ASEE 2014 Zone I Conference, April 3-5, 2014, University of Bridgeport, Bridgeport, CT, USA.

Analysis of a Counter Flow Parallel-plate Heat Exchanger

Ruoxu Jia, Junling Hu, and Abubaker E.M Elbalsohi, Department of Mechanical Engineering

University of Bridgeport, Bridgeport, CT, USA ruoxujia@gmail.com, jjhu@bridgeport.edu, aelbalos@my.bridgeport.edu

Abstract—Heat exchangers are used widely in many

industries for heat recovery or cooling purposes. This paper developed a numerical model to simulate a counter flow parallel heat exchanger. A representative repeating unit cell of the multi-channeled heat exchanger was taken as the computational domain, which includes a cold channel and a hot channel separated by plates. The model was simulated in COMSOL for an oil to water heat exchanger. Higher temperature oil and relatively lower temperature water entered two separate parallel channels in opposite directions. The detailed distributions of temperature, velocity, and pressure were used to analyze the performance of the heat exchanger. It was found the model can be used to provide guidance for designing an optimal heat exchanger.

Keywords—heat exchanger; cooling system; counter flow , CFD

I. INTRODUCTION Currently, heat exchangers have a wide range of industry

applications. They are widely used in space heating, refrigeration, power plants, petrochemical plants, petroleum refineries and sewage treatment [1]. There are many types of heat exchanger designs for various applications. The major types of heat exchanger include double pipe, shell-tube, plate and shell, plate fin, and phase change heat exchangers. The flow in a heat exchanger can be arranged as parallel flow, counter flow, and cross flow. New heat exchangers have been designed for emerging thermal engineering fields, such as miniaturized heat exchanger for cooling electronics components and systems, miniaturized heterogeneously catalyzed gas-phase reactions, thermoelectric generators, etc. [2-5] New materials, such as polymers, have been explored to develop polymer heat exchangers for better fouling and corrosion resistance [6].

Parallel-plated heat exchangers have been studied analytically and experimentally to provide formulations for heat exchanger design. Vera and Linan [3] analyzed multilayered, counterflow, parallel-plate heat exchangers numerically and theoretically. They developed a two-dimensional model to find analytical expressions and their approximations for the fully developed laminar counter flow in long parallel-plate heat exchangers. Kragh et al. [7] developed a new counter flow heat exchange for ventilation systems in

cold climates. The efficiency of the new heat exchanger was calculated theoretically and measured experimentally.

Zhan et al. [8] used an experimentally validated model to understand the influence of operational and geometric parameters of the cross-flow and counter-flow exchangers on the different metrics of cooling performance. Overall the counter-flow exchanger demonstrated better cooling effectiveness and higher cooling capacity than the cross-flow system. However, the energy efficiency of the counter-flow system is often seen to be lower than that of the more conventional cross-flow dew point system [8]. The shape of the cross section of the heat exchanger also has a significant effect on efficiency. Hasan et al. [9] studied the effect of channel geometry on the performance of a counter-flow MCHE (main cryogenic heat exchanger). The influences of channel shapes such as circular, square, rectangular, isotriangular, and trapezoidal were evaluated by numerical simulations. In their studies, decreasing the volume of each channel or increasing the number of channels increased the heat transfer, but the required pumping power and pressure drop were also increased. The channel with a circular shape resulted in the best overall performance. [10]

Recently, CFD analysis of heat exchanger has been used to help design heat exchangers and to analyze their thermal performance, effectiveness and temperature distributions. This paper simulated the heat transfer and fluid flow in a multilayered counter flow parallel-plated heat exchanger. The temperature distributions and heat transfer rate are analyzed to study the performance of the heat exchanger.

II. MATHEMATICAL MODEL

Fig.1 Schematic of a counter flow heat exchanger

Figure 1 shows a schematic sketch of a multilayered counter flow parallel-plated heat exchanger. Two fluids with different temperatures marked with different colors in Fig. 1 enter numerous channels in separate layers. Each channel is formed by thin folded plates and separation plates between cold and hot fluids. The thickness of the plates is t and the channels have a square shape with a size w and length L. A unit cell consists of a cold channel and a hot channel is taken as the computational domain for CFD analysis, as shown in Fig. 2.

Fig.2 side view the computational domain consisting of one cold and one hot channels

For a laminar flow in the channels, Navier-Stokes equations are solved for the heat transfer and fluid flow in the channels. The mathematical model includes conservations of mass, momentum and energy in the fluid domains and conduction in the solid domain for a steady state laminar flow.

Mass conservation

0=∂

∂+

∂

∂+

∂

∂

zuw

yuv

xuu (1)

Momentum conservation

xp

zu

yu

xu

zuw

yuv

xuu

∂

∂−⎟⎟⎠

⎞⎜⎜⎝

⎛

∂

∂+

∂

∂+

∂

∂=

∂

∂+

∂

∂+

∂

∂

ρρ1µ

2

2

2

2

2

2 (2)

yp

zv

yv

xv

zvw

yvv

xvu

∂

∂−⎟⎟⎠

⎞⎜⎜⎝

⎛

∂

∂+

∂

∂+

∂

∂=

∂

∂+

∂

∂+

∂

∂

ρρ1µ

2

2

2

2

2

2 (3)

g1µ2

2

2

2

2

2

+∂

∂−⎟⎟⎠

⎞⎜⎜⎝

⎛

∂

∂+

∂

∂+

∂

∂=

∂

∂+

∂

∂+

∂

∂

zp

zw

yw

xw

zww

ywv

xwu

ρρ (4)

Energy conservation

⎟⎟⎠

⎞⎜⎜⎝

⎛

∂

∂+

∂

∂+

∂

∂=

∂

∂+

∂

∂+

∂

∂2

2

2

2

2

2

zT

yT

xT

ck

zTw

yTv

xTu

pρ (5)

where u, v, and w are velocity components in x, y, z direction, respectively; ρ is density, µ is dynamic viscosity, p is pressure , T is the temperature , g is gravitational acceleration, k is thermal conductivity, and cp is heat capacity.

Hot fluid and cold fluids enters channels of the opposite side. Velocity inlet boundary conditions are taken at the inlets and pressure outlet boundary are set at the fluid exits. The boundary conditions for walls are set as shown in Fig. 2. Two side walls are insulated due to symmetry. The periodic boundary condition is set for the top and bottom walls.

III. CFD SIMULATION This paper simulated an oil to water heat exchanger. Hot

oil at 330K enters hot channel with an inlet velocity of 0.04 m/s. Cold water at 300K enters cold channel with an inlet velocity of 0.005 m/s. The channels have a dimension of 2 cm × 2 cm × 50 cm. Channel wall thickness is 2 mm. Table I listed the important parameters used in this simulation. The properties of oil and water were set as a function of temperature in the simulation. The properties of water at 25oC and those of oil at 40oC were listed in Table I to calculate Reynolds numbers for each channel. The Reynolds numbers in the channels are found to be 224 and 6.44 for the respective cold and hot channels.

TABLE I. TRANSLATION OF DESIGN REQUIREMENTS

Parameter Symbol Value unit Channel length L 0.2 m Channel width W 0.02 m Channel thickness t 0.002 m Density of water ρw 997 kg/m3 Density of oil ρo 876 kg/m3 Density of steel ρs 7850 kg/m3 Thermal conductivity of water kw 0.607 W/m·K Thermal conductivity of oil ko 0.145 W/m·K Thermal conductivity of steel ks 44.5 W/m·K Heat capacity of water cpw 4180 J/kg·K Heat capacity of oil cpo 1964 J/kg·K Heat capacity of steel cps 475 J/kg·K Dynamics viscosity of water µ 0.891×10-3 Kg/m·s Dynamics viscosity of oil µ 0.2177 Kg/m·s Prandtl number of water Prw 6.14 Prandtl number of oil Pro 2963 Inlet velocity of water Vinw 0.005 m/s Inlet velocity of oil Vino 0.04 m/s Reynolds number of water Rew 224 Reynolds number of oil Reo 6.44 Inlet temperature of water Tinw 300 K Inlet temperature of oil TinO 330 K

Fig.3 Computational mesh

The problem was numerically solved by using the software COMSOL 4.3. An unstructured mesh of 563707 tetrahedral elements is shown in Fig. 3. The simulations were carried out in a laptop with Intel core i7 processors and 8 GB RAM. Each simulation took 20 minutes to converge with a mesh shown in

Figure 3. Finer meshes near the wall boundaries are generated to resolve the high velocity and temperature gradients at the near wall boundaries. A structured mesh stretched in fluid direction could be used to significantly reduce the number of mesh and thus solution time, however, the general projection function in COMSOL does not work with the structured mesh.

IV. RESULTS AND DISCUSSIONS Figures 4 and 5 report the temperature distribution in the

surface of the 3D computational domain and in the x-z planes along channel length directions. It can be clearly seen tht hot oil enters the top channel with an uniform temperature of 330K and is cooled along the channel length and cold water enters the top channel with a temperture of 300K is heated along the channel length. Heat transfer between the two channels are through the channel walls. As shown in Fig. 6, heat spreads over the walls and walls serve as a media to exchange heat with fluids.

Fig. 4 Surface temperature of the channels and walls

Fig.5 Temperature fields in the x-z cut-planes along channel length.

Fig.6 Temperature fields in the solid walls in the x-z cut-planes along channel length

The average fluids temperatures and the centerline temperature cahnges in the channels along channel length direction are shown in Figs. 7 and 8. Hot oil enters the hot channel with an averaged temperature of 330K and exits the channel with an average temperature of 323.7K. Cold water enters the cold channel with an average temperature of 300K and exits with an average temperature of 310.5K. However, the temperatures at the channel centers only slightly changed along the centerline. Oil temperture at the channel center only decreased 0.3K and centerline water temperature increased 1.5K.

Fig.7 Average fluid temperatures along the channel length

Fig.8 Fluid temperature changes along channel centerlines

Fig.9 Prandtl number of fluids

The Prandtl number of the two working fluids are greater 1, especially of oil. Prandtl numbers of the two fluids calculated with their real properties are shown in Fig. 9. The Prandtl number of water varies in a range of 3.33-5.90 and that of oil varies in a range of 1235-5020 in the respective cold and hot channels. Prandtl number is defined as the ratio of momentum diffusivity to thermal diffusivity of fluid. Heat diffuses very slowly compared to momentum diffusion in high Prandtl number fluids, which result in a thinner thermal boundary relative to the velocity boundary and a longer thermal entrance length compared to the hydrodynamic length.

The normalized centerline velocities in two channels are shown in Fig. 10. Centerline velocities increase rapidly in the underdeveloped flow region near the flow entrances and the changes slow as it approaches to the fully developed region.

The flattened centerline velocities indicate hydrodynamically fully developed boundary layers have been established. The centerline velocity still changes remarkably even in the fully developed region in the oil channel because the thermal fluid

properties of oil vary significantly with temperature. The temperature field, streamwise velocity field and pressure field

in the channel x-y center planes are shown in Fig. 11. It can be seen that the thermal boundary layer of each fluid is much

thinner the fluid’s velocity boundary layer, especially for oil.

Fig. 10 Centerline velocities in two channels normalized by the inlet velocities

(a) (b)

Fig.11 Contour fields of temperature, streamwise velocity, and pressure along x-y plane: (a) cold channel and (b) hot channel

T v p T v p

The calculated pressure drop in the cold and hot channels is 0.0763 Pa and 68.0 Pa, respectively and corresponding average temperature drops in the cold and hot channels are 10.5K and 6.3K. Further, the center temperature of oil only changed 0.3K and the center temperature of water increased 1.5K. Therefore, the inlet velocity of oil is decreased to 0.02 m/s and the water inlet velocity is increased to 0.05 m/s in order to increase temperature drop and decrease pressure drop in the hot channel without significantly increase pressure drop in the cold channel.

Figures 12 and 13 show the average temperature along the channels and the temperature changes in the centerlines of the channels for the case with the increased inlet water velocity and decreased oil velocity. The average temperature and centerline temperature drop are 2K and 0.05K for the cold channel and 10K and 0.9K for the hot channel. The pressure drops are 2.5 Pa and 42.7 Pa for the corresponding cold and hot channels. The working fluid inlet velocities, channel sizes and other heat exchanger design and working conditions can be further optimized to achieve the best energy efficiency and operating requirements.

Fig.12 Average fluid temperatures along the channel length for the case with

modified inlet velocities

V CONCLUSION In this study, a 3D model of a multilayered counterflow

parallel heat exchanged was developed to simulate the heat transfer and fluid flow pattern in a unit cell of one cold channel and one hot channel. The model was simulated in COMSOL with oil and water as two working fluids. The detailed temperature, velocities, and pressure distributions in the channels can be used as guidance for an optimal heat exchanger design.

Fig.13 Fluid temperature changes along channel centerlines for the case with

modified inlet velocities

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