Two-phase experimental heat transfer studies on a water-diesel system in a shell and tube heat exchanger

Abstract

Two-phase heat transfer involving two immiscible systems is gaining importance in petrochemical and allied industries. Varying compositions of diesel and water were experimentally studied in a 1:2 shell and tube heat exchanger. The data on pure water and diesel were fitted to an equation of the form. h1φ = a NmRe.The two-phase multiplier, Φ L, was related to the Lockhart Martinelli (L-M) parameter, χtt², using the two-phase data and a correlation Φ L = b+c(χtt²)+d/(χtt²)² was established. The two-phase heat transfer coefficient was calculated based on the coefficients 'a' and 'm' for pure diesel and pure water along with ФL and the L-M parameter. The calculated values of the two-phase heat transfer coefficient h2φ based on pure diesel and pure water suggest that diesel is a better reference fluid since the average error is much smaller compared to pure water as reference.

Heat transfer coefficient; Shell and tube heat exchanger; Two-phase flow; Lockhart Martinelli parameter; Two-phase multiplier

FLUID DYNAMICS; HEAT AND MASS TRANSFER; AND OTHER TOPICS

Two-phase experimental heat transfer studies on a water-diesel system in a shell and tube heat exchanger

V. Alagesan^I; S. Sundaram^II

^ISchool of Chemical and Biotechnology, SASTRA University, Phone: + 91 9894988976, Fax: + 91 4362-264120, Thanjavur, Tamil nadu- 613402, India. E-mail: [e-mail]

^IISchool of Electrical and Electronics Engineering, SASTRA University, Phone: + 91 9894084987, Fax: + 91 4362-264120, Thanjavur, Tamil nadu- 613402, India. E-mail: [e-mail]

ABSTRACT

Two-phase heat transfer involving two immiscible systems is gaining importance in petrochemical and allied industries. Varying compositions of diesel and water were experimentally studied in a 1:2 shell and tube heat exchanger. The data on pure water and diesel were fitted to an equation of the form. h_1φ = a N^m_Re.The two-phase multiplier, Φ _L, was related to the Lockhart Martinelli (L-M) parameter, χ_tt², using the two-phase data and a correlation Φ _L = b+c(χ_tt²)+d/(χ_tt²)² was established. The two-phase heat transfer coefficient was calculated based on the coefficients 'a' and 'm' for pure diesel and pure water along with Ф_L and the L-M parameter. The calculated values of the two-phase heat transfer coefficient h_2φ based on pure diesel and pure water suggest that diesel is a better reference fluid since the average error is much smaller compared to pure water as reference.

Keywords: Heat transfer coefficient; Shell and tube heat exchanger; Two-phase flow; Lockhart Martinelli parameter; Two-phase multiplier.

INTRODUCTION

In process industries, two-phase flow has gained importance over the years. A better understanding of the rates of momentum and heat transfer in multi-phase flow is a must for the optimum design of heat exchangers. Since experimentation in two-phase flow is cumbersome, heat transfer coefficient correlations are being developed using pure fluid thermo-physical properties, dimensionless numbers such as the Reynolds number and Nusselt number.

Considerable research is being pursued in two-phase flow particularly in the area of fluid dynamics. Lockhart et al. (1949) carried out the first detailed study in gas-liquid two-phase flow and proposed a correlation for isothermal two-component flow in pipes. Thorbjon et al. (1972) presented a theoretical method for predicting the hold up in stratified and wavy two-phase flow. This theoretical solution agrees well with the generalized empirical solution developed by Lockhart and Martinelli (L-M) for all regimes. Subsequently, many researchers have used this approach for hydrodynamic and pressure drop studies in gas-liquid two-phase flow in various geometries such as vertical tube (Spedding et al., 1980; Vijayarangan et al., 2007; Xiuzhong et al., 2005), horizontal tube (Rani Hemamalini et al., 2005;), vertical and horizontal tube (Benbelk A. Shannak., 2008), across staggered rod bundles (Dowlati et al., 1992), helicoidal pipes (Awwad et al., 2000), etc. The heat transfer for gas-liquid flow in a plate type heat exchanger has also been investigated (Vlasogiannis et al., 2002). Ramachandran et al. (2006) conducted two-phase experiments in a compact heat exchanger and developed heat transfer correlations for two-phase heat transfer involving liquid-liquid systems. Ramachandran et al. (2008) developed a model for predicting the two-phase heat transfer coefficient of liquid-liquid systems using single phase data.

In this work, we propose a model formulation analogous to the L-M parameter model for heat transfer involving a liquid-liquid mixture. However, the study of heat transfer involving two immiscible liquids in a shell and tube heat exchanger has not been extensively studied. Experiments were carried out in a shell and tube heat exchanger with hot water as the heating fluid (service fluid) and two-phase mixtures of water-diesel in different ratios as the heated fluid (process fluid) on the shell side. The heat transfer coefficients on the shell side were correlated with Reynolds numbers and the relations between the Lockhart-Martinelli parameter, the quality and the two-phase multiplier were developed based on the experimental data. The work is confined to laminar flow in the present study.

EXPERIMENTAL SECTION

A schematic diagram of the 1-2 pass shell and tube heat exchanger experimental setup is shown in Figure 1, which gives in detail the size and specifications of all the units involved. Triangular pitch was used for the arrangement of tubes. Heating fluid and process fluid were pumped through the tube and shell side of the heat exchanger, respectively, using 0.25 HP pumps. Water was heated using a 2 kW heater and the temperature of the hot fluid was maintained constant at 70ºC in the tank using suitable thermostats with an accuracy of ±0.5ºC. Pumping continued through both the channels until a steady state was obtained with respect to the inlet and outlet temperatures of both the fluids. The flow rate was measured using Gallenkamp rotameters with an accuracy of ±0.1 LPM. The hot water flow rate was constantly maintained by rotameter R1 and circulated through the tube side, while the shell side test fluid mixture was metered through rotameter R2. The rotameters were calibrated before use. The flow rates of the two streams were adjusted using hand operated valves (2) and (4). The temperatures were recorded in the exit and inlet using RTD with an accuracy of ± 0.1ºC. Six compositions (0% to 100% diesel) of the water-diesel system were used in the study. The two-phase system was kept in suspension using an agitator.

CALCULATION METHODOLOGY

Tube Side

On the tube side, the heating fluid (hot water) circulated at a constant rate. The tube side Reynolds number, Nusselt number, heat transfer coefficient and heat transfer rates were calculated using Equation (1) to (4).

The properties µ, ρ, k were calculated based on the average of the inlet and outlet temperatures.

Shell Side

Various compositions of diesel and water were circulated at different flow rates. The heat transfer coefficients for the single phases were related to the Reynolds number using Equation (5) and the constants a and m established by regression analysis.

The quality (X) is defined by Equation (6),

The Reynolds number is calculated based on Equation (7) to (12):

The correction factor (F_t) is a function of the shell and tube fluid temperatures and was correlated as a function of two dimensionless temperature ratios (Sinnott, 2000):

R is equal to the shell side fluid flow rate times the fluid mean specific heat divided by the tube side fluid flow rate times the tube side fluid specific heat.

S is a measure of the temperature efficiency of the exchanger.

The true temperature difference is expressed as:

The overall heat transfer coefficient (U) and process side heat transfer coefficient (h_2φ ) are determined using Equation (15) and (16):

The single phase heat transfer coefficient was related to the Lockhart-Martinelli parameter (χ_tt²) using the slope 'm' of Equation (5).

The ratio of the two-phase heat transfer coefficient to the single phase heat transfer coefficient is expressed as the two-phase multiplier (Φ _L):

Equation (19) relates the two-phase multiplier to the L-M parameter:

The error is defined by Equation (20) as,

RESULTS AND DISCUSSION

Figure 2 shows the variation of the single and the two-phase heat transfer coefficients with Reynolds number for the shell side process fluid. It is seen that the two-phase data fall within the boundaries of the pure water and pure diesel data. In addition, the increase in agitation enhances the uniformity of the two-phase mixture, thus preventing stratification of the phases. Hence, the overall physical properties of the mixture remain uniform throughout the flow channel. The uniformity of the two-phase mixture, coupled with increased convective currents driven by higher flow velocities, results in higher heat transfer coefficients.

Figures 3 and 4 show the single phase heat transfer coefficient (h_1φ ) and Reynolds number relationship for pure diesel and pure water, respectively. The data for pure fluid (diesel or water) was fitted to Equation (5) by regression analysis and the resultant constants a and m for diesel and water are given in Table 1. Initially the L-M parameter correlation was used for predicting the pressure drop of gas-liquid two-phase systems and then the heat transfer coefficients for liquid-liquid two-phase flow were related to the L-M parameter (Ramachandran et al., 2006, 2008) in Equation (17), where 'm' represents the power to which the Reynolds number is raised to determine the single phase heat transfer coefficient. The inlet and outlet temperatures of the shell side and tube side fluid are shown in Table 2 for different compositions. We maintained the inlet temperatures constant and measured the outlet temperatures once the heat exchanger attained the steady-state condition. The two-phase multiplier Φ _L (Equation (18)) and the L-M parameter (Equation (17)) are shown in Figures 5 and 6 for 80% composition of the diesel–water system based on pure diesel and pure water, respectively, and are related by the heat capacity (Equation (19)). The variation of the two-phase multiplier (Φ _L) with the L-M parameter (χ_tt²) shows an increasing concave trend, while the h_1φ of pure diesel is less than the heat transfer coefficient of the two-phase mixture. Because h_1φ based on pure water is higher than h_2φ , the trend between Φ _L and χ_tt² is upwardly concave. The constants b, c and d of the heat capacity correlation (Equation (19)) are given in Table 3 based on pure diesel and pure water as the reference fluid. The relationship of quality to the L-M parameter and the two-phase multiplier are shown in Figures 7 and 8. An increasing L-M parameter (χ_tt²) for the diesel-water system denotes a decrease in quality(X) and implies an increase in the two-phase multiplier (Φ _L). As the proportion of the second phase increases, with a consequent decrease in the proportion of water, the viscosity of the mixture increases and the thermal conductivity, density and specific heat decrease. This brings down the heat transfer coefficient and hence the two phase multiplier decreases with quality. Tables 4 and 5 compare the two-phase heat transfer coefficients calculated based on pure diesel and pure water as the reference fluid. Table 6 summarizes the average absolute deviation of the two-phase heat transfer coefficients calculated using water and diesel as reference liquids for the data in Tables 4 and 5.

CONCLUSION

Two-phase flow through a 1-2 pass shell and tube exchanger using a water-diesel system was studied. The correlations between X, Φ _L and χ_tt² will be useful for predicting two-phase heat transfer coefficients using pure phase thermo-physical properties. The correlation developed for the diesel-water system is useful for identifying heat transfer coefficients of two-phase systems for the range of Reynolds number studied. Based on the summary in Table 6, it can be concluded that, for this system, diesel is a better reference fluid compared to water since the average absolute deviation varies from 2.24 to 2.88 percent compared to water (2.63 to 5.69 percent). Further studies on Palm oil-Water, Nitrobenzene-Water, Oleic acid-Water and Castor oil-Water are being carried out to verify whether Palm oil, Nitrobenzene, Oleic acid and Castor oil are also better reference fluids compared to water. The specific reason for diesel being a better reference fluid should be clarified by this comprehensive study of similar systems.

NOMENCLATURE

a, m

constants for pure water and pure diesel in Equation (5)

A_h

heat transfer area m²

A_s

cross flow area m²

b, c, d

constants of the heat capacity correlation Equation (19)

B_s

baffle spacing m

Cp_h

specific heat of hot water J/kg K

D_i

inner diameter of the tube m

D_o

outer diameter of the tube m

D_s

inner diameter of the shell m

D_e

equivalent diameter

F_t

temperature correction factor

G_s

mass velocity kg/m² s

h_1φ

heat transfer coefficient of pure diesel/pure water W/m² K

h_2φ

two-phase heat transfer coefficient W/m² K

h_1tφ

tube side (hot water) heat transfer coefficient W/m² K

k

thermal conductivity of hot water W/m K

k_w

thermal conductivity of the tube wall material W/m K

L

length of tube m

m_h

flow rate of hot water kg/s

N_Nu

Nusselt number

N_Pr

Prandtl number

N_Re

Reynolds number

Pt

tube pitch (m)

R, S

dimensionless temperature ratios

T_h1

inlet temperature of hot water on the tube side K

T_h2

outlet temperature of hot water on the tube side K

T_c1

inlet temperature of cold fluid on the shell side K

T_c2

outlet temperature of cold fluid on the shell side K

v_f

volumetric flow rate of diesel m³/s

v_m

flow rate of a diesel-water mixture m³/s

v_w

volumetric flow rate of water m³/s

X

quality parameter for the two-phase system

Greek Letters

χ_tt²

Lockhart-Martinelli (L-M) parameter

Φ_L

two phase multiplier

ΔT_lm

logarithmic mean temperature K

ΔT_m

true temperature difference K

ν

velocity of hot water m/s

µ

viscosity of hot water kg/m s

µ_w

viscosity of water kg/m s

µ_f

viscosity of diesel kg/m s

µ_m

viscosity of diesel-water mixture kg/m s

ρ

density of hot water

ρ_w

density of water kg/m³

ρ_f

density of diesel kg/m³

ρ_m

density of diesel-water mixture kg/m³

(Submitted: April 26, 2011 ; Revised: November 19, 2011 ; Accepted: December 29, 2011)

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Publication Dates

• Publication in this collection
  21 June 2012
• Date of issue
  June 2012

History

• Received
  26 Apr 2011
• Accepted
  29 Dec 2011
• Reviewed
  19 Nov 2011