Strength Analysis of High-Pressure SCR System Based on Thermo-Fluid-Solid Coupling

Abstract

In the operation of a high-pressure selective catalytic reduction (HP-SCR) system, variations in the internal exhaust gas flow speed result in non-uniform pressure and temperature distribution within the reactor. These fluctuations, which are neither constant nor linear, can affect the safe and reliable operation of the high-pressure selective catalytic reduction (HP-SCR) system, so the strength simulation analysis is necessary. Based on the high-pressure selective catalytic reduction system of a thermo-fluid-solid coupling marine diesel engine as the research object, this study constructs a calculation model using Space Claim and utilizes computational fluid dynamics (CFD) and computer-aided engineering (CAE) numerical simulation methods to analyze the strength of the high-pressure selective catalytic reduction (HP-SCR) reactor. The results show that the overall pressure drop of the selective catalytic reduction system is 5500 Pa, and the overall temperature rise of the reactor is 24 °C, which mainly occurs in the first layer catalyst, accounting for 62.5%. The pressure and temperature load of the reactor change along the axial direction, and the axial deformation gradient of the cylinder is more. The maximum deformation of the reactor under thermal load is 15 times that under mechanical load, and 97% of the deformation is axial.

1. Introduction

Under the background of economic globalization and the increasing prosperity of world trade, the commodities of various countries have been circulated on a large scale all over the world. Through a comparative analysis of various modes of transport, it is found that marine transport has the characteristics of high safety, a large carrying capacity and low operating cost, so marine diesel engines are increasingly widely used [1]. This has resulted in a rise in marine diesel exhaust (NO_x, PM, SO_x, etc.), which can cause serious environmental pollution. Global emissions from shipping have grown rapidly in recent years, surpassing those from land. According to statistics, the global shipping industry accounts for 15% of the global total nitrogen oxide emissions (an average of 20.9 million tons/year), of which 278,000 tons are discharged from ships docked at Chinese ports, accounting for 11.3% of the national total emissions [2]. Greenhouse gas emissions from shipping as a share of global anthropogenic emissions are on the rise, increasing from 2.76% in 2012 to 2.89% in 2018 [3]. China released the Annual Report on Environmental Management of China Mobile Sources (2022) in December 2022. According to the report, NO_x emissions from non-road mobile sources are close to that of motor vehicles, reaching 4.789 million tons. In addition, the emissions of unburned hydrocarbon, sulfur dioxide (SO₂) and PM were 429,000 tons, 168,000 tons and 234,000 tons, respectively. In order to reduce the harm of ship exhaust pollution and promote the green development of maritime trade. Different parts of the world have established corresponding emission laws and regulations [4].

People pay great attention to the above-mentioned pollutants and the treatment methods of pollutants, which makes the emission control technology of marine diesel engines face more severe challenges. The selective catalytic reduction (SCR) system is crucial for the post-combustion nitrogen oxide (NO_x) emission control of fixed and mobile sources [5]. During operation, the system is subjected to mechanical loads caused by gravity and internal pressure, thermal loads caused by high temperature and corrosive gas corrosion. In addition, uncertain loads, such as vibration loads from diesel engines, wind and waves, cannot be ignored [6]. Therefore, the design, manufacture and installation process of the marine diesel engine high-pressure SCR system must fully consider the strength conditions; if the system is damaged during the working process, the exhaust gas leakage will directly pollute the environment and threaten personal safety, resulting in economic losses. Therefore, it is of great significance to conduct strength simulation analysis for the above systems [7,8].

Compared with the automotive SCR system, the marine diesel engine SCR system has a slightly different arrangement; the system has two kinds of arrangement [9], installed in the front and the rear of the turbocharger, respectively, which are divided into the high-pressure SCR system (HP-SCR, located in the front of the turbocharger) and the low-pressure SCR system (LP-SCR, located at the rear of the turbocharger).

Under the action of a catalyst and oxygen, the SCR system can selectively reduce NO_x in the tail gas to N₂ and H₂O in a relatively low temperature range (280~420 °C), and the optimal reaction temperature is 330~350 °C [10]. The exhaust gas in the exhaust pipe drives the turbine/supercharger to do work and consumes part of the energy, so the exhaust gas temperature is reduced by 50~175 °C after passing through the device [11]. It can be observed that the high-pressure SCR system (exhaust gas temperature 300~350 °C) arranged in front of the supercharger has more advantages in temperature than the low-pressure SCR system, and its energy utilization rate is higher, which can meet the temperature requirements of the SCR system so as to achieve higher conversion efficiency when using conventional catalysts.

In terms of NO_x emission control of marine diesel engines, scholars have conducted extensive research on SCR technology [12,13,14]. The main research directions include the flow field structure design of the SCR system and structural optimization of the mixer and reactor of the SCR system [15,16]. Studies have shown that, in the temperature range of 280–420 °C, with the action of a catalyst, the evenly mixed ammonia can effectively remove NO_x from the tail gas [17].

Verhelst et al. [18] took a 4 MW, 700 rpm engine as the research object to explore the relationship between NO_x conversion efficiency and temperature. The results show that the optimal temperature range of the selective catalytic reduction reaction is 330~350 °C, and the stable operation of the SCR can be ensured by increasing the exhaust temperature. Therefore, the HP-SCR has more obvious advantages in temperature discharge. In addition, the HP-SCR has a high working pressure, which is equivalent to reducing the volume flow rate or line velocity of the exhaust gas and increasing the reaction time of the SCR [19], which can make the reaction more fully carried out. However, this system also increases the mechanical load of the reactor.

In terms of the marine diesel engine high-pressure SCR system, MAN Company (Augsburg, Germany) and Hitachi Shipbuilding took a 6S46MC-C8 diesel engine as the research object; in 2011, the marine high-pressure SCR system was verified on the ship. Shortly thereafter, MAN company first applied the high-pressure SCR system in a marine low-speed diesel engine. Gysel et al. [20] continued to study the impact of an SCR-DPF reprocessing system on ship exhaust emissions. In general, SCR technology has the potential to significantly reduce NO_x emissions in ports and nearby areas as follows: On a tugboat using two marine diesel engines, the SCR system reduced approximately 92% of NO_x [21].

It can be observed from the above that the marine diesel engine HP-SCR is subjected to a large heat engine load in the working project, and the reaction efficiency is related to temperature. Won et al. pointed out in their study that 1224 kJ of heat is released per mole of standard SCR reaction at a temperature of 300~400 °C [22]. As the reaction continues in the SCR system, there is a large temperature difference between the catalyst layers of the reactor, resulting in a large thermal stress effect on the shell [23,24,25].

China started relatively late in the research of marine SCR systems but has also achieved a series of achievements. Xia et al. [26] took a 10 WM marine low-speed, two-stroke diesel engine as the research object to explore the impact of engine performance, emission characteristics and exhaust pipe pulse effect under Tier II and Tier III modes [27]. The experiments showed that the temperature from the HP-SCR reactor to the turbine inlet dropped by 20~40 °C. The urea injection unit decreased by 36~47 °C, and the HP-SCR reactor increased by 10~18 °C, which was mainly caused by the urea solution injection and subsequent reaction. Zhu et al. [28] optimized the structure of the HP-SCR system by adding a flow guiding device in the mixer. The results showed that the flow deflector enhanced the uniformity of the upwind velocity of the SCR catalyst, with a deviation of 10.17% in the exhaust gas velocity. Therefore, it is necessary to consider the deflector at the elbow and reactor when simulating the flow field of the SCR system. In addition, when low-speed marine diesel engines burn low-quality, high-sulfur fuel, there must be a large amount of gas phase SO_x in the exhaust gas, which has a certain corrosive effect on the SCR reactor and pipeline structures [29].

The SCR reactor is generally taken as the research object above, and reasonable assumptions are adopted. However, the SCR system is subject to fluid pressure and temperature loads as a whole, so it is necessary to consider thermo-fluid-solid coupling analysis for the whole system in the analysis process [30,31,32]. Some related research has been conducted [33]. Yu et al. [34] took a curved flow pipeline as the research object to explore the influence of different coupling modes on pipeline stress and natural frequency. The results show that the difference in deformation in single and bidirectional fluid structure coupling is very small, only 0.035 mm, but the effect on stress is significant, and compared to not considering fluid structure coupling, the natural frequency of bidirectional coupling is significantly reduced. Cui et al. [35] studied the spiral heat transfer tubes of the South Korean SMART reactor steam generator and used the ANSYS Workbench platform to investigate the effect of temperature on stress and strain. The results indicate that the maximum stress mainly depends on the system temperature.

This study takes the high-pressure SCR system of marine diesel engines as the research object and uses CFD and CAE numerical simulation methods for simulation analysis. The main research content is as follows: Based on the operating parameters of the main engine and relevant criteria, the size design of the SCR system is carried out; a calculation model is built using SpaceClaim software (SpaceClaim is a 3D entity direct modeling software. Concord, MA, USA), providing theoretical calculation formulas and simulation numerical models; Exploring the influence of different simulation methods on the calculation results using the thermo-fluid-solid coupling method is explored; the reactor strength of the high-pressure SCR system is analyzed; the fundamental frequency of the engine is calculated through theoretical formulas and verified with the natural frequency of the SCR system to determine whether resonance occurs between the two.

2. Numerical Model for Strength Simulation of Marine High-Pressure SCR System

The high-pressure SCR system studied in this study is installed on a marine diesel engine with a rated power of 45,300 kW, and the exhaust temperature is 443 °C when the diesel engine is under 100% load condition. Therefore, each device of the high-pressure SCR system must withstand mechanical loads, such as gravity and internal pressure, but also suffer from high temperature loads and corrosive gases. At the same time, vibration loads from the engine and uncertain loads, such as wind and waves, cannot be ignored. Therefore, strength conditions must be fully considered in the design, manufacture and installation of the marine diesel engine high-pressure SCR system. In this study, the fourth strength theory (shape-changing specific energy theory) is used to analyze the stress of the SCR system based on the “analysis and design” method. In order to effectively evaluate the safety of the high-pressure SCR system, ANSYS Workbench simulation software (ANSYS software is a large general Finite element analysis (FEA) software developed by ANSYS company in the United States. It is the fastest growing computer Aided engineering (CAE) software in the world. It can interface with most computer Aided design (CAD, computer Aided design) software) is used to conduct numerical simulation research. The numerical model is divided into two parts: structure and fluid. The following assumptions were adopted in the simulation process: (1) The materials of the SCR system components meet the requirements of the drawings and technical documents; (2) The pipe is properly simplified, the expansion joint and other components are deleted, and the smooth transition details of the weld are ignored; (3) The radial and axial forces and moments caused by the deformation of the expansion joint are ignored; (4) An assumption is made that the SCR pipe housing is insulated from the outside world.

2.1. Numerical Model of High-Pressure SCR System Structure

2.1.1. Thermodynamic Analysis

The structural analysis mainly focuses on stress, deformation and fatigue life. Combined with the working conditions of the marine diesel engine high-pressure SCR system, the thermo-mechanical coupling analysis, statics and steady-state heat transfer modules are adopted. Statics is mainly used to analyze the structural response under fixed loads, without considering the inertia and damping of the system [36]. According to the definition of linear statics, it can be observed that the speed and acceleration of the system are 0, and the load is constant; so, its physical equation is as follows:

$$KX=F$$

(1)

where K is the system stiffness matrix; X is the displacement; and F is the external force.

Thermal analysis is mainly used to calculate the temperature distribution of a system or structural component and other physical parameters, such as heat gain or loss. All thermal analysis problems follow the law of conservation of energy in thermodynamics [37,38]. The general thermal balance matrix equation is shown in Equation (2):

$$[C(t)]\left\{\dot{T}\right\}+[K(t)]\left\{T\right\}=[Q(t)]$$

(2)

where $t$ is time; $\left\{T\right\}$ is the temperature matrix; $\left\{\dot{T}\right\}$ is the derivative of the temperature with respect to time; $[Q]$ is the heat flow vector; $[K]$ is the heat transfer matrix; and $[C]$ is the specific heat capacity matrix.

In thermal steady-state analysis, the temperature of any node does not change with time, so the dynamic phase with time change is not considered. At this time, the equilibrium equation of thermal steady-state analysis is shown in Equation (3):

$$[K]\left\{T\right\}=[Q]$$

(3)

2.1.2. Thermodynamic Coupling Analysis

When the structure is subjected to temperature changes, it will produce expansion or contraction deformation. At this time, if the structure can move freely, there will be no thermal stress inside the structure. On the contrary, if the structure is constrained at this time, thermal stress will be generated. In addition, when different materials are combined, thermal stress can also occur if the material deforms unevenly. The support of the high-pressure SCR system has a restraining effect, and the SCR system cannot deform freely, resulting in thermal stress and additional deformation of the structure [39]. Therefore, the overall deformation component of the elastomer is shown as follows:

$${\epsilon }_x={\displaystyle \frac{1}{E}}\left[{\sigma }_x-\mu \left({\sigma }_y+{\sigma }_z\right)\right]+\alpha T$$

(4)

$${\epsilon }_y={\displaystyle \frac{1}{E}}\left[{\sigma }_y-\mu \left({\sigma }_x+{\sigma }_z\right)\right]+\alpha T$$

(5)

$${\epsilon }_z={\displaystyle \frac{1}{E}}\left[{\sigma }_z-\mu \left({\sigma }_x+{\sigma }_y\right)\right]+\alpha T$$

(6)

$${\gamma }_{yz}={\displaystyle \frac{2(1+\mu )}{E}}{\tau }_{yz}$$

(7)

$${\gamma }_{xx}={\displaystyle \frac{2(1+\mu )}{E}}{\tau }_{zx}$$

(8)

$${\gamma }_{xy}={\displaystyle \frac{2(1+\mu )}{E}}{\tau }_{xy}$$

(9)

where $\sigma$ represents normal stress; $\tau$ stands for shear stress; $\epsilon$ represents positive strain; $\gamma$ represents shear strain; E stands for elastic modulus; $\mu$ stands for Poisson’s ratio; $\alpha$ represents the coefficient of thermal expansion; and $T$ stands for temperature.

2.1.3. Fatigue Analysis

Due to the reciprocating action of the alternating load, fatigue cracks appear in the parts and expand in the local position, and the phenomenon of the final fracture is called fatigue failure. Fatigue is usually divided into two categories, namely high-cycle fatigue and low-cycle fatigue, wherein stress fatigue is generally used for high-cycle fatigue and strain fatigue is generally used for low-cycle fatigue. In this study, the software mechanical working condition simulation adopts the stress fatigue theory, and the stress is defined as follows in the analysis process:

$$R={\displaystyle \frac{{\sigma }_{\min }}{{\sigma }_{\max }}}$$

(10)

$${\sigma }_a={\displaystyle \frac{{\sigma }_{\max }-{\sigma }_{\min }}{2}}$$

(11)

$$△\sigma ={\displaystyle \frac{{\sigma }_{\max }-{\sigma }_{\min }}{2}}$$

(12)

$${\sigma }_m={\displaystyle \frac{{\sigma }_{\max }+{\sigma }_{\min }}{2}}$$

(13)

where $R$ is the stress ratio; ${\sigma }_a$ is the stress amplitude; $△\sigma$ is the stress range; and ${\sigma }_m$ is the average stress.

2.2. Numerical Model of Fluid in High-Pressure SCR System

The physical and chemical processes of the SCR reactor are very complicated, so the selection of numerical models should be fully considered when doing fluid analysis. Fluid flow follows three conservation laws [40]: mass conservation equation (Equations (14)–(16)), momentum conservation equation (Equation (17)) and energy conservation equation (Equation (18)).

$${\displaystyle \frac{\partial \rho }{\partial t}}+{\displaystyle \frac{\partial \left(\rho u\right)}{\partial x}}+{\displaystyle \frac{\partial \left(\rho v\right)}{\partial y}}+{\displaystyle \frac{\partial \left(\rho w\right)}{\partial z}}=S_m$$

(14)

$$div(\overrightarrow{a})=\partial a_x/\partial x+\partial a_y/\partial y+\partial a_z/\partial z$$

(15)

$${\displaystyle \frac{\partial \rho }{\partial t}}+div(\rho \overrightarrow{u})=S_m$$

(16)

where $\rho$ is the density of working medium; $t$ is time; $S_m$ is the source term, mass added to the continuous phase; $\overrightarrow{u}$ is the velocity vector; and u, v and w are the components of the velocity vector in the x, y and z directions, respectively.

$${\displaystyle \frac{\partial }{\partial t}}\left(\partial u_i\right)+{\displaystyle \frac{\partial }{\partial x_j}}\left(\rho u_i{u}_j\right)=-{\displaystyle \frac{\partial p}{\partial x_i}}+{\displaystyle \frac{\partial {\tau }_{ij}}{\partial x_j}}+\rho g_i+F_i$$

(17)

where $P$ is the static pressure; ${\tau }_{ij}$ is the stress tensor; $\mu$ is the dynamic viscosity; $g_i$ is the acceleration of gravity in the direction; and $F_i$ is the external volume force.

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho E\right)+{\displaystyle \frac{\partial }{\partial x_i}}\left[u_i\left(\rho E+\rho \right)\right]={\displaystyle \frac{\partial }{\partial x_i}}\left(k_{eff}{\displaystyle \frac{\partial T}{\partial x_i}}-{\displaystyle \sum _j{h}_j{j}_j+u_j{\left({\tau }_{ij}\right)}_{eff}}\right)+S_h$$

(18)

where $K_{eff}$ is the effective thermal conductivity; $J_j$ is the diffusion flux of component j; $h_j$ is the enthalpy of component j; $S_h$ is the chemical reaction heat and other volumetric heat source terms; and $E$ is the internal energy of the system.

At the same time, the exhaust gas is turbulent flow in the flue, and an additional turbulent transport equation needs to be considered. The turbulence models provided by Fluent include the Spalart–Allmaras model, standard k-ε model, RNG k-ε model, k-ω model, Reynolds stress model and large eddy simulation model. Among them, the realizable k-ε model is more consistent with the real situation in the calculation of boundary layer and separation flow with directional pressure gradient, so this model is chosen. Liquid ammonia, urea and ammonia water are commonly used as reducing agents in SCR technology. In this study, a urea aqueous solution is selected, and the DPM model is used to simulate its spraying, atomization and evaporation processes. This model can calculate the trajectories of these particles as well as the mass, momentum, energy exchange and component transfer with the exhaust. The injection velocity of the urea solution is defined based on a reference coordinate system, and particle tracking is also based on this coordinate system. The specific distribution of these particles is examined using the phase coupling method.

In addition, the fluid region of the catalyst part of the reactor needs to be separated separately, defined as the porous media region and defined as laminar flow. Because the pressure drop of the fluid passing through this area is obvious, the calculation process needs to determine the viscosity coefficient and the inertia coefficient. The additional momentum source term in the momentum equation of porous media consists of two parts, namely, the viscous loss term and the internal loss term.

$$S_{\mathrm{i}}=-\left({\displaystyle \sum _{j=1}^3{D}_{ij}}\mu v_j+{\displaystyle \sum _{j=1}^3{C}_{ij}\frac{1}{2}\rho \left|v_j\right|v_j}\right)$$

(19)

where $S_{\mathrm{i}}$ is the source term in the momentum equation and $D_{ij},C_{ij}$ is the mathematical matrix in the momentum equation.

For uniform porous media, the above formula can be simplified as follows:

$$S_{\mathrm{i}}=-\left({\displaystyle \frac{\mu }{\alpha }}{v}_j+C_2{\displaystyle \frac{1}{2}}\rho \left|v_j\right|v_j\right)$$

(20)

where $\alpha$ is the permeability and $C_2$ is the inertial drag coefficient, laminar flow is 0.

If the convection and diffusion terms are ignored, the above equation can be simplified to Dacy’s law:

$$\nabla p=-{\displaystyle \frac{\mu }{\alpha }}v$$

(21)

The pressure drop of the exhaust gas through the catalyst region along the three coordinate directions is as follows:

$$\Delta p_x={\displaystyle \sum _{j=1}^3\frac{\mu }{{\alpha }_{xj}}}{v}_j\Delta n_x,\Delta p_y={\displaystyle \sum _{j=1}^3\frac{\mu }{{\alpha }_{yj}}}{v}_j\Delta n_y,\Delta p_z={\displaystyle \sum _{j=1}^3\frac{\mu }{{\alpha }_{zj}}}{v}_j\Delta n_z$$

(22)

where 1/α_ij is an element of matrix D in the momentum equation of porous media; v_j is the partial velocity of the exhaust in three directions; and Δn_x, Δn_y and Δn_z are the thicknesses of the catalyst layer in three directions.

2.3. Mesh Division and Boundary Conditions

2.3.1. Grid Division

The grid is divided into structured and unstructured grids. Mesh software (Italian 3D geometric model processing tool) is adopted in the grid division, and the division unit is mesh 200, including the structural mesh division and fluid mesh division. The method of Sweep, Tetrahedrons and Multizone is used to divide the grid, and the local grid control algorithm is used to locally encrypt the reactor guide plate and other locations. The final fluid region is divided into five layers of expansion layers, with the minimum size defined as 5 mm in the curvature control function and an overall mesh size of 9,019,089; the solid region grid division method is the same. Taking the SCR reactor as an example, a local size control method is used to ensure that the number of grids in the wall thickness direction is two layers. The curvature control function is used to set the minimum size to 2 mm in order to refine the grid at the bolt holes and transition surfaces. The final number of grids in this part is 694,682. The specific division form is shown in Figure 1 and Figure 2.

2.3.2. Setting of Boundary Conditions

After the completion of grid division, it is necessary to further set the boundary conditions of the fluid region. In the simulation, the exhaust parameters under 100% working conditions of the marine diesel engine high-pressure SCR system are taken as the boundary conditions to study the temperature and pressure changes in the above region. The specific components of exhaust gas are shown in

Table 1. Exhaust component volume fraction at 100% load.

Component	ppm
NO	1924
NO2	66
H2O	50,000
O2	140,000
CO2	50,000
SO2	600
SO3	60

.

The fluid area adopts a mass flow inlet condition, the hydraulic diameter of the pipe diameter is 1300 mm, the outlet section adopts a pressure outlet condition, and the whole wall is set as adiabatic and non-slip. See

Table 2. Boundary conditions under 100% working condition.

Parameter	Numerical Value
Inlet mass flow (kg/s)	83.79
Inlet temperature (K)	716.15
Turbulence intensity (%)	5
Outlet static pressure (bar)	3.19
Turbulence intensity (%)	3
Wall boundary	Insulation, no slip

.

In the solid region, the heat engine load and constraint mode are mainly considered. The default gravity acceleration of the software is adopted in the whole model, and the direction is straight down along the Y-axis. Meanwhile, the catalyst mass is applied to the internal support of the reactor in the form of equal effect. The internal pressure and temperature of the SCR system need to be defined separately. In the thermo-fluid-solid coupling, the above two parameter values are directly transmitted by Fluent. There are two main constraint modes: fixed support and sliding support. Fixed support restricts all degrees of freedom, and sliding support can move freely along the axis. The specific layout is shown in Figure 3.

The size of the SCR system is relatively large, and the overall calculation requires a high number of grids and computer computing power. Prior to simulation calculations, preliminary calculations were conducted on the shape variables of each pipeline using WinGD’s guidance manual. The results showed that the elastic force generated by the expansion joint was significantly different from the gravity and exhaust pressure forces of the flue itself. Therefore, the elastic force was ignored during the simulation process, and each component was calculated separately.

2.4. Grid Independence and Model Validation

2.4.1. Grid Independence Analysis

In order to ensure the accuracy of the simulation model and balance the calculation time, it is necessary to verify the grid independence of the model before calculation. The convergence of Von-mises stress was verified by using different mesh numbers in the mechanical load condition of the reactor. The specific mesh number and chamfered wall stress are shown in

Table 3. Stress sizes under different mesh numbers.

Equivalent Stress (pa)	Change (%)	Nodes	Elements
1.19 × 108	\	406,854	161,695
1.17 × 108	1.64	497,451	251,036
1.16 × 108	0.92	1,397,529	635,697
1.15 × 108	0.85	1,701,996	876,556
1.15 × 108	−0.02	2,728,734	1,575,802
1.15 × 108	−0.03	9,233,643	6,225,432

and Figure 4.

As can be observed in Figure 4 the difference between the calculated results of the two adjacent cases is less than 5%, and the results are convergent, with the maximum stress approximately 1.15 × 10⁸ Pa. On this basis, we continue to check the mesh quality and find that the mesh cell quality is approximately 0.8, which meets the calculation requirements. In addition, the above verification should be further repeated if other working conditions are calculated.

2.4.2. Model Verification

In order to demonstrate the accuracy of the model in this paper, the result values of the manual and simulation calculations are compared, as shown in Figure 5. It can be observed in the figure that the two trends are the same, and the relative error is less than 10%, which can verify the accuracy of the simulation results.

3. Strength Analysis of High-Pressure SCR System Based on Thermo-Fluid-Solid Coupling

In the actual work project, the exhaust gas flow speed inside the SCR system is not uniform, and the changes in pressure and temperature acting on the flue and reactor are not constant or linear. Therefore, this section first takes the whole system as the research object, uses Fluent to perform flow field analysis and explores the temperature changes caused by urea injection and the SCR reaction and the pressure changes caused by pipe bending and the catalyst layer. Then, the above results are taken as the boundary conditions and coupled with thermodynamic analysis. The effects of different pressure and temperature distributions on the stress and deformation of the SCR reactor were considered.

3.1. Initial Flow Field Distribution and Optimization of High-Pressure SCR System

The degree of the selective catalytic reduction reaction of the SCR system is affected by the flow rate of tail gas and mixing uniformity, so the initial scheme is to set a diversion device in the intake bend section. Make Section 1 (XZ section, Y = 0) of the SCR system through the central axis (As shown in Figure 6) and analyze the velocity distribution cloud map of this section (As shown in Figure 7). It can be observed that, compared to the part where the guide plate is added, the velocity uniformity of the exhaust gas at the outlet bend is poor, and the velocity near the bend area and outside the outlet pipe wall is higher. The exhaust gas is affected by the contraction section of the reactor, causing a decrease in pressure and an increase in flow rate, resulting in limited gas directional ability. Afterwards, under the influence of inertial force, it flows forward through the bent pipe section until it collides with the outer pipe wall and changes direction, causing fluid separation and resulting in lower flow velocity below the bent pipe. After mixing with the outside fluid, the flow rate on the lower side of the outlet pipe is higher and then gradually decreases due to the influence of viscosity. After the gas hits the wall and changes direction, it mixes with the outside fluid. The flow velocity of the pipeline and the outside wall of the reactor is faster and enters the outside direction of the reactor. However, due to inertia, the gas did not mix evenly in the flare-up section in time, and the gas flow and velocity on both sides were low, so a vortex was formed on both sides of the conical head of the reactor.

After adjusting the spacing of the baffle and adding static mixers and porous plates, the flow field distribution is relatively uniform after optimization. Figure 8 shows the velocity distribution cloud map at Section 1. It can be determined from the observation that the tail gas in the pipeline is hindered by the static mixer, and the tail gas flow rate behind and outside of the pipeline is obviously accelerated, forming a low-speed zone at the back end of the static mixer. Under the action of the porous plates, the uniformity of gas flow distribution and velocity distribution at the inlet end of the reactor is obviously increased, but the increase in the above devices will lead to the increase in pressure loss.

In this section, the unidirectional fluid-structure coupling method is used to simulate the reactor structure strength, considering the influence of flow field pressure and temperature changes. In order to make effective use of computing resources, the urea hydrolysis reaction is omitted in the following simulation calculation. Figure 9 shows the manual selection of 18 cross-sections with different spacing, mainly guided by the location of the catalyst layer. The overall pressure distribution and reactor pressure changes along the path are shown in Figure 10 and Figure 11. When the waste gas flows through the mixer, under the action of the baffle, the cross-sectional area of the flow channel changes, the flow rate increases, and the pressure decreases. Thereafter, the pressure will rise somewhat under the influence of the exhaust disturbance, and the static mixer and other diversion devices together cause an increase in the pressure loss of the SCR system. When the tail gas flows through the catalyst layer, the pressure decreases and changes linearly under the action of catalyst resistance, which follows Darcy’s law. According to Bernoulli’s principle, the flow rate of the engine exhaust increases, the pressure decreases in the retracted section of the reactor, and the change rate is higher than that in the expanded section.

Figure 12 shows the temperature distribution of the SCR system at Section 1 and the overall reactor. It can be observed that the urea solution diffuses more uniformly under the action of the static mixer and then rapidly evaporates and absorbs heat, causing a temperature drop. The low-temperature exhaust gas exchanges heat with other gases in the flue, resulting in a more uniform temperature distribution when entering the reactor cylinder. In the first catalyst region, most of NO and all NO₂ are reduced by NH3 to release heat, and the temperature rises. The remaining NO_x continues to react and exotherm in the subsequent catalyst region, but affected by the concentration of reactants, the heat released is lower than that in the first catalyst region, so the temperature rise rate shows a gradual decreasing trend. In addition, the flow speed of the engine exhaust gas in the catalyst bed is not uniform, which affects the reaction rate and leads to inconsistent temperature changes inside and outside the reactor.

Figure 13 shows the temperature variation trend of the reactor along the process. It can be observed that the temperature before Section 6 is basically constant and then sharply increases between Sections 7 and 8. This area is the first layer of the catalyst bed, and the temperature remains unchanged until Section 9. The reaction continues to release heat in the remaining catalyst area, but the rate of temperature change decreases, which is more consistent with the chemical reaction law.

3.2. Strength Analysis of Boundary SCR Reactor Based on Flow Field Calculation

3.2.1. Mechanical Stress Analysis of SCR Reactor

In the simulation calculation process, the thermo-fluid-solid coupling comprehensively considers the influence of fluid temperature, pressure and velocity changes on the structural strength of the reactor. Taking mechanical load as an example, the pressure drop in the catalyst layer of the reactor is large, and the pressure distribution is not uniform. Its fluctuations will cause slight changes in mechanical stress. As can be observed in Figure 14, the maximum stress of the reactor is 175.73 MPa, which appears at the constraint of the supporting base plate and belongs to the sharp corner of the geometric structure. According to the elastic theory, the stress here is infinite and cannot be converged by thinning the mesh, which belongs to the stress singularity. The maximum stress of the main body of the SCR reactor appears at the spherical head, which belongs to the discontinuous part of the structure and is a phenomenon of stress concentration. Figure 15 shows the stress on the inner wall of the spherical head of the reactor, and it can be observed that the maximum stress at this time is 123.47 MPa.

3.2.2. Thermal Mechanical Coupling Stress Analysis of SCR Reactor

As can be observed in Figure 16, the highest temperature of the reactor barrel is slightly higher than the initial temperature of the waste gas, 456.25 °C. Due to the heat transfer between the reactor and the support in the extension direction, there is convection heat transfer between the reactor and the external environment in the vertical extension direction. Therefore, the farther away from the cylinder, the lower the support temperature and the larger the temperature difference between the reactor and the support plate. From the reactor to the support plate, the temperature is distributed in steps. Due to the heat conduction effect of the backing plate, the temperature of the side away from the backing plate drops faster. The lowest temperature occurs in the area of the supporting plate, which is higher than the external environment temperature, specifically 43.47 °C, which decreases by approximately 90% compared with the area of the supporting plate. The temperature distribution of the cylinder in the axial direction is quite different, the difference between the highest temperature and the lowest temperature is 48 °C, and the distribution trend is not uniform. The main influencing factors are as follows: The flow velocity distribution of the tail gas deviates through the elbow and the reactor guide plate, and the fluid velocity near the outer side of the elbow is higher in the positive direction x, which leads to gasification in the pipeline and chemical reaction in the catalyst layer for heat exchange. Therefore, the temperature in the visible direction of the reactor in the following figure is lower than that on the other side, and the axial temperature distribution conforms to the temperature variation law of the flow field.

Under the action of the exhaust gas, the overall temperature of the SCR reactor rises and produces an axial temperature gradient, which generates thermal stress under the action of support and temperature difference. It can be observed in the literature that, if the device cannot move freely, the stress generated by the steel vessel is approximately 2.5 MPa for every 1 °C temperature difference. Therefore, compared with the simple mechanical load, the maximum stress on the reactor rises sharply, and the stress at the material discontinuity connecting the support and reactor barrel exceeds 300 MPa, which is higher than the yield strength. The reasons are as follows: The thermal expansion coefficient of the adjacent structures is different, resulting in excessive thermal stress; located in the discontinuity of the structure, the stress concentration occurs, and the stress singularity occurs at the sharp corners. Taking the manhole and head area of the reactor as an example, the results are shown in Figure 17. The maximum stress of the manhole is much lower than that of the first section of the seal, with a difference of approximately 140 MPa. The total stress in the head area increases by 55% compared to the mechanical stress.

3.2.3. SCR Reactor Deformation Analysis

The calculation model used in this section is arranged horizontally, with sliding supports releasing axial degrees of freedom. The specific deformation under mechanical and thermal loads is shown in Figure 18. The maximum deformation of the reactor under thermal load is 40.22 mm, and the maximum deformation under mechanical load is only 2.73 mm, which is much lower than that under thermal load. However, the deformation distribution trend of the two is the same, and the displacement of the outlet area of the reactor is large because the support of the inlet and outlet ends is a sliding support, allowing for the reactor to expand in the axial direction. At the same time, the reactor is thermally expanded under the action of temperature, and its displacement is affected by the distance from its own position to the constraint point and the temperature difference, so the reactor outlet deformation is larger under the action of thermal load.

3.2.4. SCR Reactor Modal Calculation and Analysis

The high-pressure SCR system is installed at the rear end of the main engine and is subjected to the vibration excitation of the engine, so its design and evaluation must consider the dynamic characteristics. In this section, used for numerical modal analysis, the inherent and overall characteristics of the SCR reactor are analyzed through simplified calculations. The actual operation steps are as follows: On the basis of thermo-fluid-solid coupling, the Modal module is further coupled, the material density is defined, the modal analysis with pre-stress is performed, and the natural frequency and corresponding mode of the model are output by the software.

As can be observed in

Table 4. Natural frequencies of the reactor under the thermo-fluid-solid coupling scheme.

Order	Cold Mode (Hz)	Thermal Mode (Hz)	Rate of Change (%)
1	14.16	13.72	3.13
2	16.94	16.62	1.90
3	33.45	31.70	5.46
4	39.32	38.08	3.09
5	45.08	42.96	4.79
6	48.43	46.90	3.14
7	55.02	52.03	5.35
8	58.68	55.24	5.87
9	66.20	61.92	6.30
10	69.59	65.21	6.49

, the calculation results of the cold and hot modes of the reactor differ greatly, and the natural frequency decreases with an increase in temperature, with the maximum change rate of 6.5%. The main reasons are as follows: On the one hand, nonlinear material is selected for simulation analysis in this study, and the mechanical properties of the material will change greatly if the temperature distribution is not uniform; on the other hand, the temperature load generates thermal stress, which reduces the flexural stiffness as well as the torsional stiffness of the reactor. In general, the natural frequency of the reactor decreases with an increase in temperature.

The evaluation of the simulation results shows that the first-order vibration mode distribution of the unidirectional flow thermal structure coupling and fluid structure coupling simulation calculations are basically consistent, and the deformation variables are roughly equal. Figure 19 shows the first-order vibration mode distribution with and without the addition of thermal load during the thermo-fluid-solid coupling calculation process. It can be observed that, after adding thermal load, the deformation of the reactor increases, and the areas with a relatively large deformation increase, especially in the manhole area.

3.2.5. SCR System Fatigue Analysis

The failure phenomenon that occurs under the action of alternating stress is called fatigue, which is fundamentally different from static failure. The stress strength of the marine high-pressure SCR system is lower than the static strength limit during operation and meets the pressure vessel strength evaluation criteria. However, in order to further consider the safety problems during use, it is necessary to analyze the working life of the structure, effectively extend its working life under the premise of determining safety and improve the economy of SCR reactor use. The fatigue life is closely related to the magnitude of the stress; generally speaking, the stress concentration part is more prone to failure. The stress analysis used in the above stress analysis is the Mises equivalent stress. The stress calculation is based on the fourth strength theory but cannot determine whether the stress in the above area is tensile or compressive. Since tensile stress and compressive stress have different effects on fatigue life, the distribution of the first and third principal stresses of the reactor can be roughly observed before fatigue analysis. As can be observed in Figure 20, the maximum principal stress is always dominated by the chamfer connecting the reactor head and the cylinder, and the maximum value is higher than 100 MPa. This section mainly analyzes the fatigue life because the analysis process selects a pulsating cycle and the fatigue strength factor is greater than 0.5, so the stress amplitude is less than the maximum stress solved by the software.

The materials, such as the flue, mixer and reactor barrel, of the SCR system are inconsistent with the support, so the fatigue life prediction does not conduct too much research on the support and mainly shows the life distribution of the flue, mixer, reactor barrel and head area. In addition, the design life of high-cycle fatigue analysis is generally higher than 1e6 times, so this section evaluates the damage coefficient on this basis. Figure 21 shows the prediction of the reactor life under mechanical load conditions. It can be observed in the figure that the minimum life is more than 7 × 10⁶ times. However, due to the limitation of the S-N curve data, the life is uniformly displayed as 1 × 10⁷ times in the area of stress less than 100 MPa. The area with the lowest life is the chamfer where the reactor head is connected to the cylinder, which is consistent with the stress distribution trend. In the process of analysis of the fatigue safety factor, in order to make the distribution of the factor clearer, the design life is set to 1 × 10⁷ times. As can be observed in the figure, the fatigue safety factor is lower at the head and the discontinuity of the structure, and the lowest safety factor is 0.8391, which appears at the rounded corner of the left end cylinder and is also the position where the stress is the greatest. After the addition of a thermal load, the thermal stress is formed due to the temperature gradient and constraint effect, and the stress in some regions of the reactor is higher than the yield strength. A low-cycle thermal fatigue analysis was adopted, and the strain–life curve generated was invoked after six parameters were input; the results are shown in Figure 22. The minimum life is 4247 times, which occurs in the structural discontinuity between the support and the reactor, and the distribution trend of stress and strain is the same. In addition, there are geometric sharp corners in the above areas, and some gaps can be reserved in the welding process, so it is planned to establish a model for the simulation calculation in the above areas in the future. The design life was defined as 3000 times, and the fatigue safety factor was observed. It can be observed in the figure that the fatigue safety factor was lower at the head and the discontinuity of the structure, the lowest being 1.7579, which was the same distribution trend as the fatigue life.

The analysis method of each flue in the SCR system is the same as that of the reactor. As can be observed in Figure 23, the minimum life of each flue is 3465 times, which occurs at the structural discontinuity between the support and the flue, and the distribution trend of stress and strain is the same.

4. Conclusions

With the increasing prosperity of economic globalization and world trade, the application of marine diesel engines is becoming more and more extensive, and the requirements of the International Maritime Organization (IMO) on NO_x emissions of diesel engines are becoming more and more stringent. SCR technology is an effective measure to solve the above problems. This study takes the high-pressure SCR system of a marine diesel engine as the research object, constructs a calculation model by using SpaceClaim (Concord, MA, USA) and uses CFD and CAE numerical simulation methods to explore the influence of different load conditions and system structure on SCR strength. The main conclusions are as follows:

(1)

A numerical simulation analysis was conducted on the high-pressure SCR system of a marine diesel engine using the thermo-fluid-solid coupling method. This study showed that the overall pressure drop of the SCR system calculated by the thermo-fluid-solid coupling was 5500 Pa, which met the design requirements. The overall temperature rise of the reactor was 24 °C, mainly occurring in the first layer of the catalyst, accounting for 62.5%. The pressure and temperature loads of the reactor vary axially, and the axial deformation gradient of the cylinder is greater.

(2)

Compared with the mechanical stress, the thermal coupling stress of the SCR system increases sharply, and some areas exceed the yield strength of the material. The maximum deformation of the reactor under thermal load is 40.22 mm, and the maximum deformation under mechanical load is only 2.73 mm, with the maximum deformation of the thermal load condition roughly 15 times higher than that of the mechanical load condition, and 97% of the deformation is axial.

(3)

The natural frequency of the cold and hot modes in the SCR system increases with the increase in order, and the natural frequency of the cold mode is higher than that of the hot mode. The change rate of the cold and hot modes of the reactor is up to 6.5%, the fundamental frequency of the engine is 5 Hz, which is far lower than the lowest order natural frequency of the SCR system modal analysis, and there is no resonance phenomenon between the two. The numerical simulation analysis of the fatigue life of the high-pressure SCR system is carried out, and the results show that the fatigue life of the SCR system decreases rapidly due to the heat engine load. Among them, the minimum life of the flue and reactor is 3465 times and 4247 times, respectively, which is the same as the stress and strain distribution trend.