Reynolds number effects on the wind pressure distribution on spherical storage tanks
Introduction
Spherical storage tank is one of the most commonly used equipment in petrochemical industry for inflammable, explosive, highly toxic and corrosive gas, liquefied gas and liquid materials, which may become a major source of danger related to social security when the structure is damaged. Because the structures are quite sensitive to wind actions, the wind disaster resistance is extremely important.
The spherical storage tank is of a typical bluff body shape, the aerodynamic loads of which are significantly affected by the Reynolds number. The prototype Reynolds numbers in practical engineering application could reach 107 - 108 (with a diameter of 10–40 m, a design wind velocity of 15–30 m/s) or larger. However, it is nearly impossible to simulate such a large magnitude of prototype Reynolds number in a common atmospheric turbulent boundary layer wind tunnel, which can the Reynolds numbers of the order of 105 - 106. Therefore, it is necessary to study the Reynolds number effect on the aerodynamic characteristics of the spherical storage tanks to provide guidance for the wind tunnel tests as well as an aerodynamic load model for engineering reference.
The Reynolds number effect on the aerodynamic loads on structures is one of the most discussed topics in the field of wind engineering. Researchers such as Roshko (1961) and Achenbach (1968) investigated the wind loads on a classical smooth circular cylinder with a wide range of Reynolds number in uniform flow. It was concluded that in the sub-critical Re range (300 < Re < 3 × 105), the separation angle was found to be below 90° with laminar separations on both sides. As Re increased to (3–3.5) × 105, the separation angle was found to shift from 95° to 140°on the surface where a turbulent separation occurs. The separation angle remains at approximately 120° in the super-critical Re range (3.5 × 105 < Re < 1.5 × 106) and the flow separations becomes turbulent on both sides. When Re > 4 × 106, the surface boundary layer becomes turbulent before the separation, which is defined as trans-critical range. Schewe (1983) tested the aerodynamic drag and lift coefficients in the Reynolds number range from 2 × 104 to 7 × 106, indicating that the drag coefficient was 0.52 in the trans-critical range when Re exceeded 3 × 106. Güven et al. (1980) and Duarte (1991a and 1991b) investigated the influence of surface roughness of cylinder on the aerodynamic coefficients, indicating a potential method to equivalently simulate the flow and load characteristics at high Reynolds numbers. Duarte (1992) and Zan (2008) investigated the aerodynamic loads on circular cylinders in turbulent flow, indicating that the transition of separation occurs at lower Re in turbulent oncoming flows. Qiu et al. (2014 and 2018), Liu et al. (2020), and Cheng et al. (2017) investigated the Reynolds number effect on the aerodynamic loads on cylindrical engineering structures such as cylindrical roofs, MAN type gas storage tanks, and cooling towers with different rise-to-span ratios and surface roughness in atmospheric turbulent boundary layer flows for engineering reference. Hu and Kwock (2020) collected the wind load data of various cylindrical engineering structures various Reynolds numbers to carry out predictions of aerodynamic statistics with machine learning techniques.
For a spherical bluff body, Achenbach (1972) investigated the flow and load characteristics of a smooth sphere for 4 × 104 < Re < 6 × 106 in uniform flow, the results of which were found to be similar to those for classical circular cylinders. The effects of surface roughness and wind tunnel blockage are also studied (Achenbach, 1974). The results indicated that the critical Re decreased with the surface roughness, while increased with tunnel blockage. Taneda (1978) presented the results of a visual observation on the flow past a sphere at Reynolds numbers between 104 and 106 to investigate the vortex structure. Tsutusi (2008) carried out an investigation of the flow and wind load for a smooth sphere in a plane turbulent boundary layer at Re = 8.4 × 104 and proposed an empirical formula for the drag and uplift coefficients. The experimental condition is close to the situation of spherical tanks. However, the Reynolds number is much lower than that for prototype structures. Yeung (2007) proposed a general piecewise model for the mean pressure coefficients on cylindrical and spherical bodies for engineering simplification. In addition, Taylor (1991), Letchford and Sarkar (2000), and Cheng and Fu (2010) carried out experimental researches of the mean and fluctuating wind loads on domed roofs from an engineering point of view, concluding that, in turbulent boundary layer flow, the pressure distributions on hemispherical dome become insensitive to Re when Re exceeds (1.0–2.0) × 105. The Re range where the aerodynamic characteristics are insensitive to (or independent of) Re is defined as the self-modeling Re range.
Many investigations on simulating high Reynolds number flow with surface roughness has been carried out. The surface roughness is usually implemented by adhering sandpaper (e.g. Qiu et al., 2014), stripes (e.g. Liu et al., 2020), or notching on the surface (e.g. Sun et al., 2020) on the model surface. Basic investigations are carried out mostly on cylinder-like structures, and some qualitative and quantitative conclusions were drawn to provide guidance and basic criteria for the wind tunnel simulations. However, the applicability of conclusions drawn from cylinder-like structures on more complicated three-dimensional bluff body such as sphere demand further discussion. Therefore, quantitative investigations on bluff body with more complex curved surfaces are still required.
The present research focuses on the Reynolds number effect on the aerodynamic loads of a spherical storage tank. Wind tunnel tests are carried out on spherical storage tanks with different numbers of supporting columns, surface roughness in uniform and atmospheric boundary layer flows in a Reynolds number range from 105 to 106. The characteristics of aerodynamic drag and uplift coefficients, mean and RMS wind pressure coefficients are discussed. The aerodynamic load characteristics in uniform flow provide a basic research for the Reynolds number dependent characteristics of a sphere-like bluff body. The wind pressure characteristics in ABL flow is more applied research for engineering reference. The trans-critical self-modeling Re range criteria are determined by analyzing the similarity of mean and RMS wind pressure coefficient distribution patterns, providing guidance for wind tunnel simulation for sphere-like bodies. Moreover, a model of the mean wind load in the trans-critical self-modeling Re range for spherical storage tanks is established for engineering reference.
Section snippets
Test model
In the present research, a spherical storage tank with a capacity of 25 000 m3 was modeled according to the Steel spherical storage tanks type and dimension database (GB/T 17261–2011). The diameter of prototype tank is D = 36.3 m and the height of equator is H = 20.2 m. The schematic illustration of the tank model is displayed in Fig. 1a, together with the coordinate system with its origin at the center of the sphere. The location of pressure taps on the model can be described by the
Drag coefficient
The drag coefficients of smooth spherical storage tank models are shown in Fig. 4. The influences of surface roughness on the drag coefficient are shown in Fig. 5. It is indicated that in the tested Re range (105 - 106), the drag coefficients decrease with the increment of Reynolds number in both uniform and ABL flows. With the increment of surface roughness, the drag coefficient becomes less sensitive to Re. Generally, the CD value for the lower hemisphere is larger than that for the upper
Wind pressure coefficient distribution in the circumferential direction
The distributions of wind pressure coefficients along the vertical circle parallel to the wind direction (α = 0° and 180°) of the smooth spherical storage tank in the uniform flow are shown in Fig. 8. The influences of surface roughness on the distribution are shown in Fig. 9. It is obvious that the transition from the super-critical to the trans-critical range can be found from the transition of separation angle on the upper hemi-sphere. The separation angle can be recognized by the
Conclusions
The present research investigated the Reynolds number effects on the wind pressure distributions on spherical storage tanks with different supporting columns numbers, surface roughness, and oncoming flows in a wind tunnel. The following conclusions are drawn.
- (1)
For the smooth spherical storage tank model in uniform flow, super-critical Re range is recognized as 2.5 × 105 to 6.5 × 105. When Re exceeds 6.5 × 105, the separation angle changes from 135° to 120°, indicating that the Reynolds
CRediT authorship contribution statement
Ning Su: Investigation, Visualization, Data curation, Writing - original draft. Shitao Peng: Conceptualization, Funding acquisition, Project administration, Resources. Yasushi Uematsu: Investigation, Writing - review & editing, Supervision.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
This research was supported by the China National Key R&D Program (Grant No. 2017YFE0130700) and the Fundamental Research Funds for the Central Public Welfare Research Institutes (Grant Nos. TKS190204 and TKS20200106).
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