Discrete optimal control for Birkhoffian systems

In this paper, we investigate a discrete variational optimal control for mechanical systems that admit a Birkhoffian representation. Instead of discretizing the original equations of motion, our research is based on a direct discretization of the Pfaff–Birkhoff–d’Alembert principle. The resulting discrete forced Birkhoffian equations then serve as constraints for the minimization of the objective functional. In this way, the optimal control problem is transformed into a finite-dimensional optimization problem, which can be solved by standard methods. This approach yields discrete dynamics, which is more faithful to the continuous equations of motion and consequently yields more accurate solutions to the optimal control problem which is to be approximated. We illustrate the method numerically by optimizing the control for the damped oscillator.     

Micro-blast waves using detonation transmission tubing

Micro-blast waves emerging from the open end of a detonation transmission tube were experimentally visualized in this study. A commercially available detonation transmission tube was used (Nonel tube, M/s Dyno Nobel, Sweden), which is a small diameter tube coated with a thin layer of explosive mixture (HMX $+$ traces of Al) on its inner side. The typical explosive loading for this tube is of the order of 18 mg/m of tube length. The blast wave was visualized using a high speed digital camera (frame rate 1 MHz) to acquire time-resolved schlieren images of the resulting flow field. The visualization studies were complemented by computational fluid dynamic simulations. An analysis of the schlieren images showed that although the blast wave appears to be spherical, it propagates faster along the tube axis than along a direction perpendicular to the tube axis. Additionally, CFD analysis revealed the presence of a barrel shock and Mach disc, showing structures that are typical of an underexpanded jet. A theory in use for centered large–scale explosions of intermediate strength $(10\, < \Delta {p}/{p}_0 \lesssim \, 0.02)$ gave good agreement with the blast trajectory along the tube axis. The energy of these micro-blast waves was found to be $1.25 \pm 0.94$ J and the average TNT equivalent was found to be $0.3$ . The repeatability in generating these micro-blast waves using the Nonel tube was very good $(\pm 2~\%)$ and this opens up the possibility of using this device for studying some of the phenomena associated with muzzle blasts in the near future.     

Large area impingement spray cooling from multiple normal and inclined spray nozzles

An inclined spray chamber with four multiple nozzles to cool a 1 kW 6U electronic test card has been designed and tested in this study. The multiple inclined sprays can cover the same heated surface area as that with the multiple normal sprays but halve the volume of the spray chamber. The spray cooling system used R134a as a working fluid in a modified refrigeration cycle. It is observed that increasing mass flow rate and pressure drop across the nozzles improved the heat transfer coefficient with a maximum enhancement of 117 %, and reduced the maximum temperature difference at the heated surface from 13.8 to 8.4 °C in the inclined spray chamber with a heat flux of 5.25 W/cm², while the heat transfer coefficient of the normal spray increased with a maximum enhancement of 215 % and the maximum temperature difference decreased from 10.8 to 5.4 °C under similar operating conditions. We conclude that the multiple inclined sprays could produce a higher heat transfer coefficient but with an increase in non-uniformity of the surface temperature compared with the multiple normal sprays.     

Effectiveness of a multi-channel volumetric air receiver for a solar power tower

In this study, the heat transfer performance of a multi-channel volumetric air receiver for a solar power tower was numerically analyzed. The governing equations, including the solar radiation heat flux, conduction, convection and radiation heat transfer for a single channel, were solved on the basis of valid related references and a methodology that can predict the temperature distribution of the receiver wall and the heat transfer fluid for specific dimensions and input conditions. Furthermore, a mathematical model of the effectiveness of the receiver was derived from an analysis of the temperature profiles of the wall and the heat transfer fluid. The receiver effectiveness as an appropriate criterion to assess economic feasibility regarding geometric size was investigated, as it would be applied to the design process of the receiver. The main parameters for the thermal performance simulations described in this paper are the air mass flow rate, receiver length and the influence of these parameters on the heat transfer performance from the viewpoint of receiver efficiency and effectiveness.     

Symmetric Gauss-Seidel multigrid solution of the Euler equations on structured and unstructured grids

The efficient symmetric Gauss-Seidel (SGS) algorithm for solving the Euler equations of inviscid, compressible flow on structured grids, developed in collaboration with Jameson of Stanford University, is extended to unstructured grids. The algorithm uses a nonlinear formulation of an SGS solver, implemented within the framework of multigrid. The earlier form of the algorithm used the natural (lexicographic) ordering of the mesh cells available on structured grids for the SGS sweeps, but a number of features of the method that are believed to contribute to its success can also be implemented for computations on unstructured grids. The present paper reviews, the features of the SGS multigrid solver for structured gr0ids, including its nonlinear implementation, its use of “absolute” Jacobian matrix preconditioning, and its incorporation of multigrid, and then describes the incorporation of these features into an algorithm suitable for computations on unstructured grids. The implementation on unstructured grids is based on the agglomerated multigrid method developed by Sørensen, which uses an explicit Runge-Kutta smoothing algorithm. Results of computations for steady, transonic flows past two-dimensional airfoils are presented, and the efficiency of the method is evaluated for computations on both structured and unstructured meshes.     

Two-stage fourth-order gas-kinetic scheme for three-dimensional Euler and Navier-Stokes solutions

ABSTRACT

For the one-stage third-order gas-kinetic scheme (GKS), successful applications have been achieved for the three-dimensional compressible flows [Pan, L., K. Xu, Q. Li, and J. Li. 2016. “An Efficient and Accurate Two-stage Fourth-order Gas-kinetic Scheme for the Navier-Stokes Equations.” Journal of Computational Physics 326: 197–221]. The high-order accuracy of the scheme is obtained by integrating a multidimensional time-accurate gas distribution function over the cell interface within a time step without using Gaussian quadrature points and Runge-Kutta time-stepping technique. However, to the further increase of the order of the scheme, such as the fourth-order one, the one step formulation becomes very complicated for the multidimensional flow. Recently, a two-stage fourth-order GKS with high efficiency has been constructed for two-dimensional inviscid and viscous flow computations ([Li, J., and Z. Du. 2016. “A Two-stage Fourth Order Time-accurate Discretization for Lax-Wendroff Type Flow Solvers I. Hyperbolic Conservation Laws.” SIAM Journal on Scientific Computing 38: 3046–3069]; Pan et al. 2016), and the scheme uses the time accurate flux function and its time derivatives. In this paper, a fourth-order GKS is developed for the three-dimensional flows under the two-stage framework. Based on the three-dimensional WENO reconstruction and flux evaluation at Gaussian quadrature points on a cell interface, the high-order accuracy in space is achieved first. Then, the two-stage time stepping method provides the high accuracy in time. In comparison with the formal third-order GKS [Pan, L., and K. Xu. 2015. “A Third-order Gas-kinetic Scheme for Three-dimensional Inviscid and Viscous Flow Computations.” Computers & Fluids 119: 250–260], the current fourth-order method not only improves the accuracy of the scheme, but also reduces the complexity of the gas-kinetic flux solver greatly. More importantly, the fourth-order GKS has the same robustness as the second-order shock capturing scheme [Xu, K. 2001. “A Gas-kinetic BGK Scheme for the Navier-Stokes Equations and its Connection with Artificial Dissipation and Godunov Method.” Journal of Computational Physics 171: 289–335]. Numerical results validate the outstanding reliability and applicability of the scheme for three-dimensional flows, such as the cases related to turbulent simulations.     

Further Examination of the Mechanism of Round Synthetic Jets in Delaying Turbulent Flow Separation

This paper reports the findings from a further study of the 2D and stereo PIV data obtained in the interaction zone between the separated turbulent boundary layer over a 2D ramp and round synthetic jets by the authors. The synthetic jets are operated at two actuation frequencies with one being close to the natural frequency of the separated shear layer. Both the triple decomposition technique and Q-criterion are employed to investigate how the separated flow responds to the passage of different parts of the vortical structures produced by the synthetic jets during an actuation cycle at different synthetic jet operating conditions. An attempt is made to explain the observed differences in the ways that the separated flow responds to the actuation of synthetic jets at the two actuation frequencies. A better understanding of the mechanism of flow separation delay using round synthetic jets is obtained, leading to a more complete physical model describing the interaction mechanism.     

Large-Eddy Simulations of Forced Three-Dimensional Impinging Jets

Large-eddy simulations of the flow field around twin three-dimensional impinging jets were carried out to simulate the near-ground hover configuration of a vertical takeoff and landing (VTOL) aircraft. Both the impinging jet and the upwash caused by the collision of the wall jets are modeled in this study. The evolution of the vortical structures in the impinging jet flow field, due to the introduction of axisymmetric and azimuthal perturbations at the jet exit, has been investigated. The vortical structures formed in the jet shear layer due to azimuthal forcing, show significant three-dimensional vortex stretching effects when compared to the structures formed during axisymmetric forcing. Breakdown of the large-scale structures into smaller vortices also occurs much earlier during azimuthal forcing. When compared to the upwash formed during axisymmetric forcing, the azimuthally perturbed jet forms an upwash that is less coherent and results in a weaker upload or lift-off force on the aircraft undersurface. Comparison with available experimental data indicates good agreement for the centerline velocity decay, the wall pressure variation and the phase speed of the vortical structures.     

苯胺四聚体-聚乙二醇-苯胺四聚体嵌段共聚物薄膜的自组装

以氨基封端的苯胺四聚体为基础,以甲苯2,4-二异氰酸酯(TDI)为中间体制备了苯胺四聚体-聚乙二醇-苯胺四聚体(ANI₄-PEG-ANI₄,PEG600,M_n＝600)嵌段共聚物,并溶于乙醇/N,N-二甲基甲酰胺(DMF)混合溶剂后,涂覆于导电玻璃(ITO)表面制备成薄膜,利用原子力显微镜(AFM)、紫外-可见光谱(UV-Vis)和循环伏安(CV)等研究了薄膜的自组装及电化学行为等,讨论了诱导溶剂对嵌段共聚物薄膜形态和性能的影响. 研究发现,通过改变混合溶剂比和诱导溶剂种类,ANI₄-PEG-ANI₄嵌段共聚物薄膜可以实现多种形态的转变.     

利用小行星视线矢量的火星探测光学自主导航研究

结合我国即将开展的自主火星探测计划,研究了航天器在火星探测巡航过程中利用小行星进行光学自主导航的整个过程. 根据巡航段的设计轨道,给出了导航小行星的筛选条件并筛选出可用于实际任务的导航小行星序列. 将自主导航的数据弧段长度设定为30d,数据观测周期为5d. 采用加权最小二乘滤波算法,当数据弧段长度为30d时,导航计算的位置误差在100～400km变化,速度误差不超过0.25m/s.