Effect of wavelength of sinusoidal wavy wall surface on drag and heat transfer at turbulent thermal boundary layer flow

Hiroya MAMORI, Masanari FUJIMURA, Shotaro UDAGAWA, Kaoru IWAMOTO, Akira MURATA, Yasuo KAWAGUCHI, Hirotomo ANDO, Hideki KAWASHIMA, Hirohisa MIENO
2018 Journal of Thermal Science and Technology  
Direct numerical simulations of thermal turbulent boundary layer flows over a wavy wall surface are performed to investigate the effect of a wavelength on drag coefficients and heat transfer performance. The Reynolds number based on an inlet boundary layer thickness is set to be 2820 and the Prandtl number is set to be Pr = 0.71 and 2.0. The wavy wall surface is homogeneous in the spanwise direction and the wave amplitude is fixed at 2a + = 20. The six wavelength cases of λ/2a = 7.5 ∼ 45 are
more » ... mined. As the wavelength decreases, the skin-friction drag decreases and the pressure drag and heat transfer increase. The total drag peaks at λ/2a = 12.5 and the flow separation occurs at λ/2a < 15. In the separation region, the backward flow transfers the heat and results in a negative correlation coefficient between the velocity and temperature of R(u ′ t T ′ ) at the bottom of the wavy wall. Spindle-shaped spots of the Nusselt number are also observed on the upslope of the wavy wall. Hanratty (2003) and performed LDV measurements for a flow field with the highly rough wavy wall surfaces, the intermediate roughened surfaces, and the hydraulically smooth surfaces. Günther and von Rohr (2003) conducted the PIV measurement and discussed the role of streamwise-oriented large-scale structures over the wavy wall surface. Direct numerical simulations (DNS) and large eddy simulations have also been conducted, and have revealed significant effects of the wavy boundary on flow statistics, flow structure, pressure, and skin-friction drag coefficient (e.g., de Angelis et al. (1997) , Henn and Sykes (1999) , Yoon et al. (2009) ). As discussed above, there are numerous studies of turbulent channel flow with wavy wall surface and the effect of wave amplitude. In contrast, Gong et al. (1996) investigated the turbulent boundary layer flow over the wavy wall surface numerically and experimentally, and found that the mean flow separated over each wave was approximately twodimensional for small amplitude cases. For a relatively smooth surface, however, the flow is attached after the first wave and a three-dimensional secondary flow is observed after the first few waves. In general, numerical simulations of the turbulent boundary layer flows require larger computational cost as compared to the channel flow simulation. Consequently, few studies have been conducted on the turbulent boundary layer flows over the wavy wall. In the present study, therefore, we focus on the turbulent thermal boundary layer flow over the wavy wall surface. The expected contribution is twofold. First is the drag prediction. For the prediction of the drag over the roughness, Moody's diagram (Moody, 1944) is well-known and summarizes the pressure drop of the pipe flow as a function of Reynolds number and the relative roughness. The relative roughness is defined as the ratio of roughness height to pipe diameter, and the diagram is very useful for predicting the drag if the relative roughness is known. However, if the relative roughness is not known, the Moody diagram cannot be used to predict the pressure drop straightforwardly; rather, unknown relative roughness is determined from a fitting of roughness height to match the measured pressure drop. In this study, turbulent flows over the wavy wall with a different wavelength and constant amplitude are investigated using DNS. According to the definition of relative roughness, it is unique and the diagram predicts the same drag. However, the resultant drag is a function of the wavelength, and we will discuss the reason of the variation. Second is to estimate the heat transferred by the wavy wall in the turbulent thermal boundary layer flow. Owing to the inherent similarity between momentum and heat transfer, the heat transfer enhancement is expected where turbulence is promoted. Previously, e.g., Choi and Suzuki (2005) performed the large eddy simulation of a channel flow equipped with a heated wavy wall surface and investigated the response for different wave amplitudes; as for the experiments, Günther and von Rohr (2002) used liquid crystal thermometry to quantify the temperature field and assessed the large-scale structure; Kruse and von Rohr (2006) performed a particle thermometry technique to determine the turbulent heat flux between a wavy heated bottom wall and a flat top wall in a water channel. These investigations were conducted in the channel flow, whereas our target is a spatially developed turbulent boundary layer flow. This study aims to investigate the wavelength effect on the thermal turbulent boundary layer flow by using DNS. The thermal turbulent boundary layer flow is chosen for threefold reasons: first, it is more practical than the channel flow in the real situation; second, the wavelength of the wavy wall can be easily changed in the turbulent boundary layer flow if a large computational domain is provided; third, the similarity between momentum and heat transport is held under the no-slip and isothermal boundary conditions. The rest of this paper is organized as follows: in section 2, detail of the computational condition is summarized; in section 3, we show DNS results and discuss the relation between the velocity and temperature fields; and in section 4, we draw our conclusion.
doi:10.1299/jtst.2018jtst0023 fatcat:4s2xb5niovbd7o3sxbe7y3r2he