**4. Experimental approaches for unknown variable heat flux or constant wall temperature boundary conditions**

In the case of constant wall temperature boundary conditions for the test section, the wall heat flux is subject to change. The measurement and control of local vapor quality at the outlet of a test section under uniform wall temperature boundary conditions is more challenging than that of uniform wall heat flux boundary conditions. In a single loop of internal flow boiling, the outlet vapor quality is typically measured and controlled by directly monitoring the constant amounts

*Heat Transfer - Design, Experimentation and Applications*

with the heating tapes wrapped around the tube.

qualities within the flow boiling tests.

**conditions**

recirculated.

The difference between *Qsuppl* and *Qtransf* reveals the heat losses

(*QQ Q loss suppl transf* = − ) . A correlation is then developed by plotting the variations of heat transferred to the fluid (*Qtransf* ) versus heat supplied (*Qsuppl*) , which can be used for calibrating the heat supplies as an imperative step to further measure vapor

**3. Experimental approach for known uniform wall heat flux boundary** 

After estimating heat losses and calibrating heat supplies for any of electrical heater units in a test setup, local vapor qualities at the inlet and outlet of a test section can be measured by energy balance on the enthalpy change of vaporization. **Figure 2** depicts the schematics of a typical setup to conduct measurements of vapor qualities under known constant wall heat flux boundary conditions using the electrical heating either through the direct resistance heating of the test tube or

As shown in **Figure 2**, while inlet vapor quality can be controlled using the heat-supplying unit located right before the test section (called Pre-Heater), local vapor quality at the outlet of test section may be controlled from the heat-supplying unit at the test section (called TS-Heater). The subcooled liquid at a certain pressure of Psat with a bulk temperature of Tsp is warmed up by a heat-supplying unit (i.e. SP-Heater) in order to reach the state of saturated liquid (*x* = 0%) at the saturation temperature of Tsat corresponding to the system pressure of Psat. Using the Pre-Heater located right before the test section, the saturated liquid therefore reaches a certain vapor quality at the inlet of the test section (*x*in) and is afterwards exposed to a known constant wall heat flux supplied by the TS-Heater at the test section to reach a two-phase flow of higher vapor quality at the outlet (*x*out), and then keeps

To ensure the state of saturated liquid, the subcooled liquid is warmed up by the SP-Heater to reach a temperature infinitesimally lower than the saturation temperature of Tsat targeted for the flow boiling experiments. Using the sight glass shown in **Figure 2**, the state of saturated liquid is also directly observed in order to check

whether or not there is any vapor bubble in the saturated liquid flow.

*The experimental approach to measuring vapor qualities for uniform wall heat flux boundary conditions.*

**392**

**Figure 2.**

of surface heat flux provided by heating tapes wrapped around the test section. However, the use of hot fluid heating rather than electrical heating to generate constant wall temperature conditions does not allow the direct control of outlet vapor quality due to the unknown variable surface heat flux exchanged between the hot-side fluid (e.g. external condensation of steam or single-phase hot liquid) and the cold-side fluid (i.e. internal flow boiling).

#### **4.1 Approach I: auxiliary after-heater**

**Figure 3** illustrates a typical case of constant temperature boundary conditions imposed by external condensation of steam on the test tube. The test section shown in this case is the place where external condensation and internal flow boiling occur simultaneously. The test section therefore functions as a cross flow heat exchanger whose both sides are manipulated with phase-change heat transfer processes. The test apparatus for this arrangement is to consist of two closed loops, including: external condensation loop (i.e. steam condensation over a horizontal tube) and internal boiling loop (i.e. two-phase flow boiling inside the tube).

Within the external condensation loop, saturated vapor of water at saturation temperature and pressure of Tsat,steam and Psat,steam is provided by a steam generator and then enters the test chamber. After condensation of steam on the horizontal test tube due to the temperature difference between the saturated vapor and the tube surface (called subcooling), the condensate is driven by gravity and collected in a condensate reservoir to feed the steam generator and set a steady flow circulation in the external condensation loop. Regarding the internal boiling loop, the fluid is warmed up by the SP-Heater in order to reach the saturated liquid state (*x* = 0) at the saturation temperature and pressure of Tsat and Psat, respectively (Tsat < Tsat,steam). Using the Pre-Heater located right before the test section, the saturated liquid therefore reaches a certain vapor quality at the inlet of the test section (*x*in) and is afterwards exposed to the latent heat released from the external condensation side to reach an unknown higher vapor quality at the outlet (*x*out).

The unknown outlet vapor quality can be measured by adding a calibrated heat-supplying unit (After-Heater) with power controller installed right after the test section in order to take the two-phase flow with unknown outlet quality to the known state of saturated vapor (i.e. *x* = 100%) at the same saturation temperature of Tsat. In this case, the energy balance is dictated as follows:

*Q Q Q mh h calib after suppl after loss after* − −− = −=− ( ) ( *g x*( <sup>=</sup>1) *x out* [ ] ) (4)

**395**

**Figure 4.**

**Figure 3.**

*Experimental Approaches to Measurement of Vapor Quality of Two-Phase Flow Boiling*

After-Heater, the state of saturated vapor is also directly observed in order to check whether or not there is any liquid droplet and/or humidity in the gas stream at the beginning of superheated state. Unlike the earlier approach to measuring local vapor quality at the outlet of test section under uniform wall heat flux conditions, this approach does not contain any accumulated errors arising from earlier mea-

In the second methodology for variable wall heat flux conditions, a tube-in-tube or shell-and-tube heat exchanger installed at the test section may be used for measuring and controlling local vapor quality at the outlet of test tube. Analogous to the earlier cases, the inlet vapor quality is measured and controlled by monitoring the

As represented in **Figure 4**, a hot liquid single-phase flow with known mass flow rates and known temperatures and pressures at the inlet and outlet passes through

*The experimental approach to measuring vapor qualities for variable wall heat flux boundary conditions.*

*The experimental approach to measuring vapor qualities for uniform wall temperature boundary conditions.*

*DOI: http://dx.doi.org/10.5772/intechopen.94473*

surements of inlet vapor qualities.

**4.2 Approach II: auxiliary heat exchanger**

calibrated heat supplied by the Pre-Heater using the Eq. (2).

where *Qsuppl after* <sup>−</sup> stands for the heat experimentally supplied by the After-Heater, *Qloss after* <sup>−</sup> is the corresponding heat loss from this heat-supplying unit, and *Qcalib after* <sup>−</sup> accounts for the calibrated heat which is actually transferred to the boiling flow. Having the enthalpy of saturated vapor (*hg* (x=1)) known, the only unknown parameter in Eq. (4) is the enthalpy at the outlet of the test section ( *x out* [ ] *h* ) from which the outlet vapor quality can be extracted at the operating saturation temperature and pressure. Similar to the case of constant wall heat flux boundary conditions stated earlier, the inlet vapor quality can independently be measured and controlled by adjusting the calibrated heat supplied by the Pre-Heater using the Eq. (2).

In this approach, to ensure the state of saturated vapor, the After-Heater located after the test section is adjusted to supply the required latent heat for the two-phase flow with a certain outlet quality to reach a temperature slightly higher than the constant saturation temperature, which would be the starting point of the superheated vapor state. As shown in **Figure 3**, using the sight glass installed after the

*Experimental Approaches to Measurement of Vapor Quality of Two-Phase Flow Boiling DOI: http://dx.doi.org/10.5772/intechopen.94473*

After-Heater, the state of saturated vapor is also directly observed in order to check whether or not there is any liquid droplet and/or humidity in the gas stream at the beginning of superheated state. Unlike the earlier approach to measuring local vapor quality at the outlet of test section under uniform wall heat flux conditions, this approach does not contain any accumulated errors arising from earlier measurements of inlet vapor qualities.
