Boundary layer laminarization by convex curvature and acceleration

Boundary layer measurements have been made on the concave surfaces of two constant curvature blades using hot wire anemometry. All the current experiments were performed with negligible streamwise pressure gradient. Grids were used to produce a range of freestream turbulence levels between 1% and 4%. The freestream velocity increases with distance from a concave wall according to the free vortex condition making the determination of the boundary layer edge difficult. A flat plate equivalent boundary layer procedure was adopted therefore to overcome this problem. The Taylor-Goertler (T-G) vortices resulting from the concave curvature were found to make the laminar and turbulent boundary layer profiles fuller and to increase the skin friction coefficent by up to 40% compared with flat plate values. This leads to a more rapid growth in boundary layer thickness. The evolution in the intermittency through transition is very similar to that for a flat plate, however the shape factors are depressed slightly throughout the flow due to the fuller velocity profiles. For all the current experiments, curvature promoted transition. This was very marked at low freestream turbulence level but remained significant even at the highest levels. It appears that the velocity fluctuations associated with the T-G vortices enhance the freestream turbulence resulting in a higher effective turbulence level. A new empirical correlation for start of transition based on this premise is presented. The ratio of end to start of transition momentum thickness Reynolds numbers was found to be approximately constant.

The effect of the Reynolds number, the boundary layer thickness and the gap ratio on the beginning of the periodic vortex-shedding from a circular cylinder in a laminar boundary layer was experimentally investigated. The Reynolds number Re, which was defined in terms of the cylinder diameter (d) and the free stream velocity (U0), ranged from 40 to 1000. The range of the boundary layer thickness (d/δ) was from 0.08 to 0.38. The gap ratio defined by the circular cylinder (d) and the clearance between the circular cylinder and the wall (g) was varied from 0.38 to 3.0. As a result, the frequency of the vortex-shedding from the circular cylinder in the laminar boundary layer can be determined by the gap ratio, but it does not depend on the Reynolds number and the boundary layer thickness.

We examine the response of hypervelocity boundary layers to global mechanical distortions due to concave surface curvature. Surface heat transfer and visual boundary layer thickness data are obtained for a suite of models with different concave surface geometries. Results are compared to predictions using existing approximate methods. Near the leading edge, good agreement is observed, but at larger pressure gradients, predictions diverge significantly from the experimental data. Up to a factor of five underprediction is reported in regions with greatest distortion. Curve fits to the experimental data are compared with surface equations. We demonstrate that reasonable estimates of the laminar heat flux augmentation may be obtained as a function of the local turning angle for all model geometries, even at the conditions of greatest distortion. This scaling may be explained by the application of Lees similarity. As a means of introducing additional local distortions, vortex generators are used to impose streamwise structures into the boundary layer. The response of the large scale vortices to an adverse pressure gradient is investigated. Surface streak evolution is visualized over the different surface geometries using fast response pressure sensitive paint. For a flat plate baseline case, heat transfer augmentation at similar levels to turbulent flow is measured. For the concave geometries, increases in heat transfer by factors up to 2.6 are measured over the laminar values. The scaling of heat transfer with turning angle that is identified for the laminar boundary layer response is found to be robust even in the presence of the imposed vortex structures.

An experimental investigation has been carried out on a transitional boundary layer subject to high (initially 9%) freestream turbulence, strong acceleration (K=ν/Uw2dUw/dx as high as 9×10−6), and strong concave curvature (boundary layer thickness between 2% and 5% of the wall radius of curvature). Mean and fluctuating velocity as well as turbulent shear stress are documented and compared to results from equivalent cases on a flat wall and a wall with milder concave curvature. The data show that curvature does have a significant effect, moving the transition location upstream, increasing turbulent transport, and causing skin friction to rise by as much as 40%. Conditional sampling results are presented which show that the curvature effect is present in both the turbulent and nonturbulent zones of the transitional flow.

We report high-resolution measurements of the properties of the velocity boundary layer in turbulent thermal convection using the particle image velocimetry (PIV) technique and measurements of the temperature profiles and the thermal boundary layer. Both velocity and temperature measurements were made near the lower conducting plate of a rectangular convection cell using water as the convecting fluid, with the Rayleigh numberRavarying from 109to 1010and the Prandtl numberPrfixed at 4.3. From the measured profiles of the horizontal velocity we obtain the viscous boundary layer thickness δυ. It is found that δυfollows the classical Blasius-like laminar boundary layer in the present range ofRa, and it scales with the Reynolds numberReas δυ/H= 0.64Re−0.50±0.03(whereHis the cell height). While the measured viscous shear stress and Reynolds shear stress show that the boundary layer is laminar forRa< 2.0 × 1010, two independent extrapolations, one based on velocity measurements and the other on velocity and temperature measurements, both indicate that the boundary layer will become turbulent atRa~ 1013. Just above the thermal boundary layer but within the mixing zone, the measured temperature r.m.s. profiles σT(z) are found to follow either a power law or a logarithmic behaviour. The power-law fitting may be slightly favoured and its exponent is found to depend onRaand varies from −0.6 to −0.77, which is much larger than the classical value of −1/3. In the same region, the measured profiles of the r.m.s. vertical velocity σw(z) exhibit a much smaller scaling range and are also consistent with either a power-law or a logarithmic behaviour. The Reynolds number dependence of several wall quantities is also measured directly. These are the wall shear stress τw~Re1.55, the viscous sublayer δw~Re−0.91, the friction velocityuτ~Re0.80, and the skin-friction coefficientcf~Re−0.34. All of these scaling properties are very close to those predicted for a classical Blasius-type laminar boundary layer, except that ofcf. Similar to classical shear flows, a viscous sublayer is also found to exist in the present system despite the presence of a nested thermal boundary layer. However, velocity profiles normalized by wall units exhibit no obvious logarithmic region, which is likely to be a result of the very limited distance between the edge of the viscous sublayer and the position of the maximum velocity. Compared to traditional shear flows, the peak position of the wall-unit-normalized r.m.s. profiles is found to be closer to the plate (atz+=z/δw≃ 5). Our overall conclusion is that a Blasius-type laminar boundary condition is a good approximation for the velocity boundary layer in turbulent thermal convection for the present range of Rayleigh number and Prandtl number.

Effect of leading edge bluntness on the interaction of ramp induced shock wave with laminar boundary layer at hypersonic speed

The important effects of rotation and compressibility on rotor blade boundary layers are theoretically investigated. The calculations are based on the momentum integral method and results from calculations of a transonic compressor rotor are presented. Influence of rotation is shown by comparing the incompressible rotating flow with the stationary one. Influence of compressibility is shown by comparing the compressible rotating flow with the incompressible rotating one. Two computer codes for three-dimensional laminar and turbulent boundary layers, originally developed by SSPA Maritime Consulting AB, have been further developed by introducing rotation and compressibility terms into the boundary layer equations. The effect of rotation and compressibility on the transition have been studied. The Coriolis and centrifugal forces that contribute to the development of the boundary layers and influence its behavior generate crosswise flow inside the blade boundary layers, the magnitude of which depends upon the angular velocity of the rotor and the rotor geometry. The calculations show the influence of rotation and compressibility on the boundary layer parameters. Momentum thickness and shape factor increase with increasing rotation and decrease when compressible flow is taken into account. For skin friction such effects have inverse influences. The different boundary layer parameters behave similarly on the suction and pressure sides with the exception of the crossflow angle, the crosswise momentum thickness, and the skin friction factor. The codes use a nearly orthogonal streamline coordinate system, which is fixed to the blade surface and rotates with the blade.

The influence of the boundary layer (BL) thickness on the tonal noise generated by subsonic impinging jets is investigated. For that, initially laminar jets at Mach numbers$0.6$and$0.9$with BL thicknesses$0.05r_0$,$0.1r_0$and$0.2r_0$, where$r_0$is the pipe-nozzle radius, impinging on a plate at$6r_0$from the nozzle, are simulated. For Mach number$0.9$, acoustic tones due to feedback loops of axisymmetric nature between the nozzle and the plate are generated at frequencies that do not vary with the BL thickness. The two dominant tones are, however,$17$and$26\ \mathrm {dB}$stronger for the thickest BL compared with the thinnest one. For Mach number$0.6$, for the thinnest BL no acoustic peaks appear, as observed in the experiments of the literature, but narrow peaks resulting from axisymmetric feedback loops emerge for thicker BLs. Therefore, low subsonic impinging jets can be resonant for specific nozzle-exit conditions. The increase in tone amplitude for Mach number$0.9$, and the establishment of feedback loops for Mach number$0.6$with increasing BL thickness, are found to result from two changes in the jet flow. The first change is that the shear-layer laminar–turbulent transition occurs farther downstream for a thicker BL, leading to a greater predominance of the axisymmetric aerodynamic fluctuations near the plate. The second change is that the amplification of the flow fluctuations between the nozzle and the plate at the tone frequencies is stronger for thicker BLs.

One 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.

The development of a boundary layer over a flat plate placed in a square pipe was studied in pulp suspensions at concentrations of 0.5, 1 and 1.8% at flow velocities of 0.24-0.96 m/s. Laser Doppler Anemometry (LDA) was used to measure velocities in the boundary layer from y=0-3 mm at x=0, 5, 10, 20 and 30 mm, where x=0 mm was the position where the flow met the plate. During the measurement time the pressure drop over the plate was also measured and it was concluded that the flow was in the rolling friction regime. The results of boundary layer thickness show that an increase in velocity or a decrease in concentration gave a thicker boundary layer in contrast to a laminar Newtonian boundary layer. In a power law fluid, boundary layer thickness decreases with an increase in shear thinning or velocity. Furthermore, in the pulp suspensions, a boundary layer with a constant thickness was reached 20 mm from the plate edge in contrast to a Newtonian and a shear thinning boundary layer which continued to increase along the plate. The difference in boundary layer development is believed to depend on the two-phase effects in pulp suspensions.

Inward turning hypersonic vehicle inlets have the theoretical potential to achieve higher efficiency than conventional two-dimensional geometries. However, the design of axisymmetric, streamtraced inlets depends on the capability to model boundary layer behavior over surfaces with concave curvature. In this work, we carry out a fundamental study of boundary layers flows, which are known to be significantly influenced by three-dimensional effects, at high stagnation-enthalpy, hypersonic conditions over surfaces with different concave geometry. Surface heat transfer and boundary layer visual thickness data over models with cubic, quadratic and blended concave surface curvature are compared with a flat plate baseline case. For all models, concave surface curvature produces an increase in the heat flux over flat plate laminar values. We demonstrate that reasonable estimates of the laminar heat flux augmentation due to concave surface curvature may be obtained from the local turning angle at the conditions of these experiments.

Flow in the juncture of surface mounted stream-lined slabs of various aspect ratios was studied in a low speed wind tunnel for laminar as well as turbulent approach boundary layer conditions for Reynolds number of 70,000, 90,000 and 120,000. For a laminar approach boundary layer a wavy structure along the primary separation line was observed for an aspect ratio of 1 while at higher aspect ratios and in case of the turbulent boundary layer for all aspect ratios this pattern was not visible. Mean pressures measured along the plane of symmetry on the surface exhibited influence of aspect ratio as well as boundary layer condition. While the surface pressure gradient for the turbulent case continuously increased in the direction of the slab, the laminar boundary layer case had a distinct change in slope, the location of which was aspect ratio dependent. Additionally the pressure gradient for the turbulent boundary layer was lower in comparison to the laminar boundary layer. The pressure differential at the mean vortex location for the turbulent boundary layer was higher than the laminar boundary layer case and reduced with increasing aspect ratio for both cases. The mean vortex location moved away from the slab leading edge with increasing aspect ratio for the laminar case while movement in case of the turbulent boundary layer was not discernable. The mean vortex locations for the turbulent boundary layer were further upstream as compared to the laminar boundary layer cases

Transient natural convection boundary layer flow is studied at Pr>1 and the curvature effect is specifically and fundamentally explored. Important scale laws, i.e. boundary layer thickness \ensuremath{\delta}t and characteristic velocity ${u}_{z}$ of the transient and steady states and the cut-off time ${t}_{s}$ of the initial growth, are proposed and validated. We find that for cylinder radius much larger than the boundary layer thickness, the present scaling relations reduce to those of the classic flat boundary layer. The most curved boundary layer we examine is 26 times thicker than the cylinder radius. We show that the present scaling set is accurate for all flow conditions bounded by the two limiting scenarios.

Direct numerical simulation is conducted to uncover the response of a supersonic turbulent boundary layer to streamwise concave curvature and the related physical mechanisms at a Mach number of 2.95. Streamwise variations of mean flow properties, turbulence statistics and turbulent structures are analysed. A method to define the boundary layer thickness based on the principal strain rate is proposed, which is applicable for boundary layers subjected to wall-normal pressure and velocity gradients. While the wall friction grows with the wall turning, the friction velocity decreases. A logarithmic region with constant slope exists in the concave boundary layer. However, with smaller slope, it is located lower than that of the flat boundary layer. Streamwise varying trends of the velocity and the principal strain rate within different wall-normal regions are different. The turbulence level is promoted by the concave curvature. Due to the increased turbulence generation in the outer layer, secondary bumps are noted in the profiles of streamwise and spanwise turbulence intensity. Peak positions in profiles of wall-normal turbulence intensity and Reynolds shear stress are pushed outward because of the same reason. Attributed to the Görtler instability, the streamwise extended vortices within the hairpin packets are intensified and more vortices are generated. Through accumulations of these vortices with a similar sense of rotation, large-scale streamwise roll cells are formed. Originated from the very large-scale motions and by promoting the ejection, sweep and spanwise events, the formation of large-scale streamwise roll cells is the physical cause of the alterations of the mean properties and turbulence statistics. The roll cells further give rise to the vortex generation. The large number of hairpin vortices formed in the near-wall region lead to the improved wall-normal correlation of turbulence in the concave boundary layer.

The work described divides itself into three parts. The first of these describes an experimental investigation into the influence of a line sink on a turbulent boundary layer, the object of which was to ascertain the overall effect on the values of boundary layer thickness and. mean velocity profile shape factor of removing a given amount of fluid. To this end, an axisymmetrical boundary layer duct was constructed. W1 thin the limitations of the experimental investigation, which was restricted to the case of only one initial value of shape-factor, it was found possible to represent the effect of a suction strip on a boundary layer in a semi-empirical manner. It was also apparent that the transient effects as represented by the lack of universality of the mean velocity distribution only persisted for a limited extent downstream of the suction strip. The second part of this work considers the problem of the optimum . distribution of suction in order to suppress the separation of a boundary layer. A fairly comprehensive theoretical treatment of this problem is presented which can be used to define the distribution of suction for any surface over which the boundary layer flow is essentially two dimensional. The basis of this approach is that the suction distribution can be defined by specifying .an upper limit on the value of either one of the two parameters which are normally taken as defining the state at a boundary layer, i.e., momentum thickness and shape factor. The precise value lot this upper limit is defined. by the condition that the suction power required should be a minimum. A series of calculations have been Wldertaken which illustrate the general validity of this approach and. which :f'urther result in a prediction of the minimum suction quantity necessary in order to obtain a given lift coefficient. These results may be used as the basis tor a project study of an aircraft which utilises this type o£' boundary layer control, and also as a starting point for an experimental investigation which would introduce the influence of the various methods of attaining an idealised porous surface in practise. The third part of the work considers the alternative of boundary layer control by tangential blowing. Experimental measurements on a plane wall jet are compared with Glauert' s theoretical predictions and it is noted that, whereas the basic idea behind Gl.auert's approach is confirmed, some of the detailed predictions show significant discrepancies. The existence of a region of universal mean velocity distribution near the surface is confirmed. A method of caloulating the streamwise variation of the maximum velocity of a wall jet is proposed which is based on the principles of similarity of the mean velocity distribution, continuity and variation of momentum due to the action of the surface shearing force. consideration is made of the effects of . surface curvature and the superposition of a tree stream on the development of a wall jet and it is noted that the latter effect is small. In the case of :flap blowing, it is shown that the non-dimensional blowing momentum coefficient can be interpreted directly in terms of the value of the ratio of maximum jet velocity to local stream velocity where both are measured at the trailing edge.