Numerical Simulation of Impinging Jets

**Principal Investigator:**

Jörn Sesterhenn

**Affiliation:**

Institut für Strömungsmechanik und Technische Akustik, Technische Universität Berlin

**Local Project ID:**

JetCool

**HPC Platform used:**

Hazel Hen of HLRS

**Date published:**

**Abstract**

An effective cooling of the gas turbine components subject to high thermal stresses is vital for the success of new engine and combustion concepts, whose implementation is widely deemed the only viable solution to achieve further improvements in the energy conversion efficiency of the overall machine. To this end, novel and more efficient cooling mechanisms shall be developed and optimized. A promising approach is, for instance, the use of pulsating impinging jets, which have been shown to enlarge vortex structures, which naturally occur in the impinging jet flow when no pulsation is enforced. It has been indeed shown that such vortices provide a significant contribution to the cooling rate of impinging jets. However, it was still unclear how the vortex system behaves under realistic conditions which entail, for example, a turbulent inflow. Here, we perform a DNS of a non-pulsating impinging jet flow with fully turbulent inflow conditions and compare its results with a reference case with a laminar inflow. It was found that a turbulent inflow strongly modifies the vortex dynamics within the flow and changes the main mechanism of heat transfer at the impingement plate.

**Background**

Given the growing political sensitivity to the environmental issues, the share of renewable sources in the global energy mix to electricity supply has sensibly increased. Most of renewable sources are nonetheless fluctuating and could jeopardize the stability of the electrical networks, which is based on the instantaneous supply-demand balance. Gas turbine power plants play a crucial role in balancing the networks because they can be quickly switched on to compensate unpredicted supply losses. Efficient gas turbines are also needed for the airplanes, which still constitute an irreplaceable means of transport for long-haul journeys. In recent decades, thanks to the progress in the thermo-fluid dynamic design of turbomachinery, the efficiency of gas turbines has considerably improved. For instance, the overall efficiency of today's gas turbine power plants is approximatively 40%: twice that of their early ancestors. In order to save fuel and reduce greenhouse gas emissions, further efficiency improvements are strongly desirable. The Brayton cycle used in such heat engines hardly changed since the construction of the first prototypes and is responsible for the largest share of the energy conversion losses. On the other hand, the mechanical components have reached by now very high efficiency.

For this reason, the purpose of the Collaborative Research Center (CRC) 1029 is to improve the performance of gas turbines by using unsteady combustion and flow dynamics. In particular, a pulsed detonation approach is investigated in order to achieve a quasi-constant-volume combustion, which can lead to an increase of the overall efficiency of more than 10%. The use of an unsteady combustion, however, will not only affect the combustor, but also the functionality of all the components of the turbine, which will undergo stronger thermal and mechanical stresses.

**Introduction**

The gas turbine section that is subjected to high thermal stresses must be supplied with secondary air from the compressor in order to address safety-critical tasks such as protection against hot-gas injection and adequate cooling. A non-stationary pressure-increasing combustion, such as a pulsed detonation, aggravates this problem, because it will enhance the demand in secondary air. However, since the bleeding of secondary air significantly reduces the achievable thermal efficiency of the entire machine, it is necessary to limit this additional effort to an absolute minimum. Impinging air jets are used to cool down the inner walls of the turbine blade and the optimization of the impingement cooling technique offers a high potential to solve this issue. Technical applications of impinging jets are not only limited to gas turbines. They are used as efficient heat transfer devices in several additional engineering configurations and scopes (electronics, drying of textiles and paper, etc.)

Several studies focused on the development of techniques aimed at improving the impingement cooling efficiency. A promising approach consists in enforcing a pulsating inflow to the impinging jet. It has been shown that a pulsating impinging jet can provide up to 40% higher heat transfer than a non-pulsating one [1]. In general, impinging jets are able to provide a high heat flux not just near the stagnation point, but also at higher distances from the jet axis *r*/*D*, where *D* is the jet diameter. The extra heat transfer originates from a vortex system impinging on the plate (primary vortices), which couples with secondary vortices generated close to the impingement plate and forms bunches of vortices travelling over the impingement plate in radial direction (vortex rings) [2]. Such vortices occur naturally when a non-pulsating inflow is enforced. In both cases (i.e. pulsating and non-pulsating inflow), very high temperature gradients are observed in the region where the vortex rings generate. In the non-pulsating case, the vortex rings lead to a secondary maximum* ^{[1]}* of the heat flux at

* ^{[1]}* The primary (local) maximum always occurs at the impingement point (

**Motivation**

Despite the strong research effort, it has not been made clear yet what is the effect of the flow regime (laminar or turbulent) of the jet at its exit on the heat transfer at the plate. This is particularly relevant because in real applications the inflow will likely not be laminar.

**Configuration**

We consider a fully turbulent compressible impinging jet flow with Reynolds and Mach numbers of 8000 and 0.8, respectively. The jet is vertically confined between two isothermal walls and issues from a pipe of diameter *D* through an orifice in the uppermost wall. The lowermost wall serves as impingement plate. The temperature of the walls is approximately 80 K higher than the average total temperature of the jet at the pipe outlet. The distance between the pipe outlet and impingement plate is set to 5*D*.

In previous computations carried out at our research group [2], an identical configuration with laminar inflow conditions was studied. In the present case, we prescribe turbulent inflow conditions by coupling the impinging jet simulation with an upstream pipe of length 3*D* (injection pipe). The inflow of the pipe is enforced by copying time-dependent density and velocity profiles from an auxiliary fully developed turbulent pipe flow simulation. When compared with synthetic turbulence generation methods, this procedure offers the advantage of not requiring any external calibration parameter and of giving a very accurate representation of all turbulence scales.

**Methods**

The phenomena responsible for the heat and mass transfer near the plate occur at very small time and length scales. For this reason, they are often not detectable in experiments and not at all resolved in RANS or LES computations. As a matter of fact, such simulation approaches do not aim at solving the smallest physical scales but use turbulence models to account for the non-negligible effects of them on the largest scales. The limit of turbulence models is that they cannot tell us anything more than what has been already observed, because they are themselves based on previous observations. Therefore, we perform a Direct Numerical Simulation (DNS) of the impinging jet flow. DNS, by solving the fluid dynamic equations down to the smallest existing scales, is the only method that allows us to fully investigate the complex fluid dynamics of the impinging jet.

However, the resolution of the smallest scales of turbulence requires the space (computing domain) to be discretized into a very large number of discrete grid points, which can overcome the hundreds of millions. In the present case, more than 1 billion grid points are needed, therefore requiring the simulation to be solved in parallel on thousands of CPUs, in order to obtain results in a reasonable time period. The DNS run for a total time summing up to approximately 100 days on 8000 to 16000 CPUs in parallel. This is only possible thanks to the powerful resources provided by the most performant supercomputers of the world, such as Hazel-Hen at HLRS.

**Numerical setup**

The simulation is performed by solving the compressible Navier-Stokes equations on a 1024 × 1024 × 1024 rectilinear grid in the main simulation block, whereas 144 × 756 × 144 points are used for the injection pipe. We use skew-symmetric 4th-order finite differences for the space differentiation and a 4th-order Runge-Kutta method for advancing in time. Characteristic non-reflecting boundary conditions are applied at the lateral outflow. A sketch of the computational domain is shown in Figure 1.

**Results**

In this section, results of the present study are compared with those presented by Wilke and Sesterhenn [2] who analysed the identical configuration by applying laminar inflow conditions.

By looking at Figure 2, which compares the instantaneous values of the second invariant of the velocity gradient tensor* ^{[2]}*of the laminar and turbulent-inflow simulations, we note that the coherent structures, so called primary vortices, are only observable in the free jet region of the laminar inflow case. On the other hand, the flow close to the impingement plate appears strongly more chaotic in the turbulent inflow case. Although the wall jet region is fully turbulent in both cases, we observe a recurrent aggregation of vortices flowing downstream (vortex rings) only in the laminar-inflow case.

* ^{[2]}*The second invariant of the velocity gradient tensor

As shown in Figure 3, this reflects in the mean local heat flux distribution at the wall, expressed in terms of Nusselt number* ^{[3]}*. Here, the characteristic shoulder (i.e. inflection point) is not observable for the turbulent-inflow case. We found that in the latter case, the Nusselt number is approximately 20% higher at distances from the jet axis lower than 1.2, whereas the laminar-inflow case features a 5% larger heat flux at distances larger than 1.8.

Surprisingly, the total heat flow rate through the plate is, in the two cases, approximatively equal. This can be explained by considering that the round impingement jet flow is characterized by a cylindrical symmetry. By using a cylindrical coordinate system, whose longitudinal axis corresponds to the jet axis, the surface of a generic annulus of width *Δr* is equal to *2**πr _{m}*

^{[3]}The Nusselt number *Nu* is the heat flux, non-dimensionalised with the temperature difference *ΔT*, the orifice diameter *D* and the thermal conductivity of the fluid *k*, where *ΔT* is the difference between the wall temperature and the mean total temperature of the fluid at the pipe outlet.

**Conclusions**

We reported on a DNS comparing two impinging jet flows with respectively a laminar and a turbulent inflow, under otherwise identical conditions. For the first time, turbulent inflow conditions were enforced by coupling an impinging jet simulation with a fully turbulent pipe flow DNS. In particular, we focused on the comparison of the cooling effectiveness of the cold jet impinging on a hot impingement plate. At large distance from jet axis, the laminar-inflow jet provides a higher heat flux through the plate, due to the formation of vortex rings over the wall, stemming from Kelvin-Helmholtz vortices which originate in the free jet region. On the contrary, both Kelvin-Helmholtz instabilities and vortex rings cannot be observed in the turbulent-inflow case. The surprising result is that both jets provide about the same heat flow rate (in the considered area), because the region where the turbulent-inflow jet has a much better cooling rate (approx. 20% higher) is much smaller, too (approx. 2.5 times smaller). Nonetheless, the local changes in the heat flux indicate that for the optimal design of impingement cooling devices, the inflow conditions play a key role.

**Project-related publications**

G. Camerlengo & J. Sesterhenn, DNS study of the turbulent inflow effects on the fluid dynamics and heat transfer of a compressible impinging jet flow. In: *High Performance Computing in Science and Engineering ́19* (Springer, forthcoming).

**Bibliography**

1. T. Janetzke, *Experimentelle Untersuchungen zur Effizienzsteigerung von Prallkühlkonfigurationen durch dynamische Ringwirbel hoher Amplitude*, PhD Thesis, TU Berlin, 2010.

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

3. R. Viskanta, Heat transfer to impinging isothermal gas and flame jets. *Experimental thermal and fluid science*, **6** (1993) 111–134.

4. J. C. Hunt, A. A. Wray, & P. Moin, Eddies, Streams, and Convergence Zones in Turbulent Flows. *Studying Turbulence Using Numerical Simulation Databases-I1*, (1988) 193.

**Principal investigator**

Jörn Sesterhenn^{1}

**Project contributor**

Gabriele Camerlengo^{1}

^{1 }Institut für Strömungsmechanik und Technische Akustik, Fachgebiet Numerische Fluiddynamik, Technische Universität Berlin

**Scientific Contact**

Gabriele Camerlengo (M.Sc.)

Institut für Strömungsmechanik und Technische Akustik

Fachgebiet Numerische Fluiddynamik

Technische Universität Berlin

Müller-Breslau-Str. 15, D-10623 Berlin (Germany)

e-mail: gabriele.camerlengo [@] tu-berlin.de

*HLRS project ID: JetCool*

*February 2020*