A method for calculating conjugate heat transfer of SCR system based on secondary development of OpenFOAM

Abstract

The application discloses an SCR system conjugate heat transfer calculation method based on OpenFOAM secondary development, and the secondary development is carried out based on an open source CFD library OpenFOAM; a temperature solving method of a solid field is implanted on the basis of an original fluid field solving method, so as to solve the problem that a solver for the flow field conjugate heat transfer characteristics of a diesel engine aftertreatment system has not been developed maturely in the prior art. On the basis of the gas field solver of the computational fluid dynamics open source library OpenFOAM, the heat conduction calculation method of the solid field is implanted, the numerical calculation of the diesel engine exhaust aftertreatment SCR system conjugate heat transfer problem is realized, and the application range is effectively widened.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of fluid mechanics, and particularly relates to a SCR system conjugate heat transfer calculation method based on OpenFOAM secondary development. BACKGROUND

[0002] The rapid development of the automobile industry has exacerbated the energy crisis and air pollution problems. Diesel engines have good power performance, low carbon emissions and good economy, and are widely used in commercial vehicles, engineering machinery, agricultural machinery and other fields. However, diesel engine exhaust is one of the main sources of atmospheric nitrogen oxides (NOx) and particulate matter (PM). Since 2020, the national VI emission standard for heavy-duty diesel engines has been implemented, which has put forward higher standards and technical requirements for diesel engine emission control. At present, the SCR (selective catalytic reduction) technology has been relatively mature and is widely used in various medium and heavy-duty diesel vehicles.

[0003] Using the computational fluid dynamics (CFD) numerical simulation method, the information of urea solution atomization, exhaust flow and component distribution can be obtained, which can provide basis for SCR catalyst structure design and optimization, shorten the research and development cycle and save development cost. At present, commonly used commercial software such as Ansys Fluent, Star CCM and AVL can be used to solve various types of fluid mechanics problems, and has certain applicability, accuracy and robustness, and the calculation results can meet the engineering requirements. However, the program source code of these commercial software has been encapsulated, and the program details cannot be known, and the source code cannot be modified, which greatly limits the in-depth study of specific problems. OpenFOAM as a CFD open source library completely opens the user's customization rights, which has a natural advantage in the research of SCR system conjugate heat transfer problems.

[0004] However, the solvers in OpenFOAM for SCR system conjugate heat transfer problems have not been developed maturely. Therefore, it is necessary to carry out secondary development based on OpenFOAM to improve the numerical simulation accuracy of SCR system conjugate heat transfer problems, so as to meet the needs of current diesel engine exhaust SCR system conjugate heat transfer problem research. SUMMARY

[0005] At present, the numerical simulation of the internal flow of diesel engine exhaust aftertreatment system structure is mostly based on commercial software, and the self-defined model is inevitably limited by the software itself. At the same time, the research on the temperature field of the flow field of the aftertreatment system is basically carried out by engine bench test, and the conjugate heat transfer phenomenon actually existing in the system is less considered in numerical simulation. Based on the open source CFD library OpenFOAM, the temperature solving method of the solid domain is implanted on the basis of the original fluid domain solving method to solve the problem that the solver for the conjugate heat transfer characteristics of the flow field of the diesel engine aftertreatment system is not mature in the prior art.

[0006] An SCR system conjugate heat transfer calculation method based on secondary development of OpenFOAM is as follows:

[0007] S1: initialize the calculation domain, start the calculation at t=t start ;

[0008] S2: start spraying and establish a spray model;

[0009] S3: obtain the intermediate density ρ temp ; the intermediate density ρ temp is obtained from the continuity equation ; wherein, ρ is the gas density, U is the gas velocity, t is the time, and Sc is the mass equation source term;

[0010] S4: based on the intermediate density ρ temp and the momentum equation , the intermediate velocity U temp of the flow field at this time is solved;

[0011] S5: construct and solve the gas phase transport equation , thereby updating the component Y i of the gas domain; wherein, Sc is the mass equation source term, Yi is the mass fraction of the i-th component, μ eff is the effective viscosity coefficient, and Si is the component source term;

[0012] S6: construct the fluid energy equation and solve to obtain the specific enthalpy h, and according to h, the temperature distribution T of the fluid domain is obtained, and the density ρ temp1 of the fluid domain is obtained through the state equation p=ρRT; wherein, K is the specific mechanical energy, α eff is the effective thermal diffusivity, e is the specific internal energy, S heat is the energy equation source term, and R is the gas constant;

[0013] S7: model the heat conduction process in the solid domain to obtain the specific enthalpy of each grid element in the solid domain, and simultaneously obtain the temperature distribution of the solid domain;

[0014] S8: According to U temp and p temp1 , construct the pressure Poisson equation, where the pressure term p and gravity term g are numerically processed to define p rgh = p - pg.h, and then solve to obtain the pressure p of the flow field rgh temp , and update the flow field velocity U temp’ at this time according to the pressure Poisson equation

[0015] S9: According to the continuity equation and U temp’ , obtain the corrected flow field density p temp2 ;

[0016] S10: If p temp2 does not satisfy the convergence condition, return to S4 for iteration until convergence, and the convergence condition is that p temp2 and p temp1 tend to be consistent, that is, the density of the flow field at this time.

[0017] S11: If t does not satisfy t > t end , it needs to return to S1 to continue, if t > t end , the calculation is completed.

[0018] Preferably, the spray model comprises:

[0019] Liquid droplet motion model:

[0020] In the formula, m d is the mass of the liquid droplet, u d is the velocity of the liquid droplet, and ∑F is the total external force received by the liquid droplet, including drag force and gravity;

[0021] Liquid droplet evaporation model:

[0022] When the temperature of the liquid droplet is less than the boiling temperature of water, the evaporation rate of the liquid droplet is:

[0023]

[0024] When the temperature rises greater than or equal to the boiling temperature of water, the evaporation rate of the liquid droplet becomes:

[0025]

[0026] In the formula, D d is the diameter of the liquid droplet, p m is the density of the mixed gas, Γ is the diffusion coefficient, Sh is the Sherwood number, B M is the mass transport number, λ is the thermal conductivity of the gas, Nu is the Nusselt number, and cvap B is the specific heat capacity of water vapor at constant pressure T is the mass transport number.

[0027] Preferably, the heat conduction process in the solid domain is modeled, in particular:

[0028] Urea pyrolysis model:

[0029] (NH2)2CO (1) → (NH2)2CO (s) + H2O (g)

[0030] (NH2)2CO (s or l) → NH3 (g) + HCNO (g)

[0031] The heat transfer governing equation in the solid domain is:

[0032] where ρs, hs and αs are the density, specific enthalpy and effective thermal diffusivity of the solid domain, respectively, and t is time. s s eff,s

[0033] Preferably, in the solving process, the boundary treatment at the interface between the solid and gas domains is as follows:

[0034]

[0035] where kg and ks are the thermal conductivities of the gas and solid, respectively, T is the temperature, and n is the normal vector of the grid cell at the boundary.

[0036] Compared with the prior art, the present application has the beneficial effect that, on the basis of the gas domain solver of the open source library of computational fluid dynamics OpenFOAM, the heat conduction calculation method of the solid domain is implanted, the numerical calculation of the conjugate heat transfer problem of the diesel engine exhaust aftertreatment SCR system is realized, and the application range is effectively widened. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 is the flowchart of the present application, wherein t start , t end are the start and end times of the numerical calculation, respectively;

[0038] Figure 2 is the distribution of NH3 without considering the heat transfer of the solid domain, and considering the heat transfer of the solid domain (conjugate heat transfer);

[0039] Figure 3 is the cross-sectional NH3 volume fraction distribution cloud map;

[0040] Figure 4 is the temperature distribution map of the model symmetry plane considering the conjugate heat transfer. DETAILED DESCRIPTION ​​​

[0041] One specific embodiment of the present application is described in detail below with reference to the accompanying drawings, but it should be understood that the scope of the present application is not limited by the specific embodiment.

[0042] The present application simulates the process of exhaust and injection of urea aqueous solution in a certain elbow model, as follows:

[0043] The calculation domain is initialized, and the calculation starts at t=t start , and the calculation is completed when t>t end (If not, continue to calculate), in particular:

[0044] The intermediate density ρ temp is obtained through the continuity equation.

[0045] Continuity equation:

[0046] Based on the intermediate density ρ temp and the momentum equation, the intermediate velocity U temp is derived and obtained.

[0047] Momentum equation:

[0048]

[0049] The gas phase transport equation is constructed and solved, so as to update the composition Y i of the gas domain.

[0050] Gas phase transport equation:

[0051] The fluid domain energy equation is constructed and solved to obtain the specific enthalpy h.

[0052] Fluid domain energy equation:

[0053]

[0054] State equation: p=ρRT (6)

[0055] In the formula, ρ is the gas density, U is the gas velocity, t is the time, Sc is the mass equation source term, p is the gas pressure, S is the momentum equation source term, Y i is the mass fraction of the i-th component, μ eff is the effective viscosity coefficient, S i is the component source term, h is the specific enthalpy, K is the specific mechanical energy, α eff is the effective thermal diffusion coefficient, e is the specific internal energy, and S heat is the energy equation source term.

[0056] The heat transfer process in the solid domain is modeled to obtain the specific enthalpy of each grid cell in the solid domain, while the temperature distribution of the solid domain is obtained, as follows:

[0057] The simulation of the urea solution is performed using the discrete droplet model (DDM), and the calculation object is the droplet group, which is considered to have the same properties as the single droplet, i.e., the change of the entire droplet group is represented by the change of the single droplet. The processes of spraying atomization, evaporation, and pyrolysis reaction are simulated during the calculation, and the specific model includes:

[0058] Droplet movement model (ignoring the effect of buoyancy on the droplet):

[0059]

[0060] In the formula, m d is the droplet mass, u d is the droplet velocity, and ∑F is the total external force acting on the droplet, including drag force and gravity.

[0061] Droplet evaporation model:

[0062] When the droplet temperature is less than the boiling temperature of water, the droplet evaporation rate is:

[0063]

[0064] When the temperature rises to equal or greater than the boiling temperature of water, the droplet evaporation rate becomes:

[0065]

[0066] In the formula, D d is the droplet diameter, ρ m is the density of the mixed gas, Γ is the diffusion coefficient, Sh is the Sherwood number, B M is the mass transport number, λ is the gas thermal conductivity, Nu is the Nusselt number, c vap is the constant-pressure specific heat capacity of water vapor, and B T is the mass transport number.

[0067] Urea pyrolysis model:

[0068] (NH2)2CO(1)→(NH2)2CO(s)+ H2O(g) (10)

[0069] (NH2)2CO(s or l)→ NH3(g)+ HCNO(g) (11)

[0070] In order to realize the numerical calculation method of the conjugate heat transfer problem of the diesel engine SCR system, the heat conduction process in the solid domain is considered on the basis of the original solver, the model is programmed by using C++ language in the OpenFOAM open source library, and the heat transfer control equation of the solid domain is as follows:

[0071]

[0072] In the formula, rho s , h s And alpha eff,s The density, specific enthalpy and effective thermal diffusivity of the solid domain are respectively.

[0073] When the conjugate heat transfer is solved, the boundary treatment at the solid-gas domain interface is as follows:

[0074]

[0075] In the formula, k g , k s The thermal conductivity of gas and solid respectively, T is temperature, and n is the normal vector of the grid unit at the boundary.

[0076] According to U temp And rho temp1 The pressure Poisson equation is constructed The pressure term p and the gravity term g are calculated and defined as p rgh =p-ρg·h, and then the pressure p of the flow field is solved rgh temp , and the flow field velocity U temp’ is updated according to the pressure Poisson equation; wherein h represents the position vector of the grid unit center;

[0077] According to the continuity equation and U temp’ The modified flow field density rho temp2 ;

[0078] If rho temp2 Does not meet the convergence condition, iteration is carried out again until convergence, and the convergence condition is that rho temp2 And rho temp1 Tend to be consistent, that is, the density of the flow field at this time.

[0079] In addition, it should be understood that, although the present specification is described according to the embodiments, not every embodiment contains only one independent technical solution, and the description manner of the specification is only for the sake of clarity, and the person skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can be combined to form other embodiments which can be understood by the person skilled in the art.

Claims

1. An SCR system conjugate heat transfer calculation method based on OpenFOAM secondary development, characterized in that, Specifically as follows S1: Compute domain initialization, by t t start starting at time instant​ S2: Start spraying, and establish a spray model; S3: Obtain intermediate density ρ temp ; intermediate density ρ temp from the continuity equation ; where, is the gas density, U is the gas velocity, t is time, is the mass equation source term; S4: Based on the intermediate density ρ temp and momentum equations , , the intermediate velocity of the flow field is solved ; S5: Construct and solve the gas phase transport equations , thereby updating the composition of the gas domain ; where, is the mass equation source term, is the mass fraction of the i-th component, is the effective viscosity coefficient, is the composition source term; S6: Construct the fluid domain energy equation and solve to get the specific enthalpy h , and according to h get the temperature distribution of the fluid domain T , and through the state equation get the density of the fluid domain ρ temp1 ; wherein, K is the specific mechanical energy, is the effective thermal diffusion coefficient, e is the specific internal energy, is the energy equation source term, R is the gas constant; S7: Model the heat conduction process in the solid domain to obtain the specific enthalpy of each grid cell in the solid domain, and simultaneously obtain the temperature distribution of the solid domain; S8: According to and ρ temp1 Constructing pressure Poisson equation where the pressure term p is coupled with the gravity term g After numerical treatment, define and then solve to obtain the pressure of the flow field ， and update the flow field velocity at this time according to the pressure Poisson equation ; wherein, h represents the position vector of the grid unit cell center. S9: according to the continuity equation and obtaining a modified flow field density ρ temp2 ; S10: If ρ temp2 If the convergence condition is not met, go back to S4 for iteration until convergence, the convergence condition is ρ temp2 and ρ temp1 converge, i.e. the density of the flow field at this time; S11: If t not satisfied then it is necessary to return to S1 to continue, if then the calculation is complete; Wherein, the spray model comprises: Droplet motion model: ; wherein m d is the droplet mass, u d is the droplet velocity, is the resultant external force on the droplet, including drag and gravity; A droplet evaporation model: When the droplet temperature is less than the boiling temperature of water, the droplet evaporation rate is: When the temperature rise is greater than or equal to the boiling temperature of water, the droplet evaporation rate becomes: wherein D d is the droplet diameter, is the density of the mixture, is the diffusion coefficient, Sh is the Sherwood number, B M is the mass transport number, is the gas thermal conductivity, Nu is the Nusselt number, c vap is the specific heat capacity of water vapor at constant pressure, B T is the mass transport number; Modeling the heat conduction process in the solid domain, specifically: A urea pyrolysis model: (NH2)2CO (1)→ (NH2)2CO (s) + H2O (g) (NH2)2CO (s or l)→ NH3 (g) + HCNO (g) The heat transfer control equation for the solid domain is: wherein , and are the density, the specific enthalpy and the effective thermal diffusivity of the solid domain, respectively, t is the time.

2. The SCR system conjugate heat transfer calculation method based on OpenFOAM secondary development according to claim 1, characterized in that, In solving, the boundary at the solid-gas domain interface is processed as follows: wherein kg , ks are the thermal conductivities of the gas, solid, respectively, T is the temperature, n is the normal vector of the grid cell at the boundary.

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