Active Turbulence Grid-Controlled Inﬂow Turbulence and Replication of Heat Exchanger Flow Fields in Fan Applications

: A novel active turbulence grid of the Institute of Fluid Mechanics at FAU Erlangen-Nuremberg is introduced. The focus of this grid is not on basic investigations of ﬂuid mechanics, as is usually the case with active turbulence grids, but the generation of deﬁned inﬂow conditions for axial fans. Thus, by means of the active turbulence grid, individual turbulence characteristics in the ﬂow to the fan can be changed; therefore, fundamental interactions between the ﬂow mechanics at the axial fan and the sound radiation can be analyzed. In addition, the replication of the ﬂow ﬁelds of heat exchangers by the active turbulence grid is the focus of the investigations. The investigations showed that it is possible to use the active turbulence grid to generate deﬁned inﬂow conditions for axial fans. It was also possible to reproduce the heat exchanger ﬂow ﬁelds both for the mean turbulence values and for the spatial distributions. It was found that the grid induces tonal components due to the drive motors, but also that the inherent noise has no signiﬁcant inﬂuence on the spectrum of the fans under investigation. Based on selected turbulence characteristics, direct correlations were found between the spatial distribution of the turbulence level and sound radiation at the ﬁrst blade passing frequency of the axial fan. As the variance of the turbulence level increases, the sound radiation of the tonal components becomes more pronounced. The total sound pressure level, however, is mainly determined by the low-frequency broadband sound. A linear relationship between the spatial mean value of the turbulence level and the total sound pressure level was found for the investigated axial fan.


Introduction
Turbulence grids are used in wind tunnels and axial fan test rigs to generate increased turbulence intensities, modified length scales and defined flow fields [1,2]. A distinction is made between active and passive turbulence grids. The passive turbulence grids consist of rigid struts, which generate a defined orifice and blocking of the flow field [3]. Active turbulence grids (ATG), on the other hand, consist of shafts with attached wings called turbulence generators. The shafts are driven by motors located outside the flow. The motors generate a rotational motion, which is transmitted onto the shafts and the turbulence generators. The rotation of the turbulence generators can influence the turbulence intensity, the turbulent length scale and the homogeneity of the flow field [4]. The great advantage of the active turbulence grid is that a large number of different flow conditions can be generated with one grid [5,6]. The turbulence parameters are adjusted by changing the rotational speed of individual shafts. Active turbulence grids have been used since 1991 for fundamental investigations of flows and turbulence properties in wind tunnels [7,8]. They are usually operated in a square channel and the flow generated by the grids is analyzed downstream. In a novel approach an active turbulence grid will be used to replicate real flow fields and to generate variable inflow turbulence for axial fans. Thus, the high variability in the flow field due to the active turbulence grid is used and investigated in the context of axial fans. Two questions arise from this, which are to be explored by means of this approach. On the one hand, it is to be studied to what extent it is possible to replicate real flow fields of heat exchangers. This also raises the question of how the sound radiation of the fan differs between the real flow field and the imitated flow field. This realworld application of axial fans with suction-side heat exchangers is of particular importance because, on the one hand, they are used in a variety of devices in close proximity to humans, such as heat pumps [9]. On the other hand, it is not yet fully understood why a suctionside heat exchanger can increase the sound radiation of axial fans [10,11]. Additionally, complete CFD simulations of the flow field through heat exchangers are not possible until now [12,13]. If the imitation of real flow fields by means of the ATG would be successful, then in future experimental investigations in the scope of heat pumps and air conditioning it would be possible to avoid cumbersome changes between many heat exchangers. This would save time in research as well as in industrial companies. A second question, which should be answered by means of active grids, is how the physical interactions between inflow turbulence to the axial fans and the resulting sound generation are [14]. With the active turbulence grid, it is possible to adjust the turbulence characteristics of the flow independently, in contrast to rigid turbulence grids. Thus, it has been shown in the literature that at low rotational speeds of the turbulence generators, the integral length scale can be varied while the turbulence level remains constant. On the other hand, at high rotational speeds, it was possible to vary the turbulence level, while the length scale remained unchanged [15]. This feature offers the possibility to investigate the influences of the individual turbulence parameters on the sound pressure spectrum of axial fans and thus to derive a better understanding of the sound generation mechanisms. However, for the use of the active turbulence grid in this context, it must be investigated on the one hand whether a modification of the inflow conditions can occur if a circular duct is arranged behind the square duct of the active turbulence grid. Active turbulence grids have a square shape. Axial fans, on the other hand, require a circular duct. Such a change in the cross-sectional area has so far unexplained effects on the generated turbulence of the active turbulence grid. In other studies with a cross-sectional change applied to axial fans, local turbulence spots were generated which changed the sound radiation at the tonal components of the fan [16]. Furthermore, for the investigation of the sound radiation of axial fans, it must be ensured that the inherent noise of the active turbulence grid is so low that no significant influence on the sound pressure spectrum takes place. Since no acoustic investigations with active turbulence grids have been carried out up to now, no data are available in the literature on the acoustic characteristics. The sound radiation of the active turbulence grid changes with the rotational speed of the turbulence generators. For the correct interpretation of the effects of the flow field on the sound emissions from the axial fans, the sound emission of the grid must be known. This radiation must be taken into account from the very beginning because it represents a distortion quantity and must be reduced as much as possible in the design process of the grid.
The structure of the paper consists of the following. First, the experimental fan used is described and its design parameters are discussed. In a further subchapter, the experimental setups for determining the sound field and for characterizing the inflow conditions are described. Then, the novel active turbulence grid is presented, and the constructional details are discussed in detail. This is followed by a subchapter on the sound radiation of the grid and how this changes as a function of the turbulence generator speed. Proceeding from these constitutive setups, the two questions from the introduction are then addressed and a comparison is made between active turbulence grid and heat exchangers. Subsequently, the basic physical interactions between inlet turbulence and sound radiation in the axial fan are discussed. Both questions are discussed with regard to flow fields and sound radiation in the axial fan. The paper is closed by a summary and conclusion.

Forward Skewed Axial Fan
A forward skewed axial fan, which operates in a short duct segment with a diameter of D duct = 500 mm, is used for the investigations. The axial fan, its specific blade energy and its sweep angle are shown in Figure 1. The forward skew increases from an angle of λ = 0 • at the hub to λ = 55 • at the blade tip. The total diameter of the fan is D fan = 495 mm, which means that the tip gap is s tip = 2.5 mm. The hub diameter of the fan is D hub = 247.5 mm [17]. As is common in heat exchanger applications, the fan operates within a short inlet nozzle, which causes the tip gap to vary along the axial length of the inlet nozzle. As shown in Figure 1, the fan has z = 9 blades and is designed for a flow rate of . V = 1.4 m 3 /s at a rotational speed of n fan = 1486 rpm and a total-to-static pressure rise of p fan = 140 Pa [18]. The blades are based on a NACA 4510 profile and designed according the blade element theory [19]. In the investigations, this axial fan was chosen intentionally because, on the one hand, its forward skew is very similar to the fans currently used in industry and, on the other hand, it is very well documented in the literature. The precise knowledge of the behavior of the axial fan in inflow turbulence makes it possible to better classify effects caused by the disturbed inflow conditions of the ATG and to better understand and interpret the physical effects. The aerodynamic and aeroacoustics characteristics of the used axial fan can be found in the literature at various inflow conditions and in interaction with heat exchangers [11,16,19,20].

Forward Skewed Axial Fan
A forward skewed axial fan, which operates in a short duct segment with a diameter of Dduct = 500 mm, is used for the investigations. The axial fan, its specific blade energy and its sweep angle are shown in Figure 1. The forward skew increases from an angle of λ = 0° at the hub to λ = 55° at the blade tip. The total diameter of the fan is Dfan = 495 mm, which means that the tip gap is stip = 2.5 mm. The hub diameter of the fan is Dhub = 247.5 mm [17]. As is common in heat exchanger applications, the fan operates within a short inlet nozzle, which causes the tip gap to vary along the axial length of the inlet nozzle. As shown in Figure 1, the fan has z = 9 blades and is designed for a flow rate of = 1.4 m 3 /s at a rotational speed of nfan = 1486 rpm and a total-to-static pressure rise of pfan = 140 Pa [18]. The blades are based on a NACA 4510 profile and designed according the blade element theory [19]. In the investigations, this axial fan was chosen intentionally because, on the one hand, its forward skew is very similar to the fans currently used in industry and, on the other hand, it is very well documented in the literature. The precise knowledge of the behavior of the axial fan in inflow turbulence makes it possible to better classify effects caused by the disturbed inflow conditions of the ATG and to better understand and interpret the physical effects. The aerodynamic and aeroacoustics characteristics of the used axial fan can be found in the literature at various inflow conditions and in interaction with heat exchangers [11,16,19,20].

Experimental Setup for the Determination of Sound Emission and Aerodynamic Properties
The sound radiation and the aerodynamic properties of the axial fan are investigated together. For this purpose, the axial fan is installed in the axial fan test rig of the Friedrich-Alexander University Erlangen (see Figure 2). The operating point of the fan can be adjusted by means of a butterfly throttle and an auxiliary fan. The volume flow can be measured with a standardized volume flow measuring device at the inlet. Within the non-reflecting chamber, which is located on the suction side of the test fan, the pressure buildup between the suction side and the ambient pressure is measured. Additionally, within this chamber, the sound radiation of the fan is recorded by five free-field microphones from B&K. The microphones are placed at a distance of one meter from the axial fan. They

Experimental Setup for the Determination of Sound Emission and Aerodynamic Properties
The sound radiation and the aerodynamic properties of the axial fan are investigated together. For this purpose, the axial fan is installed in the axial fan test rig of the Friedrich-Alexander University Erlangen (see Figure 2). The operating point of the fan can be adjusted by means of a butterfly throttle and an auxiliary fan. The volume flow can be measured with a standardized volume flow measuring device at the inlet. Within the non-reflecting chamber, which is located on the suction side of the test fan, the pressure build-up between the suction side and the ambient pressure is measured. Additionally, within this chamber, the sound radiation of the fan is recorded by five free-field microphones from B&K. The microphones are placed at a distance of one meter from the axial fan. They are located on a hemisphere, with one microphone directly on the axis of rotation of the fan. Two additional microphones are arranged in ϕ = 22.5 • angular segments on a horizontal and a vertical circular arc. The microphones record the acoustic pressure at a sampling rate of f s = 48 kHz for a duration of t = 30 s. The speed and torque of the fan can be monitored via the shaft drive, which is located on the pressure side. The pressure, flow rate, rotational speed, torque, density and temperature are recorded at a sampling rate of f s = 1 kHz for t = 10 s. Heat exchangers or the active turbulence grid can be positioned in front of the axial fan. Thus, the influence of different inflow conditions on the aerodynamic and acoustic properties of the fan can be investigated. monitored via the shaft drive, which is located on the pressure side. The pressure, flow rate, rotational speed, torque, density and temperature are recorded at a sampling rate of fs = 1 kHz for t = 10 s. Heat exchangers or the active turbulence grid can be positioned in front of the axial fan. Thus, the influence of different inflow conditions on the aerodynamic and acoustic properties of the fan can be investigated.

Determination of Inflow Turbulence and Turbulence Parameters
The inflow conditions to the axial fan are determined at the position where the leading edge of the axial fan is located. At the leading edge, the fan interacts directly with inflow turbulence, and dominant sound sources are generated there, which emit sound primarily in the broadband, low-frequency range [22,23]. The sound source can be attributed to pressure fluctuations at the surface. Since the fan blades block the way to the measuring plane, the fan is replaced by a bladeless hub for the investigation of the flow field [24]. The flow field is determined by means of 3D hot-wire anemometry [25]. For this purpose, one third of a circular segment is measured inside the duct. A total of 80 measuring points with equidistant spacing are distributed in this circular segment (see Figure  3). The measuring points are accessed via a traverse from the pressure side. For each measuring point, the flow velocities in the three spatial directions are measured at a sampling rate of fs = 48 kHz for a period of t = 30 s [12,16]. The hot-wire system used, manufactured by Dantec, is calibrated before the measurements [26]. From the data of the flow velocity ( , ) the fluctuations of the flow velocity ( , ) can be calculated by Equation (1). ( ) is the time average value of one flow component [27].
With these, the global turbulence intensity can be calculated based on Equation (2).

Determination of Inflow Turbulence and Turbulence Parameters
The inflow conditions to the axial fan are determined at the position where the leading edge of the axial fan is located. At the leading edge, the fan interacts directly with inflow turbulence, and dominant sound sources are generated there, which emit sound primarily in the broadband, low-frequency range [22,23]. The sound source can be attributed to pressure fluctuations at the surface. Since the fan blades block the way to the measuring plane, the fan is replaced by a bladeless hub for the investigation of the flow field [24]. The flow field is determined by means of 3D hot-wire anemometry [25]. For this purpose, one third of a circular segment is measured inside the duct. A total of 80 measuring points with equidistant spacing are distributed in this circular segment (see Figure 3). The measuring points are accessed via a traverse from the pressure side. For each measuring point, the flow velocities in the three spatial directions are measured at a sampling rate of f s = 48 kHz for a period of t = 30 s [12,16]. The hot-wire system used, manufactured by Dantec, is calibrated before the measurements [26]. From the data of the flow velocity u j (x i , t) the fluctuations of the flow velocity u j (x i , t) can be calculated by Equation (1). u j (x i ) is the time average value of one flow component [27].  With these, the global turbulence intensity can be calculated based on Equation (2). In this context, the global turbulence intensity Tu glo means that turbulent fluctuations are related to the spatial mean value of the main flow component u x1 for all 80 measurement points [11].
The integral length scale of the turbulent flow is determined per measurement point from the time data of the main flow velocity. In this case, the length scale is calculated from the energy spectrum E( f ) according to Equation (3) and the approach of El-Gabry et al. [28].
This procedure refers to isotropic flows, but according to Kurian et al. [29] it can also be used for not completely ideal isotropic flows. The calculation of the integral length scale on the basis of autocorrelation is not an option in these investigations with active turbulence grid. Due to the small distance between the measuring plane and the ATG and the rotation of the turbulence generators, cyclic components are included in the flow data. These would lead to the autocorrelation being a function of the rotational speed of the turbulence generators and thus the length scale would be calculated incorrectly. In addition to these basic parameters of the turbulence theory, a new parameter is presented in this paper, which should provide further insight into the interaction between the axial fan and the flow field. For this purpose, the formula of the variance σ 2 according to Equation (4) is applied to the time average values of the turbulence intensity Tu and the length scale Λ per measuring point (see Equations (5) and (6)). This results in a spatial variance, which combines the temporal and spatial data from the flow field into one value.

Constructional Design of the Active Turbulence Grid
An active turbulence grid is used to generate defined inflow conditions. The basic form of the grid is shown as CAD in Figure 4. The turbulence generators, which are shown in orange in the center, are in the closed state, i.e., the maximum blocking of the grid is present. The basic structure of the grid consists of an outer frame and an inner frame, through which the flow passes. The drive motors and their controls are located on the outer frame. A total of 20 stepper motors are used, which are equipped with encoders and heat sinks. Vibration damping couplings are attached to the stepper motors. These couplings reduce the vibrations on the shaft, which are generated by the stepper motor. The outer frame is mounted on vibration dampers. The stepper motors and the space between the inner and outer frames are shielded by foam and motor enclosures so that as little sound as possible can be emitted to the outside from these components.

Constructional Design of the Active Turbulence Grid
An active turbulence grid is used to generate defined inflow conditions. The ba form of the grid is shown as CAD in Figure 4. The turbulence generators, which are sho in orange in the center, are in the closed state, i.e., the maximum blocking of the grid present. The basic structure of the grid consists of an outer frame and an inner fram through which the flow passes. The drive motors and their controls are located on outer frame. A total of 20 stepper motors are used, which are equipped with encoders a heat sinks. Vibration damping couplings are attached to the stepper motors. These co plings reduce the vibrations on the shaft, which are generated by the stepper motor. T outer frame is mounted on vibration dampers. The stepper motors and the space betwe the inner and outer frames are shielded by foam and motor enclosures so that as li sound as possible can be emitted to the outside from these components.  Figure 5 shows a partial section of the active turbulence grid, where the flange be ings are visible. These are located outside the flow on the inner frame and guide the sha on which the turbulence generators are located. In the center of the flow field, the sha are additionally supported by sliding bearings, which have vibration damping propert The center cross is designed as a symmetrical airfoil. This prevents stall at the center cro which is necessary for stability reasons. As shown in Figure 5, there is a front and a r row of turbulence generators. After the turbulence generators are 3D printed and slid o the shaft to be centered, there must be a gap between the vertical and horizontal axes. B the horizontal and vertical axes are positioned 6.5 mm off center. Thus, the shafts hav distance of 13 mm from each other in flow direction.  Figure 5 shows a partial section of the active turbulence grid, where the flange bearings are visible. These are located outside the flow on the inner frame and guide the shafts on which the turbulence generators are located. In the center of the flow field, the shafts are additionally supported by sliding bearings, which have vibration damping properties. The center cross is designed as a symmetrical airfoil. This prevents stall at the center cross, which is necessary for stability reasons. As shown in Figure 5, there is a front and a rear row of turbulence generators. After the turbulence generators are 3D printed and slid over the shaft to be centered, there must be a gap between the vertical and horizontal axes. Both the horizontal and vertical axes are positioned 6.5 mm off center. Thus, the shafts have a distance of 13 mm from each other in flow direction.  Figure 5. Partial view of the active turbulence grid, in which the distance between the two rows o turbulence generators can be seen. Figure 6 illustrates a turbulence generator with shaft. The turbulence generators ar square wings, which are located on the shaft. Each 2.5 wings consist of a joint 3D printe part and can be slid onto the shaft and fixed there by means of screws. The inner frame o the active turbulence grid, where the flow passes through, has square dimensions of 80 × 800 mm. The turbulence generators are shortened by a total of 7.5 mm. For this reason there is a space of 3.75 mm between the two ends of a turbulence generator shaft and th respective frame wall. This clearance, as well as the distance between the horizontal an vertical axes, is necessary so that the turbulence generators do not drag or collide wit each other during operation. By means of the individually controllable stepper motor each of the 20 drive shafts, with the turbulence generators located on them, can be ad justed independently of each other. These settings include the direction of rotation, th rotational speed, the start position, the acceleration, a standstill position or relative move ments to other drive shafts. The number of individual shafts determines the mesh size of the active turbulenc grid, which is M = 80 mm. The axial length of the active turbulence grid is L = 260 mm. B Figure 5. Partial view of the active turbulence grid, in which the distance between the two rows of turbulence generators can be seen. Figure 6 illustrates a turbulence generator with shaft. The turbulence generators are square wings, which are located on the shaft. Each 2.5 wings consist of a joint 3D printed part and can be slid onto the shaft and fixed there by means of screws. The inner frame of the active turbulence grid, where the flow passes through, has square dimensions of 800 × 800 mm. The turbulence generators are shortened by a total of 7.5 mm. For this reason, there is a space of 3.75 mm between the two ends of a turbulence generator shaft and the respective frame wall. This clearance, as well as the distance between the horizontal and vertical axes, is necessary so that the turbulence generators do not drag or collide with each other during operation. By means of the individually controllable stepper motors, each of the 20 drive shafts, with the turbulence generators located on them, can be adjusted independently of each other. These settings include the direction of rotation, the rotational speed, the start position, the acceleration, a standstill position or relative movements to other drive shafts.  Figure 5. Partial view of the active turbulence grid, in which the distance between the two rows of turbulence generators can be seen. Figure 6 illustrates a turbulence generator with shaft. The turbulence generators are square wings, which are located on the shaft. Each 2.5 wings consist of a joint 3D printed part and can be slid onto the shaft and fixed there by means of screws. The inner frame of the active turbulence grid, where the flow passes through, has square dimensions of 800 × 800 mm. The turbulence generators are shortened by a total of 7.5 mm. For this reason, there is a space of 3.75 mm between the two ends of a turbulence generator shaft and the respective frame wall. This clearance, as well as the distance between the horizontal and vertical axes, is necessary so that the turbulence generators do not drag or collide with each other during operation. By means of the individually controllable stepper motors, each of the 20 drive shafts, with the turbulence generators located on them, can be adjusted independently of each other. These settings include the direction of rotation, the rotational speed, the start position, the acceleration, a standstill position or relative movements to other drive shafts. The number of individual shafts determines the mesh size of the active turbulence grid, which is M = 80 mm. The axial length of the active turbulence grid is L = 260 mm. By means of adapters on the inner frame, the square channel of the grid can be extended as desired both at the front and at the rear. In the tests presented here, a total length of L = The number of individual shafts determines the mesh size of the active turbulence grid, which is M = 80 mm. The axial length of the active turbulence grid is L = 260 mm. By means of adapters on the inner frame, the square channel of the grid can be extended as desired both at the front and at the rear. In the tests presented here, a total length of L = 330 mm was selected, with an extension of 70 mm in the direction of flow (see Figure 3). The dimensions of the heat exchanger, which also plays a role in these investigations, are 800 × 800 × 330 mm, which thus corresponds to the same flow area and expansion as with the ATG. After the housing of the grid there is a transition to a circular duct with D = 500 mm diameter [11,16]. The transition is realized by an inlet nozzle. The axial fan to be investigated is operated in the round duct. If the axial fan is installed, the distance between it and the center plane of the two rotation planes of the active turbulence grid is d = 200 mm. Figure 7 shows the active turbulence grid within the anechoic chamber of the axial fan test rig at the University of Erlangen-Nuremberg [30]. The active turbulence grid is shown in its basic shape without sound enclosure. Additionally, the five free-field microphones for measuring the sound radiation on the suction side are visible.

uls. Power 2023, 8, x FOR PEER REVIEW
The dimensions of the heat exchanger, which also plays a role in these in 800 × 800 × 330 mm, which thus corresponds to the same flow area and e the ATG. After the housing of the grid there is a transition to a circular d mm diameter [11,16]. The transition is realized by an inlet nozzle. The a vestigated is operated in the round duct. If the axial fan is installed, the it and the center plane of the two rotation planes of the active turbulen mm. Figure 7 shows the active turbulence grid within the anechoic cha fan test rig at the University of Erlangen-Nuremberg [30]. The active t shown in its basic shape without sound enclosure. Additionally, the five phones for measuring the sound radiation on the suction side are visible

Intrinsic Noise of the Active Turbulence Grid
In order to better separate the acoustic influence of the active turbu measurement results of the sound pressure from the axial fans under inherent noise of the active turbulence grid was determined. The noise is it can be assumed that the intrinsic noise of the grid is masked by the Figure 8 displays a comparison between the sound radiation of the axial f box in front and selected operating conditions of the ATG.
The spectra in Figure 8 are the inherent noise of the active turbulenc

Intrinsic Noise of the Active Turbulence Grid
In order to better separate the acoustic influence of the active turbulence grid on the measurement results of the sound pressure from the axial fans under investigation, the inherent noise of the active turbulence grid was determined. The noise is low enough that it can be assumed that the intrinsic noise of the grid is masked by the fan noise [14,31]. Figure 8 displays a comparison between the sound radiation of the axial fan with an empty box in front and selected operating conditions of the ATG.
The spectra in Figure 8 are the inherent noise of the active turbulence grid at constant speeds. In this case, all motors rotate at the same speed and the grid blockage is constantly set to 50% blockage. A blockage of 50% is achieved by starting half of the turbulence generators at 90 • offset to the others. Operating modes in which all shafts rotate at the same speed are usually the noisiest. Thus, the case with the maximum speed of 800 rpm of the ATG is also the acoustically worst case. As a reference value, the noise of the axial fan is chosen when an empty box (an empty heat exchanger housing) is positioned in front of the axial fan on the suction side. With the ATG, a corresponding housing is always positioned in front of the axial fan due to the inner frame. Thus, this case represents a better comparison case, than the free inflow, because so also the influence of the changed directional characteristics is considered [32]. Only for the maximum speed of 800 rpm are there a few frequencies at which the spectrum of the axial fan does not mask the noise of the ATG. The overall sound pressure level is 11 dB away from the ATG's inherent noise at 800 rpm, far enough away that it can be assumed that the fan's sound radiation is not affected by the inherent noise of the turbulence grid. In the high-frequency range, tonal components appear individually through the spectrum of the axial fan. Through a run-up and a resulting Campbell plot (see Figure 9), it can also be determined that the tonal components generated by the active grid are related to the speed of the shafts. In addition, the linear relationship between the tonal components in the sound spectrum and the motor speed is related to the steps and micro steps of the motors used. These perform 200 steps and 3200 micro steps per revolution. The corresponding sound radiation of the tonal components can be calculated using Equation (7). The rotational speed n and the step size goes into the calculation of the respective frequency. The tonal sound radiation due to the microstep is the 16th harmonic (k = 16) of the fundamental frequency. Through a run-up and a resulting Campbell plot (see Figure 9), it can also be determined that the tonal components generated by the active grid are related to the speed of the shafts. In addition, the linear relationship between the tonal components in the sound spectrum and the motor speed is related to the steps and micro steps of the motors used. These perform 200 steps and 3200 micro steps per revolution. The corresponding sound radiation of the tonal components can be calculated using Equation (7). The rotational speed n and the step size δ goes into the calculation of the respective frequency. The tonal sound radiation due to the microstep is the 16th harmonic (k = 16) of the fundamental frequency.
spectrum and the motor speed is related to the steps and micro steps of the motors used These perform 200 steps and 3200 micro steps per revolution. The corresponding sound radiation of the tonal components can be calculated using Equation (7). The rotationa speed n and the step size goes into the calculation of the respective frequency. Th tonal sound radiation due to the microstep is the 16th harmonic (k = 16) of the fundamenta frequency.

Generation of Defined Inflow Conditions
In many literatures in the field of sound radiation from axial fans, the inflow conditions are defined by spatial mean values of turbulence intensity and length scale [33,34]. These two values are also used for empirical sound prediction models for the axial fan and are essential for its sound radiation [35,36]. Thus, when the spatial mean values of these two quantities are plotted against each other, a characteristic map for the inflow conditions of the axial fan can be generated. In Figure 10, the global values of turbulence level and integral length scale are plotted in a characteristic map. Different operating modes of the active turbulence grid are shown with red dots in the map. The black squares are representative of four different heat exchangers with the dimensions of 800 × 800 mm. The distribution of the red dots shows that the active turbulence grid can vary the turbulence level in the range of [6.7%; 16.3%] and the length scale in the range of [3.7 mm; 36.2 mm]. In addition, a kind of pareto front [37] is recognizable in the measurement data. In total, more than 60 different operating conditions with different flow fields were generated with an active turbulence grid. Since at this point the basic functionality of the grid for the application in the field of turbulent inflow conditions of axial fans should be demonstrated, the individual flow fields and how they were generated will not be discussed. As different operating modes were used rigid modes, i.e., without rotation of shafts, uniform modes, where all shafts rotate at the same speed, staged modes, where different shafts have different speeds, and partially rotating modes, where only one part of the shaft rotates while the other part is stationary. The relationship that at constant slow speed the length scale can be adjusted and at constant high speed the turbulence intensity can be controlled independently, which is described in the literature [15], could also be found in this application. Thus, the characteristic map of the active turbulence grid (see Figure 10) proves that, for example, the length scale can be varied in the region of Tu glo = 14% turbulence level, whereas the average turbulence level remains almost constant at this value. At a length scale of about Λ = 5 mm, the opposite pattern is seen. In this range, the turbulence level can be changed while the length scale remains constant. Thus, the active turbulence grid allows a separation of the influences of the different turbulence characteristics on the sound spectrum of axial fans to be investigated independently of each other. the turbulence level can be changed while the length scale remains co active turbulence grid allows a separation of the influences of the diff characteristics on the sound spectrum of axial fans to be investigated i each other.

Reproduction of the Flow Fields of Heat Exchangers
The four heat exchangers from Figure 10 are industrial devices, which are used, for example, in heat pumps or refrigeration systems. The turbulence intensity decreases with decreasing pipe diameter. Thus, the heat exchanger with the highest turbulence intensity has a tube diameter of 12 mm, the two black squares in the middle have a tube diameter of 9.52 mm, and the heat exchanger with the lowest turbulence intensity has a tube diameter of 5 mm. A detailed description of the heat exchangers can be found in the literature [16]. Especially the heat exchanger with the highest turbulence level can be reproduced very well in the mean values by the active turbulence grid. Here, the mean values in the length scale between heat exchanger and active turbulence grid deviate by only 2 mm. For the two heat exchangers in the turbulence range of 6.5%, the active turbulence grid can reproduce the turbulence level, but the length scale deviates by 6 mm. The heat exchanger with the low turbulence level of 4.3% cannot yet be reproduced by the active turbulence grid so far. Further investigations will show whether this range can be achieved in the map via other operating modes.
Since the active turbulence grid seems to be able to reproduce the average flow values of heat exchangers, a comparison between the flow field downstream of a heat exchanger (Tu glo = 8.12%, Λ = 8.34 mm) and the most similar operating mode of the active turbulence grid (Tu glo = 8.15%, Λ = 10.48 mm) is shown in Figure 11. In addition, the flow pattern of a free inlet flow is shown as a reference (Figure 11c). grid so far. Further investigations will show whether this range can be achieved in the map via other operating modes.
Since the active turbulence grid seems to be able to reproduce the average flow values of heat exchangers, a comparison between the flow field downstream of a heat exchanger (Tuglo = 8.12%, Λ = 8.34 mm) and the most similar operating mode of the active turbulence grid (Tuglo = 8.15%, Λ = 10.48 mm) is shown in Figure 11. In addition, the flow pattern of a free inlet flow is shown as a reference (Figure 11c). The surface plots of the turbulence level display that flow conditions similar to those of heat exchangers can be created with the active turbulence grid. It is noticeable that the flow field seems to be rotated by 90° in the plots shown. Nevertheless, inhomogeneities in the flow field, which are mainly generated by the square housing of the heat exchanger and the active grid, can be reproduced [16,38]. The two-dimensional distribution of turbulence values also shows similar tendencies. Compared to the free inflow, the turbulence intensity increases through the heat exchanger as well as through the active turbulence grid. The inhomogeneity in the distribution increases in both cases compared to the free inflow.

Heat Exchanger and Active Turbulence Grid
The active turbulence grid is not only intended to reproduce the flow field of the heat exchangers, but also to reproduce the sound radiation of axial fans positioned downstream of heat exchangers as best as possible. The sound pressure spectrum is used to evaluate the sound emissions on the suction side of the axial fans. A comparison of the active turbulence grid and the heat exchanger should only be made at the operating point The surface plots of the turbulence level display that flow conditions similar to those of heat exchangers can be created with the active turbulence grid. It is noticeable that the flow field seems to be rotated by 90 • in the plots shown. Nevertheless, inhomogeneities in the flow field, which are mainly generated by the square housing of the heat exchanger and the active grid, can be reproduced [16,38]. The two-dimensional distribution of turbulence values also shows similar tendencies. Compared to the free inflow, the turbulence intensity increases through the heat exchanger as well as through the active turbulence grid. The inhomogeneity in the distribution increases in both cases compared to the free inflow.

Heat Exchanger and Active Turbulence Grid
The active turbulence grid is not only intended to reproduce the flow field of the heat exchangers, but also to reproduce the sound radiation of axial fans positioned downstream of heat exchangers as best as possible. The sound pressure spectrum is used to evaluate the sound emissions on the suction side of the axial fans. A comparison of the active turbulence grid and the heat exchanger should only be made at the operating point at which the flow data are available. A change in the flow velocity within the active turbulence grid leads to a change in the grid Reynolds number, which in turn changes the turbulence level and the length scale generated by the grid [15]. Figure 12 shows the sound pressure spectrum of the forward skewed axial fan at the design point. Here, the spectrum that is induced when a heat exchanger is placed in front of the axial fan and the spectrum when an active turbulence grid generates similar flow conditions are presented. In both cases, the sound measurements were made inside the anechoic chamber, on the suction side of the axial fan. Accordingly, the sound is influenced during its propagation to the microphones by the heat exchanger or the active turbulence grid, which are also located on the suction side of the axial fan. In this operating point there is a difference of 0.7 dB in the overall sound pressure level of the two variants. From this, follows that the overall sound pressure level is reproduced well by means of active turbulence grids. In addition, the sound pressure spectra have similar trends, in which the subharmonic peak and the higher harmonic blade passing frequencies are reproduced. Only the first blade passing frequency (1.BPF) is higher in the case with the active turbulence grid. This could be due to a higher turbulence spot in the flow field, which is not detected by the measurement in the third segment of the duct [16]. At higher frequencies, the heat exchanger consistently induces a lower sound pressure level. However, this difference is not due to the flow field, but to the sound guiding properties of the heat exchanger. Czwielong et al. [32] have identified that the differences in the high frequencies are due to the periodic arrangement of the coolant tubes in the heat exchanger and to the thermoviscous losses due to the high number of cooling fins. Thus, the differences in the high frequency range can be corrected by knowledge of the heat exchanger's sound transmission characteristics. frequency (1.BPF) is higher in the case with the active turbulence grid. This could be due to a higher turbulence spot in the flow field, which is not detected by the measurement in the third segment of the duct [16]. At higher frequencies, the heat exchanger consistently induces a lower sound pressure level. However, this difference is not due to the flow field, but to the sound guiding properties of the heat exchanger. Czwielong et al. [32] have identified that the differences in the high frequencies are due to the periodic arrangement of the coolant tubes in the heat exchanger and to the thermoviscous losses due to the high number of cooling fins. Thus, the differences in the high frequency range can be corrected by knowledge of the heat exchanger's sound transmission characteristics.

Fundamental Investigations between Flow Field and Axial Fan Sound Radiation
Based on the flow field investigations, the sound emissions of the axial fan were investigated in nineteen selected operating modes of the active turbulence grid. The sound

Fundamental Investigations between Flow Field and Axial Fan Sound Radiation
Based on the flow field investigations, the sound emissions of the axial fan were investigated in nineteen selected operating modes of the active turbulence grid. The sound pressure spectra obtained at the design point were analyzed, for example, on the basis of the sound radiation at the first blade passing frequency (1.BPF = z = n/60 = 222.9 Hz, with z = 9 blades and n = 1486 rpm) and the total sound pressure level up to 1 kHz, which is mainly determined by the low-frequency broadband sound. The first blade passing frequency is often a dominant tonal component in the sound pressure spectrum of lowpressure axial fans and should be kept as low as possible so that the fan noise is not perceived as annoying [39]. Figure 13a displays the relationship between the acoustic emission of the axial fan at the first blade passing frequency and the spatial mean value of the turbulence level. From the data distribution, it can be concluded that no correlation between the mean spatial turbulence level and the sound emission at the first BPF can be found. This indicates that it is often not sufficient to give only mean turbulence levels when the sound pressure spectra of axial fans are discussed in the literature. Figure 13b displays the relationship between the first BPF and the spatial variance of the turbulence level. It can be clearly identified that as the variance increases, the acoustic radiation of the axial fan increases at the first BPF. A linear fit is given as a red dashed line in the plot. Equation (8) is the equation of the linear fit curve, in which the turbulence level in percent is inserted. The coefficient of determination has a value of R 2 = 77.66% for the fit. The relationship between the total sound pressure level between 0.1 kHz and 1 kHz, which is mainly determined by the broadband noise at the leading edge of the fan, and the spatial mean value as well as the spatial variance of the turbulence intensity is shown in Figure 13c,d.
For the total sound pressure level, no linear relationship to the spatial variance of the turbulence intensity can be found. In fact, the total sound pressure level remains almost independent of this parameter because a horizontal tendency develops. However, the total sound pressure level is influenced to a certain extent by the spatial mean value of the turbulence intensity. Here, a linear fit can be performed, which is given in Equation (9) and has a value of R 2 = 34.10%. The fit is shown as a dashed red line in Figure 13c. The existence of a linear relationship between the sound radiation at the first BPF and the spatial variance of the turbulence level indicates that the knowledge and specification of spatial parameters is critical for the understanding of the sound emission of axial fans. The spatial variance offers the possibility not only to represent discontinuities in the turbulence level by surface plots but also to describe these discontinuities in a statistical value. A high spatial variance means that spatial gradients in the turbulence level are present. When the fan blade moves through these gradients, it experiences a change in the blade forces, which in turn leads to a change in the sound radiation of the 1.BPF. Low values of the spatial variance of the turbulence level indicate a homogeneously distributed turbulence level. The fan blade moves through fewer gradients; therefore, experiences fewer changes in blade forces as it rotates through the flow field. As a result, the sound emission decreases at the 1.BPF. In heat exchanger applications, strong inhomogeneities in the flow field may occur. To minimize sound radiation at the 1.BPF, these inhomogeneities in the flow field should be avoided as far as possible. For the total sound pressure level, no linear relationship to the spatial variance of the turbulence intensity can be found. In fact, the total sound pressure level remains almost independent of this parameter because a horizontal tendency develops. However, the total sound pressure level is influenced to a certain extent by the spatial mean value of the turbulence intensity. Here, a linear fit can be performed, which is given in Equation (9) and has a value of R 2 = 34.10%. The fit is shown as a dashed red line in Figure 13c.
The existence of a linear relationship between the sound radiation at the first BPF and the spatial variance of the turbulence level indicates that the knowledge and specification of spatial parameters is critical for the understanding of the sound emission of axial fans. The spatial variance offers the possibility not only to represent discontinuities in the turbulence level by surface plots but also to describe these discontinuities in a statistical value. A high spatial variance means that spatial gradients in the turbulence level are present. When the fan blade moves through these gradients, it experiences a change in the blade forces, which in turn leads to a change in the sound radiation of the 1.BPF. Low values of the spatial variance of the turbulence level indicate a homogeneously distributed turbulence level. The fan blade moves through fewer gradients; therefore, experiences fewer changes in blade forces as it rotates through the flow field. As a result, the sound emission decreases at the 1.BPF. In heat exchanger applications, strong inhomogeneities Figure 13. Influence of spatial mean turbulence intensity and spatial variance of turbulence intensity on sound radiation of axial fan at first blade passing frequency (1.BPF) and total sound pressure level between 0.1 kHz and 1 kHz. (a) BPF in dependence of the spatial mean value of the turbulence intensity, (b) BPF as a function of spatial variance of turbulence intensity with linear fit function, (c) BPF as a function of the spatial mean value of the turbulence intensity with linear fit function and (d) OSPL in dependence of the spatial variance of turbulence intensity.

Conclusions
An active turbulence grid was presented, which can be used for the generation of inflow turbulence of axial fans. The acoustic characterization of the active turbulence grid showed that the inherent noise of the grid is low enough and no significant influence on the sound pressure spectra of the axial fans under investigation is to be expected. In addition, it was found that the tonal peaks of the active turbulence grid depend on the rotational speed of the shafts and the number of steps of the stepper motors. On the basis of 3D hot-wire investigations, it was demonstrated that the active turbulence grid can be used to generate a large number of different inflow conditions, and that the mean turbulence characteristics and the spatial turbulence characteristics induced by heat exchangers can be reproduced by means of the active turbulence grid. The sound radiation of the investigated forward skewed axial fan between a heat exchanger and the active turbulence grid, which both induce comparable inflow conditions, also had similar tendencies. Here, differences in the high frequency range could be attributed to the absence of cooling fins. Based on a large number of sound radiation investigations, a linear relationship was found between the sound pressure level at the first blade passing frequency and the spatial variance of the turbulence level. No correlation was found between the sound radiation at the 1. BPF and the spatial mean of the turbulence level. This result indicates on the one hand that the spatial flow field significantly influences the sound radiation of axial fans and on the other hand that for the understanding of the sound generation mechanisms at the axial fan not only mean values are sufficient. However, the total sound pressure level up to 1 kHz did not depend on the spatial variance of the turbulence level, but on the spatial average of the turbulence level. The derived value of spatial variances of turbulence level and length scale should be considered in future studies on inflow turbulence of axial fans to achieve a better understanding between the sound radiation and the flow field.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.