Effects of Guide Vane Placement Angle on Hydraulic Characteristics of Flow Field and Optimal Design of Hydraulic Capsule Pipelines
2. Theoretical Analysis
2.1. Design of the Piped Carriage
2.2. Force Analysis
- The gravity of the piped carriage Gc was related to the basic materials of the piped carriage.
- The pressure gradient force acting on the front and rear ends of the piped carriage Fp, which can be expressed as
- The support force of the pipe wall against the piped carriage Fn. Six support forces acting on the contact points between the universal balls of the piped carriage and the inner wall of the pipes in different directions, and the directions of these support forces pointed towards the center of the conveying pipes from its interior wall.
- The buoyancy of the piped carriage Fb was related to the internal volume of the barrel.
- The rolling frictional resistance fc was decomposed into an axial force fcz and a circumferential force fcθ. These two forces can be expressed respectively as
- The shear stress of the annular slit flow acting on the sidewall of the guide vanes τv was decomposed into an axial force τvz and a circumferential force τvθ. These two forces can be expressed respectively as
- The shear stress of the annular slit flow acting on the sidewall of the barrel τb was decomposed into an axial force τbz and a circumferential force τbθ. These two forces can be expressed respectively as
- The fluid thrust acting on the guide vanes Rv was decomposed into an axial force Rvz and a circumferential force Rvθ. These two forces can be expressed respectively as
- The lift acting on the piped carriage Fl was related to the hydrodynamic pressure and the average axial velocity of the pipe fluid.
2.3. Motion Model
2.4. Rotating Characteristics
3. Materials and Methods
4. Bidirectional Fluid–Structure Interaction Calculation
4.1. Mathematical Model
4.2. Governing Equations of Fluid Domain
4.3. Motion Equations of Structural Domain
4.4. Bidirectional Fluid–Structure Interaction Algorithm
- First of all, the motion parameters of the piped carriage needed to be set at the initial time t, including the instantaneous axial speed, ; the instantaneous angular speed, ; the instantaneous angle, ; and the instantaneous displacement, .
- The instantaneous axial speed and the instantaneous angular speed at time t were regarded as the boundary conditions for the next iteration. The hydraulic characteristics at time t + ∆t were solved based on the governing equations and the turbulent model of the fluid domain. When the internal flow field was fully converged, the instantaneous resultant force and the instantaneous moment acting on the piped carriage at time t + ∆t were obtained.
- The instantaneous axial speed and the instantaneous displacement of the piped carriage at t + ∆t were calculated, which were expressed as
- The instantaneous angular speed and the instantaneous angle of the piped carriage at time t + ∆t were calculated, which were expressed as
- Combined with the instantaneous displacement and the instantaneous angle at time t + ∆t, the piped carriage moved to a new location, and then the meshes of the fluid domain were updated by using the moving mesh technology.
- The instantaneous axial speed and instantaneous angular speed at time t + ∆t were used as the boundary conditions for the next iteration. The above calculation steps were repeated again until the piped carriage arrived at the pre-defined locations in the computational domains.
5. Verification of the Simulated Results
5.1. Instantaneous Speed
5.2. Piezometric Heads
5.3. Velocity Distributions
6. Results and Discussion
6.1. Average Speed Analysis
6.2. Axial Velocity Distributions
6.3. Radial Velocity Distribution
6.4. Circumferential Velocity Distribution
6.5. Pressure Distributions
6.6. Vorticity Magnitude Distributions
6.7. Pressure Drop Characteristics
6.8. Mechanical Efficiencies
6.9. Force Statistics
7. An Optimization Model of HCPs
7.1. Cost of Pipeline
7.2. Cost of Piped Carriage
7.3. Cost of Power
7.4. Optimization Method
- Assume the diameter of the pipeline Dc.
- Obtain the total length of the conveying pipe through the dropping and receiving position of the piped carriage Lc.
- Calculate the cost of pipelines and the piped carriage by adopting Equations (68) and (69) based on the materials for the pipelines and the piped carriages and market prices of these materials.
- Determine and configure the physical parameters such as the diameter ratio of the piped carriage, the length of the barrel, the height of the guide vane, the length of the guide vane, the placement angle of the guide vane, as well as the transport loading based on the experimental schemes in Section 2.
- Determine the diameter of the barrel dc, combined with the diameter of the pipelines.
- Assume the value of the efficiency for the centrifugal pumping unit (0.6–0.75).
- Calculate the total pressure drop of transporting the piped carriage by using the bidirectional fluid–structure interaction method ΔPtotal.
- Assume the mixed pipe discharge Qm, based on the pipe discharge.
- Calculate the cost of power consumption by using Equations (70) and (71) based on the unit price of electricity and the service life of the centrifugal pumping unit.
- Calculate the total cost of HCPs, CostTotal, using Equations (64) and (65).
- Repeat above Steps 1 to 10 for the various values of the pipe diameters to obtain the minimum value of the total cost of HCPs and its corresponding pipe diameter Dc.
- Find out the optimal diameter of the conveying pipes in order to determine the various indicators for the optimization model of HCPs.
7.5. Design Example
- With the increase of the guide vane placement angle, the average axial speeds of the piped carriage showed a logarithmic growth trend, while the average angular speeds showed an exponential growth trend.
- With the increase of the guide vane placement angle, the affected areas of the axial velocity and radial velocity gradually decreased, and the affected areas of the circumferential velocity and vorticity magnitude gradually increased near the front end of the piped carriage. With the increase of the guide vane placement angle, both the average drag coefficient and the average lift coefficient of the piped carriage showed exponential growth.
- The combined effects of both the energy dissipation and the energy conversion caused the local low-pressure areas to develop near the front end of the piped carriage, and the energy conversion caused the downstream pressure of the piped carriage to rise sharply again. With the increase of the guide vane placement angle, the average pressure drop coefficient of transporting the piped carriage first decreased and then increased, while the mechanical efficiency of transporting the piped carriage first increased and then decreased. The average pressure drop coefficient and mechanical efficiency of the piped carriage collectively indicated that the optimal placement angle of the guide vanes was 21° when the transport loading was 0.6 kg and the pipe discharge was 50 m3·h−1.
- In the near-wall areas of the piped carriage, the axial velocity distributions, radial velocity distributions, circumferential velocity distributions, and vorticity magnitude distributions were basically the same, while the pressure distributions showed a gradually decreasing trend, when the piped carriage moved through the pipelines.
- Based on the least cost principle, the optimization model of HCPs can output the optimal pipe diameter. A practical example has been completed in order to demonstrate the usage and effectiveness of this optimization model.
Conflicts of Interest
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|Model of Piped Carriage||Model 1||Model 2||Model 3|
|Guide vane||Placement angle/°||3/6/9/12/15/18/21/24/27/30/33/36|
|Mesh Size/m||Average Pressure of Inlet Cross-Section/Pa|
|φv = 6°||φv = 12°||φv = 18°||φv = 24°||φv = 30°||φv = 36°|
|Boundary Name||Boundary Condition|
|Inlet of the horizontal pipe model||Velocity Inlet|
|Outlet of the horizontal pipe model||Pressure Outlet|
|Static wall of the horizontal pipe model||Stationary Wall|
|Moving wall of the piped carriage||Translating Wall|
|Connecting cross-sections of different pipes||Interface|
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Zhang, C.; Sun, X.; Li, Y.; Zhang, X.; Zhang, X.; Yang, X.; Li, F. Effects of Guide Vane Placement Angle on Hydraulic Characteristics of Flow Field and Optimal Design of Hydraulic Capsule Pipelines. Water 2018, 10, 1378. https://doi.org/10.3390/w10101378
Zhang C, Sun X, Li Y, Zhang X, Zhang X, Yang X, Li F. Effects of Guide Vane Placement Angle on Hydraulic Characteristics of Flow Field and Optimal Design of Hydraulic Capsule Pipelines. Water. 2018; 10(10):1378. https://doi.org/10.3390/w10101378Chicago/Turabian Style
Zhang, Chunjin, Xihuan Sun, Yongye Li, Xueqin Zhang, Xuelan Zhang, Xiaoni Yang, and Fei Li. 2018. "Effects of Guide Vane Placement Angle on Hydraulic Characteristics of Flow Field and Optimal Design of Hydraulic Capsule Pipelines" Water 10, no. 10: 1378. https://doi.org/10.3390/w10101378