A study on optimization of the air supply system for the electric heating solid heat storage unit

Abstract

An experimental and simulation study was carried out on the air supply system of the electric heating solid heat storage unit, aiming to improve the uniformity of the air supply system, thereby increasing the overall heating efficiency of the solid heat storage unit. The experiments show that non-uniform air distribution of the air system may cause non-uniform heat release of the heat accumulator, and the uniformity of the air supply system is greatly affected by the air supply structure and air inlet. By establishing a model of the heat storage device and conducting numerical simulation, the air distribution law of the air supply system was studied. According to the study results, the uniformity index of the air system was effectively improved by increasing the air cabin width and the air inlet angle, and adding a static pressure box at the air supply outlet, so that the flow velocity distribution of the air supply system was more uniform, which is of great significance to the overall optimization of the solid heat storage and heating system.

Keywords

Electric heating solid heat storage unit flow velocity distribution uniformity index experiments numerical simulation

1. Introduction

In response to the proposal of the State’s “emission peak” and “carbon neutrality” goals, we will accelerate the industrial innovation of energy and ecological environment, vigorously promote the “wind-water-thermal-solar power storage, and source-network-load storage” integrated development, focus on supporting technological breakthroughs of heat storage, efficient photovoltaics, hydrogen energy, intelligent energy and other core technologies, effectively drive the innovation and development of the energy revolution, and facilitate the construction of zero carbon villages and towns in China, to achieve sustainable development of the ecological environment. Since electricity is a stable green and clean energy, the electric heat storage technology has been widely applied in the heating industry, which is also to respond to China’s policy of Peak Cut. Using the electric heating solid heat storage unit as a heating method to replace the way of heating with coal, can effectively alleviate the fossil energy crisis and air pollution resulting from heating.

However, the solid heat storage technology is emerging and not mature enough, and there are no systematic national norms and standards to regulate it. In China today, research and engineering applications of heat storage materials, heat storage mode, heat storage characteristics of the heat storage electric heating system have gradually increased. The air supply system is an important part of the heat exchange system in an electric heating solid heat storage unit. The air supply mode and structure of the unit greatly affect the operating efficiency of the whole system. The solid heat accumulator has dozens to hundreds of air vents inside it. The uniform air supply system is designed in such way that the flows of the fluid supplied into each vent tend to be consistent. In case of disordered air distribution, the temperature distribution of the heat accumulator will be in a non-uniform state, affecting the efficiency of heat exchange of the entire unit. Besides, due to the high temperature resistance, the heat storage temperature of the heat accumulator can reach 700 to 800 ${{}^{\circ}}$ C. However, the maximum primary-side air supply temperature of the finned heat exchanger commonly used in the electric heating solid heat storage system should not exceed 350 to 400 ${{}^{\circ}}$ C, and excessive air temperature will cause the heat exchanger’s heat tubes and fins to deform and even melt. By regulating the air flow of the air supply system, the air temperature of the heat accumulator can be effectively controlled, to maintain the primary- side air temperature and flow of the heat exchanger are uniform and relatively stable, thereby, guaranteeing a stable heat supply for users.

Therefore, the study on optimization of the air supply system of the electric heating solid heat storage unit is of great significance to the improvement of system efficiency and heating supply effect. In this study, an experimental study was carried out, combined with an actual project, and a model for the air system of the heat storage device was established to conduct numerical simulation. Through experimental study and simulation data, the air distribution law of the air system was summarized and an optimization study was carried out. On this basis, a better way of air supply is proposed.

2. Electric heating solid heat storage unit

2.1 Introduction of the system and operation principle

The electric heating solid heat storage unit mainly consists of an electric heating system, a heat storage system and a heat exchange system. The operation principle of heating system is shown in Fig. 1.

Figure 1.

A diagram indicating the operation principle of the heating system of the electric heating solid heat storage unit.

(1)

The electric heating system is mainly composed of high temperature-resisting resistance wires with an appropriate surface load. Each resistance wire goes through a thread hole reserved in the heat accumulator, converting electrical energy into heat energy and then transmitting the heat to the heat storage brick. The resistance wires from each thread hole are connected in parallel, and achieve confluence through a copper busbar. The high voltage electricity is supplied by a high voltage cabinet and is started and stopped through control of a low voltage switch cabinet.

(2)

The heat storage brick of the heat storage system is mainly made with high temperature and high voltage-resistant, large heat storage material sintered at high temperature. It can achieve heat storage and release just with its own heat, and the form of it does not change with temperature. The most commonly-used heat storage material is a magnesium brick. The heat storage bricks are reserved with brick holes during fabrication, which are to be used for constructing connected air vents and as the holes for resistance wires to go through.

(3)

The heat exchange system is used to perform heat exchange with the heat storage bricks of the unit, using air as the medium. The high temperature air flows into the heat exchanger through the air duct, and exchanges heat with the secondary-side water, during which, heat is transferred. After the heat accumulator completes the electric heating process, the heat release and heat supply process will start. At this time, the fan is started, to drive the low temperature and low pressure air which has been subject to heat release through the air-water heat exchanger, to flow into the air inlet cabin of the heat storage device. Under the pressure of the air inlet cabin, the air flows through the heat dissipation hole in the middle of the heat storage module, and enters the air outlet cabin. At this time, the low temperature air has completed the heat exchange with the heat storage module, and its temperature has reached the air supply outlet condition. Through the heat storage device at the air outlet of the air outlet cabin, it returns to the steam-water heat exchanger to release heat. Thus, the whole circulating process of the air system is completed. The uniformity and flow regulation of the air supply system greatly affect the heat efficiency and heat exchange effect of the heating system.

2.2 Evaluation indicators of the air system

Flow Velocity Distribution Uniformity Index:

This uniformity evaluation indicator is an evaluation standard for the flow velocity uniformity of a flow field established in the early 90’s, which is based on the definition of statistical deviation, can fully reflect the fluid velocity distribution characteristics across the whole flow-through cross-section, featuring a high comparability and a wide range of applications. Its expression is:

$\displaystyle W=1-\frac{1}{2n}\sum_{i=1}^{n}\frac{\sqrt{(v_{i}-\bar{v})^{2}}}{% \bar{v}}$ (1)

Where, $W$ is the air distribution uniformity index of the air supply system, with a value of [0,1].

$v_{i}$ is the fluid velocity at the $i^{\text{th}}$ measuring point, in m/s; and

$\bar{v}$ is the average velocity across the measurement cross-section, in $m/s$ ;

The larger the W is, the better the flow uniformity will be, and the closer the temperature distribution of each part of the heat accumulator at the same depth will be, so that the heat of the heat accumulator may be fully released. 1 means uniform flow in the ideal state, 0 means that the fluid only passes 1 measuring point. Both cases are supposed conditions and do not actually exist.

3. Experimental study

3.1 Experimental purpose

To collect the temperature parameters of heat storage bricks and air volume parameters of heat dissipation holes in various parts of the heat accumulator by reasonably arranging the measuring points; summarize the overall distribution state of heat accumulator parameters based on data; and verify the rationality of the boundary conditions set by the numerical simulation and the rationality of the physical model through the feedback data from each measuring point in the experiment.

3.2 Experimental platform

3.2.1 Equipment and parameters of the heating system

This experimental platform undertakes the task of heating to a building area of 24,000 square meters near the boiler room, where heating radiators are used for heat radiance.

(1) Heat load

The overall heat indicator of the heating building is 61 W/m ${}^{2}$ , and the heating load of this system is 1.46 MW.

(2) Calculation of year-round heat consumption

The heating period of Zhangjiakou City is from November 1 to March 31, totaling 151 days. The average outdoor temperature during the heating period is $-$ 3.9 ${{}^{\circ}}$ C, the calculated outdoor and indoor temperatures of the heating-supplied room are $-$ 13.6 ${{}^{\circ}}$ C and 18 ${{}^{\circ}}$ C, respectively. The annual heat consumption was calculated based on a continuous time, which was 13, 240 GJ according to the meteorological parameters of Zhangjiakou City.

(3) Physical parameters of heat accumulator

Designed maximum heat storage temperature: 700 ${{}^{\circ}}$ C;

Designed temperature difference between heat storage and release: 500 ${{}^{\circ}}$ C;

Power withstood by the single-phase heat accumulator: 0.5 MW;

Size of heat dissipation hole: 50 mm in diameter, and 3.15 m in length;

Number of heat dissipation holes: horizontally arranged: 32; vertically arranged: 10;

Total volume of single-phase heat storage bodies: 15.32 m ${}^{3}$ ;

(4) Selection of fan types

Table 1
Parameters for selection of fan types

Fan type	Power (kW)	Air volume (m ${}^{3}$ /h)	Full pressure (pa)	Number (units)
4-72 4.5A	7.5	5712–10562	2554–1673	3

3.2.2 Size parameters of the experimental platform

This experimental platform is located in Zhangjiakou City, and the computer room is set in the basement of a building. Due to space confinement and the original intention of achieving the functions of a multi-function platform, the experimental platform is set with the heat storage module, heat exchanger and fan separated, and the main studied item in this work is the heat storage module.

The casing of the heat storage module has overall dimensions as 9460 mm $\times$ 5340 mm $\times$ 2760 mm, air supply outlet dimensions as 500 mm $\times$ 300 mm, and the number of air supply outlets is 3. The heat storage device is divided into three phases of heat storage modules internally, each of which corresponds to a separate air supply outlet and has an independent air supply fan.

3.3 Experimental scheme

The air distribution uniformity is only related to the structure of the air system itself. When the structure and relevant dimensions of the system are determined, the characteristics of the air system will be basically determined. In this case, the flow distribution of each heat dissipation hole of the heat accumulator is only related to the air inlet velocity of the unit. According to this principle, the flow distribution of the whole heat accumulator at a certain frequency can be obtained, as long as the velocity $v$ at each heat dissipation hole on the upwind cross-section of the heat accumulator is measured at the certain frequency above mentioned, by regulating the fan frequency to control the air velocity of the existing unit. When the fan frequency is changed, a series of velocities of all the heat dissipation holes under different air inlet velocities can be measured, based on which, the structure of the unit can be evaluated.

3.3.1 Test items

The tests in this part included the cold boiler flow velocity test and the hot boiler temperature test.

(1) Cold boiler flow velocity test

Based on the principle of symmetry, the cold boiler test was conducted with a half boiler as the test object, and the test items mainly include flow velocities and air flows of each air supply outlet and air vent inlet. Such flow velocities and flows were obtained by using a multi-point velocity indicator and a multi-throat flow meter. On this basis, the air distribution characteristics of the air system were analyzed.

This test was divided into two parts according to the fan running control mode, namely the case with one fan running, and the case with three fans running. The inlet flow velocity of each heat dissipation hole was measured with the total flow constant, when one fan was running and when three fans were running, respectively. The specific arrangement of the measuring points is shown in Fig. 2.

Figure 2.

Arrangement of measuring points for the half-boiler test.

According to the fan performance parameters, the effects of fans on the flow velocity distribution of the heat storage body under the two control modes described above were analyzed. When the total flow was selected as 9900 m ${}^{3}$ /h, 8400 m ${}^{3}$ /h, 6600 m ${}^{3}$ /h and 5400 m ${}^{3}$ /h, respectively, the corresponding frequencies with one fan running were 49 Hz, 43.6 Hz, 37.1 Hz and 32.8 Hz, respectively. When three fans with the same frequency were running simultaneously, the corresponding frequencies were 25.2 Hz, 23.4 Hz, 21.2 Hz and 19.8 Hz, respectively. The set testing conditions are given Table 2. The values of each measuring point were recorded once every 10 s, and the test lasted 5 min at each frequency. The average of the values from each measuring point during the testing was taken as the test result for the corresponding measure point.

Table 2

Test conditions

Control form no.	Control form	Air vent	Fan	Test frequency (Hz)
I	One fan running	1/3 off, 2 on	1/3 off, 2 on	49.0/43.6/37.1/32.8
II	Three fans running simultaneously	1/2/3 on	1/2/3 on	25.2/23.4/21.2/19.8

(2) Hot boiler temperature test

This test was to obtain the temperature changes at various positions of the heat accumulator in each heat release stage. The temperature values were mainly obtained by the heat feedback of the high temperature K-type thermocouples in contact with the heat storage brick, which were buried in different positions of the heat accumulator. The positions of all measuring point are as shown in Fig. 3. Before testing, it was ensured that all the valves of the front and rear air ducts of the heat storage device were closed. Then the electric heating mode was initiated, and set as that the heating would stop when the maximum heating temperature 300 ${{}^{\circ}}$ C was reached. The heat release duration was set 120 min. Sampling was conducted once every 10 min at each temperature measuring point. The temperatures of the heat storage bricks were recorded during the whole heat release period.

3.3.2 Meters for the test

The meters used in the test are listed as follows.

Table 3
Main meters and parameters

Meter	Model	Measuring range	Accuracy
Type K thermocouple	PT100 universal	0 to 1300 ${{}^{\circ}}$ C	Level 1
Air velocity sensor	SYSTEM 6242	0.00 to 25.00 m/s	$\pm$ 0.5%FS
Multi-throat flow meter	HQJLV-ZYL	$-$ 40 ${{}^{\circ}}$ C to 550 ${{}^{\circ}}$ C, and 0.5 to 60 m/s	Level 0.5

Figure 3.

Arrangement of temperature measuring points of heat accumulator.

3.4 Test results and analysis

3.4.1 Half-boiler flow velocity test

(1) Test results and analysis

The half-boiler flow velocity test was to obtain the flow velocity at each measuring point, at each specific frequency when only fan was running, and when three fans were running simultaneously, respectively. The test results are as shown in Fig. 4a and b. The maximum flow velocity difference for the upwind cross-section was calculated, as shown in Fig. 4c and d.

Figure 4.

Half-boiler flow test results.

Through analysis of Fig. 4a and c, it is known that the flow velocities at measuring points F1 and E1 which were located nearest to the open air vent (Fan 2) were obviously higher than those at other measuring points when only one fan was running and the total air volume was constant. The averaged flow velocity of the measuring points except for F1 and E1 was within the 0 $\sim$ 2.5 m/s range of which, measuring points D1 and F3 had the lowest flow velocities. When the frequency of the medium-located fan was 49 Hz, the maximum flow velocity difference on the upwind cross-section of the heat accumulator reached up to 13 m/s; when the frequency was 43.6 Hz, the maximum flow velocity difference reached 11.78 m/s; when the frequency was 37.1 Hz, the maximum flow velocity difference reached 10.2 m/s; and when the frequency was 32.8 Hz, the maximum flow velocity difference reached 8.95 m/s. Therefore, the flow velocity difference at the heat dissipation hole on the upwind cross-section of the three phases of heat accumulators when only one fan was running was quite large, and it increased with the rise of the fan frequency.

Similarly, according to the analysis of Fig. 4b and d, it is known that the flow velocities at each measuring point when three fans were running simultaneously, were obviously more concentrated than those when only the medium-located fan was running, and they were all within 0 $\sim$ 4 m/s range. Of all the measuring points, F1 located at the medium phase air inlet had the highest air inlet flow velocity, and D5 located at the corner of the air cabin had the lowest air inlet flow velocity. When the frequency of the fan was 25.2 Hz, the maximum flow velocity difference on the upwind cross-section of the heat accumulator reached 2.75 m/s; when the frequency was 23.4 Hz, the maximum flow velocity difference reached 2.85 m/s; when the frequency was 21.2 Hz, the maximum flow velocity difference reached 2.63 m/s; and when the frequency was 19.8 Hz, the maximum flow velocity difference reached 2.39 m/s. Compared to the case with only one fan running with the same air volume, the maximum flow velocity on the upwind cross-section of the heat accumulator at different frequencies decreased by 75.5%. Besides, the flow velocities at F1 and F4 located nearest to the two air inlets showed $V_{\textit{F1}}＞V_{\textit{F4}}$ . The flow velocities at measuring points E3 and E5, as well as F3 and F5 which were respectively located on both sides of the air vent symmetrically were basically the same. The flow velocities at D3 and D5 which were located at the two upper corners of the heat accumulator showed that $V_{\textit{D3}}$ was slightly larger than $V_{\textit{D5}}$ . According to the above comparison, it can be seen that the flow velocities of the measuring points which were located at the opposite positions on both sides with the vertical center of the air vent as the axis of symmetry were basically the same. The fluids for the three phases of air cabins affected each other, so the flow velocity of the heat dissipation hole of the medium-phase heat accumulator was slightly different from those of the side-phase heat storage bodies located in the same position.

In both forms, the flow velocity at each measuring point was gradually increased with the rise of the fan frequency. However, it can be seen that in the case of only one fan running, the flow velocity distribution was quite non-uniform among heat dissipation holes of the heat storage bodies. The calculated nonuniformity coefficient corresponding to each experimental condition are given in the table below:

Table 4

Nonuniformity coefficient corresponding to each experimental condition

No.	Total flow	Number of fans in operation	Nonuniformity coefficient
1	9900	One	0.608
		Three	0.874
2	8400	One	0.607
		Three	0.874
3	6600	One	0.612
		Three	0.866
4	5400	One	0.612
		Three	0.871

By comparing the non-uniformity coefficient in Table 4, it can be found that when the total air volume is the same, the non-uniformity coefficient when three fans are running is significantly higher than the value when only one fan is running. After calculation, the average flow velocity uniformity index on the upwind cross-section of the heat accumulator when three fans are opened at the same time is 42.8% higher than that when only one fan is opened. It indicates that the wind speed distribution in each heat dissipation hole of the heat accumulator is more uniform when three fans are running at the same time.

(2) Summary of the half-boiler flow test

By analysis and comparison of flow velocities at all measuring points in the heat dissipation holes in the case with two fan running, we can conclude that the distribution of flow velocities at the heat dissipation holes of the heat accumulator is quite non-uniform when only one fan is running, but this problem can be greatly alleviated by making three fans operate simultaneously. In both fan running modes, the measured velocity increased with the rise of the fan’s frequency. In the same fan running mode, the air distribution nonuniformity coefficient increased slightly with the decrease of the fan frequency. On this basis, it can be concluded that the simultaneous running of the three fans is conductive to the uniform heat dissipation of the heat accumulator, when the total flow of the heat exchange system is constant. In addition, When three fans are running simultaneously, the output flows from both sides overlay and couple with each other, and get concentrated to the middle, which will pose an extrusion force to the middle air outlet, so that the flow there is increased quickly. Therefore, the flow velocity measured at the measuring point of middle air outlet is larger than that measured at the air outlet on either side. The torque of the fan located at the middle air outlet is larger than that of the fans located on either side, and the working air resistance of the corresponding fan is increased as well. From normal operation and uniform air distribution of the whole heat accumulator, it is recommended that the air cabins of three phases of heat storage bodies should be separated and supply air independently.

3.4.2 Hot boiler temperature test

(1) Test results and analysis

One of the main manifestations of a heat accumulator’s heat storage capacity is the temperature drop rate of each part thereof. The brick temperatures at the measuring points were obtained through experiments. Table 5 shows the experimental record data of measuring points 1 to 3.

Table 5
Experimental temperature test results of measuring points 1 to 3

Time/min	Measuring point 1	Measuring point 2	Measuring oint 3
0	300.9	300.4	299.1
10	299.7	294.6	286.7
20	286.6	275.9	259.4
30	265.5	250.3	230.9
40	242.8	227.6	211.7
50	221.1	199.1	187.1
60	199.5	180.3	170.4
70	184.7	171.8	156.2
80	176.6	159.2	148.3
90	162.6	147.1	138.4
100	151.6	133.7	122.6
110	143.4	125.9	111.9
120	134.2	119.7	97.80

To observe the changes in brick temperature, the experimental data were plotted as below. Figure 5 shows actual temperature changes at measuring points 1 to 3.

Figure 5.

Temperature changes at measuring points 1 to 3.

As seen from Fig 5, the initial temperature values of the three measuring points were basically the same, and there was a significant difference in the temperatures of the same points after a period of heating. When the brick temperature dropped to below 200 ${{}^{\circ}}$ C, the heat release rates of the heat storage bricks in each position slowed down, and the heat release ended 120 min later. The temperature difference between measuring point 1 and measuring point 3 on the same cross-section of the heat accumulator reached 36.4 ${{}^{\circ}}$ C. Through analysis, it is known that when the heat accumulator was performing pure heat release, its brick temperature was not affected by the electric heating wire. The heat release rate is only related to the air flow velocity at each heat dissipation hole. The heat release rate of the heat storage bricks around the heat dissipation hole with a large flow velocity was faster. After a period of time, the temperature around the heat dissipation hole with a slow flow velocity was still in high, while the temperature difference between the heat accumulator and the fluid around the heat dissipation hole with a high flow velocity decreased gradually, and the heat taken away by the fluid was getting less and less, as the result, the non-uniform distribution of heat accumulator temperature has appeared in the whole heat release process.

(2) Summary of the boiler temperature test

The air distribution uniformity is a decisive factor affecting the heat exchange performance of the heat accumulator. The difference in the inlet flow velocity at the heat dissipation hole of the heat accumulator resulted in a large difference in the heat release rate of the heat storage bricks in different positions. After several rounds of heat storage and release cycles, the temperature inside the heat storage bodies not located at any measuring point was far higher than the value indicated by the monitor, exceeding the temperature tolerance of the electric heating wire and monitoring thermocouples, which will increase the operating and maintenance costs, while greatly limiting the use performance of the electric heating solid heat storage device. The first task of optimizing the heat release process is to increase the air distribution capacity of the equipment and improve the non-uniform heat release condition of the heat accumulator.

4. Simulation study

4.1 Control equation

The flowing of the air flow in the model simulated in this study met the conditions that the flow process of the incompressible viscous fluid follows the law of momentum conservation, the law of the momentum conservation, the law of energy conservation and the law of mass conservation. The corresponding forms of these laws are as follows:

(1) Mass conservation equation

The casing structure covering the heat storage module has a good tightness, the air flow meets the law of mass conservation, that means, the increase of fluid mass within unit time is equal to the net mass flowing into the volume in unit time. The formula is as follows:

$\displaystyle\frac{\partial\rho}{\partial t}+\frac{\partial\left({\rho u}% \right)}{\partial x}+\frac{\partial\left({\rho\upsilon}\right)}{\partial y}+% \frac{\partial\left({\rho\omega}\right)}{\partial z}=0$ (2)

(2) Momentum conservation equations

$\displaystyle u\frac{\partial\left({\rho u}\right)}{\partial x}+v\frac{% \partial\left({\rho u}\right)}{\partial y}+w\frac{\partial\left({\rho u}\right% )}{\partial z}=-\frac{\partial p}{\partial x}+\frac{\partial}{\partial x}\left% ({\mu\frac{\partial u}{\partial x}}\right)+\frac{\partial}{\partial y}\left({% \mu\frac{\partial u}{\partial y}}\right)+\frac{\partial}{\partial z}\left({\mu% \frac{\partial u}{\partial z}}\right)$ (3) $\displaystyle u\frac{\partial\left({\rho v}\right)}{\partial x}+v\frac{% \partial\left({\rho v}\right)}{\partial y}+w\frac{\partial\left({\rho v}\right% )}{\partial z}=-\frac{\partial p}{\partial y}+\frac{\partial}{\partial x}\left% ({\mu\frac{\partial v}{\partial x}}\right)+\frac{\partial}{\partial y}\left({% \mu\frac{\partial v}{\partial y}}\right)+\frac{\partial}{\partial v}\left({\mu% \frac{\partial v}{\partial z}}\right)$ (4) $\displaystyle u\frac{\partial\left({\rho w}\right)}{\partial x}+v\frac{% \partial\left({\rho w}\right)}{\partial y}+w\frac{\partial\left({\rho w}\right% )}{\partial z}=-\frac{\partial p}{\partial x}+\frac{\partial}{\partial x}\left% ({\mu\frac{\partial w}{\partial x}}\right)+\frac{\partial}{\partial y}\left({% \mu\frac{\partial w}{\partial y}}\right)+\frac{\partial}{\partial v}\left({\mu% \frac{\partial w}{\partial z}}\right)-\rho g$ (5)

(3) Energy conservation equation

$\displaystyle u\frac{\partial\left({\rho T}\right)}{\partial x}+v\frac{% \partial\left({\rho T}\right)}{\partial y}+w\frac{\partial\left({\rho T}\right% )}{\partial z}=\frac{\partial}{\partial x}\left({\frac{\lambda}{C_{P}}\frac{% \partial T}{\partial x}}\right)+\frac{\partial}{\partial y}\left({\frac{% \lambda}{C_{P}}\frac{\partial T}{\partial y}}\right)+\frac{\partial}{\partial z% }\left({\frac{\lambda}{C_{P}}\frac{\partial T}{\partial z}}\right)$ (6)

Where, $\rho$ is fluid density, in kg/m ${}^{3}$ ; $p$ is pressure intensity, in Pa; and $\mu$ is power viscosity, in $Pa\cdot s$

(4) $\kappa-\varepsilon$ Equations

$\displaystyle\frac{\partial(\rho k)}{\partial t}+\frac{\partial(\rho ku_{i})}{% \partial x_{i}}=\frac{\partial}{\partial x_{j}}\left[{\left({\mu+\frac{\mu_{t}% }{\sigma_{k}}}\right)\frac{\partial k}{\partial x_{j}}}\right]+G_{k}+G_{b}-% \rho\varepsilon-Y_{M}+S_{k}$ (7) $\displaystyle\frac{\partial(\rho\varepsilon)}{\partial t}+\frac{\partial(\rho% \varepsilon u_{i})}{\partial x_{i}}=\frac{\partial}{\partial x_{j}}\left[{% \left({\mu+\frac{\mu_{t}}{\sigma_{\varepsilon}}}\right)\frac{\partial% \varepsilon}{\partial x_{j}}}\right]+C_{1\varepsilon}\frac{\varepsilon}{k}% \left({G_{k}+C_{3\varepsilon}G_{b}}\right)-C_{2\varepsilon}\rho\frac{% \varepsilon^{2}}{k}+S_{\varepsilon}$ (8)

Where, $G_{k}$ refers to the turbulent kinetic energy generated by the average velocity gradient; $G_{b}$ refers to the turbulent kinetic energy generated by the buoyancy effect; $Y_{M}$ refers to the effect of compressible turbulence pulsation expansion on the total diffusion rate; and the turbulence viscosity coefficient $\mu t=\rho C\mu\frac{k^{2}}{\varepsilon}$ .

C1-Epsilon and C2-Epsilon are empirical constants, and their default values are C1-Epsilon $=$ 1.44 and C2-Epsilon $=$ 1.92, respectively.

The transport equation of the standard K- $\varepsilon$ model, where, C1-Epsilon $=$ C1 $\varepsilon$ and C2-Epsilon $=$ C2 $\varepsilon$ .

The standard $k-\varepsilon$ model is the simplest complete turbulence model, and is the model of two equations. To solve two variables, i.e. velocity and length, this standard $\kappa-\varepsilon$ model is only suitable for the simulation of the flow process of complete turbulence.

4.2 Physical model

The model of the heat storage device was established by referring to a complete heat storage structure. The structure of this device is symmetrical, so simplifying the model is to simplify the calculation steps. In the study, the model was established using the heat accumulator on one side. When the 3D model for fluid motion was established, it was reasonably simplified. A half model was built with the central line of a single-phase heat accumulator as the symmetrical axis, by making the gas phase of the heat storage module along the direction of fluid flow, and the symmetrical side has the same flow characteristics. Figure 6 is the three-dimensional view of the heat accumulator model, Fig. 7 shows the structure on the upwind cross-section of the heat dissipation hole.

Figure 6.

3D view of the model of heat accumulator.

Figure 7.

Upwind cross-section of the Heat accumulator.

The physical model of the solid heat storage device was established by setting the boundary conditions with the measured data, in which:

(1)

Dimensions of Heat accumulator: 2960 mm $\times$ 1800 mm $\times$ 3150 mm;

(2)

Dimensions of Heat Dissipation Hole: D-50 mm;

(3)

The air inlet and outlet cabins have the same dimensions, as: 2960 mm $\times$ 1800 $\times$ 600 mm; and

(4)

The casing of the heat accumulator was insulated.

During meshing of the physical model, the meshes in the area around the heat dissipation hole and hole opening were set denser that those in other areas, while in the middle part of the air cabin, the meshes were enlarged, which is to make the simulation model as close to the actual situation as possible, and guarantee the reliability of the simulation and the rationality of the calculation time.

The standard turbulence model $k-\varepsilon$ was used for the fluid in the air duct, and the coupling relationship was solved with the SIMPLE algorithm. For the area near the wall, the standard wall function was used. The turbulent kinetic energy, turbulence dissipation item, and momentum equation were dispersed by the second order upwind scheme.

4.3 Simulation and result analysis

In this part, the air inlet velocity conditions were changed relative to the existing heat accumulator, to simulate the airflow organization, where, the air inlet flow velocity was set to 3 m/s, 6 m/s, 9 m/s, and 12 m/s, respectively.

With the flow state at the air inlet flow velocity of 3 m/s as an example, a qualitative analysis was conducted on the air cabin.

Figure 8.

Flow velocity contour map of the case with air inlet velocity of 3 m/s, and z-0.55 m.

When the air inlet velocity was 3 m/s, the contour map for the velocity at the first 50 mm section of the upwind cross-section of the heat accumulator, is as shown in Fig. 8, and the overall velocity distribution trend was: decreasing progressively while fanwise radiating upward, leftward and rightward. The fluid area was divided into high flow velocity zone, step-descent zone and low flow velocity zone according to the flow velocity. The low speed zone appears in the middle of the high-speed flow field under the air vent, the highest speed is about 480 mm on both sides of the air vent centerline, the maximum value is 1.8 m/s, The lowest speed is the upper and lower corners of the section, the minimum is 0 m/s, the maximum speed difference for the same section is 1.8 m/s, and the average speed is 0.7 m/s. Position is 3/4 above the bottom. A low velocity zone appeared in the middle of the high velocity flow field, under the air inlet. The largest velocity occurred the positions on both sides of the air inlet central line, which were about 480 mm to the air inlet central line. The lowest velocity appeared at left and right upper corners of the cross-section. The velocity difference on the same cross-section was 2 m/s while the average velocity was 0.7 m/s, which appeared at the 3/4 position to the bottom.

The velocity distribution was further observed after the air inlet velocity was changed, and the intervals with the same gradient were set. The changing law of the fluid at different flow velocities on the same cross-section was similar to the case when the air inlet velocity was 3 m/s. With the increasing of the air inlet velocity, the area of the step-descent velocity zone rose increasingly, and the low flow velocity area decreased increasingly as well. From this point of view, the increase of the flow velocity is beneficial for heat dissipation of the heat accumulator in the low-flow velocity area. According to the range of flow velocity, the maximum flow velocity difference across the cross-section increase with the increase of the flow velocity.

In order to understand the specific flow velocity at the inlet of the heat dissipation hole at different flow velocities, the typical heat dissipation hole was selected to output the hole outlet cross-section velocity. Considering the structure of the air supply system is symmetrical and the position of the air outlet is lower, the position of the hole opening was selected as shown in Fig. 9, and the flow velocity are as shown in Fig. 10.

Figure 9.

Arrangement of measuring points on half-phase upwind cross-section.

Figure 10.

Simulated flow velocity at hole port of the heat accumulator under different inlet conditions.

The air flow state in the heat storage device at different flows was simulated by changing the air inlet flow velocity, and the conclusion was drawn as that: for this model, the flow velocity distribution on the upwind cross-section of the storage body is basically fixed when the structure of the heat storage device has been fixed. The lower the inlet flow velocity is, the closer the flow velocities are to each other. In this case, increasing the fan frequency can reduce the area with a low flow velocity, which is conducive to heat release at the flow velocity dead zone of the heat accumulator heating, but there is still a low velocity zone that cannot be reduced. The maximum flow velocity difference also increases, indicating that the air distribution of the heat accumulator is limited by the structure. To improve the air distribution in the heat dissipation holes of the heat accumulator, it is necessary to change the structure of the heat storage device.

4.4 Comparison of experimental and simulation results

4.4.1 Error analysis

The error of test data refers to the difference between the measured value and the real value of the measured parameters during the experiment. Error analysis can be used to evaluate the accuracy of experimental data, find out the affecting factors of the error and its source, and try to eliminate or reduce the error to improve the accuracy of experimental results.

Error can be divided into systematic error, random error and gross error. Systematic errors include the errors caused by the measuring instrument itself, installation and use, test environment, measurement method and operation process. Systematic errors can be eliminated through rigorous experimental process and multiple experiments.

Random errors may cause the fluctuation of measured data values, but scattered data generally show statistical rules. In engineering, data can be sorted out by calculating the average value, as shown in Eq. (9).

$\displaystyle\bar{x}=\frac{x_{1}+x_{2}+\ldots+x_{n}}{n}=\frac{\sum\limits_{i=1% }^{n}{x_{i}}}{n}$ (9)

Where, $x_{1}\cdot,x_{2}\ldots x_{n}$ is the measured data values for each experiment;

$n$ is the number of measurements.

Gross error is caused by the operator’s carelessness, fatigue, inattention, etc., which is manifested in the partial measurement value obviously deviates from the overall measurement result, and it can not be reasonably explained by objective conditions. Experimental personnel strengthen the sense of responsibility, careful operation can avoid the occurrence of gross error.

4.4.2 Comparison and analysis of experimental and simulation results

By comparing the experimental results with the simulation results, the relationship and differences between the two were analyzed. The figure below shows the changes of the air inlet velocity of the heat dissipation hole at the measuring points of the heat accumulator.

Figure 11.

Experimental data.

Figure 12.

Simulation data.

As seen from Figs 11 and 12, the flow velocity at each measuring point was proportional to the fan frequency in both experimental and simulation conditions. Due to uneven upwind surface of the heat accumulator, the velocity field was greatly affected by interference. When the fan frequency was greater than 25 Hz, the simulated flow velocity was larger than the experimental velocity, and the fan frequency was less than 25 Hz, the simulated velocity was less than the experimental velocity. The slope of the experimental velocity is less than the simulation data, and the maximum difference between the experimental velocity and the velocity at the simulated measuring point was not more than 1 m/s. The maximum velocity occurred at the hole channel corresponding to the air inlet, and the minimum velocity appeared at the left upper corner away from the air inlet. The simulation value was slightly higher than the experimental value, but both conformed to the trend of jet velocity attenuation.

By comparing the simulation data with the experimental results, the overall velocity distribution and change trend can better depict the real velocity field, which indicates that the model is correct for the content and purpose of this study. However, the simulation results are relatively high than the measured velocity, as the effect of irregular bumps formed on the upwind surface and surface electric heating wire of the heat accumulator during the construction of the heat storage brick was ignored in the model, which is the main reason for the simulated flow velocity was slightly larger.

5. Optimization of air distribution uniformity of the heat storage device

In order to improve the heat release performance of the solid heat storage device, the concept of air flow organization is introduced in this article. The air flow organization of the solid heat storage device is to reasonably arrange the air supply outlets, return air inlets, and oriented guiding device so that the low temperature air which has been subject to heat exchange flows into multiple heat dissipation hole uniformly in the heat accumulator, following the oriented flow guiding, diffusion and buoyancy lift. The unit flows of all heat dissipation holes tended to be consistent. The temperature decrease speeds of the bricks on the same cross section were synchronous, and the heat stored in the heat storage module could be fully released.

The air flow organization is not reasonable in the current heat storage device: the air enters the air inlet cabin from the air inlet, where it flows in an unorganized state, and enters the heat dissipation holes between the heat storage bodies, which results in obvious difference in the flow between heat dissipation holes, and non-uniform heating of the heat accumulator. In this case, the component damage and safety problems of the heating wire will be caused due to partial excessively high temperature and the stored heat cannot be used fully and efficiently.

5.1 Effect of the air cabin width on the air distribution of the heat storage device

There are no relevant execution standards for the specific setting of the air cabin of the electric heating solid heat storage device. In actual projects, the width of the air cabin of the heat storage device is determined with two considerations, one of which is full heat exchange between air and the heat accumulator, and the other of which is internal maintenance to be carried out by the personnel.

The air cabin width of the heat storage device in this project is 0.6 m. To explore the effect of the air cabin width on the flow distribution uniformity of the device, the air cabin within the flow velocity range of the air inlet was simulated with different widths. The uniformity coefficient of the flow velocity was calculated, and the law of change was observed. The air cabin width was selected as 0.6 m, 1 m, 1.4 m, 1.8 m, 2.2 m, and 3 m, respectively, and the air inlet velocity was taken as 3 m/s, 9 m/s, and 15 m/s to simulate the flow field with different air cabin widths and calculate the velocity difference between them.

Figure 13.

Mesh model with 1 m air reservoir width.

Figure 14.

maximum flow velocity difference at hole opening at different inlet velocities.

Under the conditions with large, medium and small flow velocities respectively, the maximum flow velocity difference at the hole opening of the upwind cross-section decreased with the rise of the air cabin width, and it reached the minimum value when the air cabin width was 2.2 m. At large and medium flow velocities, the maximum flow velocity difference showed an increase. Just judging from the maximum flow velocity difference curves, the flow velocity range was more concentrated when the air cabin width was 2.2 m. The extreme values alone cannot reflect the discrete relationship between the flow velocity and the average. In this study, the relationship between the velocity at the inlet and the air inlet cabin width was explored by calculating the flow velocity distribution uniformity index. The calculation results are as shown in Fig. 15.

Figure 15.

Flow velocity distribution uniformity index on the cross-section at different air inlet flow velocities.

From the figure above, it can be seen that the flow velocity distribution uniformity index increases with the rise of the air inlet cabin width. The change rate of the exponential value tends to be stable when the cabin width reaches 2.2 m. Besides, the larger the flow velocity is, the smaller the flow velocity distribution uniformity index will be. According to the characteristic that the maximum flow velocity difference and the flow velocity distribution uniformity index changed with the air cabin width, it can be considered that the flow distribution uniformity of each heat dissipation hole is better when the air cabin width of the heat storage device in this project is 2.2 m.

Combined with the knowledge learned, the larger the air inlet cabin is, the smaller the effect of the air outlet on the upwind cross-section, the more uniform the flow velocity distribution of all heat dissipation hone on the upwind cross-section of the heat accumulator. When the air inlet cabin width is large enough, so that the whole air cabin becomes a static pressure box, the flow velocity distribution uniformity will no longer be affected by the air cabin width. In the actual project, however, the air cabin width cannot be large enough normally due to limited space. Therefore, we have to seek other methods to improve the air flow distribution uniformity based on the actual situation.

5.2 Effect of air inlet angle on the air distribution of the heat storage device

The air inlet has a great effect on the flow velocity distribution uniformity on the upwind cross-section. In this project, the air inlet dimensions are 500 mm $\times$ 300 mm, the heat accumulator’s dimensions on the upwind cross-section of the heat accumulator are 2960 mm $\times$ 1800 mm, the axial length of the square gradually-expanding opening is 270 mm, and the opening angles are as follows: left and right sides: 45 ${}^{\circ}$ ; upper edge: uptilting by 50 ${}^{\circ}$ ; and lower edge: uptilting by 5 ${}^{\circ}$ . The mesh model for the air inlet is as shown in Fig. 16.

Based on the aspect ratio of the upwind cross-section of the heat accumulator and the position of the air inlet, the opening angle settings of the air inlet are shown in Table 6.

Table 6
Air inlet angle settings

No.	Opening angle
	Left and right sides	Upper edge	Lower edge
1	0	0	5
2	15	20	5
3	25	30	5
4	35	40	5
5	45	50	5
6	55	58	5
7	65	68	5

Figure 16.

Air inlet mesh model.

The flow field with different angles was simulated by selecting the air inlet velocity as 3 m/s, 9 m/s and 15 m/s respectively. Through calculation, the relationship between the flow velocity nonuniformity coefficient and the air inlet angle was determined, as shown in Figs 17 and 18. As seen from the figure, the flow velocity distribution uniformity index at the inlet of the dissipation hole showed an overall decrease trend with the rise of the angle, after the angle was 15 ${}^{\circ}$ /20 ${}^{\circ}$ , under the conditions of different air inlet velocities. Before the angle was 15 ${}^{\circ}$ /20 ${}^{\circ}$ , the flow velocity distribution uniformity index was greatly affected by the air inlet velocity. Combined with the effect of different air flow velocities within the air inlet angle and fan frequency range on the flow velocity distribution uniformity index, it may be considered that the flow velocity distribution uniformity is higher when the angle is 15 ${}^{\circ}$ /20 ${}^{\circ}$ than the case with any other angle value.

Figure 17.

Different air inlet angles and distribution uniformity on the upwind cross-section.

Figure 17 shows the maximum flow velocity difference between the heat dissipation holes on the upwind cross-section of the heat accumulator at different air inlet angles and velocities.

Figure 18.

The maximum flow velocity difference for the cut-off face at different air intake angles.

As seen from the figure above, the maximum flow velocity difference of air inlets on the upwind cross-section had the minimum value when the air inlet angle was 15 ${}^{\circ}$ /20 ${}^{\circ}$ under the same air inlet velocity condition. And, it increased with the rise of the air inlet velocity.

Through the analysis on simulations of different air inlet angles and flow velocities, it is found that changing the air inlet angle of the electric heating solid heat storage device can change the flow velocity distribution at heat dissipation hole openings to a certain extent, but it is not possible to eliminate the effect of the structure position and flow velocity. The greater the air inlet flow velocity is, the larger the maximum flow velocity difference between heat dissipation hole openings on the upwind cross-section will be. The velocity distribution of the heat storage device is still not ideal viewing from the maximum air inlet velocity difference.

5.3 Study on the effect of the addition of a baffle at the inlet on the air distribution of the heat storage device

An ideal air distribution uniformity cannot be obtained only by changing the air inlet opening angle. It is required to reduce the flow velocity at the heat dissipation hole opening near the air inlet, and improve the flow velocity at the heat dissipation hole opening near the flow velocity dead zone. Therefore, adding a flow guiding device in the air inlet cabin of the heat storage device is necessary.

In order to balance the flow of each opening on the cross-section of the heat accumulator, a static pressure box was set at the air inlet of the heat storage device. For the static pressure box, the overall dimensions are 2 m $\times$ 0.3 m $\times$ 1 m (L $\times$ W $\times$ H), the diameter of the circular air hole is 40 mm, and the dimensions of the strip-like air inlet on sides are 0.2 m $\times$ 0.03 m (L $\times$ W). The 3D model of the static pressure box and the mesh division model are shown in Figs 19 and 20.

Figure 19.

3D model of the static pressure box and the mesh division model.

The flow velocity at heat dissipation hole openings on the upwind cross-section of the heat accumulator was analyzed from flow velocity vector and size. For the heat storage device model with the static pressure box added, the simulation was conducted for the cases with the air inlet velocity of 3 m/s, 9 m/s, 15 m/s and 18 m/s, respectively. The flow velocities at heat dissipation hole openings on the upwind cross-section were obtained and compared. Such flow velocities are as shown in Fig. 20. The flow velocity uniformity indexes at openings on the upwind cross-section of the heat accumulator under different air inlet flow velocity conditions were calculated, and the calculation results are shown in Fig. 21.

Figure 20.

Air inlet flow velocities under different air inlet velocity conditions.

Figure 21.

Flow velocity distribution uniformity index.

As seen in the figure, the flow velocities at each measuring point tended to be consistent after the static pressure box was added. The degree to which the flow velocity distribution at heat dissipation hole openings on the upwind cross-section of the heat accumulator was affected by the position of the air inlet structure and the flow velocity was reduced. The maximum flow velocity differences between hole openings under different flow velocity conditions were all decreased. When the air inlet flow velocity was 3 m/s, the maximum flow velocity difference was 0.17 m/s, and the flow velocity distribution uniformity index on the upwind cross-section of the heat accumulator was 0.975. When the air inlet flow velocity a was 9 m/s, the maximum flow velocity difference between hole opening was 0.56 m/s, and the flow velocity distribution uniformity index on the upwind cross-section of the heat accumulator was 0.978. When the air inlet flow velocity a was 15 m/s, the maximum flow velocity difference between hole openings was 1.01 m/s, and the flow velocity distribution uniformity index on the upwind cross-section of the heat accumulator was 0.975. And, when the air inlet flow velocity a was 18 m/s, the maximum flow velocity difference between hole opening was 1.15 m/s, and the flow velocity distribution uniformity index on the upwind cross-section of the heat accumulator was 0.974. From the numerical calculation results, the air flow velocity distribution of the heat storage device of the air supply system was significantly optimized after the static pressure box was added.

6. Conclusions

In this article, experiments were carried out, combined with a heating project, in view of the air distribution uniformity in an electric heating solid heat storage device, and the numerical simulation and optimization of the factors affecting the flow velocity distribution uniformity of the heat storage device was also conducted. The conclusions are drawn as follows:

(1)

In the hot-state brick temperature test, the brick temperatures at different positions of the heat accumulator were initially the same, but showed a significant difference finally. The temperature difference between measuring points 1 and 3 reached 36.4 ${{}^{\circ}}$ C, which proved non-uniform heat release at different positions of the heat accumulator in the heat storage unit due to non-uniform air distribution of the air system.

(2)

In the cold-state flow velocity test, the averaged flow velocity distribution uniformity index of the heat dissipation holes on the upwind cross-section when three fans were running, but the middle fan resistance increased. From the perspective of good operation of fans and air distribution uniformity of the whole heat accumulator, the independent air supply by the separated air cabin based on the modularization of the heat accumulator is conductive to the operation of the unit.

(3)

When the air cabin width was greater than 2.2 m, and the air inlet angle was 15 ${}^{\circ}$ /20 ${}^{\circ}$ , the flow velocity distribution uniformity on the upwind cross-section of the heat accumulator was better, but it was significantly affected by the site space and the air inlet flow, and the air inlet flow velocity distribution uniformity was limited.

(4)

By adding a static pressure box with a conductive effect at the air outlet, the flow velocity difference on the upwind cross-section caused by the air supply structure and characteristics was reduced, eliminating the effect of site space. As the result, the uniformity index of the air system was increased by 13.2%, and the heat dissipation flow velocity on the upwind cross-section of the heat accumulator were more uniform after such improvement.

Footnotes

Acknowledgments

This work is supported by Hebei innovation capability improvement project (19244503D).

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A study on optimization of the air supply system for the electric heating solid heat storage unit

Abstract

Keywords

1. Introduction

2. Electric heating solid heat storage unit

2.1 Introduction of the system and operation principle

3.1 Experimental purpose

3.2 Experimental platform

3.2.1 Equipment and parameters of the heating system

Table 1 Parameters for selection of fan types

3.3 Experimental scheme

3.3.1 Test items

Table 3 Main meters and parameters

3.4.1 Half-boiler flow velocity test

Table 5 Experimental temperature test results of measuring points 1 to 3

4.1 Control equation

4.4.1 Error analysis

5.1 Effect of the air cabin width on the air distribution of the heat storage device

Table 6 Air inlet angle settings

Footnotes

Acknowledgments

References

Table 1
Parameters for selection of fan types

Table 3
Main meters and parameters

Table 5
Experimental temperature test results of measuring points 1 to 3

Table 6
Air inlet angle settings