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This paper presents a robust adaptive boundary layer thickness (BLT) of sliding mode control (SMC) for a secure communication of chaos-based system. First, chaotic system was remodeled into the Takagi–Sugeno (T-S) fuzzy format. Second, a novel SMC with an adaptive finite time reaching phase and an adaptive BLT of fixed time sliding phase was proposed to synchronize the master and slave systems (MSSs). The matched disturbances on three channels of the secure communication system (SCS) were rejected by the proposed method. To prove that the proposed theories are corrected, the Lyapunov condition was used to meet the goal. Furthermore, the simulation study was used to verify the correction and effectiveness of the proposed algorithm. The tracking errors and reaching times are very small. The sent and received data were precisely tracked each other in the short time.

The aerodynamic characteristics are concerned with the fuel consumption rate and the stability of a high speed vehicle. The current research aims at studying the aerodynamic behavior of a typical SUV vehicle model mounted with the vortex generator (VG) at various linear positions with reference to its rear roof edge. The flow field around the vehicle model was observed at different wind speed conditions. It had been determined that at the instance of lower wind speed, the VG had minimal effects of aerodynamic drag on the vehicle body. However, at the instance of higher wind speed conditions the magnitude of the drag force decreased significantly. Vehicles move at higher speeds in the highways, location of the VG varied towards the upstream of the vehicle due to early flow separation. Therefore test were conducted at different wind speeds and locations of VG. The numerical simulation conduced in this study provides flow characteristics around the vehicle model for different wind speeds. The realizable k−ε model was used to simulate and validate the empirical results in an effective manner. By using experimental data, the drag was reduced by 9.04 % at the optimized VG location. The results revealed that the induced aerodynamic drag would determine the best car shape. This paper provides a better understanding of VG positioning for enhanced flow separation control.

In order to improve the accuracy of the original full-range equation for wave boundary layer thickness, with special reference to increasing its applicability to tsunami-scale waves, a theoretical investigation is carried out to derive a dimensionless expression which is valid under both smooth and rough turbulent regimes. A coefficient in the equation is determined through a comparison with k-ω  model computation results for tsunami-waves along with laboratory scale oscillatory flow experiments. Thus, the improved full-range equation for wave boundary layer thickness enables us to cover a wide range of wave periods from wind-wave to tsunami.

The aim of this work is to highlight the significance of Fluid–Thermal–Structural Interaction (FTSI) as a diagnosis of existing designs, and as a means of preliminary investigation to ensure the feasibility of new designs before conducting experimental and field tests. The novelty of this work lies in the multi-physics simulations, which are, for the first time, performed on rectangular nozzles. An existing experimental supersonic rectangular converging/diverging nozzle geometry is considered for multi-physics 3D simulations. A design that has been improved by eliminating the sharp throat is further investigated to evaluate its structural integrity at design Nozzle Pressure Ratio (NPR 3.67) and off-design (NPR 4.5) conditions. Static structural analysis is performed by unidirectional coupling of pressure loads from steady 3D Computational Fluid Dynamics (CFD) and thermal loads from steady thermal conduction simulations, such that the simulations represent the experimental set up. Structural deformation in the existing design is far less than the boundary layer thickness, because the impact of Shock wave Boundary Layer Interaction (SBLI) is not as severe. FTSI demonstrates that the discharge coefficient of the improved design is 0.99, and its structural integrity remains intact at off-design conditions. This proves the feasibility of the improved design. Although FTSI influence is shown for a nozzle, the approach can be applied to any product design cycle, or as a prelude to building prototypes.

Free-stream turbulence (FST) and its effect on boundary-layer transition is an intricate problem. Elongated unsteady streamwise streaks of low and high speed are created inside the boundary layer and their amplitude and spanwise wavelength are believed to be important for the onset of transition. The transitional Reynolds number is often simply correlated with the turbulence intensity (${Tu}$), and the characteristic length scales of the FST are often considered to have a small to negligible influence on the transition location. Here, we present new results from a large experimental measurement campaign, where both the ${Tu}$ and the integral length scale ($\\Lambda _x$) are varied ($1.8\\,\\% < {Tu}< 6.2\\,\\%$; $16\\ \\textrm {mm}< \\Lambda _x < 26\\ \\textrm {mm}$). In the current experiments it has been noted that on the one hand, for small $Tu$, an increase in $\\Lambda _x$ advances transition, which is in agreement with established results. On the other hand, for large $Tu$, an increase in $\\Lambda _x$ postpones transition. This trend can be explained by the fact that an optimal ratio between FST length scale and boundary-layer thickness at transition onset exists. Furthermore, our results strengthen the fact that the streaks play a key role in the transition process by showing a clear dependence of the FST characteristics on their spanwise scale. Our measurements show that the aspect ratio of the streaky structures correlates with an FST Reynolds number and that the aspect ratio can change by a factor of two at the location of transition. Finally, we derive a semi-empirical transition prediction model, which is able to predict the influence of $\\Lambda _x$ for both small and high values of ${Tu}$.

We perform direct numerical simulations of wall sheared Rayleigh–Bénard convection for Rayleigh numbers up to $Ra=10^{8}$, Prandtl number unity and wall shear Reynolds numbers up to $Re_{w}=10\\,000$. Using the Monin–Obukhov length $L_{MO}$ we observe the presence of three different flow states, a buoyancy dominated regime ($L_{MO}\\lesssim \\unicode[STIX]{x1D706}_{\\unicode[STIX]{x1D703}}$; with $\\unicode[STIX]{x1D706}_{\\unicode[STIX]{x1D703}}$ the thermal boundary layer thickness), a transitional regime ($0.5H\\gtrsim L_{MO}\\gtrsim \\unicode[STIX]{x1D706}_{\\unicode[STIX]{x1D703}}$; with $H$ the height of the domain) and a shear dominated regime ($L_{MO}\\gtrsim 0.5H$). In the buoyancy dominated regime, the flow dynamics is similar to that of turbulent thermal convection. The transitional regime is characterized by rolls that are increasingly elongated with increasing shear. The flow in the shear dominated regime consists of very large-scale meandering rolls, similar to the ones found in conventional Couette flow. As a consequence of these different flow regimes, for fixed $Ra$ and with increasing shear, the heat transfer first decreases, due to the breakup of the thermal rolls, and then increases at the beginning of the shear dominated regime. In the shear dominated regime the Nusselt number $Nu$ effectively scales as $Nu\\sim Ra^{\\unicode[STIX]{x1D6FC}}$ with $\\unicode[STIX]{x1D6FC}\\ll 1/3$, while we find $\\unicode[STIX]{x1D6FC}\\simeq 0.30$ in the buoyancy dominated regime. In the transitional regime, the effective scaling exponent is $\\unicode[STIX]{x1D6FC}>1/3$, but the temperature and velocity profiles in this regime are not logarithmic yet, thus indicating transient dynamics and not the ultimate regime of thermal convection.

Large-scale secondary flows can sometimes appear in turbulent boundary layers formed over rough surfaces, creating low- and high-momentum pathways along the surface (Barros & Christensen, J. Fluid Mech., vol. 748, 2014, R1). We investigate experimentally the dependence of these secondary flows on surface/flow conditions by measuring the flows over streamwise strips of roughness with systematically varied spanwise spacing. We find that the large-scale secondary flows are accentuated when the spacing of the roughness elements is roughly proportional to the boundary layer thickness ${\\it\\delta}$ , and do not appear for cases with finer spacing. Cases with coarser spacing also generate ${\\it\\delta}$ -scale secondary flows with tertiary flows in the spaces in between. These results show that the ratio of the spanwise length scale of roughness heterogeneity to the boundary layer thickness is a critical parameter for the occurrence of these secondary motions in turbulent boundary layers over rough walls.

Turbulent separation bubbles over and behind a two-dimensional forward–backward-facing step submerged in a deep turbulent boundary layer are investigated using a time-resolved particle image velocimetry. The Reynolds number based on the step height and free-stream velocity is 12 300, and the ratio of the streamwise length to the height of the step is 2.36. The upstream turbulent boundary layer thickness is 4.8 times the step height to ensure a strong interaction of the upstream turbulence structures with the separated shear layers over and behind the step. The velocity measurements were performed in streamwise–vertical planes at the channel mid-span and streamwise–spanwise planes at various vertical distances from the wall. The unsteady characteristics of the separation bubbles and their associated turbulence structures are studied using a variety of techniques including linear stochastic estimation, proper orthogonal decomposition and variable-interval time averaging. The results indicate that the low-frequency flapping motion of the separation bubble over the step is induced by the oncoming large-scale alternating low- and high-velocity streaky structures. Dual separation bubbles appear periodically over the step at a higher frequency than the flapping motion, and are attributed to the inherent instability in the rear part of the mean separation bubble. The separation bubble behind the step exhibits a flapping motion at the same frequency as the separation bubble over the step, but with a distinct phase delay. At instances when an enlarged separation bubble is formed in front of the step, a pair of vertical counter-rotating vortices is formed in the immediate vicinity of the leading edge.

The effect of spanwise heterogeneous surface geometry on turbulent boundary layer secondary flows and on skin friction is investigated experimentally. The surfaces consist of smooth streamwise-aligned ridges of different shapes and widths with spanwise wavelengths comparable to the boundary layer thickness ($S/\\unicode[STIX]{x1D6FF}\\approx O(1)$). Cross-stream stereoscopic particle image velocimetry combined with oil-film interferometry is used to investigate the flow field and assess the drag. Results show that the spanwise distribution of the skin friction varies as a consequence of the mean flow heterogeneity and is highly dependent on surface geometry. The swirling strength maps revealed remarkable changes in the secondary flow structures for different ridge shapes. For wide ridges, topological changes occur showing the appearance of tertiary vortices coexisting with the large-scale secondary structures. An imbalance in favour of these tertiary structures occurs over a certain width which take over the secondary structures, causing a swap in the locations of the low- and high-momentum pathways. Furthermore, the results indicate that the spanwise spacing alone is insufficient to characterise the surface heterogeneity. A new parameter ($\\unicode[STIX]{x1D709}$), which is based on the ratio of the perimeter over and below the mean surface height, is shown to adequately capture the changes in skin friction and streamwise circulation of the secondary motions. Triple decomposition allowed the quantification of the dispersive stresses for all these cases, which can contribute up to$55\\,\\%$of the total shear stress when strong secondary motions occur.

Trip-resolved large-eddy simulations of the DARPA SUBOFF are performed to investigate the development of turbulent boundary layers (TBLs) in model-scale studies. The primary consideration of the study is the extent to which the details of tripping affect statistics in large-eddy simulations of complex geometries, which are presently limited to moderate Reynolds number TBLs. Two trip wire configurations are considered, along with a simple numerical trip (wall-normal blowing), which serves as an exemplar of artificial computational tripping methods often used in practice. When the trip wire height exceeds the laminar boundary layer thickness, shedding from the trip wire initiates transition, and the near field is characterized by an elevation of the wall-normal Reynolds stress and a modification of the turbulence anisotropy and mean momentum balance. This trip wire also induces a large jump in the boundary layer thickness, which affects the way in which the TBL responds to the pressure gradients and streamwise curvature of the hull. The trip-induced turbulence decays along the edge of the TBL as a wake component that sits on top of the underlying TBL structure, which dictates the evolution of the momentum and displacement thicknesses. In contrast, for a trip wire height shorter than the laminar boundary layer thickness, transition is initiated at the reattachment point of the trip-induced recirculation bubble, and the artificial trip reasonably replicates the resolved trip wire behaviour relatively shortly downstream of the trip location. For each case, the inner layer collapses rapidly in terms of the mean profile, Reynolds stresses and mean momentum balance, which is followed by the collapse of the Reynolds stresses in coordinates normalized by the local momentum thickness, and finally against the 99 % thickness. By this point, the lasting impact of the trip is the offset in boundary layer thickness due to the trip itself, which becomes a diminishing fraction of the total boundary layer thickness as the TBL grows. The importance of tripping the model appendages is also highlighted due to their lower Reynolds numbers and susceptibility to laminar separations.