Experimental and numerical study of convection heat transfer of CO2 at super-critical pressures during cooling in small vertical tube

Convection heat transfer of CO₂ at super-critical pressures during cooling in a vertical small tube with inner diameter of 2.00 mm was investigated experimentally and numerically. The local heat transfer coefficients were determined through a combination of experimental measurements and numerical simulations. This study investigated the effects of pressure, cooling water mass flow rate, CO₂ mass flow rate, CO₂ inlet temperature, flow direction, properties variation and buoyancy on convection heat transfer in small tube. The results show that the local heat transfer coefficients vary significantly along the tube when the CO₂ bulk temperatures are in the near-critical region. The increase of specific heat and turbulence kinetic energy due to the density variation leads to the increase of the local heat transfer coefficients for upward flow. The buoyancy effect induced by density variation leads to a different variation trend of the local heat transfer coefficients along the tube for upward and downward flows. The numerical simulations were conducted using several k–ε turbulence models including the RNG k–ε model with a two-layer near wall treatment and three low-Reynolds number eddy viscosity turbulence models. The simulations using the low-Reynolds number k–ε model due to Yang–Shih has been found to be able to reproduce the general features exhibited in the experiments, although with a relatively large overestimation of measured wall temperatures. A better understanding of the mechanism of properties variation and buoyancy effects on convection heat transfer of CO₂ at super-critical pressures in a vertical small tube during cooling has been developed based on the information generated by the simulation on the detailed flow and turbulence fields.     

Development of a new forced convection heat transfer correlation for CO2 in both heating and cooling modes at supercritical pressures

Experimental and numerical investigations on forced convection heat transfer of carbon dioxide at supercritical pressures in a prototypic printed circuit heat exchanger under both cooling and heating conditions have been performed in this present study. The experiment test section has nine semi-circular channels with a hydraulic diameter of 1.16 mm and a length of 0.5 m. Primary operational parameters include inlet pressure of 7.5–10 MPa, mass fluxes of 326 kg/m² s and 762 kg/m² s, inlet temperatures from 10 °C to 90 °C and the average heat flux was 30 kW/m². Beyond reproducing the regular experimental cases, numerical modeling also implemented higher heat fluxes of 60 kW/m² and 90 kW/m² in order to investigate the effect of heat flux. Good agreement was found between the experiments and FLUENT simulations using an SST k–w model with the near-wall region being completely resolved. The distinctive behavior of convection heat transfer at supercritical pressures between heating and cooling modes was systematically analyzed. A more physically reasonable property-averaging technique, Probability Density Function (PDF)-based time-averaged property, was developed to account for the effect of nonlinear dependency of properties on instantaneous local temperature. Furthermore, experimental and computational data were compared to empirical predictions by the Dittus–Boelter and Jackson correlations. The results showed that Dittus–Boelter correlation has better precision for the average value of the predicted heat transfer coefficient but cannot take account of the effect of heat flux. In contrast, the Jackson correlation, with property ratio correction terms to account for the distribution of the properties in the radial direction, could predict the distinction of heat transfer characteristics under heating and cooling conditions. However, it overestimates the average value of heat transfer coefficient in the whole range of the experiment conditions. Finally, a new correlation evaluated by PDF-based time-averaged properties for forced convection heat transfer of CO₂ in both heating and cooling mode at supercritical pressures was developed. Comparison of experimental and computational data with the prediction results by the new developed correlation reveals that it works quite well; i.e., more than 90% data in either heating or cooling mode with various heat fluxes are predicted within an accuracy of ±25%.     

Experimental validation of CFD modelling for heat transfer coefficient predictions in axial flux permanent magnet generators

This paper describes the experimental validation of CFD modelling for heat transfer coefficients in an axial flux permanent magnet (AFPM) generator. A large scale low speed test rig was designed and constructed. The geometric parameters and the rotational speed of the test rig were determined by dimensional analysis, to ensure the flow characteristic remains unchanged as compared with commercial AFPM generators. The heat transfer coefficients in the test rig were measured at rotational Reynolds number, Re_ω from 0 to 2 × 10⁶, non-dimensional flow rate, C_w up to 11,000 and gap ratio, G = 0.016, by using the combination of heat flux sensors and thermocouples. Due to the large size of the scaled-up rig, natural convection played a significant part in the heat transfer and this had to be compensated for in the forced convection heat transfer coefficient calculations. Extra experiments were designed and conducted to identify the effect of natural convection on the machine’s cooling. The experimentally determined results were compared to heat transfer coefficients predicted by CFD models and good agreement was obtained.     

Study of the heat transfer characteristics in turbulent combined wall and offset jet flows

The heat transfer study of a combined wall jet and offset jet flow with different wall jet and offset jet flow velocities are considered. The flow is considered two-dimensional, steady, incompressible, turbulent at high Reynolds number with negligible body forces. The streamline curvature modification of the standard k–ε model is used to carry out the turbulence modeling. The Reynolds number is varied from 10⁴ to 4 × 10⁴ and Pr = 0.71 is taken for all computations. Constant wall temperature and constant wall heat flux boundary conditions are considered. The results are presented in the form of local Nusselt number, local heat flux, surface temperature in case of constant heat flux condition, average Nusselt number and total heat transfer.     

Turbulent heat transfer characteristics of supercritical n‐decane in a vertical tube under various operating pressures

To explore the effect of the operating pressure on the flow and thermal characteristics in a vertical tube with supercritical n‐decane, the inner wall temperature along the streamwise direction, the applicability of empirical correlations and buoyancy criteria are studied firstly. The mechanisms in views of density distribution, velocity field, turbulence intensity, the thickness of the thermal boundary layer, and secondary flow are then analyzed. It is observed that the buoyancy is helpful for the phenomenon of heat transfer deterioration at lower operating pressures but higher operating pressures can diminish this tendency. According to this reason, the empirical correlation proposed by Bae and Kim is suitable for the higher operating pressures but cannot well predict the occurrence of heat transfer deterioration. However, it can be evaluated by the buoyancy criterion Gr/Re² = 0.01 qualitatively. The decrease of turbulence intensity, the thickened thermal boundary layer, and secondary flow generation make contributions to the heat transfer deterioration in particular. Similarly, this situation can be diminished and even removed by the higher operating pressures.     

Fluid‐to‐fluid scaling of heat transfer to mixed convection flow of supercritical pressure fluids

Fluid‐to‐fluid scaling for supercritical heat transfer can effectively reduce the difficulty and cost of heat transfer experiments in supercritical boilers and supercritical water reactors and can reduce the number of experiments by converting experimental data of the model fluid to the prototype fluid in organic Rankine cycles. Currently, most existing scaling methods are only suitable for forced convection, while few are developed for mixed convection where buoyancy significantly affects the heat transfer. This paper attempts to extend the applicability of scaling method to mixed convection with the aid of computational fluid dynamic simulations. The scaling parameters were analyzed first and then the shear‐stress transport k‐ω model was used to analyze the supercritical heat transfer characteristics of water and R134a to provide further information for developing a dimensionless number. The results show that significant variations of properties and flow parameters occur in the layer of y⁺ = 5 to 100 and the axial velocity gradient in this layer changes in quite a similar manner to the wall temperature. Based on numerical results, the axial velocity gradient was used with a thermal resistance analogy to derive a new dimensionless number, Re^?0.9π_A , to scale the mass flux. Then, a set of fluid‐to‐fluid scaling laws were developed to predict the heat transfer to supercritical fluids. To validate the newly proposed scaling laws, well‐developed correlations were used for forced convection flow and a direct validation method was developed for buoyancy‐influenced flow. Results show that this new scaling method exhibits reasonable accuracy for both forced and mixed convection heat transfer with supercritical fluids.     

The effects of different entrance sections lengths and heating on free and forced convective heat transfer inside a horizontal circular tube

An experimental study was done for hydrodynamically fully developed and thermally developing laminar air flows in a horizontal circular tube has a 30 mm inside diameter and 900 mm heated length (L/D = 30) under a constant wall heat flux boundary condition, with different aluminum entrance section pipes (calming sections) having the same inside diameter as test section pipe but with variable lengths of 600 mm (L/D = 20), 1200 mm (L/D = 40), 1800 mm (L/D = 60), and 2400 mm (L/D = 80). The Reynolds number ranged from 400 to 1600 and the heat flux is varied from 60 W m^− 2 to 400 W m^− 2. This paper examines the effects of the entrance sections lengths and heating on the free and forced convection heat transfer process. The surface temperature data were measured and heat transfer rates at different heat flux levels as well as different Reynolds numbers were calculated and correlated in the form of relevant parameters. The buoyancy force has a significant effect on the heat transfer and the combined convection factor was approximately varied form 0.13 ≤ Gr/Re² ≤ 7.125. It was found that the surface temperature increases as the entrance section length increases. It was inferred that the heat transfer decreases as the entrance section length increases due to the flow resistance and the mass flow rate. The proposed correlation was compared with available literature and with laminar forced convection and showed satisfactory agreement.     

Boiling heat transfer and critical heat flux of ethanol–water mixtures flowing through a diverging microchannel with artificial cavities

This paper presents an experimental study on the convective boiling heat transfer and the critical heat flux (CHF) of ethanol–water mixtures in a diverging microchannel with artificial cavities. The results show that the boiling heat transfer and the CHF are significantly influenced by the molar fraction (x_m) as well as the mass flux. For the single-phase convection region except for the region near the onset of nucleate boiling with temperature overshoot, the single-phase heat transfer coefficient is independent of the wall superheat and increases with a decrease in the molar fraction. After boiling incipience, the two-phase heat transfer coefficient is much higher than that of single-phase convection. The two-phase heat transfer coefficient shows a maximum in the region of bubbly-elongated slug flow and deceases with a further increase in the wall superheat until approaching a condition of CHF, indicating that the heat transfer is mainly dominated by convective boiling. A flow-pattern-based empirical correlation for the two-phase heat transfer coefficient of the flow boiling of ethanol–water mixtures is developed. The overall mean absolute error of the proposed correlation is 15.5%, and more than 82.5% of the experimental data were predicted within a ±25% error band. The CHF increases from x_m = 0–0.1, and then decreases rapidly from x_m = 0.1–1 at a given mass flux of 175 kg/m² s. The maximum CHF is reached at x_m = 0.1 due to the Marangoni effect, indicating that small additions of ethanol into water could significantly increase the CHF. On the other hand, the CHF increases with increasing the mass flux at a given molar fraction of 0.1. Moreover, the experimental CHF results are compared with existing CHF correlations of flow boiling of the mixtures in a microchannel.     

Investigation of mixed convection heat transfer in a horizontal channel with discrete heat sources at the top and at the bottom

Mixed convection heat transfer from arrays of discrete heat sources inside a horizontal channel has been investigated experimentally. Each of the lower and upper surfaces of the channel was equipped with 8 × 4 flush mounted heat sources subjected to uniform heat flux. Sidewalls, lower and upper walls are insulated and adiabatic. The experimental parametric study was made for aspect ratios of AR = 2, 4 and 10, at various Reynolds and Grashof numbers. From the experimental measurements, row-average surface temperature and Nusselt number distributions of the discrete heat sources were obtained and effects of Reynolds and Grashof numbers on these numbers were investigated. From these results, the buoyancy affected secondary flow and the onset of instability have been discussed. Results show that top and bottom heater surface temperatures increase with increasing Grashof number. The top heater average-surface temperatures for AR = 2 are greater than those of bottom ones. For high values of Grashof numbers where natural convection is the dominant heat transfer regime (Gr¹/Re² ≫ 1), temperatures of top heaters can have much greater values. The variation of the row-average Nusselt numbers for the aspect ratio of AR = 4, show that with the increase in the buoyancy affected secondary flow and the onset of instability, values of Nusselt number level off and even rise as a result of heat transfer enhancement especially for low Reynolds numbers.     

Flow boiling of liquid nitrogen in micro-tubes: Part II – Heat transfer characteristics and critical heat flux

This paper is the second portion of a two-part study concerning the flow boiling of liquid nitrogen in the micro-tubes with the diameters of 0.531, 0.834, 1.042 and 1.931 mm. The contents include the heat transfer characteristics and critical heat flux (CHF). The local wall temperatures are measured, from which the local heat transfer coefficients are determined. The influences of heat flux, mass flux, pressure and tube diameter on the flow boiling heat transfer coefficients are investigated systematically. Two regions with different heat transfer mechanism can be classified: the nucleate boiling dominated region for low mass quality and the convection evaporation dominated region for high mass quality. For none of the existed correlations can predict the experimental data, a new correlation expressed by Co, Bo, We, K_p and X is proposed. The new correlation yields good fitting for 455 experimental data of 0.531, 0.834 and 1.042 mm micro-tubes with a mean absolute error (MAE) of 13.7%. For 1.931 mm tube, the flow boiling heat transfer characteristics are similar to those of macro-channels, and the heat transfer coefficient can be estimated by Chen correlation. Critical heat flux (CHF) is also measured for the four tubes. Both the CHF and the critical mass quality (CMQ) are higher than those for conventional channels. According to the relationship that CMQ decreases with the mass flux, the mechanism of CHF in micro-tubes is postulated to be the dryout or tear of the thin liquid film near the inner wall. It is found that CHF increases gradually with the decrease of tube diameter.     

Oscillatory thermocapillary flow in liquid bridges of high Prandtl number fluid with free surface heat gain

Oscillatory thermocapillary flow in liquid bridges of high Prandtl number fluid is studied. The effect of free surface heat transfer, especially heat gain, on the oscillation phenomenon is investigated experimentally and numerically. It is shown that the critical temperature difference (ΔT_cr) changes substantially when the free surface heat transfer changes from loss to gain in the case of nearly straight liquid bridges. In contrast, ΔT_cr is not affected by the free surface heat transfer with concave liquid bridges. The free surface heat transfer rate is computed numerically by simulating the interaction of the liquid and the surrounding air. The oscillatory flow is also investigated numerically by analyzing the liquid flow in three-dimensions for straight bridges. The computed results agree well with the experimental data. The simulation shows that the free surface heat gain enhances the surface flow and that the oscillatory flow is a result of interactions between the convection effect and buoyancy. The flow does not become oscillatory if there is no net heat gain at the free surface in the range of Marangoni number of the present work (⩽1.8 × 10⁴), so the present cause of oscillations is different from that in the free surface heat loss case we investigated in the past.     

Deteriorated turbulent heat transfer (DTHT) of gas up-flow in a circular tube: Experimental data

The major focus of this paper is to present experimental data, collected for three gases – nitrogen, helium, and carbon dioxide, at the deteriorated turbulent heat transfer (DTHT) regime in gas up-flow with near uniform heat flux. The data were collected for a range of (1) inlet Reynolds number from 1800 to 42,700, (2) inlet buoyancy number Bo¹ up to 1 × 10^?5and (3) inlet acceleration parameter K_v up to 5 × 10^?6. Based on the new experimental data, the traditional thresholds for the DTHT regimes are updated, and a new heat transfer regime map is proposed and compared to the existing experimental data.     

Mixed convection on jet impingement cooling of a constant heat flux horizontal porous layer

In the present study, numerical investigation of jet impingement cooling of a constant heat flux horizontal surface immersed in a confined porous channel is performed under mixed convection conditions, and the Darcian and non-Darcian effects are evaluated. The unsteady stream function-vorticity formulation is used to solve the governing equations. The results are presented in the mixed convection regime with wide ranges of the governing parameters: Reynolds number (1 ≤ Re ≤ 1000), modified Grashof number (10 ≤ Gr¹ ≤ 100), half jet width (0.1 ≤ D ≤ 1.0), Darcy number (1 × 10^?6 ≤ Da ≤ 1 × 10^?2), and the distance between the jet and the heated portion (0.1 ≤ H ≤ 1.0). It is found that the average Nusselt number (Nu_avg) increases with increase in either modified Grashof number or jet width for high values of Reynolds number. The average Nusselt number also increases with decrease in the distance between the jet and the heated portion. The average Nusselt number decreases with the increase in Da for the non-Darcy regime when Re is low whereas Nu_avg increases when Re is high. It is shown that mixed convection mode can cause minimum heat transfer unfavorably due to counteraction of jet flow against buoyancy driven flow. Minimum Nu_avg occurs more obviously at higher values of H. Hence the design of jet impingement cooling through porous medium should be carefully considered in the mixed convection regimes.     

Numerical Investigation of Conjugate Heat Transfer to Supercritical CO2 in a Vertical Tube-in-Tube Heat Exchanger

Conjugate heat transfer to supercritical CO₂ in a vertical tube-in-tube heat exchanger was numerically investigated. The results demonstrate that most models considered are able to reproduce the heat transfer processes qualitatively, and the Abe, Kondoh, and Nagano model shows optimal agreement with the experimental data. The influences of hot fluid mass flux and temperature of the shell side, supercritical fluid mass flux of the tube side, flow direction, and pipe diameter on conjugate heat transfer were investigated based on velocity and turbulence fields. It is concluded that hot fluid mass flux and temperature of the shell side significantly affect heat transfer of the tube side. Mixed convection is the main heat transfer mechanism for the supercritical CO₂ conjugate heat transfer process when the inner diameter of the tube is greater than 1 mm. In addition, density variation is highly significant for heat transfer of supercritical CO₂ while high viscosity hinders the distortion of the flow field and reduces deterioration in heat transfer.     

Upflow turbulent mixed convection heat transfer in vertical pipes

The present work deals with the results of an experimental investigation on heat transfer in water cooled vertical pipes, for thermal–hydraulic conditions ranging from forced convective flow to mixed convective flow. The flow of water in the pipe is upwards.Experimental data confirm the reduction in the heat transfer rate for mixed convection in upward heat flow, mainly due to the laminarization effect in the near-wall region (buoyancy effect) . They are in a very good agreement with numerical methods, such as the k–-model.A new method for the calculation of the heat transfer coefficient in upward mixed convection heated flow is proposed. It is based on the well-known superposition method (heated downflow) modified accounting for the phenomenology of the upward heated flow in comparison with downflow heated conditions.     

Heat transfer characteristics of gaseous flows in microtube with constant heat flux

Heat transfer characteristics of gaseous flows in a microtube with constant heat flux whose value is positive or negative are investigated on two-dimensional compressible laminar flow for no-slip regime. The numerical methodology is based on the Arbitrary–Lagrangian–Eulerian (ALE) method. The computations are performed for tubes with constant heat flux ranging from −10⁴ to 10⁴ W m⁻². The tube diameter ranges from 10 to 100 μm and the aspect ratio of the length and diameter is 200. The stagnation pressure, p_stg is chosen in such away that the Mach number at the exit ranges from 0.1 to 0.7. The outlet pressure is fixed at the atmosphere. The wall and bulk temperatures in microtubes with positive heat flux are compared with those of negative heat flux case and also compared with those of the incompressible flow in a conventional sized tube. In the case of fast flow, temperature profiles normalized by heat flux have different trends whether heat flux is positive or negative. A correlation for the prediction of the wall temperature of the gaseous flow in the microtube is proposed. Supplementary runs with slip boundary conditions for the case of D = 10 μm conducted and rarefaction effect is discussed. With increasing Ma number, the compressibility effect is more dominant and the rarefaction effect is relative insignificant where Kn number is less than Kn = 0.0096. And, the magnitudes of viscous dissipation term and compressibility term are investigated along the tube length.     

Experimental study of R-134a evaporation heat transfer in a narrow annular duct

An experiment is carried out here to investigate the evaporation heat transfer and associated evaporating flow pattern for refrigerant R-134a flowing in a horizontal narrow annular duct. The gap of the duct is fixed at 1.0 and 2.0 mm. In the experiment, the effects of the duct gap, refrigerant vapor quality, mass flux and saturation temperature and imposed heat flux on the measured evaporation heat transfer coefficient h_r are examined in detail. For the duct gap of 2.0 mm, the refrigerant mass flux G is varied from 300 to 500 kg/m² s, imposed heat flux q from 5 to 15 kW/m², vapor quality x_m from 0.05 to 0.95, and refrigerant saturation temperature T_sat from 5 to 15 °C. While for the gap of 1.0 mm, G is varied from 500 to 700 kg/m² s with the other parameters varied in the same ranges as that for δ = 2.0 mm. The experimental data clearly show that the evaporation heat transfer coefficient increases almost linearly with the vapor quality of the refrigerant and the increase is more significant at a higher G. Besides, the evaporation heat transfer coefficient also rises substantially at increasing q. Moreover, a significant increase in the evaporation heat transfer coefficient results for a rise in T_sat, but the effects are less pronounced in the narrower duct at a low imposed heat flux and a high refrigerant mass flux. Furthermore, the evaporation heat transfer coefficient increases substantially with the refrigerant mass flux except at low vapor quality. We also note that reducing the duct gap causes a significant increase in h_r. In addition to the heat transfer data, photos of R-134a evaporating flow taken from the duct side show the change of the dominant two-phase flow pattern in the duct with the experimental parameters. Finally, an empirical correlation for the present measured heat transfer coefficient for the R-134a evaporation in the narrow annular ducts is proposed.     

Heat transfer and pressure drop during HFC refrigerant saturated vapour condensation inside a brazed plate heat exchanger

This paper presents the heat transfer coefficients and the pressure drop measured during HFC refrigerants 236fa, 134a and 410A saturated vapour condensation inside a brazed plate heat exchanger: the effects of saturation temperature (pressure), refrigerant mass flux and fluid properties are investigated. The heat transfer coefficients show weak sensitivity to saturation temperature (pressure) and great sensitivity to refrigerant mass flux and fluid properties. A transition point between gravity controlled and forced convection condensation has been found for a refrigerant mass flux around 20 kg/m²s that corresponds to an equivalent Reynolds number around 1600–1700. At low refrigerant mass flux (G_r < 20 kg/m²s) the heat transfer coefficients are not dependent on mass flux and are well predicted by the Nusselt [20] analysis for vertical surface: the condensation process is gravity controlled. For higher refrigerant mass flux (G_r > 20 kg/m²s) the heat transfer coefficients depend on mass flux and are well predicted by Akers et al. [21] equation: forced convection condensation occurs. In the forced convection condensation region the heat transfer coefficients show a 25–30% increase for a doubling of the refrigerant mass flux.The frictional pressure drop shows a linear dependence on the kinetic energy per unit volume of the refrigerant flow and therefore a quadratic dependence on mass flux.HFC-410A shows heat transfer coefficients similar to HFC-134a and 10% higher than HFC-236fa together with frictional pressure drops 40-50% lower than HFC-134a and 50–60% lower than HFC-236fa.     

Study of turbulent heat transfer of aviation kerosene flows in a curved pipe at supercritical pressure

The flow and heat transfer characteristics of China No. 3 aviation kerosene in a heated curved tube under supercritical pressure are numerically investigated by a finite volume method. A two-layer turbulence model, consisting of the RNG k–ε two-equation model and the Wolfstein one-equation model, is used for the simulation of turbulence. A 10-species kerosene surrogate model and the NIST Supertrapp software are applied to obtain the thermophysical and transport properties of the kerosene at various temperature under a supercritical pressure of 4 MPa. The large variation of thermophysical properties of the kerosene at the supercritical pressure make the flow and heat transfer more complicated, especially under the effects of buoyancy and centrifugal force. The centrifugal force enhances the heat transfer, but also increases the friction factors. The rise of the velocity caused by the variation of the density does not enhance the effects of the centrifugal force when the curvature ratios are less than 0.05. On the contrary, the variation of the density increases the effects of the buoyancy.