4th International Conference On Building Energy, Environment

Modeling Particle Deposition on a Plate-Fin Heat Exchanger

Q. Cao 1, Q. Xu

1, C.H. Lin

2, D. Wei

3 and Q. Chen

1, 4*

1School of Environmental Science and Engineering, Tianjin University, Tianjin 300072, China

2The Boeing Company, Seattle, USA

3Boeing Research & Technology-China, Beijing, China

4School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907, USA

SUMMARY The particles deposited on the surfaces of the aircraft environmental control systems (ECS) could affect their thermal performance and lead to component failures. This study aimed to predict the particle deposition on the surfaces of complex ECS components, such as a heat exchanger. Three Reynolds Averaged Navier Stokes (RANS) models with a modified Lagrangian method were used to simulate the deposition rate of particles ranging from 1 to 8 μm in diameter in the plate-fin heat exchanger. The computed results were compared and validated with the experimental data. The results showed that the RSM model with a near-wall correction provided the most accurate prediction of the particle deposition rate in the heat exchanger. The location and number of deposited particles mainly depend on the particle size and flow velocity. This investigation provided guidelines for selecting appropriate procedure for simulating micro-particle deposition in ECS components.

INTRODUCTION Commercial airplanes use environmental control systems (ECS) to provide conditioned outside air into the cabin for maintaining a suitable air pressure and temperature. However, most of the airplanes do not have HEPA filters for filtering outside air because outside air at cruising altitude is very clean (Bull, 2008). Airborne particulate matter from or close to the ground in heavily polluted airports could deposit on the surfaces of the ECS components, such as heat exchangers, condensers, fans, turbochargers and ducts (Cao et al., 2016). Due to heavy traffic in air, the ground operation time for mid-size airplanes could be comparable to that in air. The particles accumulated on the various surfaces of the ECS components can affect their thermal performance and lead to component failures. For example, the accumulated particulate fouling on the heat exchangers may increase air side thermal resistance and pressure drop, which results in a significant deterioration of their long-term heat exchange performance (Pu et al., 2009). The particle mass loading rate on an ECS component is very important for the maintenance of the component. Therefore, to assess the impact of particle accumulation on the ECS components, it is important to know the particle deposition rate.

Although some studies (Zhan et al. 2016, Qureshi and Zubair 2012) investigated particle deposition on air-conditioning systems of buildings, few were conducted on particle deposition rates for ECS components in an airplane. Cao et al. (2016) experimentally investigated the overall particle deposition rate in the ECS of different commercial airplanes and showed that as much as 90% of PM2.5 would deposit on the ECS when the outside air quality on ground was poor. However, there was no detailed information on what size and how many particles deposited on different components of ECS. Heat exchanger is the main part of the air-conditioning

pack in ECS, where the hot bleed air is cooled with the ram air. The compact cross-flow plate-fin heat exchangers are usually used in aircraft due to their high heat exchange efficiency, small size and light weight. Our literature search did not find studies about particle deposition on this type of heat exchanger. However, some studies (Inamdar et al.,2016; Nasr and Balaei, 2015; Siegel and Nazaroff, 2003) have reported particle deposition in air side of fin-and-tube heat exchangers typically used for HVAC systems in buildings. The studies tried to understand fouling on the outside tube surfaces due to particulate deposition from air. However, the geometric structures of the plate-fin heat exchangers used in ECS are different from the fin-and-tube heat exchangers. It is thus essential to investigate particle deposition on the plate-fin heat exchangers.

Although both experimental measurements and numerical simulations can be used to investigate particle deposition, computational fluid dynamics (CFD) simulations can provide detailed and accurate information of airflow, particle deposition and movement on the plate-fin heat exchangers with complex geometries. The key for correctly predicting particle deposition is the accurate simulation of airflow.

Therefore, many studies (Taler and Ocłoń, 2014; Chen et

al., 2013; Ma ET AL., 2012) have used CFD, especially RANS turbulence models, to study the airflow in a heat exchanger. In those studies, the renormalization group (RNG) k-ε model (Yakhot and Orszag, 1986), the shear stresstransport (SST) k-ω model (Menter, 1994), and the Reynoldsstress model (RSM) model (Gibson and Launder, 1978) weremost popular. Nevertheless, there is unclear if thoseturbulence models could be used for studying airflow in aplate-fin heat exchanger.

This paper reports our effort in assessing CFD method with various turbulence models for predicting airflow in a plate-fin heat exchange and in using Lagrangian method for computing particle deposition rate on the heat exchanger.

METHODS Based on previous studies on airflow through a heat exchanger, this study further assessed three commonly used RANS turbulence models: the RNG k-ε model, the SST k-ω model, and the RSM model, to predict airflow in a plate-fin heat exchanger. By using the Lagrangian method with the predicted flow, we can determining the particle deposition rate on the heat exchanger. Then the computed deposition rates were compared with the measured data in order to find a suitable turbulence model.

Brief Description of the Turbulence Models

The three turbulence models are all based Reynolds averaged Navier-Stokes equations. The RNG k-ε model calculates turbulence kinetic energy (k) and its dissipation rate (ε) by two independent transport equations. The model

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4th International Conference On Building Energy, Environment

is isotropic but very stable. The SST k-ω model calculates turbulence kinetic energy (k) and its specific dissipation rate (ω) again by two independent transport equations. The model applies the standard k-ω model in the near-wall region and the transformed k-ε model in the free shear region (Menter, 1994). Abandoning the isotropic eddy-viscosity hypothesis that was used in the RNG k-ε model and the SST k-ω model, the RSM model closes the Reynolds-averagedNavier-Stokes equations by solving six independenttransport equations for the Reynolds stresses and oneadditional transport equation for the dissipation rate ofturbulence kinetic energy. More detailed information of thetransport equations for the three turbulence models can befound in Shi et al. (2016).

Particle Movement Model

This investigation used the Lagrangian method to track the individual particle motion directly based on the airflow distribution calculated from CFD with turbulence model. The turbulent flow field is treated as a continuous phase and simulated in the Eulerian frame. The Lagrangian method determines the particle model based on Newton’s law:

( ) (1)

where the first term and the second term on the right-hand

side represent the drag force and gravity term, respectively,

FB Brownian motion force, FS Saffman’s lift force, µα air

viscosity, dp particle diameter, up particle velocity, ua air

velocity, g gravitational acceleration, ρp particle density, ρa

air density, and Cc the Cunningham correction factor, which

can be expressed as:

(2)

where λ is the mean free path of air molecules.

Particle turbulent dispersion is a main mechanism of particle deposition, which is associated with the instantaneous flow fluctuations. This study used the discrete random walk (DRW) model to calculate the particle turbulent dispersion. In the DRW model, the interaction of a particle with a succession of discrete stylized fluid phase turbulent eddies is simulated. Each eddy is characterized by a Gaussian distributed random velocity fluctuation, ui’, vi’ and wi’. The values of ui’, vi’

and wi’ that prevail during the lifetime of the turbulent eddy

are sampled by assuming that they obey a Gaussian probability distribution.

The RNG k-ε model and the SST k-ω model assume the turbulent fluctuations to be isotropic. Thus, the turbulent fluctuating air velocity can be calculated as:

√ √ (3)

The RSM model calculates separately anisotropy of the stresses so the fluctuation velocity, u’i, can be determined by:

√ (4)

√ (5)

√ (6)

where ζi is a standard normal random number.

With the above equations, one is able to determine particle trajectory in turbulence flow including turbulence dispersion. The proper simulation of the turbulent fluctuating velocity in the near-wall region is crucial to the particle deposition modeling. However, the turbulent fluctuating velocity in the near-wall region simulated by the RANS models is less accurate than the direct numerical simulation (DNS) which is hardly used in practical applications due to the excessive requirement in computing resources (Lin and Ahmadi, 2007). Previous studies (Chen et al., 2016; Gao et al., 2012) adopted curve-fitted DNS values to correct the turbulent fluctuating velocity in the near-wall region. For the two-equation models, RNG k-ε model and SST k-ω model, near-wall corrections were used for the turbulence kinetic energy due to the assumption of isotropic turbulence. Chen et al. (2016) combined the findings in the literatures (Lai and Chen, 2006; Kim et al., 1987) and proposed a method to modify the turbulence kinetic energy in near-wall region:

In the region of y+

≤ 2.5,

( ) (7)

In the region of 2.5 <y+

≤ 80,

(

) (8)

where u* is the friction velocity and y+ the dimensionless wall

distance.

For the RSM model, the correction is only needed for the fluctuating velocity in the direction normal to the wall due to the anisotropic assumption. This study used the correction proposed by Li and Ahmadi (1993a) based on the results from Ounis et al. (1993):

In the region of y+

< 4,

√ (9)

Calculation Method for the Particle Deposition Rate

With the near-wall corrections, the particle deposition can be accurately calculated. In this study, the calculated total particle deposition rates in a plate-fin heat exchanger were validated by the experimental data from our previous investigation (Cao et al. 2017). Figure 3 shows the schematic of the test rig used for measuring the particle deposition on the heat exchanger. The test rig includes a HEPA filter, a particle generator (MAG 3000), a mixing box, two sampling boxes, a centrifugal fan and a plate-fin heat exchanger. The monodisperse particle deposition rates were obtained by measuring the particle concentration at the upstream and downstream of the heat exchanger with the weighing method. The particles tested were of different sizes ranging from 1.0

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to 8.5 μm in diameter. The air velocity through the heat

exchanger was set to be the same as that for the ECS. The experiments and analysis are described in greater details by Cao et al. (2017).

Figure 1. Schematic of the experimental rig

In the experiment, the total particle deposition rate in the heat exchanger was calculated by:

(10)

where Pdeposition is the particle deposition rate in the heat exchanger; Cdownstream the particle concentration downstream of the heat exchanger, g/m

3; Cupstream the particle

concentration upstream of the heat exchanger, g/m3;

Δmdownstream the mass gain of the filter in the downstream sampling box, g; Δmupstream the mass gain of the filter in the upstream sampling box, g; Gdownstream the sampling mass flow rate in the downstream sampling box, m

3/s; Gupstream the

sampling mass flow rate in the upstream sampling box, m3/s;

and t the sampling time, s.

Figure 2 shows the size distribution of particles generated by the particle generator for the monodisperse particles with a diameter of 2.4 μm. The monodisperse diameter was the weighted average of particle size distribution. Note that 11 different particle sizes were used in the experiment and the diameter distributions of the particles for each size look similar to that shown in Figure 2. The relationship between the particle concentration and the aerodynamic diameter was skewed normal distribution. The particles diameter distribution was sufficiently concentrated to be regarded as monodisperse. Therefore, in the CFD modeling, the particle deposition rate in the heat exchanger for each diameter can be calculate as the particle number deposited on the inner surfaces divided by the total particle number released at the inlet.

Figure 2. The size distribution of the particles measured by the aerodynamic particle sizer: the monodisperse diameter was 2.4 μm in CFD modeling

Particle Deposition Velocity Modeling

To better understand where and how many particles deposited on the inner surfaces of the heat exchanger, this investigation modelled the local particle deposition velocity on the surfaces. The local particle deposition velocity on a given computing mesh, i, can be calculated by (Zhang and Chen, 2009):

(11)

where Ai the area of the local computing mesh, Nd,i the number of particles depositing onto this mesh within the time

t, N the average number of particles in the calculated space within t, and V the volume of the inner space in heat exchanger.

CASE SETUP The plate-fin heat exchanger used in the experiment was shown in Fig. 3 (a). Although the plat-fin heat exchanger selected was not exactly the same as those used in aircraft, it had the same working principle as the heat exchangers in the ECS. This kind of heat exchangers was characterized by high heat transfer area per unit volume and high heat transfer coefficients. Fig. 3 (b) shows the schematic of the offset strip fin structure in the plate-fin heat exchanger. The fin had a rectangular cross section and was cut into small strips of length direction. Every alternative strip was offset by about 50% of the fin pitch in the transverse direction. The fin transverse spacing s, fin length l and fin height h of the selected heat exchanger were 4 mm, 5 mm and 6 mm, respectively. This study ignored the thicknesses of fins and walls.

(a) (b) Figure 3. (a) The plate-fin heat exchanger selected for this study (b) schematic of the offset strip fin structure

Due to the symmetric geometry, this study modelled a half of the heat exchanger as shown in Fig. 4. The calculation domain was extended 150 mm (about 3 times of the inlet and outlet diameter) at both side of the inlet and outlet of the heat exchanger to obtain fully developed flow and to avoid the reversed flow. The inlet velocity was uniform and set to 21.95 m/s, which was the same as that in the experiment. A turbulent intensity of 3.9% and a length scale of 58 mm (equal to the diameter of the inlet) were used for the inlet boundary conditions. This study used the tetrahedral grids in the whole computational domain. Three grid resolutions (4.31, 8.05 and 12.28 million) were tested and found that a grid number of 8.05 million provided grid-independent results.

HEPA filter

MAG 3000

Mixing box

APS

Fan

Plate fin heat exchanger

Sample Pumps

Isokinetic nozzles

with sample filters

1.5 m 1.6 m 1.7 m 1.8 m 2 m 2.1 m 2.3 m 2.5 m 2.6 m 2.8 m 3.1 m0

60

120

180

240

Pa

rtic

le n

um

be

r (#

/cm

3)

Particle diameter

s

hl

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4th International Conference On Building Energy, Environment

Figure 4. Computational domain and boundary conditions used in this study

As the particle concentration investigated in this study was low, the effect of particles on the turbulence could be neglected. One-way coupling was used for the interaction between the airflow and particles. The density of the particle was 912 kg/m

3, which was according to that used in the

experiment. After the near-wall turbulence corrections, monodisperse particles were released at the inlet into the heat exchanger. To obtain a statistical particle deposition result, this study calculated 160,572 particle trajectories for each particle size. As the particles usually cannot accumulate enough rebound energy to overcome the adhesion force, this study assumed no particle resuspension in the simulation. The wall boundaries for all the surfaces of the heat exchanger including the fins and guide walls were set to be ―trap‖ as shown in Fig. 4, which means the calculation of particle trajectory was terminated as the particles reached the wall surface. The particles could rebound into the flow when they reached the extended walls because they were set to be ―reflect‖. When the particles passed through the outlet, the calculations of the trajectory were terminated and the particles escaped from the outlet.

This study used a commercial CFD program, ANSYS Fluent 16.0, to calculate the airflow field and particle trajectories. The near-wall turbulence correction and calculation of particle deposition velocity were implemented by the user-defined functions. The governing equations for the airflow were solved by the finite volume method. The SIMPLE algorithm was used for pressure and velocity coupling of the transport equations, and the second-order discretization schemes were used for solving all the independent variables.

RESULTS

Flow Field Simulation in Heat Exchanger

Fig. 5 shows the airflow distribution in a cross section and a longitudinal section of the heat exchanger predicted by the three turbulence models. The airflow results by the RNG k-ε and RSM were similar. The SST k-ω model provided a smaller vortex in the inlet guide part and a little more uniform airflow distribution than the other two models. The flow distribution at the cross section (interface of the guide part and fin channel inlets) was not uniform due to the guide part. For the five fin channels, the inlet velocities were different from each other. In each fin channel, the velocity distribution was not uniform, which means the particle fouling level was different in the five fin channels. The detailed information of particle deposition in the heat exchanger could be obtained by the modeling of particle deposition velocity on each computing meshes on the surfaces by using Eq. (10), which will be described below. Unfortunately, it was hard to obtain the experimental airflow distribution in the heat exchanger, thus this study did not compare the calculated flow with experimental data.

(a) (b) (c) Figure 5. Comparison of the airflow fields in the cross section and longitudinal section of the heat exchanger predicted by (a) the RNG model, (b) the SST model and (c) the RSMmodel.

Particle Simulation Results

This study compared the total particle deposition rate in the heat exchanger predicted by three different turbulence models and validated the simulation results with the measurement data. As shown in Fig. 6, without the near-wall corrections, the particle deposition rates predicted by the three turbulence models were higher than the experimental data, especially for particles with a diameter smaller than 3.8 μm. For particles with a diameter larger than 7.2 μm, all of the three models agree with the measurement results very well, with or without the near-wall correction. After the near-wall corrections, the modelling results of the three turbulence models were obviously improved and the RSM model produced most accurate particle deposition rate in the plate-fin heat exchanger. Even with the near-wall correction, the SST k-ω model over-predicted the particle deposition rate for most sizes, which may be not suitable for modeling the particle deposition on the plate-fin heat exchanger.

Velocity inlet 21.95 m/s

(Particle injection)

Outflow (Escape)Symmetry

Fins (Trap)Outlet guide wall

(Trap) Inlet guide wall

(Trap)

Fin Channels

(Trap)

Inlet

Outlet

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4th International Conference On Building Energy, Environment

Figure 6. Comparison of the total particle deposition rate in the heat exchanger predicted by different turbulence models with the measurement data.

To obtain the detail information of where, how many, and what size of the particles deposited on the surfaces of the plate-fin heat exchanger, this study calculated the deposition velocities for monodisperse particles according to Eq. (11). As the RSM model with a near-wall correction predicted the most accurate total particle deposition rate, this study adopted this model to calculate the local particle deposition velocity on each computational cell of the surfaces. Figs. 7(a) (b) (c) and (d) show the predicted particle deposition velocitydistributions onto the inner surfaces of the heat exchangerfor particles with a diameter of 1.0 μm, 3.2 μm, 6.5 μm and8.1 μm, respectively. It can be seen that the depositionpatterns for particles with different diameters were different.For small particles, the deposition distribution was uniform onthe fins and guide walls as shown in Figs. 7(a) and (b), whichwere predominantly caused by Brownian diffusion. Largeparticles were likely to deposit by impact on the fins and inletguide wall of the heat exchanger. The particles mainlydeposited on the inlet guide wall and near the positionconnecting the fin channels with inlet guide wall. In the finchannels, the deposition distribution was similar to the airflowpattern as shown in Fig. 5. Higher velocities led to moredeposition by impact. Large particles contributed significantlyto the bulk of fouling because of their large size and highdeposition fraction. For the plat-fin heat exchangerinvestigated, the fouling risk was highest near the inlets ofthe fin channels.

(a)

(b)

(c)

(d) Figure 7. The predicted pattern of particle deposition velocity on the inner surfaces of the plate-fin heat exchanger for particles with a diameter of (a) 1.0 μm, (b) 3.2 μm, (c) 6.5 μm, and (d) 8.1 μm

By comparing with the experimental data, the RSM model with a near-wall correction combining with the Lagrangian method is recommended to model the particle deposition in a plate-fin heat exchanger. The average relative error between the simulated and measured deposition rates for the particles at 11 different diameters was about 25%. The simulated results in this study showed that the particle deposition in the plate-fin heat exchanger was serious and the deposition distribution was not uniform especially for large particles. The particles mainly accumulated at the inlet guide part and near the position connecting the fin channels with inlet guide wall. The inlets of the five fin channels may be the positions first to be blocked by the particles.

DISCUSSION This study conducted the particle deposition modeling under isothermal condition with an air temperature of 293 K. However, the heat exchangers in the aircraft ECS may work at a temperature as high as 500 K. Yang et al. (2008) experimentally investigated the effect of temperature on PM2.5 deposition in the rectangular duct. They found that the radial force thermophoresis pushed the particles to the cold wall and enhanced the PM2.5 deposition. The deposition efficiency increases with the increase of the ratio of the air temperature at the inlet of the test section to the cold wall temperature. As the heat exchangers in the aircraft ECS are used to cool the hot bleed air, the actual particle deposition in the heat exchanger during operating in the aircraft may be higher than the predicted results shown in this study, which should be further verified.

CONCLUSIONS This study adopted three commonly used RANS turbulence models with a Lagrangian method to predict particle deposition in a plate-fin heat exchanger. The simulated results were validated by the experimental data obtained previously from our group. The particle deposition velocities and distributions on the inner surfaces were also simulated and analyzed. The study led to the following conclusions:

Among the three RANS models, the RSM model with a near-wall correction provided the most accurate prediction of the total particle deposition rate in the plate-fin heat exchanger.

1.7 2.4 2.8 3.2 3.8 4.4 5.1 6.5 7.2 8.10

20

40

60

80

100

Experimental data

RSM & Eq.(9)

RNG k-& Eq.(7)(8)

SST k-& Eq.(7)(8)

RSM

RNG k-

SST k-To

tal p

art

icle

de

po

sitio

n r

ate

(%

)

Particle diameter (m)

1.0

Particle deposition velocity (m/s)

Inlet

Outlet

Inlet

Outlet

Inlet

Outlet

Inlet

Outlet

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Even with the near-wall correction, the SST k-ω model over-predicted the particle deposition rates.

For small particles, the deposition distribution was uniform on the fins and guide walls, which were predominantly caused by Brownian diffusion. Large particles deposited mainly on the inlet guide wall and near the position connecting the fin channels with inlet guide wall. Higher velocities led to more deposition by impact for large particles. For the plat-fin heat exchanger investigated, the fouling risk was the highest near the inlets of the fin channels.

ACKNOWLEDGEMENT The research presented in this paper was partially supported by the National Key R&D Program from the Ministry of Science and Technology, China, on ―Green Buildings and Building Industrialization‖ through Grant No.

2016YFC0700500.

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