adverse pressure gradients. The wall law has been obtained by performing a one-dimensional analysis on the turbulent kinetic energy equation with assumptions of local similarity. The analysis relates the diffusional flux to the shear stress gradient. Physical limiting conditions and known experimental results are used to evaluate unknown constants appearing in the derived equation. The resulting wall law is particularly suited for the near-wall treatment in the numerical calculations.

Turbulent spot growth in favorable pressure gradients

Abstract: Experimental results are presented on the lateral growth of turbulent spots in a series of flows with favorable pressure gradients. It is shown that the wedge angle increases slowly with the Reynolds number and that a favorable pressure gradient inhibits the growth of turbulent spots and, in general, results in a nonlinear turbulent wedge. As soon as the pressure gradient decreases to the point where the flow becomes supercritical, however, spot growth increases rapidly and the associated turbulent wedge becomes linear.