Fluid Mass Ratio Research Articles

Vibration behavior prediction of submerged nanobeams with axially traveling supports: numerical, analytical, and machine learning approaches

This work surveyed the vibration behavior and stability analysis of an underwater moving flexible nanosize beam, implementing numerical and analytical methods as well as tree-based machine learning (ML) algorithms. Dynamic modeling is performed based on the nonlocal stress-strain gradient theory (NSSGT), incorporating variable environmental conditions, surface energy, and rotational inertia effects. The natural frequencies and instability threshold are computed numerically. The exact closed-form mathematical expression for the critical towing velocity of the nanosize beam is determined analytically. Also, decision tree regression and least-squares boosting tree (LSBT) regression algorithms are exploited to predict stability boundaries and the fundamental vibration frequency, and their efficiency is surveyed accordingly. Comparative studies and parametric investigations are conducted. The impressions of geometry, added mass coefficient, scale ratio parameter, surface layer characteristics, fluid mass ratio, humidity, temperature rise, and external magnetic field intensity on the nanosystem dynamics are examined and illuminated. It is detected that the results of the analytical method and ML-based approaches are consistent with those reported by the numerical technique and literature. The results asserted that the proposed ML algorithms have acceptable performance and excellent effectiveness in computational time and cost. It is comprehended that the dynamic features of submerged traveling nanobeams drastically depend on the rotational inertia effects and thickness-dependent scale effects. The stability of the immersed movable nanoscale beams is perceived to improve by increasing the scale ratio parameter and the added mass coefficient. From the perspective of the optimal design of engineering instrumentation tools, the outcomes of the current article can be applied as an inclusive benchmark.

An inerter-based concept of locally resonant fluid-conveying pipe

Preventing damage or failure caused by vibrations in periodic fluid-conveying pipes needs appropriate mitigation strategies. This paper proposes a novel concept of locally resonant fluid-conveying pipe resting on periodically spaced inerter-based resonant supports, each including an inerter and linear springs. On adopting a Timoshenko beam model for the pipe, two types of inerter-based resonant supports are investigated, differing by the arrangement of the internal components, i.e., inerter and springs. For both types, elastic wave dispersion analyses of the infinite pipe demonstrate the existence of two low-frequency band gaps in the frequency response. The second band gap, caused by local resonance, exhibits better attenuation over a relevant part of its frequency range; its lower/upper edge frequencies and amplitude may be suitably changed depending on the parameters of the inerter-based resonant supports, and very considerable amplitudes can be obtained thanks to the large inertia effects warranted by the grounded inerter. The influence on the band gaps of key parameters such as fluid velocity and ratio of fluid mass to total pipe mass is assessed. Moreover, the effect of damping is considered, assuming a Kelvin–Voigt viscoelastic behavior for the pipe material and including viscous dashpots in parallel with the springs within the inerter-based resonant supports. An original exact dynamic-stiffness method is formulated for computational purposes, targeting wave dispersion analysis of the infinite pipe as well as frequency-domain analysis of the finite pipe. In particular, the main novelty is the derivation of the exact dynamic-stiffness matrix and exact load vector of the unit cell of the Timoshenko pipe with Kelvin–Voigt viscoelastic behavior. Remarkably, the transmittance of the finite pipe confirms the predictions from wave dispersion analysis of the infinite pipe and substantiates the effectiveness of the proposed concept of locally resonant fluid-conveying pipe.

Path curvature enhances the flow-induced vibrations of a cylinder without structural restoring force

A cylinder immersed in a current and free to translate along a circular arc is considered to investigate the impact of path curvature on the flow-induced vibrations (FIV) occurring without structural restoring force. Path curvature magnitude ( $\kappa$ , inverse of path radius non-dimensionalized by the body diameter $D$ ) is varied from $0$ (transverse rectilinear path) to $20$ , over a wide range of values of the structure to displaced fluid mass ratio, $m^\star \in [0.05,10]$ . The exploration is carried out numerically at subcritical and postcritical values of the Reynolds number ( $Re$ , based on $D$ and the inflow velocity), i.e. below and above the critical value $47$ for the onset of flow unsteadiness when the body is fixed, up to $100$ . Path curvature triggers a desynchronized regime of the flow–body system in addition to the synchronized regime typical of vortex-induced vibrations, and alters the composition of fluid forcing. The most prominent effect uncovered here is, however, a global enhancement of FIV, with three principal results: (i) vibrations and flow unsteadiness are found to arise at lower subcritical $Re$ along a curved path, down to $19.5$ versus $31$ for $\kappa =0$ ; (ii) the $m^\star$ range where substantial responses develop is considerably extended and encompasses the entire interval under study, which contrasts with the narrow band of low $m^\star$ identified for $\kappa =0$ ; (iii) the vibrations are amplified, $+45\,\%$ relative to the peak amplitude measured along a rectilinear path at $Re =100$ .

A wind tunnel investigation of the effects of end and laminar/turbulent inflow conditions on cylinder vortex-induced vibrations

The influence of end and inflow conditions on the vortex-induced vibrations of a cylinder is studied on the basis of wind tunnel experiments, combining measurements of the body displacement and flow velocity in its wake. The cylinder of length-to-diameter aspect ratio 5.5 has one end exposed to the current. It is elastically mounted in the cross-flow direction, with low damping. The structure to displaced fluid mass ratio is close to 1000. The behavior of the system is explored over a range of values of the reduced velocity, U⋆, defined as the inverse of the oscillator natural frequency, non-dimensionalized by the inflow velocity (U∞) and the cylinder diameter (D), typically between 4 and 8, at a Reynolds number of the order of 104, based on U∞ and D. Three end conditions are examined: two free-end conditions with either a flat or a hemispherical shape, and a condition where a fixed plate is placed close to the flat end. Three inflow states are considered: a laminar condition and two grid-generated turbulent conditions of different turbulence intensity levels (up to 10%) and comparable integral length scales, around 30% of D. Vibrations characterized by bell-shaped evolutions of their magnitude with U⋆ develop, under flow-body synchronization (lock-in), in all conditions, with peak amplitudes ranging from 4% to 12% of D. The free end causes a shift of the response bell-shaped curve towards higher U⋆ values. The shift may be such that there is no overlap between the vibration domains in the end-plate and free-end conditions. The passage from laminar to turbulent inflow conditions is found to attenuate this shift. A clear reduction of vibration amplitude is observed when the end plate is removed, and the amplitude is further reduced when the flat end is replaced by the hemispherical one. On the other hand, turbulent inflows induce a global enhancement of the vibration amplitudes, which may reach +45% relative to the laminar stream condition. The end/inflow conditions are also shown to impact the regularity of the structural responses.

Dynamics of spinning pipes conveying flow with internal elliptical cross-section surrounded by an external annular fluid by considering rotary inertia effects

In this work, the vibration and stability of spinning pipes with an internal elliptical cross-section concurrently subjected to internal flow and external annular fluid are analyzed by considering rotary inertia effects and the non-uniformity of internal flow velocity distribution. To model the system, axial force, internal pressure, hygro-thermal loads, viscoelastic properties, and gravitational effects were incorporated. The coupled dynamic equations of transverse motions of the pipe were derived by exploiting the extended Hamilton's principle. With the aid of the Laplace transform and Galerkin discretization method, eigenvalues and stability conditions of the system were determined. Moreover, the divergence instability conditions of the system were acquired analytically. Then, the current investigation results were compared and verified with existing experimental and theoretical data in open literature. The impacts of key parameters, such as stabilizer characteristics, boundary conditions, geometrical features, and external fluid mass ratio, on the vibration frequencies and instability thresholds, were evaluated. It was concluded that, contrary to the internal circular cross-section case, the divergence instability region can be observed in the stability evaluation of the system with the internal elliptical cross-section. It was found that considering the rotary inertia effects reduces the critical velocities of the system. Also, the results showed that by increasing the stabilizer damping, the detached stable region is detected in the stability map of cantilevered pipes. The present research results can be beneficial for the optimal design of industrial equipment such as drill string pipes.

Analysis of vibration stability of fluid conveying pipe on the two-parameter foundation with elastic support boundary conditions

In this study, the vibration stability of fluid conveying pipe resting on two-parameter foundation is investigated under four different elastic support boundary conditions. The harmonic differential quadrature (HDQ) method is applied to solve the governing vibration equation derived based on Euler–Bernoulli beam theory subject to the elastic foundation and boundary conditions. As a result, a general set of second-order ordinary differential equations emerges, and by appropriately setting the stiffness of the end springs, one can easily study the dynamics of various systems with classical or non-classical boundary conditions. The numerical simulations are conducted to study the pipe instability performance with respect to various boundary conditions, elastic support parameters, elastic foundation parameters and fluid mass ratios. The numerical model is validated by comparison with published data. It is found that the elastic support boundary conditions have significant effects on the stability of pipe resting on elastic foundation. The pipe stability performance is very sensitive to the two elastic foundation parameters. Larger fluid mass ratio enhances the pipe flutter stability performance but has no effects on the divergence.

Investigation of energy consumption reduction in multistage compression process and its solutions

During hot seasons the inlet temperature of Nitrogen increases, as a result compressor consumes more power for compressing a specific mass ratio of fluid and consequently total energy consumption of the compressor increases as well. In this research, a three stage centrifugal compressor with intercooler was modeled thermodynamically in order to decreases the energy consumption of the compressor. In each compressor, isentropic efficiency, outlet temperature of the Nitrogen gas and power compression was investigated. The effect of inlet Nitrogen temperature and cooling water temperature on intercoolers’ efficiency were investigated. In this study, Nitrogen gas is considered as an ideal gas. It is found that, in each compressor any growth in inlet temperature of the Nitrogen gas will result in linear increase in the outlet temperature of the Nitrogen gas and power compression furthermore, it is observed that increasing the temperature of Nitrogen gas has the most negative effect on efficiency and power compression of the first compressor in comparison to the second and the third compressor consequently, it will result in a 10 percent decrease in special power compression specially during summer time. According to the results, it is figured out that any growth in inlet Nitrogen temperature causes a smooth decline in isentropic and Power Compression of the first, second and third compressors besides increasing the temperature of the Nitrogen gas increases the isentropic efficiency up to 3 Percent and increasing the cooling water temperature decreases the intercooler efficiency up to 7 Percent.

Quantifying Ca exchange in gypsum using a 45Ca tracer: Implications for interpreting Ca isotopic effects in experimental and natural systems

Abstract Mineral-solution exchange rates of Ca were determined using a 45Ca tracer technique for three types of gypsum: natural cm-long gypsum needles, natural microcrystalline gypsum, and synthetic microcrystalline gypsum. Batch reactors containing the gypsum crystals were equilibrated with a saturated 45Ca spiked solution (Ωgypsum ≈ 1) for 30 days and were sequentially sacrificed to estimate exchange rates. The percentage of gypsum that exchanged was determined using a time-dependent box model, which simulated mineral dissolution and reprecipitation over time with variable extents of back reaction. Large natural needles exhibited no detectable exchange over 30 days, whereas a significant percentage of the Ca in the synthetic and natural micro-crystals exchanged. According to our model-based calculations, 45% of the synthetic gypsum and 20% of the natural gypsum exchanged; because of our experimental design, these extents are not affected by the model framework. The surface area normalized exchange rates were faster over the first five days (1.04 · 10−5 ± 5.84 · 10−6 mol/m2/d in the synthetic micro-crystals and 8.97 · 10−5 ± 7.45 · 10−5 mol/m2/d in the natural micro-crystals) than during the remainder of the experiment (2.37 · 10−6 ± 6.03 · 10−7 mol/m2/d in the synthetic micro-crystals and 2.69 · 10−5 ± 1.23 · 10−5 mol/m2/d in the natural micro-crystals). As the Ca concentration in solution remained constant over the experiment, the observed exchange is thought to be a result of dissolution/reprecipitation at the mineral-solution interface rather than due to net dissolution or net precipitation. The gypsum exchange rates that we constrain are consistent with those of other sulfate minerals, irrespective of their hydration state, but are considerably faster than carbonates over similar time scales. It is not clear if this is a result of the interpretive model framework, which can strongly influence both the derived rate and the extent of reaction, or whether it is a real phenomenon. Because the influence of the model framework is so important, we detail the importance of the solid to fluid mass ratio and the role of a back-reaction flux to the accurate quantification of recrystallization rates and extents. Finally, we apply our numerical model to the reinterpretation of past work and constrain the Ca isotopic fractionation factor associated with extremely slow rates of gypsum precipitation/exchange to be between 0 and −0.1‰.

Stability analysis of thin-walled spinning reinforced pipes conveying fluid in thermal environment

Abstract The divergence and flutter instabilities of the thin-walled spinning pipes reinforced by single-walled carbon nanotubes in thermal environment are investigated. The material properties of carbon nanotube-reinforced composites are assumed to be uniform distribution as well as two types of functionally graded distribution patterns. The thermal effects are also considered and the material properties of carbon nanotube-reinforced composites are assumed to be temperature-dependent. The cantilever pipe conveying fluid is spinning along its longitudinal axis and subjected to an axial force at the free end. Based on the thin-walled Timoshenko beam theory, the governing equations of motion are derived using the extended Hamilton's principle and discretized via the Galerkin method. The resulting thermal-structural-fluid eigenvalue problem is solved and the frequency and the critical fluid velocities are calculated. The effects of carbon nanotubes distributions, volume fraction of carbon nanotubes, compressive axial force, spinning speed, gravity and fluid mass ratio on the critical divergence and flutter velocities of the thin-walled spinning pipe conveying fluid are studied.

On the Stability of Spinning Functionally Graded Cantilevered Pipes Subjected to Fluid-Thermomechanical Loading

This paper studies the thermomechanical stability of a cantilevered pipe spinning along its longitudinal axis and carrying an internal axial flow. The pipe, made of functionally graded materials (FGMs), is subjected to an axial force at the free end operating in a high temperature environment. It is modeled by the Rayleigh beam theory and is considered as a hollow thin-walled beam. The equation of motion, along with the boundary conditions, for the pipe is derived by using the extended Hamilton’s principle. Further, the extended Galerkin’s method (EGM) in conjunction with a proper representation of the displacements of the pipe is used to solve the eigenvalue problem. Depending upon the nature of the eigenvalues, i.e. real or complex-conjugate, the conditions for occurrence of instability by flutter or by divergence are derived. The effects of spin rate and velocity of fluid flow are studied on the stability regions, i.e. the critical flutter and divergence boundary, by the numerical method. Also, the effects of parameters, such as fluid mass ratio, compressive axial force, volume fraction index of the FGM and temperature gradient through the pipe thickness, are considered in developing the stability map for the spinning cantilever pipe. The results are compared with those available in the literature and good agreement has been achieved.

Dynamic stress-intensity factors of an in-plane shear crack in saturated porous medium

Based on the classical Biot theory of propagation of elastic waves in fluid-saturated porous media, two classes of plane problem are considered. One is the transient problem of a finite crack subjected to a suddenly applied in-plane shear, and another one is dealing with diffraction of transverse SV-wave by the same crack. The formulation utilizes the Laplace and integral transforms to reduce the mixed boundary-value problems to Fredholm integral equations of the second kind. The equations are then solved numerically for time and frequency dependent dynamic stress-intensity factors (mode II), and the influence of pore fluid on the dynamic stress-intensity factor is investigated. Pore fluid is found to have impact on the magnitude of the stress-intensity factor the extent of which depends on the two fluid parameter values, namely ratio of fluid mass with respect to the whole bulk mass and viscosity-to-permeability ratio. Comparisons of the solutions obtained from the present study with the corresponding known solutions of dry elastic medium are also provided to verify the validity of the present solution scheme.

The effects of diagenesis and dolomitization on Ca and Mg isotopes in marine platform carbonates: Implications for the geochemical cycles of Ca and Mg

The Ca, Mg, O, and C isotopic and trace elemental compositions of marine limestones and dolostones from ODP Site 1196A, which range in depth (∼58 to 627mbsf) and in depositional age (∼5 and 23Ma), are presented. The objectives of the study are to explore the potential for non-traditional isotope systems to fingerprint diagenesis, to quantify the extent to which geochemical proxies are altered during diagenesis, and to investigate the importance of diagenesis within the global Ca and Mg geochemical cycles. The data suggest that Ca, which has a relatively high solid to fluid mass ratio, can be isotopically altered during diagenesis. In addition, the alteration of Ca correlates with the alteration of Mg in such a way that both can serve as useful tools for deciphering diagenesis in ancient rocks.Bulk carbonate δ44Ca values vary between 0.60 and 1.31‰ (SRM-915a scale); the average limestone δ44Ca is 0.97±0.24‰ (1SD), identical within error to the average dolostone (1.03±0.15 1SD ‰). Magnesium isotopic compositions (δ26Mg, DSM-3 scale) range between −2.59‰ and −3.91‰, and limestones (−3.60±0.25‰) and dolostones (−2.68±0.07‰) are isotopically distinct. Carbon isotopic compositions (δ13C, PDB scale) vary between 0.86‰ and 2.47‰, with average limestone (1.96±0.31‰) marginally offset relative to average dolostone (1.68±0.57‰). The oxygen isotopic compositions (δ18O, PDB scale) of limestones (−1.22±0.94‰) are substantially lower than the dolostones measured (2.72±1.07‰).The isotopic data from 1196A suggest distinct and coherent trends in isotopic and elemental compositions that are interpreted in terms of diagenetic trajectories. Numerical modeling supports the contention that such trends can be interpreted as diagenetic, and suggests that the appropriate distribution coefficient (KMg) associated with limestone diagenesis is ∼1 to 5×10−3, distinctly lower than those values (>0.015) reported in laboratory studies. With respect to Mg isotopes, the modeling also suggest that diagenetic fractionation factors of ∼0.9955 (−4.5‰) and 0.9980 (−2‰) are appropriate for limestone diagenesis and dolomitization, respectively.

Hydroelastic response and energy harvesting potential of flexible piezoelectric beams in viscous flow

Electroactive polymers such as piezoelectric elements are able to generate electric potential differences from induced mechanical deformations. They can be used to build devices to harvest ambient energy from natural flow-induced deformations, e.g., as flapping flags subject to flowing wind or artificial seaweed subject to waves or underwater currents. The objectives of this study are to (1) investigate the transient hydroelastic response and energy harvesting potential of flexible piezoelectric beams fluttering in incompressible, viscous flow, and (2) identify critical non-dimensional parameters that govern the response of piezoelectric beams fluttering in viscous flow. The fluid-structure interaction response is simulated using an immersed boundary approach coupled with a finite volume solver for incompressible, viscous flow. The effects of large beam deformation, membrane tension, and coupled electromechanical responses are all considered. Validation studies are shown for the motion of a flexible filament in uniform flow, and for a piezoelectric beam subject to base vibration. The predicted flutter velocities and frequencies also compared well with published experimental and numerical data over a range of Reynolds numbers for varying fluid and solid combinations. The results showed that for a heavy beam in a light fluid (i.e., high βρ regime), flutter incepts at a lower critical speed with a lower reduced frequency than for a light beam in a heavy fluid (i.e., low βρ regime). In the high βρ regime, flutter develops at the second mode and is only realized when the fluid inertial forces are in balance with the solid elastic restoring forces, which leads to large amplitude oscillations and complex wake patterns; the flutter speed is practically independent of the Reynolds number (Re) and solid to fluid mass ratio (βρ), because the response is dominated by the solid inertial forces. In the low βρ regime, fluid inertial forces dominate, flutter develops at higher modes and is only realized when the solid inertial forces are proportioned to the solid elastic restoring forces; the flutter speed depends on both Re and βρ, and viscous force and beam tension effects tend to delay flutter and reduce vibration amplitudes, leading to thinner, more simplified wake patterns. The results demonstrate that energy extraction via fluttering piezoelectric beams is possible. The overall efficiency was observed to be influenced by the piezoelectric circuit resistance, which is known to be directly related to the square of the piezoelectric coupling factor. The results show that the maximum strain limit of piezoelectrics may be exceeded, and hence careful optimization of the material and geometry is recommended to maximize the energy capture for a given range of expected flow conditions while satisfying safety and reliability requirements.

THERMOMECHANICAL STABILITY ANALYSIS OF FUNCTIONALLY GRADED THIN-WALLED CANTILEVER PIPE WITH FLOWING FLUID SUBJECTED TO AXIAL LOAD

In this study, the thermomechanical stability of functionally graded thin-walled cantilever pipes conveying flow and loading by compressive axial force is investigated. The governing equations of motion and boundary conditions are derived via the Hamilton's variational principle. The thin-walled structure is formulated based on Rayleigh's theory. Moreover, quasi-steady flow pressure loadings and steady surface temperature are considered and the temperature gradient through the wall thickness of the pipe is included. The partial differential equations of the pipe are transformed into a set of ordinary differential equations using the extended Galerkin method. Finally, having solved the resulting thermal-structural-fluid eigenvalue system of equations, the effects of the compressive axial force, fluid speed, fluid mass ratio, volume fraction index of functionally graded materials (FGMs), and temperature change through the thickness of the pipe on the stability boundary are investigated. Numerical comparisons are also performed with the available data in the literature and good agreement is observed.

Fluids in the peridotite–water system up to 6 GPa and 800°C: new experimental constrains on dehydration reactions

The phase assemblages and compositions in a K-free lherzolite + H2O system were determined between 4 and 6 GPa and 700–800°C, and the dehydration reactions occurring at subarc depth in subduction zones were constrained. Experiments were performed on a rocking multi-anvil apparatus using a diamond-trap setting. The composition of the fluid phase was measured using the recently developed cryogenic LA–ICP–MS technique. Results show that, at 4 GPa, the aqueous fluid coexisting with residual lherzolite (~85 wt% H2O) doubles its solute load when chlorite transforms to the 10-Å phase between 700 and 750°C. The 10-Å phase breaks down at 4 and 5 GPa between 750 and 800°C and at 6 GPa between 700 and 750°C, leaving a dry lherzolite coexisting with a fluid phase containing 58–67 wt% H2O, again doubling the total dissolved solute load. The fluid fraction in the system increases from 0.2 when a hydrous mineral is present to 0.4 when coexisting with a dry lherzolite. Our data do not reveal the presence of a hydrous peridotite solidus below 800°C. The directly measured fluid compositions demonstrate a fundamental change in the (MgO + FeO) to SiO2 mass ratio of fluid solutes occurring at a depth of ca. 120–150 km (in the temperature window of 700–800°C), from (MgO–FeO)-dominated at 4 GPa [with (MgO + FeO)/SiO2 ratio of 1.41–1.56] to SiO2-dominated at 5–6 GPa (ratios of 0.61–0.82). The mobility of Al2O3 increases by more than one order of magnitude across this P–T interval and demonstrates that Al2O3 is compatible in an aqueous fluid coexisting with the anhydrous ol-opx-cpx ± grt assemblage. This shift in the fluid composition correlates with changes in the phase assemblage of the residual silicates. The hitherto unknown fundamental change in (MgO + FeO)/SiO2 ratio and prominent increase in Al2O3 of the aqueous fluid with progressive subduction will likely inspire novel concepts on mantle wedge metasomatism by slab fluids.

The distribution of sulfur between haplogranitic melts and aqueous fluids

Abstract The distribution of sulfur between haplogranitic melt and aqueous fluid has been measured as a function of oxygen fugacity (Co–CoO-buffer to hematite–magnetite buffer), pressure (0.5–3 kbar), and temperature (750–850 °C). Sulfur always strongly partitions into the fluid. At a given oxygen fugacity, pressure and temperature, the distribution of sulfur between melt and fluid can be described by one constant partition coefficient over a wide range of sulfur concentrations. Oxygen fugacity is the most important parameter controlling sulfur partitioning. While the fluid/melt partition coefficient of sulfur is 468 ± 32 under Co–CoO buffer conditions at 2 kbar and 850 °C, it decreases to 47 ± 4 at an oxygen fugacity 0.5–1 log unit above Ni–NiO at the same pressure and temperature. A further increase in oxygen fugacity to the hematite–magnetite buffer has virtually no effect on the partition coefficient (Dfluid/melt = 49 ± 2). The dependence of Dfluid/melt on temperature and pressure was systematically explored at an oxygen fugacity 0.5–1 log units above Ni–NiO. At 850 °C, the effect of pressure on the partition coefficient is small (Dfluid/melt = 58 ± 3 at 0.5 kbar; 94 ± 9 at 1 kbar; 47 ± 4 at 2 kbar and 68 ± 5 at 3 kbar) and temperature also has only a minor effect on partitioning. The data show the “sulfur excess” observed in many explosive volcanic eruptions can easily be explained by the presence of a small fraction of hydrous fluid in the magma chamber before the eruption. The sulfur excess can be calculated as the product of the fluid/melt partition coefficient of sulfur and the mass ratio of fluid over melt in the erupted material. For a plausible fluid/melt partition coefficient of 47 under oxidizing conditions, a 10-fold sulfur excess corresponds to a 17.6 wt.% of fluid in the erupted material. Large sulfur excesses (10-fold or higher) are only to be expected if only a small fraction of the magma residing in the magma chamber is erupted. The behavior of sulfur, which seems to be largely independent of pressure and temperature under oxidizing conditions is very different from chlorine, where the fluid/melt partition coefficient strongly increases with pressure. Variations in the SO2/HCl ratio of volcanic gases, if they reflect primary processes in the magma chamber, therefore provide an indicator of pressure variations in a magma. In particular, major increases in the S/Cl ratio of an aqueous fluid coexisting with a felsic magma suggest a pressure reduction in the magma chamber and/or magma rising to the surface.

Aerodynamic-Rotordynamic Interaction in Axial Compression Systems—Part II: Impact of Interaction on Overall System Stability

This paper presents an integrated treatment of the dynamic coupling between the flow field (aerodynamics) and rotor structural vibration (rotordynamics) in axial compression systems. This work is motivated by documented observations of tip clearance effects on axial compressor flow field stability, the destabilizing effect of fluid-induced aerodynamic forces on rotordynamics, and their potential interaction. This investigation is aimed at identifying the main nondimensional design parameters governing this interaction, and assessing its impact on overall stability of the coupled system. The model developed in this work employs a reduced-order Moore-Greitzer model for the flow field, and a Jeffcott-type model for the rotordynamics. The coupling between the fluid and structural dynamics is captured by incorporating a compressor pressure rise sensitivity to tip clearance, together with a momentum based model for the aerodynamic forces on the rotor (presented in Part I of this paper). The resulting dynamic model suggests that the interaction is largely governed by two nondimensional parameters: the sensitivity of the compressor to tip clearance and the ratio of fluid mass to rotor mass. The aerodynamic-rotordynamic coupling is shown to generally have an adverse effect on system stability. For a supercritical rotor and a typical value of the coupling parameter, the stability margin to the left of the design point is shown to decrease by about 5% in flow coefficient (from 20% for the uncoupled case). Doubling the value of the coupling parameter not only produces a reduction of about 8% in the stability margin at low flow coefficients, but also gives rise to a rotordynamic instability at flow coefficients 7% higher than the design point.

A THEORY OF REACTIVE CONTROL OF LOW-FREQUENCY DUCT NOISE

A theoretical prediction is undertaken for low-frequency duct noise control by a compact reactive muffler. The muffler achieves a pressure-release condition over a broad frequency band (from near zero to the first cut-on frequency of the duct) by four flush-mounted pistons, one on each duct wall, with a structure to fluid mass ratio of the order of unity. The concept of a magnetic device is introduced to allow the stiffness of the system to be made sufficiently small, leading to a high transmission loss near the DC frequency. Interactions among the pistons yield negative virtual mass which neutralizes the structural inertia. The inertia neutralization is nearly perfect over a wide frequency band, so that the high transmission loss extends to the first cut-on frequency of the duct. The near-field analysis reveals that the negative virtual mass derives from the plane wave mode of sound radiation due to the mirror effect of the opposite duct wall, an effect which can be maximized by the pairing of pistons on the two opposing walls. For relatively heavy pistons a minimum transmission loss of 14 dB may be obtained for plane waves, while that of relatively compact and light pistons could exceed 30 dB. The effects of residual system stiffness required by the system stability, and of structural damping are shown to be insignificant except for a narrow band near the DC frequency.

TRANSVERSE VIBRATIONS OF TENSIONED PIPES CONVEYING FLUID WITH TIME-DEPENDENT VELOCITY

In this study, the transverse vibrations of highly tensioned pipes with vanishing flexural stiffness and conveying fluid with time-dependent velocity are investigated. Two different cases, the pipes with fixed–fixed end and fixed–sliding end conditions are considered. The time-dependent velocity is assumed to be a harmonic function about a mean velocity. These systems experience a Coriolis acceleration component which renders such systems gyroscopic. The equation of motion is derived using Hamilton's principle and solved analytically by direct application of the method of multiple scales (a perturbation technique). The natural frequencies are found. Increasing the ratio of fluid mass to the total mass per unit length increases the natural frequencies. The principal parametric resonance cases are investigated in detail. Stability boundaries are determined analytically. It is found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system. When the velocity fluctuation frequency is close to zero, no instabilities are detected up to the first order of perturbation. Numerical results are presented for the first two modes.

Validation of Hyperbolic Model for Water-Hammer in Deformable Pipes

A mathematical formulation is presented to describe the transient flow of homogeneous gas–liquid mixtures in deformable pipes. The mixture density is defined by an expression averaging the two-component densities where isothermal evolution of the gaseous phase is admitted. Instead of the void fraction, which varies with pressure, the gas–fluid mass ratio (or the quality), assumed to be constant, is used. By application of the conservation of mass and momentum laws, a nonlinear hyperbolic system of two differential equations is obtained for the two principal dependent variables, which are the fluid pressure and velocity. Consideration is given in this paper to the numerical solution of these equations by the method of characteristics and the finite difference conservative scheme. The finite difference scheme computes the pressure by using a Newton–Raphson iterative formula, where the pressure wave speed takes place explicitly. To verify the validity of the computed results, comparison has been made with those of the numeric-experimental example of Chaudry et al. “Analysis of Transient in Bubbly Homogeneous Gas–Liquid Mixtures,” 1990. ASME J. Fluids Eng., 112, pp. 225–231. [S0098-2202(00)00301-1]