Abstract:
A method for accurate estimation of a gas temperature at transient conditions includes measuring temperature sensor readings in a gas flow and estimating the gas temperature by equating the specific heat properties of the temperature sensor to the sum of conductive heat, convective heat, and radiative heat acting upon the temperature sensor and solving for the gas temperature.

Description:
TECHNICAL FIELD 
       [0001]    This disclosure is related to temperature measurement of a gas flow at transient conditions. 
       BACKGROUND 
       [0002]    Combustion within an engine produces heat and a flow of chemical by-products as an exhaust gas flow. Various methods exist for modulating the combustion process to improve fuel efficiency and control exhaust gas emissions. One important property used to monitor the combustion process and the aftertreatment of the exhaust gas flow is the exhaust gas temperature. Temperature sensors are well known for monitoring temperature in a gas flow. However, temperature sensors measure the temperature of the temperature sensor and not the temperature of the gas flow. Heat energy must flow between the gas flow and the temperature sensor for temperature changes in the gas flow to be measured. This resulting temperature response in the temperature sensor to the flow of heat energy introduces a delay or lag relative to temperature changes in the gas flow. Additionally, the temperature of the temperature sensor is a result or a summation of historical heat flows. This summing or averaging effect upon temperature sensor temperatures masks high speed or alternating changes in temperature in the gas flow, reducing the sensitivity of the temperature sensor readings. Results of the lag and averaging errors of temperature sensor readings in an exhaust gas flow include compromises in engine control and management of exhaust gas aftertreatment. 
       SUMMARY 
       [0003]    A method for accurate estimation of a gas temperature in a gas flow at transient conditions based on temperature sensor readings includes measuring the temperature sensor readings from a temperature sensor in the gas flow and estimating the gas temperature on the basis of the temperature sensor readings, wherein the estimating includes equating the specific heat properties of the temperature sensor to the sum of conductive heat, convective heat, and radiative heat acting upon the temperature sensor and solving for the gas temperature. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0004]    One or more embodiments will now be described, by way of example, with reference to the accompanying drawings, in which: 
           [0005]      FIG. 1  is a schematic diagram of an exemplary vehicle equipped with a temperature sensor in accordance with the present disclosure; 
           [0006]      FIG. 2  is a graphical representation of test results of an exemplary known system utilizing a temperature sensor to measure exhaust gas temperatures in accordance with the present disclosure; 
           [0007]      FIG. 3  is a cross-sectional schematic diagram of an exemplary temperature sensor located inside an exhaust pipe in accordance with the present disclosure; 
           [0008]      FIG. 4  is a flowchart illustrating an exemplary process utilizing an estimated exhaust gas temperature in accordance with the present disclosure; and 
           [0009]      FIG. 5  is a graphical representation depicting test results of exemplary estimated exhaust gas temperatures as compared to simulated exhaust gas temperatures in accordance with the present disclosure. 
       
    
    
     DETAILED DESCRIPTION 
       [0010]    Referring now to the drawings, wherein the showings are for the purpose of illustrating certain exemplary embodiments only and not for the purpose of limiting the same,  FIG. 1  schematically illustrates vehicle  10  equipped with temperature sensor  40  in accordance with the disclosure. Vehicle  10  includes engine  20 , engine control module  25 , exhaust manifold  30 , exhaust aftertreatment system  35 , and temperature sensor  40 . Engine  20  combusts fuel to propel vehicle  10 . Exhaust system  30  and exhaust aftertreatment system  35  provide a path for the exhaust gas generated in the combustion process to be processed for certain emission reductions and then to be expelled from vehicle  10 . 
         [0011]    Modern engines utilize various schemes to improve fuel efficiency and to reduce the emissions from the combustion process. Engine control module  25  processes information from various inputs and modulates the operation of engine  20  and processes in exhaust aftertreatment system  35  referred to as aftertreatment. The temperature of the exhaust gas flow is an important property to the various schemes run by engine control module  25  as exhaust gas temperature reflects both conditions within the combustion process of engine  20  and properties of the exhaust gas flow itself important to aftertreatment the exhaust gas. Engine  20  is also dynamic in as much as an engine may change from an idle state to a full-open throttle condition in a very short period of time. Schemes run by engine control module  25  must be able to react to the dynamic conditions of engine  20  in order to accurately control the various processes to keep engine  20  running efficiently and to manage exhaust gas flow aftertreatment. Therefore, accurate and timely estimation of the exhaust gas temperature is important to fuel and emission efficient operation of an engine. It should also be appreciated that while an embodiment is described utilizing temperature sensor  40  in an internal combustion engine exhaust gas flow process, the disclosure is equally valid in any flow of material in any process. 
         [0012]      FIG. 2  graphically depicts test results of a known system wherein readings are taken from temperature sensor  40  in the form of a thermocouple. An engine is operated in various states of operation and readings are taken from a thermocouple located in the exhaust system. The simulated gas temperature illustrated on the graph is generated by an off-line computer model and estimates the actual exhaust gas temperature. The actual temperature of the exhaust gas as simulated quickly changes over 400 Kelvin in around seven seconds. Both the readings of the thermocouple temperature and a simulation of the thermocouple temperature show that the thermocouple temperature lags several seconds behind the actual exhaust gas temperature and embodies an average temperature for the exhaust gas over time. The behavior of the thermocouple in the heated exhaust gas and the lag in thermocouple temperature readings can best be described by the specific heat equation, 
         [0000]        Q=m·c·ΔT    [1] 
         [0000]    wherein Q describes the heat energy applied to an object, m describes the mass of the object, c describes the property of specific heat of the object, and ΔT describes the resulting change in temperature to the object. The specific heat term, c, describes how much energy a mass unit of the material requires to increase temperature by a set amount. Heat energy, Q, flowing from high temperature exhaust gas, is transferred to the thermocouple, causing the thermocouple to rise by a temperature ΔT. The temperature of the thermocouple does not instantly change to the temperature of the exhaust gas flow, but rather the temperature of the thermocouple rises as heat flows into the thermocouple from the exhaust gas flow. This specific heat equation may used to show the relationship of heat to temperature rise per unit time by taking the time derivative of the equation. This equation becomes, 
         [0000]    
       
         
           
             
               
                 
                   
                     
                        
                       Q 
                     
                     
                        
                       t 
                     
                   
                   = 
                   
                     m 
                     · 
                     c 
                     · 
                     
                       
                          
                         T 
                       
                       
                          
                         t 
                       
                     
                   
                 
               
               
                 
                   [ 
                   2 
                   ] 
                 
               
             
           
         
       
     
         [0000]    showing that the rate of heat energy flow into an object with mass m and specific heat c is directly proportional to the rate of temperature increase. 
         [0013]    As described above, the rate of heat flow into the thermocouple dictates the resulting increase in temperature. Heat flow is described by three general forms of heat transfer: conduction, convection, and radiation. Conduction describes the flow of heat energy from one object to another object in direct connection to each other. The rate of heat transfer by conduction may be described by Fourier&#39;s Law, stating, 
         [0000]    
       
         
           
             
               
                 
                   
                     
                        
                       Q 
                     
                     
                        
                       t 
                     
                   
                   = 
                   
                     U 
                     · 
                     A 
                     · 
                     
                       ( 
                       
                         Δ 
                          
                         
                             
                         
                          
                         T 
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   3 
                   ] 
                 
               
             
           
         
       
     
         [0000]    wherein U equals conductance and A equals the cross-sectional area of contact between the two objects. Convection describes heat flow through a fluid or gaseous medium to an object. The rate of heat transfer by convection may be described by Newton&#39;s Law of Cooling, stating, 
         [0000]    
       
         
           
             
               
                 
                   
                     
                        
                       Q 
                     
                     
                        
                       t 
                     
                   
                   = 
                   
                     h 
                     · 
                     A 
                     · 
                     
                       ( 
                       
                         
                           T 
                           medium 
                         
                         - 
                         
                           T 
                           object 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   4 
                   ] 
                 
               
             
           
         
       
     
         [0000]    wherein h equals a heat transfer coefficient and A equals the surface area of the object exposed to the medium. Radiation describes heat flow from a hot object to another object across a gap in the form of electromagnetic radiation, for example infrared energy. The rate of heat transfer by radiation to a relatively small object enclosed by a larger surface may be described by the Stefan-Boltzmann Law, stating, 
         [0000]    
       
         
           
             
               
                 
                   
                     
                        
                       Q 
                     
                     
                        
                       t 
                     
                   
                   = 
                   
                     ɛ 
                     · 
                     σ 
                     · 
                     
                       A 
                       object 
                     
                     · 
                     
                       ( 
                       
                         
                           T 
                           surface 
                           4 
                         
                         - 
                         
                           T 
                           object 
                           4 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   [ 
                   5 
                   ] 
                 
               
             
           
         
       
     
         [0000]    wherein ε equals emissivity and σ equals Stefan&#39;s constant. One may sum the three previous equations to describe the total rate of heat transfer to an object. For a relatively small object surrounded by a surface and immersed in a gaseous medium, one may form an equation showing the effect of heat transfer upon the object to the temperature of that object by equating the specific heat equation to the sum of the heat transfer equations. The resulting equation, describing the relationship of the temperature of the object to the various forms of heat transfer, would be the following: 
         [0000]    
       
         
           
             
               
                 
                   
                     m 
                     · 
                     c 
                     · 
                     
                       
                          
                         
                           T 
                           object 
                         
                       
                       
                          
                         t 
                       
                     
                   
                   = 
                   
                     
                       U 
                       · 
                       A 
                       · 
                       
                         ( 
                         
                           Δ 
                            
                           
                               
                           
                            
                           T 
                         
                         ) 
                       
                     
                     + 
                     
                       h 
                       · 
                       
                         A 
                         object 
                       
                       · 
                       
                         ( 
                         
                           
                             T 
                             medium 
                           
                           - 
                           
                             T 
                             object 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       ɛ 
                       · 
                       σ 
                       · 
                       
                         A 
                         object 
                       
                       · 
                       
                         ( 
                         
                           
                             T 
                             surface 
                             4 
                           
                           - 
                           
                             T 
                             object 
                             4 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   [ 
                   6 
                   ] 
                 
               
             
           
         
       
     
         [0014]    Heat transfer rates are dependant upon the specific properties of the system being utilized.  FIG. 3  illustrates in cross-section an exemplary embodiment of a temperature sensor  40  in the form of a thermocouple located within an exhaust system  30  in accordance with the disclosure. Exhaust system  30  comprises an exhaust pipe  50  with walls  55 . Exhaust pipe  50  as depicted is assumed round in cross-section, however with only minor variations to resulting calculations by means well known in the art, exhaust system  30  could take virtually any shape and still be valid within this disclosure. Temperature sensor  40  is located within exhaust pipe  50  and is connected to outside devices by electrical lead  45 . As is well known in the art, the flow of gas through exhaust pipe  50  follows a cross-sectional profile, and it is preferable to use some means such as electrical lead  45  to place temperature sensor  40  within some portion of the flow away from wall  55 . The exhaust gas flow travels through exhaust pipe  50  and travels around temperature sensor  40 . Heat from the exhaust gas flow enters electrical lead  45  which may then transfer heat to temperature sensor  40  in the form of conductance. However, the cross-section of electrical lead  45  leading into the thermocouple in this particular embodiment is so small that this heat transfer by conductance can be said to be negligible. Heat from the exhaust gas flow enters temperature sensor  40  directly through convection, and this heat transfer may be described by Newton&#39;s Law of Cooling. Heat from the exhaust gas flow is transferred to walls  55 , which then radiate heat to temperature sensor  40 . This heat by radiation may be described by the Stefan-Boltzmann Law. The resulting equation describing the relationship of the change in temperature of a temperature sensor (“T TS ”) to the various sources of heat transfer becomes, 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       m 
                       TS 
                     
                     · 
                     
                       c 
                       TS 
                     
                     · 
                     
                       
                          
                         
                           T 
                           TS 
                         
                       
                       
                          
                         t 
                       
                     
                   
                   = 
                   
                     
                       
                         U 
                         TS 
                       
                       · 
                       
                         A 
                         contact 
                       
                       · 
                       
                         ( 
                         
                           
                             T 
                             lead 
                           
                           - 
                           
                             T 
                             TS 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       
                         h 
                         TS 
                       
                       · 
                       
                         A 
                         TS 
                       
                       · 
                       
                         ( 
                         
                           
                             T 
                             TS 
                           
                           - 
                           
                             T 
                             exhaustgas 
                           
                         
                         ) 
                       
                     
                     + 
                     
                       ɛ 
                       · 
                       σ 
                       · 
                       
                         A 
                         TS 
                       
                       · 
                       
                         ( 
                         
                           
                             T 
                             walls 
                             4 
                           
                           - 
                           
                             T 
                             TS 
                             4 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   [ 
                   7 
                   ] 
                 
               
             
           
         
       
     
         [0000]    One may solve this equation for an estimated exhaust gas temperature (“T exhaustgas ”), yielding, 
         [0000]    
       
         
           
             
               
                 
                   
                     T 
                     exhaustgas 
                   
                   = 
                   
                     
                       T 
                       TS 
                     
                     + 
                     
                       
                         
                           
                             m 
                             TS 
                           
                           · 
                           
                             c 
                             TS 
                           
                         
                         
                           
                             h 
                             TS 
                           
                           · 
                           
                             A 
                             TS 
                           
                         
                       
                       · 
                       
                         
                            
                           
                             T 
                             TS 
                           
                         
                         
                            
                           t 
                         
                       
                     
                     - 
                     
                       
                         
                           ɛ 
                           · 
                           σ 
                         
                         
                           h 
                           TS 
                         
                       
                       · 
                       
                         ( 
                         
                           
                             T 
                             walls 
                             4 
                           
                           - 
                           
                             T 
                             TS 
                             4 
                           
                         
                         ) 
                       
                     
                     - 
                     
                       
                         
                           
                             U 
                             TS 
                           
                           · 
                           
                             A 
                             contact 
                           
                         
                         
                           
                             h 
                             TS 
                           
                           · 
                           
                             A 
                             TS 
                           
                         
                       
                       · 
                       
                         ( 
                         
                           
                             T 
                             lead 
                           
                           - 
                           
                             T 
                             TS 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   [ 
                   8 
                   ] 
                 
               
             
           
         
       
     
         [0000]    In the particular embodiment described above, wherein the heat transfer by conductance is said to be negligible, the term in the above equation related to conductance drops out, and the equation becomes, 
         [0000]    
       
         
           
             
               
                 
                   
                     T 
                     exhaustgas 
                   
                   = 
                   
                     
                       T 
                       TS 
                     
                     + 
                     
                       
                         
                           
                             m 
                             TS 
                           
                           · 
                           
                             c 
                             TS 
                           
                         
                         
                           
                             h 
                             TS 
                           
                           · 
                           
                             A 
                             TS 
                           
                         
                       
                       · 
                       
                         
                            
                           
                             T 
                             TS 
                           
                         
                         
                            
                           t 
                         
                       
                     
                     - 
                     
                       
                         
                           ɛ 
                           · 
                           σ 
                         
                         
                           h 
                           TS 
                         
                       
                       · 
                       
                         ( 
                         
                           
                             T 
                             walls 
                             4 
                           
                           - 
                           
                             T 
                             TS 
                             4 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   [ 
                   9 
                   ] 
                 
               
             
           
         
       
     
         [0000]    T TS  is a measured value from the temperature sensor. dT TS /dt is a simple time derivative of the measured values from the temperature sensor which may be generated by a simple operation within a processor. T walls  is the temperature of walls  55  and is a value which is frequently modeled at different engine conditions and is readily available in the art. T lead  can be similarly derived and will frequently be a function of T walls . A TS , A contact , m TS , and ε are known values which may be programmed for a given temperature sensor. c TS , h TS , U TS  and σ are constants which may also be programmed. Because all of the values of the above equation may be determined in an in-vehicle setting on the basis of an incoming stream of T TS  values, T exhaustgas  may be calculated in real-time. The resulting T exhaustgas  value may then be used to adjust engine or aftertreatment parameters according to actual exhaust temperatures. 
         [0015]    The exemplary embodiment of temperature sensor  40  illustrated in  FIG. 3  is commonly known as an exposed junction thermocouple. However, it will be appreciated that the methods disclosed herein are widely applicable in any gas flow across varied designs of thermocouples as well as resistive temperature detection (RTD) devices such as wire RTD or semiconductor thermistors. For example, thermocouples and resistive temperature detection sensors can also be constructed with an exposed sensing element or with a sheath which covers the sensing element. The sensing element can be insulated from or in contact with the internal wall of the protective sheath. In these sheathed designs, the additional conductive energy flow across the sheath and an insulation layer could be accounted for using the same methods disclosed herein. Numerous methodologies are utilized in the design of temperature sensors, and this disclosure is not intended to be limited to the examples here described. By summing the energy flows entering and leaving the temperature sensor and equating these energy flows to the thermal properties of the temperature sensor, one may solve for the estimated actual gas temperature. In this way, various types of temperature sensors may be used to accurately estimate actual gas temperatures. 
         [0016]      FIG. 4  is a flowchart depicting an exemplary process  100  in accordance with the disclosure. At step  102 , temperature sensor  40  measures a temperature reading T TS . At step  104 , a processor is employed to apply a function estimating T exhaustgas  as a function of T TS . T exhaustgas  is then fed at step  106  to an engine control module or, in the case of a hybrid drive application, a powertrain control module. It should be noted that the processor of step  104  could be a physically independent unit from the control module of step  106 , or the processor could be integral to the control module. The control module of step  106  then issues control commands to the engine and to the aftertreatment components in step  108  in order to affect the engine controls and exhaust processing controls for improved fuel and emission efficiencies. Process  100 , in terms of information flow, ends at step  108 ; however, the dotted line at step  110  reflects that the control commands affected at step  108  clearly have an effect on exhaust temperature as engine operation is modulated. 
         [0017]      FIG. 5  graphically depicts test results of a system wherein engine readings from temperature sensor  40  are used to estimate T exhaustgas  in accordance with the disclosure. This graph compares the T exhaustgas  estimate generated by actual thermocouple readings applied to the above equation and a simulated exhaust gas temperature generated by an off-line computer model simulating actual exhaust gas temperatures. The graph shows T exhaustgas  closely tracking the simulated exhaust gas temperature without the lag or averaging effect apparent to the results of  FIG. 2 . 
         [0018]    The disclosure has described certain preferred embodiments and modifications thereto. Further modifications and alterations may occur to others upon reading and understanding the specification. Therefore, it is intended that the disclosure not be limited to the particular embodiment(s) disclosed as the best mode contemplated for carrying out this disclosure, but that the disclosure will include all embodiments falling within the scope of the appended claims.