Design Process

In using high speed cascades, few compromises are needed to achieve a model of the real blade in the turbomachine. Indeed, true similarity can be obtained sometimes. In the case of low speed cascades, more compromises are required and the shape of the resulting low speed blade usually differs greatly from the real blade to be modelled. Typical sizes of the resulting LPT blades for both high and low speed cascade testing at the Whittle laboratory are shown in Table 1.

1.1 Choosing the bars

To achieve a realistic simulation of the rotor-stator interaction, several sim­ilarity parameters must be correctly matched. The method used to choose the size and the pitch of the bars is the same in low and high speed cascade testing and it is presented below. Only by following this procedure is a good simula­tion of the rotor-stator interaction situation achieved.

To reproduce the kinematics of the wake-blade interaction, the fbw angle ві in the bar relative frame of reference, is matched to that of the upstream bladerow in the LPT. The relative and absolute inlet ft>w angles and the inlet axial velocity to the cascade, V, i • then give the speed of the bars, U, from the velocity triangles at the inlet of the cascade.

The reduced frequency of the machine not only sets the ratio of the con­vection time scale to the wake passing time scale, but it also sets the ratio of the viscous diffusion time scale to the wake passing time scale. Therefore, it must be matched if a realistic rotor-stator interaction is to be achieved. The reduced frequency, F, and the bar passing frequency, f, are related according to the expression

F = fC/V2 = U/Sbar • C/V2 « f • x/U (1)

where C is the chord of the airfoil. Equation 1 provides the bar passing fre­quency and the pitch of the bars, sbar. The reduced frequency is defined in terms of the exit velocity of the cascade, V2. This is because the most im­portant wake-blade interactions tend to occur in the latter half of the blade passage. Typical values of the bar passing frequencies for high speed and low speed cascades are given in Table 1.

Pfeil and Eifer (1976) showed that the structure of the far wake of an air­foil and that of a cylindrical body of the same drag is almost the same. If an estimation of the stagnation pressure losses of the blade row to be simulated is known, Yp, the diameter of the bars, d, can be obtained according to

Yp = d • Cd/(Sbar • CosA) (2)

which is exact for low speed ft>ws. An estimation of the drag coefficient of the bars, Cd, at the relative conditions that Yp represents, must be known. Typical dimensions of the resulting diameters of the bars are given in Table 1. These values are of the same order than the trailing edge thickness of the upstream blade row.

Once all the previous values are fixed, the ratio between the pitch of the cascade, s, and the pitch of the bars is known. Also, the fbw coefficient of the bars, ф, is given by

ф = Vxi/U (3)

and this is fixed by the inlet angle in the cascade frame of reference.