Concentration and Temperature Profile of LiBr Aqueous Solution Flowing Over Horizontal Tube with Film Redistribution

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Concentration and Temperature Profile of LiBr Aqueous Solution Flowing Over Horizontal Tube with Film Redistribution

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Anil Kumar Sharma1, Bimal Kumar Mishra2, Abhinav Dinesp, Ashok Misra4 1Department of Production Engineering, Birla Institute of Technology, Deoghar, India 2Department of Applied Mathematics, Birla Institute of Technology, Mesra, Ranchi, India

3Department of Electronics & Communication Engineering, Birla Institute of Technology, Jaipur, India

4Department of Mechanical Engineering, Birla Institute of Technology, Mesra, Ranchi, India

Abstract:- The paper presents a numerical investigation on water vapor absorption by an aqueous Lithium Bromide solution flowing over horizontal tubes with film redistribution. The model is developed based on continuity, momentum, energy and mass diffusion equations for certain boundary conditions and assumptions. Dimensionless variables are used to transform the calculation domain into a rectangular grid that normalizes the spatial derivatives in x and y directions. Profile for variation of Lithium Bromide mass fraction and temperature across the solution film thickness are generated. Concentration profile across film thickness reveals that the mass fraction boundary layer is thin at interface and does not penetrate much into the film. To enhance absorption in such state, redistributors approach is proposed. Simulation results show an increment in absorption of vapor. Temperature profile shows non uniformity for larger value of , probably due to dominating gravitational force in this region which leads to flow separation.

Keywords: Film flow; Horizontal tube; Absorption; Redistribution; Mathematical Model

Nomenclature

Cp specific heat (J kg-1K-1)

D mass diffusivity (m2s-1)

g gravitational acceleration (m s-2) ha heat of absorption (J kg-1)

hcw cooling water side heat transfer coefficient (W m-2 K-1) k thermal conductivity (W m-1 K-1)

m mass (kg)

P pressure (Pa)

r radius (m)

T Temperature (K)

U overall heat transfer coefficient between cooling water and tube (Wm-2 K-1) vx velocity in flow direction (m s-1)

vy velocity in film thickness direction (m s-1) X LiBr mass fraction (%)

x flow direction coordinate

y coordinate perpendicular to flow direction thermal diffusivity (m2 s-1)

film thickness(m)

specific film flow rate (kg m-1 s-1) dynamic viscosity (kg m-1 s-1) kinematic viscosity (m2 s-1) density (kg m-3)

angle (radian)

non dimensional coordinate in x-direction non dimensional coordinate in y-direction

Subscripts

i inlet or inner

if interference

o outer

t tube

1. INTRODUCTION

Increased global warming and environmental effect of chlorofluorocarbon has stimulated interest in development of vapor absorption systems to generate cooling effect. In such systems, waterlithium bromide (H2OLiBr) is most widely used working fluid pair. Vapor absorption cycle for the system is explained in fig. 1. In this cycle, vapor evaporates and separates from aqueous LiBr solution in generator by gaining heat from external source. These vapors shift towards condenser and condensed by releasing heat to cooling water. The condensed water is throttled to evaporator at low pressure, where it changes its phase from liquid to vapor by gaining latent heat of vaporization from surroundings that generates cooling effect. These vapors are then absorbed by aqueous LiBr solution supplied from generator in the absorber. The absorption of water vapor is an exothermic process and released heat is passed to the cooling water. From exit of absorber, solution with reduced concentration of LiBr is pumped to generator at higher pressure and continues the cycle.

A review of absorption refrigeration technologies was presented by Srikhirin et al. [1]. Design and construction methodology of a LiBrwater absorption system was discussed by Florides et al. [2]. Sharma et al. [3, 4] had proposed an absorption system configuration with certain capacity and performed sensitivity analysis.

In above discussed cycle, absorption is an exothermic process and excess of heat needs to be removed from film. This simultaneous heat and mass transfer make the absorber critical and have significant effects on overall system efficiency. An experimental study on absorber with film flowing over vertical surface was performed by Kim et al. [5]. A model of water- cooled vertical plate absorber was developed by Yoon et al. [6] and by Yigit [7] on vertical tube absorber. Islam et al. [8] discussed a linearized coupled model for falling film absorbers. In water cooled horizontal tube type configuration, absorption phenomenon depends on solution properties and its flow rate. Other contributing factors which govern flow around and between the tubes are tube diameter, tube spacing and surface wetting. Oxygen gas absorption on completely wetted horizontal tubes was experimentally investigated by Nosoko et al. [9]. A detailed review of heat and mass transfer models for falling film absorption was done by Killion et al. [10]. Wassenaar [11] had conducted experimental work on the performance of horizontal tube absorber. Absorption by a wavy film flow was discussed in the model of Patnaik et al. [12].

The aim of present study is to simulate the heat and mass transfer process in water cooled horizontal tube absorber. Two- dimensional governing equations were formulated and solved for the falling film regime over a smooth horizontal tube. Using finite difference method temperature and concentration distributions were found along the film thickness. A redistribution approach had been proposed to enhance the absorption of vapor by aqueous LiBr solution.

2. PROBLEM GEOMETRY AND ASSUMPTION

Geometry of the problem and flow regime on a representative absorber tube is shown in fig. 2. The LiBr solution is injected from a distributor at the absorber inlets on the first tube and flows down by gravity forming a thin falling film over horizontal tube. The vapors present in surroundings of the tube are absorbed at the interface of the falling film and reduces the concentration of lithium bromide in the solution. Release of absorption heat at film interface is transferred to the cooling water flowing inside the tube. At bottom of tube, film breaks into drops and falls on the next tube.

In above geometry, redistributors are placed in form of small diameter wire at specific positions along the length of horizontal tube and perpendicular to the flow direction of falling film. This agitates the falling film and homogenizes LiBr concentration throughout the film thickness and afterward provides a fresh surface for absorption of vapor at the interface. Considering gravitational effect on falling film, redistributors are positioned on upper half of the tube. Exposed surface area of film and time of exposure at interface are critical for absorption of vapors and influence the number of redistribution positions. Hence for illustration purpose, four redistributions position symmetrically placed at 300 and 600 had been selected (Fig.3). Properties of solution were referred from ASHRAE handbook of fundamentals [13].

3. MATHEMATICAL FORMULATION

3.1 Governing equations3.2 Derived equations3.3 Transformation of derived and governing equations

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