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## B03: Dynamic impingement cooling by pulsed impinging jet arrays

**Principal investigator: **Dr.-Ing. Frank Haucke (mail)

### Summary

The experimental investigation of dynamic impingement cooling in three-dimensional array arrangements is to be further advanced. The high flow-mechanical complexity of the impinging jet interaction is to be extended by the influence of a dynamically imposed cross-flow, which increases the flow-mechanical similarity to turbine blades through which the flow passes. In order to further improve the similarity to the inner geometry of real turbine blades, the influence of a curved flow path on convective heat transfer will be analysed in detail. In cooperation with the numerical subproject B04 and the control engineering subproject B06, a significant reduction of the measurement time for the parametric variations is aimed at.

## 2nd funding period 2016-2020

Within the first project phase of the subproject a test facility for the investigation of dynamically forced impinging jet arrays was designed and built. The main focus of the design process was the inclusion of a 7x7 impinging jet array as well as the variation of the nozzle distance (S/D<=5), the variation of the impingement distance (H/D<=5) and the variation of dynamic parameters, such as frequency (f_{D}<=1000 Hz), phase shift of adjacent impinging jets (Φ<=100 %), Reynolds number (Re_{D} <= 7200) and duty cycle (DC<=100 %), planned in the second funding phase. The developed test rig has the possibility to freely traverse the target and the nozzle plate, which allows both the adjustment of the impingement distance andthe accurate positioning of the nozzle array to the target plate.

The compressed air supply to the nozzle array was implemented via four mass flow, each supplying a cooling air distributor, which in turn distributed the cooling air to 12 or 13 nozzles. The implementation of the required dynamics within the cooling air mass flow was achieved by 49 modified solenoid switching valves, whereby each nozzle could be controlled individually with regard to the required dynamic parameters. The impinging jet nozzles used [18] [23] [19] were based on the nozzle design presented by Janetzke [5] [6].

For the determination of the wall temperatures and thus for the evaluation of the cooling effect, liquid crystal thermography (LCT) is also used as a measuring method in the second funding phase. In this method, the impingment plate consists of an electrically heated 0.5 mm thick metal foil, which is equipped with a self-adhesive liquid crystal film (LCT film) on the back. The foil construct is fixed on a glass plate. This provides a stable base and favourable thermal and optical properties for heat transfer investigations (see Figure 2). To exclude an isolation effect between the individual layers, all air between the glass plate and the foils is evacuated. The LCT film is a film with encapsulated liquid crystals, which reflect different wavelengths of the illuminating light source depending on the local wall temperature, resulting in a defined, visible temperature-dependent color distribution. This can be recorded through the glass plate with a colour camera and converted into a two-dimensional temperature distribution under consideration of a colour temperature calibration. With the help of the flat temperature distribution, the local Nusselt number distribution can be calculated with the help of the known electrical heating power, the ambient parameters and the cooling fluid temperature, provided that the measurement has taken place in a state of thermal equilibrium. This similarity parameter is used to evaluate the increase of the convective heat transfer of the system by the respective set parameter combinations.

In addition to the LCT measurements, a phase-triggered stereo PIV system is used to gain insight into the flow field and the physical mechanisms responsible for the change in heat transfer (see Figure 3). For each case studied, 40 equidistantly distributed phase points within an actuation phase are recorded. To make the tracer particles (di-ethyl-hexyl-sebacate (DEHS)) visible, a Δz = 1.5mm thick light section is positioned centrally under the central row of nozzles using a Nd:YLF laser. The tracer particles are introduced into the cooling air at the cooling air distributor (see figure 4 left), whereby each nozzle is evenly supplied with seeding. The two cameras (resolution: 2560 x 2150 pixels) are stereoscopically arranged at an angle of 37° to the measuring plane and each takes 100 images for averaging. This results in an optical resolution for the measurements of Res = 0.94 vectors per mm.

The required optical components are positioned downstream of the nozzle array, whereby an influence of the flow by the components can be excluded. Two measurement planes are recorded to obtain the data. The first covers nozzles three, four and five and the second covers nozzles five, six and seven. A recording of all seven nozzles is optically not possible due to structural conditions. The overlapping of both measuring planes is used to couple the recorded data by interpolation in the overlap area.

### Constructional and metrological extension of the impingement cooling test stand.

For reasons of noise and laser protection, a housing was provided around the test facility. In addition, a thermal barrier was installed around the test stand to improve the measuring accuracy and repeatability of the results. The 60 mm thick thermal insulation used has a thermal conductivity of L=0.04 W/mK and allows improved repeatability of the measured values, even under fluctuating environmental conditions. Due to the reduced heat and fluid exchange with the environment, less time is required to reach the thermal equilibrium required for the measurement, which allows for more efficient measurement operation. Furthermore, the cooling air mass supply was modified. While the original supply allowed four individual cooling air streams, seven cooling air streams with seven nozzles each can now be operated independently. Each line can be individually controlled by a mass flow controller with an accuracy of 0.1 % - 0.5 % full-scale-error. In addition to the improved accuracy of the cooling air supply, the distributor system for the impinging jet nozzles has also been further developed. By extending the cooling air supply from four to seven mass flow controllers, it was possible to reduce the number of connected cooling air nozzles from 12 or 13 to seven per cooling air distributor on the basis of the cooling air distributors used at the beginning, which enabled a considerable improvement in reliability and accuracy during parameter variations. The integration of a triggerable camera system, in connection with a new LabView-based control software, enables a fully automatic measurement with time-synchronous acquisition of image and temperature data. Thus, the accuracy of the measurement results, in particular the colour calibration required for the LCT measurement method, can be additionally increased, which in turn positively influences the repeatability of the measurement results. Due to the presented optimizations, the current maximum deviation between comparable measurements could be determined to σ_{max} = 2.79 % (see Figure 4 right). The investigation was based on eight repeat measurements, which were carried out under different atmospheric conditions (humidity, temperature, air pressure). It is also evident that the repeatability at higher actuation frequencies is marginally decreased than at frequencies below f_{D} = 700 Hz.

In addition to the described optimizations, the flat experimental setup was supplemented by a cross-flow frame for the second funding phase (see Figure 5 left). This cross-flow frame is located between the nozzle plate and the flapper plate and encloses the nozzle array on three sides. The entire outgoing cooling mass flow is channeled in one direction, thus superimposing a frequency-dependent dynamic cross-flow on the array, which is comparable in its formation and thus in its flow physical properties to that inside a turbine blade. This means that the cross-flow velocity is coupled to the cross-sectional area of the flow channel. Therefore, the widening or reduction of the impingement distance H/D results in a decrease or increase of the prevailing cross-flow velocity (see Figure 5, right). The total transverse mass flow is thereby inevitably formed successively from the individual mass flows of the nozzle rows in x-direction. This leads to an increase in the cooling air mass flow rate dependent on the nozzle rows and thus also to an increase in the locally prevailing cross-flow velocity. A further optimization of the measurement methodology used was developed and implemented in cooperation with subproject B06. The thermal conditions in the vicinity of the test stand within the enclosure can be adjusted almost independently of external weather conditions by means of a controllable heat source. By adjusting the ambient temperature, both heat loss flows and the necessary measuring time can be minimized.

### Variation of the plane impingement jet array arrangement with dynamic cross flow

In the first step of the second work package, the classification of the test stand is the focus of the investigation. For this purpose, the internationally accepted empirical function presented by Florschuetz et al. [2] is used to predict the Nusselt numbers in a static cross-flow nozzle array. A comparison of the function values Nu_{FL} with own experimental data Nu_{exp} is, due to the definition of the empirical function, possible in the setup presented for the mean value of the Nusselt number below the first row of nozzles, 90 degrees to the cross-flow direction. Figure 6 on the left shows the calculation basis for different Nusselt numbers used within the investigated impingement jet array. The estimation function presented by Florschuetz et al. has been established for impingement distances H/D >> 3 and large Reynolds numbers and shows a possible error of up to 11 % in these areas.

Figure 6 on the right shows that the test stand behaves equivalently to the function of Florschuetz. For large impingement distances the deviation between the theoretical and the experimentally determined values is below 5%, for a reduced impingement distance the deviation increases up to 9.6% if the Reynolds number is reduced. A further reduction of the rebound distance, which lies far outside the validity range of the estimation function, shows that only the highest experimentally mapped Reynolds number is still within the error window of the function. All in all, the presented comparison shows that the experimental setup represents the estimation function well within its validity range according to Florschuetz [20]. The second step of the test stand classification was focused on the determination of the cross-flow influence on the convective heat transfer within the array. For the static case the influence is shown in figure 7. The left side shows the spatial development of the convective heat transfer in cross-flow direction within the statically operating array without a cross-flow frame and the right side shows the development with an integrated cross-flow frame. The effect is shown as a function of the impingement distance H/D. It can be seen that the convective heat transfer is significantly reduced with increasing cross-flow velocity, i.e. with the number of nozzle rows passed. Furthermore, it can also be seen that the additionally channeled cross-flow causes a shift of the local maxima in the convective heat transfer downstream. This shift grows with the reduction of the impingement distance, i.e. with the increase of the cross-flow velocity. The implementation of a dynamic impingement cooling, here exemplarily shown for f_{D} = 500 Hz, minimizes the heat transfer reducing effects.

Figure 8 shows the spatial Nusselt number distribution, normalized to a Reynolds number of Re_{D} = 2150, for the dynamic cases compared to the static case with a Reynolds number of Re_{D} = 7200. It can be seen that the dynamics can completely compensate for the reduction of the maxima in the cross-flow direction. Furthermore, the observed shift of the maxima in convective heat transfer is also significantly reduced. The normalization to the lower Reynolds number allows the identification of the Reynolds number dependent increase of the local cooling effect. This leads to the conclusion that the vortex systems created by the dynamics are able to penetrate the cross-flow with reduced interaction, allowing more cooling fluid to reach the impingement plate. This can be attributed to the temporarily increased exit velocity of each impingement jet compared to the steady blowing case, which results in an increase of the impulse ratio between the impingement jet and the cross-flow on a time average. The effects derived from Figure 8 can also be observed in corresponding PIV data.

Figure 9 shows the mean velocity fields for the static case f_{D} = 0 Hz and for an exemplary dynamic case f_{D} = 500 Hz. In both cases an identical cooling air mass flow rate was used. From this it follows that the mean discharge velocities of both cases are identical. As a result of the periodic interruption, depending on the selected pulse width, a pulse increase in the respective impingement jet results both temporarily and on a time average, whereby the local pulse ratio between jet and cross-flow is increased compared to the stationary case. This can be seen from the increased jet velocities near the impingement plate and the associated reduced jet deflection in the cross-flow direction. Due to the increased velocities close to the wall, increased wall shear stresses are also associated, which in turn mean increased convective heat transfer at the wall [14]. After the basic classification of the test rig and the determination of the cross-flow influence, the convective heat transfer was maximized depending on the frequency, the impingement distance and the Reynolds number. For this purpose, all parameters are varied within the following limits: f_{D} = 0...1000 Hz, Δf_{D} = 100 Hz, H/D = 2, 3, 5 and Re_{D} = 3200, 5200, 7200.

Figure 10 shows the global effect of variation on the convective heat transfer within the array, as a function of the actuation frequencies f_{D}. A global averaged Nusselt number Nu (see Figure 6 left) is formed and normalized to the global average Nusselt number of the corresponding static case Nu_{0}. The data shows that the global frequency-dependent course of all cases shows a high degree of similarity. Each parameter combination examined displays an increased convective heat transfer compared to the static case and shows a growth maximum of 51% at f_{D} = 700Hz. Furthermore, the data show that the growth potential is reduced with the impingement distance, whereas the increase in the Reynolds number for the impingement distances of H/D = 3 and H/D = 5 shows a potential increase in growth [15, 16, 21].

Figure 11 shows the vorticity fields averaged over 40 phase points of the last five nozzles in cross-flow direction for the static (f_{D} = 0 Hz), the f_{D} = 500 Hz and for the f_{D} = 700 Hz case. It can be seen that specific actuation frequencies clearly influence the resulting vorticity in the shear layer. An increased vorticity near the wall generally leads to increased local wall shear stresses and thus to an increased convective heat transfer. This effect can also be observed between the impingement zones, whereby the spatial cooling effect within the array can be significantly increased by the implementation of a dynamic [22]. In addition to the global frequency influence, the phase shift between the individual rows of nozzles is also a relevant factor for optimizing the global convective heat transfer. In order to analyse this, the phase position between the individual nozzle rows is varied within the limits Φ = 0 ... 90 %. The variation takes place, depending on the Reynolds number and the impingement distance, at three representative actuation frequencies. These are f_{D} = 300Hz, f_{D} = 500Hz and f_{D} = 700Hz, which corresponds to a weak, a moderate and the most effective actuation frequency.

Figure 12 shows the development of the global Nusselt number for the representative impingement distance of H/D = 2 for the investigated Reynolds numbers and frequencies. Especially for high Reynolds numbers a considerable additional potential for the most effective frequency f_{D} = 700Hz can be observed. By varying the phase shift, which symbolizes the time-controlled sequence of adjacent ring vortices, the vortex interaction can be optimized with respect to the resulting heat transfer at the wall. With a phase shift of Φ = 50%, an additional increase in convective heat transfer of up to 12% can be recorded. The two other frequencies shown also show significant increases in convective heat transfer. Depending on the phase offset, a further increase of up to 16% can be generated [16]. The increase in the cooling effect, especially at Φ = 50%, is one of the driving factors for the use of fluidic actuators in the further development of the system, since these have a functionally fixed phase shift of Φ = 50%.

An equally relevant parameter is the spatial distance between the nozzles (see Figure 13). Investigations show that the frequency-dependent convective heat transfer is influenced by the reduction of the nozzle distance S/D in such a way that for small impingement distances H/D = 2, a reduction of the nozzle distance to S/D = 3 allows a potential increase of 60 % at specific frequencies. However, when larger distances are investigated, a deterioration is seen for almost all frequencies investigated. This trend continues when the nozzle distance is reduced to S/D = 2.5. In this case, even for the small impingement distance only a maximum increase of 35% is possible. In addition, the increase can only be generated in a frequency range up to f_{D} = 400Hz. This indicates that with the running length of the vortex and the associated vortex diameter increase, there are increased interactions between adjacent vortices, which can have a negative influence on the fluid transport properties of the vortex structures. Corresponding PIV data as well as data regarding the influence of phase shift at reduced nozzle distance have already been recorded and are currently in the evaluation and publication phase.

### Variation of the 2D curved impingement jet array arrangement with dynamic cross flow

Following the flat test configuration, work package three focuses on a curved configuration. The selected radius of curvature of r = 1 m is based on a radius of curvature of an impingement-cooled inner surface of a NASA E3 turbine blade profile scaled to the nozzle outlet. Figure 14 shows the modified impingement plate, nozzle plate, and cross-flow frame. The curvatures take into account that the radius of the nozzle plate must be adjusted with the impingement distance to ensure a 90° angle between the target plate and the exiting impingement jet. The target plate is a curved glass plate allowing the use of both LCT and PIV test setups, which are equivalent to those shown in Figures 2 and 3.

First results regarding convective heat transfer and the resulting cooling effect in terms of the global Nusselt number are shown in Figure 15. Here, the general trend with regard to the frequency-dependent increase of the cooling effect is comparable to that of the plane configuration under the same geometric conditions (see Figure 15 left). The difference between the two global frequency-dependent Nusselt number curves of the curved and the plane plate is shown in Figure 15 left. It can be seen that the global growth maximum is at f_{D} = 800 Hz and that for most frequencies below f_{D} = 600 Hz the difference between both configurations is less than 5 %. The exceptions are f_{D} = 200 Hz and fD = 400 Hz, with the first frequency showing a Nusselt number reduction of about 34% and the higher frequency a Nusselt number improvement of 15%. This surprising and as yet unexplained behaviour will be investigated in more detail by means of a finer frequency resolution. In addition to the first effects, frequencies above f_{D} = 600 Hz also show a Nusselt number reduction; however, this is almost constant at 16%, independent of frequency.

At this point it is also to be noted that the cooling maxima found in this configuration at f_{D} = 350 Hz and f_{D} = 800 Hz are similar to the numerically determined results of subproject B04. In subproject B04 the most receptive modes were found at Strouhal numbers of Sr_{D} = 0.46 and Sr_{D} = 0.92. If the found most effective frequencies of this configuration are converted to the Strouhal numbers Sr_{D} related to the nozzle outlet, Strouhal numbers of Sr_{D} = 0.46 and Sr_{D} = 1.05 result for both the plane and the curved surface despite different exit Mach number and impingement distance. Thus, for the first preliminary results of the curved test configuration it can be stated that the global behavior of the frequency-dependent Nusselt number development is similar to the plane configuration. However, a comparison of the absolute growth rates, especially at high frequencies, shows a lower increase in cooling effect in the case of the curved test body. Furthermore, it can be seen that the experimental and numerical results show a similarity with regard to the expected frequencies for the cooling maxima.

### Optimization and control of the dynamically forced impingement cooling

For the optimization and control of the dynamic impingement cooling, cooperation with subproject B06 is underway. Thereby it is necessary to be able to evaluate the changes of the cooling capacity in real-time. This is possible by using Pt-100 sensors instead of liquid crystal thermography. Figure 16 on the left shows the modification of the experimental setup presented in detail in Figure 2. Here, the LCT foil is replaced by 15 Pt-100 sensors, which are positioned at an even distance below the center section of the nozzle array. Compared to the LCT film, the sensors have a much higher bandwidth, which means that the dynamics of the surface temperature are better resolved by the measurement. The heat conduction from the plate surface to the rest of the experimental setup is much slower. It can therefore be assumed that this only slightly distorts the determination of convective heat transfer from the plate using the measured surface temperature. In order to guarantee the real-time capability of the measurements, it is not possible to wait for a thermal equilibrium of the entire system. Therefore, only general qualitative trends can be detected and not quantitative ones. Within this work package, in cooperation with subproject B06, an innovative Fast Extremum Seeking algorithm has been developed in such a way that it is possible to estimate the thermal response of the investigated overall system by using pertubated parameter ramps. The acquisition of a ramp takes only five minutes, which represents an elementary time saving compared to the measurement methods used so far [17]. The experiments performed show that the developed algorithm is able to detect the frequency-dependent course of the cooling capacity with good accuracy (see Figure 16 right). Thus, it is possible for an impingement cooling system to detect maxima and minima in the heat transfer due to changed operating conditions in a comparatively short time and to store the thermal behavior as a data matrix [17].

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**[5]** T. Janetzke and W. Nitsche and J. Täge. Experimental investigations of flow field and heat transfer characteristics due to periodically pulsating impinging air jets. Heat and Mass Transfer, 45:193–206, 2008. DOI: 10.1007/s00231-008-0410-8

**[6]** T. Janetzke and W. Nitsche. Time resolved investigations on flow field and quasi wall shear stress of an impingement configuration with pulsating jets by means of high speed piv and surface hot wire array. Int. J. Heat and Fluid Flow, 30:877–885, 2009.

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## Own publications relevant to the project

**[14]** **A. Berthold (B03) **and **F. Haucke (B03)**. Experimental investigation of dynamically forced impingement cooling. In Proceedings of ASME Turbo Expo 2017, volume 5A: Heat Transfer. ASME Turbo Expo 2017: Turbomachinery Technical Conference and Exposition, 2017.

**[15]** **A. Berthold (B03) **and **F. Haucke (B03)**. Experimental study on the alteration of cooling effectivity through excitation-frequency variation within an impingement jet array with side-wall induced crossflow. Active Flow and Combustion Control 2018, Ch: Springer International Publishing.:(S.339–354), 2018.

**[16]** **A. Berthold (B03) **and **F. Haucke (B03)**. Influence of excitation frequency, phase-shift and duty cycle on cooling ration in a dynamically forced impingement jet array. In ASME Turbo Expo 2019, number GT2019-90695. ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition, 2019.

**[17]** **B. Fietzke (B06)**, **M. Kiesner (B06)**, **A. Berthold (B03)**, **F. Haucke (B03)**, and **R. King (B06)**. Map estimation for impingement cooling with a fast extremum seeking algorithm. Active Flow and Combustion Control 2018, Ch: Springer International Publishing.:(S.367–378), 2018.

**[18]** **F. Haucke (B03)**, H. Kroll, **I. Peltzer (B01)**, and **W. Nitsche (B03)**. Experimental investigation of a 7 by 7 nozzle jet a array for dynamic impingement cooling. In Active Flow and Combustion Control 2014, Editor R. King, dx.doi.org/10.14279/depositonce-39. Springer, 2014.

**[19]** **F. Haucke (B03)**,** W. Nitsche (B01)**, and **D. Peitsch (B03)**. Enhanced convective heat transfer due to dynamically forced impingement jet array. In Proceedings of ASME Turbo Expo 2016, number GT2016-57360, 2016.

**[20]** **F. Haucke (B03) **and **A. Berthold (B03)**. Experimental investigation of a dynamically forced impinging jet array. New Results in Numerical and Experimental Fluid Mechanics XI, Notes on Numerical Fluid Mechanics and Multidisciplinary Design 136, 136:209–218, 2016.

**[21]** B. Ataseven, **A. Berthold (B03)**, and **F. Haucke (B03)**. Influence of system resonance on a dynamically forced impinging jet. In ASME Turbo Expo 2019: Turbomachinery Technical Conference and Exposition,, number Poster No. GT2019-92266, 2019.

**[22]** **A. Berthold (B03), F. Haucke (B03), **and J. Weiss. Flow field analysis of a dynamically forced impingement jet array. In 2020 AIAA SciTech Forum, 2020.

**[23]** **F. Haucke (B03)**,** W. Nitsche (B03)**, **R. Wilke (B04)**, and **J.L. Sesterhenn (B04)**. Experimental and numerical investigation regarding pulsed imipingement cooling. In Deutscher Luft- und Raumfahrt Kongress Rostock, 2015.