CN106481446B - Method for calculating the pressure drop across a flow-blocking component - Google Patents

Method for calculating the pressure drop across a flow-blocking component Download PDF

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CN106481446B
CN106481446B CN201610721263.0A CN201610721263A CN106481446B CN 106481446 B CN106481446 B CN 106481446B CN 201610721263 A CN201610721263 A CN 201610721263A CN 106481446 B CN106481446 B CN 106481446B
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flow
pressure drop
function
pressure
interpolation
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CN106481446A (en
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A.布劳恩
R.迪尔施维格尔
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Robert Bosch GmbH
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F02—COMBUSTION ENGINES; HOT-GAS OR COMBUSTION-PRODUCT ENGINE PLANTS
    • F02D—CONTROLLING COMBUSTION ENGINES
    • F02D41/00—Electrical control of supply of combustible mixture or its constituents
    • F02D41/0002—Controlling intake air
    • F02D41/0007—Controlling intake air for control of turbo-charged or super-charged engines
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F02—COMBUSTION ENGINES; HOT-GAS OR COMBUSTION-PRODUCT ENGINE PLANTS
    • F02B—INTERNAL-COMBUSTION PISTON ENGINES; COMBUSTION ENGINES IN GENERAL
    • F02B37/00—Engines characterised by provision of pumps driven at least for part of the time by exhaust
    • F02B37/12—Control of the pumps
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F02—COMBUSTION ENGINES; HOT-GAS OR COMBUSTION-PRODUCT ENGINE PLANTS
    • F02B—INTERNAL-COMBUSTION PISTON ENGINES; COMBUSTION ENGINES IN GENERAL
    • F02B37/00—Engines characterised by provision of pumps driven at least for part of the time by exhaust
    • F02B37/12—Control of the pumps
    • F02B37/18—Control of the pumps by bypassing exhaust from the inlet to the outlet of turbine or to the atmosphere
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F02—COMBUSTION ENGINES; HOT-GAS OR COMBUSTION-PRODUCT ENGINE PLANTS
    • F02B—INTERNAL-COMBUSTION PISTON ENGINES; COMBUSTION ENGINES IN GENERAL
    • F02B37/00—Engines characterised by provision of pumps driven at least for part of the time by exhaust
    • F02B37/12—Control of the pumps
    • F02B37/24—Control of the pumps by using pumps or turbines with adjustable guide vanes
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F02—COMBUSTION ENGINES; HOT-GAS OR COMBUSTION-PRODUCT ENGINE PLANTS
    • F02D—CONTROLLING COMBUSTION ENGINES
    • F02D41/00—Electrical control of supply of combustible mixture or its constituents
    • F02D41/02—Circuit arrangements for generating control signals
    • F02D41/14—Introducing closed-loop corrections
    • F02D41/1438—Introducing closed-loop corrections using means for determining characteristics of the combustion gases; Sensors therefor
    • F02D41/1444—Introducing closed-loop corrections using means for determining characteristics of the combustion gases; Sensors therefor characterised by the characteristics of the combustion gases
    • F02D41/1445—Introducing closed-loop corrections using means for determining characteristics of the combustion gases; Sensors therefor characterised by the characteristics of the combustion gases the characteristics being related to the exhaust flow
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F02—COMBUSTION ENGINES; HOT-GAS OR COMBUSTION-PRODUCT ENGINE PLANTS
    • F02D—CONTROLLING COMBUSTION ENGINES
    • F02D41/00—Electrical control of supply of combustible mixture or its constituents
    • F02D41/02—Circuit arrangements for generating control signals
    • F02D41/14—Introducing closed-loop corrections
    • F02D41/1438—Introducing closed-loop corrections using means for determining characteristics of the combustion gases; Sensors therefor
    • F02D41/1444—Introducing closed-loop corrections using means for determining characteristics of the combustion gases; Sensors therefor characterised by the characteristics of the combustion gases
    • F02D41/1446—Introducing closed-loop corrections using means for determining characteristics of the combustion gases; Sensors therefor characterised by the characteristics of the combustion gases the characteristics being exhaust temperatures
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F02—COMBUSTION ENGINES; HOT-GAS OR COMBUSTION-PRODUCT ENGINE PLANTS
    • F02D—CONTROLLING COMBUSTION ENGINES
    • F02D41/00—Electrical control of supply of combustible mixture or its constituents
    • F02D41/02—Circuit arrangements for generating control signals
    • F02D41/14—Introducing closed-loop corrections
    • F02D41/1438—Introducing closed-loop corrections using means for determining characteristics of the combustion gases; Sensors therefor
    • F02D41/1444—Introducing closed-loop corrections using means for determining characteristics of the combustion gases; Sensors therefor characterised by the characteristics of the combustion gases
    • F02D41/1448—Introducing closed-loop corrections using means for determining characteristics of the combustion gases; Sensors therefor characterised by the characteristics of the combustion gases the characteristics being an exhaust gas pressure
    • F02D41/145—Introducing closed-loop corrections using means for determining characteristics of the combustion gases; Sensors therefor characterised by the characteristics of the combustion gases the characteristics being an exhaust gas pressure with determination means using an estimation
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F02—COMBUSTION ENGINES; HOT-GAS OR COMBUSTION-PRODUCT ENGINE PLANTS
    • F02D—CONTROLLING COMBUSTION ENGINES
    • F02D41/00—Electrical control of supply of combustible mixture or its constituents
    • F02D41/24—Electrical control of supply of combustible mixture or its constituents characterised by the use of digital means
    • F02D41/2406—Electrical control of supply of combustible mixture or its constituents characterised by the use of digital means using essentially read only memories
    • F02D41/2409—Addressing techniques specially adapted therefor
    • F02D41/2416—Interpolation techniques
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F02—COMBUSTION ENGINES; HOT-GAS OR COMBUSTION-PRODUCT ENGINE PLANTS
    • F02D—CONTROLLING COMBUSTION ENGINES
    • F02D41/00—Electrical control of supply of combustible mixture or its constituents
    • F02D41/02—Circuit arrangements for generating control signals
    • F02D41/14—Introducing closed-loop corrections
    • F02D41/1401—Introducing closed-loop corrections characterised by the control or regulation method
    • F02D2041/1433—Introducing closed-loop corrections characterised by the control or regulation method using a model or simulation of the system
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F02—COMBUSTION ENGINES; HOT-GAS OR COMBUSTION-PRODUCT ENGINE PLANTS
    • F02D—CONTROLLING COMBUSTION ENGINES
    • F02D23/00—Controlling engines characterised by their being supercharged
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/10—Internal combustion engine [ICE] based vehicles
    • Y02T10/12—Improving ICE efficiencies

Abstract

The invention relates to a pressure drop (4) for a first flow-blocking module (4) and a second flow-blocking module (5) arranged parallel thereto, for a turbine of a charging device, in particular driven by exhaust gas
Figure 100004_DEST_PATH_IMAGE002
) Method for determining, the turbine having a variable turbine geometry and a bypass line with a controllable cross section, the method comprising the following steps: -providing a first flow function (f) for the first component (4)
Figure 100004_DEST_PATH_IMAGE004
) Critical first pressure drop of (c) ((
Figure 100004_DEST_PATH_IMAGE006
) And a second flow function for the second component (5) ((
Figure 100004_DEST_PATH_IMAGE008
) Critical second pressure drop of (c) ((
Figure 100004_DEST_PATH_IMAGE010
) (ii) a -at normalized first and second flow functions (c:)
Figure 100004_DEST_PATH_IMAGE012
) And critical first and second pressure drops (
Figure 100004_DEST_PATH_IMAGE014
) A pressure drop function is preset on the basis of the pressure drop; -in dependence of said pressure dropThe function determines (S7-S11) the pressure drop by applying an approximation (S7-S11)
Figure DEST_PATH_IMAGE002A
）。

Description

Method for calculating the pressure drop across a flow-blocking component
Technical Field
The present invention relates generally to the calculation of state variables in gas conducting systems with flow-blocking components, in particular for internal combustion engines with supercharging devices driven by exhaust gases. The invention further relates to the field of actuating a supercharger regulator of a supercharging device for an internal combustion engine.
Background
In order to regulate the charging pressure in a supercharged internal combustion engine, in particular a diesel engine, a supercharging device, for example a turbocharger, which is driven by exhaust gas is used. The efficiency of the charging device or the proportion of the mechanical power extracted from the exhaust gas enthalpy which is used to drive the compressor can be set by means of the supercharger regulator. The exhaust-gas-driven charging device, which is used in particular for the variable adjustment of the efficiency of the charging device, may have a controllable variable turbine geometry, a controllable wastegate valve or a combination thereof. Different charging topologies are currently used for motor vehicles, which provide, for example, a single-stage charging, a two-stage charging with two turbochargers connected in series, or a two-stage charging with two turbochargers connected in parallel (stepped charging).
The variable adjustment of the charging device can be realized, for example, by a turbine having a variable geometry (VTG regulator, variable turbine geometry). VTG is used to denote all types of turbines, the efficiency of which can be varied by means of a housing geometry that is variable during operation. This can be done, for example, by means of variable guide vanes.
At present, multi-stage supercharging systems are mainly used to improve the dynamic driving behavior of the vehicle. For example, the series connection of two charging devices allows the use of a charging device with a lower output and a charging device with a higher output, wherein the charging device with the lower output accelerates more quickly due to a lower moment of inertia and thus can produce the motor torque more quickly. For higher motor speeds, this charging device is bypassed due to the higher mass flow, so that the charging pressure is formed only with a charging device having a higher output. In this case, it is currently the case with VTG turbines that the turbine bypass is opened in a regulated manner only when the turbine is no longer able to be regulated by the VTG due to the higher mass flow.
The current regulation strategy takes advantage of all of the boosting topologies described above. A new development describes a single-stage supercharging device having a VTG turbine which additionally has a bypass line. The bypass line distinguishes the charging device from a previously known single-stage charging device. The bypass valve in this bypass line should be operated unregulated. In other words, the bypass should be opened only under controlled conditions, while the regulation of the charging device takes place via the VTG turbine at each time.
In the case of an exhaust-gas-driven charging device and in other components of a gas conducting system in an internal combustion engine, a flow-blocking component acting as a throttle valve can be arranged in parallel in the gas conducting means. Since the state variables of the gas conducting system are constantly regulated, it is necessary to know the pressure drop over the entire parallel arrangement, which occurs from the two flow-blocking components.
Disclosure of Invention
According to the invention, a method is provided for determining the pressure drop over two parallel-connected flow-blocking components of a turbine of a charging device, in particular driven by exhaust gas, wherein the turbine has a variable turbine geometry and a bypass line with a controllable cross section, and a device and a control system are provided for carrying out the method according to the invention.
Other designs include: determining the pressure drop by applying an approximation method on the basis of the other state variable; the approximation corresponds to an interpolation method using a predetermined interpolation function; giving an upper limit value for a solution of the pressure drop functionAnd a lower limit value by: -equating a normalized first flow function to a normalized second flow function and equating the normalized second flow function to the normalized first flow function, wherein an interpolation is performed between the upper limit value and the lower limit value; selecting the interpolation function as a relative term
Figure 100002_DEST_PATH_IMAGE001
A monotonic function wherein
Figure 100002_DEST_PATH_IMAGE002
Corresponding to the total mass flow through the modules arranged in parallel, T corresponding to the temperature on the inlet side, pDsCorresponding to the output pressure on the outlet side, R corresponding to a specific gas constant, A1Corresponding to an effective first flow cross-section through said first component and A2Corresponding to an effective second flow cross-section A through said second component2(ii) a The interpolation function is equivalent to
Figure 100002_DEST_PATH_IMAGE003
Or
Figure 100002_DEST_PATH_IMAGE004
And x and y correspond to an upper limit value and a lower limit value, and w corresponds to a predefined scaling of the width of the interpolation function; using an interpolation method having the characteristics of monotonicity and fixed point iteration of the function and a derivative of the function on the pressure drop; the pressure drop is determined by means of an iterative solution by: according to
Figure 100002_DEST_PATH_IMAGE005
Using the result of the interpolation as a starting value for a fixed-point iteration and in dependence on the slope
Figure 100002_DEST_PATH_IMAGE006
Insert it in
Figure 100002_DEST_PATH_IMAGE007
And
Figure 100002_DEST_PATH_IMAGE008
to (c) to (d); the approximation is used only if the ratio of the output pressure to the input pressure at the module is greater than the critical first and second pressure drops as data of the actual pressure drop; if the pressure drop is between the critical first and second pressure drops, the following form is used to determine the pressure drop
Figure 100002_DEST_PATH_IMAGE009
Of wherein
Figure 100002_DEST_PATH_IMAGE010
Corresponding to data on pressure drop as a proportion of output pressure to input pressure, and
Figure 100002_DEST_PATH_IMAGE011
a first pressure ratio corresponding to a threshold of the first component having a smaller threshold value of the flow function; the further state variable is one or more of the mass flow, the temperature upstream of the component, the pressure downstream of the component, the effective first flow cross section and the effective second flow cross section.
According to a first aspect, a method for determining pressure drop data on a first flow-blocking component and a second flow-blocking component arranged parallel thereto of a turbine of a charging device, in particular driven by exhaust gas, having a variable turbine geometry and a bypass line with a controllable cross section, is provided, comprising the following steps:
-providing a first pressure drop critical for a first flow function of the first component and a second pressure drop critical for a second flow function of the second component;
-predetermining a pressure drop function on the basis of the first and second flow functions and the critical first and second pressure drops;
-determining the pressure drop from the pressure drop function by applying an approximation.
In particular, for exhaust-gas-driven charging devices having a turbine with a variable turbine geometry and a bypass line short-circuiting the turbine, a novel control strategy for controlling the turbine is possible. With such an arrangement, instead of operating the bypass line in a regulated manner, it is possible to control the bypass line only, and the regulation of the charging device takes place at each time by regulating the turbine geometry. In particular in the case of exhaust-gas-driven charging devices having a bypass line, it is necessary to determine the pressure drop over the parallel arrangement in order to set the turbine geometry of the turbine of the exhaust-gas-driven charging device. Knowing the pressure drop, the power of the turbine can be determined, which can be used to characterize the dynamics of the supercharging device. From the pressure drop, the distribution of the mass flow through the branches of the parallel arrangement and thus the turbine power and the exhaust gas temperature downstream of the turbine can be determined. The trajectory of the supercharger speed can thus be calculated given the effective turbine area and bypass area.
In particular for exhaust-gas-driven charging devices with a bypass, the pressure drop with the bypass open depends only on the effective turbine area, which in turn depends on the set turbine geometry.
The pressure drop or the pressure ratio over the parallel arrangement of the components can be determined according to the method described above, if the pressure drop is to be calculated from the effective cross-sectional area of the components.
In the case of conventional regulation of exhaust-gas-driven charging devices with variable turbine geometry without a bypass line, the effect of the turbine bypass is ignored. In this case, although it is also possible to adjust the desired charge pressure statically, charge pressure undershoots and overshoots occur dynamically, since the adjustment only reacts to charge pressure deviations that have already occurred due to changes in the bypass position. Knowing the pressure drop existing across the parallel arrangement, the effect of the opening of the bypass line on the pressure drop can be determined prospectively and the regulation for the turbine geometry can be determined accordingly. In particular, it is thereby possible to suppress charge pressure disturbances due to changes in the effective orifice cross section in the bypass line, since model-based pilot control can already react to changes in the effective orifice cross section in the bypass line.
In particular, further state variables, in particular mass flow, temperature upstream of the component, pressure downstream of the component, effective first flow cross section and/or effective second flow cross section, can be specified, wherein the pressure drop is determined from the further state variables by using an approximation.
Furthermore, the approximation may correspond to an interpolation method using a predetermined interpolation function.
In particular, an upper limit value and a lower limit value can be given to the solution of the pressure drop function by: the normalized first flow function is made equal to the normalized second flow function and the normalized second flow function is made equal to the normalized first flow function, wherein the interpolation is performed between the upper limit value and the lower limit value.
Provision may be made for the interpolation function to be selected relative to the terms
Figure 26682DEST_PATH_IMAGE001
A monotonic function wherein
Figure 456526DEST_PATH_IMAGE002
Corresponding to the total mass flow, T, through the modules arranged in parallelUsCorresponding to the temperature of the inlet side, pDsCorresponding to the output pressure of the outlet sideForce, R corresponding to a specific gas constant, A1Corresponding to an effective first flow cross-section through said first component and A2Corresponding to an effective second flow cross-section through said second component.
Furthermore, the interpolation function may be equivalent to
Figure 100002_DEST_PATH_IMAGE012
Or may for example, as an alternative, correspond to
Figure 100002_DEST_PATH_IMAGE013
Wherein the weighting of the values to be interpolated depends on the function variables x and y and w corresponds to a predetermined constant scaling of the width (Breite) of the interpolation function, tanh is the hyperbolic tangent, erf corresponds to the error function
Figure 100002_DEST_PATH_IMAGE014
。
According to one specific embodiment, the approximation method can be used in particular only when the ratio of the output pressure at the component to the input pressure, as a function of the actual pressure drop, is greater than the critical first and second pressure drops.
Furthermore, the pressure drop can be determined by means of an iterative solution by: using the result of said interpolation as a reference for
Figure 307939DEST_PATH_IMAGE005
And according to the slope
Figure 848641DEST_PATH_IMAGE006
Insert it in
Figure 492112DEST_PATH_IMAGE007
And
Figure 30541DEST_PATH_IMAGE008
in the meantime.
If the pressure drop lies between the critical first and second pressure drops, the following forms can be used in order to determine the pressure drop
Figure 759463DEST_PATH_IMAGE009
Of wherein
Figure 244802DEST_PATH_IMAGE010
Corresponding to data (Angabe) on the pressure drop as a proportion of said output pressure to the input pressure, and
Figure 742779DEST_PATH_IMAGE011
a first pressure ratio corresponding to a threshold of the first component with a smaller threshold value of the flow function.
According to another aspect, an apparatus for carrying out one of the above-described methods is provided. In particular, the device is configured for:
-providing a first pressure drop critical for a first flow function of the first component and a second pressure drop critical for a second flow function of the second component;
-predetermining said pressure drop function on the basis of said normalized first and second flow functions and critical first and second pressure drops;
-determining the pressure drop from the pressure drop function by applying an approximation.
Drawings
The embodiments are explained in detail below with the aid of the figures. The figures show:
FIG. 1 is a schematic illustration of a parallel arrangement of two components of a gas conducting means acting as throttle valves;
FIG. 2 is a flow chart illustrating a method for calculating a pressure ratio over the parallel arrangement of FIG. 1; and is
FIG. 3 is a graph illustrating an approximation method for determining a pressure ratio over the parallel arrangement of FIG. 1.
Detailed Description
Fig. 1 schematically shows a parallel arrangement 1 of lines for conducting a gaseous medium by means of a first branch line 2 and a second branch line 3. The two branch lines 2, 3 are connected in parallel and each have a component, namely a first flow-blocking component 4 in the first branch line 2 and a second flow-blocking component 5 in the second branch line 3. The flow-blocking assemblies 4, 5 may comprise, for example, simple control valves, variable controllable control valves or turbines having a variably adjustable turbine geometry.
At a mass flow rate
Figure 100002_DEST_PATH_IMAGE015
At a temperature TUsAnd an input pressure pUsFeeding gaseous medium to the parallel arrangement and at the same mass flow rate
Figure 780005DEST_PATH_IMAGE015
Output temperature TDsAnd an output pressure pDsThe gaseous medium is conducted away from the parallel arrangement. The mass flow rate generated in the branch lines 2, 3 corresponds to the first mass flow rate
Figure 100002_DEST_PATH_IMAGE016
And a second mass flow rate
Figure 100002_DEST_PATH_IMAGE017
。
In particular in an application in which the first component 4 of the VTG turbine corresponds to a charging device driven by exhaust gas, it can be determined from the pressure drop that "the flow has an effective first flow cross section a1Or through a second flow cross-section a having an effective cross-section2Second of (2)First and second partial mass flows of the assembly 5
Figure 340431DEST_PATH_IMAGE016
、
Figure 222936DEST_PATH_IMAGE017
"aspect of division, and from said first portion mass flow
Figure 106579DEST_PATH_IMAGE016
Determining the turbine power P outputTrbAnd the exhaust gas temperature T after the turbineDs. The pressure drop is defined as the pressure ratio
Figure 100002_DEST_PATH_IMAGE018
Figure 100002_DEST_PATH_IMAGE019
So that the magnitude of the pressure drop is smaller when the pressure difference between the output pressure and the input pressure is higher than when the pressure difference is smaller.
The method for determining the pressure ratio is described below in conjunction with the flowchart of FIG. 2.
The following mass flow equation is used as a starting point:
Figure 100002_DEST_PATH_IMAGE020
Figure 100002_DEST_PATH_IMAGE021
Figure DEST_PATH_IMAGE022
wherein
Figure DEST_PATH_IMAGE023
、
Figure DEST_PATH_IMAGE024
Is equivalent toThe flow rate functions of the first and second partial lines 2, 3 are different.
With a reduced pressure on the parallel arrangement, the pressure is self-critical when the gas flows through the flow-blocking component
Figure DEST_PATH_IMAGE025
In contrast, ultrasonic flow may occur. At this point, the flow rate characteristic curve
Figure DEST_PATH_IMAGE026
Typically becomes constant and has a value
Figure DEST_PATH_IMAGE027
. These two critical values depend on the specific heat c of the gas flowing throughPAnd a specific gas constant R.
By transformation of the equation:
Figure DEST_PATH_IMAGE028
in which a normalized flow function is used
Figure DEST_PATH_IMAGE029
And wherein
Figure DEST_PATH_IMAGE030
Wherein
Figure DEST_PATH_IMAGE031
、
Figure DEST_PATH_IMAGE032
Is at said critical first or second pressure ratio
Figure DEST_PATH_IMAGE033
、
Figure DEST_PATH_IMAGE034
Flow through the first or second componentNumerical values of the amounts. Therefore, for
Figure DEST_PATH_IMAGE035
In this case, the application
Figure DEST_PATH_IMAGE036
。
For the pressure loss through the turbine of the exhaust-gas-driven charging device, it can be assumed that the functional relationship between mass flow and pressure ratio is the same as for the case when passing through other types of throttle valves, where appropriate for the critical value
Figure DEST_PATH_IMAGE037
And
Figure DEST_PATH_IMAGE038
and (6) carrying out calibration. In general, critical values are predefined for the first and second components 4, 5 in step S1
Figure 977624DEST_PATH_IMAGE033
、
Figure DEST_PATH_IMAGE039
And
Figure 946717DEST_PATH_IMAGE031
、
Figure 505350DEST_PATH_IMAGE032
。
in addition, in step S2, the state variable, in particular the mass flow, is provided
Figure 977920DEST_PATH_IMAGE015
Upstream of the components 4, 5UsDownstream of the assemblies 4, 5, a pressure pDsEffective first flow cross section A1And an effective second flow cross section A2。
For a turbine having a variable turbine geometry (with flow function)
Figure DEST_PATH_IMAGE040
Critical value of) and a turbocharger of a bypass line in which there is an adjustable bypass valve (having a flow function) operating with exhaust gas
Figure DEST_PATH_IMAGE041
Critical value of) for the turbine (first component) and the bypass valve (second component) yields:
Figure DEST_PATH_IMAGE042
under the following assumptions:
Figure DEST_PATH_IMAGE043
next, the cases can be distinguished in step S3 into three cases:
case 1:
Figure DEST_PATH_IMAGE044
case 2:
Figure DEST_PATH_IMAGE045
case 3:
Figure DEST_PATH_IMAGE046
the case distinction can be implemented in the following manner:
once the cover is closed
Figure 497894DEST_PATH_IMAGE010
Pressure ratio greater than the two critical values
Figure 626387DEST_PATH_IMAGE033
、
Figure DEST_PATH_IMAGE047
One of, the function
Figure DEST_PATH_IMAGE048
Strictly monotonically decreases. This results from the two flow characteristic curves
Figure DEST_PATH_IMAGE049
The two flow characteristic curves are in a subcritical range (i.e., the flow characteristic curves are in a subcritical range)
Figure DEST_PATH_IMAGE050
) Also strictly monotonically decreasing. In the range of
Figure DEST_PATH_IMAGE051
And
Figure DEST_PATH_IMAGE052
inner, the two
Figure DEST_PATH_IMAGE053
Is constantly 1, and thus
Figure DEST_PATH_IMAGE054
Is also constant.
From the fixed-point iteration, we derive: as long as the initial value
Figure DEST_PATH_IMAGE055
Is physically meaningful (that is to say that
Figure DEST_PATH_IMAGE056
) Then all pairs
Figure DEST_PATH_IMAGE057
Comprises that
Figure DEST_PATH_IMAGE058
The contributions of (a) are all real-valued (reelwertig). That is to say that the position of the first electrode,
Figure DEST_PATH_IMAGE059
or is largeIs either less than or equal to
Figure 335848DEST_PATH_IMAGE055
。
Assumed solution to the fixed-point equation
Figure DEST_PATH_IMAGE060
Said, can be based on said function
Figure DEST_PATH_IMAGE061
The monotonically decreasing trend of (a) leads to the following conclusion: for any one with
Figure DEST_PATH_IMAGE062
Physical starting value of
Figure DEST_PATH_IMAGE063
In the case of a composite material, for example,
Figure DEST_PATH_IMAGE064
and to have to
Figure DEST_PATH_IMAGE065
In the case of (a) to (b),
Figure DEST_PATH_IMAGE066
。
thus, case discrimination can now be implemented by: as
Figure DEST_PATH_IMAGE067
Using said critical first pressure ratio
Figure 879568DEST_PATH_IMAGE033
And said critical second pressure ratio
Figure DEST_PATH_IMAGE068
And can thus identify the different uses for the case differentiation
Figure 429498DEST_PATH_IMAGE010
The range of (1). The numerical value of the iteration step thus determines which of the above ranges is within.
In the first case, the two flow characteristic curves do not depend on
Figure DEST_PATH_IMAGE069
. Whereby it can be easily calculated in step S4
Figure DEST_PATH_IMAGE070
Because of
Figure DEST_PATH_IMAGE071
And
Figure DEST_PATH_IMAGE072
both become 1. The following applies here:
Figure DEST_PATH_IMAGE073
the same applies to the second case, provided that the flow rate characteristic curve is assumed in step S5
Figure DEST_PATH_IMAGE074
In the non-critical range of the flow characteristic curve, the shape is approximately elliptical:
Figure DEST_PATH_IMAGE075
an approximation of an ellipse for the flow characteristic curve is a common approximation. The above-mentioned formula can thus be solved in a simple manner as a quadratic equation in step S6.
Figure DEST_PATH_IMAGE076
For the third case, no algebraic solution exists and therefore an approximate scheme is to be chosen. Since the above-mentioned function can be differentiated and strictly monotonically decreased, not only an iterative solution but also an interpolated solution can be applied. However, the solution of the interpolation has the following advantages: it incurs less computational overhead.
An upper limit and a lower limit can be given to the solution by the above equation by: in step S7
Figure DEST_PATH_IMAGE077
To replace
Figure DEST_PATH_IMAGE078
And used in the next step S8
Figure 996352DEST_PATH_IMAGE078
To replace
Figure 24351DEST_PATH_IMAGE077
The equation is thus obtained in both cases by being drawn from parenthesis:
Figure DEST_PATH_IMAGE079
in step S9, two approximate solutions can thus be given to the above equation, of which one solution is respectively provided
Figure DEST_PATH_IMAGE080
On top of the exact solution and one solution
Figure DEST_PATH_IMAGE081
Under the exact solution. This is illustrated in fig. 3, where curve K1 corresponds to
Figure DEST_PATH_IMAGE082
And curve K2 corresponds to:
Figure DEST_PATH_IMAGE083
。
fixed point equation (Fixpunktgleichung)
Figure DEST_PATH_IMAGE084
Corresponds to the first intersection point SP1 of the curve K1 with a standard straight line and is fixed-point equation
Figure DEST_PATH_IMAGE085
Corresponds to the second intersection point SP2 of the curve K2 with the standard straight line. The solution is
Figure DEST_PATH_IMAGE086
Now it can also be obtained by interpolation between the intersection points SP1 and SP 2.
Now, interpolation between the two limits can be performed using a suitable interpolation method in step S10. In this case, the interpolation should depend on the two variables, if differentiation is always possible
Figure 815721DEST_PATH_IMAGE077
、
Figure 5394DEST_PATH_IMAGE078
Anterior factor of
Figure DEST_PATH_IMAGE087
、
Figure DEST_PATH_IMAGE088
And should be chosen such that the two preceding factors X are1、X2In the extreme case where one is much smaller than the other preceding factor, the interpolation is always made close to an exact solution. Furthermore, the interpolation function should be strictly monotonically dependent on the two preceding factors X1、X2The difference of (a). From these requirements follows: the interpolation function being preceded by the two preceding factors X1And X2Has a value of 0 or a value of 1 in the extreme case of a relatively large spacing if the interpolation is by the following expression
Figure DEST_PATH_IMAGE089
To express (A), (B) and
Figure DEST_PATH_IMAGE090
equivalent to the interpolated solution). Therefore, a corresponding function must be selected in step S11. These requirements are satisfied, for example, by interpolation functions of the following type:
Figure DEST_PATH_IMAGE091
。
the function variables x and y defining the limit values
Figure DEST_PATH_IMAGE092
And
Figure 187108DEST_PATH_IMAGE081
with what weight to enter the interpolation. Here, w corresponds to a scaling of the width of the interpolation function and can be selected appropriately. The accuracy of this approximation can be checked numerically by: solution to interpolation
Figure DEST_PATH_IMAGE093
The exact solution can be determined, for example, in an iterative manner, using a sufficiently large number of iteration steps, with any precision, compared to the exact solution.
Furthermore, provision may be made for the result of the interpolation to be used
Figure DEST_PATH_IMAGE094
Used as starting value for a suitable iterative method in order to improve the accuracy of the solution. Alternatively, the fixed point characteristic of the above equation may be related to the function
Figure DEST_PATH_IMAGE095
Slope of (2)
Figure DEST_PATH_IMAGE096
In combination of (A), (B) and (C)
Figure 425322DEST_PATH_IMAGE096
Is equivalent to the function
Figure 258149DEST_PATH_IMAGE095
Derivative of (d). By passing
Figure DEST_PATH_IMAGE097
A fixed-point iteration is defined. Because of the fact that
Figure DEST_PATH_IMAGE098
Is always satisfied in the non-critical range, so that
Figure 819056DEST_PATH_IMAGE094
And
Figure DEST_PATH_IMAGE099
and then
Figure DEST_PATH_IMAGE100
Upper and lower limits are given for the solution of the above equation. Using said slope
Figure DEST_PATH_IMAGE101
To obtain a solution of the above equation
Figure DEST_PATH_IMAGE102
Relative to
Figure DEST_PATH_IMAGE103
And
Figure DEST_PATH_IMAGE104
in between
Figure 488066DEST_PATH_IMAGE100
The range of relative positions (Ma β).
Figure DEST_PATH_IMAGE105
The larger the size of the tube is,
Figure 123446DEST_PATH_IMAGE102
the closer to
Figure 14042DEST_PATH_IMAGE094
。
Figure 217621DEST_PATH_IMAGE105
The closer to zero the more closely,
Figure 826457DEST_PATH_IMAGE102
the closer to
Figure 203212DEST_PATH_IMAGE104
. If it is not
Figure DEST_PATH_IMAGE106
Has a value of-1, then
Figure 479472DEST_PATH_IMAGE102
Is substantially centered.
Thus, again, the values may be interpolated by suitable interpolation
Figure DEST_PATH_IMAGE107
And
Figure 853953DEST_PATH_IMAGE104
interpolation is performed in between. Suitably means that the above requirements are met in this case with a biased parameterization of the interpolation function:
Figure DEST_PATH_IMAGE108
。

Claims (13)

1. (pressure drop) across a first flow-blocking module (4) and a second flow-blocking module (5) arranged in parallel thereto for the turbine of a supercharging device driven by exhaust gas
Figure DEST_PATH_IMAGE001
) Method for determining, the turbine having a variable turbine geometry and a bypass line with a controllable cross section, the method comprising the following steps:
-providing a first flow function (f) for the first component (4)
Figure DEST_PATH_IMAGE002
) Critical first pressure drop of (c) ((
Figure DEST_PATH_IMAGE003
) And a second flow function for the second component (5) ((
Figure DEST_PATH_IMAGE004
) Critical second pressure drop of (c) ((
Figure DEST_PATH_IMAGE005
）；
-at normalized first and second flow functions (c:)
Figure DEST_PATH_IMAGE006
) And critical first and second pressure drops (
Figure DEST_PATH_IMAGE007
) A pressure drop function is preset on the basis of the pressure drop;
-determining (S7-S11) the pressure drop (S7-S11) by applying an approximation method according to the pressure drop function
Figure 493969DEST_PATH_IMAGE001
）。
2. The method of claim 1, wherein a further state variable is specified, wherein the pressure drop is determined by using an approximation method on the basis of the further state variable (
Figure 489738DEST_PATH_IMAGE001
）。
3. A method as claimed in claim 1 or 2, wherein the approximation corresponds to an interpolation using a predetermined interpolation function.
4. A method according to claim 3, wherein upper and lower limit values for the solution of said pressure drop function are given by: normalized first flow function (
Figure DEST_PATH_IMAGE008
) A second flow function equal to the normalization (a)
Figure DEST_PATH_IMAGE009
) And a second flow function (f) normalizing said second flow
Figure 738317DEST_PATH_IMAGE009
) Equal to the normalized first flow function (
Figure 461422DEST_PATH_IMAGE008
) Wherein an interpolation is performed between the upper limit value and the lower limit value.
5. The method according to claim 4, wherein said interpolation function is selected (S11) as a relative term
Figure DEST_PATH_IMAGE010
A monotonic function wherein
Figure DEST_PATH_IMAGE011
Corresponding to the total mass flow through the modules arranged in parallel, T corresponding to the temperature on the inlet side, pDsCorresponding to the output pressure on the outlet side, R corresponding to a specific gas constant, A1Corresponding to an effective first flow cross section through the first component (4) and A2Corresponding to an effective second flow cross section A through the second component (5)2。
6. The method of claim 5, wherein said interpolation function is equivalent to
Figure DEST_PATH_IMAGE012
Or
Figure DEST_PATH_IMAGE013
And x and y correspond to an upper limit value and a lower limit value, and w corresponds to a predefined scaling of the width of the interpolation function.
7. The method of claim 3, wherein using has a function
Figure DEST_PATH_IMAGE014
Interpolation of the characteristics of monotonicity and fixed-point iteration of (a) and the function versus pressure drop (b:)
Figure 413810DEST_PATH_IMAGE001
) The derivative of the calculation.
8. The method according to claim 3, wherein the pressure drop is determined by means of an iterative solution method (
Figure 236273DEST_PATH_IMAGE001
) The method comprises the following steps: according to
Figure DEST_PATH_IMAGE015
Using the result of the interpolation as a starting value for a fixed-point iteration and in dependence on the slope
Figure DEST_PATH_IMAGE016
Insert it in
Figure DEST_PATH_IMAGE017
And
Figure DEST_PATH_IMAGE018
in the meantime.
9. Method according to claim 1 or 2, wherein the actual pressure drop(s) is (are) only determined if the ratio of the output pressure over the components (4, 5) relative to the input pressure
Figure 50776DEST_PATH_IMAGE001
) Is greater than the critical first and second pressure drops (
Figure 577572DEST_PATH_IMAGE007
) Only approximation is used.
10. The method of claim 1 or 2, wherein if said pressure drop is critical first and second pressure drops (f &)
Figure 246451DEST_PATH_IMAGE007
) In order to determine the pressure drop, the following form is used
Figure DEST_PATH_IMAGE019
Of wherein
Figure 443077DEST_PATH_IMAGE001
Corresponding to about as the output pressure (p)Ds) Relative to the input pressure (p)Us) Proportional pressure drop of (a)
Figure 541614DEST_PATH_IMAGE001
) And is provided with
Figure DEST_PATH_IMAGE020
A first pressure ratio (C/F) corresponding to the first component (4) critical with a lower threshold value of the flow function
Figure DEST_PATH_IMAGE021
）。
11. The method of claim 2, wherein said other state parameter is mass flow rate (b
Figure 75364DEST_PATH_IMAGE011
) Temperature upstream of the component (4, 5), pressure downstream of the component (4, 5), effective first flow cross section (A)1) And an effective second flow cross-section (A)2) One or more state quantities.
12. Apparatus for carrying out one of the methods according to any one of claims 1 to 11.
13. A machine-readable storage medium, on which a computer program is stored, which computer program is designed to carry out all the steps of the method according to any one of claims 1 to 11.
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