Calculation of Three Dimensional Incompressible Turbulent Flow Field in Impeller of Overload Centrifugal Pump

0 Preface Low speed centrifugal pumps with a rotational speed between 30 (even smaller) and 80 have the characteristics of low flow and high lift. 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 two-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 equations Centrifugal pump impeller rotation at a uniform angle, the establishment of synchronous rotation with the impeller and the z axis coincides with the axis of rotation of the rectangular Cartesian coordinate system, the relative flow impeller in the steady flow [5]. According to Raynaud's theory, the mean turbulent current momentum Reynolds equation at this time can be written as a general form for calculation with continuity equation Ex + Fy + Gz = S (1) where P - pilot pressure, including influent Pressure p and centrifugal force FCx, FCy - Coriolis Force FCx = -2vω FCy = 2uω The k-ε turbulence model is used in combination with engineering practice [6] (2) μef - effective viscosity coefficient i = 1, The turbulent kinetic energy generation term Gk for 2,3 (x, y, z directions) is defined as Gk = μt (uy + vx) 2+ (vz + wy) 2+ (wx + uz) 2 + 2 (u2x + v2y + w2z) The constants in the above formulas are: Cμ = 0.09, σk = 1.0, σε = 1.3, C1 = 1.44, and 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 Solution of Control Equation 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 method of generating turbulent kinetic energy based on the standard k-ε turbulence model is better. Is also relatively simple. Referring to the computational experience of Howard [7] and others, the source term (4) is added to the standard k-ε equation where τω is the component of the shear stress perpendicular to the acceleration direction τθ, which is perpendicular to the curvature of streamline The stress component ρ - the radius of curvature In the solution of ρ, suppose the coordinate axis ζ coincides with the streamline near the wall, which of course is compatible with the mesh used in this paper. Thus, the source terms of the k-ε equation are given as follows: Sk = Gk-ρε + Gc (6) 2.2 Mesh generation In this paper, we use a point on a given grid wall with the corresponding first interior point And the distance between the two lines and the curve of the wall as the boundary conditions, by solving the elliptic differential equations generated 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 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. Fig.1 Turbine grid without overloading centrifugal pump 2.4 Discrete and solution of control equations Second-order central difference discrete diffusion term and source term; mixed differential discrete convection term [6]. The discrete algebraic equations are solved iteratively by implicit alternating direction (ADI). 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 of 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 no-slip conditions, that is, the relative speed w = 0; pressure taken as the first

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