The effect of transversal velocity fluctuations on the thermoacoustic response of reheat flames

Abstract

Thermoacoustic analysis remains a key component during the development process of new combustion chambers. Whereas a vast amount of literature exists on the interaction of planar acoustic and propagation-stabilized flames, research on reheat flames, especially, on how they respond to transverse modes is scarce. With the study presented here, we show the isolated effect of transversal velocity perturbations on a reheat flame. This is done for two distinct flame stabilization cases occurring in a lab-scale reheat combustor. For the first, the flame is partly autoignition-stabilized but also has propagation-stabilized regions in the shear layer because of recirculation zones induced by a backward-facing step. The second features only a minimal step height and therefore only minor recirculation zones, leading to an almost purely autoignition-stabilized flame. The two different flame stabilization cases are investigated using Reynolds–averaged Navier–Stokes simulations integrating an in-house reheat combustion model. The analysis shows that transverse velocity perturbations have no effect on flames that are purely stabilized by autoignition. In the presence of propagation-stabilized flame regions within the shear layer, transverse velocity perturbations do induce heat release rate fluctuations, as expected.

Keywords

Thermoacoustic autoignition CFD transverse eigenmodes high-frequency

Novelty and significance statement

To date three approaches^1–3 exist to model the dynamic response of one-dimensional autoignition flames to longitudinal/planar acoustic waves. Recent studies^4,5 showed for one of these models an adaptation and integration in an FEM-based framework to capture the thermoacoustic effects that the transverse acoustic eigenmodes of the combustion chamber have on non-compact autoignition flames. In this work, the dynamic heat release rate response of reheat flames perturbed by transversal velocity fluctuations was neglected. This paper addresses this gap by providing new insight into how autoignition flames behave when perturbed by transversal velocity fluctuations. The significance of this work is twofold: firstly, it provides a more profound understanding of the influence that transverse eigenmodes have on autoignition flames. Secondly, it constitutes a valuable contribution to research in this field. These findings can support the industrial development of novel low-emissions gas turbine combustion chambers.

Introduction

In order to comply with the Paris agreement,⁶ the future energy landscape must be based on renewable energy systems to ensure low emissions.^7–9 Gas turbines firing alternative carbon-free fuels can be an ideal asset to balance and stabilize the power grid.^8,10–14 To fire a variety of fuels with very different combustion properties, extensive combustion chamber development is needed. When developing a new combustor, a critical challenge is a detailed thermoacoustic analysis to mitigate combustion instabilities.¹⁵ Thus, the need for more detailed and sophisticated thermoacoustic analysis tools is apparent.

The thermoacoustic analysis of longitudinal/planar acoustic waves on propagation stabilized flames has been extensively studied in the past.^16–24 Nicoud et al.¹⁶ showed how the thermoacoustic stability of combustion chambers with propagation-stabilized flames can be assessed using the finite element method (FEM) and an $n - τ$ model, first introduced by Crocco.²⁵ Schuermans¹⁸ showed how the acoustics of complex geometries can be segmented into simpler subdomains described by a state-space representation and then concatenated in a network model to perform thermoacoustic analysis of acoustically compact flames with high accuracy. In contrast, reheat flames have recently received increased attention.^1,3,26–31 Ni et al. observe and describe the influence of pressure pulsations on a reheat flame.³² Bothien et al.²⁸ reconstructed the acoustic transfer matrix from a LES simulation of a backward-facing-step reheat combustor. Zellhuber et al.,²⁶ Gant et al.¹ and Gopalakrishnan et al.³ derived frameworks to characterize the HRR response of 1D reheat flames perturbed by planar waves. Heinzmann et al.^4,33 extended the numerical Lagrangian framework of Gopalakrishnan to compute modeshape dependent FTFs of transverse modes accurately.

In general, propagation-stabilized flames and autoignition flames react very differently to acoustic perturbations. However, the differentiation thereof is not trivial. Reheat flames in industrial gas turbine combustion chambers are usually composed of different heat release rate (HRR) regions. Certain regions of a reheat flame are solely stabilized by autoignition, others are stabilized by propagation. The propagation-stabilized HRR regions of reheat flames are typically located in the shear layers, which form due to recirculation zones at geometrical area jumps or around bluff bodies. The core of the reheat flame is autoignition-stabilized within the bulk flow. The overall HRR distribution between the different zones is not fixed and can vary. With higher inlet temperatures in a sequential combustion chamber the overall HRR zone becomes more autoignition driven with characteristic shorter ignition delay times; and vice versa for colder conditions. While the propagation-stabilized HRR regions are governed by the balance of flame consumption speed and local flow velocity, the autoignition is governed by the balance between chemical and residence time scales. Acoustic fluctuations can have a large impact on both flame zones.

With respect to perturbations in transverse direction, transversal acoustic waves can significantly affect the flame shape and HRR. Close to geometric discontinuities, such as area jumps, transversal acoustic eigenmodes can induce vortex shedding and modulate the reactive shear layers. This leads to HRR fluctuations locally within the propagation-stabilized part of the flame.³⁴ The autoignition-stabilized HRR regions are sensitive to acoustic pressure and isentropic temperature fluctuations, which modify the local ignition delay time and therefore shift the flame back and forth.^3,4 Heinzmann et al.^4,5 developed a framework to model the dynamic effect that such modes have on reheat flames. They assessed transverse eigenmode stability and validated it with experiments. An assumption of the framework is that transverse velocity perturbations have negligible effect on a one-dimensional (1D) autoignition flame. This assumption is based on the fact that reheat flames react significantly weaker to velocity fluctuations in flow direction when compared to temperature and pressure fluctuations. This can be seen by the low value of the FTF with respect to velocity perturbations in Ref.²⁸ The mechanism responsible for the HRR response due to in-flow-oriented velocity perturbation is the modulation of the equivalence ratio.^1,2,26,35 However, no equivalence ratio fluctuations are present in the case of transverse velocity perturbations in fully premixed conditions. A homogeneous premixed mixture upon entry into the combustion chamber was confirmed by a prior study for the investigated combustor.³⁶ In-house CFD simulations also concluded a good mixing of fuel and air before entering the combustor. Thus, the modeshape-dependent FTF $F_{ψ_{Ω}} (ω)$ for a certain eigenmode $Ω$ to compute the fluctuating instantaneous heat release rate (HRR) ${\hat{\dot{q}}}_{a, ψ_{Ω}}$ of Eq. (1) is assumed to remain unaffected by transverse velocity perturbations.⁴

{\hat{\dot{q}}}_{a, ψ_{Ω}} (z) = {\dot{q}}_{0, a} (z) F_{ψ_{Ω}} (ω) \frac{\hat{p} (x_{r e f}, z)}{p_{0}}

(1)

To the best of our knowledge, there is no literature to date stating whether transverse velocity perturbations have an effect on 1D reheat flames. In this paper, we identify the dynamic HRR response for two distinct cross-sections of a rectangular lab-scale reheat combustion chamber.³⁷ This is done by acoustically exciting the first transverse modes for both dimensions of a rectangular combustion chamber (i.e. in $x y$ - and $x z$ -direction) in unsteady compressible RANS simulations. To identify and isolate whether transverse velocity fluctuations have negligible effect on a pure reheat flame, two different simulations are performed for each of the dimensions (four in total). Non-compact Fourier decomposition is done of the results to identify the flame response of both the autoignition-stabilized flame parts as well as the propagation-stabilized assisted flame regions.

Methodology

The methodology section describes how the RANS computation is set up. First, the geometry is shown. Second, the combustion model is introduced. Third, the numerical setup is discussed. Fourth, the mean fields are shown and lastly, the implementation of the transverse forcing is discussed.

Combustor geometry

The atmospheric combustor of the Technical University of Munich (TUM)³⁷ shown in Figure 1 consists of a vitiator followed by a reheat combustor. The vitiator is operated with a lean, perfectly premixed, preheated mixture of hydrogen and methane. The vitiated air enters the reheat combustor and passes through a mixing section where the fuel is injected into the hot gas in a jet-in-cross-flow arrangement. To improve mixing, delta wing-shaped vortex generators are placed upstream of the fuel injection. The mixture then passes through a convergent section before entering the reheat combustion chamber through a diffuser-shaped outlet. The rectangular combustion chamber mainly expands in $y$ -direction (Figure 1 first schematic), which leads to strong upper and lower recirculation zones downstream of the area jump. In $z$ -direction (Figure 1 second schematic), the combustion chamber does not expand significantly, and thus no significant recirculation zones are observed. The flow-direction is aligned with the $x$ -axis. For more details on the sequential combustor, the reader is referred to Refs.^4,34,37,38

Figure 1.

Geometry of the reheat combustion chamber at TUM. The $x y$ -cross-section is shown on the top, and the $x z$ -cross-section on the bottom. Qualitative experimental flame images are shown solely for the visualization purpose (different operating point).

RANS computation

The RANS CFD computations are performed for the presented rectangular reheat combustion chamber (Figure 1) burning a mixture of 50% methane and 50% hydrogen by weight at lean and autoignitive conditions. The CFD is done using ANSYS Fluent 2024 R1³⁹ using the realizable $k - ϵ$ model for turbulence with an adaptive Schmidt number to obtain better mixing results at the jet-in-crossflow fuel injection. A RANS version of the combustion model derived by Kulkarni et al.^40,41 was implemented and extended to capture the effects of acoustic waves.

This combustion model is based on a transported normalized progress variable ( $P V$ ) which represents intermediate species reactions that govern the ignition delay. In contrast to using a linear $P V$ , reaction species from the radicals ( $C H_{2} O$ , $C O$ , $H O_{2}$ ) and product pool ( $C O_{2}$ , $H_{2} O$ ) are used to properly capture the ignition process. The advantage of including the (hot) products is that the propagation-stabilized flames in the shear layer of the recirculation zones are captured more accurately. The normalized $P V$ is obtained by dividing the sum of the included species mass fractions ( $Y_{i}$ ) by its sum at equilibrium ( $Y_{i, eq}$ ):

P V = \frac{\sum Y_{i}}{\sum Y_{i, eq}}

(2)

The $P V$ source term ( ${\dot{ω}}_{P V}$ ) can be computed using finite differencing. For the model to work, the source term must be strictly positive and only depend on known parameters like the local fuel mass fraction $f_{F}$ , hot gas mass fraction $f_{H}$ , temperature $T$ , pressure $p$ and the value of the $P V$ itself. By splitting the temperature and pressure into its mean and fluctuating part ( $T_{0, init}, T^{'}, p_{0}, p^{'}$ ), and under the assumption that the mean value of the temperature and pressure are constant during the radical buildup, the $P V$ source can be expressed as:

{\dot{ω}}_{P V} = {\dot{ω}}_{P V} (f_{i}, T_{0, init}, T^{'}, p_{0}, p^{'}, P V)

(3)

In their combustion models, Brandt^42,43 and Kulkarni⁴⁰ assumed that the transport of energy scales the same as the transport of mass, and that the change of specific heat capacity $c_{p}$ upstream of the flame is negligible. Therefore, the initial temperature can be expressed through the mass fractions $f_{i}$ and the known initial temperatures $T_{i, init}$ :

T_{0, init} = \sum T_{i, init} f_{i}

(4)

Assuming an isentropic correlation of pressure and temperature for acoustic waves, $T^{'}$ can be expressed through $p^{'}$ , and as the operating pressure $p_{0}$ is known, the $P V$ source can be simplified to:

{\dot{ω}}_{P V} = {\dot{ω}}_{P V} (f_{i}, p^{'}, P V)

(5)

To model the turbulence chemistry interaction (TCI) a PDF approach for the mass fractions $f_{i}$ and the $P V$ is used. The mean turbulent source term is obtained by folding the sources over a probability distribution:

{\bar{\dot{ω}}}_{P V} = \int_{0}^{1} (\int_{0}^{1} {\dot{ω}}_{P V} (f_{i}, p^{'}, P V) P (f_{i}) d f_{i}) P (P V) d P V

(6)

The HRR is then obtained by using the mixed is burned approximation and delaying it by multiplying the reaction rate with the PV.

The major advantage of this approach is that it is computationally cheap. The source terms, which can be computed using 0D reactors, and the integration can be done a priori and stored. Therefore, only the educts, products, $P V$ , its variance and the mass fractions with their variances need to be transported, and no expensive reaction rate computations are necessary. Using this approach, it is assumed that there is no interaction between the individual reactors during computations. Performing 0D reactor mixing studies, Brandt⁴³ verified this assumption and obtained an overall error below 10%.

In this paper, the $P V$ source terms were computed using the GRI30⁴⁴ mechanism and the probability distributions for integration were created using modified curl mixing of particles.⁴⁵ To reduce $P V$ source lookup time during the simulation, a Residual Network is used to retrieve the sources. Residual Networks are neural networks where each block adds a skip connection. The skip connection helps with the training stability and accuracy for deeper networks by mitigating vanishing gradients and overfitting. The network used here consists of an input block followed by three residual blocks, each consisting of two fully connected layers with a skip connection, and an output layer.⁴⁶

Four simulations are computed in total. Table 1 displays the naming convention, depending on the orientation of the first eigenmode as well as the HRR effects accounted for. The T1y- and T1z-simulations are computed for the first transverse eigenmode in $y$ - and $z$ -direction (Figure 1), respectively, with the inclusion of local acoustic pressure and temperature fluctuations effects. The T1yNPE- and T1zNPE-simulations (NPE: no pressure effects) do not account for a change in HRR due to local pressure and temperature fluctuations in the CFD progress variable. Thus, the flame only reacts to velocity and equivalence ratio fluctuations. For the NPE cases, $p^{'}$ is set to zero for the source term lookup. Therefore, the effect of the pressure and temperature change induced by acoustic waves is ignored during the simulation.

Table 1.

Simulation nomenclature depending on eigenmode and accounted HRR effects.

First transverse eigenmode	Simulation nomenclature
	All effects	Without $p^{'}$ and $T^{'}$ effects
y-Direction	T1y	T1yNPE
z-Direction	T1z	T1zNPE

The computational domain (Figure 3) is half of the reheat combustor³⁷ making use of the symmetry planes $x z$ and $x y$ for efficiency. The mesh is made up of approximately 1.3*10 $^{6}$ cells with refinements at the walls, the area changes and the fuel injection. A mesh independence study comparing the fuel mixture fractions at the dump plane as well as the magnitude and position of the HRR shows no variation for a finer mesh. Time and space are discretized in second order and the timestep is set to 4e $-$ 7s to obtain an acoustic CFL below one. The operating point, which is shown in Table 2, is equal to the $N G_{50 m e d}$ operating point from Franke et al.³⁷ Temperature and mass flow rate are prescribed at the inlets, and pressure is prescribed at the outlet. Non-reflecting boundary conditions are applied at both boundaries.

Figure 3.

Half of the CFD mesh and computational domain.

Table 2.

Gas properties

Property	Hot gas	Fuel premixed with additional air
$\dot{m}$ [g/s]	366.46	8.55
$T$ [K]	967	283.15
$Y_{O_{2}}$	0.168	0.123
$Y_{N_{2}}$	0.76	0.461
$Y_{C O_{2}}$	0.039	-
$Y_{H_{2} O}$	0.032	-
$Y_{C H_{4}}$	-	0.208
$Y_{H_{2}}$	-	0.208

The excitation is achieved in a similar way as was shown by Zellhuber et al.⁴⁷ On the combustor walls, which coincide with the antinodes of the first transversal eigenmode, small porous zones with high resistance are added, Figures 2 and 3. Within these zones, sinusoidal momentum source terms are applied to force the fluid domain. Due to the high resistance, the gas motion within the porous zones is strongly restricted; therefore, the prescribed momentum fluctuations are converted into pressure fluctuations. The precise forcing frequencies of the T1y and T1z modes are calculated by solving the homogeneous Helmholtz equation Eq. (7) in COMSOL 6.2, where $ρ_{0}$ and $p_{0}$ are the time-averaged quantities of the density and the pressure. Further, $\hat{p}$ is the pressure fluctuation and $ω$ the angular frequency.

\begin{matrix} \nabla \cdot (\frac{1}{ρ_{0}} \nabla \hat{p}) + \frac{ω^{2}}{γ p_{0}} \hat{p} = 0 \end{matrix}

(7)

Figure 2.

Porous zones and momentum source terms.

The time averaged flame is accounted for in the FEM study by inclusion of the time averaged temperature field in the combustion chamber, which is taken from the steady CFD computation.

Results

First the CFD mean field results are shown and the time averaged HRR field is validated for the $x y$ -cross-section using experimental data from Franke et al.³⁷ Subsequently, observations are made for two distinct geometrical planes of the combustion chamber. Then, the $x y$ -plane ( $z$ = 0) is analyzed where the flame response is composed of autoignition and propagation-stabilized flame regions for both the T1y and T1yNPE simulations. The subsequent section presents the results of the analysis of the $x z$ -plane ( $y$ = 0). Here, the flame is predominantly autoignition-stabilized,^4,29 and comparisons are drawn between the T1z and T1zNPE simulations.

CFD steady HRR mean field validation

Figure 4 shows the temperature, $x$ -velocity and $P V$ contours from the RANS computation for the $x z$ -cross-section. Figure 4(a) shows a uniform temperature distribution at the inlet of the combustion chamber. Figure 4(b) indicates that the recirculation zones induced by the step are small. Figure 4(c) shows the result of the in-house combustion model. The earlier timed ignition at the corner of the area jump is captured because of the inclusion of (recirculating) hot products. On the $x$ -axis the flame is purely autoignition-driven and the position matches with the analytical mean ignition delay time also reported in Ref.³⁷

Figure 4.

CFD mean fields for the $x z$ -cross-section: (a) temperature field, (b) x-velocity field, and (c) progress variable (PV).

The time averaged flow field and flame shape of the CFD simulation is validated using experimental data.³⁷ Figure 5 compares the time-averaged HRR on the $x y$ -plane from a) line-of-sight-integrated chemiluminescence and b) the RANS simulation. The mean ignition length is estimated from Gaussian kernel fits of the HRR along $x$ . At $y = 0$ , the peak is located 0.16m downstream of the dump plane, which is in good agreement with the experiment. This agreement indicates that the mean flame location is predicted accurately by the implemented in-house combustion model. Toward the combustor walls, the flame is shifted upstream, consistent with the reduced axial velocity caused by recirculation downstream of the area change at the dump plane. The shear-layer flames are captured by the simulation, but the strongest shear-layer HRR is predicted slightly farther upstream. This offset is most likely attributed to the implemented combustion model. A more pronounced autoignition-stabilized core is also predicted by the simulation compared to the experiment. One likely reason is that the mixing predicted by the simulation may not have reproduced the actual mixing in the experiment. Also, as the amount of shielding air used in the experiment is not known, the jet-in-crossflow fuel injection momentum predicted by the simulation might differ slightly from the experiment. Reduced jet momentum would decrease fuel penetration toward the combustor centerline and reduce the fuel mass fraction there. Further, line-of-sight-integrated chemiluminescence results are compared to the CFD HRR. While the comparison of these values is state-of-the-art, they describe different quantities and are therefore not identical. Despite these differences, the simulated time-averaged HRR reproduces the main structure of the measured field. For the $x z$ -plane (Figure 5(c)), no experimental measurements are available for validation. However, the identical combustor geometry was used in McClure et al.,⁴⁸ where a similar flame shape was reported at a different operating point burning methane and propane. The near-wall HRR is likely predicted too far upstream in the RANS result, but the mean field is considered sufficiently accurate for the present study.

Figure 5.

(a) Time averaged HRR mean field on the $x y$ -plane of the experimental line-of-sight-integrated chemiluminescence imaging,³⁷ (b) time averaged HRR mean field on the $x y$ -plane of the RANS computation, (c) the time averaged HRR mean field on the $x z$ -plane of the RANS computation.

The excitation frequencies were determined by solving Eq. (7) in FEM, analogously to Heinzmann et al.⁴ The effect of the flame is accounted for by including the time-averaged temperature field in the combustion chamber. For the T1y-mode the forcing frequency is 1426Hz and for the T1z-mode 2660Hz. Figure 6(a) shows the first transverse eigenmode of the $x z$ -plane obtained by the eigenfrequency study using FEM. Figure 6(b) shows the instantaneous pressure perturbations of the excited first transverse mode at an identical frequency of 2660Hz. The comparison shows an excellent match between the modeshapes. The same is the case for the T1y mode (not shown). Thus, it is confirmed that the first transverse eigenmodes are correctly excited in the CFD simulation.

Figure 6.

a) T1z acoustic eigenmode of the FEM computation, b) T1z acoustic eigenmode of the RANS computation.

Propagation- and autoignition-stabilized flame regions on the $x y$ -plane

Analyzing the flame response on the $x y$ -plane (which is the symmetry plane of the T1y simulation), distinct observations can be made. Figure 7(a) shows the pressure perturbations in the first column, the transverse velocity perturbations in the second column, and the HRR perturbations in the third column for the T1y-simulation. All quantities are plotted for half an oscillation from 90° to 270°. It is visible that the first transverse acoustic mode has an effect on the partly autoignition-stabilized reheat flame. An alternating HRR perturbation pattern is clearly visible at a phase of 180°. At this phase, the upper ( $y > 0$ ) HRR perturbation in the shear layer flame is around 180° out of phase with the transverse velocity perturbation. The lower ( $y < 0$ ) HRR perturbation in the shear layer flame is in phase with the velocity perturbation. The same behavior is not observed for the T1yNPE-simulation shown in Figure 7(b). Therefore, the clearly observable HRR perturbation pattern in the T1y-simulation is believed to occur due to pressure and temperature effects. The very local and small HRR fluctuations right after the dump plane ( $x$ = 0) are very similar in both simulations, and no qualitative differences are observed. Most likely, they are induced by vortical structures that originate right after the dump plane. This behavior was also observed in prior experiments of the experimental setup by McClure et al.³⁴ The tracking of more/less intense HRR perturbation patches revealed that these vortical structures are transported with the mean flow.³⁴ They are contained between the shear layers of the recirculation zones, that is, in the propagation-stabilized shear layer flames. With respect to the central symmetry line ( $y$ = 0), no HRR fluctuations are present in both simulations. This is interesting to observe, because the central symmetry line is a nodal line of the pressure modeshape and an antinode for the velocity perturbations. Thus, on this line, a fluid particle experiences no pressure fluctuation, but indeed the strongest velocity fluctuations. Therefore, it is found, that the transverse velocity fluctuations have no influence on a solely autoignition-stabilized reheat flame segment at ( $y$ = 0). This is further supported by the experimental results from McClure et al.³⁴ for the same combustion chamber. In the experiment, the identical first transverse mode was measured in the combustor and no flame modulation was found of the autoignition core region.

Figure 7.

a) Pressure perturbations (first column), transverse velocity perturbations (second column), and HRR perturbations (third column) for the T1y-simulation and half an oscillation. The same variables are plotted in b) for the T1yNPE-simulation.

Quantitative comparisons between the simulations can also be made. By integrating the HRR for multiple cross-sections parallel to the $x$ -axis (i.e. integrating along lines that are parallel to the $x$ -axis) and relating the integral quantity to the local velocity perturbations at the flame front (0.1m), specific local FTFs can be computed. Figure 8 shows the local FTFs for a) the T1y-simulation and b) the T1yNPE-simulation. The integrated HRR is plotted by the dashed black line to identify which locations correspond to the more strongly pronounced flame regions, such as the shear layer flames. The following observations are made:

The transverse velocity fluctuations do not induce HRR fluctuations at the center cross-section ( $y = 0$ ), which is visible from the gain of 0. This is the case in both simulations shown in Figure 8(a) and (b). This is particularly important, because the cross-section at $y = 0$ coincides with the antinode of the transverse velocity perturbation field, where the velocity fluctuations are strongest. At the same time, this identical cross-section ( $y = 0$ ) is a nodal line for pressure and temperature fluctuations. Thus, if the transverse velocity had an effect on the reheat flame, it would be expected to appear in the most isolated manner and most strongly at this cross-section. At the outer edges of the flame (toward $y = \pm 0.1 m$ ), the flame is predominantly propagation-stabilized. Thus, this region is expected to respond to velocity fluctuations due to the different flame stabilization type. Indeed, both simulations show these kernel-like HRR zones toward the combustor walls. In the intermediate region, the flame is stabilized by autoignition and additionally anchored by the outer shear-layer flame regions. However, even in such not fully autoignition-stabilized flame regions, a strong effect of pressure and isentropic temperature is observed, whereas the effect of transverse velocity remains negligible (Figure 8(a)). If transverse velocity was the main driver of the observed HRR fluctuations, these fluctuations would also need to appear in the T1yNPE (Figure 8(b)) simulation, which is not the case. From this the conclusion that the transverse velocity has a negligible effect on pure reheat flames (as for the central cross-section) is evident.

The phase of the T1y-HRR response in the shear layer flames oscillates around $0$ for the flame located on the negative $y$ -axis, and $- π / 2$ for the flame located on the positive $y$ -axis. Whilst the velocity perturbation has the same phase on the investigated plane, the pressure and resulting isentropic temperature perturbations are out of phase toward the combustor walls (antinodes are at the walls). This is most likely the reason for the different phase in the HRR-response compared to the T1yNPE-simulation. For the T1yNPE-simulation, the phases of the HRR-response of the shear layer flames appear similar at around $- π / 2$ .

The peaks in the FTF gain coincide with the stronger shear layer HRR flame regions.

The gain of the HRR-response of the shear layer flames is significantly higher in the T1y-simulation compared to the T1yNPE-simulation. This is due to the fact that no HRR-response due to pressure and isentropic temperature perturbations is accounted for in the latter. Further, the shear layer flames are located closely to the pressure antinodes, which suggests a pronounced HRR-response.

Toward the combustor walls, the transverse velocity field has its nodes. Hence, as the $y$ -coordinate approaches the location of the combustor walls, the transverse velocity measures low values which can result in a high sensitivity of the computed FTF.

Figure 8.

The local FTFs to velocity fluctuations for a) the T1y-simulation and b) the T1yNPE-simulation. The integrated HRR is plotted by the dashed black line.

Autoignition-stabilized flame regions on the $x z$ -plane

Similar comparisons as for the $x y$ -plane can be made for the $x z$ -plane (which is the symmetry plane of the T1y simulation). The main difference between the cross-sections is that the $x z$ -HRR field is predominantly stabilized by autoignition. The minimal area jump at the dump plane induces smaller recirculation zones. Therefore, only a small portion of the flame is propagation stabilized in the shear layer. Figure 9(a) shows the same quantities plotted as in Figure 7(a) for the $x z$ -plane and the T1z-simulation. A very distinct pattern of the HRR-response on the upper and lower flame regions are observed. The HRR perturbations intensify toward the outer combustor walls and are out of phase with the transverse velocity for the upper flame regions and in phase for the lower flame regions. The HRR fluctuation pattern looks very similar to the numerical computations and the experimental data in Heinzmann et al.⁴ In contrast, the T1zNPE-simulation does not reproduce the same HRR-response. Without inclusion of the pressure and isentropic temperature effects on the flame, the HRR-response is near 0 for most of the flame region. This is to be expected, as the analysis for the $x y$ -plane already showed no effect of the transverse velocity on the central cross-section. Hence, it is also confirmed for the $x z$ -plane that the transverse velocity fluctuations have no effect on the HRR of the flame. The experimental data shown in Heinzmann et al.⁴ for the same cross-section further supports this.

Figure 9.

a) Pressure perturbations (first column), transverse velocity perturbations (second column), and HRR perturbations (third column) for the T1z-simulation and half an oscillation. The same variables are plotted in b) for the T1zNPE-simulation.

The local FTFs of the integrated HRR (integrated along the $x$ -axis) and the velocity perturbation upstream of the flame are shown in Figure 10(a) for the T1z-simulation, and in Figure 10(b) for the T1zNPE-simulation. In a) it is clearly observable that the central cross-section at $z$ = 0 has a gain close to zero, meaning that the flame response is negligible. The same observation is made for the T1zNPE-simulation. The small gain of 0.07 for $z$ = 0 of the T1zNPE-simulation arises from a slight decrease of the T1z modeshape amplitude over one harmonic cycle. As a result, the HRR of the first 50% of the cycle does not average to zero with the second 50% of the cycle, as is the case for the other simulations. For the T1zNPE simulation, obtaining a close to constant modeshape amplitude for multiple cycles remained more challenging compared to the other simulations. Nonetheless, the negligible gain can be attributed to these numerical difficulties, and the results support the same findings from the other simulations. Therefore, the initial hypothesis of Heinzmann et al.,^4,33 that transverse velocity perturbations have no effect on a solely autoignition-stabilized flame, is confirmed.

Figure 10.

The local FTFs to velocity for a) the T1z-simulation and b) the T1zNPE-simulation. The integrated HRR is plotted by the dashed black line.

Conclusion

The effect of transverse acoustic eigenmodes on autoignition flames has been investigated in recent studies.^4,33 In this paper, we specifically further analyze the effect that transversal velocity fluctuations have on fully- and partly- autoignition-stabilized flames. For this, unsteady forced RANS computations are performed in Fluent of a lab-scale reheat combustor²⁹ and the mean fields validated with experimental measurements. The analysis shows that transverse velocity perturbations have no effect on flames solely stabilized by autoignition. This was confirmed in all four simulations. Therefore, the initially stated hypothesis is confirmed. For partly autoignition-stabilized flames, where propagation-stabilized parts are present in the shear layer, transverse velocities can have an effect. Still, the local effects of pressure and isentropic temperature tend to have a significantly stronger effect compared to the transverse velocity.

Footnotes

ORCID iDs

Simon M Heinzmann

Nino A Leder

Mirko R Bothien

Funding

The research work presented in this manuscript was carried out within the FLEX4H2 project. The FLEX4H2 project is supported by the Clean Hydrogen Partnership and its members European Union, Hydrogen Europe and Hydrogen Europe Research (GA 101101427), and the Swiss Federal Department of Economic Affairs, Education and Research, State Secretariat for Education, Research and Innovation (SERI). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or any other granting authority. Neither of them is liable for any use that may be made of the information contained therein.

Declaration of conflicting interests

The authors declare no potential conflicts of interest with respect to research, authorship, and publication of this article.

Nomenclature

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The effect of transversal velocity fluctuations on the thermoacoustic response of reheat flames

Abstract

Keywords

Novelty and significance statement

Introduction

Methodology

Combustor geometry

RANS computation

Results

CFD steady HRR mean field validation

Propagation- and autoignition-stabilized flame regions on the x y -plane

Autoignition-stabilized flame regions on the x z -plane

Conclusion

Footnotes

ORCID iDs

Funding

Declaration of conflicting interests

Nomenclature

References

Propagation- and autoignition-stabilized flame regions on the $x y$ -plane

Autoignition-stabilized flame regions on the $x z$ -plane