裝配圖胡軍雄,裝配,胡軍雄 Mass flow rate measurement in heterogeneous diphasic flows by using the slurry pumps behavior S. Kouidri, , F. Bakir and R. Rey LEMFI-UPRESA CNRS 7067 ENSAM, Laboratoire d’Energétique et de Mécanique des Fluides Interne, 151 Boulevard de L’H?pital, 75013, Paris, France Received 17 May 2000;? revised 10 January 2001;? accepted 22 February 2002.? Available online 26 April 2002. Abstract This study lies within the scope of a European project, with the objective of studying and designing a tunnel boring machine able to function in continuous mode. This operating mode allows reduction of discontinuities of excavation in order to obtain greater efficiency by reducing the excavation time. The extraction of rubble is carried out by means of a hydraulic circuit composed of a set of special pumps for slurry and of a horizontal hydraulic pipe. The optimal control of the whole installation, pumps included, requires continuous assessment of the mass flow rate of the solid–liquid mixture. During this study, we aimed to develop a methodology of mass flow rate measurement to replace the existing limited method of gamma-densitometer, as the irregularities noticed during various phase measurement reduce the reliability of this technique. This paper presents a theoretical and experimental study which will make it possible to improve the accuracy of measurement carried out by the gamma-densitometer and the development of a method based on the power consumed by the engines driving the pumps. Author Keywords: Gamma-densitometer; Flow rate; Pump C volumetric concentration of solid CD drag coefficient D pipe diameter d particles diameter H slurry head g acceleration of gravity L pipe length Pabs shaft power qv flow rate Rep Reynolds number R(z) means radius S solid/liquid density ratio Rext extemal radius of the impeller VC minimum building bed flow velocity VH minimum homogeneous flow velocity VS minimum heterogeneous flow velocity Ω angular speed Φ pressure coefficient ρ flow rate coefficient η efficiency τ power coefficient α radiation beam angle with horizontal ν kinematic viscosity μ absorption factor ρ density I liquid m mixture s solid Article Outline Nomenclature 1. Introduction 2. The gamma-densitometer with a single beam 2.1. Influence of the inclination of the device 2.2. Influence of the kind of flow 2.2.1. Different kinds of flows 2.2.2. Application to typical flows 2.2.3. Measurement of the density by control of the power absorbed by the pump 2.3. Behavior of the centrifugal pumps with slurry flow 2.4. Validation of the procedure 3. Conclusion Acknowledgements References 1. Introduction In the last 20 years, the development of tunnel boring machines has led to high performance machines handling greater and greater flow rates and therefore using the best technology available. The use of this type of machine requires the use of a slurry circuit allowing the evacuation of rubble to the exterior of the tunnel. The advance of the digging depends on several parameters and in particular on the correct operation of the slurry system. Pumps located all along the horizontal hydraulic piping ensure the flow of the liquid charged with rubble. The concentration in solid does not exceed critical values of 25%. One of the key points from an economical point of view is to proceed in continuous operation. However, there are still several phenomena to be mastered before building a machine able to work in this type of operating mode, these include: To control the functioning conditions of the pumps, master the position of the working point on the characteristic curve: outlet pressure, intensity consumed by the engine and conditions of wear of the impeller and the volute [1, 2 and 3]; To control the flow conditions inside pipes for a given type of hydraulic transport, and to avoid blocking [2]; To measure the mass flow rate in order to detect the release of a subsidence: crumbling of rubble occurring with the front of head of the rotary digger shield, a very important phenomenon at the origin of damage for the site being worked. 2. The gamma-densitometer with a single beam To measure the density of a liquid or of a homogeneous two-phase flow, the gamma-densitometer is based on the absorption principle. The intensity of photons arriving at a detector is given by an exponentially decreasing law: Ig=I0e?μρl (1) where Ig is the radiation collected by the detector, I0 is the radiation of origin, and I is the thickness of the absorbing matter. This gamma-densitometer presents many disadvantages: Its precision depends on the hydraulic transport conditions but errors can be partially composed by optimizing orientation of the apparatus relative to the pipe. The cost of this method is high and it presents considerable difficulties in handling, transport control and administrative management connected with its radioactive load. For such devices, the radiation beam angle is approximately 10°. 2.1. Influence of the inclination of the device Considering that the gamma-densitometer is located horizontally when it takes the measurements, it seems logical to think that an improvement of its accuracy could be achieved by inclining the device (Fig. 1). This part of the study will determine the influence of different orientations α on the measures given by the gamma-densitometer. (7K) Fig. 1. Assumptions for numerical computation. The mass that will be calculated is the mass of matter contained in 1 m of the pipe. The next step concerns the calculation of the matter which can be “seen” by the gamma-densitometer in 1 m of a pipe. The error which appears by using this method and due to the different geometrical assumptions is less than 0.8% of what ever the angle is. The average density contained in the cone is compared with the average density from the pipe. We can thus give the relative error between both densities. To calculate the best angular position, a few different density configurations which cover all the cases which can appear in the pipe, have been used. 2.2. Influence of the kind of flow 2.2.1. Different kinds of flows Concerning the hydraulic characteristics of slurries, it must be remarked that there is a great difference between a homogeneous liquid flow and that of a mixture of solids and liquids. The characterization of a homogeneous liquid flow is more or less easy, providing that the physical properties of the fluid and the circuit are known [1]. This is not so in the case of a slurry flow. Here, it is necessary to consider not only the properties of the liquid but also those of the solid and the effect of the particles on the mixture’s properties. In this way, a range of slurry behaviors can be observed depending on the flow’s homogeneity and velocity. The descriptions of both extremes of this range follows, though many slurries present a mixed character which combines the characteristics of both extremes. Thus, coarse size particles are suspended heterogeneously in the carrier fluid while finer particle size fractions join with the liquid to form the homogeneous vehicle. ? Homogeneous flow. This type of flow appears when solids are uniformly distributed in the liquid media. The presence of the solids can result in a sharp increase in viscosity as compared to that of the carrier fluid. Analyzing the Δp (pressure drop)?V (velocity), a similar response to that of a single phased liquid is observed. Thus, there is a linear variation in the turbulent regime and a flat laminar response. The velocity corresponding to the transition from turbulent to laminar flow is known as the transition velocity. This velocity tends to increase with slurry viscosity and therefore to increase with increasing solids concentration and decreasing particle size. The condition on velocity is V>VH, with VH representing the minimum homogeneous flow velocity. In this case, the flow speed is high enough to homogenize the rubble and the carrier fluid. In this study, this case is only a theoretical case, the speed being insufficient to blend both phases. ? Heterogeneous flow. In this case, solids are not evenly distributed and are in horizontal flow. Pronounced concentration gradients exist along the vertical axis of the pipe even at high velocities. The fluid and solid phases largely retain their separate identities, and the increase in the system viscosity over that of the carrier liquid is usually quite small. At pipeline velocities, where full movement of the solids occurs, the pressure drop response tends towards a position parallel to the response of the carrier fluid and the solids distribution. The condition on velocity is VH>V>VS, where VS is the minimum heterogeneous flow velocity ? Building and sliding bed. As the mean pipeline velocity decreases the solids are less and less uniformly distributed, arriving at a point when a stationary or building bed appears on the bottom of the pipe. The critical velocity at which a bed of particles begins to form is called the deposition velocity. It is directly related both to the fall velocity of the particles and to the degree of turbulence in the system. Therefore, it increases with increasing particle size, particle density and solids concentration and increasing pipe diameter. The significance of this velocity is that it represents the limit of safe operation. Operating with velocities lower than that could lead to the building up of a solid bed in the pipe, with consequent fluctuating friction losses or even plugging of the pipe. The conditions on velocities are VS>V>VC for the building bed and VC>V for the sliding bed, where VC is the minimum building bed flow velocity ? Deposit. In this case, the pumps are in operation. But as the valves are closed, there is no flow in the pipes and the particles form a deposit at the bottom of the pipe. (This process takes a long time: this explains why when the pump rotation speed is zero or slow, the density curve decreases slowly.) The condition on velocity is V≈0. Many correlations are available to define these different critical speeds [3 and 4]. 2.2.2. Application to typical flows Fig. 2 and Fig. 3 represent five density configurations that could appear in the extract circuit where the pipe diameter is R=300 mm. ? Assumption 1: homogeneous flow. This case is included only to confirm that the computation works correctly. ? Assumption 2: heterogeneous flow. ? Assumption 3: building bed configuration 1. Linear decreasing law, ? Assumption 4: building bed configuration 2. Parabolic decreasing law: ρ(r)=9.98R2?2.9R+1.3 ? Assumption 5: deposit. This case is not useful for the optimization of the angular position, but it does fit with a working case (when the pumps must be stopped for a long time). (51K) Fig. 2. Different kinds of flows. (11K) Fig. 3. Density configurations. The aim of these computations is to calculate the mass which is really seen by the device. In fact, if the device cannot measure the density on a representative sample, the given value cannot be the true value. All computation use numerical primitive computation, the radiation beam is a cone of 10°-vertex angle, its base radius is 45.5 mm and its vertex radius is 20 mm. The mass of matter contained in 1 m of the pipe will be calculated. As we know the volume intercepted by the beam we can then deduce the theoretical density. Fig. 4 presents the results obtained using a mixture of a solid and liquid having as an average density 1.25. It shows how, for assumptions 2–4, the relative error varies following the same law. This is explained by the fact that the density variation law is similar for the three assumptions. (6K) Fig. 4. Errors versus inclination angle. Assumptions 1 and 5 correspond respectively to two unusual working cases: that of homogeneous flow, and that of the pump not being in use. They have been calculated to give an overall image of the working of the circuit. 2.2.3. Measurement of the density by control of the power absorbed by the pump Tunnel boring machines have to evacuate large quantities of matter while in use. It is this fact that gives such an importance to the slurry circuit, which is the quickest and most convenient means of evacuating the rubble. The slurry circuit is divided into two different circuits, the first carries the bentonite to the boring chamber while the second extracts the carrying fluid and the rubble from the head of the machine. The data analyzed come from boring sites in Sidney (Australia) and Lille (France). The diameter of the machine is nearly 8 m. 2.3. Behavior of the centrifugal pumps with slurry flow The pumps used for the hydraulic circuit of transport are centrifugal pumps with volute and their inlet power is about 800 kW. The dimensionless parameters allow us to characterize the operation of the pump and are defined below: ? Coefficients of pressure and flow rate, respectively Ψ and : (2) (3) where H and qv are the head in meters of the mixture and the flow rate volume of the pump. ? Volumetric concentration of solid materials c and average density of the mixture ρm. By indicating by qvs the flow rate of the solid and by qVl the flow rate of the liquid (here the bentonite): (4) and (5) where ρs is the density of the solid phase and ρI is the density of the liquid phase. ? Concerning the pump, the coefficient of power and the global efficiency are defined by: (6) and (7) According to the concentration in the solid, the characteristic head-flow rates are degraded by appearance of complementary hydraulic losses resulting primarily from the difference in speed between the particles of the dispersed phase and the liquid phase [4 and 5]. On the other hand, as the power absorbed is proportional to the moment of momentum being exerted on the impeller, the latter is proportional to the average density of the mixture. The coefficient of power is thus, in its form (6), independent of the concentration. This remarkable property was the subject of many experimental validations, including in the presence of a diphasic mixture of liquid–gas [6, 7, 8 and 9]. For a given pump, as long as the wear of the impeller is moderate (the characteristic of power being invariable), it is possible to calculate the coefficient of flow rate and the coefficient of power τ, by beginning with the measurement of total flow rate (Fig. 5). (11K) Fig. 5. Characteristics of a centrifugal pump according to the solid material concentration. The simultaneous measurement of the input shaft power directly gives the density of the mixture ρm Relations ((4) and (5)) make it possible to calculate the various flow rates, the volumic concentration of transport, the total mass flow rate, etc. 2.4. Validation of the procedure To allow validation of this procedure, two work sites using a slurry-shield machine were explored. The shield diameter varied between 8 and 11 m, the pipe diameter for the extract and feeding circuit were respectively 400 and 350 mm, and the slurry pumps were equipped with vortex impellers. Throughout the boring time, many experimental data were recorded. One could thus carry out several months of operation of the slurry circuit and record physical parameters such as the speed of rotation, the intensity, the voltage of the electric motors, and the pressures recorded on the various manometers on all the important points of the circuit. As we have already indicated, the control of the tunneller and the control of its operation require knowledge of the flow rate and the density of the mixture. Fig. 6 shows a qualitative comparison between the density of the mixture measured by gamma densitometer at the Sydney site and the electric power absorbed by the pump. After treatment and adjustment of the signal of power (integration of the speed of rotation, volumetric flow rate and characteristics of the pump), and installation of the gamma-densitometer under satisfactory angular conditions, comparison of the measurements becomes satisfactory. Fig. 7 shows a comparison between the density measured by the gamma-densitometer installed on pipes having 300 mm diameter and the density calculated by the method described in this paper and calling upon the behavior of the pump. (17K) Fig. 6. Correlation between gamma-densitometer values and measured power. (18K) Fig. 7. Comparison between the density given by the gamma-densitometer and the pump behavior. 3. Conclusion The results showing the comparison between the evolution of the mass flow rate calculated starting from the shaft power absorbed by the pump and the mass flow rate given by the gamma-densitometer are very satisfactory. The behavior of the pump with respect to the fluid which crosses it allowed an evolution of the mass flow rate in a sufficiently precise way. The simplicity and the additional equipment to be installed give clear advantages to this method of measurement. Nevertheless, preliminary work is necessary in order to calibrate the various intervening parameters in calculation of the mass flow rate. Acknowledgements The present study was supported by the Commission of the European Communities Union in the framework of the Brite Euram project BE95-1735. The authors would like to thank the “Laboratoire de Robotique de Paris” for allowing us to do this work. References 1. A. Shekarriz, D.M. Sheen, Slurry pipe flow measurements using tomographic ultrasonic velocimetry and densitometry, Proceedings of FEDSM’98, ASME Fluids Engineering Division Summer Meeting, 21–25 June 1998, Washington, DC. 2. M.C. Roco, P. Nair and G.R. Addie , Casing headloss in centrifugal slurry pumps. Journal of Fluids Engineering 108 (1986), pp. 453–464. 3. P. Hergt, S. Brodersen, K. Patthivarti, V and R.J. Visintainer , A study of the outlet velocity characteristics of slurry pump impellers. Liquid-Solid Flows, ASME FED 198 (1994), pp. 197–205. 4. C.I. Walker, P.J. Wells, C. Pomat, The effect of impeller geometry on the performance of centrifugal slurry pumps, International Conference on Bulk Materials Handling and Transportation; Symposium on Freight Pipelines Wollongong, Australia, 6–8 July 1992, pp. 97–101. 5. F. Bakir, P. Weiss, R. Noguera, R. Rey, Etude théorique et expérimentale de I’écoulement diphasique dans les pompes centrifuges, Revue Fran?aise de Mécanique No. 1999–3, pp. 227–234. 6. V.K. Gahlot, V. Seshadri and R.C. Malhotra , Effect of density, size distribution, and concentration of solid on the characteristics of centrifugal pumps. Journal of Fluids Engineering 114 (1992), pp. 386–389. 7. K.K. Sheth, G.L. Morrison and W.W. Peng , Slip factors of centrifugal slurry pumps. Journal of Fluids Engineering 109 (1987), pp. 313–317. 8. P. Weiss, R. Rey, R. Noguera, The 6th Asian Congress of Fluid Mechanics, Centrifugal Pumps Problems when Conveying Gas Bubbles, Singapore, 1995. 9. J.L. Anderson, A.G. Stephens, Densitometer System Description and Uncertainty Analysis for Savannah River Tank/Muff/Pump Separate Effects Tests, EG&G-NRE-10958, September 1993.