Peristaltic transport in circular cylindrical tubes
Long wave approximation for peristaltic transport in circular cylindrical tube, noting inertia and wavelength effects on backward flow
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Long wave approximation for peristaltic transport in circular cylindrical tube, noting inertia and wavelength effects on backward flow
Plane-acoustic-wave propagation in small tubes with a cross section in the shape of a flattened oval is described. Theoretical descriptions of a plane wave propagating in a tube with circular cross section and between a pair of infinite parallel plates, including viscous and thermal damping, are expressed in similar form. For a wide range of useful duct sizes, the propagation constant (whose real and imaginary parts are the amplitude attenuation rate and the wave number, respectively) is very nearly the same function of frequency for both cases if the radius of the circular tube is the same as the distance between the parallel plates. This suggests that either a circular-cross-section model or a flat-plate model can be used to calculate wave propagation in flat-oval tubing, or any other shape tubing, if its size is expressed in terms of an equivalent radius, given by g = 2 x (cross-sectional area)/(length of perimeter). Measurements of the frequency response of two sections of flat-oval tubing agree with calculations based on this idea. Flat-plate formulas are derived, the use of transmission-line matrices for calculations of plane waves in compound systems of ducts is described, and examples of computer programs written to carry out the calculations are shown.
A waveguide feed has been designed to provide specified illumination patterns for a dual-reflector antenna in two wavelength bands: 8 to 9 GHz and 30 to 40 GHz. The feed (see figure) has a coaxial configuration: A wider circular tube surrounds a narrower circular tube that serves as a waveguide for the signals in the 30-to-40-GHz band. The annular space between the narrower and the wider tube serves as a coaxial waveguide for the signals in the 8-to-9-GHz band. The nominal design frequencies of the outer and inner waveguides are 8.45 and 32 GHz, respectively. Each of the two waveguides is terminated in a component that is sized and shaped to help focus the radiation in its respective frequency band into the specified illumination pattern. For the outer waveguide, the beam-shaping termination is a corrugated horn; for the inner waveguide, the beam-shaping termination is a dielectric rod insert.
A compact heat exchanger was constructed consisting of circular tubes in parallel brazed to a grooved base plate. This tube specimen heat exchanger was tested in an apparatus which radiatively heated the specimen on one side at a heat flux of up to 54 W/sq cm, and cooled the specimen with helium gas at 3.5 MPa and Reynolds numbers of 3000 to 35,000. The measured friction factor of the tube specimen was lower than that of a circular tube with fully developed turbulent flow, although the uncertainty was high due to entrance and exit losses. The measured Nusselt number, when modified to account for differences in fluid properties between the wall and the cooling fluid, agreed with past correlations for fully developed turbulent flow in circular tubes.
A streak tube having circular scan was designed, built and tested. Continuous circular scan, easily derived from out of phase sine waves applied to the conventional deflection plates, permits the timing of pulses traveling long baselines. At the tube's output a circular array of 720 elements is scanned to provide 30 to 40 picosecond resolution. Initial difficulties with electron bombarded silicon arrays were circumvented by using microchannel plates within the streak tube to provide the needed electronic amplification and digital sensitivity and coupling the 720 element arrays to the electron beam by means of a phosphor on a fiber optics. Two ceramic body tubes with S-20 photocathodes were tested and delivered.
Annular two-phase flow inside circular tubes for estimating liquid film thickness and calculating heat transfer coefficient of pure fluid
The results of a semi-analytical and experimental study of adiabatic tube flow and an analytical and experimental investigation of the thermal entrance region for gas flowing through electrically heated circular tubes are presented. Emphasis is placed on the low Reynolds number turbulent flow regime--defined as fully turbulent flow at bulk Reynolds numbers from 3,000 to about 15,000. Adiabatic air velocity and friction data and localized heat transfer measurements for air and helium, at low heating rates, are presented for this range. The adiabatic data were obtained in a 1.61 inch 1D tube for flow at bulk Reynolds numbers from 3,000 to 15,000. A continuous, Reynolds number-dependent, profile is developed from the data by using a modification of Reichardts' wall and middle law eddy diffusivity expressions. The velocity profile satisfies continuity. It is valid for all Reynolds numbers in excess of 3,000 for which the flow is fully turbulent and the Blasius friction factor expression is valid. The thermal entrance problem for a fully developed velocity profile is solved analytically by the method of Sparrow, Hallman, and Siegel. The solution is based on the profile developed from the velocity study. Tabular values of the eigenvalues and normalized Nusselt numbers for gases are presented for it range of Reynolds numbers from 3,000 to 50,000. The axial variation of Nusselt number is found to be correlated by [Nu/Nu_(∞)] = 1 + 0.8 (1+ 70,000 Re^(-3/2)) ((x/D)^(-1)) to within ± 5 per cent for x/D ≥2. The fully developed value agrees with the Dittus - Boelter correlation, Nu_(∞) = 0.021 Re^(0.8) Pr^(0.4) For the eigenvalues, λ^(2)_(n), and the associated constants, A_(n), correlations of the form λ^(2)_(n) =A_(1,n) Re^(-b_(1,n) + C_(1,n) Re^(-d_(1,n)) A_(n) = -A_(2,n) Re^(-b_(2,n) + C_(2,n) Re^(-d_(2,n)) are obtained. The coefficients and powers are presented in tabular form. Heat transfer data are presented, primarily for helium, for the low Reynolds number turbulent range. A one-quarter inch, resistively heated, vertical, circular tube was used for the study. The data cover an axial range from 1.2 to 96 diameters; wall-to-bulk temperature ratios vary from 1 to 1.4. In the low Reynolds number turbulent regime, these data clearly support the present analytical solution rather than the prediction obtained by applying the eddy diffusivity distribution used by Sparrow, Hallman, and Siegel.
A variational method is presented for solving eigenvalue problems which arise in connection with the analysis of convective heat transfer in the thermal entrance region of ducts. Consideration is given, to both situations where the temperature profile depends upon one cross-sectional coordinate (e.g. circular tube) or upon two cross-sectional coordinates (e.g. rectangular duct). The variational method is illustrated and verified by application to laminar heat transfer in a circular tube and a parallel-plate channel, and good agreement with existing numerical solutions is attained. Then, application is made to laminar heat transfer in a square duct as a check, an alternate computation for the square duct is made using a method indicated by Misaps and Pohihausen. The variational method can, in principle, also be applied to problems in turbulent heat transfer.
An accurate finite-difference scheme has been utilized to investigate oscillatory, laminar and incompressible flow between two-parallel-plates and in circular tubes. The two-parallel-plates simulate the regenerator of a free-piston Stirling engine (foil type regenerator) and the channel wall was included in the analysis (conjugate heat transfer problem). The circular tubes simulate the cooler and heater of the engine with an isothermal wall. The study conducted covered a wide range for the maximum Reynolds number (from 75 to 60,000), Valensi number (from 2.5 to 700), and relative amplitude of fluid displacement (0.714 and 1.34). The computational results indicate a complex nature of the heat flux distribution with time and axial location in the channel. At the channel mid-plane we observed two thermal cycles (out of phase with the flow) per each flow cycle. At this axial location the wall heat flux mean value, amplitude and phase shift with the flow are dependent upon the maximum Reynolds number, Valensi number and relative amplitude of fluid displacement. At other axial locations, the wall heat flux distribution is more complex.
Superheater tubes are critical boiler components that operate at relatively higher temperatures and pressure. Amongst the primary concerns for these tubes is the deposition of ash particles on the tube surface, leading to the reduced thickness of the tube due to material corrosion, consequently causing early creep failure of the component. In this research, a novel tube design has been proposed which resembles a teardrop or ogive shape to reduce the drag and concurrently improve the creep life of the superheater tubes. To administer the practicality of novel tubes, metal additive manufacturing (AM), for instance, laser-powder bed fusion (L-PBF), has been proposed. These unconventional designs were assessed and compared with the baseline circular tube design for mechanical design requirements (hoop stress and creep life) and the particle and flue gas flow characteristics around the differently shaped tubes. A thermomechanical finite element (FE) analysis was performed for hoop stress calculations. This study also emphasizes on effect of circumferential thermal variation on hoop stress distribution in tubes. Therefore, a detailed two-dimensional (2D) thermal simulation has been performed to report the circumferential thermal variation on the tube. A computational fluid dynamics (CFD) analysis coupled with particle tracing was performed for gas flow visualization and particle tracing around the proposed shapes and baseline circular-shaped tube design. The Schlieren optic setup was built and leveraged for qualitative validation of the proposed design. The complete design methodology established in the paper shows teardrop-shaped tubes better in terms of drag and creep life in contrast to the circular-shaped tube.
Local heat transfer for water in turbulent forced flow in entrance region of circular tubes
Low density phenomena effect on heat transfer for laminar flow in flat duct or circular tube with uniform wall heat flux
Torsion creep theory for circular and noncircular tubes using Bredt equation, measuring anisotropy in tubes, calculating torsion stresses
Transient heat transfer between thin circular tube and incompressible fluid, considering radial conduction and heat loss
Specular radiation exchange within a circular tube subject to thermal radiation at the tube ends and a uniform heat flux at the walls
Gas and surface temperature distributions for laminar flow in circular tube, considering conduction, convection and radiation effects
A circular-scan streak tube designed for use in a laser ranging system is described. Electrostatic focusing is used between the photocathode and a microchannel plate, and electrons from the microchannel plate are proximity focused onto an output phosphor screen. Electron beam deflection is achieved by driving two orthogonal sets of deflection plate assemblies in phase quadrature at a frequency of 200 MHz. The light intensity in the output beam trace is measured by using a circular Reticon array of 720 photodiodes, which is fiber-optically coupled to the output phosphor screen of the tube. Sample measurements of frequency-doubled Nd:YAG laser-pulse waveforms are given. Also the output beamwidth has been measured at the 200-MHz deflection frequency. The results suggest a limiting resolution of 33 psec for the circular-scan streak tube used for these tests.
A heat transfer analysis of a transparent gas flowing through a circular tube of finite thickness is presented. This study includes the effects of wall conduction, internal radiative exchange, and convective heat transfer. The natural mathematical formulation produces a nonlinear, integrodifferential equation governing the wall temperature and an ordinary differential equation describing the gas temperature. This investigation proposes to convert the original system of equations into an equivalent system of integral equations. The Green's function method permits the conversion of an integrodifferential equation into a pure integral equation. The proposed integral formulation and subsequent computational procedure are shown to be stable and accurate.