Flow boiling is considerably more complicated than pool boiling, owing to the coupling between hydrodynamics and boiling heat transfer processes. A sequence of two-phase and boiling heat transfer regimes takes place along the heated channels during flow boiling, as a result of the increasing quality. The two-phase flow regimes in a boiling channel are therefore “developing” everywhere and are morphologically different than their namesakes in adiabatic two-phase flows.

Forced-Flow Boiling Regimes

The preferred configuration for boiling channels is vertical upflow. In this configuration buoyancy helps the mixture flow, and the slip velocity between the two phases that is caused by their density difference actually improves the heat transfer. However, flow boiling in horizontal and even vertical channels with downflow are also of interest. Horizontal boiling channels are not uncommon, and flow boiling in a vertical, downward configuration may occur under accident conditions in systems that have otherwise been designed to operate in liquid forced convection heat transfer conditions.

Figure 12.1 displays schematically the heat transfer, two-phase flow, and boiling regimes that take place in a vertical tube with upward flow that operates in steady state and is subject to a uniform and moderate heat flux. The mass flow rate is assumed constant. When the fluid at the inlet is a highly subcooled liquid, at a very low heat flux, the flow field in the entire channel remains subcooled liquid [Fig. 12.1(a)].

Minichannel- and Microchannel-Based Cooling Systems

Compact heat exchanges, refrigeration systems, the cooling systems for microelectonic devices, and the cooling systems for the first wall of fusion reactors are some examples for the applications of minichannel- and microchannel-based cooling systems. Compact heat exchanges and refrigeration systems in fact represent an important current application of minichannels. Figure 14.1 displays typical minichannel flow passages in compact heat exchanges. In this chapter, flow boiling and CHF in channels with 10 μm ≲ DH ≲ 3 are discussed.

Distinction should be made between minichannel- and microchannel-based systems because they are different for several phenomenological and practical reasons. Some important differences between the two channel size categories with respect to the basic two-phase flow phenomena, in particular the flow patterns and the gas–liquid velocity slip, were discussed in Section 3.7 and Chapter 10. Other important differences between the two categories are as follows:

1. For practical reasons microchannel cooling systems are typically designed as arrays of parallel channels connected at both ends to common inlet and outlet plena, manifolds, or headers. Multiple parallel channels with common inlet and outlet mixing volumes are susceptible to instability, flow maldistribution, and oscillations. Minichannel cooling systems, in contrast, are designed both as parallel arrays as well as individual channels with independent flow controls.

2. Also for practical reasons, microchannels operate under low-flow conditions. Minichannel systems can operate over a wide range of coolant flow rates, however.

3. […]

Pioneering work on flapping-wing aerodynamics was done by Lighthill (1969) and Weis-Fogh (1973). Recent works, both in experiments and simulations, were documented by Katz (1979), Ellington (1984a), DeLaurier (1993), Smith (1996), Vest and Katz (1996), Liu and Kawachi (1998), Dickinson et al. (1999), Jones and Platzer (1999, 2003), Wang (2000), and Chasman and Chakravarthy (2001). A review of the characteristics of both flapping wings and fixed wings was given by Shyy et al. (1999a). The spectrum of animal flight with flapping wing was presented by Templin (2000). Ho et al. (2003) further reviewed the recent effort in developing flapping-wing-based MAVs. Computational and experimental studies regarding rotating-wing MAVs were made by Bohorquez et al. (2003).

The quasi-steady theory is constructed based on the instantaneous velocity, wing geometry, and AoA when the steady-state aerodynamic model is used.

Introductory Remarks

In Chapter 4 the basic gas–liquid two-phase flow regimes along with flow regime maps were reviewed. The discussion of flow regimes was limited to empirical methods applicable to commonly applied pipes and rod bundles. In this chapter mechanistic two-phase flow regime models will be discussed.

Empirical flow regime models suffer from the lack of sound theoretical or phenomenological bases. Mechanistic methods, in contrast, rely on physically based models for each major regime transition process. These models are often simple and rather idealized. However, since they take into account the crucial phenomenological characteristics of each transition process, they can be applied to new parameter ranges with better confidence than purely empirical methods. Some important investigations where regime transition models for the entire flow regime map were considered include the works of Taitel and Dukler (1976), Taitel, Bornea, and Dukler (1980), Weisman and co-workers (1979, 1981), Mishima and Ishii (1984), and Barnea and co-workers (1986, 1987). The derivation of simple mechanistic regime transition models often involves insightful approximations and phenomenological interpretations. The review of the major elements of the successful models can thus be a useful learning experience.

In this chapter only conventional flow passages (i.e., flow passages with) will be considered. There are important differences between commonly applied channels and mini- or microchannels with respect to the gas–liquid two-phase flow hydrodynamics. Two-phase flow regimes and conditions leading to regime transitions in mini- and microchannels will be discussed in Chapter 10.

This book is the outcome of more than fifteen years of teaching graduate courses on nuclear reactor thermal-hydraulics and two-phase flow, boiling, and condensation to mechanical, and nuclear engineering students. It is targeted to be the basis of a semester-level graduate course for nuclear, mechanical, and possibly chemical engineering students. It will also be a useful reference for practicing engineers.

The art and science of multiphase flow are indeed vast, and it is virtually impossible to provide a comprehensive coverage of all of their major disciplines in a graduate textbook, even at an introductory level. This textbook is therefore focused on gas–liquid two-phase flow, with and without phase change. Even there, the arena is too vast for comprehensive and in-depth coverage of all major topics, and compromise is needed to limit the number of topics as well as their depth and breadth of coverage. The topics that have been covered in this textbook are meant to familiarize the reader with a reasonably wide range of subjects, including well-established theory and technique, as well as some rapidly developing areas of current interest.

Gas–liquid two-phase flow and flows involving change-of-phase heat transfer apparently did not receive much attention from researchers until around the middle of the twentieth century, and predictive models and correlations prior to that time were primarily empirical. The advent of nuclear reactors around the middle of the twentieth century, and the recognition of the importance of two-phase flow and boiling in relation to the safety of water-cooled reactors, attracted serious attention to the field and led to much innovation, including the practice of first-principle modeling, in which two-phase conservation equations are derived based on first principles and are numerically solved.

Boundary layers are an elemental concept of high Reynolds number flow. They are a framework for discussing viscous fluid dynamics by separating the flow into distinct regions. That is the essential nature of boundary layer theory. The seminal ideas were described by Prandtl in 1904. He recognized that viscous flow along surfaces could be divided into two regions: a vortical layer next to the wall and a potential flow farther from the surface. Modern theories have expanded that to multilayered structure; but the basic notion always is of a thin, vortical layer next to the surface and an inviscid outer flow.

The boundary layer concept brought clarity to the puzzle of the high Reynolds number limit. High Reynolds number can be interpreted as low viscosity. Is inviscid flow the correct limit? Without viscosity, fluid flows freely over a surface, slipping relative to the wall. Hence, the tangential velocity is discontinuous between the stationary wall and the flowing fluid. The shear is infinite. Adding the smallest amount of viscosity would cause an infinite stress. Inviscid flow cannot be the correct high Re limit of viscous flow.

Any amount of viscosity will diffuse the velocity discontinuity: the fluid velocity will be brought smoothly to zero at the stationary wall. Even at the highest Reynolds numbers, viscous stresses cannot be ignored. How, then, is high Reynolds number flow to be constructed?

This puzzle is solved by recognizing that viscous influence is confined to a very thin layer next to the wall. The layer of viscous influence becomes increasingly thin as Re becomes increasingly large.