Laminar Boundary Layer Thickness Research Articles

Linear and nonlinear receptivity mechanisms in boundary layers subject to free-stream turbulence

Large-eddy simulations of a flat-plate boundary layer, without a leading edge, subject to multiple levels of incoming free-stream turbulence are considered in the present work. Within an input–output model, where nonlinear terms of the incompressible Navier–Stokes equations are treated as an external forcing, we manage to separate inputs related to perturbations coming through the intake of the numerical domain, whose evolution represents a linear mechanism, and the volumetric nonlinear forcing due to triadic interactions. With these, we perform the full reconstruction of the statistics of the flow, as measured in the simulations, to quantify pairs of wavenumbers and frequencies more affected by either linear or nonlinear receptivity mechanisms. Inside the boundary layer, different wavenumbers at near-zero frequency reveal streaky structures. Those that are amplified predominantly via linear interactions with the incoming vorticity occur upstream and display transient growth, while those generated by the nonlinear forcing are the most energetic and appear in more downstream positions. The latter feature vortices growing proportionally to the laminar boundary layer thickness, along with a velocity profile that agrees with the optimal amplification obtained by linear transient growth theory. The numerical approach presented is general and could potentially be extended to any simulation for which receptivity to incoming perturbations needs to be assessed.

Optimization of Laminar Boundary Layers in Flow over a Flat Plate Using Recent Metaheuristic Algorithms

Heat transfer is one of the most fundamental engineering subjects and is found in every moment of life. Heat transfer problems, such as heating and cooling, where the transfer of heat between regions is calculated, are problems that can give exact solutions with parametric equations, many of which were obtained by solving differential equations in the past. Today, the fact that heat transfer problems have a more complex structure has led to the emergence of multivariate models, and problems that are very difficult to solve with differential equations have emerged. Optimization techniques, which are also the subject of computer science, are frequently used to solve complex problems. In this study, laminar thermal boundary layers in flow over a flat plate, a sub-problem of heat transfer, is solved with recent metaheuristic algorithms. Teaching learning-based optimization (TLBO), sine cosine optimization (SCO), gray wolf optimization (GWO), whale optimization (WO), salp swarm optimization (SSO), and Harris hawk optimization (HHO) algorithms are used in the study. In the optimization problem, the laminar boundary layer thickness, heat flow, and distance from the leading edge are determined. These three models’ minimum, maximum, and target values are found under the specified design variables and constraints. In the study, 540 optimization models are run, and it is seen that HHO is the most suitable optimization technique for heat transfer problems. Additionally, SSO and WO algorithms gave results close to HHO. Other algorithms also set model targets with an average of less than 0.07% and acceptable error rates. In addition, the average problem solution time of all optimization algorithms and all models was 0.9 s. To conclude, the recent metaheuristic algorithms are found to be powerful and fast in solving heat transfer problems.

Suppression of vortex-induced vibration of a rigid cylinder using flexible shrouding

Experimental investigations were conducted to address the reduction of vortex-induced vibration (VIV) and mean drag coefficient (Cd mean) acting on the oscillating cylinder fitted with a shroud of various parameters. The effectiveness of the shrouds in suppressing the VIV of a short rigid cylinder was investigated by varying the mesh size (B) and mesh thickness (H). The experiments were performed in water flume in NAHRIM and data analysis of Cross-Flow (CF) and In-Line (IL) vibration amplitudes, IL and CF frequencies, mean drag coefficient responses were carried out. Calculation of the laminar boundary layer thickness around a circular cylinder was carried out as a benchmark in deciding the thickness of the mesh. The effect of mesh size and mesh thickness of shrouds was also addressed in this article. From the results obtained, it can be observed that the shroud with mesh size B = 0.2D and mesh thickness H = 0.03D achieved an optimum condition where it was able to suppress the amplitude without increasing Cd mean, with 76.62% of amplitude reduction and 48.40% of Cd mean reduction.

Heat transfer intensification by low or high frequency ultrasound: Thermal and hydrodynamic phenomenological analysis

The aim of this work is to quantitatively demonstrate the intensification of heat transfer in forced convection by mean of ultrasonic irradiation at low (25 kHz) or high (2 MHz) frequency. High frequency ultrasound induces convective acoustic streaming while low frequency ultrasonic waves produce mainly cavitation effects. These hydrodynamic phenomena are at the origin of strongly different observations in terms of flow pattern modification and thereby in Nusselt number values. A link is tentatively established between hydrodynamic behaviors at both ultrasonic frequencies and corresponding thermal results. Hydrodynamic approach was performed with a 2D-2C PIV device while thermal one was carried out under uniform heat flux conditions. It seems that thermal enhancement effect of acoustic streaming (2 MHz) decreases as flow rate increases. This behavior is consistent with the decrease of turbulent kinetic energy produced by acoustic streaming in the same conditions. In the contrary, thermal enhancement effect produced by acoustic cavitation (25 kHz), increases as flow rate increases. This result could be due to the increase of relative size of acoustic bubbles with respect to laminar boundary layer thickness as flow rate increases. In conclusion, the two different ultrasound frequencies, which lead to two different hydrodynamic effects, also lead to two different thermal and turbulence trend with respect to flow rate modifications.

Improved velocity and temperature profiles for integral solution in the laminar boundary layer flow on a semi‐infinite flat plate

AbstractOne of the most important problems in Mechanical Engineering is the determination of laminar boundary layer thickness over a flat plate. Integral solution and similarity solutions are two well‐known methods for calculation of boundary layer thickness. However, integral solution method is a computational cost‐effective method rather than the similarity solution method. Velocity and temperature profiles must be determined for the integral solution method. Velocity boundary layer thickness can be determined by the velocity profile whereas for determination of thermal boundary layer thickness both velocity and temperature profiles must be used. Available velocity profiles do not give an exact value for velocity boundary layer thickness, while the Nusselt number is affected by these profiles. In this study, a new velocity profile is proposed which gives an exact value for laminar boundary layer thickness on a flat plate. In addition, two temperature profiles are proposed that give the exact values of the Nusselt number over a flat plate for uniform temperature and uniform heat flux boundary conditions. The calculated constants in the velocity boundary layer thickness equation and the Nusselt relations are validated with the results of the similarity solution method. Excellent agreement between the results of the two methods is observed.

Numerical analysis on initial development of longitudinal vortices over a heated horizontal plate in uniform downward flow

Fluid flow and heat transfer from an upward-facing horizontal two-dimensional heated plate in uniform downward forced flow are analyzed by means of numerical simulation. We focus our attention to a case where the plate is heated so strongly that the effect of the buoyancy force is not negligible. The Reynolds number based on the plate length is 200 and 500, and the modified Grashof number ranges from 3×106 up to 1.5×108. Assuming that the working fluid is air at room condition, the Prandtl number is kept at 0.71. Longitudinal vortices, discovered in the recent experimental study, are successfully simulated. Typical structures appear as pairs of counter-rotating vortices in the vicinity of the plate with hot fluid ejection in between. They are elongated over the whole plate and regularly allocated in spanwise direction with almost uniform height. Special attention is focused on initial formation of these structures. At the beginning, germs of the structures appear either at the center or on the edge of the plate one by one until the number of them reaches a certain value. The value is subject to the natural convection instability unless the radius of the relevant vortex becomes significantly smaller than the laminar boundary layer thickness of forced stagnation flow. Streamwise contiguity of the structure is established before the power of the relevant spanwise mode comes to a stage of exponential growth inside the boundary layer.

Hot Wire Sensor-Based Data Acquisition System for Controlling the Laminar Boundary Layer Near Plant Leaves Within a Greenhouse

Monitoring a greenhouse needs frequent measurements of inside wind speed, temperature, and moisture. The best growing conditions for cultures are then reached by irrigating them properly. However, the resulting excess of humidity also favors the proliferation of small beasts that cause cryptogrammetric diseases. Instead of using fungicides to destroy them, an ecological approach is implemented, where the boundary layer near the plant leaves is modeled. It consists in reducing the thickness of laminar boundary layer to only a few millimeters, so that the parasite population is rarefied. To experiment such a solution, a data acquisition system equipped with hot wire silicon sensors is implemented so as to control the air ventilation over the plant leaves. These sensors were built using the microelectromechanical system technology and employed to automatically measure humidity, temperature, and wind speed near the plants within the greenhouse. Such sensors, which are very small (100 μm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), do not disturb the measurements. Thanks to such a system, the air ventilation is suitably controlled and the boundary layer thickness, minimized near the plant leaves.

Experimental investigation of nanofluid free convection over the vertical and horizontal flat plates with uniform heat flux by PIV

This paper applies the particle image velocimetry (PIV) to measure the laminar boundary layer thickness of TiO2–water nanofluid free convection over the vertical and horizontal flat plates with constant heat flux. The results are presented for two values of heat flux strength equal to 3000 and 7000w/m2. The effects of nanoparticles and heat flux strength on the boundary layer thickness and velocity profiles are investigated in details. Finally, a comparison is performed between the experimental, theoretical and numerical results for different conditions. The obtained results revealed that the velocity boundary layer decreases by adding the nanoparticles to the base fluid. These reductions, at ϕ=0.1%, are in the vicinity of 7.5% and 5.2% for q″=3000and7000wm-2, respectively. Also, the maximum reductions in the vertical velocity component by adding the nanoparticles at ϕ=0.1% are in the vicinity of 4% and 3.3% for q″=3000and7000wm-2, respectively.

Visualization of a Laminar Necklace Vortex System in Front of a Vertical Rectangular Plate on a Ground Wall

Various properties of a necklace vortex system formed around a rectangular plate standing vertically on a flat ground wall were investigated by visualizations produced by injecting fluorescent dye into a water channel flow. As a result, it was found that the necklace vortex pattern had three steady systems depending on the Reynolds number Reh, the relative height h/δ of the rectangular plate compared with the laminar boundary layer thickness and the aspect ratio w/h. As it is expected that the aspect ratio of the rectangular plate will typify the projected area configuration of various three-dimensional bodies, the aspect ratio is varied widely from 0.5 to 7.0. The transitional boundaries of Reh and h/δ in the 2-vortex, 4-vortex and 6-vortex systems for each aspect ratio decreased when w/h < 3.0, and increased when w/h ≥ 3.0 as w/h increased. The x-direction length of the main vortex position XV1/h was almost constant when w/h < 3.0, and decreased when w/h ≥ 3.0 as Reh increased. Then, the separation length r1/h increased when w/h < 3.0 and Reh < 1000, and became almost constant when w/h ≥ 3.0 and Reh ≥ 1000 as w/h and Reh increased. Moreover, the increase of r1/h is notably rapid when w/h < 3.0.

Investigation on the effectiveness of helical strakes in suppressing VIV of flexible riser

The effectiveness of the strakes in suppressing the vortex-induced vibration (VIV) of a long flexible cylinder is investigated by varying the pitch (p) and height (h) of the strakes. Measurements of cross-flow (CF) vibration amplitude, in-line (IL) and CF frequency responses, and hydrodynamic forces are presented for low mass flexible cylinders with helical strakes. Cylinders with aspect ratio of 162 were applied with constant pre-tension to restrict the vibration in IL and CF directions. Six cases with about 180 runs were executed under subcritical Reynolds number (Re = 0.144to 1.384) of uniform flow. Calculation on the laminar boundary layer thickness around a circular cylinder was performed as a benchmark in deciding the height of strakes. Present study shows that at certain strakes’ height which is larger than the laminar boundary layer thickness, significant VIV mitigation is found. However, the suppression effectiveness of helical strakes on flexible cylinder is less notable compared to a rigid cylinder. The change on pitch of strakes affects the occurrence of lock-in region and prevents the frequency to switch into higher mode. On the other hand, increase on the height of strakes narrows the lock-in region and plays the most major role in suppressing the vibration of a cylinder. The hydrodynamics forces indicate an unexpected phenomenon where the bare cylinder possesses higher force coefficients compared to cylinders with helical strakes. However, large drag penalty is still found in a particular case at higher reduced velocity. The most effective configuration of strakes in terms of the dynamic responses is p = 10D and h = 0.15D model. However, model of p = 10D and h = 0.10D performs better in reducing the hydrodynamic forces.

Effect of flow dynamics on the growth kinetics of CdS thin films in chemical bath deposition

During chemical bath deposition of CdS thin films, the solution is typically stirred to prevent unnecessary concentration gradient and precipitates sticking onto the film surface. Stirring rate changes the thickness of laminar boundary layer over the substrate, affecting the diffusion length of the reactants toward the substrate. It can also change hydrodynamic condition in the bath between laminar and turbulent flow. Interestingly, effect of stirring rate on the deposition kinetics of CdS thin films reported in the literature is conflicting. In this study, we showed that the diffusion-limited deposition kinetics has created a decreasing profile of film thickness along the sample as a function of boundary layer thickness when the substrate was under laminar flow and deposition temperature was between 45°C and 63°C. On the other hand, the deposition became feed-limited when the substrate was under turbulent flow and the deposition temperature was between 45°C and 63°C. While the hydrodynamic condition changed the deposition rate significantly, all the CdS films deposited showed a cubic crystal structure and the optical bandgap was slightly lower than that of single crystalline cubic CdS. The tensile stress in film probed by Raman spectroscopy can explain the low bandgap.

Analytical, Experimental and Numerical Study on formation of Laminar Boundary Layer over a Flat Plate Using Air as Working Fluid

The work presents in this paper is related to comparison of laminar boundary layer thickness of flow of air over a horizontal flat plate at different points among Analytical, Experimental and Numerical approaches.

Conservation-Law Approach to Prediction of Boundary Layer Transition

The boundary layer transition is predicted using the law of mass conservation. The increasing ratio of the boundary layer thickness to the laminar boundary layer thickness at the transition is introduced. Formulas and equations for laminar and turbulent boundary layers are used to predict the transition Reynolds number. The effect of the momentum deficit at the leading edge is also incorporated in this approach under compressible flow conditions. The calculated transition Reynolds number shows reasonable agreement with the experimental results. Under the compressible flow conditions, the calculation simulates the bucket of the transition Reynolds number with a Mach number, the change in the transition Reynolds number due to wall cooling, and the increase in the transition Reynolds number with increase in the bluntness Reynolds number.

Acoustical response of orifices under grazing flow: Effect of boundary layer profile and edge geometry

The effect of mean grazing flow on the acoustical response of a single rectangular slot in a wall to imposed sound is investigated experimentally. For this purpose an accurate multi-microphone impedance tube set-up is employed. In particular the influence of the mean grazing flow characteristics as well as the orifice's (edge) geometry is examined. For this purpose different boundary layer flows and slot geometries are used. Hot-wire boundary layer- and shear layer measurements are carried out. Care has been taken as to remain in the regime of linear acoustic perturbations. The change of the orifice's acoustic impedance due to the mean grazing flow shows an oscillating behaviour as function of the Strouhal number. It is found that, when the Strouhal number is based on the phase velocity of the spatial hydrodynamic instability of the shear layer, these oscillations coincide for different boundary layer flows. The amplitudes of the oscillations increase with decreasing laminar boundary layer thickness. The oscillations disappear when the shear layer, according to linear theory, becomes stable. Furthermore, especially the downstream edge—rather than the upstream edge—of the slot is of influence: oscillations in impedance increase up to a factor five in amplitude when the edges are sharp.

Flow and Heat Transfer around a Square Block Simulating a Package of Electronic Equipment.

An experimental study was performed to investigate the flow and heat transfer around a square block, simulating a package of electronic equipment. The height and the side length of the block were H=2 mm and L=45 mm, respectively. The mean velocity of air in the rectangular duct, Um, ranged from 0.24 to 4 m/s, and the duct height, HD, ranged from 3.8 to 10mm. The thickness of laminar boundary layer was greater than the block height. It was found that the heat transfer distribution on the top face of the block was approximately correlated to the distribution based on the theory of laminar flat boundary layer. The average Nusselt number on the top face was correlated by Num=0.61Pr1/3(Re*L)0.5, where Re* is the modified Reynolds number considering the effect of the opening ratio. This correlation was confirmed by many previous researches, performed under the similar condition of flow field.

An Interferometric Study of the Boundary Layer on a Turbine Nozzle Blade

Abstract The boundary layer on a turbine nozzle blade was investigated with an optical interferometer over a range of Reynolds numbers and subsonic downstream Mach numbers. The ratio of laminar boundary-layer thickness to distance downstream from the minimum pressure point on the suction side of the blade was found to be essentially a unique function of a length Reynolds number based on this distance. Thickness critical Reynolds numbers for transition increased, with throat Reynolds number, from 3000 to 9000 on the suction side and from 1200 to 3100 on the pressure side. A laminar velocity profile was computed from a density profile measured at a point of zero pressure gradient, and satisfactory agreement with theoretical profiles was obtained.