Frost formation on fin- and- tube heat exchangers. Part II—Experimental investigation of frost formation on fin- and- tube heat exchangers

This paper presents some comparisons of the experimental data obtained with the analytical model presented in Part I of this paper. The comparisons are made in terms of airside pressure drop and the overall heat transfer coefficient.     

Modeling non-uniform frost growth on a fin-and-tube heat exchanger

A semi-empirical model that predicts non-uniform frost growth on heat exchangers is developed and experimentally validated. The model is based on a scaling approach that uses the average frost layer properties to predict growth in a quasi-steady state, heat and mass balance based segment-by-segment coil simulation. The air redistribution algorithm in the model improved frost thickness predictions by 20%-50% and coil capacity predictions by 42% compared to the same model without air redistribution. The model along with an empirical frost delay predicted the frost thickness for different inlet refrigerant temperatures, air relative humidities and air velocities under non-uniform frosting with a root mean square error of 3.7%, 9.8% and 5.2% respectively.     

The effect of hydrophilicity on condensation over various types of fin-and-tube heat exchangers

An experimental study on the behavior of water hold-up by condensation on various shapes of fin-and-tube heat exchangers with different surface hydrophilicity, i.e. dynamic contact angle of surface, was conducted. Condensation experiments were conducted, and the amount of water hold-up was measured. Condensation flow patterns on fins with different surface hydrophilicity were visualized. Results showed that the water hold-up of a heat exchanger could be reduced by the enhancement of the surface hydrophilicity and the design of a heat exchanger with a lower number of fins and fins with slant ends.     

Empirical correlations for heat transfer and flow friction characteristics of herringbone wavy fin-and-tube heat exchangers

This study presents an empirical correlation describing the airside performance of herringbone wavy fin pattern. A total of 61 samples containing approximately 570 data points are used in the regression analysis. The proposed heat transfer correlation can describe 91% of the test data within ±15% with a mean deviation of 6.98% while the proposed friction correlation can describe 85% of the database within ±15% with a mean deviation of 8.82%.     

Heat transfer analysis of fin-and-tube heat exchangers with flat and louvered fin geometries

This paper analyzes the fluid flow and heat exchange on the air side of a multi-row fin-and-tube heat exchanger. A comparison is given between fin-and-tube heat exchanger characteristics with flat and louvered fins in a wider range of operating conditions defined by Reynolds number (based on fin spacing and air frontal velocities). The detailed representation of calculated data for the louvered heat exchanger shows significantly better heat transfer characteristics and a slightly higher pressure drop. The CFD procedure was validated by comparing the numerical simulation results with the experimental results showing the minimal average Nusselt number deviation and an almost perfectly corresponding pressure drop.     

Numerical simulation of dehumidifying fin-and-tube heat exchangers: Semi-analytical modelling and experimental comparison

The aim of this paper is to present a developed semi-analytical model for the simulation of dehumidifying air–liquid fin-and-tube heat exchangers. The simulation strategy and the mathematical methodology are described in detail. The model is based on -NTU method, and formulated in a compact way for dry and wet surface situations (temperature or enthalpy driven, respectively). Both rating and design procedures have been developed for fully dry, partially wet, or fully wet surface conditions. The model predictions are compared with experimental data obtained on a wavy and a plain finned heat exchanger, giving reasonably accurate results. The limitations of the empirical information used are clearly identified in the work. The aim of this model is to provide a fast but reliable rating and design numerical tool for air–liquid heat exchanger applications.     

An experimental investigation of heat transfer and friction losses of interrupted and wavy fins for fin-and-tube heat exchangers

The present paper discusses the results of an extensive investigation about the performance of various fin configurations, carried out in the Luve Contardo experimental facilities and aimed to enhance the heat transfer capabilities of air-cooled condensers and liquid coolers. Test results here discussed are relative to 15 coil prototypes, having the same tube and fin geometry (25×21.65 mm staggered 5/8” tube banks, 2 mm fin spacing) but different fin surface geometry, from flat to wavy to louvered to “winglet”. Different rates of heat transfer and pressure loss enhancement were obtained, also depending on the quality of the pressing process. General approaches to evaluate the “goodness” of one fin design with respect to another one provided questionable results: pressure loss influence on the air flow cannot be properly evaluated unless the actual fan head curve and the coil dimensions (front area and rows number) are stipulated. The performance of air-cooled condensers was therefore predicted and compared, for various fin design and for coil arrangements of practical interest. The type of fin adopted strongly influences the heat exchanger performance and louvered fins generally provide the best results.     

Selection of Work Sampling Observation Times: Part I—Stratified Sampling

Various methods of selecting observation times in work sampling studies are presented, including simple random, systematic, and stratified sampling, and a new method called restricted random sampling. The attributes of these sampling methods are evaluated, particularly statistical efficiency, and the important advantages of stratification are demonstrated. Finally, the analysis of variance is recommended for statistical analysis of work sampling data to account for the presence of several sources of variation, in addition to sampling error.     

Reproducing kernel hierarchical partition of unity,Part I—formulation and theory

This work is concerned with developing the hierarchical basis for meshless methods. A reproducing kernel hierarchical partition of unity is proposed in the framework of continuous representation as well as its discretized counterpart. To form such hierarchical partition, a class of basic wavelet functions are introduced. Based upon the built‐in consistency conditions, the differential consistency conditions for the hierarchical kernel functions are derived. It serves as an indispensable instrument in establishing the interpolation error estimate, which is theoretically proven and numerically validated. For a special interpolant with different combinations of the hierarchical kernels, a synchronized convergence effect may be observed. Being different from the conventional Legendre function based p‐type hierarchical basis, the new hierarchical basis is an intrinsic pseudo‐spectral basis, which can remain as a partition of unity in a local region, because the discrete wavelet kernels form a ‘partition of nullity’. These newly developed kernels can be used as the multi‐scale basis to solve partial differential equations in numerical computation as a p‐type refinement. Copyright © 1999 John Wiley & Sons, Ltd.     

The behaviour of Kevlar fibre-epoxy laminates under static and fatigue loadings. Part I—experimental

Kevlar 49 fibre and unidirectional Kevlar fibre reinforced plastic (KFRP) laminates both show an increase in stiffness under monotonic tensile loading. This stiffening effect is time-dependent and is reversible once the load is removed. In contrast, the modulus of a cross-ply KFRP laminate is affected primarily by matrix cracking of the transverse (90°) ply, and is sensitive to strain-rate and temperature. In cyclic (tensile) loading, however, the modulus of the cross-ply laminate depends on a combination of the fibre stiffening effect and transverse matrix cracking.     

Design sensitivity analysis and optimization of non‐linear transient dynamics. Part I—sizing design

A continuum‐based sizing design sensitivity analysis (DSA) method is presented for the transient dynamic response of non‐linear structural systems with elastic–plastic material and large deformation. The methodology is aimed for applications in non‐linear dynamic problems, such as crashworthiness design. The first‐order variations of the energy forms, load form, and kinematic and structural responses with respect to sizing design variables are derived. To obtain design sensitivities, the direct differentiation method and updated Lagrangian formulation are used since they are more appropriate for the path‐dependent problems than the adjoint variable method and the total Lagrangian formulation, respectively. The central difference method and the finite element method are used to discretize the temporal and spatial domains, respectively. The Hughes–Liu truss/beam element, Jaumann rate of Cauchy stress, rate of deformation tensor, and Jaumann rate‐based incrementally objective stress integration scheme are used to handle the finite strain and rotation. An elastic–plastic material model with combined isotropic/kinematic hardening rule is employed. A key development is to use the radial return algorithm along with the secant iteration method to enforce the consistency condition that prevents the discontinuity of stress sensitivities at the yield point. Numerical results of sizing DSA using DYNA3D yield very good agreement with the finite difference results. Design optimization is carried out using the design sensitivity information. Copyright © 2000 John Wiley & Sons, Ltd.     

A new shock damage model: Part I—Model formulation and analysis

In this paper we formulate a new model for system failure due to shock damage and study some aspects of analysis and parameter estimation for the model proposed.     

Linked interpolation for Reissner-Mindlin plate elements: Part I—A simple quadrilateral

In most plate elements using the Reissner-Mindlin assumptions, the interpolations used for the lateral displacements (w) and the rotation (θ) involve the independent representation of each variable by its nodal values, usually with identical interpolations. To ensure a higher order of expansion for displacement w its representation is linked in the present paper with both sets of nodal variables. Conditions necessary for the use of such expansions are established here and the paper shows the development of a linear quadrilateral element (Q4BL) whose performance and robustness are good (although it possesses one singularity if only three degrees of freedom are prescribed). In Part II we apply the identical formulation to develop a triangular element (T3BL) which performs equally well and is fully robust.     

Frost formation and heat transfer on circular cylinders in cross-flow

When humid air comes into contact with a surface whose temperature is below the dew point of water vapour in air and also below the freezing point, frost deposition takes place over the surface. Previous studies indicate that the heat transfer rate increases at the initial stages of deposition since the rough frost surface acts as a finned one. As the frost thickens, however, the insulating effect of the frost layer predominates resulting in a reduction in the heat transfer rate. This paper presents a transient model to predict the frosting process over a circular cylinder in a cross-flow of humid air. the transfer parameters are computed employing a numerical solution of the momentum, energy and diffusion boundary-layer equations along with the continuity equation, using a finite difference scheme. Empirical correlations for thermal conductivity and density are utilized for closure purposes. Model results are compared with existing experimental data and with numerical data of previous investigators and are found to agree well in the applicable temperature and humidity ranges of the frost density and conductivity correlations.     

Partition experimental designs for sequential processes: Part I—First‐order models

The output quality or performance characteristics of a product often depend not only on the effect of the factors in the current process but on the effect of factors from preceding processes. Statistically‐designed experiments provide a systematic approach to study the effects of multiple factors on process performance by offering a structured set of analyses of data collected through a design matrix. One important limitation of experimental design methods is that they have not often been applied to multiple sequential processes. The objective is to create a first‐order experimental design for multiple sequential processes that possess several factors and multiple responses. The first‐order design expands the current experimental designs to incorporate two processes into one partitioned design. The designs are evaluated on the complexity of the alias structure and their orthogonality characteristics. The advantages include a decrease in the number of experimental design runs, a reduction in experiment execution time, and a better understanding of the overall process variables and their influence on each of the responses. Copyright © 2001 John Wiley & Sons, Ltd.     

Optimal control of vortex shedding using low‐order models. Part I—open‐loop model development

An approach to developing active control strategies for separated flows is presented. The methodology proposed is applied to the incompressible unsteady wake flow behind a circular cylinder at a Reynold's number of 100. Control action is achieved via cylinder rotation. Low‐order models which are amenable to control and which incorporate the full non‐linear dynamics are developed by applying the proper orthogonal decomposition technique to data provided by numerical simulation. This process involves extensions to the usual POD approach and the results are therefore assessed for two ‘open‐loop’ test cases. The predictions are found to be satisfactory for control purposes, assuming the model can be reset periodically. The use of these models for optimal control is discussed in a companion paper, Part II. Copyright © 1999 John Wiley & Sons, Ltd.     

Complex variable boundary integral method for linear viscoelasticity: Part I—basic formulations

The basic formulations (direct and indirect) of the complex variable boundary integral method for linear viscoelasticity are presented. Complex variable temporal integral equations for the formulations are obtained for viscoelastic solids whose behavior in shear is governed by a Boltzmann model while the bulk behavior is purely elastic. The functions involved in the integral equations are the time-dependent complex boundary tractions and displacements for the direct approach and the unknown time-dependent complex density functions for the indirect approaches. The temporal integral equations give the displacements and stresses at a point inside a viscoelastic region in terms of time convolution and space integrals over the boundary of this region. The equations are valid for the boundaries of arbitrary shapes provided that these boundaries are sufficiently smooth. Complex variable temporal boundary equations are obtained by taking the inner point to the boundary. Numerical treatment of spatial and time convolution integrals involved in the boundary equations is discussed.     

Enhanced solution control for physically and geometrically non‐linear problems. Part I—the subplane control approach

Geometrically or physically non‐linear problems are often characterized by the presence of critical points with snapping behaviour in the structural response. These structural or material instabilities usually lead to inefficiency of standard numerical solution techniques. Special numerical procedures are therefore required to pass critical points. This paper presents a solution technique which is based on a constraint equation that is defined on a subplane of the degrees‐of‐freedom (dof's) hyperspace or a hyperspace constructed from specific functions of the degrees‐of‐freedom. This unified approach includes many existing methods which have been proposed by various authors. The entire computational process is driven from only one control function which is either a function of a number of degrees‐of‐freedom (local subplane method) or a single automatically weighted function that incorporates all dof's directly or indirectly (weighted subplane method). The control function is generally computed in many points of the structure, which can be related to the finite element discretization. Each point corresponds to one subplane. In the local subplane method, the subplane with the control function that drives the load adaptation is selected automatically during the deformation process. Part I of this two‐part series of papers fully elaborates the proposed solution strategy, including a fully automatic load control, i.e. load estimation, adaptation and correction. Part II presents a comparative analysis in which several choices for the control function in the subplane method are confronted with classical update algorithms. The comparison is carried out by means of a number of geometrically and physically non‐linear examples. General conclusions are drawn with respect to the efficiency and applicability of the subplane solution control method for the numerical analysis of engineering problems. Copyright © 1999 John Wiley & Sons Ltd.     

Design-oriented analysis of imperfect truss structures—part I—accurate analysis

An accurate nonlinear analysis procedure for calculating the displacement stresses and system buckling loads of geometrically imperfect truss structures is developed. The investigation considers both local and system imperfections. This nonlinear analysis takes first-order geometrically nonlinear effects into account. The accuracy of the analysis procedure is confirmed by comparison with analytical and experimental results for truss structures drawn from the literature. The results show that local and system imperfections can have strong influence on the behaviour of truss structures and therefore should be taken into account. It is shown that nonlinear effects play a major role in the phenomena and therefore simplified analyses that neglect nonlinear effects are inadequate.