Research on Thermal Balance Design of Mechanical Seals in Slurry Pumps and Optimization of Water Tank Dimensions

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Abstract: Based on the theories of thermodynamics and fluid mechanics, this study developed a thermal balance model for the mechanical seal system of slurry pumps, and proposed a design method for minimizing the surface area of cylindrical water tanks, using the shaft diameter (D), rotational speed (n), and medium temperature (T_{\text{in}}) as input parameters. Through theoretical derivation and practical verification, it ensures that the temperature rise of the water tank (\Delta T \leq 55^\circ \text{C}), providing a basis for rapid selection in engineering applications. I. Introduction The thermal balance of the mechanical seal system in slurry pumps is crucial for its stable operation. Properly designing the thermal balance of mechanical seals and optimizing the size of the water tank can effectively improve the performance and reliability of slurry pumps. This article conducts an in-depth study on this topic. II. Thermal equilibrium theoretical model (I) Heat generation mechanism The total heat generation power (Q_{\text{total}}) of a mechanical sealing system consists of frictional heat and disturbance heat, with the calculation formula being: {\text{Frictional heat}} + \underbrace{\mu{\text{water}} \left( \frac{\pi D n}{60 \delta} \right)^2 \cdot \pi D L \delta}_{\text{Disturbance heat}}. Here, (\mu = 0.08) for a cemented carbide friction pair ； ( P_c = 0.5 , \text{MPa} ) (end face specific pressure) ； ( \delta = 6 , \text{mm} ) (seal chamber gap) ； ( L = 0.15 , \text{m} ) (length of the sealed chamber). (II) Heat dissipation mechanism: The heat dissipation power is determined by both the convective heat dissipation from the water tank and the conductive heat dissipation from the pump, and is expressed as: {\text{Water tank heat dissipation}} + \underbrace{\frac{\Delta T}{R{\text{cond}}}}{\text{Pump conductive heat dissipation}}. Here, (h{\text{water}} = 80, \text{W/(m}^2\text{·K)}), which is the coefficient of natural convection heat transfer ； ( R_{\text{cond}} = 0.274 , \text{K/W} ) (conduction thermal resistance including contact thermal resistance). III. Case Study Verification (Shaft diameter: 100 mm, Rotational speed: 730 rpm)
(A) Input Parameters
Parameter Value: Shaft diameter (D): 0.1 m; Rotational speed (n): 730 rpm; Medium temperature (T_{\text{in}}): 30°C
(B) Thermal Balance Calculation
Values for heat generation: Frictional heat (Q_{\text{friction}}): 192 W; Vortex heat (Q_{\text{vortex}}): 153 W; Total heat generation (Q_{\text{total}}): 345 W
Values for heat dissipation: Heat dissipation through the water tank (Q_{\text{tank}}): 224 W; Heat conduction from the pump (Q_{\text{pump}}): 16.9 W; Total heat dissipation (Q_{\text{cooling}}): 240.9 W
(C) Temperature Rise Verification and Recommended Water Tank Size
The temperature rise is calculated using the formula (ΔT = \frac{Q_{\text{total}}}{\rho_{\text{water}} C_p Q_{\text{flow}}} + \frac{Q_{\text{total}}}{h_{\text{water}} S_{\text{tank}}}), resulting in a temperature rise of ΔT = 52.3°C, which is within the limit of 55°C. The recommended size for the water tank is a diameter of 280 mm and a height of 350 mm. IV. Universal Design Model (I) Objective Function and Constraints The objective function is ( \min \left( S_{\text{tank}} = \pi D_{\text{tank}} H_{\text{tank}} + \frac{\pi D_{\text{tank}}^2}{2} \right) ), while the constraints include: ( \Delta T \leq 55^\circ \text{C} ) and thermal siphon flow rate ( Q_{\text{flow}} \geq 1.5 , \text{L/min} ). (II) Parametric Design Formulas These formulas are applicable for shaft diameter ( D \in , \text{mm} ), rotational speed ( n \in , \text{rpm} ), and medium temperature ( T_{\text{in}} \in ^\circ \text{C} ). V. Recommended Dimensions Table for the Engine: Diameter (D) (mm), Rotational Speed (n) (rpm), Tank Diameter (D_{\text{tank}}) (mm), Tank Height (H_{\text{tank}}) (mm): 60, 580, 180, 220; 100, 730, 280, 350; 120, 1450, 400, 450. VI. Conclusions and Recommendations: Model effectiveness: Temperature rise error in practical applications