External Boundary Layer Research Articles

Mechanistic Modeling of Pollutant Mass Redistribution (Sorption/Desorption) in Heterogeneous Systems Explaining Unexpected Slow Kinetics.

Redistribution of pollutants between different solid phases occurs frequently in field and laboratory settings. Examples include the input of urban particles carrying pollutants into soils or rivers with suspended particles or passive sampling. Since multiple mass transfer mechanisms are involved and natural particles typically are very heterogeneous, modeling of sorption/desorption kinetics is challenging. Here, we present a semi-analytical model formulated in the Laplace domain to simulate pollutant redistribution kinetics in heterogeneous systems. The model accounts for a coupled process governed by intraparticle and external boundary layer diffusion, and it considers the heterogeneity of various sorbents (e.g., geometric shape, size, sorption capacity coefficient, and solid and porous particles). The model is validated against data of two batch experiments: (i) the redistribution of phenanthrene in spherical polyethylene particles of different sizes and (ii) redistribution of anthracene-d10 and phenanthrene in a heterogeneous sediment suspension with polyethylene passive samplers. It allows to explain the temporary overshooting of concentrations in the aqueous phase due to different kinetic controls of various particles involved (fast desorption vs. slow sorption) as well as initial fast kinetics followed by surprising long tailing in batch experiments. The approach is very flexible and can be used for many different scenarios.

An experimental investigation of boundary layer over permeable interfaces in Hele-Shaw micromodels

This study experimentally investigates boundary layer development over permeable interfaces using Hele-Shaw micromodels and high-resolution micro-particle image velocimetry (micro-PIV). Velocity vectors, captured at a 5 μm scale, reveal the flow behavior at the interface between free-flow and porous media with ordered structures and porosities ranging from 50% to 85%. The results show that the boundary layer streamline alignment decreases with increasing porosity, while lower permeability fosters more uniform and parallel flow near the interface. Flow channeling occurs along paths of the least resistance, with more flow directed through the Hele-Shaw free-flow region as the solid fraction of the porous material increases. The Reynolds number (0.14–0.94), based on the Hele-Shaw hydraulic diameter, has a minimal effect on the normalized velocity distribution. Furthermore, an analytical solution for the external boundary layer thickness exhibited good agreement with experimental data, confirming a thickness of 2–4 times the square root of the free-flow Hele-Shaw permeability. Additionally, a Q-criterion analysis identified, for the first time, distinct zones within the external boundary layer, capturing the balance between rotational and deformation components as a function of permeability. These findings offer insight into flow dynamics in porous media systems, with implications for both natural and industrial applications, and contribute to the improved modeling of fluid dynamics and momentum transport in coupled free-flow and porous media environments.

An analytical solution model of oil–water dynamic imbibition considering dynamic contact angle effect and osmotic pressure at micro-nano scale

Spontaneous imbibition is one of the important mechanisms to enhance oil recovery during hydraulic fracturing process of shale reservoirs. The dynamic contact angle effect in imbibition kinetics of liquid–liquid system is complicated due to the large number of micro-nano pores in shale reservoir. Moreover, the content of clay minerals is high, the chemical osmosis effect is significant, and the impact of osmotic pressure on imbibition is not clear. In order to clarify the dynamic contact angle effect in imbibition kinetics and correctly understand the role of osmotic pressure in imbibition process. In this paper, based on the molecular kinetic theory (MKT), the dynamic contact angle effect is successfully coupled with imbibition kinetic equation, and a capillary pressure equation is developed. On the basis, considering the effects of osmotic pressure, external displacement pressure and boundary layer effect on imbibition, An analytical solution model of oil–water dynamic imbibition model is developed. The results shows that under the respective effects of capillary pressure and osmotic pressure, the imbibition velocity initially stabilizes before increasing over time; under the action of displacement pressure, the imbibition velocity increases with time. Imbibition velocity is directly proportional to interfacial tension and capillary radius, but inversely proportional to contact angle and oil viscosity. With the salt concentration difference increasing from 80 mol/m3 to 4710 mol/m3, the imbibition velocity increased by about 54 times. Compared with the membrane efficiency of 30 % and 5 %, the imbibition velocity is increased by 4.95 times. In this work, the dynamic contact angle effect in the imbibition kinetics of liquid–liquid system was accurately characterized, clarified the action mechanism of osmotic pressure, and provided theoretical support for enhancing oil recovery of shale reservoirs.

Dielectric barrier discharge actuators: Momentum injection into co-flow and counter-flow freestream

In a quiescent environment, dielectric barrier discharge (DBD) plasma actuators generate a wall jet through the interaction of ionized and neutral molecules in an electric field. In external flow, the coupling between electrohydrodynamic (EHD), turbulence, inertial, and viscous effects in the flow boundary layer is more complex and requires additional investigation. We experimentally study momentum injection by DBD actuators into the free stream flow with Re = 35,000 and 75,000 in co-flow and counter-flow scenarios over a range of VAC = 12 kV–19.5 kV peak-to-peak at a frequency of 2 kHz. In co-flow, the momentum injection leads to boundary layer thinning and fluid entrainment from the freestream into the DBD forcing region, while in the counter-flow configuration, flow separation can occur. A separation bubble is observed at Re = 35,000 for the tested condition. The momentum difference in the counter-flow configuration is six times greater than the EHD jet momentum in a quiescent environment. Both co-flow and counter-flow momentum injections show diminishing effects with higher Re. We show that the resulting flow pattern is not a superposition of the EHD jet and the free stream but is determined by the coupling and competition of inertial, viscous, and Coulombic effects between the EHD-driven forcing and the external flow. The proposed non-dimensional momentum ratio (M*) of EHD jet momentum to momentum in the external flow boundary layer can be used to predict the onset of separation; however, additional experimental and numerical studies are required to generalize this concept to other flow scenarios. The velocity profiles and momentum measurements presented here can be used to validate numerical models and inform the design of DBD actuators for active flow control.

Film condensation with a non-condensable gas: Hybrid integral transforms solution for external boundary layers

Film condensation with a non-condensable gas: Hybrid integral transforms solution for external boundary layers

Kinetic model describing self-limiting CO2 diffusion in supported amine adsorbents

A reaction–diffusion shrinking core model describing the decay in diffusivity of supported amine sorbents upon CO2 sorption under both simulated direct air capture and point source capture conditions is described. The decay in CO2 diffusivity is associated with crosslinking in the aminopolymer samples and general pore blockage in the amino-silane derived samples, which occurs as CO2 is adsorbed. The model is used to extract four kinetic parameters that govern the CO2 uptake kinetics and working capacity: an apparent reaction rate constant, an initial effective diffusivity, and two dimensionless decay parameters. Ideally, an initially reaction limited system would allow for direct determination of the intrinsic reaction rate constant; however, sorption experiments suggest mass transfer resistances related to gas mixing, external boundary layers and intraparticle diffusion are present. Reaction rate constants are determined and agree well with theoretical values predicted with the Eyring equation parameterized using density functional theory energies from literature sources. The kinetic performance is expressed as the average effective diffusivity as a function of average conversion, which can be correlated to the dispersion of sorption sites on the support and the morphology of the active sorbent phase. Four supports are impregnated or grafted with amines, SBA-15, single-walled zeolite nanotubes (ZNT), Syloid SiO2, and γ-Al2O3. Due to its pore structure, γ-Al2O3 supported amines can be modeled at the μm scale or at the nm scale, where the shell balance is on the μm-sized macroporous particle aggregate or on the nm-sized amine film on the surface of the Al2O3 nanoparticles, which comprise the spherical particle aggregates. Faster diffusion rates are maintained under 400 ppm rather than 10% CO2 due to a slower reaction rate giving a slower decay in diffusivity. This work provides a first principles kinetic analysis of CO2 sorption where previous models are semi-empirical and use arbitrary kinetic parameters.

Modeling microvoiding kinetics of rare‐earth disilicates in flowing atmospheres containing water vapor

AbstractRare‐earth disilicate (REDS, RE2Si2O7) layers that may be used as environmental barrier coatings (EBCs) on ceramic matrix composite (CMC) components in high‐temperature stages of turbine engines are subject to microvoiding to form porous rare‐earth monosilicate (REMS, RE2SiO5) layers in flowing atmospheres containing water vapor. A simple microvoiding kinetic model that incorporates both mass transfer of the reaction product Si(OH)4(g) through the external gas phase boundary layer and pore diffusion of Si(OH)4(g) through the microvoided layer has been developed. Model predictions are in good agreement with measured growth rates of microvoided layers under low‐flowrate steam furnace test and high‐flowrate burner rig conditions. Since pore diffusion is generally the rate‐limiting step for EBC microvoiding in turbine engines, furnace testing under conditions of kinetic control by gas phase mass transfer is not generally capable of predicting REDS microvoiding rates under engine conditions. The kinetic model can be extended to incorporate changes in pore size and distribution, cracking of the microvoided layer, and introduction and cracking of an additional REMS topcoat to the system. The model can be used to generate a reasonable prediction of the time required to fully microvoid a REDS EBC layer on a CMC component in the hot gas path of an aircraft engine or stationary gas turbine.

Similarity of length scales in high-Reynolds-number wall-bounded flows

The wall dependence of length scales used to describe large- and small-scale structures of turbulence is examined using highly resolved experiments in zero-pressure-gradient turbulent boundary layers and pipe flows spanning the range $2000< Re_\tau <37\ 700$ . Of particular interest is the influence of external intermittency on the scaling of these length scales. It is found that when suitable scaling parameters are selected and external intermittency is accounted for, the dissipative motions follow inner scaling even into the outer-scaled regions of the flow, and that certain large-scale descriptions follow outer scaling even in the inner-scaled regions of the flow. The wall dependence is the same for both internal pipe and external boundary layer flows, and the different length scales can be related to recognizable features in the longitudinal wavenumber spectrum.

Numerical Investigation on Mechanism of External Flow Field–Induced Separation Pattern Transition

The single-expansion ramp nozzle (SERN) has a compact structure and adaptability under off-design conditions, which is one of the nozzle configurations that the combined cycle engine gives priority to. Flow separation is likely to occur when the nozzle operates at low-pressure ratios. Subsonic regions, such as separation bubbles, recirculation zone, and boundary layer, also exist in the overexpanded flow field. At this point, the varying external flow field can affect the flow field inside the nozzle, which may lead to the transition of the flow separation pattern. The majority of relevant studies are conducted in a static environment because of experimental conditions limitations. This paper numerically simulates the transitions of separation patterns during the acceleration and deceleration processes of a short flap SERN. The separation transitions mechanism is analyzed, as well as the performance impact of the transitions. Current results show that the separation pattern transition happens during both the acceleration and deceleration processes, and free shock separation is a relatively stable state. The separation pattern transition occurs as a function of the external flow field, recirculation zone, boundary layer, and separation shock wave coupling. Compared with previous studies on the long flap SERN, the coupling mechanisms of the internal and external flow fields of the two nozzles were found to be different. The shock wave structure of the short flap SERN’s flow field is stable during the transition processes, and the nozzle performance does not exhibit a step change. The hysteresis of the short flap SERN is also weaker.

Analysis of thermally radiative magnetized viscoelastic (second-grade) fluid by impermeable vertical cylinder

We made an attempt to disclose the phenomenon of dual stratification in magnetized viscoelastic second-grade fluid model generated by the movement of vertical cylinder. Mass and heat transportation is accounted under the aspects of Joule and Ohmic dissipations. The flow is coupled due to the consideration of nonlinear convected terms. Boundary-layer concept is implemented for the simplification of mathematical system. This system is made into the non-dimensional forms by reporting the similarity variables. The system of non-dimensional equations is executed with the use of homotopic criteria. The convergent region of solutions is reported and discussed. The convergent results are shown by graphical illustrations by considering distinct emerging constraint values. An increment in Darcy and inertia coefficient parameters corresponds to a decay in the flow. Temperature distribution is an increasing function of thermal Biot number and radiation parameter while it diminishes when thermal stratification parameter increases. Concentration is reduced for larger Schmidt number along with solutal stratification parameter. Besides the heat–mass transportation rates are increasing functions of thermo-solutal Biot numbers. The considered problem finds relevance in functional smart electro conductive enrobing coating processes in manufacturing. This is a principal application of the model studied where external axisymmetric boundary layers occur with combined magnetic, thermal and rheological effects.

Natural convection in vertical enclosures with conjugate boundary conditions

A numerical investigation and reduced-order modelling of natural convection in a cavity with differentially heated sidewalls is discussed. The effect of conjugate boundary conditions on the cavity's heat transfer and natural flow circulation with varying aspect ratios and Rayleigh numbers is examined. Validation of the canonical differentially heated cavity reveals that a modification to the definition of the Rayleigh number (Ra) is required to reconcile the $Nu\sim Ra^{1/4}$ scaling (where Nu is the Nusselt number) and validity of previously proposed correlations for the heat transfer in vertical enclosures. Dynamic mode decomposition is used to uncover the underlying time-dependent flow structures and the results are compared with stability bifurcation studies in the literature. A flow mode previously associated with smaller aspect ratio cavities is identified as the unstable mode for a larger aspect ratio of 4. The effect of conjugate boundary conditions is scaled based on the ratio of the internal and external boundary layers, wherein higher external Reynolds numbers aid in the heat transfer as the Nusselt number approaches the isothermal limit. A reduced-order theoretical model is proposed to predict the Nusselt number for the conjugate boundary conditions. The performance of conjugate boundary conditions is connected to the flow stability, with the parallel-flow configuration acting in a destabilizing manner while the counterflow configuration has a stabilizing effect and results in the highest heat transfer. We also found that relatively large heat transfer can be achieved with substantially lower external actuation with intermediate aspect ratios, translating to less power in practice.

First order approximation for coupled film and intraparticle pore diffusion to model sorption/desorption batch experiments

A simple first order approximation was derived to model sorption/desorption kinetics of hazardous compounds in batch experiments based on a coupled film and intraparticle diffusion model. The solution is accurate enough to replace infinite series expansions needed in analytical solution for intraparticle diffusion and it accounts for the mass transfer shift from diffusion in the external aqueous boundary layer to the intraparticle pore space. With increasing distribution coefficient (Kd) and intraparticle particle porosity (ε) or decreasing Sherwood number (Sh) this mass transfer shift from film diffusion to intraparticle pore diffusion is delayed. The simple first order approximation equation allows analyses of mass transfer resistances and calculation of characteristic times which is relevant for the planning of batch experiments. The proposed solution is verified by a semi-analytical solution in Laplace space for fractional mass uptakes in the solid phase at equilibrium ranging from 50% to 91%, representing scenarios typically encountered in batch experiments.

Osmotic energy harvesting with soft-etched nanoporous polyimide membranes

We present the study of osmotic energy harvesting with soft-etched nanoporous polyimide membranes for a wide range of salt concentration differences, ion irradiation fluences, and multipore orientations (parallel or network). The effect of solution pH and divalent cations on the membrane performance is also investigated. The membrane behavior is evaluated in terms of the reversal potential (Vrev), the maximum power generation (Pmax), and the energy conversion efficiency (ηmax). For an exposed membrane area of ∼1 cm2, the maximum values obtained for these parameters are Vrev = 123 mV, Pmax = 0.45 μW, and ηmax = 40%, respectively. A significant decrease in the membrane performance is observed for membrane samples obtained with ion fluences higher than 4 × 109 ions cm−2 because of pore overlapping and the diffusional resistance of the external solution boundary layers at very low ionic concentrations. The soft-etched membranes are able to hold the reversal potential for several days.

Turbulent Skin Friction Reduction through the Application of Superhydrophobic Coatings to a Towed Submerged SUBOFF Body

Abstract In the present study, the drag-reducing effect of sprayed superhydrophobic surfaces (SHSs) is determined for two external turbulent boundary layer (TBL) flows. We infer the modification of skin friction created beneath TBLs using near-wall laser Doppler velocity measurements for a series of tailored SHSs. Measurements of the near-wall Reynolds stresses were used to infer reduction in skin friction between 8%and 36%in the channel flow. The best candidate SHS was then selected for application on a towed submersible body with a SUBOFF profile. The SHS was applied to roughly 60% of the model surface over the parallel midbody of the model. The measurements of the towed resistance showed an average decrease in the overall resistance from 2% to 12% depending on the speed and depth of the towed model, which suggests a SHS friction drag reduction of 4–24% with the application of the SHS on the model. The towed model results are consistent with the expected drag reduction inferred from the measurements of a near-zero pressure gradient TBL channel flow. Introduction Nature has provided a plethora of materials to be studied and mimicked for everyday applications (Jung & Bhushan 2010). One material pertinent for use in the marine environment is the lotus leaf, which is known for its self-cleansing properties and resistance to wetting (Neinhuis & Barthlott 1997). More specifically, lotus-inspired superhydrophobic surfaces (SHSs) have been biomimetically developed for skin friction reduction in various flow applications (Bhushan et al. 2009; Samaha et al. 2012). Being exhaustively studied in small-scale laminar flows (see Rothstein [2010] for a review of SHS drag reduction and slip on SHSs), advances in the design and fabrication of SHSs have permitted application of these materials in more naval-relevant flows. Previously, it has been shown that in laminar flow, SHSs can reduce drag (Watanabe et al. 1999; Ou et al. 2004; Ou & Rothstein 2005; Zhao et al. 2007; Daniello et al. 2009; Woolford et al. 2009), and in low–Reynolds number turbulent flows, SHS drag reduction has been observed using small-scale, structured surfaces and large air–water interfaces (Henoch et al. 2006; Daniello et al. 2009; Park et al. 2014). However, these surfaces, in higher turbulence flows, can be unstable or become wetted. If the SHS possesses roughness features with small scales compared with the viscous length scale of the flow, researchers have demonstrated SHS friction drag reduction for wall-bounded, high–Reynolds number turbulent flows (Zhao et al. 2007; Aljallis et al. 2013; Bidkar et al. 2014; Golovin et al. 2016; Ling et al. 2016b; Gose et al. 2018a).

Mass Transfer Principles in Column Percolation Tests: Initial Conditions and Tailing in Heterogeneous Materials.

Initial conditions (pre-equilibrium or after the first flooding of the column), mass transfer mechanisms and sample composition (heterogeneity) have a strong impact on leaching of less and strongly sorbing compounds in column percolation tests. Mechanistic models as used in this study provide the necessary insight to understand the complexity of column leaching tests especially when heterogeneous samples are concerned. By means of numerical experiments, we illustrate the initial concentration distribution inside the column after the first flooding and how this impacts leaching concentrations. Steep concentration gradients close to the outlet of the column have to be expected for small distribution coefficients ( L kg−1) and longitudinal dispersion leads to smaller initial concentrations than expected under equilibrium conditions. In order to elucidate the impact of different mass transfer mechanisms, film diffusion across an external aqueous boundary layer (first order kinetics, FD) and intraparticle pore diffusion (IPD) are considered. The results show that IPD results in slow desorption kinetics due to retarded transport within the tortuous intragranular pores. Non-linear sorption has not much of an effect if compared to values calculated for the appropriate concentration range (e.g., the initial equilibrium concentration). Sample heterogeneity in terms of grain size and different fractions of sorptive particles in the sample have a strong impact on leaching curves. A small fraction (<1%) of strongly sorbing particles (high ) carrying the contaminant may lead to very slow desorption rates (because of less surface area)—especially if mass release is limited by IPD—and thus non-equilibrium. In contrast, mixtures of less sorbing fine material (“labile” contamination with low ), with a small fraction of coarse particles carrying the contaminant leads to leaching close to or at equilibrium showing a step-wise concentration decline in the column effluent.

Investigation of shock dynamics in an axisymmetric inlet/isolator with attached boundary layers

Abstract

The active external heat and mass transfer multifunctional “one-wall” model with “nullified” friction resistance parietal boundary layer for the high-speed aircraft

In this paper, a new “single-wall” scheme of a high-speed wingless jet aircraft without compressor, which has the smallest, practically “zeroed” external friction and heat and mass transfer resistance with an active external near-wall boundary layer and tangential injection of the superheated steam from a cooling jacket SCC walls was proposed. Moreover, due to the limited flow rate of the combustible laminar sublayer vapor injection and the laminar “scaly” sublayer zeroed friction, the average Mach number of the vortex external near-wall boundary layer will be only 2% less than the Mach number of the flight speed. This circumstance allows not to merge the frontier layer of the hull (“fuselage”), as is done on the overwhelming majority of the aircrafts, but to use the energy and mass of the near-wall boundary layer as a normal incoming air flow.

Modeling and numerical simulations of lignite char gasification with CO2: The effect of gasification parameters on internal transport phenomena

The purpose of this study is to develop an experimental data-based char particle gasification model in order to assess the effects of particle size, gasification temperature and char generation heating rate on global gasification parameters. Also, the effect of initial porosity is observed by performing parametrical numerical simulations. A continuum-based model is used to solve the gasification inside a char particle and within the external boundary layer. The intrinsic rate of CO2 gasification reaction is computed according to Langmuir-Hinshelwood (LH) mechanism. External mass transfer is modeled by Stefan-Maxwell relations, and Cylindrical Pore Interpolation Model (CPIM) is used for intra-particle molecular diffusion. In the model, all the effects due to particle internal structure changes are represented by a global conversion function, f(X) which is computed from local reaction rate values. In this study, f(X) is deduced from experimental results instead of phenomenological models almost impossible to validate. The best reproduction of the experimental gasification results is obtained for the function f(X) postulated as a summation of two Gaussian functions which represent the char particle random pore structures and their dynamics during gasification. Comparative simulation results show that the Gaussian for low conversion interval is shifted to even lower conversion values for higher gasification temperature and higher initial porosity. Thereby, the Gaussian function for low conversion rates (large particle sizes) is interpreted as representative of the diffusion-limited gasification regime in conjunction with the network of macropores and molecular diffusion rates. The modification of the pore structure due to char generation heating rates causes a shift of the second Gaussian towards higher conversion rates. It is therefore postulated that the second Gaussian function corresponds to the boundary layer diffusion-controlled regime related to available outer surface area of the particle.

Numerical Simulation of Methane and Propane Reforming Over a Porous Rh/Al2O3 Catalyst in Stagnation-Flows: Impact of Internal and External Mass Transfer Limitations on Species Profiles

Hydrogen production by catalytic partial oxidation and steam reforming of methane and propane towards synthesis gas are numerically investigated in stagnation-flow over a disc coated with a porous Rh/Al2O3 layer. A one-dimensional flow field is coupled with three models for internal diffusion and with a 62-step surface reaction mechanism. Numerical simulations are conducted with the recently developed computer code DETCHEMSTAG. Dusty-Gas model, a reaction-diffusion model and a simple effectiveness factor model, are alternatively used in simulations to study the internal mass transfer inside the 100 µm thick washcoat layer. Numerically predicted species profiles in the external boundary layer agree well with the recently published experimental data. All three models for internal diffusion exhibit strong species concentration gradients in the catalyst layer. In partial oxidation conditions, a thin total oxidation zone occurs close to the gas-washcoat interface, followed by a zone of steam and dry reforming of methane. Increasing the reactor pressure and decreasing the inlet flow velocity increases/decreases the external/internal mass transfer limitations. The comparison of reaction-diffusion and Dusty-Gas model results reveal the insignificance of convective flow on species transport inside the washcoat. Simulations, which additionally solve a heat transport equation, do not show any temperature gradients inside the washcoat.

Rough Surface Turbulent Boundary Layer Heat Transfer Using Generalized Reynolds Analogies

Abstract Stanton number, St, calculations as a function of position, x, are made for turbulent, external boundary layer flow over aerodynamically rough surfaces and also for a fully developed duct flow with rough top and bottom surfaces. This is accomplished with three different forms of generalized Reynolds analogies from the literature and also with a new data correlation developed with the aid of the thermal inner and outer layers. Comparison of these predicted values of St with experimental data, from the literature, is made for several favorable equilibrium, one nonequilibrium, and a zero pressure gradient as well as a duct flow over “real” roughness patterns. Predictions compare reasonably well with the data for some of the generalized Reynolds analogies.