Transient and Spatial Evolution of Clogging of Porous Material by

Article Cite This: Ind. Eng. Chem. Res. 2019, 58, 12261−12271

pubs.acs.org/IECR

Transient and Spatial Evolution of Clogging of Porous Material by Filtrating Particles H. Najmi,*,†,# N. Gascoin,† K. Chetehouna,† E. El-Tabach,§ and S. Akridiss† †

INSA Centre Val de Loire, Universite Orléans, PRISME EA 4229, F-18022, Bourges, France Universite Orléans, INSA-CVL, PRISME, EA 4229, F45072, Orléans, France

Downloaded via NOTTINGHAM TRENT UNIV on August 13, 2019 at 07:24:31 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

§

ABSTRACT: In hypersonic vehicles, regenerative cooling is used to handle the thermal load encountered in the combustion chamber. In this method, the fuel itself flows through a cooling channel and is circulated around the combustion chamber. The channel is made of porous material that enables fuel to also partially flow directly from the channel to the chamber by transpiration, which cools the wall by internal convection. The exposure of the fuel to high temperatures results in fuel pyrolysis producing carbon particles (coke). These particles are transported by the fuel and deposit inside the pores of the material resulting in a decrease of permeability of the medium. This process is very complex since it affects the heat transfers which generate the fuel pyrolysis and the formation of the particles. A test bench is developed in the current work to study the transient effect of the key parameters (i.e., filtrating mass flow rate, a load of particles in the flow) on the particles’ transport and on their spatial distribution inside the material. In the first part of the study, a porous medium with 3 mm thickness is used. It is found that with an increase in operational time, the powder mass accumulated inside the porous medium increases. In the second part of the study, different thicknesses (6, 9, and 12 mm) of porous medium are tried, to study its effect on particle transport. Particle transport is a function of pressure drop; therefore, the thickness of the porous medium is progressively increased at the same inlet mass flow rate which in turn modifies the pressure drop across the porous medium. More interestingly, the particles accumulate in the first 3 mm thickness of the upstream, while in the downstream on the opposite side of the porous material, almost no powder is found. Additionally, the pore Reynold’s number inside the porous media and the Reynold’s number of the fluid inside the permeation cell are determined to explain the transient and spatial evolution of clogging inside the porous media. In all the studied cases, the amount of powder transported through the porous media or collected downstream remains absent. pore structure resulting in a change in fluid flow and decrease in cooling efficiency. This results in the following disadvantages: (i) decrease in heat transfer efficiency (due to thermal insulation of carbon, the thermal conductivity of which is 4−6 times less than that of steel metallic materials),10 (ii) decrease in endothermicity of fuel decomposition reactions,9 (iii) increase in pressure drop (or system failure) due to the blocking of cooling channels or fuel injectors.11 Considering porous material for the cooling channel, a transpiration cooling is then used as a complementary cooling technique because it enables enhancing heat transfer due to internal convection obtained by the flow of fuel directly from the cooling channel to the combustion chamber due to a very strong pressure gradient (over 30 bar).10 During the course of operation, more and more coke particles are formed and get deposited not only in the main cooling channel but also in the porous material which affects the efficiency of the transpiration cooling. The clogging of the medium by particles modifies the

1. INTRODUCTION Hypersonic flights powered with a Supersonic Combustion Ramjet (SCramjet) permits the aircraft to attain a speed above Mach 5.1 Scramjet is very simple in design with no rotating parts (Figure 1). Air enters into the combustion chamber at a very high speed and is compressed due to the forward motion of the vehicle. As the flight velocity increases more than supersonic velocity, the combustion chamber is subjected to a very high thermal load, sometimes even more than 4500 K.2−4 To counter this, various cooling techniques are used, out of which regenerative cooling is widely used.5,6 In this cooling method, the onboard fuel is used as a coolant which results in the reduction of aircraft weight and increase in efficiency. The fuel, acting as the coolant, flows through cooling channels located between the inner and the outer walls of the engine, before being ignited in the engine (Figure 1). A counter-flow heat exchange between the fuel-coolant and the combustion gases causes the fuel to decompose into several small species such as hydrogen, ethane, and ethylene.7,8 In addition to these species, carbon particles are also formed; this process is known as coking.9−13 These solid carbon particles flow through the porous wall and deposit inside the combustion chamber wall pores. Further, they modify the © 2019 American Chemical Society

Received: Revised: Accepted: Published: 12261

March 29, 2019 June 11, 2019 June 13, 2019 June 13, 2019 DOI: 10.1021/acs.iecr.9b01746 Ind. Eng. Chem. Res. 2019, 58, 12261−12271

Article

Industrial & Engineering Chemistry Research

Figure 1. Schematic of transpiration cooling in scramjets.

pressure, and residence time in the cooling channels). The obtained results confirmed that with the increase in fuel mass flow rate there is an increase in the heat flux. This enhances the decomposition of the fuel which is highly dependent on temperature and further results in an increase in coking activity.18 The typical order of residence time in the cooling channel of the SCRamjet engine is about 1 s.10 Gascoin et al. and Maurice et al. confirmed a logarithmic relationship between the coking rate and residence time.9,10 It was also found that the effect of operating pressure is difficult to analyze because it cannot be dissociated from other parameters (residence time, flow regime, convective transfers). Indeed, by increasing the pressure, the density increases and for a given mass flow rate this corresponds to a decrease of the flow velocity, thus an increase of the residence time.10 This means it is difficult to study the effect of a single parameter on coke formation and its transport. The coking activity that occurs during the thermal cracking of a hydrocarbon is studied in a number of literature works.19 This is also observed in various industry applications9 but the industrial cracking is significantly different from the one observed in an aircraft. Industrial cracking typically occurs at near-atmospheric pressure with steam-diluted hydrocarbons in large tubes (internal diameter > 2.5 cm). However, in aircrafts, the fuel system pressures are 35−70 bar, the fuel is undiluted, and the channel diameter is much smaller in the order of millimeters.20,21 The aircraft fuels at high temperatures experience a number of environmental conditions that are significantly different than the typical industrial fuel applications. Therefore, there is a need of a separate study in which the effect of all the above explained parameters on particle transport can be studied. Particle transport in porous media is of significance in many industrial applications such as geothermal energy,22 oil recovery,23 leaching mining,24 coal bed gas mining,25 sand production in oil recovery,26 water treatment,27−30 and drug delivery.31 In a few studies, the Monte Carlo model is developed to study the particle transport processes in flow through a porous medium.32−34 The particle transport and capture are due to several effects depending on particle size.22 In the case of particles larger than 10 μm, hydrodynamics, gravity, and inertial effects are dominant.22 On the contrary, smaller particles are preferentially submitted to physicochem-

porosity and the permeability of the porous walls. The place of coke formation and deposition can be different because of the transport of particles into the porous material. Therefore, in addition to the coking activity, the fluid flow inside the porous media is also of great importance. The following are some common parameters which can influence coking as well as fluid flow through the porous media:10 temperature distribution of the walls, mass flow rate of fluid, fluid pressure, operation time, and characteristics of the porous medium (thickness, porosity, permeability). Through the interaction of these parameters, the residence time in the material, the relative quantity of particles flowing in the medium, the flow regime, and the ratio of particles’ diameter on material pore diameter are the four main driving indicators to be followed for a better understanding of the phenomena and quantitative evaluation of them.14,15 Langener et al. investigated the transpiration cooling efficiency of C/C materials for different porosity (ε = 10.7% up to ε = 16.1%). The materials were exposed to subsonic (M = 0.7) and supersonic (M = 2.1) flow conditions at moderate total temperature levels of up to 750 K. They found that neither the main-flow total-temperature nor material thickness of the sample has a significant effect on the cooling efficiency, but they are a function of the mass flow rate of the coolant and the properties of the ceramic material (i.e., porosity and permeability).16 In another study by Dittert et al., it was found that the bottom part of a sharp leading edge of an atmospheric re-entry vehicle is subjected to higher thermal load compared to the top part and transpiration cooling can be used to cool down the material. As the cooling depends upon the mass flow rate of the coolant, higher mass flow is required at the bottom side compared to the top side to have an optimized cooling. In order to achieve this, either the wall thickness should be increased or a different pressure reservoir should be used.17 Gascoin et al. show that high operating temperature, up to 1500 K allows producing interesting species for combustion, such as hydrogen and ethylene. These are highly hydrogenated species (with a hydrogen/carbon mass ratio of respectively infinite and 0.25) compared to the initial n-dodecane (H/C ratio of 0.15). Nevertheless, they are accompanied by high coke production (lowly hydrogenated).10 Taddeo et al. developed an experimental test bench to study the thermal management of a regeneratively cooled Scramjet. They developed analytical relationships between the operating parameters (fuel mass flow rate and equivalence ratio) and the measured outputs (fuel temperature, flame temperature, 12262

DOI: 10.1021/acs.iecr.9b01746 Ind. Eng. Chem. Res. 2019, 58, 12261−12271

Article


Figure 2. Filtration bench used to monitor the time and space clogging of porous material by solid particles dispersed in liquid flow.

residence time of flow in the material (controlled through the mass flow rate) and the porous medium thickness are varied. The experimental study is divided into two parts. In the first part, a porous medium of 3 mm thickness is used and the effect of various operating parameters such as operation time, mass flow rate, and particle loading is studied on the particle transport. Additionally, the effect of pore Reynolds number and Reynolds number is also studied. In the second part of the study, different thicknesses (6, 9, and 12 mm) of porous media are used. This allows the user to study the effect of pressure drop without modifying the inlet mass flow rate. In the last part, the effects of deposited mass and cake formation on the accumulated mass are studied.

ical forces such as double layer and van der Waals forces and to Brownian diffusion.22 The particle transport in a porous medium can be described by the following three steps (if the diameter of particle is lower than the pore diameter; assuming uniform distributions):15 1. Transported mass: In the first step, particles flow across the porous media and get deposited downstream in the so-called collecting jar (see Figure 2). 2. Accumulated mass: After some time, the particles start to get deposited inside the pores resulting in a sudden decrease in permeability and an increase in flow resistance. 3. Deposited mass: After the pores become saturated, the particles start to deposit on to the porous surface forming a cake. For particles that have a diameter greater than that of the pores, step 1 and 2 will be absent. After the cake formation, the analysis of surface filtration is based on the accumulation of a permeable filter cake above the medium as particles are retained. Under constant pressure the flow through this filter cake decreases with time as the cake thickens and the porosity decreases during compression.15 In the case of groundwater filtration, Sakthivadivel et al. [1970] found that the most critical factor determining straining within porous media (gravel matrix) was the ratio of the media diameter to the particle diameter, dm/dp.35 For a dm/dp less than 10, or relatively large particles compared to the media size, no particle penetration into the media was observed, that is, cake filtration. Within the narrow window of particle size 10 < dm/dp< 20, they found permeability reductions by a factor of 7−15, and deposited particles occupied more than 30% of the pore volume. The particles’ deposit was probably even much greater near the surface. For relatively small particles, dm/dp > 20, only 2−5% of the pore volumes were occupied by retained particles under equilibrium conditions, and permeability reductions were limited to only 10−50% of the clean porous media value. If influent particle size distributions contained a broad distribution in sizes from dm/dp < 10 to dm/dp > 20, then retained larger particles acted as strainers for smaller particles, leading to effective particle filtration at or near the media surface in a combination of surface and straining filtration.35 In the present work, a new experimental bench and test methodology are developed to study the particles’ transport inside a porous medium. It is intended to understand the effect of the operating parameters independently on particle transport and distribution as a function of time and space. Space distribution is important for later being able to analyze the temperature gradient in a system under clogging. The particles’ size and the properties of the material (porosity and permeability) are chosen to reproduce the conditions expected in aerospace applications. The input parameters such as the

2. MATERIALS AND METHODS 2.1. Experimental Setup. The experimental setup used for this work is presented in Figure 2. It is composed of an injection system which consists of an autoclave pressurized by a high-pressure nitrogen bottle (Air Liquide) from 0 to 100 bar. The autoclave is equipped with a stirrer with a variable speed controller to ensure homogeneous dispersion of the powder into the liquid. The maximum capacity of the autoclave is 2 L and the powder is mixed with water before the test. The injection system is connected to the permeation cell with Swagelok stainless steel 1/8 in. tubing. The permeation cell is composed of two parts separated by the porous medium (high-pressure chamber (HPC) for the inlet and low-pressure chamber (LPC) for the outlet). Further information regarding the cell can be obtained in previous works.36,37 A total of four different types of pressure transducers are used. The first has a measuring range of 0− 100 bar (ABB 2600T) and it is attached to the autoclave in order to measure the pressure of the gas pressurizing the mixture (liquid + powder) in the autoclave. The second has a range of 0−60 bar (Rosemount) placed at the inlet of the cell in order to monitor the upstream pressure of the mixture entering the cell. The last two are the differential pressure transducers having a range of 0−650 mbar (Rosemount) and 0−100 bar (Rosemount), placed in parallel across the permeation cell to measure the pressure drop across the porous medium. These two differential pressure transducers measure the pressure drop simultaneously to avoid any loss of data in the case of saturation of the low range transmitter or in case of low accuracy of the high range transducer. The mass flow rate is measured at the permeation cell entrance by a Coriolis flow meter (Micro Motion 2700R) and the outflow is collected using a measuring jar at the outlet. A K-type thermocouple (Omega TJ36-CASS-18U-6) measures the temperature of the fluid exiting the permeation cell. All the sensors to monitor transient variations of mass flow rate, pressure, and temperature are connected to a data acquisition 12263


Article


porous media of required thickness is that it will allow studying the depth of particle transport during the experiments by weighing each “slice” of porous material. Thus, instead of using a single 12 mm material with a single value of trapped particles weight, a spatial distribution can be obtained by using four 3 mm-thickness materials. The tightness seal is used between the “layers” of materials when tested in the preliminary phase of the work. Before starting each test, all the parts of the permeation cell are properly cleaned in an ultrasonic cleaning machine (J B Sonic 18F) to make sure that no foreign particle is present inside the cell (35 min cycle). Thereafter, all the parts are dried and small droplets of water or any other particle left (if any) are removed by blowing high-pressure gas (10 bar). Then all the components of the permeation cell including porous media are weighed using the digital mass balance (Kern ABT 1005NM and 440-53N), and their respective weight is noted. The parts which weigh less than 101 g (such as porous media, lock nut, powder) are weighed using a Kern ABT 100-5NM (range of 1 mg to 101 g, accuracy of 0.01 mg) instrument, while the parts heavier than 101 g (such as HPC and LPC) are weighed using the Kern 440-53N mass balance (range of 1 to 6000 g, accuracy of 1 g). For each test 3.75 g of SiC powder is weighed and mixed with 1.5 L of water in the autoclave by turning the stirrer on and by adding the powder progressively in the water to ensure a homogeneous dispersion. The amount of powder present in the liquid is 0.25% of the mass of water, which is a representative value of the typical coke concentration found during fuel pyrolysis.10 The cell is then prepared by placing the porous media with the carbon seal and the rubber seal. The carbon and rubber seals are placed before and after the porous media to make sure that there is no leakage around the edges of the porous sample. After preparation, the whole cell is also weighed. At the beginning of the test, the outlet valve is closed and high-pressure nitrogen is injected into the system to verify that all the joints and connections are leak proof. After this, all the valves are closed and constant gas pressure is applied to the autoclave in order to achieve the respective inlet mass flow rates of the mixtures (liquid+powder) as per the test requirement. As the experiments start, all the valves are opened, data acquisition is run, and the start time is noted. The inlet flow tends to fluctuate due to continuous deposition of powder particles on the porous surface. Therefore, it is constantly monitored through digital display and manually adjusted in real time using a micrometer valve placed on the inlet side, just after the mass flow meter (Figure 2). The experiment duration depends upon the test case (Table 2). At the end, the cell is dismounted from the bench and the mass of the whole cell is noted down. Thereafter the cell is disassembled in order to weigh each part of the cell separately (i.e., HPC, LPC, and locknut), after which all the parts are

system (Keithley 2400:1 Hz, 16 bits, 48 channels). Particle transport and Darcy’s permeability determination are studied on porous stainless steel (SS20) of grade 20 (supplied by Sintertech). The specification of the material is given in Table 1. Table 1. Physical and Geometrical Characteristics of the SS20 grade thickness diameter porosity pore diameter

20 3 mm 30 mm 35.63% 88 μm

In this study, silicon carbide (SiC) powder of a particle size of 35 μm and the specific density of 3210 kg·m−3 is used. The SiC powder is selected because it is nonmiscible in water (similar to coke in hydrocarbon fuel) and has a particle to liquid density ratio similar to the realistic conditions. The particle to liquid density ratio for SiC/water is 3.21 (3210/ 1000), while for coke/fuel it is around 3.23 (2000/620).3 2.2. Test Methodology. A number of tests have been performed by varying operational time, mass flow rate, and porous media thickness, of which nine are presented here. These nine tests are divided into four phases (see Table 2). All the tests are performed at room temperature (300 K). Phase 0 represents the test which is specifically performed to develop the test methodology. Table 2. Test Matrix for Particle Transport

Varying of the material thickness is achieved by having multiple porous media in series. For example, for achieving a 6 mm thickness, two porous media of thickness 3 mm are placed inside the permeation cell one over another, and similarly the 9 mm and 12 mm thicknesses are achieved (Figure 3). The idea of using multiple porous media (in series) instead of one

Figure 3. Test configuration to study the effect of porous media thickness on particle transport. 12264


Article

Industrial & Engineering Chemistry Research dried in Memmert UN 11 oven at 120 °C for 180 min and weighed again in order to evaluate only the deposit of powder and avoid any perturbation by the liquid weight. The porous material is first weighed with the low-pressure chamber and then by itself (to avoid loss of powder particles while disassembling). At times, some of the particles can be deposited on the surface of the porous material. In such a case, the particles are removed and the porous material is weighed again a last time in order to estimate the mass of accumulated particles inside the porous material. It should be noted that the deposited mass does not always correspond to the mass of cake formed outside the porous media. 2.3. Permeability Determination. The Brinkman equation is used in a considerable amount of literature to describe the macroscopic fluid flow in large range flow regimes:8 ΔP V V2 =μ +ρ L KD KF

pressure drop is very small (i.e., 0 to 1.5 bar). To determine the permeability using Brinkman’s equation, the ISO method considers the evolution of ΔP as a function of ρV . Since the

μV ΔP = L KD

(1)

Table 3. Darcy’s Permeability Determined Experimentally According to eq 1 and eq 3 KD (m2) spplier’s value

calculated using eq 1

calculated using eq 3

8.70 × 10−12

9.95 × 10−12

8.88 × 10−12

respectively between the calculated and the supplier’s permeability values. The relative error is higher for eq 1 because the flow is less turbulent,8 while in case of eq 3 there is no Forchheimer’s term hence the determination of permeability is more accurate. To validate the test bench further the measured pressure drop (using differential pressure transducer) is compared with the theoretical pressure drop (estimated using eq 3) for different inlet mass flow rates (see Table 4). It can be seen

ρd pV μ

(3)

2.4. Test Bench Validation. Some tests with pure water have been performed similarly to test conditions shown in Table 2 in order to determine the Darcy’s permeability using eq 1 and eq 3. The obtained permeability value is compared with the supplier’s value in order to ensure the reliable operation of the bench. It is found to be in good agreement (Table 3). Discrepancies of 14% and 2% are observed

where ΔP = Pin − Pout is the pressure drop through the porous medium, L is the external mean sample thickness, μ is the fluid viscosity (calculated using NIST data), ρ is the mean density (based on mean pressure), V is the superficial velocity, KD and KF are the Darcy’s and Forchheimer’s terms. The right term of eq 1 is composed of two parts, one related to the Darcy’s law for low velocity regime filtration (Darcian flows) and the quadratic one is related to the Stokes’s law (non-Darcian flows) which takes into account the inertial effects related with flow resistance. The flow regime inside the porous media is characterized on the basis of the pore Reynold’s Number (ReP). Therefore, the pore Reynold’s Number is determined for all the studied test cases using the following relation. ReP =

μ

Lμv

change in density and viscosity is negligible during the respective test case, Brinkman’s equation cannot be applied to the current study. Therefore, the quadratic part of Brinkman’s equation is neglected and a one-dimensional form of Darcy’s equation is considered in the present work which is as follows:

(2)

where ReP is the pore Reynolds number and dp is the pore diameter. In all the test cases ReP is found to be ≈1, which means flow is always in a laminar regime8 and the pressure gradient is linearly proportional to the fluid velocity in the porous material.8 The Reynold’s number represents the ratio of the momentum flux to the viscous stress. This can also be interpreted as the ratio between the inertial forces and the viscous forces. For a low Reynolds number, the viscous forces are dominant and for a high Reynolds number the inertial forces will become dominant. It is expected that when viscous stress dominates, the relation between pressure drop and velocity is linear. However, for higher flow velocities, the linear pressure drop does not follow the Darcy equation. In eq 1 the pressure term (i.e., lhs) is a function of Darcy’s term and Forchheimer’s term. When the pore Reynold’s number is less than the critical Reynold’s number (i.e., 1 in the case of porous stainless steel) the contribution to the pressure gradient is dominated by the Darcy’s term (90 to 98%). Therefore, at the low velocity the Forchheimer’s term is neglected. Additionally, during the current study the mass flow rate in each of the cases is fixed, it is not changed during the respective case study and hence all the fluid parameters (i.e., mass flow rate, inlet pressure, and temperature) throughout the test remains constant except the pressure drop. The change in pressure drop can impact the fluid properties such as density and viscosity but as the fluid used here is water the change in those properties are not very significant because the change in

Table 4. Comparison of Experimental and Theoretical Values of Pressure Drop measured experimentally no. 1 2 3 4 5

inlet mass flow rate (g/s) 2.09 2.51 3.16 3.64 4.31

± ± ± ± ±

0.002 0.004 0.003 0.004 0.003

estimated using eq 3

pressure drop (mbar)

pressure drop (mbar)

± ± ± ± ±

33.60 40.35 50.80 58.51 69.28

32.09 39.28 51.20 60.71 72.45

0.03 0.08 0.15 0.25 0.14

from the table that the measured and estimated values of the pressure drop are quite close to each other even for a very small pressure drop such as 32 mbar. These results confirm that the test bench is very accurate and reliable. Hence, this test bench is used for the particles’ transport study.

3. RESULTS AND DISCUSSIONS The amount of powder transported through the porous media or collected downstream remains unobservable in all the studied test cases which is probably due to the inlet pressure which is not high enough to push the powder particles through the porous medium, even for a small thickness like 3 mm. 12265


Article


Figure 4. (a) Repartition of the powder mass for four different time steps and (b) time evolution of clogging.

uncertainty,39 so from an engineering and operational point of view, 13% is acceptable. The clogging effect of the particles’ deposition is observed through the material permeability (Figure 5). Darcy’s

The repartition of the powder mass for four different operational times at 2 g/s and 3 mm thickness is first presented in Figure 4. The injected mass is estimated on the basis of the total inlet mass flow rate through the porous media during the respective cases (considering a 0.25% load of powder into the liquid which is a constant value during the test due to the stirrer in the autoclave). Some of the powder particles also stick to the cell surface and to the lock nut due to the scattering of the inlet flow inside the cell. It is considered as a “lost” mass in the process and is only of interest when calculating the global mass balance in the system. From Figure 4, as the operation time increases, the accumulated mass also increases. The longer is the operational time, the higher is the injected mass and therefore a longer operation time results in a higher accumulated mass. The accumulated mass also depends upon the type of cake formation38 (incompressible, compressible, or no cake). The type of cake formation can be determined on the basis of the permeability profile.38 The permeability profile is linear for 30 s, has an increasing slope for 60 s, and has a decreasing slope for 75 and 120 s test cases. Linear profile means the presence of an incompressible external filter cake, an increasing slope results in a compressible external filter cake, and a decreasing slope leads to no external filter cake formation but a deeper particle-invasion depth.38 Another reason for obtaining a higher accumulated mass in the 75 and 120 s test cases is the absence of external filter-cake formation. It is also quite important to note that increase in operational time results in a change in flow dynamics, which eventually affects the accumulated mass. In all the four cases (i.e., 30, 60, 75, 120 s), the accumulated mass is about 8.6% of the injected mass. As the experimental time is increased by a factor of 2 for the 60 s case and by a factor 4 for the 120 s case, the accumulated mass is increased by 60% (i.e., 1.59 times) and 209% (i.e., 3.09 times) compared to the 30 s test case. The fact that the accumulation process is not linear with the time of experiment shows that there are unsteady phenomena which act microscopically (like the saturation of the material). The ratio of the recovered mass (i.e., deposited + accumulated + stuck) to injected mass should be 1 for 100% of recovery. If the recovery is not 100%, the deflected amount is considered as lost and is presented in the lost column of Figure 4. The lower is the lost part, the better is the mass balance of the experiment. The amount of mass lost is 0% and 1% for the 30 s and the 60 s cases, respectively, and 13% for the 120 s case. Due to the very low amount of powder considered in the experiment, even the 13% loss is considered as a good result. For example, the determination of the permeability is good even when obtained with 30% of

Figure 5. Time evolution of Darcy’s permeability due to clogging.

permeability is calculated by eq 3 on the basis of real time measured parameters (i.e., pressure drop, temperature, and inlet mass flow rate). Figure 5 is plotted on the logarithmic scale in order to see the evolution of Darcy’s permeability more clearly (i.e., Y-axis is scaled from higher to lower). Darcy’s permeability decreases as a function of time because the deposited and the accumulated masses increase. There is a steep decrease in permeability for the first 15−20 s, which is about 80% of the initial value. Even after 20 s, the permeability value continues to decrease in all the test cases, but the magnitude of the decrease is lower. This is because most of the active permeating surface (active filtration area) is already covered with the powder particles in the first 20 s, due to which the incoming powder hardly penetrates inside the porous material and hence the decrease in permeability gets limited. To have a reference, the permeability of pure water without particles loadis also presented in Figure 5. The results are repeatable, particularly for the first 30 s when the three test cases have very similar quantitative trends and from 30 to 60 s, when the two cases still show a good agreement. Thus, it can be considered that doing a test, stopping it to measure the mass distribution in the system, and starting a new test for a longer duration would enable us to get the mass distribution for different time steps of the operation. The effect of the mass flow rate of a mixture is observed. It can be seen from Figure 6a that the pressure drop in the case of 2.5 g/s is higher compared to the 2.0 g/s test case which is in line with the theory (see eq 3). In addition, a higher inlet flow means that the amount of particles injected per second is also higher. This may decrease the permeability by clogging 12266


Article


Figure 6. (a) Evolution of pressure drop and (b) repartition of powder mass at an inlet mass flow rate of 2.0 and 2.5 g/s.

formation of a compressible filter cake in the 2 g/s test case and no external filter-cake formation in the 2.5 g/s test case. To isolate the effect of the powder load (higher for higher flow rate) and the effect of the flow itself (hydrodynamic pressure on the medium and turbulence regime in the system), the 2.5 g/s and 60 s case is compared with the 2 g/s and 75 s test case (see Figure 8). It can be observed from Figure 8a that the rise in pressure drop value of the 2g/s and 75 s test case (no. 3) is similar to the 2.0 g/s and 60 s test case (no. 2) because of the same flow rate. The injected powder mass in test case 3 is slightly higher (i.e., 8.5%) than in case 5 but finally the pressure drop remains lower. That means that the particles load is not the only parameter to play a role on the particles transport and the mass flow rate and that the pressure of the flow and the flow regime also have to be considered. The accumulated mass in case no. 3 is 58.5% higher than in case no. 5 (see Figure 8b). This means that the accumulation is facilitated by a slow motion flow of fluid (low turbulence regime) rather than by a fast moving and turbulent one. In the case of a small inlet mass flow rate, the amount of particles injected per second is lower. Hence, it allows more filtration surface area to get exposed to the incoming particles per time unit. This results in a steady rise in pressure drop (instead of the sudden increase in pressure drop like that observed in the case of 2.5 g/s), which finally results in more accumulated mass.15 To confirm the above statement the average pore Reynold’s number inside the porous media and average Reynold’s number inside the permeation cell is determined for the total duration of the test (see Table 5). It can be seen from Table 5, as the operational time increases (cases 1 to 4) the average pore Reynold’s number and Reynold’s number decreases. It means that the lower is the Reynold’s number, the higher will be the accumulated mass.

and thus increase the pressure drop. The repartition of mass in the process, for both cases, is observed (Figure 6b). The accumulated mass is 9.4% higher in the case of 2.5 g/s, which is obvious because even the injected powder mass is 32.7% higher compared to the 2.0 g/s test case. This means that with a higher mass flow rate and a higher inlet pressure, the accumulation in the porous material is greater. This may be due to the hydraulic strength applied on the flow and on the particles which thus gets further forced to penetrate the porous material. The deposited quantity of particles is higher in the case of a higher flow rate, which is related to the quantity of available powder being injected in the system. The decrease in permeability for 2.5 g/s is more rapid compared to the 2.0 g/s test case (Figure 7) due to the higher

Figure 7. Evolution of Darcy’s permeability at an inlet mass flow rate of 2.0 and 2.5 g/s.

accumulated and deposited mass. It is difficult to differentiate between the permeability profiles of the 2.5 g/s and 2 g/s test cases but the pressure drop profile (Figure 6a) suggests the

Figure 8. (a) Evolution of pressure drop and (b) repartition of powder mass for an identical injected powder mass. 12267


Article


monitoring the global Darcy permeability as a function of time shall be permitted to evaluate the permeability changing under clogging in the 3 mm thickness. The evolution of Darcy’s permeability for different thicknesses of porous media can be seen in Figure 11. It illustrates the fact that the first clogged layer is playing the main role as the thickness has a minor role in the permeability evolution when comparing these four test cases. In addition to this, the thickness of accumulation inside the porous material is determined using the following equation:40

Table 5. Average Pore Reynold’s Number and Reynold’s Number for Different Test Cases average test case no.

pore Reynold’s number (inside the porous media)

Reynold’s number (inside the cell)

1 2 3 4 5

0.98 0.91 0.93 0.83 1.13

335 313 318 284 386

e=

This conclusion is also valid when case 5 is compared with case 3 for which the injected mass is almost the same, but instead of a higher inlet mass flow rate in case 5 the accumulated mass is lower compared to case 3. Finally, the effect of different thicknesses (6, 9, and 12 mm) of porous media on particles’ transport is studied for the same inlet mass flow rate (2.0 g/s) and operational time (75 s). It should be noted that as the porous media thickness increases, the time required to stabilize the inlet flow also increases. Figure 9a shows that the accumulated mass varies as the thickness of the porous media increases. As the injected powder mass is not exactly the same in all the test cases (3, 6, 9, and 12 mm) because of the bench fluctuations explained above, the repartition of mass is observed in terms of percentage with respect to the injected mass to draw a conclusion (Figure 9b). The fact that the operating conditions fluctuate during the test, because of the regulation and because of the clogging, strongly impacts the results. For example, the 6 mm case shows higher pressure drop (Figure 10) and its trend is clearly responsible for it (regulation of the process). When analyzing further what happened spatially in the 6, 9, 12 mm samples, it is found that that in all the cases (6, 9, and 12 mm) the accumulated mass is limited to the first sample (inside the first 3 mm layer of material) placed upstream (Table 6). The pressure drop profile for case 7 (i.e., 9 mm) is with a decreasing slope compared to the other cases (cases 3, 6, and 8) which means that the external filter-cake formation remains absent which results in a higher accumulated mass. It can be concluded that the filtration of particles impacts the first layer of the material while the remaining depth of the material mostly plays a hydraulic role similar to what happens in pure water liquid flow following the Darcian theory. As a consequence, when monitoring the clogging, the Darcian change can be attributed to the first layer (here the 3 mm upstream part of the porous medium). As a consequence,

mpowder π

ρpowder 4 d 2ε

(4)

where mpowder and ρpowder are respectively the mass and the volumic mass of the accumulated powder, d is the diameter of the sample, and ε is the total porosity of the material. It clear from Table 7 that the accumulated mass is limited to the first layer of the porous media (i.e., 3 mm); therefore, the mass transported through the porous media remains absent in all the studied test cases. The accumulation thickness increases with the increase in operational time (cases 1 to 4) due to the change in flow dynamics as explained above. This result also confirms that the absence of an external filter-cake results in a deeper particle-invasion depth (cases 4 and 7); the results are in line with the conclusion made in the previous studies.38,41−43 In a previous work44 transport of 35 μm particles through the BR30 was studied where the transported mass was observed in all the test cases. While in the present study, even though the particle-to-pore diameter ratio is similar to the previous study,44 the transported mass remains absent. The primary reason behind this is the deposited mass which is about 42% (Figures 4a and 9b) compared to the previous study44 where it was merely 13%. As the Darcy’s permeability of the SiC particle is much lower than (10−15 m2) the porous media, it does not allow the particle to penetrate inside the porous media easily; hence, the transported mass remains absent. It is important to note that in the previous study the inlet mass flow rate used was twice the flow rate used in the present study. This means the Reynold’s number was also higher and maybe that is the reason why the deposited mass was significantly lower in the previous study44 which is in line with the conclusion made in the section above.

Figure 9. Repartition of powder mass in terms of (a) mass and (b) percentage with respect to the injected mass for different thicknesses of porous media. 12268


Article


Figure 10. Space evolution of clogging (left) and evolution of pressure drop in the case of particle transport for different thicknesses of porous media at a constant inlet mass flow rate of 2.0 g/s (right).

Table 6. Measured Weights of the Porous Samples before and after the Test weight (g) sample 1

sample 2

sample 3

sample 4

thickness (mm)

before

after

before

after

before

after

before

after

3 6 9 12

9.94639 10.6807 9.9716 10.6803

9.98855 10.6933 10.0242 10.7171

10.6479 10.2865 9.9646

10.6453 10.2865 9.9646

10.2914 10.2787

10.2914 10.2787

10.6375

10.6375

between the wall and the filtrating fluid, knowing the permeability dependence on clogging is required. Since this is a time and space dependency, an experimental work is developed to get a better insight into these complex hydraulic phenomena on very small scales of space. Tests were done with constant particle diameters and constant material characteristics. The powder load inside the liquid was fixed. The fluid flow rate was varied as was the material thickness. Three important conclusions were derived. First, it is possible to do successive tests to get the time evolution of mass distribution in the system. Second, it is confirmed by the estimated pore Reynold’s number and Reynold’s number values that the clogging is affected by fluid profile inside as well as outside the porous media. The flow turbulence outside the porous media reduces the deposit of particles inside the material and a lowspeed laminar regime favors the deposit; thus the clogging. The lower is the Reynold’s number the higher will be the accumulated mass. The type of cake formation is responsible for the respective pressure drop and permeability profile. The profile changes with the change in operational time. The absence of a filter-cake formation results in a deeper particleinvasion depth. Third, it was found that the clogging mostly appears on the upstream part of the porous material. It is basically due to the cake formation or deposited mass. The lower permeability of cake restricts particle transport. As a consequence, it could be possible to determine, as a function of time, the depth of the penetration of the particles in the material. Such information would be useful in future works to investigate the heat transfer in porous materials undergoing fuel pyrolysis with coke formation.

Figure 11. Evolution of Darcy’s permeability for different thicknesses of porous media.

Table 7. Penetration Depth of the SiC Particle Inside the Material for Different Test Cases test case no.

accumulation thickness (mm)

1 2 3 4 5 6 7 8

0.066 0.105 0.183 0.204 0.115 0.092 0.228 0.160

■

4. CONCLUSION In transpiration cooling various complex phenomena occur out of which the formation of solid carbon particles is the most important. These carbon particles modify the pore structure resulting in a change in the fluid flow and decrease in the cooling efficiency. To further study the clogging effect of particles on the heat transfer inside the porous material and

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +33 752537470. ORCID

H. Najmi: 0000-0003-1478-2392 12269


Article

Industrial & Engineering Chemistry Research Present Address

(19) Crynes, B. L.; Albright, L. R.; Tan, L. Thermal Cracking. Enc. Physical Sci. Technol. 1987, 3, 627. (20) Beal, E. J.; Hardy, D. R.; Burnett, J. C. Results and Evaluation of a Jet Fuel Thermal Stability Flow Device which Employs Direct Gravimetric Analysis of Both Surface and Fuel Insoluble Deposits. 4th International Conference on Stability and Handling of Liquid Fuels, Orlando, Florida, November 1991; pp 245−259. (21) Ronald, T. Status and Applications of Materials Developed for NASP, AIAA-95−6131. International Aerospace Planes and Hypersonics Technologies, Chattanooga, TN, U.S.A, April 1995. (22) Frey, J. M.; Schmitz, P.; Dufreche, J.; Pinheiro, I. Particle Deposition in Porous Media: Analysis of Hydrodynamic and Weak Inertial Effects. Transport in Porous Med. 1999, 37, 25. (23) Qiu, Y.; Wu, F.; Wei, M.; Kang, W.; Li, B. Lessons Learned from Applying Particle Gels in Mature Oilfields. SPE-169161-MS; SPE Improved Oil Recovery Symposium, Tulsa, Oklahoma, April 2014. (24) Mcbride, D.; Gebhardt, J.; Croft, N.; Cross, M. Heap Leaching: Modelling and Forecasting Using CFD Technology. Mineral. 2018, 8, 1. (25) Nie, B.; Fan, P.; Li, X. Quantitative Investigation of Anisotropic Characteristics of Methane-Induced Strain in Coal Based On Coal Particle Tracking Method with X-Ray Computer Tomography. Fuel 2018, 214, 272. (26) Papamichos, E.; Vardoulakis, I.; Tronvoll, J.; Skjaerstein, A. Volumetric Sand Production Model and Experiment. Int. J. Numer. Anal. Methods Geomech. 2001, 25, 789. (27) Zamani, A.; Maini, B. Flow of Dispersed Particles through Porous Media-Deep Bed Filtration. J. Pet. Sci. Eng. 2009, 69, 71. (28) Boccardo, G.; Marchisio, D. L.; Sethi, R. Microscale Simulation of Particle Deposition in Porous Media. J. Colloid Interface Sci. 2014, 417, 227. (29) Gitis, V.; Rubinstein, I.; Livshits, M.; Ziskind, G. Deep-Bed Filtration Model with Multistage Deposition Kinetics. Chem. Eng. J. 2010, 163, 78. (30) Shapiro, A. A.; Bedrikovetsky, P. G. A Stochastic Theory for Deep Bed Filtration Accounting For Dispersion and Size Distributions. Phys. A 2010, 389, 2473. (31) Kleinstreuer, C.; Yu, F.; Childress, E. Drug-Targeting Methodologies with Applications: A Review. World J. Cl. Cases. 2014, 2, 742. (32) Imdakm, A.; Sahimi, M. Computer Simulation of Particle Transport Processes in Flow Through Porous Media. Chem. Eng. Sci. 1991, 46, 1977. (33) Sahimi, M.; Imdakm, A. Hydrodynamics of Particulate Motion in Porous Media. Phys. Rev. Lett. 1991, 66, 1169. (34) Imdakm, A.; Sahimi, M. Transport of Large Particles in Flow Through Porous Media. Phys. Rev. A: At., Mol., Opt. Phys. 1987, 36, 5304. (35) Sakthivadivel, R.; Einstein, H. A. Clogging of porous column of spheres by sediment. J. Hydr. Div. ASCE 1970, 96, 461. (36) Najmi, H.; El-Tabach, E.; Chetehouna, K.; Gascoin, N.; Akridiss, S.; Falempin, F. Flow Configuration Influence on Darcian and Forchheimer Permeabilities Determination. In Innovative Design and Development Practices in Aerospace and Automotive Engineering; Lecture Notes in Mechanical Engineering; Bajpai, R. P., Chandrasekhar, U., Eds.; Springer: Singapore, 2017; pp 87−94. (37) Najmi, H. Selectivity of Porous Composite Materials for Multispecies Mixtures: Application to Fuel Cells. Ph.D. Dissertation, University of Orleans, France, 2018. (38) Pang, S.; Sharma, M. M. A Model for Predicting Injectivity Decline in Water Injection Wells. SPE Form. Eval. 1997, 12, 194. (39) Gascoin, N.; Fau, G.; Gillard, P.; Kuhn, M.; Bouchez, M.; Steelant, J. Comparison of Two Permeation Test Benches and of Two Determination Methods for Darcy’s and Forchheimer’s Permeabilities. J. Porous Media 2012, 15, 705. (40) Tabach, E.; Chetehouna, K.; Gascoin, N.; Gaschet, F. Modeling the Spatio-Temporal Evolution of Permeability during Coking of Porous Material, AIAA 2015-3663. 20th AIAA International Space

#

Institut Pprime, UPR 3346 CNRS, Department Fluides, Thermique, Combustion, ENSMA, BP 40109, 86961 Futuroscope, France. Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Curran, E. Scramjet Engines: The First Forty Years. J. Propul. Power 2001, 17, 1138. (2) Daniau, E.; Sicard, M. Experimental and Numerical Investigations of an Endothermic Fuel Cooling Capacity for Scramjet Application, AIAA 2005-3404. 13th AIAA/CIRA International Space Planes and Hypersonics Systems and Technologies Conference, Capua, Italy, May 2005. (3) Ulas, A.; Boysan, E. Numerical Analysis of Regenerative Cooling In Liquid Propellant Rocket Engines. Aerosp. Sci. Technol. 2013, 24, 187. (4) Hou, L.; Dong, N.; Sun, D. Heat Transfer and Thermal Cracking Behavior of Hydrocarbon Fuel. Fuel 2013, 103, 1132. (5) Bao, W.; Li, X.; Qin, J.; Zhou, W.; Yu, D. Efficient Utilization of Heat Sink of Hydrocarbon Fuel for Regeneratively Cooled Scramjet. Appl. Therm. Eng. 2012, 33−34, 208. (6) Bouchez, M. Scramjet Thermal Management Scramjets or Dual Mode Ramjets for High Speed Atmospheric Flight; NATO Science and Technological Organization, 2010. (7) Gascoin, N.; Gillard, P. Dynamic Study of Coupled Heavy Hydrocarbon Pyrolysis and Combustion. Combust. Sci. Technol. 2012, 184, 2136. (8) Najmi, H.; El Tabach, E.; Chetehouna, K.; Gascoin, N.; Falempin, F. Effect of Flow Configuration on Darcian and Forchheimer Permeabilities Determination in a Porous Composite Tube. Int. J. Hydrogen Energy 2016, 41, 316. (9) Maurice, L.; Edwards, T.; Griffiths, J. Liquid Hydrocarbon Fuels for Hypersonic Propulsion. In Scramjet propulsion; Murthy, S. N. B., Curran, E. T., Eds.; American Institute of Aeronautics and Astronautics, 2001; pp 757−822. (10) Gascoin, N.; Gillard, P.; Bernard, S.; Bouchez, M. Characterization of Coking Activity During Supercritical Hydrocarbon Pyrolysis. Fuel Process. Technol. 2008, 89, 1416. (11) Spadaccini, L.; Sobel, D.; Huang, H. Deposit Formation and Mitigation in Aircraft Fuels. J. Eng. Gas Turbines Power 2001, 123, 741. (12) Song, C.; Eser, S.; Schobert, H.; Hatcher, P. Pyrolytic Degradation Studies of a Coalderived and a Petroleum-Derived Aviation Jet Fuel. Energy Fuels 1993, 7, 234. (13) Chin, J. S.; Lefebvre, H. Influence of Flow Conditions on Deposits from Heated Hydrocarbon Fuels. J. Eng. Gas Turbines Power 1993, 115, 433. (14) Zhu, Y.; Yan, S.; Zhao, R.; Jiang, P. Experimental Investigation of Flow Coking and Coke Deposition of Supercritical Hydrocarbon Fuels In Porous Media. Energy Fuels 2018, 32, 2941. (15) McDowell-Boyer, L. M.; Hunt, J. R.; Sitar, N. Particle Transport through Porous Media. Water Resour. Res. 1986, 22, 1901. (16) Langener, T.; von Wolfersdorf, J.; Laux, T.; Steelant, J. Experimental Investigation of Transpiration Cooling with Subsonic and Supersonic Flows at Moderate Temperature Levels, AIAA 20085174. 44th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Hartford, CT, July 2008. (17) Dittert, C. Wall Thickness Optimization of a TranspirationCooled Sharp Leading Edge at Atmospheric Re-entry. In 5th International Conference on Porous Media and Their Applications in Science, Engineering and Industry; Vafai, K., Bejan, A., Nakayama, A., Manca, O., Eds; Engineering Conferences International, 2014. (18) Taddeo, L.; Gascoin, N.; Chetehouna, K.; Ingenito, A.; Stella, F.; Bouchez, M.; Le Naour, B. Experimental Study of PyrolysisCombustion Coupling in a Regeneratively Cooled Combustor: Heat Transfer And Coke Formation. Fuel 2019, 239, 1091. 12270


Article

Industrial & Engineering Chemistry Research Planes and Hypersonic Systems and Technologies Conference, Glasgow, Scotland, July 2015. (41) Kalantariasl, A.; Bedrikovetsky, P. Stabilization of External Filter Cake by Colloidal Forces in a “Well−Reservoir” System. Ind. Eng. Chem. Res. 2014, 53, 590. (42) Kalantariasl, A.; Farajzadeh, R.; You, Z.; Bedrikovetsky, P. Nonuniform External Filter Cake in Long Injection Wells. Ind. Eng. Chem. Res. 2015, 54, 3051. (43) Kalantariasl, A.; Zeinijahromi, A.; Bedrikovetsky, P. AxiSymmetric Two-Phase Suspension-Colloidal Flow in Porous Media during Water Injection. Ind. Eng. Chem. Res. 2014, 53, 15763. (44) Akridiss, S.; Tabach, E.; Chetehouna, K.; Gascoin, N.; Kadiri, M. S. Experimental Transient Clogging of Brass Porous Disks by Silicium Particles. Exp. Therm. Fluid Sci. 2018, 98, 112.

12271


Transient and Spatial Evolution of Clogging of Porous Material by

Recommend Documents