CFD simulation of complex phenomena containing suspensions and flow throughporous media

There is an increasing reliance on computers to solve complex engineering problems. This is because computers, in addition to supporting the development and implementation of adequate and clear models, can especially minimize the financial support required. The ability of computers to perform complex calculations at high speed has enabled the creation of highly complex systems to model real-world phenomena. The complexity of the fluid dynamics problem makes it difficult or impossible to solve equations of an object in a flow exactly. Approximate solutions can be obtained by construction and measurement of prototypes placed in a flow, or by use of a numerical simulation. Since usage of prototypes can be prohibitively time-consuming and expensive, many have turned to simulations to provide insight during the engineering process. In this case the simulation setup and parameters can be altered much more easily than one could with a real-world experiment. The objective of this research work is to develop numerical models for different suspensions (fiber suspensions, blood flow through microvessels and branching geometries, and magnetic fluids), and also fluid flow through porous media. The models will have merit as a scientific tool and will also have practical application in industries. Most of the numerical simulations were done by the commercial software, Fluent, and user defined functions were added to apply a multiscale method and magnetic field. The results from simulation of fiber suspension can elucidate the physics behind the break up of a fiber floc, opening the possibility for developing a meaningful numerical model of the fiber flow. The simulation of blood movement from an arteriole through a venule via a capillary showed that the model based on VOF can successfully predict the deformation and flow of RBCs in an arteriole. Furthermore, the result corresponds to the experimental observation illustrates that the RBC is deformed during the movement. The concluding remarks presented, provide a correct methodology and a mathematical and numerical framework for the simulation of blood flows in branching. Analysis of ferrofluids simulations indicate that the magnetic Soret effect can be even higher than the conventional one and its strength depends on the strength of magnetic field, confirmed experimentally by Völker and Odenbach. It was also shown that when a magnetic field is perpendicular to the temperature gradient, there will be additional increase in the heat transfer compared to the cases where the magnetic field is parallel to the temperature gradient. In addition, the statistical evaluation (Taguchi technique) on magnetic fluids showed that the temperature and initial concentration of the magnetic phase exert the maximum and minimum contribution to the thermodiffusion, respectively. In the simulation of flow through porous media, dimensionless pressure drop was studied at different Reynolds numbers, based on pore permeability and interstitial fluid velocity. The obtained results agreed well with the correlation of Macdonald et al. (1979) for the range of actual flow Reynolds studied. Furthermore, calculated results for the dispersion coefficients in the cylinder geometry were found to be in agreement with those of Seymour and Callaghan.

The Regulation of Skeletal and Cardiac Muscle Blood Flow in Humans. Studies by positron emission tomography with special reference to exercise, adenosine and nitric oxide

Virtually every cell and organ in the human body is dependent on a proper oxygen supply. This is taken care of by the cardiovascular system that supplies tissues with oxygen precisely according to their metabolic needs. Physical exercise is one of the most demanding challenges the human circulatory system can face. During exercise skeletal muscle blood flow can easily increase some 20-fold and its proper distribution to and within muscles is of importance for optimal oxygen delivery. The local regulation of skeletal muscle blood flow during exercise remains little understood, but adenosine and nitric oxide may take part in this process. In addition to acute exercise, long-term vigorous physical conditioning also induces changes in the cardiovasculature, which leads to improved maximal physical performance. The changes are largely central, such as structural and functional changes in the heart. The function and reserve of the heart’s own vasculature can be studied by adenosine infusion, which according to animal studies evokes vasodilation via it’s a_2A receptors. This has, however, never been addressed in humans in vivo and also studies in endurance athletes have shown inconsistent results regarding the effects of sport training on myocardial blood flow. This study was performed on healthy young adults and endurance athletes and local skeletal and cardiac muscle blod flow was measured by positron emission tomography. In the heart, myocardial blood flow reserve and adenosine A_2A receptor density, and in skeletal muscle, oxygen extraction and consumption was also measured. The role of adenosine in the control of skeletal muscle blood flow during exercise, and its vasodilator effects, were addressed by infusing competitive inhibitors and adenosine into the femoral artery. The formation of skeletal muscle nitric oxide was also inhibited by a drug, with and without prostanoid blockade. As a result and conclusion, it can be said that skeletal muscle blood flow heterogeneity decreases with increasing exercise intensity most likely due to increased vascular unit recruitment, but exercise hyperemia is a very complex phenomenon that cannot be mimicked by pharmacological infusions, and no single regulator factor (e.g. adenosine or nitric oxide) accounts for a significant part of exercise-induced muscle hyperemia. However, in the present study it was observed for the first time in humans that nitric oxide is not only important regulator of the basal level of muscle blood flow, but also oxygen consumption, and together with prostanoids affects muscle blood flow and oxygen consumption during exercise. Finally, even vigorous endurance training does not seem to lead to supranormal myocardial blood flow reserve, and also other receptors than A_2A mediate the vasodilator effects of adenosine. In respect to cardiac work, atheletes heart seems to be luxuriously perfused at rest, which may result from reduced oxygen extraction or impaired efficiency due to pronouncedly enhanced myocardial mass developed to excel in strenuous exercise.

Separation of Gas Bubbles from Circulation Waters and Pulp Suspensions in Open Channel Flow

The objective of this thesis was to study the removal of gases from paper mill circulation waters experimentally and to provide data for CFD modeling. Flow and bubble size measurements were carried out in a laboratory scale open gas separation channel. Particle Image Velocimetry (PIV) technique was used to measure the gas and liquid flow fields, while bubble size measurements were conducted using digital imaging technique with back light illumination. Samples of paper machine waters as well as a model solution were used for the experiments. The PIV results show that the gas bubbles near the feed position have the tendency to escape from the circulation channel at a faster rate than those bubbles which are further away from the feed position. This was due to an increased rate of bubble coalescence as a result of the relatively larger bubbles near the feed position. Moreover, a close similarity between the measured slip velocities of the paper mill waters and that of literature values was obtained. It was found that due to dilution of paper mill waters, the observed average bubble size was considerably large as compared to the average bubble sizes in real industrial pulp suspension and circulation waters. Among the studied solutions, the model solution has the highest average drag coefficient value due to its relatively high viscosity. The results were compared to a 2D steady sate CFD simulation model. A standard Euler-Euler k-ε turbulence model was used in the simulations. The channel free surface was modeled as a degassing boundary. From the drag models used in the simulations, the Grace drag model gave velocity fields closest to the experimental values. In general, the results obtained from experiments and CFD simulations are in good qualitative agreement.

Numerical modelling of small supersonic axial flow turbines

Supersonic axial turbine stages typically exhibit lower efficiencies than subsonic axial turbine stages. One reason for the lower efficiency is the occurrence of shock waves. With higher pressure ratios the flow inside the turbine becomes relatively easily supersonic if there is only one turbine stage. Supersonic axial turbines can be designed in smaller physical size compared to subsonic axial turbines of same power. This makes them good candidates for turbochargers in large diesel engines, where space can be a limiting factor. Also the production costs are lower for a supersonic axial turbine stage than for two subsonic stages. Since supersonic axial turbines are typically low reaction turbines, they also create lower axial forces to be compensated with bearings compared to high reaction turbines. The effect of changing the stator-rotor axial gap in a small high (rotational) speed supersonic axial flow turbine is studied in design and off-design conditions. Also the effect of using pulsatile mass flow at the supersonic stator inlet is studied. Five axial gaps (axial space between stator and rotor) are modeled using threedimensional computational fluid dynamics at the design and three axial gaps at the off-design conditions. Numerical reliability is studied in three independent studies. An additional measurement is made with the design turbine geometry at intermediate off-design conditions and is used to increase the reliability of the modelling. All numerical modelling is made with the Navier-Stokes solver Finflo employing Chien’s k ¡ ² turbulence model. The modelling of the turbine at the design and off-design conditions shows that the total-to-static efficiency of the turbine decreases when the axial gap is increased in both design and off-design conditions. The efficiency drops almost linearily at the off-design conditions, whereas the efficiency drop accelerates with increasing axial gap at the design conditions. The modelling of the turbine stator with pulsatile inlet flow reveals that the mass flow pulsation amplitude is decreased at the stator throat. The stator efficiency and pressure ratio have sinusoidal shapes as a function of time. A hysteresis-like behaviour is detected for stator efficiency and pressure ratio as a function of inlet mass flow, over one pulse period. This behaviour arises from the pulsatile inlet flow. It is important to have the smallest possible axial gap in the studied turbine type in order to maximize the efficiency. The results for the whole turbine can also be applied to some extent in similar turbines operating for example in space rocket engines. The use of a supersonic stator in a pulsatile inlet flow is shown to be possible.

Simulating Fluid Flow in a Compressed Valve

The objective of the work is to study fluid flow behavior through a pinch valve and to estimate the flow coefficient (KV ) at different opening positions of the valve. The flow inside a compressed valve is more complex than in a straight pipe, and it is one of main topics of interest for engineers in process industry. In the present work, we have numerically simulated compressed valve flow at different opening positions. In order to simulate the flow through pinch valve, several models of the elastomeric valve tube (pinch valve tube) at different opening positions were constructed in 2D-axisymmetric and 3D geometries. The numerical simulations were performed with the CFD packages; ANSYS FLUENT and ANSYS CFX by using parallel computing. The distributions of static pressure, velocity and turbulent kinetic energy have been studied at different opening positions of the valve in both 2D-axisymmetric and 3D experiments. The flow coefficient (KV ) values have been measured at different valve openings and are compared between 2D-axisymmetric and 3D simulation results.

Alpha2-Adrenoceptor-mediated vascular responses induced by dexmedetomidine

Alpha2-Adrenoceptors are cell-surface G protein coupled receptors that mediate many of the effects of the catecholamines noradrenaline and adrenaline. The three human α2-adrenoceptor subtypes are widely expressed in different tissues and organs, and they mediate many different physiological and pharmacological effects in the central and peripheral nervous system and as postsynaptic receptors in target organs. Previous studies have demonstrated that α2-adrenoceptors mediate both vascular constriction and dilatation in humans. Large inter-individual variation has been observed in the vascular responses to α2-adrenoceptor activation in clinical studies. All three receptor subtypes are potential drug targets. It was therefore considered important to further elucidate the details of adrenergic vascular regulation and its genetic variation, since such knowledge may help to improve the development of future cardiovascular drugs and intensive care therapies. Dexmedetomidine is the most selective and potent α2-adrenoceptor agonist currently available for clinical use. When given systemically, dexmedetomidine induces nearly complete sympatholysis already at low concentrations, and postsynaptic effects, such vasoconstriction, can be observed with increasing concentrations. Thus, local infusions of small doses of dexmedetomidine into dorsal hand veins and the application of pharmacological sympathectomy with brachial plexus block provide a means to assess drug-induced peripheral vascular responses without interference from systemic pharmacological effects and autonomic nervous system regulation. Dexmedetomidine was observed to have biphasic effects on haemodynamics, with an initial decrease in blood pressure at low concentrations followed by substantial increases in blood pressure and coronary vascular resistance at high concentrations. Plasma concentrations of dexmedetomidine that significantly exceeded the recommended therapeutic level did not reduce myocardial blood flow below the level that is observed with the usual therapeutic concentrations and did not induce any evident myocardial ischaemia in healthy subjects. Further, it was demonstrated that dexmedetomidine also had significant vasodilatory effects through activation of endothelial nitric oxide synthesis, and thus when the endothelial component of the blood vessel response to dexmedetomidine was inhibited, peripheral vasoconstriction was augmented. Hand vein constriction responses to α2-adrenoceptor activation by dexmedetomidine were only weakly associated with the constriction responses to α1-adrenoceptor activation, pointing to independent cellular regulation by these two adrenoceptor classes. Substantial inter-individual variation was noted in the venous constriction elicited by activation of α2-adrenoceptors by dexmedetomidine. In two study populations from two different continents, a single nucleotide polymorphism in the PRKCB gene was found to be associated with the dorsal hand vein constriction response to dexmedetomidine, suggesting that protein kinase C beta may have an important role in the vascular α2-adrenoceptor signalling pathways activated by dexmedetomidine.

The Effects of Anesthetic Induced Loss of Consciousness on Quantitative Electroen Cephalogram, and Bispectral and Spectral Entropy Indices. Studies on Healthy Male

Changes in the electroencephalography (EEG) signal have been used to study the effects of anesthetic agents on the brain function. Several commercial EEG based anesthesia depth monitors have been developed to measure the level of the hypnotic component of anesthesia. Specific anesthetic related changes can be seen in the EEG, but still it remains difficult to determine whether the subject is consciousness or not during anesthesia. EEG reactivity to external stimuli may be seen in unconsciousness subjects, in anesthesia or even in coma. Changes in regional cerebral blood flow, which can be measured with positron emission tomography (PET), can be used as a surrogate for changes in neuronal activity. The aim of this study was to investigate the effects of dexmedetomidine, propofol, sevoflurane and xenon on the EEG and the behavior of two commercial anesthesia depth monitors, Bispectral Index (BIS) and Entropy. Slowly escalating drug concentrations were used with dexmedetomidine, propofol and sevoflurane. EEG reactivity at clinically determined similar level of consciousness was studied and the performance of BIS and Entropy in differentiating consciousness form unconsciousness was evaluated. Changes in brain activity during emergence from dexmedetomidine and propofol induced unconsciousness were studied using PET imaging. Additionally, the effects of normobaric hyperoxia, induced during denitrogenation prior to xenon anesthesia induction, on the EEG were studied. Dexmedetomidine and propofol caused increases in the low frequency, high amplitude (delta 0.5-4 Hz and theta 4.1-8 Hz) EEG activity during stepwise increased drug concentrations from the awake state to unconsciousness. With sevoflurane, an increase in delta activity was also seen, and an increase in alpha- slow beta (8.1-15 Hz) band power was seen in both propofol and sevoflurane. EEG reactivity to a verbal command in the unconsciousness state was best retained with propofol, and almost disappeared with sevoflurane. The ability of BIS and Entropy to differentiate consciousness from unconsciousness was poor. At the emergence from dexmedetomidine and propofol induced unconsciousness, activation was detected in deep brain structures, but not within the cortex. In xenon anesthesia, EEG band powers increased in delta, theta and alpha (8-12Hz) frequencies. In steady state xenon anesthesia, BIS and Entropy indices were low and these monitors seemed to work well in xenon anesthesia. Normobaric hyperoxia alone did not cause changes in the EEG. All of these results are based on studies in healthy volunteers and their application to clinical practice should be considered carefully.

Pressure drop coefficients for elliptic and circular sections in one, two and three-row arrangements of plate fin and tube heat exchangers

The objective of the present work is the experimental determination of pressure drop coefficients (loss coefficients) for elliptic and circular sections in one, two and three-row arrangements of plate fin and tube heat exchangers. The experiments permitted to correlate the dimensionless loss coefficient with the flow Reynolds number in the rectangular channel formed by the plate fins. The experimental technique consisted of the measurement of the longitudinal pressure distribution along the flow channel, for several values of air mass flow rate. The total number of data runs, each one characterized by the flow Reynolds number, was 216. The present geometry is used in compact heat exchangers for air conditioning systems, heaters, radiators, and others. Also, it is verified the influence of the utilization of elliptic tubes, instead of circular ones, in the pressure drop. The measurements were performed for Reynolds numbers ranging from 200 to 1900.

Turbulent heat transfer and pressure drop in pinned annular regions

Experiments were performed to determine average heat transfer coefficients and friction factors for turbulent flow through annular ducts with pin fins. The measurements were carried out by means of a double-pipe heat exchanger. The total number of pins attached to the inner wall of the annular region was 560. The working fluids were air, flowing in the annular channel, and water through the inner circular tube. The average heat transfer coefficients of the pinned air-side were obtained from the experimental determination of the overall heat transfer coefficients of the heat exchanger and from the knowledge of the average heat transfer coefficients of the circular pipe (water-side), which could be found in the pertinent literature. To attain fully developed conditions, the heat exchanger was built with additional lengths before and after the test section. The inner circular duct of the heat exchanger and the pin fins were made of brass. Due to the high thermal conductivity of the brass, the small tube thickness and water temperature variation, the surface of the internal tube was practically isothermal. The external tube was made of an industrial plastic which was insulated from the environment by means of a glass wool batt. In this manner, the outer surface of the annular channel can be considered adiabatic. The results are presented in dimensionless forms, in terms of average Nusselt numbers and friction factors as functions of the flow Reynolds number, ranging from 13,000 to 80,000. The pin fin efficiency, which depends on the heat transfer coefficient, is also determined as a function of dimensionless parameters. A comparison of the present results with those for smooth sections (without pins) is also presented. The purpose of such a comparison is to study the influence of the presence of the pins on the pressure drop and heat transfer rate.

Horizontal Slug Flow in a Large-Size Pipeline: Experimentation and Modeling

The knowledge of the slug flow characteristics is very important when designing pipelines and process equipment. When the intermittences typical in slug flow occurs, the fluctuations of the flow variables bring additional concern to the designer. Focusing on this subject the present work discloses the experimental data on slug flow characteristics occurring in a large-size, large-scale facility. The results were compared with data provided by mechanistic slug flow models in order to verify their reliability when modelling actual flow conditions. Experiments were done with natural gas and oil or water as the liquid phase. To compute the frequency and velocity of the slug cell and to calculate the length of the elongated bubble and liquid slug one used two pressure transducers measuring the pressure drop across the pipe diameter at different axial locations. A third pressure transducer measured the pressure drop between two axial location 200 m apart. The experimental data were compared with results of Camargo's1 algorithm (1991, 1993), which uses the basics of Dukler & Hubbard's (1975) slug flow model, and those calculated by the transient two-phase flow simulator OLGA.

Modeling of Liquid-Solid Flow in Industrial Scale

In the present work, liquid-solid flow in industrial scale is modeled using the commercial software of Computational Fluid Dynamics (CFD) ANSYS Fluent 14.5. In literature, there are few studies on liquid-solid flow in industrial scale, but any information about the particular case with modified geometry cannot be found. The aim of this thesis is to describe the strengths and weaknesses of the multiphase models, when a large-scale application is studied within liquid-solid flow, including the boundary-layer characteristics. The results indicate that the selection of the most appropriate multiphase model depends on the flow regime. Thus, careful estimations of the flow regime are recommended to be done before modeling. The computational tool is developed for this purpose during this thesis. The homogeneous multiphase model is valid only for homogeneous suspension, the discrete phase model (DPM) is recommended for homogeneous and heterogeneous suspension where pipe Froude number is greater than 1.0, while the mixture and Eulerian models are able to predict also flow regimes, where pipe Froude number is smaller than 1.0 and particles tend to settle. With increasing material density ratio and decreasing pipe Froude number, the Eulerian model gives the most accurate results, because it does not include simplifications in Navier-Stokes equations like the other models. In addition, the results indicate that the potential location of erosion in the pipe depends on material density ratio. Possible sedimentation of particles can cause erosion and increase pressure drop as well. In the pipe bend, especially secondary flows, perpendicular to the main flow, affect the location of erosion.

Changes in the electrophysiological parameters of the posterior intestine of Anguilla anguilla (Pisces) induced by oxytocin, urotensin II and aldosterone

In view of the importance of the intestine in the osmoregulation of freshwater fishes, we determined the effects of oxytocin, urotensin II (UII), and aldosterone added to the serosal side of the isolated posterior intestine of the freshwater-adapted teleost Anguilla anguilla on electrophysiological parameters. Oxytocin decreased the short-circuit current (SCC) and transepithelial potential difference (TPD) at concentrations of 1 and 10 mU/ml (to 50% and 42% of control values, respectively), but did not alter these parameters at a concentration of 0.1 mU/ml. UII reduced SCC and TPD at concentrations of 10 nM, 50 nM and 100 nM (to 85% of control values), but increased these parameters at the concentration of 500 nM (to 115% of control values). Aldosterone did not alter SCC or TPD at the concentrations tested (10 nM and 100 nM). Oxytocin may open Na+ channels in the apical membrane, allowing the flow of Na+ to the serosa, reducing SCC and TPD. Should this hypothesis be correct, oxytocin would be important for freshwater adaptation, since it would increase Na+ absorption. The reduction of SCC and TPD in the posterior intestine of A. anguilla induced by UII is evidence that this neurohormone is also important for freshwater adaptation in teleosts. Aldosterone did not show this effect probably due to the lack of receptors in this organ

Validation of transit-time flowmetry for chronic measurements of regional blood flow in resting and exercising rats

The objective of the present study was to validate the transit-time technique for long-term measurements of iliac and renal blood flow in rats. Flow measured with ultrasonic probes was confirmed ex vivo using excised arteries perfused at varying flow rates. An implanted 1-mm probe reproduced with accuracy different patterns of flow relative to pressure in freely moving rats and accurately quantitated the resting iliac flow value (on average 10.43 ± 0.99 ml/min or 2.78 ± 0.3 ml min-1 100 g body weight-1). The measurements were stable over an experimental period of one week but were affected by probe size (resting flows were underestimated by 57% with a 2-mm probe when compared with a 1-mm probe) and by anesthesia (in the same rats, iliac flow was reduced by 50-60% when compared to the conscious state). Instantaneous changes of iliac and renal flow during exercise and recovery were accurately measured by the transit-time technique. Iliac flow increased instantaneously at the beginning of mild exercise (from 12.03 ± 1.06 to 25.55 ± 3.89 ml/min at 15 s) and showed a smaller increase when exercise intensity increased further, reaching a plateau of 38.43 ± 1.92 ml/min at the 4th min of moderate exercise intensity. In contrast, exercise-induced reduction of renal flow was smaller and slower, with 18% and 25% decreases at mild and moderate exercise intensities. Our data indicate that transit-time flowmetry is a reliable method for long-term and continuous measurements of regional blood flow at rest and can be used to quantitate the dynamic flow changes that characterize exercise and recovery

Acute extracellular fluid volume changes increase ileocolonic resistance to saline flow in anesthetized dogs

We determined the effect of acute extracellular fluid volume changes on saline flow through 4 gut segments (ileocolonic, ileal, ileocolonic sphincter and proximal colon), perfused at constant pressure in anesthetized dogs. Two different experimental protocols were used: hypervolemia (iv saline infusion, 0.9% NaCl, 20 ml/min, volume up to 5% body weight) and controlled hemorrhage (up to a 50% drop in mean arterial pressure). Mean ileocolonic flow (N = 6) was gradually and significantly decreased during the expansion (17.1%, P<0.05) and expanded (44.9%, P<0.05) periods while mean ileal flow (N = 7) was significantly decreased only during the expanded period (38%, P<0.05). Mean colonic flow (N = 7) was decreased during expansion (12%, P<0.05) but returned to control levels during the expanded period. Mean ileocolonic sphincter flow (N = 6) was not significantly modified. Mean ileocolonic flow (N = 10) was also decreased after hemorrhage (retracted period) by 17% (P<0.05), but saline flow was not modified in the other separate circuits (N = 6, 5 and 4 for ileal, ileocolonic sphincter and colonic groups, respectively). The expansion effect was blocked by atropine (0.5 mg/kg, iv) both on the ileocolonic (N = 6) and ileal (N = 5) circuits. Acute extracellular fluid volume retraction and expansion increased the lower gastrointestinal resistances to saline flow. These effects, which could physiologically decrease the liquid volume being supplied to the colon, are possible mechanisms activated to acutely balance liquid volume deficit and excess.

Heterogeneity of glomerular perfusion and filtration induced by epinephrine and norepinephrine

The role of catecholamines in the distribution of intrarenal blood flow and in single-nephron glomerular filtration rate (SNGFR) was evaluated in anesthetized Wistar rats by the Hanssen technique. Epinephrine (EPI) and norepinephrine (NOR) were infused to produce elevations of 20-30 mmHg in mean arterial pressure. Superficial and juxtamedullary nephron perfusion and filtration were determined by the presence of Prussian blue dye. In the control group, 100% of the nephrons presented a homogeneous pattern of perfusion and filtration. In contrast, a heterogeneous distribution of the dye was found even in the larger arteries (arciform and radial), indicating variable perfusion and filtration in both superficial and juxtamedullary nephrons. The effects of EPI and NOR were also evaluated in the superficial cortex by the micropuncture technique in two additional groups of Munich-Wistar rats. Mean SNGFR was 27% and 54% lower in the EPI- and NOR-treated groups, respectively. No change in mean intraglomerular hydraulic pressure was observed after EPI or NOR infusion in spite of a highly scattered pattern, indicating an important variability in perfusion along the superficial cortex, and/or different sensitivity of the pre- and post-glomerular arterioles. The present data suggest that EPI and NOR may affect intrarenal hemodynamics by modifying perfusion and filtration in both superficial and juxtamedullary glomeruli and not by shifting blood flow from superficial to juxtamedullary nephrons. The heterogeneous pattern of perfusion was a consequence of differential vasoconstriction along the intrarenal arteries, probably due to different density and/or sensitivity of the adrenergic receptor subtypes present in the intrarenal vascular tree.