Turbulence statistics from three different nacelle lidars

Atmospheric turbulence can be characterized by the Reynolds stress tensor, which consists of the second-order moments of the wind field components. Most of the commercial nacelle lidars cannot estimate all components of the Reynolds stress tensor due to their limited number of beams; most can estimate the along-wind velocity variance relatively well. Other components are however also important to understand the behavior of, e.g., the vertical wind profile and meandering of wakes. The SpinnerLidar, a research lidar with multiple beams and a very high sampling frequency, was deployed together with two commercial lidars in a forward-looking mode on the nacelle of a Vestas V52 turbine to scan the inflow. Here, we compare the lidar-derived turbulence estimates with those from a sonic anemometer using both numerical simulations and measurements from a nearby mast. We show that from these lidars, the SpinnerLidar is the only one able to retrieve all Reynolds stress components. For the two- and four-beam lidars, we study different methods to compute the along-wind velocity variance. By using the SpinnerLidar's Doppler spectra of the radial velocity, we can partly compensate for the lidar's probe volume averaging effect and thus reduce the systematic error of turbulence estimates. We find that the variances of the radial velocities estimated from the maximum of the Doppler spectrum are less affected by the lidar probe volume compared to those estimated from the median or the centroid of the Doppler spectrum.

Stress-weighted spatial averaging of random fields in geotechnical risk assessment

Effects of spatial fluctuations of soil parameters are considered in a new context – considering variability of soil parameters in conjunction with non-uniform stress fields, which can locally amplify (or suppress) subsoil inhomogeneities. In this way, several design situations for the Coulomb frictional material with random tan(φ(x)) reveal a reduction of variance, which is less significant than for the standard volume averaging. When looking for an ‘effective’ random variable [tan(φ)]a – that is, a random variable, which is equivalent to the random field tan(φ( x )) – the Vanmarcke averaging by simple volume integrals is insufficient; it systematically overestimates effects of variance reduction, thus causing potentially unsafe situations. The new proposed approach is coherent, formally defined and more realistic.

Effects of the Porous Microstructure on the Drag Coefficient in Flow of a Fluid with Pressure-Dependent Viscosity

Equations governing the flow of a fluid with pressure-dependent viscosity through an isotropic porous structure are derived using the method of intrinsic volume averaging. Viscosity of the fluid is assumed to be a variable function of pressure, and the effects of the porous microstructure are modelled and included in the pressure-dependent drag coefficient. Five friction factors relating to five different microstructures are used in this work

Two-Pressure Model of Particle-Fluid Mixture Flow with Pressure-Dependent Viscosity in a Porous Medium

Equations governing the flow of a fluid-particle mixture with variable viscosity through a porous structure are developed. Method of intrinsic volume averaging is used to average Saffman’s dusty gas equations. A modelling flexibility is offered in this work by introducing a dust-phase partial pressure in the governing equations, interpreted as the pressure necessary to maintain a uniform particle distribution in the flow field. Viscosity of the fluid-particle mixture is assumed to be variable, with variations in viscosity being due to fluid pressure. Particles are assumed spherical and Stokes’ coefficient of resistance is expressed in terms of the pressure-dependent fluid viscosity. Both Darcy resistance and the Forchheimer micro-inertial effects are accounted for in the developed model

Analytical Solutions of a Two-Compartment Model Based on the Volume-Average Theory for Blood Toxin Concentration during and after Dialysis

Accurate prediction of blood toxin concentration during and after dialysis will greatly contribute to the determination of dialysis treatment conditions. Conventional models, namely single-compartment model and two-compartment model, have advantages and disadvantages in terms of accuracy and practical application. In this study, we attempted to derive the mathematical model that predicts blood toxin concentrations during and after dialysis, which has both accuracy and practicality. To propose the accurate model, a new two-compartment model was mathematically derived by adapting volume-averaging theory to the mass transfer around peripheral tissues. Subsequently, to propose a practical model for predicting the blood toxin concentration during dialysis, an analytical solution expressed as algebraic expression was derived by adopting variable transformation. Furthermore, the other analytical solution that predicts rebound phenomena after dialysis was also derived through similar steps. The comparisons with the clinical data revealed that the proposed analytical solutions can reproduce the behavior of the measured blood urea concentration during and after dialysis. The analytical solutions proposed as algebraic expressions will allow a doctor to estimate the blood toxin concentration of a patient during and after dialysis. The proposed analytical solutions may be useful to consider the treatment conditions for dialysis, including the rebound phenomenon.

Normal BOLD Response to a Step CO2 Stimulus After Correction for Partial Volume Averaging

Cerebrovascular reactivity (CVR) is defined as the change in cerebral blood flow induced by a change in a vasoactive stimulus. CVR using BOLD MRI in combination with changes in end-tidal CO2 is a very useful method for assessing vascular performance. In recent years, this technique has benefited from an advanced gas delivery method where end-tidal CO2 can be targeted, measured very precisely, and validated against arterial blood gas sampling (Ito et al., 2008). This has enabled more precise comparison of an individual patient against a normative atlas of healthy subjects. However, expected control ranges for CVR metrics have not been reported in the literature. In this work, we calculate and report the range of control values for the magnitude (mCVR), the steady state amplitude (ssCVR), and the speed (TAU) of the BOLD response to a standard step stimulus, as well as the time delay (TD) as observed in a cohort of 45 healthy controls. These CVR metrics maps were corrected for partial volume averaging for brain tissue types using a linear regression method to enable more accurate quantitation of CVR metrics. In brief, this method uses adjacent voxel CVR metrics in combination with their tissue composition to write the corresponding set of linear equations for estimating CVR metrics of gray matter (GM), white matter (WM), and cerebrospinal fluid (CSF). After partial volume correction, mCVR and ssCVR increase as expected in gray matter, respectively, by 25 and 19%, and decrease as expected in white matter by 33 and 13%. In contrast, TAU and TD decrease in gray matter by 33 and 13%. TAU increase in white matter by 24%, but TD surprisingly decreased by 9%. This correction enables more accurate voxel-wise tissue composition providing greater precision when reporting gray and white matter CVR values.

Heat Dissipation Performance of Micro-channel Heat Sink with Various Protrusion Designs

This research will focus on studying the effect of aperture size and shape of the micro-channel heat sink on heat dissipation performance for chip cooling. The micro-channel heat sink is considered to be a porous medium with fluid subject inter-facial convection. Derivation based on energy equation gives a set of governing partial differential equations describing the heat transfer through the micro-channels. Numerical simulation, including steady-state thermal analysis based on CFD software, is used to create a finite element solver to tackle the derived partial differential equations with properly defined boundary conditions related to temperature. After simulating three types of heat sinks with various protrusion designs including micro-channels fins, curly micro-channels fins, and Micro-pin fins, the result shows that the heat sink with the maximum contact area per unit volume will have the best heat dissipation performance, we will interpret the result by using the volume averaging theorem on the porous medium model of the heat sink.