Relative Pressure Difference Research Articles

Evaluation of Aortic Hemodynamics Using Four-Dimensional Flow of Magnetic Resonance Imaging in Rabbits with Liver Fibrosis.

Liver fibrosis (LF) precipitates systemic hemodynamic alterations, however, its impact on the aorta remaining undefined. To assess aorta hemodynamics changes during LF development in a rabbit model. Prospective, experimental. Thirty 7-month-old male rabbits underwent bile duct ligation (BDL) to induce LF. Biweekly four-dimensional (4D) flow imaging incorporating a 3D gradient-echo at 3.0 T scanner for 14 weeks post-BDL. Histopathological exams for 2-5 rabbits were performed at each time point, following each MRI scan. LF was graded using the Metavir scale by a pathologist. 4D flow was analyzed by two radiologists using dedicated postprocessing software. They recorded 4D flow parameters at four aorta sections (aortic sinus, before and after bifurcation of aortic arch, and descending aorta). The linear mixed model; Bonferroni correction; Pearson correlation coefficient (r); receiver operating characteristic (ROC) curve; Delong test. The level of significance was set at P < 0.05. Following BDL, the wall shear stress (WSS) (0.23-0.32 Pa), energy loss (EL) (0.27-1.55 mW) of aorta significantly increased at the second week for each plane, peaking at the sixth week (WSS: 0.35-0.49 Pa, EL: 0.57-2.0 mW). So did the relative pressure difference (RPD) (second week: 1.67 ± 1.63 mmHg, sixth week: 2.43 ± 0.63 mmHg) in plane 2. Notably, the RPD in plane 2 at the second week displayed the highest area under ROC curve of 0.998 (specificity: 1, sensitivity: 0.967). LF were found at the second, fourth, and sixth week after BDL, with grade F2, F3, and F4, respectively. The RPD in plane 2 was most strongly correlated with the severity of LF (r = 0.86). The occurrence of LF could increase WSS, EL, and RPD of aorta as early as the second week following BDL. 1 TECHNICAL EFFICACY: Stage 2.

Influence of Inlet and Outlet Area Ratio on Intake Port Flow Capacity

The flow capacity of the intake port has a great influence on the charging efficiency of the internal combustion engine, affecting the engine’s performance, so it is critical to improve the intake port flow capacity. In this paper, the intake port numerical model was established, and the influence of the inlet and outlet area ratio on intake port flow capacity was studied. The results show that, under the same condition of relative pressure difference, the intake port discharge coefficient increases sharply and then slowly with an increase in area ratio. Under the same condition of area ratio, the discharge coefficient is only determined by relative pressure difference and decreases with an increase of relative pressure difference when the inlet and outlet area ratio&gt;1. The optimal area ratio decreases and then converges with an increase in relative pressure difference. When the intake port is designed, the optimal area ratio under the working condition of a smaller relative pressure difference should be applied in order to ensure the discharge coefficient is optimal under all working conditions.

Enhanced echocardiographic assessment of intracardiac flow in congenital heart disease.

4D flow magnetic resonance imaging (4D flow MRI) can assess and measure the complex flow patterns of the right ventricle (RV) in congenital heart diseases, but its limited availability makes the broad application of intracardiac flow assessment challenging. Color Doppler imaging velocity reconstruction from conventional echocardiography is an emerging alternative, but its validity against 4D flow MRI needs to be established. To compare intracardiac flow parameters measured by color Doppler velocity reconstruction (DoVeR) against parameters measured from 4D flow MRI. We analyzed 20 subjects, including 7 normal RVs and 13 abnormal RVs (10 with repaired Tetralogy of Fallot, and 3 with atrial-level shunts). Intracardiac flow parameters such as relative pressure difference, vortex strength, total kinetic energy, and viscous energy loss were quantified using DoVeR and 4D flow MRI. The agreement between the two methods was determined by comparing the spatial fields and quantifying the cross-correlation and normalized difference between time-series measurements. The hemodynamic parameters obtained from DoVeR and 4D flow MRI showed similar flow characteristics and spatial distributions. The time evolutions of the parameters were also in good agreement between the two methods. The median correlation coefficient between the time-series of any parameter was between 0.87 and 0.92, and the median L2-norm deviation was between 10% to 14%. Our study shows that DoVeR is a reliable alternative to 4D flow MRI for quantifying intracardiac hemodynamic parameters in the RV.

Toward the realization of a primary low-pressure standard using a superconducting microwave resonator.

We describe a primary gas pressure standard based on the measurement of the refractive index of helium gas using a microwave resonant cavity in the range between 500Pa and 20kPa. To operate in this range, the sensitivity of the microwave refractive gas manometer (MRGM) to low-pressure variations is substantially enhanced by a niobium coating of the resonator surface, which becomes superconducting at temperatures below 9K, allowing one to achieve a frequency resolution of about 0.3Hz at 5.2GHz, corresponding to a pressure resolution below 3 mPa at 20Pa. The determination of helium pressure requires precise thermometry but is favored by the remarkable accuracy achieved by ab initio calculations of the thermodynamic and electromagnetic properties of the gas. The overall standard uncertainty of the MRGM is estimated to be of the order of 0.04%, corresponding to 0.2Pa at 500 and 8.1Pa at 20kPa, with major contributions from thermometry and the repeatability of microwave frequency measurements. A direct comparison of the pressures realized by the MRGM with the reference provided by a traceable quartz transducer shows relative pressure differences between 0.025% at 20kPa and -1.4% at 500Pa.

Abstract 14957: Validation of Echocardiography Color Doppler Velocity Reconstruction Against 4d Flow Mri in Assessment of Right Ventricular Intracardiac Flow

Introduction: Intracardiac flow imaging of the right ventricle [RV] may improve the management of congenital heart disease like repaired Tetralogy of Fallot [rTOF] or atrial shunts that cause RV dilation [RVD]. However, this is mostly performed via 4D flow magnetic resonance imaging [MRI], which has limited availability and is resource intensive. We propose the use of conventional echocardiography as a viable alternative to assess RV intracardiac flow. Hypothesis: We hypothesize that a velocity reconstruction algorithm implemented for conventional color Doppler echocardiography can resolve flow quantities with good agreement to 4D flow MRI. Methods: We retrospectively collected echos for children with rTOF/RVD and age-matched controls. Color Doppler echos of the RV were evaluated using an in-house algorithm called Doppler Velocity Reconstruction [DoVeR]. Measurements from 4D flow MRI and DoVeR were post-processed to collect hemodynamics parameters for relative pressure difference , vortex strength , total kinetic energy , and viscous energy loss . Agreement between modalities was performed by cross-correlation and L2-norm difference between indexed chamber-average timeseries measurements. Results: 10 rTOF subjects, 3 RVD, and 7 age-matched controls were identified. There was qualitative agreement in spatial and time series measurements between DoVeR and 4D flow MRI (Figure 1). For timeseries measurements, there was strong correlation (median R &gt; 0.85) with low differences (median L2 &lt; 15%) between DoVer and 4D flow MRI. Conclusions: A color Doppler reconstruction method, DoVeR, can effectively measure hemodyanmics parameters using conventional color Doppler echocardiography, with strong agreement against 4D flow MRI. Figure 1: Left – Flow field overlaid onto pressure reconstruction and pressure difference estimates between DoVeR and 4D flow modalities. Right – Correlation coefficient and difference between modality timeseries measurements.

Effect of Retainer Ring Pressure in Ceria Based CMP

Consumable of Chemical mechanical polishing (CMP) process for global planarization can be divided by pad, conditioner, and slurry. Wafer is applied to pressure on the pad with Slurry. Among the abrasives contained the slurry, although ceria has a low concentration, the removal rate is higher than the silica on inter-layer dielectric (ILD)/inter-metal dielectric (IMD) CMP process. Removal rate (RR) increased by Preston’s equation in proportion to the pressure and rpm (RR=KPV). Where K is a Preston’s constant, P is the main pressure, and V is the relative velocity. Yield improvement method in the semiconductor is a large uniform area after CMP process. In other words, wafer edge area should be minimized. It is important to control uniform pressure distribution. Head structure can be divided by main pressure for removal and retainer ring pressure for prevention out of course. In this research, pressure distribution is demonstrated by controlling the different pressure wafer pressure and retainer ring in a single pressure structure. Removal rate changed by different pressure due to pad deformation. Relative pressure difference changed from 150 to 30 g/cm2 to demonstrate for the reason. In case of the low pressure (1, 2psi), the smaller relative pressure difference increases the uniformity, but the removal rate is decreased. In the high pressure (3, 4 psi), the removal rate and uniformity are not big changes according to relative pressure difference. But parameters of temperature and coefficient of friction are not same. This research investigated the mechanism of how to affect the ceria in ILD/IMD CMP through each parameter.Figure 1. Removal rate according to relative pressure difference of retainer ring, (a) low pressure, and (b) high pressure. Figure 1

A Mathematical Model of the Hydrodynamic Pressure Acting on a Turbine Runner Blade under the Rotor-Stator Interaction Based on the Quasi-Three-Dimensional Finite Element Method

In this paper, a turbine runner blade under hydraulic excitation was taken as the object of study and the mathematical hydrodynamic pressure model of a turbine runner blade under the rotor-stator interaction was established using quasi-three-dimensional finite element model. The regularity of the distribution of the hydrodynamic pressure was then investigated. First, the quasi-three-dimensional finite element model of a runner blade was established using the quasi-three-dimensional theory. Next, according to the pressure distribution from the numerical simulation, the mathematical mean pressure model of a node was established using the relative pressure difference method; the pressure fluctuation was then established taking the rotor-stator interaction into consideration. Then, based on the mean pressure and the pressure fluctuation of a node, the mathematical hydrodynamic pressure model for any position of a runner blade was obtained. Finally, the feasibility of the mathematical model was verified by an example analysis, and the internal relationship between the hydrodynamic pressure and its hydraulic parameters and the structural parameters of the blade was revealed, which provides a theoretical basis for further study of the dynamic characteristics of turbine runner blades under the rotor-stator interaction.

Non-invasive estimation of relative pressure for intracardiac flows using virtual work-energy.

Intracardiac blood flow is driven by differences in relative pressure, and assessing these is critical in understanding cardiac disease. Non-invasive image-based methods exist to assess relative pressure, however, the complex flow and dynamically moving fluid domain of the intracardiac space limits assessment. Recently, we proposed a method, νWERP, utilizing an auxiliary virtual field to probe relative pressure through complex, and previously inaccessible flow domains. Here we present an extension of νWERP for intracardiac flow assessments, solving the virtual field over sub-domains to effectively handle the dynamically shifting flow domain. The extended νWERP is validated in an in-silico benchmark problem, as well as in a patient-specific simulation model of the left heart, proving accurate over ranges of realistic image resolutions and noise levels, as well as superior to alternative approaches. Lastly, the extended νWERP is applied on clinically acquired 4D Flow MRI data, exhibiting realistic ventricular relative pressure patterns, as well as indicating signs of diastolic dysfunction in an exemplifying patient case. Summarized, the extended νWERP approach represents a directly applicable implementation for intracardiac flow assessments.

Utility of Saline-Induced Resting Full-Cycle Ratio Compared with Resting Full-Cycle Ratio and Fractional Flow Reserve.

Background The saline-induced distal coronary pressure/aortic pressure ratio predicted fractional flow reserve (FFR). The resting full-cycle ratio (RFR) represents the maximal relative pressure difference in a cardiac cycle. Therefore, the present study aimed to compare the results of saline-induced RFR (sRFR) with FFR. Methods Seventy consecutive lesions with only moderate stenosis were included. The FFR, RFR, and sRFR values were compared. The sRFR was assessed using an intracoronary bolus infusion of saline (2 mL/s) for five heartbeats. The FFR was obtained after an intravenous injection of papaverine. Results Overall, the FFR, sRFR, and RFR values were 0.78 ± 0.12, 0.79 ± 0.13, and 0.83 ± 0.14, respectively. With regard to anatomical morphology were 40, 18, and 12 cases of focal, diffuse, and tandem lesion. There was a significant correlation between the sRFR and FFR (R = 0.96, p < 0.01). There were also significant correlations between the sRFR and FFR in the left coronary and right coronary artery (R = 0.95, p < 0.01 and R = 0.98, p < 0.01). Furthermore, significant correlations between sRFR and FFR were observed in not only focal but also in nonfocal lesion including tandem and diffuse lesions (R = 0.93, p < 0.01 and R = 0.97, p < 0.01). A close agreement on FFR and sRFR was shown using the Bland–Altman analysis (95% CI of agreement: −0.08–0.07). In the receiver operating characteristic curve analysis, the cutoff value of sRFR to predict an FFR of 0.80 was 0.81 (area under curve, 0.97; sensitivity 90.6%; and specificity 98.2%). Conclusion The sRFR can accurately and safely predict the FFR and might be effective for diagnosing ischemia.

Flow Analysis and Theoretical Design of Diesel Engine Exhaust Port

Exhaust port is an important part of a diesel engine which affects the combustion and emission. It is important to have a good design for exhaust port. In this paper, the calculation formula of the optimal area ratio (Kopt) of outlet and inlet of exhaust port was derived. The formula shows that Kopt is only determined by relative pressure difference (RPD). Then influence of the area ratio (K) of outlet and inlet on flow capacity of exhaust port and the trend of Kopt with relative pressure difference were studied numerically to verify the validity and applicability of the formula. The numerical results shows that the mass flow rate increases first and then keeps constant with the increase of K at the same RPD. Kopt exists and decreases first and then keeps constant with the increase of RPD. The numerical trend is consistent with theoretical trend and the errors between maximum mass flow rates of numerical results and actual mass flow rates at theoretical optimal area ratios are all less than 5% meeting engineering accuracy. It is indicated that the derived formula is correct and applicable. When an exhaust port is designed, the outlet area can be estimated by this formula.

Wireless Interrogation of Implantable SAW Sensors.

Implantable sensors provide long-term, accurate physiological measurements after a minimally invasive procedure, particularly when designed as transponders. Wireless interrogation of deeply implanted transponders with RF remains a challenge due to the high loss at the skin-air interface and large tissue RF absorption. This paper presents a system for wirelessly interrogating surface acoustic wave (SAW) sensors implanted in the main pulmonary artery (PA), where the pressure (PAP) is a very important parameter in the management of heart failure patients. The proposed PAP monitoring system consists of an implantable SAW pressure sensor integrated with an antenna and anchor in a housing, an external antenna and an electronic interrogator. The PAP is determined by measuring the frequency of the echo signal from SAW sensor accurately. An asymmetric antenna was designed and integrated with the sensor. The combination of simulation, theoretical calculation and phantom measurement indicates that the path loss to the implant location, about 6cm below the skin, is around 25dB. A portable interrogator was designed based on a dual conversion receiver and single echo high frequency sampling approach to assess achievable frequency estimation accuracy predicted by Cramer-Rao Lower Bound (CRLB) analysis. The system was characterized using a high quality (Q) factor SAW sensor, fabricated at wafer level, wire-connected to the interrogator via an attenuator to simulate path loss. The signal-to-noise ratio (SNR) of captured echo signals was calculated and used in CRLB analysis. The analysis indicates that without using signal post processing, the sensor sensitivity has to be at least 440Hz/mmHg in order to achieve a target 1mmHg accuracy. Although the current sensor sensitivity is only 200Hz/mmHg, the in vivo measurement showed that acceptable accuracy can be obtained by signal post processing. The results from an invasive catheter tip transducer measured simultaneously with the SAW sensor showed that the differences in pulse pressure and relative mean pressure are 0.8mmHg and 1.4mmHg, respectively. The accuracy could be further improved by increasing the sensor Q factor and sensitivity and reducing path loss.

Determination of an Injection Sprayer's Technological Parameters

Agricultural boom sprayers are equipped with injection sprayers of mainly foreign origin. The main parameters of the injection sprayers shown in the catalogs display the consumption characteristics in cer­tain ranges without taking into account the design parameters.(Research purpose)Determination of the design and technological parameters of an injection sprayer for the introduction of pesticides.(Materials and methods)The injection sprayer belongs to the class of two­phase liquid­gas isothermal jet devices with the formation of an air­gas mixture at the outlet. It has been established that the design model of the working process of an injection sprayer is based both on the laws of the conservation of mass, energy, momentum, as well as theoretical relation­ships in the form of equations describing two­phase jet devices, and empirical relationships characterizing flow parameters, geometric transverse and longitudinal dimensions of the spray channels.(Results and discussion)The following analytical relationships have been obtained: the relative pressure difference generated by an injec­tion sprayer and the volume injection coefficient for different surface area ratios of the working nozzle to the flow section of the sprayer; the ratio between the cross­sectional area of the mixing chamber to the area of the working nozzle outlet and the injection ratio; relative pressure difference and the injection ratio; the ratio be­tween the cross­sectional area of the mixing chamber and the working nozzle and the relative pressure difference. The authors have determined a set of dimensionless pressure characteristics of the injection sprayer for different ratios between the cross­sectional areas of the working nozzle and the mixing chamber. It has been established that the ratio between the cross sections of the mixing chamber area and the working nozzle area increases as the injection ratio increases. It has been shown that for each injection coefficient, there is an achievable relative pressure difference in the injection sprayer.(Conclusions)The authors have proposed the design equations that determine the characteristics of an injection sprayer and its main design parameters – the diameters of nozzle and mixing chambers. They have calculated the main dimensions of the sprayer for aerial top­dressing by introducing working solutions of pesticides.

Pressure Mapping and Hemodynamic Assessment of Intracranial Dural Sinuses and Dural Arteriovenous Fistulas with 4D Flow MRI.

The feasibility of 4D flow MR imaging to visualize flow patterns and generate relative pressure maps in the dural venous sinus in healthy subjects (n = 60) and patients with dural arteriovenous fistulas (n = 7) was investigated. Dural venous drainage was classified based on torcular Herophili anatomy by using 4D flow MR imaging-derived angiograms and magnitude images. Subjects were scanned in a 3T clinical MR imaging system. 4D flow MR imaging enabled noninvasive characterization of dural sinus anatomy and mapping of relative pressure differences.

Relative pressure estimation from velocity measurements in blood flows: State-of-the-art and new approaches.

The relative pressure difference across stenotic blood vessels serves as an important clinical index for the diagnosis of many cardiovascular diseases. While the clinical gold standard for relative pressure difference measurements is invasive catheterization, Phase-Contrast Magnetic Resonance Imaging has emerged as a promising tool for enabling a noninvasive quantification, by linking highly spatially resolved velocity measurements with relative pressures via the incompressible Navier-Stokes equations. In this work, we provide a review and analysis of current methods for relative pressure estimation and propose 3 additional techniques. Methods are compared using synthetic data from numerical examples, and sensitivity to subsampling and noise was explored. Through our analysis, we verify that the newly proposed approaches are more robust with respect to spatial subsampling and less sensitive to noise and therefore provide improved means for estimating relative pressure differences noninvasively.

Decline or stability of obligate freshwater elasmobranchs following high fishing pressure

Despite elasmobranchs are a predominantly marine taxon, several species of sharks and rays are regularly found in fresh water. Although there is ample evidence of declining elasmobranch populations around the world, this evidence comes exclusively from marine and euryhaline species; the ecology and conservation status of obligate freshwater elasmobranchs is far from being understood. River stingrays (Potamotrygoninae, 32 species) live exclusively in South American rivers and represent the overwhelming majority of freshwater elasmobranch diversity. Here, we present evidence of a decline in the abundance of river stingrays in the middle and lower Paraná River, an extensive wetland mosaic of approximately 35,000km2. By taking advantage of a stingray-manipulation procedure widespread among South American fishermen, we were able to estimate spatial differences in relative fishing pressure and found that the observed decline is related to fishing pressure. The highest fishing effort and lowest relative abundance occurred in areas where fisheries operate on the river floodplain. The lowest fishing effort and highest relative abundances occurred in areas where fisheries operate in the main channel. The only species with a stable trend was Potamotrygon motoro. This evidence confirms the long-presumed vulnerability of obligate freshwater elasmobranchs and suggests that some species, e.g. P. motoro, can be exploited sustainably. Our results also indicate that negative effects on freshwater elasmobranchs can be minimized by adjusting fishing grounds.

Urban air pollution and meteorological factors affect emergency department visits of elderly patients with chronic obstructive pulmonary disease in Taiwan

Both air pollution and meteorological factors in metropolitan areas increased emergency department (ED) visits from people with chronic obstructive pulmonary disease (COPD). Few studies investigated the associations between air pollution, meteorological factors, and COPD-related health disorders in Asian countries. This study aimed to investigate the relationship between the environmental factors and COPD-associated ED visits of susceptible elderly population in the largest Taiwanese metropolitan area (Taipei area, including Taipei city and New Taipei city) between 2000 and 2013. Data of air pollutant concentrations (PM10, PM2.5, O3, SO2, NO2 and CO), meteorological factors (daily temperature, relative humidity and air pressure), and daily COPD-associated ED visits were collected from Taiwan Environmental Protection Administration air monitoring stations, Central Weather Bureau stations, and the Taiwan National Health Insurance database in Taipei area. We used a case-crossover study design and conditional logistic regression models with odds ratios (ORs), and 95% confidence intervals (CIs) for evaluating the associations between the environmental factors and COPD-associated ED visits. Analyses showed that PM2.5, O3, and SO2 had significantly greater lag effects (the lag was 4 days for PM2.5, and 5 days for O3 and SO2) on COPD-associated ED visits of the elderly population (65–79 years old). In warmer days, a significantly greater effect on elderly COPD-associated ED visits was estimated for PM2.5 with coexistence of O3. Additionally, either O3 or SO2 combined with other air pollutants increased the risk of elderly COPD-associated ED visits in the days of high relative humidity and air pressure difference, respectively. This study showed that joint effect of urban air pollution and meteorological factors contributed to the COPD-associated ED visits of the susceptible elderly population in the largest metropolitan area in Taiwan. Government authorities should review existing air pollution policies, and strengthen health education propaganda to ensure the health of the susceptible elderly population.

Two-dimensional numerical analysis of active flow control by steady blowing along foil suction side by different urans turbulence models

The effects of active separation control by steady blowing jets were investigated numerically on three different examples: subsonic flow past Aerospatiale A airfoil at 13? angle-of-attack, transonic flow past NACA 0012 airfoil at 4? angle-ofattack, and transonic flow in linear compressor/turbine cascade. Performed analyses are two-dimensional, flow is turbulent (or transitional) while fluid is viscous and compressible. Jets are positioned along the suction sides of the foils, the first one being located just upstream of the separation point, and modeled by source terms added to flow equations. Several different jet diameters and intensities are investigated. As the choice of turbulence model affects the final solution of Reynolds equations, turbulence is modeled by four different models: Spalart- Allmaras, realizable k-?, k-? SST, and ?-Re?, and a comparison of obtained results is performed. Goals of the study include definition of an adequate numerical setting that enables sufficiently correct simulation of the problems in question as well as evaluation of the possible increase in aerodynamic performances. Lift coefficients, lift-to-drag ratios or relative pressure differences are improved for all controlled cases.

Experimental and computational investigation of the patient-specific abdominal aortic aneurysm pressure field

The objective of the present manuscript is three-fold: (i) to study the detailed pressure field inside a patient-specific abdominal aortic aneurysm (AAA) model experimentally and numerically and discuss its clinical relevance, (ii) to validate a number of possible numerical model options and their ability to predict the experimental pressure field and (iii) to compare the spatial pressure drop in the AAA before and after the formation of intraluminal thrombus (ILT) for a late disease development timeline. A finite volume method was used to solve the governing equations of fluid flow to simulate the flow dynamics in a numerical model of the AAA. Following our patient-specific anatomical rapid prototyping technique, physical models of the aneurysm were created with seven ports for pressure measurement along the blood flow path. A flow loop operating with a blood analogue fluid was used to replicate the patient-specific flow conditions, acquired with phase-contrast magnetic resonance imaging, and measure pressure in the flow model. The Navier–Stokes equations and two turbulent models were implemented numerically to compare the pressure estimations with experimental measurements. The relative pressure difference from experiments obtained with the best performing model (unsteady laminar simulation) was ∼1.1% for the AAA model without ILT and ∼15.4% for the AAA model with ILT (using Reynolds Stress Model). Future investigations should include validation of the 3D velocity field and wall shear stresses within the AAA sac predicted by the three numerical models.

Thermobarometric constraints on pressure variations across the Plattengneiss shear zone of the Eastern Alps: implications for exhumation models during Eoalpine subduction

Forward and inverse mineral equilibria modelling of metapelitic rocks in the hangingwall and footwall of the Plattengneiss, a major shear zone in the Eastern Alps, is used to constrain their tectonometamorphic evolution and assess models for their exhumation. Forward (pseudosection) modelling of two metapelitic rocks suggests a steep clockwise P–T path with a near-isothermal decompression segment from a pressure peak at ~18–19 kbar and 670 °C to the metamorphic peak at 680–720 °C and 11–13 kbar. A subsequent decrease to 600–645 °C and 8–9 kbar is inferred from the late growth of staurolite in some samples. Conventional thermobarometric calculations (inverse modelling) on 18 samples with the inferred peak assemblage garnet + plagioclase + muscovite + biotite + quartz + rutile ± ilmenite ± kyanite are associated with large 2σ uncertainties, and absolute pressures calculated for all samples are statistically indistinguishable. However, calculations constraining relative pressure differences (ΔP) between samples sharing a common mineral assemblage are associated with much smaller uncertainties and yield pressure differences that are statistically meaningful. Although the overall pattern is complicated, the results suggest a pressure gradient of up to 3 kbar across the shear zone that is consistent with volume loss and a model of exhumation related to slab extraction for the Plattengneiss shear zone.

A numerical investigation of moment coefficient and flow structure in a rotor–stator cavity with rotor-mounted bolts

The torque associated with overcoming the losses on a rotating disc is of particular importance to the designers of gas turbine engines. Not only does this represent a reduction in useful work, but it also gives rise to unwanted heating of metal surfaces and the adjacent fluid. This article presents a numerical study on the effect of rotor-mounted bolts on the moment coefficient and velocity distributions within a rotor–stator cavity under conditions representative of modern gas turbine engine design. Steady-state, two-dimensional and three-dimensional, computational fluid dynamics simulations are obtained using the FLUENT commercial code with a standard k–ɛ turbulence model. The model is validated against experimental data and then used to investigate the effects of varying the number of bolts and also a continuous ring. Two test cases are investigated: one corresponds to where the flow structure is dominated by the superimposed flow ( λT = 0.35); and the other, where rotation is expected to govern the flow structure ( λT = 0.35). The principal flow phenomena in the vicinity of the bolts were described using the simulation results. Increasing the number of bolts will decrease the relative total pressure difference around bolts and increase the tangential velocity of the core of fluid between the rotor and stator. It was also found out that the free-stream Reynolds number of the flow approaching the bolts decreases and angle of attack increases with increasing number of bolts. As a consequence, the bolts’ wake character changes leading to a situation where the wake of one bolt is not fully collapsed in advance of the following bolt. The occurrence of Taylor columns were also investigated in the rotor–stator system with rotor-mounted bolts. It was found that while increasing the number of bolts can decrease the Rossby number to produce an intermediate rotation in the system, the Taylor columns will not be produced even for 60 bolts under the both flow conditions. The contribution of skin friction to the overall moment coefficient reduces as the number of bolts increases and the pressure-related losses increase. Increasing the number of bolts will decrease the moment produced by each individual bolt. However, since there are more bolts in the system the total moment of all bolts will increase by increasing their number. There also appears to be a point where increasing the number of bolts does not bring about an increase in the overall moment coefficient. It is also interesting to report that the moment coefficient associated with a continuous ring is similar to that for a plain disc.