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ABSTRACT
The transient critical heat flux (CHF) of subcooled water flowing in a narrow channel was measured. A small tube with an inner diameter of 1.0 mm was heated by a direct current. The effects of the subcooling, pressure, flow velocity, and e-folding times of the heat generation rate on the transient CHF were investigated. The experimental result showed that an initial temperature overshoot appeared as the e-folding time of the heat generation rate decreased. The CHF increased with a shorter e-folding time of the heat generation rate. Finally, an empirical correlation for the transient CHF was obtained.
Nomenclature
| A | = | inner surface area of the tube, m2 |
| b | = | systematic standard uncertainty, (-) |
| C | = | constant in Eq. (8), (-) |
| Csf | = | constant in Eq. (9), (-) |
| ch | = | specific heat of the tube, J/kg K |
| cp | = | specific heat at constant pressure for water, J/kg K |
| D* | = | = d/{σ/g(ρl ρg)}0.5, non-dimensional diameter, (-) |
| d | = | inner diameter, m |
| G | = | mass velocity, kg/m2 s |
| f | = | friction factor, (-) |
| g | = | acceleration of gravity, m/s2 |
| h | = | = q/(Ts - Tb), heat transfer coefficient, W/m2K |
| hfg | = | latent heat of vaporization, J/kg |
| I | = | direct current, A |
| K | = | constant in Eq. (13) |
| L | = | length, m |
| MAE | = | mean absolute error, % |
| m | = | exponent in Eq.(9), (-) |
| N | = | number of experimental data, (-) |
| n | = | exponent in Eq.(9), (-) |
| Nu | = | = hd/λ, Nusselt number, (-) |
| P | = | pressure, kPa |
| Pin | = | pressure at the inlet of the heated section, kPa |
| Pout | = | pressure at the outlet of the heated section, kPa |
| Pr | = | = μcp/λ, Prandtl number, (-) |
| = | heat input per unit volume, W/m3 | |
| Q | = | heat transfer rate, W |
| Q0 | = | initial exponential heat input, W/m3 |
| q | = | heat flux, W/m2 |
| R0 | = | electrical resistance at 0 °C, Ω |
| R | = | electrical resistance of the double bridge circuit, Ω |
| Ra | = | average roughness, μm |
| Rs | = | standard electrical resistance, Ω |
| Ry | = | maximum roughness depth, μm |
| Rz | = | mean roughness depth, μm |
| Re | = | = ud/v, Reynolds number, (-) |
| RMSE | = | root mean square error, % |
| r | = | radius of the tube, m |
| s | = | random standard uncertainty of the mean of N measurements, (-) |
| Sc | = | = cplΔTsub,out /hfg, non-dimensional outlet subcooling, (-) |
| Sp | = | = ρlcplΔTsub,out /ρghfg, non-dimensional parameter for the outlet subcooling, (-) |
| T | = | temperature, K |
| Ta | = | average temperature of the tube, K |
| Tin | = | inlet liquid temperature, K |
| Tb | = | = (Tin+Tout)/2, bulk temperature, K |
| Tout | = | = |
| Tsat | = | saturation temperature, K |
| t | = | time, s |
| t95 | = | Student’s t value at a specified confidence level, (-) |
| ΔTsat | = | = Ts−Tsat, surface superheat, K |
| ΔTsub,in | = | = Tsat−Tin, inlet liquid subcooling, K |
| ΔTsub,out | = | = Tsat−Tout, outlet liquid subcooling, K |
| URSS | = | = (b2+t95s2)0.5, expanded uncertainty, (-) |
| u | = | flow velocity, m/s |
| V | = | volume of the tube, m3 |
| VI | = | voltage of the standard resistor, V |
| VR | = | voltage of the tube, V |
| VT | = | unbalanced voltage, V |
| w | = | weighting factor, (-) |
| We | = | = G2d/ρl σ, Weber number, (-) |
| α | = | coefficient, (-) |
| β | = | coefficient, (-) |
| ε | = | emissivity of platinum |
| λ | = | thermal conductivity, W/mK |
| μ | = | viscosity, N s/m2 |
| ν | = | kinematic viscosity, m2/s |
| τ | = | e-folding time, s |
| ρ | = | density, kg/m3 |
| σ | = | surface tension, N/m |
| σsb | = | Stefan–Boltzmann constant, (-) |
Subscripts
| AMP | = | Amplifier |
| cr | = | CHF |
| exp | = | experiment |
| g | = | vapor |
| h | = | heater |
| i | = | inner |
| in | = | inlet |
| l | = | liquid |
| o | = | outer |
| out | = | outlet |
| pred | = | prediction |
| rad | = | radiation |
| s | = | surface |
| sub | = | subcooling |
| surround | = | surrounding |
| TC | = | thermocouple |