Optimized Runge-Kutta Methods with Automatic Step Size Control for Compressible Computational Fluid Dynamics

We develop error-control based time integration algorithms for compressible fluid dynam-ics(CFD)applications and show that they are efficient and robust in both the accuracy-limited and stability-limited regime.Focusing on discontinuous spectral element semidis-cretizations,we design new controllers for existing methods and for some new embedded Runge-Kutta pairs.We demonstrate the importance of choosing adequate controller parameters and provide a means to obtain these in practice.We compare a wide range of error-control-based methods,along with the common approach in which step size con-trol is based on the Courant-Friedrichs-Lewy(CFL)number.The optimized methods give improved performance and naturally adopt a step size close to the maximum stable CFL number at loose tolerances,while additionally providing control of the temporal error at tighter tolerances.The numerical examples include challenging industrial CFD applications.

Direct Digital Frequency Control Based on the Phase Step Change Characteristic between Signals

We present a new digital phase lock technology to achieve the frequency control and transformation through high precision multi-cycle group synchronization between signals without the frequency transformation circuit. In the case of digital sampling, the passing zero point of the phase of the controlled signal has the phase step characteristic, the phase step of the passing zero point is monotonic continuous with high resolution in the phase lock process, and using the border effect of digital fuzzy area, the gate can synchronize with the two signals, the quantization error is reduced. This technique is quite different from the existing methods of frequency transformation and frequency synthesis, the phase change characteristic between the periodic signals with different nominal is used. The phase change has the periodic phenomenon, and it has the high resolution step value. With the application of the physical law, the noise is reduced because of simplifying frequency transformation circuits, and the phase is locked with high precision. The regular phase change between frequency signals is only used for frequency measurement, and the change has evident randomness, but this randomness is greatly reduced in frequency control, and the certainty of the process result is clear. The experiment shows that the short term frequency stability can reach 10-12/s orders of magnitude.

Microstructure and Growth Kinetics of Silicide Coatings for TiAl Alloy

In order to improve the oxidation resistance of Ti Al alloy, silicide coatings were prepared by pack cementation method at 1273, 1323, and 1373 K for 1-3 hours. Scanning electron microscopy（SEM）, energy dispersive spectrometry（EDS） and X-ray diffraction（XRD） were employed to investigate the microstructures and phase constitutions of the coatings. The experimental results show that all silicon deposition coatings have multi-layer structure. The microstructure and composition of silicide coatings strongly depend on siliconizing temperatures. In order to investigate the rate controlling step of pack siliconizing on Ti Al alloy, coating growth kinetics was analyzed by measuring the mass gains per unit area of silicided samples as a function of time and temperature. The results showed that the rate controlling step was gas-phase diffusion step and the growth rate constant（k） ranged from 1.53 mg^2/（cm^4·h^2） to 2.3 mg^2/（cm^4·h^2）. Activation energy（Q） for the process was calculated as 109 k J/mol, determined by Arrhenius＇ equation： k = k0 exp[–Q/（RT）].

Simple PID Parameter Tuning Method Based on Outputs of the Closed Loop System

Most of the existing PID parameters tuning methods are only effective with pre-known accurate system models, which often require some strict identification experiments and thus infeasible for many complicated systems. Actually, in most practical engineering applications, it is desirable for the PID tuning scheme to be directly based on the input-output response of the closed-loop system. Thus, a new parameter tuning scheme for PID controllers without explicit mathematical model is developed in this paper. The paper begins with a new frequency domain properties analysis of the PID controller. After that, the definition of characteristic frequency for the PID controller is given in order to study the mathematical relationship between the PID parameters and the open-loop frequency properties of the controlled system. Then, the concepts of M-field and θ-field are introduced, which are then used to explain how the PID control parameters influence the closed-loop frequency-magnitude property and its time responses. Subsequently, the new PID parameter tuning scheme, i.e., a group of tuning rules, is proposed based on the preceding analysis. Finally, both simulations and experiments are conducted, and the results verify the feasibility and validity of the proposed methods. This research proposes a PID parameter tuning method based on outputs of the closed loop system.

The Mechanism of the Formation and Transformation of Ettringite

The formation and transformation of ettringite were studied by measuring the ion concentration in liquid phase and analyzing the composition in solid phase. The effects of C3A, gypsum lime and C-S-H gel on ettringite formation and transformation were also investigated. The experimental results shuw, that, when gypsum was presented in solid phase, the composition of liquid phase was in favor of ettringite formation. Ettringite formation consisted of three reactions including the formation of [ Al （OH）6 ]^3- octahedral, formation of Ca-Al polyhedra prism in which Ca and Al polyhedra arranged alternately, as well as entrance of SO4^2- into the channel of polyhedra. [ Al （OH）6 ]^3- formation, which was the slowest reaction, controlled ettringite formation. The concentration of AlO2^- was a main factor that influenced ettringite formation. After gypsum in solid phase was consumed, [ SO4^2- ] decreased quickly and [ AlO2^- ] increased, and it was possible that ettringite transformed into hydrated monsulfate calcium aluminate （ be called M in short） in thermodymanics. The rate of transformation was controlled by diffusion of AlO2^- .

Adaptive explicit Magnus numerical method for nonlinear dynamical systems

Based on the new explicit Magnus expansion developed for nonlinear equations defined on a matrix Lie group, an efficient numerical method is proposed for nonlinear dynamical systems. To improve computational efficiency, the integration step size can be adaptively controlled. Validity and effectiveness of the method are shown by application to several nonlinear dynamical systems including the Duffing system, the van der Pol system with strong stiffness, and the nonlinear Hamiltonian pendulum system.

Picard-Newton Iterative Method with Time Step Control for Multimaterial Non-Equilibrium Radiation Diffusion Problem

For a new nonlinear iterative method named as Picard-Newton(P-N)iterative method for the solution of the time-dependent reaction-diffusion systems,which arise in non-equilibrium radiation diffusion applications,two time step control methods are investigated and a study of temporal accuracy of a first order time integration is presented.The non-equilibrium radiation diffusion problems with flux limiter are considered,which appends pesky complexity and nonlinearity to the diffusion coef-ficient.Numerical results are presented to demonstrate that compared with Picard method,for a desired accuracy,significant increase in solution efficiency can be obtained by Picard-Newton method with the suitable time step size selection.

Kinetics of Oxidation Reaction for Magnetite Pellets

An experiment for the oxidation process of single magnetite pellet and theoretical analysis based on modi lied unreacted core shrinking （MUCS） model were carried out, and the controlling mechanisms of the initial and de veloping reactions were examined, respectively. From the study of the initial reaction, it was found that the chemical reaction of surface is the controlling step of the overall reaction when the temperature is up to about 750 K, while the mass transfer through the gaseous boundary layer dominates the reaction rate when the temperature is above 750 K. As the reaction developing within the pellet, the mass transfer through the produced layer becomes the controlling step. In addition, the effects of reaction conditions （such as oxygen concentration, temperature） on the fractional oxidation of magnetite pellet were determined.