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Silica particle deposition in superheated steam in an annular flow: Computational modeling and experimental investigation
Geothermics 86 (2020) 101802
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Silica particle deposition in superheated steam in an annular flow: Computational modeling and experimental investigation
T
Vijay Chauhan*, Maria Gudjonsdottir, Gudrun Saevarsdottir School of Science and Engineering, Reykjavik University, Menntavegur 1, 101 Reykjavík, Iceland
ARTICLE INFO
ABSTRACT
Keywords: Deposition Geothermal Silica Steam Superheat
The work presents computational modeling and an experimental investigation of silica deposition occurring in geothermal systems with superheated steam flows. An advection diffusion model was implemented for predicting silica particle transport and deposition in turbulent flows. The model includes the effect of Brownian diffusion, turbulent diffusion, turbophoresis, Saffman lift force, and drag force on particle motion. Simulation results for deposition of silica particles in superheated steam flow were validated experimentally. An experimental setup consisting of a superheated steam generating system, silica injection system and test section assembly was designed and constructed. Deposition velocity was measured for silica fume particles ranging from 1 to 20 μm in diameter. The measured data shows agreement with the implemented model simulation results showing an increase in deposition velocity with increase in particle relaxation time in diffusion impaction regime.
1. Introduction High enthalpy fluids extracted from an unconventional vapor dominated geothermal system in a superheated state offer the potential to obtain more power, with greater efficiency, than from fluids extracted from conventional geothermal systems. The Icelandic Deep Drilling Project (IDDP) was established in year 2000 to investigate the technical and economic feasibility for utilization of an unconventional, very high temperature steam from deeper wells (Palsson et al., 2014). The geothermal well designated IDDP-1 was drilled at the Krafla geothermal field in northwest Iceland in an attempt to obtain supercritical steam. The well did not produce supercritical steam, but rather superheated steam with an enthalpy greater than 3170 kJ/kg and at pressures up to 15 MPa. Due to its high pressure, the steam contained a considerable amount of dissolved silica (up to 66 ppm) in gaseous form. The high concentration of silica in superheated steam occurs due to increase in silica solubility with increase in pressure near to the supercritical region (Bahadori and Vuthaluru, 2010). Lowering the steam pressure causes silica to precipitate, as was observed in IDDP-1 (Markusson and Hauksson, 2015). The precipitated silica is found as particles carried within the superheated steam flow. The particles deposited on the surface of different components causing scaling. Silica scaling in geothermal heat exchangers has an impact on pressure and performance, such that the pressure drop increases and performance
⁎
decreases with increase in silica scaling. This was seen at the Wairakei power plant in New Zealand, studied by Zarrouk el al. (2014). Studies shows scaling has major long term effects on power plant performance. It is therefore necessary to take measures to control silica scaling to maintain the design output of a geothermal power plant. Controlling silica scaling by chemical means is suggested in the literature (Gallup and Barcelon, 2005). The addition of inhibitors to control scaling relates to two phase geothermal fluid as it requires the presence of a liquid phase where mineral solubility can be influenced. For superheated steam, similar to that obtained from IDDP-1, considerable amount of liquid injection required for adding inhibitors would cause quenching of the superheated steam and hence reduce the exergy of the geothermal fluid. A different method to control silica scaling occurring in superheated steam flow is therefore proposed. Application of heat recovery system to retain steam superheat, utilizing salt solution with high boiling point elevation as a scrubbing medium was proposed by Chauhan et al. (2019). The feasibility of utilizing a heat recovery system, however, depends on the hydrodynamic characteristics of silica particles in the superheated steam flow, which plays a vital role in the phenomena of deposition, causing scaling. A study on hydrodynamics characteristics of silica particles in superheated flow is therefore proposed. The process of silica scaling involves precipitation, agglomeration and then deposition on a surface. Developing methods to control silica
Corresponding author. E-mail address: [email protected] (V. Chauhan).
https://doi.org/10.1016/j.geothermics.2020.101802 Received 7 January 2018; Received in revised form 23 December 2019; Accepted 5 January 2020 0375-6505/ © 2020 Elsevier Ltd. All rights reserved.
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scaling requires an understanding of silica particle transport in superheated steam flow and the factors controlling it. A study on scaling under controlled hydrodynamic conditions was done by Brown and Dunstall (2000) to understand the effect of different hydrodynamic parameters on particle transport. The study showed that the scaling increased with an increase in particle diameter. Their study however does not provide a definite theory or model to predict the silica scaling rate. An insight into the mechanisms of silica particle transport in superheated steam flow can be obtained through computational modeling. Predicting particle transport and deposition in a two phase flow is also important in other engineering applications and scientific studies. The particle deposition in gas flows is observed in many processes, including chemical aerosol transportation and in atmospheric pollutants. Researchers have proposed various approaches to model particle deposition in a two-phase flow. Friedlander and Johnstone (1957), for example, introduced a free flight model in order to predict deposition of small particles suspended in gas flow in a pipeline. The free flight model assumes diffusion of particles in a flow up to a certain distance, called stop distance, after which they are assumed to have free flight to the wall. Various modifications have been made in the model depending upon the prescription of free flight velocity (Davies, 1966; Beal, 1970). The free flight model however suffer problems as the particle size increases. The free flight model shows a monotonic increase in deposition velocity with an increase in particle relaxation time, which contradicts experimental values showing a third regime where the particle velocity decreases as relaxation time increases. Another approach for predicting particle transport in gaseous medium is the Euler-Euler two phase method, in which both particles and the gas phase are assumed as continuous, and equations are modeled in Eulerian field. Considerable progress has been made in the development and modeling of the EulerEuler two phase approach (Reeks, 2005). In this method, equations are obtained by averaging instantaneous equations of mass, momentum and energy for the particle phase. The averaged equations obtained are coupled and require closure relations for particle Reynolds stress and carrier flow velocity field. Despite high computational efficiency, application of the Eulerian two fluid approach relies on constitutive relations, or closure equations, to be obtained by a heuristic or empirical approach. A simplified Eulerian model called the diffusion-inertia model was developed for isothermal flows (Zaichik et al., 1997a) and flows involving heat transfer (Zaichik et al., 1997b) for low inertia particles. Later improvements were made in the model by two waycoupling to include back effects of particles on fluid (Zaichik et al., 2010). The model suffers, however, from the disadvantage of application to low inertia particles only. Complexity in Euler two fluid model was reduced by using the simple advection-diffusion equation shown in the independent work done by both Guha (1997) and Young and Leeming (1997). The advection-diffusion approach for modeling particle deposition on a vertical wall was first applied by Johansen (1991). Major mechanisms contributing to deposition such as Brownian and turbulent diffusion, turbophoresis, Saffman lift and electrostatic force were accounted for in the model. The most important feature of this model is that the advection-diffusion equation is uncoupled from the equation for mean particle velocity, which is used in advection-diffusion equation itself. Deposition features were successfully reproduced by both models (Guha, 1997 and Young and Leeming, 1997) for a case of turbulent flow through a pipe. Despite the simplicity in solving the equations of the advection-diffusion model, however, difficulties arise in solving problems with particle discontinuities and in the treatment of boundary conditions. Issues related to the Eulerian approach are discussed and addressed in the work of Slater and Young (2001). A similar approach for computation including the effect of turbulence was presented in the work of Slater et al. (2003). The work involves deriving an advectiondiffusion model using the theoretical approach described in Young and Leeming (1997) with the particle continuum equations averaged using
the density-weighted method, and shows the application of a derived model for more complicated geometry involving solid particle in gas flow through a turbine. As these models relate to particles flowing with air, it is important to have an experimental validation of a general two-phase flow computational model, particularly for its application in study involving silica particles in superheated steam flow. Extensive experimental studies on particle deposition in vertical tubes with air flow exist in the literature, which were used to inform the design of experiments within this study. A study of particle deposition on a vertical glass tube coated with petroleum jelly was done by Stavropoulos (1954). Measurements of deposition velocities in flows with varying Reynolds numbers were made by Postma and Schwendiman (1960) for 2−4 μm diameter ZnS particles and 30 μm glass spheres: aluminum, steel, and brass tubes of different diameters were used in the study. Experiments on the effect of surface roughness on deposition were done by Wells and Chamberlain (1967), using particle sizes ranging from 0.17 to 15 μm and with different densities. Deposition on surfaces with different levels of microscale roughness were also studied by El-Shobokshy (1983). The studies found that surface roughness substantially affected deposition rates. On effect of surface roughness on deposition, Sehmel (1968) showed an increase in deposition in one experiment and no effect in another experiment due to changes in surface roughness. The deposition of olive oil aerosols in vertical turbulent flows over a wide range of flow conditions was studied by Liu and Agarwal (1974). They showed the variation of deposition as a function of relaxation time in the diffusion impaction and inertia regime. Data related to deposition in the diffusion regime is provided by Shimada et al. (1993). Lee and Gieseke (1994) conducted experiments on particle deposition onto pipe walls in turbulent flow. The measurement covers both turbulent diffusion and the diffusion impaction regimes. An experimental study on the deposition rate of non-spherical particles in laminar flow was reported by Gallily and Cohen (1979). Investigation of the deposition of non-spherical particles was done by Kvasnak el al., (1993). Deposition measurements for spherical beads and irregular shaped dust particles were compared with the results from empirical models. Experimental validation of these deposition models, as reported in the literature above, was carried out with air as a flow medium. This is not surprising as most relevant systems refer to particles in air. The experiment designs used in the various studies cannot be used for studies involving superheated steam application. This is due to the limitation of the equipment’s and measurement technique used in the experiments for low temperature applications involving air as a flow medium. The current work focuses on the study of deposition occurring in geothermal systems which consist of superheated steam as a transport medium, with precipitated silica particles in a dispersed phase. The particles occurring in the geothermal steam flow consist of silica agglomerates of irregular shapes and varying sizes, depending upon the degree of agglomeration. The flow medium, that is superheated steam, has different hydrodynamic properties to air. The computation model validation for geothermal system applications therefore requires an experimental investigation involving silica particles in superheated steam flow. The work implements an advection-diffusion model for modeling silica particle transport and deposition in superheated steam flow using OpenFoam (OpenFOAM, 2014), an open source Computational Fluid Dynamics (CFD) package. Continuum equations for particle flow were written in OpenFoam notation and existing turbulence models and solvers in the software were used to solve for the required fluid flow variables. An experimental setup was designed and constructed, and a study was performed to determine silica deposition in superheated steam flow for different relaxation times. The experimental measurements were compared to data from the literature as well as the computational model simulation.
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2. Computational model
inertia, particle slip velocity must be taken into consideration by incorporating a drag coefficient into the equation. The drag coefficient (Clift et al., 1978) can be expressed as:
Simulation of advection-diffusion model requires solving conservation equations for the fluid (steam) and the particle (silica) phase. The solver in OpenFoam consists of fluid phase equations which are solved independently to obtain the fluid flow variables. The conservation equations for the particle phase however, needs to be implemented. Equations for both phases are described as follows:
Cd =
p, inertial
In a Eulerian frame, for incompressible turbulent flow, the well know expressions for Reynolds averaged mass and momentum conservation equation are:
1 p + f xi
f
2u ¯
i
x i xj
+
(2)
3
t
cp vi t
xi
+
=0
(cp vi vj ) xj
= cp (Fdrag , i + Flift , i )
c¯p t
(3)
=
xi
=
xi
uj
vj p
(9)
c¯p
(DB + DT ) ( u¯i uj ) xj
+
(10)
xi v¯ic
u¯ i p
j =1 j i
f p
p
u¯ j xi
1 2
v¯jc
u¯ j p
(11)
where is the density-averaged particle convective velocity, DB is the coefficient of Brownian diffusion, DT is the coefficient of turbulent diffusion and is the ratio of particle mean square velocity to the fluid mean square velocity. The detailed expressions for the coefficients are available in the literature (Slater and Young, 2003). Fluid flow equations were solved using existing solver and utility functions in OpenFoam to obtain fluid velocity field, fluid root mean square velocity and turbulent diffusivity. These variables are required in the particle continuum equations, which are also written in OpenFoam notation. The values of concentration, velocity field, and their flux are updated in the runtime loop until a steady-state solution is achieved. To obtain the physical requirement of an absorbing boundary condition, zero wall normal gradients of particle density and velocity are applied to generate the required particle fluxes at the boundary. Such conditions corresponds to zeroth order extrapolation from the flow to the wall.
v¯ic
vi (5)
2 p rp2 9µ f
(cp v¯ic )
+ 0.725
Where p is the particle relaxation time which for the Stokes regime is expressed as: p
p
3
The drag force is a mechanism causing particles to approach a velocity equal to that of the surrounding fluid due to viscosity of the fluid. The force acts opposite to the direction of the relative velocity of a particle with respect to the fluid and is given as:
p
1/2
xi
(4)
2.3. Drag force
ui
+
v¯ic (v¯ic ) + vjc = xj t
Where vi is the particle velocity along direction i , cp is the particle concentration in mass per unit volume and Fi represents the force per unit mass acting on particle along direction i . The forces (per unit mass) acting on particles, shown on the righthand side of Eq. (4), are defined in the following two subsections.
Fdrag, i =
uj
p
After inserting the above expressions for the forces in Eq. (4), Eqs. (3) and (4) need to be averaged in order to obtain the final equations. Various approaches have been applied in the literature for averaging. Non-density-weighted based Reynolds averaging was applied in Cartesian coordinates by Guha (1997) and in cylindrical coordinates by Young and Leeming (1997). Density-weighted averaging was used in the work of Slater and Young (2003). The method offers the advantage of producing fewer turbulence terms. The averaged equations can be simplified further separating particle flux into its convective and diffusive components; however, the final equations obtained are similar to those obtained using the non-density weighted averaged method. The detailed derivation can be found in Slater and Young (2003). The final equations are written as:
For the particle phase, conservation equations are required for particle concentration and momentum balance. The equations are expressed in a Cartesian tensor form as:
(cp vi )
(8)
g
j=1 j i
2.2. Particle phase conservation equations
+
p
Flift , i = 0.725
where u¯i is the Reynolds averaged fluid velocity along direction i, p is the fluid pressure, and f and f are the fluid density and kinematic viscosity, respectively. The last term in Eq. (2) represents the gradient of velocity fluctuations. Velocity fluctuations and the scalar property for eddy viscosity can be obtained using two equation turbulence models. A number of turbulence models are available in OpenFoam. Commonly used two equation models include k-ε model and k-ω model. Details of the models can be found in the literature (Launder and Spalding, 1974). For obtaining the fluid velocity field, boundary conditions of a fixed inlet velocity and a velocity gradient of zero at the outlet and on the walls are assumed.
cp
24
Rep Cd
The lift force causes particle to move perpendicular to the direction of flow. The expression for shear induced lift force as derived by Saffman (1965) is given as:
ui¯uj xi
=
2.4. Lift force
(1)
u¯ i u¯ + u¯ j i = t xj
(7)
Where Rep is the slip Reynolds number. The resulting expression for particle relaxation time considering the slip velocity factor is given as:
2.1. Fluid phase conservation equations
u¯ i =0 xi
24 (1 + 0.15Rep0.687) Rep
(6)
3. Experimental setup
Where p and rp are the density and radius of a particle, respectively, and µ f is the dynamic viscosity of the fluid. For particles with large
Fig. 1 shows a schematic diagram of the experimental setup. The 3
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V. Chauhan, et al.
Fig. 1. Schematic diagram of the experimental setup.
setup consists of three sub-systems: the steam generating system, the particle injection system and the test section assembly. The steam generating system consists of an 18 kW electric boiler with a water storage tank for continuous supply. An airflow line from the compressor with a control valve (Cv2) is connected to the steam flow line after the gate valve (Cv1). This is required to run the setup with air flow at the beginning and at the end of the experiment. The wetness in the steam coming out from the boiler is removed in the cyclone separator (S1). The saturated steam is then passed through a throttle valve (Tv) and a 500 W superheater (SH) to attain the superheat. The particle injection system consists of a micro-screw feeder with a variable speed motor drive to control the feed rate. The micro-screw feeding mechanism provides an almost constant average feed rate of 40 mg kg−1. The particles delivered by the screw feeder are injected into the main line by suction in the ejector. The ejector system provides an easy way to inject particles into steam by mixing a small quantity of air into the steam. This overcomes the drawback of using aerosol generators with air as the only carrying medium, as used in experiment studies from the literature discussed earlier. The mixing of a small quantity of air into the superheated steam is justified by the fact that the geothermal steam from the well also consists of additional non-condensable gases. The particle and steam mixture is sent to another cyclone separator (S2). The separator works as a mixing chamber giving time for larger agglomerated particles to breakup forming a uniform mixture and reducing eddies in flow. The particle deposition test section consists of two 1.5 m long concentric steel pipes, where the inner diameter of the outer pipe is 22.5 mm and the outer diameter of the inner pipe is 17.5 mm. To sample particles from the inner pipe surface, the ends of the pipe were fitted with a thread and screw attachments for closure, making pipe removal easy as required for sampling. The outer pipe consists of a conical section such that the annulus area decreases by a ratio of 1:10 at the entrance. The conical surface of the outer pipe contains an inlet to which a stainless-steel probe is attached, which is used for collecting particles and for measurement of the mean concentration of the mixture. The probe, which has a length of 10 cm and inner diameter of 3.65 mm is sharpened at the front, while the other end is connected to a cone shaped flask made of cast iron. The material selection allows the flask to be heated in order to avoid condensation on the filter paper. The flask contains a wired mesh serving as a seat for the filter paper to collect particles. A membrane filter paper with 0.45 μm pore size and 47 mm diameter is used for collection. The filter is stable in steam up to a temperature of 180 ̊C. The flowing steam is passed through a control valve (Cv5) to control the flow rate through the probe. The steam is then passed through a condenser (C1) and then collected to measure the flow
rate through the probe. The steam from the test section is also collected after condensation in the condenser (C2) to measure the total flow rate. The system is well insulated and heated using heating tape to avoid heat loss from the flow. 4. Measurement procedure The system is run with air in the beginning. The superheater is switched on to heat the setup using air. This will ensure that there is no condensation in the test section at the start when the system is run using steam. Once the surface temperature of the equipment approaches the set-point temperature for the experiment, the airflow line is shut down and the steam flow line is opened. The steam is initially run through the system with air suction in the ejector and without particle feeding. This is done until steady mass flow, temperature and pressure are obtained. The boiler capacity limits the steam flow rate and so the system is always run constantly at a saturated pressure of 4.5 bar to achieve a steady state. A large pressure drop occurs in the ejector due to an expansion of steam from the ejector nozzle. The inlet mixture to the test section is at 160 ̊C and 1.4 bar. The volume flow rate of steam at the inlet of the test section is 150 l min−1. This corresponds to mass flow rate of 0.105 kg min−1. The mixture therefore has a considerable degree of superheat at the inlet of the test section. The flow has a Reynolds number of 3800. The particles used in the experiment are silica fume of density 2200 kg m-3 and with 97 % purity. Silica fume is an amorphous polymorph of silica dioxide and thus possess similar characteristics to silica found in geothermal systems precipitated from solution in superheated geothermal steam. It has a grey color due to minute percentage of impurities which increase its visibility on filter paper. The maximum particle concentration is kept less than 0.5 % by weight, similar to the concentration observed in IDDP-1. This corresponds to a volume fraction of less than 10-6 to ensure one way coupling between particle and flow turbulence (Elghobashi, 1994). Once the experiment was run using steam and particles for an average duration of an hour, the steam flow and particle injection were shut down. Finally air was run again for a few seconds to remove all steam from the test section to avoid condensation upon cooling. The deposited particles were collected on a polished pipe surface in test section, coated with polytetrafluoroethylene (PTFE) lubricant. The lubricant is thermally stable and insoluble in water. Coating causes a decrease in the coefficient of restitution and an increase in the energy loss of particles striking the surface, hence reducing the effect of rebound or re-entrainment. A particle sampling and counting technique using a digital microscope and image processing was used. The surface of the pipe was 4
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V. Chauhan, et al.
heated using an induction heater before taking images. This was done to remove the lubricant by vaporization, enhancing visibility. The particle flux Jw on the wall is calculated using the following equation:
Jw =
Nw t Aimage
IDDP-1. A small difference in the injected and measured concentration is observed due to chances of silica particles of small size escaping the filter surface while sampling and some particles depositing along the surface of equipment before entering the test section.
(12)
5. Results and discussion
where Nw is the number of particles of specific size on surface image, Aimage is the area of image and t is the time duration of the sampling. To determine the mean flow concentration, flow samples were taken using the probe over a time span of 15 min. For isokinetic sampling, flow velocity through the probe was kept consistent with that inside the pipe. The required flow rate through the probe was obtained by adjusting control valve (Cv5). The filter paper images were taken carefully after removing the filter paper from the flask. The mean particle concentration was determined with the following formula:
c¯p =
Nfilter Afilter 1 Aimage Aprobe t Vprobe
Fig. 3 shows the experimental results for deposition velocities of the silica particles in the superheated steam flow for varying relaxation times. A comparison of the experimental results for silica in superheated steam can be made with experimental data from the literature for aerosol in air flow by normalizing the relaxation time. To the author’s knowledge, no results are available in the literature for particle deposition in steam. The figure shows three different regimes of deposition for two phase flow with particles in dispersed phase. First, the turbulent diffusion regime where deposition occurs mainly due to Brownian and turbulent diffusion for particles with low relaxation time. A decrease in deposition velocity in this region occurs with increasing relaxation time due to a decrease in Brownian diffusion, which is the dominating mechanism for particle motion near to the wall. This decrease in Brownian motion occurs due to an increase in particle size. The second regime, called the diffusion impaction regime, consists of a steep increase in deposition with relaxation time due to lift and turbophoretic forces. The third regime, called the inertia regime consists of particle inertia, where deposition velocity slows down due to a decrease in the time of interaction with eddies as particle inertia increases with increase in particle size. As seen from the figure, the data from studies in the literature consists of experimental results on deposition for a specific range of relaxation time. The relaxation time range is limited by fluid velocity and the chosen range of particle sizes as seen from Eq. 16. The experiment was carried out for silica particles with sizes ranging from 1 μm to 20 μm and the superheated steam as a flow medium. The flow velocity was kept constant for the given design setup and electric boiler unit capacity. The relaxation time range was therefore obtained using the available particle size distribution. For the available particle size range, the setup was designed to obtain flow velocity such that the relaxation time range correspond to the impaction diffusion regime, where an increase in deposition is expected. The experimental results for silica and superheated steam flow show a steep increase in deposition rate with increasing relaxation time in the diffusion impaction regime. In geothermal systems with superheated steam, silica particles precipitated from superheated steam have chances to agglomerate due to collision and attachment along the flow after precipitation. This can be observed from the suspended silica particles sampled from IDDP-1, having size of the micro scale (Hauksson et al., 2014) obtained from the condensed steam as well as from the dry dust collected from the silencer rock and the silencer line. This agglomeration causes particle size to increase which increases its relaxation time. As observed from the results, an agglomerated particle with larger relaxation time have higher deposition velocity than smaller particle. Thus for the same concentration, the scaling rate increases with increase in degree of agglomeration. Results for the non-dimensional deposition velocity obtained in the current work are consistent with results from the literature involving aerosols in air flow for the same non-dimensional relaxation time range. An error is expected for low relaxation times due to the likelihood of small particles sticking to the surface of the probe due to bends and its small cross sectional area. This causes decrease in particle concentration (c¯p ) collected on the filter paper and hence measuring higher deposition velocity as given by Eq. 14. A simulation was performed using the implemented model based on the experimental conditions and boundary constraints. Results from the simulation show agreement with the experimental data in the diffusion impaction regime, as shown in Fig. 3. The simulated deposition curve for all three
(13)
where Nfilter is the number of particles of specific size on filter paper image, Afilter is the filter area, Aprobe is the inlet cross section area of the probe and Vprobe is the flow velocity through the probe. The non-dimensional deposition velocity is given by:
V+ =
Jw u *c¯p
where
u*
(14) is the friction velocity, defined as:
f 2
u* = Vav
(15)
where Vav is the average fluid velocity and f is the Fanning friction factor calculated using Blasius law for turbulent flows and smooth walls. The non-dimensional particle relaxation time is given by: +
=
*2 pu
(16)
f
Digital images with an area of 384 μm by 288 μm were captured of the pipe surface and the filter paper and were statistically analyzed using ImageJ (Schneider et al., 2012). Fig. 2 shows the resulting images from various steps of image processing, which are: original image (Fig. 2a), filtered image (Fig. 2b), threshold reverse image (Fig. 2c) and the analyzed image (fig.2d). The silica particles were agglomerated, making their shape irregular. This approach assumes projected area diameter as the diameter of a particle. A similar technique, assuming the particles to be spherical, was used by Kvasnak et al. (1993) for measuring the size of dust particle of irregular shape. The result shows small compact irregular shape dust particles follow the same trend of variations as those of spherical particles. Images are averaged for each particle size with a band width of ± 0.5 μm considering each image as one sample. Sample images averaged along the surface were used to obtain deposition rate of particles of different size. Verification of the mean flow concentration, to be within the range of concentration, as measured in IDDP-1 is done by calculating the concentration using the particle size distribution obtained from pictures of filter paper. The equation for mass concentration can be obtained by summing up concentration for particles of each size obtained using Eq. (13), expressed as follows:
cmean =
Afilter 1 1 Aimage Aprobe Vprobe . t 6
p s
(
Ni,di3)
(17)
where Ni is the number of ith size particle on filter paper image with diameter di. The concentration measured from the filter paper is found to be 33.7 mg kg−1 which is close to the inlet injection concentration of 40 mg kg−1 and is within the range of particle concentration found in 5
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Fig. 2. (a) Original image (b) filtered image (c) threshold reversed image (d) analyzed image.
which causes their concentration distribution to evolve uniformly if external forces are absent. However, the presence of turbulence causes formation of dense clusters of particles (Eaton and Fessler, 1994). The degree of preferential concentration depends upon the ratio of particleto-fluid inertia. The preferential concentration of silica particles in superheated steam is high due to high density ratio of silica and steam. Very small particles follow all motions of turbulence and disperse with fluid elements as shown in fig. (4a). As the particle size increases the particles do not follow curved streamlines, which causing preferential concentration (fig. (4b)); however, as inertia increases with further increase in particle size, the particles become too sluggish to have a longer response during an eddy’s lifetime, hence the preferential concentration decreases (Fig. (4 c), fig. (4d)). The computational model successfully captures the concentration distribution. The model however predicts excessive particle concentration near the wall as the particle size increases. This is because the model assumes local equilibria, such that it ignores the so called the memory effect in which a particle retains the turbulent characteristics of an eddy it previously passed through before. An improved model for turbophoretic force is required to avoid this limitation; however, the limitation is overshadowed by the fact that assumption of local equilibrium is effective in predicting the gross features of the deposition process correctly. The wall normal particle velocity increases continuously with an increase in particle relaxation time. For low relaxation time, flux towards the wall is mainly due to diffusion, as shown by concentration gradient near the wall (Fig. (4 a), fig. (4b)). The turbophoretic force provides acceleration to particles against the direction of viscous drag. For higher relaxation times, lift forces increases causing the convective velocity of silica particles towards the wall to increase. In this range, particle motion is mainly governed by impaction (Fig. (4 c), fig. (4d)). The negative value of velocity and forces in the graph represents
Fig. 3. Variation of non-dimensional deposition velocity with non-dimensional particle relaxation time.
regimes is consistent with the results from the literature involving aerosol in air flow for the same non-dimensional relaxation time. A better understanding of the deposition process and different aspects of silica particle transport in superheated steam flow can be obtained from the simulation. Fig. 4 shows the variation of non-dimensional silica particle concentration, wall normal velocity and forces per unit mass along wall normal distance for different dimensionless particle relaxation times. Very small silica particles have Brownian motion, 6
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Fig. 4. Particle concentration non-dimensionalized by bulk mean concentration (c¯p ), Wall normal velocity and Forces per unit mass for different dimensionless particle relaxation times (a) 0.5 (b) 2.0 (c) 7.8 (d) 60.
7
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direction towards the wall. The net particle acceleration can be obtained by subtracting the drag force from the sum of all forces acting towards the wall.
Sci. Eng. 40 (1), 1–11. Brown, K., Dunstall, M., 2000. Silica scaling under controlled hydrodynamic conditions. In: Proceedings World Geothermal Congress. Kyushu-Tohoku, Japan, May 28 – June 10.. Chauhan, V., Gudjonsdottir, M., Saevarsdottir, G., 2019. Silica scrubbing from uperheated steam using aqueous potassium carbonate solution: an experimental investigation. Geothermics 80, 1–7. Clift, R., Grace, J.R., Weber, M.E., 1978. Bubbles, Drops and Particles. Academic Press, New York. Davies, C.N., 1966. Aerosol Science. Academic Press, London. Eaton, J., Fessler, J., 1994. Preferential concentration and settling of heavy particles by turbulence. Int. J. Multiph. Flow 20, 169–209. Elghobashi, S., 1994. On predicting particle laden turbulent flows. Appl. Sci. Res. 52, 309–329. El-Shobokshy, M.S., 1983. Experimental measurements of aerosol deposition to smooth and rough surfaces. Atmos. Environ. 17, 639–644. Friedlander, S.K., Johnstone, H.F., 1957. Deposition of suspended particles from turbulent gas streams. Ind. Eng. Chem. 49 (7), 1151–1156. Gallily, I., Cohen, A.H., 1979. On the orderly nature of the motion of nonspherical large droplet and axially symmetrical elongated particles. J. Colloid Interface Sci. 68, 338–356. Gallup, D.L., Barcelon, E., 2005. Investigations of organic inhibitors for silica scale control from geothermal brines-II. Geothermics 34, 756–771. Guha, A., 1997. A unified Eulerian theory of turbulent deposition to smooth and rough surfaces. J. Aerosol Sci. 28 (8), 1517–1537. Hauksson, T., Sigurdur, M., Einarsson, K., Karlsdottir, S.N., Einarsson, A., Moller, A., Sigmarsson, T., 2014. Pilot testing of handling the fluids from the IDDP-1 exploratory geothermal well, Krafla, N.E. Iceland. Geothermics 49, 76–82. Johansen, S.T., 1991. The deposition of particles on vertical walls. Int. J. Multiph. Flow 17 (3), 355–376. Kvasnak, W., Ahmadi, G., Bayer, R., Gaynes, M., 1993. Experimental investigation of dust particle deposition in a turbulent channel flow. J. Aerosol Sci. 24, 795–815. Launder, B., Spalding, D., 1974. The numerical computation of turbulent flows. Comput. Methods Appl. Mech. Eng. 3 (2), 269–289. Lee, K.W., Gieseke, J.A., 1994. Deposition of particles in turbulent pipe flows. J. Aerosol Sci. 25, 699–709. Liu, B.Y., Agarwal, J.K., 1974. Experimental observation of aerosol deposition in turbulent flow. J. Aerosol Sci. 5 (2), 145–155. Markusson, S.H., Hauksson, T., 2015. Utilization of the hottest well in the world, IDDP-1 in Krafla. In: Proceedings World Geothermal Congress. Melbourne, Australia, 19-25 April. OpenFOAM, 2014. Userguide, 2nd ed.). OpenCFD Ltd. Palsson, B., Holmgeirsson, S., Gudmundsson, A., Boasson, H.A., Ingason, K., Sverrisson, H., Thorhallsson, S., 2014. Drilling of the well IDDP-1. Geothermics 49, 23–30. Postma, A.K., Schwendiman, L.C., 1960. Studies in micrometrics. I. Particle Deposition in Conduits As a Source of Error in Aerosol Sampling. Report HW-65308. Handford Laboratory., Richland, Washington. Reeks, M.W., 2005. On model equations for particle dispersion in inhomogeneous turbulence. Int. J. Multiph. Flow 31 (1), 93–114. Saffman, P.G., 1965. The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385–400. Schneider, C.A., Rasband, W.S., Eliceiri, K.W., 2012. NIH Image to ImageJ: 25 years of image analysis. Nat. Methods 9 (7), 671–675. Slater, S.A., Young, J.B., 2001. The calculation of inertial particle transport in dilute gasparticle flows. Int. J. Multiph. Flow 27 (1), 61–87. Sehmel, G.A., 1968. Aerosol Deposition From Turbulent Airstreams in Vertical Conduits. Report BNWL-578. Pacific Northwest Laboratory, Richland, Washington. Shimada, M., Okuyama, K., Asai, M., 1993. Deposition of submicron aerosol particles in turbulent and transitional flow. Aiche J. 39, 17–26. Slater, S.A., Leeming, J.B., Young, J.B., 2003. Particle deposition from two-dimensional turbulent gas flows. Int. J. Multiph. Flow 29 (5), 5721–5750. Stavropoulos, N., 1954. Deposition of Particles From Turbulent Gas Streams. M.Sc Thesis. Columbia University, New York. Wells, A.C., Chamberlain, A.C., 1967. Transport of small particles to vertical surfaces. Br. J. Appl. Phys. 18, 1793–1799. Young, J., Leeming, A., 1997. Particle deposition in turbulent pipe flow. Journal of Fluid Mech 340, 129–159. Zaichik, L.I., Pershukov, V.A., Kozelev, M.V., Vinberg, A.A., 1997a. Modeling of dynamics, heat transfer, and combustion in two-phase turbulent flows: 1. Isothermal flows. Exp. Therm. Fluid Sci. 15 (4), 291–310. Zaichik, L.I., Pershukov, V.A., Kozelev, M.V., Vinberg, A.A., 1997b. Modeling of dynamics, heat transfer, and combustion in two-phase turbulent flows: 2. Flows with heat transfer and combustion. Exp. Therm. Fluid Sci. 15 (4), 311–322. Zaichik, L.I., Drobyshevsky, N.I., Filippov, A.S., Mukin, R.V., Strizhov, V.F., 2010. A diffusion-inertia model for predicting dispersion and deposition of low-inertia particles in turbulent flows. Int. J. Heat Mass Transf. 53, 154–162. Zarrouk, S.J., Woodhurst, B.C., Morris, C., 2014. Silica scaling in geothermal heat exchangers and its impact on pressure drop and performance: wairakei binary plant, New Zealand. Geothermics 51, 445–459.
6. Conclusion Based on the work, the following conclusions can be drawn concerning silica particle deposition in superheated steam flows: (1) Silica particles in a superheated steam flow represent a case of two phase flow with particles as a dispersed phase in a gas medium. (2) As shown by the simulation and the experimental measurement, deposition velocity increases with particle relaxation time in the diffusion impaction regime. For a system involving silica particles in superheated steam flow, relaxation time increases with increase in particle size caused by agglomeration. (3) The developed experimental setup with sampling and image processing techniques offers a promising method for study of silica deposition in superheated steam flows. (4) Results from the computational advection diffusion model agrees with the experimental results for silica particles in superheated steam flows. The implemented computation model can be used to study silica particle transport and deposition in superheated steam for more complicated geometries. (5) The implemented model in OpenFoam offers an advantage of computational time and cost saving due to its Eulerian approach. The model may be applied to the design and analysis of geothermal systems involving silica and superheated steam flows. CRediT authorship contribution statement Vijay Chauhan: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation. Maria Gudjonsdottir: Resources, Visualization, Writing - original draft. Gudrun Saevarsdottir: Funding acquisition, Supervision, Writing - review & editing. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement The work was funded by GEORG, Landsvirkjun, Reykjavik Energy, HS Orka, Orkustofnun and the IDDP project. The authors wish to thank Landsvirkjun staff for providing valuable support and technical advice. They are also grateful to staff of the Innovation Center of Iceland for their technical support. Appendix A. Supplementary data Supplementary material related to this article can be found, in the online version, at doi:https://doi.org/10.1016/j.geothermics.2020. 101802. References Bahadori, A., Vuthaluru, H.B., 2010. Prediction of silica carry-over and solubility in steam of boilers using simple correlation. Appl. Therm. Eng. 30, 250–253. Beal, S.K., 1970. Deposition of particles in turbulent flow on channel or pipe walls. Nucl.
8
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Silica particle deposition in superheated steam in an annular flow: Computational modeling and experimental investigation
T
Vijay Chauhan*, Maria Gudjonsdottir, Gudrun Saevarsdottir School of Science and Engineering, Reykjavik University, Menntavegur 1, 101 Reykjavík, Iceland
ARTICLE INFO
ABSTRACT
Keywords: Deposition Geothermal Silica Steam Superheat
The work presents computational modeling and an experimental investigation of silica deposition occurring in geothermal systems with superheated steam flows. An advection diffusion model was implemented for predicting silica particle transport and deposition in turbulent flows. The model includes the effect of Brownian diffusion, turbulent diffusion, turbophoresis, Saffman lift force, and drag force on particle motion. Simulation results for deposition of silica particles in superheated steam flow were validated experimentally. An experimental setup consisting of a superheated steam generating system, silica injection system and test section assembly was designed and constructed. Deposition velocity was measured for silica fume particles ranging from 1 to 20 μm in diameter. The measured data shows agreement with the implemented model simulation results showing an increase in deposition velocity with increase in particle relaxation time in diffusion impaction regime.
1. Introduction High enthalpy fluids extracted from an unconventional vapor dominated geothermal system in a superheated state offer the potential to obtain more power, with greater efficiency, than from fluids extracted from conventional geothermal systems. The Icelandic Deep Drilling Project (IDDP) was established in year 2000 to investigate the technical and economic feasibility for utilization of an unconventional, very high temperature steam from deeper wells (Palsson et al., 2014). The geothermal well designated IDDP-1 was drilled at the Krafla geothermal field in northwest Iceland in an attempt to obtain supercritical steam. The well did not produce supercritical steam, but rather superheated steam with an enthalpy greater than 3170 kJ/kg and at pressures up to 15 MPa. Due to its high pressure, the steam contained a considerable amount of dissolved silica (up to 66 ppm) in gaseous form. The high concentration of silica in superheated steam occurs due to increase in silica solubility with increase in pressure near to the supercritical region (Bahadori and Vuthaluru, 2010). Lowering the steam pressure causes silica to precipitate, as was observed in IDDP-1 (Markusson and Hauksson, 2015). The precipitated silica is found as particles carried within the superheated steam flow. The particles deposited on the surface of different components causing scaling. Silica scaling in geothermal heat exchangers has an impact on pressure and performance, such that the pressure drop increases and performance
⁎
decreases with increase in silica scaling. This was seen at the Wairakei power plant in New Zealand, studied by Zarrouk el al. (2014). Studies shows scaling has major long term effects on power plant performance. It is therefore necessary to take measures to control silica scaling to maintain the design output of a geothermal power plant. Controlling silica scaling by chemical means is suggested in the literature (Gallup and Barcelon, 2005). The addition of inhibitors to control scaling relates to two phase geothermal fluid as it requires the presence of a liquid phase where mineral solubility can be influenced. For superheated steam, similar to that obtained from IDDP-1, considerable amount of liquid injection required for adding inhibitors would cause quenching of the superheated steam and hence reduce the exergy of the geothermal fluid. A different method to control silica scaling occurring in superheated steam flow is therefore proposed. Application of heat recovery system to retain steam superheat, utilizing salt solution with high boiling point elevation as a scrubbing medium was proposed by Chauhan et al. (2019). The feasibility of utilizing a heat recovery system, however, depends on the hydrodynamic characteristics of silica particles in the superheated steam flow, which plays a vital role in the phenomena of deposition, causing scaling. A study on hydrodynamics characteristics of silica particles in superheated flow is therefore proposed. The process of silica scaling involves precipitation, agglomeration and then deposition on a surface. Developing methods to control silica
Corresponding author. E-mail address: [email protected] (V. Chauhan).
https://doi.org/10.1016/j.geothermics.2020.101802 Received 7 January 2018; Received in revised form 23 December 2019; Accepted 5 January 2020 0375-6505/ © 2020 Elsevier Ltd. All rights reserved.
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scaling requires an understanding of silica particle transport in superheated steam flow and the factors controlling it. A study on scaling under controlled hydrodynamic conditions was done by Brown and Dunstall (2000) to understand the effect of different hydrodynamic parameters on particle transport. The study showed that the scaling increased with an increase in particle diameter. Their study however does not provide a definite theory or model to predict the silica scaling rate. An insight into the mechanisms of silica particle transport in superheated steam flow can be obtained through computational modeling. Predicting particle transport and deposition in a two phase flow is also important in other engineering applications and scientific studies. The particle deposition in gas flows is observed in many processes, including chemical aerosol transportation and in atmospheric pollutants. Researchers have proposed various approaches to model particle deposition in a two-phase flow. Friedlander and Johnstone (1957), for example, introduced a free flight model in order to predict deposition of small particles suspended in gas flow in a pipeline. The free flight model assumes diffusion of particles in a flow up to a certain distance, called stop distance, after which they are assumed to have free flight to the wall. Various modifications have been made in the model depending upon the prescription of free flight velocity (Davies, 1966; Beal, 1970). The free flight model however suffer problems as the particle size increases. The free flight model shows a monotonic increase in deposition velocity with an increase in particle relaxation time, which contradicts experimental values showing a third regime where the particle velocity decreases as relaxation time increases. Another approach for predicting particle transport in gaseous medium is the Euler-Euler two phase method, in which both particles and the gas phase are assumed as continuous, and equations are modeled in Eulerian field. Considerable progress has been made in the development and modeling of the EulerEuler two phase approach (Reeks, 2005). In this method, equations are obtained by averaging instantaneous equations of mass, momentum and energy for the particle phase. The averaged equations obtained are coupled and require closure relations for particle Reynolds stress and carrier flow velocity field. Despite high computational efficiency, application of the Eulerian two fluid approach relies on constitutive relations, or closure equations, to be obtained by a heuristic or empirical approach. A simplified Eulerian model called the diffusion-inertia model was developed for isothermal flows (Zaichik et al., 1997a) and flows involving heat transfer (Zaichik et al., 1997b) for low inertia particles. Later improvements were made in the model by two waycoupling to include back effects of particles on fluid (Zaichik et al., 2010). The model suffers, however, from the disadvantage of application to low inertia particles only. Complexity in Euler two fluid model was reduced by using the simple advection-diffusion equation shown in the independent work done by both Guha (1997) and Young and Leeming (1997). The advection-diffusion approach for modeling particle deposition on a vertical wall was first applied by Johansen (1991). Major mechanisms contributing to deposition such as Brownian and turbulent diffusion, turbophoresis, Saffman lift and electrostatic force were accounted for in the model. The most important feature of this model is that the advection-diffusion equation is uncoupled from the equation for mean particle velocity, which is used in advection-diffusion equation itself. Deposition features were successfully reproduced by both models (Guha, 1997 and Young and Leeming, 1997) for a case of turbulent flow through a pipe. Despite the simplicity in solving the equations of the advection-diffusion model, however, difficulties arise in solving problems with particle discontinuities and in the treatment of boundary conditions. Issues related to the Eulerian approach are discussed and addressed in the work of Slater and Young (2001). A similar approach for computation including the effect of turbulence was presented in the work of Slater et al. (2003). The work involves deriving an advectiondiffusion model using the theoretical approach described in Young and Leeming (1997) with the particle continuum equations averaged using
the density-weighted method, and shows the application of a derived model for more complicated geometry involving solid particle in gas flow through a turbine. As these models relate to particles flowing with air, it is important to have an experimental validation of a general two-phase flow computational model, particularly for its application in study involving silica particles in superheated steam flow. Extensive experimental studies on particle deposition in vertical tubes with air flow exist in the literature, which were used to inform the design of experiments within this study. A study of particle deposition on a vertical glass tube coated with petroleum jelly was done by Stavropoulos (1954). Measurements of deposition velocities in flows with varying Reynolds numbers were made by Postma and Schwendiman (1960) for 2−4 μm diameter ZnS particles and 30 μm glass spheres: aluminum, steel, and brass tubes of different diameters were used in the study. Experiments on the effect of surface roughness on deposition were done by Wells and Chamberlain (1967), using particle sizes ranging from 0.17 to 15 μm and with different densities. Deposition on surfaces with different levels of microscale roughness were also studied by El-Shobokshy (1983). The studies found that surface roughness substantially affected deposition rates. On effect of surface roughness on deposition, Sehmel (1968) showed an increase in deposition in one experiment and no effect in another experiment due to changes in surface roughness. The deposition of olive oil aerosols in vertical turbulent flows over a wide range of flow conditions was studied by Liu and Agarwal (1974). They showed the variation of deposition as a function of relaxation time in the diffusion impaction and inertia regime. Data related to deposition in the diffusion regime is provided by Shimada et al. (1993). Lee and Gieseke (1994) conducted experiments on particle deposition onto pipe walls in turbulent flow. The measurement covers both turbulent diffusion and the diffusion impaction regimes. An experimental study on the deposition rate of non-spherical particles in laminar flow was reported by Gallily and Cohen (1979). Investigation of the deposition of non-spherical particles was done by Kvasnak el al., (1993). Deposition measurements for spherical beads and irregular shaped dust particles were compared with the results from empirical models. Experimental validation of these deposition models, as reported in the literature above, was carried out with air as a flow medium. This is not surprising as most relevant systems refer to particles in air. The experiment designs used in the various studies cannot be used for studies involving superheated steam application. This is due to the limitation of the equipment’s and measurement technique used in the experiments for low temperature applications involving air as a flow medium. The current work focuses on the study of deposition occurring in geothermal systems which consist of superheated steam as a transport medium, with precipitated silica particles in a dispersed phase. The particles occurring in the geothermal steam flow consist of silica agglomerates of irregular shapes and varying sizes, depending upon the degree of agglomeration. The flow medium, that is superheated steam, has different hydrodynamic properties to air. The computation model validation for geothermal system applications therefore requires an experimental investigation involving silica particles in superheated steam flow. The work implements an advection-diffusion model for modeling silica particle transport and deposition in superheated steam flow using OpenFoam (OpenFOAM, 2014), an open source Computational Fluid Dynamics (CFD) package. Continuum equations for particle flow were written in OpenFoam notation and existing turbulence models and solvers in the software were used to solve for the required fluid flow variables. An experimental setup was designed and constructed, and a study was performed to determine silica deposition in superheated steam flow for different relaxation times. The experimental measurements were compared to data from the literature as well as the computational model simulation.
2
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V. Chauhan, et al.
2. Computational model
inertia, particle slip velocity must be taken into consideration by incorporating a drag coefficient into the equation. The drag coefficient (Clift et al., 1978) can be expressed as:
Simulation of advection-diffusion model requires solving conservation equations for the fluid (steam) and the particle (silica) phase. The solver in OpenFoam consists of fluid phase equations which are solved independently to obtain the fluid flow variables. The conservation equations for the particle phase however, needs to be implemented. Equations for both phases are described as follows:
Cd =
p, inertial
In a Eulerian frame, for incompressible turbulent flow, the well know expressions for Reynolds averaged mass and momentum conservation equation are:
1 p + f xi
f
2u ¯
i
x i xj
+
(2)
3
t
cp vi t
xi
+
=0
(cp vi vj ) xj
= cp (Fdrag , i + Flift , i )
c¯p t
(3)
=
xi
=
xi
uj
vj p
(9)
c¯p
(DB + DT ) ( u¯i uj ) xj
+
(10)
xi v¯ic
u¯ i p
j =1 j i
f p
p
u¯ j xi
1 2
v¯jc
u¯ j p
(11)
where is the density-averaged particle convective velocity, DB is the coefficient of Brownian diffusion, DT is the coefficient of turbulent diffusion and is the ratio of particle mean square velocity to the fluid mean square velocity. The detailed expressions for the coefficients are available in the literature (Slater and Young, 2003). Fluid flow equations were solved using existing solver and utility functions in OpenFoam to obtain fluid velocity field, fluid root mean square velocity and turbulent diffusivity. These variables are required in the particle continuum equations, which are also written in OpenFoam notation. The values of concentration, velocity field, and their flux are updated in the runtime loop until a steady-state solution is achieved. To obtain the physical requirement of an absorbing boundary condition, zero wall normal gradients of particle density and velocity are applied to generate the required particle fluxes at the boundary. Such conditions corresponds to zeroth order extrapolation from the flow to the wall.
v¯ic
vi (5)
2 p rp2 9µ f
(cp v¯ic )
+ 0.725
Where p is the particle relaxation time which for the Stokes regime is expressed as: p
p
3
The drag force is a mechanism causing particles to approach a velocity equal to that of the surrounding fluid due to viscosity of the fluid. The force acts opposite to the direction of the relative velocity of a particle with respect to the fluid and is given as:
p
1/2
xi
(4)
2.3. Drag force
ui
+
v¯ic (v¯ic ) + vjc = xj t
Where vi is the particle velocity along direction i , cp is the particle concentration in mass per unit volume and Fi represents the force per unit mass acting on particle along direction i . The forces (per unit mass) acting on particles, shown on the righthand side of Eq. (4), are defined in the following two subsections.
Fdrag, i =
uj
p
After inserting the above expressions for the forces in Eq. (4), Eqs. (3) and (4) need to be averaged in order to obtain the final equations. Various approaches have been applied in the literature for averaging. Non-density-weighted based Reynolds averaging was applied in Cartesian coordinates by Guha (1997) and in cylindrical coordinates by Young and Leeming (1997). Density-weighted averaging was used in the work of Slater and Young (2003). The method offers the advantage of producing fewer turbulence terms. The averaged equations can be simplified further separating particle flux into its convective and diffusive components; however, the final equations obtained are similar to those obtained using the non-density weighted averaged method. The detailed derivation can be found in Slater and Young (2003). The final equations are written as:
For the particle phase, conservation equations are required for particle concentration and momentum balance. The equations are expressed in a Cartesian tensor form as:
(cp vi )
(8)
g
j=1 j i
2.2. Particle phase conservation equations
+
p
Flift , i = 0.725
where u¯i is the Reynolds averaged fluid velocity along direction i, p is the fluid pressure, and f and f are the fluid density and kinematic viscosity, respectively. The last term in Eq. (2) represents the gradient of velocity fluctuations. Velocity fluctuations and the scalar property for eddy viscosity can be obtained using two equation turbulence models. A number of turbulence models are available in OpenFoam. Commonly used two equation models include k-ε model and k-ω model. Details of the models can be found in the literature (Launder and Spalding, 1974). For obtaining the fluid velocity field, boundary conditions of a fixed inlet velocity and a velocity gradient of zero at the outlet and on the walls are assumed.
cp
24
Rep Cd
The lift force causes particle to move perpendicular to the direction of flow. The expression for shear induced lift force as derived by Saffman (1965) is given as:
ui¯uj xi
=
2.4. Lift force
(1)
u¯ i u¯ + u¯ j i = t xj
(7)
Where Rep is the slip Reynolds number. The resulting expression for particle relaxation time considering the slip velocity factor is given as:
2.1. Fluid phase conservation equations
u¯ i =0 xi
24 (1 + 0.15Rep0.687) Rep
(6)
3. Experimental setup
Where p and rp are the density and radius of a particle, respectively, and µ f is the dynamic viscosity of the fluid. For particles with large
Fig. 1 shows a schematic diagram of the experimental setup. The 3
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V. Chauhan, et al.
Fig. 1. Schematic diagram of the experimental setup.
setup consists of three sub-systems: the steam generating system, the particle injection system and the test section assembly. The steam generating system consists of an 18 kW electric boiler with a water storage tank for continuous supply. An airflow line from the compressor with a control valve (Cv2) is connected to the steam flow line after the gate valve (Cv1). This is required to run the setup with air flow at the beginning and at the end of the experiment. The wetness in the steam coming out from the boiler is removed in the cyclone separator (S1). The saturated steam is then passed through a throttle valve (Tv) and a 500 W superheater (SH) to attain the superheat. The particle injection system consists of a micro-screw feeder with a variable speed motor drive to control the feed rate. The micro-screw feeding mechanism provides an almost constant average feed rate of 40 mg kg−1. The particles delivered by the screw feeder are injected into the main line by suction in the ejector. The ejector system provides an easy way to inject particles into steam by mixing a small quantity of air into the steam. This overcomes the drawback of using aerosol generators with air as the only carrying medium, as used in experiment studies from the literature discussed earlier. The mixing of a small quantity of air into the superheated steam is justified by the fact that the geothermal steam from the well also consists of additional non-condensable gases. The particle and steam mixture is sent to another cyclone separator (S2). The separator works as a mixing chamber giving time for larger agglomerated particles to breakup forming a uniform mixture and reducing eddies in flow. The particle deposition test section consists of two 1.5 m long concentric steel pipes, where the inner diameter of the outer pipe is 22.5 mm and the outer diameter of the inner pipe is 17.5 mm. To sample particles from the inner pipe surface, the ends of the pipe were fitted with a thread and screw attachments for closure, making pipe removal easy as required for sampling. The outer pipe consists of a conical section such that the annulus area decreases by a ratio of 1:10 at the entrance. The conical surface of the outer pipe contains an inlet to which a stainless-steel probe is attached, which is used for collecting particles and for measurement of the mean concentration of the mixture. The probe, which has a length of 10 cm and inner diameter of 3.65 mm is sharpened at the front, while the other end is connected to a cone shaped flask made of cast iron. The material selection allows the flask to be heated in order to avoid condensation on the filter paper. The flask contains a wired mesh serving as a seat for the filter paper to collect particles. A membrane filter paper with 0.45 μm pore size and 47 mm diameter is used for collection. The filter is stable in steam up to a temperature of 180 ̊C. The flowing steam is passed through a control valve (Cv5) to control the flow rate through the probe. The steam is then passed through a condenser (C1) and then collected to measure the flow
rate through the probe. The steam from the test section is also collected after condensation in the condenser (C2) to measure the total flow rate. The system is well insulated and heated using heating tape to avoid heat loss from the flow. 4. Measurement procedure The system is run with air in the beginning. The superheater is switched on to heat the setup using air. This will ensure that there is no condensation in the test section at the start when the system is run using steam. Once the surface temperature of the equipment approaches the set-point temperature for the experiment, the airflow line is shut down and the steam flow line is opened. The steam is initially run through the system with air suction in the ejector and without particle feeding. This is done until steady mass flow, temperature and pressure are obtained. The boiler capacity limits the steam flow rate and so the system is always run constantly at a saturated pressure of 4.5 bar to achieve a steady state. A large pressure drop occurs in the ejector due to an expansion of steam from the ejector nozzle. The inlet mixture to the test section is at 160 ̊C and 1.4 bar. The volume flow rate of steam at the inlet of the test section is 150 l min−1. This corresponds to mass flow rate of 0.105 kg min−1. The mixture therefore has a considerable degree of superheat at the inlet of the test section. The flow has a Reynolds number of 3800. The particles used in the experiment are silica fume of density 2200 kg m-3 and with 97 % purity. Silica fume is an amorphous polymorph of silica dioxide and thus possess similar characteristics to silica found in geothermal systems precipitated from solution in superheated geothermal steam. It has a grey color due to minute percentage of impurities which increase its visibility on filter paper. The maximum particle concentration is kept less than 0.5 % by weight, similar to the concentration observed in IDDP-1. This corresponds to a volume fraction of less than 10-6 to ensure one way coupling between particle and flow turbulence (Elghobashi, 1994). Once the experiment was run using steam and particles for an average duration of an hour, the steam flow and particle injection were shut down. Finally air was run again for a few seconds to remove all steam from the test section to avoid condensation upon cooling. The deposited particles were collected on a polished pipe surface in test section, coated with polytetrafluoroethylene (PTFE) lubricant. The lubricant is thermally stable and insoluble in water. Coating causes a decrease in the coefficient of restitution and an increase in the energy loss of particles striking the surface, hence reducing the effect of rebound or re-entrainment. A particle sampling and counting technique using a digital microscope and image processing was used. The surface of the pipe was 4
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V. Chauhan, et al.
heated using an induction heater before taking images. This was done to remove the lubricant by vaporization, enhancing visibility. The particle flux Jw on the wall is calculated using the following equation:
Jw =
Nw t Aimage
IDDP-1. A small difference in the injected and measured concentration is observed due to chances of silica particles of small size escaping the filter surface while sampling and some particles depositing along the surface of equipment before entering the test section.
(12)
5. Results and discussion
where Nw is the number of particles of specific size on surface image, Aimage is the area of image and t is the time duration of the sampling. To determine the mean flow concentration, flow samples were taken using the probe over a time span of 15 min. For isokinetic sampling, flow velocity through the probe was kept consistent with that inside the pipe. The required flow rate through the probe was obtained by adjusting control valve (Cv5). The filter paper images were taken carefully after removing the filter paper from the flask. The mean particle concentration was determined with the following formula:
c¯p =
Nfilter Afilter 1 Aimage Aprobe t Vprobe
Fig. 3 shows the experimental results for deposition velocities of the silica particles in the superheated steam flow for varying relaxation times. A comparison of the experimental results for silica in superheated steam can be made with experimental data from the literature for aerosol in air flow by normalizing the relaxation time. To the author’s knowledge, no results are available in the literature for particle deposition in steam. The figure shows three different regimes of deposition for two phase flow with particles in dispersed phase. First, the turbulent diffusion regime where deposition occurs mainly due to Brownian and turbulent diffusion for particles with low relaxation time. A decrease in deposition velocity in this region occurs with increasing relaxation time due to a decrease in Brownian diffusion, which is the dominating mechanism for particle motion near to the wall. This decrease in Brownian motion occurs due to an increase in particle size. The second regime, called the diffusion impaction regime, consists of a steep increase in deposition with relaxation time due to lift and turbophoretic forces. The third regime, called the inertia regime consists of particle inertia, where deposition velocity slows down due to a decrease in the time of interaction with eddies as particle inertia increases with increase in particle size. As seen from the figure, the data from studies in the literature consists of experimental results on deposition for a specific range of relaxation time. The relaxation time range is limited by fluid velocity and the chosen range of particle sizes as seen from Eq. 16. The experiment was carried out for silica particles with sizes ranging from 1 μm to 20 μm and the superheated steam as a flow medium. The flow velocity was kept constant for the given design setup and electric boiler unit capacity. The relaxation time range was therefore obtained using the available particle size distribution. For the available particle size range, the setup was designed to obtain flow velocity such that the relaxation time range correspond to the impaction diffusion regime, where an increase in deposition is expected. The experimental results for silica and superheated steam flow show a steep increase in deposition rate with increasing relaxation time in the diffusion impaction regime. In geothermal systems with superheated steam, silica particles precipitated from superheated steam have chances to agglomerate due to collision and attachment along the flow after precipitation. This can be observed from the suspended silica particles sampled from IDDP-1, having size of the micro scale (Hauksson et al., 2014) obtained from the condensed steam as well as from the dry dust collected from the silencer rock and the silencer line. This agglomeration causes particle size to increase which increases its relaxation time. As observed from the results, an agglomerated particle with larger relaxation time have higher deposition velocity than smaller particle. Thus for the same concentration, the scaling rate increases with increase in degree of agglomeration. Results for the non-dimensional deposition velocity obtained in the current work are consistent with results from the literature involving aerosols in air flow for the same non-dimensional relaxation time range. An error is expected for low relaxation times due to the likelihood of small particles sticking to the surface of the probe due to bends and its small cross sectional area. This causes decrease in particle concentration (c¯p ) collected on the filter paper and hence measuring higher deposition velocity as given by Eq. 14. A simulation was performed using the implemented model based on the experimental conditions and boundary constraints. Results from the simulation show agreement with the experimental data in the diffusion impaction regime, as shown in Fig. 3. The simulated deposition curve for all three
(13)
where Nfilter is the number of particles of specific size on filter paper image, Afilter is the filter area, Aprobe is the inlet cross section area of the probe and Vprobe is the flow velocity through the probe. The non-dimensional deposition velocity is given by:
V+ =
Jw u *c¯p
where
u*
(14) is the friction velocity, defined as:
f 2
u* = Vav
(15)
where Vav is the average fluid velocity and f is the Fanning friction factor calculated using Blasius law for turbulent flows and smooth walls. The non-dimensional particle relaxation time is given by: +
=
*2 pu
(16)
f
Digital images with an area of 384 μm by 288 μm were captured of the pipe surface and the filter paper and were statistically analyzed using ImageJ (Schneider et al., 2012). Fig. 2 shows the resulting images from various steps of image processing, which are: original image (Fig. 2a), filtered image (Fig. 2b), threshold reverse image (Fig. 2c) and the analyzed image (fig.2d). The silica particles were agglomerated, making their shape irregular. This approach assumes projected area diameter as the diameter of a particle. A similar technique, assuming the particles to be spherical, was used by Kvasnak et al. (1993) for measuring the size of dust particle of irregular shape. The result shows small compact irregular shape dust particles follow the same trend of variations as those of spherical particles. Images are averaged for each particle size with a band width of ± 0.5 μm considering each image as one sample. Sample images averaged along the surface were used to obtain deposition rate of particles of different size. Verification of the mean flow concentration, to be within the range of concentration, as measured in IDDP-1 is done by calculating the concentration using the particle size distribution obtained from pictures of filter paper. The equation for mass concentration can be obtained by summing up concentration for particles of each size obtained using Eq. (13), expressed as follows:
cmean =
Afilter 1 1 Aimage Aprobe Vprobe . t 6
p s
(
Ni,di3)
(17)
where Ni is the number of ith size particle on filter paper image with diameter di. The concentration measured from the filter paper is found to be 33.7 mg kg−1 which is close to the inlet injection concentration of 40 mg kg−1 and is within the range of particle concentration found in 5
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Fig. 2. (a) Original image (b) filtered image (c) threshold reversed image (d) analyzed image.
which causes their concentration distribution to evolve uniformly if external forces are absent. However, the presence of turbulence causes formation of dense clusters of particles (Eaton and Fessler, 1994). The degree of preferential concentration depends upon the ratio of particleto-fluid inertia. The preferential concentration of silica particles in superheated steam is high due to high density ratio of silica and steam. Very small particles follow all motions of turbulence and disperse with fluid elements as shown in fig. (4a). As the particle size increases the particles do not follow curved streamlines, which causing preferential concentration (fig. (4b)); however, as inertia increases with further increase in particle size, the particles become too sluggish to have a longer response during an eddy’s lifetime, hence the preferential concentration decreases (Fig. (4 c), fig. (4d)). The computational model successfully captures the concentration distribution. The model however predicts excessive particle concentration near the wall as the particle size increases. This is because the model assumes local equilibria, such that it ignores the so called the memory effect in which a particle retains the turbulent characteristics of an eddy it previously passed through before. An improved model for turbophoretic force is required to avoid this limitation; however, the limitation is overshadowed by the fact that assumption of local equilibrium is effective in predicting the gross features of the deposition process correctly. The wall normal particle velocity increases continuously with an increase in particle relaxation time. For low relaxation time, flux towards the wall is mainly due to diffusion, as shown by concentration gradient near the wall (Fig. (4 a), fig. (4b)). The turbophoretic force provides acceleration to particles against the direction of viscous drag. For higher relaxation times, lift forces increases causing the convective velocity of silica particles towards the wall to increase. In this range, particle motion is mainly governed by impaction (Fig. (4 c), fig. (4d)). The negative value of velocity and forces in the graph represents
Fig. 3. Variation of non-dimensional deposition velocity with non-dimensional particle relaxation time.
regimes is consistent with the results from the literature involving aerosol in air flow for the same non-dimensional relaxation time. A better understanding of the deposition process and different aspects of silica particle transport in superheated steam flow can be obtained from the simulation. Fig. 4 shows the variation of non-dimensional silica particle concentration, wall normal velocity and forces per unit mass along wall normal distance for different dimensionless particle relaxation times. Very small silica particles have Brownian motion, 6
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Fig. 4. Particle concentration non-dimensionalized by bulk mean concentration (c¯p ), Wall normal velocity and Forces per unit mass for different dimensionless particle relaxation times (a) 0.5 (b) 2.0 (c) 7.8 (d) 60.
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direction towards the wall. The net particle acceleration can be obtained by subtracting the drag force from the sum of all forces acting towards the wall.
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6. Conclusion Based on the work, the following conclusions can be drawn concerning silica particle deposition in superheated steam flows: (1) Silica particles in a superheated steam flow represent a case of two phase flow with particles as a dispersed phase in a gas medium. (2) As shown by the simulation and the experimental measurement, deposition velocity increases with particle relaxation time in the diffusion impaction regime. For a system involving silica particles in superheated steam flow, relaxation time increases with increase in particle size caused by agglomeration. (3) The developed experimental setup with sampling and image processing techniques offers a promising method for study of silica deposition in superheated steam flows. (4) Results from the computational advection diffusion model agrees with the experimental results for silica particles in superheated steam flows. The implemented computation model can be used to study silica particle transport and deposition in superheated steam for more complicated geometries. (5) The implemented model in OpenFoam offers an advantage of computational time and cost saving due to its Eulerian approach. The model may be applied to the design and analysis of geothermal systems involving silica and superheated steam flows. CRediT authorship contribution statement Vijay Chauhan: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation. Maria Gudjonsdottir: Resources, Visualization, Writing - original draft. Gudrun Saevarsdottir: Funding acquisition, Supervision, Writing - review & editing. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement The work was funded by GEORG, Landsvirkjun, Reykjavik Energy, HS Orka, Orkustofnun and the IDDP project. The authors wish to thank Landsvirkjun staff for providing valuable support and technical advice. They are also grateful to staff of the Innovation Center of Iceland for their technical support. Appendix A. Supplementary data Supplementary material related to this article can be found, in the online version, at doi:https://doi.org/10.1016/j.geothermics.2020. 101802. References Bahadori, A., Vuthaluru, H.B., 2010. Prediction of silica carry-over and solubility in steam of boilers using simple correlation. Appl. Therm. Eng. 30, 250–253. Beal, S.K., 1970. Deposition of particles in turbulent flow on channel or pipe walls. Nucl.
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