Computing mean fields with known Reynolds stresses at steady state

With the rising of modern data science, data-driven turbulence modeling with the aid of machine learning algorithms is becoming a new promising field. Many approaches are able to achieve better Reynolds stress prediction, with much lower modeling error( M), than traditional Reynolds-averaged Navier-Stokes(RANS) models, but they still suffer from numerical error and stability issues when the mean velocity fields are estimated by solving RANS equations with the predicted Reynolds stresses. This fact illustrates that the error of solving the RANS equations( P) is also very important for a RANS simulation. In the present work, the error P is studied separately by using the Reynolds stresses obtained from direct numerical simulation(DNS)/highly resolved large-eddy simulation to minimize the modeling error M, and the sources of P are derived mathematically. For the implementations with known Reynolds stresses solely, we suggest to run an auxiliary RANS simulation to make a first guess on ν*t and S 0 i j. With around 10 iterations, the error of the streamwise velocity component could be reduced by about one-order of magnitude in flow over periodic hills. The present work is not to develop a new RANS model, but to clarify the facts that obtaining mean field with known Reynolds stresses is nontrivial and that the nonlinear part of the Reynolds stresses is very important in flow problems with separations. The proposed approach to reduce P may be very useful for the a posteriori applications of the data-driven turbulence models.     

计及轴颈倾斜的径向滑动轴承湍流润滑分析

分析了轴颈倾斜状态下，径向滑动轴承的湍流润滑性能. 基于轴颈倾斜的统一Reynolds方程和能量方程，应用有限差分法求解了不同轴颈倾斜方位角、轴颈倾斜度、偏心率和平均雷诺数下的径向滑动轴承湍流润滑性能. 结果表明:轴颈倾斜方位角α=0°时，随着轴颈倾斜度的增大，轴承油膜的压力峰向轴承一端移动，轴承一端的轴向油膜温度梯度增大；α=90°时，随着轴颈倾斜度的增大，轴承油膜压力逐渐出现双峰分布，且向轴承两端移动，轴承两端的轴向温度梯度也不断增大. 在相同轴颈倾斜度增量下，轴承最大油膜压力、最高油膜温度、承载力和稳定工作力矩的增量随轴承中央截面偏心率的增大而增大. 相同轴颈倾斜度增量下，轴承最大油膜压力增量、最高油膜温度增量、承载力增量、摩擦系数减量和稳定工作力矩增量随平均雷诺数的增大而增大. 可见，径向滑动轴承湍流润滑分析中有必要考虑轴颈倾斜因素的影响.      

A formulation of PANS capable of mimicking IDDES

The partially averaged Navier–Stokes (PANS) model, proposed in Girimaji (2006), allows to simulate turbulent flows either in RANS, LES or DNS mode. The PANS model includes $f_k$ which denotes the ratio of modeled to total kinetic energy. In RANS, $f_k=1$ while in DNS it tends to zero. In the present study we propose an improved formulation for $f_k$ based on the H-equivalence introduced by Friess et al. (2015). In this formulation the expression of $f_k$ is derived to mimic Improved Delayed Detached Eddy Simulation (IDDES). This new formulation behaves in a very similar way as IDDES, even though the two formulations use different mechanisms to separate modeled and resolved scales. They show very similar performance in separated flows as well as in attached boundary layers. In particular, the novel formulation is able to (i) treat attached boundary layers as properly as IDDES, and (ii) “detect” laminar initial/boundary conditions, in which case it enforces RANS mode. Furthermore, it is found that the new formulation is numerically more stable than IDDES.     

Acousto-mechanical behaviour of ex-vivo skin: Nonlinear and viscoelastic properties

The mechanical behaviour of skin is significant for some applications including dermatology, surgery, and impact biomechanics science. In this work, we have investigated the study of the acousto-mechanical viscoelastic properties of skin. For that, both tensile-relaxation and ultrasonic tests were conducted on porcine tissue samples in fibre directions. To understand the complex skin aging phenomena, we used strength tensile test correlated with the Nonlinear Time Reversal signal processing tool extension “TR-NEWS”. Uniaxial tensile tests were carried out at a strain rate of $5?{10}^{?3}\text{ mm}{\text{s}}^{?1}$ on skin using a load-relaxation-discharge load path with increasing amplitude and offset. This work is also under way to extend the frequency range of ultrasounds to 50 MHz. Digital Image Correlation was used for 2D strain measurement of the dermis. From this analysis, we conclude that fresh porcine skin should be modelled as a nonlinear viscoelastic material with strain-rate dependence. The obtained hysteresis loop shall be taken as significant skin damage.     

Global stability analysis of a 90°-bend pipe flow

The present work investigates the stability properties of the flow in a 90°-bend pipe with curvature $\delta =R/R_c=1/3$, with R being the radius of the cross-section of the pipe and $R_c$ the radius of curvature at the pipe centreline. Direct numerical simulations (DNS) for values of the bulk Reynolds number ${\mathit{Re}}_b=U_{b}D/\nu$ between 2000 and 3000 are performed. The bulk Reynolds number is based on the bulk velocity $U_b$, the pipe diameter D, and the kinematic viscosity $\nu$. The flow is found to be steady for ${\mathit{Re}}_b⩽2500$, with two main pairs of symmetric, counter-rotating vortices in the section of the pipe downstream of the bend. The presence of two recirculation regions is detected inside the bend: one on the outer wall and the other on the inner side. For ${\mathit{Re}}_b⩾2550$, the flow exhibits a periodic behaviour, oscillating with a fundamental non-dimensional frequency $\mathit{St}=\mathit{fD}/U_b=0.23$. A global stability analysis is performed in order to determine the cause of the transition from the steady to the periodic regime. The spectrum of the linearised Navier-Stokes operator reveals a pair of complex conjugate eigenvalues with positive real part, hence the transition is ascribed to a Hopf bifurcation occurring at ${\mathit{Re}}_{b,\mathit{cr}}\approx 2531$, a value much lower than the critical Reynolds number for the flow in a torus with the same curvature. The velocity components of the unstable direct and adjoint eigenmodes are investigated, and they display a large spatial separation, most likely due to the non-normality of the linearised Navier-Stokes operator. Thus, the core of the instability, also known in the literature as the wavemaker, is sought performing an analysis of the structural sensitivity of the unstable eigenmode to spatially localised feedbacks. The region located 15° downstream of the bend inlet, on the outer wall, is the most receptive to this kind of perturbations, and thus corresponds to where the instability originates. Since this region coincides with the outer-wall separation bubble, it is concluded that the instability is linked to the strong shear by the backflow phenomena. The present results are relevant for technical applications where bent pipes are frequently used, and their stability properties have hitherto not been studied.