Two-phase Heat Transfer Model Research Articles

Bubble dynamics in high-pressure flow boiling conditions

High resolution measurements of key parameters relevant to bubble departure processes in high-pressure water systems has been a major challenge over the past several decades due to the small size and fast motion of vapor bubbles, making conventional optical measurements unreliable. Addressing this difficulty is critical, as accurate bubble departure data and computationally inexpensive models are needed for future two-phase heat transfer models. To close this gap, we use high-speed imaging to track bubble size and velocity in high-pressure flow boiling conditions (10 – 40 bar). It is observed that bubbles are almost always perfectly spherical in shape and slide along the boiling surface immediately after nucleating. To predict sliding, we conduct a force balance on the bubble and derive an equation of motion in the direction of the bulk flow. Interestingly, we find that at high pressure conditions, the equation of motion can be significantly simplified, resulting in an analytical expression for the bubble motion, growth time and departure diameter, allowing us to develop simple and computationally efficient equations. The applicability of the model and departure criterion across a broader range of high-pressure conditions is discussed, and recommendations for further characterization of bubble departure processes are made.

Heat Transfer Included Simulation of Carbonate Rock Acidizing Using Two-Scale Continuum Model with Varying Rock Physics Curves

Summary Matrix acidizing is the commonly used method to enhance permeability of a damaged zone around the well. Acid injection will dissolve the rock, creating narrow, high-permeability channels, called wormholes, to bypass the damaged zone. The pattern of wormhole generation indicates the efficiency of the well stimulation process. Although the injection rate has the most important role in this process, there are other factors such as rock properties, presence of an immiscible phase, and temperature variation that could also affect the dissolution pattern. A few studies have considered the simultaneous effects of all phenomena involved in the acidizing process. We have developed a two-phase heat transfer model coupled with a two-scale continuum model considering capillary and gravity forces for the first time, to simulate the wormhole dissolution pattern. It could be used to analyze the dissolution phenomenon of carbonate rock. A new two-phase relative permeability model is implemented to take the effect of dissolution on relative permeability curves into account. The influence of acid-rock temperature difference, reaction heat, nonisothermal condition, phase saturation, formation porosity, intrinsic permeability and heterogeneity on dissolution pattern, and number of injected pore volumes (PVs) before acid breakthrough is investigated in the developed model. The simulation results show that both optimum injection rate and required PV of acid to breakthrough are strongly dependent on acid and rock temperatures. High formation temperature increases both the optimum injection rate and the optimum number of injected PVs before breakthrough. Injection of acid at lower temperatures will decrease both the optimum injection rate and the optimum number of injected PVs to break through. Simulation results show that the optimum number of injected PVs to break through is 8% higher when reaction heat is considered. Formation properties and degree of heterogeneity influence the number of required injected PVs to breakthrough. Low porosity formations with high heterogeneity correspond to the lowest number of injected PVs to breakthrough. The results indicated that formations with higher permeability will have a higher optimum number of injected PVs to break through and an optimum injection rate. Simulated results show that increasing the initial water saturation will increase the volume of acid to breakthrough. Variation in initial water saturation has a minor effect on wormhole shape, but it does not change the dissolution regime.

Experimental investigation, CFD and theoretical modeling of two-phase heat transfer in a three-leg multi-channel heat pipe

Muti-channel flat heat pipe is an innovative technology recently used at the rear of photovoltaic cells to absorb and reuse the wasted heat. To better understand the fundamentals of two-phase heat transfer (boiling and condensation) taking place inside multi-channel heat pipes, a unique three-leg heat pipe has been built. This one-of-a-kind heat pipe was used to develop both computational fluid dynamic (CFD) and theoretical models of a multi-channel heat pipe. To simulate the heat pipe operation with ANSYS Fluent, the Volume of Fluid (VOF) approach and Lee model were investigated. Different types of Lee models using user defined function (UDF) were compared and the influence of the condenser's boundary condition, saturation temperature, and mass transfer coefficient on the simulations was studied. For the first time, major limits of the Lee model for the simulation of heat pipes are identified. It is concluded that the available Lee model cannot predict the heat pipe temperature as it shows low physical meaning and can easily be manipulated to adjust the simulation's results. Based on the three-leg heat pipe experimental data, a new multi-channel theoretical model was developed that uses the thermal-electrical resistance analogy to predict the three-leg heat pipe thermal resistance. By selecting the optimum correlations for pool boiling and filmwise condensation, the developed iterative theoretical model was able to predict the three-leg heat pipe thermal resistance with an error of 8.2%.

Heat transfer model and cooling performance of converter oxygen lance affected by slag sticking

The heat transfer mechanism and water-cooling effect during oxygen lance blowing changes by slag sticking at the nozzle. In order to effectively overcome this problem, in this study, the equivalent heat transfer method was applied to modify the heat transfer coefficient of the oxygen lance nozzle under different slag thicknesses and steel slag thermal conductivities. In addition, the gas–liquid two-phase heat transfer model was established by computational fluid dynamics numerical simulation, and the cooling effects for different types of oxygen lance nozzles were calculated by the improved model. The results show that the error rate between the calculated value of the modified model and the field measured value was reduced to 3.3%–4.6%. The nozzle with double angle and double flow design was found to be conducive to the improvement of the cooling system. In this study, the best cooling effect was obtained when the flow ratio of large nozzles and small nozzles is 60%/40% and the angle is 12°/17°.

An improved thermal model for predicting wellbore temperature distribution in deep-water gas well

Accurate prediction of wellbore temperature plays an extremely important role in the production design of deep-water gas wells. This study overcomes the shortcomings of the previous literature in temperature calculations, comprehensively studies the heat transfer mechanism in the annulus and tubing, and an improved thermal model for predicting wellbore temperature in deep-water gas well is established. This model includes two important innovations: the natural convection heat transfer model in the annulus and the gas–liquid two-phase heat transfer model in the tubing. Firstly, the mechanism of heat transfer through natural convection in annulus is revealed by a numerical study, and a new calculation method for the annulus convective-heat-transfer coefficient, which can be applied to non-Newtonian fluids, is proposed. Secondly, considering that the two-phase flow in the tubing often presents an annular-mist flow in water-bearing gas well, a heat transfer model of the annular-mist flow in the tubing is developed considering the gas–liquid distribution characteristics and droplet dynamics. The results obtained using this improved thermal model are in good agreement with the field data of deep-water gas well, and the model prediction error is within 10%. Further, the sensitivity analysis is carried out on the parameters of annulus testing fluid that affect the wellbore temperature, and a novel solution for the annular insulation testing fluid was designed. Compared with ordinary annulus testing fluids, the wellbore temperature are more than doubled after adopting the new solution, thereby providing effective guidance for the development of insulation testing fluid system during deep-water gas well testing.

Research on air-water coordinated operation of water side free cooling system based on improved particle swarm optimization algorithm

Water side free cooling is an important technology for cooling water system to use natural cooling source for energy saving, especially in the field of data center and industrial production. However, the operation regulation of water side free cooling system was lack of scientific basis. This process involves the two-phase circulation of air and cooling water, which requires the coordinated operation of air and water to further optimize the energy consumption. The coordinated operation of air and water includes the coordination of air and water flow in each cooling tower and the matching of the operating numbers of equipment in the system. Firstly, based on the characteristics of the cooling tower, the key equipment in the water side free cooling system, the air-water two-phase heat transfer model in the cooling tower was established. Then, according to the heat transfer model and power model of each equipment in the system, the optimization objectives and constraints are established. An improved particle swarm optimization (PSO) algorithm was proposed to solve the problem of wind water collaborative optimization of water side free cooling system. Finally, this paper takes a small data center cooling water system as an example to analyze the optimization performance of the improved particle swarm optimization algorithm. The simulation results showed that the excellent rate obtained by the improved algorithm can be increased by 36.9%, which is more energy-saving. This method can provide a reference for the energy-saving optimization of water side free cooling system.

Temperature gradients within the packed bed affect cumulative supercritical CO2 extraction plots for oilseeds

We studied the effect of temperature gradients within a packed bed on the SuperCritical (SC) CO2 extraction of oil from pelletized cranberry seeds. Temperature gradients were imposed on the extractor by using different temperatures for the SC-CO2 flow and the extractor vessel wall in heating and cooling experiments (60 and 40 °C, and viceversa) for oilseed pellets and glass beads at 48 MPa. A two-phase heat transfer model and a linear-driving-force mass transfer model described temperature profiles and oil extraction curves. Overall, temperatures in the packed bed were more affected by the vessel wall than the SC-CO2 inlet condition. Extraction curves for heating and cooling experiments were between the isothermal extraction curves for 40 and 60 °C, being affected by the vessel wall temperature in the solubility-controlled period of the extraction and approaching each other after 1-h of dynamic extraction. Both heat and mass transfer models allowed a satisfactory prediction of such a behavior and represent a step forward in the prediction of SC-CO2 oil extraction course.

Two-phase heat transfer model of a beam-down gas-solid fluidized bed solar particle receiver

Beam-down concentrating solar power for thermochemical and energy absorption applications stands as an attractive approach that can enhance the renewable energies deployment. This work explores the integration of beam-down optics with fluidized bed technology proposing a model to calculate both gas and bed temperatures. The beam-down system concentrates the energy from the solar field into a fluidized bed receiver. A novel phenomenological model is proposed to adapt the well-known two-phase theory to the heat transfer process of a bed operating in the bubbling regime while it is directly irradiated from the top. In this way, this simple model can be used as a design tool for beam-down fluidized bed receivers. The top bed surface is considered as an opaque diffuse layer formed by gray particles. A single layer model is applied to estimate the effective emissivity between the heterogeneous bed surface and the ambient conditions in the freeboard. The vertical temperature profile is obtained considering particle phase heat conduction, particle to gas heat convection, solid convection, bubble convection and radiation heat transfer mechanisms. The model is validated using silicon carbide and zirconia fluidized bed experiments reported in the literature. The model shows that the solid convection is the dominant heat transfer mechanism for a beam-down fluidized bed receiver. Further results explore the influence of the operating conditions on the fluidized bed receiver for a bed of silicon carbide particles, showing that energy concentration fluxes of 35 · 104 W/m2 can reach bed temperatures of 1000 °C when operating at a gas velocities of 3·Umf.

Development and validation of a semi-empirical model for two-phase heat transfer from arrays of impinging jets

Two-phase jet impingement is a compact cooling technology that provides high-heat-flux dissipation at manageable pressure drop, with applications in cooling power electronics and server modules. The extensive set of geometrical parameters and operating conditions that determine the heat transfer behavior of jet impingement systems provide an attractive level of design flexibility. In the present study, a semi-empirical approach is developed to predict heat transfer from arrays of jets of liquid that undergoes phase change upon impingement. In the modeling approach developed, the jet array is divided into unit cells centered on each orifice that are assumed to behave identically. Based on prior experimental observations, the impingement surface in each unit cell is divided into two distinct regions: a single-phase heat transfer region directly under the jet, and a surrounding boiling heat transfer region along the periphery. Single-phase convection and boiling heat transfer correlations available in the literature are used to estimate the heat transfer coefficient distribution in each region, and the mean surface temperature of the unit cell is estimated via area-averaging. An analysis is performed to show that the model outputs are sensitive to the heat transfer coefficient correlations used as inputs, with the choice depending on the heat flux input and the expected operating regime. Experiments are performed to validate the area-averaged thermal performance predictions. The model results are also compared against experimental data in the literature. The semi-empirical modeling approach developed in this work successfully represents the different heat transfer modes and transitions that occur during two-phase jet impingement. The location of transition to boiling predicted by the model is consistent with prior experimental observations of an inward-creeping boiling front with increasing heat flux. The predicted temperature difference between the surface and the jet inlet across all experimental comparisons has a mean absolute percentage error of 3.88%. The proposed modeling approach is demonstrated to be a practical tool in the development of two-phase jet array impingement devices, allowing for parametric exploration across the expansive design space.

A heat transfer model for condensation accounting for non-equilibrium effects

A heat transfer model is proposed in this paper for condensation of annular and stratified flow in horizontal smooth round tubes accounting for the non-equilibrium effects. The model is based on a non-equilibrium flow regime map and void fraction correlation that is developed from diabatic flow visualization and film thickness measurement. The model unifies single-phase and two-phase heat transfer models into one continuous function throughout the superheated, condensing-superheated, two-phase, condensing-subcooled and subcooled regions with seamless transition in between. Film heat transfer coefficient based on the interfacial temperature of the flow is used as a tool for the modeling in the presence of two-phase flow, which is later converted back to heat transfer coefficient based on the bulk temperature of the flow. The two-phase flow model is developed for the annular and stratified flow. The effects of interfacial waviness, liquid entrainment, wall subcooling, gravity, tube diameter as well as non-equilibrium are discussed in separated sections. Data obtained from different refrigerants and working conditions are used for the validation of the model.

Two-phase heat transfer model for multiprobe cryosurgery

Cryosurgery has been studied as an effective alternative to the conventional chemo and radiotherapies for treating various diseases including cancer. However, it is difficult to accurately quantify the temperature for determining the cell injury in tissue during cryosurgery. One way to overcome this difficulty is to develop numerical models to predict the temperature distribution during cryosurgery. However, contemporary models do not account for the fluid flow and heat transfer inside the cryoprobe(s) and its coupling with the heat transfer in the tissue outside the cryoprobe. In this study, we developed a two-phase flow model to predict the temperature distributions within multiple cryoprobe(s) and further coupled it with the heat transfer in the tissue, to reveal the synergistic effects among the cryoprobes on multi-probe cryosurgery. Our results show that coupled modeling of the heat transfer inside and outside the cryoprobes is crucial for accurate prediction of the cooling power of cryoprobes during multi-probe cryosurgery. The coupled model developed in this study represents a major step forward in mechanistically modeling cryosurgery and may be a valuable tool for optimizing the design of cryoprobes and the procedure of cryosurgery for treating various diseases.

The effect of reduced gravity on cryogenic nitrogen boiling and pipe chilldown.

Manned deep space exploration will require cryogenic in-space propulsion. Yet, accurate prediction of cryogenic pipe flow boiling heat transfer is lacking, due to the absence of a cohesive reduced gravity data set covering the expected flow and thermodynamic parameter ranges needed to validate cryogenic two-phase heat transfer models. This work provides a wide range of cryogenic chilldown data aboard an aircraft flying parabolic trajectories to simulate reduced gravity. Liquid nitrogen is used to quench a 1.27 cm diameter tube from room temperature. The pressure, temperature, flow rate, and inlet conditions are reported from 10 tests covering liquid Reynolds number from 2,000 to 80,000 and pressures from 80 to 810 kPa. Corresponding terrestrial gravity tests were performed in upward, downward, and horizontal flow configurations to identify gravity and flow direction effects on chilldown. Film boiling heat transfer was lessened by up to 25% in reduced gravity, resulting in longer time and more liquid to quench the pipe to liquid temperatures. Heat transfer was enhanced by increasing the flow rate, and differences between reduced and terrestrial gravity diminished at high flow rates. The new data set will enable the development of accurate and robust heat transfer models of cryogenic pipe chilldown in reduced gravity.

Numerical investigations of high temperature packed bed TES systems used in hybrid solar tower power plants

Packed bed thermal energy storage systems with air as high-temperature heat transfer fluid are a cost effective technology for air-based hybrid solar tower plants. A scheme of this plant has been proposed and an optimal mathematical heat transfer model has been formulated to investigate the cyclic thermal behavior of two packed bed TES systems within this plant. The first TES system stores energy at high-temperature (around 1000°C) and at high pressure (around 10bars), while the second one stores energy at 650°C and under atmospheric pressure. The developed model in this study is a dynamic 1-dimensional two-phase heat transfer model, which incorporates variable thermophysical properties for both fluid and solid phases, and hence, enables an accurate prediction of the TES system dynamic. A numerical method for solving the model equations is described in this effort, as well as the required physical correlations. Based on this model a simulation tool was developed in the environment of MATLAB R2011b, and was validated with previous experimental and simulation studies. This calculation tool is fast compared to previous models; thus, it enables the prediction of the cyclic performance of packed bed TES technology at high temperature and pressure working ranges in a relatively short simulation time.

A theoretical analysis of local thermal equilibrium in fibrous materials

The internal heat exchange between each phase and the Local Thermal Equilibrium (LTE) scenarios in multi-phase fibrous materials are considered in this paper. Based on the two-phase heat transfer model, a criterion is proposed to evaluate the LTE condition, using derived characteristic parameters. Furthermore, the LTE situations in isothermal/adiabatic boundary cases with two different heat sources (constant heat flux and constant temperature) are assessed as special transient cases to test the proposed criterion system, and the influence of such different cases on their LTE status are elucidated. In addition, it is demonstrated that even the convective boundary problems can be generally estimated using this approach. Finally, effects on LTE of the material properties (thermal conductivity, volumetric heat capacity of each phase, sample porosity and pore hydraulic radius) are investigated, illustrated and discussed in our study.

Design of packed bed thermal energy storage systems for high-temperature industrial process heat

A previously validated quasi-one-dimensional transient two-phase heat transfer model is used to assess the effect of operational and design parameters on the performance of thermocline thermal energy storage (TES) based on a packed bed of rocks and high-temperature air from process heat as heat transfer fluid. The performance indicators are thermal losses, pumping work, discharge outflow temperature, and overall storage efficiency. A 7.2GWhth TES unit is used as a baseline design. It is found that initial charging of the TES prior to cyclic operation significantly improves its performance at the expense of additional storage material. The temperature drop during the discharge phase is reduced and the efficiency is increased by decreasing the tank diameter-to-height ratio and the rock diameter at the expense of increased pressure drop and pumping work. Increasing the cone angle results in reduced storage size, but increases the temperature drop during discharging. It is shown that thin insulation layers are sufficient to ensure low thermal losses. For all investigated cases, the overall efficiency of the storage stays above 95%.

Mathematical modelling and parameter optimization of pulsating heat pipes

Proper heat transfer management is important to key electronic components in microelectronic applications. Pulsating heat pipes (PHP) can be an efficient solution to such heat transfer problems. However, mathematical modelling of a PHP system is still very challenging, due to the complexity and multiphysics nature of the system. In this work, we present a simplified, two-phase heat transfer model, and our analysis shows that it can make good predictions about startup characteristics. Furthermore, by considering parameter estimation as a nonlinear constrained optimization problem, we have used the firefly algorithm to find parameter estimates efficiently. We have also demonstrated that it is possible to obtain good estimates of key parameters using very limited experimental data.

Update on advances in flow pattern based two-phase heat transfer models

The flow pattern, simplified flow structure based evaporation model of Kattan et al. [J. Heat Transfer 120 (1998) 140; J. Heat Transfer 120 (1998) 148; J. Heat Transfer 120 (1998) 156] has been updated several times since its original publication and also generalized to intube condensation. The current status of our work on this heat transfer prediction model and flow pattern map is described here, covering the following topics: the onset of nucleate boiling, elimination of iterative calculations, evaporation of CO 2 up to pressures as high as 64 bars for tube diameters from 0.9 to 10.0 mm, convective condensation inside horizontal tubes, and the recent experimental verification of the drift flux void fraction model used by the flow pattern map and heat transfer model.

NUMERICAL INVESTIGATION OF HEAT TRANSFER IN INTENSIVE COOLING TUBES WITH TURBULENCE BUSHES

The heat transfer in intensive cooling tubes with turbulence bushes is studied numerically. Based on experimental data, a two-dimensional, two-phase heat transfer model was developed, which describes the coupled temperature fields in the wire and the annulus. Due to the very high wall temperature of the wire and the special flow conditions, convection-controlled film boiling occurs, in which the heat transfer depends mainly on the parameters of single-phase convection. The asymmetric turbulent flow is described by an appropriate one-dimensional model. In order to investigate shape variations of the bushes, additional experiments or two-dimensional flow simulations are required. Therefore, further modeling is focused on the single-phase heat transfer considering the two-dimensional flow. This numerical model is also validated by experimental results. The numerical experiments show the mechanism of the shape influence of the turbulence bushes on the pressure drop and the heat transfer coefficient. They permit optimization of newly designed turbulence bushes and deliver the characteristic bush parameters for the two-phase model.