Method for the Synthesis of Adaptive Algorithms for Estimating the Parameters of Dynamic Systems Based on the Decomposition Principle and the Joint Maximum Methodology

A method of synthesis of a filter for estimating the state of dynamic systems of Kalman type with an adaptive model built on the basis of the principle of decomposition of the system using kinematic relations from the condition of constancy of motion invariants has been developed. The structure of the model is determined from the condition of the maximum function of the generalized power up to a nonlinear synthesizing function that determines the rate of dissipation and, accordingly, the degree of structural adaptation. The resulting model has an explicit relation with the gradient of the estimation error functional, which makes it possible to adapt to the intensity of regular and random influences and can be used to construct a filter for estimating the state of the Kalman structure. On the basis of the developed method, a discrete algorithm is obtained and its comparative analysis with the classical Kalman filter is carried out.

Validation of RANS Turbulence Models for Labyrinth Seal Flows by Means of Particle Image Velocimetry

Accurate prediction of labyrinth seal flows is important for the design and optimisation of turbomachinery. However, the prediction of such flows with RANS turbulence models is still lacking. The identification of modelling deficits and the development of improved turbulence models requires detailed experimental data. Consequently, a new test rig for straight labyrinth seals was built at the Institute for Turbomachinery and Fluid Dynamics which allows for non-intrusive measurements of the three dimensional velocity field in the cavities. Two linear eddy viscosity models and one algebraic Reynolds stress turbulence model have been tested and validated against global parameters, local pressure measurements, and non-intrusive measurements of the velocity field. While some models accurately predict the discharge coefficient, large local errors occurred in the prediction of the wall static pressure in the seal. Although improved predictions were possible by using model extensions, significant errors in the prediction of vortex systems remained in the solution. These were identified with the help of PIV results. All turbulence models struggled to accurately predict the size of separations and the swirl imposed by viscous effects at the rotor surface. Additionally, the expansion of the leakage jet in the outlet cavity is not modelled correctly by the numerical models. This is caused by a wrong prediction of turbulent kinetic energy and, presumably, its rate of dissipation.

A model for a solid undergoing rate-independent dissipative mechanical processes

A thermodynamic framework is proposed to capture the dissipative response of metals. In contrast to the conventional practice, a stressed reference configuration is assumed instead of a stress-free configuration. The second law of thermodynamics is converted into equality by prescribing a non-negative rate of dissipation function. Stress in the reference configuration evolves with time to satisfy the second law of thermodynamics. Appropriate constitutive prescriptions are made to model the experimentally observed cyclic response of metals such as mild steel, aluminum alloy, and titanium, to uniaxial loading. An appropriate choice of material parameters captures well the experimentally observed response for different loading protocols.

Numerical investigation of mixture generation due to different inlet and outlet positions

A numerical simulation is a method carried out to study the flow characteristics of compressible fluid through different channels. Two approaches using air as a working substance were used to study the flow characteristics. In the first approach, two inlets and one outlet horizontally in the x direction was depended on to generate different flow characteristics; the flow properties were calculated along the diagonal line inside the channel. In the second approach, one inlet and outlet horizontally with sudden change in the area of the channel was employed. In this research, the flow properties were calculated along the center line inside the channel and the flow fields have been investigated. A non-linear k-Є model is employed to solve the flow characteristics by using the finite difference method with a curvilinear coordinate system near the dead zone and the k-Є and Reynolds stress model area semi-empirical model based on modeling of the equations of transport that contain the dissipation rate (ε) as well as turbulent kinetic energy (k). The derivation of turbulent kinetic energy and its rate of dissipation derived from the Navier–Stokes equation. In this work, the simulation outcomes of the proposed k-ε turbulence model indicated a good compatibility with published correlations. In order to get an accurate solution, the value of 10–8 for the maximal normalized equation residual was considered to be the convergence between computation and steady solution. The model applied for flow velocity 30 m/s and the obtained results presented as curves, surface and contours for velocities turbulent kinetic energy, rate of dissipation of turbulent kinetic energy and vortices. The builder model can be utilized for academic purposes since it is widely used for many physical and engineering applications.

Evolution of Oceanic Near-Surface Stratification in Response to an Autumn Storm

Understanding the processes that control the evolution of the ocean surface boundary layer (OSBL) is a prerequisite for obtaining accurate simulations of air–sea fluxes of heat and trace gases. Observations of the rate of dissipation of turbulent kinetic energy (ε), temperature, salinity, current structure, and wave field over a period of 9.5 days in the northeast Atlantic during the Ocean Surface Mixing, Ocean Submesoscale Interaction Study (OSMOSIS) are presented. The focus of this study is a storm that passed over the observational area during this period. The profiles of ε in the OSBL are consistent with profiles from large-eddy simulation (LES) of Langmuir turbulence. In the transition layer (TL), at the base of the OSBL, ε was found to vary periodically at the local inertial frequency. A simple bulk model of the OSBL and a parameterization of shear driven turbulence in the TL are developed. The parameterization of ε is based on assumptions about the momentum balance of the OSBL and shear across the TL. The predicted rate of deepening, heat budget, and the inertial currents in the OSBL were in good agreement with the observations, as is the agreement between the observed value of ε and that predicted using the parameterization. A previous study reported spikes of elevated dissipation related to enhanced wind shear alignment at the base of the OSBL after this storm. The spikes in dissipation are not predicted by this new parameterization, implying that they are not an important source of dissipation during the storm.

On the inference of the state of turbulence and mixing efficiency in stably stratified flows

Scaling arguments are presented to quantify the widely used diapycnal (irreversible) mixing coefficient $\unicode[STIX]{x1D6E4}=\unicode[STIX]{x1D716}_{PE}/\unicode[STIX]{x1D716}$ in stratified flows as a function of the turbulent Froude number $Fr=\unicode[STIX]{x1D716}/Nk$. Here, $N$ is the buoyancy frequency, $k$ is the turbulent kinetic energy, $\unicode[STIX]{x1D716}$ is the rate of dissipation of turbulent kinetic energy and $\unicode[STIX]{x1D716}_{PE}$ is the rate of dissipation of turbulent potential energy. We show that for $Fr\gg 1$, $\unicode[STIX]{x1D6E4}\propto Fr^{-2}$, for $Fr\sim \mathit{O}(1)$, $\unicode[STIX]{x1D6E4}\propto Fr^{-1}$ and for $Fr\ll 1$, $\unicode[STIX]{x1D6E4}\propto Fr^{0}$. These scaling results are tested using high-resolution direct numerical simulation (DNS) data from three different studies and are found to hold reasonably well across a wide range of $Fr$ that encompasses weakly stratified to strongly stratified flow conditions. Given that the $Fr$ cannot be readily computed from direct field measurements, we propose a practical approach that can be used to infer the $Fr$ from readily measurable quantities in the field. Scaling analyses show that $Fr\propto (L_{T}/L_{O})^{-2}$ for $L_{T}/L_{O}>O(1)$, $Fr\propto (L_{T}/L_{O})^{-1}$ for $L_{T}/L_{O}\sim O(1)$, and $Fr\propto (L_{T}/L_{O})^{-2/3}$ for $L_{T}/L_{O}<O(1)$, where $L_{T}$ is the Thorpe length scale and $L_{O}$ is the Ozmidov length scale. These formulations are also tested with DNS data to highlight their validity. These novel findings could prove to be a significant breakthrough not only in providing a unifying (and practically useful) parameterization for the mixing efficiency in stably stratified turbulence but also for inferring the dynamic state of turbulence in geophysical flows.

Turbulent kinetic energy production and flow structures in flows past smooth and rough walls

Data available in the literature from direct numerical simulations of two-dimensional turbulent channels by Lee & Moser (J. Fluid Mech., vol. 774, 2015, pp. 395–415), Bernardini et al. (J. Fluid Mech., 742, 2014, pp. 171–191), Yamamoto & Tsuji (Phys. Rev. Fluids, vol. 3, 2018, 012062) and Orlandi et al. (J. Fluid Mech., 770, 2015, pp. 424–441) in a large range of Reynolds number have been used to find that $S^{\ast }$ the ratio between the eddy turnover time ($q^{2}/\unicode[STIX]{x1D716}$, with $q^{2}$ being twice the turbulent kinetic energy and $\unicode[STIX]{x1D716}$ the isotropic rate of dissipation) and the time scale of the mean deformation ($1/S$), scales very well with the Reynolds number in the wall region. The good scaling is due to the eddy turnover time, although the turbulent kinetic energy and the rate of isotropic dissipation show a Reynolds dependence near the wall; $S^{\ast }$, as well as $-\langle Q\rangle =\langle s_{ij}s_{ji}\rangle -\langle \unicode[STIX]{x1D714}_{i}\unicode[STIX]{x1D714}_{i}/2\rangle$ are linked to the flow structures, and also the latter quantity presents a good scaling near the wall. It has been found that the maximum of turbulent kinetic energy production $P_{k}$ occurs in the layer with $-\langle Q\rangle \approx 0$, that is, where the unstable sheet-like structures roll-up to become rods. The decomposition of $P_{k}$ in the contribution of elongational and compressive strain demonstrates that the two contributions present a good scaling. However, the good scaling holds when the wall and the outer structures are separated. The same statistics have been evaluated by direct simulations of turbulent flows in the presence of different types of corrugations on both walls. The flow physics in the layer near the plane of the crests is strongly linked to the shape of the surface and it has been demonstrated that the $u_{2}$ (normal to the wall) fluctuations are responsible for the modification of the flow structures, for the increase of the resistance and of the turbulent kinetic energy production.

Computationally generated constitutive models for particle phase rheology in gas-fluidized suspensions

Developing constitutive models for particle phase rheology in gas-fluidized suspensions through rigorous statistical mechanical methods is very difficult when complex inter-particle forces are present. In the present study, we pursue a computational approach based on results obtained through Eulerian–Lagrangian simulations of the fluidized state. Simulations were performed in a periodic domain for non-cohesive and mildly cohesive (Geldart Group A) particles. Based on the simulation results, we propose modified closures for pressure, bulk viscosity, shear viscosity and the rate of dissipation of pseudo-thermal energy. For non-cohesive particles, results in the high granular temperature $T$ regime agree well with constitutive expressions afforded by the kinetic theory of granular materials, demonstrating the validity of the methodology. The simulations reveal a low $T$ regime, where the inter-particle collision time is determined by gravitational fall between collisions. Inter-particle cohesion has little effect in the high $T$ regime, but changes the behaviour appreciably in the low $T$ regime. At a given $T$, a cohesive particle system manifests a lower pressure at low particle volume fractions when compared to non-cohesive systems; at higher volume fractions, the cohesive assemblies attain higher coordination numbers than the non-cohesive systems, and experience greater pressures. Cohesive systems exhibit yield stress, which is weakened by particle agitation, as characterized by $T$. All these effects are captured through simple modifications to the kinetic theory of granular materials for non-cohesive materials.