Numerical Simulation of Frosting on Fin-and-Tube Heat Exchanger Surfaces

Probably not a substantial claim: may not pass S3 (load-bearing).

Lee and Ro [10] modeled the air gaps in the frost as cylindrical capillary tubes to model water vapor diffusion in the frost layer.

“Lee and Ro [10] modeled the air gaps in the frost as cylindrical capillary tubes to model the water vapor diffusion in the frost layer.”

• cites [10] 2005, Analysis of the Frost Growth on a Flat Plate by Simple Models of Saturation and Supersaturation, Exp. Therm. Fluid Sci. sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing).

The calculation method proposed by O'Neal and Tree [6] was improved by Webb and coworker [7], Lee et al. [8], and Yao et al. [9].

“The calculation method proposed by O'Neal and Tree [6] was improved by Webb and coworker [7], Lee et al. [8], and Yao et al. [9].”

• cites [6] 1984, Measurement of Frost Growth and Density in a Parallel Plate Geometry, ASHRAE Trans.Not checked yet

  Not checked in the free run.

• cites [7] 2004, New Model for Frost Growth Rate, Int. J. Heat Mass Transfer sourcePartly supported

  The Abstract (p. 1) and Conclusions (p. 11) describe Na and Webb’s new frost-growth model and its improved thermal-conductivity correlation. But the discussion on p. 2 identifies O’Neal and Tree as authors of a review of thermal-conductivity correlations, not as proposers of the calculation method that Na and Webb improved. The cited paper therefore supports the improvement, but not the claimed lineage from O’Neal and Tree. (LLM, conf=0.84)

  Experimental — accuracy not yet measured
• cites [8] 2003, Prediction of the Frost Formation on a Cold Flat Surface, Int. J. Heat Mass Transfer sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

Kandula [13] incorporated empirical correlations for frost density and effective thermal conductivity applicable for a wide range of frost circumstances.

“Kandula [13] incorporated empirical correlations for the frost density and the effective thermal conductivity, which were applicable for a wide range of frost circumstances.”

• cites [13] 2011, Frost Growth and Densification in Laminar Flow Over Flat Surfaces, Int. J. Heat Mass Transfer sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The model of Lee et al. [11] assumed that the humid air was saturated at the frost surface, while Webb and coworker [7,12] assumed that the humid air was supersaturated at the frost surface.

“The model assumed that the humid air was saturated at the frost surface, while Webb and coworker [7,12] assumed that the humid air was supersaturated at the frost surface.”

• cites [11] 1997, A One-Dimensional Model for Frost Formation on a Cold Flat Surface, Int. J. Heat Mass Transfer sourceNot checked — no full text of the source
• cites [7] 2004, New Model for Frost Growth Rate, Int. J. Heat Mass Transfer sourceSupported
• cites [12] 2004, Mass Transfer On and Within a Frost Layer, Int. J. Heat Mass Transfer sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

Wu et al. [5] assumed that the driving force for water vapor condensation into ice was the difference between water vapor partial pressure in the humid air and water vapor saturation pressure corresponding to the frost surface temperature, related to vapor concentration difference [3,5,7].

“They assumed that the driving force for the water vapor condensation into ice was the difference between the water vapor partial pressure in the humid air and the water vapor saturation pressure corresponding to the frost surface temperature, which was related to the vapor concentration difference [3,5,7].”

• cites [3] 2007, Visual and Theoretical Analyses of the Early Stage of Frost Formation on Cold Surfaces, J. Enhanced Heat Transfer sourceNot checked — no full text of the source
• cites [5] 2016, Phase Change Mass Transfer Model for Frost Growth and Densification, Int. J. Heat Mass Transfer sourceNot checked — no full text of the source
• cites [7] 2004, New Model for Frost Growth Rate, Int. J. Heat Mass Transfer sourceSupported

May combine two claims.

The model predicts frost distributions on heat exchanger surfaces, temperature distributions, and air flow pressure drop.

“The model predicts the frost distributions on the heat exchanger surfaces, the temperature distributions, and the air flow pressure drop.”

May combine two claims.

Frost is thicker and frost density is higher on fin surfaces on the windward side near the tubes, while frost is thinner and density is lower near the inlet.

“The results show that the frost is thicker and the frost density is higher on the fin surfaces on the windward side near the tubes, while the frost is thinner and the density is lower near the inlet.”

• Also stated in: § 4 Results and Discussion · p. 5 · plain

  “Figure 8 shows that the frost density is higher near the tubes on the windward side and lower near the inlet.”

• Also stated in: § 5 Conclusions · p. 6 · plain

  “The frost is thicker and the frost density is higher on the fin surface on the windward side near the tubes, while the frost is thinner and the density is lower near the inlet.”

May combine two claims.

Frost on fin-and-tube heat exchanger surfaces restricts airflow and about doubles the pressure drop after frosting for 50 min.

“Frost on the fin-and-tube heat exchanger surfaces restricts the airflow and about doubles the pressure drop after frosting for 50 min.”

• Also stated in: § 5 Conclusions · p. 6 · plain

  “The frost on the fin-and-tube heat exchanger surfaces restricts the airflow and the pressure drop is about doubled for a frosting time of 50 min.”

May combine two claims.

The frost layer growth process is affected by the flow field of the humid air, and the humid air flow field changes due to frost on the tubes.

“The frost layer growth process is affected by the flow field of the humid air. On the other hand, the humid air flow field changes due to the frost on the tubes as shown in Fig. 5.”

May combine two claims.

The air temperature decreases along the flow direction because of the cold tubes and fin, and is lowest downwind of the tubes.

“The air temperature decreases along the flow direction because of the cold tubes and fin. The air temperature is then lowest downwind of the tubes.”

May combine two claims.

There is very little humid air flow just downwind of the tubes and the low velocity area expands after frost appears on the tubes.

“The streamlines show that there is very little humid air flow just downwind of the tubes and that the low velocity area expands after the frost appears on the tubes.”

May combine two claims.

The velocities in the core are higher after frosting as the flow region becomes smaller due to frost growth on the fins, which creates a larger wake region.

“The velocities in the core are higher after frosting as the flow region becomes smaller due to the frost growth on the fins, which creates a larger wake region.”

• Also stated in: § 5 Conclusions · p. 6 · plain

  “The velocities increase as the frost layer grows and the wake expands.”

May combine two claims.

There is very little humid air flow in the wake behind the tubes and water vapor motion there mostly depends on diffusion, so water vapor concentration is relatively low.

“As shown in Fig. 5, there is very little humid air flow in the wake behind the tubes and the water vapor motion there mostly depends on diffusion so the water vapor concentration is relatively low.”

May combine two claims.

The maximum velocity in the flow passage is 4.3 m/s after frosting for 50 min, but just 2.8 m/s before frosting.

“The maximum velocity in the flow passage is 4.3 m/s after frosting for 50 min, but just 2.8 m/s before frosting.”

May combine two claims.

The measured pressure drop before frosting was 10.8 Pa and after frosting was 20.0 Pa.

“The measured pressure drop before frosting was 10.8 Pa and after frosting was 20.0 Pa.”

May combine two claims.

The overall pressure drop before frosting is 8.8 Pa and after frosting is 18.7 Pa in the simulations.

“The simulations show that the overall pressure drop before frosting is 8.8 Pa and after frosting is 18.7 Pa.”

May combine two claims.

The frost thickness on the tube wall and on the fin surface increases with time.

“The frost thickness on the tube wall and on the fin surface increases with time.”

May combine two claims.

The water vapor motion on the downwind side is mostly by diffusion, so water vapor concentration there is relatively low.

“The water vapor motion on the downwind side is mostly by diffusion; so, the water vapor concentration there is relatively low as shown in Fig. 7.”

May combine two claims.

Both fin temperature and humid air temperature are lower near the tubes, with the highest air temperature far from the tubes and the fin at the flow passage inlet.

“Both the fin temperature and the humid air temperature are lower near the tubes with the highest air temperature far from the tubes and the fin at the flow passage inlet.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Multifluid models in CFD have been used to solve mass, momentum, energy, and species conservation equations in multiphase flow [19-21].

“With the development of the computational fluid dynamics (CFD) capabilities, the multifluid models in CFD have been used to solve mass, momentum, energy, and species conservation equations in multiphase flow [19-21].”

• cites [19] 2013, Development of a Generalized Numerical Framework for Simulating Biomass Fast Pyrolysis in Fluidized-Bed Reactors, Chem. Eng. Sci. sourceNot checked — no full text of the source
• cites [20] 2015, Characterizing Effects of the Shape of Screw Conveyors in Gas–Solid Fluidized Beds Using Advanced Numerical Models, ASME J. Heat Transfer sourceNot checked — no full text of the source
• cites [21] 2014, Modeling Effects of Interphase Transport Coefficients on Biomass Pyrolysis in Fluidized Beds, Powder Technol. sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

O'Neal and Tree [6] modeled frost as a porous media consisting of ice crystals and air gaps.

“O'Neal and Tree [6] modeled frost as a porous media consisting of ice crystals and air gaps.”

• cites [6] 1984, Measurement of Frost Growth and Density in a Parallel Plate Geometry, ASHRAE Trans.Not checked yet

  Not checked in the free run.

Classified as probably not a substantial claim.

Accurate predictions of the mass transfer rate from water vapor in the air to ice are important in frosting simulation.

“Accurate predictions of the mass transfer rate from the water vapor in the air to the ice are important in frosting simulation.”

May combine two claims.

Previous frosting models did not take the interaction between the humid air flow field change and the frost layer growth into consideration, so they may not be used to simulate frost layer growth on complicated structure surfaces.

“However, these models did not take the interaction between the humid air flow field change and the frost layer growth into consideration. Thus, these models may not be used to simulate the frost layer growth on complicated structure surfaces.”

May combine two claims.

The mass transfer model proposed by Wu et al. [5] is more reasonable and can better reflect the frosting mechanism, making it suitable for simulating frost formation on complicated structure surfaces such as heat exchanger surfaces.

“Since the mass transfer model proposed by Wu et al. [5] is more reasonable and can better reflect the frosting mechanism, it is suitable for simulating frost formation on complicated structure surfaces, such as heat exchanger surfaces.”

• cites [5] 2016, Phase Change Mass Transfer Model for Frost Growth and Densification, Int. J. Heat Mass Transfer sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

Lee et al. [11] presented a model that only considered the frost layer when calculating frost formation on a cold flat surface.

“Lee et al. [11] presented a model that only considered the frost layer when calculating the frost formation on a cold flat surface.”

• cites [11] 1997, A One-Dimensional Model for Frost Formation on a Cold Flat Surface, Int. J. Heat Mass Transfer sourceNot checked — no full text of the source

May combine two claims.

The air flow passage was gradually blocked with increasing frost layer thickness, which increased air velocity and reduced boundary layer thickness; therefore, the air velocity gradient in the boundary layer increased and the frost layer thickness growth rate slowed.

“In addition, the air flow passage was gradually blocked with the increasing frost layer thickness, which increased the air velocity and reduced the boundary layer thickness. Therefore, the air velocity gradient in the boundary layer increased and the frost layer thickness growth rate slowed.”

Probably not a substantial claim: may not pass S3 (load-bearing).

These coupled models considered both the frost layer region and the humid air region without interface conditions with the same governing equations for both regions.

“These models considered both the frost layer region and the humid air region without interface conditions with the same governing equations for both regions.”

Classified as probably not a substantial claim. May combine two claims.

After grid independence tests, the cell size in the humid air domain was chosen as D x = 0.05 mm, D y = 0.05 mm, and D z = 0.05 mm near the tubes and D x = 0.3-0.5 mm, D y = 0.3-0.5 mm, and D z = 0.05 mm for the rest of the domain.

“After grid independence tests, the cell size in the humid air domain was chosen as D x ¼ 0.05 mm, D y ¼ 0.05 mm, and D z ¼ 0.05 mm near the tubes and D x ¼ 0.3-0.5 mm, D y ¼ 0.3-0.5 mm, and D z ¼ 0.05 mm for the rest of the domain.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Wu et al. [5] proposed a phase change mass transfer model for frost layer growth and densification.

“Wu et al. [5] proposed a phase change mass transfer model for frost layer growth and densification.”

• cites [5] 2016, Phase Change Mass Transfer Model for Frost Growth and Densification, Int. J. Heat Mass Transfer sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Kim et al. [23] assumed that mass transfer at the frost surface occurs due to the water vapor concentration gradient and used the mass transfer rate per unit volume as a volumetric source or sink term to describe mass transfer.

“Kim et al. [23] assumed that the mass transfer at the frost surface occurs due to the water vapor concentration gradient and used the mass transfer rate per unit volume as a volumetric source or sink term to describe the mass transfer.”

• cites [23] 2015, Frosting Model for Predicting Macroscopic and Local Frost Behaviors on a Cold Plate, Int. J. Heat Mass Transfer sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

Cui et al. [22,24] proposed a frost mass transfer model based on nucleation theory to model the frosting process on flat plates and fin-and-tube heat exchangers.

“Cui et al. [22,24] proposed a frost mass transfer model based on nucleation theory to model the frosting process on flat plates and fin-and-tube heat exchangers.”

• cites [22] 2011, A New Time- and Space-Dependent Model for Predicting Frost Formation, Appl. Therm. Eng. sourceNot checked — no full text of the source
• cites [24] 2011, A New Model for Predicting Performance of Fin-and-Tube Heat Exchanger Under Frost Condition, Int. J. Heat Fluid Flow sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

Kim et al.'s [23] simulations calculated the frost layer density and thickness separately starting from an initial frost layer.

“Their simulations calculated the frost layer density and thickness separately starting from an initial frost layer.”

• cites [23] 2015, Frosting Model for Predicting Macroscopic and Local Frost Behaviors on a Cold Plate, Int. J. Heat Mass Transfer sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S4 (based).

Frost will grow on fin-and-tube heat exchanger surfaces when fin and tube surface temperatures are below zero and below the dew point of the air.

“Frost will grow on the fin-and-tube heat exchanger surfaces when the fin and tube surface temperatures are below zero and below the dew point of the air.”

May combine two claims.

In the humid air flow region, the air velocity was relatively large, so Y_v - Y_vs <= B u_a was satisfied and no frost appeared because the mass transfer rate was zero.

“The air velocity was relatively large in the humid air flow region. Thus, the relation Y v Y vs B u a was satisfied and no frost appeared because the mass transfer rate was zero.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Some frosting models have been coupled with multiphase flow models in CFD simulations [5,22,23].

“Some frosting models have been coupled with multiphase flow models in CFD simulations [5,22,23].”

• cites [5] 2016, Phase Change Mass Transfer Model for Frost Growth and Densification, Int. J. Heat Mass Transfer sourceNot checked — no full text of the source
• cites [22] 2011, A New Time- and Space-Dependent Model for Predicting Frost Formation, Appl. Therm. Eng. sourceNot checked — no full text of the source
• cites [23] 2015, Frosting Model for Predicting Macroscopic and Local Frost Behaviors on a Cold Plate, Int. J. Heat Mass Transfer sourceNot checked — no full text of the source

May combine two claims.

The frost density is generally higher with lower humid air temperature and higher water vapor concentration.

“The frost density is generally higher with lower humid air temperature and higher water vapor concentration.”

May combine two claims.

Lower temperatures on the windward area near the tubes lead to larger phase change driving forces and water vapor quickly condenses to ice, resulting in faster frost growth and densification.

“Thus, lower temperatures on the windward area near the tubes lead to larger phase change driving forces and the water vapor quickly condenses to ice resulting in faster frost growth and densification.”

May combine two claims.

The pressure drop increases because the frost layer occupies part of the flow passage, increasing velocities, and because ice crystals on the frost layer surface create a rougher surface.

“The pressure drop increases not only because the frost layer occupies part of the flow passage which increases the velocities but also because the ice crystals on the frost layer surface create a rougher surface.”

May combine two claims.

The phase change driving force is very low on the downwind side and the water vapor mass transfer rate is too small to form much frost.

“Thus, the phase change driving force is very low on the downwind side and the water vapor mass transfer rate is too small to form much frost.”