## MARIANGELA DE MAIO

Dottoressa di ricerca**ciclo**: XXXVI

**supervisore**: Prof. Sergio Pirozzoli

**Titolo della tesi:**Numerical investigation of flow in ducts with realistic large roughness at the wall

We conduct a numerical study of turbulent flow in rough ducts to highlight the limitations of Reynolds averaged Navier-Stokes equations (RANS) in heat exchange and to define a possible path for the correction of heat transfer. This research is necessary because current RANS models are not always suitable for predicting heat exchange when wall roughness is very high. The need for this study is a consequence of technological advances in the field of metal additive manufacturing, which allows the fabrication of small and complex geometries, such as channels for the regenerative cooling of liquid rocket engines, obtained at lower cost and less production time.
These techniques generate high roughness, which significantly affects pressure losses and heat transfer. Currently, the high roughness model is the only model that can handle such large roughness, but it must be calibrated and corrected, especially for the thermal effects.
We carry out direct numerical simulations (DNS) of turbulent flow in ducts with circular, square, and rectangular cross-sections, which serve as a reference due to their high degree of accuracy. The results are reported for fully-developed flows. The ducts are made of rough wall and three types of irregular roughness are investigated, namely a grit-blasted and a graphite and an Inconel surface. A finite-differences approach and the immersed-boundary method are adopted to solve the governing equations in the computational domain. The flow and heat transfer phenomena in the ducts are studied in detail for laminar and turbulent regimes at Pr = 0,71, as representative of air.
The simulations highlighted some disparities between the mean streamwise velocity and temperature fields, resulting in lower values for the temperature roughness function compared to the velocity roughness function. These differences arise due to the decrease in the heat transfer efficiency with increasing Reynolds number, causing the Reynolds analogy to break down. Since the heat transfer in RANS model relies on the Reynolds analogy, the need for a correction is expected. Then, a comparative analysis between the RANS and DNS is presented.
In the RANS simulations, we examine the flow as it develops within the ducts. However, we compare these RANS results to the DNS in the region where the flow is fully developed. We find errors in smooth ducts both on the friction factor (about 6%) and Stanton number (about −3% for the circular pipes and −9% for the square ducts) relative to the DNS. Errors are very high in square ducts, where the heat transfer is strongly underestimated. Some inaccuracies are also found in the rough ducts, when the high roughness model is used, which yields lower value of friction coefficient when the equivalent sand-grain roughness found through the DNS model is used. Indeed, to match the friction coefficient observed in the DNS, the relative roughness height in the RANS simulations needs to be increased by 60% compared to that used in the DNS. Moreover, errors in a range from −8% to 12% are also
found in the Stanton number for the square ducts, whereas the error in the case of circular pipes with large roughness is always larger and goes from 20% to 40%.
For this reason, a method for applying a thermal correction is proposed and tested to replicate the DNS results. The test shows that the correction can be used in a
specified range of the parameters. Last, the next steps for extending the correction to a broader range are defined.

**Produzione scientifica**