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An experimental investigation was performed to investigate two-dimensional axial velocity field at downstream of the 90
° double bend pipe with and without inlet swirling condition. The main objectives are to find separation region and observe the influence of inlet swirling flow on the velocity fluctuation using ultrasound technique. The experiments were carried out in the pipe at Reynolds number Re = 1 × 10
^{4}. In case of inlet swirling flow condition, a rotary swirler was used as swirling generator, and the swirl number was setup
*S *= 1. The ultrasonic measurements were taken at four downstream locations of the second bend pipe. Phased Array Ultrasonic Velocity Profiler (Phased Array UVP) technique was applied to obtain the two-dimensional velocity of the fluid and the axial and tangential velocity fluctuation. It was found that the secondary reverse flow became smaller at the downstream from the bend when the inlet condition on the first bend was swirling flow. In addition, inlet swirling condition influenced mainly on the tangential velocity fluctuation, and its maximum turbulence intensity was 40%.

Pipeline systems in many industries and power plants are usually characterized by its layout complexity, which consists of many main long straight pipes and secondary pipes connected by sharp bends. In nuclear power plants, the flow downstream of a 90˚ bend is essential for the primary and secondary cooling systems, where many sharp bends are used to interconnect the components. However, fluid flows through a 90˚ sharp bends are a very complex phenomenon. As the fluid flows through a bend, the centrifugal force acting on the fluid develops a radial pressure gradient. Because of the pressure gradient in the fluid, the secondary flow is generated downstream of the bend. In addition, a significant pressure gradient produces swirling flow downstream the bend pipe [

The structure of the secondary flow in the bends is dependent on the bend curvature radius (R_{c}) and Reynolds number (Re). Some researchers have investigated the flow characteristics in the 90˚ single bend pipe flow with curvature ratio of R_{c}/D > 1.3 (R_{c}: curvature radius, D: pipe diameter) both experimentally and numerically [_{c}/D = 1.1, 2, 4. The experiments were done by using Laser Doppler Velocimetry (LDV) at Reynolds numbers of 5 × 10^{4} < Re < 1 × 10^{5}. They revealed that the flow separation occurred at R_{c}/D = 1 and did not occur at R_{c}/D = 2 and R_{c}/D = 4. Also, they found that the power spectrum of the turbulence intensity downstream near the elbow with any curvature ratio and Reynolds number had a distinct peak at the reduced frequency of about 0.5. Later on, Ono et al. [_{c}/D = 1 and R_{c}/D = 1.5) in order to investigate the interaction between flow separation and the secondary flow due to the elbow curvature. Particle Image Velocimetry (PIV) was used in their experiment, and they confirmed that the flow separation always occurred in the short-elbow (R_{c}/D = 1) while the flow separation occurred intermittently in the long-elbow case (R_{c}/D = 1.5).

The experiments on the above previous studies mainly were conducted under the inlet condition of fully developed flow and flat velocity profile. However, non-uniform velocity profile on the inlet condition might be appeared in a specific condition. Kubo et al. [^{5} with three types of curvature ratio R_{c}/D = 1, 1.5, 2. They found that the swirl intensity of the swirling flow, which was generated in the dual elbow, became high and fluctuated largely as the curvature ratio was small. The influence of inlet swirling flow on 90˚ bend pipe was studied in order to understand the flow structure downstream the bend pipe flow [^{4} with a curvature ratio of R_{c}/D = 2 under the weak inlet swirling flow condition. They found that inlet swirl flow affected the behavior of secondary flow generating at the downstream of the bend pipe flow. Later, Kalpakli and Orlu [_{c}/D = 1. They found that the flow separation region was deflected at the downstream from the bend when the inlet condition on the first bend was swirling flow. Later, Mizutani et al. [_{c}/D = 1 was used to be close to an actual condition and to accumulate knowledge towards optimization of a prospective piping layout in the conceptual design of Japan Sodium Fast Reactor (JSFR) [

In the previous studies, the researchers mostly used the optical system to measure the velocity field and velocity fluctuation. However, the optical system has some challenges to apply in non-transparent wall channel or pipe. Also, it is difficult for the applications in actual plant process. Thus, another measurement technique should be developed to evaluate the velocity field and velocity fluctuation. In addition, the influence of the strong swirling inlet on the double bend with curvature ratio R_{c}/D < 1 has not been done yet. So in this study, the influence of the strong swirling inlet condition on the velocity fluctuation at the 90˚ double bend pipe with curvature ratio R_{c}/D = 0.5 is investigated with ultrasound technique. Ultrasound technique measurement is used because its advantages which can be applied in the non-transparent pipe and opaque liquid flow [

Initially, conventional Ultrasonic Velocity Profiler (UVP) method only measures one-dimensional velocity profile in the measurement line. In the case of two-dimensional velocity vector measurement, Takeda and Kikura [

The main objectives of this study are to clarify the reattachment point of secondary swirling flow that occurs just downstream of the double bend pipe and to observe the influence of strong swirling inlet flow on the velocity fluctuation of the 90˚ double bend pipe flow using ultrasound technique. The bend curvature caused the secondary swirling flow, and the high-velocity fluctuation occurs near the reattachment point region. To achieve this purpose, Phased Array UVP system is utilized to measure the two-dimensional velocity and the axial and tangential velocity fluctuation at the secondary flow region.

The working principle of Phased Array UVP system based on Doppler shift frequency detection along ultrasound beam lines. Phased array sensor emits an ultrasonic pulse, and each piezoelectric element of sensor receives the echo reflected from the surface of a particle. The exciting element emits a spherical ultrasonic wave. When adjacent elements emit within a close second, interference of wave fronts occurs as shown in _{s} and the time delay Δt is related with the speed of sound in a medium c and inter-element spacing d as shown in Equation (1).

θ s = sin − 1 [ c Δ t d ] (1)

Basic equation of Doppler shift is derived from Doppler equation as shown below:

f d = 2 * s * f 0 c (2)

where f_{d} is the Doppler frequency, s is the speed at which object is approaching the transducer, f_{0} is the basic frequency of the transducer, and c is the speed of sound in the medium, i.e., water (c = 1480 m/s at 20˚C).

If the object is moving at an angle θ to the transducer, then s = V *cosθ. By substitution, we get the Doppler shift equation for a single transducer:

f d = 2 * f 0 * V * cos θ c (3)

Equation (3) can be rewritten as:

f d = ( f 0 * V c ) * 2 * cos θ (4)

where 2 *cosθ applies to a roundtrip Doppler shift using a single transducer.

If two transducers are used, one receiver and one transmitter, as shown in

The Doppler equation becomes:

f d = ( f 0 * V c ) * [ cos θ + cos ( θ − α ) ] (5)

Using the trigonometric identity:

cos ( θ − α ) = cos θ * cos α + sin θ * sin α (6)

The Doppler Equation (5) becomes:

f d = ( f 0 * V c ) * [ cos θ + cos θ * cos α + sin θ * sin α ] (7)

In this paper, phased array sensor is used as transmitter and receiver (transceiver). As shown in

For measuring two-dimensional velocity vector, the development system uses two piezoelectric elements as transceivers to calculate the actual velocity magnitude and angle from the returned signal at specific measuring volume, i.e., Channel 4 (Ch 4). The Doppler shift equation for the piezoelectric element number 8 is identical to Equation (7):

f d 8 = ( f 0 ∗ V c ) ∗ [ cos θ + cos θ ∗ cos α + sin θ ∗ sin α ] (8)

where f_{d}_{8} is the Doppler frequency received by the piezoelectric element number 8 at angle α (measured clockwise from the axis of the transmitting beam), f_{0} is basic frequency, V is the magnitude of the velocity of the particle travelling at angle θ (measured clockwise from the axis of the transmitting beam), and c is the speed of sound in fluid i.e. water.

The Doppler shift equation for the piezoelectric element number 1 is:

f d 1 = ( f 0 ∗ V c ) ∗ [ cos θ + cos θ ∗ cos β + sin θ ∗ sin β ] (9)

where f_{d}_{1} is the Doppler frequency received by the piezoelectric element number 1 at angle β (measured clockwise from the axis of the transmitting beam), and all other terms are identical to those of the piezoelectric element number 8.

The signals from both of these transceivers are demodulated with the transmitted frequency f_{0} to produce four quadrature signals. It should be noted

that at a given depth (channel) from the surface of both piezoelectric elements f_{0}, c, α, and β are all-constant due to the fixed geometry of the piezoelectric elements. The real velocity vector V is calculated by multiplying the four-quadrature signals from the two transceivers elements number 1 and 8. The multiplying produces two subcomponents, which are the sum of the frequencies and the difference between the frequencies. Using trigonometry:

cos f d 1 ∗ cos f d 8 = 1 2 [ cos ( f d 1 + f d 8 ) + cos ( f d 1 − f d 8 ) ] (10)

From Equation (8) and Equation (9), we will get the equations for the sum and difference as follow:

f d 1 + f d 8 = f 0 ∗ V c [ cos θ + cos θ ∗ cos β + sin θ ∗ sin β + cos θ + cos θ ∗ cos α + sin θ ∗ sin α ] (11)

If sin β = −sinα and cosβ = cosα, then Equation (11) becomes

f d 1 + f d 8 = f 0 ∗ V c [ cos θ + cos θ ∗ cos β + sin θ ∗ sin β + cos θ + cos θ ∗ cos α + sin θ ∗ sin α ] f d 1 + f d 8 = f 0 ∗ V c [ 2 ∗ cos θ ( 1 + cos θ ) ] f d 1 + f d 8 = 2 ∗ f 0 c ( 1 + cos θ ) ∗ V ∗ cos θ (12)

f d 1 − f d 8 = f 0 ∗ V c [ cos θ + cos θ ∗ cos β + sin θ ∗ sin β − cos θ − cos θ ∗ cos α − sin θ ∗ sin α ] (13)

If sinβ = −sinα and cosβ = cosα, then Equation (13) becomes

f d 1 − f d 8 = f 0 ∗ V c [ cos θ + cos θ ∗ cos β + sin θ ∗ sin β − cos θ − cos θ ∗ cos α − sin θ ∗ sin α ] f d 1 − f d 8 = f 0 ∗ V c [ − 2 ∗ sin θ ∗ sin α ] f d 1 − f d 8 = − 2 ∗ f 0 c ∗ sin α ∗ V ∗ sin θ (14)

If V_{x} = V * sinθ and V_{y} = V * cosθ, then from Equations (12) and (14):

V x = − ( f d 1 − f d 8 ) 2 ∗ f 0 c sin α (15)

V y = ( f d 1 + f d 8 ) 2 ∗ f 0 c ( 1 + cos α ) (16)

Since these V_{x} and V_{y} are orthogonal, the real magnitude can be determined by vector addition, and simple trigonometry can determine the angle:

V = V x 2 + V y 2 (17)

δ = tan − 1 ( V y V x ) (18)

The spatial resolution or channel distance is defined as:

Δ y = N c y c l e 2 ∗ f 0 ∗ c (19)

where Δy is channel distance, N_{cycle} is a number of cycles per pulse, c is the speed of sound, and f_{0} is the basic frequency of the transducer. If N_{cyle} = 2, c = 1480 m/s, and f_{0} = 2 MHz, then channel distance (Δy) is 0.74 mm.

Phased Array UVP system is showed in

In Phased Array UVP system, we have to consider the effect of the near field oscillation. The high oscillation burst occurs near the active elements surface. It influences the accuracy of the measurement close to the sensor (near-field region). The near-field boundary of phased array sensor has been numerically investigated as shown in _{oscillation} of phased array sensor.

N oscillation = k a b 2 8 λ (20)

where, k_{a} is correction factor, and b is piezoelectric total element width. The correction factor can be calculated from the rectangular element ratio (b/c) = 1

as shown in

The experiment was conducted in a horizontal water circulation system at atmospheric pressure, which consisting of the cooling system, electromagnetic flow meter, pump, ball valve, a bypass pipe, and flow conditioner as shown in

effects of the elbow. The length of straight pipe before entering the first bend is 42D (D = 50 mm) in order to achieve fully developed turbulent pipe flow condition at the inlet of the first bend. In this experiment, the double bend pipe is utilized to investigate the secondary swirling flow. The double bent pipe has a bent angle of 90 degrees and curvature ratio R_{c}/D = 0.5. The Reynolds number is Re = 1 × 10^{4}, based on the bulk velocity and the pipe diameter. The cooling system is used to control and maintain a constant water temperature. The temperature is recorded using thermocouple during the measurements, and it is confirmed that the water temperature fluctuation is ±1˚C.

For the generation of swirling flow, some different methods exist (e.g., pipe rotation, tangential injection, guide-vane, twisted tape, helical turbulators, and propeller-type), which have a different effect on the main flow [

The swirl generator is installed at 12D upstream of the double bent pipe. The rotary swirler consists of a 150 mm long aluminum pipe with inner diameter 50

mm. Small tubes of diameter 3 mm and 50 mm long are inserted into the aluminum pipe. The small tubes are packed as tightly as possible, and their number is approximately 95. The pipe can be rotated about its axis at speed varying from 15 to 1,100 r.p.m. by induction motor (5IK90SW-5 Oriental Motor Co., Ltd.) and a timing belt (K40L50BF) connects it. With the pipe rotating, the growth of the boundary layer on the pipe walls establishes an azimuthal velocity distribution corresponding to the solid-body rotation in the core. Whereas the rotary swirler allows the solid rotation of the small tubes in peripheral direction, while the axial velocity distribution is made uniform by the function of the small tubes structure [

For axisymmetric flow, swirl intensity is usually defined by its swirl number (S). A parameter S that is used by several researchers [

S = 2 π ρ ∫ 0 R v x v y r 2 d r 2 π ρ R ∫ 0 R r v x 2 d r (21)

where r is the radial distance from a pipe axis, v_{x} is the streamwise mean velocity and v_{y} is the circumferential mean velocity.

An alternative to the parameter S on the rotating swirleris defined as follow [

S = ω D 2 U m (22)

Equation (22) indicates that the swirl intensity can be evaluated directly from the angular velocity ω of the rotary pipe, the diameter D of the pipe and the bulk velocity U_{m} of the flow through the pipe.

A phased array sensor, which has basic frequency 2 MHz, is installed through the pipe wall. Thus, there is a direct contact between sensor and fluid to overcome the refraction in the pipe wall. The cross-sectional plane measurement is performed at 7D downstream of the swirling generator to observe developed swirling flow. The angular velocity of rotating pipe is measured by a digital optical tachometer (AD-5172 A & D Company) with accuracy ± 0.01% ± 1 digit (10 - 6000 r.p.m.). According to the literature [

Parameters | Value |
---|---|

Reynolds number [Re = ρ *D *U_{m}/μ] | 10,000 |

Dean number [De = Re *(R_{c}/D)^{0.5}] | 7071 |

Fluid (water) temperature | 25˚C ± 1˚C |

Angular velocity of rotation pipe ω | 0, 480 min^{−1} |

Swirl number S | 0, 1 |

Frequency of phased array transducer | 2 MHz |

Steering angle θ_{s} | 0˚, −5˚, −10˚ |

Pulse repetition frequency f_{prf} | 1 kHz |

Number of repetition N_{rep} | 256 |

Spatial resolution Δy | 0.74 mm |

Time resolution Δt [N_{rep}/f_{prf}] | 0.256 s |

Number of velocity profiles | 10,000 |

x/D = 0.6, x/D = 1 and x/D = 1.5 downstream of the double bend. After the measurement is done at the first position, the sensor is moved to another position. The maximum steering angle of the phased array sensor is −10 degree to 0 degree. In each measurement position, we measured 3 measurement lines, and the interval between each measurement lines is 5 degree as shown in

The experiments were done in the case of with and without inlet swirling flow condition. In the case of without inlet swirling flow condition,

Ten thousand instantaneous velocities are averaged in each velocity profile. The vertical axis indicates the dimensionless distance of measurement line through the pipe. The horizontal axis is the dimensionless axial and tangential velocity normalized by the average axial velocity and the average tangential velocity respectively. According to

At the center of the pipe (y/D = 0.5), the velocity magnitude is relatively lower compared to the end wall regions. The reason is that the bend pipe curvature generate the centrifugal force and it enhances tangential velocity magnitude near the pipe walls.

Two-dimensional velocity measurement results are plotted to know the flow structure downstream of 90˚ double bend pipe in the condition of with and without inlet swirling flow.

Firstly, to confirm the inlet swirling condition, we visualized two-dimensional radial velocity as shown in

downstream from the swirling generator. It is confirmed that the generated swirling flow is symmetric, and the velocity distribution is homogenous. In the core region of the pipe, the velocity magnitude is lower than near wall region. The highest velocity magnitude is between the core and near wall region.

After confirming inlet swirling flow, we investigated the influence of swirling flow on the flow structure downstream of the double bend.

For the investigation of velocity fluctuation, we calculated turbulent intensity for axial velocity and tangential velocity in the condition of without inlet swirling flow and with inlet swirling flow respectively. The x-axis represents the normalized distance, and the y-axis represents turbulent intensity. The turbulent intensity of axial velocity and tangential velocity fluctuation is very effective to analyze the velocity fluctuation.

the tangential velocity fluctuation is high near the extrados sidewall and at the center of the pipe. When the fluid touches the extrados sidewall, the flow direction changes. Some fluids flow as the main flow and some fluids change as the secondary flow. Therefore in the main flow region (near the extrados) and at the core of the secondary swirling flow (at the pipe center) occurs the high tangential velocity fluctuation. Here, the maximum turbulent intensity is around 40% with inlet swirling flow, and the maximum turbulent intensity is around 25% without swirling flow. Therefore, the velocity fluctuation of inlet swirling flow is stronger than without inlet swirling flow. It seems that swirling flow enhances tangential velocity fluctuation.

Phased Array UVP system was applied for two-dimensional velocity measurements in the condition of without inlet swirling flow and with inlet swirling flow on the double bend pipe flow. According to one-dimensional velocity profiles, the velocity magnitude of inlet swirling flow is much stronger than without inlet swirling flow in the secondary flow region. These differences are due to the influence of the inlet swirling flow. In two-dimensional velocity of without inlet swirling flow, the flow separation occurs around x/D = 0.1, and the reattachment point is located at x/D = 1.5. In case of inlet swirling flow, the flow separation phenomenon is same as the condition of without inlet swirling flow, but the reattachment point is located at x/D = 1. Therefore, the reverse flow region is narrow. At x/D = 1.5, the fluid becomes the accelerated swirling flow. In the condition of without inlet swirling flow, the axial velocity fluctuation is higher than with inlet swirling flow, but tangential velocity fluctuation is lower than inlet swirling flow.

We are grateful to Professor Nobuyuki Fujisawa in Niigata University, Japan, for his advice on the design of swirling generator.

Shwin, S., Hamdani, A., Takahashi, H. and Kikura, H. (2017) Experimental Investigation of Two- Dimensional Velocity on the 90˚ Double Bend Pipe Flow Using Ultrasound Technique. World Journal of Mechanics, 7, 340-359. https://doi.org/10.4236/wjm.2017.712026