Design and Evaluation of an Improved Mixer for a Selective Catalytic Reduction System

Transcription

1 Design and Evaluation of an Improved Mixer for a Selective Catalytic Reduction System by David M. Stelzer A thesis submitted in conformity with the requirements for the Degree of Masters of Applied Science Graduate Department of Mechanical Engineering & Industrial Engineering University of Toronto Copyright by David M Stelzer (2014)

2 Design and Evaluation of an Improved Mixer for a Selective Catalytic Reduction System David M Stelzer Masters of Applied Science Graduate Department of Mechanical Engineering & Industrial Engineering University of Toronto 2014 Abstract More stringent environmental regulations have created a requirement for Selective Catalytic Reduction (SCR) after-treatment technology on stationary Diesel engines. In this work, Computational Fluid Dynamics (CFD) is used in conjunction with a separate 1-D catalyst reaction model to evaluate the overall performance of the combined High Efficiency Vortab (HEV) mixer and U-bend design. This model yielded mixing results with a Uniformity Index (UI) of 97% while generating less than 10 ppm of NH3 slip. The compact nature of the combined design creates an SCR that is easy to install and manufacture. Pressure drop, was also determined to be less than 10 of water (WC) over the range of operating conditions. The performance from this design will assist engineers in meeting current and next generation environmental regulations. ii

3 Acknowledgements The author wishes to express his sincere appreciation for all of the help and direction provided by Professor James S. Wallace and Professor Pierre E. Sullivan toward this thesis. The author is also grateful for the funding and support provided by the Ontario Center of Excellence for this project and for supporting business development in Ontario. Safety Power Inc, has also been an invaluable resource for developing this work. Special thanks to Henry Pong, Safety Power Engineer, who has provided an incredible amount of support and assistance to this research project. iii

4 Table of Contents 1 Introduction Selective Catalytic Reduction Organization of thesis SCR Simulations SCR Performance Evaluation NOx Reduction Chemistry Injection Approaches Catalyst Reaction Kinetics Mixing Numerical Set-Up U-bend SCR Design Geometry Flow Regime Meshing Injection Dimensional Catalytic Reaction Model Numerical Error Results and Discussion HEV Model HEV and U-bend Performance NOx and NH3 Results from UWS Simulation Conclusions and Recommendations Future Recommendations References: iv

5 List of Figures Figure 1-1: US EPA Off Road Emissions Regulations (Xinqun et al. 2010)... 3 Figure 2-1: HEV Based Static Mixer Figure 3-1: Overall SCR Geometry Figure 3-2: Upstream DPF Box Figure 3-3: Side View of the Complete Mesh Figure 3-4: Horizontal Mid-Plane Contour Plot of Y+ Values Figure 3-5: Urea Decomposition with UWS Model (Birkhold et al. 2007) Figure 3-6: Overall SCR Modeling (Faltsi & Mutyal 2012) Figure 3-7: Geometric Configuration of SCR Only Design Figure 3-8: Extrapolated Value of Axial Velocity across Catalyst Face Figure 3-9: Extrapolated Value of NH3 Concentration across Catalyst Face Figure 3-10: Extrapolated Value of Static Pressure across Catalyst Face Figure 3-11: GCIfine with Error Bars of Axial Velocity across Catalyst Face Figure 3-12: GCIfine with Error Bars of NH3 Concentration across Catalyst Face Figure 3-13: GCIfine with Error Bars of Static Pressure across Catalyst Face Figure 3-14: Residual Plot for Fine Mesh with Injection Figure 4-1: HEV Only Mixer Figure 4-3: HEV Mixer Full Load Performance Figure 4-4: Mid-Plane Total Pressure Contour Plot of HEV Only Mixer Figure 4-5: HEV Mixer, Water Spray Partial Loading Performance Figure 4-6: Pathlines for Full Load U-Bend Model Figure 4-7: Pathlines for Full Load Combined HEV and U-Bend Model Figure 4-8: U-bend Only Model, Molar Feed Ratio across Catalyst Figure 4-9: Combined HEV and U-bend Model, Molar Feed Ratio across Catalyst Figure 4-10: Mid-Plane Contour Plot of Axial Velocity Figure 4-11: Mid-Plane Contour of Total Pressure Figure 4-12: Mid-Plane Contour Plot of Temperature Figure 4-13: Mid-Plane Contour of Full Load HNCO Concentrations Figure 4-14: Mid-Plane Contour of Full Load NH3 Concentrations Figure 4-15: Normalized Axial Flow Velocity Across Catalyst Face Figure 4-16: Normalized HNCO Concentration Across Catalyst Face Figure 4-17: Normalized NH3 Concentration Across Catalyst Face v

6 Nomenclature Latin letters A Ag Ai pre-exponential factor (1/s) cross-sectional area of catalyst wall (μm) cell area (m2) Ap surface area of droplet (m 2 ) Aw cross sectional area of void channel (μm) C i, vapour concentration in bulk gas (kmol/m 3 ) Ci,s vapour concentration at droplet surface (kmol/m 3 ) cp Cp,g Cp,w d dh dm Dm e i Ea Ea d Ea o Ea r h hc hf g k kc L md ṁvap n N P pa pd specific heat (J/kg-K) specific heat of gas (J/kg-K) specific heat of gas at wall (J/kg-K) droplet diameter (μm) hydraulic diameter (m) mean droplet diameter (μm) mass diffusion coefficient (m 2 /s) unit vector activation energy (kj/mol) activation energy of desorption reaction (kj/mol) activation energy of oxidation reaction (kj/mol) activation energy of reduction reaction (kj/mol) non-dimensionalized mesh size convective heat transfer coefficient (W/m 2 -K) latent heat of vaporization (kj/kg) thermal conductivity of continuous phase (W/m-K) mass transfer coefficient(m/s) catalyst length (m) mass of droplet (kg) mass flow of vaporization (kg/s) spread parameter number of cell elements pressure (Pa) pre-exponential factor for absorption (1/s) pre-exponential factor for desorption (1/s) vi

7 po pre-exponential factor for oxidation (1/s) pstat saturated vapour pressure (Pa) R Universal gas constant (J/mol-K) ri j ratio of h values, (hj/hi) s storage sites per meter (m -1 ) Δt time step (s) t time (s) temperature of bulk gas (K) T Tg Tp Tw udarcy U V temperature of gas (K) temperature of particle (K) temperature of gas at wall (K) Darcy friction factor x component of velocity (m/s) y component of velocity (m/s) ΔVi element volume (m 3 ) v cell velocity vector (m/s) V Velocity field (m/s) W z component of velocity (m/s) Y+ non-dimensional distance from wall mass fraction of droplet greater than d Yd Y i, Yi,s Yu vapour mass fraction in bulk gas vapour mass fraction at surface Mass fraction of urea Greek letters Øi α εp θ θr del operator cell field property molar feed ratio particle emissivity fraction of ammonia storage radiation temperature, (I/4σ) 1/4, where I is the radiation intensity μ molecular viscosity (kg /s 2 ) ρ density in bulk gas (kg/m 3 ) ρg density in gas (kg/m 3 ) ρw density in gas at wall (kg/m 3 ) σ Stefan Boltzmann constant (5.67 x 10-8 W/m 2 -K 4 ) vii

8 Dimensionless numbers Pr Prandtl number, (cp μ/k ) Re Reynolds number, (ρg dh U/μ) Sc Schmidt number, (μ/ρg-dm) Sh Sherwood number, (kc L/Dm) viii

9 1 Introduction 1.1 Selective Catalytic Reduction NOx emissions are one of the key contributors to the formation of smog and greenhouse gases. This has been related to several adverse health conditions, global warming, acid rain and is the reason for new environment regulations. NOx emissions are comprised of two gases that can form in high temperature combustion process; these two gases are Nitric Oxide (NO) and Nitrogen Dioxide (NO2). In most current engine applications, NOx is created by the high temperature level achieved in the combustion chamber. The chemical reactions that form the gases at high temperatures (the thermal mechanism for NOx formation) are (Heywood 2011): (1-1) O + N 2 NO + N (1-2) N + O 2 NO + O (1-3) N + OH NO + H (1-4) NO + HO 2 NO 2 + OH (1-5) NO 2 + O NO + O 2 1

10 In the past, NOx emissions have been controlled within the combustion process; some examples for diesel engines include: High Pressure Direct Injection, with multiple injections during combustion cycle reducing peak pressure and temperature (Fang et al. 2008). Exhaust Gas Recirculation (EGR), recycled gas reduces peak combustion temperatures by increasing the heat capacity of intake gases. Engine intercoolers or aftercoolers, reduce the temperature of turbocharged intake air (Heywood 2011). Current regulations are too stringent to achieve with combustion process control alone. Some form of exhaust after-treatment is required. At temperatures between 1,200K and 1,300K NOx can be reduced into Nitrogen Gas by injecting ammonia into the exhaust stream, this is referred to as the Selective Non-Catalytic Reduction (SNCR) process (Zamansky et al. 1999). Reduction can be carried out at the lower temperatures typical of engine exhaust through the use of a catalyst in a process known as Selective Catalytic Reduction (SCR). Lower temperature SCR after-treatment technologies were first employed to reduce NOx in industrial power plants in the 1980s (Depcik & Assanis 2005). Since then, the technology has been extended to the automotive industry where it was first introduced in the Mercedes G-Class Bluetech vehicle (Chatterjee et al. 2008). In automotive and stationary engine technologies, ammonia is provided in the form of ureawater solution, a liquid that is easy to store and handle. SCR technology has several advantages in delivering a high degree of NOx reduction: Durability No additional burner or oxidation catalyst required 2

11 No additional fuel input Low Pressure Drop The use of SCRs in large stationary engines is relatively new and is largely driven by regulatory requirements. Constantly improving engines and after treatment technologies have resulted in more stringent regulations. Figure 1-1, illustrates the United States Environmental Protection Agency (US EPA) regulatory requirements for off road Diesel Engines over the past decade (Xinqun et al. 2010). Figure 1-1: US EPA Off Road Emissions Regulations (Xinqun et al. 2010) The latest US regulatory iteration is the Tier 4 Non-Road Diesel Engine Regulation requiring NOx levels of 0.67 g/kwh (US EPA 2013). This aggressive reduction requires more innovative SCR design, especially to achieve improved mixing. The Uniformity Index (UI) is a measure of the non-dimensionalized mixing effectiveness of an SCR, this allows researchers to compare designs of different proportions. Creating an SCR design that delivers a water spray UI greater than 97% 3

12 would surpass current designs (Pong 2010). Relating the UI to the Tier 4 regulation, involves combining the UI with specific engine characteristics and catalyst reaction kinetics. SCR technology has become a widely accepted approach for reducing NOx emissions associated with large stationary engines. Computational Fluid Dynamics (CFD) is increasingly used to optimize SCR design through modelling. Modelling an SCR requires describing injection, mixing and the reaction kinetics important to reducing NOx. The goal of this thesis is to create a novel mixing design that improves SCR performance for large stationary engines. 1.2 Organization of thesis Enhancing SCR mixing using CFD modeling is the goal of this thesis. This thesis will first focus on understanding the NOx reduction process and the current approaches for achieving this. A description of the geometric design and modelling approach will then be outlined. A specific design will then be evaluated using this model and analyzed to show an increase in performance. 4

13 2 SCR Simulations This chapter summarizes the phenomena underlying operation of an SCR system, including NOx reduction chemistry, urea injection approaches, catalyst reaction kinetics and mixing. Finally, two criteria for SCR performance valuation are presented. 2.1 NOx Reduction Chemistry The SCR catalyst is referred to as selective as it only absorbs NH3 resulting in reduced NOx emissions from the exhaust. Non-selective Oxidation catalysts are often used in conjunction with an SCR to remove excess hydrocarbons (King 2007). There are six reactions that can occur when NOx comes into contact with ammonia over a selective catalyst: (2-1) 4NH3 + 2NO + 2NO2 -> 4N2 + 6H2O (2-2) 2NH3 + NO + NO2 -> 2N2 + 3H2O (2-3) 8NH3 + 6NO2 -> 7N2 + 12H2O (2-4) 4NH3 + 3O2 -> 2N2 + 6H2O (2-5) 2NO + O2 <-> 2NO2 (2-6) 2NH3 + 2NO N2 + N2O + 3H2O 5

14 Equations (2-1) and (2-4) are the most prevalent in the SCR process; they are respectively referred to as the ammonia reduction and oxidation reactions. The remaining equations have slow rates of reaction and are neglected in modelling(faltsi & Mutyal 2012). 2.2 Injection Approaches Initially, industrial based SCRs used pure ammonia gas for injection. To reduce the risks associated with storing liquid ammonia, a low concentration urea solution is now used for commercial applications. A standard urea solution containing 32.5% by weight of ammonia solution in water is used for these applications. Urea water solutions are easy to transport as they are non-volatile (King 2007). For the urea to be useful in the SCR, it must be converted into ammonia gas and this process occurs in three steps. First, water is vaporized from the droplet and evaporates from water-urea droplets at 373 K at 1 atm. Continued water evaporation increases the urea concentration of the droplet until saturation occurs. A thin layer of urea salt is then created; further saturation forms a hollow sphere urea particle structure (Kulmala & Wagner, 1996). Equation (2-7) models the water evaporation from urea which occurs before the exhaust flow encounters the catalyst. The second step, takes place when the remaining solid urea melts at 425 K at 1 bar and decomposes to form isocyanic acid (HNCO) and ammonia gas. The production of isocyanic acid and ammonia (Equation ((2-8)) occurs quickly before the exhaust stream contacts the catalyst (Birkhold et al. 2006). The last step, is the decomposition of isocyanic acid into ammonia gas and carbon dioxide. The corresponding chemical formula is shown in Equation (2-9). This reaction typically takes place on the catalyst surface. Summating the entire process yields 2 moles of gaseous ammonia per mole of solid urea (Ström et al. 2009). 6

15 (2-7) (NH2)2CO (aq) (NH2)2CO(s or l) + 6.9H2O(g) (2-8) (NH2)2CO(s or l) NH3(g) + HNCO(g) (2-9) HNCO(g) + H2O(g) NH3(g) + CO2(g) Research has focused on modeling the urea water decomposition process using CFD (Birkhold et al. 2006; Wang et al. 2009; Kim et al. 2004). The simplest way to simulate this process is the Water Spray Model, which treats the urea as water droplets. This model over-predicts urea decomposition, at it assumes that all evaporated water will be immediately converted into ammonia. In practice, decomposition occurs quickly, but not until the urea particle reaches 425K at 1 atm. This model also does not distinguish between ammonia and isocyanic acid and assumes that the urea decomposition occurs in one step (Helden et al. 2004). Generally catalysts are designed with larger axial distances allowing the isocyanic acid to decompose. Since most isocyanic acid decomposes on the catalyst surface, ignoring the proceeding rate of reaction is a fairly good approximation. The advantage of using a Water Spray model is a large reduction in computational expense as no reaction kinetics are required. The Water Spray approach has been used to accurately evaluate SCR design using CFD (Helden et al. 2004) More inclusive Urea decomposition models account for both the urea and water constituents and are referred to as Urea Water Solutions (UWS). There are two prevalent models that have been used for describing this decomposition process. The first is the Wet-Solid Combustion Model which evaluates the UWS particle as solid urea and liquid water. This model is well established in 7

16 modeling reactions in combustion chambers and uses diffusion and convection to model the evaporation of the water from the UWS particle. At the same time, a single rate based equation is employed to describe the melting of urea into ammonia. The wet-solid approach to model urea decomposition is employed in this thesis and is described in detail in Section 3.5. Experimentation using a long tube with several longitudinal samplings ports was used to verify that this model yields accurate results (Kim et al. 2004). A Multi-Component UWS Model has also been utilized to describe urea decomposition. This model treats the UWS droplet as a homogenous liquid urea and water particle. Diffusion and convection or rapid mixing are used to describe the vaporization of the entire particle solution. Thermolysis of the solution is described using Raoult s Law and Dalton s Law for partial and total vapour pressures (Birkhold et al. 2006). Birkhold investigated the performance of a Rapid Mixing Model versus a Diffusion Limit Model for a multi component Urea Water Solutions (UWS). A single droplet analysis was used to validate both models. The rapid mixing model assumes infinitely high transport terms during the liquid phase. Equation (2-10) was used to evaluate the Rapid Mixing Model, which uses mass conservation: (2-10) dy u dt = m vap Y m u d where: Yu is the mass fraction of urea, m vap is the mass flow of vapourization and md is the mass of the droplet. The Diffusion Limit Model evaluates concentration by applying energy conservation to find the total and partial pressures of all prevalent species. Birkhold estimated that 8

17 both models yield similar results. The one exception, is that the Diffusion Limit model predicts a slightly higher urea concentration at the catalyst face; he concluded that this small increase in performance is not worth the extra computational power required. Birkhold estimates that the Diffusion Limit Model is 10 times more computationally expensive. Both of these models were compared to experimental results and were determined to align accurately (Birkhold et al. 2007). Droplet size can also affect the decomposition process. Experiments have determined that particles less than 150 µm in diameter behave as described by the 3 part decomposition process, presented earlier in this Section. Larger particles break down differently and have been shown to form a protective surface skin when heated. This protective skin inhibits the regular evaporation and eventually causing the droplet to explode when sufficient heat has been supplied. This protective skin requires more energy to decompose and results in a longer evaporation period (Vahid 2011). Air assisted injectors are commonly used for urea injection for Stationary Engine SCRs. These injectors combine compressed air with liquid urea to atomize the solution. An upstream urea pump works in conjunction to deliver the correct quantity of solution. Air assisted injectors produce small droplets (mean diameter of 30 µm) when compared to automotive airless injection systems. Small droplets are advantageous as they evaporate quickly allowing a reduction in the SCR mixing length (Helden et al. 2004). Similar SCR designs utilizing these injectors have also not exhibited any flashed urea within the injector (Safety Power Inc 2013). Droplets from air assisted injectors have been shown to behave in accordance with a Rosin Rammler statistical distribution. This statistical model has been widely used to predict the size of 9

18 urea droplets injected into a SCR as it accurately models droplet formation. The Rosin-Rammler model is (Jeong et al. 2008): Y d = exp [ ( d n ) ] d m (2-11) where: Yd is the mass fraction of the droplet greater the d, d is the droplet diameter, dm is the mean droplet diameter and n is the spread parameter. 2.3 Catalyst Reaction Kinetics Understanding the reaction kinetics within the catalyst is essential for determining the corresponding effectiveness and also vital for creating control strategies in commercial designs. Catalyst based reaction models were initially developed for 3 way automotive catalysts in the early 1970s. These models have been accurately applied to evaluate SCR catalyst performance (Depcik & Assanis 2005). Initial models neglected catalyst ammonia storage terms, limiting them to steady state situations. The requirement for better SCR control has focused on the effects of modulating the amount of injectant compared to NOx in the exhaust stream. Too much injectant leads to excellent NOx reduction, but creates NH3 slip and it has been found that the ideal injection rates are slightly less than stoichiometric (Helden et al. 2004). Transient SCR injection models are much more complex as the catalyst is able to store ammonia. To evaluate a suitable model, Hsieh set up an experimental reactor with NH3 sensors positioned before, after and at the midpoint of the catalyst. He compared the experimental results to a 1D Continuously Stirred Tank Reactor (CSTR) model and found that 10

19 the results agreed well (Hsieh & Wang 2011). External 1-dimenional models can be used to predict final NOx and NH3 slip concentrations (Depcik & Assanis 2005). This thesis utilizes this (described in Section 3.6). Recent literature has focused on solving models of these transient catalysts quickly so that they can be adopted into real time control systems. Linearized 1-D models with catalyst storage terms have shown particularly good computational performance for solving these control problems (Na 2010). 2.4 Mixing Straight mixing chambers with few mixing features were used in early commercial SCRs to satisfy the initial regulations of NOx conversion rates of approximately 50%. Since then, SCR designs have become much more innovative to meet increasing requirements (King 2007). Understanding mixing geometry and the addition of mixing features to improve NOx conversion is essential to produce a competitive SCR product. Flow in the mixing portion of the SCR is highly turbulent with Reynolds numbers ranging from 50,000 to 250,000. Mixing can be enhanced by angling the injector or modifying the flow around the injector. Ström et al. (2009) performed his analysis on a straight reactor with an injecting lance mounted at 45 o. This design was evaluated using CFD and variable duct lengths. The longest duct length yielded the best results with a 65% conversion rate. Helden et al. (2004), created a custom injector lance with 8 ports. The injection lance was mounted parallel to the flow so that the injector ports sprayed at acute angles towards the flow. This design was also combined with a 90 o geometric bend after the injection. The combination of these two mixing features yielded conversion rates over 90% (Helden et al. 2004). 11

20 Pong et al. (2012) used a 3D Fluent model to evaluate the performance of a U-bend design. The U-bend creates a 180 o bend between the injector location and the catalyst inlet. This design worked extremely well, as it created a recirculation zone on the far side of the U-bend. This recirculation zone resulted in a pressure gradient that bent the flow evenly onto the surface of the catalyst. Three variants of the design were created by modifying the cross sectional ratio of height to width. The best performing cross sectional design involved a slightly higher height to width ratio of At high engine loads this design yielded UI values of 95% with minimal amounts of NH3 slip. Pong also experimentally verified his results and did not observe any appreciable wall wetting (Pong et al. 2012). Geometric features can also be used to enhance the dispersion of the injectant in the reactor. Oh et al. (2012), used mixing plates to enhance the mixing in a Lean NOx trap. A Lean NOx trap is another type of NOx after-treatment system. The NOx trap contains a catalyst that has the ability to store NOx during lean combustion conditions and release the accumulated NOx during rich fuel conditions. NOx released in high concentrations will have a high NO2 conversion rate. This experiment utilized a fuel injector before the lean NOx trap to create rich conditions for a direct injection gasoline engine. The injector dynamics described above have similar flow characteristics to an SCR; the mixer behavior can therefore be utilized to improve SCR performance. This experiment used high speed photography to evaluate the performance of the mixing plates that were placed downstream of the injector. Two types of mixing plates were investigated, a gridplate mixer and a vortex mixer with a helical contour. The vortex mixer, actually reduced performance of the lean NOx trap as it created a destabilization of the flow and resulted in wall wetting. It was theorized that this destabilisation was likely the result of the helical design and the 12

21 placement of the injector. The grid-plate mixer enhanced the UI index by 15-20% over a range of engine loading conditions (Oh et al. 2012). To push the boundaries of SCR design, different processes with similar type mixing conditions were researched to see if other relevant mixing enhancements or technologies could be introduced. Commercial natural gas turbines used in power generation were of interest. NOx concentrations are also a concern in modern day power generation turbines. One way of reducing NOx is to employ a lean-premix strategy in the combustor. Much like an SCR, fuel is injected through a lance into the combustor portion of the turbine; uniform mixing in 1.5 diameters is required for this process. Eroglu et al. (2001) used Laser Doppler Anemometry and Laser Induced Florescence to optically evaluate the performance of up-stream delta wing vortex generators in gas turbines. This experiment used similar types of flows (Re = 50,000) and experimentally simulated the flow using a water channel experimentation apparatus. In this apparatus a constant flow of die injected water is passed over the plates and evaluated using the optical devices mentioned above. The images obtained were then examined using commercial imaging and statistical software packages. Pressure drop was also calculated by determining the vorticity and circulation of the flow using Equations (2-12) and (2-13). (2-12) ω = V = ( e x + e x y + e y z ) (Ue x + Ve y + We z ) z (2-13) ℶ = ω ds s 13

22 where: e x, e y and e z are Cartesian unit vectors and U, V and W are the corresponding velocity components. It was determined that delta wing generators with a cross section of 50% more length than width yielded the best results with little recirculation. This configuration of delta wing yielded uniform mixing at 3 diameters with a 5% pressure drop. In order to obtain uniform mixing in the required 1.5 diameters, 4 parallel delta wing generators were combined. Combining the delta wings increased the pressure drop to 30%. Another interesting observation is that the resulting flows did not have any flow impingement after the delta wing vortex generators, which is analogous to no wall wetting in an SCR design (Eroglu et al. 2001). Another interesting mixer design was found investigating static mixers used in industrial process based applications. In particular, the High Efficiency Vortab (HEV) mixer developed by Vortab Corporation is used in similar flow regimes to enhance mixing (Smith 1990). Figure 2-1, illustrates the geometry of a HEV mixer Figure 2-1: HEV Based Static Mixer 14

23 The HEV mixer contains 2 circular mixer areas that each have several angled vanes. The vanes contained within each circular mixer area are all the same size and at the same angle with respect to the axial length. The HEV mixer has been previously modeled in CFD and has shown excellent turbulent liquid to gas mixing. A HEV mixer was one of the mixing components utilized in this thesis as it has shown excellent mixing with relatively little pressure drop or swirl. (Bakker & Laroche 2000). 2.5 SCR Performance Evaluation The two most critical SCR design variables that evaluate overall performance are NOx reduction and NH3 slip. NH3 slip occurs when excess ammonia is emitted to atmosphere. Regulations generally dictate a maximum allowable ammonia slip of 10ppm for SCR design Ammonia is dangerous as it toxic. It is also extremely volatile and will combine to form harmful substances like ammonium sulfate and ammonium nitrate salts (King 2007). Designing an SCR that does not meet ammonia slip requirements would be unsafe; therefore minimizing NH3 slip is a fixed design criteria. NOx reduction depends on how effectively ammonia mixes with exhaust gas. Large NOx reduction or conversion is the goal of any SCR design. A high degree of uniformity at the entrance of the catalyst also results in longer catalyst life and reduces the amount of the catalyst required for overall NOx conversion. The UI is an effective way of evaluating the mixing process as is can be used to non-dimensionally compare different SCR designs (Oh et al. 2012). The UI is calculated at the inlet of the catalyst portion of the SCR using Equation (2-14). 15

24 (2-14) UI = 1 n i=1 [( i m )( A i )] 2 m n [ A i ] i=1 where: Øi is the property of interest, Øm is the mean value of that properties and Ai is the cell area. The following specific performance criteria have been selected for the enhanced mixing SCR design: Able to reduce NOx emission by creating pre-catalyst mixing water spray concentration with a UI greater than 97% for particular loading conditions. Achieve this NOx reduction while maintaining concentrations of less than 10 PPM of ammonia slip in the treated exhaust stream. Achieve these performance characteristics with a pressure drop less than 10 of water. Use a single urea injector to achieve the results. Minimize axial mixing lengths so that the design is compact and easy to apply in retrofit applications. 16

25 3 Numerical Model This chapter presents the U-bend SCR design, geometry and the mesh used in the simulation. The flow regime in the SCR is calculated for three engine loads. Input data for urea injection and the one-dimensional catalyst model are summarized and discussed. Finally, the results of a comprehensive error analysis are presented to demonstrate the adequacy of the mesh used in the simulations. 3.1 U-bend SCR Design The SCR design studied in this thesis uses a U-bend for improved flow uniformity across the catalyst face. The 180 o bend performs this by creating a recirculation zone in the middle of the bend, guiding the flow around it and generating mixing. A U-bend type design has been shown to deliver UI values over 95% (Pong et al. 2012) with low pressure loss, pressure loss is a major concern to large scale commercial Diesel engines. Market dominant inline SCRs require mixing lengths similar to that of a U-bend design, creating an overall mixer requiring twice the axial length. The compact design of the U-bend reduces production costs and enables SCRs to easily be retrofitted to existing space-constrained stationary Diesel engines (Pong et al. 2012). To achieve a higher degree of mixing, an HEV based static mixer was added to a U-bend design to enhance upstream mixing and overall performance. A multiple injector design was also considered, but limited availability of commercial urea injectors with flow rates less than 1 kg/hour (Spraying Systems Co, 2013) constrained the commercialization of this type of design. Multiple injector designs also create complicated control strategies as there is an increase in the number of control points. For these reasons the addition of an upstream HEV mixer was researched as a way to achieve a Tier 4 level of performance. 17

26 3.2 Geometry The geometry consists of three main parts: An upstream Diesel Particulate Filter (DPF). While not the focus of this thesis, it is important to understand the behaviour as the DPF outlet area establishes the SCR inlet boundary conditions A mixing duct, which is a combination of a tubular HEV mixer and a square duct U-bend. The Urea injector is also located near the front of this assembly. A catalyst section, which consists of a Vanadium Titania (V2O5-WO3/TiO2) based monolithic porous catalyst. The final geometry is shown in Figure 3.1. Figure 3-1: Overall SCR Geometry 18

27 The green rectangular section in Figure 3.1 represents an exhaust inlet for the SCR. There are two identical inlets, the second one is not shown in Figure 3.1, but is identical except that it is mirrored across the Z-axis. The outlet is represented by the green circle on top of the SCR. The complete upstream DFP is not shown in Figure 3.1. A DPF would be placed over the area combining the inlets with the hollow rectangular area, or DPF pressure box. The DPF works by distributing the pressurized flow through several small porous channels, removing particulate matter from exhaust gas. A pressure drop of 2 to 6 of water column has been observed with similar stationary DPFs (Mansour 2005); however, it seemed to result in uniform velocity distribution across the SCR system inlet boundaries. The porous channels contained within the DPF, are typically cm in length, resulting in an exit flow normal to the SCR system inlets. Figure 3-2 shows the geometry of the DPF box. Figure 3-2: Upstream DPF Box 19

28 Exhaust gas enters the SCR system inlet faces shown in Figure 3.1 and is then directed towards the tubular opening of the HEV mixer. At the front of the mixer is an aqueous urea injector. Downstream of the mixer there is an expansion zone followed by the U-bend that turns the flow 180 o before reaching the catalyst face. After the flow has passed through the catalyst zone, there is a collection area and vertical outlet stack. The exhaust outlet vents to atmosphere and the outlet was assumed to have a uniform normal flow distribution. Engine emission characteristics for a Cummins QSK50-54 were used and are shown in Table 3.1 below (Cummins 2013): Engine Load (%) Exhaust Flow Rate (kg/h) Exhaust Temperature (K) 10 3, , , Table 3-1: Engine Exhaust Flow Rates and Temperature The chemical composition of exhaust entering the SCR was modeled with: 74% N2, 10% O2, 9% CO2 and 7% H2O by volume. The SCR inlet composition was kept constant for all engine loading conditions shown in Table 3.1, as varying load performance was not published by Cummins. All flow in the SCR was assumed to be incompressible. Flow through the catalyst section was modeled as flow through a porous media. The small cross sectional size of the catalyst channels causes the flow to behave in the laminar regime with a Reynolds Number around Convection, acceleration and diffusion can all be neglected in the catalyst, allowing Darcy`s Law to be utilized. Darcy s Law (Equation (3-1) is used to determine the resistance coefficients (1/α) for the catalyst. 20

29 (3-1) P L = 1 α μ u darcy where: P is pressure, L is the axial catalyst length, α is the molar feed ratio, μ is the molecular viscosity and udarcy is the Darcy friction factor. 3.3 Flow Regime ANSYS Fluent V14.5 was used to model the SCR design, as it is widely used (Kuehlert et al. 2008)(Jiang et al. 2011)(Gröhn et al. 2012). A k-ϵ RANS model was selected as the flow is highly turbulent; the Reynolds Numbers corresponding to the range of engine loads simulated are shown in Table 3-2. The k-ϵ model is widely accepted and has been used to model SCRs and HEV mixers (Bakker & Laroche 2000). The k-ϵ model constants that were used are shown in Table

30 Engine Load (%) Engine Flow (kg/h) Re 10 3, x , x , x 10 5 Table 3-2: Engine Load and Reynolds Values k-ϵ Model Constants Value C 0.09 C C TKE Prandtl Number 1 TDR Prandtl Number 0.85 Wall Prandtl Number 0.85 Turbulent Schmidt Number 0.7 Table 3-3: k-ϵ Model Constants A steady-state RANS model was used, as steady-state behaviour was the focus of this thesis. Transient conditions could be considered in future work to improve start up conditions, model variable loading and evaluate control sequences. The engine loads and temperatures listed were selected as they cover a broad range of engine operation allowing a complete perspective on overall SCR performance. A standard Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) based pressure coupling was used as the flow is incompressible and steady-state. A second order upwind solver was also used to limit truncation error across the solution. A 3-dimensional species transport model was utilized to capture the physical interactions between the multiple exhaust gasses. The viscosity was calculated using Sutherland s Law with a reference viscosity (µref) of x 10 5 Pa s and a Sutherland Constant of K (Shahraeeni & Raisee 2010). 22

31 3.4 Meshing The final mesh corresponding to the geometry shown in Figure 3.1 contains 9,010,221 elements created using an unstructured cut-cell method, which is ideal for geometries with rectangular features. Automated meshing algorithms that employ the cut-cell method are also more accurate and require less computational power then standard tetrahedral based algorithms (Berger et al. 1998). The mesh size of approximately 9 million elements was due to memory limitations. Figure 3.2 below displays the final mesh used. Figure 3-3: Side View of the Complete Mesh The geometry in Figure 3.1 was sub-divided into several small bodies, so that high gradient areas could be accurately captured by the automated cut-cell algorithm. 23

32 The complete DPF box shown in Figure 3-2 was not included in the mesh due to memory limitations. This DPF design involves multiple directional changes in the flow, resulting in high gradient velocity changes and an extremely large mesh. As described in Section 3.2, several simplifications were made to accurately model the inlet conditions for the SCR. A standard wall function was used during the turbulence simulation to model the boundary layer interactions. Special attention was given to the y+ values to ensure that simulation was accurate. The overall mesh was designed so that the majority of wall elements had a y+ value between 10 and 100, under all operating conditions outlined in Table 3.1. Figure 3.3, below is a horizontal contour plot of the full load y+ values at the bottom of the SCR. The catalyst sections have a y+ of zero as porous medium assumption is used. 24

33 Figure 3-4: Horizontal Mid-Plane Contour Plot of y+ Values 25

34 3.5 Injection A 32.5% by weight aqueous urea solution was injected into the center of the HEV mixer. The injector was held by a lance that protrudes from the side of the SCR. Most studies reported in literature do not include the addition of the lance into the CFD analysis, as it has been shown to have a negligible effect on the overall flow field (Jeong et al. 2008). The lance is also not permanently integrated into the mixing design; this allows future refinement if evidence of mixing degradation is shown in the mock-up phase. Therefore, the lance was not modeled in the current study. To simplify the simulation the injector modeled has multiple point injections with properties listed in Table 3.2. Injector Properties Cone Injection Angle 21 o Number of injection holes 6 Attack Angle 0 o Velocity 40 m/s Compressed Air Pressure 50 PSI Mean Diameter 32 μm Table 3-4: Injector Properties (Safety Power Inc 2013) The information presented in Table 3-1 was modeled after a 6 hole injector from Spraying Systems with part number ¼ Ln SS (Spraying Systems Co 2013). This injector was selected as it is commercial available and appropriately sized for this application. A multiple hole injector was selected as they have shown much better performance over single hole injectors (Jeong et al. 2008). Several simulations were conducted on increasing the cone angle and varying the angle of attack; these simulations resulted in a negligible effect as the momentum of the exhaust flow exhibited a dominating effect over the injection. 26

35 A discrete, random walk turbulent dispersion model was utilized to describe the trajectory of droplets exiting the injector. A Rosin-Rammler distribution was used to describe the range of droplet diameters (Equation (2-11), the mean diameter, d was obtained from Table 3-4 and a spread factor of 3.27 was used (Birkhold et al. 2007). Aqueous urea was injected at 298K with a molar feed rate proportional to the NOx concentration in the exhaust stream. Storage of feed urea is typically done in a climate controlled space to prevent freezing and salting. Molar feed rates were chosen based on the results of the 1-D simulation outlined in Section 3.6 of this thesis. NH3 slip production was the limiting variable for urea injection quantities; the small amount of allowable NH3 slip resulted in molar feed rates close to stoichiometric. Fluent V14.5 contains a wet-solid Urea Water Solution (UWS) injection model. This model has been verified against experimental work performed by Kim, Birkhold and Wang (Faltsi & Mutyal 2012). The UWS model has been well documented in the Fluent Manual and is based on the work of Birkhold et al. 2006; Wang et al. 2009; Kim et al The wet-solid UWS model assumes a particle or droplet containing both solid urea and liquid water; an example is shown in (Birkhold et al. 2007) below: 27

36 Figure 3-5: Urea Decomposition with UWS Model (Birkhold et al. 2007) Fluent utilizes the following 4 mechanisms to mathematically describe the decomposition process (ANSYS 2012): 1) Droplet vaporization, begins once the droplet reaches the vaporization temperature. 2) Mass transfer of evaporated droplet material by convection and diffusion processes. 3) Droplet boiling, occurs when boiling temperature of droplet has been reached. 4) Devolatilization of solid urea into ammonia, begins when the droplet surpasses the vaporization temperature. Fluent utilizes the Clapeyron-Clausius relationship to determine the enthalpy of vaporization for the water portion of droplet vaporization (ANSYS 2012). Mass transfer from the evaporated droplet is one of the more mathematically complex stages, as it is highly dependent on both convective and diffusive interactions with the bulk gas flow. Equation (3-2) below defines the rate of mass change for the droplet or particle. 28

37 (3-2) dm d dt = k ca p ρ ln (1 + B m ) where md is the mas of the droplet, kc is the mass transfer coefficient, Ap surface area of the droplet, ρ is the density of the bulk gas and Bm is the Spalding mass, given by Equation (3-3): B m = Y H2O,s Y H2O, 1 Y H2O,s (3-3) where YH2O,s is the water vapour mass fraction on the particle surface and Y H2O, is the water vapour mass fraction of the bulk gas. The diffusion controlled portion of the model is governed by Equation (3-4), the corresponding droplet surface concentration is determined using Equation (3-5). N H2O = k c (C H2O,s C H2O, ) (3-4) (3-5) C H2O,s = p stat(t p) RT p where: CH2O,s is the water vapour concentration at the droplet surface, C H2O, is the water vapour concentration of the bulk gas, pstat is the saturated vapour pressure, Tp is the temperature of the particle and R is the Universal gas constant. Heat transfer between the bulk gas and the droplet relies on convective and latent heat transfer and is outlined using Equation (3-6). 29

38 (3-6) m d c p dt p dt = h ca p (T T p ) dm d dt h fg + A p ε p σ(θ R 4 T p 4 ) where cp is the specific heat, hc is the convective heat transfer coefficient, T is the temperature of the bulk gas, hf g is the latent heat of vaporization, θr is the radiation temperature, σ is the Boltzmann constant and εp is the particle emissivity. The Fluent model has the capability to model radiation, however it was ignored during this simulation to conserve computational resources. The heat transfer coefficient used in Equation (3-6) was calculated using Equation (3-7) below: Nu = h cd k = ( Re 1/2 Pr 1/3 ) (3-7) where: k is the thermal conductivity of the continuous phase and d is the droplet diameter. The Wet-Solid UWS model predicts urea devolatilization using a single kinetic reaction described by Equation (3-8). (3-8) k = A exp [ E a RT ] where Ar is the pre exponential factor equal to 800 and E is the activation energy equal to 2.94 x 10-7 kj/kmol (Kim et al. 2004) 30

39 3.6 One-Dimensional Catalytic Reaction Model ASNSY Fluent 14.5 does not currently have a built-in capability to model the reaction kinetics that occur in the catalyst portion of an SCR. As a result, a separate model was used to evaluate the performance of the SCR using the CFD catalyst inlet conditions. An overview of the modelling approach used is shown in Figure 3-6. Figure 3-6: Overall SCR Modeling (Faltsi & Mutyal 2012). The SCR catalyst is composed of several small channels, approximately 1 mm in cross sectional length. Each of these channels has a monolith structure supporting a Vanadium Titania catalyst that interacts with the NOx. Above the catalyst is a porous media or wash coat that guides the NH3 laced exhaust gas onto the catalyst surface. This particular type of catalyst is referred to as selective as it only absorbs NH3 resulting in only the oxidation of NOx (Depcik & Assanis 2005). These catalyst properties allow us to make the follow assumptions for modeling (Na 2010): 31

40 Individual channels are geometrically identical Negligible heat loss conducted through catalyst walls, as all channels are close in temperature Flow in channels is assumed to be 1-dimensional and laminar, as the channels are small and have Reynolds Numbers in the laminar regime Flow is fully developed NO2 concentration is negligible Gas phase chemical reactions are negligible. Ideal gases Heat generation from NO conversion is negligible, as less than 0.001% of the exhaust gas is comprised of ammonia and convective heat transfer is much more dominant. Operational temperatures are always greater than 250 o C. The SCR process breaks down at temperatures lower than this. The Eley-Rideal Mechanism governs the interaction of ammonia with the catalyst surface and has been experimentally verified to apply between 250 o C and 400 o C (Nova et al. 2006). There are 4 dominant interactions with that the catalyst and ammonia gas; these are described below: Absorption (Ra), Ammonia molecules are absorbed onto the catalyst surface. Desorption (Rd), Previously absorbed ammonia is released from the catalyst surface. Reduction (Rr), Absorbed ammonia interacts with NO gas. Oxidation (Ro), Absorbed ammonia reacts with Oxygen in exhaust gas. The chemical formulas that apply to the Eley-Rideal interactions are: 32

41 (3-9) (Ra) NH3(g) NH3(s) (3-10) (Rd) NH3(s) NH3(g) (3-11) (Rr) 4NH3(s) + 4NO(g) + O2(g) 6H2O(g) + 4N2(g) (3-12) (Ro) 4NH3(s) + 3O2(g) 2N2(g) + 6H2O(g) The rates of the reactions outlined in Equations (3-9) through (3-12) can be described by the Arrhenius Equation shown in Equation (3-13). k = A e Ea/(RT) (3-13) where k is the rate constant of the reaction, A is the pre-exponential factor, Ea is the Activation Energy, and R is the Universal Gas Constant. Catalyst manufacturers do not publish the rate constants and pre-exponential factors associated with their products, so experimental values were used from the literature (Chatterjee et al. 2005). Combining the Eley-Rideal Catalyst Mechanism with the Arrhenius Rate Equations allows the derivation of differential equations that describes the SCR process. In total, five equations are required to close the SCR system utilizing the assumptions outlined in the beginning of this 33

42 section. Equations (3-14) and (3-15) were derived by applying Conservation of Energy over the respective wall and gas portions of the catalyst: (3-14) T g x = h c P ρ g A g c p,g U (T g T w ) T w t = h c P ρ w A w c p,w (T w T g ) (3-15) where: Tg is the temperature of the gas, P is the pressure, ρg is the density of the gas, Ag is the cross sectional area of the catalyst wall, cp,g is the specific heat of the gas, U is the axial velocity, Tw is the temperature of the gas at the wall, ρw is the density of gas at the wall and cp,w is the specific heat of gas at the wall. Equations (3-16) and (3-17) were derived by applying the law of mass conservation to the respective NH3 and NO species, these equations are listed below: (3-16) C NH3 x = s A g U [ p a(1 θ)c NH3 + p d exp ( E a d(1 αθ) )θ] RT w (3-17) C NO x = s A g U [ p rexp ( E a r RT w )θc NO ] where, s the number of molecular storage sites per axial meter, C is the concentration of the corresponding species, pa is the pre-exponential factor for absorption, pd is the pre-exponential factor for desorption, Ea d is the activation energy of the desorption reaction, Ea r is the activation 34

43 energy of the reduction reaction, θ is the fraction of ammonia storage and α is the molar feed ratio of ammonia. along the direction of flow in a channel. Equation (3-18) is also derived by applying the law of mass conservation to the ammonia absorbed on the catalyst (θ) and is shown below: (3-18) θ t = [p a(1 θ)c NH3 p d exp ( E a d(1 αθ) ) θ p RT r exp ( E r ) θc w RT NO w p o exp ( E a,o RT w )θc O2 ] where: Ea o is the activation energy of the oxidation reaction and po is the pre-exponential factor for oxidation. Equations (3-14) through (3-18) were solved using a Matlab script developed by Safety Power Inc (Safety Power Inc 2013). This script uses Gear s Algorithm to solve Equations (3-15) and (3-18) or the time dependent part of the system. The built in Matlab ODE solver is then used to evaluate Equations (3-14), (3-16) and (3-17) that reside in the spatial domain. The catalyst was divided into 1,156 individual elements, as this was the number available from the Fine Grid Resolution mesh CFD solution. More elements would increase the accuracy of the analysis based on an asymptotic relationship outlined in Section 3.7 (Celik et al. 2008). 3.7 Numerical Error ASME has defined a method to quantify discretization error, ensuring confidence in CFD results (Celik et al. 2008). The ASME discretization error method uses both the Richardson Extrapolation (RE) and the Fine Grid Convergence Index (GCI) methods. The ASME method have been used in 35

44 several publications (Sekavc nik et al. 2010; Veluri et al. 2009; Zamora et al. 2011). The Grid Convergence Index (GCI) defines a non-dimensionalized quantity h that represents the size of a mesh; this value is calculated in Equation (3-19). N 1/3 h = [ 1 N ( V i) ] i=1 (3-19) where N is the number of cell elements and Vi is the element volume. ASME advises that three separate mesh sizes be created to evaluate a CFD problem. A large difference between the h values of respective meshes improves the accuracy of this analysis; memory constraints limited the overall size of these values to the ones listed in Table 3-5 (Celik et al. 2008). This Table, also lists other mesh properties used in this analysis. Mesh # Name Number of Elements 1 Fine 8,187,946 2 Medium 4,512,221 3 Coarse 1,966,216 h 7.84E E E-02 ri j = (hj/ hi) Table 3-5: Mesh Properties for ASME Error Calculations ASME outlines that the three non-structured mesh sizes should be created using an identical systematic approach, such that the meshes only differ by respective element size (Celik et al. 2008). Available computer memory was capable of solving a 9 Million element mesh; however it was not 36

45 possible to create a fine mesh this size without deviating from the systematic element size scaling approach. To satisfy both the ASME numerical error analysis and capture the inlet behaviour resulting from the upstream DPF, the modeling was done in two parts: 1) The ASME numerical error analysis was performed on the SCR-only portion that is the research focus of this analysis; the corresponding geometry is shown in Figure ) The resulting Medium SCR mesh from the ASME Error Analysis was combined with the simplified DPF mesh from upstream DPF to capture an accurate SCR system inlet profile. This mesh is utilized to evaluate the final results presented in this thesis. Figure 3-7: Geometric Configuration of SCR Only Design The smallest SCR-only mesh, outlined in Table 3-5 is approximately 2 million elements; adding the DPF section to the SCR creates a coarse mesh of approximately 6.5 million elements. 37

46 Performing the ASME numerical error analysis on this complete SCR and DPF mesh would require a fine mesh with of over 30 million elements (Celik et al. 2008). Given the memory constraints described above it was not computationally possible to solve a mesh of this size for this research project and as a result the SCR-only mesh was created. The numerical error process uses the Equations (3-20) through (3-22) to determine the apparent order, p of the discretization method: (3-20) p = 1 ln (r 21) ln ε 32 ε 21 + q(p) (3-21) q(p) = ln ( r p 21 s r p 32 s ) (3-22) s = 1 sgn( ε 32 ε 21 ) where ε 32 = 3 2 ; ε 21 = 2 1 and i is respective solution point of interest of the i th size mesh. The mesh sizes are labeled from 1 to 3 with 1 representing the fine mesh size and 3 representing the coarse mesh size. Equations (3-20) through (3-22) were solved iteratively until a converged solution was achieved. The final value of p was then used to determine the extrapolated exact solution of the CFD model (referred to as the extrapolated value), using Equation (3-23): (3-23) ext 21 = r 21 p 1 2 r 21 p 1 38

47 The goal of SCR design is to create a constant distribution of NH3 and exhaust gasses across the catalyst face. Most research utilizes CFD to determine these properties and then utilize a separate 1-D analysis to evaluate overall SCR performance and NOx reduction (Pong et al. 2012; Depcik & Assanis 2005). The quantities for axial velocity, static pressure and NH3 concentration were sampled across the horizontal mid plane of the catalyst face. The results of this process are shown in Figure 3-8 through Figure Please note that H2O concentration was used in this analysis to represent NH3. Figure 3-8: Extrapolated Value of Axial Velocity across Catalyst Face 39

48 Figure 3-9: Extrapolated Value of NH3 Concentration across Catalyst Face Figure 3-10: Extrapolated Value of Static Pressure across Catalyst Face Overall the extrapolation yields solutions consistent with the Fine Mesh Solution. The largest deviation was 9.5 % or 0.028% concentration by volume of NH3 occurring at a lateral position of approximately 1.0 m. The average difference in extrapolated values across the Axial Velocity, 40

49 NH3 Concentrations and Static Pressure plots was 0.49% deviation from the Fine Mesh Solution. Aside from the injection, all other values were determined to be well within acceptable errors The RE Method that is utilized in the above figures has some inherent errors. These errors are highlighted in Figure 3-8 and Figure 3-10, in the regions where the extrapolated values peak or deviate from the fine grid solutions. The 6 points in Figure 3-9 where there is an apparent deviation between the Extrapolation and Fine Mesh solutions can be explained by examining Equation (3-23). This equation breaks down when the value of r 21 p approaches one, resulting in a solution that approaches infinity. All 6 points where deviation is observed, produce a r 21 p close to one. One of the underlying assumptions in using the RE Method is for a solution in the asymptotic range. This error is likely the result of the solution deviating from the asymptotic range. Fortunately, these deviations occur infrequently and result in a small overall effect on the results (Celik et al. 2005). The ASME Error Uncertainty Method uses the following approach to solve the Fine Grid Convergence Index (GCIfine): (3-24) e a 21 = GCI fine 21 = 1.25e a 21 r 21 p 1 (3-25) 41

50 Below are identical representations of numerical error for the Axial Velocity, NH3 Concentration and Static Pressure across the face of the catalyst. The error is shown in the form of error bars on top of the fine grid solution. Figure 3-11: GCIfine with Error Bars of Axial Velocity across Catalyst Face Figure 3-12: GCIfine with Error Bars of NH3 Concentration across Catalyst Face 42

51 Figure 3-13: GCIfine with Error Bars of Static Pressure across Catalyst Face Similar to the RE results, Figure 3-11 through Figure 3-13 have a small numerical error. The average error across the Axial Velocity, H2O Concentration and Static Pressure is 0.63%. The maximum error is 13.16% and occurs at the exact same point as the highest deviation in the RE method. This error is small and is equal to an overall % difference in NH3 concentrations by volume. Since the GCI method is based on the Richardson Expansion, the same points where r 21 p approaches one are attributed to higher error. This breakdown of the model is one of the limitations of the RE method and allows these individual predicted values to be neglected (Ferziger & Peric 1996). Overall the numerical error identified from both the Richardson Expansion and GCIfine methods are less than 1%. This indicates that the mesh size and orientation have been appropriately selected as they yield acceptable numerical error. Low error in these critical design variables indicates low numerical error in the overall SCR and NOx reduction process. 43

52 The method also recommends that convergence be achieved with 4 th order residuals. All numerical solutions presented in this thesis have achieved this level of convergence, with the exception of computations involving an injection. Injecting species into the solution introduces an additional source of mass that affects the convergence of the continuity equation. To minimize this effect, the injection is performed on a small time scale, this yields residuals that approximate 4 th order. Below is a plot of the fine grid solution residuals. Figure 3-14: Residual Plot for Fine Mesh with Injection 44

53 4 Results and Discussion The computational modeling methodology outlined in Chapter 3 has been used to evaluate an HEV only mixer, a U-bend only mixer and a combined HEV and U-bend design. These simulations were chosen to isolate the performance of the individual mixing components so that the associated contribution to performance could be identified. Due to the large computational expense associated with fully modeling these components a simplified water spray simulation was selected. The water spray simulation is well suited to compare overall bulk mixing trends. A full single injection rate, urea water spray simulation was then used to evaluate the final design. A comparison between the results of the water spray and full single rate model has also been made. The 1-D model outlined in Section 3.6 was then employed to predict the final NOx reduction and NH3 slip of the overall design. 4.1 HEV Model The HEV mixer was modeled separately to identify the individual effect of this component on performance and to establish a suitable mixing length. A long mixing length is ideal as it will generate a high degree of mixing, but is not spatially practical for a U-bend type design. The desired mixer is one that generates a fair degree of mixing with the least spatial impact on the overall U-bend design. 45

54 Figure 4-1, shows the geometry used to evaluate the HEV only model. Flow enters at the far end located by the mixing vanes, an injection point then occurs, flow then passes through the two sets of mixing and a pressure outlet located 2.2 m downstream. The injection point was selected at an axial distance of 30 cm before the first set of HEV vanes so that the combined flow would have as ample time to interact with the mixing vanes. To evaluate mixing performance and mixing distance, the injected water spray UI was sampled at measurement slices in 0.1 m axial increments after the mixing vanes. Contours of the water spray injection are shown in Figure 4-1. Initially the modeled water spray concentrations are highly concentrated in the center of the mixing tube. The effectiveness of the HEV mixer is demonstrated by the relatively even water spray concentration near the end of the mixer. Figure 4-1: HEV Only Mixer 46

55 UI The full performance of the HEV only mixer is shown in, Figure 4-2. The performance is measured by taking the UI of the axial velocity and water spray concentrations at the measurement slices. The UI for velocity and spray concentrations peak at the end of the tube at 97.8% and 96.8% respectively. It was observed that the modeled UI performance increases at a high rate until a mixing length of 0.7 m. After 0.7 m, the overall increase in UI is gradual. As a result, a 0.7 m mixing length was selected for the overall combined HEV mixer and U-bend design. The corresponding UI of velocity and water spray at 0.7 m are 93.2% and 93.4% respectively. HEV Mixer, UI Vs. Mixing Length Distance (m) Velocity H2O Injection Figure 4-2: HEV Mixer Full Load Performance Pressure loss is a major concern with the SCR design. Figure 4-3, represents a mid-plane contour plot of the overall HEV mixer. A pressure loss of 805 Pa or 3.31 WC was predicted across the mixing vanes. This pressure loss was calculated by taking the difference between the mass averaged cross-sectional value at the inlet and after the second set of vanes. Little pressure loss 47

56 was predicted after the second set of vanes; the associated pressure loss was calculated to be 13 Pa or 0.05 WC. This indicates that the overall length downstream of the mixing tube has little effect on overall pressure loss. Figure 4-3: Mid-Plane Total Pressure Contour Plot of HEV Only Mixer Effective mixing performance under partial loading conditions was a goal of this work. Performances metrics were utilized to evaluate the UI of water spray concentrations at 45% and 10% loads. The corresponding UI was calculated to be 89.1% for both loading conditions; Figure 4-4, presents the results. This represents a 4.3% reduction in UI at these loading conditions. Partial loading UIs are critical to the overall design, this partial loading performance degradation is an important design limitation that will be address further in Section

57 UI HEV Mixer, UI Vs. Mixing Length Distance (m) 100% Load 45% Load 10% Load Figure 4-4: HEV Mixer, Water Spray Partial Loading Performance 4.2 HEV and U-bend Performance The geometry in Figure 3-1 was used to model the performance differences between a U-bend only mixer and a combined HEV and U-bend mixer. In the U-bend only design, the mixing vanes were treated as interior space instead of walls, resulting in an identical geometric model except without the vanes. Pathlines were utilized to display the overall similarities and differences between the two models. The U-bend only and combined models are shown in Figure 4-5 and Figure 4-6, respectively. Colours are utilized to represent the starting position of individual pathlines. Both of these models are evaluated at full load performance. Overall these two designs produce similar flow patterns. The major difference is emphasized in the magnified HEV mixer section shown in Figure 4-6, where pathlines mix as shown by the greater distribution of colours near the end of the HEV mixer. This increased mixing aligns with the findings of the HEV only mixer shown in Section

58 Figure 4-5: Pathlines for Full Load U-Bend Model Figure 4-6: Pathlines for Full Load Combined HEV and U-Bend Model As discussed in Section 3.7, the most important metric to determine the effectiveness of an SCR system is the molar concentration of the injectant at the face of the catalyst. The ideal profile would have a constant molar feed ratio (α) equal to one, indicating that the proportion of NOx is equal to 50

59 that of NH3. The molar feed ratios for both the U-bend only and combined HEV and U-bend designs are shown in Figure 4-7 and Figure 4-8 respectively with the vertical scale for α kept constant. Comparing the shape of the profiles it is evident that the addition of the HEV mixer improves performance by creating a much flatter profile that better approaches the ideal case. This is illustrated by examining the local minimum and maximum values of both graphs. In Figure 4-7 the maximum molar feed ratio is and the minimum is ; in Figure 4-6 the maximum is and the minimum is Both of the values in the combined HEV and U-bend design are closer to one indicating a more even distribution. Figure 4-7: U-bend Only Model, Molar Feed Ratio across Catalyst 51

60 Figure 4-8: Combined HEV and U-bend Model, Molar Feed Ratio across Catalyst The performance increase is further analyzed by examining the UI for velocity and water spray across the catalyst face. The modeled water spray UI for the U-bend only and combined design are 93.6% and 97.8% respectively. The addition of the HEV mixer increases the overall full load UI by 4.2%; a substantial increase in performance. The velocity UIs for the two models are 98.0% and 97.3% respectively, representing a 0.7% decrease in modeled performance. This slight decrease in the overall velocity profile is caused by the HEV mixing effect observed in Section 4.1. The overall impact in NOx reduction can be approximated by evaluating the UI of the molar feed ratio α. The UI of the molar feed ratio is evaluated utilizing the resulting data obtained by multiplying the normalized water concentration by the normalized axial velocity profile across the catalyst face. The increase in molar feed ratio UI resulting from the combined HEV and U-bend design is equated at 3.4%. The overall molar feed ratio UI for this design was calculated to be 95.7%. This means that this model predicts a theoretical full load NOx conversion level of 95.7%. This helps show that the increase in water spray UI outweighs the decrease in velocity UI. The values are theoretical as they do not include catalytic reactions; it also assumes that the injection 52

61 flow has a negligible physical influence on overall bulk exhaust flow. Section 4.3 calculates the overall NOx reduction with a model that includes these variables. A 2.3 WC increase in pressure drop was predicted using the combined HEV and U-bend design. The combined design model produces a total pressure drop of 7.7 WC, representing a 42% increase over the U-bend only design. This pressure drop level is well below the design target of 10 WC. An overall increase in pressure drop is expected as the increased mixing process dissipates energy. Partial loading conditions were evaluated with the water spray model. Table 4-1, displays the partial loading velocity and water spray UIs. All calculated UI values are above the thesis design goal of 97%. This is particularly interesting as a notable decrease in performance was observed at lower loads using the HEV only design with the same mixing tube length. This decreased in performance was does not exist in Table 4-1, indicating that the U-bend was able to compensate for this variation Load UI of H2O UI of Velocity 100% 97.8% 97.3% 45% 97.5% 97.0% 10% 97.6% 98.0% Table 4-1: Partial Loading Performance of Combined HEV U-bend Design 4.3 NOx and NH3 Results from UWS Simulation A single rate based urea water solution model was used to model the full load performance of the combined HEV and U-bend design. Figure 4-9, is a contour plot showing the mid-plane velocity magnitude. The velocity significantly increases in the HEV mixer area, as a result of the smaller 53

62 diameter and flow obstructions caused by the mixing vanes. A recirculation area is identified by a zero velocity magnitude. This recirculation zone is responsible for the mixing action of the U- bend, causing the flow to become relatively uniform across the catalyst surface. Figure 4-9: Mid-Plane Contour Plot of Axial Velocity A similar mid-plane contour for the total pressure is shown in Figure As discussed in the HEV only model, pressure decreases substantially across the HEV mixer. There is also a fairly large pressure loss at the beginning of the catalyst region; this makes sense as the porous nature of the catalyst is more resistant. The total pressure drop utilizing UWS model was calculated at 7.8 WC, which represents a 1.3% difference from the water spray model. 54

63 Figure 4-10: Mid-Plane Contour of Total Pressure Temperature loss was evaluated using the Fluent outer wall convective heat loss model (ANSYS 2012). The outside free stream temperature was set to 250 K so that the thermal loss was evaluated under extreme winter conditions. Less heat loss would occur in more realistic operating conditions as there would be less of a temperature difference between the outside air and the exhaust stream. The outside walls were modeled with the conductive properties of 2.5 mm thick stainless steel. Figure 4-11 represents a mid-plane contour of the temperature throughout the SCR design. An 18 K loss of temperature was predicted over the whole SCR. This temperature loss equates to 48.1 kw of heat loss to the surroundings. This heat loss has a small effect on the overall flow field, as it represent a 4.0% heat loss when compared to the overall 1,202 kw of thermal energy passing through the SCR. 55

64 Figure 4-11: Mid-Plane Contour Plot of Temperature Urea was injected into the SCR at an axial distance of 30 cm before the first set of HEV mixing vanes. The full load injection rate was kg/s of the urea solution. Figure 4-12 represents a mid-plane contour plot of the HNCO concentrations across the SCR. HNCO concentrations increase near the beginning of the injection point as the 32 μm urea droplets are quickly evaporated by the 700 K exhaust gas. The total HNCO concentration peaks at the beginning of the catalyst. The HNCO decomposition that would occur through the catalyst is not shown as catalyst reactions are modeled separately using the 1-D model. Figure 4-13 shows a mid-plane contour plot of the NH3 concentration across the SCR. The NH3 concentrations are an order of magnitude higher than the HNCO concentration; this aligns with Equations (2-7) through (2-9) as decomposition yields double the amount of NH3. The lack of built in catalytic reactions in the model results in continually climbing ammonia concentrations after the flow interacts with the porous catalyst. Similar to the HNCO concentrations, this model is only valid up until the face of the catalyst. 56

65 Concentrations after this should be neglected as the separate 1-D reaction model was used to evaluate the catalytic reactions. Figure 4-12: Mid-Plane Contour of Full Load HNCO Concentrations Figure 4-13: Mid-Plane Contour of Full Load NH3 Concentrations 57

66 The inputs to the 1-D catalyst reaction kinetics model are obtained from the urea water CFD simulation. These model inputs are temperature, axial velocity, NH3 concentration and HNCO concentration at each element on the catalyst face. Figure 4-14 shows the normalized axial velocity across this face. The normalized axial velocity is calculated relative to the average axial velocity over the entire catalyst face. The normalized velocity was bias towards the outer edge of the U-bend and is symmetrical across the y-axis. The overall UI for the axial velocity was determined to be 97.1%. Figure 4-14: Normalized Axial Flow Velocity Across Catalyst Face The urea water simulation yields concentrations for both NH3 and HNCO. Figure 4-15 displays the normalized HNCO concentration across the catalyst face. This concentration like the velocity profile has a bias towards the outer edge of the U-bend. The UI of the HNCO concentration was predicted to be 93.1%. Figure 4-16 represents a contour plot of the normalized NH3 concentration across the same face. As shown in Figure 4-13, NH3 concentrations are of an order of magnitude higher than HNCO concentrations, making them much more influential on the final NOx reduction result. The total UI of the NH3 across the catalyst face is 95.3%. The combined UI of HNCO and 58

67 NH3 across the catalyst is 95.0%. This represents a 2.8% reduction of the water spray analysis conducted in Section 4.2. Figure 4-15: Normalized HNCO Concentration Across Catalyst Face Figure 4-16: Normalized NH3 Concentration Across Catalyst Face The major difference between the water spray and UWS model is the urea decomposition time. The water spray model simulates a droplet with a 100% water content resulting in a longer H2O 59