Conical Duct Research Articles

Flow separation in a diverging conical duct: Effect of Reynolds number and divergence angle

Fluid flows in passages whose cross-sectional area increases in the streamwise direction are prone to separation. Here, the flow in a conical diffuser fed by a fully developed velocity at its inlet and mated at its downstream end to a long circular pipe is investigated by means of numerical simulation. A universal flow-regime model was used to accommodate possible laminarization of flows having moderate-turbulent and transitional Reynolds numbers at the diffuser inlet. It was found that flow separation occurred for a diffuser expansion angle of 5° for inlet Reynolds numbers less than about 2000. This finding invalidates a prior rule-of-thumb that flow separation first occurs at a divergence angle of seven degrees. Results from the 10 and 30° simulations showed separation at all investigated Reynolds numbers. The largest streamwise length of the separation zones occurred at the lower Reynolds numbers.

On the one-dimensional acoustic propagation in conical ducts with stationary mean flow

This paper proposes a direct time-domain calculation of the time-domain responses of anechoic conical tubes with steady weak mean flow. The starting point is the approximated linear one-dimensional wave equation governing the velocity potential for the case of steady flow with low Mach number. A traveling solution with general space-dependent propagation velocity is then proposed from which the inward and outward pressure and velocity impulse responses can be obtained. The results include the well-known responses of conical and cylindrical ducts with zero mean flow.

Magnetic booster fast ignition macron accelerator

A new fast ignition scheme was recently proposed where the ignition is done by the impact of a small solid projectile accelerated to velocities in excess of 108cm∕s, with the acceleration done in two steps: first, by laser ablation of a flyer plate, and second by injecting the flyer plate into a conical duct. The two principal difficulties of this scheme are as follows: first, the required large mass ratio for the laser ablation rocket propelled flyer plate, and second, the Rayleigh-Taylor instability of the flyer plate during its implosive compression in the conical duct. To overcome these difficulties, it is suggested to accelerate a projectile by a magnetic fusion booster stage, made up of a dense, wall-confined magnetized plasma brought to thermonuclear temperatures. After ignition, this plasma undergoes a thermonuclear excursion greatly increasing its pressure, resulting in the explosion of a weakened segment of the wall, with the segment becoming a fast moving projectile. The maximum velocity this projectile can reach is the velocity of sound of the booster stage plasma, which at a temperature of 108K is of the order 108cm∕s.

A semi-implicit conservation element–solution element method for chemical species transport simulation to tapered ducts of internal combustion engine

In order to obtain a reliable numerical solution, with low computational cost, for a differential equation system modelling the unsteady flow with chemical species tracking in tapered ducts of reciprocating internal combustion engine, three characteristics of numerical resolution schemes have to be considered. Firstly, the scheme must show a total variation decreasing (TVD) behavior, also the internal calculations have to be simple and finally, the mass conservation property of each species has to be carried out. With these requirements, a semi-implicit numerical method based in the conservation element–solution element (CE–SE) method is presented. This method helps to obtain a solution where the mass conservation property of each species is improved in relation to the CE–SE method. This last improvement is studied in several real examples with two species in conical ducts.

An iterative method to obtain analytical-numerical approximation of the one-dimensional gas flow transport solution in conical ducts

In this paper, an analytica-numerical approximation of the one-dimensional gas flow Euler equations in conical ducts, is obtained by an iterative method based on the Cauchy-Kovalev-skaya theorem. This method has been applied in [1] for the constant ducts case. In this paper, the algorithm and the theoretical results are adapted and some examples for different types of ducts are presented.

Comparison between Monte Carlo and analytical calculation of Clausing functions of cylindrical and conical tubes

In a previous work (J. Vac. Sci. Technol. A 21 (2003) 1452), we calculated the transmission probabilities for cylindrical and conical ducts, solving numerically the Clausing integral equation and integrating the resulting Clausing function. It is also important to obtain the Clausing function itself, because it is proportional to the distribution of molecular collisions with the walls of the system, as we show in this contribution. Besides, the density profile of the gas inside the duct can be calculated using the Clausing function, as shown by Davies and Lucas (J. Phys. D: Appl. Phys. 16 (1983) 1). We have calculated the Clausing functions for different cylindrical and conical ducts using a Monte Carlo simulation method and we have compared these results to the numerical ones, finding a very good agreement, within statistical uncertainties.

Percutaneous angiography of Patent Ductus Arteriosus in dogs: techniques, results and implications for intravascular occlusion

Objectives To evaluate the percutaneous angiography and the morphology of patent ductus arteriosus (PDA) in dogs. Background In contrast to surgical ligation the knowledge of angiographic morphology is necessary for intravascular PDA occlusion. Methods Forty-nine dogs with a left to right shunting PDA were included in a three-year, prospective study. In 43 dogs with a body weight ≥ 3.0 kg a percutaneous approach to brachial artery was tested. In six miniature dogs (< 3.0 kg) placement of angiographic catheter from femoral vein antegrade through the PDA was studied. Angiographic morphology and dimensions of PDA were analyzed. Results Percutaneous approach to brachial artery was performed successfully in 41/43 (95%) dogs, in the remaining 2 dogs this approach was not possible and the femoral artery had to be used. Two dogs did not survive the procedure. Arterial bleeding was not a problem in any of the 39 cases in which percutaneous brachial artery catheterization was performed. Two dogs developed transient radial nerve paralysis that resolved 4 to 6 days later. The transvenous technique was successful in all 6 small dogs. In 39 dogs there was an elongated conical duct (type E). A conical duct (type A) was found in nine dogs and one dog had a PDA with two constrictions (type D). The mean PDA minimal diameter was 3.78 ± 1.55 mm (range 1.5 to 6.9), in 20/49 dogs (41%) the minimal PDA diameter measured more than 4.0 mm. Conclusions Percutaneous catheterization of the brachial artery using a vascular introducer is feasible and entails minimal risk of hemorrhage. Angiographic evaluation of the ductus arteriosus is easily performed with this technique, but coilimplantation is not possible by this approach. The frequency of PDA-types is different in dogs and humans and the PDA minimal diameter is larger in dogs.

Comparison between Monte Carlo and analytical calculation of the conductance of cylindrical and conical tubes

The accurate calculation of transmission probabilities of ducts in the molecular flow regime has become a need of vacuum standards on the ultrahigh vacuum region. The usual approach is to simulate a molecular flow of molecules with a Monte Carlo method, because of the difficulties that arise trying to find a solution of the Clausing integral equation in a system of a given geometry. As modern computers increase their speed, the accuracy of Monte Carlo methods is getting higher. It is therefore important to compare simulation results with data obtained by other methods to check that pseudorandom numbers generated are uniformly distributed and not correlated. We have applied both a Monte Carlo method and numerical methods to solve the Clausing integral equation for cylindrical and conical tubes. Both Monte Carlo and numerical methods are consistent within estimated uncertainties. In the case of conical ducts, we obtain values which agree very well with values found in the literature and with uncertainties several orders of magnitude smaller. In the case of cylinders, very accurate transmission probabilities are obtained solving numerically the Clausing integral equation. Comparing with other values found in the literature using a variational method, our values are near the upper bound and quite far away from the lower bound.

Convergent-Flow-Derived Waveriders

Results are presented of a study on the aerodynamics of a new type of waverider derived from supersonic axisymmetric e ows inside constricting ducts, specie cally conical trumpet ducts. In such a duct, an initial shock wave arises from its leading edge, and the compression e ow downstream of this shock has streamlines converging toward the e ow axis. This e ow is chosen as a basic e ow for the waverider design. The simplest convergent-e owderived waveriders are constructed with a lifting surface with a transverse-concave arc-shaped contour. They are compared with known types of waveriders constructed based on uniform e ows behind plane oblique shock waves or divergent e ows behind axisymmetric conical shock waves. The characteristics of convergent waveriders as lifting cone gurations are analyzed with the lift and drag coefe cients, the lift-to-drag ratio, and the integral heat e uxes through the waverider surfaces determined. The possibilities of using these new waveriders as forebodies for hypersonic vehicles powered by airbreathing engines are also estimated. The e owe eld characteristics near the lower lifting surface of the waverider as a precompression surface arranged upstream of the inlet are considered in this connection.

Sound propagation in a conical duct with flow

The variations of acoustical exergy and acoustical mass velocity are used for a description of three-dimensional sound propagation in quasi one-dimensional moving medium in a conical duct of a different cross-sectional shape. Solution for the sound propagation in this system is represented by the solution for a matched slightly deformed conical waveguide without flow (reciprocity part of the propagation) corrected by nonreciprocity time delay that takes into account convection of the sound by flow. Equivalent circuit for a sound propagation in a conical duct is represented by two successive separate elements: reciprocity one, which describes a sound propagation in the matched waveguide, and a nonreciprocity part represented by the element of nonreciprocity delay. For the particular dependencies of the cross-sectional area against duct axis, the solution for propagating sound is found as two propagated noninteracted advancing and backward waves. The Green’s functions and equivalent circuits for internal and external sound excitations are found as their decomposition by the eigenmodes of the matched waveguide.

Modern methods for attenuation in ductwork and silencers

Silencers in power plant ductwork should find a good compromise between the (generally rather high) needed sound transmission loss and the static flow pressure loss induced by them. The annual costs of the electric power consumption created by a silencer may exceed the costs of investment. Modern design possibilities will be displayed. All of them can be computed with the instrument of mode analysis. On the classical background, that attenuation is concentrated in broadband silencers with straight, homogeneous linings, the following improvements will be illustrated with examples. First, because a broadband silencer needs thick linings for low frequencies and small free duct width for high frequencies, both increasing the static pressure loss, subdivide the silencer in sections for different frequency subbands, with stepping lining thicknesses and duct widths. It will be indicated how such steps can be computed Second, insert the necks of Helmholtz resonators between lining sections designed for medium and high frequencies. The resonator volumes are behind the lining sections. The increase in silencer length is very small; the increase in thickness is small, because the main extension of the resonator volumes is in the duct direction. Such resonators may be designed for an efficient low-frequency additional attenuation. Third, duct elbows with their static pressure losses exist anyhow in most ductworks. They can be designed as very efficient high-frequency silencers, thus permitting to avoid the narrow lining spacings in the silencer. Criteria for good corner silencers will be illustrated. Fourth, most silencers in a ductwork begin and end with a conical duct transition. If they are rigid, their combined effects are small. If, however, they are suitably lined, they can produce remarkable additional attenuation.

MODES IN LINED WEDGE-SHAPED DUCTS

The computation of sound fields in wedge-shaped spaces with an absorbing boundary (the seabed) is a classical problem of underwater acoustics, covered by a large number of publications. All known solutions are approximations which are restricted to very small wedge angles θ0, typically less than 3°. In underwater acoustics it is further assumed thatk0r⪢1. The background of the present paper is the performance of lined conical duct sections in silencers. There the wedge angle can attain values around 45°, and the assumptionk0r⪢1 cannot be made. The absorber of the lined boundary here is supposed to be locally reacting (for reasons of simplicity); it can be characterized by a normalized surface admittanceG0. The problems of the analysis arise from the fact, that the fundamental field solutions (modes) can no longer be separated in the cylindrical co-ordinatesr, θ if a boundary is absorbing. This paper describes analytical solutions for the construction of modes in lined wedge-shaped ducts; they can be applied for wedge angles up to about 15° (a subsequent paper will describe a method for angles up to about 45° but only moderatek0rvalues). In the solutions, use is made of “fictitious modes”, which satisfy the boundary conditions and solve a part of the wave equation. They must be completed by a “modal rest” to satisfy approximately the full wave equation. In the first solution, the rest is synthesized by fictitious modes; in the second solution, a separate function is introduced for the rest. Modes for typical underwater acoustics conditions will arise as side products.

Venturi Tubes: Acoustic Attenuation With Flow Loss Considerations

The acoustic wave attenuation performance of Venturi tubes with zero mean fluid flow is investigated by: (1) combining analytical solutions for one-dimensional wave propagation in conical reducers, diffusers, and straight ducts; (2) employing a computational time-domain technique; and (3) conducting experiments in an extended impedance tube setup with four fabricated Venturi tubes and matching contraction chambers. The results from both analytical and computational approaches compare well with each other and the experimental data. The numerical technique is also applied to address the effects of a compressible mean flow on the acoustic behavior. Finally, the flow performance of the fabricated Venturi tubes is measured and the trade-offs are discussed between flow efficiency and acoustic performance.

Supersonic flow of hydrogen and air in a duct with variable area

A chemically nonequilibrium supersonic flow of hydrogen and air has been investigated in a duct with conically divergent or convergent walls. Elementary reaction schemes of radicals involved in reaction of hydrogen-air have been considered and solved through the CHEMKIN code. The aim was to promote an understanding of characteristics of chemically nonequilibrium supersonic flow by introducing a simple mathematical formulation. The temperature, pressure, and density all were found to decrease for divergent ducts as the flow was accelerated, whereas they increased for a slightly convergent duct or a constant cross-sectional area duct. For the divergent nozzle with a greater degree the flow became chemically frozen. But it was quite necessary to take account of the effect of chemical nonequilibrium in a moderately expanded or all convergent conical ducts. As was expected, it was found that the temperature, pressure and Mach number were reduced for a fuel-lean mixture.

Computation of axisymmetric confined jets in a diffuser

AbstractThe paper reports on a numerical study of turbulent confined jets in a conical duct with a 5° divergence. The flow has a large ratio of jet to ambient velocities at the entrance so that it gives rise to strong recirculation. The calculations are carried out with a general finite volume method designed for calculating incompressible elliptic flows with complex boundaries. Turbulence is simulated by the standard κ–ϵ model. The sensitivity of the solution to numerical discretization errors is examined using three convection schemes, i.e. hybrid central/upwind differencing, QUICK and SOUCUP, on two grids consisting of 68 × 50 and 102 × 82 points respectively. An examination is also made of the influence of inlet boundary conditions on the predicted flow field. The computed results are compared with experimental data for mean axial velocity, turbulent shear stress and turbulent kinetic energy profiles. It is shown that the calculations reproduce the essential features of the flow observed in the experiments.

Transfer matrix modeling of hyperbolic and parabolic ducts with incompressible mean flow

A general differential equation for the propagation of sound in a variable area duct or nozzle carrying incompressible mean flow (of low Mach number) is derived and solved for hyperbolic and parabolic shapes. Expressions for the state variables of acoustic pressure and acoustic mass velocity of the shapes are derived. Self-consistent expressions for the four-pole parameters are developed. The conical, exponential, catenoidal, sine, and cosine ducts are shown to be special cases of hyperbolic ducts. Finally, it is shown that if the mean flow in computing the transmission loss of the mufflers involving hyperbolic and parabolic shapes was not neglected, little practical benefit would be derived.

A comment on ‘‘Conical bores. Part I: Reflection functions associated with discontinuities’’ [J. Acoust. Soc. Am. 84, 1613–1619 (1988)] and ‘‘Alternatives to the impulse response h(t) to describe the acoustical behavior of conical ducts’’ [J. Acoust. Soc. Am. 84, 1606–1612 (1988)

According to J. Martínez and J. Agulló [J. Acoust. Soc. Am. 84, 1613–1619 (1988)] and Agulló et al. [J. Acoust. Soc. Am. 84, 1606–1612 (1988)], reflection functions and modified impulse responses can always be obtained from the corresponding frequency‐domain functions through a Fourier transform. The following letter is a revision of that conclusion.

The Sampling of Ions from an Atmospheric‐Pressure Flame into a Vacuum Chamber

AbstractOne atmospheric‐pressure flame of H2 + O2 + N2 has been burnt with a final temperature of 2400 K. Small amounts of caesium were added to the burner supplies, which resulted in free electrons and Cs−+ ions being formed in the flame. The burnt gases were continuously sampled through a tiny (diam. 80 ‐ 200 μm) orifice at the tip of a hollow conical nozzle. Subsequently the gases pass inside the nozzle and down a conical expansion duct into a vacuum chamber. A pointed needle is located axially inside the hollow sampling nozzle and collects either the positively or negatively charged species which had passed through the inlet hole to the vacuum chamber. It was found that, for optimal sampling of negative ions, the sampling nozzle should be at a positive potential with respect to the burner. However, the sampling of positive ions from a flame is best achieved when the burner and nozzle are at the same potential. The effect of varying the inlet orifice's diameter is also investigated. All the observations can be explained in terms of there being either an ion or an electron sheath adjacent to the sampling nozzle. Moreover, the thickness of such a sheath varies inversely with the square root of the electron density in the flame. One important conclusion is that when the electron concentration is low, it is usually impossible for electrons to pass through the inlet hole; instead they are collected by the sampling nozzle. However, for large electron densities (∼ 10−10/ml) and a big orifice, electrons can pass through the sampling hole into the vacuum chamber. By contrast the losses of positive or negative ions, whether atomic or molecular, are almost negligible.

Flow field due to a row of vortex and source lines spanning a conical annular duct

Analytical expressions are derived for the incompressible flow due to a row of vortex and source lines spanning a duct whose walls are coaxial conical surfaces of revolution with a common vertex. The singularity lines have the shape of an arc of circle meeting the walls perpendicularly, and are defined by the intersection of a spherical surface with a series of equally spaced meridional planes. Although source lines of spanwisely varying strength are in general assumed, only vortex lines of constant circulation are considered. Simpler expressions are derived for the limiting two-dimensional cases when the flow is axisymmetric (actuator disc), and when the angular distance between the conical walls becomes vanishingly small. The expressions for the latter case are used in an example to obtain numerical results by a panel method for the velocity distribution of the flow about the inlet guide vane system of a water turbine of bulb type.

Alternatives to the impulse response h(t) to describe the acoustical behavior of conical ducts

In unidimensional acoustical systems, the impulse response h(t) at the input section, which describes the pressure evolution originated at this section by the introduction of a flow unit impulse through it, relates pressure p(t) and flow u(t) at the input section by means of the convolution product p=h*u. If damping and radiation are small, it is interesting to find other functions of faster decay than h(t) in order to improve the convolution convergence. As alternatives to h(t), this article studies the impulse responses h′(t) and h″(t), which correspond to the modified systems that result when coupling the original acoustical system input section to a cylindrical anechoic termination and a conical anechoic termination, respectively. These functions h′(t) and h″(t) are related to the plane-wave reflection function Rp−(t) and spherical-wave reflection function Rs−(t), respectively. The comparison of these three impulse responses shows that the use of h′(t) and h″(t), though of faster decay than h(t) in principle, is not always advisable. For conical bores with small truncation, the convolution with h′(t) may lead to numerical instability more easily than that with h(t). On the other hand, the impulse response h″(t) turns out to be divergent for certain geometrical duct configurations, and thus it is useless as a kernel function in a convolution in these cases.