Thermodynamic Analysis and Calculation of the Drying and Heating System of Automatic Stirring Equipment

Automatic stirring equipment is a kind of important machinery in building construction projects, and its power and fuel consumption take the largest proportion in the total energy consumption of all kinds of building construction equipment [1-5]. The installed power of automatic stirring equipment with an annual mixture output of 200,000 tons can reach more than 820 kW, and it will consume at least 5 million kWh of electricity every year. At present, more than 20,000 automatic stirring equipment of different types have been put on stream in China [6-11]. In this context, how to effectively reduce the power consumption of automatic stirring equipment is an issue requiring the attention from the construction machinery industry [12-15]. The function of DHS is to heat and dry the cold materials, it is the core component of automatic stirring equipment, and analyzing its thermodynamics is a necessity for improving the heating and drying efficiency of the drying drum and reducing its energy consumption; it is the key to increase the efficiency of the automatic stirring equipment [16-23].

Ruby and Sutrisno [24] firstly discussed the problems of how to establish and solve heat equation models, then, it built a heat equation model for rice dryer, and employed the variable separation method to solve it; and the simulation and experiment were conducted under both steady and unsteady state conditions. Souza et al. [25] analyzed a developed non-traditional rotary dryer and used a two-phase model and a set of constitutive equations to describe the drying process, the equations were numerically solved using normal configuration technique, experiment proved that the simulation results were in good agreement with the experimental data. Novak et al. [26] studied the motion of fabrics in the drum of household heat pump drum-type dryer and its influence on the performance parameters of the dryer under different load masses and drum speeds; then multiple regression analysis was performed and a condensate water mass flow model was constructed, as a function of drum speed, load mass, and drying stage, its results can optimize the operating parameters of the dryer, including energy efficiency, drying time for per kilogram of fabric, and condensate water mass flow. For the drying cylinder in the dryer section of paper machine, in order to get a cross-sectional shape of channels with better drainage and heat transfer performance, Dong et al. [27] selected channels with two different cross-sectional shapes to study the steam flow and heat transfer in the channels and compare the changes in heat transfer coefficient of the channels under different working conditions, and the results showed that the heat transfer effect of U-shaped channels in the multi-channel dryer was better than that of other channels. Kumar et al. [28] analyzed the thermodynamics of natural convection dryers made of heat storage materials with and without sensible heat, aiming to take pebbles as sensible heat storage medium to improve the performance of the dryer, the paper also gave energy and exergy analysis to investigate the loss size of pebbles and whether they are suitable for acting as the sensible heat storage material. Singh et al. [29] used 3D computational fluid dynamics simulation to study the gas-solid fluidization behavior and heat transfer characteristics in a non-slit rotating solid bed; in ANSYS FLUENT 14.5, numerical simulation was carried out based on the Euler-Eulerian method, and the experimental results showed that, main factors affecting the volume of reactor include air inlet velocity, inlet pressure, temperature, and heat transfer coefficient; after comparing the numerical calculation results with experimental results, it is found that the maximum error of temperature was 6.98%.

Compared with foreign countries, the domestic drying and heating technology still lags behind. After reviewing the studies of some scholars concerning DHS, it’s found that the existing empirical thermodynamic formulas generally take certain working conditions as prerequisites, and substituting relevant parameters of DHS into calculation can cause large errors, so we need more accurate numerical simulation methods to analyze the working process of DHS and study the changes in its heat efficiency and energy consumption. For this reason, this paper performed thermodynamic analysis and calculation on the DHS of automatic stirring equipment. The second part of the paper analyzed the material ratio of the automatic stirring equipment. The third part divided the drying and heating process of mixture into three stages of mixture preheating, mixture drying, and heating mixture to the working temperature; and measured and calculated the energy consumption of the DHS. The fourth and fifth parts calculated the heat consumption of fuel combustion, the consumption rate of the fuel, and the heat efficiency of DHS. The last part gave the thermodynamic analysis results of the DHS of automatic stirring equipment, and verified the effectiveness of the proposed measurement and calculation methods.

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Figure 1. Division of different processing sections of drying drum

The drying and heating process of stirred mixture can be divided into three stages: mixture preheating, mixture drying, and heating mixture to the working temperature, and the three stages respectively correspond to the three processing sections A, B, and C of the drying drum. Section A is for preheating the materials to be stirred, it is located on the side close to the outlet of hot gas and water vapor. Section B is for drying the mixture, it is located in the middle part of the drying drum. Section C is for heating the mixture to the working temperature, and it is located at the side of the hot gas inlet. Figure 1 shows the division of the different processing sections of the drying drum.

The hot gas used for heating the mixture enters Section A from Section C, then the residual heat, plus the water vapor generated in Section B, can be used to preheat the cold mixture that has just entered Section A. The heat consumed by preheating includes two parts: the heat consumed by preheating the mixture, and the heat consumed by preheating the water contained in the mixture. Assuming: W'_A represents the total amount of heat consumed by preheating the stirred cold mixture per unit time, W''_A represents the amount of heat absorbed by the preheating of water within per unit time, D_n represents the specific heat of the mixture, D_q represents the specific heat of water, τ₁ represents the temperature when the materials are just fed, τ₂ represents the temperature when the water is strongly evaporated, then Formula 4 gives the formula for calculating the heat consumed by preheating the mixture:

$W_{A}^{'}={{D}_{n}}{{H}_{n}}\left( {{\tau }_{2}}-{{\tau }_{1}} \right)$       (4)

Formula 5 gives the formula for calculating the heat consumed by preheating the water contained in the mixture:

$W_{A}^{''}={{D}_{q}}{{H}_{q}}\left( {{\tau }_{2}}-{{\tau }_{1}} \right)$      (5)

Therefore, the heat consumption of the stirred mixture in Section A is:

${{W}_{A}}=W_{A}^{'}+W_{A}^{''}$      (6)

The heat consumption of preheated mixture in Section B contains two parts: the heat consumed by evaporating the water contained in the mixture, and the heat consumed for heating the water vapor to the temperature of output hot gas. Assuming: W'_B represents the amount of heat consumed by evaporating the water contained in the mixture within per unit time, W''_B represents the amount of heat for heating the water vapor to the temperature of wasted gas, ζ represents the latent heat for forming water vapor, D_u represents the specific heat of water vapor, τ_A represents the temperature of hot gas output from the drying drum, then the amount of heat consumed by evaporating the water in the mixture can be calculated by Formula 7:

$W_{B}^{'}={{H}_{q}}\zeta $     (7)

The heat consumed for heating water vapor to the temperature of output hot gas can be calculated by Formula 8:

$W_{B}^{''}={{D}_{u}}{{H}_{q}}\left( {{\tau }_{a}}-{{\tau }_{2}} \right)$      (8)

Therefore, the total heat consumption of mixture in Section B is:

${{W}_{B}}=W_{B}^{'}+W_{B}^{''}$      (9)

The mixture heated to the working temperature is output from Section C, assuming τ₃ represents the temperature when the materials are discharged, then the heat consumption of mixture in Section C can be calculated by Formula 10:

${{W}_{C}}={{D}_{n}}{{H}_{n}}\left( {{\tau }_{3}}-{{\tau }_{2}} \right)$       (10)

To sum up, the effective total heat required by the DHS of the automatic stirring equipment can be calculated by Formula 11:

${{W}_{TOTAL}}={{W}_{A}}+{{W}_{B}}+{{Q}_{C}}$       (11)

Assuming: W_HR represents the total amount of heat supplied to the drying drum during fuel combustion, τ'_D represents the fuel combustion temperature, when the hot gas produced by fuel combustion exchanges heat with the cold mixture, the amount of heat released for per 1°C temperature drop of the hot gas can be calculated by Formula 12:

${{w}_{0}}=\frac{{{W}_{HR}}}{\tau _{D}^{'}-{{\tau }_{A}}}$       (12)

In the process of drying and heating the mixture, the heat consumption of mixture heating, and the heat loss of the drying drum wall are the main factors for the changes in the heat of hot gas. Assuming τ'_C represents the hot gas temperature of Section C, then the value of temperature drop of the hot gas can be calculated by Formula 13:

$\Delta {{\tau }_{C}}=\frac{{{W}_{C}}+{{W}_{HL}}}{{{w}_{0}}}$      (13)

$\tau _{C}^{'}=\tau _{D}^{'}-\Delta {{\tau }_{C}}$      (14)

Assuming: τ'₃ represents the hot gas temperature in Section B when the water contained in the mixture starts to evaporate, then the following heat balance equations can be constructed:

${{w}_{0}}\left( \tau _{C}^{'}-\tau _{B}^{'} \right)=W_{B}^{'}+{{D}_{u}}{{H}_{w}}\left( \tau _{B}^{'}-\tau _{B}^{{}} \right)$        (15)

$\tau _{B}^{'}=\frac{{{w}_{0}}\tau _{C}^{'}+{{D}_{u}}{{H}_{q}}-W_{B}^{'}}{{{w}_{0}}+{{D}_{u}}{{H}_{q}}}$        (16)

At last, τ_A, the temperature of mixed gas containing hot gas and water vapor discharged from Section A was calculated from the perspective of heat balance, then there is:

${{w}_{0}}\left( \tau _{2}^{'}-{{\tau }_{a}} \right)+{{D}_{u}}{{H}_{q}}\left( \tau _{2}^{'}-{{\tau }_{a}} \right)={{W}_{\tau }}$         (17)

Combining with Formula 13, we can get:

${{\tau }_{a}}=\frac{\left( {{w}_{0}}+{{D}_{u}}{{H}_{q}} \right)\tau _{2}^{'}-{{W}_{1}}}{{{w}_{0}}+{{D}_{u}}{{H}_{q}}}$         (18)

According to the law of energy conservation, the heat generated by fuel combustion satisfies equation W_l=F_k+n_gD_gτ_g + n_xD_xτ_x, then the total heat consumption of per unit time satisfies equation W=W_l×n_τ; the effective utilization rate of heat of Section A can be calculated by Formula 25:

${{w}_{A}}=\frac{{{W}_{A}}+{{D}_{u}}{{D}_{q}}\left( \tau _{B}^{'}-{{\tau }_{A}} \right)}{W}\times 100%$        (25)

The effective utilization rate of heat of Section B can be calculated by Formula 26:

${{w}_{B}}=\frac{{{W}_{B}}+{{D}_{u}}{{D}_{q}}\left( \tau _{B}^{'}-{{\tau }_{B}} \right)}{W}\times 100%$        (26)

The effective utilization rate of heat of Section C can be calculated by Formula 27:

${{w}_{C}}=\frac{{{W}_{C}}}{W}\times 100%$      (27)

The heat loss rate of the drying drum wall can be calculated by Formula 28:

${{w}_{HL}}=\frac{{{W}_{HL}}}{W}\times 100%$       (28)

The heat loss rate of mixed gas containing discharged hot gas and water vapor can be calculated by Formula 29:

${{w}_{A}}=\frac{{{W}_{A}}}{W}\times 100%$       (29)

In summary, the heat efficiency Ω of DHS of the automatic stirring equipment is the sum of the effective heat consumption of each processing section, namely:

$\Omega ={{w}_{A}}+{{w}_{B}}+{{w}_{C}}$      (30)