Transient convective droplet removal from condenser surfaces has the potential to significantly enhance thermal transport. Despite a century of progress in understanding of steady-state condensation, less is known about transient condensation. Here, we study transient pulse condensation of ethanol vapor. Using rigorous two-phase heat transfer measurements, we characterize transient heat transfer performance for filmwise and dropwise condensation of ethanol on smooth copper and nanostructured copper oxide lubricant-infused surfaces, respectively. We demonstrate an 8X and 5X enhancement in the condensation heat transfer coefficient during transient operation for dropwise and filmwise modes, respectively, when compared to the steady state. Beyond transient heat transfer enhancement, repeated cycles or pulses of dropwise condensation led to 30% higher time-averaged heat transfer performance due to higher nucleation site density and convective effects. Our work not only demonstrates transient condensation as a method to enhance heat transfer but also develops a methodology for enabling enhanced condensers for high power density thermal management systems for applications employing transient energy dissipation.

Vapor condensation is a ubiquitous phenomenon in many industrial processes such as power generation,1 air conditioning,2,3 natural gas processing,4 desalination,5 water harvesting,6 and thermal management.7,8 Phase change heat transfer enhancement promises significant energy and economic gains.9 The higher heat transfer coefficients during phase change enable a lower heat transfer area (QhA, where Q is the overall heat transfer, h is the heat transfer coefficient, and A is the heat transfer area), while the near-constant temperature during phase change (low dT) yields additional benefits.10,11 From an economic standpoint, the high h enables compact system development (low A) as well as high power density, resulting in smaller and lighter energy-efficient systems.12,13 In the past, much attention has been devoted to developing non-wetting superhydrophobic surfaces promoting dropwise14–16 or droplet jumping condensation,17,18 which have an order of magnitude higher heat transfer performance when compared to filmwise condensation.15,16 However, despite significant progress in the understanding of steady-state condensation, relatively little is known about transient condensation. Here, we study transient “pulse” condensation as a method to enhance droplet removal and nucleation density. By operating the process in vapor inlet-evacuation cycles (pulses), we demonstrate an 8X and 5X enhancement in the transient condensation heat transfer coefficient for dropwise and filmwise condensation of ethanol, respectively.

To enable a comparison of the transient pulse and steady state, we investigated the condensation heat transfer performance of ethanol on state-of-the-art (SOA) smooth functionalized copper (Cu) surfaces and fluorinated lubricant infused (LIS) nanostructured copper oxide (CuO) surfaces.19–21 Considering the high boiling point of steam at atmospheric pressure, we chose ethanol (hfg 846 kJ/kg) as the working fluid. The lower boiling point of ethanol makes it a promising candidate for thermal management applications such as electronics cooling. The LIS was chosen due to its ability to promote stable dropwise condensation of low-surface-tension fluids such as toluene,21,22 ethanol,20 and hexane.20,22 Functionalized nanostructured CuO tubes (dOD = 6.35 mm, dID = 4.72 mm, and L = 76.2 cm) were infused with fluorinated Krytox VPF 1525 oil (Chemours, γ= 19 mN/m, μ= 498 mPa·s) by dip coating the tubes for 10 min20 (Sec. S2, supplementary material). Contact angle measurements using 100 nl ethanol droplets on the smooth Cu and LIS surfaces showed apparent advancing and receding contact angles of θa=36.5±2°/θr=23.4±4° and θa=71.1±3°/θr=69.3±3°, respectively.

Condensation heat transfer performance was determined by testing the Cu and LIS tubes in a controlled environment chamber (Secs. S3 and S4, supplementary material). Prior to running the condensation experiments, a separate vapor generator (8″ OD standard CF Tee) filled with ethanol (200 Proof) was vigorously boiled, and the environmental chamber [Fig. 1(a)] evacuated to a pressure of P < 2 ± 1 Pa to eliminate noncondensable gases (NCGs). An external water cooling loop independently controlled the tube sample surface temperature. The cooling water flow rate was maintained at 10.5±0.15 l/min, and the chiller (Neslab System III, Thermo Fisher) inlet temperature was kept constant at 7±0.5°C for all experiments. The selected flow rate resulted in a highly turbulent flow with the Reynolds number of RedID=ρwU¯dID/μw=30000, ensuring a well-mixed flow with rapid temperature equilibration of the coolant inside the condensing tube sample. This ensured that the transient response of the inlet and outlet temperatures were measurable by the resistance temperature detectors (RTDs). Both the thermal and electrical response time of the class A RTDs used to measure the cooling water inlet and outlet temperatures were significantly faster than the experimental time scale (Sec. S5, supplementary material). Steady-state condensation heat transfer performance on the Cu [Fig. 1(b)] and LIS [Fig. 1(c)] tubes was tested within the vapor pressure range of 4.5 <Pv,steady< 9 kPa. The temperature difference between the cooling water inlet and outlet (dT=ToutTin) for all transient experiments was within the range of 0.714°C. For details regarding the experimental design, initial operation, steady state condensation experiments, and a rigorous uncertainty analysis, please refer to Secs. S3–S6 of the supplementary material.

FIG. 1.

(a) Schematic of the experimental setup (not to scale). Photographs of condensation of saturated ethanol vapor on horizontally oriented (b) smooth Cu tubes (filmwise) and (c) LIS tubes (dropwise).

FIG. 1.

(a) Schematic of the experimental setup (not to scale). Photographs of condensation of saturated ethanol vapor on horizontally oriented (b) smooth Cu tubes (filmwise) and (c) LIS tubes (dropwise).

Close modal

After evacuating the chamber, the vacuum-line valve [connecting the chamber to the vacuum pump, Fig. 1(a)] was closed and the vapor-inlet valve [connecting the secondary vapor generator to the chamber, Fig. 1(a)] instantly opened. For pulse condensation experiments, the vapor-inlet valve was completely opened to allow a surge of saturated ethanol vapor into the condensation chamber. Ethanol vapor was allowed to enter the chamber for time topen, after which the vapor-inlet valve was completely closed, and the vacuum-line valve opened. This setting was maintained for time tclose, during which time ethanol vapor was continuously removed by the vacuum pump, resulting in a rapid pressure drop inside the chamber. After time tclose, which marked the end of one pulse cycle, the vacuum-line valve was once again completely closed, and the vapor-inlet valve opened. To achieve high fidelity data during pulse condensation runs, six consecutive pulse cycles were performed for each experiment. The input power of the vapor generator remained constant throughout the experiment. To eliminate the initial effect of vapor injection into the evacuated dry chamber, transient heat transfer calculations were performed for five consecutive pulse cycles starting from the second cycle, i.e., after the initial topen+tclose, as indicated by the vertical dashed line t=0 in Fig. 2.

FIG. 2.

Ethanol vapor pressure (Pv, red solid line), measured U¯pulse (green solid line), and hpulse (blue solid line) as a function of time during a typical pulse condensation operation on LIS with topen=tclose= 60 s. The horizontal dashed lines indicate the arithmetic mean Pv¯ (red dashed line), Upulse¯ (green dashed line), and hpulse¯ (blue dashed line) for the entire operation.

FIG. 2.

Ethanol vapor pressure (Pv, red solid line), measured U¯pulse (green solid line), and hpulse (blue solid line) as a function of time during a typical pulse condensation operation on LIS with topen=tclose= 60 s. The horizontal dashed lines indicate the arithmetic mean Pv¯ (red dashed line), Upulse¯ (green dashed line), and hpulse¯ (blue dashed line) for the entire operation.

Close modal

The ethanol vapor pressure (Pv) continuously increased throughout the time ethanol vapor was allowed to enter the chamber (topen, Figs. 2 and S6). Once the vapor-inlet valve was closed after time topen and the vacuum-line valve opened, Pv started to decrease, reaching its initial pressure after time topen+tclose. The overall measured condensation heat flux (qpulse), however, did not follow a similar trend [Fig. S7(a)]. At the instant of opening the vapor-inlet valve, qpulse increased rapidly for 10–15 s. Thereafter, even though a constant supply of fresh ethanol vapor entered the chamber for the remaining time topen, qpulse decreased from its peak value. The overall heat transfer coefficient, defined as U¯pulse=qpulse/ΔTLMTD, was calculated from the measured qpulse and calculated log mean vapor-to-liquid temperature difference (Sec. S6, supplementary material). The internal forced convection heat transfer coefficient was estimated using the Petukhov correlation, which is relevant to the coolant flow conditions and has an accuracy of 6%. It is worth noting that the correlation, in general, is applicable for thermally and hydrodynamically fully developed flow. Our experiments are in the hydrodynamically developed—thermally developing regime, leading to overestimation of the convective thermal resistance. For practical purposes, the Petukhov correlation is widely used to estimate the convective heat transfer coefficient and thermal resistance20,21 for both steady and transient condensation, allowing for a fair comparison. By knowing the thermal resistances of internal forced convection and radial conduction through the tube wall, the condensation heat transfer coefficient (hpulse) at the tube outer surface was calculated. Note that both the tube wall and the additional coating thermal resistances are significantly lower than the condensation and internal forced convection thermal resistances (Sec. S6, supplementary material), enabling us to neglect them in our calculation. By neglecting the coating thermal resistance, we overestimate the condensation thermal resistance, thereby underestimating the condensation heat transfer coefficient (hpulse), and providing a conservative estimate of heat transfer performance. As shown in Fig. 2 for dropwise pulse condensation of ethanol on LIS, both U¯pulse and hpulse showed a sudden rise at the instant the vapor inlet valve was opened after time tclose for each cycle, reaching a maximum of hpulse,peak 19 kW/(m2·K) right after the start of the vapor-inlet cycle. After reaching the peak values in the initial few seconds of the vapor-inlet cycle, U¯pulse and hpulse began to decrease gradually. Note that even though Pv rises during the remainder of time of the vapor-inlet cycle (topen), U¯pulse and hpulse continue to decrease from their initial peak values. The initial enhancement occurs due to the large pressure difference at the start of vapor-inlet cycle, resulting in higher vapor velocity and higher supersaturation S. Furthermore, during the start of the vapor-inlet cycle, minimal condensate exists on the tube surface for a small time interval (∼20 s), as discussed later. After time topen, when the vapor-inlet valve is closed and the chamber is connected to the vacuum line, ethanol vapor is rapidly evacuated from the chamber, resulting in a sharp fall of U¯pulse and hpulse. The brief surge of hpulse increases the time-averaged hpulse¯ 8.36 kW/(m2·K) over the entire pulse cycle time (topen+tclose), as indicated by the blue dotted line in Fig. 2.

To further investigate the magnitude of hpulse,peak, we performed condensation experiments for tclose = 60, 120, 180, and 240 s, while keeping topen = 60 s. As expected, the average vapor pressure during the entire pulse cycle (Fig. S6) decreases with increasing tclose due to the longer time periods for ethanol vapor removal for the same vapor supply time interval. More importantly, the chamber vapor pressure at the start of every pulse cycle (after time topen+tclose) decreased with increasing tclose (Pv = 5.6, 4, 3.4, and 3.1 kPa for tclose = 60, 120, 180, and 240 s, respectively) due to the fixed topen. This resulted in a surge in heat transfer at the beginning of the subsequent vapor-inlet cycle, resulting in higher hpulse,peak values (Fig. 3 and Table I). In fact, the heat transfer enhancement during the initial vapor inlet period for tclose= 240 s, hpulse,peak 52 kW/(m2·K), was 8× greater than the corresponding steady state condensation heat transfer coefficient hsteady¯ 6.4 kW/(m2·K) for the same average vapor pressure (Pv¯= 4.74 kPa) during dropwise condensation of ethanol on LIS.

FIG. 3.

Transient condensation heat transfer coefficient, hpulse, as a function of time (t) for topen = 60 s and different tclose during 1 pulse cycle of ethanol condensation on LIS. The longer the tclose, the lower the Pv at the start of the pulse cycle and the higher the hpulse,peak. Dashed lines indicate hpulse¯ for five consecutive pulse cycles.

FIG. 3.

Transient condensation heat transfer coefficient, hpulse, as a function of time (t) for topen = 60 s and different tclose during 1 pulse cycle of ethanol condensation on LIS. The longer the tclose, the lower the Pv at the start of the pulse cycle and the higher the hpulse,peak. Dashed lines indicate hpulse¯ for five consecutive pulse cycles.

Close modal
TABLE I.

Heat transfer performance during pulse condensation. Average chamber pressure (Pv¯) and peak and average heat transfer coefficients (hpulse,peak and hpulse¯) during pulse condensation, along with steady state condensation heat transfer coefficients (hsteady¯). Chamber vapor pressure Pv,steady¯Pv¯ for the steady-state measurements. Each experiment was repeated three times to ensure reproducibility.

LIS (dropwise)Cu (filmwise)
tclose [s]Pv¯ [kPa]hpulse,peak [kW/(m2·K)]hpulse¯ [kW/(m2·K)]hsteady¯ [kW/(m2·K)]Pv¯ [kPa]hpulse,peak [kW/(m2·K)]hpulse¯ [kW/(m2·K)]hsteady¯ [kW/(m2·K)]
60 7.94 ± 0.12 18.98 ± 1.14 8.36 ± 0.61 6.45 ± 0.39 9.13 ± 0.11 6.42 ± 0.46 3.61 ± 0.31 2.94 ± 0.23 
120 6.26 ± 0.11 25.96 ± 1.81 7.53 ± 0.65 6.58 ± 0.41 7.89 ± 0.11 10.69 ± 0.49 3.48 ± 0.36 3.18 ± 0.28 
180 5.26 ± 0.12 37.28 ± 2.02 7.23 ± 0.62 6.63 ± 0.37 6.94 ± 0.12 13.26 ± 0.54 3.43 ± 0.34 3.27 ± 0.26 
240 4.74 ± 0.13 51.62 ± 2.19 6.91 ± 0.58 6.36 ± 0.44 6.51 ± 0.12 18.34 ± 0.43 3.37 ± 0.4 3.33 ± 0.27 
LIS (dropwise)Cu (filmwise)
tclose [s]Pv¯ [kPa]hpulse,peak [kW/(m2·K)]hpulse¯ [kW/(m2·K)]hsteady¯ [kW/(m2·K)]Pv¯ [kPa]hpulse,peak [kW/(m2·K)]hpulse¯ [kW/(m2·K)]hsteady¯ [kW/(m2·K)]
60 7.94 ± 0.12 18.98 ± 1.14 8.36 ± 0.61 6.45 ± 0.39 9.13 ± 0.11 6.42 ± 0.46 3.61 ± 0.31 2.94 ± 0.23 
120 6.26 ± 0.11 25.96 ± 1.81 7.53 ± 0.65 6.58 ± 0.41 7.89 ± 0.11 10.69 ± 0.49 3.48 ± 0.36 3.18 ± 0.28 
180 5.26 ± 0.12 37.28 ± 2.02 7.23 ± 0.62 6.63 ± 0.37 6.94 ± 0.12 13.26 ± 0.54 3.43 ± 0.34 3.27 ± 0.26 
240 4.74 ± 0.13 51.62 ± 2.19 6.91 ± 0.58 6.36 ± 0.44 6.51 ± 0.12 18.34 ± 0.43 3.37 ± 0.4 3.33 ± 0.27 

The enhancement in the heat transfer coefficient results in higher overall heat transfer during transient operation as compared to the steady state. The sudden surge in hpulse,peak is attributed to three factors. At the instant of the opening of the vapor-inlet valve at the start of vapor incoming cycle, a large pressure difference exists between the vapor generator and the condensation chamber. The pressure inside the vapor generator is the highest at the end of time tclose when disconnected from the condensation chamber. The vapor pressure inside the condensation chamber, on the other hand, is the lowest at the end of time tclose. The large pressure difference results in a sudden influx of saturated vapor into the chamber having a significant velocity at the start of the pulse cycle. The forced convection condensation23,24 results in rapid sweeping of existing droplets from the tube surface, thereby creating a large number of fresh nucleation sites. The longer the tclose, the larger the pressure difference, resulting in a larger velocity of incoming vapor and rapid nucleation at the start of the vapor inlet cycle. In addition, at the start of the vapor inlet cycle, the supersaturation S (ratio of the vapor pressure to the saturation pressure corresponding to the surface temperature, S=Pv/Pwall) is the highest. The large supersaturation generates a vapor flux toward the condensing tube surface, further increasing the rate of nucleation and condensation heat transfer during the initial stages of vapor injection. The longer the tclose, the larger the S, resulting in higher heat flux. Finally, the longer the tclose, more the time for droplet evaporation from the condensing surface. During tclose, the condensate droplets on the tube surface have a higher saturation pressure when compared to the evacuated surroundings at Pv. The vapor pressure difference between the saturation pressure at the droplet liquid-vapor interface, corresponding to the saturation pressure at the coolant temperature, and surrounding vapor pressure leads to evaporation of the residual condensate droplets during evacuation. The more the time given for droplet evaporation, the higher the reduction in the time averaged droplet size distribution on the tube surface (videos S1–S4) at the end of time tclose. Furthermore, since the chamber remains below saturation conditions during the vapor-evacuation cycle, minimal heat transfer to the cooling water exists, resulting in a uniform cooling water temperature at the inlet and the outlet at the start of the vapor-inlet cycle (Fig. S5). Indeed, one of the main advantages of transient condensation is the ability to initiate condensation on a subcooled tube having a uniform coolant temperature and a clean surface. The transient nature of the condensation as droplets nucleate and grow inherently lends itself to higher heat transfer performance, analogous to transient conduction between semi-infinite bodies. These benefits of rapid nucleation and vapor condensation are eliminated within 20 s of the start of the vapor-inlet cycle. Thereafter, the vapor generator and the condensation chamber reach a quasi-equilibrium pressure difference, resulting in lower vapor inlet velocity insufficient to sweep away condensate droplets on the surface. Moreover, due to continuous condensation, fewer nucleation sites are available, resulting in decreased U¯pulse and hpulse when compared to the initial peak value.

It is important to note that although our results show that hpulse,peak increases with increasing tclose, hpulse¯ decreased with increasing tclose, since the chamber remains below saturation conditions for longer time periods. Figure 3 shows that for the same total time, shorter evacuation cycles (tclose) lead to a greater frequency in pulses with more peaks of hpulse,peak, resulting in higher hpulse¯ (area under the hpulset curve) as summarized in Table I. For results of the overall heat transfer coefficient and heat flux, refer to Sec. S7 of the supplementary material.

Transient ethanol condensation experiments on smooth hydrophobic Cu tubes showed similar trends to those observed during dropwise condensation on LIS. However, due to the presence of a condensate film instead of discrete droplets [Fig. 1(b)], the heat transfer rates decreased. Due to the lower condensation rates, the average chamber vapor pressure during the entire pulse cycle, Pv¯, was higher for filmwise condensation as compared to dropwise condensation for the same topen and tclose (Fig. S8). Similar to dropwise condensation, a sudden surge in heat transfer existed at the start of the vapor inlet cycle, which subsequently decreased (Fig. S9).

To quantify the heat transfer enhancement during transient pulse condensation, we performed continuous steady-state ethanol condensation on smooth Cu and LIS for 30 min at a fixed saturation pressure Pv,steady¯. Table I summarizes the steady state Pv,steady¯ (≈Pv¯) and corresponding heat transfer coefficient (hsteady¯) for ethanol filmwise and dropwise condensation. For the shortest pulse cycles (topen=tclose= 60s), transient dropwise and filmwise condensation of ethanol showed a 30% and 23% higher hpulse¯, when compared to hsteady¯, respectively. As the length of the pulse cycle extended (i.e., topen= 60 s, tclose= 240 s), the transient to steady enhancement for dropwise and filmwise condensation diminished to 8% and 2%, respectively. The higher hpulse¯ when compared hsteady¯ is due to the optimization between the larger hpulse,peak at the start of the vapor-inlet cycle and the reduced condensation time due to intermittency of closing and opening. Thus, though our results show increasing hpulse¯ with decreasing tclose, we hypothesize that for very short tclose, there would be a reduced sudden influx of vapor at the start of the vapor-inlet cycle due to the lack of a significant pressure difference between the incoming vapor and the chamber and, hence, a reduced hpulse,peak. The gain in time averaged HTC, hpulse¯, would be subsequently lost, indicating an optimum closing condition to attain the highest hpulse¯.

The present study offers insight into heat transfer enhancement obtained from transient condensation, which provides design guidelines for compact condensers and thermal management systems. Transient condensation behavior has analogous benefits for a variety of systems, which operate in a highly transient manner and dissipate high heat loads for short periods of time.25 For instance, high-power-density systems involving dynamically actuated high-heat-flux devices require transient active cooling mechanisms to maintain system temperatures within a specified range.26,27 Laser diode arrays, where a lasing event is implemented as a series of quasi-continuous wave pulses, require uniform temperature to reduce wavelength shift and spectral broadening. The spectral output of such semiconductor lasers can shift with drifting device mean temperature when the average power with a longer timescale response is utilized to deal with this short timescale thermal behavior.25,28 By designing the system for transient behavior and taking advantage of pulse condensation, condenser sizing can be reduced. Current systems are designed to handle the peak load at all times, resulting in over sizing of the thermal management system.29,30 Given that the overall heat flux is a direct function of the condensing area, by designing the system for transient behavior and taking advantage of pulse condensation, condenser sizing can be reduced. A second consideration is the design of the system itself to enable transient condensation. Specifically, the control strategies and accumulators needed to hold vapor generated at the heat source for distribution to a downsized condenser in a transient fashion. Significant work is needed in terms of both system integration strategies and control theory for transient operation.31,32 It is interesting to note that recent theoretical work has indeed shown that transient condensation can be an effective alternative for improving waste heat recovery from power plant flue gases.33,34 Furthermore, recent work on flash boiling cooling mechanisms designed for transient performance has been shown to significantly improve device performance.26,35 A closed system utilizing the developed flash boiling technique will require condensers capable of handling high vapor fluxes in a transient manner. Although studied here for ethanol condensation, future work is needed to characterize transient condensation for a variety of other relevant fluids such as steam and refrigerants. Moreover, even though our results show similar heat transfer performance for LISs infused with different viscosity lubricants (supplementary material, Sec. S2), the lubricant drainage rate may vary. In the future, long term condensation experiments (∼months) are needed to quantify the longevity of the lubricant layer and determine the loss of heat transfer performance. Additionally, although the effect of condensate evaporation in enhancing transient heat transfer performance is evident, the process involves several contributing factors such as working fluid properties, chamber dimensions, pump size, and vacuum pump-chamber connection methodology. More extensive work is needed in the future to quantify the evaporation effects on the heat transfer performance. Furthermore, although developed here for external condensation, further work is needed to characterize internal transient condensation, which represents a large fraction of condenser applications in stationary and mobile applications.

See the supplementary material for video of pulse condensation experiment, additional experimental details, heat transfer data, and error analysis.

The authors thank Dr. Timothy S Fisher of UCLA for fruitful discussions regarding pulse condensation. This work was funded by the Center of Excellence for Integrated Thermal Management of Aerospace Vehicles. N.M. gratefully acknowledges funding support from the National Science Foundation under Award No. 1554249 and the International Institute for Carbon Neutral Energy Research (No. WPI-I2CNER), sponsored by the Japanese Ministry of Education, Culture, Sports, Science and Technology.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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