Axisymmetric Tube Research Articles

Mathematical Modelling of the Impact of IR Laser Radiation on an Oncoming Flow of Nanoparticles with Methane

Introduction. The study is devoted to the numerical investigation of laser radiation’s effect on an oncoming two-phase flow of nanoparticles and multicomponent hydrocarbon gases. Under such exposure, the hydrogen content in the products increases, and methane is bound into more complex hydrocarbons on the surface of catalytic nanoparticles and in the gas phase. The hot walls of the tube serve as the primary source of heat for the reactive two-phase medium containing catalytic nanoparticles. Materials and Methods. The main method used is mathematical modelling, which includes the numerical solution of a system of equations for a viscous gas-dust two-phase medium, taking into account chemical reactions and laser radiation. The model accounts for the two-phase gas-dust medium’s multicomponent and multi-temperature nature, ordinary differential equations (ODEs) for the temperature of catalytic nanoparticles, ODEs of chemical kinetics, endothermic effects of radical chain reactions, diffusion of light methyl radicals CH3 and hydrogen atoms H, which initiate methaneconversion, as well as absorption of laser radiation by ethylene and particles. Results. The distributions of parameters characterizing laminar subsonic flows of the gas-dust medium in an axisymmetric tube with chemical reactions have been obtained. It is shown that the absorption of laser radiation by ethylene in the oncoming flow leads to a sharp increase in methane conversion and a predominance of aromatic compounds in the product output. Discussion and Conclusion. Numerical modelling of the dynamics of reactive two-phase media is of interest for the development of theoretical foundations for the processing of methane into valuable products. The results obtained confirm the need for joint use of mathematical modelling and laboratory experiments in the development of new resource-saving and economically viable technologies for natural gas processing.

Benchmark problems for simulating Hyperloop aerodynamics

Hyperloop is proposed as the next generation of sustainable high-speed transport. Recently, an increasing body of literature has been amassed on Hyperloop aerodynamics, however, the vast majority of this work is numerical. Experimentally, there are few relevant studies and none are suitable for validating computational approaches. This paper presents three benchmark cases to provide a framework for computational research and to address this significant gap. Benchmark 1 provides experimental data from existing work on a projectile traveling at Mach 1.1 in ground effect. This incorporates many of the flow characteristics of a Hyperloop system, including (i) transonic Mach numbers, (ii) wall confinement, and (iii) shock formation/reflection. These experimental data are compared to Computational Fluid Dynamics simulations with a very good match seen. Next, Benchmark 2 is proposed which extends these simulations toward a baseline Hyperloop pod design operating in an axisymmetric low-pressure tube environment. This is achieved in stages by adding a full tube, scaling up the domain, reducing the air pressure, and introducing a baseline pod design. It is shown that the enclosed tube environment causes the most significant change in aerodynamic characteristics via flow choking. Nevertheless, a number of aerodynamic similarities remain, compared to Benchmark 1. Finally, Benchmark 3 is proposed to explore the impact of ground clearance of the pod. This aspect has a significant influence on the flow by deflecting the wake and the downstream shock pattern. Furthermore, the drag, downforce, and pitching moment are all found to increase with lower ground clearances.

Numerical investigation of partial cavitation in a Venturi tube by Eulerian-Lagrangian multiscale modelling

The cavitating flow in a Venturi tube has a complex flow structure. In this paper, the partial cavitation in an axisymmetric Venturi tube, dominated by bubbly shock, is investigated by utilizing Eulerian-Lagrangian multiscale modelling. The unsteady partial cavitation is simulated by Large Eddy Simulation coupled with the Volume of Fluid and the Discrete Bubble Model. The numerical results show a well agreement with the high-speed photography. Through a comprehensive analysis of the development and transportation of macro cavities and micro bubbles, a detailed explanation of the cavity shedding process triggered by bubbly shock is provided. The results highlight the precise capability of the multi-scale method in elucidating the intricate flow field induced by partial cavitation. The findings may pave the way for the further investigations on the underlying mechanisms of partial cavitation, fostering a deeper understanding of bubbly shock dominated cavitating flow.

Numerical Study of Forced Nonlinear Acoustic Gas Oscillations in a Tube under the Action of Two Pistons with Phase Shift

Nonlinear acoustic oscillations of large amplitude created in a gas-filled tube under the action of two pistons located at the ends of the pipe are numerically investigated. The pistons oscillate according to the harmonic law at one of the natural frequencies and with different values of phase shift. The movement of the gas is described by mathematical equations of conservation for the main determining relations for the flow, which are estimated by applying the finite volume method based on OpenFOAM package. The non-stationary forced oscillatory motion of a gas inside an axisymmetric tube from a state of rest to a periodic steady motion is investigated. The features of nonlinear acoustic fluctuations of gas in cylindrical duct under the action of two pistons are found. The effect of the phase shift value has a strong effect on the oscillation amplitude of gas, when pistons oscillating at equal natural frequencies, in turn, when the pistons oscillate at different natural frequencies, the effect is very small. In particular, resonant oscillations are detected when the pistons vibrate at the same frequency values equal to odd values of their own higher harmonics in the absence of a phase shift value. In the case when the frequency values are equal to even values of the natural harmonics, resonant oscillations occur when the pistons move in anti-phase. The numerical method appears to work well and would be hoped for practical computations of different resonators.

A Study of Anchor Cable and C-Shaped Tube Support for the Roadway of Shuangliu Coal Mine

Active support using highly prestressed cable bolts and anchor cables has become a mainstream support technology for coal mine roadways. However, the ability of bolts and anchor cables to withstand transverse shear decreases with the prestress level, jeopardizing mining safety. This study proposed a technical solution to this problem featuring anchor cables enclosed in an axisymmetrical tube with a C-shaped cross-section (ACC), which are highly prestressed and can withstand high transverse shear. The ACC mechanical performance was tested in the #318 gas extraction roadway of the Shuangliu Coal Mine, China, characterized by extensive deformation under original support conditions. Theoretical analysis, laboratory tests, numerical simulation, and field tests were performed to analyze the shear mechanical properties of the ACC and anchor cables alone. The double shear test results revealed that the proposed ACC scheme increased the transverse shear resistance and stiffness by 10–25% and 20–40%, respectively. The FLAC3D numerical simulation showed that the roof-and-floor and rib-to-rib convergences decreased by 9.53 and 25.11%, respectively. The area of the stress concentration zone also decreased. Field monitoring showed that the ACC achieved good support performance. During the monitoring period, the maximum roof-and-floor and rib-to-rib displacements were 40 and 49 mm, respectively. The ACC scheme offered adequate shear resistance and effectively controlled surrounding rock deformation in the gas extraction roadway under study, making it applicable to similar engineering scenarios.

Experimental and Numerical Study of Pulse Detonation Engine with Ethylene as a Fuel

This paper presents an insight on the study of transient, compressible, intermittent pulsed detonation engine with one-step overall reaction model to reduce the computational complexity in detonation simulations. Investigations are done on flow field conditions developing inside the tube with the usage of irreversible one-step chemical reactions for detonations. In the present simulations one and two-dimensional axisymmetric tubes are considered for the investigation. Studies are also performed with different grid sizes which influence the prediction of Von-Neumann spike, CJ Pressure and detonation velocity. Numerical studies are conducted using 66mm diameter tube and compared with the literature values. The simulation result from the single-step reaction model agrees well with the previous published literature of multi-step reaction models. The present studies shows that one-step overall reaction model is sufficient to predict the flow properties with reasonable accuracy. Experiments are conducted in a 25mm dia. tube with Ethylene/Air mixtures. The reactants are premixed and injected into the detonation tube using solenoid valves. The equivalence ratio of the fuel/oxidizer mixture and the length of the detonation tube are varied to understand their effects on detonation parameters. Finally the results from the present numerical study are compared and validated using NASA CEA and experiments.

Bandwidths of vocal tract resonances in physical models compared to transmission-line simulations.

This study investigated how the bandwidths of resonances simulated by transmission-line models of the vocal tract compare to bandwidths measured from physical three-dimensional printed vowel resonators. Three types of physical resonators were examined: models with realistic vocal tract shapes based on Magnetic Resonance Imaging (MRI) data, straight axisymmetric tubes with varying cross-sectional areas, and two-tube approximations of the vocal tract with notched lips. All physical models had hard walls and closed glottis so the main loss mechanisms contributing to the bandwidths were sound radiation, viscosity, and heat conduction. These losses were accordingly included in the simulations, in two variants: A coarse approximation of the losses with frequency-independent lumped elements, and a detailed, theoretically more precise loss model. Across the examined frequency range from 0 to 5 kHz, the resonance bandwidths increased systematically from the simulations with the coarse loss model to the simulations with the detailed loss model, to the tube-shaped physical resonators, and to the MRI-based resonators. This indicates that the simulated losses, especially the commonly used approximations, underestimate the real losses in physical resonators. Hence, more realistic acoustic simulations of the vocal tract require improved models for viscous and radiation losses.

Stability of the aneurysm-type solution in a membrane tube with localized wall thinning filled with a fluid with a non-constant velocity profile

We perform the stability analysis of bulging localized structures on the wall of a fluid-filled axisymmetric membrane elastic tube. The wall of the tube is assumed to be subjected to localized thinning. The problem has no translational invariance anymore, hence the stability of a bulging wave centered in the point of the localization of imperfection is usual, and not orbital stability up to a shift as in the case of translationally invariant governing equations. Motionless wave solutions of the governing equations having the form of a localized bulging are called throughout the paper aneurysm solutions. We assume that the fluid is subjected to the power law for viscous friction of a non-Newtonian fluid, and also that the viscosity of the fluid does not play a significant role and it can be neglected. The velocity profile remains not constant along the cross section of the tube (even in the absence of the viscosity) because no-slip boundary conditions are performed on the tube walls. Stability is established by demonstrating the non-existence of the unstable eigenvalues with a positive real part of the linearized problem. This is achieved by constructing the Evans function depending only on the spectral parameter, analytic in the right half of the complex plane Ω+ and which zeroes in Ω+ coincide with the unstable eigenvalues of the problem. The non-existence of zeroes of the Evans function is performed using the argument principle from the analysis of complex variable. Finally, we discuss the possibility of applying of the results of the present analysis to the aneurysm formation in damaged human vessels under the action of the internal pressure.

Unsteady stretching of a glass tube with internal channel pressurization

Mathematical modeling is used to examine the unsteady problem of heating and pulling an axisymmetric cylindrical glass tube with an over-pressure applied within the tube to form tapers with a near uniform bore and small wall thickness at the tip. To allow for the dependence of viscosity on temperature, a prescribed axially varying viscosity is assumed. Our motivation is the manufacture of emitter tips for mass spectrometry which provide a continuous fluid flow and do not become blocked. We demonstrate, for the first time, the feasibility of producing such emitters by this process and examine the influence of the process parameters, in particular the pulling force and over-pressure, on the geometry. There is not a unique force and over-pressure combination to achieve the desired geometry at the tip but smaller over-pressure (hence force) yields a more uniform bore over the entire length of the emitter than does a larger over-pressure (and force). However, the sensitivity of the geometry to small fluctuations in the parameters increases as the over-pressure decreases. The best parameters depend on the accuracy of the puller used to manufacture the tapers and the permissible tolerances on the geometry. The model has wider application to the manufacture of other devices.

A meshless solution of the compressible viscous flow in axisymmetric tubes with varying cross-sections

The meshless Diffuse Approximate Method (DAM) is for the first time formulated and applied to simulate the compressible Newtonian flow of an ideal gas in an axisymmetric tube with varying cross-sections. The problem is structured by coupled partial differential equations for conservation of mass, momentum and energy, and the equation of state closure. These equations are solved in primitive variables and strong form. DAM is formulated on irregular node arrangement by using the second and third-order polynomial shape functions and Gaussian weights, leading to weighted least squares approximation on overlapping local subdomains. Pressure-velocity coupling is performed by the Pressure Implicit with Splitting of Operators (PISO) scheme. The solution of the represented novel application of DAM is verified by matching the meshless results with the fine-mesh finite-volume method results. The characteristics of meshless DAM for this kind of problem are systematically assessed by a detailed investigation of the varying node density, shape function order, Gaussian weight's shape, and the number of nodes in a local subdomain. The sensitivity study of DAM parameters shows that for the tested problems, the most suitable values of the Gaussian weight function and the number of nodes in a local subdomain are 5.0 and 13, respectively. Third-order convergence rate with better results is observed while using third-order polynomial shape functions.

Bubbles in capillaries: Relaxing traditional assumptions

<h2>Abstract</h2> The dynamics of long gas bubbles and thin liquid films in confined channels is a classical problem in fluid mechanics and has been studied extensively under the assumptions of two-dimensional (Hele-Shaw cells or axisymmetric tubes) geometries, very viscous flows, negligible inertial and gravitational effects, and isothermal conditions. However, recent engineering applications such as microfluidics, where channels present angular cross-sections, or two-phase cooling via microchannel flow boiling, where low-viscosity fluids are utilised, require relaxation of these assumptions to deliver robust design principles. This work presents new insights into bubbles and thin films dynamics that emerge when studying this flow in unconventional settings. When bubbles propagate in noncircular capillaries, liquid films are much thinner than what observed in pipes and cross-stream film drainage induces a monotonic film thinning towards the bubble rear. Inertial forces cause the appearance of undulations at the bubble rear, which are described well by augmenting the traditional lubrication theory. Gravitational forces are impactful already when the Bond number is much smaller than unity, despite Bo<1 being a popular criterion to disregard the impact of gravity. Finally, these insights are exploited to explain heat transfer trends emerging from numerical simulations of flow boiling in microchannels for thermal management applications.

The effect of inlet pressure distortion on the performance of an axisymmetric compact tube heat exchanger with radial counter flow type for hypersonic pre-cooled aero-engine

The effect of inlet pressure distortion on the performance of an axisymmetric compact tube heat exchanger with radial counter flow type for hypersonic pre-cooled aero-engine

CFD simulation of an integrated PCM-based thermal energy storage within a nuclear power plant connected to a grid with constant or variable power demand

The current numerical study investigates the integration of a phase change material (PCM)-based thermal energy storage (TES) system within a nuclear power plant (NPP) to enhance the capability of such proposed plant to better follow the variations of power grid demand especially in countries with a high share of nuclear in their energy mix. This study focuses on the transient behavior of the PCM during the simultaneous charging and discharging (SCD) operation mode during one day. For this, an enthalpy-porosity method is used to simulate the SCD operation mode of PCM within an axisymmetric vertical triplex tube. Hot and cold heat transfer fluids (HTFs) are simultaneously co-circulating within the TES for downward-inner heating and upward-outer cooling. Constant and variable loads are considered to study the load-following ability of the coupled system. During the SCD mode with a constant load, results show that an equilibrium between melting and solidification (charging and discharging) is established and the liquid fraction (20%) is not changing with time. Under the variable load, the suggested TES system is able to follow the daily variation of the grid demand and, hence, fill the gap between reactor supplied energy and grid power demand with the reactor constantly operated at full rated capacity. During the variable load, the liquid fraction within PCM is altering from solid to liquid phases and vice versa depending on the deviations of the grid as expected.

Hydrothermal analysis of non-Newtonian fluid flow (blood) through the circular tube under prescribed non-uniform wall heat flux

The present article aims to investigate the Graetz-Nusselt problem for blood as a non-Newtonian fluid obeying the power-law constitutive equation and flowing inside the axisymmetric tube subjected to non-uniform surface heat flux. After the flow field is determined by solving the continuity and the momentum equations, the energy equation is handled by employing the separation of variables method. The resulting Eigen functions and Eigen values are numerically calculated using MATLAB built-in solver BVP4C. The analysis is first conducted for the situation of constant heat flux and subsequently generalized to apply to the case of sinusoidal variation of wall heat flux along the tube length, using Duhamel's Theorem. Furthermore, an approximate analytic solution is determined, employing an integral approach to solve the boundary layer equations. With respect to the comparison, the results of approximate solution display acceptable congruence with those of exact solution with an average error of 7.4%. Interestingly, with decreasing the power-law index, the discrepancy between the two presented methods significantly reduces. Eventually, the influences of the controlling parameters such as surface heat flux and power-law index on the non-Newtonian fluid flow's thermal characteristics and structure are elaborately discussed. It is found that switching from constant wall heat flux to non-uniform wall heat flux that sinusoidally varies along the tube length significantly improves the simulation's accuracy due to the better characterization of the heat transport phenomenon in non-Newtonian fluid flow through the tube. In the presence of sinusoidally varying wall heat flux with an amplitude of 200 W/m2and when the power-law index is 0.25, the maximum arterial wall temperature is found to be about 311.56 K.

Bursting on a vortex tube with initial axial core-size perturbations

Axisymmetric rectilinear vortex tubes develop twist waves if their core size varies along the centerline. These twist waves propagate, and when two opposite-signed twist waves meet their interaction leads to vortex bursting. We perform numerical simulations of vortex tubes with a range of initial core-size perturbation amplitudes, and provide a detailed analysis of the bursting dynamics. Our results explain the main mechanisms driving and subsequently arresting the bursting process; quantify the accelerated energy dissipation due to bursting; and show that bursting is susceptible to non-axisymmetric instabilities that further accelerate the decay of the vortex tube.

Thermal entrance problem for blood flow inside an axisymmetric tube: The classical Graetz problem extended for Quemada's bio-rheological fluid with axial conduction.

The heat-conducting nature of blood is critical in the human circulatory system and features also in important thermal regulation and blood processing systems in biomedicine. Motivated by these applications, in the present investigation, the classical Graetz problem in heat transfer is extended to the case of a bio-rheological fluid model. The Quemada bio-rheological fluid model is selected since it has been shown to be accurate in mimicking physiological flows (blood) at different shear rates and hematocrits. The steady two-dimensional energy equation without viscous dissipation in stationary regime is tackled via a separation of variables approach for the isothermal wall temperature case. Following the introduction of transformation variables, the ensuing dimensionless boundary value problem is solved numerically via MATLAB based algorithm known as bvp5c (a finite difference code that implements the four-stage Lobatto IIIa collocation formula). Numerical validation is also presented against two analytical approaches namely, series solutions and Kummer function techniques. Axial conduction in terms of Péclet number is also considered. Typical values of Reynolds number and Prandtl number are used to categorize the vascular regions. The graphical representation of mean temperature, temperature gradient, and Nusselt numbers along with detail discussions are presented for the effects of Quemada non-Newtonian parameters and Péclet number. The current analysis may also have potential applications for the development of microfluidic and biofluidic devices particularly which are used in the diagnosis of diseases in addition to blood oxygenation technologies.

Experiment on flow dynamics and cavitation structure in an axisymmetric venturi tube based on x-t diagrams and proper orthogonal decomposition

The shedding mechanisms of unsteady cavitation flow in venturi tubes are key problems in the study of cavitation flow, and cavitation dynamics in different venturi tubes differs owing to the difference of operating conditions and geometric parameters, so different results still exist among academics. In this paper, the flow dynamics and cavitation structure induced by shedding of sheet/cloud cavitation in an axisymmetric venturi tube under different flow conditions were investigated experimentally by combining x-t diagrams and the proper orthogonal decomposition (POD) method. The cavitation dynamic shows that the combination of shock waves and re-entrant flow resulted in the shedding and collapse of the sheet/cloud cavitation in the tested venturi tube. Furthermore, the characteristic cavity length, shedding frequency are analyzed under different operating conditions. The relationships for predicting two typical cavity lengths Lt* and Lc* was proposed, and the transition cavitation number for Lt* and Lc* was constant (σc = 0.54). Finally, the feature information of the sheet/cloud cavitation flow and POD modes were extracted through proper orthogonal decomposition (POD) analysis, reducing the dimensionality of the complex process. The coherent structure of sheet cavitation, transition region and cloud cavitation and the characteristics of these structures with displacement versus period time were illustrated, and the irregular perturbation process of the microstructure induced by the periodic shedding of cavitation clouds was demonstrated. In summary, the shedding mechanisms of sheet/cloud cavitation and coherent cavitation structure in venturi are greatly clarified through this research, and the findings provide theoretical guidance for the application of venturi tubes from the perspective of cavitation prevention and utilization.

Flow Nonuniformities Behind Accelerating and Decelerating Shock Waves in Shock Tubes

Shock tubes are used to investigate the chemical kinetics and radiative properties of gasses. Analyses of the flow conditions produced in shock tubes typically assume a single, constant shock speed even though the shock speed varies due to driver effects, boundary-layer growth, and diaphragm rupture effects. This paper will investigate the dependence of flow properties upon the entire shock speed history for a 100-mm-diam, 8-m-long shock tube using the FROSST axisymmetric shock tube Navier–Stokes code. A perfect gas is applied to remove the complexity of thermochemistry and allow a focus upon the flow details. Shock speed profiles ranging from accelerating to decelerating are simulated to qualitatively represent different experimental conditions, and the resulting test slugs compared. All shocks reach the test section at the same final shock Mach number of 6.53. Pressure variations caused by the accelerating shock are found to combine with entropy gradients introduced by the changing shock strength, yielding differences in maximum temperature of the test slug by as much as 56%, and differences in maximum pressure as high as 22% despite the shared tube-end Mach number. Local temperature and pressure around gas packets in the test slug are found to relax significantly through time in response to changing postshock conditions. Test slug variations due to boundary-layer effects are found to be present, but overwhelmed by the relaxation processes under many conditions.

MATHEMATICAL ANALYSIS OF VISCOSITY AND REABSORPTION ON URINE FLOW THROUGH A STRAIGHT NARROW TUBE

This study investigates the effect of variable viscosity (exponential and linear) and constant reabsorption for the urine flow through a narrow tube. The inertial free flow of viscous fluid has been governed by the momentum and mass conservation through the cross-section of axisymmetric tube. The governing partial differential equations have been simplified with the help of stream function and stress components with exponential and linear variable viscosity. The resulting partial differential equations have been solved by the inverse method and give the explicit expressions for velocity, pressure, shear stress, flux and leakage of flow. It has been observed that flow in transverse direction increases with the increase in reabsorption velocity at wall, whereas horizontal flow, shear stress and volume flow rate become slow with the increase in uniform reabsorption velocity. Effect of viscosity is significant near the walls of tube because the axial velocity accelerates by increasing viscosity parameter due to the pressure gradient near the center of tube but it decelerates near the walls of tube due to surface friction. Also, the special case of variable viscosity is discussed by assuming the linear type of viscosity. The derived data for the velocity and flow rate have been used to measure the fractional reabsorption in proximal tube with varying viscosity near the wall.

Numerical Simulation of Shock Tubes Using Shock Tracking in an Overset Formulation

An axisymmetric viscous shock tube simulation code is developed that keeps the shock and the contact discontinuity stationary in suitably constructed moving frames of reference. The flowfield around the discontinuities is represented on fine grids that move with the frames attached to the waves. These moving grids are overset upon a coarse background grid of the entire facility, allowing efficient computation of the main discontinuities as they traverse the tube. Focus is placed upon accurate capture of the influence of wave speeds and viscous effects upon the shock and contact discontinuity as they traverse the tube. The code is extensively validated against experiments ranging from Mach 1.6 to 2.7 in a 26.8-mm-diameter shock tube with argon driver/driven gases and an initial pressure of 66.66 Pa. Agreement within 2% is seen in velocity throughout the tube’s length. Test times are predicted to within 6% across a broad range of test conditions. Unsteady diaphragm opening effects as well as turbulent transition are demonstrated to substantially influence experimental results of the well-known experiments of Duff (“Shock-Tube Performance at Low Initial Pressure,” Physics of Fluids, Vol. 2, No. 2, 1959, pp. 207–216).