### Page Content

### Summary

A pulsating impinging jet has substantially higher heat transfer than a non pulsating jet. The extra heat transfer comes from a vortex system impinging on the plate. This vortex system was shown to be related to the eigenmodes of the jet but it is unclear how it behaves under cross flow and curvature like in the realistic case in the turbine blade. On top of that it is not the linear eigenmode rather than a saturated limit cycle which is of interest. We investigate this limit cycle and its receptivity in order to optimize saturation. The interaction of several jets under cross flow and curvature is investigated numerically for a line array.

## 2nd Funding period 2016 - 2020

- Fig. 1: Turbulent structures highlighted through the contours of the second invariant of the instantaneous velocity gradient tensor Q on a plane passing through the jet axis.
- © TUB

**Analysis of an impinging with fully turbulent inlet conditions**

The inflow of impinging jets in engineering applications, such as the internal cooling of gas turbines, are certainly not laminar. Therefore, we study the effects of a turbulent inlet on the impinging cooling efficiency. A direct numerical simulation is performed at Re=8000 and results are compared with experimental and numerical data that have been found during the 1st funding period.

The presence of a turbulent inlet affects significantly the free jet region of the flow (Fig. 1). The different evolution of the free jet affects subsequently the wall region, where a general increase of the turbulence intensity emerges. This leads in turn to an increase of the heat transfer at the wall, when compared to the laminar inlet case. Fig. 2 shows the average dimensionless heat flux (Nusselt number Nu) distribution at the wall as a function of the distance from the jet axis for both cases. It can be seen that the there is no proportional relation between the two curves, since the heat flux remains relatively higher over a greater area when turbulent inlet conditions are prescribed.

- Fig. 2: Average Nusselt number distribution at the wall as a function of the dimensionless distance from the jet axis r/D (turbulent inlet case).
- © TUB

Root mean squares (RMS) of the velocity in the shear layer are in good agreement when experimental and numerical data are compared. In the laminar inlet case, as a result of the laminar shear layer profile, natural modes of the impinging jet can develop undisturbed. In particular, modal structures appear in form of axis-symmetric ring vortices, which are accompanied with strong RMS of axial and radial velocity fluctuations in the free and wall jet regions. In the experiments, however, several different modes are induced by the turbulent inlet. They prevent the free development of natural modes so that the ring vortices in the experiment occur only in weakened and irregular form. As a result, the corresponding RMS in the shear layer areas are smaller.

**Stability analysis of the impinging jet**

In the 1st funding period we carried out a dynamic mode decomposition (DMD) of our DNS flow field. With this method, a dominant mode which has same non-dimensional frequency as the most effective inlet pulsation in the experiment could be detected. It is known that the application of the DMD in a linear system gives the eigenfunctions of the system. The linear stability analysis of the impinging jet system showed that global modes exist, whose the frequencies of correspond to the DMD frequencies. It is noteworthy that the sensitivity to external forcing is attained in the proximity of the jet inlet (Fig. 3). This feature can be gainfully exploited for the purpose of devising cooling efficiency enhancement methods.

- Fig. 4: Average Nusselt number Nu on the target plate as a function of the non-dimensional distance from jet axis r/D (curved plate case).
- © TUB

**Effects of plate curvature**

In order to resemble the internal configuration of a gas turbine blade, a DNS of a jet impinging on flat plate has been performed. The analysis focused on assessing how good is the common hypothesis by which curved plates can be approximated as flat when estimating the heat transfer efficiency through them. It has been found that integral heat flux (integrated on the plate up to a distance from the jet axis of 5 jet diameters) differs from the flat plate case (reference case) by just 0.03% (Fig. 4). On the other hand, peak frequencies of the instantaneous Nusselt number appear reduced by 40% and 50% when compared to the flat plate case. A dynamic mode decomposition (DMD) of the system showed, as observed in the reference case, that the modes oscillating at the aforementioned peak frequencies are those responsible for the characteristic heat flux profile at the wall. It can be consequently affirmed that if only averaged properties are of interest, it is possible to model curved impingement plates as flat surfaces. On the contrary, when the dynamic response of the system is addressed in order to implement, for instance, dynamic heat transfer enhancement techniques, the presence of the curved plate can not be disregarded.

### Publications

Camerlengo, G., Borello, D., Salvagni, A., & Sesterhenn, J. (2019). Effects of Wall Curvature on the Dynamics of an Impinging Jet and Resulting Heat Transfer. In *Active Flow and Combustion Control 2018* (pp. 355-366). Springer, Cham.

Wilke, R., & Sesterhenn, J. (2017). Statistics of fully turbulent impinging jets. *Journal of Fluid Mechanics*, *825*, 795-824.

### Summary

An effective cooling of turbine components subject to high thermal stresses is vital for the success of new engine and combustion concepts. Therefore efficient cooling mechanisms have to be developed and optimized. A promising approach is the use of pulsating impinging jets. The impinging jets generates vortices which encapsulate the hot fluid at the wall and effectively transport the pockets of hot fluid away from the wall. This project investigates the underlying mechanisms of pulsating impinging jets by direct numerical simulation and optimizes them with the aim of improved cooling efficiency.

- Fig. 1: Computational domain with iso-surfaces at Ma=0.2 coloured with pressure and at Q=10^5 m^2s^-4 coloured with radial velocity. Re=8000.
- © TUB

In order to investigate the heat transfer of a confined round impinging jet (not pulsating) as a reference, two direct numerical simulations are performed at Reynolds numbers Re=3300 and Re=8000 using a grid of 512 × 512 × 512 respectively 1024 × 1024 × 1024 points.

Figure 1 shows the computational domain including a snapshot of the turbulent structures of the impinging jet at Reynolds number Re=8000. The two walls are isothermal. All other boundaries are non-reflecting. The computation is done on a grid with more than 1 billion points. Much more than a quarter of a million time steps are required to reach convergence in turbulent statistics.

- Fig. 2: Mean radial distributions of the local Nusselt number Nu (top) and turbulent heat flux (bottom). Re=3300.
- © TUB

Each configuration features two annular regions with local maxima of heat transfer at the impinging plate (Figure 2). The periodical appearance and disap-pearance of the vortex pairs (Figure 3) lead to a high averaged turbulent heat flux exactly where the averaged Nusselt number reaches its local maxima.

- Fig. 3: Snapshots at Re=3300. Slice through the jet axis: temperature. Impingement plate: Nusselt number.
- © TUB

Given these results, the aim for future work is to enhance the vortices by applying an pulsating inlet condition and thereby the wall normal turbulent heat flux concluding in a more efficient cooling of the impinging plate.

### Acknowledgement

The simulations were performed on the national supercomputer Cray XE6 at the High Performance Computing Centre Stuttgart (HLRS) under the grant number GCS-NOIJ/12993.

### Publications

Wilke, R. und J. L. Sesterhenn: Direct Numerical Simulation of Heat Transfer of a Round Subsonic Impinging Jet. In: Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Bd. 127, S. 147–159. Springer, 2015.

Wilke, R. und J. L. Sesterhenn: Numerical Simulation of Impinging Jets. In: High Performance Computing in Science and Engineering ‘14, S. 275–287. Springer International Publishing, 2015.

Wilke, R. und J. L. Sesterhenn: Numerical Simulation of Subsonic and Supersonic Impinging Jets. Akzeptiert f ¨ ur High Performance Computing in Science and Engineering ‘15), 2016.

Haucke, F., W. Nitsche, R. Wilke und J. L. Sesterhenn: Experimental and Numerical Investigations Regarding Pulsed Impingement Cooling. In: Deutscher Luft- und Raumfahrt Kongress, Rostock, Germany, 2015.

Hossbach, S., R. Wilke und J. L. Sesterhenn: Identification of Material Vortices. In: Turbulence, Heat and Mass Transfer 8, isbn 978-1-56700-428-8, 2015.

### Zusatzinformationen / Extras

## Quick Access:

## Auxiliary Functions

## Office

Steffi Stehrsec. ER 2-1

Room 107

Hardenbergstr. 36a

10623 Berlin

+49 (30) 314 23110

e-mail query