Cross-flow Tube Research Articles

Computational study of solid particle erosion for a single tube in cross flow

Erosion of boiler tubes causes serious problems in many pulverized coal-fired utility boilers. The Eulerian approach was employed to predict the behaviour of the particulate phase. Traditionally, the Eulerian approach shows deficiencies when used in the numerical prediction of erosion, because of a lack of an appropriate wall boundary condition for the particulate phase. Comparison of the numerical prediction for a single tube erosion with experimental data shows very good agreement.

Numerical Simulation of the Lock-In Effect of a Fixed-Fixed Tube in Cross Flow

This paper deals with the development of a numerical calculation code that is able to simulate the three-dimensional flow through a heat exchanger tube bundle and therefore allows a coupled calculation of fluid-structure interaction between the flow and the tube bundle. The incompressible flow field is calculated by a Navier-Stokes solver using a first-order power law scheme, a SIMPLEC algorithm to calculate the pressure and velocity correction fields, and a line-by-line Gauss-Seidl tridiagonal algorithm to solve the linearised system of equations. The transient parts of the Navier-Stokes equations are discretised by a second-order forward finite differencing scheme. The turbulence is examined with the aid of a large-eddy turbulence model. The transient fluid forces acting on the tubes are calculated by integration of all local flow pressure values on the surfaces of the tubes. As an example a single fixed-fixed cylinder in a flow channel is considered using the structural calculation part already developed as well as the new flow field and flow forces subroutines. The time series of the tube's motion and the fluid forces acting on the tube are analysed by Fourier's transformation. The lock-in effect occurring when the vortex shedding frequency approaches the first natural frequency of the tube can be excellently demonstrated by varying the inflow velocity over a wide range of Reynolds numbers.

Numerical Simulation of the Lock-In Effect of a Fixed-Fixed Tube in Cross Flow

Numerical Simulation of the Lock-In Effect of a Fixed-Fixed Tube in Cross Flow

The combined effects of wall longitudinal heat conduction, inlet fluid flow nonuniformity and temperature nonuniformity in compact tube–fin heat exchangers: a finite element method

A finite element analysis of a crossflow tube–fin compact heat exchanger is presented. The analysis takes into account the combined effects of one-dimensional longitudinal heat conduction through the exchanger wall and nonuniform inlet fluid flow and temperature distributions on both hot and cold fluid sides. A mathematical equation is developed to generate different types of fluid flow⧹temperature maldistribution models considering the possible deviations in fluid flow. Using these fluid flow⧹temperature maldistribution models, the exchanger effectiveness and its deterioration due to the combined effects of longitudinal heat conduction and flow⧹temperature nonuniformity are calculated for various design and operating conditions of the exchanger. It was found that the performance deteriorations are quite significant in some typical applications due to the combined effects of longitudinal heat conduction, temperature nonuniformity and fluid flow nonuniformity on crossflow tube–fin heat exchanger.

FLUID DAMPING CONTROLLED INSTABILITY OF TUBES IN CROSSFLOW

The mathematical model for fluid damping controlled instability of tubes in crossflow presented in this paper is based on unsteady flow theory. Motion-dependent fluid forces are measured in a water channel. From the measured fluid forces, fluid stiffness and fluid damping coefficients are calculated as a function of reduced flow velocity, oscillation amplitude, and Reynolds number. Once these coefficients are known, the mathematical model can be applied to predict structural instability due to fluid damping. The cases considered are a single tube, twin tubes, tube row, triangular array, and square arrays. The results show instability regions that are based on the fluid damping coefficients and provide answers to a series of questions on fluidelastic instability of tube arrays in crossflow.

Vibration and Stability of Two Tubes in Cross-Flow

Two tubes in tandem and normal to flow were studied on the basis of the unsteady-flow theory. Motion-dependent fluid forces were measured in a water channel, and the pitch-to-diameter ratio was 1.35. From the measured fluid forces, fluid damping and stiffness were calculated as a function of reduced flow velocity and several Reynolds numbers. Once the fluid-damping and fluid-stiffness coefficients are known, coupled vibration and stability of the two tubes in cross-flow can be predicted.

Flow-Induced Vibration of Tubes in Cross-Flow

Abstract This paper presents an unsteady-flow theory for flow-induced vibration of tubes in cross-flow. It includes a general description of motion-dependent fluid forces, characteristics of fluid-force coefficients, and mathematical models. Detailed results are presented for the constrained mode in the lift direction for various tube arrangements.

Theoretical analysis of the thermal resistance of non-uniform fouling on cross-flow heat exchanger tubes

A theoretical analysis of steady-state heat conduction through homogenous fouling on the external surface of tubes in cross-flow has been made. Modelling the fouling geometry as an eccentric annulus, a finite difference procedure in bipolar coordinates has been developed to predict the effect of fouling on the thermal performance. Theoretical predictions for a range of geometry, thermal conductivity and variable convection boundary conditions are presented. It is shown how, for a range of foulant thickness, eccentricity and thermal conductivity, the rate of heat transfer to a given size tube can be reduced or increased. The case of non-homogeneity of the fouling is explored with a view to extending the analysis towards varying thermal conductivity.

Local enhancement of heat transfer in a particulate cross flow—II Experimental data and predicted trends

Results from an experimental investigation of the effect of solid particles on heat transfer at the first row of a staggered tube array in cross flow are compared with those determined for equivalent conditions from correlations derived previously by the author. Comparison of the experimental data with the predicted levels of heat transfer enhancement from a range of heat transfer mechanisms suggests that the transport of thermal energy by rebounding particles is responsible for much of the measured increase in heat transfer. The total enhancement based on this model of the suspension flow compares well with the experimental data for particles of 46 and 58 μ m dia, although the agreement is not as good for 127 μm dia particles. The fine particle model of suspension flow gives levels of enhancement of the correct order for some flow conditions but fails to predict the effect of Reynolds number and particle size. In the light of these results, the suspension heat transfer mechanisms for tubes in cross flow are re-assessed and the dominant effects on enhancement are identified for specific flow conditions.

Local enhancement of heat transfer in a particulate cross flow—I Heat transfer mechanisms

The mechanisms associated with the enhancement of heat transfer over the front of a tube in a gas-particle cross flow are investigated. A correlation derived in a previous study of enhancement from the increased thermal capacity of the suspension is modified to take account of local particle residence times and the calculations of gas-to-particle heat transfer are refined. The influence on the enhancement of conduction between an impacting particle and the tube wall is analysed and the correlation is modified to include the effect of energy transport by rebounding particles. In addition, the effects of changes in the gas flow structure and boundary-layer characteristics on local heat transfer are explored.

An Experimental Investigation on Forced Convection Heat Transfer From a Cylinder Embedded in a Packed Bed

Forced convection heat transfer from a cylinder embedded in a packed bed of spherical particles was studied experimentally. With air as the working fluid, the effects of particle diameter and particle thermal conductivity were examined for a wide range of thermal conductivities (from 200 W/m K for aluminum to 0.23 W/m K for nylon) and three nominal particle sizes (3 mm, 6 mm, and 13 mm). In the presence of particles, the measured convective heat transfer coefficient was up to seven times higher than that for a bare tube in crossflow. It was found that higher heat transfer coefficients were obtained with smaller particles and higher thermal conductivity packing materials. The experimental data were compared against the predictions of a theory based on Darcy’s law and the boundary layer approximations. While the theoretical equation was moderately successful at predicting the data, improved correlating equations were developed by modifying the form of the theoretical equation to account better for particle diameter and conductivity variations.

Radiative heat transfer in pulverized-coal-fired boilers—Development of the absorptive/reflective character of initial ash deposits

Emission Fourier transform, infrare (FTIR) spectroscopy data provide in situ, time-resolved, spectralemissivity measurements for ash deposits generated from two U.S. Powder River Basin coals. The first 3h of deposit growth on a tube in cross flow in a pilot-scale furnace detail the development of surface emissivity with time. Measured emissivities vary significantly with wavelength, indicating the influence of the physical properties and chemical composition of the deposit. At long wavelength (>7 μm), emission features exhibit characteristics of silica, sulfates, and silicates. The spectral emissivity measured in this region approaches a steady value due to an increase in deposit thickness and the size of particles in the deposit. In contrast, deposits are not opaque at shorter wavelengths where the measured emissivity is influenced by the properties of the underlying metal surface. Theoretical predictions of the emsivity of a particulate layer were performed, and results are compared to the measured values. The theory adequately predicts the general features of spectral variation of the emissivity. The predicted trends in emissivity with particle size and deposit composition are also consistent with exerimental observations. Total (Planck-weighted) emissivities are calculated from the measured spectral values for the deposits at the tube temperatures. They increase with time from the clean tube value (0.2–0.3) to values typicals of deposits formed from western U.S. coal (0.45–0.55). Calculated total absorptivities are found to be lower than the correspoding emissivities.

Non-Linear Dynamics Of Loosely Supported Tubes In Crossflow

By means of the unsteady flow and a bilinear mathematical model, a theoretical study was conducted of the chaotic dynamics associated with the fluid-elastic instability of loosely supported tubes. Calculations were performed for the r.m.s. of tube displacement, bifurcation diagram, phase portrait, power spectral density and Poincaré map. Analytical results show the existence of chaotic, quasi-periodic and periodic regions when the flow velocity exceeds a threshold value.

In situ, real-time characterization of coal ash deposits using Fourier transform infrared emission spectroscopy

In situ Fourier transform infrared (FTIR) emission spectroscopy is used to identify the presence of silica, sulfates, and silicates as a function of time in coal ash deposits generated in Sandia's multifuel combustor, a pilot-scale reactor. Ash deposits are formed on a cylindrical tube in cross flow under experimental conditions which correspond to convection pass (fouling) regions of a commercial coal-fired boiler. The gas temperature, gas composition, particle loading, and extent of particle reaction in the combustor are typical of commercial boiler operation. The major classes of inorganic species deposited on the tube, including silicates and sulfates, are identified using the FTIR emission spectroscopy technique

An Unsteady Theory For Fluidelastic Instability in an Array of Flexible Tubes in Cross-Flow. Part I: Theory

An unsteady theoretical model for fluidelastic instability in an array of tubes in cross-flow is presented. The model is based on concepts developed by Lever and Weaver, but is extended to overcome some of the problems encountered with that earlier work. A perturbation decay function is introduced to account for decay of disturbances away from a moving tube, and the theory includes the effects of neighbouring tube motion. The theory is applicable to all standard array geometries and is shown to reduce to a model of a single flexible tube in a rigid array which includes static instability as a special case.

An Unsteady Theory for Fluidelastic Instability in an Array of Flexible Tubes in Cross-Flow. Part II: Results and Comparison With Experiments

A relatively simple unsteady theory of fluidelastic instability in a flexible array of tubes in cross-flow was developed in Part 1 of this study. In this part, numerical results are computed and compared with experimental data from the literature. It is shown that the single flexible tube in a rigid array model predicts a tendency towards divergence at high values of the mass-damping parameter and is, therefore, not a suitable model for a flexible array of tubes at such values. The results for a flexible array of tubes show reasonable agreement with experiments for all standards array geometries.

Chaotic Vibrations of Nonlinearly Supported Tubes in Crossflow

Chaotic vibrations associated with the fluidelastic instability of nonlinearly supported tubes in a crossflow is studied theoretically on the basis of the unsteady-flow theory and a bilinear mathematical model. Effective tools, including phase portraits, power spectral density, Poincare maps, Lyapunov exponent, fractal dimension, and bifurcation diagrams, are utilized to distinguish periodic and chaotic motions when the tubes vibrate in the instability region. The results show periodic and chaotic motions in the region corresponding to fluid-damping-controlled instability. Nonlinear supports, with symmetric or asymmetric gaps, significantly affect the distribution of periodic, quasi-periodic, and chaotic motions of a tube exposed to various flow velocities in the instability region of the tube-support-plate-inactive mode.

Local Heat Transfer Behavior and Its Impact on a Single-Row, Annularly Finned Tube Heat Exchanger

Experimental studies of the local mass transfer characteristics of annularly finned tubes in crossflow are presented. Variations due to boundary layer development, forward-edge separation, the tube wake, horseshoe vortices, and tip vortices are discussed. In addition, regularly located local maxima in mass transfer rates associated with the horseshoe vortex system are found, and conjecture as to their mechanism is offered. Inferring heat transfer behavior from the mass transfer results, we find that the true fin efficiency is always less than that obtained with an assumed constant convective heat transfer coefficient. The difference is 3–7 percent for high-conductivity materials such as aluminum alloys, and 9–17 percent for low-conductivity materials such as mild steels.

Heat transfer and pressure drop in single rows of tubes in cross-flow

Results of experimental investigations on the influence of turbulence intensity and pitch-to-diameter ratio on heat transfer and pressure drop in single rows of plain tubes are presented. Vertically arranged tubes with 16 different pitch-to-diameter ratios between 1.26 and 5.73 were heated by saturated steam, condensing inside, and cooled outside by air in cross-flow. The turbulence intensity in the entrance cross-section was enhanced by means of different biplanar grids installed in the test section of a wind tunnel upstream of the single rows. The mean streamwise turbulence intensity behind the grids, measured with a constant temperature hot-wire anemometer, varied between 0.8% and 38.8%. Reynolds numbers ranged from 4X10 3 to 2X10 5 . For single rows, the measurements show that the Nusselt number for a given turbulence intensity increases with increasing Reynolds number. In the investigated range of Reynolds numbers, the drag coefficient is only slightly influenced by the inlet turbulence intensity. The use of turbulence grids thus leads to higher efficiencies of heat exchangers

Heat transfer from a cylinder and finned tube in a pulsating crossflow

Experiments have shown that the convective heat transfer from heated cylinders and finned tubes is very sensitive to the frequency of pulsation of the approaching crossflow. A specially developed wind tunnel, which had facility for generating a time-dependent flow, was used for the experimental testing. The circular cylinder and finned tube test specimens had isothermal surfaces, and tests were performed over a Reynolds number range of 2,000–14,000 to determine average heat transfer coefficients. The effect of a pulsating flow on the forced convective heat transfer from the cylinder was to decrease the heat transfer relative to the steady-flow case with the same mean flow conditions for low dimensionless frequencies and to increase the heat transfer for high dimensionaless frequencies. In the case of the finned tube, a significant increase in the heat transfer was noted for high values of the dimensionless frequencies. At low dimensionless frequencies, the heat transfer did not vary appreciably. In general, the data obtained indicated that heat transfer is enhanced at higher dimensionless frequencies and diminished at lower ones. This study has stimulated interest in a numerical study that will consider the effects of the so-called ac boundary layers and, for the case of the finned tube, the effects of vorticity amplication on the convective heat transfer. The vorticity is generated by the boundary layer flow over the fins, and the amplification would be due to the flow accelerating over the cylindrical core.