FLOW-INDUCED VIBRATIONS OF A TRASHRACK

 

ROLAND HOLLENSTEIN

 

VAW ETH Zürich, Gloriastrasse 37-39, CH-8092 Zürich,

Tel.: 0041-1-632 41 76, e-mail: hollen@vaw.baum.ethz.ch

 

 

ABSTRACT

The Tiroler Kraftwerke AG (TIWAG) constructed a new power plant on the river Inn at Langkampfen, close to Kufstein, Austria. A 1 : 2 scale trashrack model was built and tested at the Laboratory of Hydraulics, Hydrology and Glaciology (VAW) of the Swiss Federal Institute of Technology (ETH) in Zurich to investigate the potential of flow-induced vibrations.

A portion of the grid structure including eight bars was considered to give accurate information. With two degrees of freedom in the streamwise and the crossflow directions, the trashrack model reproduced the main vibration modes of the prototype. The single bars had an aspect ratio of 1 : 5.6. Investigations regarding vortex shedding reproduced a maximum Strouhal number of 0.24.

The mutual interaction of the formation of single vortices, the angle of incidence and the flow turbulence affected the rack vibration characteristics. The multiple-mode vibrations were caused by either Impinging Leading-Edge Vortex Shedding (ILEV) or Alternate-Edge Vortex Shedding (AEVS), with the transition from ILEV to AEVS occuring between angles of incidence of 15^o - 30^o.

 

INTRODUCTION

This investigation illustrates the flow-induced vibrations of the trashrack at the Lang-kampfen power plant. These vibrations may be vortex- or turbulence-induced.

A trashrack section of the Langkampfen power plant is 17.7 m high and 13.0 m wide. The maximum discharge is 260 m³/s, with an average inflow velocity v_m = 1.1 m/s. The single bars are rectangular shaped, with a length l = 140 mm and a thickness d = 25 mm. The space between the bar axes is s_a = 135 mm. The single bars and the entire rack section can be forced by the flow to bending vibrations in the streamwise and the crossflow directions, and to torsional vibrations.

 

MODEL CONSTRUCTION AND INSTRUMENTATION

 

Scaling criteria

Dynamic similarity between model and prototype is ensured when similarity in geometry and the ratios of major forces are satisfied. The essential forces in an open channel flow are gravity and inertia. The ratio between these forces is characterised by the Froude number Fr (Petrikat, 1966). The similarity of small-scaled flow patterns near the bars is caused by the viscous force. In this case the Reynolds number Re as the ratio between viscous and inertial forces, is significant (Petrikat, 1966). With Reynolds numbers based on the bar thickness as large as Re = 2·10³ - 1.5·10⁴, the influence of viscous forces can be neglected.

Similarity between model (subscript M) and prototype (subscript N) referring to vibrations requires a correct scaling of the model frequencies. For this trashrack model the Froude similarity was applied to define the frequency ratio as

 

f_N / f_M = 1 / l_L^1/2. (1)

 

f_N: prototype frequency; f_M: model frequency; l_L: scale factor of the length.

 

Description of the trashrack model

To investigate the movement in the streamwise and the crossflow directions, a system with two degrees of freedom is required. The rack model had eight single bars of rectangular shape. Four bars in the center portion were flexibly mounted in bearings with small sheet metal pieces to allow for bar bending in the crossflow direction. The transverse movement of the rack in the streamwise direction was modelled as a strustural pendulum (Figure 1).

 

 

Figure 1 : Vibration modes.

a) In the streamwise direction as a pendulum.

b) In the crossflow direction as a bending movement.

 

The effect of the angle of incidence was modelled by deflecting the rack model with an angle a to the streamwise direction. The flow in the wake of the rack was always directed parallel to the bar sides by flow straighteners.

 

EXPERIMENTAL RESULTS

 

Natural frequency of the trashrack model

A comparison of shaker tests with the trashrack vibrating in air and water shows the influence of the added mass (Table 1). The added mass is an additional weight of the fluid vibrating with the bars and reduces the natural frequencies in water.

 

Table 1 Natural frequencies of the trashrack model.

	in air		in water
	f0x	f0y	fwx	fwy
Natural frequency	11.6 Hz	16.9 Hz	10.9 Hz	14.4 Hz

 

Vortex shedding

The frequency of periodic vortex shedding is proportional to the inflow velocity. A dimensionless number for the periodic vortex shedding is the Strouhal number

Sh = . (2)

f_s: frequency of the vortex shedding; L: characterstic length; V: characteristic velocity.

 

Two different vortex shedding phenomena may occur. For an angle of incidence a = 0^o, the vortices form "Impinging Leading-Edge Vortices" (ILEV), where the vortices from the leading edge propagate along the sides of the bar and cause vibrations in the crossflow direction due to pressure fluctuations (Figure 2b). At an angle of incidence a = 45^o the vortex shedding is an "Alternate-Edge Vortex Shedding" (AEVS), without an interaction between the vortices from the leading edge and the sides of the bar (Figure 2a). AEVS causes vibrations in the streamwise and the crossflow directions. For angles a = 15^o and 30^o neither of these vortex shedding phenomena dominate.

 

 

Figure 2:

a) AEVS at high angles of incidence a (a > 30^o).

b) ILEV for small angles of incidence a (a < 15^o).

d' = l·sina + d·cosa.

 

To determine the Strouhal number of a trashrack from the Strouhal number of a single bar, the velocity v_eff close to the sides of the bar is considered. Because of the space reduction between the bars at a given angle of incidence, the velocity v_eff is larger than the average inflow velocity v_m. Naudascher and Rockwell (1994) determined v_eff for small angles of incidence, i.e. s_a - tana·l - d >> 0, as

 

v_eff = . (3)

v_m: average inflow velocity; d' = l·sina + d·cosa; s_a: space between the bar axes.

 

For the present trashrack model equation 3 is only valid up to a = 30^o.

Table 2 shows the Strouhal numbers of various investigations for a single bar. For ILEV vortex shedding one or two vortices can propagate along the sides of the bar. The Strouhal number for AEVS is constant for various angles of incidence.

Vortex shedding is also dependent on the turbulence level Tu = v'/v_m up- and downstream of the rack, where v' is the fluctuating velocity in the streamwise direction. With increasing turbulence level the Strouhal number increases (Wang, 1992).

The turbulence level in the model was 7-8 %. For a prototype trashrack turbulence levels are about 10 %, so that the present investigation with 8 % compares well with the trashrack at the Langkampfen power plant.

 

Table 2 Strouhal numbers for single bars; Re = 10³ - 10⁵, Tu = 0.3 % - 1.0 %.

Angle of	Sh'(d'); l/d = 10.0 Wang (1992)			Sh'(d'); l/d = 5.0 Knisely (1990)		Sh(l); l/d = 5.6 Nakamura et al. (1991)
incidence a	ILEV with 1 Vortex	ILEV with 2 Vortices	AEVS	ILEV with 1 Vortex	AEVS	ILEV with 1 Vortex	ILEV with 2 Vortices
0o	0.12	0.20		0.12		0.6	1.2
15o	0.18		0.16	0.14	0.14
30o			0.16	0.16	0.16
45o			0.16		0.16

 

EXCITATION AT THE NATURAL FREQUENCY

Crossflow direction

The acceleration peaks in Figure 3 denoted with the dashed line correspond to ILEV vortex shedding. The natural frequency f_wy of the crossflow direction is the resonant frequency in spite of a lower natural frequency f_wx of the streamwise direction. ILEV thus only cause crossflow vibrations. The other peaks are turbulence-induced.

 

Figure 3: Acceleration spectrum in crossflow direction for a = 0o. The dashed line marks the excitation due to vortex shedding. The vortex shedding is ILEV. fwx: natural frequency in the streamwise direction fwy: natural frequency in the crossflow direction Note: The acceleration scale is distorted.

 

Streamwise direction

At an angle of incidence a = 45^o (Figure 4) a vortex shedding similar to a = 0^o in the crossflow direction may be noticed. The phenomenon of the vortex shedding is AEVS, whereas the other peaks are turbulence-induced.

 

 

From the spectra, the Strouhal numbers for the rack are as given in

Table 3. The Strouhal numbers Sh'(d') of the rack are larger than the Strouhal numbers Sh'(d') of the single bar (

Table 2). This results from the mutual interaction of the vortex formations by the single bars, and from the increasing velocities near the sides of the bar. Considering the velocity v_eff, the Strouhal number Sh'_eff(d') of the trashrack model is even larger than the Strouhal number Sh'(d') of the single bar. This is caused by the higher turbulence level in the model.

 

Table 3 Strouhal numbers as a function of d, d' und l; Re = 2·10³-1.5·10⁴, Tu = 8 %. Sh(d) as a function of v_m, and Sh'_eff(d') as a function of v_eff according to equation 3. For a = 15^o und 30^o no definite Strouhal numbers could be determined.

 

Effect of the vibration

The excitation of the trashrack bars may result from both vortex shedding in the crossflow (ILEV) and in the streamwise directions (AEVS), and due to turbulence. If resonance (f_s = f_w) is allowed to develop, the rack will vibrate with increasing amplitude. The second mode can be forced by the first mode, where the mutual interaction depends on the ratio f_wx / f_wy between the natural frequencies of the modes.

To quantify the failure due to fatigue from the DIN Norm 4150/3 (1986) a maximum vibration velocity of 5 mm/s is recommended. The vortex induced resonant vibrations in the rack model at f_wy = 14.4 Hz causes a maximum vibration velocity of 20 mm/s at an angle of incidence a = 0^o. The maximum vibration velocity due to turbulence-in­duced vibrations, however, is smaller than 1 mm/s. If vortex induced excitation is pre­vented, the rack may not fail due to fatigue.

The comparison between natural frequencies f_w and vortex shedding frequencies f_s specifies the design condition for the onset of flow-induced resonant vibration. To ensure that resonant vibration will not occur, the natural frequency f_w is limited to some value larger than the exciting frequency f_s, such as

 

0.5 to 0.65 · f_w > f_s. (4)

 

f_w: natural frequency, f_s: exciting frequency

 

The exciting frequencies for the trashrack in Langkampfen are reproduced in

Table 4 for an average inflow velocity v_m = 1.1 m/s.

 

Table 4 Strouhal number Sh = Sh(d) and vortex shedding frequency f_s for v_m = 1.1 m/s.

 

CONCLUSIONS

The critical frequency for trashrack excitation with large amplitudes is the vortex shedding resonant frequency. For angles of incidence a < 15^o the ILEV phenomenon may cause periodic excitation. For angles of incidence a > 30^o, the AEVS phenomenon occurs. The Strouhal number of a single bar with l/d = 5.6 and a = 0^o is smaller than the Strouhal number of the trashrack considered, due to the combined influence of the single vortex formation and the larger velocity between the bars. The transition from ILEV to AEVS is between a = 15^o - 30^o. The Strouhal number for AEVS is smaller than the largest Strouhal number for ILEV. Turbulence may have a large influence on the vortex shedding. By an increasing turbulence level the Strouhal number and the exciting frequency increase too.

The main design consideration is to limit the natural frequency to some value larger than the exciting frequency, where the natural frequency f_w is twice the vortex induced exciting frequency f_s. The turbulence-induced excitation seems not to be important for structural stability.

 

ACKNOWLEDGEMENTS

The supply of prototype data by and excellent collaboration with TIWAG are kindly acknowledged.

 

Symbols

Index M: Model data

Index N: Prototype data

Index x: Streamwise direction

Index y: Crossflow direction

 

a [deg] Angle of incidence

n [m²/s] Kinematic viscosity

l_L [-] Scale factor

r_w [kg/m³] Weight of water (1'000 kg/m³)

d [m] Bar thickness

d' [m] Reduced bar thickness

d' = l · sina + d·cosa

g [m/s²] Gravity, g = 9.81 m/s²

f_s [Hz] Vortex shedding frequency

f₀ [Hz] Natural frequency in air

f_w [Hz] Natural frequency in water

Fr [-] Froude number, Fr = V / (g·L)^1/2

L [m] Characteristic length

l [m] Bar length

Re [-] Reynolds number, Re = V·L / n

s_a [m] Space between the bar axes

Sh [-] Strouhal number, Sh = f·L / V

Sh' [-] Strouhal number with L = d'

Sh'_eff [-] Strouhal number with L = d' und V = v_eff

Tu [-] Turbulence level

V [m/s] Characteristic velocity

v_m [m/s] Average inflow velocity

v_eff [m/s] Inflow velocity on the bar sides

 

References

Knisely C.W., (1990). Strouhal numbers of rectangular cylinders at incidence, Journal of Fluids and Structures, Vol.4, pp.371-393.

Nakamura Y., Ohya Y., Tsuruta H., (1991). Experiments on vortex shedding from flat plates with square leading and trailing edges, Journal of Fluid Mechanics, Vol. 222, pp.437-447.

Naudascher E., Rockwell D., (1994). Flow-induced vibrations - an engineering guide, IAHR Hydraulic Structures Design Manual 7, A.A.Balkema, Rotterdam.

DIN Norm 4150/3 (1986). Erschütterungen im Bauwesen, Deutsches Institut für Normung e.V., Beuth Verlag GmbH Berlin.

Petrikat K. (1966). Möglichkeiten und Grenzen des wasserbaulichen Versuchswesens, Mitteilung 4, TH Stuttgart.

Wang Y., (1992). Schwingungen von schräg angeströmten Rechenstäben quer zu und in Strömungsrichtung, SFB Bericht No. 210/E/74, Universität Karlsruhe, Germany.