Diabatic flow

Fig. 2.32 Diabatic flow pattern map for vaporizing flow in uniformly heated micro-channel, R-134a, d = 0.5 mm, L = 70 mm, Tg = 30 °C, = 50 kW/m without subcooling at inlet. Flow patterns isolated bubble regime (IB), coalescing bubble regime (CB), annular (completely coalesced) regime (A), post-dryout regime (PD). Reprinted from Thome et al. (2006) with permission...

The plot of the pressure drop depending on the bulk velocity in adiabatic and diabatic flows is shown in Fig. 3.6a,b. The data related to the adiabatic flow correspond to constant temperature of the fluids Tjn = 25 °C, whereas in the diabatic flow the fluid temperature increased along micro-channel approximately from 40 to 60 °C. It is seen that in both cases the pressure drop for Habon G increases compared to clear water. The difference between pressure drop corresponding to flows of a surfactant solution and solvent increases with increasing bulk velocity. 

Fig. 3.6a,b Dependence of pressure drop on fluid bulk velocity in (a) adiabatic flow, and (b) diabatic flow. Reprinted from Hetsroni et al. (2004) with permission... 

Void Fraction and Slip Ratio in Diabatic Flow 147... 

Figure 3.14 illustrates the transition of flow regimes in a horizontal diabatic flow (Becker, 1971). The asymmetric phase distribution and possible phase separation have a severe effect on heat transfer. 

Figure 3.14 Flow regimes for horizontal diabatic flow. (From Becker, 1971. Copyright 1971 by Studsvik AB, Nykoping, Sweden. Reprinted with permission.)...

VOID FRACTION AND SLIP RATIO IN DIABATIC FLOW... 

For a diabatic flow case, as in the high heat flux, boiling water system typical of reactor cores, Tarasova et al. (1966) proposed the following correlation for the effect of wall heat flux on friction factors by a correction factor ... 

For diabatic flow, that is, one-component flow with subcooled and saturated nucleate boiling, bubbles may exist at the wall of the tube and in the liquid boundary layer. In an investigation of steam-water flow characteristics at high pressures, Kirillov et al. (1978) showed the effects of mass flux and heat flux on the dependence of wave crest amplitude, 8f, on the steam quality, X (Fig. 3.46). The effects of mass and heat fluxes on the relative frictional pressure losses are shown in Figure 3.47. These experimental data agree quite satisfactorily with Tarasova s recommendation (Sec. 3.5.3). 

The annular flow model is useful for diabatic flow beyond critical heat flux (CHF). Hewitt and Govan (1990) introduced a model for the CHF state that is... 

The choice of MPE tubes for the test section allowed easier measurements and results closer to industrial reality. Further studies should put the stress on the accurate influence of channel geometry and confinement on heat transfer with diabatic flow visualisation and a large variety of channels configurations. 

The steady two-dimensional diabatic flow is described by the equations for mass, momentum and energy in conservation form (Schnerr and Dohrmann [7], Dohrmann [8]). Real gas effects are not yet included and inviscid fluids are assumed. Here the classical nucleation theory of Volmer [9] is used which gives a good qualitative representation of the behavior of condensing in the supersaturated state (Wegener [iO]). Oswatitsch [11] introduced this theory into the calculation of flow processes, a summary of all basic relationships for compressible flows with heat addition is given by Zierep [12]. To compute the nucleation rate J per unit time and volume, we take... 

Here two different airfoils are Investigated, the circular arc CA-0.1 (thickness ratio of 10 %) and the NACA-0012, Due to the approximately constant cooling rate at local Mach numbers close to one the circular arc airfoil allows some simplifications. The value at Mach number one, denoted by the star, represents the time scale at the entire transonic airfoil section, whereas the cooling rate at the NACA-0012 changes considerably. Condensation onset Mach numbers very close to one are correlated with higher cooling rates and vice versa (Table 1). Usually it is assumed that the temperature gradients in adiabatic flow and with heat addition are identical up to the condensation onset for free stream Mach numbers M < 1, too. However, the numerical results of diabatic flows show a more or less pronounced precompression... 

Another problem associated with the initialization of diabatic flow is that the moisture field must also be properly initialized in such a way that the initial precipitation rate calculated from the prediction model agrees with observed. The problem is often compounded by the fact that the precipitation rates on global scale are not easily available through conventional rainfall measurements. However, progress has been made recently in the moisture initialization owing to the advent of satellite observations, such as the TRMM (Section VI), and the development of variational data assimilation described in the next subsection. 

R. Revellin, J. R. Thome, A new type of diabatic flow pattern map for boiling heat transfer in microchannels, J. Micromech. Microeng., 2007, 17, 788-796. 

For the case of diabatic flow (involving heat input to the transfer line), Martinelli and Nelson showed that a modification of Eq. (7.76) can be used to relate the total pressure drop in the transfer line to that experienced by a flow that is only liquid with a total flow rate equal to the sum of and The modification has the form... 

---