A method of modeling a nitrogen oxide sensor nox pump unit

Abstract

The application discloses a modeling method for a nitrogen oxygen sensor NOx pump unit, and belongs to the field of automobile sensors. The method comprises the following steps: considering the reduction reaction of NO and O2 on an electrode to establish an electrochemical sub-model of the NOx pump unit, wherein the electrochemical sub-model comprises Nernst voltage, cathode and anode concentration loss, cathode and anode activation loss and Ohm loss; considering gas diffusion and early decomposition of NO in a second chamber to establish a gas diffusion sub-model of the NOx pump unit, wherein the gas diffusion sub-model comprises diffusion of gas in a diffusion channel and diffusion of gas in the electrode; combining the electrochemical sub-model and the gas diffusion sub-model through a limiting current to obtain a combined model, and the combined model is used for parameter setting and working control of the nitrogen oxygen sensor. Through the combined model which considers all characteristics in the pump unit and eliminates the intermediate variable of gas concentration, the precision and calculation speed of the sensor model are improved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of automobile sensors, and more particularly relates to a modeling method of a nitrogen oxide sensor NOx pump unit. BACKGROUND

[0002] Due to environmental protection requirements, the engine exhaust emission standards are becoming higher and higher, and the nitrogen oxide NOx emission has become a major challenge for engines to meet the emission standards. In order to reduce NOx emission, motor vehicles are equipped with exhaust aftertreatment systems, among which the selective catalytic reduction technology based on urea is a common means for diesel engines, which can maximize the reduction of NOx emission. However, this system must ensure its correct operation by measuring the current NOx concentration. Therefore, NOx sensors are installed in the exhaust treatment system of the automobile to detect the NOx concentration.

[0003] In order to meet the increasingly stringent emission standards, the accuracy of the NOx sensor needs to be improved, which requires a more comprehensive understanding of the electrochemical pump unit in the sensor. Existing researches mostly only study the performance of the NOx sensor from the electrochemical parameters such as electrode material, electrolyte characteristics, battery voltage, and most of these researches are experimental researches without establishing a physical-based model. Although there are some researches on sensor models, they do not fully consider all the internal characteristics of the sensor, nor do they combine the electrochemical model and the diffusion model, so there is a large space for improving the model accuracy and calculation speed. SUMMARY

[0004] In view of the defects and improvement needs of the prior art, the present application provides a modeling method of a nitrogen oxide sensor NOx pump unit, which aims to improve the accuracy and calculation speed of the sensor model by constructing a combined model that considers all the internal characteristics of the pump unit and eliminates the intermediate variable of gas concentration.

[0005] To achieve the above-mentioned purpose, according to one aspect of the present application, a modeling method of a nitrogen oxide sensor NOx pump unit is provided, the nitrogen oxide sensor comprising three cavities connected in sequence, the NOx pump unit being in the third cavity, the modeling method comprising: S1, considering the reduction reaction of NO and O2 on the electrode to establish an electrochemical sub-model of the NOx pump unit, the electrochemical sub-model comprising Nernst voltage, cathode and anode concentration loss, cathode and anode activation loss and Ohm loss; S2, considering gas diffusion and NO decomposition in advance in the second cavity to establish a gas diffusion sub-model of the NOx pump unit, the gas diffusion sub-model comprising diffusion of gas in the diffusion channel and diffusion in the electrode; S3, combining the electrochemical sub-model and the gas diffusion sub-model by limiting current to obtain a combined model, the combined model being used for parameter setting and working control of the nitrogen oxide sensor.

[0006] Further, the electrochemical sub-model is:

[0007] V P2 = E N + η act，c + η act，a + η ohm + η con，c + η con，a

[0008] wherein V P2 is the pump voltage, E N is the Nernst voltage, η act，c is the cathode activation overpotential, η act，a is the anode activation overpotential, η ohm is the ohmic overpotential, η con，c is the cathode concentration overpotential, and η con，a is the anode concentration overpotential.

[0009] Further, the Nernst voltage E N is:

[0010]

[0011] wherein E0is the base electromotive force, R is the universal gas constant, T is the working temperature of the nitrogen-oxygen sensor, F is the Faraday constant, and In denotes the logarithmic function, P NO，th , are the gas partial pressures of N2, NO, and O2 in the third chamber, respectively, is the gas partial pressure of O2 in the external sample gas, are the 0.5th powers of P , respectively.

[0012] Further, the cathode concentration overpotential η con，c and the anode concentration overpotential η con，a are:

[0013]

[0014]

[0015] wherein R is the universal gas constant, T is the working temperature of the nitrogen-oxygen sensor, F is the Faraday constant, and In denotes the logarithmic function, P NO，th , are the gas partial pressures of NO and O2 in the third chamber, respectively, P NO，tpb，c , are the gas partial pressures of NO and O2 at the cathode three-phase interface, respectively, is the gas partial pressure of O2 at the anode three-phase interface, The gas partial pressure of O2 in the external sample gas.

[0016] Further, the cathode activation loss η act，c and the anode activation loss η act，a are respectively:

[0017]

[0018]

[0019] wherein R is a universal gas constant, T is the working temperature of the nitrogen-oxygen sensor, F is a Faraday constant, n c is the number of exchanged electrons in the cathode chemical reaction, n a is the number of exchanged electrons in the anode chemical reaction, i c is the cathode current density, i 0，c is the cathode exchange current density, i a is the anode current density, i 0，a is the anode exchange current density, sinh -1 represents the inverse hyperbolic sine function.

[0020] Further, the ohmic loss η ohm is:

[0021] η ohm = I P R e

[0022] wherein I P is the pump current, R e is the electrolyte resistance.

[0023] Further, the gas diffusion sub-model is:

[0024]

[0025]

[0026] wherein, P NO，sc，0 are respectively the gas partial pressures of O2 and NO in the second chamber, P NO，tpb，c are respectively the gas partial pressures of O2 and NO at the cathode three-phase interface, R is a universal gas constant, T is the working temperature of the nitrogen-oxygen sensor, F is a Faraday constant, is the diffusion coefficient of oxygen in the third diffusion channel, is the diffusion coefficient of oxygen in the cathode, I NO are respectively the pump currents of O2 and NO, L1, L2, L cD1, D2, D3, D4 are the diffusion lengths of the first, second, third diffusion channels, the third chamber NOx pump cell cathode, respectively, D1, D2, D3, D c S1, S2, S3, S4 are the diffusion coefficients of NO in the first, second, third diffusion channels, the third chamber NOx pump cell cathode, respectively, S1, S2, S3, S c A1, A2, A3, A4 are the diffusion cross-sectional areas of the first, second, third diffusion channels, the third chamber NOx pump cell cathode, respectively, A1, A2, A3, A4

[0027] Further, when reaching the limit state, P NO，tpb，c = 0, I NO = I L，NO , the gas diffusion sub-model is equivalent to:

[0028]

[0029]

[0030] wherein, I L，NO are the limit currents of O2, NO formation, respectively.

[0031] Further, the combined model is:

[0032]

[0033] wherein, V P2 is the pump voltage of the NOx pump cell, V oc is the pump voltage of the NOx pump cell at zero current, R is the universal gas constant, T is the working temperature of the nitrogen oxide sensor, F is the Faraday constant, In is the logarithm function, I P2 is the pump current of the NOx pump cell, I L is the limit current of the NOx pump cell, n c is the number of exchanged electrons of the cathode chemical reaction, n a is the number of exchanged electrons of the anode chemical reaction, sinh -1 denotes the inverse hyperbolic sine function, S c , S a are the cross-sectional areas of the third chamber NOx pump cell cathode, anode, respectively, i 0，ca , i 0，an are the exchanged current densities of the third chamber NOx pump cell cathode, anode, respectively, R e is the electrolyte resistance.

[0034] In general, the above technical solutions conceived by the present application can achieve the following beneficial effects: the electrochemical sub-model and the gas diffusion sub-model of the NOx pump unit of the nitrogen oxygen sensor are constructed, all characteristics inside the pump unit are fully considered, the constructed model is more comprehensive, the model precision is improved, and thus the precision of the NOx concentration detection is improved; the electrochemical sub-model and the gas diffusion sub-model are combined together through the limiting current, the intermediate variable of the gas concentration which is difficult to directly measure is eliminated, a more simple combined model is formed, the calculation difficulty of the model is reduced, the calculation speed of the model is improved, the real-time operation of the model is facilitated, and thus the precision and the calculation speed of the sensor model are improved. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 The flow chart of the NOx pump unit modeling method of the nitrogen oxygen sensor provided in the embodiment of the present application is shown in

[0036] Figure 2 The cross-sectional view of the sensing element of the nitrogen oxygen sensor provided in the embodiment of the present application is shown in DETAILED DESCRIPTION

[0037] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and should not be used to limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0038] In the present application, the terms "first", "second", etc. (if any) in the present application and the accompanying drawings are used to distinguish similar objects, and do not necessarily describe a specific order or sequence.

[0039] Figure 1 The flow chart of the NOx pump unit modeling method of the nitrogen oxygen sensor provided in the embodiment of the present application is shown in Figure 1 , combined with Figure 2 , the NOx pump unit modeling method in the embodiment is described in detail.

[0040] Referring to Figure 2 In the embodiment, the nitrogen oxygen sensor includes three cavities connected in sequence, which are a first cavity, a second cavity and a third cavity in sequence, the three cavities are connected through a second diffusion channel and a third diffusion channel, exhaust gas enters the first cavity through a first diffusion channel, and the diffusion channel is a slit diffusion. Each cavity has a pump unit, wherein the first cavity is a main pump oxygen unit, the second cavity is an auxiliary pump oxygen unit, and the third cavity is a NOx pump unit. The nitrogen oxygen sensor further includes three Nernst units, a heater and a reference gas chamber.

[0041] The main pump unit, consisting of the common outer electrode P+ and the negative electrode P-, can pump out most of the oxygen from the first chamber. At the same time, the Nernst voltage between the negative electrode P- and the reference electrode Ref can reflect the oxygen concentration in the first chamber. The auxiliary pump unit, consisting of the common outer electrode P+ and the negative electrode M1, can pump out the remaining small amount of oxygen from the second chamber, promoting the reduction and conversion of all NOx types into NO in the second chamber. The NOx pump unit, consisting of the common outer electrode P+ and the negative electrode M2, can measure the concentration of NOx in the exhaust gas.

[0042] The embodiments of the present application model the NOx pump unit, including operations S1-S3.

[0043] In operation S1, the reduction reactions of NO and O2 on the electrodes are considered to establish an electrochemical sub-model of the NOx pump unit, including the Nernst voltage, the cathode and anode concentration losses, the cathode and anode activation losses, and the ohmic loss.

[0044] According to embodiments of the present application, the established electrochemical sub-model is:

[0045] V P2 = E N + η act，c + η act，a + η ohm + η con，c + η con，a

[0046] where V is the pump voltage, E is the Nernst voltage, η is the cathode activation loss, η is the anode activation loss, η is the ohmic loss, η is the cathode concentration loss, and η is the anode concentration loss. P2 N act，c act，a ohm con，c con，a

[0047] The Nernst voltage E N is:

[0048]

[0049] where E0 is the base electromotive force, i.e., the electromotive force under standard conditions, R is the universal gas constant (8.3145 J mol - 1 K -1 ), T is the working temperature of the nitrogen oxide sensor (in K), F is the Faraday constant (96485.33 C / mol), and In represents the logarithmic function, P NO，th , ​​​​​​​These represent the partial pressures of N2, NO, and O2 in the third chamber, respectively. The partial pressure of O2 in the external sample gas. They are respectively 0.5.

[0050] Cathode concentration loss η con，c and anode concentration loss η con，a They are respectively:

[0051]

[0052]

[0053] Among them, P NO，th , P represents the partial pressures of NO and O2 in the third chamber, respectively. NO，tpb，c , These represent the partial pressures of NO and O2 at the cathode three-phase interface, respectively. This represents the partial pressure of O2 at the anode three-phase interface. This represents the partial pressure of O2 in the external sample gas. Studies have shown that the anode concentration loss is negligible compared to the cathode concentration loss. Therefore, the anode and cathode concentration losses in this embodiment can also be directly represented by the cathode concentration loss.

[0054] The activation loss can be described by the Butler-Volmer method, where the cathode activation loss η is... act，c and anodic activation loss η act，a They are respectively:

[0055]

[0056]

[0057] Where, n c n represents the number of electrons exchanged in the cathode chemical reaction. a i represents the number of electrons exchanged in the anodic chemical reaction. c i is the cathode current density. 0，c i is the cathode exchange current density. a i is the anode current density. 0，a For the anode exchange current density, sinh -1 This represents the inverse hyperbolic sine function.

[0058] Ohm loss η ohm This is generated by the resistance of the electrolyte and can be expressed as:

[0059] η ohm =I P R e

[0060] where I P is the pump current, R e is the electrolyte resistance.

[0061] Operation S2, considering the gas diffusion and the pre-decomposition of NO in the second chamber, a gas diffusion sub-model of the NOx pump unit is established, which includes the diffusion of the gas in the diffusion channels and the diffusion within the electrode.

[0062] According to an embodiment of the present application, the established gas diffusion sub-model is:

[0063]

[0064]

[0065] where, P NO，sc，0 are the gas partial pressures of O2 and NO in the second chamber, respectively, P NO，tpb，c are the gas partial pressures of O2 and NO at the cathode three-phase interface, respectively, is the diffusion coefficient of oxygen in the third diffusion channel, is the diffusion coefficient of oxygen in the cathode, I NO are the pump currents formed by O2 and NO, respectively, L1, L2, L c are the diffusion lengths of the first diffusion channel, the second diffusion channel, the third diffusion channel, and the cathode of the third-chamber NOx pump unit, respectively, D1, D2, D c are the diffusion coefficients of NO in the first diffusion channel, the second diffusion channel, the third diffusion channel, and the cathode of the third-chamber NOx pump unit, respectively, S1, S2, S c are the diffusion cross-sectional areas of the first diffusion channel, the second diffusion channel, the third diffusion channel, and the cathode of the third-chamber NOx pump unit, respectively, and λ is the decomposition rate of NO in the second chamber.

[0066] When reaching the limit state, P NO，tpb，c = 0, I NO = I L，NO , the gas diffusion sub-model is equivalent to:

[0067]

[0068]

[0069] where, I L，NO are the limit currents formed by O2 and NO, respectively.

[0070] Since the pump current formed by O2 and NO gradually reaches the limit current state from the zero current state, and the diffusion environment and conditions of the two gases are consistent, it can be considered that the change processes of the two pump currents are consistent, that is:

[0071]

[0072] In operation S3, the combined model is obtained by combining the electrochemical sub-model and the gas diffusion sub-model through the limit current, and the combined model is used for parameter setting and working control of the nitrogen oxygen sensor.

[0073] Preferably, the NOx pump unit combined model is:

[0074]

[0075] Studies have shown that η con，a η con，c can be ignored. Therefore, the combined model established in the embodiment of the present application is:

[0076]

[0077] wherein V P2 is the pump voltage of the NOx pump unit, V oc is the pump voltage of the NOx pump unit at zero current, I P2 is the pump current of the NOx pump unit, I L is the limit current of the NOx pump unit, n c is the number of exchanged electrons of the cathode chemical reaction, n a is the number of exchanged electrons of the anode chemical reaction, sinh-1 represents the inverse hyperbolic sine function, S c , S a are the cross-sectional areas of the cathode and anode of the third chamber NOx pump unit respectively, i 0，ca , i 0，an are the exchange current densities of the cathode and anode of the third chamber NOx pump unit respectively.

[0078] The pump voltage V oc of the NOx pump unit at zero current satisfies:

[0079]

[0080] The model establishment processes of the main pump oxygen unit and the auxiliary pump oxygen unit are the same as the principle of the model establishment process of the NOx pump unit, which will not be repeated here.

[0081] The NOx pump unit combination model constructed in the embodiment characterizes the size of the influence of each characteristic on the sensor in the working of the sensor. The device parameters of the nitrogen oxygen sensor can be determined according to the established combination model, and the working process of the nitrogen oxygen sensor is controlled to reduce the influence of the cathode and anode concentration loss, the cathode and anode activation loss and the ohmic loss of the nitrogen oxygen sensor, and improve the detection accuracy of the nitrogen oxygen sensor.

[0082] Those skilled in the art can understand that the above description is only preferred embodiments of the present application, and is not used to limit the present application, and any modifications, equivalent replacements and improvements made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method of modeling a nitrogen oxide sensor NOx pump unit, the nitrogen oxide sensor comprising three chambers in series, the NOx pump unit being in the third chamber, characterized in that, The modeling method comprises: S1, considering the reduction reactions of NOx on the electrodes and to establish an electrochemical sub-model of the NOx pump unit, the electrochemical sub-model including Nernst voltage, anode and cathode concentration losses, anode and cathode activation losses, and ohmic losses; S2, taking into account the gas diffusion and pre-decomposing in the second chamber to establish a gas diffusion sub-model of the NOx pump unit, the gas diffusion sub-model including diffusion of the gas in the diffusion channel and within the electrodes; S3, combining the electrochemical sub-model and the gas diffusion sub-model through a limiting current to obtain a combined model, the combined model being used for parameter setting and working control of the nitrogen-oxygen sensor; The electrochemical sub-model is: wherein, is the pump voltage, is the Nernst voltage, is the cathode activation loss, is the anode activation loss, is the ohmic loss, is the cathode concentration loss, is the anode concentration loss; The gas diffusion sub-model is: wherein , are respectively , partial pressure of gas in the second chamber, , are respectively , partial pressure of gas at the triple phase boundary of the cathode, is the universal gas constant, is the operating temperature of the nitrogen oxide sensor, is the Faraday constant, is the diffusion coefficient of oxygen in the third diffusion channel, is the diffusion coefficient of oxygen in the cathode, , are respectively , pump current formed, , , , are respectively the diffusion length of the first diffusion channel, the second diffusion channel, the third diffusion channel, the cathode of the third chamber NOx pump unit, , , , are respectively the diffusion coefficient of the first diffusion channel, the second diffusion channel, the third diffusion channel, the cathode of the third chamber NOx pump unit, , , , are respectively the diffusion cross-sectional area of the first diffusion channel, the second diffusion channel, the third diffusion channel, the cathode of the third chamber NOx pump unit, is the decomposition rate of NO in the second chamber; The combined model is: wherein, is the pump voltage of the NOx pump unit, is the pump voltage of the NOx pump unit at zero current, is the universal gas constant, is the operating temperature of the nitrogen oxide sensor, is the Faraday constant, is the logarithm function, is the pump current of the NOx pump unit, , is the limiting current of the NOx pump unit, is the number of exchanged electrons of the cathode chemical reaction, is the number of exchanged electrons of the anode chemical reaction, denotes the inverse hyperbolic sine function, , are the cross-sectional areas of the cathode and anode of the third chamber NOx pump unit, respectively, , are the exchange current densities of the cathode and anode of the third chamber NOx pump unit, respectively, is the electrolyte resistance.

2. The nitrogen oxide sensor NOx pump unit modeling method of claim 1, wherein, nernst voltage is: wherein is the background electromotive force, is the universal gas constant, is the operating temperature of the nitrogen oxide sensor, is the Faraday constant, denotes the logarithm function, , , are respectively , , the gas partial pressure in the third chamber, is the gas partial pressure of in the ambient sample gas, , are respectively , the 0.5th power of 3. The nitrogen oxide sensor NOx pump unit modeling method of claim 1, wherein, cathode concentration losses and anode concentration losses respectively. wherein is the universal gas constant, is the operating temperature of the nitrogen oxide sensor, is the Faraday constant, denotes the logarithm function, , are , is the gas partial pressure in the third chamber, , are , is the gas partial pressure at the cathode three-phase interface, is is the gas partial pressure at the anode three-phase interface, is the gas partial pressure of in the ambient sample gas.

4. The method of claim 1, wherein: cathode activation loss and anode activation loss respectively. wherein, is the universal gas constant, is the operating temperature of the nitrogen oxide sensor, is the Faraday constant, is the number of exchanged electrons for the cathode chemical reaction, is the number of exchanged electrons for the anode chemical reaction, is the cathode current density, is the cathode exchange current density, is the anode current density, is the anode exchange current density, denotes the inverse hyperbolic sine function.

5. The method of claim 1, wherein, ohmic losses is: wherein, is the pump current, is the electrolyte resistance.

6. The method of claim 1, wherein: When the limit state is reached, , , , , the gas diffusion sub-model is equivalent to: wherein , are respectively , the limiting current formed.

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