Experimental study on the relation of water rivulet-reynolds number effect-cable vibration

Transcription

1 The Seventh International Colloquium on Bluff Body Aerodynamics and Applications (BBAA7) Shanghai, China; September -, Experimental study on the relation of water rivulet-reynolds number effect-cable vibration Qingkuan Liu, Yi Wang, Yunfei Zheng, Wenyong Ma Wind Engineering Research Center, Shijiazhuang Tiedao University, 7 Northeast Second Inner Ring, Shijiazhuang, Hebei China ABSTRACT: Rain-wind induced vibration of stay-cables is a worldwide problem of great concern in bridge engineering. In all factors that induce this vibration, water rivulet formed on cable surface in rainy and windy condition is considered as the most inportant one. Taking drag/lift force coefficients and vibration amplitudes in different Reynolds numbers as parameters, by wind tunnel tests, the influence of water rivulet on Reynolds number effect and mechanism of vibration caused by such facters were studied by means of force-measurement and vibrationmeasurement tests of stay-cable models with water rivulets attached in different positions. Resrults show that water rivulet has great influence upon changing rules of force coefficients with different Reynolds numbers; force coefficients value and changing rule have very close relationship with vibration. KEYWORDS: stay cable; rain-wind induced vibration; wind force coefficients; water rivulet; Reynolds number INTRODUCTION Inclined cables often show violent vibration in rainy and/or windy days due to low structural damping. Among cable vibrations, rain-wind induced vibration is a worldwide problem, as its large amplitude and serious harm to cable-stayed bridges. To make clear the mechanism and control methods of this vibration, by field observation [- ],wind tunnel tests [-] and numerical analysis [-], reseach work have have been carried out for more than two decades, and galloping theory of water rivulet [,], high wind speed vortex induced vibration [], water rivulet movement theory [,7,9,] have been put forward by different researchers. In all the factors that induce this vibration, water rivulet formed on cable surface in rainy and windy condition is considered as the most inportant one, as it can change the cabel shape and wind force. As we know that Reynolds number is a key parameter in study of fluid mechanics, particularly for the structures which have smooth surface, since flow fields around such structures vary with Reynolds number, as well as the aerodynamic force and vibration characteristics. In this research, from the viewpoint of Reynolds number effect, taking drag/lift force coefficients and vibration amplitudes in different Reynolds numbers as parameters, the influence of water rivulet on Reynolds number effect, the influence of Reynolds number on cable vibration were studied by means of force-measurement and vibration-measurement tests. The cable model used is a circular cylinder with water rivulets attached in different positions. The aim of this paper is tried to understand the mechanism of rain-wind induced vibration of stay-cables from the new viewpoint of Reynolds number effect. 7

2 WIND TUNNEL TEST Two series of wind tunnel tests were performed to determine the exact relationship between Reynolds number effect and cable vibration. One series of tests is aerodynamic force measurements using fixed rigid cable models; the other one is vibration amplitude measurements using spring supported rigid cable models. The wind tunnel used in this study is a open/closed circuit type with two sections, located at Shijiazhuang Tiedao University. The tests were performed using the small section of the wind tunnel, which is.m in width and.m in height and can reach a wind velocity up to 8m/s. The cable model in wind tunnel, the water position and shape are shown in Fig.. The wind tunnel test cases are shown in Table. Wind θ mm mm Fig. Cable model, water rivulet position and shape Table. Wind tunnel test cases force-measurement test vibration-measurement test ) Re range ( ) Re step ( ) ( ) Re range ( ) Re step ( ) 8~. 8~. ~ 7~7. ~7 8~. 7~7..~7 ~7. RELATION BETWEEN WATER RIVULET POSITION AND REYNOLDS NUMBER EFFECT Drag and lift force coefficients of cable model with water rivulet in different positions are shown in Fig.. It can be seen that the Reynolds number effects of force coefficients have a very close relation with water rivulet position Re( x) Re(x) Re( x) = =. = 7

3 The Seventh International Colloquium on Bluff Body Aerodynamics and Applications (BBAA7) Shanghai, China; September -, Re( x) Re( x) -.8 Re( x) =7. = = Re( x) Re( x) Re( x) = =7. = Re( x) - Re( x) - Re( x) =. = = Re( x) - Re( x) - Re( x) = =. = Re( x) - Re( x) - Re( x) =. = =. 7

4 Re( x) Re( x) Re( x) = =7. = Re( x) Re( x) Re( x) =. = =7. Fig. Drag and lift force coefficients of each water rivulet position The results of Fig. can be classified into two types based. on drag/lift force coefficients changing with Reynolds number, one type is results from water rivulet position = to =, -. the another type is other water rivulet positions. - In the first type, the changing rule of drag force coefficients with Reynolds number is steady-decreasing-steady- -. Re( x) decreasing-steady, the changing rule of lift force coefficients is =7 steady-increasing-steady-decreasing-steady. Refering to the changing rule of force coefficients of cable with smooth surface [9], it can be deduced that the first steady range of the two force coefficients belongs to subcritical Reynolds number range, and the following range belongs to critical Reynolds number range with the decreasing of drag force coefficient and increasing of lift force coefficient, the last steady range of the two force coeffients belongs to super-critical Reynolds number range. In the second type, from the Reynold number range shown in the figures, the first stage of the two coefficients (drag force decreasing and lift force increasing) is not shown, the process of the two coefficients are steady-decreasing-steady. Based on all the cases, defining the maximum of drag force coefficient as Dmax (ex. Point in Fig., case of = ), minimum of drag force coefficient as Dmin (Point ), the drag force valve when it begins to decrease in the last decreasing stage as Dst (Point ), the decreasing amplitude of drag force in the last decreasing stage as DA (drag force difference from Point to Point ), maximum of lift force as Lmax (Point ), minimum of lift force as Lmin (Point ), lift force value when it begins to decrease as Lst (Point ), the decreasing amplitude of lift force in the last decreasing stage as LA (drag force difference from Point to Point ), the Reynolds number when drag force coefficient begins to decrease in the last stage as Dstre (Reynolds number of Point ), Reynolds number when drag force coefficient gets its minimum as Dminre (Rey-. 7

5 The Seventh International Colloquium on Bluff Body Aerodynamics and Applications (BBAA7) Shanghai, China; September -, nolds number of Point ), the distance of Reynolds number when drag force coefficient shows steady range as Lpl (Reynold number difference from Point 7 to ), Reynolds number when lift force coefficient gets its maximum as Ltre (Reynolds number of Point 7), these parameters changing rule with water rivulet are concluded in Fig.. Base on Fig. and Fig., it can be seen that the change of water rivulet can induce obvious change of drag/lift force coefficients; the coefficients value and parameters obove-mentioned are different in different water rivulet positions..8.. Dmax Dmin Dst DA.. Lmax Lmin Lst LA Dstre Dminre Lpl Ltre.. Re(x) a Parameters of drag force coefficient b Parameters of lift force coefficient c Reynolds number of key point Fig. Variation of force coefficient parameters with rivulet positions RELATION BETWEEN WATER RIVULET POSITION AND AERODYNAMIC STABILITY /d and vibration amplitude of cable model with water rivulet in different positions are shown in Fig.. Here, /d is galloping coefficient, calculated from drag and lift force coefficients. A/cm A/cm A/cm - - Re( x) - Re( x) - Re( x) = =. = A/cm A/cm A/cm - - Re( x) Re( x) - Re( x) =7. = =. 7

6 A/cm A/cm A/cm - Re( x) - Re( x) - Re( x) = =7. =. 7. A/cm 8 A/cm. A/cm Re( x) -. Re( x) - Re( x) =. = =7... A/cm.. A/cm A/cm -. - Re( x) Re( x) - Re( x) = =. = 8 A/cm - - A/cm - A/cm Re( x) -8 Re( x) - Re( x) =7. = =. A/cm A/cm A/cm Re( x) Re( x) Re( x) = =7. = 7

7 The Seventh International Colloquium on Bluff Body Aerodynamics and Applications (BBAA7) Shanghai, China; September -, 8 8 A/cm 8 A/cm A/cm - - Re( x) - Re( x) - Re( x) =. = =7. Fig. /d and vibration amplitude of each water rivulet position From Fig., it can be seen that there are two main vibration types of cable model. When water rivulet is at a low position ( is small), with the increasing of Reynolds number, drag force coefficient decreases and lift force coefficient increases dramatically. The similar critical Reynolds number effect occurs. The change of force coefficients induce minus /d he large amplitude vibration of cable model under such condition can be explained by both critical Reynolds number effect and galloping. When Reynolds number is relatively high (between and ), with the decreasing of drag force coefficient and lift force coefficient, varying amplitude vibrations of cable model occur for every water rivulet position test cases. The vibration under such condition is similar to the vibration induced by critical Reynolds number effect. A/cm Re( x) =7 CONCLUSION Base on Reynolds number effect, water rivulet effect on Reynolds number effect and mechanism of water rivulet effect on cable vibration are studied, the conclusions are as follows: () Water rivulet can influnce the changing rule of force coefficients with Reynolds number; there is close relationship between cable vibration and coefficients value and their changing rules. () In low water rivulet positions, with the increasing of Reynolds number, drag force decrease and lift force increase, the galloping coefficients are minus, cable shows large amplitude vibration. This vibration can be explained by Reynolds number effect and galloping. () In high water rivulet positions, with the decreasing of drag force coefficient, lift force coefficient changes heavily; cable vibrates in different amplitude in each water rivulet position. The mechanism of these vibrations is similar to vibration induced by Reynold number effect. ACKNOWLEDGEMENTS This work was supported by National Science Foundation of China (878), New Century Training Program Foundation for Talents from the Ministry of Education of China (NCET-- ). 77

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