Development of unsteady multi-hole pressure probes based on fiber-optic pressure sensors

For measurements of unsteady flow phenomena with multi-hole pressure probes, pressure transducers are integrated in the probe near the probe tip. The application of additive manufacturing enables a wide variation in probe geometries for complex use cases. The spatial characteristics of the unsteady probe are determined by the steady state calibration in a known free-jet wind tunnel. Furthermore, the acoustic/pneumatic line-cavity system, that emerges inside the channels of the probe, is investigated in detail in the temporal calibration. In order to realize multi-hole probes with higher temporal resolution, which can be operated in harsh environments, a fiber-optic pressure sensor is developed. The measurement principle of the fiber-optic sensor is based on the Fabry-Pérot interferometer effect. The sensor is operated differentially with a pressure capillary by either pressurizing the sensor or using the surrounding static pressure as the reference pressure. Besides calibration of the sensor, comparisons with a state-of-the-art piezo-resistive pressure transducer have been performed. The focus of this work is on the reproducibility of both frequency response and amplitude.


Introduction
Highly fluctuating flow fields are caused for example by interactions of rotating and non-rotating components in turbo machines. Sources of unsteadiness, like rotor-stator interaction, secondary flows or blade wake shedding, have to be understood either by means of numerical simulations or measurements. Even though the development and optimization of computational fluid dynamics (CFD) simulations enables the unsteady flow patterns to be handled numerically, experimentally gained data are still of interest for academic and industrial research. The reason why experiments can be still justified alongside numerical simulations is twofold: firstly, experimental results often serve as a database for the validation for CFD solutions. Secondly, live monitoring of machines (e.g. turbines in operation) is only possible experimentally. Certain requirements have to be met by probes for unsteady flow measurement in turbomachines. This ensures that all sources of unsteadiness can be resolved precisely. For example, bandwidths corresponding to blade passing frequencies of up to f=10 kHz are the benchmark for the temporal resolution. For aerodynamic measurements of flow fields, measurement techniques can basically be divided into non-intrusive/optical and intrusive techniques. Particle image velocimetry (PIV) and laser Doppler anemometry (LDA) are the main representatives of optical measurements, which are used to examine the velocity field. However, in some cases they are disadvantageous because of high calibration efforts and significant set up costs. Furthermore, the need for optical access in the test section rules out optical measurement techniques in various test situations. Of the intrusive measuring methods, hot-wire probes and multi-hole pressure probes are most commonly used. On the one hand, hot-wire anemometry is characterized by its high temporal resolution. On the other hand, hot-wires lack of mechanical robustness when being set in harsh environments. In contrast, multi-hole pressure probes are cost-efficient and easy to use. Since

Multi-hole probe geometry and additive manufacturing
In the following, the main steps regarding the multi-hole probe geometry and the usage of an additive manufacturing process are presented. The working principle of multi-hole pressure probes relies on the stagnation of the flow around the probe, when being inserted in the flow of any fluid. The pressure distribution around the bluff probe body varies from the maximum pressure at the location of stagnation to lower values, that can even be lower that the static pressure in the undisturbed flow far upstream of the bluff probe body. At the stagnation point maximum pressure, the stagnation or total pressurep t , is equal to the sum of the static pressurep s and the dynamic pressure far away from the probeq.
Here, ¥ U is the free-stream velocity and ρ the density of the fluid. Similar to the well-known Pitot probe, where the stagnation pressure is measured at a single pressure port, multi-hole probes measure the total pressure of the flow at various locations at the probe tip. In figure 1(a) the schematic cross-section of a multi-hole probe under an angle-of-attack is depicted. In this flow situation the bottom and central hole would experience higher pressures than the upper hole. By measuring all pressures and setting these pressures into relation, the general flow properties at the location of the probe tip can be concluded. For a five-hole probe, which can measure both, pitch and yaw, angles, the pressures p 1 , p 2 , ..., p 5 are measured at the depicted pressure ports (see figure 1(b)). In the present research project, a multi-hole pressure probe is developed for its use in unsteady flows (see figure 2). It is designed for measurements in turbomachinery and wind tunnels. In contrast to steady pressure acquisitions, long pressure lines cannot be used to connect the probe holes to the acquisition manometers/pressure sensors for unsteady flows as the time-dependent pressure fluctuations would be attenuated entirely. Therefore, differential pressure sensors are installed in close proximity to the probe tip-often in the probe shaft. Turbomachinery use cases with signal frequencies of up to 10 kHz define the temporal characteristics. Intrusive effects, as they occur when placing probes in flows, can be avoided by miniaturizing the fast-response pressure probe (FRAP) and its shaft. Using additive manufacturing enables the realization of arbitrary probe shapes, which counteract the limitations of probes manufactured in conventional cutting processes [21].
Fabrication of complex geometries can be realized with additive manufacturing. For the manufacturing of the probe shown in figure 2, the powder-bed fusion method, more precisely the selective laser melting (SLM) method, was used. Thereby, metal or ceramic powders are melted and sintered. Further terminologies for SLM in the literature are direct metal laser sintering or laser cusing [21]. In the SLM process, thin layers of powder are stacked on top of each other and selectively melted by a laser. Considering the design of aerodynamic probes, the narrow internal channels and the required tightness make certain manufacturing settings necessary. Layer thicknesses under 50 μm and focal laser diameters of around 100 μm provide good results with relatively small probe diameters. The orientation of the probe during the additive manufacturing process is crucial to obtain a smooth surface, as well. Low angles and overhangs must be avoided when possible. Depending on the potentially harsh environments during probe applications, e.g. high temperatures, different materials can be used in the printing process. The materials, which can be used in the powder-bed-fusion process, have to show adequate melting and resolidifying properties [21]. Materials like titanium, Inconel 718, or stainless steel are most commonly used for aerodynamic applications [22]. In this work's case, it was decided to use the standard alloy  316L, since no special temperature requirements were present. Nevertheless, there are still some limitations regarding the probe's geometry and its channel configuration when setting up the additive manufactoring process. Hence, many iterations are required to achieve acceptable results. These limitations range from powder accumulation within cavities to excessive porosity or rough surfaces in some structures. Research efforts targeting those problems have enabled the manufacturing of arbitrary multi-hole probes with tip diameters of 1.2mm and channel diameters of D=1 mm [22]. As the final step of the manufacturing, different details in the probe design can be realized in a post manufacturing cutting process (see figure 3). Such details can be, for example, different probe tip shapes, which can vary from the application of the probe, or the connection to a probe holder. Most commonly only the probe head is manufactured through SLM, since it is the critical part of the probe and sensible to geometric variations. For most unsteady applications, a hemispheric probe tip is beneficial. Probe geometries can be adopted to special measurement instrumentations. Börner et al realized a 3D-printed miniaturized wedge probe for transonic wake flows [18]. Furthermore, Bach et al designed a SLMmanufactured guide vane with an integrated Kiel probe [23]. Improvements in the 3D-printing process can lead to further miniaturized probes, which reduce intrusive effects of the probe in the flow field.

Sensor specifications
As already mentioned, due to the measurement task in highly unsteady flows, the placement of pressure sensors inside the probe is necessary, since long pressure lines to manometers would attenuate signal contents of high frequencies entirely. In the following, the state-of-the-art pressure sensor type, namely piezo-resistive sensors, are introduced. Furthermore, the development of a new fiber-optic pressure sensor, that should overcome the downsides of the electric counterparts, is described.

Piezo-resistive sensor
In figure 4(a) the working principle of a piezo-resistive sensor is depicted [24]. Due to the application of pressure, the sensor membrane will be deformed. Therefore, the piezoresistor will experience bending stresses and, hence, changes in electrical resistivity of the sensor material due to the piezo-resistive effect. A Wheatstone bride is embedded in the piezoresistor membrane (often silicon). The change in resistance of the bridge leads to a change in the output voltage V out (see figure 4(b)). Even though piezo-resistive sensors are easy to use and the state-ofthe-art solution for pressure measurements, there are several downsides, which lead to the idea to develop a sensor based on another measurement technique, as described in the following chapter. Piezo-resistive sensors show not negligible cross-sensitivities to external influences, like temperature and humidity changes or electromagnetic disturbance. Furthermore, the Wheatstone bridge has to be operated actively. In addition, due the spatial restrictions inside a pressure probe, the wiring of the multiple sensors is time-consuming and complex. Commercially available differential sensors are seldom smaller than 2-3 mm in diameter, considering the desired pressure range of up to psig 2 for low-speed wind tunnel use-cases.

Fiber-optic pressure sensor
A major part of the probe improvement activities is the enhancement of the sensor performance. Therefore, optical principles are applied to surpass the limits of conventional electrical pressure transducers with respect to resolution and cross-sensitivities. The characteristics of the optical sensors are expected to outperform state-ofthe-art piezo-resistive sensors.
In previous developments, fos4X GmbH has developed a durable pure glass absolute fiber-optic pressure sensor for surface pressure measurements [19,20]. The cuboid pressure sensor, which is wall mounted, operates without any conductive material. Due to its absence, the sensor is inherently immune to electro-magnetic interference. Furthermore, it is robust against water, humidity, and corrosion. The miniature sensor with dimensions of 1.6 mm×3 mm×10 mm is capable of measuring aerostatic, aerodynamic and aeroacoustic events as a pressure sensor and as a microphone at the same time [19]. The flat design allows for integration in surfaces with minimal aerodynamic disturbance of the air flow. The fully exposed membrane of 1.65 mm diameter at the surface of the sensor enables pressure measurements without any spectral characterization, because of constant frequency response to 80% of the natural frequency of 250 kHz [19,20].
In contrast to the existing cuboid absolute pressure sensor, a new cylindrical, differential pressure sensor is developed and tested, in this work. It is intended to be installed in five-hole probes as a replacement for state-ofthe-art piezo-resistive sensors.

Fabry-pérot effect for pressure sensing
A fiber-optic pressure transducer at the end of a common telecommunication fiber works in principle similar to their electrical counterparts: The fiber-optic sensor is a passive MOEMS glass chip, which consists of a diaphragm/membrane, a resonance cavity and two mirrors. One mirror is attached on the diaphragm, while the second is half transparent and fixed. Applied pressure p bends the diaphragm and changes the cavity length L c between the two mirrors (see figure 5). The end of the fiber and the inner part of the membrane represent the two mirrors. The maximum deflection of the membrane is [20]: Here, E is the Young's modulus, ν the Poisson's ratio and r m and h m radius and thickness of membrane. Thus, the performance of the measurement system, e.g. its sensitivity, is predominantly defined by the mechanical  displacement of the membrane. The miniaturization of the sensor design will therefore considerably affect the sensitivity. A broadband infrared light source illuminates the transducer from the fiber-optic cable. Optical interference modulates the reflecting light spectrum depending on the cavity length and therefore, the deflection of the membrane due to the applied pressure. Each wavelength λ of incoming light, which fulfills the Fabry-Pérot resonance condition will interfere destructively [25]. The ratio of the reflecting light spectrum I R to the incoming light spectrum I 0 is dependent on the phase δ and can be calculated as follows: Here, F depicts the coefficient of finesse, which describes the quality of the Fabry-Pérot filter. M refers to the 'mismatch' of the reflectance values in the interferometer [26,27]. An increasing cavity length shifts the phase condition of the destructively interfered wavelength in the spectrum to larger wavelengths, while a smaller cavity length shifts the spectrum to smaller wavelengths [19,28]. The modulated light is guided back in the same single fiber to the optical measurement device, where it is split in two parts. While the first part is focused directly on a photodiode, the second part is optically filtered and focused on a second photodiode. The reflected spectrum of the sensor is matched to the operating point of an edge-filter interrogator, also known as the Q-point of the device. Therefore, the edge-filter interrogator is filtering a single destructive interference in the optical spectrum in the C-band. The ratio of the light intensities reveals the phase shift of the reflected spectrum. The correlation of this ratio to the applied pressure can be determined in a calibration. The optical filtering process ensures sampling frequencies up to f s =50 kHz. Each analog signal is converted to a digital value by an analog to digital converter.

Sensor design and assembly
In the development process conducted within this work, a gauge/differential fiber-optic pressure sensor, which is based on the optical principles of a Fabry-Pérot interferometer, is manufactured. As an aim the main specifications of the presented five-hole FRAP shall be improved regarding its measurement abilities by replacing the piezo-resistive sensors with the fiber-optic ones. The fiber-optic sensor casing and membrane are fabricated out of two fused silica (SiO 2 ) wafers, which are bonded together. Further information regarding the selective laser etching (SLE) bonding process is given in [29]. Furthermore, the optical fiber is fixed to fit the Q-Point of the measurement device in the micromachined wafer. A capillary is bonded to either pressurize the cavity and therefore measure the differential pressure or work as a gauge sensor with the surrounding static pressure as the reference pressure (see figure 5). In figure 6, a fiber-optic pressure sensor of the 1st generation is shown, which has a diameter of 2 mm. The light is reflected by a mirror and terminated.

Probe calibration process
Using the probe in an experiment with unknown flow conditions requires a calibration of the probe beforehand.
In the calibration process, a separation of spatial and temporal behavior of the probe is assumed. Hence, besides an aerodynamic/spatial calibration, a dynamic/temporal calibration has to be conducted as well. The temporal calibration characterizes the acoustic system in the channels between the tip and the sensors. Both calibration approaches are explained in more detail in the following sections.

Spatial calibration in a free-jet
Within the spatial calibration, the correlation between the mean free-stream flow conditions and the measured pressures at the probe is determined. Therefore, various combinations of the free-stream velocity ¥ U and the flow angles α and β are set in the free-jet calibration wind tunnel, which is illustrated in figure 7. Table 1 depicts the specifications of the calibration free-jet facility. Depending on the expected angle and velocity range in later experiments, angle combinations at certain velocities are calibrated. Figure 8 shows the calibration grid for the straight five-hole probe in figure 2. Figure 9 shows the two interchangeable coordinate systems: pitch(α)-yaw(β) or roll(f)-cone(θ). Figure 7. Free-jet calibration facility at Vectoflow [22].  In order to determine the actual flow conditions at the probe tip in an experiment, the acquired pressures have to be post-processed. In the literature, there are multiple ways how the calibration data is used for reconstructing the flow-field properties. The most commonly used one is an interpolation scheme, which is applied on the gathered pressures in order to calculate the properties at the probe tip. System identification approaches with the use of neural networks can also be found in the literature. Both approaches will be discussed and compared subsequently: Non-dimensional calibration coefficients can be calculated, which are the basis for the interpolation. The interpolation routines can be divided in global or local interpolations, depending on whether to use all calibration points or solely points in the surrounding with similar calibration coefficient values, respectively. Based on Johansen [30], a local interpolation method is used and the calibration data is divided in a low-angle and high-angle regime. The pressure port with the highest measured pressure determines the set of calibration coefficients, that are used for the reconstruction. In the case that multiple pressure ports see similar pressures within a pre-specified margin, overlap segments are defined, in which the coefficients are calculated for every dominant pressure port (see figure 10). For the low-angle regime, where the central port p 1 measures the highest pressure, the coefficients are as follows:  Thus,q denotes the pseudo dynamic pressure, which is used to non-dimensionalize the coefficients. The high-angle regime, where one of the circumferential ports p i measures the highest pressure, can be described by the following coefficients: Thereby, p + and p − denote the pressures at the circumferential pressure ports in clockwise and counterclockwise direction.
In the reconstruction procedure, the pressure data at the test point is acquired , , for low-or high-angle regimes are calculated as defined above, respectively. In the following step, a local-least square interpolation determines the quantities A t T , , A s, T and α T , β T or θ T , f T as functions of , . The Mach number Ma can be calculated as follows (shown for the high-angle regime): Here, c is the speed of sound, κ the specific heat ratio and R the specific gas constant. Lastly, the velocity components u, v and w can be calculated: A possible way to implement the basic interpolation functionality in MATLAB is to use the built-in Delauney triangulation function delauneyTriangulation from a set of points. Using its object function pointLocation, the triangle enclosing a test point and the barycentric coordinates of the test point can be determined. Thus, a fast interpolation can be ensured. A further method how the measured pressures can be post-processed is the usage of system identification methods. Neural network approaches have been used in the field of multi-hole probes for the reconstruction of the flow conditions [31,32]. An artificial neural network (ANN) application is based on training data to set the weights of connected neurons/nodes. So-called weights and biases determine the strength of the connections between different neurons and layers. MATLAB offers the neural network fitting application nftool [33]. Figure 11 shows the structure of the trained neural network for a single calibration Mach number. As input data, the five measured pressures are given. The output of the ANN are the flow angles (α and β) and the static and total pressure (p s and p t ). The neural network is trained with the function trainlm, which trains a shallow two layer feed-forward network with sigmoid hidden neurons and linear neurons. For this purpose, the Levenberg-Marquardt backpropagation algorithm is applied to update the weight w and bias b values [34]. The division between training, validation and test data for the neural network fitting is random. The number of hidden neurons is set to N=25.

Temporal calibration
In addition to the spatial calibration, the dynamic characteristics of the multi-hole probe has to be determined. The acoustic system inside the pressure channels has a significant influence on the measurement of unsteady flow phenomena. Figure 12 illustrates the properties, which mainly describe the acoustic system between the tip and the location of the sensor inside the probe shaft: the length L, the diameter D=2r and the volume in front of the sensor V. The acoustic system is mainly dominated by two different forms of pressure distortion, resonance and attenuation.
A way to describe the dynamic behavior of pneumatic line-cavity systems was introduced by Bergh and Tijdeman [35]. They analytically formulated a recursive solution for small disturbances and for tubes with small diameters compared to the tube length L/D?1. Furthermore, a laminar flow and a fluid governed by the ideal gas law was assumed. The complex ratio P sensor /P tip describes the attenuation and phase shift for the acoustic wave propagation inside a system of a single tube and is denoted as transfer function (TF) of the system H(ω): ( ) i r 25 3 2 Thereby, J i denotes the Bessel function of ith order, κ the specific heat ratio and Pr, ρ and μ the Prandtl number, the density and dynamic viscosity of the fluid, respectively. In the case of longer pneumatic lines, the signal noise can get dominant in the deconvolution. Semaan and Scholz compare the Bergh and Tijdeman correction with a method using a Wiener filter. This approach is called Wiener deconvolution [36]. They come to the conclusion that only for a length bigger than L>150 mm the Wiener deconvolution is beneficial. Since the probe presented in this paper has shorter tubes, the Bergh and Tijdeman solution is used as a reference in the following.
Experiments with additive manufactured probes have shown that due to imperfections inside the tubing, analytic solutions can solely serve as a first guess. The need for more accurate transfer functions leads to the experimental verification of the acoustic system. In a frequency test-rig the investigated object (e.g. the multihole probe) and a reference sensor are mounted in close proximity to each other (see figure 13). Furthermore, it contains a speaker connected to an amplifier. Sinusoidal waves are emitted and recorded at specified frequency steps, and hence, the amplitude ratio as well as the phase shift are obtained.
When measuring in unknown unsteady flows, the reconstruction process of the actual time signal at the tip is shown in figure 14 [10]. The quasi-periodic signal at the sensor p sensor (t) represents the input. Before the timedomain signal is processed into the frequency domain by applying a fast Fourier transformation (FFT), a windowing function is applied. The TF is then used to calculate the Fourier-transformed pressure at the tip P tip (ω) from the Fourier-transformed pressure at the sensor P sensor (ω): Furthermore, digital signal conditioning, like low-pass filtering, can be applied in this step. Lastly, the signal is transferred into time space by applying the inverse FFT. The pressure at the tip p tip (t) is obtained as the output and can be further processed by utilizing the spatial calibration data. In order to show the functionality of the reconstruction procedure, the transfer function of a narrow silicone tubing is determined. Two sinusoidal signals with f 1 =4000 Hz and f 2 =5000 Hz with differing weights are superposed and emitted by the speaker in the frequency test-rig. Figure 15 shows the reconstructed pressure at the tubing tip p tip recon , after applying the TF on the pressure detected at the sensor p sensor . It is compared to a reference signal measured in close proximity to the tip with another sensor p tip ref , . The reconstructed signal matches the reference signal very well.

Sensor tests
In the following, all experiments are conducted with ten sensors of the first sensor generation (depicted in figure 6). Tests include the determination of the calibration coefficient and comparisons to piezo-resistive sensors.

Static and dynamic calibration
In the sensor calibration process, the correlation between the optic output value ρ opt and the applied pressure p is determined for the linear pressure range by If the operating point is set correctly, the characteristic should be linear, since it is mainly dependent on the mechanic deformation of the sensor membrane. In addition, the operating point has been set to match the quasi-linear range of the edge-filter. By applying predefined pressures, either statically or dynamically, the calibration coefficient k is calculated. First calibration tests have shown that the sensor's behavior strongly depends on the ambient conditions and the installation situation. Therefore, it is important to know the influence of these conditions during calibration and to separate them in the best possible way. Temperature resistance is limited due to the use of adhesive when attaching the optical fiber and the pressure capillary to the ferrule. In addition, the temperature sensitivities vary from sensor to sensor, but behave linearly. For the static calibration procedure, a sealed box, in which the sensor was integrated, was pressurized. The sensors' output values are linear with pressure in a pressure range specific for each sensor. The width of this range depends mostly on the sensitivity of the sensor and the Q-point. Outside of the range, non-linear behavior sets in. Figure 16 shows the static calibration curves for two sensors. One of the sensors shows a linear correlation between pressure and the optical output value r r opt opt,0 over the whole shown pressure range. The linear range of the other sensor is less extensive, so that an overall non-linear behavior in the shown measurement range was observed. For future sensor generations, the sensor assembly and setting of the operating point is one of the most challenging tasks in order to have reproducible linear behavior ranges for sensors in the same batch. Nevertheless, even for sensors with non-linear static calibration behavior, small, dynamic disturbances around the operating point can be regarded linear. The sensors are tested on their dynamic behavior with a sound generator that produces a specific sinusoidal signal at a prescribed sound pressure level L p .

Comparison to piezo-resistive sensors
As a first comparison of the fiber-optic pressure sensors to state-of-the-art piezo-resistive sensors, both sensors are placed next to each other in the frequency test-rig. Sinusoidal excitations in the frequency range of f s =[100, 1000] Hz are measured and compared. The signal frequencies can be exactly reproduced by both sensor types with relative errors smaller than 1% in the whole frequency range. Figure 17 shows the dynamic pressure amplitudes measured by both sensors. Furthermore, the relative deviation of the fiber-optic pressure sensor to the piezo-resistive sensor is depicted. It can be observed that the amplitudes also match very well. Larger deviations at f s =100, 400 Hz could be due to acoustic modes in the frequency test-rig, that have been observed in previous measurements, as well. Furthermore, those errors could be traced back to the small excitation magnitudes, which are in the range of the minimum transducer resolution.
Tests examining the noise level of the measurement chain are conducted. The piezo-resistive sensor is connected to a NI 9237 module and shows better signal-to-noise ratios (SNR) than the fiber-optic pressure sensors. This is due to the lack of enhanced signal conditioning in the optic measurement acquisition. The optic Figure 16. Fiber-optic pressure sensor static calibration. measurement chain is still under development and efforts concerning bandwidth and noise specifications have to be addressed either by changes in hard-or software.
In table 2, a short comparison of the 1st generation fiber-optic pressure sensor specifications, which are observed in the sensor batch, to the Meggitt Endevco 8507C-2 piezo-resistive sensor is shown.

Transfer function of a silicone tubing
A more realistic test application for the fiber-optic pressure sensors is the determination of the transfer function of a silicone tubing with L=200 mm and D=1.5 mm. Experiments are conducted in the aforementioned frequency test-rig. Variations of the combination of the reference sensor and the sensor at the end of the tubing are compared. Different frequency step sizes were used for the different combinations: 20 Hz for piezo-piezo and 100 Hz for the piezo-optic and optic-optic cases, respectively. Moreover, the analytical solution for the attenuationˆp p tube ref by Bergh and Tijdeman is displayed in figure 18. For the two cases, in which the fiber-optic sensor is mounted at the end of the tubing, the resonance frequencies match the ones of the analytical and the piezo-piezo solution, which can be seen as the state-of-the-art and validated solution. The qualitative trend is reproduced well, however, the amplitudes of the attenuation are underpredicted by the optic sensors. A possible reason for this can be a systematic error, which is attributed to a modification of the operating point of the sensor while installing it in the test-rig. The fiber-optic sensor is deformed by the surrounding silicone tubing marginally but sufficient enough to cause a change in the calibration coefficient. This leads to the conclusion that   the assembly of the sensor into a test object is crucial regarding its behavior and therefore has to be addressed in the future carefully.

Fast response probe tests
Lastly, the characteristics of a conventional unsteady probe, which is equipped with state-of-the-art piezoresistive sensors, are shown. For applications with limited space for the probe installation, a miniaturization of the probe dimensions would be beneficial. In addition, a smaller probe head leads to less intrusive and disturbing effects in the flow field. Thus, the reduction of the tip size would enhance the aerodynamic/spatial resolution of the probe [16]. Non-uniform flow conditions, like shear and gradient dominated flows, can be represented in more detail with an increased resolution. Moreover, corrections for flow phenomena due to the intrusion of the probe, like inertial effects of the probe, have a smaller contribution to the pressure measurement. Yet, the reduction of the probe size has also antagonistic effects: Two major problems concerning the temporal characteristic emerge, which affect the acoustic system inside the probe and therefore, predominantly change the unsteady behavior of the pressure probe. First, a reduction of the acoustic channel diameter leads to a high attenuation of the acoustic wave for higher frequencies (see figure 19). Second, sensor dimensions have to be reduced as well when reducing the overall dimensions of the probe and keeping the channel length constant. Flush mounted sensors could counteract the described attenuation. Nevertheless, by placing the sensors in close proximity to the probe tip, the packaging effort and the probe dimensions would increase. Therefore, the performance of future sensors has to be optimized, which is one major driver in the already mentioned development of a new fiber-optic pressure sensor.

Design of a conventional unsteady multi-hole probe
An unsteady five-hole pressure probe, which is displayed in figure 2, has been designed for testing its unsteady aerodynamic measurement behavior. Table 3 summarizes the major design aspects, which are described in more detail in the following. The straight probe has a tip diameter of D tip =3 mm. The additive manufactured probe head is attached to a shaft with an outer diameter of D shaft =15 mm. Five cavities are drilled into the rear part of the probe head, which contain the unsteady differential pressure sensors. For this pressure probe, state-of-theart piezo-resistive Meggitt Endevco 8507C-2 transducers are installed inside the cavities [37]. A challenging task in the design is the integration of the sensors inside the probe. Considering the miniaturization of the probe, the sensor, which has a diameter of 2.3 mm, limits the geometric design. A further reduction of the size of the probe shaft, which contains five sensors in a compact pattern, is restricted by mechanical stability. In order to avoid leakage, the sensor is surrounded with a thin silicone tubing and pressed into the cavity (see figure 20). The Figure 19. Analytical estimate for the attenuationˆp p sensor tip for L=100 mm, V=2 mm 3 and varying tubing diameters. reference pressure lines of the differential transducer are merged in a manifold, so only one pressure tubing is connected to the reference pressure. In general, maximum calibrated angles for five-hole probes range up to 60°. Precise reconstructions with absolute angular errors smaller than 1°and velocity errors smaller than 1 m s −1 can be ensured up to α, β=±55°, as it is noted in the subsequent chapter .

Spatial and temporal characteristic
In the following, the post-processing accuracy and time consumption of the two different spatial reconstruction approaches, the local interpolation and neural network, are compared. As a test, data for 258 test points are acquired after the probe calibration for a defined Mach number of Ma=0.10. Figure 21 depicts the postprocessed angles compared to the actual angles set in the free-jet wind tunnel. Both methods show mean absolute errors below 1°for both angles. Table 4 shows maximum absolute (maxabs) errors, root-mean-squared (rms) values and standard deviations (std) for both angles. The Delauney triangulated interpolation calculation result in smaller deviations compared to the ANN approach. This is due to a limited amount of neurons in the ANN training of 25 neurons. Nevertheless, both methods show acceptable errors for tested angles up to 60°. The reconstructed velocities match the fixed velocity in the free-jet with relative errors smaller than 1% for both methods. Applying the MATLAB built-in functions for both methods results in a speed-up factor of up to 5 for the neural network processing in comparison to the Delauney triangulated interpolation method. The demand of fast data processing increases, when measuring in highly unsteady flows with sampling frequencies bigger than f s >50 kHz. Though interpolation methods are optimized and represent the state-of-the-art solution for multi-hole probe post-processing, the neural network approach may lead to reduced calculation times.
As described in the chapter for the probe calibration, besides a spatial calibration, the temporal characteristic has to be determined in the frequency calibration test-rig. For the determination of the transfer function, a   frequency step size of the input sinusoidal signal is set to 20 Hz. Figure 22 exemplarily shows the amplitude ratiôp p sensor tip and the phase shift j for three of the five sensors of the five-hole FRAP. For frequencies up to 10 kHz, the attenuation does not fall below 0.15. This value is assumed to be appropriate to reconstruct signals within the frequency range. Having calibrated both, the spatial and temporal, characteristics, the fast-response multi-hole pressure probe is ready to be used in unsteady, unknown flow-fields.

Discussion and outlook
A reference five-hole pressure probe with piezo-resistive sensors that can measure unsteady phenomena up to 10 kHz was developed, as a preliminary stage towards a fiber-optic based multi-hole probe. Additive manufacturing (selective laser melting) enables the realization of arbitrary probe shapes. Hence, even in probe installation situations with massive spatial restrictions, appropriate probe designs can be achieved and produced. The spatial and temporal calibrations of the five-hole probe ensure a precise reconstruction of the flow-field parameters at the probe tip. The spatial calibration data represents the correlation between the port pressures to the flow conditions that were set during the calibration in the free-jet wind tunnel. When measuring an unknown flow field, the calibration data set can be used to reproduce the unknown conditions, either by interpolation or neural network approaches. During the temporal calibration, the acoustic system inside the probe pressure channels is characterized. A transfer function that determines the amplitude ratio and the phase shift of the pressures in the channels is obtained experimentally in a frequency test-rig. The development of an unsteady fiber-optic pressure sensor is presented. The gauge/differential fiber-optic sensor is based on the optical principles of a Fabry-Pérot interferometer. Details on the optic theory are given. Tests with the fiberoptic pressure sensors of the 1st sensor generation already show good dynamic behavior and appropriate specifications in comparison to state-of-the-art electrical sensors. The static calibration shows the importance of a precise sensor assembly in order to fit the operating point of the sensor to the linear part of the edge-filter interrogator spectrum. In case of discrepancies in the assembly, the sensor output could behave non-linear when larger pressure amplitudes are applied. In future developments, further sensor investigations have to be carried out with respect to fixed mounting and assembly conditions. In addition, improvements concerning signal conditioning within the optical measurement chain will be examined. In future development steps, a smaller unsteady multi-hole probe equipped with the differential fiber-optic pressure sensors will be assembled, calibrated and tested.