Abou El-Azm et al.[9] investigated the pressure drop after such fractal orifices and measured the pressure recovery at different stations downstream the orifice. Jankowski et al.[10] developed a simple model to predi-

ct the pressure drop and the discharge coefficient for incompressible flow through orifices with length-to- diameter ratio greater than zero (orifice tubes) over wide ranges of Reynolds number.

The tortuous passage is widely used to reduce the fluid pressure through multistage throttling in many engineering applications. In our previous work, diffe- rent passages were used to produce the multistage pre- ssure drop and they were studied by experimental  and

CFD approaches[11,12]. Xia et al.[13] proposed a new modified relation for predicting the pressure drop     in

the helical rectangle channel. Moraczewski and Shapley[14] investigated the pressure drop of concen- trated suspensions flowing through an axisymmetric contraction-expansion   channel   at   a   low Reynolds

number. The passage structure and the boundary con- ditions are both the key factors that determine the pre- ssure drop results. Adachi and Hasegawa[15]  studied the transition of the flow in a symmetric channel with periodically expanded grooves. Zhang et al.[16] perfor- med a multi objective optimization to improve the structure of trapezoidal labyrinth channels. Pfau et al.[17] presented a highly resolved experimental data set taken  in  an  inlet  cavity of  a  rotor tip labyrinth seal.

Novak et al.[20] focused on the flow at the side weir in a narrow flume.

In this paper, the tortuous passage investigated is different from previous studies, especially, the geome- tric configuration and the passage size. The distinctive feature of the passage is the narrow dimension, with the smallest cross section being only 0.0025 m× 0.0040 m. Based on this structure, the CFD approach will be used to analyze the pressure drop and the pre- ssure loss coefficient under different operation condi- tions.

Fig.2 The geometric configuration of a labyrinth passage (pro- totype)

1. The geometric features of labyrinth passage

The sketch of a labyrinth passage is shown in Fig.2, where the flow direction and path are shown. The flow enters the tortuous pathway and flows in- wardly to the plug. Each flow channel consists of several right angle turns (stages), which accounts for more than one velocity head of the pressure drop. With the flow area continually increasing, the fluid pressure decreases. Thus the velocity is continuously reduced to a very reasonable level at the expanding passage section. There are no local pressure recovery points for the cavitation to take place in the pathway such as what occurs with a drilled hole type pathway. This is the one of the great advantages of the labyrinth pass- age as compared to the hole type ones.

There are 24 right angle turns in this labyrinth passage. In order to illustrate the features of right angle turns and expanding passage size, along the flow dire- ction, a series of dimension sizes are defined in  Fig.2,

Parvaneh et al.[18] revealed the hydraulic performance of asymmetric labyrinth side weirs located on a   strai-

such as the inlet

S0  , the first throttling section

L1, D ,

ght  channel.  Crookston  and  Tullis[19]   increased  the

and  the  first  expanding  space  in  the  tangential and

discharge capacity and the hydraulic efficiency of a

normal directions

S1 ,

L1, R

and so on. All these sizes

labyrinth  weir  with  an  Arced  cycle   configuration.