Polymer Solution with Very Low Relaxation Time: A Combined Numerical-Experimental Determination Strategy

For very low relaxation time (i.e. lesser than a microsecond) viscoelastic fluid experimental determination is difficult, if not impossible. In the present work the relaxation time measurement of a weakly elastic polymer solution, too low to be measured using classical rheometry techniques, is assessed using a mixed experimental-numerical strategy. First the fluid is rheologically assessed, by measuring its shear viscosity, surface tension and density. Then the relaxation time is determined by comparing the jetting of polymer solution from a Continuous Ink-Jet (CIJ) device experimentally and numerically. The numerical approach is first validated using test case and a viscoelastic Oldroyd-B model is then used to model the experimental solution. The relaxation time is then a parameter allowing us to fit numerical simulation onto experimental results. This mixed strategy is particularly convenient for weakly elastic solution for which physical parameters can not be measured using experimental rheometry setup.

Numerical Investigation on Radiation Effect in Transpiration Cooling

This paper proposed a numerical strategy which could achieve the coupled modeling and solving of transpiration cooling with external high-temperature gas flow and especially take the radiation effect into account. Based on the numerical strategy, the heat and mass transfer characteristics of the transpiration cooling in a high-temperature gas channel were studied, and the radiation effect and corresponding influence factors were analyzed. The results indicated that the radiative heat flux takes an important role in the heat transfer between the transpiration cooling and external high-temperature gas flow which may reach 40% under the operating condition considered in this work, and the radiation absorption from the coolant is more obvious near the downstream wall. As the wall emissivity increases, the radiation heat transfer in the downstream area of the porous wall is enhanced significantly and thereby the wall temperature there increases, as the result, the uniformity of the temperature distribution on the whole porous wall is improved to some extent.

Development of a Harmonic Balance Method-Based Numerical Strategy for Blade-Tip/Casing Interactions: Application to NASA Rotor 37

In this study, a frequency-domain approach based on the harmonic balance method coupled to a predictor-corrector continuation algorithm is implemented for the qualitative analysis of blade-tip/casing contacts in aircraft engines. Unilateral contact and dry friction are taken into account through a regularized penalty law. To enhance the robustness of the methodology, particular attention is paid to the mitigation of the Gibbs phenomenon. To this end, the employed Alternating Frequency/Time scheme features a Lanczos σ-approximation so that spurious oscillations of the computed nonlinear contact forces become negligible. This approach is applied in combination with a model reduction technique on an industrial compressor blade: NASA rotor 37. In order to assess the influence of both the contact law regularization and the Lanczos σ-approximation, obtained results are thoroughly compared to an existing time integration-based numerical strategy relying on a Lagrange multiplier-based approach for contact treatment and that was previously confronted to experimental results. Presented results underline the very good agreement between the proposed methodology and the reference time integration numerical strategy. The proposed developments thus complement existing results on blade-tip/casing contact adding a much needed qualitative understanding of the interaction and an accurate assessment of the contact stiffening phenomenon.

Shear coefficient of spin viscosity estimation through velocity profiles of a ferrofluid under the effect of an external rotating magnetic field of low amplitude and frequency

The present article describes a numerical strategy for the estimation of the shear coefficient of spin viscosity for a ferrofluid sample confined to a cylindrical container and exposed to the effect of an external rotating magnetic field with a low amplitude and frequency. As far as we know, there are no experimental measurements of such coefficient. Furthermore, the few analytical values reported differ in several orders of magnitude. First, we describe briefly the mathematical model of the system and its numerical solution. Then, the definition of the direct and inverse problems is given as a part of the methodology for estimating such coefficient. Finally, we solve the inverse problem using simulated measurements and two global optimization algorithms. We generate this type of measurements by adding white Gaussian noise signals to the numerical solution of the ferrohydrodynamic mathematical model. Several noise levels in the range of 10 to 40 dB were used to increase the number of scenarios for validation purpose. Results showed an excellent agreement between the estimated values and those used in the numerical solution of the mathematical model. A statistical analysis revealed a normal distribution that was dependent on the noise level. This variation did not affect the results, but showed instead the validity of the proposed method. Additionally, this strategy stands as a computational tool for validating experimental results of the future in situ measurements. Tables 7, Figs 11, Refs 17.

PI/PID controller stabilizing sets of uncertain nonlinear systems: an efficient surrogate model-based approach

Closed forms of stabilizing sets are generally only available for linearized systems. An innovative numerical strategy to estimate stabilizing sets of PI or PID controllers tackling (uncertain) nonlinear systems is proposed. The stability of the closed-loop system is characterized by the sign of the largest Lyapunov exponent (LLE). In this framework, the bottleneck is the computational cost associated with the solution of the system, particularly including uncertainties. To overcome this issue, an adaptive surrogate algorithm, the Monte Carlo intersite Voronoi (MiVor) scheme, is adopted to pertinently explore the domain of the controller parameters and classify it into stable/unstable regions from a low number of nonlinear estimations. The result of the random analysis is a stochastic set providing probability information regarding the capabilities of PI or PID controllers to stabilize the nonlinear system and the risk of instabilities. The minimum of the LLE is proposed as tuning rule of the controller parameters. It is expected that using a tuning rule like this results in PID controllers producing the highest closed-loop convergence rate, thus being robust against model parametric uncertainties and capable of avoiding large fluctuating behavior. The capabilities of the innovative approach are demonstrated by estimating robust stabilizing sets for the blood glucose regulation problem in type 1 diabetes patients.