Abstract:
Methods and systems for regenerating an after treatment device are disclosed. In one example, the possibility of introducing fuel to oil during after treatment device regeneration is reduced. The methods and systems may reduce engine degradation and improve engine emissions.

Description:
BACKGROUND/SUMMARY 
       [0001]    Diesel engines have relatively high efficiency as compared to other internal combustion engines. With the higher engine efficiency comes lower engine exhaust temperatures. Lower exhaust temperatures can make regeneration of after treatment devices more difficult because after treatment devices often begin to regenerate at higher temperatures. One way to produce higher temperatures in an exhaust system is to inject fuel late in a cylinder cycle (e.g., during an exhaust stroke) so that the fuel can oxidize in the exhaust system, thereby increasing the exhaust system temperature. However, when liquid fuel is injected in an exhaust stroke, some portion of the injected fuel can impinge on cylinder walls in liquid form. Fuel that encounters cylinder walls in liquid form may degrade the oil film on the cylinder wall and increase cylinder wall wear. Further, liquid fuel may enter the engine crankcase and dilute engine oil. Consequently, it may be desirable to reduce the amount of injected liquid fuel that reaches cylinder walls during injection. 
         [0002]    In European patent application EP 1,798,404 A1, a method for regenerating an after treatment device via post injection control is described. The method estimates a fuel spray brakeup length based on a differential pressure between an interior and exterior of an injector hole. The method adjusts fuel injection time so that the fuel spray brakeup length is less than a distance S to a cylinder wall. However, the fuel spray brakeup length as determined via a delta pressure may not be as accurate as is desired. Consequently, fuel spray may still impinge on cylinder walls during some conditions. 
         [0003]    The inventor herein has recognized the above-mentioned disadvantages and have developed a method for regenerating an exhaust after treatment device, comprising: performing combustion in a cylinder of an engine during a cylinder cycle; injecting an amount of fuel in a fuel injection pulse after a combustion event in the cylinder and before exhaust valve closing during the cylinder cycle, the amount of fuel in the fuel injection pulse adjusted for a density of a gas mixture in the cylinder; and regenerating an after treatment device via the amount of fuel. 
         [0004]    By adjusting a post injection fuel quantity in response to cylinder mixture density, it may be possible to better estimate an amount of fuel injected that impinges on a cylinder wall in liquid form so that fuel injected for after treatment device regeneration is less than the amount that impinges on the cylinder wall in liquid form when injected. In particular, an estimate of fuel spray penetration may be improved by accounting for cylinder density and temperature. Cylinder mixture density and temperature provide a more accurate estimate of fuel spray penetration than cylinder pressure or injector delta pressure since cylinder mixture density and temperature account for both fuel evaporation and momentum transfer. 
         [0005]    Additionally, the inventor has also determined that cylinder volumetric efficiency is another parameter that may be accounted for to improve fuel spray penetration estimates. Cylinder volumetric efficiency can affect temperature of gases in a cylinder as well as fractions of air and residual exhaust gas that make up a cylinder mixture. In this way, cylinder volumetric efficiency can affect density and temperature within the cylinder at the time of injection. Consequently, by considering cylinder mixture density, cylinder volumetric efficiency, and temperature, timing of a post injection fuel amount may be improved so that fuel spray more closely approaches a cylinder wall, yet does not impinge on the cylinder wall in liquid form. As a result, larger amounts of fuel may be injected into a cylinder without causing fuel to impinge on cylinder walls in liquid form. 
         [0006]    The present description may provide several advantages. In particular, the approach may reduce engine degradation. Further, the present approach may reduce engine emissions by reducing engine oil dilution. Further still, the approach may be applied without costly in-cylinder sensors. Additionally, the approach may increase an engine oil change interval and/or allow for a smaller oil sump containing less oil. 
         [0007]    The above advantages and other advantages, and features of the present description will be readily apparent from the following Detailed Description when taken alone or in connection with the accompanying drawings. 
         [0008]    It should be understood that the summary above is provided to introduce in simplified form a selection of concepts that are further described in the detailed description. It is not meant to identify key or essential features of the claimed subject matter, the scope of which is defined uniquely by the claims that follow the detailed description. Furthermore, the claimed subject matter is not limited to implementations that solve any disadvantages noted above or in any part of this disclosure. 
     
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         [0009]      FIG. 1  shows a schematic depiction of an engine; 
           [0010]      FIG. 2  shows an example fuel spray penetration length; 
           [0011]      FIGS. 3A-3B  show example plots of how cylinder mixture density and temperature can affect fuel spray penetration length; and 
           [0012]      FIG. 4  shows an example method for regenerating an after treatment device. 
       
    
    
     DETAILED DESCRIPTION 
       [0013]    The present description is related to regenerating an exhaust after treatment device.  FIG. 1  shows one example of a boosted diesel engine where the method of  FIG. 4  initiates after treatment device regeneration via controlling post combustion fuel injection.  FIG. 2  shows an example fuel spray penetration length which provides a basis for an amount of fuel that may be injected to initiate after treatment device regeneration.  FIGS. 3A-3B  illustrate how cylinder mixture density and pressure influence fuel spray penetration. Finally,  FIG. 4  is an example method for regenerating a particulate filter. 
         [0014]    Referring to  FIG. 1 , internal combustion engine  10 , comprising a plurality of cylinders, one cylinder of which is shown in  FIG. 1 , is controlled by electronic engine controller  12 . Engine  10  includes combustion chamber  30  and cylinder walls  32  with piston  36  positioned therein and connected to crankshaft  40 . Combustion chamber  30  is shown communicating with intake manifold  44  and exhaust manifold  48  via respective intake valve  52  and exhaust valve  54 . Each intake and exhaust valve may be operated by an intake cam  51  and an exhaust cam  53 . The position of intake cam  51  may be determined by intake cam sensor  55 . The position of exhaust cam  53  may be determined by exhaust cam sensor  57 . 
         [0015]    Fuel injector  66  is shown positioned to inject fuel directly into combustion chamber  30 , which is known to those skilled in the art as direct injection. Fuel injector  66  delivers fuel in proportion to the pulse width of signal from controller  12 . Fuel is delivered to fuel injector  66  by a fuel system (not shown) including a fuel tank, fuel pump, fuel rail (not shown). Fuel pressure delivered by the fuel system may be adjusted by varying a position valve regulating flow to a fuel pump (not shown). In addition, a metering valve may be located in or near the fuel rail for closed loop fuel control. A pump metering valve may also regulate fuel flow to the fuel pump, thereby reducing fuel pumped to a high pressure fuel pump. 
         [0016]    Intake manifold  44  is shown communicating with optional electronic throttle  62  which adjusts a position of throttle plate  64  to control air flow from intake boost chamber  46 . Compressor  162  draws air from air intake  42  to supply boost chamber  46 . Exhaust gases spin turbine  164  which is coupled to compressor  162  via shaft  161 . In some examples, a charge air cooler may be provided. Compressor speed may be adjusted via adjusting a position of variable vane control  72  or compressor bypass valve  158 . In alternative examples, a waste gate  74  may replace or be used in addition to variable vane control  72 . Variable vane control  72  adjusts a position of variable geometry turbine vanes. Exhaust gases can pass through turbine  164  supplying little energy to rotate turbine  164  when vanes are in an open position. Exhaust gases can pass through turbine  164  and impart increased force on turbine  164  when vanes are in a closed position. Alternatively, wastegate  74  allows exhaust gases to flow around turbine  164  so as to reduce the amount of energy supplied to the turbine. Compressor bypass valve  158  allows compressed air at the outlet of compressor  162  to be returned to the input of compressor  162 . In this way, the efficiency of compressor  162  may be reduced so as to affect the flow of compressor  162  and reduce intake manifold pressure. 
         [0017]    Combustion is initiated in combustion chamber  30  when fuel ignites without an externally provided spark as piston  36  approaches top-dead-center compression stroke. In some examples, a universal Exhaust Gas Oxygen (UEGO) sensor  126  may be coupled to exhaust manifold  48  upstream of emissions device  70 . In other examples, the UEGO sensor may be located downstream of one or more exhaust after treatment devices. Further, in some examples, the UEGO sensor may be replaced by a NOx sensor that has both NOx and oxygen sensing elements. 
         [0018]    At lower engine temperatures glow plug  68  may convert electrical energy into thermal energy so as to raise a temperature in combustion chamber  30 . By raising temperature of combustion chamber  30 , it may be easier to ignite a cylinder air-fuel mixture via compression. 
         [0019]    Emissions device  70  can include a particulate filter and catalyst bricks, in one example. In another example, multiple emission control devices, each with multiple bricks, can be used. Emissions device  70  can include an oxidation catalyst in one example. In other examples, the emissions device may include a lean NOx trap or a selective catalyst reduction (SCR), and/or a diesel particulate filter (DPF). 
         [0020]    Exhaust gas recirculation (EGR) may be provided to the engine via EGR valve  80 . EGR valve  80  is a three-way valve that closes or allows exhaust gas to flow from downstream of emissions device  70  to a location in the engine air intake system upstream of compressor  162 . In alternative examples, EGR may flow from upstream of turbine  164  to intake manifold  44 . EGR may bypass EGR cooler  85 , or alternatively, EGR may be cooled via passing through EGR cooler  85 . In other, examples high pressure and low pressure EGR system may be provided. 
         [0021]    Controller  12  is shown in  FIG. 1  as a conventional microcomputer including: microprocessor unit  102 , input/output ports  104 , read-only memory  106 , random access memory  108 , keep alive memory  110 , and a conventional data bus. Controller  12  is shown receiving various signals from sensors coupled to engine  10 , in addition to those signals previously discussed, including: engine coolant temperature (ECT) from temperature sensor  112  coupled to cooling sleeve  114 ; a position sensor  134  coupled to an accelerator pedal  130  for sensing accelerator position adjusted by foot  132 ; a measurement of engine manifold pressure (MAP) from pressure sensor  121  coupled to intake manifold  44 ; boost pressure from pressure sensor  122  exhaust gas oxygen concentration from oxygen sensor  126 ; an engine position sensor from a Hall effect sensor  118  sensing crankshaft  40  position; a measurement of air mass entering the engine from sensor  120  (e.g., a hot wire air flow meter); and a measurement of throttle position from sensor  58 . Barometric pressure and exhaust pressure may also be sensed (sensor not shown) or inferred for processing by controller  12 . In a preferred aspect of the present description, engine position sensor  118  produces a predetermined number of equally spaced pulses every revolution of the crankshaft from which engine speed (RPM) can be determined. 
         [0022]    During operation, each cylinder within engine  10  typically undergoes a four stroke cycle: the cycle includes the intake stroke, compression stroke, expansion stroke, and exhaust stroke. During the intake stroke, generally, the exhaust valve  54  closes and intake valve  52  opens. Air is introduced into combustion chamber  30  via intake manifold  44 , and piston  36  moves to the bottom of the cylinder so as to increase the volume within combustion chamber  30 . The position at which piston  36  is near the bottom of the cylinder and at the end of its stroke (e.g. when combustion chamber  30  is at its largest volume) is typically referred to by those of skill in the art as bottom dead center (BDC). During the compression stroke, intake valve  52  and exhaust valve  54  are closed. Piston  36  moves toward the cylinder head so as to compress the air within combustion chamber  30 . The point at which piston  36  is at the end of its stroke and closest to the cylinder head (e.g. when combustion chamber  30  is at its smallest volume) is typically referred to by those of skill in the art as top dead center (TDC). In a process hereinafter referred to as injection, fuel is introduced into the combustion chamber. In some examples, fuel may be injected to a cylinder a plurality of times during a single cylinder cycle. In a process hereinafter referred to as ignition, the injected fuel is ignited by compression ignition resulting in combustion. During the expansion stroke, the expanding gases push piston  36  back to BDC. Crankshaft  40  converts piston movement into a rotational torque of the rotary shaft. Finally, during the exhaust stroke, the exhaust valve  54  opens to release the combusted air-fuel mixture to exhaust manifold  48  and the piston returns to TDC. Note that the above is described merely as an example, and that intake and exhaust valve opening and/or closing timings may vary, such as to provide positive or negative valve overlap, late intake valve closing, or various other examples. Further, in some examples a two-stroke cycle may be used rather than a four-stroke cycle. 
         [0023]    Thus, the system of  FIG. 1  provides for an engine including a cylinder and an exhaust system; an after treatment device in an exhaust system; a fuel injector supplying fuel to the cylinder; and a controller including instructions stored in non-transitory memory to regenerate an after treatment device, the controller including additional instructions to adjust an amount of fuel supplied to the cylinder via the fuel injector in response to cylinder volumetric efficiency and a temperature of gas in the cylinder after a combustion event in the cylinder during a present cycle of the cylinder, the amount of fuel injected after the combustion event and before an exhaust valve closing of the cylinder during a cycle of the cylinder. 
         [0024]    The system of  FIG. 1  includes where the amount of fuel injected is less than an amount of injected fuel that leads to liquid fuel impingement on cylinder wall. The engine system further comprises additional controller instructions for providing a plurality of fuel injections after the combustion event and before the exhaust valve closing. The engine system further comprises additional controller instructions to inject fuel to a second cylinder after a combustion event in the second cylinder during a present cylinder cycle of the second cylinder and in response to volumetric efficiency of the second cylinder. The engine system further comprises evenly distributing a remainder of a post injection fuel quantity for a cylinder cycle between a maximum number of fuel injections that occur after combustion in the cylinder and before exhaust valve closing in the cylinder. 
         [0025]    Referring now to  FIG. 2 , an example fuel spray penetration length is shown. Fuel injector nozzle  216  provides fuel to combustion chamber  30  in the form of a spray that has an upper spray cone boundary  210 , spray cone centerline  211 , and a lower spray cone boundary  214 . The distance between nozzle  216  and the cylinder wall  230  via the spray cone centerline  211  is indicated by L 1 . Distance L 1  is the distance of greatest fuel spray penetration into the cylinder. Thus, distance L 1  is a distance that determines how far fuel spray penetration is allowed to go before fuel impinges on the cylinder wall. Consequently, fuel penetration length is adjusted to a distance less than L 1  via controlling the fuel injector on time. 
         [0026]    Referring now to  FIG. 3A , it shows a plot of a relationship between fuel liquid penetration and cylinder temperature for a constant density injection environment. The X axis represents cylinder mixture temperature and the Y axis represents fuel liquid penetration length or distance. It can be observed that fuel liquid penetration decreases with increasing injection environment temperature (e.g., increasing cylinder temperature). 
         [0027]      FIG. 3B  shows a plot of fuel spray liquid penetration versus fuel density at a constant temperature. The X axis represents cylinder mixture density and the Y axis represents fuel spray liquid penetration. The plot shows that fuel spray liquid penetration increases with decreasing cylinder density. Therefore, if the cylinder mixture density is at a higher level, the fuel spray liquid cannot penetrate into the cylinder as far as when cylinder density is lower, during constant temperature conditions. Consequently, the fuel injector on time may be increased at higher cylinder densities so that more fuel may be injected without encountering the cylinder walls. Thus,  FIGS. 3A-3B  show that cylinder mixture density and temperature are useful for determining fuel spray penetration distance. 
         [0028]    Referring now to  FIG. 4 , it shows an example method for regenerating an after treatment device while reducing the possibility of fuel in oil. The method of  FIG. 4  is described in terms of a single cylinder, but it may be applied to all engine cylinders. The method of  FIG. 4  may be stored as executable instructions in non-transitory memory of controller  12  shown in  FIG. 1 . Further, the method of  FIG. 4  may provide the operating sequence shown in  FIG. 3 . 
         [0029]    At  401 , method  400  judges whether or not after treatment device regeneration is desired. In one example, the after treatment device is a diesel particulate filter (DPF). In another example, the after treatment device is a LNT. In the example where the after treatment device is a DPF, method  400  may judge that DPF regeneration is desired when a pressure drop across the DPF is greater than a threshold value. If method  400  judges that it is desirable to regenerate the DPF, the answer is yes and method  400  proceeds to  402 . Otherwise, the answer is no and method  400  proceeds to exit. 
         [0030]    At  402 , method  400  injects and combusts a main fuel injection pulse. The main fuel injection pulse may be injected to the cylinder during a compression stroke of the cylinder, or during both the compression and expansion strokes. Further, in some examples pilot injections precede the main injection. The main injection may take place during the compression stroke, the expansion stroke, or during both the compression and expansion strokes. Further still, in some examples, one or more injections that participate in combustion in the cylinder during a cylinder cycle may be injected after the main fuel injection amount. These injections may be described as combusting post injections. 
         [0031]    At  404 , method  400  determines a post injection fuel quantity. The post injection fuel quantity is a fuel amount in defined in mg/stroke or similar units. A post injection fuel quantity is an amount of fuel injected to a single cylinder, and fuel delivered to the after treatment device may be injected to one or more cylinders. Fuel may be injected to each cylinder of a group of cylinders during a time period after combustion in the cylinder and before the exhaust valve of the cylinder closes. 
         [0032]    In one example, the post injection fuel quantity is an amount of fuel injected to a cylinder after a combustion event in the cylinder and before intake valves of the cylinder open. The post fuel injection amount or quantity is determined via a table of empirically determined values that are indexed based on engine speed and load. Additionally, fuel injected after combustion may be injected in response to after treatment device temperature such that the fuel injection amount is adjusted to increase or decrease the after treatment device temperature. Method  400  proceeds to  406  after the desired post injection fuel quantity is determined. 
         [0033]    At  406 , method  400  determines mass in a cylinder receiving a post fuel injection quantity at the time fuel is injected to the cylinder. In one example, in-cylinder mass is determined as a function of mass air flow into the cylinder, cylinder EGR amount, engine speed, exhaust pressure, volumetric efficiency, and an amount of fuel injected to the cylinder before combustion in the cylinder during a cycle of the cylinder (e.g., fuel injected before post injection). In particular, air mass in the cylinder is determined from a mass air flow sensor, cylinder EGR mass is determined from air intake oxygen concentration, exhaust oxygen concentration, intake manifold pressure, intake manifold temperature, engine speed, and mass air flow into the engine. In one example, EGR mass is determined according to the following equation: 
         [0000]    
       
         
           
             EGR 
             = 
             
               
                 1 
                 - 
                 
                   
                     O 
                     
                       2 
                       , 
                       int 
                     
                   
                   20.95 
                 
               
               
                 1 
                 - 
                 
                   
                     O 
                     
                       2 
                       , 
                       exh 
                     
                   
                   20.95 
                 
               
             
           
         
       
     
         [0000]    where O 1, int  is intake oxygen concentration, O 2, exh  is exhaust oxygen concentration, and 20.95 is an approximation of oxygen percentage in air. In another example, EGR amount may be determined according to the following equation: 
         [0000]    
       
         
           
             EGR 
             = 
             
               1 
               - 
               
                 
                   
                     m 
                     air 
                   
                   · 
                   R 
                   · 
                   
                     T 
                     man 
                   
                   · 
                   2 
                   · 
                   1000 
                 
                 
                   
                     P 
                     man 
                   
                   · 
                   N 
                   · 
                   60 
                   · 
                   
                     V 
                     disp 
                   
                   · 
                   
                     η 
                     vol 
                   
                 
               
             
           
         
       
     
         [0000]    where m air  is mass of air entering the engine, R is a gas constant, T man  is intake manifold temperature, Pman is intake manifold pressure, N is engine speed, V displ  is engine displacement, and η vol  is volumetric efficiency. 
         [0034]    The portion of mass in the cylinder attributable to injected fuel is based on the mass of fuel that is injected before the post injection fuel. The amount of fuel injected before the post injected fuel may be determined from a desired fuel injection quantity for combustion. 
         [0035]    Mass in the cylinder is further adjusted in response to engine volumetric efficiency. In one example, engine volumetric efficiency is estimated based on empirical data stored in tables or functions in controller memory. The volumetric efficiency data may be indexed based on engine speed, engine load, and engine valve timing. Alternatively, volumetric efficiency may be adjusted based on sampled or inferred exhaust pressure. Cylinder density is adjusted based on the determined engine volumetric efficiency. For example, if engine volumetric efficiency is determined to be reduced, it may be determined that additional residual is in the cylinders, thereby increasing the cylinder temperature and/or lowering cylinder mixture density. Volumetric efficiency adjust the mass of residuals (e.g., internal EGR) in the cylinder and then fuel mass, air mass, and external EGR mass (are summed together to determine mass of the cylinder mixture. Method  400  proceeds to  408  after determining the in cylinder mass. 
         [0036]    The above cylinder mass determination process applies if fuel injection occurs before EVO. However, if fuel injection occurs after EVO the above estimate of cylinder mixture mass may be reduced in response to time since EVO, engine speed, and crankshaft angle change since EVO. In one example, the change in cylinder mixture mass is adjusted based on an empirically determined multiplier that is stored in memory and indexed according engine speed, time since EVO, and crankshaft angle change since EVO. In an alternative example, in cylinder mixture density can be estimated via exhaust pressure and temperature according to the ideal gas law if fuel injection is after EVO. In particular, the cylinder pressure and exhaust pressure may be assumed as equal when determining cylinder mixture density. 
         [0037]    At  408 , method  400  estimates in cylinder temperature at the time fuel is injected for the post fuel injection during a cylinder cycle. In one example, temperature in a cylinder is determined according to the following equations: 
         [0000]      PV n =C 
         [0000]    where P is cylinder pressure, V is cylinder volume at a specific crankshaft angle, n is a constant between 1.3 and 1.4, and C is a constant. Constant C can be equated to a cylinder pressure at a cylinder volume such that the following equation may be formed: 
         [0000]      P 1 V 1   n =P 2 V 2   n    
         [0000]    Solving for the ratio of pressures: 
         [0000]    
       
         
           
             
               
                 P 
                 1 
               
               
                 P 
                 2 
               
             
             = 
             
               
                 ( 
                 
                   
                     V 
                     2 
                   
                   
                     V 
                     1 
                   
                 
                 ) 
               
               n 
             
           
         
       
     
         [0000]    According to the ideal gas law: 
         [0000]    
       
         
           
             
               
                 P 
                 1 
               
                
               
                 V 
                 1 
               
             
             = 
             
               
                 
                   mRT 
                   1 
                 
                 ⇒ 
                 
                   
                     
                       P 
                       1 
                     
                      
                     
                       V 
                       1 
                     
                   
                   
                     T 
                     1 
                   
                 
               
               = 
               mR 
             
           
         
       
       
         
           
             
               
                 P 
                 2 
               
                
               
                 V 
                 2 
               
             
             = 
             
               
                 
                   mRT 
                   2 
                 
                 ⇒ 
                 
                   
                     
                       P 
                       2 
                     
                      
                     
                       V 
                       2 
                     
                   
                   
                     T 
                     2 
                   
                 
               
               = 
               mR 
             
           
         
       
     
         [0000]    where m is a number of moles of a gas, R is the gas constant, and T 1  and T 2  are temperatures of the gas at P 1  V 1  and P 2  V 2 . In particular T 1  is temperature at exhaust valve opening, V 1  is cylinder volume at exhaust valve opening, V 2  is a cylinder volume at a time in the exhaust stroke, and T 2  is a cylinder temperature during the exhaust stroke. Substituting yields: 
         [0000]    
       
         
           
             
               
                 
                   P 
                   1 
                 
                  
                 
                   V 
                   1 
                 
               
               
                 T 
                 1 
               
             
             = 
             
               
                 
                   
                     
                       P 
                       2 
                     
                      
                     
                       V 
                       2 
                     
                   
                   
                     T 
                     2 
                   
                 
                 ⇒ 
                 
                   
                     P 
                     1 
                   
                   
                     P 
                     2 
                   
                 
               
               = 
               
                 
                   
                     V 
                     2 
                   
                    
                   
                     T 
                     1 
                   
                 
                 
                   
                     V 
                     1 
                   
                    
                   
                     T 
                     2 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 and 
                  
                 
                   
 
                 
                 ( 
                 
                   
                     V 
                     2 
                   
                   
                     V 
                     1 
                   
                 
                 ) 
               
               n 
             
             = 
             
               
                 
                   
                     
                       V 
                       2 
                     
                      
                     
                       T 
                       1 
                     
                   
                   
                     
                       V 
                       1 
                     
                      
                     
                       T 
                       2 
                     
                   
                 
                 ⇒ 
                 
                   
                     ( 
                     
                       
                         V 
                         2 
                       
                       
                         V 
                         1 
                       
                     
                     ) 
                   
                   
                     n 
                     - 
                     1 
                   
                 
               
               = 
               
                 
                   T 
                   1 
                 
                 
                   T 
                   2 
                 
               
             
           
         
       
     
         [0000]    which given T 1  can be solved for T 2 . T 1  can be estimated via lookup tables that are indexed based on engine speed and load. Method  400  proceeds to  410  after cylinder temperature is estimated. 
         [0038]    In the cylinder temperature estimate of  408 , temperature T 1  is at or before EVO, and T 1  decreases as a function of time since EVO, crankshaft angle after EVO, and ECT when fuel injection is after EVO. The amount that T 1  is decreased after EVO may be empirically determined and stored in memory for later use. The T 1  temperature adjustment may be indexed via time since EVO, crankshaft angle since EVO, and ECT. 
         [0039]    At  410 , method  400  determines start of fuel injection timing for the post injection fuel quantity. In one example, the start of fuel injection timing is empirically determined and stored in table or functions in controller memory. The tables or functions may be indexed via engine speed, engine load, injection timing during the intake and compression strokes, engine temperature, and intake air temperature. For example, start of injection timing for injecting post combustion fuel may be based on an amount of time or crankshaft degrees since end of combustion. End of combustion time may be estimated based on empirically determined cylinder temperatures and pressures. When multiple post injections to a cylinder are provided during a single cycle of the cylinder, start of injection timing for each post fuel injection after the first post fuel injection occur at a start of injection time that is the end of injection time for the last injection event of the cylinder plus an amount of time that it take to reopen the fuel injector. The start of fuel injection timing for each post fuel injection is determined and method  400  proceeds to  412 . Note again that post fuel injections occur after combustion in the cylinder and before exhaust valve closing. 
         [0040]    At  412 , method  400  determines the quantity of post injection fuel that may be injected in a single injection without liquid fuel in fuel spray impinging on the cylinder wall. As noted above, the desired post injection fuel quantity determined at  404  may be injected to one or more engine cylinders via a plurality fuel injections. For example, each cylinder of a cylinder bank may provide two post injections for four cylinder cycles until the total desired post injection fuel quantity is injected to regenerate a DPF. 
         [0041]    In one example, the quantity limit for one fuel injection provided to a cylinder is determined via looking up calculated or empirically determined fuel injection amounts that are stored in functions or tables that are indexed via cylinder mixture temperature, cylinder density, and bio-fuel content in the fuel being injected. In one example, the post injection fuel quantity is expressed as: 
         [0000]        Q   post, max   =f (ρ( CA ),  T ( CA ))
 
         [0000]    where Q post, max  is a maximum post injection fuel amount for a single injection event after combustion and before exhaust valve closing, ρ is cylinder mixture density as a function of crankshaft angle, T is cylinder gas mixture temperature as a function of crankshaft angle. The cylinder density is based on mass in the cylinder and cylinder volume. In some examples, the post injection fuel amount final crankshaft angle may be estimated and iteratively adjusted so that the post injection quantity can be determined based on the cylinder density and temperature at the end of injection timing. Thus, in one example, the post fuel injection amount is based on end of post fuel injection timing. 
         [0042]    At  414 , method  400  injects as many maximum post injection amounts as determined at  410  as is possible during a cylinder cycle limited by the post injection fuel quantity at  404 . If the post injection fuel quantity cannot be injected during as many fuel injections as may be provided in a cylinder cycle, the remaining fuel is split between all post injections during the present cylinder cycle. Thus, for a given cylinder during a given cycle, there is a target or desired post fuel injection quantity specified in mg. The target or desired post fuel injection quantity is split into multiple pulses after combustion in the cylinder and before EVC. Any remainder fuel is determined via equations that subtract the maximum post fuel injection quantity for a given pulse from the target or desired total post fuel injection quantity for one cylinder and one cycle. This operation is performed iteratively until there is no more fuel or no more pulses available. Since the desired post fuel injection quantity must be reached, the remaining fuel is split between the pulses. For example, any remaining fuel that does not fit in the amount of time between end of combustion in the cylinder and EVC is added to the injection quantity of each fuel injection after combustion in the cylinder and before EVC. Such an operation may minimize the possibility of wall wetting. For example, in one example, the desired post injection fuel quantity can be updated via the following equations: 
         [0000]    
       
      
       Q 
       post 
       −Q 
       inj 
       =Q 
       re 
       
         m  
       
      
     
         [0000]      Q post =Q rem    
         [0000]    where Q post  is the desired amount of post injection fuel as determined at  404 , where Q inj  is the amount of fuel injected during a most recent individual post fuel injection, and where Q rem  is a remainder resulting from subtracting the most recent fuel injection amount from the desired amount of post injection fuel. Method  400  proceeds to exit after the post fuel injections for a cylinder cycle are scheduled and/or injected. 
         [0043]    Thus, the method of  FIG. 4  provides for a method for regenerating an exhaust after treatment device, comprising: performing combustion in a cylinder of an engine during a cylinder cycle; injecting an amount of fuel in a fuel injection pulse after a combustion event in the cylinder and before exhaust valve closing during the cylinder cycle, the amount of fuel in the fuel injection pulse adjusted for a density of a gas mixture in the cylinder; and regenerating an after treatment device via the amount of fuel. The method includes where the density is adjusted for an amount of exhaust gas in the cylinder before performing combustion in the cylinder of the engine during the cylinder cycle. The method also includes where the density is adjusted for an amount of fuel injected to the cylinder that participates in combustion during the cylinder cycle. 
         [0044]    In some examples, the method further comprises providing additional fuel injections to the cylinder during the cylinder cycle after the combustion event and before exhaust valve closing during the cylinder cycle and adjusting the amount of fuel in the fuel injection pulse in response to a temperature of the gas mixture in the cylinder. The method includes where the fuel injection pulse is one of a plurality of fuel pulses that sum to a desired post injection fuel quantity to regenerate an after treatment device, and further comprising adjusting the amount of fuel in the fuel injection pulse in response to a cylinder air amount inducted into the cylinder. The method further comprises adjusting the amount of fuel in the fuel injection pulse in response to a volumetric efficiency of the engine. The method includes where the amount of fuel injected is less than an amount of injected fuel that leads to liquid fuel impingement on cylinder wall. The method further comprises where the amount of fuel in the fuel injection pulse is adjusted in response to an estimated temperature in the cylinder at a time when the amount of fuel in the fuel injection is injected. 
         [0045]    The method of  FIG. 4  also provides for regenerating an exhaust after treatment device, comprising: performing combustion in a cylinder of an engine during a cylinder cycle; injecting an amount of fuel in a fuel injection pulse after combustion in the cylinder and before exhaust valve closing during the cylinder cycle, the amount of fuel in the fuel injection pulse adjusted for a cylinder volumetric efficiency; and regenerating an after treatment device via the amount of fuel. In this way, the amount of post injected fuel accounts for a change in engine volumetric efficiency that can change liquid fuel penetration in the cylinder. 
         [0046]    In one example, the method further comprises additional fuel injections to the cylinder during the cylinder cycle after combustion and before exhaust valve closing during the cylinder cycle and adjusting the amount of fuel injected in the fuel injection pulse in response to a temperature of a gas mixture in the cylinder. The method includes where the fuel injection pulse is one of a plurality of fuel pulses that sum to a desired post injection fuel quantity to regenerate an after treatment device. The method further comprises adjusting a subsequent fuel injection pulse that is injected to the cylinder after combustion and before exhaust valve closing in the cylinder during a subsequent cylinder cycle, the subsequent fuel injection pulse based on an amount of fuel remaining to be injected that when added to an amount of fuel already injected equals the desired post injection quantity. The method includes were the volumetric efficiency of the cylinder is estimated based on engine speed and load. The method includes where the volumetric efficiency is further based on cam timing. The method further comprises reducing a desired post injection fuel amount based on the amount of fuel in the fuel injection pulse and iteratively further reducing the desired post injection fuel amount based on fuel injected to the cylinder after injecting the amount of fuel in the fuel injection pulse. 
         [0047]    As will be appreciated by one of ordinary skill in the art, the method described in  FIG. 4  may represent one or more of any number of processing strategies such as event-driven, interrupt-driven, multi-tasking, multi-threading, and the like. As such, various steps or functions illustrated may be performed in the sequence illustrated, in parallel, or in some cases omitted. Likewise, the order of processing is not necessarily required to achieve the objects, features, and advantages described herein, but is provided for ease of illustration and description. Although not explicitly illustrated, one of ordinary skill in the art will recognize that one or more of the illustrated steps, methods, or functions may be repeatedly performed depending on the particular strategy being used. 
         [0048]    This concludes the description. The reading of it by those skilled in the art would bring to mind many alterations and modifications without departing from the spirit and the scope of the description. For example, single cylinder, 12, 13, 14, 15, V6, V8, V10, V12 and V16 engines operating in natural gas, gasoline, diesel, or alternative fuel configurations could use the present description to advantage.