Variable Cross-sectional Area Research Articles

Static and dynamic solar coronal loops with cross-sectional area variations

ABSTRACT The Enthalpy Based Thermal Evolution of Loops approximate model for static and dynamic coronal loops is developed to include the effect of a loop cross-sectional area which increases from the base of the transition region (TR) to the corona. The TR is defined as the part of a loop between the top of the chromosphere and the location where thermal conduction changes from an energy loss to an energy gain. There are significant differences from constant area loops due to the manner in which the reduced volume of the TR responds to conductive and enthalpy fluxes from the corona. For static loops with modest area variation the standard picture of loop energy balance is retained, with the corona and TR being primarily a balance between heating and conductive losses in the corona, and downward conduction and radiation to space in the TR. As the area at the loop apex increases, the TR becomes thicker and the density in TR and corona larger. For large apex areas, the coronal energy balance changes to one primarily between heating and radiation, with conduction playing an increasingly unimportant role, and the TR thickness becoming a significant fraction of the loop length. Approximate scaling laws are derived that give agreement with full numerical solutions for the density, but not the temperature. For non-uniform areas, dynamic loops have a higher peak temperature and are denser in the radiative cooling phase by of order 50 per cent than the constant area case for the examples considered. They also show a final rapid cooling and draining once the temperature approaches 1 MK. Although the magnitude of the emission measure will be enhanced in the radiative phase, there is little change in the important observational diagnostic of its temperature dependence.

Augmented Renal Clearance, Muscle Catabolism and Urinary Nitrogen Loss: Implications for Nutritional Support in Critically Ill Trauma Patients.

The main objective of this pilot study was to determine the association between augmented renal clearance (ARC), urinary nitrogen loss and muscle wasting in critically ill trauma patients. We conducted a retrospective analysis of a local database in 162 critically ill trauma patients without chronic renal dysfunction. Nutritional-related parameters and 24 h urinary biochemical analyses were prospectively collected and averaged over the first ten days after admission. Augmented renal clearance was defined by a mean creatinine clearance (CLCR) > 130 mL/min/1.73 m2. The main outcome was the cumulated nitrogen balance at day 10. The secondary outcome was the variation of muscle psoas cross-sectional area (ΔCSA) calculated in the subgroup of patients who underwent at least two abdominal CT scans during the ICU length of stay. Overall, there was a significant correlation between mean CLCR and mean urinary nitrogen loss (normalized coefficient: 0.47 ± 0.07, p < 0.0001). ARC was associated with a significantly higher urinary nitrogen loss (17 ± 5 vs. 14 ± 4 g/day, p < 0.0001) and a lower nitrogen balance (−6 ± 5 vs. −4 ± 5 g/day, p = 0.0002), without difference regarding the mean protein intake (0.7 ± 0.2 vs. 0.7 ± 0.3 g/kg/day, p = 0.260). In the subgroup of patients who underwent a second abdominal CT scan (N = 47), both ΔCSA and %ΔCSA were higher in ARC patients (−33 [−41; −25] vs. −15 [−29; −5] mm2/day, p = 0.010 and −3 [−3; −2] vs. −1 [−3; −1] %/day, p = 0.008). Critically ill trauma patients with ARC are thus characterized by a lower nitrogen balance and increased muscle loss over the 10 first days after ICU admission. The interest of an increased protein intake (>1.5 g/kg/day) in such patients remains a matter of controversy and must be confirmed by further randomized trials.

Median Nerve Neuritis after Infection by the SARS-CoV-2 Virus

Background: The spectrum of neurological complications from SARS-CoV-2 infection is under constant investigation. According to numerous publications, occurrence of neurological complications can be about 36.4%. There are no reports to date of the occurrence of bilateral median nerve neuritis in the wrist after SARS-CoV-2 infection. Case: A previously healthy 24 years old female was observed in March 2021 due to dysesthesias in both hands, associated with nocturnal discomfort and decreased grip strength. The symptoms started a month earlier with acroparesthesias. SARS-CoV-2 virus infection was in January 2021 and evolved favorably, with progressive remission in about 10 days. Prior to the infection she didn’t have any of the hand symptoms; denied diabetes or metabolic diseases. Negative tests for SARS-CoV-2 infection since February. April 2021, the patient returned with persistent dysesthesias in her hands. Normal EMG, however with Sensitive Conduction Speed (SCS) of 50 m/sec on the right wrist; on the left SCS 55 m/sec. Sensitive latency 2.8 on the right and 2.6 on the left. Amplitude 17 on the right and 24 on the left. MRI detected an increase in signal in PDFS sequences in both median nerves, in the carpal tunnel, with no detected variations in cross-sectional areas or masses. The treatment was a 30 days 150 mg benfotiamine in two daily doses. Discussion: There is a wide variation in the clinical presentation of SARS-CoV-2 infection, ranging from asymptomatic patients to death. Most frequent symptoms are fever, dry cough, sore throat, dyspnea, myalgia, fatigue, chills, diarrhea, chest pain and vomiting, and the most common complications pneumonia and acute respiratory distress syndrome. Neurological manifestations of viral infection can occur in about 36.4% and in 45.5% in severe disease. They include Guillán-Barré and Miller Fischer syndrome; however, these conditions usually occur in more severe cases of the disease, but this patient hadn’t the typical picture of ataxia, ophthalmoplegia and areflexia. Benfotiamine is a synthetic derivative of thiamine with a multifaceted therapeutic profile, with a therapeutic role especially in diabetic neuropathy. Conclusion: Knowledge and recognition of neurological manifestations of SARS-CoV-2 infection and early detection of secondary peripheral neuropathies result in improvement of patients' clinical results and development of ideal ways of treatment. Although only a small percentage of patients develop peripheral neuropathy, in a pandemic this can result in a major social and health impact. The reported case is the first case of bilateral secondary median nerve neuritis in the literature. Level of evidence 4.

Clausius-Duhem inequality for quasi-1D transient flows in variable cross-section area deformable pipes

This paper presents the derivation of the Clausius-Duhem inequality for quasi-1D transient flows of compressible fluids in radially deformable pipes of varying cross-section area. To do so, a decomposition of the normal stress in spherical and deviatoric components was considered, so that the power expended to radially deform the fluid could be properly accounted for in the first law of thermodynamics, generating a coherent Clausius-Duhem inequality. Based on the derived inequality for Newtonian-Fourier fluids, we focus on their implications and applications. As implications we show that the restrictions imposed on the dynamic and bulk viscosities are different from those retrieved from the 1D and 3D contexts. As applications, we present two distinct studies concerning pipe flows. The first shows by appealing to numerical simulations that the weighting-function and local-balance unsteady friction models violate the second law of thermodynamics since they present negative local rate of energy dissipation. The second presents an analysis to estimate upper bounds of the local rate of energy dissipation associated with shear, and volumetric and axial deformations for laminar and turbulent transient regimes, under flow conditions characterized by the Ghidaoui's dimensionless parameter P^, for liquids with different bulk to shear viscosity ratios. Although the dissipation is dominated by shear, that one due to volumetric deformation may become more relevant for laminar flows, when small numbers P^ and high bulk viscosities liquids are considered.

Transient thermal behavior of a segmented thermoelectric cooler with variable cross‐sectional areas

In this work, a simulation model based on finite element analysis for a one-dimensional p-type segmented semiconductor element with different cross-sectional areas is analyzed to predict transient thermal behavior for thermoelectric coolers (TECs). The proposed model considers all thermoelectric effects, including the Peltier effect, Thomson effect, Joule heating, and Fourier's heat conduction. The supercooling occurs when a pulse current higher than the steady-state optimum current is applied to a TEC. Dynamic characteristics, such as minimum cold side temperature and holding time of transient state, which arise in transient supercooling are very important to be considered for the design and operation of TECs. In this study, we present a new approach of transient performance based on leg geometry shape, considering variable cross-sectional areas, as well as individual element lengths of two different thermoelectric materials using a segmentation model proposed. A variety of model designs are analyzed, considering rectangular, trapezoidal, and inverse trapezoidal legs, where also optimum pulse current is found as a function of the element lengths. It is demonstrated that an improvement of 4.75% in the cooling is possible when using trapezoidal legs compared with conventional rectangular systems. Our presented model is mainly a new alternative in characterizing Peltier supercooling as a function of both pulse current ratio as well as the leg shape.

Analytical Solutions for Side-branch Impedance Producing Spatial Localization of Acoustic Waves in Ducts with Varying Cross Sections

Analytical mathematical models and solutions for spatial localization of acoustic waves through an impedance discontinuity produced by an intermediate damped side branch are studied in stationary media in ducts with varying cross sections. Three specific geometries, namely, with polynomial, sinusoidal, and exponential longitudinal variations, are investigated. The sound fields inside the ducts are modeled by Webster's horn equation. Traveling-wave solutions are obtained by appropriate transformations. The side-branch impedances required for spatial localization (confinement) of traveling and standing waves are found analytically and verified numerically using three-dimensional finite element analysis. The impact of the longitudinal variation of the duct's cross-sectional area (CSA) on the side-branch impedance is examined. It was found that the required side-branch resistance changes more than the reactance with the variation of the duct CSA. A measure of a traveling wave is defined to quantitatively examine the spatial localization of acoustic waves. It was found that the CSA corrections on the side-branch impedances are important. The results of this study reveal the quantitative relationships between the side-branch impedance and the CSA variations for zero reflection from the impedance discontinuity. The mathematical approach presented is potentially helpful for a design of a full anechoic termination and energy localization in duct systems.

INFLUENCE OF RUNNER CROSS-SECTION ON AIR ENTRAPMENT IN PRESSURE DIE CASTS VOLUME

Technology of metal die casting is characterized by production of casts complicated as to shape yet with positive mechanical properties and with high repeatability of production. However, casts are porous to a certain extent which eventually reduces their mechanical properties. One of the significant methods of porosity reduction of casts rests in correct design of a gating system. The submitted paper studies the influence of cross-section area of a runner on air entrapped in the cast volume. Seven alternatives of runners with the identical structural organization and variable cross-section area were compared. In case of a gating system design there was an assumption made that the runner with the largest cross section would deliver the lowest possible velocity to the melt before reaching the runner which would result in the lowest possible values of air entrapment. The air entrapment in the cast volume is evaluated behind the cores which were evaluated as critical points with regards to further processing. The results reached during examination of the melt flowing through runners proved the aforementioned assumption, yet the values of air entrapment in die casts volume did not show remarkable differences. In its final part, the paper clarifies the reached results and recommendations which should be taken into consideration when designing the gating system structure.

Theoretical analysis on the dynamic compressive behavior of cellular solids with non-linear variation in cross-sectional area

The dynamic compressive behavior of foams with a non-linear variation in the cross-sectional area profiles is studied. A theoretical model has been developed based on the one-dimensional shock theory and the rigid, perfectly-plastic, and locking (RPPL) material model, to establish the governing equations of motion of an initially stationary foam struck by a rigid projectile. Both decreasing and increasing cross-sectional area profiles with various power-law exponents are considered. The numerical simulations suggest that the decreasing area profiles, referred to as the convergent foams, exhibit a double-shock mode. In contrast, the foams with an increasing area-profile, referred to as the divergent foams, exhibit a single-shock mode. The theoretical predictions of both the double-shock and the single-shock cases are validated against the finite element simulations. Compared to the foam with a uniform cross-sectional area, the convergent foams transmit lower mean forces at the distal end, and the divergent foams transmit higher forces at higher impact velocities. An interesting phenomenon observed is that the mean force at the distal end decreases with an increase in the impact velocity beyond the densification velocity, for the convergent foams. An expression for the plastic energy dissipated by convergent foams has been derived, and we observe that the convergent foams dissipate less energy than the divergent foams. The performance of the foams has been compared through the dissipation performance parameter, defined as the ratio of non-dimensional plastic energy dissipated at the end of the crushing process to the mean non-dimensional force at the distal end. Convergent foams with low gradients and high power-law exponents have the highest dissipation performance. A special case of a decreasing density-gradient combined with an increasing area-gradient is shown (through finite element simulations) to be beneficial for structural protection.

PARAMETRIC STUDY ON SEISMIC PERFORMANCE OF COLUMN BASE WITH SHEAR TYPE ENERGY DISSIPATION DEVICES

To study the seismic performance of the steel column base with shear type energy dissipation device, the ABAQUS is used to analyze the parameters of nine column base joint models. The results of finite element calculation are compared with the test results to verify the model accuracy. The influences of the variation of cross-sectional area, width-thickness ratio and the axial compression ratio of the column, on the seismic performance of the column base, such as the resistance capacity, initial stiffness, energy dissipation capacity and self-reset capacity, are studied by using effective column base joint model. The results show that the resistance capacity of the column base is less affected by the width-thickness ratio; when the section area of the weakened section of the energy dissipation device increases to 1.1 times, the resistance capacity can be increased by 36%; when the axial compression ratio of the column base becomes 4 times larger, the resistance capacity can be increased by 58%. The results show that the energy dissipation capacity of column base joint is less affected by the axial compression ratio of steel column; when the section area of the weakened section of energy dissipation device becomes about 2.1 times of the original, the energy consumption of column base joint increases about 79%; when the width-thickness ratio of shear type energy dissipation device increases 3.1 times, the energy consumption of column base joint increases nearly 20%. In addition, the residual deformation of the column base has little influence on the width-thickness ratio of the energy dissipation device. When the weakened section area of the column base increases by one time, the residual displacement angle of the column base node increases by 209%; when the axial compression ratio of the steel column increases by two times, the residual displacement angle of the column base decreases by 54%. In conclusion, when the axial compression ratio is constant, the resistance capacity and energy dissipation capacity of the steel column base can be improved by increasing the cross-sectional area of the shear type energy dissipation device or increasing the width-thickness ratio of the shear type energy dissipation device.

Bond properties of steel angles in concrete filled steel tubes

The performance of concrete filled steel tubes (CFSTs) in tensile actions can effectively be improved by inner steel L-profiles embedded in the core concrete. In order to investigate the bond properties between the steel angle and core concrete, 24 pull-out specimens with variable bond length and cross-section area were tested. The results suggest that the peak value of the pull-out load increases with the bond length and the cross-section area when the peak load is reached before yielding and the average bond strength and the average residual strength are not dependent on the two parameters referred to. A formula is proposed to calculate the characteristic pull-out resistance of steel angles embedded in CFSTs, and the bond-slip constitutive relationship is obtained based on the analysis of interfacial bond stress and slipping. Further comparisons with previous studies illustrate that the circumferential constraint provided by the steel tube can effectively increase the residual bond strength and the bond ductility.

Numerical schemes for quasi-1D steady nozzle flows

In this work we construct high-resolution numerical schemes for the calculation of the quasi-1D unsteady flow in pipes with variable cross-sectional area. This is an example of non-homogeneous hyperbolic systems of conservation laws that admit stationary solutions. We use the strategy developed by the authors in [1] which is to transform the non-homogeneous system into homogeneous writing the source term in divergence form, so that it can be incorporated into the flux vector of the homogeneous system and discretized in the same way. As a result, the source terms are automatically discretized to achieve perfect balance with flux terms, obtaining well-balanced schemes that produce very robust and accurate solutions. Concretely, the mentioned strategy will be used to extend the flux limiter technique [2] and the Harten, Lax and van Leer (HLL) Riemann solver [3] to the quasi-1D flow in ducts of variable cross-section. The numerical results confirm the capacity of these methods to construct well-balanced schemes.

Performance comparison of TEGs for diverse variable leg geometry with the same leg volume

The product development process consists of all the steps required to transform a product from concept to market availability. The volume used to make a product is one of the most important factors affecting the final price of a product and has to be taken into account in the design stage. In this context, a study based on the finite element method was carried out using different geometrical shapes of the same volume by considering the five following shapes: rectangle, I-leg, X-leg, trap-leg, and Y-leg. To achieve this, two cases were examined. In the first case, all five shapes of the same volume (47.915 mm3) were studied by considering an identical length of X-leg (6 mm) and the variable cross-sectional area of the hot ceramic junction. The results obtained show that the rectangular leg model generates the highest efficiency and output power with 5.482% and 0.041 W respectively. In the second case, all shapes of identical volume (47.915 mm3) were analyzed by condensing a variable leg length and a fixed cross-sectional area of the hot ceramic junction of X-leg. The results also show that the rectangular leg model generates the highest output power, which is approximately 0.114 W. In addition, in order to optimize the best model found, the length of the legs allowing to obtain the optimal internal resistance and thermal conductivity has been determined. The findings indicate that the rectangular leg model with a leg length of 6 mm gives the best performance.

On the Leakage and Dynamic Force Coefficients of a Novel Stepped Shaft Pocket Damper Seal: Experimental and Numerical Verification

Abstract High-performance turbomachinery favors annular seals with a large damping coefficient to ensure rotor system stability. Pocket damper seals (PDSs), a variation of labyrinth seals with axial blades (ribs) and adding circumferential partition walls (ridges), produce a favorable damping performance. To further enhance the damping characteristic and reduce leakage, a novel stepped shaft PDS is hereby introduced. The invention has a unique arrangement of steps on the rotor surface, each facing an upstream rib in a pocket row. Thus, the step and a blade tip form a tight clearance (c1), while the rotor surface and the downstream blade tip make a larger clearance (c2). The convergence–divergence variation of cross-sectional areas along the flow direction increases the PDS damping coefficient. To validate the performance of the novel design, a stepped shaft PDS (c1/c2 = 0.5) with four axial ribs and eight circumferential pockets is built and tested. A comprehensive investigation, experimental and computational, produces the seal leakage and dynamic force coefficients for the stepped shaft PDS, as well as similar performance characteristics for an identical PDS with a smooth rotor surface (c1/c2 = 1, i.e., a uniform clearance PDS). The stepped shaft PDS operates with air at supply pressure (PS) ranging from 1.1 bar to 3.2 bar. The measured leakage for the stepped shaft PDS is 50% of that for the uniform clearance PDS. Computational fluid dynamics (CFD) and bulk flow model (BFM) predictions of leakage agree well with the test data. For PS = 2.3 bar, the test damping coefficient (C) for the stepped shaft PDS is ~1.5 times greater than the one for the uniform clearance PDS. With an increase in PS to 3.2 bar, the stepped shaft PDS shows a two and one half increase in damping coefficient. In comparison to the test data, a CFD model overestimates C by 29% for operation at PS = 3.2 bar, though capturing the variation trend versus whirl frequency. The BFM largely underpredicts C for the stepped shaft PDS and is abandoned for future work. Both the test data and CFD predictions demonstrate the superior damping performance of the stepped shaft PDS, thus providing a novel alternative seal configuration for turbomachinery usage.

Free high-frequency vibrations of nonlocally elastic beam with varying cross-section area

In the framework of the two-phase theory of nonlocal elasticity we study free high-frequency vibrations of nanobeams with varying cross section. Considering the Helmholtz kernel in the constitutive equation, we reduce the original integro-differential equation to an equivalent six-order differential equation with variable coefficients and derive the pair of additional boundary conditions accounting for the nonlocal edge effects. Applying WKB method, a solution of the boundary-value problem is constructed in the form of superposition of the outer expansion and edge effect integrals with high variability along the beam axis. As an example, a clamped nanobeam with a shape matching to the shape of a slab waveguide in a photonic crystal beam laser is considered. The derived relations for natural frequencies and performed calculations revealed strong effect of both the nonlocal model fraction and the cross-section variability on the correction to natural frequencies calculated within the classical beam theory

Numerical Modelling of Laminar Forced Convection in a Variable Cross-Section Circular Pipe

A study of three dimensional laminar forced convection with conjugated heat transfer for water flowing inside a circular pipe with variable cross-section area has been numerically conducted. The thermal performance and pressure drop under constant heat flux are also estimated. In this paper, using FLUENT ANSYS, the finite volume method (FVM) is used to evaluate the continuity, momentum, and energy governing equations. For a range of Reynolds numbers less than 2000, heat transfer rates were computed, and Prandtl number equal to 3.7. The effects of Reynolds number and divergent angles (ratio) on the convection coefficient of heat transfer (h) drop in pressure (ΔP), and the thermal-hydraulic performance (η) are analyzed and discussed. The results showed that the use of the divergent ratio increases the thermal-hydraulic performance. Compared to the uniform pipe, it is increased by 23% with a maximum pressure drop decrease by about 240% for ratio=1.8. With the empirical Shah equation, the current model is validated, and the results showed excellent agreement.

Direct measurement of the effect of non-submerged rigid vegetation-induced flow cross-section area variations on flow force in compound channel

In this experimental work, flow force in compound channel in presence of non-submerged vegetation was obtained via direct measurement method. The direct measurement method was used to address the inefficiency of the conventional energy-based methods for measuring the force within the body of highly rough flows. On this basis, the study was performed using a specially designed flume called knife-edge flume with a length of 14 m, a width of 1.07 m, and a height of 1.05 m at a stream bed grade of 10-3. The flow force measurements were performed directly using a load cell in absence of the common errors that were otherwise associated with velocity measurement by inserting an external body into the flow. In this study, we examined non-submerged rigid vegetation layers with five different diameters (i.e., 20, 25, 30, 40, and 50 mm), three values of crossline spacing (i.e., 6, 8, and 10 cm), five values of crossline spacing (i.e., 8, 10, 12, 15, and 20 cm), and two different arrangements (i.e., ordered and non-ordered or cruciform) at three different positions (i.e., in the floodplain, in the main channel, and simultaneously in the floodplain and the main channel) by performing a total of 451 tests. The flow force exhibited the highest sensitivity to the increase in vegetation volume under the non-ordered arrangement. In this respect, the improvement in the flow force with increasing the percent volume of vegetation was much larger when the vegetation was arranged in a non-ordered rather than ordered fashion, with the effect of the vegetation been even more pronounced in the floodplain rather than the main channel. In addition, at a certain percent change of the flow force, the trough-vegetation flow velocity was higher under the ordered arrangement rather than the non-ordered arrangement, reflecting the more difficulty encountered by the flow as it passed through the non-ordered vegetation. Based on the analysis results, it was found that the flow force would change by 060% when the vegetation had grown in the floodplain with λ* values in the range of 0–1. In cases where the vegetation had grown in the main channel and simultaneously in the main channel and the floodplain, the flow force variations increased to 10–70% and 20–80% as the λ* changed from 0 to 10, respectively. Analyzing the results of the experiments and the vegetation-modified Reynolds number, a relationship was further presented for calculating the flow force in presence of non-submerged rigid vegetation in a compound channel.

Delay and Power Estimations of Magnetic Tunnel Junction based Random Access Memory and Sense Amplifier Circuit

The paper starts with the principle of operation of magnetic tunnel junctions in magnetoresistive random access memories. The simulation of a sense amplifier circuit made up of magnetic tunnel junctions for application in MRAM array has been presented in this paper. The circuit has been implemented with six different tunnel junctions, simulating the sense amplifier circuit with one tunnel junction at a time, to estimate the power and delay. The effect of variation of cross sectional area of the tunnel junctions on the power consumption and delay time of the sense amplifier circuit has been presented. Out of the six tunnel junctions, it is observed that the sense amplifier circuit with Fe/MgO/Fe magnetic tunnel junction consumes minimal power with impressive delay time estimation. The R & C values used for simulating the circuit have been obtained from the LSDA band structure simulations of the six tunnel junctions.

Numerical method for solving the problem of the gas-dynamic state of a main gas pipeline section relief of a variable cross-sectional area

The paper proposes a numerical method for solving the problem of the gas-dynamic state of a main gas pipeline linear section, which is characterized by a path change in the diameter and leveling height of the pipeline axis. The quasi-one-dimensional equations of gas pipeline transport are derived with account for the local and convective components of the inertia force, the quadratic law of resistance and the force of gravity at a variable cross-sectional area of the pipeline. At the inlet to the section, a time change in hydrostatic pressure is set, and at the outlet from the section a mass rate of gas flow is set. The initial distribution of gas-dynamic indices was taken for a stationary mode of operation. The equations were transformed to the equations of direct and reverse traveling waves presented in dimensionless variables, and approximated by an implicit scheme, taking into account the direction of excitation propagation. The iterative processes were formed by virtue of the nonlinearity of equations and boundary conditions, A calculation program was developed that allowed studying the process dynamics depending on the time change in the inlet pressure and the outlet mass flow rate under a path change in the diameter and leveling height of the pipeline axis. The results of separate calculations on transient processes were presented, when, at the section outlet the mass flow rate increases abruptly, and the pipe diameter has a local increase according to a sinusoidal law.

Studying free hight-frequency vibrations of an inhomogeneous nanorod based on the nonlocal theory of elasticity

Free high-frequency longitudinal vibrations of an inhomogeneous nanosized rod are studied on the basis of the nonlocal theory of elasticity. The upper part of spectrum with the wavelength comparable to the internal characteristic dimension of a nanorod is examined. An equations in the integral form with the Helmholtz kernel, incorporating both local and nonlocal phases, is used as the constitutive one. The original integro-differential equation is reduced to the forth-order differential equation with variable coefficients, the pair of additional boundary conditions being deduced. UsingWKB-method, a solution of the boundaryvalue problem is constructed in the form of the superposition of a main solution and edge effect integrals. As an alternative model, we consider the purely nonlocal (one-phase) differential model which allows estimating the upper part of spectrum of eigen-frequencies. Considering the nanorod with a variable cross-section area, we revealed a fair convergence of eigen-frequencies found in the framework of two models when the local fraction in the two-phase model vanishes.

Влияние деформации проточной части эластомерных элементов самодействующих клапанов на характеристики тихоходных длинноходовых компрессорных ступеней

The results of the study of the influence of changes in the area of the flow section in the seat of selfacting valves with elastomeric elements on the characteristics of low-speed compressor stages are presented. A method of experimental research of low-speed compressor stages with the possibility of obtaining instantaneous parameters of the gas state in the working chamber of the stage and its integral characteristics and an experimental stand for its implementation have been developed. The results of comparative experimental studies have confirmed the effectiveness of the valve design with a variable cross-sectional area of the seat in comparison with known designs — an increase in the feed coefficient and isothermal indicator efficiency is at least 10...15%.