Flow rate distribution in evaporating parallel pipes—modeling and experimental

doi:10.1016/j.ces.2006.08.026

Chemical Engineering Science

Volume 61, Issue 22, 20 November 2006, Pages 7249-7259

https://doi.org/10.1016/j.ces.2006.08.026 Get rights and content

Abstract

The motivation for the present work is related to the use of parabolic trough solar power technology for direct steam generation (DSG). So far, commercial plants use liquid oil to absorb heat from the collectors, and steam is produced in heat exchangers. A more efficient process of direct steam generation in the collectors is not used due to possible uneven flow rate distribution and other instabilities, related to liquid–vapor flow in parallel pipes.

In this work we present an analysis and experimental results for the flow rate distribution of water flowing and evaporating in two parallel pipes with common inlet and outlet manifolds.

A new simplified model that yields the pressure drop versus the flow rate in a single pipe is developed. This model is the basis for the calculation of steady-state solutions, stability analysis and transient simulations in two parallel pipes.

Multiple steady-state solutions may be obtained depending on the flow rate and the heating power. Linear stability analysis and transient simulation allow to differentiate between the stable steady states and the unstable ones. It is also shown that when few stable state solutions are possible the one that takes place depends on the history of the inlet flow rate. Experimental results compare well with the theoretical solutions.

Introduction

Simultaneous flow of two-phases, vapor and liquid, in parallel pipes has many engineering applications. Fluids flowing in parallel pipes, undergoing evaporation or condensation take place in heat exchangers, boilers and condensers, power plants and cooling systems. In the nuclear industry, evaporating two-phase flow in parallel channels is of major interest related to nuclear instability in boiling water reactors (BWR) and loss of cooling accident (LOCA). Evaporating two-phase flow in parallel micro-channels is considered for heat removal in micro-electronic devices.

The main motivation of the present work is associated with the use of solar energy collected in long lines. In this technology, an array of parallel pipes is located at the focal center of parabolic mirrors that focus solar radiation on the pipes. The pipes are placed at the center of glass pipes, under vacuum conditions, which allows radiant heat to reach the pipes but minimizes convective and radiant losses to the surroundings. Since the objective of this system is to produce steam, one would expect that water should enter the inlet manifold and steam will be produced in the heated pipes. However, commercial plants use oil as the primary heated fluid and steam is produced in a steam generator. The reason direct steam generation (DSG) is not used is due to the lack of understanding of two-phase flow behavior within the absorbing pipes and the fear of possible occurrence of circumferential temperature distribution, instabilities and uneven flow rate distribution.

Renewed interest in solar energy production based on the parabolic trough concept stimulated intensive research in this area. May and Murphy (1983) used the homogeneous model to analyze the benefits of direct generation of steam in line-focus solar collectors. Almanza and Lentz (1998), Almanza et al. (2002) and Odeh et al. (2000) were concerned with the flow pattern in the heated pipe and the circumferential temperature gradient that is generated during stratified flow.

Flow in real large-scale experiments of a single pipe DSG operation is described by Zarza et al. (2002), Eck and Steinmann (2002), Price et al. (2002), and Eck et al. (2003). These papers bring to our attention the up-to-date status of the direct solar steam (DISS) test facility at the Plataforma Solar de Almeria (PSA). Apparently, the flow in parallel pipes is still not well analyzed. The operation of parallel rows under steady-state and transient conditions, remain one of the main open questions concerning DSG (Zarza et al., 2002; Eck et al., 2003).

During evaporation in a single pipe flow excursion, pressure and flow rate oscillations may occur. Comprehensive reviews of two-phase flow instability in a single heated pipe are included in many papers like Yadigaroglu (1981), Kakaç and Veziroglu (1983), Yüncü and Kakaç (1988), Ozawa (1999), and Pederson and May (1982), where the last one is concerned specifically with solar energy. According to the last two reviews the main instabilities that may appear in a single pipe are: density wave oscillation (DWO), pressure drop oscillation (PDO), and flow excursion.

Two-phase flow instabilities in parallel pipes were investigated primarily for flow in vertical pipes since there was no special interest in horizontal flows. Boiling two-phase flow in horizontal pipes differ from boiling two-phase flow in vertical pipes by the flow patterns (Lock, 1996; Collier, 1981) and by the absence of gravitational pressure drop. Dominant gravitational pressure drop avoid flow rate mal-distribution as reported by Ozawa et al. (1979).

Akagawa et al. (1971) investigated flow distribution and stability for the case of Freon-113 flowing in three parallel vertical tubes. A simplified stability analysis was performed and was shown to compare favorably with the experimental results. Ozawa et al. (1979) performed a similar experiment with refrigerant R-113 in a five vertical pipe system. They observed density oscillations in the range where pressure drop versus flow rate increases monotonously and uneven distribution in the range where pressure drop versus flow rate decreases.

Tong (1975) indicated that it is possible to avoid flow rate mal-distribution in vertical pipes by a suitable adjustment of the operating conditions. Ozawa et al. (1979) experimentally overcame the mal-distribution in vertical parallel pipes by increasing the pipes diameter in order to decrease the frictional pressure drop and Profos (1959) offered to overcome the mal-distribution by increasing the pipes inlet hydraulic resistance.

Tanaka et al. (1979) investigated experimentally two-phase flow of refrigerant R-11 in two parallel horizontal tubes. They observed flow rate oscillations in the common inlet pipe, but unfortunately they did not place flow meters at the parallel pipes. Nakanishi et al. (1983) performed evaporation tests with refrigerant R-113 on a system of five, four and three vertical parallel pipes. Their main conclusion is that if the flow is distributed uniformly among all channels, they oscillate with the same amplitude and equal phase lag. They performed an additional study on air water flow in parallel pipes and mentioned that results obtained for air water should not apply directly to actual boiling systems.

Natan et al. (2003) analyzed a system of two parallel pipes with common inlet and outlet manifolds that undergoes a process of heating and evaporation. They developed a model for the prediction of flow rate distribution in two parallel pipes at steady state. The pressure drop versus flow rate curves are calculated based on the local flow pattern along the pipe while Akagawa et al. (1971) and Ozawa et al. (1979) obtained it experimentally. The analysis was performed for horizontal and near horizontal inclinations, up to $10^{\circ}$ . The results show that the solution is not unique and one can obtain multiple solutions even for the case of equal heating of the two pipes.

Minzer et al. (2004) measured the flow rate distribution and the pressure drop in a set of two parallel horizontal evaporating pipes. The experimental results compare well with the theoretical steady-state analysis of Natan et al. (2003). The stability criteria offered by Akagawa et al. (1971) was used to distinguish between stable and unstable steady states.

Flow transients in evaporating parallel channels that are related to nuclear reactor safety were studied by several researchers like Kakaç et al. (1976), Aritomi et al., 1977a, Aritomi et al., 1977b, Fukuda and Kobori (1978), and Xiao et al. (1993). In these works, flow oscillations in vertical upward flow systems were investigated. There was no evidence for flow rate mal-distribution. Few researchers like, Aritomi et al. (1979) and Wedekind and Kobus (1994) investigated theoretically and experimentally transients under imposed unequal flow rate distribution.

Aritomi et al. (1981) investigated experimentally instabilities in two, U shape, parallel channels with boiling in a down comer. They obtained unequal flow distribution with new type of oscillations. These phenomena are caused by the development of a stagnant vapor slug at the down comer of one tube.

The main objective of this work is to determine when uneven distribution takes place for evaporating flows in horizontal and slightly inclined parallel pipes with common inlet and outlet manifolds. A simplified theoretical analysis for the solution of the flow distribution is carried out followed by a stability analysis and transient simulations. Experimental data are collected and compared with the theoretical results.

Section snippets

Basic approach

The geometry involved is presented schematically in Fig. 1. Two pipes are placed in parallel and have a common input manifold and a common output manifold. Subcooled water enters the input manifold and the flow splits into the two parallel pipes. Heating and evaporation takes place in the two pipes. Water can exit the outlet as hot liquid, liquid–vapor mixture or superheated vapor, depending on the flow rate and heating power. It is assumed that the liquid input, $W_{in}$ , and the pressure at the

Experiments

An experimental apparatus was built in order to check the validity of the theory and to determine the actual steady-state solutions that will be obtained in practice. A schematic diagram of the experimental system is presented in Fig. 4. The experimental facility consists of two parallel stainless steel pipes, 6 m long 5 mm in diameter with a common inlet manifold. The pipes are open to the atmosphere at the exit. Water at room temperature enters the inlet manifold and splits into the two pipes

Single pipe pressure drop

In Fig. 5, the pressure difference along a single horizontal pipe is plotted versus the total flow rate for the case of heating power of 1 kW/m and for the case of no heating. The symbols denote the experimental results of Minzer et al. (2004) and the solid lines are the result of the present model. Despite its simplicity the model agrees well with the experimental data. In the theoretical model we use $S = \sqrt{ρ_{L} / ρ_{G}}$ (Lahey Jr. and Moody, 1977). Note that the results are not sensitive to the exact

Summary and conclusions

A simplified model for calculating the pressure drop versus flow rates for evaporating fluid in a single heated pipe is presented. Good agreement is obtained with the experimental data.

The model is extended to the analysis of fluid flow in two parallel pipes and the steady-state solutions for flow distribution and inlet pressure are calculated. The simplified model is presented as time-dependent equations allowing linear stability analysis and transient simulations. The stability analysis

Notation

$A$	cross section
$B$	variable defined by Eq. (5)
$C_{M}$	Chisholm coefficient
$D$	pipe diameter
$f$	friction factor
$F$	function of $W$ , Eq. (18)
$g$	gravitational constant
$h$	enthalpy
$L$	length
$m$	$= L / A$
$P$	pressure
$Q$	heat absorbed (per unit length)
$R$	flow rate ratio $(W_{R} / W_{in})$
$s$	periphery
$S$	slip ratio
$t$	time
$U$	velocity
$w$	perturbed mass flow rate
$W$	mass flow rate
$x$	axial coordinate
$X$	quality
$X_{M}$	Lockhart–Martinelli parameter $((d P / d x)_{FS} / (d P / d x)_{GS})^{1 / 2}$

Greek letters

$α$	void fraction, also $d P / d W$
$β$	angle of inclination (positive for upflow)
$δ$	perturb amplitude
$λ$	eigenvalue
$ρ$

Acknowledgments

The authors would like to thank Prof. Mamoru Ozawa for his helpful comments. The financial support of the Gordon Center for Energy Studies is appreciated.

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Citation Excerpt :
Ledinegg instability is also classified as static instability by Boure et al. [14]. Mechanistic models for the calculations of the characteristic pressure drop versus flow rate in an evaporating single pipe as well as for the steady state flow rate distribution and stability analysis in parallel pipes were presented by Natan et al. [15], Minzer et al. [16,17], Baikin et al [18], Zhang et al. [19] and Oevelen et al. [20]. A transient model for flow rate distribution in multiple evaporating parallel pipes based on the instantaneous local flow pattern in each pipe was developed by Taitel and Barnea [21,22].
Evaporation of liquid in parallel heated pipes with common inlet and outlet manifolds was investigated mainly for co-current horizontal and upward flow. Almost no work was published on parallel heated pipes with an upper inlet header where sub cooled liquid is injected. In the present work such a system has been investigated. It seems that the Ledinegg excursion instability and the transient simulations used for co- current horizontal flow (Hayat et al. [1]) are not fully sufficient to predict the behavior of parallel heated pipes with vertical downward flow. In the present case the flow rate distribution between the parallel pipes include also solutions for counter current flow, where the flow in one of the pipe is directed upwards.
Experimental results of the characteristics pressure drop curve, the steady state flow rate distribution as well as the transient response of the system to changes in the operational conditions are presented. At certain regions of inlet flow rates a cyclic process, similar to a geysering phenomenon, was observed where pressure drop and flow rate oscillations take place in both pipes. It occurs when upward flow is observed in one of the pipes.
A theoretical model based on the local instantaneous flow pattern was used for calculating the characteristic pressure drop curve for both downward and upward flows. The theoretical pressure drop curve compares quite well with the experimental results. The characteristic pressure drop, a linear stability analysis and transient simulations were used to predict the flow rate distribution between the pipes at steady state and under transient conditions. The model predicts correctly the experimental results as long as there is no upward flow in one of the pipes.

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Flow rate distribution in evaporating parallel pipes—modeling and experimental

Abstract

Introduction

Section snippets

Basic approach

Experiments

Single pipe pressure drop

Summary and conclusions

Notation

Acknowledgments

Solar Energy

International Journal of Heat and Mass Transfer

Solar Energy

International Journal of Multiphase Flow

International Journal of Multiphase Flow

International Journal of Multiphase Flow

Study on distribution of flow rates and flow stabilities in parallel long evaporators

Bulletin of the Japan Society of Mechanical Engineers

DSG under two phase and stratified flow in a steel receiver of a parabolic trough collector

Transactions of the ASME, Journal of Solar Energy Engineering

Instabilities in parallel channel of forced-convection upflow system (I). Mathematical model

Journal of Nuclear Science and Technology

Instabilities in parallel channel of forced-convection upflow system (II). Experimental results

Journal of Nuclear Science and Technology

Instabilities in parallel channel of forced-convection upflow system (III). System with different flow conditions between two channels

Journal of Nuclear Science and Technology

Instabilities in parallel channel of forced-convection upflow system (IV). Instabilities in multi-channel of system and with boiling in downcomer

Journal of Nuclear Science and Technology

Convective Boiling and Condensation

Direct steam generation in parabolic troughs: first results of DISS project

Transactions of the ASME, Journal of Solar Energy Engineering

A review of two-phase flow instabilities