The theory of boiling is complex and not yet fully understood. The boiling process depends on factors such as mass flow, vapor content and the temperature difference between the refrigerant and the heating surface. The available research is based on empirical experiments on smooth tubes. Understanding the evaporation process inside plate heat exchangers is further complicated by the swirling flow that the plate pattern induces.
However, the processes of evaporation could be explained by a combination of the available research on pool boiling and flow boiling. SWEP has developed algorithms based on these theories and empirical laboratory tests that resemble the heat transfer.
The heat transfer coefficient for pool boiling has a characteristic curve that displays heat flux versus the temperature difference between the evaporating and the secondary media (see Figure 6.4). As the temperature difference increases, the energy flow per heat transfer area (kW/m2) will increase until an unstable maximum value for heat transfer is reached, the critical heat flux. At this point, vapor will form to such an extent that it hinders contact between the liquid refrigerant and the heat transfer area. As the temperature difference increases, a continuous gas film will form and the heat flux will reach a minimum. A further increase in the temperature difference will increase the heat flux only slowly, because the heat transfer coefficient will depend on radiation. High heat transfer coefficients after this point are achieved only with a temperature difference of >800K, where BPHEs are not a suitable heat transfer solution. Preferably, a BPHE evaporator should be designed to operate below the critical heat flux to avoid the unstable performance of partial film boiling and the low heat transfer coefficient of complete film boiling.
The different boiling regimes in Figure 6.4 are explained below:
- Free convection evaporation. Heat is transferred between the wall and the refrigerant without bubble formation. The liquid close to the surface wall becomes slightly superheated and evaporates in the interface between liquid and gas.
- Sub-cooled nucleate boiling region. Heat transfer between the wall and the refrigerant is sufficiently large to create bubbles, but they collapse in contact with the liquid bulk.
- Nucleate boiling region. This is the most important boiling region for technical applications. The temperature difference required to enter this region is approximately 3K. Superheated liquid overcomes the surface tension, forming unstable vapor bubbles that collapse in contact with the sub-cooled refrigerant liquid. The additional turbulence caused by forming and collapsing bubbles increases the heat transfer. The heat transfer increases as the temperature difference between the refrigerant and the secondary medium increases to reach a maximum critical heat flux at the burnout point.
- Partial film boiling. Increasing the temperature difference further, beyond the burnout point, will cause the refrigerant to evaporate too quickly to allow new liquid refrigerant access to the heat transfer surface. The partial vapor blanket acts as insulation, causing the heat transfer coefficient to drop greatly and reducing the overall heat flux. This is an unstable region that should be avoided, because performance is uncertain and may fluctuate substantially. Complete film boiling. With a very high temperature difference, a stable film of refrigerant vapor will form on the heat transfer area. The film will act as an effective insulation layer hindering any direct contact between the heat surface and the liquid refrigerant. Although the heat transfer coefficient reaches a minimum here, this evaporation region is preferable over the unstable partial film-boiling region, because predictions of the heat transfer coefficient are more reliable.
- Radiation. At very high temperatures, the heat flux will increase again due to radiation.
The theory of flow boiling inside tubes or channels is more complex than that of pool boiling. The gas phase has a much lower density than the liquid phase, and thus the evaporation of the refrigerant causes an acceleration of the fluid. Different flow regimes have been identified in experiments with different mechanisms of heat transfer. The different flow regimes are shown in Figure 6.5.
The different flow regimes are discussed below:
- Sub-cooled boiling. The temperature difference is not sufficient to initiate stable vapor bubbles that will collapse in contact with subcooled liquid. If the vapor content is small (>5-8%), the heat transfer mechanism will be similar to that of pool boiling.
- Bubble or emulsion flow. Vapor nucleates form and grow as a result of evaporation at the gas/liquid interface. For evaporators with small temperature differences (> 3K), this flow regime dominates the initial part of the evaporator before enough vapor is formed to increase the turbulence.
- Slug flow. Vapor forms spontaneously and merges into big bubbles. This flow is typical of evaporators with conventional temperature differences (5-10 K) between the refrigerant and the secondary fluid.
- Annular flow (regions 4 and 5). The vapor phase accelerates and forms a "chimney" that pushes the liquid phase upwards. Annular flow is often found at the top of BPHE evaporators, where the vapor quality is high. However, the liquid phase remains in contact with the surface area, ensuring a high heat transfer coefficient.
- Mist flow: the vapor velocity becomes high enough to tear the liquid film from the heat transfer area; this results in greatly reduced heat transfer coefficients.
For a BPHE evaporator working in a direct expansion (DX) system, refrigerant vapor is already present at the inlet. Flow regimes 2-5 are therefore most applicable to BPHEs. Flooded evaporators also have flow types 1 and 2 at the beginning.
Flow boiling heat transfer mechanisms are explained as a combination of nucleate and convective boiling from the pool boiling theory. The heat transfer coefficient for nucleate boiling is higher than for convective boiling, but nucleate boiling requires a larger temperature difference between the refrigerant and the secondary medium. To simplify the relation between convective and nucleate flow boiling, it is possible to assume that the heat transfer coefficient is the net effect of the two mechanisms, as shown in Figure 6.6.
At the beginning of the evaporator, where there is normally only 15- 30% vapor, nucleate boiling is the dominant heat transfer mechanism. When the vapor content is high, i.e. higher up in the evaporator or in evaporators with a very high inlet vapor quality, the convective heat transfer mechanism becomes dominant. This is easily understood, because convective boiling depends on the total liquid/gas interface area, which increases with the vapor quality.
As Figure 6.7 indicates, the heat transfer coefficient for an evaporator operating in the convective regime is almost independent of heat flux, but highly influenced by the mass flow and turbulence in the liquid phase. At a certain heat flux, the vapor pressure is sufficiently high to overcome the surface tension, and nucleate boiling is initiated. At this point, the heat transfer coefficient increases with increasing heat flux.