Subproject B02

Transport of heat and species near solid walls is of central importance in various industrial applications including those in the focus of the present Collaborative Research Centre. Presence of a solid wall particularly adds to the complexity of the problem as it imposes different types of boundary conditions for different transported variables (Dirichlet or mixed boundary condition for temperature and Neumann for species). Subproject B02 aims at using high fidelity Direct Numerical Simulations (DNS) to shed light on these complexities by studying a canonical but highly relevant flow configuration – impingement of two parallel jets on a solid wall. The jets can possess different temperatures and concentrations of species, what leads to wall-parallel gradients in the near wall region that is required for the purpose of this study. Effect of surface roughness in the impingement area is also a central topic in this subproject.

DNS provides an absolute access to the details of flow, thermal and concentration fields that is nearly impossible to achieve in experiments. Also use of DNS makes possible studying extreme cases that are too costly for experimental studies. In view of the above, by using DNS two main goals are followed in this subproject:

1) studying the detailed physics of a problem in a wide parameter range,

2) providing unique data for development of engineering models in other subprojects.

In the first project period, this subproject was focused on momentum and heat transfer in flows over rough walls. To this end, DNS results based on a canonical plane channel flow configuration were employed to study the effect of roughness morphology on the near wall momentum and heat transfer and, specifically, to characterize roughness due to combustion chamber deposits.

Sample instantaneous inner scaled velocity field out of DNS in a channel over roughness elements. The exact roughness geometry is resolved using the Immersed Boundary Method. Friction Reynolds number equals 500; x, y and h₀ denote streamwise direction, wall-normal direction and channel half height, respectively.

Spectral Element Navier Stokes solver NEK5000 will be used in this research. Spectral Element Method (SEM) combines the high accuracy of spectral schemes with a much higher geometrical flexibility compared to the widely used pseudo-spectral codes. Low-Mach number approximation will be employed to take into account the variation of thermophysical properties with temperature. In this subproject the problem will be solved for non-reactive scalars. To mimic the realistic inflow conditions in the parallel experiments, a Synthetic Eddy Method (SyEM) will be implemented that makes possible generation of anisotropic turbulent inflow.

This subproject closely cooperates with subproject A06N (twin experiments) on cross-validation of the results and with subproject B03 (hybrid RANS/VLES simulations) – on delivery of turbulence statistics required for model-adjustment and also on the development of the SyEM.

In addition, the present subproject supports subprojects B04, C03, C03, B06 and B07 by delivering DNS data required for development of models and understanding of the physical mechanisms.

• von Deyn, L.H., Schmidt, M., Örlü, R., Stroh, A., Kriegseis, J., Böhm, B., Frohnapfel, B.: Ridge-type roughness: from turbulent channel flow to internal combustion engine. Exp Fluids, 10.1007/s00348-021-03353-x, 2022.
• Schäfer, K., Stroh, A., Forooghi, P., Frohnapfel, B.: Modelling spanwise heterogeneous roughness through a parametric forcing approach. J. Fluid Mech., 10.1017/jfm.2021.850, 2022.
• Secchi, F., Häber, T., Gatti, D., Schulz, S., Trimis, D., Suntz, R., Frohnapfel, B.: Turbulent impinging jets on rough surfaces. GAMM-Mitteilungen, 10.1002/gamm.202200005, 2022.
• Samkhaniani, N., Stroh, A., Holzinger, M., Marschall, H., Frohnapfel, B., Wörner, M.: Bouncing drop impingement on heated hydrophobic surfaces. International Journal of Heat and Mass Transfer, 10.1016/j.ijheatmasstransfer.2021.121777, 2021.
• Wörner, M., Samkhaniani, N., Cai, X., Wu, Y., Majumdar, A., Marschall, H., Frohnapfel, B., Deutschmann, O.: Spreading and rebound dynamics of sub-millimetre urea-water-solution droplets impinging on substrates of varying wettability. Applied Mathematical Modelling, 10.1016/j.apm.2021.01.038, 2021.
• Chedevergne, F., Forooghi, P.: On the importance of the drag coefficient modelling in the double averaged Navier-Stokes equations for prediction of the roughness effects. Journal of Turbulence, 10.1080/14685248.2020.1817465, 2020.
• Schäfer, K., Forooghi, P., Straub, S., Frohnapfel, B., Stroh, A.: Direct Numerical Simulations of a Turbulent Flow over Wall-Mounted Obstacles – A Comparison of Different Numerical Approaches. In: Garc a-Villalba, M., Kuerten, H. and Salvetti, M. V. (Eds.): Direct and Large Eddy Simulation XII, Bd. 27. Cham: Springer International Publishing (ERCOFTAC Series), 91–96, 10.1007/978-3-030-42822-8_12, 2020.
• Stroh, A., Schäfer, K., Frohnapfel, B., Forooghi, P.: Rearrangement of secondary flow over spanwise heterogeneous roughness. J. Fluid Mech., 10.1017/jfm.2019.1030, 2020.
• Bender, A., Stroh, A., Frohnapfel, B., Stephan, P., Gambaryan-Roisman, T.: Combined direct numerical simulation and long-wave simulation of a liquid film sheared by a turbulent gas flow in a channel. Physics of Fluids, 10.1063/1.5064423, 2019.
• Forooghi, P., Frohnapfel, B., Magagnato, F., Busse, A.: A modified Parametric Forcing Approach for modelling of roughness. International Journal of Heat and Fluid Flow, 10.1016/j.ijheatfluidflow.2018.03.019, 2018.
• Forooghi, P., Stripf, M., Frohnapfel, B.: A systematic study of turbulent heat transfer over rough walls. International Journal of Heat and Mass Transfer, 10.1016/j.ijheatmasstransfer.2018.08.013, 2018.
• Forooghi, P., Stroh, A., Schlatter, P., Frohnapfel, B.: Direct numerical simulation of flow over dissimilar, randomly distributed roughness elements: A systematic study on the effect of surface morphology on turbulence. Phys. Rev. Fluids, 10.1103/PhysRevFluids.3.044605, 2018.
• Forooghi, P., Weidenlener, A., Magagnato, F., Böhm, B., Kubach, H., Koch, T., Frohnapfel, B.: DNS of momentum and heat transfer over rough surfaces based on realistic combustion chamber deposit geometries. International Journal of Heat and Fluid Flow, 10.1016/j.ijheatfluidflow.2017.12.002, 2018.
• Luan, Y., Olzmann, M., Magagnato, F.: Simulation of a shock tube with a small exit nozzle. J. Therm. Sci., 10.1007/s11630-018-0981-8, 2018.
• Forooghi, P., Magagnato, F., Frohnapfel, B.: Reynolds analogy in turbulent flows over rough walls – a DNS investigation, Proceedings of the 16th Int. Heat Transfer Conference, Beijing, China, 10.1615/IHTC16.cov.021429, 2018.
• Forooghi, P., Stroh, A., Magagnato, F., Jakirlić, S., Frohnapfel, B.: Toward a universal roughness correlation. Journal of Fluids Engineering, 10.1115/1.4037280, 2017.
• Forooghi, P., Flory, M., Bertsche, D., Wetzel, T., Frohnapfel, B.: Heat transfer enhancement on the liquid side of an industrially designed flat-tube heat exchanger with passive inserts – Numerical investigation. Applied Thermal Engineering, 10.1016/j.applthermaleng.2017.05.144, 2017.
• Forooghi, P., Frohnapfel, B., Magagnato, F.: Simulation of a gaseous jet impinging on a convex heated surface – effect of inlet condition. Applied Thermal Engineering, 10.1016/j.applthermaleng.2016.01.048, 2016.