Impact of Mixing on the Signature of Combustor Defects

Abstract

Defects in the combustion chamber can negatively influence the performance of an aircraft engine and increase component stress in the turbine. One aim of the Collaborative Research Center 871 is to provide early prediction about the condition of the engine by analysing the signature of the exhaust gas jet. This includes the usage of machine learning techniques and helps to optimise maintenance times and to reduce costs. This topic is linked to the question, how defects in the combustion chamber affect the flow field and how the defect signature is mixed out in the hot gas path. Examples are shown for a simplified ring burning chamber, where several experimental and numerical studies have been done. Additionally, one failure case is described in detail here, where the methodology is applied to a real size gas turbine burning chamber and its subsequent turbine. Furthermore the diffusion theory is generalized to situations with complex geometrical boundary conditions, for instance from the turbine passage channel geometry. This approach is applied on the investigated example case and shows complex thermal diffusion coefficients, being in the order of 10,000–100,000 times larger than the molecular diffusion coefficient. Even these large values allow the determination of burning chamber defects from the exhaust flow pattern.

1 Influence of Defects on the Exhaust Gas and Temperature

Defects in the combustion chamber produce specific signatures in the distribution of exhaust gas components and temperatures. In order to investigate how these signatures are created, numerical and experimental investigations were carried out on an atmospheric model combustion chamber. The model combustion chamber consists of eight swirl burners in a ring array, from which one is individually operable, to simulate a burner defect in a defined way (von der Haar et al. 2016; Hennecke et al. 2017; Hennecke 2018). The model combustion chamber is capable to produce up to 25 different defects with variations in the thermal power, fuel–air-ratio and burner position of this variable burner. A model of the combustion chamber and the manipulated burner can be seen in Fig. 1.

Fig. 1

Geometry of the model combustion chamber with eight burners, the manipulated burner is marked in the red circle (von der Haar et al. 2021; von der Haar 2021)

For the lab experiments the concentration of certain species was measured using the Fourier Transform Infrared Spectroscopy (FTIR). This is an invasive 0-dimensional measurement technique where a ceramic suction tube is placed in the exhaust jet to collect samples. The exhaust gas composition is then determined at this measurement point. Figure 2 shows the model combustion chamber in operation with the ceramic suction tube for the FTIR measurements. Using a robotic arm, nine different measuring positions are approached to obtain a certain spatial resolution. A schematic view of the model combustion chamber with the burner and measurement position can be seen in Fig. 3. The red burner can be manipulated in the power or it can be tilted. For some experiments instead the blue burner is shifted from its ideal position.

Fig. 2

Model combustion chamber in operation with ceramic suction tube for FTIR experiments

Fig. 3

Schematic top view of the model combustion chamber with burner positions, points of measuments (x), manipulated and tiltable burner (red) and shiftable burner (blue) (von der Haar et al. 2021; von der Haar 2021)

In parallel, three-dimensional numerical CFD simulations were carried out for the model combustion chamber. For this purpose, a tetrahedral mesh was generated for the swirl burners and a hexahedral mesh for the combustion chamber which consist of 9 million elements in total. A mesh independence study was performed (von der Haar 2021). The investigated defects in the experiments were passed on as boundary conditions for the simulations. The meshing was carried out in the software ANSYS ICEM while the calculations were performed in ANSYS Fluent 17.2. In the combustion chamber, transient Scale-Adaptive-Simulations (SAS) were carried out with a pressure based solver. The 2-step mechanism 2S-CH4-CM2 (Boudier 2007) was used for the calculation of the main combustion process, while NOx was simulated in a postprocessing step with the model include in ANSYS Fluent.

Figure 4 shows the exhaust gas concentrations from the FTIR measurements and the CFD simulations at the positions according to Fig. 3. The dashed red line indicates the position of the manipulated burner. Some defects demonstrated here are listed in Table 1. A complete list of defects used for damage detection and classification and additional information about this work can be found in (von der Haar et al. 2021; von der Haar 2021). P is the thermal power and λ is the air–fuel ratio for the manipulated burner (Single) and the remaining seven burners (Array). Typically, the “normal” burners were operated with 15 kW thermal power each. The profiles show great similarity, even when the exact concentrations are not obtained by the simulation. The comparison of the experimental and the numerical data shows, that the simulation predicts the processes qualitatively correctly. The position of the disturbance by the manipulated burner agrees well in the simulation and experiment. Furthermore, each defect produces a specific distribution and the different cases can be distinguished from each other on the basis of the obtained results. Both, the experimental and numerical data sets can be used for defect detection and classification. After demonstrating that burner defects have a specific influence on the local exhaust gas composition in the model combustion chamber, this method is transferred to the combustion chamber of the V2500 engine (Hennecke 2018; von der Haar 2021). For this purpose, a numerical model of a 90° segment is build and discretised with a Delaunay mesh with 45 million elements. The numerical domain used for the CFD simulations can be seen in Fig. 5. The segment includes five burners, with the middle one being manipulated. The investigated defects include a partially or completely clogged fuel line (P50, P0), which result in a reduced thermal power and a cold gas streak. Furthermore, defects in the flame stabilisation were investigated. Two swirled air streams are generated in the fuel spray nozzle, which stabilise the flame through recirculation in the primary zone. The outer swirler (see Fig. 6, yellow arrows) is manipulated for the investigation. For this purpose, the swirler blades are removed (P100-Swirl) or the swirl air duct is blocked (P100-AirDuct), which leads to a destabilisation of the flame, creating a hot jet.

Fig. 4

Circumferential profile of the exhaust gas concentrations from the FTIR measurements (left) and the CFD simulations (right) (von der Haar et al. 2021; von der Haar 2021)

Table 1 Some investigated operating points and defects (selection) (von der Haar et al. 2021; von der Haar 2021)

Fig. 5

Numerical domain of the V2500 combustion chamber, manipulated burner marked in red (Ignatidis et al. 2022)

Fig. 6

Cross section view of the fuel spray nozzle. Air flow is marked in blue, fuel flow marked in green

Only the middle burner will be manipulated, the remaining burner operate in normal mode. Steady-State RANS and transient SAS simulations were performed for these defects. The resulting outlet temperature and CO profiles from the RANS simulations can be seen in Figs. 7, 8 and 9. The temperature and CO₂ distribution correlates very strongly, so that the CO₂ distribution is not shown. Both can be used for damage classification. It can be seen that a clogged fuel line leads to a significant local temperature decrease. Damages in the swirler blades and the combustion air duct lead create local hot spots and increased CO concentrations. The circumferential position of the defective fuel spray nozzle and the signature on the combustor outlet remains constant at for all defects. The impact position in the combustion chamber outlet remains static at 45°.

Fig. 7

Temperature contour plot at the combustion chamber outlet for reference case P100 (top), P50 (middle) and P0 (bottom)

Fig. 8

Temperature contour plot at the combustion chamber outlet for reference case P100 (top), P100-AirDuct (middle), P100-Swirler (bottom)

Fig. 9

CO contour plot at the combustion chamber outlet for defect P100-AirDuct (top) and P100-Swirl (bottom)

2 Damage Detection and Classification

The investigations on the model combustion chamber and the V2500 combustor show that defects have a specific influence on the exhaust jet. This allows a clear assignment of the defect from the exhaust gas. A method was developed with which damage detection and classification can be performed using machine learning techniques (von der Haar et al. 2021; von der Haar 2021). A Support-Vector-Machine (SVM) algorithm was applied on the model combustion chamber with the data sets from the FTIR measurements. The detection and classification was carried out with the CO, CO₂ and NO concentrations at three positions (180°, 202.5° and 225°, see Fig. 3).

First, a defect detection was done using a One-Class SVM. For that, all defects are seen as one class. Only the reference data is used for training. A big advantage of this method is that no damage library has to be created and that unknown defects can also be detected. With the help of this method, defects can be detected but not classified. A proper selection of features is necessary for a reliable defect detection and classification. The CO, CO₂ and NO concentrations are available at three evaluation positions, resulting in ten different feature combinations. The possible feature combinations can be found in Table 2. The damage detection and classification is performed with all combinations in order to select the best features.

Table 2 Feature combinations for defect detection and classification (von der Haar et al. 2021; von der Haar 2021)

In 85% of the cases it was possible to correctly detect the defects. The best classification rate is achieved for the combination #1 (3 × CO₂). The One-Class-SVM results for all feature combinations are shown in Figs. 10 and 11 (von der Haar et al. 2021; von der Haar 2021).

Fig. 10

One-Class-SVM FTIR

Fig. 11

One-Class-SVM CFD

In the next step, a defect classification was done using Multi-Class SVM. For this purpose, each defect is seen as a separate class. The SVM is trained on a damage library using the defects (listed above). Compared to the one-class SVM, the damages are not only recognised but also classified. The results of the Multi-Class SVM are shown in Figs. 12 and 13 (von der Haar et al. 2021; von der Haar 2021). In over 85% of the cases, the defects were correctly classified with the exception of feature combination #2. With feature combination #9, all test data are correctly classified.

Fig. 12

Multi-Class-SVM FTIR

Fig. 13

Multi-Class-SVM CFD

The method was transferred to the defects in the V2500 combustion chamber. The damage detection and classification here is also based on the CO, CO₂ and NO concentrations at three evaluation points. Figure 14 shows the CO₂ distribution at the combustor outlet and the evaluation points. The defect detection with the One-Class-SVM and damage classification using Multi-Class-SVM performed well. Apart from the defect ‘P100-AirDuct’, all defects were classified correctly. The Multi-Class-SVM result matrix can be seen in Fig. 15.

Fig. 14

CO₂ distribution at combustor outlet for defect ‘P0’ with evaluation points for classification (von der Haar 2021)

Fig. 15

Result matrix for Multi-Class-SVM classification of defects (von der Haar 2021)

Defect detection with One-Class-SVM and classification with Multi-Class-SVM worked very well with both the model combustor and the V2500 combustor. The method is suitable to reliably detect and classify defects based on exhaust concentrations (von der Haar 2021).

3 Defect Signature Propagation in the Turbine

Now that it is known how defects in the combustion chamber affect the flow field and how the defects can be detected and classified, it remains to be clarified how these defect signatures are propagated through the turbine to the outlet. For this purpose, an approach was developed to quantify the defect signatures in order to understand their progression through the turbine. In cooperation with the Institute of Turbomachinery and Fluid Dynamics (TFD), simulations of the downstream turbine were carried out and the approach applied (Ignatidis et al. 2022, Ignatidis 2024). The defect of the clogged fuel line was investigated, which produces a cold gas streak. The resulting flow field at the combustion chamber outlet is used as an inlet boundary condition for the turbine simulation. The temperature field was evaluated in each row in the turbine. For every angle, spatial averaging was done in radial direction. The cold gas streak produces a temperature profile that decreases locally and can be fitted with a Gaussian distribution curve according to Eq. 1.

$$\theta \left(\upxi \right)={T}_{0} + \frac{{\theta }_{0}}{\sqrt{2\pi {\sigma }^{2}}}{\text{exp}}\left(-\frac{{\left(\xi -\varphi \right)}^{2}}{2{\sigma }^{2}}\right).$$

(1)

Here, ξ is the circumferential position, φ represents the streak position, T₀ is the mean temperature of the surrounding gas and θ₀ a normalization factor (negative for cold gas streaks). The standard deviation σ is a measure of the gas streak width and can be used to calculate the full-width at half maximum (minimum) FWHM using $2\sqrt{2 \ln 2\sigma}$. The progression of the streak position and the FWHM now provide information about the mixing of the signature in the turbine. Figure 16 shows the circumferential temperature at the combustor outlet with the corresponding fitted Gaussian curve. The defective burner is at ξ = 45°.

Fig. 16

Temperature distribution at combustion chamber outlet (left), circumferential temperature with Gaussian curve (right) (Ignatidis et al. 2022)

The propagation and the mixing of the cold gas streak through the turbine is influenced by the blade curvature and the blade rotation. In order to examine these influences in a differentiated manner, two turbine simulations were carried out. A steady simulation with frozen-rotor was performed to show the geometric influences. An unsteady simulation shows how the mixing and streak shift is affected by the blade rotation. For both simulations, the width of the streak (its FWHM) and the streak position φ were determined at all rows. The progression is shown in Figs. 17 and 18. The rows R1–R4 represent the high-pressure turbine (HPT), R5–R15 the low-pressure turbine (LPT) and ‘HPTLPT’ the interface between HPT and LPT. The evaluation positions are located upstream of the corresponding row. Both blade curvature and speed are higher in the HPT than in the LPT which will affect the propagation of the gas streak.

Fig. 17

Disturbance FWHM for steady and unsteady simulation (Ignatidis et al. 2022)

Fig. 18

Streak position for steady and unsteady simulation (Ignatidis et al. 2022)

The FWHM plot (Fig. 17) shows that the disturbance width increases in the HPT, while it remains almost constant in the LPT for the steady simulation case and only slightly increases for the unsteady simulation case. Thus, the mixing increases with the blade curvature and rotational speed. The displacement of the streak position φ (Fig. 18) is minimal in the steady simulations, showing little influence from the blade curvature. However, the influence of the blade rotation becomes clear for the unsteady simulation. The streak shifts differently in the HPT and LPT, which is due to the different rotational speeds. The total mixing and streak displacement in the turbine is determined to be FWHM(R15) – FWHM(R1) = 9.7° and φ(R15) – φ(R1) = 81.4°. In addition, the mixing and streak displacement are considered per stage and can be found in Table 3.

Table 3 FWHM and streak position φ in HPT and LPT (Ignatidis et al. 2022)

Now that the mixing and streak displacement per stage are known for that rotational speed, it is possible to determine the total streak displacement and mixing for this operating point using a generalized approach with the number of stages n. To do this, Eqs. 2 and 3 are first used to calculate the total displacement φ_Total and total mixing FWHM_Total.

$${\text{WHM}}_{{{\text{total}}}} = {\text{n}}_{{{\text{HPT}}}} \left( {{\text{FWHM}}/{\text{Stage}}} \right)_{{{\text{HPT}}}} { }\,{\text{n}}_{{{\text{LPT}}}} \left( {{\text{FHWM}}/{\text{Stage}}} \right){ }_{{{\text{LPT}}}}$$

(2)

$$\varphi_{{{\text{total}}}} = {\text{n}}_{{{\text{HPT}}}} \left( {\varphi /{\text{Stage}}} \right)_{{{\text{LPT}}}} \,{\text{n}}_{{{\text{LPT}}}} \left( {\varphi /{\text{Stage}}} \right)_{{{\text{LPT}}}}$$

(3)

$${\varphi }_{{\text{Defect}}}={\varphi }_{{\text{EGV}}}-{\varphi }_{{\text{Total}}}$$

(4)

If a cold gas streak is detected in the exhaust gas jet and its position is determined, Eq. 4 can be used to calculate the position of the defective burner backwards. The method will be demonstrated using the temperature distribution downstream of the Exhaust Guide Vane (EGV, Fig. 19). Here, a cold gas streak is determined at the position φ_EGV = 35°. Equation 4 results in the defect burner position φ_Defect of 50°. The actual defective burner position is at 45° (see Fig. 16). Despite the error of 5°, the defective burner can be determined from the temperature distribution downstream the EGV, since the burner segments have a width of 18°.

Fig. 19

Normalized temperature distribution at EGV outlet (Ignatidis et al. 2022)

It should be mentioned that the values for the mixing and streak displacement per stage in Table 3 are only valid for the examined rotational speeds at this engine operating point. The HPT has a higher rotational speed than the LPT. For a more general statement, investigation with additional operating points will be needed to be carried out.

The analysis of the temperature distribution in the turbine shows how the blade curvature and the rotational speed influence the mixing and the position of the gas streak. This new approach allows the localization of a defective fuel spray nozzle from the temperature distribution in the exhaust gas.

4 Complex Diffusion Model for Defect Propagation

The above example shows that the width of the defect signature remains relatively limited (Fig. 17), while a first order assumption could be that for instance the cold gas streak mixes rather soon away, so that it would not be visible anymore at the exit of the turbine. In order to be able to generalize the mixing behaviour of such disturbances, an approach is developed, which is based on a generalized diffusion theory (Dinkelacker 2022).

In flows without any turbulence, a thermal streak (and similarly a streak of another type of chemical species) would mix out based on molecular diffusion processes, which are induced from thermal diffusion (or species diffusion), and which are described by Fourier’s law of thermal diffusion (or Fick’s law of species diffusion). The molecular diffusion process is typically very small, for gases at normal temperature and pressure (300 K, 1 bar) the molecular diffusion coefficient is in the order of 20 × 10⁻⁶ m²/s. For the typical passage time through the turbine (in the order of 5 ms) this diffusional process would not be observable at all due to its very small value.

In flows with turbulence it has become common, to model the effects of turbulent mixing on such diffusional mixing processes with the help of a turbulent viscosity concept. For instance for Reynolds averaged numerical simulations a turbulent viscosity parameter ν_t is modeled as a function of two turbulence parameters k and ϵ with ν_t = c_μ · k²/ϵ, with the constant c_μ = 0.09. Such approaches are leading to estimations of turbulent mixing, which work as an approximation, if the turbulent flow is not too far away from straight flows with sufficiently developed turbulence conditions (Ferziger and Perić 2002).

For flows within burning chambers of jet engines or within turbines, the boundary conditions are leading to very complex flow pattern with recirculation, dilution jets, and complex wall boundary layers between the turbine channels, such that an approximation of the resulting turbulent mixing process seems to be nearly impossible. Within our project we proposed to generalize the procedure of turbulent mixing to such complex situations with the aim to reach a reduced modeling approach. We label this approach as “complex diffusion model”, see Fig. 20.

Fig. 20

Concept of complex diffusion for the turbulent mixing of the defect flow within the complex boundary conditions of a turbine. They lead to a complex mixing behaviour, being described as a generalized complex diffusion process with an effective complex diffusion constant D*

As it is clear that here the details of the boundary situation will influence the turbulent mixing process significantly, such an approach can assist for the description of first order approximations only. We developed this approach empirically from the results of numerical simulation of the defect propagation process, either within the burning chamber or within the subsequent turbine segments.

The complex diffusion approach is based on the diffusion theory, where the diffusion equation is given for the number density n of molecules of one type with (Bird et al. 2007).

$$\frac{\partial n}{\partial t}=D\cdot \frac{{\partial }^{2}n}{\partial {x}^{2}}$$

(5)

Here the species diffusion equation form, 2. Fick’s law, is described, but for thermal diffusion the same is valid for the temperature field, if the thermal diffusion constant is used instead of the species diffusion constant. The mathematical solution depends on the initial and boundary conditions. For the example of an initial delta function of the defect pattern, the solution (obtained within the Fourier space, see mathematics textbooks) leads to a stable Gaussian distribution—similar to Eq. 1, where the denominator within the exponent contains the product 4 · D · t, with the diffusion constant D and time t. For a defect pattern within the ring-shaped geometry of a typical aviation engine (both within the combustor and the turbine passage section) a circumferential defect pattern can be described with the width B or the corresponding circumferential angle β (see Fig. 21). The mixing process within the complex flow and geometry conditions in the combustor and the turbine section leads to an increase of the disturbance width, being described with the generalized effective diffusion constant D^∗. It can be shown, that the increase of the width from B₁ to B₂ within a certain section can be described analytically as solution of the generalised diffusion law (Dinkelacker 2022). If the width of the disturbance (described by its FWHM) is expressed in the form of the corresponding angles β₁ and β₂ and the mean radius r₁ of the channel at the first cross section, and if the flow passage time between the two cross sections t₂ − t₁ is known from the mean velocity and distance, than the effective diffusion coefficient can be determined with the following equation

$$D^{*} = 14.24 \cdot \frac{{r_{1}^{2} \cdot \left[ {\left( {\frac{{\beta_{2} }}{{360^{^\circ } }}} \right)^{2} - \left( {\frac{{\beta_{1} }}{{360^{^\circ } }}} \right)^{2} } \right]}}{{t_{2} - t_{1} }}$$

(6)

Fig. 21

Determination of the effective diffusion coefficient from measurement of the width B₁ and B₂ (FWHM) of a defect disturbance at two different downstream positions 1 and 2 in a ring channel

With this approach it is possible to evaluate the resulting effective diffusion coefficient D^∗ even under the complex boundary conditions occurring within the burning chamber or the turbine of the airjet engine (Dinkelacker 2022).

The approach has been applied for the following situations for the determination of the effective thermal diffusion coefficient.

• Flow within the burning chamber

• High pressure turbine section (HPT)

• Low pressure turbine section (LPT)

Within the burning chamber the third part of the combustor is analysed, where the dilution air is added to the exhaust gas to cool it down before the turbine inlet. For the high pressure and low pressure turbine, the transient simulations shown above are analysed. In Table 4 the width of the disturbance is given for the analysed planes (X7 and X12 are two relevant planes within the burning chamber, not in detail shown in this report) together with the necessary geometry data and the approximated transit time of the flow. It is found that the resulting complex thermal diffusion coefficient reaches values between 0.24 and 1.82 m²/s for the burning chamber section and the turbine section. These values are significantly larger than the molecular thermal diffusion coefficients, which are also given in the table as a function of temperature and pressure for the relevant conditions. The ratio between complex diffusion coefficient and molecular diffusion coefficient reaches values of 13,000 for the burning chamber, 95,000 for the HPT and 30,500 for the LPT section. These large values are on one hand coming from the turbulent mixing in the flow, being commonly described with the turbulent viscosity, which is typically known to reach values of 100–1000 times that of the molecular viscosity. On the other hand here the influence of the complex additional mixing processes is included, coming from the irregular mixing flow within the combustor and from the multichannel flow within the moving turbine blade sections.

Table 4 Determination of the effective thermal diffusion coefficient for the third part of the burning chamber (mixing of dilution air), high pressure turbine (HPT) and low pressure turbine (LPT). Also the ratio to the molecular thermal diffusion coefficient is given

Experimental confirmations are not yet given. Real size gasturbines experiments have been planned in subproject A3, but have not been possible so far.

The advantage of this concept of complex diffusion is, that it would allow already from low-dimensional estimations the predetermination of the complex diffusion coefficient. With that it would be easy to predict the possible detectability of defect pattern also in other geometries.

5 Conclusions

In subproject ‘A6: Mixing and Combustor Signature’ it was investigated, how damage signatures are created in the combustion chamber and how they can be detected and classified from the exhaust gas jet. The initially asked questions were answered. How does the damage in the combustion chamber affect the exhaust gas composition and temperature distribution? The experimental and numerical investigations on the model combustion chamber and the V2500 combustor show that defects create a characteristic signature in the temperature and species distribution, which allows a clear allocation of damages. How is a combustion chamber damage detected and classified? Applying Support-Vector-Machine methods allow the automatic detection and classification of defects based on the distribution of the exhaust gas components. How does the disturbance signature propagate through the turbine section and how is it mixed out? The numerical investigations on the V2500 turbine show how defect signatures propagate in the hot gas path and how the mixing and displacement are affected by the blade curvature and rotating speeds. In addition, an approach was developed with which a defective fuel spray nozzle can be localised from the temperature distribution in the exhaust gas jet at a known rotational speed.

Furthermore the diffusion theory is generalized to situations as in the burning chamber or turbine, where the turbulent flow mixing process is not only determined from molecular diffusion and turbulent mixing but also from the complex geometrical boundary conditions, for instance from the turbine passage channel geometry. This approach is applied on the investigated example case. It is found that the complex thermal diffusion coefficient of the investigated cold gas defect is in the order of 10,000–100,000 larger than the molecular diffusion coefficient, being especially large in the high pressure turbine section. Even these large values still allow the determination of burning chamber defects from the exhaust flow pattern.