Steady-state Turbulent Heat Transfer Research Articles

Conductive sublayer of turbulent heat transfer for heating of water in a circular tube

The steady-state and transient turbulent heat transfer coefficients in circular platinum (Pt) test tubes (inner diameters: 3 and 6 mm; heated lengths: 66.5 and 100 mm and 69.6 mm, respectively) were systematically measured using an experimental water loop for a wide range of flow velocities, inlet liquid temperatures, Prandtl numbers, inlet pressures, and exponentially increasing heat inputs (Q 0 exp(t/τ), τ: exponential period). The Reynolds-averaged Navier–Stokes equations and the k–e turbulence model for unsteady turbulent heat transfer in circular test sections were numerically solved for heating of water with heated sections of diameter 3 and 6 mm and length 67 and 100 mm and 70 mm, respectively, by using computational fluid dynamics code under the same conditions as those in the experiment and with temperature-dependent thermophysical fluid properties. The thickness of the conductive sublayer, δ CSL,st and δ CSL [=(Δr) out /2], and the nondimensional thickness of the conductive sublayer, (y , + ) TEM [=(f F /2)0.5 ρ l u δ CSL,st /μ l ] and (y + ) TEM [=(f F /2)0.5 ρ l u δ CSL /μ l ], for steady-state and transient turbulent heat transfer at various heated length-to-inner diameter ratios, inlet liquid temperatures, and exponential periods were measured on the basis of the numerical solutions. The correlations of the thickness of the conductive sublayer, δ CSL,st , and nondimensional thickness of the conductive sublayer, (y , + ) TEM , for steady-state turbulent heat transfer and those of the thickness of the conductive sublayer, δ CSL , and nondimensional thickness of the conductive sublayer, (y + ) TEM , for transient turbulent heat transfer in a circular tube were derived.

Heat transfer and critical heat flux of subcooled water flow boiling in a HORIZONTAL circular tube

The steady-state turbulent heat transfer (THT) due to exponentially increasing heat inputs with various exponential periods (Q=Q0exp(t/τ), τ=6.55–21.81s) were systematically measured with the flow velocities, u, of 4.15, 7.05, 10.07 and 13.50m/s by an experimental water loop flow. Measurements were made on a 6mm inner diameter, a 59.2mm effective length and a 0.4mm thickness of HORIZONTAL Platinum (Pt) circular test tube. The relation between the steady-state turbulent heat transfer and the flow velocity was clarified. The steady state nucleate boiling heat transfer (NBHT) and the steady state critical heat fluxes (CHFs) of the subcooled water flow boiling for HORIZONTAL SUS304 circular test tube were systematically measured with the flow velocities (u=3.93–13.86m/s), the outlet and inlet subcoolings (ΔTsub,out=60.40–130.30K and ΔTsub,in=81.30–154.20K), the inlet pressures (Pin=786.29–960.93kPa) and the increasing heat input (Q0exp(t/τ), τ=8.36s). The HORIZONTAL SUS304 test tube of inner diameter (d=6mm), heated length (L=59.4mm), effective length (Leff=48.4mm), L/d (=9.9), Leff/d (=8.06) and wall thickness (δ=0.5mm) with surface roughness (Ra=3.89μm) was used in this work. The NBHT and the steady state CHFs of the subcooled water flow boiling for the HORIZONTAL SUS304 circular test tube were clarified at the flow velocities, u, ranging from 3.93–13.86m/s. The steady-state THT data, the NBHT ones and the steady state CHF ones were compared with the values calculated by authors’ THT correlation, their NBHT ones and their transient CHF ones against outlet and inlet subcoolings based on the experimental data for the VERTICAL circular test tubes with the flow velocities, u, ranging from 4.0 to 42.4m/s. The influences of test tube orientation on the THT, the NBHT and the subcooled flow boiling CHF are investigated into details and the widely and precisely predictable correlations of the THT, the NBHT and the transient CHFs against outlet and inlet subcoolings in a HORIZONTAL circular test tube are derived based on the experimental data. The THT correlation, the NBHT ones and the transient CHF ones for the HORIZONTAL test tube can describe the THT data, the NBHT ones and the subcooled flow boiling CHF ones for the wide ranges of ΔTsub,out, ΔTsub,in and u obtained in this work within ±15% difference.

Computational study of turbulent heat transfer for heating of water in a short vertical tube under velocities controlled

The steady-state turbulent heat transfer coefficients in a short vertical Platinum (Pt) test tube for the flow velocities (u = 4.11–41.07 m/s), the inlet liquid temperatures (Tin = 296.47–310.04 K), the inlet pressures (Pin = 810.40–1044.21 kPa) and the increasing heat inputs (Q0 exp(t/τ), exponential periods, τ, of 6.04–23.66 s) were systematically measured by an experimental water loop comprised of a multistage canned-type circulation pump with high pump head. Measurements were made on a 59.2 mm effective length and its three sections (upper, mid and lower positions), which were spot-welded four potential taps on the outer surface of the Pt test tube of a 6 mm inner diameter, a 69.6 mm heated length and a 0.4 mm thickness. Theoretical equations for turbulent heat transfer in a circular tube of a 6 mm in diameter and a 636 mm long were numerically solved for heating of water with heated section of a 6 mm in diameter and a 70 mm long by using PHOENICS code under the same condition as the experimental one considering the temperature dependence of thermo-physical properties concerned. The surface heat flux, q, and the average surface temperature, Ts,av, on the circular tube solved theoretically under the flow velocities, u, of 4.11–41.07 m/s were compared with the corresponding experimental values on heat flux, q, versus the temperature difference between average inner surface temperature and liquid bulk mean temperature, ΔTL [=Ts,av − TL, TL = (Tin + Tout)/2], graph. The numerical solutions of q and ΔTL are almost in good agreement with the corresponding experimental values of q and ΔTL with the deviations less than ±10% for the range of ΔTL tested here. The numerical solutions of local surface temperature, (Ts)z, local average liquid temperature, (Tf,av)z, and local liquid pressure drop, ΔPz, are within ±10% of the corresponding experimental data on (Ts)z, (Tf,av)z and ΔPz. The thickness of the thermal boundary layer, δTBL [=(Δr)out/2], and the non-dimensional thickness of thermal boundary layer, yTBL+[=(fF/2)0.5(ρluδVSL/μl)], for the turbulent heat transfer in a short vertical tube under velocities controlled are clarified based on the numerical solutions. It was confirmed in this study that authors’ steady-state turbulent heat transfer correlation based on the experimental data (Hata and Noda, 2008) can not only describe the experimental data of steady-state turbulent heat transfer but also the numerical solutions within ±10% difference for the wide ranges of temperature differences between heater inner surface temperature and liquid bulk mean temperature (ΔTL = 5–200 K) and flow velocities (u = 4.01–41.07 m/s).

Computational Study of Turbulent Heat Transfer for Heating of Water in a Vertical Circular Tube

The steady-state turbulent heat transfer coefficients in a vertical circular Platinum (Pt) test tube for the flow velocities (u=4.22 to 21.45 m/s), the inlet liquid temperatures (Tin=308.20 to 311.77 K), the inlet pressures (Pin=834.04 to 910.23 kPa) and the increasing heat inputs (Q0exp(t/τ), exponential periods, τ, of 6.04 to 32.13 s) were systematically measured by an experimental water loop comprised of a multistage canned-type circulation pump with high pump head. Measurements were made on Pt test tubes of 3, 6 and 9 mm inner diameters, 32.7, 69.6 and 49.6 mm heated lengths and 0.5, 0.4 and 0.3 mm thicknesses, respectively. Theoretical equations for turbulent heat transfer in circular tubes of 3, 6 and 9 mm in diameter and 492, 636 and 616 mm long were numerically solved for heating of water with heated sections of 3, 6 and 9 mm in diameter and 33, 70 and 50 mm long by using PHOENICS code under the same condition as the experimental one considering the temperature dependence of thermo-physical properties concerned. The surface heat flux, q, and the average surface temperature, Ts,av, on the circular tubes solved theoretically under the flow velocities, u, of 4.22 to 21.45 m/s were compared with the corresponding experimental values on heat flux, q, versus the temperature difference between average inner surface temperature and liquid bulk mean temperature, ΔTL [=Ts,av-TL, TL=(Tin+Tout)/2], graph. The numerical solutions of q and ΔTL are almost in good agreement with the corresponding experimental values of q and ΔTL with the deviations less than ±10 % for the range of ΔTL tested here. The numerical solutions of local surface temperature, (Ts)z, and local average liquid temperature, (Tf,av)z, are within ±10 % of the corresponding experimental data on (Ts)z and (Tf,av)z. The thickness of the conductive sub-layer, δCSL [=(Δr)out/2], and the non-dimensional thickness of conductive sub-layer, y+CSL [=(fF/2)0.5ρluδCSL/µl], for the turbulent heat transfer in various vertical tubes are clarified based on the numerical solutions. It was confirmed in this study that authors’ steady-state turbulent heat transfer correlation based on the experimental data [Hata and Noda, 2008] can not only describe the experimental data of steady-state turbulent heat transfer but also the numerical solutions within ±10 % difference for the wide ranges of tube inner diameters (3, 6 and 9 mm), temperature differences between average inner surface temperature and liquid bulk mean temperature (ΔTL=8 to 145 K) and flow velocities (u=4.22 to 21.45 m/s).

ICONE19-43301 COMPUTATIONAL STUDY OF TURBULENT HEAT TRANSFER FOR HEATING OF WATER IN A SHORT VERTICAL TUBE

The steady-state turbulent heat transfer coefficients in a short vertical Platinum (Pt) test tube for the flow velocities (u=4.01 to 13.62 m/s), the inlet liquid temperatures (T_<in>=294.00 to 304.29 K), the inlet pressures (P_<in>=802.12 to 859.08 kPa) and the increasing heat inputs (Q_0exp(t/τ), exponential periods, τ, of 6.04 to 25.67 s) were systematically measured by an experimental water loop comprised of a multistage canned-type circulation pump with high pump head. Measurements were made on a 59.2 mm effective length and its three sections (upper, mid and lower positions), which was spot-welded four potential taps on the outer surface of a 6 mm inner diameter, a 69.6 mm heated length and a 0.4 mm thickness of the Pt test tube. The outer surface temperature distribution of the Pt test tube was also simultaneously observed by an infrared thermal imaging camera at intervals of 3 seconds. Theoretical equations for turbulent heat transfer in a circular tube of a 6 mm in diameter and a 636 mm long were numerically solved for heating of water with heated section of a 6 mm in diameter and a 70 mm long by using PHOENICS code under the same condition as the experimental one considering the temperature dependence of thermo-physical properties concerned. The surface heat flux, q, and the surface temperature, T_s, on the circular tube solved theoretically were compared with the corresponding experimental values on heat flux, q, versus the temperature difference between heater inner surface temperature and liquid bulk mean temperature, ΔT_L [=T_s-T_L, T_L=(T_<in> + T_<out>)/2], graph. The theoretical solutions of q and ΔT_L are almost in good agreement with the corresponding experimental values of q and ΔT_L with the deviations less than ±10 % for the range of ΔT_L tested here. The theoretical solutions of local surface temperature, (T_s)_z, local average liquid temperature, (T_<f,av>)_z, and local liquid pressure drop, ΔP_z, were also compared with the corresponding experimental data on (T_s)_z, (T_<f,av>)z and ΔP_z versus heated length, L, or distance from inlet of the test section, Z, graph, respectively. The theoretical solutions of local surface temperature, (T_s)z and local average liquid temperature, (T_<f,av>)_z are within ±10 % of the corresponding experimental data on (T_s)_z and (T_<f,av>)_z, although those of local liquid pressure drop, ΔP_z, become 37.6 % lower than the experimental ones. It was confirmed in this study that authors' steady-state turbulent heat transfer correlation, Eq. (1), based on the experimental data (Hata and Noda, 2008) Nu_d=0.02Re^<0.85>_dPr^<0.4>(L/d)^<-0.08>(μ_1/μ_w)^<0.14> (1) can not only describe the experimental data of steady-state turbulent heat transfer but also the theoretical solutions within ±10 % difference for the wide ranges of temperature differences between heater inner surface temperature and liquid bulk mean temperature (ΔT_L=5 to 200 K) and flow velocity (u=4.01 to 13.62 m/s).

Transient Turbulent Heat Transfer for Heating of Water in a Short Vertical Tube

The transient turbulent heat transfer coefficients in a short vertical Platinum test tube were systematically measured for the flow velocities (u=4.0 to 13.6 m/s), the inlet liquid temperatures (Tin=296.93 to 304.81 K), the inlet pressures (Pin=794.39 to 858.27 kPa) and the increasing heat inputs (Q0 exp(t/τ), exponential periods, τ, of 18.6 ms to 25.7 s) by an experimental water loop comprised of a multistage canned-type circulation pump with high pump head. The Platinum test tubes of test tube inner diameters (d=3 and 6 mm), heated lengths (L=66.5 and 69.6 mm), effective lengths (Leff=56.7 and 59.2 mm), ratios of heated length to inner diameter (L/d=22.16 and 11.6), ratios of effective length to inner diameter (Leff/d=18.9 and 9.87) and wall thickness (δ=0.5 and 0.4 mm) with average surface roughness (Ra=0.40 and 0.45 µm) were used in this work. The surface heat fluxes between the two potential taps were given the difference between the heat generation rate per unit surface area and the rate of change of energy storage in the test tube obtained from the faired average temperature versus time curve. The heater inner surface temperature between the two potential taps was also obtained by solving the unsteady heat conduction equation in the test tube under the conditions of measured average temperature and heat generation rate per unit surface area of the test tube. The transient turbulent heat transfer data for Platinum test tubes were compared with the values calculated by authors’ correlation for the steady state turbulent heat transfer. The influence of inner diameter (d), ratio of effective length to inner diameter (Leff/d), flow velocity (u) and exponential period (τ) on the transient turbulent heat transfer is investigated into details and the widely and precisely predictable correlation of the transient turbulent heat transfer for heating of water in a short vertical tube is given based on the experimental data and authors’ studies for the transient critical heat fluxes (CHFs) of subcooled water flow boiling in a short vertical tube caused by exponentially, ramp-wise and stepwise increasing heat inputs. The correlation can describe the transient turbulent heat transfer coefficients obtained in this work for the wide range of the temperature difference between heater inner surface temperature and average bulk liquid temperature, ΔTL, of 10 to 160 K with d=3 to 6 mm, Leff/d=9.87 to 18.9, u=4.0 to 13.6 m/s and τ=18.6 ms to 25.7 s within ±15 % difference.

ICONE19-43190 TRANSIENT TURBULENT HEAT TRANSFER FOR HEATING OF WATER IN A SHORT VERTICAL TUBE

The transient turbulent heat transfer coefficients in a short vertical Platinum test tube were systematically measured for the flow velocities (u=4.0 to 13.6 m/s), the inlet liquid temperatures (T_<in>=296.93 to 304.81 K), the inlet pressures (Pin=794.39 to 858.27 kPa) and the increasing heat inputs (Q_0 exp(t/τ), exponential periods, τ, of 18.6 ms to 25.7 s) by an experimental water loop comprised of a multistage canned-type circulation pump with high pump head. The Platinum test tubes of test tube inner diameters (d=3 and 6 mm), heated lengths (L=66.5 and 69.6 mm), effective lengths (L_<eff>=56.7 and 59.2 mm), ratios of heated length to inner diameter (L/d=22.16 and 11.6), ratios of effective length to inner diameter (L_<eff>/d=18.9 and 9.87) and wall thickness (δ=0.5 and 0.4 mm) with average surface roughness (Ra=0.40 and 0.45 μm) were used in this work. The surface heat fluxes between the two potential taps were given the difference between the heat generation rate per unit surface area and the rate of change of energy storage in the test tube obtained from the faired average temperature versus time curve. The heater inner surface temperature between the two potential taps was also obtained by solving the unsteady heat conduction equation in the test tube under the conditions of measured average temperature and heat generation rate per unit surface area of the test tube. The transient turbulent heat transfer data for Platinum test tubes were compared with the values calculated by authors' correlation for the steady state turbulent heat transfer. The influence of inner diameter (d), ratio of effective length to inner diameter (L_<eff>/d), flow velocity (u) and exponential period (τ) on the transient turbulent heat transfer is investigated into details and the widely and precisely predictable correlation of the transient turbulent heat transfer for heating of water in a short vertical tube is given based on the experimental data and authors' studies for the transient critical heat fluxes (CHFs) of subcooled water flow boiling in a short vertical tube caused by exponentially, ramp-wise and stepwise increasing heat inputs. The correlation can describe the transient turbulent heat transfer coefficients obtained in this work for the wide range of the temperature difference between heater inner surface temperature and average bulk liquid temperature (ΔT_L=10 to 160 K) with the inner diameters (d=3 to 6 mm), L_<eff>/d (=9.87 to 18.9), the flow velocities (u=4.0 to 13.6 m/s) and the exponential periods (τ=18.6 ms to 25.7 s) within ±15 % difference.