Alkali Vapor Condensation on Heat Exchanging Surfaces: Laboratory

Article pubs.acs.org/EF

Alkali Vapor Condensation on Heat Exchanging Surfaces: LaboratoryScale Experiments and a Mechanistic CFD Modeling Approach Ulrich Kleinhans,*,† Roman Rück,† Sebastian Schmid,† Thomas Haselsteiner,† and Hartmut Spliethoff†,‡ †

Institute for Energy Systems, Technische Universität München, 85748 Garching, Germany Bavarian Center for Applied Energy Research, 85748 Garching, Germany

‡

ABSTRACT: Inorganic vapors and their condensation can lead to severe operational problems in pulverized fuel systems such as integrated gasification and combined-cycle power plants or a conventional pulverized fuel combustion system. In order to understand these phenomena, a laboratory-scale cooling line for hot gases is used to measure and quantify the deposition of alkali vapors caused by heterogeneous condensation on a horizontal probe. The cooling line consists of two zones, an isothermal evaporation zone for the vaporization of alkali salts and a condensation zone. A condensation probe equipped with steel rings is placed inside the condensation zone with a gradually decreasing temperature. Different concentrations of inorganic vapors are studied under controlled conditions, and condensation rates on a probe, maintained at different temperatures, are quantified. A computational fluid dynamics model is developed and used to validate a heterogeneous condensation model based on Ficks’ law of diffusion. Numerical modeling can predict the location and amount of condensed inorganic vapors. The model shows a high sensitivity to the wall temperature which needs to be predicted accurately. A calculation procedure for saturation pressures and diffusion coefficients for gaseous alkali salts is presented and discussed. With this fundamental model it is possible to predict condensation rates of inorganic vapors. The model can also be applied for the calculation of condensation of vapors on existing fly ash particles. The model is essential for the prediction of hot gas cleaning systems for future integrated gasification combinedcycle plants or the formation of an initial layer on a superheater tube in pulverized fuel boilers firing alkali-rich biomass. The present study can serve as a development case for simplified empirical models in which the boundary layer is not resolved with a high number of nodes, e.g., for a model of a full-scale boiler.

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INTRODUCTION The combustion or gasification of solid fuels leads to the formation of ash particles and inorganic vapors. Both, inorganic vapors and ash particles are causing a number of problems associated with their deposition on surfaces. The main concern is excessive deposit formation on heat exchanging surfaces of pulverized fuel systems. Within combined cycles such as integrated gasification combined-cycle (IGCC) power plants, alkali vapors are known to be a limiting parameter in the gas turbine. The condensation of these vapors on turbine blades can cause sulfuror chlorine-induced high-temperature corrosion.1−3 Therefore, relatively strict limits for the contamination of the product gas with alkali vapors are found in literature. For instance, Korobov4 mentions a limit of 70 ppbv of Na- or K-compounds in the combustible gas. In general, ash deposition is strongly dependent on the presence of ash particles and inorganic vapors at heat exchanging surfaces. The main mechanisms leading to deposit formation on a surface are5−7 • inertial impaction including eddy impaction, • thermophoresis of small particles due to a temperature gradient, • diffusion of aerosols due to gradients in the flow • diffusion of inorganic vapors and their heterogeneous condensation, as well as • the heterogeneous chemical reaction of inorganic vapors with deposits. The first three listed mechanisms are caused by particle deposition, where the latter two are due to inorganic vapors. © XXXX American Chemical Society

Deposit formation is often initiated by a sticky initial layer. This layer is mainly caused by condensation of inorganic vapors directly on the heat exchanging surfacecalled heterogeneous condensationor by the particle formation, also referred to as nucleation, directly from the gas phase during coolingcalled homogeneous condensation. Therefore, condensation is expected to be crucial during early stages of deposit formation. Figure 1 illustrates typical deposit formation on a superheater tube in solid fuel fired power plants. The very early stages of

Figure 1. Deposit formation over time on a superheater tube.

deposit formation are dominated by the condensation of inorganic vapors. They either deposit directly on the surface or form aerosols during cooling which are then transported to the surface by diffusion effects or a temperature gradient, called thermophoresis. Large particles impact; however, they do not stick due to their high viscosity at low steel surface temperatures of around 450− 600 °C. Only if the surface temperature increases due to an Received: July 8, 2016 Revised: September 9, 2016

A

DOI: 10.1021/acs.energyfuels.6b01658 Energy Fuels XXXX, XXX, XXX−XXX

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obtained by the excimer laser-induced fluorescence (ELIF) technique. A semiempirical model, based on the work of Hansen,15 using mass transfer correlations for the estimation of condensation rates was applied. These equations were implemented in a computational fluid dynamics (CFD) code to calculate condensation rates on a probe for the straw firing case. Calculated condensation rates were in the range of 10−8 kg/(m2 s) and dominated during early stages.14 A recent publication by Lindberg et al.16 presented a vaporization and condensation model of alkali salts in laminar conditions using mass transport equations and CFD. The aim was to study the effect of temperature gradients in a synthetic deposit composed of KCl and K2SO4 on chemistry and morphology inside a tube furnace. Experimental results were explained and confirmed using CFD methods showing that outer, hot particles release alkali chloride vapors, which then condense on cooler particles near the steel/deposit interface.16 There are a number of further modeling studies, mostly CFD, using empirical mass transfer calculations. They include the work of Scharler et al.,17 Schulze et al.,18 Tomeczek and Wacławiak,19 and Leppänen et al.20 or the work of Weber et al.,21 who proposes simple correlations. However, there is no fundamental approach calculating the diffusion rates to the wall and resolving the concentration boundary layer in order to predict condensation rates on surfaces. Therefore, the present contribution applies a detailed modeling approach, predicting the concentration boundary layer and the saturation and condensation rates. The CFD model builds upon the work of Balan et al.22 and is validated using a laboratory-scale cooling line for syngases from an entrained flow gasifier. The test rig, developed by Haselsteiner23 for future hot product-gas cleaning systems in IGCC power plants, can be applied to study the condensation behavior of alkali vapors on a condensation probe with welldefined and -controlled conditions. The presence of ash particles is eliminated, enabling high-quality measurements on condensation rates. This work is organized as follows: In the beginning the theoretical background on mass transfer equations and their mathematical description is discussed. This section is followed by the description of the experimental setup and a method for the quantification of condensation rates. The mechanistic model is presented in the subsequent section in combination with a validation against measurements. In the end, results are discussed, an outlook on future work is given, and conclusions are drawn.

initial layer, larger particles become softer and sticky enough to remain on the deposit surface. Sarofim and Helble8 estimated the time needed for the formation of a 2 mm layer caused by condensation to around 46 days. This is in line with reports from power plants stating a long period for the initial layer built-up upon commissioning of a power plant. Inorganic vapors are predominantly formed by the vaporization of inorganic fuel components. The origin of the inorganic elements or compounds can be from mineral matter, organically bound inorganics, or salts dissolved in fuel moisture. Typical elements are alkali metals Na and K, earth alkali metals Ca and Mg, and nonmetals such as S, P, or Cl. The amount of vaporizable elements is strongly dependent on the fuel type. Low-rank fuels, such as biomass or lignites, have higher quantities of organically bound inorganics and, thus, produce increased concentrations of alkali vapors.9 High values of alkali vapors can be expected when using biomass such as straw or wood. Direct measurements on alkali vapor concentrations in full-scale systems are very complex. Sorvajärvi10 used collinear photofragmentation spectroscopy for the quantification of gaseous KCl in a 100 MWth bubbling fluidized bed boiler firing wastes together with wood bark. He found KCl concentrations in the range of 50−100 mg/m3 at a gas temperature of 800 °C. These values translate to around 59−118 ppmv. Values for coal-fired boilers are expected to be considerably lower, but reliable measurements were not found in literature. Particularly waste-based fuels and straw have a high chlorine content, which can react to gaseous alkali chlorides, known as a corrosive species when in contact with the steel surface. Furthermore, aluminosilicates can affect the amount of gaseous alkali chlorides by the adsorption and/or reaction of alkali metals at high temperatures.11 The amount of vaporization is also dependent on the peak temperature and the residence time. Mims et al.12 found an exponential temperature-dependence for the amount of inorganic elements released from a Montana lignite. Alkali and heavy metals showed the highest fractions vaporized. For instance, around 10 wt % Na was released from a high-rank coal to the gas phase at a temperature of 2000 K and a residence time of 2 s. Experimental investigations on condensation and its rates are rare in the literature. Often it is just mentioned that a ”white” initial layer, composed of salts and rich in alkali metals, is observed. One of the few fundamental investigations was conducted by Nielsen et al.13 They studied the deposition behavior of K-, Cl-, and S-based salts during wheat straw combustion in a 30 kWth laboratory-scale test rig at 900−1400 °C. The gaseous sulfur content was varied by separate SO2 addition. With this approach, the sulfation of KCl to K2SO4 could be investigated. A sophisticated deposition probe with two vertical metal plates and a protection shield above was used. This prevents inertial impaction and enables the investigation of condensation effects and the deposition of aerosols due to thermophoresis. The temperature of the uncooled plates was in the region of 300−400 °C and is measured using thermocouples. Scanning electron microscopy results indicate the deposition of 1−2 μm KCl particles and a sponge-like matrix of sub-micrometer K2SO4 particles, which may be formed by homogeneous condensation and agglomeration.13 They assumed that KCl condenses heterogeneously on existing K2SO4 particles and then melts, forming relatively large salt particles. Akbar et al.14 conducted an experimental and modeling study on the release and the condensation of KCl during straw firing in a 500 kWth pulverized fuel combustion test facility. The release model was validated using K-vapor concentration measurements

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THEORETICAL BACKGROUND AND MATHEMATICAL DESCRIPTION The condensation of alkali vapors takes place on ”cold” heat exchanging surfaces (e.g., steel temperatures of 400−600 °C), when the flue gas is saturated or supersaturated with the condensing species. A fluid is saturated when the vapor pressure of the condensing species “A” exceeds the saturation vapor pressure of species A at a given temperature. Vapors in the vicinity of a surface are transported by diffusion through the boundary layer to the surface. A thin, sticky film develops, which might change the pick-up of other solids,6 as discussed earlier. The amount and chemical composition of vapors strongly depends on the flue gas temperatures. In the radiant superheater region of a pulverized fuel boiler with gas temperatures around 1100 °C, these inorganic vapors are primarily compounds of alkali metals K and Na:6,24 alkali chlorides (KCl, NaCl); alkali sulfates (K2SO4, Na2SO4); alkali carbonates (K2CO3, Na2CO3); alkali hydroxides (KOH, NaOH); and depending on the fuel, vapors of heavy metals and their compounds (Zn, Pb, ZnCl2, etc.). Most of the B


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with Sh being the Sherwood number, which is a function of the Reynolds number (Re) and Schmidt number (Sc), analogous to heat transfer equations. The parameter DAB is again the diffusion coefficient and D a characteristic length, in this case the diameter of a heat exchanger tube. The Sherwood number for a tube in a crossflow can be expressed by the empirical correlation:

vapors listed above are formed by chemical reactions in the gas phase. According to Sarofim and Helble,8 inorganic constituents in coal will vaporize at flame temperatures, in amounts that are governed by the vapor pressures of the constituents in the char. This is enhanced, when for instance a reduction from SiO2 to SiO occurs, due to the higher vapor pressure of SiO. However, inorganic vapors based on Si, Al, or Fe species typically do not form in such a quantity that heterogeneous condensation on heat exchanging surfaces is relevant. Metal temperatures are too cold (400−600 °C), and condensation, if it occurs, will take place in the surrounding gas phase. Mass transfer of a species within a gas mixture to a surface can be caused by concentration, temperature, or pressure gradients. In laminar boundary layerstypical for clean superheater tubes with Reynolds numbers in the range of 500 < Retube ≤ 200021 diffusion is the dominant mechanism. It is described by Ficks’ first law of diffusion: jA = −DAB∇cA

Sh = c(Re m)(Sc n)(Sc/ScW )0.2

(6)

where the coefficient c, m, and n are dependent on the Reynolds number; see, e.g., Baehr and Stephan.27 The last term in eq 6 is a correction for differences in the Schmidt number of the free-stream Sc, and the wall ScW. The Schmidt number is defined as the ratio of momentum to mass transport as Sc = νg/DAB = μg/(ρgDAB). The saturation pressure psat given in eq 4 is dependent on the gas temperature and the species itself. Saturation pressures of relevant species are shown in Figure 2. The saturation or vapor pressure of

(1)

where jA is the diffusive flux of species A (mol/(m s)), DAB describes the molecular diffusion coefficient of species A in species B, and ∇cA is the concentration gradient in all spatial directions. By integrating eq 1 over the concentration boundary layer thickness δc,A and multiplying it with the gas density ρg one can obtain the following expression: 2

mȦ = ρg

DAB ⎛ 1 − wA, W ⎞ ⎟⎟ ln⎜⎜ δc ,A ⎝ 1 − wA, ∞ ⎠

(2)

where ṁ A is the mass flux to the wall, wA,W and wA,∞ are the mass fractions of species A at the wall (index W) and in the bulk flow (index ∞). The mass fraction can be expressed as wA = cAMA/ρg, with MA being the molar mass of gas A. The molecular diffusion coefficient DAB is temperature- and pressure-dependent and can be calculated using kinetic theory equations or empirical correlations such as the one from Wilke and Lee25 given by the following expression:

DAB =

(

M +M 0.0043T 2/3 MA M B A B

Figure 2. Saturation pressures for different alkali compounds as a function of temperature. Calculations made with data from Scandrett and Clift.26

1/2

)

p(VA̅ 1/3 + VB̅ 1/3)2

(3)

species A can be approximated using the following form of the Antoine equation:

Here the variables V̅ A and V̅ B stand for the molar volume of species A and B, p is the total pressure, and T the gas temperature in kelvin. Strictly, eq 3 is valid for two component, binary gases. In the case of real flue gases a multicomponent diffusion coefficient should be used instead. However, sometimes eq 3 is applied for combustion systems assuming that nitrogen is the most abundant species by approximating the diffusion coefficient with DA,N2. There are different equations available in literature to estimate the rate of condensation. Tomeczek and Wacławiak19 give the following equation, based on mass transfer laws: pA − psat ,A mȦ = ρg βA p (4)

⎛ 10000 ⎞ log psat ,A = A⎜ − B⎟ + C ⎝ T ⎠

where A, B, and C are fitting coefficients, and T is the temperature (°C). Often the supersaturation ratio SA of the gas phase with species A is used to estimate the type of condensation. It can be calculated using the vapor pressure by the following expression: pA SA = psat ,A (T ) (8) At high supersaturation ratios SA ≫ 1, homogeneous condensation is very likely to occur, whereas at SA = 1 the system is in equilibrium. Wieland28 showed that homogeneous condensation (nucleation) starts at a gas temperature of Tg = 1000 °C at supersaturation ratios SA around 10, depending on the conditions and equations applied. Thus, deposit formation due to heterogeneous condensation is expected to play a key role in the region of 1 < SA < 10. At higher values of SA > 10, both, particle nucleation and condensation on walls are assumed to occur.

where βA is the mass transfer coefficient, pA is the partial pressure, psat,A is the saturation pressure (or vapor pressure) of species A, and p is the total pressure. Sarofim and Helble8 state the saturation vapor pressure is small enough to be neglected, which would simplify eq 4. The mass transfer coefficient βA can be calculated by

βA = Sh

DAB D

(7)

(5) C


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the device of type AAS FL 5 of the company Analytik-Jena is used. The deposition rates are then calculated by dividing the deposited mass from the AAS analysis with the ring surface area and the experiment time of 4 h. Thus, the condensation can be expressed as a rate in mass per unit area and time or simply by mass per unit area. For more details on the procedure, see the work of Haselsteiner.23 Experimental results are given in the next section together with a validation of the CFD model. Geometry and flow rates of the cooling line experiments and needed for the numerical model are summarized in Table 2.

Table 1. Coefficients for the Calculation of Alkali Vapor Saturation Pressures and Estimation of Diffusion Coefficientsa

Table 2. Geometry, Boundary Conditions, and Material Properties for the CFD Model

Equation 3 is fitted to values of Scandrett and Clift.26 Molar volumes are calculated from data of Gilliland.29. a

variable

Table 1 gives coefficients A, B, and C for the calculation of saturation pressures for alkali chlorides and alkali sulfates. Data are fitted toward values of Scandrett and Clift.26 Furthermore, Table 1 provides estimates for molar volumes of alkali vapors and nitrogen for the estimation of diffusion coefficients.

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EXPERIMENTAL SETUP

A laboratory-scale test rig is used to study the cooling and condensation behavior of alkali vapors. The test rig is located at the Institute for Energy Systems at the Technische Universität München. Figure 3 shows a schematic of relevant components. It is composed of two zones, the evaporation zone with constant temperatures and the condensation zone in which the gas is cooled under controlled conditions. Nitrogen gas flow rates are set and regulated by mass-flow controllers, supplying the carrier gas for alkali vapors. Nitrogen is used to prevent the steel probe from oxidation, and it enables the use of eq 3 for the calculation of the diffusion coefficients in a binary system. The cooling line has five heating elements, used to set the desired temperature and profile for the evaporation and condensation zone. The wall temperature in the evaporation zone is set and controlled by the first two heating elements to a value of T1/2 = 1000 °C. The temperature in the crucibles is measured to a constant value of TEC = 750 °C. Two ceramic crucibles with a known amount of finely ground salt, 4 g of NaCl in the upper and 4 g of KCl in the lower crucible, are placed above each other in the flow. The condensation zone is used to cool the gas and study the condensation behavior of gaseous salts. The temperature in this zone is controlled using three heating elements, which are regulated and set to 850, 600, and 300 °C, respectively. A condensation probe is placed in the center and temperatures of the probe are recorded. The probe uses 14 type ”K” thermocouples, distributed equally along the probe length and attached to the inner wall. The condensation probe is equipped with small steel segments of 30 mm length and a diameter of 12 mm, which can be easily disassembled and analyzed. After each test run, the rings with salt depositions are dissolved for 2 h in deionized water. In the next step, the flame atomic absorption spectroscopy (AAS) is used to quantify the amount of salts originally deposited on each ring. For this,

symbol

unit

value

length evaporation zone length condensation zone diameter evaporation zone diameter condensation zone diameter condensation probe position evaporation cup

lEZ lCZ dEZ dCZ dCP xEC

mm mm mm mm mm mm

1300 2500 40 50 12 965

evaporated salt KCl evaporated salt NaCl concentration of KCl concentration of NaCl mass flow rate nitrogen

ṁ KCl ṁ NaCl xKCl xNaCl ṁ N2

kg/s kg/s ppmv ppmv kg/s

8.775 × 10−8 7.903 × 10−9 102.1 11.7 3.23 × 10−4

temperature inlet temperature evaporation crucible wall temperature evaporation zone wall temperature condensation zone wall temperature condensation zone wall temperature condensation zone emissivity wall condensation zone emissivity condensation probe

Tinlet TEC T1/2 T3 T4 T5 εCZ εCP

°C °C °C °C °C °C

20 750 1000 850 600 300 0.16 0.20

A crucial aspect is the alkali vapor concentration. It has to be ensured that the evaporation rate, and thus the concentration in the gas phase, is constant over the entire experiment period. Typically, a 4 h test run is conducted. The temperature of the evaporation zone is used to change the salt evaporation and thus adjust the concentration. The mass of evaporated salt is determined by weight difference. Here, it has to be guaranteed that salt is left in the crucible after the experiment. An ELIF measurement device and an optical port shown in Figure 3 are used to control the alkali concentration. Details on the ELIF system can be found in a previous work of Erbel et al.30 Figure 4 shows the qualitative signal over a time period of 6 h. In the beginning, the temperature in the evaporation crucible is fixed to 800 °C and the signal remained almost constant. A slight decrease is observed, which is due to structural changes in the surface area of salt crystals. After the experiments, the

Figure 3. Experimental setup to study the cooling and condensation behavior of inorganic vapors. Adapted with permission from ref 22. Copyright 2013 American Chemical Society. Probe thermocouples are not shown. D


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mass-flow rate from the crucible shown in Figure 3. This is justified by Figure 4 showing constant concentrations over time via optical measurements. The numerical grid, its geometry, and components in the model are shown in Figure 5. The grid is built in ANSYS ICEM v16 using block-structured hexahedral elements. Grids with different levels of detail are compared for grid sensitivity. Three grids with 0.86, 1.65, and 8.16 million cells are tested. The difference is mainly due to the number of cells in the radial and axial directions. The spacing at the probe is kept at a high resolution. Focus is on the boundary layer of the probe, in particular the number of nodes inside the boundary layer. The number of nodes is adjusted to ensure a y+ value below unity. The differences in the results between the grids with 1.65 and 8.16 million cells were marginal (maximum difference in the probe’s surface temperature is 2 K). However, computational time is more than five times higher. Therefore, the grid with 1.65 million nodes is applied for the numerical simulation. A more detailed graphical illustration of this grid can be seen in Figure 6. It shows the beginning of the deposition probe colored in blue.

Figure 4. Qualitative measurement of alkali concentration in the cooling line using ELIF spectroscopy.23 remaining salt inside the crucibles was molten. In addition, it is shown that a decrease in temperature leads to lower concentrations. The amount of gaseous alkali compounds is almost constant over time, enabling a simple constant mass release for the numerical model. The concentrations of KCl and NaCl in the experiment were set to 102.1 and 11.7 ppmv, respectively. These concentrations are typical for biomass combustion systems, and they are calculated assuming perfect mixing with the carrier nitrogen gas.

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NUMERICAL SIMULATION A heterogeneous condensation model is investigated and developed using the cooling line experiments. The condensation model is based on eqs 1, 3, and 7. It calculates the molar flux to the wall using eq 1 in the following form: cA − cA,sat jA ≈ −DAB (9) Δx where cA − cA,sat is the supersaturation of the wall-adjacent cell and Δx is the normal distance between the first node and the wall. The saturation concentration can be calculated using the saturation pressure, the molar mass, the gas density, and the mass fraction of the relevant species, which is accessible in the CFD code. When using eq 9, it is crucial that the boundary layer is resolved in detail and the first node in the radial direction is placed within the viscous sublayer. If this is fulfilled, the calculation becomes accurate as long as the surface temperature is predicted accurately. In the next step, the condensing species is removed from the calculation (sink at the surface) leading to the formation of a concentration boundary layer. The first version of the model, published in the work of Balan et al.,22 had no concentration boundary layer and had to introduce a correction factor. This correction can be neglected if the condensing species is removed. Further parameters required are the temperaturedependent saturation pressure psat,A and the diffusion coefficients DA,N2, where A stands for the condensing species. The saturation pressure for the alkali species is described by eq 7, which is fitted to values from Figure 2. The diffusion coefficients are estimated using the empirical eq 3. Since boundary layers inside the cooling line are laminar, turbulent effects on the condensation rate are neglected. The evaporation is modeled using a constant

Figure 6. Grid details at the beginning of the condensation probe.

Stationary CFD simulations are carried out using ANSYS Fluent v16.31 Convergence is monitored using temperature and velocity values, condensation rates, and residuals. Monitors have to become stable and residuals must be below 10−5 to fulfill our requirements. Spatial discretization is realized using the second order upwind scheme, and pressure−velocity coupling is achieved with the SIMPLE algorithm.31 Selected models and equations considered are summarized in Table 3. Species transport equations are activated and gas properties are calculated

Figure 5. Geometry and computational grid of the cooling line showing the main features: inlet, evaporation crucible, condensation probe, and the outlet. E


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Energy & Fuels Table 3. Selected Models and Main Boundary Conditions for the Numerical Model general turbulence species radiation boundary conditions evaporation

gravity, ideal gas with temperature-dependent properties k−ω SST model species transport with thermal diffusion discrete ordinates model mass-flow inlet, pressure outlet, and no-slip walls mass-flow inlet with constant evaporation rate from a plane

temperature- and composition-dependent. Turbulence is modeled using the k−ω SST model, which is known to provide better results in wall-dominated flows. The impact of thermal radiation and thermal diffusion is studied separately. If radiation is activated, the discrete ordinates (DO) model is used to describe the interaction between walls. Geometry and boundary conditions are summarized in Table 2. The inlet is described using a mass-flow inlet with specified inlet turbulence. The Reynolds number strongly depends on the location and temperature. A typical value for the condensation zone is Re ≈ 800, which is laminar. However, turbulent effects are expected in the inlet region and therefore included. A test of a laminar case revealed 20% higher condensation rates due to less mixing in the evaporation zone. The evaporation crucible is modeled as a box with a mass-flow inlet, where the amount of gaseous salt is calculated based on mass-loss measurements. The outlet is set to an outlet vent, where pressure and flow rates are calculated. The walls inside the cooling line are no-slip boundary conditions. The temperature in the evaporation zone is fixed and set to the regulated value from the experiment. The temperature at the condensation zone wall is set stepwise to measured values. The temperature of the condensation probe is calculated inside the CFD code considering radiation, heat convection, and conduction. The condensation model is implemented using so-called userdefined functions (UDF). The UDF type “DEFINE_PROFILE” is applied to calculate diffusion coefficients, saturation pressures depending on the surrounding gas conditions, and the mass flux to the wall in combination with a sink for the condensing species. The UDF type ”EXECUTE_AT_END” is used to loop over all cells and calculate the local saturation pressure and supersaturation ratios. A crucial aspect is the condensation on the outer walls. If it is neglected, condensation rates are overestimated by a factor of around 10. The main reason is that the outer wall surface area is large compared to the probe. Thermal diffusion was found to only slightly change the condensation rates.

Figure 7. Measured and simulated temperature profiles on the condensation probe within the cooling line.

of the surface temperature. It seems that heat transfer rates from the probe to the wall are too high in the region of 0.5−1.0 m, probably induced by too high emissivity values. However, changing the coefficient only shifts the profile leading to disagreement in other regions. Without thermal radiation the surface temperature of the condensation probe is overpredicted. The best results might be obtained using a zone- and temperature-dependent emissivity value. In addition, it is known that a condensing layer changes the surface structure and the emissivity. A sensitivity study is too elaborate and therefore not carried out. Instead one case with a fitted temperature profile is studied. The effect of different surface temperature profiles on the heterogeneous condensation rate is shown in Figure 8.

Figure 8. Measured and simulated heterogeneous condensation rates for NaCl and KCl for a 4 h experiment.

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The points are derived from measurements, where the condensation rate is expressed by deposited mass per ringsegment surface area for a 4 h test run. The error is estimated based on the measurement system. The temperature influence and the impact of thermal radiation are shown for NaCl. As expected, the best agreement is obtained using a fitted temperature profile. The case including the DO model overpredicts condensation rates and is shifted upstream. The shift is due to low temperatures of around 750 °C at x = 0.5 m, which is the onset temperature for heterogeneous condensation of NaCl at given concentrations. The higher peak is due to less mixing with surrounding nitrogen; inorganic vapor remains concentrated in the center of the cooling line. The opposite behavior can be observed for the case without radiation effects. The temperature profile and condensation is shifted further

RESULTS AND DISCUSSION Results in this section are obtained for the grid consisting of 1.65 million nodes. Figure 7 shows measured temperature values and three results from the numerical simulation. The differences in Figure 7 arise form the radiation treatment. One case fits the temperature profile to measured values. The second case includes thermal radiation interaction of walls and uses an emissivity value of εsteel = 0.2 for the condensation probe composed of polished steel. And a third case neglects radiation effects by deactivating the DO model. The resulting temperatures of the condensation probe along the axis of the test rig are shown by the dashed and continuous lines in Figure 7. Best results are, as expected, obtained by using a polynomial fit of the wall temperature. Including radiation effects leads to an underprediction F


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Figure 9. Comparison of predicted and observed condensation: (a) predicted condensed mass per unit area for a 4 h experiment and (b) photographs of the condensation probe showing a solid, white layer of alkali chloride deposition on the top (left) and dendritic structures for higher salt concentrations (right). Photographs taken from the work of Haselsteiner.23

downstream. In addition, the peak is lower compared with measurements. As already mentioned, a good agreement can be seen when the temperature profile of the condensation probe is fitted to measurements. The condensation rate agrees well in location and amount. The same can be seen for the KCl. Hence, the model works well, as long as the surface temperature is predicted accurately. Heterogeneous condensation shows a high sensitivity toward the surface temperature. Furthermore, it is found that condensation on the outer walls has to be included; otherwise the condensation rates are far too high. Thus, condensation on fly ash particles has to be considered when modeling condensation in a PF combustion system. A graphical illustration of computed deposition rates on the probe’s surface is shown in Figure 9. The maximum is at around x = 1 m, where the temperature is approximately 605 °C. The measured and calculated condensation rates, expressed in mass per unit time and area, are in the same region of 10−8 kg/(m2s) compared to the work of Akbar et al.14 A graphical comparison of simulation results and photographs from the experiment can be seen in Figure 9a,b. The left photograph shows a typical white layer forming on top of the probe as predicted by the simulation. Haselsteiner23 used higher concentrations and/or longer experiment times and observed a dendritic layer growth illustrated by the photograph on the right-hand side. This dendritic structure changes the emissivity values, and the flow conditions as well as condensation behavior. Hansen et al.32 observed a similar KCl finger formation and assumed that these fingers may form by condensation effects or thermophoresis of small particles. This study supports the assumption that the dendritic structure forms by heterogeneous condensation. The saturation pressure shown in Figure 2 can be used to calculate the supersaturation ratio SA for different salt concentrations as a function of temperature. Figure 10 shows the values of SKCl and SK2SO4 for concentrations of 1, 10, and 100 ppmv. The region leading to heterogeneous and homogeneous condensation is filled gray. It can be seen that the experiment with xKCl ≈ 102 ppmv yields supersaturation ratios of SKCl(T=800°C) ≈ 0.1 up to values of SKCl(T=600°C) ≈ 24. Thus, the main mode of condensation is heterogeneous condensation on existing surfacesin this case, the condensation probe. When evaluating the curves for K2SO4, one can see much higher supersaturation ratios up to SK2SO4(T=600°C) ≈ 107. In this area,

Figure 10. Supersaturation ratios of potassium species showing typical regions of condensation (colored in gray).

homogeneous condensation, aerosol collision, and agglomeration are dominant effects and have to be included in the CFD model. Future work should therefore be directed toward this issue. The application of the condensation model presented in this work to PF combustion requires the evaporation of inorganic elements. A possible idea could be the release of inorganic compounds based on chemical fractionation results. Water- and ammonium acetate-leachable components are assumed to vaporize during the combustion. The elements are vaporized proportionally to the fuel conversion. However, a validation of this assumption is needed in particular for biomass and lignite. Future work should be directed toward an aerosol formation model or possible alkali getter such as aluminosilicates or kaolin. In addition, the forming layer and its impact on condensation rates should be included in the model. The layer can have a dendritic structure with changed pick-up of vapors or particles and a changed emissivity. G


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SUMMARY AND CONCLUSIONS This work presents a mechanistic condensation model for inorganic vapors on heat exchanging surfaces. A well-defined and controlled laboratory-scale cooling line is used to vaporize salts and study their cooling and condensation behavior on a steel probe. The condensation rates are quantified and compared to numerical simulations. The model considers the formation of a concentration boundary layer and provides requirements for an accurate prediction. The model needs temperature-dependent saturation pressures and diffusion coefficients of alkali species in the surrounding gas. Methods for their calculation are presented. The model is able to accurately predict the location and amount of condensation. It is important to consider condensation on all surfaces in a combustion system, i.e., including ash particle surfaces. Furthermore, condensation rates are highly sensitive to the temperature, which needs to be predicted carefully.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +49 89 28916268. Fax: +49 89 28916271. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is related to the project HotVeGas II, which is supported by the BMWi and industrial partners (Air Liquide, EnBW, RWE, Siemens, and Vattenfall) under Contract No. 0327773E. We thank all partners of HotVeGas II, the TUM Graduate School, and Christoph Wieland for their support.

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Alkali Vapor Condensation on Heat Exchanging Surfaces: Laboratory

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