Numerical investigation of the flow in a straight and bended hydrofoil cascade of an inducer.

Stuparu, Adrian ; Muntean, Sebastian ; Baya, Alexandru 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". 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 and bended hydrofoil cascade for the construction of the blades of the inducer satisfies these requirements. We investigated two inducers, one with the blades constructed from straight hydrofoil cascade and one with the blades manufactured from bended hydrofoil cascade. Each inducer has two blades.

In order to validate the numerical investigations of the flow, the results obtained are compared with experimental results from investigations performed in a wind tunnel upon two inducers which respect the geometrical similitude laws.

2. COMPUTATIONAL DOMAIN, FLOW EQUATIONS AND BOUNDARY CONDITIONS

The computational domain, figure 1 and figure 2, was generated using the pre-processor GAMBIT from FLUENT, based on the existing geometry. The geometrical characteristic of the two types of hydrofoil corresponding to the middle radius of the blade and the investigated operating condition are given in table 1.

The generated mesh for the computational domains is structured and has 60,000 cells each. A boundary layer was attached to the two hydrofoils in order to be able to compute the flow near a solid wall, (Thomson et al., 1997).

The periodic boundaries of the domains are positioned at a distance, regarding the chord.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

This distance is equal with the space of the cascade, while the inlet is positioned at a distance equal with half of the space of the cascade and the outlet at a distance equal with four times the space of the cascade, (Susan-Resiga&Muntean, 1999)

A steady relative 2D flow is computed in the computational domain:

[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, using a Reynoldsaveraged Navier-Stokes (RANS) solver.

First the inviscid flow is calculated, that means that the viscosity of the water is not take into account.

After that, the flow is calculated using two models of turbulence: standard k-[epsilon] and Reynolds Stress Model.

The standard k-[epsilon] model is a two-equation model in which the solution of two separate transport equations allows the turbulent velocity and length scales to be independently determined.

The Reynolds Stress Model (RSM) is the most elaborate turbulence model that FLUENT provides. Abandoning the isotropic eddy-viscosity hypothesis, the RSM closes the Reynolds-averaged Navier-Stokes equations by solving transport equations for the Reynolds stresses, together with an equation for the dissipation rate. This means that five additional transport equations are required in 2D flows, (Fluent, 2001).

We imposed on the inlet section the two components of the velocity, corresponding to the prescribed flow rate and flow angle, together with the turbulence parameters,

[w.sub.x] = Q/[S.sub.IN] (3)

[w.sub.y] = [w.sub.x]/tg[[beta].sub.0] (4)

On the outlet section of the computational domain and of the computational domain a radial equilibrium condition is chosen, (Gostelow, 1984).

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

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] (5)

A comparison between the pressure coefficient obtained from the numerical investigation of the flow with different types of turbulence and from experimental investigation (Anton, 1994) is made, in order to validate the numerical results. It can be observed that the pressure coefficient distribution obtained with the RSM turbulence model is most similar to the distribution obtained from measurements, for both hydrofoil cascades, as presented in figure 3 and 4.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

In figure 5 and 6 the streamlines for the two hydrofoil cascades are presented. It can be observed that for the straight hydrofoil appears a recirculation on the suction side which leads to the partial blockage of the flow channel. This phenomenon is eliminated by using a bended hydrofoil cascade, as shown in figure 6.

4. CONCLUSIONS

From the comparison of the numerical data with the experimental data regarding the pressure coefficient distribution along the two hydrofoils it results a good agreement for the RSM turbulence model. The numerical investigation of the flow predicts the presence of a dead zone of the flow on the suction side of the straight hydrofoil. This dead zone is not present at the bended hydrofoil.

This leads to the conclusion that the bended hydrofoil is suited for the construction of the blade of the inducer and that the use of the RSM turbulence model for numerical investigation is recommended.

5. REFERENCES

Anton, L. E. (1994). Determination of pressure distribution on the blades of an inducer, Proceedings of XVII 1AHR Symposium, pp. 321-328, China, September, 1994, Beijing

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

Gostelow, J.P.(1984). Cascade Aerodynamics, Pergamin Press, Oxford

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

Thomson, J.F.; Warsi, Z.U.A.; Mastin, C.W. (1997). Numerical Grid Generation, Elsevier Science Publishing Co.

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

Hydrofoil Q D d s
 [m.sub.3]/h [mm] [mm] [mm]

Straight 100 300 100 3
Bended 100 300 100 3

Hydrofoil [[beta] [[beta] t/l
 .sub.s] .sub.0] [-]
 [[degrees]] [[degrees]]

Straight 36.5 20.52 0.804
Bended 31.5 20.52 0.804