# The Wind Loading Characteristics of MAN Type Dry Gas Storage Tank

Authors: Xinpeng Liu; Zhitao Yan; Zhengliang Li; Junfan Chen; Jingbo Liu
Journal: Advances in Civil Engineering
 (2020)

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## Abstract

The effects of Reynolds number (Re) and surface roughness on the wind pressure coefficient on a MAN type dry gas tank were analyzed in detail by wind tunnel tests. A wind load calculation model was then established, which is suitable for the wind resistant design of the gas tanks. The test results revealed that in the range of 7 × 105 < Re < 1.0 × 106 (supercritical regimes), the drag coefficient (Cd) and wind pressure coefficient remained constant, consistent with 2D cylinders in a uniform flow. However, in common with 2D cylinder flows, the surface roughness with the spacing ratio (λ) greater than 0.9 had a significant effect on the wind pressures coefficient. The minimum pressure coefficient (Cpmin) sharply increased from −2.3 to −0.65 with increasing surface roughness. The corresponding angle for the minimum pressure coefficient θmin was in between 140°and 90°, which was in a gradual decreasing trend with the increase in surface roughness of the model. The calculation method of the wind pressure coefficient with vary surface roughness was proposed, based on which, the calculation results were in good agreement with the test data.


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## Body

## 1. Introduction

Gas tank is an important industrial structure. This structure is mainly made up of tank dome, cylindrical cabinet, internal piston, and supporting members. As shown in Figure1, the gas tank is a simple circular cross-section structure. When it comes to aerodynamics, simple circular cross-section always brings a complex behavior [1], as the features of flow separation strongly depend on Reynolds number. The aerodynamics of circular cylinders is characterized by abrupt transitions in the flow pattern and in the force parameters, depending only on Reynolds number and defining the aerodynamic regimes. The aerodynamic regimes and the related flow characteristics around a circular cylinder are shown in Table 1.Figure 1
Geometry model of the gas tank.Table 1
Aerodynamic regimes and flow characteristics around a circular cylinder. Data from Wieselsberger [2]; Schewe [3]; Williamson [4]; Roshko [5]; Norberg [6]; Demartino and Ricciardelli [7].
Regime
No separation
Pair of stationary vortex
Laminar vortex shedding
Turbulent vortex shedding
Re range
0 < Re < 5
0 < Re < 5
0 < Re < 5
0 < Re < 5
C
d
∞ >Cd > 4
4 >Cd > 2.1
2.1 >Cd > 1.5
1.5 >Cd > 1.3
C
l
0
0
0
0
St
—
—
0.1 < St < 0.2
0.2 ≌ St ≌ 0.2
Sketch
Regime
Subcritical
Critical
Supercritical
Transcritical
Re range
300 < Re < 3 × 105
3 × 105 < Re < 3.5 × 105
3.5 × 105 < Re < 4.5 × 106
4.5 × 106 < Re < ∞
C
d
1.3 >Cd > 1.2
1.2 >Cd > 0.3
0.3 <Cd < 0.5
C
d > 0.5
C
l
0
≌1.3
0
0
St
0.2 ≌ St ≌ 0.2
0.2 < St < 0.45
0.45 > St > 0.25
St < 0.25
SketchWith the variety of Reynolds number, the development of flow transition around a cylinder experiences three states: wake transition (TrW), shear layer transition (TrSL), and boundary layer transition (TrBL). In Eiffel’s [8] study of spheres in the air, it was found that when Re = 120, the resistance of spheres would suddenly decrease. Wieselsberger [2] explained that the sudden drop of resistance was related to the transition of the boundary layer near the separation point. Taylor [9] first reported the average pressure distribution on the surface of a cylinder in the TrBL state. Fage and Johansen [10] carried out more detailed experimental studies and found a very complex coupling phenomenon between transition and separation. Cantwell [11] repeated the average pressure distribution measurements test in TrBL states. The test results show that the minimum pressure coefficient decreases sharply with the increase of the Reynolds number. Korotkin [12] took a short cylinder with end plates as the research object and simultaneously tested the surface pressure distribution of the cylinder at 35 positions. The experimental results showed that the local bubble rupture had a significant effect on the pressure coefficient distribution. Roshko [5], Schmidt [13], Jones and Knudsen [14], and Warschauer and Leene [15] tested the reference pressure of a cylinder in the transcritical region. Due to the breakdown of separated bubbles, the experimental data points showed very large dispersion. In addition, Roshko [5] revealed a high Reynolds number transition in which the drag coefficient changed dramatically, which indicated the effect of Reynolds number on the drag coefficient of the circular cylinder was significant. Through reconfirming Roshko’s [5] experimental results, Achenbach [16] measured the local pressure and skin friction distribution around the cylinder. From the results the total drag, the pressure drag, and the friction drag were calculated. According to the skin friction distribution, the position of the separation points, separation bubbles, and transition points can be localized, which allow one to define three typical states of the flow. Bearman [17] found that onset of mean lift force caused by a one-side separation from one side of the cylinder. Although there was agreement about the flow features around a circular cylinder depending on the Reynolds number, the description about steps by which the transition from laminar to turbulent occurs was not understood until four regimes were proposed by Achenbach [18].On the other hand, surface irregularities, commonly termed roughness, are another important factor affecting aerodynamic characteristics of the circular cylinder. Pioneering experiments on the effects of uniform roughness on the aerodynamics of circular cylinders in cross flow were performed by Fage and Warsap [19]. They determined Cd for 2.5 × 104 < Re < 2.5 × 105 and for 5 × 10−4 ≤ Re ≤ 2 × 10−2. It was observed that in the subcritical regime roughness has no influence on Cd, while in the supercritical regime Cd increases with increasing k/D. The most significant differences are in the critical regime, where the minimum value of Cd increases and Rec decreases with increasing k/D. It was observed that in the subcritical regime roughness has no influence on Cd, while in the supercritical regime Cd increases with increasing k/D. The most significant differences are in the critical regime, where the minimum value of Cd increases and Rec decreases with increasing k/D. To better understand the effects of roughness on the boundary layer over a circular cylinder with uniform roughness, different researchers measured surface pressures and shear stresses. Similarly to smooth cylinders, in the range 4 × 104 < Re < 3 × 106, for the rough cylinders, shear stresses contributed only a few percent to the total drag [18]. In the case of rough cylinders, Buresti [20] defined the critical regime as the absence of regular vortex shedding, the upper transition regime as the appearance of vortex shedding, and postcritical regime as the independence of St and Cd on Re. In the subcritical regime, separation was found to be laminar and to occur in the front portion of the cylinder, as a consequence of the shear stresses [18]. However, the transition boundary between subcritical and critical is strongly affected by roughness, which was pointed out by Achenbach [18]. The strongest influence of roughness occurs in the critical regime, where roughness itself is the cause producing local turbulence, as it inhibits the formation of the separation bubble and hence obliterates the one and two bubble regimes [21]. Ribeiro [22] studied the roughness generated by ribs, wire mesh screen, and sand paper and demonstrated that variety of roughness textures produced major changes of roughness, even the same physical scale. After reviewing a large amount of investigations on the flow features around a circle cylinder, Zdravkovich [23] presented a relationship between Cd and Re, by which the variation of Cd against Re has been well described in a range of Re up to over 107. Moreover, it is well known that the onset of surface roughness has evident affect to the typical flow features, Achenbach and Heinecke [24] revealed the differences between the Reynold number regimes for rough and smooth surfaces. Zou et al. [25] proposed a new definition of surface roughness (k/s) and a conversion formula with the original definition of surface roughness. Cheng et al. [26] carried out a pressure measurement experiment of the cooling tower in the uniform flow field and atmospheric boundary layer respectively, in which surface roughness effects on both static and dynamic wind loads were studied and quantified.As discussed above, there were a large number of studies on the aerodynamic characteristics of a single circular cylinder, but there are few research studies concerning the effect of Re and surface roughness on flow features and wind pressure distribution of the gas tank.In this paper, the effects of the Re and surface roughness on the wind characteristic of the gas tank has been investigated by the wind tunnel test. Based on the analytical results, the wind load calculation method for the gas tank structure was proposed for the first time. This calculation method could be widely used in the wind resistance design of the gas tank structure.


## 2. Wind Tunnel Experiment

### 2.1. Overview of the Experiment

To understand wind pressure distributions, the whole gas tank is simplified into the tank dome, the cylindrical cabinet, and the supporting members. In order to simulate the real Re characteristics of the gas tank [27, 28] as much as possible, the geometrical scale of the gas tank rigid model was determined to be 1/50.The total height (L) and diameter (D) of the model are 2.4 m and 1.32 m, respectively. The radius of curvature of the dome is 1.76 m. The corresponding rigid model is shown in Figure 2.Figure 2
(a) Rigid model of the gas tank. (b) Detailed model surface.
(a)
(b)There were 416 pressure measurement points arranged on the rigid model. Eleven layers of measurement points were set up along the height of the model, spaced 180 mm apart. Thirty-two measurement points were arranged evenly along the circumferential direction at each layer. The layout and geometric design dimensions of the model are shown in Figure3.Figure 3
Layout of measurement point.The wind tunnel test was conducted in the uniform flow and atmospheric boundary layer (ABL) turbulent flow field of Type A according to Chinese Codes, respectively. The longitudinal integral scale is about 0.9 m∼1.8 m. The simulation results of Type A wind field are listed in Figure4.Figure 4
Simulation of Type A flow field in the wind tunnel. (a) Average wind velocity profile. (b) Turbulence intensity profile. (c) Power-spectrum function for along-wind component of wind speed.
(a)
(b)
(c)


### 2.2. Experiment Cases

For each experiment case, pressure measurement tests in both uniform and Type A flow fields were conducted with different 5 test reference wind speeds 4.5 m/s, 6 m/s, 7.6 m/s, 9.2 m/s, and 10.5 m/s. The corresponding Re are 4.0 × 105, 5.5 × 105, 7.0 × 105, 8.4 × 105, and 9.6 × 105.


#### 2.2.1. In the Uniform Flow

To compare with the results of the previous literature, the smooth circular cylinder rigid model was placed on the center turntable of the test section, and the wind pressure measurement experiment was conducted with different 5 reference wind speeds.To study the surface roughness effects, different 9 surface roughness (γ) which would be defined below were simulated on the model by sticking rough strips. The height range of the rough strip was 1–6 mm. The width of the rough strip was 5 mm. The experiment cases are listed in Table 2.Table 2
Relative roughnessγ for different cases.
Case
Number of rough strips along the circular direction
Height of strip
Surface roughness (γ=k/s)
Wind field
U-1
0
0
0
Uniform flow
U-2
32
1
0.0077
U-3
32
2
0.0154
U-4
32
3
0.0231
U-5
32
4
0.0308
U-6
32
5
0.0386
U-7
32
6
0.0463
U-8
64
4
0.0617
U-9
64
5
0.0771
U-10
64
6
0.0926
T-1
0
0
0
Type A turbulent flow
T-2
32
1
0.0077
T-3
32
2
0.0154
T-4
32
3
0.0231
T-5
32
4
0.0308
T-6
32
5
0.0386
T-7
32
6
0.0463
T-8
64
4
0.0617
T-9
64
5
0.0771
T-10
64
6
0.0926


#### 2.2.2. In the ABL Turbulent Flow Field

To understand the characteristic wind pressure distribution of the gas tank, the same experiments were conducted in the ABL turbulent flow field.


### 2.3. Experiment Equipment

The Digital Service Module and Electronic pressure scanning module were used to acquire pressure data at measurement points. Each ZOC33 module incorporates 64 individual silicon pressure sensors, calibration valving, a high-speed multiplexer (45 kHz), and an instrumentation amplifier. An integral “duplexing” valve is available to allow the ZOC33’s 64 sensors to service up to 128 input pressures.


### 2.4. Experiment Arrangement

In order to meet the maximum of blockage requirement, the wind tunnel test was conducted in the XNJD-3 wind tunnel of Southwest Jiao Tong University. The width and height of the wind tunnel are 22.5 m and 4.5 m. The distance from the top of the model to the ceiling of the wind tunnel is 2.1 m. The maximum test wind speed is 16 m/s. The wind tunnel experiment was conducted in the uniform flow and atmospheric boundary layer (ABL) turbulent flow field of Type A according to Chinese Codes, respectively. The spires and rough elements were used to simulate the ABL turbulent field flow.The spires were made of the isosceles triangular wood structure with height of 4.2 meters. The rough elements were made of cubic wood blocks. The lengths of one side of the large and small rough element were 0.2 m and 0.1 m. The installation of turbulent field and simulation results of wind field are shown in Figure5.Figure 5
Arrangement of wind field. (a) Layout of turbulent field (unit: mm). (b) Realistic arrangement of turbulent field.
(a)
(b)


### 2.5. Parameters Definition

#### 2.5.1. Wind Pressure Coefficient

The instantaneous wind pressure coefficient of theith measurement point on the surface of the model is given by(1)Cpit=pit−p∞ZρV∞2Z/2,where pit indicates the instantaneous surface wind pressure of the ith measurement point that is positive inwards and negative outwards, Z represents the height of the ith measurement point, p∞Z and V∞Z denote the freestream static pressure and oncoming air velocity at high Z, respectively, and ρ is the density of the air.The mean wind pressure coefficient of theith measurement point is given by(2)Cpi=1m∑t=1mCpit,where m indicates the samples number of wind pressure data.The fluctuating wind pressure coefficient of theith measurement point is given by(3)CpiRMS=1m∑t=1mCpit−Cpi21/2.


#### 2.5.2. Characteristic Parameters of Wind Pressure Distribution

The characteristic parameters of mean wind pressure distribution on the gas tank surface are shown in Figure6.Figure 6
Definition of the characteristic parameters.


#### 2.5.3. Surface Roughness

The surface roughness is given by(4)γ=ks,where k is average height of rough bar and s is the distance between the rough bar, which are shown in Figure 7.Figure 7
Diagram of surface roughness definition.


## 2.1. Overview of the Experiment

To understand wind pressure distributions, the whole gas tank is simplified into the tank dome, the cylindrical cabinet, and the supporting members. In order to simulate the real Re characteristics of the gas tank [27, 28] as much as possible, the geometrical scale of the gas tank rigid model was determined to be 1/50.The total height (L) and diameter (D) of the model are 2.4 m and 1.32 m, respectively. The radius of curvature of the dome is 1.76 m. The corresponding rigid model is shown in Figure 2.Figure 2
(a) Rigid model of the gas tank. (b) Detailed model surface.
(a)
(b)There were 416 pressure measurement points arranged on the rigid model. Eleven layers of measurement points were set up along the height of the model, spaced 180 mm apart. Thirty-two measurement points were arranged evenly along the circumferential direction at each layer. The layout and geometric design dimensions of the model are shown in Figure3.Figure 3
Layout of measurement point.The wind tunnel test was conducted in the uniform flow and atmospheric boundary layer (ABL) turbulent flow field of Type A according to Chinese Codes, respectively. The longitudinal integral scale is about 0.9 m∼1.8 m. The simulation results of Type A wind field are listed in Figure4.Figure 4
Simulation of Type A flow field in the wind tunnel. (a) Average wind velocity profile. (b) Turbulence intensity profile. (c) Power-spectrum function for along-wind component of wind speed.
(a)
(b)
(c)


## 2.2. Experiment Cases

For each experiment case, pressure measurement tests in both uniform and Type A flow fields were conducted with different 5 test reference wind speeds 4.5 m/s, 6 m/s, 7.6 m/s, 9.2 m/s, and 10.5 m/s. The corresponding Re are 4.0 × 105, 5.5 × 105, 7.0 × 105, 8.4 × 105, and 9.6 × 105.


### 2.2.1. In the Uniform Flow

To compare with the results of the previous literature, the smooth circular cylinder rigid model was placed on the center turntable of the test section, and the wind pressure measurement experiment was conducted with different 5 reference wind speeds.To study the surface roughness effects, different 9 surface roughness (γ) which would be defined below were simulated on the model by sticking rough strips. The height range of the rough strip was 1–6 mm. The width of the rough strip was 5 mm. The experiment cases are listed in Table 2.Table 2
Relative roughnessγ for different cases.
Case
Number of rough strips along the circular direction
Height of strip
Surface roughness (γ=k/s)
Wind field
U-1
0
0
0
Uniform flow
U-2
32
1
0.0077
U-3
32
2
0.0154
U-4
32
3
0.0231
U-5
32
4
0.0308
U-6
32
5
0.0386
U-7
32
6
0.0463
U-8
64
4
0.0617
U-9
64
5
0.0771
U-10
64
6
0.0926
T-1
0
0
0
Type A turbulent flow
T-2
32
1
0.0077
T-3
32
2
0.0154
T-4
32
3
0.0231
T-5
32
4
0.0308
T-6
32
5
0.0386
T-7
32
6
0.0463
T-8
64
4
0.0617
T-9
64
5
0.0771
T-10
64
6
0.0926


### 2.2.2. In the ABL Turbulent Flow Field

To understand the characteristic wind pressure distribution of the gas tank, the same experiments were conducted in the ABL turbulent flow field.


## 2.2.1. In the Uniform Flow

To compare with the results of the previous literature, the smooth circular cylinder rigid model was placed on the center turntable of the test section, and the wind pressure measurement experiment was conducted with different 5 reference wind speeds.To study the surface roughness effects, different 9 surface roughness (γ) which would be defined below were simulated on the model by sticking rough strips. The height range of the rough strip was 1–6 mm. The width of the rough strip was 5 mm. The experiment cases are listed in Table 2.Table 2
Relative roughnessγ for different cases.
Case
Number of rough strips along the circular direction
Height of strip
Surface roughness (γ=k/s)
Wind field
U-1
0
0
0
Uniform flow
U-2
32
1
0.0077
U-3
32
2
0.0154
U-4
32
3
0.0231
U-5
32
4
0.0308
U-6
32
5
0.0386
U-7
32
6
0.0463
U-8
64
4
0.0617
U-9
64
5
0.0771
U-10
64
6
0.0926
T-1
0
0
0
Type A turbulent flow
T-2
32
1
0.0077
T-3
32
2
0.0154
T-4
32
3
0.0231
T-5
32
4
0.0308
T-6
32
5
0.0386
T-7
32
6
0.0463
T-8
64
4
0.0617
T-9
64
5
0.0771
T-10
64
6
0.0926


## 2.2.2. In the ABL Turbulent Flow Field

To understand the characteristic wind pressure distribution of the gas tank, the same experiments were conducted in the ABL turbulent flow field.


## 2.3. Experiment Equipment

The Digital Service Module and Electronic pressure scanning module were used to acquire pressure data at measurement points. Each ZOC33 module incorporates 64 individual silicon pressure sensors, calibration valving, a high-speed multiplexer (45 kHz), and an instrumentation amplifier. An integral “duplexing” valve is available to allow the ZOC33’s 64 sensors to service up to 128 input pressures.


## 2.4. Experiment Arrangement

In order to meet the maximum of blockage requirement, the wind tunnel test was conducted in the XNJD-3 wind tunnel of Southwest Jiao Tong University. The width and height of the wind tunnel are 22.5 m and 4.5 m. The distance from the top of the model to the ceiling of the wind tunnel is 2.1 m. The maximum test wind speed is 16 m/s. The wind tunnel experiment was conducted in the uniform flow and atmospheric boundary layer (ABL) turbulent flow field of Type A according to Chinese Codes, respectively. The spires and rough elements were used to simulate the ABL turbulent field flow.The spires were made of the isosceles triangular wood structure with height of 4.2 meters. The rough elements were made of cubic wood blocks. The lengths of one side of the large and small rough element were 0.2 m and 0.1 m. The installation of turbulent field and simulation results of wind field are shown in Figure5.Figure 5
Arrangement of wind field. (a) Layout of turbulent field (unit: mm). (b) Realistic arrangement of turbulent field.
(a)
(b)


## 2.5. Parameters Definition

### 2.5.1. Wind Pressure Coefficient

The instantaneous wind pressure coefficient of theith measurement point on the surface of the model is given by(1)Cpit=pit−p∞ZρV∞2Z/2,where pit indicates the instantaneous surface wind pressure of the ith measurement point that is positive inwards and negative outwards, Z represents the height of the ith measurement point, p∞Z and V∞Z denote the freestream static pressure and oncoming air velocity at high Z, respectively, and ρ is the density of the air.The mean wind pressure coefficient of theith measurement point is given by(2)Cpi=1m∑t=1mCpit,where m indicates the samples number of wind pressure data.The fluctuating wind pressure coefficient of theith measurement point is given by(3)CpiRMS=1m∑t=1mCpit−Cpi21/2.


### 2.5.2. Characteristic Parameters of Wind Pressure Distribution

The characteristic parameters of mean wind pressure distribution on the gas tank surface are shown in Figure6.Figure 6
Definition of the characteristic parameters.


### 2.5.3. Surface Roughness

The surface roughness is given by(4)γ=ks,where k is average height of rough bar and s is the distance between the rough bar, which are shown in Figure 7.Figure 7
Diagram of surface roughness definition.


## 2.5.1. Wind Pressure Coefficient

The instantaneous wind pressure coefficient of theith measurement point on the surface of the model is given by(1)Cpit=pit−p∞ZρV∞2Z/2,where pit indicates the instantaneous surface wind pressure of the ith measurement point that is positive inwards and negative outwards, Z represents the height of the ith measurement point, p∞Z and V∞Z denote the freestream static pressure and oncoming air velocity at high Z, respectively, and ρ is the density of the air.The mean wind pressure coefficient of theith measurement point is given by(2)Cpi=1m∑t=1mCpit,where m indicates the samples number of wind pressure data.The fluctuating wind pressure coefficient of theith measurement point is given by(3)CpiRMS=1m∑t=1mCpit−Cpi21/2.


## 2.5.2. Characteristic Parameters of Wind Pressure Distribution

The characteristic parameters of mean wind pressure distribution on the gas tank surface are shown in Figure6.Figure 6
Definition of the characteristic parameters.


## 2.5.3. Surface Roughness

The surface roughness is given by(4)γ=ks,where k is average height of rough bar and s is the distance between the rough bar, which are shown in Figure 7.Figure 7
Diagram of surface roughness definition.


## 3. Discussion of Experimental Result

### 3.1. Effect of Reynolds Number on Drag Coefficient and Minimum Pressure Coefficient

The effects of Reynolds number on the drag coefficient (Cd) and minimum pressure coefficient (Cpmin) were shown in Figures 8 and 9. For space reasons, only partial test results are listed.Figure 8
Effect of the Reynolds number on the drag coefficient of each measurement layer. (a, c, e) Uniform flow and (b, d, f) Type A turbulent flow field. (a, b)γ = 0, (c, d) γ = 0.0386, and (e, f) γ = 0.0771.
(a)
(b)
(c)
(d)
(e)
(f)Figure 9
Effect of the Reynolds number on minimum negative wind pressure coefficient. (a, c, e) Uniform flow and (b, d, f) Type A turbulent flow field. (a, b)γ = 0, (c, d) γ = 0.0386, and (e, f) γ = 0.0771.
(a)
(b)
(c)
(d)
(e)
(f)


#### 3.1.1. Drag CoefficientCd

The drag coefficient of each measurement layer of the gas tank was obtained by weighted averaging the wind pressure data of each measurement point:(5)Cd=πN∑i=1nCpicosθ,where θ represents the azimuthal angle of the ith measurement point and n and N represent the number of weighted average points and total points for each layer. In this section, n = N = 32.(1) Detail Results Obtained in Uniform Flow Field. Figure 8(a) shows the drag coefficient (Cd) of the gas tank model with smooth surface (γ=0) in the uniform flow field as well as the results of the previous studies obtain from Yao et al. [29], Liu et al. [30], Güven et al. [31], and Wieselsberger [2]. When Re < 6.0 × 105, the Cd is basically unchanged. With the increase of the Reynolds number (6.0 × 105 < Re < 1.0 × 106), the Cd increases slowly, but the trend is not significant. When Re > 1.0 × 106, the Cd gradually kept constant. Generally, in the region of 4.0 × 105 < Re < 1.0 × 106, the change of Cd of the gas tank model with the smooth surface is not significant, and the value of Cd is approximately equal to 0.3–0.35. The test results are close to those obtained by Liu et al. [30] and Wieselsberger [2]. However, the test results of Cd in this paper are smaller than those obtained by Yao et al. [29] in the whole Reynolds number region (4.0 × 105<Re < 1.0 × 106). In order to suppress the end effect of the flow field of the test model, Yao et al. [29] fixed the two square end plates on the upper and lower ends of the smooth cylindrical model. Therefore, the results of deviation are mainly caused by the three-dimensional effect of the model.TheCd of the gas tank model with surface roughness (γ=0.0386,0.0771) in the uniform flow field are shown in Figures 8(c) and 8(e), respectively, and the results were compared with those obtained by Fage and Warsap [19] and Güven et al. [31]. The Cd of the gas tank model with surface roughness decreased from 0.9 to 0.7 slowly with the increase of the Reynolds number (3.0 × 105 < Re < 9.0 × 105). The variety trend of Cd is almost the same in two different surface roughness. When γ=0.0386, the Cd of this paper is smaller than those obtained by Güven et al.[31]. This is mainly due to the different surface roughness of these two tests. When γ=0.0771, the test results in this paper are smaller than the results obtained by Güven et al. [31], but it is closer to the results obtained by Fage and Warsap [19].(2) Detail Results Obtained in ABL. In order to further analyze the effect of the Reynolds number on Cd, the Cd of the gas tank model with the smooth surface in Type A flow field are shown in Figure 8(b) and the results were compared with those obtained by Cheng et al. [26]. Cheng et al. [26] placed a cooling tower model similar to the gas tank with different surface roughness in Type B flow field to study the wind load characteristics in this paper. It is difficult to find the same experimental results as the wind field type in this paper; therefore, the comparison of Cd between Cheng et al. [26] and this paper is still necessary. Due to turbulence, the Cd results of the smooth surface in the ABL are more dispersed than those in uniform flow. The Cd of the measurement point with different Z/L keep constant basically in the whole region of the Reynolds number (4.0 × 105 < Re < 1.0 × 106). The Cd of the smooth surface in this paper are larger than those obtained by Cheng et al. [26] in the whole region of the Reynolds number. But the deviation is not significant.TheCd of the gas tank model with surface roughness (γ=0.0386,0.0771) in ABL are shown in Figures 8(d) and 8(f), respectively, and the results were compared with those obtained by Cheng et al. [26]. When γ=0.0386, the Cd of the gas tank decreased from 1.0 to 0.75 with the increase of the Reynolds number (3.0 × 105 < Re < 9.0 × 105). In the region of 5.0 × 105 < Re < 9.0 × 105, the Cd in this paper are small than those obtained by Cheng et al. [26]. And the deviation increases in the high Reynolds number region. When γ=0.0771, the Cd keeps constant in the whole region of the Reynolds number. The value of the Cd is approximately equal to 0.8. However, there is a deviation between the test results of this paper and Cheng et al. [26], which is mainly caused by the large difference in the surface roughness of the model.


#### 3.1.2. Minimum Pressure CoefficientCpmin

(1) Detail Results Obtained in Uniform Flow Field. Figure 9(a) shows Cpmin results of the gas tank model with the smooth surface (γ=0) in the uniform flow field as well as the those of previous studies obtained by Cheng et al. [26], Güven et al. [30], and Van Nunen et al. [32]. When γ=0, the Cpmin in the middle section of the gas tank model is close to the results obtained by et al. [26], Güven et al. [31], and Van Nunen et al. [32]. For the smooth surface model, the Cpmin increases from −2.7 to −2.3. However, there is a deviation between the Cpmin of the upper and lower measuring points and that of the middle measuring points, which is mainly due to the three-dimensional effect of the test.With the increase of surface roughness, theCpmin of the gas tank model increases significantly to −0.7 and keep constant in the whole region of the Reynolds number, which is consist with those obtained by Cheng et al. [26]. The deviation of Cpmin between the end and middle section of the gas tank model is not significant.(2) Detail Results Obtained in ABL. Different from the test results in the uniform flow field, the deviation of Cpmin on end and middle section of the gas tank model gradually decreases. When γ=0, the Cpmin of the gas tank model increases slowly from −2.7 to −2.4 with the increase of the Reynolds number, which is consist with the results obtained by Cheng et al. [26].With the increase of surface roughness, theCpmin of the gas tank model in ABL increases from −2.5 to −0.75, which is same as the results in the uniform flow field. Whether the surface roughness is 0.0386 or 0.0771, the Cpmin results of this paper are very close to those obtained by Cheng et al. [26].To sum up, theCd and Cpmin tended to keep constant in high Re region. When Re > 6 × 105, reference wind speed had little effect on the Cd and Cpmin. The Cd and Cpmin of the gas tank had the same trend in uniform flow and turbulent flow field. With the increase of Re, the height of measurement points had little effect on wind pressure distribution of the gas tank. The Cd and Cpmin of different measuring layers were gradually approaching in the high Re regime.In the uniform flow field, theCd and Cpmin of both the smooth and rough surface were close to that of the previous literature. In the ABL turbulent flow field, roughness on the surface promotes the transition of the boundary layer from laminar to turbulent, and the minimum value of Cd increases with increasing k/s.The turbulence of flow field made theCpmin increase. This phenomenon was most obvious in the smooth surface model. For the smooth surface model, the Cpmin increases from −2.7 to −2.3. However, with the increase of surface roughness, the effects of turbulence on Cpmin was not significant. For γ=0.0771, in both uniform and ABL turbulent flow field, the Cpmin was approximately equal to −0.7, which remained basically unchanged.TheCd and Cpmin tended to be stable in high Re region. When Re > 0.6 × 106, reference wind speed had little effect on the Cd and Cpmin. The Cd and Cpmin of the gas tank had the same trend in the uniform flow and turbulent flow field.With the increase of Re, the height of measurement points had little effect on wind pressure distribution of the gas tank. TheCd and Cpmin of different measuring layers were gradually approaching in the high Re regime.


#### 3.1.3. Effect of Reynolds Number on Wind Pressure Coefficient

Figure10 showed the fluctuating (CpRMS) and mean wind pressure (Cp) distribution along the annular angle of each layer. For space reasons, only the typical height of wind pressure distribution was listed (1440 mm from ground level).Figure 10
Effect of the Reynolds number on (a, c, e) fluctuating and (b, d, f) local mean wind pressure coefficient. (a, b)γ = 0, (c, d) γ = 0.0386, and (e, f) γ = 0.0771.
(a)
(b)
(c)
(d)
(e)
(f)As shown in Figure10, when the experimental wind speed was greater than 7.6 m/s, the corresponding Re > 6 × 105, the effects of Re on CpRMS and Cp were limited, which were different from theoretical research about flow around the cylinder. This is because the existence of roughness promotes makes the wind load keep constant.


### 3.2. Effect of Roughness on Wind Pressure Coefficient

When Re > 6 × 105, the variation of the wind pressure coefficient was not significant. In order to simulate the realistic Re effect, the experimental reference wind speed would be determined to 10.5 m/s (corresponding Re ≈ 1.0 × 106), which ensure that the Reynolds number of the flow around the gas tank had been in the supercritical region.It should be noted that there is an experiment worst point which is always the one at the lowest Re (lowest velocity) when any pressure measurement and any velocity measurement will have the biggest uncertainty as a percentage of that measured value. Because of the definition ofCp, there will be uncertainty in any measured surface pressure which can be quantified by the stated accuracy of the pressure transducer. Often it is stated as X% of the full-scale range of the transducer. Thus, if the transducer can measure a differential pressure up to a stated maximum of 1000 Pa and any measurement is accurate to 0.5% of that value, then any pressure can be measured to the nearest 5 Pa. It means that if, during a measurement, the measured pressure is only 100 Pa, the accuracy will be +/−(5/100) × 100% = 5% of the measured value.On top of this, there will be a statistical uncertainty based on the total number of samples used to form an average pressure. Usually, in order to ensure the accuracy of data, it is necessary to have enough samples.


#### 3.2.1. Effect of Measurement Point Height on Wind Pressure Coefficient

Figure11 showed the effects of height of measurement point on the wind pressure coefficient (CpRMS and Cp) with different surface roughness under reference wind speed (10.5 m/s).Figure 11
Effect of measurement point height on the fluctuating and local mean wind pressure coefficient. (a, c, e) Type A turbulent flow field and (b, d, f) uniform flow. (a, b)γ = 0, (c, d) γ = 0.0386, and (e, f) γ = 0.0771.
(a)
(b)
(c)
(d)
(e)
(f)As shown in Figure11, when the surface roughness of the structure was determined, the CpRMS and Cp of middle measurement layers of the model were coincident with each other. However, because of the three-dimensional effect, the wind pressure coefficient of the top and bottom measurement layer had a slight deviation. It was found that when the Re of the gas tank model was in the supercritical regime, the height of the measurement layer had little effect on the wind pressure distribution of the gas tank model. Therefore, in the subsequent analysis about the effect of surface roughness on the wind pressure distribution of the gas tank structure, the 8th level (Z/L = 0.525) measuring experimental results under reference wind speed (10.5 m/s) was used to analyze the wind load uniformly.


#### 3.2.2. Effect of Spacing Ratio on Wind Pressure Coefficient

If the width of the rough strip increases gradually, the roughness value would be close to the center pitchs, which would lead to form a smooth surface cylinder with a new diameter. In this state, it is obviously not suitable to analyze the effects of roughness on wind pressure distribution without preconditions. Therefore, a new parameter named as spacing ratio would be discussed in this section, by which the applicable condition of roughness effecting the wind pressure distribution would be determined:(6)λ=s−Bs,where s is the center distance of rough strip and B is the width of the rough strip.As shown in Figure12, when λ<0.9, the effect of roughness on the wind pressure coefficient was limited. Therefore, experimental data with the spacing ratio greater than 0.9 would be used to investigate the effects of roughness on the wind pressure coefficient on the model surface.Figure 12
Effects of the spacing ratio on wind pressure distribution. (a, c, e) Fluctuating wind pressure coefficient and (b, d, f) mean wind pressure coefficient. (a, b)γ = 0, (c, d) γ = 0.0386, and (e, f) γ = 0.0771.
(a)
(b)
(c)
(d)
(e)
(f)


#### 3.2.3. Effects of Ring Reinforcing Strip on Wind Pressure Coefficient

As shown in Figure13, no matter in the ABL turbulent flow field or uniform flow field, the effects of reinforced strips on the mean wind pressure coefficient was limited. In the test cases, the Cpmax for the upwind surface was about 0.95, the Cpmin was 0.65, the Cpb was -0.39, and the θb was basically around 95°. The wind pressure coefficient of the structure was unchanged when the circular reinforcing strip was removed and only the rough condition of the vertical rough strip was present. However, the vertical rough strip conditions were removed, the Cpmin had a significant change, from the initial −0.65 to −2.3, the Cpb increased slightly to about 0.28, and the θb increased to 140°. For the fluctuating wind pressure coefficient, the effects of the reinforcing strip were limited. And the fluctuating wind pressure coefficient was almost coincident under two ceases.Figure 13
Effects of stiffeners on the wind pressure coefficient: (a) fluctuating wind pressure coefficient and (b) mean wind pressure coefficient.
(a)
(b)Whether in the ABL turbulent or smooth flow, compared with the column, the ring reinforcement had limited effects on the wind pressure coefficient. So, the impact of ring reinforcement would be ignored.Based on the abovementioned analysis, the wind tunnel test results with the spacing ratio greater than 0.9 would be analyzed in this section.Figure14 showed the Cpmax affected by roughness was limited, and its value was about 0.95. However, the effects of roughness on the negative pressure area was significant, the Cpmin was 2.3 without roughness, and with an increase of roughness, its value increased to 0.65 significantly. The θmin was 90° under the case of the smooth wall, whereas considering the rough case, the angle was about 80°. The θb was continuously moved forward with the increase of roughness, the θb was shifted from 140° to 90°, and the Cpb was reduced from 0.28 to −0.4.Figure 14
Effects of roughness on wind pressure: (a) fluctuating wind pressure coefficient and (b) mean wind pressure coefficient.
(a)
(b)The main parameters of the wind pressure coefficient distribution were listed in Figure15.Figure 15
Effects of roughness onCpmin and θb: (a) minimum pressure coefficient and (b) azimuthal angle of separation point.
(a)
(b)To sum up, with the structural surface roughness increased, theCpmin and Cpb increased, and the θb constantly reduced. According to Figure 15, the results of Cpmin in this paper is larger than those obtained by Zou et al. [25], which may be caused by different structure shape and spacing ratios. The separation angel test results in this paper are consistent with those obtained by Zou et al. [25].As a result, the increase of roughness makes the gas tank structure wind load distribution tend to be uniform, which was advantageous to wind resistant design.Figure16 showed the comparison between the measured data of the wind pressure on the surface of the real gas tank, in which gas tank capacity is 300000 m3 and the surface roughness is about 0.0772. The figure showed that the measured wind pressure coefficient agrees well with the experiment value.Figure 16
Comparison with the measured value and test value for the wind pressure coefficient.


## 3.1. Effect of Reynolds Number on Drag Coefficient and Minimum Pressure Coefficient

The effects of Reynolds number on the drag coefficient (Cd) and minimum pressure coefficient (Cpmin) were shown in Figures 8 and 9. For space reasons, only partial test results are listed.Figure 8
Effect of the Reynolds number on the drag coefficient of each measurement layer. (a, c, e) Uniform flow and (b, d, f) Type A turbulent flow field. (a, b)γ = 0, (c, d) γ = 0.0386, and (e, f) γ = 0.0771.
(a)
(b)
(c)
(d)
(e)
(f)Figure 9
Effect of the Reynolds number on minimum negative wind pressure coefficient. (a, c, e) Uniform flow and (b, d, f) Type A turbulent flow field. (a, b)γ = 0, (c, d) γ = 0.0386, and (e, f) γ = 0.0771.
(a)
(b)
(c)
(d)
(e)
(f)


### 3.1.1. Drag CoefficientCd

The drag coefficient of each measurement layer of the gas tank was obtained by weighted averaging the wind pressure data of each measurement point:(5)Cd=πN∑i=1nCpicosθ,where θ represents the azimuthal angle of the ith measurement point and n and N represent the number of weighted average points and total points for each layer. In this section, n = N = 32.(1) Detail Results Obtained in Uniform Flow Field. Figure 8(a) shows the drag coefficient (Cd) of the gas tank model with smooth surface (γ=0) in the uniform flow field as well as the results of the previous studies obtain from Yao et al. [29], Liu et al. [30], Güven et al. [31], and Wieselsberger [2]. When Re < 6.0 × 105, the Cd is basically unchanged. With the increase of the Reynolds number (6.0 × 105 < Re < 1.0 × 106), the Cd increases slowly, but the trend is not significant. When Re > 1.0 × 106, the Cd gradually kept constant. Generally, in the region of 4.0 × 105 < Re < 1.0 × 106, the change of Cd of the gas tank model with the smooth surface is not significant, and the value of Cd is approximately equal to 0.3–0.35. The test results are close to those obtained by Liu et al. [30] and Wieselsberger [2]. However, the test results of Cd in this paper are smaller than those obtained by Yao et al. [29] in the whole Reynolds number region (4.0 × 105<Re < 1.0 × 106). In order to suppress the end effect of the flow field of the test model, Yao et al. [29] fixed the two square end plates on the upper and lower ends of the smooth cylindrical model. Therefore, the results of deviation are mainly caused by the three-dimensional effect of the model.TheCd of the gas tank model with surface roughness (γ=0.0386,0.0771) in the uniform flow field are shown in Figures 8(c) and 8(e), respectively, and the results were compared with those obtained by Fage and Warsap [19] and Güven et al. [31]. The Cd of the gas tank model with surface roughness decreased from 0.9 to 0.7 slowly with the increase of the Reynolds number (3.0 × 105 < Re < 9.0 × 105). The variety trend of Cd is almost the same in two different surface roughness. When γ=0.0386, the Cd of this paper is smaller than those obtained by Güven et al.[31]. This is mainly due to the different surface roughness of these two tests. When γ=0.0771, the test results in this paper are smaller than the results obtained by Güven et al. [31], but it is closer to the results obtained by Fage and Warsap [19].(2) Detail Results Obtained in ABL. In order to further analyze the effect of the Reynolds number on Cd, the Cd of the gas tank model with the smooth surface in Type A flow field are shown in Figure 8(b) and the results were compared with those obtained by Cheng et al. [26]. Cheng et al. [26] placed a cooling tower model similar to the gas tank with different surface roughness in Type B flow field to study the wind load characteristics in this paper. It is difficult to find the same experimental results as the wind field type in this paper; therefore, the comparison of Cd between Cheng et al. [26] and this paper is still necessary. Due to turbulence, the Cd results of the smooth surface in the ABL are more dispersed than those in uniform flow. The Cd of the measurement point with different Z/L keep constant basically in the whole region of the Reynolds number (4.0 × 105 < Re < 1.0 × 106). The Cd of the smooth surface in this paper are larger than those obtained by Cheng et al. [26] in the whole region of the Reynolds number. But the deviation is not significant.TheCd of the gas tank model with surface roughness (γ=0.0386,0.0771) in ABL are shown in Figures 8(d) and 8(f), respectively, and the results were compared with those obtained by Cheng et al. [26]. When γ=0.0386, the Cd of the gas tank decreased from 1.0 to 0.75 with the increase of the Reynolds number (3.0 × 105 < Re < 9.0 × 105). In the region of 5.0 × 105 < Re < 9.0 × 105, the Cd in this paper are small than those obtained by Cheng et al. [26]. And the deviation increases in the high Reynolds number region. When γ=0.0771, the Cd keeps constant in the whole region of the Reynolds number. The value of the Cd is approximately equal to 0.8. However, there is a deviation between the test results of this paper and Cheng et al. [26], which is mainly caused by the large difference in the surface roughness of the model.


### 3.1.2. Minimum Pressure CoefficientCpmin

(1) Detail Results Obtained in Uniform Flow Field. Figure 9(a) shows Cpmin results of the gas tank model with the smooth surface (γ=0) in the uniform flow field as well as the those of previous studies obtained by Cheng et al. [26], Güven et al. [30], and Van Nunen et al. [32]. When γ=0, the Cpmin in the middle section of the gas tank model is close to the results obtained by et al. [26], Güven et al. [31], and Van Nunen et al. [32]. For the smooth surface model, the Cpmin increases from −2.7 to −2.3. However, there is a deviation between the Cpmin of the upper and lower measuring points and that of the middle measuring points, which is mainly due to the three-dimensional effect of the test.With the increase of surface roughness, theCpmin of the gas tank model increases significantly to −0.7 and keep constant in the whole region of the Reynolds number, which is consist with those obtained by Cheng et al. [26]. The deviation of Cpmin between the end and middle section of the gas tank model is not significant.(2) Detail Results Obtained in ABL. Different from the test results in the uniform flow field, the deviation of Cpmin on end and middle section of the gas tank model gradually decreases. When γ=0, the Cpmin of the gas tank model increases slowly from −2.7 to −2.4 with the increase of the Reynolds number, which is consist with the results obtained by Cheng et al. [26].With the increase of surface roughness, theCpmin of the gas tank model in ABL increases from −2.5 to −0.75, which is same as the results in the uniform flow field. Whether the surface roughness is 0.0386 or 0.0771, the Cpmin results of this paper are very close to those obtained by Cheng et al. [26].To sum up, theCd and Cpmin tended to keep constant in high Re region. When Re > 6 × 105, reference wind speed had little effect on the Cd and Cpmin. The Cd and Cpmin of the gas tank had the same trend in uniform flow and turbulent flow field. With the increase of Re, the height of measurement points had little effect on wind pressure distribution of the gas tank. The Cd and Cpmin of different measuring layers were gradually approaching in the high Re regime.In the uniform flow field, theCd and Cpmin of both the smooth and rough surface were close to that of the previous literature. In the ABL turbulent flow field, roughness on the surface promotes the transition of the boundary layer from laminar to turbulent, and the minimum value of Cd increases with increasing k/s.The turbulence of flow field made theCpmin increase. This phenomenon was most obvious in the smooth surface model. For the smooth surface model, the Cpmin increases from −2.7 to −2.3. However, with the increase of surface roughness, the effects of turbulence on Cpmin was not significant. For γ=0.0771, in both uniform and ABL turbulent flow field, the Cpmin was approximately equal to −0.7, which remained basically unchanged.TheCd and Cpmin tended to be stable in high Re region. When Re > 0.6 × 106, reference wind speed had little effect on the Cd and Cpmin. The Cd and Cpmin of the gas tank had the same trend in the uniform flow and turbulent flow field.With the increase of Re, the height of measurement points had little effect on wind pressure distribution of the gas tank. TheCd and Cpmin of different measuring layers were gradually approaching in the high Re regime.


### 3.1.3. Effect of Reynolds Number on Wind Pressure Coefficient

Figure10 showed the fluctuating (CpRMS) and mean wind pressure (Cp) distribution along the annular angle of each layer. For space reasons, only the typical height of wind pressure distribution was listed (1440 mm from ground level).Figure 10
Effect of the Reynolds number on (a, c, e) fluctuating and (b, d, f) local mean wind pressure coefficient. (a, b)γ = 0, (c, d) γ = 0.0386, and (e, f) γ = 0.0771.
(a)
(b)
(c)
(d)
(e)
(f)As shown in Figure10, when the experimental wind speed was greater than 7.6 m/s, the corresponding Re > 6 × 105, the effects of Re on CpRMS and Cp were limited, which were different from theoretical research about flow around the cylinder. This is because the existence of roughness promotes makes the wind load keep constant.


## 3.1.1. Drag CoefficientCd

The drag coefficient of each measurement layer of the gas tank was obtained by weighted averaging the wind pressure data of each measurement point:(5)Cd=πN∑i=1nCpicosθ,where θ represents the azimuthal angle of the ith measurement point and n and N represent the number of weighted average points and total points for each layer. In this section, n = N = 32.(1) Detail Results Obtained in Uniform Flow Field. Figure 8(a) shows the drag coefficient (Cd) of the gas tank model with smooth surface (γ=0) in the uniform flow field as well as the results of the previous studies obtain from Yao et al. [29], Liu et al. [30], Güven et al. [31], and Wieselsberger [2]. When Re < 6.0 × 105, the Cd is basically unchanged. With the increase of the Reynolds number (6.0 × 105 < Re < 1.0 × 106), the Cd increases slowly, but the trend is not significant. When Re > 1.0 × 106, the Cd gradually kept constant. Generally, in the region of 4.0 × 105 < Re < 1.0 × 106, the change of Cd of the gas tank model with the smooth surface is not significant, and the value of Cd is approximately equal to 0.3–0.35. The test results are close to those obtained by Liu et al. [30] and Wieselsberger [2]. However, the test results of Cd in this paper are smaller than those obtained by Yao et al. [29] in the whole Reynolds number region (4.0 × 105<Re < 1.0 × 106). In order to suppress the end effect of the flow field of the test model, Yao et al. [29] fixed the two square end plates on the upper and lower ends of the smooth cylindrical model. Therefore, the results of deviation are mainly caused by the three-dimensional effect of the model.TheCd of the gas tank model with surface roughness (γ=0.0386,0.0771) in the uniform flow field are shown in Figures 8(c) and 8(e), respectively, and the results were compared with those obtained by Fage and Warsap [19] and Güven et al. [31]. The Cd of the gas tank model with surface roughness decreased from 0.9 to 0.7 slowly with the increase of the Reynolds number (3.0 × 105 < Re < 9.0 × 105). The variety trend of Cd is almost the same in two different surface roughness. When γ=0.0386, the Cd of this paper is smaller than those obtained by Güven et al.[31]. This is mainly due to the different surface roughness of these two tests. When γ=0.0771, the test results in this paper are smaller than the results obtained by Güven et al. [31], but it is closer to the results obtained by Fage and Warsap [19].(2) Detail Results Obtained in ABL. In order to further analyze the effect of the Reynolds number on Cd, the Cd of the gas tank model with the smooth surface in Type A flow field are shown in Figure 8(b) and the results were compared with those obtained by Cheng et al. [26]. Cheng et al. [26] placed a cooling tower model similar to the gas tank with different surface roughness in Type B flow field to study the wind load characteristics in this paper. It is difficult to find the same experimental results as the wind field type in this paper; therefore, the comparison of Cd between Cheng et al. [26] and this paper is still necessary. Due to turbulence, the Cd results of the smooth surface in the ABL are more dispersed than those in uniform flow. The Cd of the measurement point with different Z/L keep constant basically in the whole region of the Reynolds number (4.0 × 105 < Re < 1.0 × 106). The Cd of the smooth surface in this paper are larger than those obtained by Cheng et al. [26] in the whole region of the Reynolds number. But the deviation is not significant.TheCd of the gas tank model with surface roughness (γ=0.0386,0.0771) in ABL are shown in Figures 8(d) and 8(f), respectively, and the results were compared with those obtained by Cheng et al. [26]. When γ=0.0386, the Cd of the gas tank decreased from 1.0 to 0.75 with the increase of the Reynolds number (3.0 × 105 < Re < 9.0 × 105). In the region of 5.0 × 105 < Re < 9.0 × 105, the Cd in this paper are small than those obtained by Cheng et al. [26]. And the deviation increases in the high Reynolds number region. When γ=0.0771, the Cd keeps constant in the whole region of the Reynolds number. The value of the Cd is approximately equal to 0.8. However, there is a deviation between the test results of this paper and Cheng et al. [26], which is mainly caused by the large difference in the surface roughness of the model.


## 3.1.2. Minimum Pressure CoefficientCpmin

(1) Detail Results Obtained in Uniform Flow Field. Figure 9(a) shows Cpmin results of the gas tank model with the smooth surface (γ=0) in the uniform flow field as well as the those of previous studies obtained by Cheng et al. [26], Güven et al. [30], and Van Nunen et al. [32]. When γ=0, the Cpmin in the middle section of the gas tank model is close to the results obtained by et al. [26], Güven et al. [31], and Van Nunen et al. [32]. For the smooth surface model, the Cpmin increases from −2.7 to −2.3. However, there is a deviation between the Cpmin of the upper and lower measuring points and that of the middle measuring points, which is mainly due to the three-dimensional effect of the test.With the increase of surface roughness, theCpmin of the gas tank model increases significantly to −0.7 and keep constant in the whole region of the Reynolds number, which is consist with those obtained by Cheng et al. [26]. The deviation of Cpmin between the end and middle section of the gas tank model is not significant.(2) Detail Results Obtained in ABL. Different from the test results in the uniform flow field, the deviation of Cpmin on end and middle section of the gas tank model gradually decreases. When γ=0, the Cpmin of the gas tank model increases slowly from −2.7 to −2.4 with the increase of the Reynolds number, which is consist with the results obtained by Cheng et al. [26].With the increase of surface roughness, theCpmin of the gas tank model in ABL increases from −2.5 to −0.75, which is same as the results in the uniform flow field. Whether the surface roughness is 0.0386 or 0.0771, the Cpmin results of this paper are very close to those obtained by Cheng et al. [26].To sum up, theCd and Cpmin tended to keep constant in high Re region. When Re > 6 × 105, reference wind speed had little effect on the Cd and Cpmin. The Cd and Cpmin of the gas tank had the same trend in uniform flow and turbulent flow field. With the increase of Re, the height of measurement points had little effect on wind pressure distribution of the gas tank. The Cd and Cpmin of different measuring layers were gradually approaching in the high Re regime.In the uniform flow field, theCd and Cpmin of both the smooth and rough surface were close to that of the previous literature. In the ABL turbulent flow field, roughness on the surface promotes the transition of the boundary layer from laminar to turbulent, and the minimum value of Cd increases with increasing k/s.The turbulence of flow field made theCpmin increase. This phenomenon was most obvious in the smooth surface model. For the smooth surface model, the Cpmin increases from −2.7 to −2.3. However, with the increase of surface roughness, the effects of turbulence on Cpmin was not significant. For γ=0.0771, in both uniform and ABL turbulent flow field, the Cpmin was approximately equal to −0.7, which remained basically unchanged.TheCd and Cpmin tended to be stable in high Re region. When Re > 0.6 × 106, reference wind speed had little effect on the Cd and Cpmin. The Cd and Cpmin of the gas tank had the same trend in the uniform flow and turbulent flow field.With the increase of Re, the height of measurement points had little effect on wind pressure distribution of the gas tank. TheCd and Cpmin of different measuring layers were gradually approaching in the high Re regime.


## 3.1.3. Effect of Reynolds Number on Wind Pressure Coefficient

Figure10 showed the fluctuating (CpRMS) and mean wind pressure (Cp) distribution along the annular angle of each layer. For space reasons, only the typical height of wind pressure distribution was listed (1440 mm from ground level).Figure 10
Effect of the Reynolds number on (a, c, e) fluctuating and (b, d, f) local mean wind pressure coefficient. (a, b)γ = 0, (c, d) γ = 0.0386, and (e, f) γ = 0.0771.
(a)
(b)
(c)
(d)
(e)
(f)As shown in Figure10, when the experimental wind speed was greater than 7.6 m/s, the corresponding Re > 6 × 105, the effects of Re on CpRMS and Cp were limited, which were different from theoretical research about flow around the cylinder. This is because the existence of roughness promotes makes the wind load keep constant.


## 3.2. Effect of Roughness on Wind Pressure Coefficient

When Re > 6 × 105, the variation of the wind pressure coefficient was not significant. In order to simulate the realistic Re effect, the experimental reference wind speed would be determined to 10.5 m/s (corresponding Re ≈ 1.0 × 106), which ensure that the Reynolds number of the flow around the gas tank had been in the supercritical region.It should be noted that there is an experiment worst point which is always the one at the lowest Re (lowest velocity) when any pressure measurement and any velocity measurement will have the biggest uncertainty as a percentage of that measured value. Because of the definition ofCp, there will be uncertainty in any measured surface pressure which can be quantified by the stated accuracy of the pressure transducer. Often it is stated as X% of the full-scale range of the transducer. Thus, if the transducer can measure a differential pressure up to a stated maximum of 1000 Pa and any measurement is accurate to 0.5% of that value, then any pressure can be measured to the nearest 5 Pa. It means that if, during a measurement, the measured pressure is only 100 Pa, the accuracy will be +/−(5/100) × 100% = 5% of the measured value.On top of this, there will be a statistical uncertainty based on the total number of samples used to form an average pressure. Usually, in order to ensure the accuracy of data, it is necessary to have enough samples.


### 3.2.1. Effect of Measurement Point Height on Wind Pressure Coefficient

Figure11 showed the effects of height of measurement point on the wind pressure coefficient (CpRMS and Cp) with different surface roughness under reference wind speed (10.5 m/s).Figure 11
Effect of measurement point height on the fluctuating and local mean wind pressure coefficient. (a, c, e) Type A turbulent flow field and (b, d, f) uniform flow. (a, b)γ = 0, (c, d) γ = 0.0386, and (e, f) γ = 0.0771.
(a)
(b)
(c)
(d)
(e)
(f)As shown in Figure11, when the surface roughness of the structure was determined, the CpRMS and Cp of middle measurement layers of the model were coincident with each other. However, because of the three-dimensional effect, the wind pressure coefficient of the top and bottom measurement layer had a slight deviation. It was found that when the Re of the gas tank model was in the supercritical regime, the height of the measurement layer had little effect on the wind pressure distribution of the gas tank model. Therefore, in the subsequent analysis about the effect of surface roughness on the wind pressure distribution of the gas tank structure, the 8th level (Z/L = 0.525) measuring experimental results under reference wind speed (10.5 m/s) was used to analyze the wind load uniformly.


### 3.2.2. Effect of Spacing Ratio on Wind Pressure Coefficient

If the width of the rough strip increases gradually, the roughness value would be close to the center pitchs, which would lead to form a smooth surface cylinder with a new diameter. In this state, it is obviously not suitable to analyze the effects of roughness on wind pressure distribution without preconditions. Therefore, a new parameter named as spacing ratio would be discussed in this section, by which the applicable condition of roughness effecting the wind pressure distribution would be determined:(6)λ=s−Bs,where s is the center distance of rough strip and B is the width of the rough strip.As shown in Figure12, when λ<0.9, the effect of roughness on the wind pressure coefficient was limited. Therefore, experimental data with the spacing ratio greater than 0.9 would be used to investigate the effects of roughness on the wind pressure coefficient on the model surface.Figure 12
Effects of the spacing ratio on wind pressure distribution. (a, c, e) Fluctuating wind pressure coefficient and (b, d, f) mean wind pressure coefficient. (a, b)γ = 0, (c, d) γ = 0.0386, and (e, f) γ = 0.0771.
(a)
(b)
(c)
(d)
(e)
(f)


### 3.2.3. Effects of Ring Reinforcing Strip on Wind Pressure Coefficient

As shown in Figure13, no matter in the ABL turbulent flow field or uniform flow field, the effects of reinforced strips on the mean wind pressure coefficient was limited. In the test cases, the Cpmax for the upwind surface was about 0.95, the Cpmin was 0.65, the Cpb was -0.39, and the θb was basically around 95°. The wind pressure coefficient of the structure was unchanged when the circular reinforcing strip was removed and only the rough condition of the vertical rough strip was present. However, the vertical rough strip conditions were removed, the Cpmin had a significant change, from the initial −0.65 to −2.3, the Cpb increased slightly to about 0.28, and the θb increased to 140°. For the fluctuating wind pressure coefficient, the effects of the reinforcing strip were limited. And the fluctuating wind pressure coefficient was almost coincident under two ceases.Figure 13
Effects of stiffeners on the wind pressure coefficient: (a) fluctuating wind pressure coefficient and (b) mean wind pressure coefficient.
(a)
(b)Whether in the ABL turbulent or smooth flow, compared with the column, the ring reinforcement had limited effects on the wind pressure coefficient. So, the impact of ring reinforcement would be ignored.Based on the abovementioned analysis, the wind tunnel test results with the spacing ratio greater than 0.9 would be analyzed in this section.Figure14 showed the Cpmax affected by roughness was limited, and its value was about 0.95. However, the effects of roughness on the negative pressure area was significant, the Cpmin was 2.3 without roughness, and with an increase of roughness, its value increased to 0.65 significantly. The θmin was 90° under the case of the smooth wall, whereas considering the rough case, the angle was about 80°. The θb was continuously moved forward with the increase of roughness, the θb was shifted from 140° to 90°, and the Cpb was reduced from 0.28 to −0.4.Figure 14
Effects of roughness on wind pressure: (a) fluctuating wind pressure coefficient and (b) mean wind pressure coefficient.
(a)
(b)The main parameters of the wind pressure coefficient distribution were listed in Figure15.Figure 15
Effects of roughness onCpmin and θb: (a) minimum pressure coefficient and (b) azimuthal angle of separation point.
(a)
(b)To sum up, with the structural surface roughness increased, theCpmin and Cpb increased, and the θb constantly reduced. According to Figure 15, the results of Cpmin in this paper is larger than those obtained by Zou et al. [25], which may be caused by different structure shape and spacing ratios. The separation angel test results in this paper are consistent with those obtained by Zou et al. [25].As a result, the increase of roughness makes the gas tank structure wind load distribution tend to be uniform, which was advantageous to wind resistant design.Figure16 showed the comparison between the measured data of the wind pressure on the surface of the real gas tank, in which gas tank capacity is 300000 m3 and the surface roughness is about 0.0772. The figure showed that the measured wind pressure coefficient agrees well with the experiment value.Figure 16
Comparison with the measured value and test value for the wind pressure coefficient.


## 3.2.1. Effect of Measurement Point Height on Wind Pressure Coefficient

Figure11 showed the effects of height of measurement point on the wind pressure coefficient (CpRMS and Cp) with different surface roughness under reference wind speed (10.5 m/s).Figure 11
Effect of measurement point height on the fluctuating and local mean wind pressure coefficient. (a, c, e) Type A turbulent flow field and (b, d, f) uniform flow. (a, b)γ = 0, (c, d) γ = 0.0386, and (e, f) γ = 0.0771.
(a)
(b)
(c)
(d)
(e)
(f)As shown in Figure11, when the surface roughness of the structure was determined, the CpRMS and Cp of middle measurement layers of the model were coincident with each other. However, because of the three-dimensional effect, the wind pressure coefficient of the top and bottom measurement layer had a slight deviation. It was found that when the Re of the gas tank model was in the supercritical regime, the height of the measurement layer had little effect on the wind pressure distribution of the gas tank model. Therefore, in the subsequent analysis about the effect of surface roughness on the wind pressure distribution of the gas tank structure, the 8th level (Z/L = 0.525) measuring experimental results under reference wind speed (10.5 m/s) was used to analyze the wind load uniformly.


## 3.2.2. Effect of Spacing Ratio on Wind Pressure Coefficient

If the width of the rough strip increases gradually, the roughness value would be close to the center pitchs, which would lead to form a smooth surface cylinder with a new diameter. In this state, it is obviously not suitable to analyze the effects of roughness on wind pressure distribution without preconditions. Therefore, a new parameter named as spacing ratio would be discussed in this section, by which the applicable condition of roughness effecting the wind pressure distribution would be determined:(6)λ=s−Bs,where s is the center distance of rough strip and B is the width of the rough strip.As shown in Figure12, when λ<0.9, the effect of roughness on the wind pressure coefficient was limited. Therefore, experimental data with the spacing ratio greater than 0.9 would be used to investigate the effects of roughness on the wind pressure coefficient on the model surface.Figure 12
Effects of the spacing ratio on wind pressure distribution. (a, c, e) Fluctuating wind pressure coefficient and (b, d, f) mean wind pressure coefficient. (a, b)γ = 0, (c, d) γ = 0.0386, and (e, f) γ = 0.0771.
(a)
(b)
(c)
(d)
(e)
(f)


## 3.2.3. Effects of Ring Reinforcing Strip on Wind Pressure Coefficient

As shown in Figure13, no matter in the ABL turbulent flow field or uniform flow field, the effects of reinforced strips on the mean wind pressure coefficient was limited. In the test cases, the Cpmax for the upwind surface was about 0.95, the Cpmin was 0.65, the Cpb was -0.39, and the θb was basically around 95°. The wind pressure coefficient of the structure was unchanged when the circular reinforcing strip was removed and only the rough condition of the vertical rough strip was present. However, the vertical rough strip conditions were removed, the Cpmin had a significant change, from the initial −0.65 to −2.3, the Cpb increased slightly to about 0.28, and the θb increased to 140°. For the fluctuating wind pressure coefficient, the effects of the reinforcing strip were limited. And the fluctuating wind pressure coefficient was almost coincident under two ceases.Figure 13
Effects of stiffeners on the wind pressure coefficient: (a) fluctuating wind pressure coefficient and (b) mean wind pressure coefficient.
(a)
(b)Whether in the ABL turbulent or smooth flow, compared with the column, the ring reinforcement had limited effects on the wind pressure coefficient. So, the impact of ring reinforcement would be ignored.Based on the abovementioned analysis, the wind tunnel test results with the spacing ratio greater than 0.9 would be analyzed in this section.Figure14 showed the Cpmax affected by roughness was limited, and its value was about 0.95. However, the effects of roughness on the negative pressure area was significant, the Cpmin was 2.3 without roughness, and with an increase of roughness, its value increased to 0.65 significantly. The θmin was 90° under the case of the smooth wall, whereas considering the rough case, the angle was about 80°. The θb was continuously moved forward with the increase of roughness, the θb was shifted from 140° to 90°, and the Cpb was reduced from 0.28 to −0.4.Figure 14
Effects of roughness on wind pressure: (a) fluctuating wind pressure coefficient and (b) mean wind pressure coefficient.
(a)
(b)The main parameters of the wind pressure coefficient distribution were listed in Figure15.Figure 15
Effects of roughness onCpmin and θb: (a) minimum pressure coefficient and (b) azimuthal angle of separation point.
(a)
(b)To sum up, with the structural surface roughness increased, theCpmin and Cpb increased, and the θb constantly reduced. According to Figure 15, the results of Cpmin in this paper is larger than those obtained by Zou et al. [25], which may be caused by different structure shape and spacing ratios. The separation angel test results in this paper are consistent with those obtained by Zou et al. [25].As a result, the increase of roughness makes the gas tank structure wind load distribution tend to be uniform, which was advantageous to wind resistant design.Figure16 showed the comparison between the measured data of the wind pressure on the surface of the real gas tank, in which gas tank capacity is 300000 m3 and the surface roughness is about 0.0772. The figure showed that the measured wind pressure coefficient agrees well with the experiment value.Figure 16
Comparison with the measured value and test value for the wind pressure coefficient.


## 4. Calculation Method

### 4.1. Approximate Calculation of Wind Pressure Coefficient of the Gas Cabinet

The main parameters of the wind pressure coefficient [33, 34] were Cpmax, Cpmin, Cpb, θb, and θmin; through the abovementioned analysis, the effects of roughness on the Cpmax, Cpb, and θmin was limited. The Cpmax was 0.95, the Cpb was −0.35, and the θmin occurred at 80°.Based on the test results, theCpmin and the θb were fitted by empirical equations (7) and (8), respectively:(7)Cpmin=aγb,where a = −0.35 and b = −0.23.(8)θb=b+a−b1+γ/cd,where a = 139.49, b = 79.76, c = 0.02116, and d = 1.172.Obviously, if the surface is smooth (γ=0), it is mathematically meaningless for equation (7), which is not consistent with the results of the flow around a smooth surface cylinder. To ensure the applicability of equation (7), the range of γ should be studied. When γ = 0, according to the results of flow around a cylinder, the Cpmin is about equal to −2.3, which could be used to deduce the applicable range of γ. Therefore, it can be determined that the lower limit value of γ is 3E − 4. In addition, the upper limit value of γ is 0.01. Therefore, in the range of 3E − 4< γ < 0.01, the equation (7) is applicable.The fitting results were shown in Figure17. There was some deviation between the results fitted by equations (7) and (8). For minimum pressure coefficient (Cpmin), due to the limited number of measurement point arranged along the circumference, the real minimum pressure coefficient value may be missed. The fitting uncertainty of θb is mainly due to the definition of θb. According to Figure 6, θb is the angle corresponding to the intersection of two tangent lines which causes some data errors.Figure 17
Fitting results ofCpmin and θb.
(a)
(b)Formula (9) was used to estimate the surface mean wind pressure coefficient along the cyclic distribution curve of the gas cabinet. The fitting result was shown in Figure 18.(9)Cp=Cpmin+1−Cpminsin20.5πθ−θminθmin,0<θ<θmin,Cpmin+Cb−Cpminsin2−0.5πθ−θminθb−θmin,θmin<θ<θb,Cb,θb<θ<π.Figure 18
Fitting results of the shape coefficient at different test conditions (a)γ=0.0386 and (b) γ=0.0771.
(a)
(b)From Figure18, comparing with the results of the previous literature from Niemann [35], the fitting results proposed by the present article were in good agreement with the experimental values. Therefore, the proposed method of estimating the mean wind pressure coefficient of the gas tank could predict the distribution of the wind pressure coefficient on the gas tank surface.


## 4.1. Approximate Calculation of Wind Pressure Coefficient of the Gas Cabinet

The main parameters of the wind pressure coefficient [33, 34] were Cpmax, Cpmin, Cpb, θb, and θmin; through the abovementioned analysis, the effects of roughness on the Cpmax, Cpb, and θmin was limited. The Cpmax was 0.95, the Cpb was −0.35, and the θmin occurred at 80°.Based on the test results, theCpmin and the θb were fitted by empirical equations (7) and (8), respectively:(7)Cpmin=aγb,where a = −0.35 and b = −0.23.(8)θb=b+a−b1+γ/cd,where a = 139.49, b = 79.76, c = 0.02116, and d = 1.172.Obviously, if the surface is smooth (γ=0), it is mathematically meaningless for equation (7), which is not consistent with the results of the flow around a smooth surface cylinder. To ensure the applicability of equation (7), the range of γ should be studied. When γ = 0, according to the results of flow around a cylinder, the Cpmin is about equal to −2.3, which could be used to deduce the applicable range of γ. Therefore, it can be determined that the lower limit value of γ is 3E − 4. In addition, the upper limit value of γ is 0.01. Therefore, in the range of 3E − 4< γ < 0.01, the equation (7) is applicable.The fitting results were shown in Figure17. There was some deviation between the results fitted by equations (7) and (8). For minimum pressure coefficient (Cpmin), due to the limited number of measurement point arranged along the circumference, the real minimum pressure coefficient value may be missed. The fitting uncertainty of θb is mainly due to the definition of θb. According to Figure 6, θb is the angle corresponding to the intersection of two tangent lines which causes some data errors.Figure 17
Fitting results ofCpmin and θb.
(a)
(b)Formula (9) was used to estimate the surface mean wind pressure coefficient along the cyclic distribution curve of the gas cabinet. The fitting result was shown in Figure 18.(9)Cp=Cpmin+1−Cpminsin20.5πθ−θminθmin,0<θ<θmin,Cpmin+Cb−Cpminsin2−0.5πθ−θminθb−θmin,θmin<θ<θb,Cb,θb<θ<π.Figure 18
Fitting results of the shape coefficient at different test conditions (a)γ=0.0386 and (b) γ=0.0771.
(a)
(b)From Figure18, comparing with the results of the previous literature from Niemann [35], the fitting results proposed by the present article were in good agreement with the experimental values. Therefore, the proposed method of estimating the mean wind pressure coefficient of the gas tank could predict the distribution of the wind pressure coefficient on the gas tank surface.


## 5. Conclusion

(1)
When the Reynolds number of the gas tank was in the supercritical regime, the wind load of the gas tank tended to be stable; the effects of Re onCd, Cpmin, CpRMS, and Cp were not significantly. The height of the measuring point had little effect on the wind pressure coefficient.
(2)
Based on the definition of the equivalent roughness, it was suggested that the space ratio of roughness greater than 0.9 should be used to analyze the wind pressure coefficient on the gas tank. By comparing theCpRMS and Cp of the gas tank, the effects of the ring reinforcement on the wind pressure coefficient was limited, which should be ignored.
(3)
The effects of roughness onCpmin and θb was evident; the Cpmin increased from −2.3 to 0.65 with the increase of roughness, and the θb moved from 140° to 90°. However, the roughness had limited effect on the Cpmax, Cpb, and θmin, the value of which was 0.95, −0.35, and 80°, respectively.
(4)
By describing the main affecting parameters of the wind pressure coefficient, a wind pressure load model of the gas tank suitable for engineering calculation was proposed. The calculation method could accurately estimate the mean wind pressure coefficient of the gas tank structure.



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*Source: 4974082-2020-02-20.xml*