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    Centrifugal pumps with a low specific speed of more than 30 (even less) to 80 have a low flow rate and a high head. The shaft power characteristics of the curve is on the rise, resulting in easy to burn out the motor at run time. As it is widely used in industrial and agricultural production, it caused huge losses. Literature [1] proposed a design method of non-overload centrifugal pump to ensure that the shaft power does not exceed a maximum value in the entire flow range, thus preventing motor overload. Its theoretical basis is that the exit angle of the blade is equal to the absolute flow angle of the exit of the blade. The angle of its leaves than the ordinary centrifugal pump to large, curved leaves more serious.
Although the design of a non-overloaded centrifugal pump is discussed in detail in [1], its internal flow characteristics have not yet been demonstrated. In [2], the two-dimensional turbulence in the impeller with rotation and curvature is approximated by the boundary layer. Wu et al. [3] calculated the turbulence in the impeller under design and non-design conditions. In [4] A kind of advanced vortex method is used to solve the two-dimensional unsteady flow in the impeller after being discretized by finite difference. In view of the fact that there is no mature calculation model at home and abroad, this paper still uses the two-equation turbulence model theory based on Reynolds-averaged method to calculate the turbulent flow in the impeller of over-load centrifugal pump for the first time. The dual equation model considers the convection and diffusion of two turbulent flows and their changes with time. It can describe the main physical features of many flows in a more realistic way and is one of the most in-depth and extensive studies in recent years.
1 control equation
Set the centrifugal pump impeller to rotate at a uniform angular velocity to establish a rotating rectangular coordinate system that rotates synchronously with the impeller and the z-axis coincides with the impeller axis. The relative flow in the impeller is a constant flow [5]. According to Raynaud's theory, the average turbulent momentum Reynolds equation at this time can be written together with the continuity equation as a general form for calculation
P - pilot pressure, including water pressure p and centrifugal force
FCx, FCy - Coriolis Force FCx = -2vω
FCy = 2uω
Combined with engineering practice k-ε turbulence model [6]
(2)
(3)
μef - effective viscosity coefficient
i = 1,2,3 (x, y, z direction)
Turbulence kinetic energy generation term Gk is defined as
2 (u2x + v2y + w2z)
σε = 1.3, C1 = 1.44, C2 = 1.92.
According to the chain guide law, the control equations in Cartesian coordinates can be transformed into the control equations in arbitrary curvilinear coordinate system without further derivation here.
2 control equations to solve
2.1 Correction of k-ε Turbulence Model Considering Rotation and Curvature In order to consider the influence of rotation and curvature, previous studies show that the correction of turbulence kinetic energy based on the standard k-ε turbulence model is better and Simpler. Referring to the computational experience of Howard [7] and others, the source term is added to the standard k-ε equation
(4)
Where τω is the shear stress component in the direction perpendicular to the acceleration τθ is the shear stress component perpendicular to the curvature of streamline Ï is the curvature radius When Ï is assumed, the coordinate axis ζ coincides with the streamline near the wall, Of course, this is also compatible with the grid used in this article. From this we can get the source terms of k-ε equation as follows
2.2 Mesh Generation - In this paper, the distance between a point on a given grid wall and the corresponding first interior point and the angle between the two lines and the wall curve are used as boundary conditions. By solving the elliptic Derivation of differential equations and grid. No overloading Centrifugal pump impeller grid shown in Figure 1 (the pump parameters: flow qV = 15m3 / h, head H = 34m, efficiency η = 55%, speed n = 2860r / min, the number of leaves 4).
2.3 Algorithm - For the incompressible fluid, there is no pressure field display equation, making the solution of the velocity field is difficult to meet the continuity equation.
The SIMPLE class of algorithms successfully solved this problem by establishing algebraic correction equations for pressure and velocity. The SIMPLE-C algorithm takes into account the influence of neighboring nodes when deriving the correction equation, which is more reasonable than SIMPLE.
In order to ensure the coupling of velocity field and pressure field and prevent the occurrence of pressure sawtooth wave, a staggered grid is adopted.
2.5 Boundary conditions The relative speed of imports is set by the law of conservation of mass and the non-rotationality. Pressure is assumed to be evenly distributed on the inlet cross section. The value of turbulent kinetic energy is taken as 0.5% -1.5% of the average kinetic energy at the inlet. The turbulent viscosity of the inlet is chosen according to the characteristic length at the inlet. The turbulent kinetic energy dissipation rate at the inlet is calculated according to the turbulent kinetic energy and the length of the inlet. The velocity at the exit is deduced from the velocity of the upper layer of the grid points, and then corrected proportionally according to the conservation of mass. The other physical quantities are taken as the values ​​of the upper layer of the grid points. Solid wall to meet the conditions of no slip, that is, the relative speed w = 0; pressure to take the second type of boundary conditions, that is p / n = 0; turbulent wall conditions using wall function boundary conditions.
3 Calculation results
3.1 Cross-section Features - Figure 2 shows a network of cross-sections of the cross-sectional velocities around, near, and in the vicinity of the inlet of the above-mentioned no-overload impellers (properly rotated in the direction of impeller rotation). It can be seen that the relative speed of the impeller is poorly distributed in the cross section. This is closely related to the structural features of the impeller such as larger curvature of the blade, narrow and long runner, serious vortexing of the blade. At the same time, the turbulence model used in this calculation, which takes into account the rotation and curvature correction, is not accurate in simulating strong and strong meandering flow, which partly reduces the simulation accuracy. However, we can still see that this simulation reflects the fact that the relative velocity of the liquid is larger near the back side (suction side) of the blade than near the working face (pressure side), and the speed near the rear cover of the impeller is higher than that near the front cover. All of these show that the impeller's external characteristics are closely related to the structure of the impeller: the structure determines the internal flow state, and the internal flow is reflected in the external characteristics. This provides a more reliable performance prediction method for further optimization of the design.
Figure 3 for the impeller near the entrance, the middle section and the outlet near the cross-section pressure network diagram. The figure shows that the pressure near the pressure surface is higher than the pressure near the suction surface, and the pressure is increased rapidly near the exit. It complies with the principle of impeller work and shows the same pressure distribution on the cross section as the relative velocity distribution of the impeller one side.
In this paper, the three-dimensional incompressible turbulent flow field in a centrifugal pump impeller without overload is calculated for the first time both in China and abroad. It is found that the flow in the impeller without over-load centrifugal pump has the following characteristics: the relative velocity decreases gradually with the flow passage; reflux occurs near the inlet; The pressure near the suction surface is higher than that near the suction surface; the pressure increases rapidly near the exit port and there is a secondary flow phenomenon near the exit port. These phenomena not only reflect some basic features of the impeller's inflow but also reveal some particularities of the inflow of the impeller without overloading, which shows that different design concepts produce different hydraulic properties, and different external characteristics correspond to different inflow fields , Change the flow model that is to change the pump performance, the results of this paper laid the foundation for the optimal design of non-overload centrifugal pump.
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Ex + Fy + Gz = S (1)
In the formula Gk = μt (uy + vx) 2+ (vz + wy) 2+ (wx + uz) 2+
The constants in the above formulas are: Cμ = 0.09, σk = 1.0, Sk = Gk-Ïε + Gc (5)
(6) Figure 1 No overload centrifugal pump impeller grid
Discrete 2.4 Solving equations with second order central difference discretization <br> diffusion and source terms; discrete differential mixed convection term [6]. The discrete algebraic equations are solved iteratively by implicit alternating direction (ADI). Figure 2 section speed
Relative velocity vector between the blades between the blade 3.2 <br> flow characteristics shown in Figure 4 can be seen near the inlet of the impeller with a reflux; relative rate decreases the flow channel; this figure also showing a vicinity of the impeller outlet with the present Impeller rotation direction of the secondary flow characteristics, which is related to the small flow of the centrifugal pump, high lift external characteristics, indicating that the pump efficiency than the pump without secondary efficiency decreased, reflecting the efficiency Reduce the shaft design power reduction. Figure 3 section pressure
Figure 4 speed vector
Pressure characteristics between the leaves shown in Figure 5. The pressure characteristics reflected in the figure are related to the larger curvature of the impeller blades and the pressure conditions on the wall surface of the blade used in this calculation. However, we still see the basic characteristics of pressure on the work surface (pressure surface) of the impeller and the larger impeller at the exit. Figure 5 pressure
4 Conclusion