Thermal prediction of transient two-phase flow in cryogenic transportation based on drift-flux model

Highlights

• The drift flux model is firstly applied to the two-phase flow in cryogenic energy transportation.

• The introduction of drift velocity can accurately describe the complex two-phase flow regimes.

• The intermittent chill-down strategy is recommended from the perspective of energy saving.

• Pressure surge brings higher challenges to the safety of cryogenic energy transportation system.

Abstract

Accurate prediction as well as effective thermal management of transient cryogenic transportation is of great importance to the safe and high-efficiency utilization of cryogenic fluids. To predict the unstable cryogenic transportation process, a one-dimensional model coupling two-phase flow with transient heat conduction of solid tube is developed in this study. The transient two-phase flow is described by a drift-flux model, and a finite volume method (FVM) with staggered grid mesh is adopted for numerical calculation. Verified by a lot of experimental data, the proposed model shows its applicability in a wide range of conditions. Then, thermal performance and pressure surge phenomenon are investigated in detail. The intermittent chill-down strategy is recommended to take full use of the sensible energy of fluid from the perspective of energy saving. Besides, the pressure surge is verified as a special physical phenomenon in cryogenic fluids transportation process, which brings higher challenges to the storage, handling and transport of cryogenic fuels.

Introduction

As environmental pollution [1] and energy shortage [2] have become the main challenges to human society, the proportion of clean and renewable energy, such as wind energy [3], nuclear energy [4], solar energy [5], is continuously increasing. Due to the great change in energy system, the cryogenic fluids are widely used in various industries for the eco-friendly and high energy density characteristics. For example, in the International Thermonuclear Experimental Reactor (ITER), which is the largest fusion reactor in the world, the magnet is cooled at 4K by supercritical helium to operate at high magnetic fields [6]. The liquid hydrogen and liquid oxygen are regarded as the most promising propellants for the flight heritage such as Saturn V, Centaur, Shuttle [7]. Liquid natural gas and liquid hydrogen provide opportunities to diversify energy supplies for fuel-cell vehicles [8]. The cryogenic fluids will play a virtual role in the future energy system, especially for the fusion, spacecraft, and fuel cell vehicle. However, due to the extremely low boiling temperature of cryogenic fluids, the complex two-phase flow encountered in the transportation process has been a challenging task for the experts in all kinds of fields [6,9]. The delivering pipeline and the associated hardware must be chilled down from room temperature to the saturation temperature prior to large flow transport of cryogenic fluids, which is defined as “chill-down” or “quenching” phenomena. Fig. 1 shows the schematic diagram of a cryogenic transportation system as well as the flow regimes during the chill-down (quenching) process. The violent phase change, transient flow regimes, and pressure instabilities during this process bring a variety of risks to the safe and high-efficiency utilization of cryogenic fuels. Therefore, accurate modeling of two-phase boiling as well as effective thermal management is the main limiting factor for the proper storage [10], handling and transport of cryogenic fuels [11], [12].

The transient two-phase flow related to cryogenic chill-down has been actively studied since 1960s with the focus on macroscopic phenomena such as the chill-down time [13], flow patterns [14], pressure drops [15], and liquid consumptions [16]. With the increasing attention of cryogenic fluids, a lot of experiments are carried out to explore the thermal and physical performance of chill-down boiling. In order to reduce the complexity, researchers usually isolate different influencing factors in experiments for mechanism analysis, including the mass flow rates, flow directions and physical properties. Hu et al. [17], Johnson et al. [18] and Darr et al. [19] investigated the influence of mass flux through lots of experiments and concluded that the chill-down time decreased with the increase of the mass flow. Darr et al. [19] pointed out that buoyancy effect should be considered in low mass flow conditions, and the effect of forced convection was gradually significant as mass flow increased. The experimental results of Darr et al. [19] also indicated that the heat transfer performance of vertical pipelines was better than that of horizontal pipelines and inclined pipelines because of the layering phenomenon. Hartwig et al. [20] revealed the special physical characteristics in liquid hydrogen chill-down process by comparing the experiments of liquid hydrogen and liquid nitrogen. Jin et al. [21], [22] carried out the line chill-down experiments using liquid nitrogen, liquid oxygen, and liquid argon separately, which provided abundant experimental data for chill-down research. Visual experiments conducted by Velat et al. [23] and Jackson et al. [24] also showed much valuable information about the two-phase flow patterns. In addition, for different optimization goals, researchers performed experiments from two aspects: chill-down strategies (continuous flow & intermittent flow) and pipeline structures (nano-porous material & coating layer). Shaeffer et al. [25] conducted experimental research on continuous flow and intermittent flow using liquid nitrogen as a working fluid. The results showed that the intermittent flow could reduce the consumption of liquid nitrogen in high Reynolds number conditions. Since liquid hydrogen flow was characterized by high Reynolds number, the intermittent flow method could save nearly 50% of the liquid hydrogen according to the experiments by Hartwig et al. [26]. Hu et al. [27] concluded that the nano-porous material improved the heat transfer efficiency in chill-down process. The experimental results conducted by Chung et al. [28] indicated that the low-thermal conductivity inner surface coating greatly enhanced the chill-down efficiency.

The experimental research greatly contributed to the development of empirical correlations and numerical simulations for chill-down process. The use of empirical correlations is one of the most popular approaches to predict two-phase flow boiling in most industries [29], [30]. The pioneering report on cryogenic empirical correlations was carried out by Klimenko et al. [31], who proposed a correlation that considered the influence of the heating surface using a lot of liquid nitrogen experimental data. Recently, Hartwig et al. [9] drew a conclusion that the existing classical correlations could not be used to predict cryogenic chill-down process through detailed comparison and review. Therefore, Darr et al. [19,32] investigated numerous chill-down experiments to explore the mechanism of each influencing factor, and presented the specialized empirical correlations for chill-down process involved in liquid nitrogen and liquid hydrogen. Furthermore, since the thermal prediction management of cryogenic transportation is of great significance in both academic and industrial views, the numerical simulation process has attracted increasing attention in the last two decades [33], [34], [35]. The general transient two-phase flow can be predicted by homogenous model, two-fluid model, and drift-flux model according the physical and thermal performance [36]. The solution strategies and governing equations of the three models are shown in Fig. 2. The homogenous model (including the one-dimensional software Generalized Fluid System Simulation Program) is the main method to simulate chill-down process. The previous efforts were made by Chi et al. [14], but the deviation was apparent due to the inappropriate correlations. Darr et al. [37] developed 1-D homogeneous model based on the correlations with a wide range of mass flux and directions, which brought great progress to the chill-down simulation. Jin et al. [38] also performed numerical simulation by homogenous model with liquid nitrogen, liquid oxygen, and liquid argon. Besides, the simulated results conducted by Wang et al. [39] matched well with a lot of experimental data from different literatures. However, due to ignoring interphase parameters, the homogeneous model is useless for many rigorous applications. In the two-fluid model, each phase is considered separately with interfacial interactions. For chill-down prediction, Liao et al. [40] developed a two-fluid model to describe stratified flow and Yuan et al. [41] established a simplified model of film boiling carrying liquid droplets. Because of the uncertainties in specifying interfacial interaction terms between two phases as well as the mathematical complexity of two sets of conservation equations, considerable difficulties are inevitable in the two-fluid model, especially for chill-down process. Comparing to the complex six-equation two-fluid model, the drift-flux model provides a simple and reliable alternative to modeling the transient two-phase flow. In drift-model, the behavior of two-phase flow is treated as a whole, rather than two separated phases, while relative motion between phases is considered by the constitutive equation [42]. The drift-flux model is widely used in many applications [43], [44], [45], due to the simplicity as well as the applicability to wide range two-phase problems.

The summary of research on cryogenic chill-down transportation process is shown in Fig. 3. A lot of cryogenic transportation experiments have been conducted, but most of the studies adopt the small-diameter pipeline and rarely involve the actual cryogenic system. For the numerical simulations, the homogenous model is not suitable for large-diameter actual delivery pipeline, and two-fluid model is limited to specific flow regimes. Thus, the purpose of this paper is to establish a drift-flux model for accurately modeling the transient two-phase flow in cryogenic transportation and revealing the thermal and physical performance, which may be the first attempt to apply drift-flux model to cryogenic fluids transportation process.