Duct Of Constant Cross-section Research Articles

Compact asymmetric treatments for perfect sound absorption in ventilated problems

This presentation introduces compact asymmetric treatments for sound absorption, i.e., simultaneous cancellation of reflection and transmission, in a lined duct of constant cross section. The treatments are composed of side by side and sub-wavelength resonators. They are thus compact, which facilitates their practical use. The simplest asymmetric treatment is formed by a pair of detuned resonators that can lead to a perfect monochromatic sound absorption. Furthermore, the combination of multiple pairs of resonators generates multiple low quality factor absorption peaks leading to an absorption plateau. Two compact asymmetric treatments are presented: one is composed of quarter-wavelength porous resonators to prove their ability to achieve perfect sub-wavelength absorption in a duct problem and the other is composed of Helmholtz resonators flush mounted on the walls of a large cross-section duct. In both cases, the evanescent coupling between the resonators has an important impact on the treatments behavior and is thus accounted for during their optimization. The experimental results are found in good agreement with the theory and a mean absorption coefficient of 99% over a large target and subwavelength frequency range is observed for each treatment.

Numerical Analysis of Spatial Hydrodynamic Stability of Shear Flows in Ducts of Constant Cross Section

A technique for analyzing the spatial stability of viscous incompressible shear flows in ducts of constant cross section, i.e., a technique for the numerical analysis of the stability of such flows with respect to small time-harmonic disturbances propagating downstream is described and justified. According to this technique, the linearized equations for the disturbance amplitudes are approximated in space in the plane of the duct cross section and are reduced to a system of first-order ordinary differential equations in the streamwise variable in a way independent of the approximation method. This system is further reduced to a lower dimension one satisfied only by physically significant solutions of the original system. Most of the computations are based on standard matrix algorithms. This technique makes it possible to efficiently compute various characteristics of spatial stability, including finding optimal disturbances that play a crucial role in the subcritical laminar–turbulent transition scenario. The performance of the technique is illustrated as applied to the Poiseuille flow in a duct of square cross section.

Entrance and Temperature-Dependent Property Effects on Laminar Duct Flows of Liquids

The results of a numerical investigation on the effects of the temperature dependence of viscosity and thermal conductivity in simultaneously developing laminar flows of liquids in straight ducts of constant cross sections are used to obtain new correlations for the axial distributions of the peripherally averaged local Nusselt number. Three different cross-sectional geometries are considered, corresponding to both axisymmetric (circular and concentric annular) and three-dimensional (square) ducts. Uniform heat flux boundary conditions are specified at the heated walls. Viscosity is assumed to vary with temperature according to an exponential relation, while a linear dependence of thermal conductivity on temperature is assumed. The other fluid properties are held constant. A superposition method is applied to obtain the values of the peripherally averaged local Nusselt number by separately considering the effects of temperature-dependent viscosity and those of temperature-dependent thermal conductivity.

Numerical Simulation of time domain wall impedance on circular and annular ducts using the immersed boundary method

In this work, time domain boundary conditions of wall impedance are simulated on circular and annular ducts of constant cross section. The discretization technique used here is the immersed boundary method in the framework of finite volume formulation. It has fourth order of precision in space and uses a third order Runge-Kutta method for time stepping. Several boundary conditions for wall impedance are tested and then compared with the analytical results of the one-dimensional resonating chamber for code validation. The impedance boundary conditions are simulated on a circular duct with wall treatment and with a synthetic sound source. Mean flow conditions include constant axial velocity and swirling flows of rigid body rotation and potential flow. The results are then compared with a fourth order eigensystem method of linearized governing equations. The results of the immersed boundary methodology are assessed along with the wall impedance boundary condition models and their linear validity is compared with the results of the eigensystem method.

Nusselt number correlations for simultaneously developing laminar duct flows of liquids with temperature dependent properties

New correlations, suitable for engineering applications, for the mean Nusselt number in the entrance region of circular tubes and square ducts with uniform heat flux boundary conditions specified at the walls are proposed. These correlations are obtained on the basis of the results of a previous parametric investigation on the effects of temperature dependent viscosity and thermal conductivity in simultaneously developing laminar flows of liquids in straight ducts of constant cross-sections. In these studies, a finite element procedure has been employed for the numerical solution of the parabolized momentum and energy equations. Viscosity and thermal conductivity are assumed to vary with temperature according to an exponential and to a linear relation, respectively, while the other fluid properties are held constant. Axial distributions of the mean Nusselt number, obtained by numerical integration from those of the local Nusselt number, are used as input data in the derivation of the proposed correlations. A superposition method is proved to be applicable in order to estimate the Nusselt number by considering separately the effects of temperature dependent viscosity and thermal conductivity. Therefore, for each of the considered cross-sectional geometries, two distinct correlations are proposed for flows of liquids with temperature dependent viscosity and with temperature dependent thermal conductivity, in addition to that obtained for constant property flows.

Entrance and temperature dependent property effects in the laminar forced convection in straight ducts with uniform wall temperature

The paper reports the results of a parametric investigation on the effects of temperature dependent viscosity and thermal conductivity on forced convection in simultaneously developing laminar flows of liquids in straight ducts of constant cross-sections. Uniform temperature boundary conditions are specified at the duct walls. Viscosity is assumed to vary with temperature according to an exponential relation, while a linear dependence of thermal conductivity on temperature is assumed. The other fluid properties are held constant. Two different cross-sectional geometries, namely circular and flat ducts, are considered. A finite element procedure is employed for the solution of the parabolized momentum and energy equations. Computed axial distributions of the local Nusselt number are presented for different values of the entrance Prandtl number and of the viscosity and thermal conductivity Pearson numbers. Moreover, a superposition method is proved to be applicable in order to obtain an approximate value of the local Nusselt number by separately considering the effects of temperature dependent viscosity and those of temperature dependent thermal conductivity.

Entrance and Temperature Dependent Viscosity Effects on Laminar Forced Convection in Straight Ducts With Uniform Wall Heat Flux

Abstract In this paper a parametric investigation is carried out on the effects of temperature dependent viscosity in simultaneously, i.e., hydro-dynamically and thermally, developing laminar flows of liquids in straight ducts of constant cross sections. Uniform heat flux boundary conditions are imposed on the heated walls of the ducts. Different cross-sectional geometries are considered, corresponding to both axisymmetric (circular and concentric annular) and three-dimensional (rectangular and trapezoidal) ducts. Viscosity is assumed to vary with temperature according to an exponential relation, while the other fluid properties are held constant. A finite element procedure is employed for the solution of the parabolized momentum and energy equations. Computed axial distributions of the local Nusselt number and of the apparent Fanning friction factor are presented for different values of the Pearson and Prandtl numbers. Numerical results confirm that, in the laminar forced convection in the entrance region of straight ducts, the effects of temperature dependent viscosity cannot be neglected in a wide range of operative conditions. Correlations are also provided for the local Nusselt number and the apparent Fanning friction factor in simultaneously developing flows in ducts of different cross sections.

Fast computation of optimal disturbances for duct flows with a given accuracy

This work is devoted to the numerical analysis of small flow disturbances, i.e. velocity and pressure deviations from the steady state, in ducts of constant cross sections. The main emphasis is put on the disturbances causing the most kinetic energy density growth, the so-called optimal disturbances, whose knowledge is important in laminar-turbulent transition and robust flow control investigations. Numerically, this amounts to computing the maximum amplification of the 2-norm of a matrix exponential exp{tS} for a square matrix S at t ≥ 0. To speed up the computations, we propose a new algorithm based on low-rank approximations of the matrix exponential and prove that it computes the desired amplification with a given accuracy. We discuss its implementation and demonstrate its efficiency by means of numerical experiments with a duct of square cross section.

Surface wrinkling of a channelized flow

We consider an inclined rectangular duct of constant cross-section conveying viscous fluid and covered by an elastic plate. The fluid is described by the Stokes equations and the plate by the Föppl–von Kármán equations. The equations admit an equilibrium solution in which the plate is flat and fluid flows underneath due to gravity. This base flow induces a varying traction across the plate, which can lead to out-of-plane buckling due to the associated in-plane shear. Linear stability analysis demonstrates that buckling occurs for sufficiently thin plates on steep slopes and deep channels. The most unstable modes take the form of either symmetric or antisymmetric downslope-directed chevron patterns that travel downstream at a fraction of the average speed of the base flow. An analogous analysis shows that similar buckling also occurs if the elastic plate is replaced by a thin skin of very viscous fluid. Our description provides a simple model for the formation of ropy pahoehoe lava.

Sound propagation in slowly varying lined flow ducts of arbitrary cross-section

Sound transmission through ducts of constant cross-section with a uniform inviscid mean flow and a constant acoustic lining (impedance wall) is classically described by a modal expansion, where the modes are eigenfunctions of the corresponding Laplace eigenvalue problem along a duct cross-section. A natural extension for ducts with cross-section and wall impedance that are varying slowly (compared to a typical acoustic wavelength and a typical duct radius) in the axial direction is a multiple-scales solution. This has been done for the simpler problem of circular ducts with homentropic irrotational flow. In the present paper, this solution is generalized to the problem of ducts of arbitrary cross-section. It is shown that the multiple-scales problem allows an exact solution, given the cross-sectional Laplace eigensolutions. The formulation includes both hollow and annular geometries. In addition, the turning point analysis is given for a single hard-wall cut-on, cut-off transition. This appears to yield the same reflection and transmission coefficients as in the circular duct problem.

Natural Convection Inside Vertical Isothermal Ducts of Constant Arbitrary Cross Section

A model for steady laminar natural convection inside vertical, arbitrarily shaped isothermal ducts of constant cross section is presented. The model is based on a combination of asymptotic solutions for fully developed and developing, boundary-layer e ow. The fully developed asymptote model utilizes forced convection, internal e ow modeling techniques, and an approximate model is presented, which is valid for a wide range of duct shapes and aspectratios.Themodelisvalidated usingexperimentaldataandnumericalresultsfrom theliteratureforavariety of duct shapes, including the triangle, square, circle, rectangle and the special case of parallel plates. The model is in good agreement with all of the data, with an rms percent difference of 10% or less in most cases.

Liquid-metal MHD flow in rectangular ducts with thin conducting or insulating walls: laminar and turbulent solutions

This paper treats the steady, fully-developed flow of a liquid metal in a rectangular duct of constant cross-section with a uniform, transverse magnetic field. Thin conducting wall boundary conditions at the top/bottom walls (perpendicular to the magnetic field) are extended to allow electrical currents to return through either the wall or the Hartmann layers. Hence, a unified analysis of flows in ducts with wall conductance ratios in the range of interest of fusion blanket applications, namely, from thin conducting to insulating wall ducts, is conducted. The flow in laminar and turbulent regimes is investigated through a composite core-side-layer spectral collocation solution which explicitly resolves the flow in the side layers (parallel to the magnetic field) even for very large Hartmann numbers. Turbulent profiles are obtained through an iterative scheme in which turbulence is introduced through an eddy viscosity model from the renormalization group theory of turbulence [Yakhot, V. and Orsag, S.A., J. Sci. Comput., 1986, 1 (1), 3]. The transition from a flow in a duct with thin conducting walls to one with insulating walls is clearly displayed by varying the wall conductance ratio from 0.05 to 0 for Hartmann numbers in the range 10 3–10 5. In turbulent regime, Reynolds numbers vary in the range 5 × 10 4–5 × 10 5. For thin conducting wall duct flows, turbulence is concentrated in the increased side layers while the core remains unperturbed. In insulating wall ducts, the flow remains in the laminar regime within the considered range of Reynolds numbers.

Friction factors for fully developed laminar flow in ducts confined by corrugated parallel walls

Straight ducts of constant cross-section with sinusoidally curved walls may be found in plate heat exchangers as well as in packing structures used in mass transfer operations or in catalytic reactors. Frictional pressure drop, in the case of fully developed laminar flow, depends on the shape of the cross-section. It is characterized by a generalized form of Poiseuilles law: ( ξ · Re) = K. Two types of cross-section formed by two parallel sinusoidally corrugated walls, with the amplitude a ̂ , the wave length A and the distance 2 a ̂ are regarded. The two sine walls may be either phase shifted by Π, so that the walls touch each other and form an arbitrary number of equal tubelike ducts, or they may be in phase, so that the duct is similar to the one formed by two parallel planes. In both limits the values of K were numerically calculated for a number of aspect ratios 2 a ̂ / A . The whole range of aspect ratios has been covered by fitting polynomials in order to allow for interpolation of the calculated values.

Calculation of the View Factors for Radiant Heat Exchange in a New Volumetric Receiver With Tapered Ducts

The need to increase efficiency of volumetric receivers for use in solar power plants by reducing reradiation losses and increasing the ``volumetric effect`` has promoted the idea of a receiver with tapered ducts. These seems to be very promising since higher efficiency and considerable saving of material can be achieved, as compared to conventional receivers perforated with ducts of constant cross-section. A finite element program is being developed to calculate stationary heat transfer in the tapered ducts by free and forced convection in the gas flow, conduction in walls and in the gas, and solar and thermal radiation. Gas and wall temperatures are considered to be varying only in the flow direction. In order to perform the highly nonlinear calculations of radiative exchange, the exact knowledge of the view factors is necessary. The aim of the present work is to evaluate analytically the view factors in tapered ducts.

Pseudoshock combustion regime

The combustion of fuels flowing with supersonic velocity in a duct of constant cross section is analyzed. Experimental data on the pressure at the duct wall are used to calculate the heat-release rates by a one-dimensional procedure that takes into account the specific characteristics of combustion in a pseudoshock. It is shown that the heat-release rate, averaged over the length of the combustion zone and normalized to the maximum possible rate, depends on the ratio of the length of the combustion zone to the pseudoshock length for the isothermal case in flow stagnation up to a Mach number M = 1.0 and not on the fuel injection technique or the length of the duct. An approach is suggested for determining the duct geometry in the pseudoshock combustion regime so as to organize the combustion process efficiently as a function of the flow parameters and the physicochemical characteristics of the field, which can be determined from specially designed experiments.

Transient acoustic pressure radiated from a finite duct

The time-dependent pressure radiated from a finite, rigid, circular duct of constant cross section is determined for the specified motion (velocity or acceleration) of a piston source within the duct. The modal composition of the internal field variables is represented as an eigenfunction expansion over the duct cross section, and a time- and space-dependent Green’s function is used to develop a generalized boundary condition which describes the effect of the external surroundings at the duct exit. Solution of this boundary value problem results in a duct transfer function which is then cascaded with the spatial transfer function connecting the duct exit port and a selected external field point. In this paper, inversion to the time domain is accomplished via the FFT algorithm. Numerical examples demonstrating the calculation of the external time-dependent pressure are presented based upon the specification of a gated sinewave piston acceleration over an assumed piston spatial profile. Confirming the theoretical analysis, the numerical results show that the time-dependent pressure for the cross modes develops its peak value off-axis and is always zero on-axis, while the plane wave mode always peaks precisely on-axis.

Pressure drop in fully developed, duct flow of dispersed liquid-vapor mixture at zero gravity

The dynamics of steady, fully developed dispersed liquid-vapor flow in a straight duct at 0- g is simulated by flowing water containing n-butyl benzoate droplets. Water and benzoate are immiscible and have identical density at room temperature. The theoretical basis of the simulation is given. Experiments showed that, for a fixed combined flow rate of water and benzoate, the frictional pressure drop is unaffected by large changes in the volume fraction of benzoate drops and their size distribution. Measured power spectra of the static wall pressure fluctuations induced by the turbulent water-benzoate flow also revealed that their dynamics is essentially unaltered by the presence of the droplets. These experimental findings, together with the theoretical analysis, led to the conclusion that the pressure drop in fully developed, dispersed liquid-vapor flow in straight ducts of constant cross section at 0- g is identical to that due to liquid flowing alone at the same total volumetric flow rate of the liquid-vapor mixture and, therefore, can be readily determined.

Blowby flow rates to assess energy loss in cascaded refrigeration-heat pump systems

Available equation to determine the mass flow rate of ideal gas in an adiabatic flow through a duct of constant cross-section is modified after introducing isentropic exponents corresponding to a real gas. The equation is then used to compute theoretical blowby rates for cascaded refrigeration-heat pump systems. Most widely used and comparatively cheaper refrigerants R-12, R-22 and R-717 are selected for the heat pump system and R-13 for refrigeration sub-system. The rates are compared with ideal gas rates over a variety of operating conditions and a considerable loss energy is found with blowby rates. This loss can be averted, if a microprocessor is used to monitor instantaneous refrigerant mass at evaporator inlet and to compare this with the preset design mass and the difference (blowby) after cooling, it is feedback by an innovated method from the crankcase side of the compressor.

Some general properties of the exact acoustic fields in horns and baffles

The propagation of the fundamental, longitudinal acoustic mode in a duct of variable cross-section is considered, and the “Webster” wave equations for the sound pressure and velocity are used to establish some general properties of the exact acoustic fields. The equipartition of kinetic and compression energies is shown (section 2.1) to hold at all stations only for (i) a duct of constant cross-section and (ii) an exponential horn; these are the two cases for which the wave equations for the acoustic velocity and pressure coincide. It is proved (section 2.3) that there are only five duct shapes, forming two dual families, which have constant cut-off frequency(ies): namely, (I) the exponential duct, which is self-dual, and is the only shape with constant (and coincident) cut-offs both for the velocity and pressure; (II) the catenoidal horns, of cross-section S∼cosh 2, sinh 2, which, with their duals (III) the inverse catenoidal ducts S∼sech 2, csch 2, have one constant cut-off frequency, respectively, for the acoustic pressure and velocity. The existence of at least one constant cut-off frequency implies that the corresponding wave equation can be transformed into one with constant coefficients, and thus the acoustic fields calculated exactly in terms of elementary (exponential, circular and hyperbolic) functions; this property also applies to the imaginary transformations of the above shapes, viz., the sinusoidal S∼sin 2 and inverse sinusoidal S∼csc 2 ducts, that have no cut-off frequency, i.e., are acoustically “transparent”. It is shown that elementary exact solutions of the Webster equation exist only (section 3.1) for these seven shapes: namely, the exponential, catenoidal, sinusoidal and inverse ducts; it is implied that for all other duct shapes the exact acoustic fields involve special functions, in infinite or finite terms, e.g., Bessel and Hermite functions respectively for power-law and Gaussian horns. Examples of the method of analysis are given by calculating, in elementary form, the exact acoustic fields in inverse catenoidal ducts, for all cases of (a) propagating waves above, (b) non-oscillating modes below and (c) transition fields at the cut-off frequency. The inverse catenoidal ducts consist of (A) the horn of cross-section S∼sech 2, ressembling the “soliton” of non-linear water wave fame, and (B) the baffle of cross-section S∼csch 2, which also matches two exponentially converging ducts, but has infinite, instead of finite, flare at the origin. The geometrical and acoustic properties of these ducts are illustrated by sets of six plots, in Figure 1(a) for the sech-horn and in Figure 1(b) for the csch-baffle; the exact acoustic fields are described by amplitude and phase decompositions of the sound velocity and pressure, plotted as functions of position along the duct, for four frequencies ranging from the cut-off condition to the ray limit (or W.K.B.J. approximation).

Air distribution from ventilation ducts under grain

Using experimental measurements and simulations, air pressures in perforated ventilation ducts under bulks of grain were related to air distribution through the grain above the ducts. In shallow grain layers and at high velocities, the static pressure in the duct close to the fans was up to 20 times that at the distant end when the air was sucked into the ducts, so producing a large difference in airflow through the grain bulk at opposite ends of the duct. When air was blown into the ducts the air distribution improved considerably, although a regain of static pressure occurred at the distant end of the duct of up to 4 times that at the fan end. In blowing systems, air distribution was acceptable at moderate air velocities in a duct of constant cross section but was improved by reducing the diameter of the ducting in stages along the store, by increasing the grain depth, by introducing partial barriers into the duct or by using ducts with higher internal friction.