## Abstract

Swirling flows are commonly used for flame stabilization in gas turbine combustors, which are hence equipped with suitable swirler units. In these units the air rotation, quantified by the swirl number, is fixed through the geometry and represents a parameter significantly affecting flame stability and dynamics. The possibility of a continuous swirl variation, on the other hand, would be advantageous for the assessment and control of thermoacoustic instabilities. This is especially true for fuel-flexible applications, for which different swirl numbers are needed to stabilize flames arising from the combustion of different fuels. Most swirl-varying systems rely on mechanical adjustments. In this work, instead, a novel swirl-stabilized burner is investigated experimentally, which is based exclusively on fluidic actuation. For the experimental assessment of the resulting flow field, the axial and azimuthal velocity components are determined through laser Doppler anemometry (LDA) measurements. The measurements are performed in a volume downstream of the burner's mixing tube. The data are processed and computed into swirl-numbers in order to quantify the degree of swirl as a function of the fluidic actuation. The characteristics of two different burner geometries are investigated, with and without a central cone within the swirler, respectively. The configuration with the cone is found to generate higher swirl over the investigated operational range. For this configuration, the technically relevant operating range is determined in which the swirl number can be continuously set from zero to around 0.9. Our experimental results show that fluidic actuation is a viable way to continuously change the swirl number, and that the achievable swirl range is quantitatively comparable to that of state-of-the-art swirl-stabilized burners.

## 1 Introduction

The performance and efficiency of modern gas turbines are tightly linked to the underlying combustion process. In order to affect fuel-air mixing processes, heat transfer mechanisms, and to stabilize and anchor the flame, swirl-stabilized flames are usually employed. The burners used to stabilize these flames feature a swirler element, through which the defined air rotation is imprinted via air flowing through the respective burner geometry [1,2]. The operating principles of swirl-stabilized flames and the effect of swirling flows on combustion have been extensively investigated and studied [2–5]. Nevertheless, since the degree of swirl is one of the parameters that significantly influences the dynamic and static stability of flames, the possibility of active and continuous swirl variation represents an advantageous contribution to the investigation and control of thermoacoustic instabilities [3].

In this context, this work demonstrates experimentally the use of fluidic actuation in a swirl-stabilized burner, allowing for an active and continuous variation of the degree of swirl. In contrast to other examples found in literature, which almost exclusively rely on mechanical and/or geometrical swirl variation [3,6–8], the novel swirl-stabilized burner presented here operates solely through fluidic actuation, i.e., the injection of a secondary air mass flow, thus entirely omitting movable parts. The use of fluidic thrust vectoring systems has been successfully used in the field of aerospace engineering (see Refs. [9] and [10]), and its working principle has been qualitatively evaluated through numerical simulations in Ref. [11]. This work aims at unveiling experimental proof for the working principle and technical relevance of the investigated concept, as well as identifying a technically relevant operating range. In the experimental investigation presented here, the axial and azimuthal velocity components are measured in various regions of interest downstream of the swirler and mixing tube by means of laser Doppler anemometry (LDA) measurements, for two different swirler geometries. All experiments are conducted at atmospheric and isothermal conditions, not involving combustion or reacting flows. The experimental data are processed to calculate swirl-numbers, in order to quantify the degree of swirl as a function of the fluidic actuation.

In Sec. 2, the principles of quantification of the degree of imposed swirl are briefly depicted, as well as the concept of LDA measurements. Then, the experimental setup and the employed techniques and methods are described. Lastly, the obtained results are presented and summarized.

## 2 Experimental Investigation

In this section, we describe the experimental setup and LDA measurement methodology used to investigate the fluidic burner concept.

### 2.1 Test Rig.

The test rig used in the experimental investigation is schematically depicted in Fig. 1.

It represents an open test facility which consists of an air plenum onto which the investigated fluidic burner is mounted. The primary air is fed to the plenum through an air filter system and the air flow is controlled by mass flow controllers. Analogously, the secondary air is induced through a separate mass flow controller directly, and varied to investigate the level of control of the induced swirl in the burner. The experiments are conducted at atmospheric conditions. The average Reynolds number, based on the tube outlet diameter *D*, is $Re\u2248105$. For every investigated operating point, the total air mass flow is kept constant at $m\u02d9tot=m\u02d9p+m\u02d9s\u2261175$ kg/h. The mass flow ratio $MFR=m\u02d9s/m\u02d9p$ between secondary and primary air, however, is varied. Within the main test rig plenum, the primary air is infused with seeding particles consisting of atomized dioctyl-sebacate (Bis(2-ethylhexyl) sebacate) droplets through a TOPAS ATM 210^{2} aerosol generator/atomizer. This oily and colorless liquid are not hazardous and are found to form stable aerosols. The distributed particles have a median diameter of well below 1 *μ*m and it can therefore be assumed that the particle movement reliably resolves the flow. The seeded primary air passes through an air-rectifying array before reaching the main air channels of the investigated burner. This setup achieves a homogeneous air-seeding mix over the entire operational range and allows for the investigation of the flow field downstream of the burner's mixing tube by means of LDA measurements. The underlying LDA measurement system is briefly described in the following section.

### 2.2 Laser Doppler Anemometry System.

A schematic overview of the LDA setup is depicted in Fig. 2. The used LDA system is a two-dimensional system by Dantec^{3}. It relies on a two-color, four-beam laser system, featuring a 490 mW argon-ion laser by Spectra-Physics^{4}. The resulting wavelengths are $\lambda 1=514.5\u2009nm$ (green) and $\lambda 2=488\u2009nm$ (blue). Each of the colored beams is split in two, of which one is led through a 40 MHz Bragg-Cell. Here, the respective beams are subjected to a frequency shift to achieve directional sensitivity of the system. All four beams are passed through an integrated transmitting and receiving optic unit, which specifies multiple beam parameters and simultaneously captures scattered light reflected from seeding particles passing through the measurement volume. The adjustable focal length is set to $f=310\u2009mm$, and the optical and geometrical specifications of the resulting measurement volume are summarized in Table 1.

Parameter | Green laser | Blue laser |
---|---|---|

Optical system | ||

Wavelength $\lambda $ (nm) | 514.5 | 488 |

Focal length f (mm) | 310 | 310 |

Beam half-angle $\theta /2$ (deg) | 3.46 | 3.46 |

Measurement volume | ||

Length L ($\mu m$) | 400 | 400 |

Width W ($\mu m$) | 23.3 | 22.1 |

Parameter | Green laser | Blue laser |
---|---|---|

Optical system | ||

Wavelength $\lambda $ (nm) | 514.5 | 488 |

Focal length f (mm) | 310 | 310 |

Beam half-angle $\theta /2$ (deg) | 3.46 | 3.46 |

Measurement volume | ||

Length L ($\mu m$) | 400 | 400 |

Width W ($\mu m$) | 23.3 | 22.1 |

For each emitted wavelength, the scattered light signals are processed through a photomultiplier, allowing for the acquisition of two orthogonal velocity components. The signal bursts are then analyzed in a burst spectrum analyzer (BSA, Model Dantec^{3} BSA F60), which computes physical velocity values for each particle passing through the measurement volume within a given measurement time *t*. The interpretation and processing of these raw velocity data sets are outlined in detail in the following section.

Due to the amount of oil seeding needed to reach adequate data acquisition rates, the used beam-focusing lens is prone to suffer from seeding particle deposition. Since the spatial resolution of the investigated flow fields requires a large number of measurement points and thus long measurement times, the particle deposition can decrease the data acquisition rate and affect the data quality. For this reason, a lens-purging mechanism is employed in which compressed air flows automatically and uniformly over the lens to prevent the deposition of seeding particles.

### 2.3 Velocity Data Acquisition and Processing.

The LDA system acquires signals of the Cartesian velocity components perpendicular to the laser-optic axis. For every measurement point, a multitude of flow velocities is acquired, since a velocity is inferred for each seeding particle (separately for each laser-/velocity-component, respectively). In order to collect a statistically significant amount of particle data, the measurement time for each measurement point is set to $t=15s$ or $t=20s$, depending on the measurement setup. To define a characteristic velocity value for each measurement point, all acquired particle velocities are generally fitted onto a Gaussian distribution. In other applications, this Gaussian distribution assumption has proven to be valid and suitable for velocity processing [12]. In the present case, however, particle velocity data for various measurement points appears to not follow a normal distribution. This is primarily caused by the highly heterogeneous and turbulent nature of the velocity field downstream of the investigated burner, incorporating areas of elevated positive and negative flow velocities, thus reaching the capability limits of the employed measurement setup. This leads to the existence of truncated or asymmetrical velocity distributions. To accommodate for these non-normal distributions, a so-called Kernel distribution is fitted to the particle velocities, which represents a nonparametric estimation of the probability density function of a random variable^{5}. Figure 3 schematically depicts the velocity distribution of an exemplary measurement point for one of the two used laser components. The standard Gaussian-distribution fit is depicted in red, and the fit based on the Kernel distribution is depicted in green.

When assuming a Gaussian velocity distribution, the velocity value characterizing the respective measurement point is computed as the mean of all particle velocity values and, in the example of Fig. 3, amounts to $8.67\u2009m/s$. The interpretation of the velocity distribution following the Kernel distribution approach involves finding the maximum value of the probability density function, amounting to $17.72\u2009m/s$. This velocity value is found to be more suitable for the characterization of the measurement point. In the case that the particle velocities actually follow a Gaussian distribution, the Kernel and Gaussian approach lead to the same characteristic velocity values.

### 2.4 Quantitative Assessment of Swirling Flows.

*S*is applied [5,13]

*R*stands for a characteristic radius of the swirling flow (e.g., the outer radius of the respective nozzle or swirler exit) [3,13]. By neglecting the pressure term in the axial momentum flux [3,5] and the contribution of turbulence, the swirl number can be simplified into the following conventional definition:

where $U\xaf\theta $ and $U\xafz$, respectively, stand for the tangential and axial velocity at the examined outlet plane averaged in the azimuthal direction. $Rref$ denotes a reference radius, chosen to be the outer radius $R=D/2$. As found by Vignat et al. [5], this definition of the swirl number is simplified and cannot reflect all underlying physical mechanisms. However, it is well suited for comparisons between applications featuring similar geometries.

As denoted in Eq. (2), the swirl number calculations rely on velocity components in cylindrical coordinates. Since the original measurement grid is of Cartesian nature, the measured velocity components are interpolated onto a cylindrical grid, and converted into corresponding cylindrical velocity components, $u,v,w\u21a6U\theta ,Ur,Uz$, which are then averaged over the azimuthal range and used to compute swirl number values according to Eq. (2).

To maximize the accuracy of the swirl estimation, the reference plane should be chosen close to the outlet of the swirler [5]. However, the LDA setup does not allow for direct measurements of the flow field within the mixing tube. The data for the computation of the swirl number are therefore chosen to be at the plane closest the swirler outlet at which the maximum number of measurement points is possible, found to be at $z=D$ (see Sec. 3). In this way, the radial integration limit $Rlim$ in Eq. (2) is maximized and chosen to include all measurement data.

### 2.5 Operating Conditions and Measurement Locations.

This section briefly outlines the measurement setup employed in the present experimental investigation. Two full-scale swirler burner models have been manufactured by means of additive manufacturing, both of which are schematically depicted in Fig. 4. In contrast to geometry (B), geometry (A) features a central cone. Both geometries are analyzed at various operating points (at constant total mass flow $m\u02d9tot=m\u02d9p+m\u02d9s$, for various $MFR=m\u02d9s/m\u02d9p$): $0%\u2264MFR\u226442%$. Two velocity components are measured by means of LDA (see Sec. 2.2), namely, the velocity component *u* in *x*-direction and the axial velocity component *w* in *z*-direction. Since the investigated burner models are axially symmetric, it is reasonable to assume that the resulting flow fields are axially symmetric. As a result, the velocity component *v* in *y*-direction, which could not be measured with the portrayed setup, is computed as a rotation of velocity *u* for each *z*-position. This assumption is partially validated with dedicated measurements, as explained in the following.

For every investigated setup, velocity data are acquired at various circular planes at constant *z*-coordinates with $x2+y2\u2264R2$, centered at $x,y=0$ mm. The measurement positions constitute a grid of points arranged on concentric circles, whose radial spacing is nonuniform and decreases toward the center of the burner outlet. Each circular measurement plane (also referred to as plane-measurement) comprises up to 302 measurement positions, at each of which the measurement time is set to $t=15s$, amounting to a substantial measurement duration for each investigated case. To reduce the measurements time, additional measurements are conducted on X-shaped grids, aligned with the *x* and *y* coordinate axes for a constant *z*, with $\u2212R\u2264x\u2264R$ when $y=0$ or vice versa. In contrast to the plane measurements, these measurements are referred to as X-measurements. For each X-measurement, the number of measurement positions is reduced to 125, but the measurement time is increased to $t=20s$ for each position. The combined investigation of circular and X-shaped grids is advantageous because it allows for a more detailed and time-optimized assessment of the investigated operating range. Moreover, the geometrical difference between the two measurement grids can be used to characterize the axial symmetry of the system and validate this assumption.

With a given mixing tube and swirler outlet diameter *D*, the measurement grids are positioned as shown in Table 2. Since the beam angle $\theta $ of the LDA system would cause light scattering from the test rig's base/reference plane, the *x*, *y* range of plane (1) is reduced to $R\u22641.2\xb7D$. The position of the first four measurement planes is schematically depicted in Fig. 5.

## 3 Experimental Results

In this section, selected results from the experimental investigation are presented and discussed. Figure 6 depicts the flow field downstream of geometry (A) for $MFR=6%$ and $30%$ at $z=D$ (plane measurement) by means of a filled contour of the axial velocity *w* and streamlines derived from *u* and *v*. The black dotted circle represents the mixing tube outlet, with diameter *D*. The case at $MFR=6%$ portrayed on the left represents an operating point at which no swirl is measured. The depicted streamlines are comprehensively radially oriented toward the geometrical center of the mixing tube, resembling air being entrained by the resulting symmetrical jet. The flow field is thus comparable to an axial jet. The case portrayed on the right, instead, involves a high magnitude of fluidic actuation (MFR = 30%) and is characterized by a strong degree of swirl. The streamlines follow a path tangential to the mixing tube outlet, with the air being subjected to a strong counterclockwise rotation, i.e., exhibiting a positive swirl. For the highly swirled flow, the axial velocity peaks within an annular region outside the mixing tube outlet. Within the center of the region, directly above the outlet, a region with a clear negative axial velocity, i.e., back-flow, can be observed. Its magnitude is found to range between $wmin,A\u2248\u221217\u2009m/s$ and $wmin,B\u2248\u221212\u2009m/s$, where the index A, B denotes the type of geometry (only A shown). This back-flow is found to be a suitable indicator for the presence of a swirl-induced vortex breakdown downstream of the reference plane, indicating the typical flame-stabilizing ability of swirling flows. This is in accordance with the plotted streamlines, indicating a strong degree of swirl. The flow field for the zero-swirl case at $MFR=6%$ does not comprise areas of axial back-flow or any tangential air displacement, thus representing an unswirled axial jet.

In order to assess the behavior of flow fields and characterize both of the investigated geometries over the entire MFR operational range, in the following the resulting swirl numbers are calculated and the trends of the underlying velocity components are discussed. In this regard, the results sourcing from plane-measurements are discussed and swirl number trends for both investigated burner geometries are compared. Subsequently, the planar measurement results are compared to results acquired through X-measurement grids, which are faster and allow us to identify a technically relevant operating range.

### 3.1 Results From Planar Measurements.

This section discusses the results obtained from plane-measurements (see Sec. 2.5). At first, the axial and tangential velocity profiles characterizing a swirling flow are discussed for selected operating points and for both investigated geometries. Then, the swirl numbers are calculated and their dependency on the intensity of the MFR is discussed for both burner geometries.

#### 3.1.1 Velocity Profiles.

The behavior of the investigated swirlers is first characterized by the trend of the azimuthally averaged cylindrical velocity components, on which the swirl number calculations are based. Figure 7 depicts the axial velocity component averaged over the azimuth range $Uz$ at the measurement plane $z=D$ for both geometries and a selection of MFR-values, plotted over the radial distance to the axial center line.

For all depicted cases, the axial velocity decreases to approximately zero toward the outer boundaries of the flow field. Depending on the degree of swirl, it increases for decreasing *r* until reaching its respective maximum in a region between $r/Rref=0.5$ and $r/Rref=1.3$. Further toward the centerline, the axial velocity is again reduced, even reaching negative levels for highly swirled operating points. For the two investigated geometries, the progression of $Uz$ over *r* is comparable. A clear trend can be distinguished for $Uz$, the maximum value of which steadily decreases with increasing MFR-values, i.e., with increasing swirl magnitude. Moreover, the location of these $Uz$-peaks is shifted outward for an increasing MFR, reflecting the expansion of the out-flowing swirling jet, indicating the presence and propagation of vortex breakdown. This is in accordance with the decrease of the minimum $Uz$ values toward higher MFR-values in vicinity of $r/Rref=0$, denoting the magnitude of the respective central back-flow. However, the profiles for $MFR=0%$ in both geometries are surprising. A decrease in the $Uz$ velocity component close to the axis ($r/Rref=0$) can be observed, which indicates a pronounced rotation of the flow field, even more pronounced compared to $MFR=5%$. An induced swirl without fluidic actuation ($MFR=0%$) was initially not expected.

Figure 8 depicts the azimuthally averaged tangential velocity $U\theta $ at the measurement plane $z=D$ for both geometries and all MFR-values. Analogously to $Uz$, the tangential velocity amounts to zero for high *r* and reaches its maximum in close vicinity to the mixing tube outlet. Toward the centerline, the tangential velocity is again reduced to reach zero, as expected for swirling flows. The trend exhibited by $U\theta $ with respect to *r* follows a similar trend as the axial velocities. For high MFR values and accordingly increased swirl, the regions of elevated tangential velocity are analogously extended over a broader radial range. In combination to, respectively, reduced axial velocities, including reversed flow for some cases, the behavior is found to comply to the expected trend. However, the behavior at $MFR=5%$ differs from the overall trend. Here, the respective tangential velocity is subjected to a change of polarity, indicating a flow swirling opposite of the envisaged direction. Moreover, as already indicated by the axial velocity profiles, the $MFR=0%$ azimuthal velocity profile exhibits nonzero values, indicating swirl. The magnitude of the tangential velocity is found to be in the same range as for $MFR=5%$, however in the opposite direction. This indicates the presence of unexpected effects at low MFR values, restraining the concept's swirl-controlling capability. More specifically, for both investigated geometries, this indicates an insufficient capability of swirl induction and control for $0%\u2264MFR\u22645%$, and is therefore further discussed in Secs. 3.1.2 and 3.2.2. As a result, this is taken into account for further measurements and the determination of a possible operating range. Since the investigated burner aims at operation under fuel-flexible conditions, a concern of the authors is represented by the central cone in geometry (A), which affects the flow field and locally decreases the axial velocity at operating conditions with reduced swirl. Locally decreased axial velocity could result in an increase risk of flashback. In the evaluation of the flow fields of both geometries at low MFR-values, however, no significant differences in the magnitudes of all acquired velocity components are noteworthy.

#### 3.1.2 Swirl Numbers.

In this section, the swirl numbers are computed from experimental velocity data from plane-measurements according to Eq. (2) for each measurement plane. Their trend as a function of the MFR and the differences between swirl numbers for the two geometries are discussed. Figure 9 gives an overview of the trend of the swirl number, calculated on plane measurements, over the axial distance to the reference plane *z*, for a selection of MFR values and for both investigated geometries. As expected, the swirl numbers maintain constant levels, independently from the axial distance to the reference plane *z*. In the considered unconfined case, i.e., without combustor walls, the swirl number is expected to slightly decrease with increasing distance to the reference plane, outside the respective proximity area [5]. The shown results, however, are evaluated at measurement planes that are not located at a sufficiently large distance from the reference plane to clearly demonstrate the expected decay. Nonetheless, for both geometries, the swirl number *S* remains within an approximately constant range. Since the radius of the measurement plane at $z=0.5D$ is reduced for both geometries (A) and (B) (see Sec. 2.5), not the entire underlying flow field could be resolved and, hence, the respective measurement points at $MFR=30%$ are omitted.

The relationship between *S* and the set MFR-values is noteworthy. In contrary to a steady progression, with increasing MFR the swirl number first decreases to negative values and, subsequently, increases until eventually complying to an expected steadily increasing correlation to the increasing MFR. This observation is in line with the anomalies found in the underlying velocity profiles (see Figs. 7 and 8). This behavior is conditioned by unsteady flow phenomena within the single channels of the underlying swirler (equally in both investigated geometries). In this respect, Fig. 10 schematically depicts selected details within one of the swirler channels. As observable from the correlations depicted in Fig. 9, at $MFR=0%$ a low positive swirl, i.e., an air rotation in the counterclockwise direction, can be seen in both geometries, indicating that parts of the in-flowing primary air mass flow is redirected toward the main Coanda surface. Due to the absence of secondary air and, thus, of a controlling wall-jet, at $MFR=0%$ this incomplete attachment is geometrically caused by the small backward-facing step presented by the secondary air injection slot (highlighted through a red circle in Fig. 10). This effect is not observable as soon as a secondary air mass flow is introduced. As discussed in Sec. 3.1.1, at $MFR=5%$, for both geometries a moderate negative swirl can be observed, denoting a flow attachment to the Coanda surface opposite of the secondary air injection. In this regard, the behavior of both swirler geometries shows a lack of flow and, thus, swirl control in this region. Instead of an increase in swirl number, at first, a decrease below zero occurs for $MFR\u21925%$. This behavior is of unsteady nature and, despite its reproducibility, it is found to be inapplicable for the operation of the investigated variable-swirl burner. The investigated burner concept aims at operating within operating conditions which allow for a well-defined control of the degree of swirl, as observed at higher MFR values. Considering the literature this is also expected, as thrust vectoring is known to be only controllable after a threshold value of MFR (see Refs. [9], [10], [14], and [15]).

In consequence, a technically relevant operating region is identified and further analyzed in Sec. 3.2.

When comparing both geometries, a slight difference in the achieved swirl magnitude over the entire investigated experimental range is visible. In Fig. 9, the swirl induced by swirler (A) (left) is found to be higher than the swirl induced by swirler (B) (right). The differences peek approximately 30% for values measured at $z=2D$. This observed difference in swirl magnitude is found to be caused by the cone-induced flow guidance within swirler (A), forcing the out-flowing air toward the mixing tube walls, resulting in higher tangential flow velocity components. This effect is maximized with increasing MFR-values and thus the increased air flow in tangential direction.

Due to its increased swirl-inducing and varying capability, geometry (A) is found to be more advantageous and is chosen as the base for further examination and development. In Sec. 3.2, a technically relevant operating range is identified and further discussed for geometry (A).

### 3.2 Results From X-Measurements.

For the identification of a suitable operating range, i.e., the in-depth characterization of the fluidic swirler with respect to the MFR range, and the validation of the employed measurement technique, results acquired through X-measurements (see Sec. 2.5) are discussed in this section.

#### 3.2.1 Comparison to Planar Measurements.

To demonstrate the validity of the employed measurement method, the data processing routine, and especially the assumption of axial symmetry of the flow field, this section depicts in detail the process for the results sourcing from an exemplary measurement point (geometry (A), $MFR=10%$, $z=D$). In this regard, results obtained from two measurement grids are compared for this point, namely, X- and plane-measurements.

As described in Sec. 2.4, the acquired Cartesian velocity components are transformed into a cylindrical framework. The resulting tangential velocity $U\theta $ and axial velocity components $Uz$ are relevant for the analysis of swirling flows. Figure 11 depicts the acquired axial and tangential velocity components for geometry (A) at $MFR=10%$ and $z=D$, azimuthally averaged and plotted over the radial position *r*, comparing the plane- and X-measurement techniques. As in Figs. 7 and 8, the two main velocity components characterizing swirling flows are depicted over the radial distance to the system's centerline. The axial velocity profiles $Uz$ (see top of Fig. 11) are comparable in magnitude and trend for both employed measurement grids. The trend with increasing *r* is consistent between both X- and plane-measurements as well as the magnitude and position of the maximum axial velocity. For the tangential velocities $U\theta $, depicted at the bottom of Fig. 11, minor differences between the two measurement grids are visible. The trend of $U\theta $ over *r*, however, is quantitatively comparable. This shows that both employed measurement methods are suitable for the analysis of the resulting flow field as well as for the quantification of the swirl.

In this respect, the X-measurement grid relies on significantly less measurement points, i.e., less data, than the comparable plane-measurements. A qualitative and quantitative agreement of both techniques regarding the derived flow fields and the resulting swirl numbers is observable, affirming the validity of the made symmetry assumption.

In the present experimental investigation, the plane-measurements have been used for the acquisition of fundamental flow field velocity data at an elevated spacial resolution, while the X-measurements allow for a time-optimized characterization of the swirl over a broad operating range. Importantly, the strong similarities between the $Uz$ and $U\theta $ velocity components for both measurement grids and all azimuthal positions favorably support the assumption of the flow field's axial symmetry.

#### 3.2.2 Operating Range.

For the identification of a technically relevant operating range, the behavior of the presented swirl-stabilized burner (geometry (A)) is further resolved over a broader range of MFR values. In this respect, the use of the X-shaped measurement grid is found to be advantageous. Figure 12 depicts swirl numbers over set MFR values for geometry (A), acquired through X-measurements. Additionally, selected measurement points acquired through full plane-measurements are depicted for comparison. Results are shown for measurements featuring MFR variations toward increasing and decreasing values, in order to further identify regions subjected to unsteady behavior regarding the dynamic change of MFR values. A clear change in the obtained swirl numbers is visible for $MFR<6%$, depending on the MFR variation direction. This indicates the presence of a hysteresis, inhibiting the possibility of a stable control of the swirl. This region is therefore not considered to be technically relevant. For $MFR=6%$, an operating point is identified in which no swirl is measured ($S\u21920$), regardless of previous MFR progression. As this point is reproducible (both for plane and X-measurements), it denotes the beginning of the technically relevant operating range of the presented concept. The flow conditions of this lower limit of the identified range is especially noteworthy, since it demonstrates the capability of the swirler to create axial jets. The symmetry of the resulting flow field can also be observed in the left plot of Fig. 6. For $6%<MFR<7%$, a steep increase of *S* is visible, followed by an approximately linear increase for $7%<MFR<32%$. For MFR values above 32%, this increase is mitigated, denoting the upper limit of the identified operating range.

The characteristics of the presented variable-swirl burner correctly resemble the behavior of fluidic thrust vectoring systems, where three main regions are distinguished [9,14]: A dead-zone for low fluidic actuation (i.e., low MFR values) in which no control is achievable, a control-zone at intermediate MFRs in with an almost linear control of the fluidic flow redirection, and a saturation-zone for high MFRs in which the degree of flow vectoring (here represented by swirl number increase) cannot be further augmented with increasing fluidic actuation.

### 3.3 Assessment of Applicability.

Since the fluidic swirl-stabilized burner concept is eventually intended for operating within actual gas turbines, its potential applicability is estimated in terms of total pressure loss. This is primarily motivated by the presence of secondary air injection slots, which present a significant flow constriction. Through measurements of the static pressure within the respective air plenum for a selection of MFR values, an approximate estimation of the total pressure loss is computed. For the secondary air mass flow, its maximum amounts to approximately 1.3 bar, whereas the pressure loss over the primary flow path lies an order of magnitude below. As a result, and especially since case-specific modifications are necessary prior to any full-operational test within a working machine, the presented concept is found to be prospectively suitable.

## 4 Conclusions

In this study, the experimental investigation of a fluidic swirl-stabilized burner allowing for continuous swirl number variations was presented. The working principle relies on fluidic thrust vectoring methods, studied in the field of aircraft propulsion systems. The amount of movable components within the novel combustor is therefore significantly reduced in comparison to alternative variable-swirl burners. The concept working principle and its capability have been experimentally demonstrated. The experimental assessment consisted of laser-optical flow velocity measurements by means of LDA. The flow fields yielded by two burner geometries have been resolved through the acquisition of velocity fields at various measurement planes located at multiple axial positions *z*. The acquired data allowed for a qualitative and quantitative analysis of the flow fields as well as for the computation of swirl numbers, suitably quantifying the degree of induced swirl. A technically relevant operating range was identified, characterizing the swirl-varying performance of the burner.

The behavior and performance of both swirler geometries have been compared and discussed. The observed characteristics resemble the behavior of state-of-the-art swirl-stabilized burners. A distinction between the two investigated geometries is mainly found in the magnitude of the generated swirl. Geometry (A), featuring a central cone within the swirler segment, yields nominally higher swirl numbers over the investigated operating range. At the same time, no significant differences concerning the flow field at low-swirl operating points could be observed. As a result, geometry (A) is found to be more advantageous and, hence, is chosen as the base for further examination and development.

Additionally, an operating range was experimentally identified allowing for a technically relevant operation of the swirl-stabilized burner in terms of achievable swirl and its active control. Within the identified range, the presented concept has the capability to generate a pure axial flow, not featuring any swirl ($S\u22480$), as well as a fully swirled flow field ($S\u22481$). Furthermore, a predominantly linear control between the aforementioned cases is possible, solely through the variation of the degree of fluidic actuation, i.e., the MFR value.

In summary, the experimental investigation of the presented fluidic swirl-stabilized burner demonstrated its swirl-varying capability within technically relevant limits. It is therefore apt to represent a useful approach for the assessment of flame dynamics and stability for a broad operating range, as well as for a safe and efficient fuel-flexible operation of modern combustors. Due to the increasing importance of highly hydrogen-enriched fuels within the field of gas turbine combustion, flame dynamics and stability gain increasing significance. In this respect, the presented concept of a swirl-stabilized burner allowing for a purely fluidic swirl variation is found to be particularly beneficial for the progress of carbon-free energy solutions.

## Acknowledgment

The authors thankfully acknowledge the funding provided by the European Research Council (ERC), as part of the Advanced Grant HYPOTHESis, Grant ID. 101019937. Special thanks go to all who supported and contributed to the successful completion of this work and especially to Dr.-Ing. Finn Lückoff for fruitful discussions on experimental challenges and to Thorsten Dessin, David Lück, and Andy Göhrs for the technical support. The authors also thank Benjamin Church for supporting the three-dimensional printing of the burner prototypes.

## Funding Data

European Research Council (Grant ID: 101019937; Funder ID: 10.13039/501100000781).

## Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

## Nomenclature

*D*=diameter of mixing tube/swirler outlet (m, mm)

*f*=focal length of laser optics (mm)

- $Gz$ =
axial flux of linear momentum (kg m s$\u22122$)

- $G\Phi $ =
axial flux of angular momentum (kg m

^{2}s$\u22122$)*L*=length of LDA measurement volume ($\mu m$)

- $m\u02d9$ =
mass flow (kg s$\u22121$, kg h$\u22121$)

*R*,*r*=radius (variable) (m, mm)

- Re =
Reynolds number

*S*=swirl number

*t*=measurement time (s)

*u*,*v*,*w*=Cartesian vel. comp. in

*x*,*y*,*z*(m s$\u22121$)- $U\theta ,Uz,Ur$ =
cylindrical vel. comp. (tangential, axial) (m s$\u22121$)

*W*=width of LDA measurement volume ($\mu m$)

*x*,*y*,*z*=Cartesian coordinate positions (m, mm)

- $\Delta $ =
difference

- $\theta $ =
beam angle (deg)

- $\lambda $ =
wavelength (nm)

- $\rho $ =
density (kg m$\u22123$)

## Footnotes

Topas GmbH, Dresden, Germany.

Dantec Dynamics A/S, Skovlunde, Denmark.

Model 177-G0232, Spectra-Physics, Mountain View, CA.

See functionality “KernelDistribution,” MATLAB^{®} Release R2020b, MathWorks Inc.^{®}, Natick, MA.