The intrinsic uncertainty of fluid properties, including the equation-of-state, viscosity and thermal conductivity, on boundary layer stability has scarcely been addressed. When a fluid is operating in the vicinity of the Widom line (defined as the maximum of isobaric specific heat) in supercritical state, its properties exhibit highly non-ideal behavior, which is an ongoing research field leading to refined and more accurate fluid property databases. Upon crossing the Widom line, new mechanisms of flow instability emerge, feasibly leading to changes in dominating modes that yield turbulence. The present work investigates the sensitivity of three-dimensional boundary layer modal instability to these intrinsic uncertainties in fluid properties. The uncertainty, regardless of its source and the fluid regimes, gives rise to distortions of all profiles that constitute the inputs of the stability operator. The effect of these distortions on flow stability is measured by sensitivity coefficients, which are formulated with the adjoint operator and validated against linear modal stability analysis. The results are presented for carbon dioxide at a representative supercritical pressure of approximately 80 bar. The sensitivity to different inputs of the stability operator across various thermodynamic regimes shows an immense range of sensitivity amplitude. A balancing relationship between the density gradient and its perturbation leads to a quadratic effect across the Widom line, provoking significant sensitivity to distortions of the second derivative of the pressure with respect to the density, $\partial ^2 p/\partial \rho ^2$. From an application-oriented point of view, one important question is whether the correct baseflow profiles can be meaningfully analysed by the simplified ideal-fluid model. The integrated modal disturbance growth – the N factor calculated with different partly idealised models – indicates that the answer depends strongly on the thermodynamic regime investigated.

The transition to turbulence induced by counter-rotating wall-normal rotating cylindrical roughness pairs immersed within a laminar boundary layer on a flat plate is investigated with direct numerical simulations, dynamic mode decomposition (DMD) and perturbation kinetic energy (PKE) analysis. As long as the cylinder stub is rotating, the wake contains a steady dominating inner vortex (DIV) surrounded by a secondary inner vortex. Its circumferential velocity accelerates the fluid on one side of the cylinder and decelerates it on the other side. With low rotation speed, the perturbation is initiated by a combination of elliptical and centrifugal instabilities in the near wake. At medium rotation speeds, Taylor–Couette-like streamwise vortices are generated on the decelerated side, resulting in a protruding reverse-flow zone. Results from DMD analysis and corresponding PKE analysis reveal the unstable nature of the deceleration region and the wake. At the largest rotation speed investigated, the onset of perturbations is directly located on the decelerated side of the cylinder stubs, where a deceleration mechanism feeds the instability. In the near wake, the mechanism gradually changes to a pure centrifugal instability when the rotation speed increases. In the far wake, both elliptical and centrifugal instabilities fade away, and the streaky flow featuring a vigorous DIV is then only subject to inviscid inflectional instability.

The multi-arm robotic systems consisting of redundant robots are able to conduct more complex and coordinated tasks, such as manipulating large or heavy objects. The challenges of the motion planning and control for such systems mainly arise from the closed-chain constraint and redundancy resolution problem. The closed-chain constraint reduces the configuration space to lower-dimensional subsets, making it difficult for sampling feasible configurations and planning path connecting them. A global motion planner is proposed in this paper for the closed-chain systems, and motions in different disconnected manifolds are efficiently bridged by two type regrasping moves. The regrasping moves are automatically chosen by the planner based on cost-saving principle, which greatly improve the success rate and efficiency. Furthermore, to obtain the optional inverse kinematic solutions satisfying joint physical limits (e.g., joint position, velocity, acceleration limits) in the planning, the redundancy resolution problem for dual redundant robots is converted into a unified quadratic programming problem based on the combination of two diff erent-level optimizing criteria, i.e. the minimization velocity norm (MVN) and infinity norm torque-minimization (INTM). The Dual-MVN-INTM scheme guarantees smooth velocity, acceleration profiles, and zero final velocity at the end of motion. Finally, the planning results of three complex closed-chain manipulation task using two Franka Emika Panda robots and two Kinova Jaco2 robots in both simulation and experiment demonstrate the effectiveness and efficiency of the proposed method.

Cylinder stubs of finite length, mounted in a wall-normal manner on a flat plate, exert considerable control on their wake when rotating around their central axis. The present paper investigates these effects with linear stability theory and a direct numerical simulation. Three configurations are considered: evenly spaced corotating roughness elements, as well as positive and negative counter-rotating roughness pairs. Here, ‘positive’ and ‘negative’ are defined in accordance with the induced high- and low-speed streaks, respectively. A primary feature of the rotating-cylinder-induced wake is a ‘dominating inner vortex’ (DIV), which intensifies the lift-up effect and creates high-amplitude streaks. Linear stability analysis shows that the modified streaky flow is capable of effectively stabilizing Tollmien–Schlichting (TS) modes. The mechanism of TS mode stabilization, as found by a perturbation kinetic energy analysis, is attributed to the reduction of the wall-normal perturbation production. On the other hand, an inviscid inflectional instability mode related to the presence of the roughness appears which destabilizes the boundary-layer flow, primarily due to an increase in wall-normal perturbation energy production, but also due to increasing spanwise energy production, depending on the case. The inflectional instability roughness mode is more amplified with thicker cylinders since the induced DIV tends to support longer-living inflection points. Regarding an imaginable laminar–turbulent transition delay, positive rotating thinner roughness pairs would be preferable.