Boundary Layer Flow Regime Research Articles

Experimental study on the heat flux of transitional shock wave–boundary layer interaction at Mach 6

The shock wave–boundary layer interaction (SWBLI) phenomenon was investigated experimentally to explore the heat flux distribution characteristics of SWBLIs under different boundary layer flow regimes and the influence/mechanism of different transition positions on peak heat flux of SWBLI. Experiments were conducted in a flow of Mach number 6. The shock generator deflected the flow by 20 °, 22 °, 25 ° and 30 ° resulting in an oblique shock impinging on a flat plate. The rough elements with different heights were arranged to achieve different transition positions. The influence of the relative position of transition and interference zone on the peak heat flux and its physical mechanism are revealed. The results demonstrated that the transitional SWBLI has a higher peak heat flux than the turbulent SWBLI, however the overshoot phenomenon is not reflected in the peak pressure. The increment of heat flux peak in transitional SWBLI is related to the relative positions of transition and interference zones. The increment of heat flux peak of transitional SWBLI compared to turbulent SWBLI can reach 25.5–38.9% and 51.9–65.1% when transition approaches the separation zone and reattachment zone, respectively. This overshoot phenomenon is caused by the streamwise vortex in transitional and so-called laminar SWBLIs, which enhances the energy exchange in the boundary layer and leads to an increase in heat flux. However, in the turbulent SWBLI, the energy mixing in the boundary layer is not significantly enhanced due to the breakup of the large scale streamwise vortex into turbulent small-scale structure.

Analytical, numerical and scale analysis study of thermal diffusion effect on free convection boundary layer flows in a slender porous layer

This paper reports an analytical, numerical and scale analysis study of free convective heat and mass transfer flows coupled with thermal diffusion effect in a slender vertical porous cavity subjected to cooperating lateral temperature and concentration gradients. The top and bottom walls of the cavity are assumed to be adiabatic and impermeable to mass transfer. This study aims to analyze the different hydrodynamic, thermal and solutal behaviors developed in laminar boundary layer flow regime reached at high Rayleigh numbers. Based on the parallel flow approximation, an analytical solution of the problem is derived in the extreme case of heat-driven (N≪1) free convection. The obtained analytical results are validated numerically by generating the solutions of the full governing differential equations by means of finite-difference method (FDM). To estimate the order of magnitudes involved in the boundary layer regime, a scale analysis of the conservation equations is performed. The order of magnitudes of boundary layer thickness, Nusselt and Sherwood numbers are derived in this study. For all these quantities, the trends predicted by the scaling law theory are found to be in good agreement with those of the parallel flow approach. The combined effects of Rayleigh and Soret numbers on the boundary layer thickness, flow intensity and heat and mass transfers are illustrated graphically for representative values of N, Le and A_r, and the main results are highlighted and discussed.

Soret-driven Convection Effect on the Boundary Layer Flow Regime within Tall Porous Enclosures

Soret-driven Convection Effect on the Boundary Layer Flow Regime within Tall Porous Enclosures

Contactless Localization of Premature Laminar–Turbulent Flow Transitions on Wind Turbine Rotor Blades in Operation

Thermographic flow visualization enables a noninvasive detection of the laminar–turbulent flow transition and allows a measurement of the impact of surface erosion and contamination due to insects, rain, dust, or hail by quantifying the amount of laminar flow reduction. The state-of-the-art image processing is designed to localize the natural flow transition as occurring on an undisturbed blade surface by use of a one-dimensional gradient evaluation. However, the occurrence of premature flow transitions leads to a high measurement uncertainty of the localized transition line or to a completely missed flow transition detection. For this reason, regions with turbulent flow are incorrectly assigned to the laminar flow region, which leads to a systematic deviation in the subsequent quantification of the spatial distribution of the boundary layer flow regimes. Therefore, a novel image processing method for the localization of the laminar–turbulent flow transition is introduced, which provides a reduced measurement uncertainty for sections with premature flow transitions. By the use of a two-dimensional image evaluation, local maximal temperature gradients are identified in order to locate the flow transition with a reduced uncertainty compared to the state-of-the-art method. The transition position can be used to quantify the reduction of the laminar flow regime surface area due to occurrences of premature flow transitions in order to measure the influence of surface contamination on the boundary layer flow. The image processing is applied to the thermographic measurement on a wind turbine of the type GE 1.5 sl in operation. In 11 blade segments with occurring premature flow transitions and a high enough contrast of the developed turbulence wedge, the introduced evaluation was able to locate the flow transition line correctly. The laminar flow reduction based on the evaluated flow transition position located with a significantly reduced systematic deviation amounts to 22% for the given measurement and can be used to estimate the reduction of the aerodynamic lift. Therefore, the image processing method introduced allows a more accurate estimation of the effects of real environmental conditions on the efficiency of wind turbines in operation.

Thermographic flow visualization by means of non-negative matrix factorization

In order to investigate the areas of different flow regimes in the boundary layer of an airfoil, thermography is a powerful flow visualization tool. However, the distinguishability between boundary layer flow regimes such as laminar or turbulent is limited due to systematic and random inhomogeneity in the measured temperature field, hindering a clear separation of the flow regimes. In order to increase the distinguishability of different flow regimes, a time series of thermographic images is evaluated by means of a non-negative matrix factorization. As a result, the non-negative matrix factorization creates images that contain the dominant features of the measured images, while reducing systematic temperature gradients within the flow regimes by up to a factor of five. This way an increase of the distinguishability between every pair of consecutive flow regimes can be achieved on the surface of a non-heated cylinder in cross-flow condition. As a further application example of the non-negative matrix factorization, the distinguishability between the flow and the laminar-turbulent transition zone on a heated helicopter airfoil is also increased by a factor of five. Hence, non-negative matrix factorization is capable of enhancing thermographic flow visualization for increasing the distinguishability of different flow phenomena.

Modeling and simulation of the transient response of temperature and relative humidity sensors with and without protective housing.

Based on the necessity for enclosure protection of temperature and relative humidity sensors installed in a hostile environment, a wind tunnel was used to quantify the time that the sensors take to reach equilibrium in the environmental conditions to which they are exposed. Two treatments were used: (1) sensors with polyvinyl chloride (PVC) enclosure protection, and (2) sensors with no enclosure protection. The primary objective of this study was to develop and validate a 3-D computational fluid dynamics (CFD) model for analyzing the temperature and relative humidity distribution in a wind tunnel using sensors with PVC enclosure protection and sensors with no enclosure protection. A CFD simulation model was developed to describe the temperature distribution and the physics of mass transfer related to the airflow relative humidity. The first results demonstrate the applicability of the simulation. For verification, a sensor device was successfully assembled and tested in an environment that was optimized to ensure fast change conditions. The quantification setup presented in this paper is thus considered to be adequate for testing different materials and morphologies for enclosure protection. The results show that the boundary layer flow regime has a significant impact on the heat flux distribution. The results indicate that the CFD technique is a powerful tool which provides a detailed description of the flow and temperature fields as well as the time that the relative humidity takes to reach equilibrium with the environment in which the sensors are inserted.

Flow visualization of natural convection in a vertical channel with asymmetric heating

A dynamical study of the flow in an asymmetrically heated vertical plane channel has been conducted experimentally. Experiments were carried out in water for three aspect ratios and for a range of modified Rayleigh numbers corresponding to the boundary layer flow regime. The flow dynamics were characterized by means of visualization techniques based on laser tomography using discrete and continuous tracers. Flow visualizations were carried out in the plane of symmetry of the channel along its entire height. The investigations focused more specifically on the influence of the aspect ratio and the modified Rayleigh number on the flow structure both in steady-state regime and during the transitional phase occurring just after the start of the heating. An upward boundary layer flow is found near the heated wall, accompanied by a reverse flow developing on the opposite side from the top open-end of the channel. In steady state, the reverse flow takes the form of an elongated eight-shaped structure with two main recirculation cells. The length of the upper cell of the eight-shape structure decreases with increasing aspect ratio. For a fixed aspect ratio, the increase in modified Rayleigh number results in a decrease in the penetration of the reverse flow. During the transient the flow structure is shown to evolve from a single cell to a final eight-shaped structure.

Soret effect on the boundary layer flow regime in a vertical porous enclosure subject to horizontal heat and mass fluxes

The combined thermo- and double-diffusive convection in a vertical tall porous cavity subject to horizontal heat and mass fluxes was investigated analytically and numerically using the Darcy model with the Boussinesq approximation. The investigation focused on the effect of Soret diffusion on the boundary layer flow regime. The governing parameters were the thermal Rayleigh number, R T, the Lewis number, Le, the buoyancy ratio, N, the Soret parameter, M, which characterized the Soret effect, and the aspect ratio of the enclosure, A r . The results demonstrated the existence of a boundary layer flow solution for which the Soret parameter had a strong effect on the heat and mass transfer characteristics. For M ≠ 1 and M ≠ −1/ Le, the profiles of the vertical velocity component, v, temperature, T, and solute concentration, S, exhibited boundary layer behaviors at high Rayleigh numbers. Furthermore, as R T increased, the temperature and solute concentration became vertically and linearly stratified in the core region of the enclosure. The thermo-diffusion effect on the boundary layer thickness, δ, was discussed for a wide range of the governing parameters. It was demonstrated analytically that the thickness of the boundary layer could either increase or decrease when the Soret parameter was varied, depending on the sign of the buoyancy ratio. The effect of R T on the fluid flow properties and heat and mass transfer characteristics was also investigated.

Experimental study of Marangoni flows in molten and solidifying Sn and Sn-Bi layers heated from the side

An experimental study of Marangoni flows in horizontal layers of tin based metallic alloys heated from the side is carried out, based on the observation of the motion of tracer particles at the surface associated with a direct measurement of temperatures in the melt. A key feature of the procedure is that the experiments are performed in a high vacuum environment to limit as much as possible the pollution of the liquid vapour interface. In pure tin, depending on the intensity of the driving force measured by the Reynolds-Marangoni number, either viscous or boundary layer flow regimes are found. In addition, the onset of temperature oscillations is found to be consistent with the hydrothermal wave instability mechanism proposed by Smith and Davis. In tin-bismuth alloys, the observed flow directions and velocities are interpreted in terms of a non linear dependence of the surface tension on temperature, and successfully compared with the dependence predicted by interpolating the available experimental surface tension data with the help of a simple thermodynamic model. During the directional solidification of the layer, the concentration gradient in the solute rich boundary layer ahead of the growth front is found to locally modify the flow pattern. For instance, when thermal and solutal driving forces act in the same direction, temperature oscillations are observed at low values of the Reynolds-Marangoni number. As for opposing driving forces, the situation is that a local reversal of the flow direction is observed in correlation with the morphological instability of the growth front.

UNSTEADY LAMINAR BOUNDARY LAYER FLOW OVER A SPINNING BODY IN FREE CONVECTION

Initial development of the unsteady laminar free-convection boundary-layer flow over an impulsively started spinning isothermal axisymmetrical vertical body is investigated. Stream function, swirl velocity and temperature are obtained in series of functions in powers of time. The general results are applied to a family of downward and upward thickening bodies to investigate the effects of the body shape on the formation of unseparated and separated boundary-layer flow regimes. The onset of flow separation is observed to take place at higher spin rates for downward thickening bodies. The surface heat flux is enhanced by the circulating flow inside the separated region. The series solutions are limited to the small values of the dimensionless time.

Effect of the Nozzle Edge Shape on the Acoustic Sensitivity of a Jet

The effect of the nozzle edge shape on the acoustic sensitivity of jets, that is, on the dependence of the jet parameters on the amplitude and frequency of the acoustic oscillations produced by an external source, is experimentally studied. The investigation was performed for nozzle edge configurations, the variation of which did not result in a change in the jet characteristics without external acoustic excitation. This means that the change in the edge shape alone had no influence on the flow pattern at the nozzle exit or the boundary layer flow regime on the nozzle walls. Measurements of the dependence of the mean velocity and the velocity fluctuation intensity on the jet axis on the distance from the nozzle exit showed that a change in the nozzle edge shape can lead to a change in the acoustic sensitivity of the jet when the jet is exposed to external acoustic action.

Investigation of the Boundary Layer Behavior In the Vicinity of the Attachment Line on a Yawed Wing and the Possibilities of Deturbulization

The results of an experimental investigation of the effect of fuselage-generated turbulence impinging on the leading edge of a swept wing on the boundary layer flow regime are presented. The possibilities of attenuating the turbulizing effect are studied. The criteria of laminar-turbulent transition are determined.

Effect of an electromagnetic field on natural convection in an inclined porous layer

An investigation is conducted to study the effect of an electromagnetic field on free convection of in inclined rectangular porous cavity saturated with an electrically conducting fluid. The enclosure has the long side walls heated isothermally, while the short ends are thermally insulated. A uniform magnetic field is applied normal to the heated walls. The porous medium, modeled according to Darcy's law, is assumed to be isotropic. The dimensionless governing equations are derived in terms of the characteristic dimensionless parameters; namely, the Rayleigh number R, the magnetic Hartmann number Ha, the cavity aspect ratio A, and the inclination angle θ. An approximate analytical solution is presented for the boundary-layer flow regime within a vertical cavity. A linear stability analysis is made to determine the effect of the magnetic field on the onset of convection in a horizontal layer heated from below. A numerical study is performed to assess and extend the results of the analytical solutions. It is found that with application of an external magnetic field, the temperature and velocity fields are significantly modified.

HYDROMAGNETIC NATURAL CONVECTION IN A TILTED RECTANGULAR POROUS ENCLOSURE

A study is made of natural convection within an inclined porous layer saturated by an electrically conducting fluid in the presence of a magnetic field. The long side walls of the cavity are maintained at a uniform heat flux condition, while the short side walls are thermally insulated. On the basis of a parallel flow model, the problem is solved analytically to obtain a set of closed-form solutions. Scale analysis is applied to the case of a boundary layer flow regime in a vertical enclosure. Comparison between the fully numerical and analytical solutions is presented for 0 ≤, Ra ≤, 103 ≤, Ha ≤, 10, and -180 ° ≤, Φ ≤, 180°, where Ra, Ha, and Φ denote the Rayleigh number, Hartmann number, and inclination of the enclosure, respectively. It is found that the analytical solutions can faithfully predict the influence of a magnetic field on the flow structure and heat transfer for a wide range of the governing parameters. For a boundary layer flow regime in a vertical cavity the results of the scale analysis agree well with approximations of the analytical solution. For this situation it is found that the Nusselt number is Nu = O.5Ra2/5 / ( 1 + Ha2) 2/5. For a horizontal cavity heated from below the critical Rayleigh number for the onset of motion, determined from a stability analysis, corresponds to that for the existence of unicellular convection using the parallel flow approximation. In general, it is demonstrated that, with the application of an external magnetic field, the temperature and velocity fields are significantly modified and the Nusselt number is decreased with increasing Ha.

Airfoil transition and separation studies using an infrared imaging system

An infrared imaging system was used to detect the thermal signature of boundary-layer flow regimes on a NACA 0012 airfoil from zero angle of attack up to separation. The boundary-layer transition from laminar to turbulent flow and the onset of separation could be seen on the airfoil thermograms. The findings were compared against the behavior of aluminum foil tufts observable both visually and with the infrared imaging system. This arrangement offers the option of using the infrared imaging system both for flow regime detection through surface thermography and flow visualization by the aluminum foil tufts. Ultimately the surface temperature changes due to variation in the angle of attack of a lifting surface provide a means for interpretation of the boundary-layer flow regimes.

Gravity-driven laminar film flow of power-law fluids along vertical walls

A theoretical analysis is presented which brings steady laminar film flow of power-law fluids within the framework of classical boundary layer theory. The upper part of the film, which consists of a developing viscous boundary layer and an external inviscid freestream, is treated separately from the viscous dominated part of the flow, thereby taking advantage of the distinguishing features of each flow region. It is demonstrated that the film boundary layer developing along a vertical wall can be described by a generalized Falkner-Skan type equation originally developed for wedge flow. An exact similarity solution for the velocity field in the film boundary layer is thus made available. Downstream of the boundary layer flow regime the fluid flow is completely dominated by the action of viscous shear, and fairly accurate solutions are obtained by the Von Karman integral method approach. A new form of the velocity profile is assumed, which reduces to the exact analytic solution for the fully-developed film. By matching the downstream integral method solution to the upstream generalized Falkner-Skan similarity solution, accurate estimates for the hydrodynamic entrance length are obtained. It is also shown that the flow development in the upstream region predicted by the approximate integral method closely corresponds to the exact similarity solution for that flow regime. An analytical solution of the resulting integral equation for the Newtonian case is compared with previously published results.

Natural convection in a vertical porous annulus

Numerical studies are reported for steady free convection in a vertical annulus filled with a saturated porous medium and whose vertical walls are at constant temperatures, the horizontal walls being insulated. Curvature effects on temperature and velocity fields are significant, and completely disturb the centro-symmetrical nature found in the vertical cavity case. Convective velocities are higher in the upper half than the lower half of the annulus, and the local rate of heat transfer is much higher near the top edge of the cold wall. The average Nusselt number always increases as the radius ratio, κ, increases, though the rate of increase diminishes with the increase in curvature effects particularly at high Rayleigh numbers, Ra ∗. In the case of a tall annulus the heat transfer rate in the boundary layer flow regime approaches that for a cylinder embedded in a porous medium, as κ increases. The Rayleigh number criteria for various flow regimes are obtained, and the average Nusselt number is correlated by a relation of the form Nu = const. Ra ∗m A nκ p , where A is the aspect (height-to-gap width) ratio. In the boundary layer regime, the heat transfer rate for a tall cavity or annulus of fixed height is a very weak function of the aspect ratio.

Radiative heat transfer in a heat generating and turbulently convecting fluid layer

The coupled problem of radiative transport and turbulent natural convection in a volumetrically heated, horizontal gray fluid medium, bounded from above by a rigid, isothermal wall and below by a rigid, adiabatic wall, is investigated analytically. An approximate method based upon the boundary layer approach is employed to obtain the dependence of heat transfer at the upper wall on the principal parameters of the problem, which, for moderate Prandtl number, are the Rayleigh number, Ra, the optical thickness, κL, and the conduction-radiation coupling parameter, N. Also obtained in this study is the behavior of the thermal boundary layer at the upper wall. At large κL, the contribution of thermal radiation to heat transfer in the layer is found to be negligible for N > 10, moderate for N ∼ 1, and overwhelming for N < 0.1. However, at small kL, thermal radiation is found to be important only for N < 0.01. While a higher level of turbulence results in a thinner boundary layer, a larger effect of radiation is found to result in a thicker one. Thus, in the presence of strong thermal radiation, a much larger value of Ra is required for the boundary layer approach to remain valid. Under severe radiation conditions, no boundary layer flow regime is found to exist even at very high Rayleigh numbers. Accordingly, the ranges of applicability of the present results are determined and the approximate method justified. In particular, the validity of the present analysis is tested in three limiting cases, i.e. those of κL /ar ∞, N /a ∞, and Ra /ar ∞, and is further confirmed by comparison with the numerical solution.

Surface Tension Flows Induced by a Moving Thermal Source

Abstract Surface tension flows induced by a thermal source moving over an otherwise stationary liquid layer are investigated. Such flows are important for fire spread over flammable liquids at sub-flash temperatures. The flow structure and parameter dependence are obtained with the aid of numerical solutions of the energy and vorticity transport equations in two space dimensions. Convergence of the solutions is established by successively refining the spatial grids. Results are presented for a range of surface tension parameters (25 ≤ S ≤ 250), Prandtl numbers (1 ≤ Pr ≤ 100) and Reynolds numbers (10 ≤ Re ≤ 2500). The Reynolds number (Re = Uh/v) is based on thermal source speed (U) and layer depth (h). The induced flow takes the form of a captured eddy just below the surface. The rate of fluid circulation in the eddy (dimensional) is found to depend linearly on S, to be essentially independent of Pr and to be functionally dependent on h. Viscous and boundary-layer flow regimes are found for small and large values of h, respectively and compare favorably with available analysis.

Wind stress and surface roughness at air-sea interface

Based on the compiled data of thirty independent oceanic observations, this article systematically presents the wind-stress coefficient, the surface roughness, and the boundary layer flow regime at the air-sea interface under various wind conditions. The air flow near the water surface is shown to be aerodynamically rough or in the transition region except at a very low wind velocity (U10 < 3 m/sec). Both the wind-stress coefficient and the surface roughness are found to increase with the wind velocity when U10 is less than 15 m/sec and to reach a saturated value for U10 greater than 15 m/sec. From the oceanic wave observations, the presence of this discontinuity at U10 = 15 m/sec is found to be due to an increase in the wind velocity (measured at the significant wave amplitude above the mean water level) beyond the average wave phase velocity. This finding provides a well-defined separation for the often quoted terms ‘light’ and ‘strong’ winds. The compiled data also show that the surface roughness is governed by the amplitude of the short gravity waves. Charnock's relationship is shown to be applicable to most of the oceanic data and Charnock's proportionality constant is determined, η/(u*2/g) = 0.0156. Finally, two approximate formulas for the windstress coefficient C10 = 0.5 × U101/2 × 10−3 for light wind and C10 = 2.6 × 10−3 for strong wind are suggested for oceanic applications.