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

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 with the heating tapes wrapped around the tube.

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 recirculated.

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.*

**393**

pressure.

quality.

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

(*x* = 0) to the two-phase flow with a desired inlet quality of *x*in as follows:

As represented in **Figure 2**, the inlet vapor quality is measured and controlled by adjusting the calibrated heat supplied by the Pre-Heater to take the saturated liquid

where *h*x accounts for the enthalpy at vapor quality of *x*, *Qsuppl pre* \_ is the heat experimentally supplied by the Pre-Heater, *Qloss pre* <sup>−</sup> is the corresponding heat loss from this heat-supplying unit, and *Qcalib pre* <sup>−</sup> stands for the calibrated heat which is actually transferred to the boiling flow. Having the enthalpy of saturated liquid (*hf* (x=0)) known, the only unknown parameter in Eq. (2) is the enthalpy at the inlet of the test section from which the inlet vapor quality can simply be derived at the

After having the inlet vapor quality known, the outlet vapor quality can be measured from the calibrated heat at the test section (TS-Heater) as follows:

where *Qsuppl ts* <sup>−</sup> is the heat experimentally supplied by the heating unit at the test section, *Qloss ts* <sup>−</sup> is the corresponding heat loss from this heat-supplying unit, and *Qcalib ts* <sup>−</sup> stands for the calibrated heat which is actually transferred to the boiling flow. Having the inlet quality already measured, the only unknown parameter in Eq. (3) is the enthalpy at the outlet of the test section ( *x out* [ ] *h* ) from which the outlet

This is important to point out that the outlet vapor quality derived from the test section contains an accumulated error arisen from earlier measurement of the inlet vapor quality. As clearly shown in Eq. (2), the inlet vapor quality can be measured and controlled by obtaining the enthalpy at the inlet of test section ( *x in*[ ] *h* ), which contains the uncertainties in measurement of mass flow rate ( *m* ), bulk fluid temperature (Tsat), and calibrated heat supplies by the Pre-Heater (*Qcalib pre* <sup>−</sup> ). This measured value of inlet vapor quality ( *x in*[ ] *h* ) is used as a known parameter in Eq. (3) to obtain the vapor quality at the outlet of test section ( *x out* [ ] *h* ). The measured value of outlet vapor quality, in turn, contains uncertainties in measurement of bulk fluid temperature and calibrated heat supplies by the test section heater (*Qsuppl ts* <sup>−</sup> ) in addition to the earlier measurement error imposed by the value of inlet vapor quality, which eventually leads to the accumulation of more errors in measurement of outlet vapor quality through Eq. (3) as compared to that of inlet vapor

**4. Experimental approaches for unknown variable heat flux or constant** 

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

**wall temperature boundary conditions**

vapor quality can be extracted at the operating saturation temperature and

*Q Q Q mh h calib pre suppl pre loss pre* − −− = − =− ( ) ( *x in*[ ] *f x*( <sup>=</sup>0) ) (2)

*Q Q Q mh h calib ts suppl ts loss ts* − −− = −= − ( ) ( *x out x in* [ ] [ ] ) (3)

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

operating saturation temperature and pressure.

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

As represented in **Figure 2**, the inlet vapor quality is measured and controlled by adjusting the calibrated heat supplied by the Pre-Heater to take the saturated liquid (*x* = 0) to the two-phase flow with a desired inlet quality of *x*in as follows:

$$Q\_{calib-pre} = \left(Q\_{apppl-pre} - Q\_{las-pre}\right) = \dot{m}\left(h\_{x[ui]} - h\_{f(x=0)}\right) \tag{2}$$

where *h*x accounts for the enthalpy at vapor quality of *x*, *Qsuppl pre* \_ is the heat experimentally supplied by the Pre-Heater, *Qloss pre* <sup>−</sup> is the corresponding heat loss from this heat-supplying unit, and *Qcalib pre* <sup>−</sup> stands for the calibrated heat which is actually transferred to the boiling flow. Having the enthalpy of saturated liquid (*hf* (x=0)) known, the only unknown parameter in Eq. (2) is the enthalpy at the inlet of the test section from which the inlet vapor quality can simply be derived at the operating saturation temperature and pressure.

After having the inlet vapor quality known, the outlet vapor quality can be measured from the calibrated heat at the test section (TS-Heater) as follows:

*Q Q Q mh h calib ts suppl ts loss ts* − −− = −= − ( ) ( *x out x in* [ ] [ ] ) (3)

where *Qsuppl ts* <sup>−</sup> is the heat experimentally supplied by the heating unit at the test section, *Qloss ts* <sup>−</sup> is the corresponding heat loss from this heat-supplying unit, and *Qcalib ts* <sup>−</sup> stands for the calibrated heat which is actually transferred to the boiling flow. Having the inlet quality already measured, the only unknown parameter in Eq. (3) 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.

This is important to point out that the outlet vapor quality derived from the test section contains an accumulated error arisen from earlier measurement of the inlet vapor quality. As clearly shown in Eq. (2), the inlet vapor quality can be measured and controlled by obtaining the enthalpy at the inlet of test section ( *x in*[ ] *h* ), which contains the uncertainties in measurement of mass flow rate ( *m* ), bulk fluid temperature (Tsat), and calibrated heat supplies by the Pre-Heater (*Qcalib pre* <sup>−</sup> ). This measured value of inlet vapor quality ( *x in*[ ] *h* ) is used as a known parameter in Eq. (3) to obtain the vapor quality at the outlet of test section ( *x out* [ ] *h* ). The measured value of outlet vapor quality, in turn, contains uncertainties in measurement of bulk fluid temperature and calibrated heat supplies by the test section heater (*Qsuppl ts* <sup>−</sup> ) in addition to the earlier measurement error imposed by the value of inlet vapor quality, which eventually leads to the accumulation of more errors in measurement of outlet vapor quality through Eq. (3) as compared to that of inlet vapor quality.
