Monitoring the thermal efficiency of fouled heat exchangers: A simplified method

Fouling is a problem whether we are aware of it or not. In an industrial plant, it is important not only to be able to measure the buildup of unwanted deposits, but also to do it in the simplest and most economically possible way. This paper addresses the question of monitoring fouling in an oil refinery plant, where the high number of heat exchanger units and the variability of the feedstock charge pose additional problems in terms of the practicability of following the energetic performance of such equipment. In this case, the flow rates and quality of the fluids flowing through the heat exchangers do not usually correspond to the design conditions, because they change with time. Therefore, to assess the fouling level of the exchangers, the day-to-day measured thermal efficiency should not be compared with the efficiency predicted in the design calculations. The latter should be recalculated by introducing whenever necessary new values of flow rates, physical properties, and so forth, and by evaluating new heat transfer coefficients. However, the procedures are too time consuming to be applied frequently. The present work describes a simplified method for following heat exchanger performances, based on the assessment of the number of transfer units and thermal efficiencies, where the effects of changing the feedstock charge, particularly the flow rates of the fluids, are taken into account. The only data that need to be collected are the four inlet/outlet temperatures of the heat exchanger unit and one of the flow rates. Several heat exchanger units in an oil refinery were successfully monitored by means of this method, and it was found that the variations in the physical properties did not significantly affect the results obtained for the particular plant under study.     

Fouling of heat exchangers in the dairy industry

A general overview is given of the main factors in the fouling of processing equipment used for heating dairy fluids. The data collected indicate that the primary step in fouling is the adsorption of a monolayer of proteins onto the wall of the heating equipment at room temperature. Real fouling (i.e., the formation of macroscopic layers of foulants), however, is caused by particle formation in the bulk of the liquid being processed. These particles include both whey protein aggregates and calcium phosphate particles. Their formation is heat induced, and the deposition takes place through diffusion toward the heating surface. Only very high flow rates are able to prevent their deposition and subsequent sticking. To better control the process of fouling, special attention is given to the parameters affecting the formation of both types of particles and how their formation can be retarded or prohibited, including the role of calcium sequestrants, pH, preheating, and flow rate herewith.     

Numerical experiments on convective heat transfer in water-saturated porous media at near-critical conditions

Fluid and heat flow at temperatures approaching or exceeding that at the critical point (374 °C for pure water, higher for saline fluids) may be encountered in deep zones of geothermal systems and above cooling intrusives. In the vicinity of the critical point the density and internal energy of fluids show very strong variations for small temperature and pressure changes. This suggests that convective heat transfer from thermal buoyancy flow would be strongly enhanced at near-critical conditions. This has been confirmed in laboratory experiments. We have developed special numerical techniques for modeling porous flow at near-critical conditions, which can handle the extreme nonlinearities in water properties near the critical point. Our numerical simulations show strong enhancements of convective heat transfer at near-critical conditions; however, the heat transfer rates obtained in the simulations are considerably smaller than data reported from laboratory experiments by Dunn and Hardee. We discuss possible reasons for this discrepancy and develop suggestions for additional laboratory experiments.     

A new numerical scheme for convective dominated heat transfer in a porous medium with strong temperature gradients

A new numerical scheme, theimplicit correction scheme, has been developed for heat transfer in a porous medium with strong temperature gradients. The scheme includes diffusion, convection and transverse heat transfer processes. By using correction coefficients which are based on transverse heat transfer, the effects of convection enthalpy flow and diffusion are modified. Under suitable limiting conditions, the implicit correction scheme can be reduced to the central-difference, upwind, or power-law scheme. The correction scheme is shown to be especially useful in calculations of the thermal effectiveness of the regenerator in Stirling cycle refrigeration.     

Flow boiling heat transfer of R134a in the multiport minichannel heat exchangers

The flow boiling heat transfer characteristics of R134a in the multiport minichannel heat exchangers are presented. The heat exchanger was designed as the counter flow tube-in-tube heat exchanger with refrigerant flowing in the inner tube and hot water in the gap between the outer and inner tubes. Two inner tubes were made from extruded multiport aluminium with the internal hydraulic diameter of 1.1 mm for 14 numbers of channels and 1.2 mm for eight numbers of channels. The outer surface areas of two inner test sections are 5979 mm² and 6171 m², while the inner surface areas are 13,545 mm² and 8856 mm² for 14 and eight numbers of channels, respectively. The outer tube of heat exchanger was made from circular acrylic tube with an internal hydraulic diameter of 25.4 mm. The experiments were performed at the heat fluxes between 15 and 65 kW/m², mass flux of refrigerant between 300 and 800 kg/m² s and saturation pressure ranging from 4 to 6 bar. For instance the boiling curve, average heat transfer coefficients are discussed. The comparison results of two test sections with different the number of channels are investigated. The results are also compared with nine existing correlations. The new correlation for predicting the heat transfer coefficient was also proposed.     

Effect of fin thickness on air-side performance of herringbone wavy fin-and-tube heat exchangers

In the present study, the effects of fin thickness on the heat transfer and friction characteristics of fin-and-tube heat exchangers having herringbone wavy fin configuration are experimentally investigated. The experimental apparatus consists essentially of a well insulated open wind tunnel and herringbone wavy fin-and-tube heat exchangers made from aluminium plate finned, copper tube. Air and water are used to be working fluids in air-side and tube-side, respectively. A total of 10 samples of the fin-and-tube heat exchangers are tested. The experimental procedures are conducted by keeping the inlet water temperature at a pre-selected value, adjusting the water volumetric flow rate at a specific value and varying the air velocity. The results are presented as plots of the Colburn factor and friction factor against the Reynolds number based on the fin collar outside diameter (Re_Dc). From the results, it is found that for number of tube rows (N) = 2, the Colburn factor increases with increasing fin thickness. For N 4, the Colburn factor decreases with increasing fin thickness when Re_Dc < 1800, and increases with increasing fin thickness when Re_Dc > 2500. The friction factor increases with increasing fin thickness when fin pitch (F_p) 1.81 mm.     

Numerical estimation of mixed convection heat transfer in vertical helically coiled tube heat exchangers

A numerical investigation of the mixed convection heat transfer from vertical helically coiled tubes in a cylindrical shell at various Reynolds and Rayleigh numbers, various coil‐to‐tube diameter ratios and non‐dimensional coil pitches was carried out. The particular difference in this study compared with other similar studies is the boundary conditions for the helical coil. Most studies focus on constant wall temperature or constant heat flux, whereas in this study it was a fluid‐to‐fluid heat exchanger. The purpose of this article is to assess the influence of the tube diameter, coil pitch and shell‐side mass flow rate on shell‐side heat transfer coefficient of the heat exchanger. Different characteristic lengths were used in the Nusselt number calculations to determine which length best fits the data and finally it has been shown that the normalized length of the shell‐side of the heat exchanger reasonably demonstrates the desired relation. Copyright © 2010 John Wiley & Sons, Ltd.     

Flow characteristics of anisotropic structures constructed with porous layers

Artificial structures, serving as the solid matrix of anisotropic porous media and satisfying the requirement needed for flow visualization, were constructed with the perforated Polypropylene plates in order to improve the understanding of transport phenomena occurring in anisotropic porous media. This paper reports the regressed correlations of the experimental pressure gradient and filtration velocity data of three anisotropic and one isotropic porous media measured along two mutually orthogonal directions, which correspond to the principal axes of the permeability tensor, for the filtration velocities ranging from 0.2 to 12 mm/s with water as the fluid. To reflect the observed data, the regression equation with two types of deviations was formulated, in which the pressure gradient is represented by the sum of the linear and nonlinear terms of the filtration velocity. The physical model developed for the linear term assumes the solid matrix as repeated circular orifices when the filtration velocity approaches zero. The exponent of the filtration velocity in the nonlinear term was determined to be that of the Forchheimer extension. Also, four models for the coefficient of the nonlinear term were examined and the results were compared. The distribution of the residuals (the differences between the observed and the correlated values) validated the suggested regression procedure and the resulting correlations.     

Conjugate model for heat and mass transfer of porous wall in the high temperature gas flow

Heat and mass transfer of a porous permeable wall in a high temperature gas dynamical flow is considered. Numerical simulation is conducted on the ground of the conjugate mathematical model which includes filtration and heat transfer equations in a porous body and boundary layer equations on its surface. Such an approach enables one to take into account complex interaction between heat and mass transfer in the gasdynamical flow and in the structure subjected to this flow. The main attention is given to the impact of the intraporous heat transfer intensity on the transpiration cooling efficiency. The project supported by the National Natural Science Foundation of China (19889209) and Russian Foundation for Basic Research (97-02-16943)     

A boundary layer analysis of combined heat and mass transfer by natural convection from a concentrated source in a saturated porous medium

A boundary layer analysis was carried out to investigate the coupled phenomena of heat and mass transfer by natural convection from concentrated heat and mass sources embedded in saturated porous media. Both line and point source problems were treated. The boundary layer equations based on Darcy's law and Boussinesq approximation were solved by means of similarity transformation to obtain the details of velocity, temperature and concentration distributions above a concentrated heat source. Two important parameters, namely the Lewis number Le and the buoyancy ratioN were identified to conduct a series of numerical integrations. For the case of small Le, a substance diffuses further away from the plume centerline, such that the mass transfer influences both velocity and temperature profiles over a wide range. For large Le, on the other hand, the substance diffuses within a narrow range along the centerline. Naturally, the influence of mass transfer is limited to the level of the centerline velocity, so that a peaky velocity profile appears for positiveN whereas a velocity defect emerges along the centerline for negativeN. For such cases of large Le, the temperature profiles are found to be fairly insensitive to Le.     

Experiments on two-phase flow distribution inside parallel channels of compact heat exchangers

Uneven distribution in heat exchangers is a cause of reduction in both thermal and fluid-dynamic performances. Many papers have dealt with single-phase flow and both flow distribution data and analytical or numerical models are available for header design. With regard to two-phase flow, phase separation in manifolds with several outlets is so complicated that, to date, there is no general way to predict the distribution of two-phase mixtures at header-channel junctions. The design of headers for new generation compact heat exchangers and multi-microchannel evaporators is still based on an empirical approach, as a number of variables act together: geometrical parameters and orientation of the manifolds and of the channels, operating conditions, fluid physical properties.     

Melting and refreezing of porous media

During severe nuclear reactor accidents similar to Three-Mile Island, the fuel rods can fragment and thus convert the reactor core into a large rubble bed composed primarily of UO₂ and ZrO₂ particles. In the present study a one-dimensional model is developed for the melting and refreezing of such a bed. The analysis includes mass conservation equations for the species of interest (UO₂ and ZrO₂); a momentum equation that represents a balance among drag, capillary and gravity forces; an energy equation that incorporates the effects of convection by the melt, radiation and conduction through the bed and internal heat generation; and a UO₂---ZrO₂ phase diagram. A few key results are that (1) capillary forces are only important in beds composed of particles smaller than a few millimeters in diameter and in such beds, melt relocates both upward and downward until it freezes, forming crusted regions above and below the melt zone; (2) as melt flows downward and freezes, a flow blockage forms near the bottom of the bed and the location of this blockage is determined by the bottom thermal boundary layer thickness; (3) the maximum thickness of the lower crust increases linearly with the height of the bed; and (4) deviations from initially uniform composition profiles occur because ZrO₂ is preferentially melted and these deviations decrease as the initial ZrO₂ concentration is increased.     

Predicting the performance of a heat-pipe heat exchanger, using the effectiveness- NTU method

An analysis of the thermal performance of a heat-pipe heat exchanger based on the effectiveness-NTU model is developed. The predicted thermal performance using this model is compared with results obtained by previous investigators. Good agreement was observed.     

Contribution of air pollution to the fouling of heat exchangers in cooling water circuits

In an open recirculating system with a cooling tower, there are favorable conditions for the development of corrosion and fouling problems. These problems arise from the operating conditions and constant contamination of cooling water. A deep analysis of the system should provide the solutions for those problems. In the Sociedade Portuguesa de Oxigénio, SA, plant, a phosphate-based cooling water treatment ensures low corrosion rates. However, the fouling of heat exchange surfaces is promoted by the cooling water contamination. This contamination may result from the makeup water or from the air scrubbed in the tower. The fouling lowers the process efficiency and makes shutdowns for cleaning necessary. The air pollution produced by a neighboring plant is the main cause for fouling. To solve this problem, a decision was made to invest in equipment for makeup water treatment and reduce the stagnation conditions in the heat exchangers. It was also decided to hold negotiations to persuade the polluting company to reduce the particle emission to the atmosphere.     

Enhancement of the critical heat flux in saturated pool boiling using honeycomb porous media

Enhancement of the critical heat flux in pool boiling by the attachment of a honeycomb-structured porous plate on a heated surface is investigated experimentally using water under saturated boiling conditions. As the height of the honeycomb porous plate on the heated surface decreases, the CHF increases to 2.5 MW/m², which is approximately 2.5 times that of a plain surface (1.0 MW/m²). Automatic liquid supply due to capillary action and reduction of the flow resistance for vapor escape due to the separation of liquid and vapor flow paths by the honeycomb-structure are verified to play an important role in the enhancement of the CHF. A simplified one-dimensional model for the capillary suction limit, in which the pressure drops due to liquid and vapor flow in the honeycomb porous plate balances the capillary force, is applied to predict the CHF. The calculated results are compared with the measured results.     

多孔介质中二维对流传热的分叉

本文利用分叉理论研究了流体饱和的二维多孔介质从底部加热所引起的自然对流,用有限差分方法确定对流的分叉进程;揭示其模式转换机理及分叉对非正常流动图象形成的影响;同时确定了矩形截面宽高比与临界端利数的关系。还提出了一个判别分支稳定笥的简明方法。     

Thermodynamic optimization of finned crossflow heat exchangers for aircraft environmental control systems

This paper shows that the main geometric features of a flow component can be deduced from the thermodynamic optimization of the global performance of the largest flow system that incorporates the component. This approach represents a departure from the usual approach, where a flow component is optimized in isolation. The example chosen is the counterflow heat exchanger of the environmental control system (ECS) used on modern aircraft. The heat exchanger is fitted with a diffuser and a nozzle for the ram air, and the ECS runs on the boot strap air cycle, employing an additional compressor and turbine. Two heat transfer surface types are considered, finned and smooth parallel plates. Numerical results are reported for the external geometric aspect ratios of the heat exchanger, and for the plate-to-plate spacing of the smooth-plates model. It is shown that the optimized geometry for the core with finned surfaces is nearly the same as the optimized geometry for the core with smooth plates. Several of the optimized geometric features are robust with respect to changes in external parameters that vary from one application to the next. The method illustrated in this paper – the thermodynamic (constructal) optimization of flow geometry – is applicable to any system that runs on the basis of a limited amount of fuel (exergy) installed onboard, e.g., automobiles, ships, portable tools.     

Finite element modelling of two-phase heat and fluid flow in deforming porous media

This paper details a finite element model which describes the flow of two-phase fluid and heat within a deforming porous medium. The coupled governing equations are derived in terms of displacements, pore pressures and temperatures, and details of the time-stepping algorithm and thermodynamic considerations are also presented. Two numerical examples are included for verification.     

Finite element analysis of convective heat transfer in porous media

The finite element method is used to analyse convective heat transfer in a porous medium. Convection past a vertical surface embedded in the medium and convection in a confined porous medium enclosure are analysed using the above method. The results are compared with those available in the literature and the agreement is found to be good. The method is applicable for two-dimensional analysis in a porous body of any arbitrary shape. The restriction of the boundary layer assumption is relaxed.     

Numerical simulation and homogenization of two-phase flow in heterogeneous porous media

A mathematically rigorous method of homogenization is presented and used to analyze the equivalent behavior of transient flow of two incompressible fluids through heterogeneous media. Asymptotic expansions and H-convergence lead to the definition of a global or effective model of an equivalent homogeneous reservoir. Numerical computations to obtain the homogenized coefficients of the entire reservoir have been carried out via a finite element method. Numerical experiments involving the simulation of incompressible two-phase flow have been performed for each heterogeneous medium and for the homogenized medium as well as for other averaging methods. The results of the simulations are compared in terms of the transient saturation contours, production curves, and pressure distributions. Results obtained from the simulations with the homogenization method presented show good agreement with the heterogeneous simulations.