Description

Introduction

In environmental and civil engineering, surface-mounted hemispherical bluff bodies are commonly used as architectural design elements. They appear in various applications such as depicted in Fig. 2. Although the hemisphere represents a simple geometry, it exhibits a rather complicated flow field including complex flow patterns. They can be roughly classified into an upstream horseshoe vortex system and a recirculation area with trailing vortices in the wake region. Furthermore, full-scale structures are often exposed to turbulent boundary layers, which increases the complexity of the flow field. The specific flow problem of a wall-mounted hemisphere was studied since the 1940s. However, due to its complexity, most of the contributions focus on a certain part of the flow. The present study published in Wood et al. (2016) includes experimental investigations and large-eddy simulations (LES) to characterize the whole three-dimensional flow field around a surface-mounted smooth hemisphere in a turbulent boundary layer at Re = 50,000.

Fig. 2: Examples of hemispherical domes in modern civil engineering.

Review of previous work

The following brief literature review is extracted from Wood et al. (2016). A full version can be found in the paper.

Previous experimental investigations

Beginning with an analysis based on the pressure distribution the first experiments were carried out by Jacobs (1938), Maher (1965) and later on by Taylor (1992) to mention only a few. They showed Reynolds number independency above a critical Re number and turbulence intensity. Another experiment by Taniguchi et al. (1982) found a relationship between the approaching boundary layer thickness and the aerodynamic forces acting on the hemisphere. Toy et al. (1983) and Savory and Toy (1986) investigated the flow past a hemispherical dome using hot-wire and pulsed-wire anemometers and brought a deeper insight into the complex flow structures occurring in the near-wake regime. Another experiment by Savory and Toy (1988) focused on the separation of the shear layer in the flow around hemispheres at a sub-critical Reynolds number of Re = 140,000. The study included different turbulent boundary layers classified in thin, smooth and rough boundary layers depending on the thickness and the turbulence intensity. A profound discussion provided a deeper understanding of the distribution of the turbulent shear stress and intensity in the wake regime. Additionally, a representative illustration of the flow field characteristics was provided. The outcome of both studies (Savory and Toy 1986, 1988) is often used as reference for experimental and numerical examinations.

Visualizations of the vortical flow structures were conducted by Tamai et al. (1987). The experiments allowed to visualize the complex vortical structures by injecting dye into the water channel. Moreover, the frequencies of the vortex formation and shedding from the separation area were recorded. Bennington (2004) examined various roughness elements and their associated effects on the turbulent boundary layer. Among the chosen elements, a hemispherical obstacle was analyzed in detail concerning statistics of the Reynolds stresses, the turbulent kinetic energy and even the triple correlations. Further visualization experiments were conducted by Yaghoubi (1991). They comprised a detailed visualization of the flow pattern around grouped hemispheres in a wind tunnel. The motivation was to achieve a deeper understanding of the flow field and the associated effects of natural ventilation of domed structures.

Previous numerical investigations

Apart from experimental investigations numerical simulations were carried out to provide enhanced insight into the flow. An early study was conducted by Tamura et al. (1990) without applying any turbulence model. The focus of the simulations lay on the visualization of the unsteady flow pattern and the time-averaged surface pressure distribution. A fundamental numerical study was carried out by Manhart (1998) using large-eddy simulation to receive more detailed information about the vortical structures. The Cartesian grid combined with the immersed boundary technique led to an artificial surface roughness on the contour of the hemisphere. The results were therefore compared with the experiments of Savory and Toy (1986, 1988) for a rough hemisphere. Another comparison of numerical and experimental data was made by Meroney et al. (2002). The wind load distributions on smooth, rough and dual domes in the shape of hemispherical caps were examined. Several RANS turbulence models were used delivering similar results. Recently, Kharoua and Khezzar (2013) performed a LES on a hemisphere with a rough and smooth surface comparing the results with the experiment of Savory and Toy (1986). A specialized approach to model the surface roughness was presented. The results of the LES allowed the visualization of instantaneous three-dimensional flow patterns illustrating the complex interaction of vortical structures in the close vicinity of the hemisphere.

Previous complementary experimental and numerical investigations

A combined experimental and numerical study was accomplished by Tavakol et al. (2010). A hemisphere was immersed in two turbulent boundary layers of different thickness. Velocity distributions and turbulence intensities were presented for the streamwise and the spanwise directions in the recirculation zone. A further velocity measurement was carried out for the area close to the front of the hemisphere investigating the horseshoe vortex that leads to a strong backflow in the near-wall region. The numerical investigation relied on the RNG k-ε turbulence model (Yakhot et al., 1992). The inflow conditions of the simulation were generated by implying the time-averaged data of the corresponding hot-wire measurements. The turbulence intensity at the inlet was also taken from the measurements. The results showed overall good agreement with the experimental data. Recently, Tavakol et al. (2014) presented a yet deeper investigation of the hemisphere flow using LES. Based on the earlier study (Tavakol et al., 2010) the main focus was to highlight the superior results of the applied LES compared to the previously performed RANS simulations. The study included a thin turbulent boundary layer δ/D = 0.15 as inflow condition. For a realistic inlet velocity distribution including fluctuations, a turbulence inflow generator based on the method of Sergent (2002) was applied. The LES results showed excellent agreement with the measurements. An updated comparison between the previous study (Tavakol et al., 2015) with the current data revealed the shortcomings of the RNG k-ε model. A presentation of time-averaged data focuses on the streamline visualization and surface pressure distribution. Unfortunately, the study does not present statistical data of the velocity field or the Reynolds stresses.

Choice of test case

The literature review presented indicates that a surface-mounted hemisphere placed in a turbulent boundary layer exhibits a very complex flow field. The key aspect of most studies listed above often remains on one specific issue such as the recirculation area or the pressure distribution. Just a few studies contain general characteristics of the flow including complementary numerical and experimental investigations.

The present UFR is based on the experimental LDA and numerical LES study of Wood et al. (2016) which focuses on the following objectives:

It provides a comprehensive view of the flow field past a hemispherical object immersed in a turbulent boundary layer at Re = 50,000 with the help of experimental and numerical investigations: All relevant regions of the flow field (horseshoe vortex system, recirculation area and wake) are studied in detail including unsteady characteristics such as vortex shedding and related spectral analysis.

To avoid uncertainties in the numerical model, the surface of the hemisphere is assumed to be smooth. The experimental data are recorded based on a very smooth aluminum model with low engineering tolerances which are expected to minimize possible influences of surface roughness during the measurements.

The characteristics of the oncoming turbulent boundary layer are taken from the wind tunnel measurements and transferred to the numerical domain. This matching ensures the comparability between the experiment and the numerical simulation, focusing on the mean velocity profile and the turbulent fluctuations of the boundary layer. The numerical simulations use a synthetic turbulent inflow generator (STIG) approach to mimic the turbulent fluctuations of the boundary layer. That is found to be an important issue, since the turbulent fluctuations have a significant impact on the overall flow-field charateristics such as reattachment and separation points.

The time-averaged flow field is analyzed in detail, focussing on the mean velocity distribution in the symmetry plane. Furthermore, the corresponding Reynolds stresses of the flow field past the hemisphere are analyzed in detail including a comparison between the experimental measurements and the numerical simulation data.

The effect of well-known and often applied subgid-scale (SGS) models is highlighted to present their influence on the results.

The test case with complementary experimental and numerical data for the surface-mounted hemisphere flow offers a novel benchmark for the evaluation and validation of numerical schemes or new turbulence models.

Finally, the investigation of the flow past the rigid structure is the first step towards an investigation of the coupled fluid-structure interaction of the flow around a flexible membranous structure. Such as study is intended for the near future.

Contributed by: Jens Nikolas Wood, Guillaume De Nayer, Stephan Schmidt, Michael Breuer — Helmut-Schmidt Universität Hamburg