Numerical simulation on geometrical parameters for closed sump

The closed sump is a typical inlet passage of middle and small pumping station. It has the characteristics of low channel height, small foundation excavation depth, simple structure, a single cross sectional shape changes, ease of construction and other features, so more and more attention and application has been paying on this closed sump in pumping station project. However the flowing pattern within the closed sump is complex, the design is not perfect in some respects, the structure size does not be optimized. Based on the background for renewal and transformation of a pumping station, according to the three-dimensional incompressible fluid Reynolds-averaged N-S equations, the RNG k-e model, the CFD technology. The study on the draught in closed sump might reduce the length of pump shaft to enhance the stability of the pump unit operation. The results reveal the effect of the change of the height of plate. The turbulence in back wall might cause vortex when the height is high. The height of plate had be recommended control in 0.65D-0.85D.The better parameter combination of geometry of closed sump had be given through comparing the results of the orthogonal test and the comprehensive test. The floor clearance should be control in 1.0D. (D is the diameter of flared pipe)


Introduction
The closed sump comes from the open sump with a plate. It have double features of traditional sump and inlet conduit due to the quartet geometric shape and the environment with pressure. So by comparison, it has the unique characteristics of low channel height, small foundation excavation depth, simple structure, a single cross sectional shape changes, ease of construction and other features [1~5], so more and more attention and application has been focused on this closed sump at pumping station project [6~10].
Jiangang Feng [10] put forward that the design of intake sump should make flow smooth-going, no harmful vortex in order to ensure the safe operation of the pump unit. Songshan Chen [11] designed five different suction open height to observe the inlet flow pattern. Charles [12] put forward the velocity in sump should be control near 0.3m/s. Iverson [13] gave the value range of draught for high specific speed pump. Matahel Ansar [14] for the flow pattern in rectangular sump in some inlet conditions. For eliminate vortex bell attached under the bottom, the experiments also designed some vortex suppression program of separator. Flow pattern of the closed sump and hydraulic performance of five different 1 Corresponding author: CHENG Li(1975-), male, PhD, Professor heights of the closed sump had be analyzed orthogonal test had be set to study the geometrical parameters of the closed pump.

Mathematical Model
Calculations are performed using the commercial code CFX ® . The numerical model is based on the Reynolds-Averaged Navier-Stokes (RANS) equations with the RNG k-ε model to calculate the Reynolds stresses. First-order upwind discretizations are used for the convective terms and turbulent kinetic energy and dissipation, while a second-order central differencing scheme is used for the diffusive terms. The temporal discretization is second-order implicit. The SIMPLE algorithm is used for the pressure-velocity coupling. Sliding interfaces up-and downstream of the impeller allow the impeller to rotate with respect to the inlet and stator. The flow in the impeller is solved in the rotating frame of reference. To this end the apparent Coriolis and centrifugal forces are added to the RANS equations as source terms.
Two basic calculation methods are adopted. The first one is a quasi-steady approach in which the flow is assumed steady in its corresponding reference frame. In this multiple reference frame (MRF) method, the transient effect of the rotor-stator interaction is neglected. The convergence criterion for all equations is set to 10 -4 . A solution normally serves as a good initial solution for the second, truly unsteady, moving mesh method. In this method, the connections between rotating and stationary part are updated each time step. The transient solution is monitored as time progresses until the solution becomes periodic at blade passing frequency.

numerical simulation
The numerical domain consists of the inlet and outlet passages, the axial flow impeller with three blades and the diffuser with seven vanes. Inflow and outflow boundaries are located sufficiently far away from the pump not to influence the flow characteristics. The extent of the domain in upstream direction is especially important to allow for inlet flow recirculation at part load. Another important part is the tip clearance gap between the impeller blades and the casing. A number of layers of cells are placed in this region to allow for leakage flow over the blade tips.
Using an extrusion method, an O-type grid of hexagonal cells is created around the impeller and stator blades to ensure good mesh quality in terms of size and skewness. Because of the complex topology of the pump, the interior of the domain is filled with an unstructured mesh of tetrahedral cells.
A mesh-sensitivity study was carried out to assess the required mesh density. Several grids were considered, ranging from a total number of cells of 2×10 5 up to 2×10 6 , where care was taken that y + values at the solid boundaries remained favorable. No further convergence was obtained for grids with more than 1.5×10 6 cells. The inlet boundary condition is specified as a uniform velocity whereas at the outlet an outflow boundary condition is applied which allows for non-uniformity in both velocity and pressure. No-slip boundary conditions and wall functions are used for the solid walls.

Calculation Results
The geometric parameters of sump are shown in Fig3. So a research about the height of the plate had be taken first. In order to reduce the influence of other geometry parameters, larger geometry parameters of the sump had be set. The calculation schemes are shown in Table 1.Five different heights of plate had be set to analyze the changes of hydraulic performance.    this orthogonal test. Preferable scheme in theoretical analysis is the parameter combination which was analyzed through observing the Ki. In pump sets, pump assembly efficiency, uniformity of velocity and average angle of velocity are the index which were bigger is better. So the preferable scheme in theoretical analysis comes from the level which the K is largest. However the preferable scheme in theoretical analysis is not in the orthogonal test which reflected the superiority of the orthogonal test.  Interaction might exist in factors. One factor changed may change the influence of other factors. So the preferable scheme in theoretical analysis should be verified. If the results are better than the preferable scheme in test, the preferable scheme in theoretical analysis should be the better scheme. Otherwise the preferable scheme in test might be the better scheme.

Comprehensive test
The table given three preferable schemes in theoretical analysis is A2B2C4D3, A2B3C3D3 and A2B3C4D3.A2 and D3 is the better level in the three schemes. B and C have two better levels. So a 2×2 comprehensive test was designed to verify the results which shown in Table 6. The better parameter combination had be given in Table 7. Through comparing the results of the orthogonal test and the comprehensive test. The floor clearance should be control in 1.0D.

Conclusion
Based on the three-dimensional numerical simulation, the effect of the height of plate and the effect of all geometrical parameters were studied. The research results can be applied in the similar closed sump of pumping stations. The hydraulic performance would be better when the height of plate is lower. The height of plate should be controlled in 0.65D-0.85D.
The better parameter combination of geometry of closed sump had be given through comparing the results of the orthogonal test and the comprehensive test. The floor clearance should be controlled in 1.0D.