Particle Resuspension Modelling in Turbulent Flows

Transcription

1 Particle Resuspension Modelling in Turbulent Flows Fan Zhang IRSN (F) - Newcastle University (UK) Ecole Centrale de Lyon (F) Abstract In the event of a severe accident (SA) affecting a light-water-cooled reactor (LWR) or other reactor technology, it is expected that mechanical resuspension of deposited particles/dust by aerodynamic forces would be a primary safety concern. The overall objective of the work here is to develop, validate and apply a mechanistic model for the aerodynamic resuspension of particles from multi-layer deposits that can account for the resuspension of clusters of particles from a bed of particles of variable size and shape. The practical application will be that of assessing resuspension of particles in a range of accident scenarios for LWRs as well as other reactor technologies. The model will probably be a hybrid development of the well-known Rock n Roll model adapted for application to multilayer deposits. The current status of this work is that a critical review of existing approaches to model the resuspension phenomena has been completed and progress is being made on an initial improvement to the Rock n Roll model using information from direct numerical simulations of a turbulent boundary layer. 1. Background In the event of a severe accident affecting a light-water-cooled reactor (LWR) or other reactor technology such as a helium-cooled high-temperature reactor (HTR or V-HTR) or a thermonuclear fusion reactor (ITER), it is expected that mechanical resuspension of radioactive deposited particles would be a primary safety concern. In a LWR this phenomenon would occur, for example, in two principal situations: within the reactor coolant system due to so-called steam spikes (rapid flow accelerations) as the degrading core collapses into remaining water in the reactor vessel; within the containment if a hydrogen deflagration takes place. The relevance of resuspension and its modelling to safety assessment of reactors such as ITER and HTR arises from the accumulation of contaminated dust in the coolant circuit/torus. For ITER, activation products will accumulate in deposited particles (graphite, beryllium, tungsten) in the torus and could, in the event of a coolant-wateringress accident, be resuspended in the flow. For a HTR, the main accident scenario of coolant-circuit depressurization would resuspend dusts contaminated with activation

2 products and small quantities of fission products released during normal operation such as silver and strontium. Numerous experiments have been carried out to predict the level of mechanical resuspension of deposited particles arising in LWR severe accidents. The most recent are the STORM tests which examined the resuspension of multi-layer aerosol particles in a pipe by high pressure dry steam flows typical of those in a LWR loss-of-coolant accident (LOCA). [4] As part of the STORM programme, the resuspension data were used to develop and test a number of resuspension models of various levels of sophistication. Of these, the most useful in terms of adaptability and predictability was the mechanistic Rock n Roll model [17] see below. The Rock n Roll was successfully fitted to STORM results (despite the significantly smaller size particles and higher flow rates of these tests relative to those used to develop the model) and those of other experiments by using the data to produce values of the surface adhesion that would be consistent with the measured resuspension. [1] Significant development has taken place since the STORM tests with regard to the modelling of resuspension of particles from multi-layer deposits. In particular Friess and Yadigaroglu [7] have developed a model for resuspension of multilayer deposits taking into account the dependence of resuspension rates on the deposit structure as well as the fact that particles are typically resuspended in clusters. The deposit structure was defined in terms of variable bed porosity and resuspending clusters of particle were identified based on a balance between forces of adhesion and turbulent burst. The objective of this work is to develop, validate and apply a physical model for the resuspension of particles from multi-layer deposits that can account for the resuspension of clusters of particles from a bed of particles of variable size and shape. The practical application will be that of assessing resuspension of particles in a range of accident scenarios for LWRs as well as other reactor technologies such as ITER and HTR. The model could be a hybrid development of the Rock n Roll model adapted for application to multilayer deposits. 2. Pure Resuspension Modelling 2.1 The Resuspension Phenomenon The resuspension of a particle from a multi-layer deposit depends on the interaction of two processes: the aerodynamic forces tending to remove the particle from the bed and the various forces (essentially due to particle-particle interactions) that resist resuspension. To some extent, these two effects can be decoupled and studied separately. The aerodynamic forces acting on a particle will depend mainly on the turbulent flow and will be largely independent of the nature of the surface so that results obtained for an isolated particle on a smooth wall can be applied to an exposed particle sitting at the surface of a multi-layer deposit.

3 For multi-layer deposits, cohesive forces between particles must be considered in order to explain the resuspension of particle clusters from such deposits under the influence of turbulent drag and lift forces. Micro- and macro-scale roughness of the multilayer deposit may have some influence on the turbulent structure of the near-wall boundary layer, thus modifying the aerodynamic forces acting on the particle. And the presence of a wide range of particle sizes within the multilayer deposit can result in additional resistance forces caused by interaction between the particles. An important consequence of this interaction is that the resistance to resuspension can vary in time the larger particles will tend to resuspend first, leaving a higher concentration of smaller. These smaller particles might then act as cement, locking in the larger particles in the lower layers, and thus modifying the threshold for particle erosion. 2.2 Critical Review of Models/Approaches A comprehensive review of resuspension was carried out by Ziskind et al. [22]. Here we give only a brief summary of the salient features of the models that have been used in severe accident studies and which we will develop in the course of this study Force-Balance Models The first statistical force balance model was proposed by Cleaver and Yates [5] who considered the role of the different forces acting on a deposited particle in a turbulent boundary layer. They defined a rate of particle removal from a surface by a gas flow based on visual observations of the spatial distribution (with 630ν f /u τ long and 135ν f /u τ wide) and frequency of turbulent ejections near the depositing surface (turbulent bursting mean time 75ν f /u τ 2 ) and the condition that resuspension occurs when the lift force [9] acting on the particle is greater than the adhesive force [21]. Similar condition is derived by Ziskind et al. [23]. Braaten et al. [2] developed a Monte-Carlo particle resuspension model, which is capable of simulating the unsteady resuspension nature. They considered the turbulent burst effect and used the mean time between bursts is approximately 300ν f /u τ 2. Wen and Kasper [20] demonstrated a kinetic model of particle reentrainment which describes resuspension as a first order reaction, similar to molecules desorption from an inhomogeneous surface with a certain rate constant. Their model showed a well agreement with experimental data and also explained observed systematic derivation of the data from the 1/t law, which the particle concentration is close to 1/t for long term resuspension. In nuclear safety studies, there are two force-balance models worthy of mention. Parozzi and Tagliaferri [14] developed a resuspension model for the ECART code based on a correlation of resuspension rate with a resultant detachment force acting on a particle which is a function of the particle radius. A statistical/force-balance model applied in the CÆSAR code was developed by Hontanon et al. [12] using a 2D Lagrangian particletracking method, which calculates particles trajectories in the viscous sublayer. This approach has been extended recently by Guingo and Minier [10].

4 2.2.2 Energy-Accumulation Models Reeks, Reed and Hall [16] developed a different approach to resuspension by considering the accumulation of vibrational energy of a particle within a surface adhesive potential well arising from the Van der Waal s adhesive and elastic restoring forces and their dependence on particle-surface deformation (this is referred to as the RRH model). A particle on a surface exposed to a turbulent flow is assumed to oscillate within this potential well due to fluctuations in the lift force arising from the near wall turbulence. The vibrational energy is made up of two parts: a resonant contribution where the particle is vibrating at the natural frequency of the potential well and an off-resonant contribution where the particle is vibrating at the frequency of the fluctuating in lift force. If resonant energy is neglected, the RRH model becomes a force-balance model where the particle is only resuspended when the lift force exceeds the adhesive force. In general however a particle is detached from a surface once it has accumulated enough vibrational energy to overcome the surface adhesive potential barrier from the balance of the adhesive and mean lift forces at the point of detachment. Unlike the force balance model, particles can be resuspended even when the adhesive force is stronger than the lift force. The formula for the resuspension rate constant turns out to be very similar in form to that proposed by Wen and Kasper [20] which is based on the formula for the desorption of molecules from a surface and is more of a statistical model than a force-balance one. The classical Rock n Roll model is reviewed below in Multilayer Deposit Models There are not many models that consider multilayer deposits. It seems that Paw [15] made the first model to predict the long term resuspension rate which is independent to the time. Fromentin [8] considered the resuspension rate as a function of time with constant a, b (F r = a * t - b ) and setup the PARESS experiment to confirm the model predictions. Lazaridis and Drossinos [13] derived an expression for the total particle resuspension rate from a multilayer deposit in terms of the resuspension rate from each layer which is based on RRH model [16]. An interaction potential is considered between each layers and the particle-particle interaction in the same layer is neglected. A generic model was developed by Friess and Yadigaroglu [6] which uses a recursion relation to calculate resuspension rate of the other layers from the first layer. The results are compared with L&D and Formentin and the method is applied to the RRH model. They concluded that the monolayer models considerably over predict the resuspended mass in a thick deposit, and this is also true for the resuspension rate in the short term. They also pointed out in [7] that the resuspension of multilayer deposits involves some effects that have not been included in the existing models like mutual obstruction of particles, clustering effects and deposit structure. 2.3 The Rock n Roll Model (R n R) From their observations of resuspension due to rolling, Vainshtein et al. [19] concluded that the drag force is a more effective agent than lift for the transfer of turbulent energy from the flow to a particle on a surface. Subsequently Reeks and Hall modified the RRH model to take account of the influence of drag due to rolling. The model is known as the

5 Rock n Roll model [17] and is based on direct measurement of the aerodynamicallyinduced forces acting on a particle in a turbulent boundary layer. Model predictions have been compared with the resuspension measurements of particles from a flat plate in a fully-developed turbulent boundary layer for which the spread of adhesive forces holding the particles to the surface had been measured in a separate experiment. In this particular set of measurements, the particle sizes involved were in the range 1 to 20 microns and the deposit was restricted to less than mono-layer coverage. In this model, the particle oscillates about the pivot point of the asperity rather than in the vertical direction (see Figure 1). Compared to the RRH model (based solely on lift), the resuspension rate is much greater. The energy spectrum of fluctuating lift and drag force used in the model is based on Hall s [11] measurements. The influence of surface roughness is also considered In the R n R model by using a log-normal distribution of adhesive forces based on measured adhesive forces for nominally smooth surfaces. To determine the resuspension rate constant which is the key to calculating resuspension rate and the particle fraction remaining, the statistical motion of a particle within the potential well must first be established, in particular the distribution of particle displacements and velocities. These are both assumed to be obtained from a Gaussian distribution in the model (which is in fact not correct practically seen below). A limitation of the R n R model is that it deals with isolated-particle resuspension (i.e resuspension from multilayer deposits of particles is not considered). Figure 1 - Geometry of Rock n Roll model (Reeks and Hall, 2001)

6 Alumina particle fraction remaining after 1s in RnR Model 1 μm 5 μm 10 μm 0.7 Fraction remaining u τ (m/s) Figure 2 - Fraction remaining after 1s (parameters from Table 3,4,5 in Reeks & Hall, 2001) Figure 3 - Comparison of Biasi s prediction with Hall s tests (10μm Alumina)

7 2.4 First Steps in Improving the Rock n Roll Model Biasi et al. [1] applied a simple mechanistic model based on Rock n Roll model for resuspension which uses a log-normal distribution of adhesive forces to analyze the resuspension measurements of experiment tuned adhesion parameters (geometric mean and standard deviation) to fit the Hall s and Braaten s [3] experiments data. Biasi s correlations have been implemented in R n R model and compared with Hall s test. (Figure 3, 4) Figure 4 - Comparison of Biasi s prediction with Hall s tests (20μm Alumina) As discussed above, there are some assumptions that can today be improved in the R n R model. The first major step is to modify the appropriate distributions for particle displacement and velocity within the potential well. Direct numerical simulation (DNS) of turbulence can be used to generate statistics improving the statistics used in the model of the fluid fluctuations next to the particles. An example is shown in the following figures 5 and 6.

8 1800 Assumption of particle velocity in Gaussian distribution probability particle velocity (m/s) Figure 5 - Distribution of particle velocity in R n R model 2500 Distribution of particle velocity in turbulent boundary layer probability particle velocity in x-direction (m/s) Figure 6 - Distribution of particle velocity practically (Data from cfd.cineca.it CFD-database)

9 3. Summary of Current Status Background and literature reviews of the crucial models have been completed where most important models have been critically examined. The RRH and the R n R (with and without resonance) models have been programmed in order to improve understanding of the different model features. Biasi s correlaions [1] for particle surface adhesion has been implemented in R n R model. The first major step of modifying the R n R model is to replace the statistics of particle motion within the potential well from the current Gaussian distribution with a distribution generated from DNS calculations. Acknowledgments This work is supervised by Prof. Reeks (Newcastle University), Prof. Perkins (Ecole Centrale de Lyon) and Dr. Kissane (IRSN).

10 References 1. Biasi, L., de los Reyes, A., Reeks, M.W. and de Santi, G.F. (2001) Use of a simple model for the interpretation of experimental data on particle resuspension in turbulent flows, Journal of Aerosol Science, Vol.32, p Braaten, D.A., Paw U, K.T. and Shaw, R.H. (1990) Particle resuspension in a. turbulent boundary layer observed and modeled, J Aerosol. Sci., Vol.21, p Braaten, D. A. (1994) Wind tunnel experiments of large particle reentrainmentdeposition and development of large particle scaling parameters, Aerosol Science and Technology, Vol.21, p Capitão, J. A. and Sugaroni, F. (1995). STORM Benchmarks. Final comparison report. EUR EN 5. Cleaver, J. W. and Yates, B. (1973) Mechanism of detachment of colloidal particles from a flat substrate in a turbulent flow, J. of Colloid and Interface Science, Vol.44(3), p Friess, H. and Yadigaroglu, G. (2001) A generic model of the resuspension of multilayer aerosol deposits by turbulent flow, Journal of Nuclear Sci. and Eng., Vol.138(2), p Friess, H. and Yadigaroglu, G. (2002) Modelling of the resuspension of particle clusters from multilayer aerosol deposits, Journal of Aerosol Science, Vol.33(6), p Fromentin, A. (1989) Particle resuspension from a multi-layer deposit by turbulent flow, Ph.D. thesis No 8971, Swiss Federal Institute of Technology, Zurich 9. Goren, S. L. (1970) The normal force exerted by creeping flow on a small sphere touching a plane, J. Fluid. Mech., Vol.41, p Guingo, M. and Minier, J. P. (2008) A new model for the simulation of particle resuspension by turbulent flows based on a stochastic description of wall roughness and adhesion forces, J. Aerosol Sci, - incomplete Hall, D. (1998) Measurements of the fluctuating lift force on a particle at a boundary in turbulent flow, J. Experimental Fluid, - incomplete Hontañón, E., de los Reyes, A. and Capitão, J. A. (2000) The CÆSAR code for aerosol resuspension in turbulent pipe flows. Assessment against the storm experiments, J. Aerosol Sci, Vol.31(9), p Lazaridis, M. and Drossinos, Y. (1998) Multilayer Resuspension of Small Identical Particles by Turbulent Flow, Aerosol Science and Technology, Vol.28(6), p Parozzi, F. and Tagliaferri, L. (2000) Improvement of the dry aerosol resuspension model of ECART code in the light of STORM results, CESI final report, A0/ Paw, U. K. T. (1982) A universal model for entrainment processes, Proceedings of the fourth international conference on precipitation scavenging, dry deposition and resuspension, St. Monica (California), p Reeks, M. W., Reed, J. and Hall, D. (1988) On the resuspension of small particles by a turbulent flow, Journal of Physics D: Applied Physics, Vol.21(4), p

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