Heating performance enhancement in panel-type radiators based on vortex generators and fin form optimization

Increasing the heat performance of heating radiators could be a valuable method for building energy conservation. This paper studied the influence of fins on the thermal performance of panel radiators (type 11). The effect of different vortex generator angles, the gap width of discontinuous fins, and different forms of staggered fins have been studied numerically and experimentally. Firstly, the simplified model of the panel radiator was analyzed by CFD simulation, the thermal performance under different geometric parameters was studied, and better geometric parameters were obtained. Research shows that optimizing the parameters of the vortex generator has a positive effect in increasing the heat dissipation of the radiator. Both discontinuous fins and staggered fins can improve the thermal performance of the radiator. The research shows that the fin shape has a significant impact on the heat dissipation of the radiator. The thermal performance of the radiator can be greatly improved by using a vortex generator with specific angles, staggered fins, and discontinuous fins. These technical routes can be directly implemented on the basis of the original radiator, which provides a direction for the technical improvement of this type of radiator.


Introduction
Low-temperature heating technology originated in North America and European countries.According to research, 85% of residential buildings in South Korea use low-temperature heating technology, 65% in Canada, 48% in Switzerland, 41% in Germany, and 20% in France [1].The operation temperature for radiators specified in European Standard EN442 is 75/50 ℃, and the future development trend is 55/45 ℃.Since 1982, it is recommended that the heating medium temperature should not be higher than 55 ℃, which will promote the application of low heat medium temperature heating systems in Europe [2].The German VDI 6030 standard is designed for the heating parameters of the radiator system, which proves that when the heating temperature difference is reduced to less than 35 K, the temperature distribution will be better, and the thermal comfort of indoor personnel will also be improved; The standard also suggests that the temperature of heat medium can be further reduced to 55~45℃ for consumption reduction of heating buildings [3].
Hasan et al. [4] studied the thermal comfort of radiator heating with the operating temperature of 45℃/35℃and found that the indoor temperature fluctuation was small, and the vertical temperature difference was about 0.3 K/m.Myhren et al. [5] of Sweden used the method of CFD simulation, and compared and analyzed the comfort of high-temperature radiator heating, medium low-temperature radiator heating, floor radiation heating, and wall radiation heating by using temperature, wind speed distribution, and PPD indicators, and concluded that the comfort of medium low-temperature radiator heating is the best in rooms with poor air tightness.Calisir et al. [6] compared the performance of panel-type radiators by using experimental and CFD simulation methods.The research results show that reducing the inlet temperature from 90℃ to 30℃ will reduce the heat output by 92%.Therefore, the amount of radiator needs to be increased to obtain the same comfortable conditions under lowtemperature heating conditions.Prek and Krese [7] carried out experimental research on the heat output regulation mechanism of multi-convection panel-type radiators and studied the concept of the influence of water flow distribution of panel radiator (Type22) on heat dissipation.Ploski et al. [8] found that the use of forced convection radiators in residential buildings can meet the building heating requirements (KW) with low water supply temperatures.Võsa et al. [9] studied the emission efficiency of panel radiators in the laboratory according to the EN442 standard.The analysis shows that indoor air temperature stratification affects the heat performance of the radiator significantly.Holmberg and Myhren [10] optimized the ventilation radiator by changing the fin distribution of the radiator.Because of the higher driving force between air panels, it can greatly improve the heat output efficiency.Calisir et al. [11] studied the effects of the shape parameters of fins experimentally and numerically.Golkarfard et al. [12] focused on the comparison of the effects of optimizing the hydraulic conditions of the radiator and increasing the heat transfer surface area.The comparison system gives acceptable results in terms of indoor thermal environment assurance.Myhren and Holmberg [13][14] studied a new type of radiator with ventilation equipment, which can resist cold air and is called ventilated radiator (VLTR).When the cold air flows through the air inlet, it is preheated to a comfortable air temperature level.The simulation and laboratory measurement results show that according to different fin geometry, the heat output provided by VLTR at 35℃ water supply temperature is the same as that provided by conventional HTR at 55℃.
The above research reveals the mechanism of improving the heat performance of radiators and points out the improvement direction.Improving the thermal performance of the radiator can compensate for the decrease in heating capacity caused by the reduction in water supply temperature.On the basis of this principle, this paper focused on radiator structural optimization to find a simple and feasible method to improve the heating capacity of the radiator.

Methodology
In this paper, the improvement of heat dissipation capacity after the optimization of fin form and the installation of a vortex generator is studied.Therefore, an improved technical route for improving the thermal performance of the radiator is given.The CFD method is used to study the thermal performance improvement path of the radiator, and the calculation software is STAR-CCM+ of Siemens.Simcenter STAR-CCM+ can simulate internal and external fluid flow for a variety of fluid types.
The continuity equation is used to describe the mass balance of the computational domain: ( ) ( ) where ρ is the mass density, and v indicates the speed of the calculated object.The momentum balance equation is defined as follows: where ⊗ denotes the outer product, σ is the stress tensor, and f b is the resultant of the body forces per unit volume.For fluids, stress tensors can usually be decomposed into normal stress and shear stress: where T is the viscous stress tensor and p is the pressure: The stress tensor should satisfy the symmetry condition: The energy equation of the control body can be written as: where q is the heat flux, E is the total energy per unit mass, and SE is the energy source per unit volume.
The Realizable Two-Layer K-Epsilon model [15] combines the Realizable K-Epsilon model with the two-layer approach.The Boussinesq model is used to simulate the change of driving force caused by density change due to temperature variation.The density change is approximated as follows in Formula (7): ( ) The Reynolds number is expressed as follows: where D h is characteristic length, and u in is reference velocity.
For the case of a panel radiator, Dh is hydraulic diameter, Dh= 4A/P, P is the perimeter of the passage, A is the air passage cross-sectional area.Other non-dimensional numbers are defined as follows: where the kinematic viscosity is μ ν ρ = , λ is thermal conductivity, Cp is specific heat, and thermal diffusivity is rounding air, β is the thermal expansion coefficient of the air, and L is the character length of the radiator.
In this paper, we combined the segregated energy model and the Surface-to-Surface radiation model together to determine the temperature field.The radiation heat transfer between two surfaces depends on their size, distance, and direction.These parameters in the software are represented by geometric functions of "view factors".The emissivity of the room wall surface and radiator surface was set to 0.9 and 0.88 respectively.

Case Setup
In this paper, the panel radiator is selected as the research object.The main reason is that the panel radiator has the highest heating utilization rate in the world at present.In Europe, there are lowtemperature heating products that have been upgraded on the basis of the panel heat exchanger.Some scholars have also reformed the panel heat exchanger to form a ventilation-type heating radiator.In terms of the heat transfer mechanism, the plate heat exchanger has the characteristics of both radiation and convection, the outer plate is mainly radiation, and the rear side has the characteristics of a convection radiator after adding fins (Figure 1, Figure 2).The panel-type radiator adopts longitudinal folding fins, and the industrial automation production level is the highest among all kinds of radiators.At the same time, the panel-type radiator has a closed shell structure.After adding a spoiler fan, the improvement of heat dissipation capacity by forced convection technology can be studied.The radiator is placed in a room with six walls at 18℃ to maintain the ambient temperature around the radiator at 18℃.The water supply temperature is 80℃, the flow rate is 3 g/s, and the outlet boundary condition is the pressure outlet (Figure 3).A fan is set at the lower part of the radiator.The outlet of the fan is the velocity boundary condition and the inlet is the pressure boundary condition (Figure 3).

Mesh Convergence Analysis and Model Test Verification
Through simulation, the average temperature of the radiator wall is 67.5℃ (Figure 5), and the ambient temperature is 18℃.Therefore, the qualitative temperature of the air is 42.75℃.Under this condition, these physical properties could be defined: the reference air density ρ= 1.1176 kg/m 3 , the dynamic viscosity µ= 1.9215×10 -5 Pa•s, the kinematic viscosity is ν= µ/ρ =1.7193×10 -5 m 2 /s, the thermal conductivity is λ= 0.02756 W/m•K, the specific heat is Cp = 1007 J/kg K, and the thermal diffusivity is α = λ/ρCp= 2.4488×10 -5 m 2 /s.The characteristic size of the panel radiator is L = 0.6 m.The following nondimensional numbers are computed: Gr= 1.1221×10 9 , Pr = 0.7021, and Ra =7.878×10 8 .It is observed by White [16] that when the Reynolds number reaches 4000, a fully turbulent flow is ensured.Additionally, in the research by Hanks and Ruo [17], the range of critical Re number is determined as 2360 ≤ Re ≤ 2960 through the experimental method.As stated in [16], if 10 5 ≤Ra≤10 9 , natural convective laminar flow occurs, and the turbulent transition range of parallel panels is 10 8 ≤Ra≤10 10 .Under this working condition, the natural convection of air around the radiator is in the transition state to turbulence.According to the calculation formula of the approximate solution of the vertical plate theory of constant heat flow natural convection, the average Nusselt number is calculated by the following equation [18]: ( ) According to the above formula, the average Nusselt number is 119.31.Calculated by Equation ( 12), the heat transfer coefficient of the radiator is 5.112 W/m 2 K, under natural convection conditions.According to the figure below, along the vertical direction, the distribution of the heat transfer coefficient is as follows, and the average value of the calculator is about 5.23 W/m 2 K (Figure 6).The deviation between the results calculated by the experimental correlation formula and the simulation results of this model is about 2.25%.This shows that the results of the simulation calculation are in good agreement with those of the experiment correlation, and it is feasible to analyze the thermal performance of the radiator by the simulation calculation method.At the same time, the temperature distribution on the outer surface of the radiator calculated by the numerical simulation method is consistent with the thermal imaging temperature distribution obtained by the infrared thermal imager.When the inlet temperature of the radiator is 80℃, the upper temperature of the radiator is about 77℃, the middle temperature is about 71℃, and the lower temperature close to the return water pipe is about 63℃.This also verifies the reliability of the calculation results of this simulation model.Three hexahedral meshes with different refinement levels are used for comparative analysis to avoid mesh quality problems, such as element deflection, element offset, and element non orthogonality.Through analysis, we determine the appropriate level of mesh refinement for this study.The same mesh generation method is used in the model.In the calculation model, 2.177 million grids are used for M1, 4.905 million for M2, and 6.046 million for M3.We use M1, M2, and M3 grids to calculate the heat transfer coefficient values at the same location (Figure 7).The calculation results of the M2 and M3 grids are close.The calculation results of M1 grids in the lower half of the radiator have a large deviation from those of other grids, and the calculation results of the upper half of the three grids are basically consistent.The calculation deviation of the heat transfer coefficient is less than 3%, so it can be considered that the three grids under consideration are independent.In order to give consideration to the calculation speed and accuracy, this paper selects a grid system with a grid number of about 4.905 million to calculate.

Wall Heat Transfer Optimization Based on Vortex Generator
The heat performance optimization method of heating radiators also follows the law of heat transfer enhancement of heat exchangers.The vortex enhancement technology is based on vortex generators to improve the flow field flow characteristics to achieve the purpose of enhancing heat transfer.The vortex is generally generated by the vortex generator (LVG) (Figure 8).The arrangement of vortex generators (VGs) embedded on the surface has two structural forms: CFD and CFU [19].Figure 10 shows the four most commonly used vortex generators, which are the delta wing, rectangular wing, delta winglet, and rectangular winglet from left to right.Generally, delta winglets and rectangular winglets appear in pairs.Panel radiator is widely used in building heating, but its heat dissipation rate is limited by the heat exchange capacity on the air side.In this simulation, temperature boundary conditions are used on all room surfaces, the outlet of the fan is set as velocity condition (1 m/s, 18℃) and the inlet of the fan is pressure condition.There are coupling boundary conditions between the water and radiator, between the radiator and the air domain, and between the vortex generators and the air domain.The components of the radiator model are shown in Figure 9.The water inlet is a mass flow inlet (3 g/s, 80℃) and the outlet is a pressure outlet.The radiator in the calculated area in the model is 600 mm high, 100 mm wide, and 50 mm thick, and the vortex generator is 20 mm long, 4 mm wide, and 0.5 mm thick.The spacing of longitudinal vortex generators is 50 mm, 10 pieces are arranged in each column, and a total of 5 columns are arranged.The distance from the vortex generator to the wall is 0.2 mm.In this paper, the effect of a vortex generator on heat transfer performance at different wing angles of attack is studied.This includes the angle between the vortex generator and the wall along the -Z axis (wing angle of attack, AoA) is 15°, 30°, 45°, 60°, 90°, 120°, 135° and 150° respectively.It can be seen from the above figure that the convection heat transfer coefficient of the radiator fins near the vortex generator is significantly improved (Figure 10-Figure 15).The enhanced heat transfer spots are generated near the vortex generators and the enhancement degree and influence range of the heat transfer coefficient change with the change of attack angle.We take the heat transfer coefficient value at the centerline of the fin in the middle of the radiator for plotting, as shown in Figure 9.When the AoA of the vortex generator is 45°, the average heat transfer coefficient reaches the maximum value, 14.64 W/m 2 K. Compared with that without VGs (11.68 W/m 2 K), the increase rate is 25.34%.The average heat transfer coefficient of the radiator at different angles of attack is calculated as follows (Table 1).Because of the high local wind speed, the VGs placed in the entrance section have a higher heat transfer coefficient.In this paper, the rectangular wing vortex generator is used to allow more incoming flow to pass through the tapered channel, which is accelerated in a channel similar to the nozzle.The accelerated high-speed fluid directly impacts the downstream heat exchange tube wall, forming jet impingement.Under the effect of jet impact, the boundary layer of the downstream heat exchange wall becomes thinner and the temperature gradient rises.Finally, the purpose of heat transfer enhancement is achieved.As shown in Figure 16, the vortex reaches a stable position downstream of the region, and the heat transfer enhancement ability of the VGs is reduced.and the thickness of the thermal boundary layer increases.The evolution process of the vortex along the incoming direction can be observed by the temperature and velocity fields.The line integral convolution (LIC) method is used to obtain the visual secondary flow to find the vortex center.This paper selected the sections normal to Z-axis to visualize the generation of the vortex (Figure 16).We can see that the strongest vortex is located near the center line of the panel, where the velocity and heat transfer coefficient are higher.When the fluid flows through the longitudinal vortex generator, a longitudinal vortex pair rotating in the opposite direction is generated, and the secondary flow generated by the vortex generator rotates in the opposite direction.When the boundary layer near the rectangular wing vortex generator is damaged, the fluid rotates towards the channel wall, and the interaction with the wall is enhanced, thus causing a strong disturbance to the fluid, leading to the destruction of the boundary layer, so that the heat transfer capacity is improved.

The Influence of Fin Form on the Improvement of Heat Dissipation Performance
This paper focuses on the effect of discontinuous fins and staggered fins on the heat dissipation of panel-type radiators.In this paper, different discontinuous gaps are set in the middle of the fins of the panel-type radiator, as shown in the figure below, to study the changes in the average heat transfer coefficient and heat dissipation of the radiator under different gap widths.It can be seen that when discontinuous fins are used, the total heat transfer quantity between the fins and the air decreases, but the average heat transfer coefficient value of the additional fin area increases (Figure 17-Figure 19).The heat transfer enhancement of the initial section of the discontinuous fin is obvious.The calculation shows that the thermal performance of the radiator can be significantly improved by shifting the position of some fins of the discontinuous fin panel-type radiator that has been welded and assembled to form a staggered heat exchange structure.This basically does not increase the manufacturing cost of the radiator.It can be clearly seen from the above figure that when staggered heat exchange fins are used at the same section position, the local vortex formed at the middle position is larger, and the area of action of high-speed rotating secondary flow is larger; The velocity boundary layer at the fin position is thinner, indicating that the boundary layer here is damaged under the action of eddy current, the boundary layer becomes thinner, the temperature gradient becomes larger, and the heat flux increases, which is conducive to strengthening heat transfer.

Discussion on Heat Transfer Enhancement of Vortex Generators
The heat transfer enhancement effect from the radiator inlet to the vertical middle position of the radiator is better than that above the middle position (Figure 21).This is because the heat transfer performance of the thermal boundary layer decreases with the increase of the flow direction.It can be seen from the sectional velocity distribution of the air domain that along the incoming direction, the thickness of the low-speed zone near the wall increases, the velocity boundary layer thickens, and the heat transfer performance decreases (Figure 22).In the area near the vortex generator, the convective heat transfer coefficient increases significantly due to the strong convection between the fluid and the heat transfer surface.When air flows from the bottom of the radiator, the vortex generator is arranged in the middle and lower part of the radiator, and obvious heat transfer enhancement results can be obtained.At the same time, the research shows that the overall heat transfer enhancement results are better when the attack angle of the vortex generator varies from 30° to 45°.

Discussion on Heat Transfer Enhancement of Discontinuous Staggered Fins
When the gap increases from 0.01 m to 0.05 m, the heat dissipation of the radiator decreases gradually, but the average heat transfer coefficient of the area with fins increases continuously (Figure 23).When the clearance is 0.02 m, the heat dissipation of fins to air decreases to 98.63%, the fin area decreases to 72% of the reference value, and the average heat transfer coefficient increases to 128.6% of the refer-ence value.When the gap area is further increased, the heat dissipation decreases significantly.When the fin area ratio decreases to 51% of the reference value, the heat dissipation decreases to 92.6% of the reference value, and the average heat transfer coefficient increases to 154.3% of the reference value.When the clearance is 0.05 m, the average heat transfer coefficient increases to 180% of the reference value.This shows that the area reduction caused by discontinuous fins can be compensated to some extent by increasing the average heat transfer coefficient.This is because the discontinuous fins act as the flow around elements in the heat transfer area, producing a heat transfer enhancement effect similar to that of the vortex generator.It can be seen from the figure below that more vortices are generated in the fluid area after the discontinuous fins are set, further damaging the thermal boundary layer on the wall, so as to achieve the purpose of enhancing heat transfer.When the gap is further increased, the fins of the panel radiator disappear, and the radiator changes into a plate-type radiator without convection (Type 10, Type 20).It can be seen that the heat dissipation capacity of the non-convection fin radiator drops sharply, and the drop rate is nearly 45% compared with the conventional continuous fin radiator (Figure 23).This shows that adding vertical longitudinal fins on the surface of the panel-type radiator can increase heat dissipation.Compared with continuous fins, when the fin gap is less than 0.03 m, the overall heat dissipation of the radiator is reduced by less than 5%, but the amount of fin material can be reduced by 42%, which is of great significance to reduce the manufacturing cost of the radiator.At the same time, compared with the heat dissipation of the radiator without fins, when the gap is 0.05 m, the fin area of the radiator increases by 18%, and the heat dissipation increases by 23.6%.This shows that adding longitudinal discontinuous fins on the surface of the panel-type radiator can greatly improve the thermal performance of the panel-type radiator.When the clearance is 0.02 m, the reduction of heat dissipation is only 1.4%, and the reduction of fin consumption is as high as 28%.Through statistical calculation, the average heat transfer coefficient of a staggered fin radiator is increased from 16.86 W/m 2 K to 19.59 W/m 2 K, with an increase rate of 16.2%.Because only the position of some radiating fins is offset, the heat transfer areas are basically the same.When reaching the steady state, the heat transfer from the radiator to the air domain increases from 133.49W to 145.36 W, an increase of 8.9%.This provides a technical route for further improving the thermal performance of panel-type radiators.

Conclusions
In this paper, the CFD method is used to research the function of the vortex generator in improving the heat transfer coefficient of the panel radiator.At the same time, the effect of discontinuous fins and staggered fins on improving the thermal performance of panel radiators is further studied.The study is focused on forced convection and the radiator inlet speed is set as 1 m/s.The mesh convergence analysis is carried out in the simplified panel radiator model to determine the element size required to accurately solve the temperature and velocity field.
Installing rectangular vortex generators on a panel radiator is a method to improve the heat transfer coefficient.When the AoA of the vortex generator is 45°, the average heat transfer coefficient reaches the maximum value, 14.64 W/m 2 K. Compared with that without VGs (11.68 W/m 2 K), the increase rate is 25.34%.Due to the high local wind speed and the strong disturbance of the vortex on the flow field, the panel surface near the VG at the entrance has a high heat transfer coefficient.
At the same time, the influence of discontinuous and staggered heat exchanger fins on the heat dissipation of panel-type radiators is further studied.Compared with continuous fins, when the fin gap is less than 0.03 m, the overall heat dissipation of the radiator is reduced by less than 5%, but the amount of fin material can be reduced by 42%, which is of great significance to reduce the manufacturing cost of the radiator.The average heat transfer coefficient of a staggered fin radiator is increased from 16.86 W/m 2 K to 19.59 W/m 2 K, with an increased rate of 16.2%.The heat transfer from the radiator to the air domain increases from 133.49W to 145.36 W, an increase of 8.9%.This provides a technical route for further improving the thermal performance of panel-type radiators.

Funding:
This research was financially supported by the National Key Technology R&D program named Study on Solar Heating and Heat Storage Technology in Rural Area(2018YFD1100701)).

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ΔT is the temperature difference between the radiator wall and the sur-NESP-2023 Journal of Physics: Conference Series 2592 (2023) 012030

Figure 1 .
Figure 1.Typical structural style.Figure 2. Sample panel radiator installed in the laboratory

Figure 2 .
Figure 1.Typical structural style.Figure 2. Sample panel radiator installed in the laboratory 3.1.CFD Simulation Model Because of the symmetrical structure of the panel type radiator, this paper starts from the panelconvection (type 11) panel-type radiator.The radiator has a radiation panel and a group of back convection fins, which can be seen as the basic component of other types of panel type radiators.The radiator model is shown in the following figure.According to the symmetrical structure of this type of radiator, to simplify the radiator model, three rows of waterways are selected for CFD calculation to verify the reliability of the CFD model.The radiator is placed in a room with six walls at 18℃ to maintain the ambient temperature around the radiator at 18℃.The water supply temperature is 80℃, the flow rate is 3 g/s, and the outlet boundary condition is the pressure outlet (Figure3).A fan is set at the lower part of the radiator.The outlet of the fan is the velocity boundary condition and the inlet is the pressure boundary condition (Figure3).The fan can simulate the heat dissipation of the radiator under different convection intensities.The height of the radiator is 600 mm.The grid details of the calculation model are shown in Fig-ure 4. In this paper, the average heat transfer coefficient of the radiator under natural convection is calculated and compared with the measured value in the laboratory to verify the reliability of the model.

Figure 3 .
Figure 3. Boundary layer settings Figure 4.The local grid design of the model

Figure 7 .
Figure 7. HTC value distribution under different grid sizes

Figure 8 .
Figure 8. Several typical VGs Figure 9. Composition of radiator fins and VG

Figure 16 .
Figure 16.Temperature and velocity fields

Figure 20 .
Figure 20.Analysis of vortex morphology of staggered radiators

Figure 21 .
Figure 21.Change the trend of HTC of the radiator at a specific location

Figure 23 .
Figure 23.Thermal performance of radiators with different gap width

Table 1 .
Average HTC at different AoA