Negligible Pressure Gradient Research Articles

Hydraulic permeation-induced water concentration gradients in ion exchange membranes

Although substantial literature has detailed transport through swollen membranes, there are still conflicting reports regarding the fundamental physics of hydraulic water transport in such materials, with a long-standing debate centered on the applicability of the pore-flow and solution-diffusion mechanisms. The critical thermodynamic distinction between these models is the presence of a membrane-phase concentration gradient. For pure solvent transport, the pore-flow model presumes that a membrane-phase pressure gradient drives transport in the absence of a concentration gradient. In contrast, the solution-diffusion model proposes that a membrane-phase concentration gradient drives transport and that there is a negligible pressure gradient through the membrane. To address this topic for ion exchange membranes, this study reports measurements of water concentration profiles in pressurized films of Nafion and a commercial membrane based on sulfonated poly (styrene-co-divinylbenzene). Several films were stacked together in a custom-built permeation cell, with the feed side pressurized to between 68.9 and 137.9 bar, and the permeate side held at atmospheric conditions. At steady state, the experiment was stopped, the films were separated, and the water content of each film was measured, revealing a water concentration gradient through the stack thickness that increased with increasing feed pressure. The experimental data were in good agreement with theoretical predictions based on Fick's law and polymer-solvent swelling theories (i.e., Flory-Huggins and Flory-Rehner). These results are consistent with the solution-diffusion model and cannot be explained by a pore-flow mechanism.

On the interplay of body-force distributions and flow speed for dielectric-barrier discharge plasma actuators

The dielectric-barrier discharge plasma actuator is a well-established device commonly operated in boundary-layer airflows for active flow control. In the present experimental investigation, their ability to cause momentum transfer to the surrounding fluid is analyzed by means of spatio-temporal body-force distributions in both quiescent air and external airflow conditions. The work is motivated by the limitation to quiescent-air operating conditions of frequent previous efforts. Available analytical velocity-information-based force derivation approaches are contrasted to investigate the actuator performance under conditions of their area of application. Results of body force in quiescent air, in agreement with literature, confirm the major taken assumption for Navier–Stokes-based body-force formulations—a negligible pressure gradient. However, the previous circumstance turns out as an invalid assumption for plasma actuation encountering an external airflow. These outcomes coincide with the findings in the numerical work of (2015 Numerical investigation of plasma-actuator force-term estimations from flow experiments J. Phys. D: Appl. Phys. 48 395203), following the recommendation to apply a vorticity-equation-based approach under such conditions. Furthermore, the shape of the spatio-temporal body-force distribution is observed to undergo changes when the airflow speed increases. On the other hand, the integral force magnitude is found to remain approximately constant. Moreover, the choice of phase resolution of the discharge cycle has an implication on the accuracy of the temporal force evolution, therefore, clarifying the importance of a priori defining the type of body-force analysis in an experiment; i.e. integral force magnitude, time-averaged or time-resolved evaluation. As a promising finding of utmost importance for the actuator performance, the actuator remains as effective as in quiescent air under presence of the external airflow, which immediately renders the actuator fluid-mechanic efficiency to increase for increasing airflow speed.

Demonstration of RANS models with wall functions in the spectral element code Nek5000

The spectral element based computational fluid dynamics (CFD) code Nek5000 has been traditionally used for high-fidelity applications, such as direct numerical simulation (DNS) and large eddy simulation (LES). These techniques require very fine numerical resolution to accurately capture turbulent fluctuations which can be prohibitively expensive for users without access to leadership class computing facilities. For broader application and adoption, significant effort has been invested to develop Reynolds-averaged Navier–Stokes (RANS) capabilities in Nek5000.This work presents details of the implementation and demonstration of the standard wall functions for the k – τ model in Nek5000. Results using the wall-modeled approach are compared to a wall-resolved approach for cases with negligible pressure gradient, viz., channel flow, pipe flow and flow in a reactor subchannel. Results show reasonably good agreement between the two approaches for friction factor and Nusselt number. Some expected differences are identified near the wall. These cases demonstrate the potential for significant computational savings by using much coarser meshes for the wall-modeled approach, with only minor differences between the predicted result. Additionally, several Reynolds numbers up to 1,000,000 are demonstrated for pipe flow and predicted friction factors and Nusselt numbers compared well to available correlations, with the worst below 10%. As the Reynolds number is increased, better agreement is observed between the correlations and the wall-modeled approach. In addition, flow in a molten salt fast reactor (MSFR) core is considered which features an adverse pressure gradient and flow separation. It showcases the inability of standard wall functions to accurately predict flows with adverse pressure gradients. The results, however, match reasonably well in trend in regions of the flow where the boundary layer is attached. Ongoing research is dedicated to include a pressure gradient correction to wall functions to improve the accuracy of flows with separation or reattachment and adverse or favorable pressure gradients.

Local topography‐induced pressure gradient effects on the wake and power output of a model wind turbine

Wind-tunnel experiments were performed to study the effect of favorable and adverse constant pressure gradients (PG) from local changes in the topography right downwind of a model wind turbine. Particle image velocimetry was used to characterize the near and intermediate wake regions. We explored five scenarios, two favorable, two adverse PG, and a case with negligible PG. Results show that the PGs induce a wake deflection and modulate the wake. They imposed a relatively small impact on the turbulence kinetic energy and kinematic shear stress but a comparatively dominant effect on the bulk flow on the flow recovery. Based on this, a simple formulation is used to describe the impact of PG on the wake. We modeled the base flow through a linearized perturbation method; the wake is obtained by solving a simplified, integrated streamwise momentum equation. This approach reasonably estimated the flow profile and PG-induced power output variations.

Testing the Accuracy of the Cell-Set Model Applied on Vane-Type Sub-Boundary Layer Vortex Generators

Vortex Generators (VGs) are applied before the expected region of separation of the boundary layer in order to delay or remove the flow separation. Although their height is usually similar to that of the boundary layer, in some applications, lower VGs are used, Sub-Boundary Layer Vortex Generators (SBVGs), since this reduces the drag coefficient. Numerical simulations of sub-boundary layer vane-type vortex generators on a flat plate in a negligible pressure gradient flow were conducted using the fully resolved mesh model and the cell-set model, with the aim on assessing the accuracy of the cell-set model with Reynolds-Averaged Navier-Stokes (RANS) and Large Eddy Simulation (LES) turbulence modelling techniques. The implementation of the cell-set model has supposed savings of the 40% in terms of computational time. The vortexes generated on the wake behind the VG; vortical structure of the primary vortex; and its path, size, strength, and produced wall shear stress have been studied. The results show good agreements between meshing models in the higher VGs, but slight discrepancies on the lower ones. These disparities are more pronounced with LES. Further study of the cell-set model is proposed, since its implementation entails great computational time and resources savings.

On the mathematical model simplification using constant Lewis number – Impact assessment on heterogeneous char conversion process

Reactive systems in a thermochemical conversion domain are modelled considering N-specie, 1-energy and 2-mass conservation equations assuming negligible pressure gradient resulting in N+3 non-linear coupled PDE system with dependency on thermodynamic and transport properties. Typically, simplistic temperature-dependent polynomials are chosen for estimating thermal conductivity and specific heat, however, the estimation of mass diffusion coefficient (Di;mix) follows a complicated procedure involving kinetic theory culminating in Chapman-Enskog equation. This renders the solution computationally intensive. The complexity is simplified by assuming a constant Lewis (Le) number, a standard practice in the analytical solution for conventional reactive systems. In fixing Le, (Di;mix) is equated to thermal diffusivity (a ratio of thermodynamic properties) resulting in the specie and energy equation yielding a similar solution and collapse of N+3 system of simultaneous equations to 3 equations. The current article explores the validity and limitation of assuming constant Le in the simulation of char conversion process in air and steam. Results of char conversion are compared for fixed Le and D estimated with Chapman{Enskog expresion. The analysis suggests that Le remains invariant only under a severely restricted set of conditions. Fixing Le influences, the conversion process either over-/under-predicting the conversion time scales and the product gas composition.

Computational modelling of TRIANGULAR sub-boundary-layer vortex generators

Vortex generators (VGs) are used increasingly more by the wind turbine manufacture industry as flow control devices to improve rotor blade aerodynamic performance. The VG height is usually designed with equal thickness of the local boundary layer at the VG position. Nevertheless, these conventional VGs may produce excess residual drag in some applications. The so-called sub boundary layer VGs can provide enough momentum transfer over a region several times their own height for effective flow-separation control with much lower drag. The main objective is to investigate how well the simulations can reproduce the physics of the flow of the primary vortex generated by a triangular VG mounted on a flat plate with negligible pressure gradient with the angle of attack of the vane to the oncoming flow β= 18. Three different device heights H= 5mm, H1= 6,25mm, H2= 4,16mm have been studied and compared both qualitatively and quantitatively. To that end, computational simulations have been carried out using RANS method and at Reynolds number Re = 2600 based on the boundary layer momentum thickness θ= 2.4 mm at the VG position. The computational results show good agreement with the experimental data available in AVATAR project.

Determination of Phase-Eigenvalues by Rational Factorization and Enhanced Simulation of Two-Phase Mass Flow

In this paper, we present simple and exact eigenvalues for both the solid- and fluid-phases of the real two-phase general model developed by Pudasaini (2012); we call these phase-eigenvalues, the solid- phase-eigenvalues and the fluid-phase-eigenvalues. Results are compared by applying the derived phase- eigenvalues that incorporate the phase-interactions in the two-phase debris movements against the simple and classical solid and fluid eigenvalues without any phase interaction. We have constructed several different set of eigenvalues including the coupled phase eigenvalues by using rational factorization method. At first, we consider for general debris height; factorizing the solid and fluid lateral pressure contributions by considering the negligible pressure gradient; negligible solid lateral pressure; negligible fluid lateral pressure; negligible solid and fluid lateral pressure. Secondly, for a thin debris ow height, we also construct the fourth set of eigenvalues in three different cases. These phase-eigenvalues incorporate strong interaction between the solid and fluid dynamics. The simulation results are produced by taking all these different sets of coupled phase-eigenvalues and are compared with the classical uncoupled set of solid and fluid eigenvalues. The results indicate the importance of phase-eigenvalues and supports for a complete description of the phase- eigenvalues for the enhanced description of real two-phase debris flows and landslide motions.

Bentonite Extrusion into Near-Borehole Fracture

In this paper, we discuss laboratory experiments of bentonite swelling and coupled finite element simulations to explicate bentonite extrusion. For the experiments, we developed a swell cell apparatus to understand the bentonite migration to the near-borehole fracture. We constructed the swell cell using acrylic, which comprised of a borehole and open fracture. Initially, the borehole of the swell cell was filled with bentonite and liquid. Then, the apparatus was sealed for observations. Due to the liquid saturation increase of bentonite, its swelling pressure increased. The developed pressure caused the extrusion of bentonite into the fracture, and the flow of bentonite from the borehole decreased with time. Moreover, for the effectiveness of bentonite-based plugging, there is a limiting condition, which represents the relation between the maximum bentonite migration length with the fracture aperture. Additionally, we also performed the bentonite free swelling test to assess the swelling potential to the fluid salinity, and we observed that with the increase of the salinity, the swelling potential decreased. In addition, we present a fully coupled two-phases fluids flow (e.g., liquid and gas) and deformation flow finite element (FE) model for the bentonite column elements and swell cell model. We also combined the Modified Cam Clay (MCC) model and the swelling model for the bentonite deformation flow model. Then, we also present the validation of the bentonite model. To model other sub-domains, we used the poro-elastic model. Additionally, we obtained the transition between the wetting phase (i.e., liquid) and non-wetting phase (i.e., gas) using the Brooks–Corey model. From the finite element results, we observed that due to the liquid intrusion into the bentonite, the developed capillary pressure gradient results in a change of the hydro-mechanical behavior of the bentonite. Initially, we observed that due to the high capillary pressure gradient, the liquid saturation and the swelling pressure increased, which also decreased with time due to a reduction in the capillary pressure gradient. Thereby, the swelling pressure-induced bentonite migration to the fracture also decreased over time, and after the equilibrium state (for a negligible pressure gradient), there was no significant transport of bentonite into the fracture.

Computational Modelling of Rectangular Sub-Boundary Layer Vortex Generators

Vortex generators (VGs) are increasingly used in the wind turbine manufacture industry as flow control devices to improve rotor blade aerodynamic performance. Nevertheless, VGs may produce excess residual drag in some applications. The so-called sub-boundary layer VGs can provide an effective flow-separation control with lower drag than the conventional VGs. The main objective of this study is to investigate how well the simulations can reproduce the physics of the flow of the primary vortex generated by rectangular sub-boundary layer VGs mounted on a flat plate with a negligible pressure gradient with an angle of attack of the vane to the oncoming flow of β = 18°. Three devices with aspect ratio values of 2, 2.5 and 3 are qualitatively and quantitatively compared. To that end, computational simulations have been carried out using the RANS (Reynolds averaged Navier–Stokes) method and at Reynolds number Re = 2600 based on the boundary layer momentum thickness θ at the VG position. The computational results show good agreement with the experimental data provided by the Advanced Aerodynamic Tools of Large Rotors (AVATAR) European project for the development and validation of aerodynamic models. Finally, the results indicate that the highest VG seems to be more suitable for separation control applications.

Entropy Generation in Steady Laminar Boundary Layers with Pressure Gradients

In an earlier paper in Entropy [1] we hypothesized that the entropy generation rate is the driving force for boundary layer transition from laminar to turbulent flow. Subsequently, with our colleagues we have examined the prediction of entropy generation during such transitions [2,3]. We found that reasonable predictions for engineering purposes could be obtained for flows with negligible streamwise pressure gradients by adapting the linear combination model of Emmons [4]. A question then arises—will the Emmons approach be useful for boundary layer transition with significant streamwise pressure gradients as by Nolan and Zaki [5]. In our implementation the intermittency is calculated by comparison to skin friction correlations for laminar and turbulent boundary layers and is then applied with comparable correlations for the energy dissipation coefficient (i.e., non-dimensional integral entropy generation rate). In the case of negligible pressure gradients the Blasius theory provides the necessary laminar correlations.

Dynamics of barotropic low-frequency fluctuations in San Francisco Bay during upwelling

Observations of wind, surface elevations, and currents in San Francisco Bay during the 1999 upwelling season are analyzed to understand the dynamics of low-frequency currents in upwelling-dominated estuaries. Principal component analysis is carried out to distinguish the different uncorrelated components of the low-frequency fluctuations in the observations. Analyses of ADCP observations at two locations in the Bay show that barotropic currents flow in the direction of winds in the shallow parts of the cross section and flow against the wind in the deeper parts of the cross-section. We ran the SUNTANS model with three forcing functions: (i) winds, (ii) low-frequency surface elevations, and (iii) winds and low-frequency surface elevations, to determine the forcing functions that best reproduce the observed low-frequency fluctuations. Analyses of observations and model simulations show that wind-driven flow in the shallow areas and upwind in the deeper areas, consistent with linear theory. Model simulations also show that the low-frequency currents in the Bay generated due to local winds capture the mean low-frequency barotropic fluctuations seen in the observations during the upwelling season. Model simulations showed that the current generated due to the coastal sea level forcing at the mouth of the Bay is small because the coastal sea levels inside the Bay are in phase with that at the mouth and thus generate weak or negligible pressure gradients. We conclude that forcing of low-frequency sea level fluctuations along the offshore boundaries in the model simulations does not lead to improvement in the prediction of low-frequency currents in San Francisco Bay.

Entropy Generation in the Viscous Parts of Turbulent Boundary Layers

The local (pointwise) entropy generation rate per unit volume S‴ is a key to improving many energy processes and applications. Consequently, in the present study, the objectives are to examine the effects of Reynolds number and favorable streamwise pressure gradients on entropy generation rates across turbulent boundary layers on flat plates and—secondarily—to assess a popular approximate technique for their evaluation. About two-thirds or more of the entropy generation occurs in the viscous part, known as the viscous layer. Fundamental new results for entropy generation in turbulent boundary layers are provided by extending available direct numerical simulations. It was found that, with negligible pressure gradients, results presented in wall coordinates are predicted to be near “universal” in the viscous layer. This apparent universality disappears when a significant pressure gradient is applied; increasing the pressure gradient decreases the entropy generation rate. Within the viscous layer, the approximate evaluation of S‴ differs significantly from the “proper” value but its integral, the entropy generation rate per unit surface area Sap″, agrees within 5% at its edge.

A model for ablated-plasma distribution and width for wire-array Z-pinch implosions

A one-dimensional radial magnetohydrodynamic model of the plasma ablated from a multi-MA wire-array Z pinch is developed. The model is used to compute the mass weighted-density width δ of the plasma at the end of the ablation phase. The wire-array cores are represented as a prescribed source of plasma injection. The plasma, beyond a thin boundary layer, is approximated as a perfect conductor experiencing only magnetic forces and negligible pressure gradients. Assuming that the current driving the Z-pinch implosion increases linearly with time t during the ablation phase, and that the mass-ablation rate varies as tν, it is shown that the density width δ is a function of the dimensionless parameter λ=ua(ta)ta∕r0, where ua is the ablation velocity, ta is the total ablation time, and r0 is the initial wire-array radius. The velocity ua is defined such that its product with the mass-ablation rate equals the magnetic force at r0, which is assumed to be the mass injection point. A solution is obtained for the plasma flow in semianalytical form when the current is an exponential function of time, and ua is constant. The ablated plasma density width δ obtained under these two sets of conditions is compared. In addition, assuming that the plasma sheath at stagnation is proportional to the width δ, scaling relationships for the peak x-ray power radiated when the pinch stagnates on axis are suggested.

Tectonic controls of metamorphic field gradients

We investigate the effects of horizontal variations in tectonic factors (heat production and rate, amount, and duration of erosion) on the magnitudes and gradients of pressure ( P), temperature ( T), and cooling ages observed in mountain belts. Horizontal gradients of P, T, and cooling ages are largely controlled by two dimensionless parameters, (1) the horizontal length scale, λ′, over which erosion, erosion rate or erosion duration varies, and (2) the Peclet number, Pe, which describes the relative rates of advection and diffusion of heat. In contrast, the magnitudes of observed P and T depend strongly on the degree of thickening and original burial depth, as well as Pe, and, since horizontal heat conduction can usually be ignored, do not depend strongly on λ′. P and T gradients generally increase with decreasing λ′ and Pe. For calculations in which either, but not both, erosion rate or erosion duration is horizontally constant, P and T gradients are moderate in magnitude and increase in the direction of increasing total erosion. In contrast, calculations with horizontally constant total erosion (but varying erosion rate and erosion duration) show small temperature and pressure gradients; pressures and temperatures can increase in the same or in opposite directions, depending on the magnitude of λ′. Calculations with horizontally varying crustal heat production show small but non-zero temperature gradients and negligible pressure gradients. These results indicate that knowledge of temperature, pressure and cooling age gradients in individual mountain belts can constrain fundamental quantities such as magnitude and horizontal gradient of the exhumation rate and the average shear strain rate occurring during exhumation. On the basis of their metamorphic field gradients, most mountain belts can be divided into one of three groups. The first and largest group shows strongly positive P and T gradients. Precambrian orogenic areas comprise the second group and have small T gradients ( < ∼ 5°C/km) but moderate to large P gradients (1–100 bar/km). A third, small group, which includes the Acadian Appalachians of New England, exhibits moderate T gradients but small P gradients ( < 1 bar/km). The horizontal variations in tectonic processes responsible for the thermal development of these three groups must have been quite distinct from each other.

Flow of a temperature dependent power‐law model fluid between parallel plates: An approximation for flow in a screw extruder

AbstractThis paper formulates concisely the problem of fully developed flow of a temperature dependent power‐law fluid between parallel plates. An exact solution, in the absence of pressure gradients, is developed. The method has been validated by a comparison with an independent numerical solution. This work is applicable to melt transport in shallow partly filled screw channels, drag flow regimes in the metering zone of a screw extruder and, generally, to flows in hydrodynamically thin layers associated with negligible pressure gradients. A numerical example is included dealing with the extrusion of polypropylene. A general discussion is given concerning the utility of the new theory. Effects of pressure gradients are included in the discussion.

Effect of wall temperature on a supersonic turbulent boundary layer

Measurement of mean flow profiles in a fully developed Mach 3 turbulent boundary layer with negligible pressure gradient is reported. Data were acquired at several streamwise locations for wall-to-total temperature ratios of 0.94, 0.71, and 0.54. The results demonstrate that the velocity defect formulation of the law-of-the-wake, which successfully correlates compressible, adiabatic boundary layers, is also valid for nonadiabatic flows. It is also shown that for adiabatic walls, the linear Crocco relation between total temperature and velocity does not provide a valid test of the nature of the boundary-layer flow for practical cases where the Prandtl number departs from unity. Finally, the turbulent shear stress, mixing length, and eddy viscosity were extracted from the 'time-averaged' conservation equations using the measured mean flow profiles and found to be insensitive to wall temperature. In particular, the latter properties are in good agreement with earlier compressible, adiabatic correlations of turbulent transport properties.

Turbulent properties of a compressible boundary layer.

Turbulent shear-stress, eddy-viscosity, mixing-length, heat-flux and Prandtl number distributions across a hypersonic turbulent boundary layer have been determined from the 'time-averaged' conservation equations using experimental mean profile data obtained at several streamwise locations in a fully developed turbulent boundary layer with negligible pressure gradient. The eddy-viscosity, mixing-length and Prandtl number results show general agreement with previous incompressible and adiabatic compressible correlations. However, when the turbulent Prandtl number is defined using total enthalpy as opposed to static enthalpy no clear correlation of the results in the outer portion of the boundary layer could be obtained.