Showing papers on "Pressure gradient published in 2013"

Pressure gradient effects on the large-scale structure of turbulent boundary layers

Abstract: Research into high-Reynolds-number turbulent boundary layers in recent years has brought about a renewed interest in the larger-scale structures. It is now known that these structures emerge more prominently in the outer region not only due to increased Reynolds number (Metzger & Klewicki, Phys. Fluids, vol. 13(3), 2001, pp. 692–701; Hutchins & Marusic, J. Fluid Mech., vol. 579, 2007, pp. 1–28), but also when a boundary layer is exposed to an adverse pressure gradient (Bradshaw, J. Fluid Mech., vol. 29, 1967, pp. 625–645; Lee & Sung, J. Fluid Mech., vol. 639, 2009, pp. 101–131). The latter case has not received as much attention in the literature. As such, this work investigates the modification of the large-scale features of boundary layers subjected to zero, adverse and favourable pressure gradients. It is first shown that the mean velocities, turbulence intensities and turbulence production are significantly different in the outer region across the three cases. Spectral and scale decomposition analyses confirm that the large scales are more energized throughout the entire adverse pressure gradient boundary layer, especially in the outer region. Although more energetic, there is a similar spectral distribution of energy in the wake region, implying the geometrical structure of the outer layer remains universal in all cases. Comparisons are also made of the amplitude modulation of small scales by the large-scale motions for the three pressure gradient cases. The wall-normal location of the zero-crossing of small-scale amplitude modulation is found to increase with increasing pressure gradient, yet this location continues to coincide with the large-scale energetic peak wall-normal location (as has been observed in zero pressure gradient boundary layers). The amplitude modulation effect is found to increase as pressure gradient is increased from favourable to adverse.

An algorithm to estimate unsteady and quasi-steady pressure fields from velocity field measurements

Abstract: We describe and characterize a method for estimating the pressure field corresponding to velocity field measurements such as those obtained by using particle image velocimetry The pressure gradient is estimated from a time series of velocity fields for unsteady calculations or from a single velocity field for quasi-steady calculations The corresponding pressure field is determined based on median polling of several integration paths through the pressure gradient field in order to reduce the effect of measurement errors that accumulate along individual integration paths Integration paths are restricted to the nodes of the measured velocity field, thereby eliminating the need for measurement interpolation during this step and significantly reducing the computational cost of the algorithm relative to previous approaches The method is validated by using numerically simulated flow past a stationary, two-dimensional bluff body and a computational model of a three-dimensional, self-propelled anguilliform swimmer to study the effects of spatial and temporal resolution, domain size, signal-to-noise ratio and out-of-plane effects Particle image velocimetry measurements of a freely swimming jellyfish medusa and a freely swimming lamprey are analyzed using the method to demonstrate the efficacy of the approach when applied to empirical data

Conditional sampling of transitional boundary layers in pressure gradients

Abstract: Statistical analysis of transitional boundary layers in pressure gradients is performed using the flow fields from direct numerical simulations of bypass transition. Laminar–turbulent discrimination separates the streaky laminar flow from turbulent regions. Individual streaks are identified and tracked in the flow field in order to obtain statistics of the amplitude of the streak population. An extreme value model is proposed for the distribution of streak amplitudes. It is also possible to differentiate those streaks which break down into turbulent spots from innocuous events. It is shown that turbulence onset is due to high-amplitude streaks, with streamwise perturbation velocity exceeding 20 % of the free stream speed. The resulting turbulent spots are tracked downstream. The current analysis allows for the measurement of the lateral spreading angles of individual spots and their spatial extent and volumes. It is demonstrated that the volumetric growth rate of turbulent spots is insensitive to pressure gradient.

Flow pattern map, heat transfer and pressure drops during evaporation of R-1234ze(E) and R134a in a horizontal, circular smooth tube: Experiments and assessment of predictive methods

Abstract: This paper presents experimental results for local heat transfer coefficients, adiabatic frictional pressure gradients and two-phase flow regimes with the low-GWP refrigerant R-1234ze(E), compared to Hydro-Fluoro-Carbon refrigerant R-134a in the same conditions. In particular the results refer to an experimental investigation carried out in a circular smooth tube of 6.00 mm of inner diameter, for saturation temperatures between −2.9 °C and 12.1 °C, mass fluxes between 146 and 520 kg m−2 s−1 and heat fluxes between 5.0 and 20.4 kW m−2. These experimental results are compared to those for R-134a at the same operating conditions. Moreover, an assessment of predictive methods is provided for local heat transfer coefficients and frictional pressure gradients; also a direct comparison of flow regimes visualizations for R-1234ze(E) with a flow pattern map available in literature is presented.

Vortex-corner interactions in a cavity shear layer elucidated by time-resolved measurements of the pressure field

Abstract: The flow structure and turbulence in an open cavity shear layer has been investigated experimentally at a Reynolds number of , with an emphasis on interactions of the unsteady pressure field with the cavity corners. A large database of time-resolved two-dimensional PIV measurements has been used to obtain the velocity distributions and calculate the pressure by spatially integrating the material acceleration at a series of sample areas covering the entire shear layer and the flow surrounding the corners. Conditional sampling, low-pass filtering and time correlations among variables enable us to elucidate several processes, which have distinctly different frequency ranges, that dominate the shear layer interactions with the corners. Kelvin–Helmholtz shear layer eddies have the expected Strouhal number range of 0.5–3.2. Their interactions with the trailing corner introduce two sources of vorticity fluctuations above the corner. The first is caused by the expected advection of remnants of the shear layer eddies. The second source involves fluctuations in local viscous vorticity flux away from the wall caused by periodic variations in the streamwise pressure gradients. This local production peaks when the shear layer vortices are located away from the corner, creating a lingering region with peak vorticity just above the corner. The associated periodic pressure minima there are lower than any other point in the entire flow field, making the region above the corner most prone to cavitation inception. Flapping of the shear layer and boundary layer upstream of the leading corner occurs at very low Strouhal numbers of ∼0.05, affecting all the flow and turbulence quantities around both corners. Time-dependent correlations of the shear layer elevation show that the flapping starts in the boundary layer upstream of the leading corner and propagates downstream at the free stream speed. Near the trailing corner, when the shear layer elevation is low, the stagnation pressure in front of the wall, the downward jetting flow along this wall, the fraction of shear layer vorticity entrained back into the cavity, and the magnitude of the pressure minimum above the corner are higher than those measured when the shear layer is high. However, the variations in downward jetting decay rapidly with increasing distance from the trailing corner, indicating that it does not play a direct role in a feedback mechanism that sustains the flapping. There is also low correlation between the boundary/shear layer elevation and the returning flow along the upstream vertical wall, providing little evidence that this returning flow affects the flapping directly. However, the characteristic period of flapping, ∼0.6 s, is consistent with recirculation time of the fluid within the cavity away from boundaries. The high negative correlations of shear/boundary layer elevation with the streamwise pressure gradient above the leading corner introduce a plausible mechanism that sustains the flapping: when the shear layer is low, the boundary layer is subjected to high adverse streamwise pressure gradients that force it to widen, and when the shear layer is high, the pressure gradients decrease, allowing the boundary layer to thin down. Flow mechanisms that would cause the flapping-induced pressure changes, and their relations to the flow within the cavity are discussed.

Response of a hypersonic turbulent boundary layer to favourable pressure gradients

Abstract: The role of streamline curvature-driven favourable pressure gradients in modifying the turbulence structure of a Mach 4.9, high-Reynolds-number ( ) boundary layer is examined. Three pressure gradient cases ( and ) are characterized via particle image velocimetry. The expected stabilizing trends in the Reynolds stresses are observed, with a sign reversal in the Reynolds shear stress in the outer part of the boundary layer for the strongest favourable pressure gradient considered. The increased transverse normal strain rate and reduced principal strain rate are the primary factors. Reynolds stress quadrant events are redistributed, such that the relative differences between the quadrant magnitudes decreases. Very little preferential quadrant mode selection is observed for the strongest pressure gradient considered. Two-point correlations suggest that the turbulent structures are reoriented to lean farther away from the wall, accompanied by a slight reduction in their characteristic size, consistent with previous flow visualization studies. This reorientation is more pronounced in the outer, dilatation-dominated region of the boundary layer, whereas the alteration in structure size is more pronounced nearer the wall, where the principal strain rates are larger. In addition, integration of a simplified form of a Reynolds stress transport closure model provided a framework to assess the role of the strain-rate field on the observed Reynolds shear stresses. Given the simple geometry, the present data provide a suitable test bed for Reynolds stress transport and large-eddy model development and validation.

Combined pressure-driven and electroosmotic flow of Casson fluid through a slit microchannel

Abstract: This study aims to develop analytical solutions for steady electroosmotic (EO) flow of a viscoplastic material, namely Casson fluid, through a parallel-plate microchannel. The flow is driven by electric as well as pressure forcings. A very thin electric double layer is assumed, and the Debye–Huckel approximation is used. The Casson yield stress makes the present problem distinct from existing studies on EO flow of other kinds of non-Newtonian such as power-law fluids. A first step of the analysis is to locate the yield surface, which divides the flow section into sheared and unsheared regions, where the stress is larger and smaller in magnitude than the yield stress, respectively. Different combinations of the electric and pressure forcings can lead to different types of distribution of stress relative to the yield stress. In this study, integrals of the nonlinear coupling terms of the two forcings are analytically expressed by uniformly valid approximations derived using the boundary-layer theory. It is shown that even a small value of the Casson yield stress, characteristic of that of blood, can considerably reduce the rate of flow of the fluid through a microchannel by electroosmosis. The decreasing effect of the yield stress on the flow is intensified by the presence of a pressure gradient, whether favorable or adverse.

Series Solutions of Magnetohydrodynamic Peristaltic Flow of a Jeffrey Fluid in Eccentric Cylinders

Abstract: In this article, the mathematical modelling on magnetohydrodynamic peristaltic flow of Jeffrey fluid in the gap between two eccentric tubes has been discussed in the presence of applied magnetic fi eld. Geometrically, we considered two eccentric tubes in which the inner tube is rigid while the tube at the outer side has a sinusoidal wave pro pagating along the wall. The governing equations for Jeffrey fluid in a cylindrical coordinates for three dimensional flow are given. The approximations of low Reynolds number and long wavelength have been employed to reduce the highly nonlinear partial differential equations. The problem has been solved with the help of homotopy perturbation method alongwith eigen function expansion method. The graphs of pressure rise, pressure gradient and velocity (for two and three dimensional flow) have been drawn. The stre amlines have also been presented to discuss the trapping bolus discipline.

MHD and gyro-kinetic stability of JET pedestals

Abstract: The pedestal profile measurements in high triangularity JET plasmas show that with low fuelling the pedestal width decreases during the ELM cycle and with high fuelling it stays constant. In the low fuelling case the pedestal pressure gradient keeps increasing until the ELM crash and in the high fuelling case it initially increases then saturates during the ELM cycle.Stability analysis reveals that both JET plasmas become unstable to finite-n ideal MHD peeling–ballooning modes at the end of the ELM cycle. During the ELM cycle, n = ∞ ideal MHD ballooning modes and kinetic ballooning modes are found to be locally stable in most of the steep pressure gradient region of the pedestal owing to the large bootstrap current, but to be locally unstable in a narrow region of plasma at the extreme edge.Unstable micro-tearing modes are found at the JET pedestal top, but they are sub-dominant to ion temperature gradient modes. They are insensitive to collisionality and stabilized by increasing density gradient.

A multifold reduction in the transition Reynolds number, and ultra-fast mixing, in a micro-channel due to a dynamical instability induced by a soft wall

Abstract: A dynamical instability is observed in experimental studies on micro-channels of rectangular cross-section with smallest dimension 100 and 160 mu m in which one of the walls is made of soft gel. There is a spontaneous transition from an ordered, laminar flow to a chaotic and highly mixed flow state when the Reynolds number increases beyond a critical value. The critical Reynolds number, which decreases as the elasticity modulus of the soft wall is reduced, is as low as 200 for the softest wall used here (in contrast to 1200 for a rigid-walled channel) The instability onset is observed by the breakup of a dye-stream introduced in the centre of the micro-channel, as well as the onset of wall oscillations due to laser scattering from fluorescent beads embedded in the wall of the channel. The mixing time across a channel of width 1.5 mm, measured by dye-stream and outlet conductance experiments, is smaller by a factor of 10(5) than that for a laminar flow. The increased mixing rate comes at very little cost, because the pressure drop (energy requirement to drive the flow) increases continuously and modestly at transition. The deformed shape is reconstructed numerically, and computational fluid dynamics (CFD) simulations are carried out to obtain the pressure gradient and the velocity fields for different flow rates. The pressure difference across the channel predicted by simulations is in agreement with the experiments (within experimental errors) for flow rates where the dye stream is laminar, but the experimental pressure difference is higher than the simulation prediction after dye-stream breakup. A linear stability analysis is carried out using the parallel-flow approximation, in which the wall is modelled as a neo-Hookean elastic solid, and the simulation results for the mean velocity and pressure gradient from the CFD simulations are used as inputs. The stability analysis accurately predicts the Reynolds number (based on flow rate) at which an instability is observed in the dye stream, and it also predicts that the instability first takes place at the downstream converging section of the channel, and not at the upstream diverging section. The stability analysis also indicates that the destabilization is due to the modification of the flow and the local pressure gradient due to the wall deformation; if we assume a parabolic velocity profile with the pressure gradient given by the plane Poiseuille law, the flow is always found to be stable.

MHD and Gyro-kinetic Stability of JET Pedestals

Abstract: The pedestal profile measurements in high triangularity JET plasmas show that with low fuelling the pedestal width decreases during the ELM cycle and with high fuelling it stays constant. In the low fuelling case the pedestal pressure gradient keeps increasing until the ELM crash and in the high fuelling case it initially increases then saturates during the ELM cycle. Stability analysis reveals that both JET plasmas become unstable to finite-n ideal MHD peeling-ballooning modes at the end of the ELM cycle. During the ELM cycle, infinite-n ideal MHD ballooning modes and kinetic ballooning modes are found to be locally stable in most of the steep pressure gradient region of the pedestal owing to the large bootstrap current, but to be locally unstable in a narrow region of plasma at the extreme edge. Unstable micro-tearing modes are found at the JET pedestal top, but they are sub-dominant to ion temperature gradient modes. They are insensitive to collisionality and stabilised by increasing density gradient.

Comparison of experiments and simulations for zero pressure gradient turbulent boundary layers at moderate Reynolds numbers

Abstract: A detailed comparison between recent direct numerical simulation (DNS) and experiments of a turbulent boundary layer under zero pressure gradient at Re θ = 2,500 and 4,000 (based on the free-stream velocity and momentum-loss thickness) is presented. The well-resolved DNS is computed in a long spatial domain (Schlatter and Orlu in J Fluid Mech 659:116, 2010a), including the disturbance strip, while the experiments consist of single hot-wire probe and oil-film interferometry measurements. Remarkably, good agreement is obtained for integral quantities such as skin friction and shape factor, as well as mean and fluctuating streamwise velocity profiles, higher-order moments and probability density distributions. The agreement also extends to spectral/structural quantities such as the amplitude modulation of the small scales by the large-scale motion and temporal spectral maps throughout the boundary layer. Differences within the inner layer observed for statistical and spectral quantities could entirely be removed by spatially averaging the DNS to match the viscous-scaled length of the hot-wire sensor, thereby explaining observed differences solely by insufficient spatial resolution of the hot-wire sensor. For the highest Reynolds number, Re θ = 4,000, the experimental data exhibit a more pronounced secondary spectral peak in the outer region (y/δ 99 = 0.1) related to structures with length on the order of 5–7 boundary layer thicknesses, which is weaker and slightly moved towards lower temporal periods in the DNS. The cause is thought to be related to the limited spanwise box size which constrains the growth of the very large structures. In the light of the difficulty to obtain “canonical” flow conditions, both in DNS and the wind tunnel where effects such as boundary treatment, pressure gradient and turbulence tripping need to be considered, the present cross-validation of the data sets, at least for the present Re θ -range, provides important reference data for future studies and highlights the importance of taking spatial resolution effects into account when comparing experiment and DNS. For the considered flow, the present data also provide quantitative guidelines on what level of accuracy can be expected for the agreement between DNS and experiments.

Ideal ballooning modes in the tokamak scrape-off layer

Abstract: A drift-reduced Braginskii fluid model is used to carry out a linear and non-linear study of ideal ballooning modes in the tokamak scrape-off layer. First, it is shown that the scrape-off layer finite connection length and boundary conditions modify the ideal stability limit with respect to the closed flux-surface result. Then, in a two-fluid description, it is found that magnetic induction effects can destabilize long wavelength resistive ballooning modes below marginal ideal stability. Non-linear simulations confirm a gradual transition from small scale quasi-electrostatic interchange turbulence to longer wavelength modes as the plasma beta is increased. The transition to global ideal ballooning modes occurs, roughly, at the linearly obtained stability threshold. The transport levels and the pressure gradient as a function of plasma beta obtained in non-linear simulations can be predicted using the non-linear flattening of the pressure profile from the linear modes as a turbulent saturation mechanism.

Seismic‐ and Tsunami‐Wave Propagation of the 2011 Off the Pacific Coast of Tohoku Earthquake as Inferred from the Tsunami‐Coupled Finite‐Difference Simulation

Abstract: The 2011 Tohoku earthquake ( M 9.0) caused significant hazards including strong ground motion, coseismic ground deformation, and tsunamis. For a deeper understanding of these phenomena, we conducted a large‐scale, parallel computer simulation by means of the finite‐difference method (FDM) with newly developed tsunami‐coupled equations of motion. This method is based on the equations of motion for an elastic medium, treating seawater as elastic material having zero S ‐wave velocity. Tsunami waves are included by taking into account gravity and their equilibrium with the pressure gradient. An effective method of FDM simulation using the state‐of‐the‐art massively parallelized K computer is also studied. With the use of a 3D layered velocity structure that includes topography and bathymetry, basement structure, Moho depth, and plate boundaries, and use of the appropriate source‐rupture model based on joint inversion of seismic waves and geodetic observations, the simulated seismic waves demonstrate anomalous seismic‐wave propagation by the thick 3D basin structure inland. We also found that the sea column acts as a strong absorber of seismic waves for shallow up‐dip slip. On the ocean side, coseismic deformation and tsunamis are dynamically generated in this simulation. Tsunami attacks on the subsided Pacific coast are simulated without any additional assumptions. We also modeled the tsunami and seismic records of ocean‐bottom pressure gauges above the fault. Because sea‐bottom tsunami and seismic observation is powerful but very complex, recording both seismic and tsunami waves, the use of these coupled numerical simulations has great potential for resolving complex source fault rupture processes in a 3D heterogeneous structure. Online Material: Mpeg movies of fault slip, seismic‐wave propagation, seafloor and ground displacement, and tsunamic propagation.

Mhd eyring–prandtl fluid flow with convective boundary conditions in small intestines

Abstract: In this paper, we have discussed the food movement in stomach with thermal boundary conditions. Eyring–Prandtl fluid model is considered. Formulation of the considered phenomena have been developed for both fixed and moving frame of references. Regular perturbation is used to find the solution of stream function, temperature profile and pressure gradient. Analysis has been carried out for velocity, "stream function, temperature, pressure gradient and heat transfer". Appearance of pressure gradient is quite complicated so to get the expression for pressure rise we have used numerical integration. It is perceived that the velocity close to the channel walls is not same in outlook of the Eyring–Prandtl fluid parameter taken as β and Hartman number M. The velocity decreases by increasing β and M.

Fitting Foam Simulation Model Parameters to Data

Abstract: Cheng et al. (2000) present a simple method to fit foam simulation parameters without oil to data for pressure gradient as a function of superficial velocities of gas and liquid. The key in this process is the identification of "high-quality" (high gas fraction) and "low-quality" foam regimes. The method is essentially the same for the foam model parameters in foam models in STARS, UTCHEM or ECLIPSE. Often, however, available data are more limited - pressure gradient for one scan of foam quality at fixed total superficial velocity. We show how to extend this method to the more limited data set. The transition in regimes occurs at the foam quality with the maximum pressure gradient. We illustrate the method by fitting parameters to several published data sets. Our approach is simple and direct. The model fit would be appropriate for an EOR process involving foam injection at finite water fraction, but not a SAG foam process involving large slugs of gas and liquid. For the latter process, model parameters should be fit to data relevant to that process, i.e. at extremely high foam quality. The approach assumes an abrupt transition between high- and low-quality foam regimes, i.e. a large value of epdry in the STARS foam model. If a smaller value is chosen for faster execution of the simulator this approach could underestimate pressure gradient near its maximum value at the transition between regimes. In that case the parameter values quickly obtained by this method could provide the initial guess for a computer-based least-squares fit of all parameters, including a smaller value of epdry, and a check on the parameters so obtained.

Characteristics of Jeffrey fluid model for peristaltic flow of chyme in small intestine with magnetic field

Abstract: In the present article we have analyzed the Jeffrey fluid model for the peristaltic flow of chyme in the small intestine. We have formulated the problem using two non-periodic sinusoidal waves of different wavelengths propagating with same speed c along the outer wall of the tube. Governing equations for the problem under consideration have been simplified under the assumptions of long wavelength and low Reynolds number approximation (such assumptions are consistent since Re (Reynolds number) is very small and long wavelength approximation also exists in the small intestine). Exact solutions have been calculated for velocity and pressure rise. Physical behavior of different parameters of Jeffrey fluid has been presented graphically for velocity, pressure rise, pressure gradient and frictional forces. The trapping phenomenon is also discussed at the end of the article.

The influence of intense electric fields on three-dimensional asymmetric magnetic reconnection

Abstract: A three-dimensional particle-in-cell simulation of magnetic reconnection in an asymmetric configuration without a guide field and with temperature ratio Ti/Te>1 demonstrates that intense perpendicular electric fields are produced on the low-density side of the current layer where there is a strong gradient in the plasma density. The simulation shows that the 3-D reconnection rate is unaffected by these intense electric fields, that the electron current layer near the X line remains coherent and does not break up, but that localized regions of strong energy dissipation exist along the low-density separatrices. Near the X line the dominant term in the generalized Ohm's law for the reconnection electric field remains the off-diagonal electron pressure gradient ∂Pexy/∂x. On the low-beta separatrix, however, the anomalous drag −⟨δnδEy⟩/⟨n⟩ makes an equally important contribution to that of the pressure gradient to the average Ey field.

Dynamics of coronal rain and descending plasma blobs in solar prominences: I. Fully ionised case

Abstract: Observations of active regions and limb prominences often show cold, dense blobs descending with an acceleration smaller than that of free fall. The dynamics of these condensations falling in the solar corona is investigated in this paper using a simple fully ionised plasma model. We find that the presence of a heavy condensation gives rise to a dynamical rearrangement of the coronal pressure that results in the formation of a large pressure gradient that opposes gravity. Eventually this pressure gradient becomes so large that the blob acceleration vanishes or even points upwards. Then, the blob descent is characterised by an initial acceleration phase followed by an essentially constant velocity phase. These two stages can be identified in published time-distance diagrams of coronal rain events. Both the duration of the first stage and the velocity attained by the blob increase for larger values of the ratio of blob to coronal density, for larger blob mass, and for smaller coronal temperature. Dense blobs are characterised by a detectable density growth (up to 60% in our calculations) and by a steepening of the density in their lower part, that could lead to the formation of a shock. They also emit sound waves that could be detected as small intensity changes with periods of the order of 100 s and lasting between a few and about ten periods. Finally, the curvature of the falling path is only relevant when a very dense blob falls along inclined magnetic field lines.

Three dimensional peristaltic flow of Williamson fluid in a rectangular duct

Abstract: In present article, three dimensional peristaltic flow of a Williamson fluid model in rectangular channel has been discussed. The flow is unsteady and caused by propagation of sinusoidal waves due to peristaltic pumping. The equations of motion are derived for constitutive relation of Williamson model and are finally simplified under restrictions of low Reynolds number and long wavelength. The highly nonlinear and nonhomogeneous partial differential equations are solved by using homotopy perturbation method with combination of eigen function expansion method. The expression for pressure rise is found numerically. The final calculations for velocity, pressure gradient, pressure rise and stream functions are narrated graphically.