Method for calculating a pressure drop across two flow-impeding components connected in parallel in a gas flow system, particularly in an exhaust gas-driven charging device for an internal combustion engine

Abstract

Method for determining a pressure drop (Π) across a first flow-restricting component (4) and a second flow-restricting component (5) arranged parallel thereto, in particular a turbine of an exhaust gas-driven charging device with variable turbine geometry and a bypass line with controllable cross-section, comprising the following steps: - Providing a first critical pressure drop (Δ1Crit) or a first flow function (Ψ1Nrm) for the first component (4) and a second critical pressure drop (Δ2Crit) or a second flow function (Ψ2Nrm) for the second component (5); - Specifying a pressure drop function based on the first and second normalized flow functions (Ψ1Nrm(Π), Ψ2Nrm(Π)) and the first and second critical pressure drops (Δ1Crit, Δ2Crit); - Determining (S7 - S11) the pressure drop (Π) by applying an approximation method depending on the Pressure drop function.

Description

Technical field

[0001] The invention relates generally to the calculation of state variables in gas flow systems that have flow-impeding components, in particular for internal combustion engines with exhaust-driven turbocharging devices. Furthermore, the present invention relates to the control of a turbocharger actuator of a turbocharging device for an internal combustion engine. Technical background

[0002] To regulate boost pressure in turbocharged internal combustion engines, especially diesel engines, exhaust gas-driven charging devices, such as turbochargers, are used. The efficiency of the charging device, or the proportion of mechanical power derived from the exhaust gas enthalpy that is used to drive a compressor, can be adjusted using turbocharger actuators. Specifically, exhaust gas-driven charging devices can incorporate a controllable variable turbine geometry, a controllable wastegate valve, or a combination thereof to variably adjust the charging device's efficiency. Currently, various charging topologies are used in motor vehicles, including single-stage charging, two-stage charging with two turbochargers in series, or two-stage charging with two turbochargers in parallel (sequential charging).

[0003] Variable adjustment of charging devices can be achieved, for example, through variable geometry turbines (VTG actuators). VTG refers to all types of turbines whose efficiency can be changed by altering the casing geometry during operation. This can be done, for example, by using variable guide vanes.

[0004] Multi-stage turbocharging systems are currently used primarily to improve the vehicle's dynamic driving characteristics. For example, connecting two turbochargers in series allows the use of one low-power and one high-power turbocharger. The low-power turbocharger accelerates quickly due to its low moment of inertia, thus enabling a rapid build-up of engine torque. At high engine speeds, this turbocharger must be bypassed due to the high mass flow rate, allowing the boost pressure to be generated exclusively by the high-power turbocharger. Currently, with variable turbine geometry (VTG) turbines, the turbine bypass is only opened when the turbine can no longer be controlled by the VTG due to the high mass flow rate.

[0005] Current control strategies can handle all the charging topologies described above. A new development describes a single-stage charging system with a VTG turbine that also features a bypass line. This bypass line distinguishes the charging system from conventional single-stage systems. The bypass valve in this bypass line is intended to operate without regulation. Instead, the bypass is only opened in a controlled manner, while the charging system is controlled at all times via the VTG turbine.

[0006] In exhaust-driven turbocharging systems and other parts of the gas flow system in an internal combustion engine, flow-restricting components acting as throttles can be arranged in parallel. Since the state variables of the gas flow system are often controlled, it is necessary to know the pressure drop resulting from the two flow-restricting components across the entire parallel arrangement. Disclosure of the invention

[0007] According to the invention, a method for determining a pressure drop across two parallel flow-impeding components, in particular a turbine of an exhaust gas-driven charging device with variable turbine geometry and a bypass line with controllable cross-section according to claim 1, as well as the device and a control system according to the dependent claims are provided.

[0008] Further details are specified in the dependent claims.

[0009] According to a first aspect, a method for determining a pressure drop across a first flow-impeding component and a second flow-impeding component arranged parallel to it, in particular a turbine of an exhaust gas-driven charging device with variable turbine geometry and a bypass line with controllable cross-section, is provided, comprising the following steps: – Providing a first critical pressure drop of a first flow function for the first component and a second critical pressure drop of a second flow function for the second component; – Specifying a pressure drop function based on the first and second flow functions and the first and second critical pressure drop; – Determining the pressure drop by applying an approximation method depending on the pressure drop function.

[0010] Particularly in the case of an exhaust gas-driven turbocharging system with a variable-geometry turbine and a bypass line that short-circuits the turbine, novel control strategies for the turbine are possible. In such arrangements, the bypass line is not operated in a controlled manner, but can only be controlled, while the turbocharging system is controlled at all times by adjusting the turbine geometry. Specifically, in the case of an exhaust gas-driven turbocharging system with a bypass line, it is necessary to determine a pressure drop across the parallel arrangement for controlling the turbine geometry of the exhaust gas-driven turbocharging system.Given a known pressure drop, it is possible to determine the turbine's power output, which can then be used to describe the dynamic behavior of the turbocharging system: From the pressure drop, the distribution of mass flows through the branches of the parallel arrangement can be determined, and consequently, the turbine power output and the exhaust gas temperature downstream of the turbine. Therefore, for given effective turbine and bypass areas, the turbocharger speed trajectory can be calculated.

[0011] In particular, with the exhaust gas-driven charging device with bypass line, the pressure drop when the bypass line is open depends solely on the effective turbine area, which depends on the set turbine geometry.

[0012] Determining the pressure drop or pressure ratio across a parallel arrangement of components according to the method described above can be applied if the pressure drop is to be calculated as a function of the effective cross-sectional areas of these components.

[0013] When using a conventional control system for an exhaust-driven turbocharger with variable turbine geometry without a bypass line, the effect of the turbine bypass is neglected. In this case, while such an approach can regulate the desired boost pressure in steady-state operation, dynamically, boost pressure undershoot and overshoot will occur because the control system can only react to a boost pressure deviation that has already occurred due to a change in the bypass position. Knowing the pressure drop across the parallel arrangement allows the effect of opening the bypass line on the pressure drop to be predicted, and the turbine geometry control can be adjusted accordingly.In particular, this can suppress boost pressure drops due to changes in the effective opening cross-section in the bypass line, since the model-based feedforward control can already react to a change in the effective opening cross-section in the bypass line.

[0014] In particular, further state variables can be specified, especially a mass flow rate, a temperature upstream of the components, a pressure downstream of the components, a first effective flow cross-section and / or a second effective flow cross-section, wherein the pressure drop is determined by applying an approximation method depending on the further state variables.

[0015] Furthermore, the approximation method can correspond to an interpolation method that uses a predefined interpolation function.

[0016] In particular, an upper limit and a lower limit for the solution of the pressure drop function can be specified by equating the first normalized flow function to the second normalized flow function and the second normalized flow function to the first normalized flow function, performing the interpolation procedure between the upper and lower limits.

[0017] It may be provided that the interpolation function is used as a function of the term A monotonic function is selected, where m is a total mass flow through the parallel components, T Us the inlet temperature, p Ds a discharge pressure, R a specific gas constant, A1 a first effective flow cross-section through the first component and A2 a second effective flow cross-section through the second component.

[0018] Furthermore, the interpolation function can or e.g. alternatively The weighting of the values ​​to be interpolated depends on the function arguments x and y, and w corresponds to a predefined, constant scaling of the width of the interpolation function. tanh is the hyperbolic tangent, and erf corresponds to an error function.

[0019] According to one embodiment, the approximation method can then, in particular only, be applied if a ratio of the output pressure to an input pressure across the component, as an indication of the actual pressure drop, is greater than the first and second critical pressure drops.

[0020] Furthermore, the pressure drop can be determined using an iterative solution method by taking a result of the interpolation method as a starting value for a fixed-point iteration according to Π. n+1 = Π^(Π n ) is used and between Π n+1 and Πn depending on a slope Π' = Π^'(Π n ) is interpolated.

[0021] Furthermore, an approximation function, particularly in the form of a function, can be used to determine the pressure drop. can be used when the pressure drop lies between the first and second critical pressure drops, where Π is a specification of the pressure drop as the ratio of the outlet pressure to an inlet pressure and Π Crit 1 corresponds to the first critical pressure ratio of the first component with the smaller critical value of the flow function.

[0022] According to another aspect, a device for carrying out one of the above procedures is provided. In particular, the device is designed to: – to provide a first critical pressure drop of a first flow function for the first component and a second critical pressure drop of a second flow function for the second component; – to specify a pressure drop function based on the first and second normalized flow functions and the first and second critical pressure drops; – to determine the pressure drop by applying an approximation method depending on the pressure drop function. Brief description of the drawings

[0023] The embodiments are explained in more detail below with reference to the accompanying drawings. These show:

[0024] Fig. 1 a schematic representation of a parallel arrangement of two components acting as throttles in a gas flow; and

[0025] Fig. 2. A flowchart illustrating a procedure for determining a pressure ratio across the parallel arrangement of the Fig. 1; and

[0026] Fig. 3. A diagram illustrating an approximation method for determining a pressure ratio over the parallel arrangement of the Fig. 1. Description of embodiments

[0027] In Fig. 1 schematically represents a parallel arrangement 1 from lines for conveying a gaseous medium with a first branch line 2 and a second branch management 3 shown. The two branch lines 2 , 3 are parallel to each other and each has one component, namely a first flow-impeding component 4 in the first branch management 2 and a second flow-impeding component 5 in the second branch management 3 up. The flow-impeding components 4 , 5 These can include, for example, a simple control valve, a variable controllable control valve, or a turbine with a variably adjustable turbine geometry.

[0028] The parallel arrangement is supplied with the gaseous medium at a mass flow rate m, at a temperature T. Usand an input pressure p Us supplied and extracted from this with the same mass flow rate m, an initial temperature T Ds and an output pressure p Ds diverted. The resulting branch lines 2 , 3 The resulting mass flows correspond to a first mass flow m.1 and a second mass flow m.2.

[0029] Especially in a use case where the first component 4 In a VTG turbine corresponding to an exhaust gas-driven charging device, the pressure drop can be used to determine the division into the first and second partial mass flow m.1, m.2 by the first component. 4 with the first effective flow cross-section A1 or through the second component 5 with the second effective flow cross-section A2 and from the first partial mass flow m.1 the turbine power output P Trb and the exhaust gas temperature T DsThe pressure drop is determined after the turbine. Here, the pressure drop is expressed as a pressure ratio Π = p. Ds / p Us specified, so that with a high pressure difference between outlet pressure and inlet pressure, the value of the pressure drop is smaller than with a low pressure difference.

[0030] The procedure for determining the pressure ratio is described below in conjunction with the flowchart of the Fig. 2 described.

[0031] Initially, mass flow equations are assumed as follows: where Ψ1, Ψ2 are the given flow functions of the first and second sub-pipes 2 , 3 which are different.

[0032] When the pressure across the parallel arrangement is reduced, flow of gas through a flow-impeding component can occur above a critical pressure ratio Π. CritSupersonic flow occurs. At this point, the flow characteristic Ψ(Π) typically becomes constant and takes the value Ψ Crit These two critical values ​​depend on the specific heat capacity c. p and the specific gas constant R of the gas flowing through.

[0033] By rearranging the equations, we obtain with standardized flow functions and with where Ψ Crit 1 , Ψ Crit 2 the values ​​of the flow rates through the first and second components at the first and second critical pressure ratios Π Crit 1 , Π Crit 2 . For the case 0 < Π < Π Crit Therefore, Ψ Nrm (Π) = 1.

[0034] For the pressure loss during flow through the turbine of the exhaust gas-driven charging device, the same functional relationship between mass flow and pressure ratio can be assumed as for flow through a differently designed throttle, whereby the critical values ​​Π Crit and Ψ CritThey must be calibrated appropriately. Generally, the critical values ​​are determined in step S1. Π Crit 1 , Π Crit 2 and Ψ Crit 1 , Ψ Crit 2 for the first and second components 4 , 5 specified.

[0035] Furthermore, in step S2 the state variables, in particular the mass flow rate m, the temperature T, are determined. Us upstream of the components 4 , 5 the pressure p Ds downstream of the components 4 , 5 , the first effective flow cross-section A1 and the second effective flow cross-section A2 are provided.

[0036] In an exhaust gas-driven charging device with a turbine with variable turbine geometry (with a critical value of the flow function) Ψ Crit 1 ) and a bypass line containing an adjustable bypass valve (with a critical value of the flow function) Ψ Crit 2 ) is located, it follows that: 0 < Π Crit 1 < Π Crit 2 < 1 for the critical pressure ratio of a turbine (first component) and the critical pressure ratio of a bypass valve (second component). Assuming that Π Crit 1 < Π Crit 2 In step S3, a case distinction can be made into three cases: Case 1: 0 < Π ≤ Π Crit 1 Case 2: Π Crit 1 < Π ≤ Π Crit 2 Case 3: Π Crit 2 < Π ≤ 1

[0037] The case distinction can be made as follows.

[0038] The function Π^(Π) is strictly monotonically decreasing as soon as Π is greater than one of the two critical pressure ratios. Π Crit 1 , Π Crit 2 This follows from the monotonicity properties of the two flow characteristic curves Ψ. Nrm (Π), which are in the subcritical region (i.e., Π Crit < Π ≤ 1) also decreases strictly monotonically. In the interval 0 < Π ≤ Π Crit 1 and 0 < Π ≤ Π Crit 2 are both Ψ Nrm Since Π^ is constant, it is also constant.

[0039] A fixed-point iteration shows that, provided a starting value Π0 is physically meaningful (i.e., 0 < Π0 ≤ 1), all contributions to Π^(Π0) including Ψ Nrm (Π0) are real values. Therefore, Π1 = Π^(Π0) is either greater than, less than, or equal to Π0.

[0040] Given an assumed solution Π of the fixed-point equation, it can be deduced, due to the monotonically decreasing behavior of the function Π^(Π), that for any physical starting value Π0 with Π0 < Π, Π1 = Π^(Π0) ≥ Π, and with Π0 > Π, Π1 = Π^(Π0) ≤ Π.

[0041] This allows the case distinction to be carried out by defining Π0 as the first critical pressure ratio. Π Crit 1 and the second critical pressure ratio Π Crit 2 This allows the different ranges for Π, as defined in the case distinction, to be identified. The value of the iteration step therefore determines in which of the above ranges one is located.

[0042] In the first case, both flow characteristics are independent of Π. Therefore, Π can be easily calculated in step S4, since Ψ Nrm 1 (Π) and Ψ Nrm 2 (Π) 1 will be. The following applies:

[0043] This also applies to the second case, provided that the flow characteristic Ψ1 in its non-critical region is approximated as an ellipse of the form in step S5. The elliptic approximation for the flow characteristic is a common approximation. This allows the above formula to be used in step S6. can be solved in a simple way as a quadratic equation.

[0044] For the third case, no algebraic solution exists, and therefore an approximate approach is chosen. Since the function above is differentiable and strictly monotonically decreasing, both an iterative and an interpolative solution method can be applied. However, the interpolative solution method has the advantage of requiring less computational effort.

[0045] The equation above allows us to specify an upper and a lower limit for the solution by determining S7 in one step. Ψ Nrm 2 through Ψ Nrm 1 and in a subsequent step S8 Ψ Nrm 1 through Ψ Nrm 2 replaced, which in both cases leads to the equation by factoring out This allows us to specify two approximate solutions for the equation above in step S9, one of which lies above and one below the exact solution. This is in Fig. 3 shown, where the curve K1 and the curve K2 are equivalent to.

[0046] The solution of the fixed-point equation corresponds to a first intersection point SP1 of the curve K1 with the standard line and the solution of the fixed-point equation This corresponds to a second intersection point SP2 of curve K2 with the standard line. The solution Π^ can now be obtained by interpolation between the intersection points SP1 and SP2.

[0047] Using a suitable interpolation method in step S10, it is now possible to interpolate between the two limitations. The interpolation should be continuously differentiable from the prefactors. the two Ψ Nrm 1 , Ψ Nrm 2 The interpolation function should depend on the difference between the two prefactors X1 and X2 and be chosen such that, in the limiting case where one of the two prefactors is much smaller than the other, the interpolation approximates the exact solution. Furthermore, the interpolation function should depend strictly monotonically on the difference between the two prefactors X1 and X2. From these requirements, it follows that in the limiting case of a relatively large difference between the two prefactors X1 and X2, the interpolation function takes on the value 0 or the value 1, respectively, if the interpolation is performed by the expression Π 1 Intp = Intp(X 1 , X 2 )· + (1 – Intp(X 1 , X 2 ))· is formulated ( Π 1 Intp (corresponds to the interpolated solution). Therefore, a suitable function must be chosen in step S11. These requirements are met, for example, by an interpolation function of the form The function arguments x and y determine the weight given to the limit values ​​Π and Π in the interpolation. Here, w corresponds to a scaling of the width of the interpolation function and can be chosen appropriately. The accuracy of this approximation method can be verified numerically by comparing the interpolated solution. Π 1 Intp is compared with the exact solution, which can be determined with arbitrary accuracy, for example, using iterative methods with a sufficiently large number of iteration steps.

[0048] Furthermore, it may be stipulated that the result Π 1 Intp The interpolation is used as a starting value for a suitable iterative procedure to improve the accuracy of the solution. Alternatively, one can exploit the fixed-point property of the above equation in combination with the slope Π^' of the function Π^(Π) (Π^' corresponds to the derivative of the function Π^(Π)). By Π n+1 = Π^(Π nA fixed-point iteration is defined. Since Π^' < 0 is always satisfied in the non-critical region, it follows that Π 1 Intp und Π 2 = (Π 1 Intp ) Again, an upper and a lower bound are given for the solution of the above equation Π = Π^(Π). With the slope Π' = '(Π 1 Intp ) One obtains a measure for the relative position of the solution Π of the above equation Π = Π^(Π) between Π 1 Intp and Π 2 The larger |Π'|, the closer Π is to Π 1 Intp ·. The closer |Π'| is to zero, the closer Π is to Π. 2 If Π' has the value –1, then Π lies approximately in the middle.

[0049] Therefore, a suitable interpolation method can be used to compare the values ​​again. Π 1 Intp and Π 2 interpolate. In this case, "suitable" means fulfilling the above requirements with a different parameterization of the interpolation function. Π 2 Intp = Intp(Π', –1)·Π 2 + (1 – Intp(Π', –1))·Π 1 Intp

Claims

[1] Method for determining a pressure drop (Π) across a first flow-impeding component ( 4 ) and a second flow-impeding component arranged parallel to it ( 5 ), in particular a turbine of an exhaust gas-driven charging device with variable turbine geometry and a bypass line with controllable cross-section, with the following steps: – Providing an initial critical pressure drop (Π Crit 1 ) a first flow function (Ψ Nrm 1 ) for the first component ( 4 ) and a second critical pressure drop (Π Crit 2 ) a second flow function (Ψ Nrm 2 ) for the second component ( 5 ); – Specifying a pressure drop function based on the first and second normalized flow functions (Ψ Nrm 1 (Π), Ψ Nrm 2 (Π)) and the first and second critical pressure drop (Π Crit 1 , Π Crit 2 ); – Determining (S7–S11) the pressure drop (Π) by applying an approximation method depending on the pressure drop function. [2] Method according to claim 1, wherein further state variables are specified, in particular one or more state variables of a mass flow rate (m.), a temperature upstream of the components ( 4 , 5 ), a pressure downstream of the components ( 4 , 5 ), a first effective flow cross-section (A1) and a second effective flow cross-section (A2), wherein the pressure drop (Π) is determined by applying an approximation method depending on the other state variables. [3] Method according to claim 1 or 2, wherein the approximation method corresponds to an interpolation method that uses a predetermined interpolation function. [4] Method according to claim 3, wherein an upper limit and a lower limit for the solution of the pressure drop function are specified by the first normalized flow function (Ψ Nrm 1 (Π)) the second normalized flow function (Ψ Nrm 2 (Π)) is equated and the second normalized flow function (Ψ Nrm 2 (Π)) the first standardized flow function (Ψ Nrm 1 (Π)) is equated, whereby the interpolation procedure is carried out between the upper and lower limits. [5] Method according to claim 4, wherein the interpolation function is related to the term A monotone function is selected (S11), where m is a total mass flow rate through the parallel components, T is the output temperature, p Ds an outlet-side outlet pressure, R a specific gas constant, A1 a first effective flow cross-section through the first component ( 4) and A2 a second effective flow cross-section A2 through the second component ( 5 ) are equivalent to [6] Method according to claim 5, wherein the interpolation function corresponds to x and y being the upper and lower limits, and w being a given scaling of the width of the interpolation function. [7] Method according to any one of claims 3 to 6, wherein the interpolation method is used with the properties of fixed-point iteration and the monotonicity of a function Π^(Π) and its derivative with respect to the pressure drop (Π). [8] Method according to any one of claims 3 to 7, wherein the pressure drop (Π) is determined using an iterative solution method by taking a result of the interpolation method as the starting value for a fixed-point iteration according to Π n+1 = Π^(Π n ) is used and between Π n+1 and Π n depending on a slope Π' = Π^'(Π n ) is interpolated. [9] Method according to any one of claims 1 to 8, wherein the approximation method is only applied if a ratio of the output pressure to an input pressure across the components ( 4 , 5 ) as a specification of the actual pressure drop (Π) is greater than the first and second critical pressure drops (Π Crit 1 , Π Crit 2 ). [10] Method according to any one of claims 1 to 8, wherein an approximation function, in particular in the form of a pressure drop, is used to determine the pressure drop is used when the pressure drop between the first and second critical pressure drop (Π Crit 1 , Π Crit 2 ) lies, where Π is a specification of the pressure drop (Π) as a ratio of the initial pressure (p Ds ) to an inlet pressure (p Us ) and Π Crit 1 the first critical pressure ratio (Π Crit 1 ) the first component ( 4 ) with the smaller critical value of the flow function. [11] Device for carrying out one of the methods according to any one of claims 1 to 10. [12] Computer program which is configured to perform all steps of a method according to any one of claims 1 to 10. [13] Machine-readable storage medium on which a computer program according to claim 12 is stored.