Heat Transfer Modelling of Plate Heat Exchanger in Solar Heating System

Plate heat exchanger can obtain higher thermal performance because of its advantages in high heat transfer coefficient, small scale, and can realize pure counter current flow. It has been widely applied in HVAC industry. In this paper, the numerical research of plate heat exchanger in solar heating system has been proposed. Aimed at the type of herringbone corrugated plate which has better thermal performance and been widely used, the three dimensional model is established by Gambit software. Using FLUENT software for numerical calculation, by studying the effect of corrugated inclination angle, corrugated depth, corrugated spacing and inlet velocity of heat exchanger on internal temperature, pressure, velocity distributions of domains, the relationship between the above parameters and the Nusselt Number and the pressure drop was obtained by simulation data. Heat transfer coefficient and pressure drop correlations used to measure the overall performance of the heat exchanger. The result shows that the optimal structure parameters is corrugated angle 60 ̊, corrugated depth 4 mm and corrugated spacing 16 mm.


Introduction
The availability of resources and energy is a serious problem of the whole world.
Because of the environment, resources and energy crisis in recent years, the requirement of saving energy and reducing consumption is increasingly high, and using efficient heat exchange equipment to reduce the energy consumption has become the focus of modern industry attention and study.Compared with the traditional shell and tube heat exchanger, the development of plate heat ex- Plate heat exchanger is a kind of efficient and compact heat exchange equipment and its application involves almost all industrial fields.In recent years, brazing type plate heat exchanger has been known by people widely by its superiority of good compactness, light weight, good heat transfer performance and low initial cost.Therefore, it is very necessary to find an effective and feasible method for the study of flow and heat transfer between heat exchanger plates.It is generally recognized that herringbone corrugated plate have higher heat transfer efficiency, big resistance and bearing capacity, because the complex change in plate flow channel section is easy to induce turbulence and the fluid flow consumes more energy in this kind of variable flow [4] [5] [6] [7].
Each plate shall be four angle hole, there are two angle hole provide flow channel on the each side of the plate.When assembling plate, angle hole is arranged into bypass duct of two fluids in proper order.In a group of channel, fluid flow between the two plate after entering angle hole and outflow from the other hole.Each kind of fluid has a single port because of sheet gasket alternant of angle hole.The most common material of plate heat exchanger is stainless steel and titanium, sometimes using nickel alloy steel [8] [9] [10].
How to use the remaining energy reasonably and improve energy utilization has become a research direction for experts and scholars from all over the world.Authors of [11] studied evaporating heat transfer characteristics and pressure drop of R-404a in brazing type plate heat exchanger and using geometry on the Nusselt Number and friction factor for correction.In the paper [12], the difference of pressure drop from the port to the channel process of steam in plate heat exchanger has been studied.In the paper [13], simulations of stirred yoghurt processing in a plate heat exchanger were performed using computational fluid dynamics (CFD) calculations and the results compared with experimental data.After analysis of the velocity field and fanning friction factors, relations are proposed for the present heat exchanger between fanning factors and Reynolds Number and between mean shear rate and mean velocity of yoghurt.The paper [14] explored the potential of using a general purpose CFD code to compute the characteristics of the flow field, and of the heat transfer augmentation in conduits with corrugated walls, encountered in PHE.
The code is validated by comparing the numerical results with experimental data on pressure drop and overall temperature differences.It is shown that the CFD code is an effective and reliable tool for studying the effect of various geometrical configurations on the optimum design of a PHE.The aim of paper [15]

Numerical Method
In the process of numerical simulation, we must first establish the mathematical model which reflects the nature of the problem, that is, reflect the differential equation and the definite condition between the various problems, and then find the high efficiency and high precision calculation method.
Combined with the characteristics of flow and heat transfer in the actual plate heat exchanger, the mathematical model based on the numerical simulation is mainly used as follows: 1) The working medium is incompressible Newtonian fluid; 2) Gravity and floating capacity due to density differences are ignored; 3) Due to the lower flow velocity of the fluid in the heat exchanger, ignore the thermal effect of the viscous dissipation when the fluid flows; 4) Assuming that the fluid inlet speed is known, the outlet pressure is constant.
The inlet pressure and outlet speed are free boundary conditions.
The control equations for the fluid motion and heat transfer in the calculation region are as follows: Conti Nuity equation: Mass conservation equation: where u, v, w is the component of flow velocity.The momentum conservation equation in the i-direction Cartesian coordinate system: where ρ is the fluid density, p is the pressure, v is the kinematic viscosity, and Ui is the velocity component in the i direction.
Energy conservation equation: where a is the thermal diffusion coefficient.
There are two main categories of turbulence models: Reynolds stress model and vortex model.In the vortex model, the Reynolds stress term is not directly processed, but the turbulence viscosity is introduced, and then the turbulence

Meshing and Boundary Conditions
The object of this study is EATB55 brazing plate heat exchanger, the size of which is 539 mm long, width of which is 123 mm, and the plate thickness of which is 2.34 mm.The model created using gambit is shown in Figure 1.As the corrugated structure of the plate heat exchanger is complex, and the arrangement of which is dense, the unstructured tetrahedral mesh is adopted to divide the grid, and the grid size should be 1 mm, which is appropriate, and the total Number of grids is about 800,000, making the computer memory reasonable.
In order to explore the main factors that affect the performance of the plate heat exchanger, the corrugated angel, the corrugated depth and the corrugated spacing are defined as shown in Figure 2. The corrugated angle is 30˚ to 70˚, the   ripple depth is 3 mm to 6 mm, and the ripple pitch is 10 mm to 20 mm.
The geometrical parameters of the plate for the stimulation of the single corrugated plate and the selection of the velocity of the plate are shown in Table 1.
Boundary condition setting: 1) Fluid inlet adopts speed inlet boundary conditions: Assuming inlet speed is 0.6 m/s and inlet temperature is set to 300 K; 2) The outlet of the fluid adopts pressure outlet boundary conditions, set the outlet pressure as 101,325 Pa; 3) The upper and lower wall is set to constant wall, temperature 340 K; 4) The remaining walls are non-slip adiabatic walls, and the fluid medium is water.

Numerical Results
The pressure distribution at different angle, when the spacing λ = 16 mm, depth h = 4 mm, v = 0.6 m/s is shown in Figure 3.
The temperature distribution at different angles is shown in Figure 4.
The velocity distribution at different angles is shown in Figure 5.
The local vector velocity at different angles is shown in Figure 6.
The corrugated angle is smaller, the local vector velocity around the corner is higher, the pressure is higher, the temperature is higher as well, the highest temperature appears at the corner.When β = 30˚ the details of local vector velocity is shown in Figure 7(a) and the temperature distribution is shown in Fig-    The temperature distribution at different spacing is shown in Figure 9.The velocity distribution at different spacing is shown in Figure 10.
The local vector velocity at different spacing is shown in Figure 11.
The temperature distribution at different depths is shown in Figure 13.
The velocity distribution at different depths is shown in Figure 14.
The local vector velocity at different depths is shown in Figure 15.
When angle β = 60˚, spacing λ = 16 mm, h = 4 mm, the pressure distribution at different inlet velocity is shown in Figure 16.
The temperature distribution at different inlet velocity is shown in Figure 17.
The velocity distribution at different inlet velocity is shown in Figure 18.

Parametric Analysis
The overall performance of the heat exchanger is determined by the heat transfer performance and hydraulic characteristics.Where Nu can be used to measure the heat transfer performance, ΔP can be used to measure the hydraulic characteristics.In this paper, the relationship between the heat transfer coefficient and the pressure drop is used to measure the overall performance of the heat exchanger, said η: Change the corrugation angle, the relationship of β with ΔP, Nu, the average heat transfer coefficient and η is shown as follow Figure 20.
With the increase of β, the flow of fluid is smoother at each inflection point between the plates, resulting in the decrease of heat transfer performance.Nu and average heat transfer coefficient decrease with the same trend, and the decrease is more obvious at 60˚.The resistance through the plate is reduced, which causes the reduction of pressure drop, and it declines rapidly when the temperature is 60˚.When the inclination is less than 60˚, the cross section of the heat exchanger is crossed, and then the transition is a meandering flow, and the flow velocity decreases at the inflection point.The overall performance of the heat exchanger is increased first and then decreased, and the maximum value of which appears at 60˚.Change the corrugation spacing, the relationship of λ with ΔP, Nu, the average heat transfer coefficient and η is shown in Figure 21.
With the increase of λ, the Number of corrugations decreases, the contact of Change corrugation depth, the relationship of h with ΔP, Nu Number, average heat transfer coefficient and η is as follows Figure 22.
With the increase of h, the distance and time of the fluid flow between the plates increases, resulting in an increase in heat transfer performance.The Nu Number and the average heat transfer coefficient increase first and then decrease at the same trend, and reach the maximum value at 4 mm, while the fluid need more flow resistance to flow through the plate, there is a larger increase when in the 5 mm, and then it becomes stable.The velocity field of different h is similar, and the flow dead zone is reduced.The overall performance of the heat exchanger first increases and then becomes stable, the maximum value of which appears at 4 mm Department.
Change the velocity of the fluid, the relationship of v with ΔP, Nu Number, average heat transfer coefficient and η is as follows Figure 23.Open Journal of Fluid Dynamics

Conclusion
In this paper, CFD method is used to predict the performance of plate heat exchanger in solar heating system.The influence of structural parameters like ripple inclination, ripple depth, ripple spacing and fluid velocity on the temperature field, pressure field and velocity field of the heat exchanger were studied by using FLUENT6.3software, further analyzing its influence on the heat transfer and resistance of the chevron plate heat exchanger.The results show that the heat transfer effect at the contact point of corrugated plate heat exchanger is the best, the turbulence is the highest, the heat transfer is strengthened, but the pressure loss after passing the contact point of the fluid reaches the maximum, which leads to the increase of the pressure drop.With the increase of corrugation angle, there are two different flow patterns appear between the plates, and the overall performance first increases and then decreases, and it is optimal at 60˚.With the increase of ripple spacing, the heat transfer coefficient
stress is expressed as a function of the turbulence viscosity, which reduces the difficulty of solving.The vortex model includes zero-equation model, one-equation model, and two-equation model.The standard k-ε model is a typical two-equation model, which is formed by introducing the turbulence dissipation rate ε on the basis of the k-equation, which is the most widely used turbulence model.In this paper, the RNG model in the k-ε turbulence model is used as the renormalization group model, can deal better with high strain rate and the flow with larger flow line bending degree, due to correct the turbulence viscosity, take into account the rotational flow in the average flow, add an item to ε, reflect the mainstream time-dependent change rate E ij .Because the RNG model is only for the turbulence with full development, so wall function method is adopted for low Reynolds Number movement near the wall, the dense and a large Number of grid layout on the wall saves memory and time, which is widely used in engineering turbulence calculation.

Figure 2 .
Figure 2. The performance of the PHE.

Figure 3 .
Figure 3. Pressure distribution at different angle.

Figure 4 .
Figure 4. Temperature distribution at different angles.

Figure 6 .
Figure 6.The local vector velocity at different angles.

Figure 7 .
Figure 7.The details of local vector velocity and temperature distribution when β = 30°: (a) Local vector velocity; (b) Temperature distribution.

Figure 8 .
Figure 8. Pressure distribution at different spacing.

Figure 9 .
Figure 9. Temperature distribution at different spacing.

Figure 11 .
Figure 11.Local vector velocity at different spacing.

Figure 12 .
Figure 12.Pressure distribution at different depths.

Figure 13 .
Figure 13.Temperature distribution at different depths.

Figure 14 .
Figure 14.Speed distribution at different depths.

Figure 19 .
Figure 19.Plate corrugation local vector velocity at different inlet velocity.

Figure 20 .
Figure 20.The relationship of β with ΔP, Nu, average heat transfer coefficient and η.

Figure 22 .
Figure 22.The relationship of h with ΔP, Nu, the average heat transfer coefficient and η.

Figure 23 .
Figure 23.The relationship of velocity with ΔP, Nu, the average heat transfer coefficient and η.
ure 7(b).Due to the plate heat exchanger has a wide range of bearing temperature, Y. Jia et al.DOI: 10.4236/ojfd.2017.73029431 Open Journal of Fluid Dynamics