Method of designing and producing a turbine

Abstract

A turbine with multiple gas inlets is designed by a process of, for a given engine, obtaining time series data characterizing the power bias of the engine, obtaining an isentropic power associated with each data point of the time series, and using the isentropic powers to obtain a design point. The turbine is then designed based on the design point, such as by optimising one or more design parameters of the turbine based on the design point.

Claims

1. A method for determining at least one design parameter of a turbine for an internal combustion engine, the turbine including a pair of gas inlet volutes for transmitting exhaust gas emitted by respective groups of one of more cylinders of the engine to a chamber of the turbine which houses a turbine wheel, the exhaust gas entering a first of the volutes having a different pressure waveform from a pressure waveform of the exhaust gas entering a second of the volutes, and the two pressure waveforms being out of phase, the method including: obtaining time series data as data points indicating the available turbine power at each gas inlet volute at each of a plurality of respective times during an engine cycle; obtaining an isentropic power value associated with each data point; obtaining a design point from the time series data and the corresponding isentropic power values; and selecting the at least one design parameter to maximise power efficiency at the design point.

2. A method according to claim 1 in which the design point is obtained based on at least one of an isentropic-power weighted mean turbine expansion ratio, and an isentropic-power weighted mean scroll pressure ratio.

3. A method according to claim 1 in which a respective candidate design point is obtained for each volute, and the design point is obtained by selecting from the candidate design points.

4. A method according to claim 1 in which the design point is obtained using a sub-set of the time series data, the sub-set of the time series data being obtained by deriving a respective scroll pressure ratio for each of a number of data points of the time series data, and filtering the data points of the time series data using the respective scroll pressure ratio.

5. A method according to claim 4, in which a respective candidate design point is obtained for each volute from isentropic data points for a portion of the engine cycle in which the pressure in the respective volute is greater than in the other volute, and the design point is obtained by selecting from the candidate design points.

6. A method according to claim 1, in which there is at least one design parameter for each respective volute which is chosen using the design point.

7. A method according to claim 1, in which the selecting the at least one design parameter includes: a first step of, for a plurality of reaction values indicative of the ratio of a critical area of the turbine housing and a critical area of the turbine wheel, generating corresponding initial parameters of the turbine based on the design point; and from the initial parameters, choosing a reaction value.

8. A method according to claim 7, further including a second design step of generating parameters of the turbine based on the design point for the chosen reaction value.

9. A method of determining at least one design parameter of a turbine for an internal combustion engine, the turbine including a pair of volutes for transmitting exhaust gas emitted by respective groups of one of more cylinders of the engine to a chamber of the turbine which houses a turbine wheel, the exhaust gas entering a first of the volutes having a different pressure waveform from a pressure waveform of the exhaust gas entering a second of the volutes, and the two pressure waveforms being out of phase, the method including: obtaining time series data as data points indicative of the available turbine power at each gas inlet volute over an engine cycle; using the time series points to obtain a design point; a first design step of, for a plurality of reaction values indicative the ratio of a critical area of the turbine housing and a critical area of the turbine wheel, generating corresponding initial parameters of the turbine based on the design point; and from the initial parameters, choosing a reaction value, the at least one design parameter being a design parameter of a turbine having the chosen reaction value.

10. A method according to claim 9, further including a second design step of generating parameters of the turbine based on the design point for the chosen reaction value.

11. A method for producing a turbine for an internal combustion engine, comprising: determining at least one design parameter of the turbine, the turbine including a pair of gas inlet volutes for transmitting exhaust gas emitted by respective groups of one of more cylinders of the engine to a chamber of the turbine which houses a turbine wheel, the exhaust gas entering a first of the volutes having different a pressure waveform from the pressure waveform of the exhaust gas entering the other volute, and the two pressure waveforms being out of phase, the determination of the at least design parameter including: (i) obtaining time series data as data points indicating the available turbine power at each gas inlet volute at each of a plurality of respective times during an engine cycle; (ii) obtaining an isentropic power value associated with each data point; (iii) obtaining a design point from the time series data and the corresponding isentropic power values; and (iv) selecting the at least one design parameter to maximise power efficiency at the design point; and forming a turbine which exhibits the determined design parameter.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) A non-limiting embodiment of the disclosure will now be described, for the sake of example only, with reference to the following figures, in which:

(2) FIG. 1 is a cross-sectional drawing of a known turbocharger;

(3) FIG. 2 illustrates how a turbine of the turbocharger of FIG. 1 is conventionally connected to an engine manifold of an internal combustion engine;

(4) FIG. 3, which is composed of FIGS. 3(a) and 3(b), illustrates equal and partial admission of exhaust gas into two gas inlets of the turbine of the turbocharger of FIG. 1;

(5) FIG. 4 illustrates the time-variation of gas pressures at the gas inlets of the turbine of the turbocharger of FIG. 1;

(6) FIG. 5 is a plot of turbine expansion ratio and scroll pressure ratio for an engine cycle of a typical internal combustion engine;

(7) FIG. 6 shows steps of a method which is an embodiment of the present disclosure;

(8) FIG. 7 illustrates the accuracy of a first numerical estimate employed by the embodiment;

(9) FIG. 8 illustrates the accuracy of a second numerical estimate employed by the embodiment;

(10) FIG. 9 illustrates numerical values produced by the embodiment of the disclosure;

(11) FIG. 10 illustrates a process for obtaining a design point for a gas inlet volute in the embodiment;

(12) FIG. 11 illustrates schematically how data points are filtered by the embodiment;

(13) FIG. 12 illustrates two design points obtained by the embodiment;

(14) FIG. 13 is a plot of turbine stage efficiency against scroll pressure ratio for a candidate turbine design produced by the embodiment;

(15) FIG. 14 shows the turbine stage efficiency of turbines designed by the embodiment for different reaction values; and

(16) FIG. 15 illustrates the effect of reaction on turbine stage efficiency in a turbine designed by the embodiment.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(17) FIG. 1 shows a schematic cross-section through a known turbocharger 1. The turbocharger 1 comprises a turbine 11 joined to a compressor 12 via a central bearing housing 13. The turbine 11 comprises a turbine wheel 14 for rotation within a turbine housing 15. The turbine wheel 14 has a rotational axis 2 (in the plane of the diagram) and blades 9. Similarly, the compressor 12 comprises a compressor wheel 16 (or “impeller”) which can rotate within a compressor housing 17. The compressor housing 17 defines a compressor chamber 38 which is largely filled by the compressor wheel 16, and within which the compressor wheel 16 can rotate. The turbine wheel 14 and compressor wheel 16 are mounted on opposite ends of a common turbocharger shaft 18 which extends through the central bearing housing 13. The turbocharger shaft 18 is rotatably supported by a bearing assembly in the bearing housing 13 which comprises two journal bearings 34 and 35 housed towards the turbine end and compressor end respectively of the bearing housing 13. The bearing assembly further includes a thrust bearing 36.

(18) The turbine housing 15 has two exhaust gas inlet volutes 19a, 19b located annularly around the turbine wheel 14, and an axial exhaust gas outlet 10. The volutes 19a, 19b are symmetrical with respect to each other in a mirror plane perpendicular to the axial direction (note that in other known turbine housings the volutes are not symmetrical; furthermore in “double entry” turbines the volutes are circumferentially spaced, such as by 180 degrees, about the rotational axis 2 of the turbine). The compressor housing 17 has an axial air intake passage 31 and a volute 32 arranged annularly around the compressor chamber 38. The volute 32 is in gas flow communication with a compressor outlet 33. The compressor chamber 38 is connected to the volute 32 by a radially-extending diffuser space 39 (also referred to here as a “diffuser”) which is a gap between a radially-extending shroud surface 25 of the housing 17, and a radially extending hub surface 26 of the bearing housing 13. The diffuser 39 is rotationally symmetric about the rotational axis 2 of the shaft 18.

(19) In use, exhaust gas is provided to the two exhaust gas inlet volutes 19a, 19b from an exhaust manifold (also referred to as an outlet manifold) of the engine (not shown) to which the turbocharger is attached. The inlet volutes 19a, 19b are divided by a divider wall 20 which extends radially inwardly from the radially outer wall 21 of the turbine housing 15, to a tip 22. The exhaust gas exits the inlet volute 19a through a gap between the tip 22 of the divider wall 20 and a first shroud surface 23 of the turbine 11. The exhaust gas exits volute 19b through a gap between the tip 22 of the divider wall 20 and a second shroud surface 24 of the turbine 11. Thus, the exhaust gas passes from the exhaust gas inlet volutes 19a, 19b to the exhaust gas outlet 10 via a turbine wheel 14, which is rotated by the exhaust gas. In variants, the second shroud 24 surface may be provided as a surface of the bearing housing or some other component, instead of being a surface of the turbine housing 15.

(20) The turbine wheel 14 in turn rotates the compressor wheel 16 which thereby draws intake air through the compressor inlet 31 and delivers boost air to an inlet manifold of the engine via the diffuser 39, the volute 32 and then the outlet 33.

(21) FIG. 2 shows the turbine 11 in use (the rest of the turbocharger 1 is omitted), connected to the engine manifold 40 of an engine. A TO (turbine outlet) gas inlet of the turbine 11 in fluid communication with the gas inlet volute 19a is denoted 3.sub.1, and a BH (bearing housing) gas inlet of the turbine 11 in fluid communication with the gas inlet volute 19b is denoted 3.sub.2. The engine manifold includes passages 41, 42, 43 for transmitting exhaust gas from a first group of three cylinders of the engine to the gas inlet 3.sub.1 of the turbine 11, and passages 44, 45, 46 for transmitting exhaust gas from a first group of three cylinders of the engine to the gas inlet 3.sub.2 of the turbine 11. The reference numeral 4 denotes the turbine outlet.

(22) It is known that through a combustion cycle, the flow entering the exhaust gas inlet volutes 19a, 19b varies. We use the following notation. A quantity with a superscript dot (e.g. {dot over (p)}) denotes a variable which takes a respective value at each of a number of respective angular positions of the turbine wheel (e.g. a respective value at angular positions spaced apart by, for example, one degree), also referred to as the crank angle. Such a quantity must be measured (or calculated) at high frequency. By contrast, a quantity with a superscript dash (e.g. p) denotes a quantity which is averaged over the rotational period of the turbine wheel (i.e. over the cycle). A quantity with a subscript 1, or 3,1, denotes a quantity measured at the gas inlet 3.sub.1, whereas a quantity with a subscript 2, or 3,2, denotes a quantity measured at the gas inlet 3.sub.2. A quantity with a subscript 4 denotes a quantity measured at the turbine gas outlet 4.

(23) FIG. 3(a) illustrates the flow from the volutes 19a, 19b towards the turbine wheel 14 when the pressures in the volutes 19a, 19b are equal. The mass flow ratio (MFR) is defined (at any instant) as

(24) $\frac{{\stackrel{.}{m}}_{\mathrm{ex},1}}{{\stackrel{.}{m}}_{\mathrm{ex},1}+{\stackrel{.}{m}}_{\mathrm{ex},2}}$
where {dot over (m)}.sub.ex,1 is the mass which flows along volute 19a per second, and {dot over (m)}.sub.ex,2 is the mass which flows along volute 19b per second. An MFR of 0.5 means that both volutes are contributing equally to the mass flow.

(25) However, a situation in which the pressures in the volutes 19a, 19b are not equal is referred to as “partial admission”. FIG. 3(b) illustrates what occurs when there is a pressure pulse in the volute 19a which means that the pressure is higher than in the volute 19b. Exhaust gas from the volute 19a not only passes towards the turbine wheel 14, but also passes to the volute 19b (“recirculation”). Thus the high pressure volute 19a has completely blocked the low pressure volute 19b, and MFR is greater than one. The recirculation causes energy losses.

(26) We use the following abbreviations: P Pressure. Thus T Temperature ER Turbine expansion ratio SPR Scroll Pressure ration Pi Turbine Expansion Ratio {dot over (W)}.sub.t(T) Turbine Power {dot over (m)}.sub.ex Exhaust mass flow rate ° CA The crank angle (measured in degrees)

(27) Thus, the pressure at the gas inlet 31 is {dot over (P)}.sub.3,1, while the pressure at the gas inlet 32 is P.sub.3,2. FIG. 4 is a plot of time series data composed of data points collectively indicating the variation over engine cycles of {dot over (P)}.sub.3,1 (line 51) and {dot over (P)}.sub.3,2 (line 52). The respective time-averaged values of these pressures are almost identical and are indicated as line 53. This time-averaged value depends upon the data points (which in turn depend on the engine operating point which depends on the fuel conditions) and the averaging method and line 54 indicates an average value of the time-average pressure at the gas inlets, as measured by a dynamometer of the engine. For various reasons, the value measured by the dynamometer is typically inaccurate. The data measured on the dynamometer typically uses pressure measuring instruments mounted at the end of a long pressure measurement line. The line attenuates the pressure signal hence the ‘mechanical averaged’ p3 is lower than the time average of the instantaneous data (taken with a close coupled transducer)

(28) The expansion ratios (ER) are defined as follows:

(29) $\begin{array}{cc}{\stackrel{.}{\mathrm{ER}}}_1=\frac{{\stackrel{.}{P}}_{3,1}}{\stackrel{\_}{P_4}}\mathrm{and}{\stackrel{.}{\mathrm{ER}}}_2=\frac{{\stackrel{.}{P}}_{3,2}}{\stackrel{\_}{P_4}}& \left(1\right)\end{array}$
where P.sub.4 is the time-averaged pressure at the outlet 4. Note that in an alternative, P.sub.4 may be replaced by {dot over (P)}.sub.4 in this definition.

(30) The (instantaneous) scroll pressure ratio (S{dot over (P)}R) is defined as the ratio of the turbine inlet pressures, which can be calculated either from partial admission maps or on-engine data by high-speed data acquisition (HSDA).

(31) $\begin{array}{cc}\stackrel{.}{\mathrm{SPR}}=\frac{{\stackrel{.}{P}}_{3,1}}{{\stackrel{.}{P}}_{3,2}}& \left(2\right)\end{array}$

(32) Typically, diagrams of this parameter are plotted using the logarithmic parameter log.sub.10 (S{dot over (P)}R), in order for the scale to be symmetric between the two volutes.

(33) The (instantaneous) turbine inlet expansion ratio is defined as:

(34) $\begin{array}{cc}\stackrel{.}{P}\mathrm{.Math.}=\frac{{\stackrel{.}{\mathrm{ER}}}_1+{\stackrel{.}{\mathrm{ER}}}_2}{2}& \left(3\right)\end{array}$

(35) It is known to plot the respective values {dot over (P)}.sub..Math. against S{dot over (P)}R over a cycle, giving a diagram such as that shown in FIG. 5.

(36) D. Luckmann, et al., “Advanced Measurement and Modeling Methods for Turbochargers”, MTZ 0612016 Volume 77 includes a plot of the efficiency of a conventional twin-entry turbine for various values of values {dot over (P)}.sub..Math. against S{dot over (P)}R. The efficiency is not symmetrical with respect to log.sub.10 (S{dot over (P)}R), but instead is typically higher when log.sub.10 (S{dot over (P)}R) is negative (i.e. the pressure is greater in the BH gas inlet volute than in the TO gas inlet volute) than when it is positive.

(37) Turing to FIG. 6, a method 100 which is an embodiment of the present disclosure is shown. The embodiment is for designing and producing a turbine for a real engine of a specific type, such as the one which generated the plot of FIG. 5. Considering the known plot discussed above of the efficiency of a twin-entry turbine for various values of {dot over (P)}.sub..Math. and S{dot over (P)}R, the embodiment's design strategy can be summarized as designing the turbine such that the regions in the {dot over (P)}.sub..Math.-S{dot over (P)}R plane for which the designed turbine has high efficiency coincide with the measured trajectory illustrated in FIG. 5. To simplify the design algorithm, the trajectory of FIG. 5 is “distilled” into a small number of representative “design points” in the {dot over (P)}.sub..Math.-S{dot over (P)}R plane, and the turbine is designed to have high efficiency for those design points.

(38) In step 101 of the method 100, the isentropic turbine power bias of the real engine is identified. Step 101 is performed by measuring {dot over (P)}.sub.3,1 and {dot over (P)}.sub.3,2 at high frequency (typically 12 to 120 kHz depending on engine speed and resolution required), and converting this time-series of data points into desired quantities as follows using mean (i.e. time-averaged over the engine cycle) quantities which are available from a supplier of the engine and/or are measured at low frequency, such as T.sub.3,1, T.sub.3,2, P.sub.4, m.sub.ex,1 and m.sub.ex,2. Note that in a variation of the embodiment, the measured data may be different. For example, high frequency data {dot over (P)}.sub.4 may be obtained and used instead of the mean value P.sub.4.

(39) In step 102, a design point is obtained as follows.

(40) The respective turbine isentropic powers for the gas inlets 19a and 19b, for any given crank angle, are defined as:

(41) $\begin{array}{cc}{\stackrel{.}{W}}_{t,1,is}={\stackrel{.}{m}}_{ex,1}\times c_p\times {\stackrel{.}{T}}_{3,1}\times \left(1-{\left(\frac{1}{{\stackrel{.}{\mathrm{ER}}}_1}\right)}^{\frac{\gamma -1}{\gamma }}\right)& \left(4\right)\\ {\stackrel{.}{W}}_{t,2,is}={\stackrel{.}{m}}_{ex,2}\times c_p\times {\stackrel{.}{T}}_{3,2}\times \left(1-{\left(\frac{1}{{\stackrel{.}{\mathrm{ER}}}_2}\right)}^{\frac{\gamma -1}{\gamma }}\right),& \left(5\right)\end{array}$
where c.sub.p is the specific heat capacity of the exhaust gas. Eqns. (4) and (5) indicate the total available power which the turbine could in principle generate using the exhaust of the real engine, rather than what the turbine actually recovers, which is a function of the design of the turbine.

(42) and are calculated straightforwardly using Eqn. (1) and the time-series of data points. Note that in a variant of the embodiment, if high frequency data {dot over (P)}.sub.4 is available, Eqn. (1) may be calculated by using {dot over (P)}.sub.4 instead of the mean value P.sub.4.

(43) Instantaneous measurements of {dot over (T)}.sub.3,1 and {dot over (P)}.sub.3,2 may be hard to obtain at high frequency, but from the ideal gas law we obtain, for an ideal gas:

(44) $\begin{array}{cc}\frac{{\stackrel{.}{T}}_{3,1}}{{\stackrel{\_}{T}}_{3,1}}={\left(\frac{{\stackrel{.}{P}}_{3,1}}{{\stackrel{\_}{P}}_{3,1}}\right)}^{\frac{\gamma -1}{\gamma }},& \left(6\right)\end{array}$
where γ is the polytropic index of the gas. In a real gas, we would expect the polytropic index to be greater than γ. We have found, from a one-dimensional engine numerical simulation illustrated in FIG. 7, that the expression

(45) $\begin{array}{cc}\frac{{\stackrel{.}{T}}_{3,1}}{{\stackrel{\_}{T}}_{3,1}}={\left(\frac{{\stackrel{.}{P}}_{3,1}}{{\stackrel{\_}{P}}_{3,1}}\right)}^{\frac{n-1}{n}}& \left(7\right)\end{array}$
is well obeyed for a value of n of 1.5. In FIG. 7, line 201 indicates the time-profile of the instantaneous pressure at the output of a simulated engine. Line 202 is the simulated instantaneous temperature of the gas, and area 203 indicates a ±1.5% error around this value. Line 204 is obtained from Eqn. (7) using n=1.5. Line 204 tracks line 202 to within the error margin indicated by area 203.

(46) The instantaneous mass flow rate {dot over (m)}.sub.ex,1 and {dot over (m)}.sub.ex,2 are also difficult to measure exactly, but they can be expressed as:

(47) $\begin{array}{cc}{\stackrel{.}{m}}_{\mathrm{ex},1}=C_d{A}_1{\stackrel{.}{P}}_{3,1}\sqrt{\frac{\gamma }{R{\stackrel{.}{T}}_{3,1}}.Math.{\left(\frac{2}{\gamma +1}\right)}^{\frac{\gamma +1}{\gamma -1}}}\mathrm{and}{\stackrel{.}{m}}_{\mathrm{ex},2}=C_d{A}_2{\stackrel{.}{P}}_{3,2}\sqrt{\frac{\gamma }{R{\stackrel{.}{T}}_{3,2}}.Math.{\left(\frac{2}{\gamma +1}\right)}^{\frac{\gamma +1}{\gamma -1}}}.& \left(8\right)\end{array}$

(48) Here A.sub.1 and A.sub.2 are the respective critical areas of the gas inlet volutes. That is, CA.sub.housing=A.sub.1+A.sub.2. C.sub.d is a parameter called the “discharge coefficient”.

(49) Thus, by approximating γ as above by n=1.5, and using values for Cd and R given in standard tables, {dot over (m)}.sub.ex,1 and {dot over (m)}.sub.ex,2 can be calculated for any crank angle using Eqn. (8).

(50) Note that C.sub.d may not be not known in advance. If not, it can be worked out by an iterative process. First, we assume a value for C.sub.d, work out what value this would imply for {dot over (m)}.sub.ex,1, then find the mean of {dot over (m)}.sub.ex,1 over time, and compare it to the known value of m.sub.ex,1. If the two are different, the C.sub.d is varied. This process is carried out iteratively until the two are the same. In a case in which m.sub.ex,1 is not available, but m.sub.ex=m.sub.ex,1+m.sub.ex,2 is known, the embodiment first finds m.sub.ex,1 and m.sub.ex,2 from m.sub.ex by assuming that

(51) $\frac{{\stackrel{\_}{m}}_{\mathrm{ex},1}}{{\stackrel{\_}{m}}_{\mathrm{ex},2}}=\stackrel{\_}{\mathrm{SPR}},$
and then uses m.sub.ex,1 or m.sub.ex,2 in the iterative process.

(52) The accuracy of this approach is demonstrated in FIG. 8. In FIG. 8, line 211 indicates the time-profile of the instantaneous mass flow rate output of a simulated engine, and area 212 indicates a ±1.5% error around this value. Line 213 is obtained from Eqn. (8), and tracks line 211 to within the error margin indicated by area 212.

(53) Inserting the calculated values of , , {dot over (T)}.sub.3,1, {dot over (T)}.sub.3,2, {dot over (m)}.sub.ex,1 and {dot over (m)}.sub.ex,2 into Eqn. (4) and (5), gives the values of {dot over (W)}.sub.t,1,is and {dot over (W)}.sub.t,2,is illustrated by lines 221 and 222 in FIG. 9. Their sum, which is the total turbine isentropic power, is illustrated by line 223.

(54) Respective candidate design points for each of the volutes 19a, 19b are calculated as follows. For each of the volutes, the sub-steps illustrated in FIG. 10 are performed to generate the respective candidate design point.

(55) In a first sub-step 301, the data points for the real engine illustrated in FIG. 5 are filtered. The filter is different for each of the volutes 19a, 19b. For the volute 19a on the turbine outlet side, the filter retains only the data points for which log.sub.10 (S{dot over (P)}R) is greater than zero. For the volute 19b on the bearing housing side only the data points for which log.sub.10 (S{dot over (P)}R) is less than zero are retained. FIG. 11 illustrates the data points remaining for the turbine outlet side volute following this filtering operation. Note that the remaining data points include the mid-point 231 on the SPR interaction plot, because it is not exactly on the log.sub.10 (S{dot over (P)}R)=0 axis.

(56) In sub-step 302, for each of the filtered (i.e. remaining) data points, the product is calculated of the respective instantaneous isentropic power for the volute (i.e. {dot over (W)}.sub.t,1,is or {dot over (W)}.sub.t,2,is respectively) and the respective scroll pressure ratio S{dot over (P)}R.

(57) In sub-step 303, an isentropic power weighted mean SPR is calculated, by:

(58) 0$\begin{array}{cc}\mathrm{isentropic}\mathrm{power}\mathrm{weighted}\mathrm{mean}\mathrm{SPR}=\frac{\Sigma S\stackrel{.}{P}R\times I\mathrm{sentropic}P\mathrm{ower}}{\Sigma \mathrm{Isoentropic}\mathrm{power}},& \left(9\right)\end{array}$
where in each case the sum is over the filtered data points, and “Isentropic power” refers to {dot over (W)}.sub.t,1,is or {dot over (W)}.sub.t,2,is respectively.

(59) In sub-step 304, for each of the filtered data points, the product is calculated of the respective instantaneous isentropic power for the volute (i.e. {dot over (W)}.sub.t,1,is or {dot over (W)}.sub.t,2,is respectively) and the respective turbine expansion ratio {dot over (P)}.sub..Math..

(60) In sub-step 305, the isentropic power weighted mean Pi is calculated, by:

(61) $\begin{array}{cc}\mathrm{isentropic}\mathrm{power}\mathrm{weighted}\mathrm{mean}\mathrm{Pi}=\frac{\Sigma \stackrel{.}{P}\mathrm{.Math.}\times \mathrm{Isentropic}P\mathrm{ower}}{\Sigma \mathrm{Isoentropic}\mathrm{power}},& \left(10\right)\end{array}$
where in each case the sum is over the filtered data points, and “Isentropic power” refers to {dot over (W)}.sub.t,1,is or {dot over (W)}.sub.t,2,is is respectively.

(62) For each gas inlet volute 19a, 19b, the candidate design point is the isentropic power weighted mean Pi and the isentropic power weighted mean SPR.

(63) FIG. 12 is the same as FIG. 5 but with the two candidate design points 241, 242 for the respective volutes 19a, 19b obtained by this process overlaid.

(64) There is then a process of selecting one of the two candidate design points as the design point to be used in the design process of steps 104-107. One or more criteria can be used for this, such as the candidate design point for which the isentropic power is highest. Alternatively, the embodiment may determine which of the two candidate design points the locus of FIG. 5 is closest to for the greatest proportion of the engine cycle period.

(65) In step 103 a determination is made of whether the design point (i.e. the selected candidate design point) exhibits one or more criteria indicating that equal flow predominates. For example, the design point may have an isentropic power weighted mean SPR with an absolute value less than a predetermined threshold. If the one or more criteria are met, then the turbine may be designed by a conventional method which does not take into account the design point obtained in step 102. This possibility is not illustrated in FIG. 6.

(66) However, if the one or more criteria are not met, the turbine is designed by the process of steps 104-107 using the design point to select parameters of the turbine.

(67) Step 104 is a first design step, based on the design points. This step may be performed using a known optimisation process which is familiar to turbine designers, to optimise the design of the wheel and/or housing subject to the design point. The shape of both the gas inlet volutes is modified during the optimization process. The optimization process is carried out multiple times, each time using a different respective value of the ratio (CA.sub.housing/CA.sub.wheel) (i.e. a different respective reaction value), thereby generating multiple respective turbine designs.

(68) FIG. 13 illustrates the normalised turbine stage efficiency for different values of log.sub.10 (S{dot over (P)}R) for a turbine produced by the design step 104, when the candidate design point 242 of FIG. 12 is selected as the design point. The point 252 is the point on the turbine efficiency curve which has the same log.sub.10 (S{dot over (P)}R) value as the design point 242. The point 251 indicates the efficiency of the turbine produced by the design step 104 at the “inverse design point”, i.e. it has a log.sub.10 (S{dot over (P)}R) value which is the negative of the log.sub.10 (S{dot over (P)}R) value at the design point 242. The turbine efficiency for point 252 is higher than for point 251.

(69) FIG. 14 is a plot of the turbine stage efficiency, versus mass flow rate of two turbines designed in step 104. The horizontal axis indicates the degree of asymmetry in the pressures P.sub.3,1 and P.sub.3,2, with the left of the figure indicating that gas only enters the turbine through a single volute, and the right of the figure indicating that the pressures P.sub.3,1 and P.sub.3,2 are equal. Points on the horizontal axis between these extremes are partial admission.

(70) The curve for a relatively low value of reaction is shown as line 261, and the curve for a relatively high value is shown as line 262. For comparison, FIG. 14 also includes corresponding lines illustrating the turbine stage efficiency which would be obtained in the case of a turbine which is designed by a known design method assuming equal admission, for a relatively low value of reaction (line 263) and a relatively high reaction (line 264). It will be seen that designing the turbine taking into account the partial admission improves the efficiency over the whole of the range. It will also be seen that whereas, for the turbine designed assuming equal admission, a low reaction has higher efficiency when the flow is equal in the two volutes, and a high reaction has higher efficiency when the mass flow is in a single volute, in the case that the design of the turbine is optimized for partial admission, it is found to be always better to have a low reaction. In a conventional design process, because line 264 is above line 263 for most levels of asymmetry, it is typical to choose the reaction to take a high value. By contrast, the design process of method 100 suggests using a lower reaction.

(71) In step 105, the distribution of turbine efficiency for each of the turbine designs obtained in step 104, is calculated. From the result, an optimal reaction value for a turbine for the real engine is selected. FIG. 15 shows a plot of the normalised turbine efficiency, for respective values of log.sub.10 (S{dot over (P)}R), for three turbines generated in step 104 using different respective values of reaction. Line 271 illustrates the efficiency of a turbine generated using a reaction value of 1.1. Line 272 illustrates the efficiency of a turbine generated using a reaction value of 1.0. Line 273 illustrates the efficiency of turbine generated using a reaction value of 0.9. Thus, a reaction value of 0.9 is found to be superior to the other two values for this engine. Surprisingly, the curve 273 has a higher efficiency than the lines 271, 272 for all values of log.sub.10 (S{dot over (P)}R), although it might have been expected only to have higher efficiency near the design points.

(72) In step 106, using the reaction selected in step 105, the critical areas of the wheel and housing are calculated. This is done using the selected reaction and another assumed constraint, such as a total mass flow associated with the real internal combustion engine (e.g. specified by a manufacturer of the engine).

(73) In step 107, an optional further design step is carried out using the design point and the critical areas obtained in step 106, to obtain a final turbine design. This optimization step can be carried out using the same optimisation process as used in step 104. Note that if the optimal reaction value selected at step 105 is one of the reaction values used in step 104, then step 107 can be omitted. That is, the corresponding one of the candidate turbine designs produced in step 104 can be used as the final turbine design.

(74) In step 108, a turbo-charger including a turbine according to the final turbine design is produced (manufactured). This can be done using a conventional manufacturing process, such as casting.

(75) The explanation of the embodiment above includes an explanation of how representative operating points 241, 242 are obtained in the embodiment. Brinkert et al, “Konsequente Weiterentwicklung von Stoss-/Stauaufladung am 4-Zylinder Ottomotor”, Dresden Supercharging Conference 2014 also describes a process for obtaining average operating points from pulsatile turbine data. However, this method does not employ isentropic power weighted points, does not involve a filtration of the design points, and is believed to be inferior. Nor does this reference disclose a use for the average operating points.

(76) Although only a single embodiment of the disclosure has been described in detail, many variations are possible within the scope of the disclosure defined by the appended claims. For example, in a variant the embodiment, S{dot over (P)}R may instead be defined as the reciprocal of the right side of Eqn. (2).

(77) In a further variant, rather than using the isentropic powers associated with the respective data points to obtain isentropic-power weighted means, it would alternatively be possible to use the isentropic power in other ways, e.g. to filter out data points for which the isentropic power is less than a threshold (e.g. a certain proportion of its maximum value), and to obtain the design points using the remaining data points.

(78) Furthermore, in other variants of the embodiment, the method of FIG. 6 may be carried out while obtaining the design point in step 102 in a different manner, e.g. as a weighted point which is not an isentropic weighted mean.

(79) Furthermore, embodiments are possible in which the designed turbine is not a twin-type (in which both gas input volutes 19a, 19b enter the wheel chamber at the same rotational position about the axis 2 of the turbine wheel), but instead are of a type in which the volutes open into the wheel chamber at angular positions which are spaced from other by a 180 rotation about the rotational axis 2 of the wheel.