3D numerical simulation of the turbulent flow in an inducer.

Anton, Liviu ; Stuparu, Adrian ; Muntean, Sebastian 等

1. INTRODUCTION

The inducer is an axial impeller which is mounted on the same shaft with the impeller of a pump. By producing a supplementary specific energy on the inlet of the impeller of the pump, because of the rising of the pressure over the vaporising pressure, it prevents or reduces the cavitation. The inducer is used for the pumps with severe suction condition and it has a "sacrificial role", (Garay, 1996). It will be replaced after a certain operating time and that is why the technology for its execution has to be simple and economical. To use straight hydrofoil cascade for the construction of the blades of the inducer satisfies these requirements.

The aim of this paper is to study the structure of the flow given by the use of a straight hydrofoil cascade for the manufacturing of the inducer blades. This study is performed by analysing the stream trace distribution inside the inducer.

We numerically investigated the flow in an inducer, which has two blades manufactured from a straight hydrofoil cascade.

In order to validate the numerical investigations of the flow, the pressure distribution along the blade is compared with the experimental pressure distribution obtained from the investigations performed in a test rig upon the inducer.

2. COMPUTATIONAL DOMAIN, FLOW EQUATIONS AND BOUNDARY CONDITIONS

The computational domain, figure 1, was generated using the pre-processor GAMBIT from FLUENT, based on the existing geometry.

The geometrical characteristic of the blades of the inducer and the investigated operating condition are given in table 1, where we have informations about the significant diameters of the inducer, the interior diameter, d, and the exterior diameter, D, and the thickness of the hydrofoil, s, used for the blades.

The investigated inducer has two blades and it is numerical investigated while it is operating in air with a given rotational speed, n, and at a certain flow rate, Q.

The generated mesh for the computational domain is structured and has 460,000 cells, (Mejri et al., 2006).

[FIGURE 1 OMITTED]

For the flow analysis presented in this paper we consider a 3D turbulent flow model. A steady relative 3D flow is computed:

[nabla] x [??] = 0 (1)

[rho] d[??]/dt = [rho]g - [nabla]p + [mu][DELTA][??] (2)

The numerical solution of flow equations (1) and (2) is obtained with the expert code FLUENT 6.3, (Fluent, 2001), using a Reynolds-averaged Navier-Stokes (RANS) solver. As a result, the viscosity coefficient is written as a sum of molecular viscosity [mu] and turbulent viscosity [[mu].sub.T], and the last term in the right-hand-side of (2) becomes [nabla] x [([mu] + [[mu].sub.T])[nabla][??]].

We solve a relative flow, in a rotating frame of reference with angular speed [??] = [omega][??] ([??] being the unit vector of the pump axis direction).

By introducing the relative velocity

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

With [??] the position vector, the left hand side of (2) becomes

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

An important assumption used in the present computation is that the relative flow is steady. This simplifies (3) by removing the first and last terms, and also allows the computation of flow on a single inter-blade channel.

The turbulent viscosity is computed using the RSM model.

We imposed on the inlet section the velocity, corresponding to the prescribed flow rate together with the turbulence parameters, (Susan-Resiga, 1999):

v = Q/[S.sub.IN] (5)

On the outlet section of the computational domain a radial equilibrium condition is chosen.

On the periodic surfaces of the domain the periodicity of the velocity, pressure and turbulence parameters were imposed:

[??] (r, [theta], z) = [??](r, [theta] + 2[pi]/[n.sub.b], z) (6)

p(r, [theta], z) = p (r, [theta] + 2[pi]/[n.sub.b], z) (7)

The remaining boundary conditions for the domain correspond to zero relative velocity on the blade.

3. NUMERICAL RESULTS

The pressure coefficient is defined by the following equation:

[c.sub.p] = p - [p.sub.IN]/[rho]/2 [w.sup.2.sub.IN] (8)

The pressure distribution is plotted on a surface placed at the radius [r.sub.m] given by the following equation:

[r.sub.m] = 1/2 [square root of [D.sup.2] + [d.sup.2]/2] (9)

From the comparison of the numerical and experimental (Anton, 1994) pressure coefficient distribution along the pressure side, PS, and suction side, SS, of the blade, figure 2, it results a very good agreement. This proves that the turbulent model and boundary conditions were adequate chosen.

The 3D effects due to the loading of the inducer blade lead to the deviation of the stream trace towards the hub on the pressure side and towards the shroud on the suction side, figure 3. The flow on the pressure side towards the blade exit is positioned at the same radius as on the inlet of the blade. Moreover, the stream trace near to the pressure side moves near to the blade, while the stream trace on the suction side is pushed away from the blade, figure 4.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

4. CONCLUSIONS

The paper presents the 3D full turbulent numerical investigation and analyse of the flow in an inducer. The numerical results are in very good agreement with the experimental data at the section situated at [r.sub.m] = 0.111 m.

The 3D effects are presented due to the loading of the blade. Consequently the stream traces on the suction side are deviated towards the shroud and the stream traces on the pressure side are deviated towards the hub.

Because these 3D effects could not be taken into account in the design process of the inducer, it results a poor operation of this type of inducer.

The numerical investigation of the structure of the internal flow for this type of inducer leads to the conclusion that it is recommended the use of another type of hydrofoil cascade for manufacturing the blades of the inducer.

5. REFERENCES

Anton, L. E. (1994). Determination of pressure distribution on the blades of an inducer, Proceedings of XVII IAHR Symposium, pp. 321-328, China, September, 1994, Beijing

Fluent Inc., (2001). FLUENT 6.3 User's Guide, Fluent Incorporated, Lebanon

Garay, P. N. (1996). Pump Application Desk Book, The Fairmont Press Inc., ISBN 0881732311

Mejri, I.; Bakir, F.; Rey, R. & Belamri, T. (2006). Comparison of Computational Results Obtained From a Homogeneous Cavitation Model With Experimental Investigations of Three Inducers. Journals of Fluid Engineering, Vol. 128, No. November 2006, 1308-1323

Susan-Resiga, R.; (1999). Periodic boundary conditions implementation for the Finite Element Analysis of cascade flows, Scientific bulletin of Politehnica University Timisoara, Vol. 44(58), pp. 151-160

Table 1. Geometrical characteristics and operating conditions
of the investigated inducer

 Q D d s n
Hydrofoil [m.sup.3]/s] [mm] [mm] [mm] [rot/min]

Straight 0.335 300 100 3 1450