Increase In Boundary Layer Thickness Research Articles

Effect of initial conditions on interaction between a boundary layer and a wall-mounted finite-length-cylinder wake

The effects of initial conditions on interaction between a boundary layer over a flat plate and flow around a wall-mounted finite-length cylinder were experimentally investigated. A square cylinder with a characteristic width (d) of 20mm and a length of H=5d was vertically mounted on a horizontal flat plate. Three different boundary layers were investigated, their momentum thickness being 0.07d, 0.13d, and 0.245d, respectively, measured at the cylinder axis in the absence of the cylinder. All the experiments were carried out in a closed-loop water tunnel at a Reynolds numbers of 11 500 based on d and the free-stream velocity U∞. It is found that initial boundary layer conditions have a profound effect on the near wake, including the flow near the cylinder free end that is well beyond the boundary layer. With increasing boundary layer thickness, the base vortex is enhanced, inducing a stronger upwash flow from the cylinder base, which acts to weaken the downwash free-end shear layer and the tip vortex. Consequently, spanwise vortices gain strength near the free end but impair near the wall, causing the ratio of symmetrically to antisymmetrically arranged vortices to vary and subsequently the Reynolds stresses to increase significantly in magnitude near the free end but to decrease near the wall.

Concentration polarization in ion-exchange membrane electrodialysisThe events arising in an unforced flowing solution in a desalting cell

Using the NaCl concentration distribution observed by measuring the refraction index in a boundary layer in an unforced flowing state in a desalting cell, ionic fluxes, current density, solution velocity and potential gradient in the boundary layer were evaluated. Solution velocity was divided into the terms of electro-osmosis, concentration-osmosis and natural convection. The greater part of the solution velocity was due to natural convection, which is a horizontal component of ascending flow produced by the decrease in the solution density near the membrane surface in the boundary layer. Ionic fluxes and current density were divided into the terms of diffusion, migration and convection. Na + ion transport in the boundary layer on the desalting surface of a cation-exchange membrane was suppressed due to the lower mobility of Na + ions. Furthermore, water dissociation was strongly restricted on the surface of the cation-exchange membrane. Accordingly, Na + ion transport on the surface of the cation-exchange membrane placed in a diluted NaCl solution was promoted at the limiting current density by the increase of boundary layer thickness, the solution velocity in the boundary layer and the intensity of NaCl concentration oscillation on the membrane surface. In this circumstance, ionic transport due to the convection fluxes, which do not carry an electrical current, converted to migration fluxes and carried an electrical current. In this instance, diffusion fluxes did not support an electrical current because of lower mobility of Na + ions comparing that of Cl − ions. On the other hand, Cl − ion transport in the boundary layer on the desalting surface of the anion-exchange membrane was not suppressed because of the greater mobility of Cl − ions. Furthermore, water dissociation was not strongly restricted on the anion-exchange membrane. Accordingly, phenomena like the increase of the boundary layer thickness and the solution velocity observed in the boundary layer on the cation-exchange membrane did not occur on the anion-exchange membrane. On the anion-exchange membrane, convection fluxes were converted to diffusion fluxes and carry an electrical current. In this instance, migration fluxes did not support an electrical current because the contribution of diffusion fluxes is sufficiently effective. The potential gradient was divided into the terms of ohmic potential and diffusion potential. The ohmic potential gradient on the cation-exchange membrane was positive, and that on the anion-exchange membrane was negative. The diffusion potential gradient was positive on both the cation-exchange membrane and the anion-exchange membrane. By integrating the potential gradient distribution in a boundary layer, a current density versus voltage drop curve was obtained.

Concentration polarization in ion-exchange membrane electrodialysis: The events arising in an unforced flowing solution in a desalting cell

Using the NaCl concentration distribution observed by measuring the refraction index in a boundary layer in an unforced flowing state in a desalting cell, ionic fluxes, current density, solution velocity and potential gradient in the boundary layer were evaluated. Solution velocity was divided into the terms of electro-osmosis, concentration-osmosis and natural convection. The greater part of the solution velocity was due to natural convection, which is a horizontal component of ascending flow produced by the decrease in the solution density near the membrane surface in the boundary layer. Ionic fluxes and current density were divided into the terms of diffusion, migration and convection. Na + ion transport in the boundary layer on the desalting surface of a cation-exchange membrane was suppressed due to the lower mobility of Na + ions. Furthermore, water dissociation was strongly restricted on the surface of the cation-exchange membrane. Accordingly, Na + ion transport on the surface of the cation-exchange membrane placed in a diluted NaCl solution was promoted at the limiting current density by the increase of boundary layer thickness, the solution velocity in the boundary layer and the intensity of NaCl concentration oscillation on the membrane surface. In this circumstance, ionic transport due to the convection fluxes, which do not carry an electrical current, converted to migration fluxes and carried an electrical current. In this instance, diffusion fluxes did not support an electrical current because of lower mobility of Na + ions comparing that of Cl − ions. On the other hand, Cl − ion transport in the boundary layer on the desalting surface of the anion-exchange membrane was not suppressed because of the greater mobility of Cl − ions. Furthermore, water dissociation was not strongly restricted on the anion-exchange membrane. Accordingly, phenomena like the increase of the boundary layer thickness and the solution velocity observed in the boundary layer on the cation-exchange membrane did not occur on the anion-exchange membrane. On the anion-exchange membrane, convection fluxes were converted to diffusion fluxes and carry an electrical current. In this instance, migration fluxes did not support an electrical current because the contribution of diffusion fluxes is sufficiently effective. The potential gradient was divided into the terms of ohmic potential and diffusion potential. The ohmic potential gradient on the cation-exchange membrane was positive, and that on the anion-exchange membrane was negative. The diffusion potential gradient was positive on both the cation-exchange membrane and the anion-exchange membrane. By integrating the potential gradient distribution in a boundary layer, a current density versus voltage drop curve was obtained.

The influence of the boundary layer thickness in the vicinity of a body streamlined by a hot gas flow on the efficiency of surface cooling by a submerged cold stream

Using numerical modeling methods, we have reproduced the experimental effect of decrease in the efficiency of a cooling gas screen with increasing boundary layer thickness in the vicinity of a body streamlined by a hot gas flow. The simulation results allow the effect to be rationalized on a physically rigorous level, avoiding simplifications common in analytical descriptions and undesired in technical applications.

The effect of changing environmental variables in the surrounding water on the physiology of Elodea nuttallii

Photosynthesis and respiration of the submerged plant Elodea nuttallii (Planch.) St. John were investigated over a wide range of environmentally-relevant conditions of pH (pH 5–9), O 2 (31–625 μM) and dissolved inorganic carbon (0.15–24 mM) concentrations. Increases in O 2 concentration produced a linear decline in photosynthesis and a linear increase in respiration. The effect of reduced CO 2 availability was substantial, and best described by the Whittingham-Hill equation. Carbon dioxide compensation point varied with O 2 concentration (6.0 μM at 62.5 μM O 2, 16.3 μM at 313 μM O 2, and 54.6 μM at 500 μM O 2). pH caused a decrease in photosynthesis above pH 7 and below pH 6. The former was attributed to low CO 2 availability under these conditions, and the latter to a direct effect of acid conditions on the plant. The same response was found using buffered and unbuffered media. Elodea canadensis responded similarly to pH except below pH 6, where no decrease was found. The influence of the boundary layer on photosynthesis was demonstrated qualitatively, photosynthesis was reduced with increased boundary layer thickness. Within the range of concentrations found in stands of E. nuttallii in the field, the effect of decreasing CO 2 availability was capable of reducing photosynthesis.

The Influence of Downstream Passage on the Flow Within an Annular S-Shaped Duct

Experimental and numerical investigations were carried out to gain a better understanding of the flow characteristics within an annular S-shaped duct, including the influence of the shape of the downstream passage located at the exit of the duct on the flow. A duct with six struts and the same geometry as that used to connect the compressor spools on our new experimental small two-spool turbofan engine was investigated. Two types of downstream passage were used. One type had a straight annular passage and the other a curved annular passage with a meridional flow path geometry similar to that of the centrifugal compressor. Results showed that the total pressure loss near the hub is large due to instability of the flow, as compared with that near the casing. Also, a vortex related to the horseshoe vortex was observed near the casing. In the case of the curved annular passage, the total pressure loss near the hub was greatly increased compared with the case of the straight annular passage, and the spatial position of this vortex depends on the passage core pressure gradient. Furthermore, results of calculation using an in-house-developed three-dimensional Navier–Stokes code with a low-Reynolds-number k–ε turbulence model were in good qualitative agreement with experimental results. According to the simulation results, a region of very high pressure loss is observed near the hub at the duct exit with the increase of inlet boundary layer thickness. Such regions of high pressure loss may act on the downstream compressor as a large inlet distortion, and strongly affect downstream compressor performance.

The effect of particle size and shape on the surface specific dissolution rate of microsized practically insoluble drugs

The effects of both particle shape and size on the dissolution rate of sparingly soluble micro-particles have been studied. Griseofulvin, three different qualities of barium sulphate, oxazepam and glibenclamide were chosen as the model substances. As these materials differed in both particle size (from 1.8 to 3.8 μm) and particle shape (from rounded, isodiametric to flaky or irregular particles), different combinations of particle size and shape were used to investigate their combined effect on the dissolution rate. The surface specific dissolution rate was determined, using a Coulter counter technique. The ratio of this value to the equilibrium solubility was calculated for all materials and its relation to the shape and size of the micro-particles was investigated. The results obtained indicated that the dissolution rates of sparingly soluble drugs are related to the particle shape as well as to the particle size. For particles of the same size, the dissolution rate decreased as the level of flakiness and irregularity increased. This phenomenon can be explained by an increase in the average hydrodynamic boundary layer thickness as the particles become more irregular. Therefore, the product of the surface shape factor and mean particle diameter was used to discuss the combined effect of these factors on the dissolution rates of sparingly soluble drugs.

Laminar free convection flow of micropolar fluids from a curved surface

The laminar free convection flow of a micropolar fluid past an arbitrary curved surface has been analysed by using the cubic spline collocation numerical method. It is found that the flow field admits similarity solutions when the power functions for the stream-wise variations of the wall temperature m and the body shape configurations n are constants, and the sum of them is equal to unity. The solutions for the flow and heat transfer characteristics are evaluated numerically for different parameters, such as the body shape parameter n, the vortex viscosity parameter N1, the spin-gradient viscosity parameter N3 and the Prandtl number Pr. Results show that the heat transfer rate increases as the body shape parameter n or the parameter N1 decreases and the Prandtl number increases. The skin friction factor increases as the value of N1 decreases. In addition, an increase in the parameter N3 leads to an increase of the angular velocity boundary layer thickness. The model may solve industrial problems with processing of polymeric liquids, lubricants and molten plastics.

Fatigue behaviour of a saffil-reinforced aluminium alloy (AA6061)

A study has been made of the effects of inlet conditions and surface roughness on the performance of transitions between square and rectangular ducts of the same cross-sectional area. The conditions at entry were varied by using different approach lengths of straight duct and by means of a square screen of woven wire cloth. The surface roughening was accomplished by coating the surface of the transition with graded waterproof silicon carbide paper, whose surface roughness was measured with a Talysurf 4 instrument. All tests were run at Reynolds number 105.The results indicate that the static pressure loss coefficient significantly increases as the inlet boundary layer thickness increases. This variation is a function of aspect ratio at the rectangular end; the loss coefficient rises as the aspect ratio falls. The pressure drop slightly increases when the wall surface is roughened and is higher at low aspect ratios.

Numerical simulation of supersonic mixing and combustion

Problems of hydrogen mixing and combustion in supersonic air streams are numerically investigated. An implicit lower-upper (LU) scheme is used for solving the full, averaged, two-dimensional Navier-Stokes and species transport equations. For turbulence closure, a two-equation low-Reynolds-number q-ω turbulence model is employed. While the chemical source terms are treated fully coupled with the fluid motion, the conservation equations for q and ω are integrated in a decoupled way. This is done by the same LU algorithm as for the main flow equations. The combustion process in chemical nonequilibrium is based on a 20-step, 9-species finite-rate chemistry model. Because of the short residence times of the gas in supersonic combustors, the kind of hydrogen supply is very important for combustion process. This paper investigates hydrogen injections axial to the main stream at subsonic, sonic, and supersonic injection velocities. In addition to an optimal mixing that is strongly influenced by the shear layer behind the injector, it is important that the main stream remains supersonic. This results in a diverging geometry that compensates for the increase in boundary-layer thickness and rise in temperature due to combustion. There is also a strong interaction with shock waves, which often induce subsonic regions. The turbulent shear flow of hydrogen and air enables the gases to interpenetrate and can improve mixing.

Spin coating with slow evaporation

The spin coating of polymer solutions is discussed, with emphasis on the nature of the evaporation boundary condition. A dimensional analysis reveals that the appropriate condition is a constant small evaporation rate, which is determined by the mass transfer in the adjacent atmosphere. An error in previous work [Phys. Fluids 31, 2786 (1988)] is brought to light, and it is shown that the previous paper would be valid for rapid evaporation, such as might occur if the ambient condition were near vacuum. The transport of solvent in the liquid film is described by a boundary layer diffusion equation with large Peclet number P0. When the dimensionless evaporation rate ê is small, the diffusion equation has a self-similar solution in which the boundary layer thickness and polymer concentration increase in proportion to the decrease in film thickness. The final film thickness is determined by the boundary layer thickness, which is controlled by P0 and is independent of ê. Thus the final film thickness is found to be the same as for the case of rapid evaporation.

Effect of Concentration Boundary Layer on Carbon Limited Algal Biofilms

A model is developed to describe mass transport resistance through a concentration boundary layer associated with an algal biofilm. This model is solved simultaneously with a model for attached algal growth subject to inorganic carbon limitation. The profile of inorganic carbon species through the boundary layer is found to be nonlinear due to the interaction of inorganic carbon speciation and pH. As CO\d2 is utilized by the algae, the pH in the biofilm increases, causing a pH gradient across the boundary layer. This pH increase across the boundary layer causes a corresponding shift of inorganic carbon species away from CO\d2, which is the form utilized by the algae. As a result of this nonlinear interaction with pH, there is an especially significant decrease in the flux of inorganic carbon into the biofilm, and thus in biofilm growth, as the boundary layer increases in thickness. These results show that models that assume constant pH will overpredict the flux of inorganic carbon. Biofilm thickness is important in determining the impact of the boundary layer. Very thin biofilms that are fully penetrated with CO\d2 are not sensitive to boundary layer thickness. As the biofilm thickness increases, sensitivity to the boundary layer thickness increases, until the flux reaches the maximum possible (J\dm\da\dx) and becomes independent of biofilm thickness. The magnitude of the effect is dependent on a complex interaction of bulk pH, bulk inorganic carbon concentration, and alkalinity.

A numerical model of the combined wave and current bottom boundary layer

A numerical model of oscillatory rough‐turbulent boundary layer flow, featuring closure via the turbulent energy equation, is used to examine the principal features of wave‐current interaction above the seabed. Results are presented from case studies carried out with water depth of 10 m, bed roughness of 0.5 cm and wave period of 8 s. The steady surface current in the absence of waves is nominally 100 cm/s, and waves having near‐bottom velocity amplitudes of 50, 100, and 150 cm/s are superimposed on this current at angles ϕ = 0, π/4, and π/2. Velocity, turbulent energy, shear stress, and eddy viscosity distributions are compared for the steady current alone, for waves alone, and for waves superimposed on the current, and the interaction in the wave‐current boundary layer is examined. Cycle‐averaged vertical profiles of horizontal velocity illustrate the extent to which the mean flow is retarded by wave‐current interaction. For the general case in which the waves are superimposed at an arbitrary angle ϕ, the mean current veers to form an angle with the wave direction greater than that of the initial steady current. Finally, the enhancement of the bed shear stress and the increase in oscillatory boundary layer thickness associated with wave‐current interaction are both quantified.

Effects of inlet conditions and surface roughness on the performance of transitions between square and rectangular ducts of the same cross-sectional area

A study has been made of the effects of inlet conditions and surface roughness on the performance of transitions between square and rectangular ducts of the same cross-sectional area. The conditions at entry were varied by using different approach lengths of straight duct and by means of a square screen of woven wire cloth. The surface roughening was accomplished by coating the surface of the transition with graded waterproof silicon carbide paper, whose surface roughness was measured with a Talysurf 4 instrument. All tests were run at Reynolds number 10 5. The results indicate that the static pressure loss coefficient significantly increases as the inlet boundary layer thickness increases. This variation is a function of aspect ratio at the rectangular end; the loss coefficient rises as the aspect ratio falls. The pressure drop slightly increases when the wall surface is roughened and is higher at low aspect ratios.

Some Consequences of Leaf Pubescence in the Andean Giant Rosette Plant Espeletia Timotensis

The effects of leaf pubescence on leaf energy exchange and transpiration were evaluated for Espeletia timotensis, a caulescent giant rosette plant that occurs in the paramo zone of the Venezuelan Andes at elevations up to 4500 m. Computer simulations using standard energy balance equations and field and laboratory measurements showed that the thick leaf pubescence (up to 3 mm) modifies energy balance mainly by increasing boundary layer thickness and resistance to convective and latent heat transfer. Effects of the pubescence on solar radiation absorption are minor compared to its influence on boundary layer resistance. The degree of coupling between leaf temperature and incident solar radiation is thus greater in pubescent than in nonpubescent leaves, despite the greater absorptance to solar radiation of the later. Vertically oriented expanding leaves, which have the thickest pubescence, also have higher stomatal resistance than the other leaves in the rosette. The higher stomatal resistance enhances coupling between leaf temperature and incident radiation. Pubescence—induced increases in leaf temperature of 5°C or more can be attained without significant increases in transpiration if stomatal resistance is maintained at the proper levels. These features may be advantageous in the native habitat of E. timotensis where incoming radiation can reach a high level but mean air temperature is °3°C and maximum air temperatures are usually below 10°C. Process of assimilate translocation and leaf growth, which normally would be severely inhibited at prevailing environmental temperatures, may be favored by the higher leaf temperatures. The ability to increase leaf temperature while at the same time avoiding increases in transpiration is also of adaptive importance, since water availability in the habitat of E. timotensis is often limited by low temperatures.

Catalyzed combustion of H 2/air mixtures in a flat plate boundary layer: II. Numerical model

A computer program has been developed to solve the boundary layer equations for laminar flow over a heated catalytic plate with H 2/air combustion. The objectives are to investigate the importance of homogeneous as opposed to surface reactions during high-temperature surface catalyzed combustion and to determine the roles of heat and mass transfer and their effect on the combustion process. Realistic transport properties and a detailed kinetic mechanism have been included in the program. Results are presented for the combustion of H 2/air at an equivalence ratio of 0.1 during flow over a noncatalytic plate with a surface temperature of 1100K. The results indicate the existence of an initial region near the plate leading edge in which radical concentrations increase with little associated heat release, and a downstream region where heat release due to gas phase combustion results in a significant increase in thermal boundary layer thickness. Boundary conditions are formulated for a catalytic surface and the resulting calculations show that surface reaction has a strong quenching effect on the initiation of gas phase combustion in the boundary layer due to removal of H 2 near the plate surface and quenching of radical species generated in the gas phase. This results in a significant reduction in gas phase heat release rates and a smaller increase in thermal boundary layer thickness than found with a noncatalytic surface.

Intraparticle effects in char combustion steady state analysis

AbstractA model is developed to study the intraparticle effects of char combustion which incorporates the reactions, C + 1/202 → CO, CO + 1/202 → CO2 and CO2 + C → 2CO with appropriate intrinsic kinetics. Based on some limiting cases a feasibility region, inside which the solution should lie, is developed. In almost all cases the major product is CO with CO2 production 2 to 3 orders of magnitude lower. A maximum of three steady states is observed for the parameters chosen. The combustion rate decreases with increase in particle size and increase in boundary layer thickness. The solution structure depends strongly on the radiation conditions which obtain and on the transport properties inside the particle. The purpose of this study is to determine the effect of intraparticle transport without the confounding effects of other phenomena.

Theoretical investigation on laminar boundary layer with combustion on a flat plate

The problems of the laminar boundary layer where combustion reaction occurs are solved theoretically taking account of the Arrhenius' theory of chemical kinetics, of the effects of the impermeable leading section, and of the fact that the properties of fluid depend on the temperature and concentrations of species contained in the boundary layer. As the result of this investigation, the following conclusions have been obtained: 1. (1) The maximum temperature obtained in the present work is lower by about several hundred degrees of centigrade than that by the method which has been used in the previously published papers, 2. (2) The combustion zone occupies about 20 per cent of the boundary layer in width, 3. (3) In the case of using the test plate with an impermeable leading section, the boundary layer thickness increases and the maximum temperature goes down compared with the case using the test plate without impermeable leading section. The impermeable leading section has a great influence on the shear stress at the wall, 4. (4) In the case of uniformly injecting the gaseous fuel from the wall, the fuel concentration at the wall and the maximum temperature change with the distance from the leading edge.

Hydromagnetic Free Convection from a Horizontal Infinite Strip Facing Downward

The problem for the laminar free convection from a horizontal isothermal infinite strip facing downward is studied by the momentum-integral method within the boundary-layer approximations when a vertical magnetic field is imposed on the plate. The solutions are presented in an integral form for the case when the induced magnetic field is negligible. The detailed calculations for Pr = 0.025 and 1 are compared with those of the nonmagnetic case. It is found that the boundary-layer thickness increases and the Nusselt number decreases with the increase of the magnetic field.

Experiments on the Efficiency of Conical Diffuser : The Initial State of Separation of Flow

When flow in diverging pipe separates from the pipe walls, there occurs an increasing loss of energy and at the same time the flow begins to vibrate, being accompanied by other trouble. In this paper we describe the results of experiments on flow in a 20° conical diffuser. In the initial state of separation a reverse flow takes place near the pipe walls, the main flow going straight ahead in the form of a jet entirely uninfluenced by the diverging walls. The points of separation of the flow can be determined by the sudden increase in boundary layer thickness (displacement thickness). In this initial state of separation, the value of efficiency of pressure recovery is slightly lower than its maximum. The efficiency increases somewhat with increasing Reynolds number and with decrease in boundary layer thickness at the pipe entrance. There is considerable variation in pressure which is the order of 5-10% and the main flow swirls around within the pipe. A comparison of the separation points calculated by the theory of one of the present authors with the experimental results shows good agreement.