# Heat-flux enhancement response for novel flow-boiler operations under resonant, sub-harmonic, and superharmonic imposition of vapor pulsation frequencies relative to a liquid flow-rate pulsation frequency

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## Abstract

This paper presents fundamental results from experimental investigations of shear/pressure-driven internal flow boiling of FC-72 in a horizontal test section of total flow channel length 1000 mm, gap height 2 mm, and width 15 mm. It compares effects of the frequencies of vapor and liquid pressure fluctuations (pulsations) on the experimentally measured heat-flux rates and heat transfer coefficients at a representative location within the flow boiler under a flow operation method in which re-circulating vapor maintains an annular flow regime over the entire length of the device. For liquid flow/pressure pulsations at 3.8–3.9 Hz, four externally imposed inlet vapor pressure fluctuation conditions were considered: (1) no externally imposed vapor pulsations and (2)–(4): high-amplitude externally imposed vapor pulsations at (2) the same, (3) half, and (4) double the inlet liquid pulsation frequency. Representative pressure differences within the flow boiler are also examined. Local time-averaged heat-flux and heat transfer coefficient responses of these flows are compared with previously published data at the same liquid pulsation frequency, but at a different inlet liquid flow rate, vapor quality, and pressure. The reported measurements, and the discussions and conclusions in this paper, enable better understanding of an established pulsation-induced heat-flux enhancement phenomenon which may be used in future cooling systems to significantly enhance average heat-flux values over the entire length of an annular flow boiler. The main conclusion is that, for the flow conditions investigated, optimal heat transfer efficiency occurs when vapor and liquid pulsations are imposed at the same frequency on the flow-boiler inlet.

## Keywords

Phase-change flow Novel flow boiling Flow pulsations Pulsatile shear-driven flow boiling Annular boiling flows Imposed flow-rate pulsation Imposed pressure pulsation Heat-flux enhancement Frequency matching## List of symbols

## Labels

- S
Separator plate

- C
_{R} Compressor

- F
_{C} Coriolis flow meter

- FC-72
Working fluid used in experiments: Fluorinert™ electronic liquid (C

_{6}F_{14}) from 3M Corp- DPT
Differential pressure transducer: measures pressure differences directly

- APT
Absolute pressure transducer: used for direct measurement of absolute pressure

- HFM-40
Heat-flux meter: used to measure heat-flux directly at a location 40 cm downstream from the flow-boiler inlet

- P
_{V} Vapor pulsator: used to induce fluctuations in vapor pressure and flow rate

- P
_{1}, P_{2} Pumps: used to circulate liquid working fluid in experimental flow loop

- TEC
Thermoelectric cooler (solid state heat pumps)

- L/V separator
Liquid–vapor separator

- V
Valve

- PID
Proportional-integral-derivative (as in the control method)

- IF
Imposed fluctuation, referring to cases in which the vapor pulsator was used to apply pressure fluctuations to the vapor entering the flow boiler

- N-IF
No-imposed fluctuation, referring to cases in which the vapor pulsator was not used

- H-IF
High-amplitude imposed fluctuation, referring to cases in which the vapor pulsator was operated at its maximum amplitude

## Variables

*h*Gap height of flow channel in test section (mm)

*L*Length of flow channel (m)

- \(a\)
Amplitude value, which is the magnitude of the FFT of a flow variable at a frequency of interest, in units associated with that flow variable

- \(f\)
Frequency (Hz)

- \(f_{\text{P:V}}\)
Primary frequency associated with imposed vapor phase flow pulsations (Hz)

- \(f_{\text{P:L}}\)
Primary frequency associated with imposed liquid phase flow pulsations (Hz)

- \(x\)
Distance from the flow channel inlet in the downstream direction (cm)

- \(\dot{m}\)
Mass flow rate (g/s)

- \(p\)
Pressure (kPa)

- \(\Delta p\)
Representative pressure difference between two locations of interest (kPa)

- \(v\)
Average velocity over a reference area (m/s)

- \(T\)
Temperature (°C)

- \(h\)
Heat transfer coefficient (W/m

^{2}K)- \(p^{{\prime }}\)
Pressure fluctuations for frequencies > 0 Hz, used in FFT graphs of absolute pressures (kPa)

- \(t\)
Time (s)

- \(\Delta T\)
Representative temperature difference between saturation temperature (taken at a pressure of interest within the flow boiler) and a corresponding heat-exchange surface temperature (°C)

- \(q^{{\prime \prime }}\)
Heat-flux (W/cm

^{2})

## Subscripts

- 0
At the \(x = 0\;{\text{cm}}\) location

- 10
At the \(x = 10\;{\text{cm}}\) location

- 40
At the \(x = 40\;{\text{cm}}\) location

- 90
At the \(x = 90\;{\text{cm}}\) location

- 0–40
Between the \(x = 0\;{\text{cm}}\) and \(x = 40\;{\text{cm}}\) locations

- 40–90
Between the \(x = 40\;{\text{cm}}\) and \(x = 90\;{\text{cm}}\) locations

- I
Inlet of the test section

- E
Exit of the test section

- R
Re-circulating vapor flow

- P
Imposed pulsations

- L
Liquid

- V
Vapor

- Sat
Saturation, as of temperature

- Avg
Representative of an average value

## Notes

### Acknowledgements

This work was supported by National Science Foundation Grant CBET-1033591. The Principle Investigator on that grant, Dr. Amitabh Narain of Michigan Technological University, has approved independent study and publication of the reported work.

### Author Contribution

Publication of this document was approved by Dr. Amitabh Narain of Michigan Technological University as stated in the acknowledgment. The experiments were conducted by Dr. Michael Kivisalu as a graduate research assistant for Dr. Narain in 2013. Dr. Aliihsan Koca was responsible for data analysis, graphing, and writing of this document as a visiting research scholar at Michigan Technological University assigned to Dr. Narain.

### Compliance with ethical standards

### Conflict of interest

On behalf of all authors, the corresponding author affirms that the preceding statements completely disclose any potential conflict of interest pertaining to this document.

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