J. Cent. South Univ. (2019) 26: 852-864

DOI: https://doi.org/10.1007/s11771-019-4054-2

Flow measurement and parameter optimization of right-angled flow passage in hydraulic manifold block

HU Jian-jun(胡建军)^{1, 2}, CHEN Jin(陈进)², QUAN Ling-xiao(权凌霄)^{1, 3}, KONG Xiang-dong(孔祥东)^{1, 3}

1. School of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China;

2. School of Civil Engineering and Mechanics, Yanshan University, Qinhuangdao 066004, China;

3. Engineering Research Center of Advanced Forging & Stamping Technology and Science Built by

Central Government and Local Government, Yanshan University, Qinhuangdao 066004, China

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Abstract: This study was conducted to investigate the flow field characteristics of right-angled flow passage with various cavities in the typical hydraulic manifold block. A low-speed visualization test rig was developed and the flow field of the right-angled flow passage with different cavity structures was measured using 2D-PIV technique. Numerical model was established to simulate the three-dimensional flow field. Seven eddy viscosity turbulence models were investigated in predicting the flow field by comparing against the particle image relocimetry (PIV) measurement results. By defining the weight error function K, the S-A model was selected as the appropriate turbulence model. Then, a three-factor, three-level response surface numerical test was conducted to investigate the influence of flow passage connection type, cavity diameter and cavity length-diameter ratio on pressure loss. The results show that the Box-Benhnken Design (BBD) model can predict the total pressure loss accurately. The optimal factor level appeared in flow passage connection type II, 14.64 mm diameter and 67.53% cavity length-diameter ratio. The total pressure loss decreased by 11.15% relative to the worst factor level, and total pressure loss can be reduced by 64.75% when using an arc transition right-angled flow passage, which indicates a new direction for the optimization design of flow passage in hydraulic manifold blocks.

Key words: flow measurement; particle image relocimetry; right-angled flow passage; parameter optimization

Cite this article as: HU Jian-jun, CHEN Jin, QUAN Ling-xiao, KONG Xiang-dong. Flow measurement and parameter optimization of right-angled flow passage in hydraulic manifold block [J]. Journal of Central South University, 2019, 26(4): 852–864. DOI: https://doi.org/10.1007/s11771-019-4054-2.

1 Introduction

Modularization, assembly, opening and integration are notable development trends in hydraulic control systems. Hydraulic manifold blocks are of great importance across many fields including chemical [1–3], biomedical [4, 5], mechanical [6–8] and civil and environmental engineering [9–11]. They play an especially vital role in the safety and efficiency of hydraulic systems. The manifold block component of such a system is usually realized by drilling, boring and other mechanical processing methods resulting in numerous right-angled flow passages with cavities. Some studies have shown that the pressure loss can reach 1 MPa through each hydraulic manifold block in the system during fluid power transmission. Reducing pressure loss in the hydraulic manifold block is the key to a truly energy-efficient hydraulic system, and there is particularly urgent demand for techniques to accurately predict the flow characteristics in right-angled flow passage to reduce energy loss in the fluid power transmission process.

Advancements in computational fluid dynamics (CFD) have provided scholars with valuable means to investigate the flow features in hydraulic manifold blocks.TOMOR et al [12] described pressure losses in hydraulic manifold blocks using several different methods including CFD, semi-empirical formulations and experimental measurement. They found that CFD analysis overestimates experimental results while numerical analysis correctly reflects pressure loss trends. These results were also confirmed by ABE et al [13], who used CFD method to explore pressure drop through a complicated internal passage with multiple elbows to which empirical formulas cannot be applied. There is a general consensus that CFD is appropriate for evaluating pressure drop despite any evident discrepancy between numerical and experimental results. WANG [14] examined the research and development of theories and methodology of flow solutions in hydraulic manifold blocks including CFD, discrete models and analytical models.

There have been many studies in recent years on the flow characteristics of hydraulic manifold blocks with curved channels. MURAKAMI et al [15] described the changes in flow direction in curved channels as they relate to centrifugal force from the center of curvature toward the outer wall. Upstream of the elbow, the passage of fluid from the straight part to said curve is accompanied by an increase in outer wall pressure and a decrease in the internal wall pressure. The “diffuser” effect leads to flow separation from the inner wall, and it is intensified by the inertia forces which act in the curved zone and tend to move the particles towards the outer wall. IDELCHIK [16] stated that when the output section is greater than the input section (expansion), the diffuser effect is intensified leading to an increase in vortices and flow separation, i.e., a decrease in velocity and an increase in the pressure downstream of the elbow. TIWARI et al [17] conducted full three-dimensional theoretical and numerical analyses of single- and two-phase dilute particle/liquid flows in U-bent and helical-curved conduits to reveal the effects of these geometries on flow field evolution and wall shear. They found that the primary curvature can cause substantial asymmetry in the radial distribution of the main flow velocity.

To date, there has been little research on the connection type and flow passage parameters such as cavity length, cavity diameter and cavity length-diameter ratio in hydraulic manifold blocks in regards to optimal energy-saving effects. This paper developed numerical model for simulating the three-dimensional flow field of right-angled flow passage. Seven eddy viscosity turbulence models were investigated in predicting the flow field by comparing against the PIV measurement results. By defining the weight error function K, the S–A model was selected as the appropriate turbulence model. The influence of the factors described above on pressure loss was analyzed based on the Box-Benhnken Design (BBD) method, and the optimal factor level was obtained. The pressure loss characteristics of the right-angled flow passage with an arc transition were also investigated to provide a reference for the optimal design of flow passage in the hydraulic manifold block.

2 Flow measurement of right-angled flow passage

2.1 Design of experimental models

To determine the influence of the length and structure of the cavity on flow characteristics in the right-angled flow passage, a gravity-driven low- speed flow field measurement test rig (Figure 1) was built. The test rig is mainly composed of an elevated water tank, inlet and outlet pipelines, an adjustable throttle valve and tested blocks with different internal structures.

It was difficult to measure the internal flow field directly due to the small size and high pressure of prototype block, so it was enlarged to facilitate measurement. Water was used as the flow medium to avoid the condensation phenomena of tracer particles in hydraulic oil. To ensure that the flow features of the enlarged block were consistent with the prototype block, the geometric parameters and operating conditions of the tested block were determined by the Reynolds similarity criterion:

                        (1)

where ρ is density; l is characteristic length of flow passage; v is inlet velocity; and u is dynamic viscosity. Subscript p denotes the prototype block and subscript m denotes the model block.

Figure 1 Flow test rig of right-angled channel

The above equation can be extrapolated as follows:

                             (2)

which contains the following definitions:

where k_p is density ratio; k_v is velocity ratio; k₁ is length ratio; and k_μ is viscosity ratio.

The above parameter definitions can be introduced into Eq. (2) as follows:

                              (3)

The parameters of the tested block were determined according to the geometry and working conditions of the prototype block under the restriction of Eq. (3). The Reynolds number of prototype block is about 3000 at typical working conditions. The calculation results are shown in Table 1. The velocity in the tested block was only 0.067 m/s based on similarity calculation, so the required driving force of the internal flow could be acquired by an elevated water tank. In the experiment, the steady flow rate of the tested block was maintained at about 1.4 L/min by adjusting the water-level of the tank and the throttle properly. Before the experiment, a certain concentration of tracer particles with an average diameter of 20 μm was uniformly added into the water tank.

Three connection types of flow passage were investigated, including the inflow or outflow face the right-angled cavity and the two sides of the cavity face each other, which were defined as connection types I, II and III, respectively. Figure 2 shows the schematic diagram of type Ⅲ, where the arrow points to the flow direction, the inlet and outlet distances from the center are 60 and 120 mm respectively, D represents the channel diameter and L indicates the length of cavity.

Six tested blocks with flow passage diameter D of 21 mm were designed and manufactured based on different connection type and cavity length as shown in Figure 2. The experimental tested block is made of polymethyl methacrylate (PMMA) with high transparency which allowed us readily use a laser light to illuminate the tracer particles. The block is blacked out at the back to highlight the particles and increase the interpretation accuracy by software.

2.2 2D-PIV system

Particle image velocimetry(PIV) is a transient, non-intrusive flow field measurement technique. Dantec PIV system was used consisting of a Nd: YAG laser, a high-resolution Dantec Flow Sense CCD camera (1600 pixels×1200 pixels) mounted with an optics lens (Nikon Nikkor r 60/2.8), and an optics filter in front of the lens to eliminate ambient light noise, as well as a signal synchronizer and Dynamic Studio V2.3 software. The laser generates a maximum of 120 MJ/pulse with 532 nm wavelength green visible light. The pulse width is 6–8 ns, which is triggered by Q-switch at a maximum repetition rate of 15 Hz.

The bursts of the laser light were synchronized with the CCD camera via the signal synchronizer.

2.3 PIV system debugging

The flow field of the middle section was measured in the flow passage by adjusting the laser head, CCD camera and tested block position properly. After the measurement area was determined, the 2D PIV system was calibrated for further analysis. The tested model is shown in Figure 3.

Table 1 Parameter selection of prototype valve block and experimental model

Figure 2 Schematic diagram of connection type III

The time interval between double pulses must be properly chosen according to the velocity magnitude of the tested flow field and the size of the interrogation zone. The displacement of tracer particles between the double pulses should be about 1/2–1/3 the edge length of the interrogation zone (32 pixels×32 pixels) [18]. The time interval between pulses △t=415 μs was used as determined by the formula △tV_MAX=250 [18].

The original double exposure particle image data were processed via the adaptive-correlation algorithm developed by Dantec Company. The interrogation zone was 32 pixels×32 pixels with an overlap rate of 25%, and the maximum frequency of the laser system is 15 Hz. The flow field measurements reported here was obtained by the statistical results of 80 pairs of original images which reflect the time-averaged flow field. Tested valve block illuminated by laser light sheet is shown in Figure 4.

2.4 Experimental results and analysis

Six kinds flow passages described above were measured by 2D-PIV technique. Figure 5 shows the velocity contours and streamlines of the middle flow section of flow passage at inlet velocity of 0.067 m/s, which were processed based on the original experimental data. It is observed that two vortices generated as fluid passing through the right-angled channel. The vortex in the cavity is defined as vortex A, and the vortex generated after the right-angled channel due to flow separation is defined as vortex B.

Figure 3 Tested valve block model:

Figure 4 Tested valve block illuminated by laser light sheet:

As shown in Figure 5, the size of vortex A increased as cavity length increased under connection type I. The liquid tended to enter already-occupied right-angled cavity due to inertia, blocking the inflowing fluid and creating an outflow section that exerted strong shear stress on the fluid in the cavity. Under the action of shear stress force, a strong counter-clockwise rotation of fluid formed, that was vortex A. The kinetic energy of the fluid was dissipated into heat due to friction between the fluid and solid wall, which is an important factor causing flow loss. Vortex B originated from the typical secondary flow forming when fluid passed through the right-angled channel. The streamline began to separate from the corner wall due to inertia, bringing about strong separation loss. These path lines did not change as cavity length changing, which means that the flow loss was not related to cavity length. These results suggest that reducing cavity length can reduce the flow loss in the cavity, but has no effect on the flow loss caused by the secondary flow.

For connection type II, cavity length appeared to have a similar influence on vortexes A and B. However, fluid passing through the right-angled bend towards the solid wall instead of the fluid in the cavity as in connection type I, so the viscous shear stress force from the fluid in the cavity was less than that in connection type I. So, there was less flow loss under connection type II than connection type I under the same cavity length.

Advancements in CFD technology have made possible a number of studies on the flow characteristics of internal flow passage in hydraulic manifold blocks. The selection of an appropriate turbulence model is very important to simulate specific flow field in engineering. At present, there is no turbulence model which can adapt to all engineering problems. The turbulence models used for simulations are not standardized, and there is no consensus on the correctness of any one turbulence model. In next study, seven eddy viscosity turbulence models were investigated in predicting the flow field of right-angled flow passage by comparing against the PIV measurement results with the purpose of establishing a reliable numerical model.

3 Numerical model

3.1 Geometry modeling and grid generation

The PIV measurement results for connection types I and II with cavity length L=50%D are shown in Figures 5(c) and (f). The vortex core position of vortexes A and B served as the index to validate the turbulence model. Three-dimensional computational models were created by Solid work software, and unstructured tetrahedral grid was used to discrete the calculation zone in GAMBIT software to account for its irregular geometry. The velocity inlet and pressure outlet were set as the boundary conditions for the numerical model.

Figure 5 PIV measurement results of connection types I and II models:

The independence of the calculated results on the grid was checked against the inlet mass flow rate. Figure 6 shows that the inlet mass flow rate changed slowly when the grid number exceeded 5×10⁵, while the Y+ of the wall ranged in 1–5 in accordance with the turbulence model and wall function. The number of grids in the subsequent model was set to about 5×10⁵ for balance between computational accuracy and cost.

Figure 6 Grid independence check

3.2 Numerical method, fluid properties and boundary conditions

The general governing equations for incompressible single-phase fluid are used in this work. The conservation equations of mass and momentum are given as:

                          (4)

       (5)

where ρ is fluid density; μ is fluid viscosity; p is pressure; v is fluid velocity and t is flow time. The energy conservation equation is given by:

              (6)

where H is enthalpy; T is temperature; k is thermal conductivity and S_V is a spatial source term regarding the heat generation induced by plastic deformation. The enthalpy H is defined in its integration form as:

                            (7)

where c_P is the specific heat; T is temperature; and T_ref is the reference temperature, which is 300 K.

Commercial software ANSYS FLUENT 12.0 was used to solve the time-averaged Reynolds N-S equation. The calculation employed the uncoupled implicit scheme and spatial discretization by finite volume method. Second-order central difference scheme was used for the source term and diffusion term, and two-order upwind scheme for the convection term in the governing equation. The convergence of the calculation is judged by the residual of equations decreasing by 5 orders of magnitude and the fluctuation of the mass flow rate of the outlet is less than 0.01 kg/s. The pressure outlet and velocity inlet were set as the boundary conditions of the numerical model, which are consistent with the experiment as shown in Table 1.

3.3 Turbulence model selection

Flow fields of connection types I and II were calculated with S–A, k-ε-Standard, k-ε-RNG, k-ε-Realizable, k-ω-Standard, k-ω-SST and Reynolds Stress Model(RSM) turbulence models. Figure 7 shows the calculation results of connection type II with the seven turbulence models. It can be found that the flow characteristics of vortexes A and B were matched with the experiment results shown in Figure 5(f) when using the turbulence models S–A, k-ω-Standard and k-ω-SST.

Figure 8 shows the core position distribution of vortex A and B with calculation and experimental measurement. For connection type II, the core position of vortexes A and B calculated by the S–A model were closer to the experimental results than the other turbulence models. For connection type I, the k-ε-Realizable and the k-ω-Standard yield closer vortex core position to the experimental results.

In order to quantitatively evaluate the turbulence model in terms of vortex core position prediction accuracy for connection type I and II, the weighted error function K is defined as follow:

K=70%K_A+30%K_B                                      (8)

where K_A and K_B are the absolute distance between the calculated position of the vortex cores A, B and the experimental measured position, respectively. The position precision weight values of A and B are 70% and 30%, respectively for the vortex A indicates the most important flow characteristic of the right-angled flow passage, which also dominates the flow loss in the flow passage.

Table 2 reports the weight error K calculation results for connection typeⅠwith seven turbulence models. The K value of k-ε-Realizable model was the least indicating that it was the most accurate model. The RSM model also performed well.

Figure 7 Streamline calculated by seven turbulence model:

Table 3 reports calculations of the weight error K of connection type II with seven turbulence models. There were significant differences in prediction performance between them: S–A model was the most accurate with a K value only 1.76, the k-ω-SST model performed well, and the RSM model deviated substantially from the experimental results. Surprisingly, the widely used k-ε-Standard model performed poorer than any other model we tested.

In conclusion, the S–A model proved to be the appropriate turbulence model to predict the flow field of a right-angled flow passage in terms of balancing computational cost and accuracy. Then, S-A turbulence model was adopted to establish the numerical models to investigate the influence of connection type, cavity length and cavity length-diameter ratio on pressure loss based on response surface test with the purpose of reducing flow loss in hydraulic manifold blocks.

4 Parameter optimization of right-angled flow passage

4.1 Response surface test design

The PIV measurement results for connection types I and II with cavity length L=50%D are shown in Figures 5(c) and (f). The vortex core position of vortex.

The S–A turbulence model was used to simulate the three-dimensional flow field of right-angled flow passage based on ANSYS FLUENT 12.0 commercial code. Mining hydraulic oil L-HM with density of 870 kg/m³ and dynamic viscosity μ of 0.04002 Pa·s was used as the medium.

Figure 8 Comparison of vortex core positions of A and B vortices:

Table 2 Weight error K of connection type I

Table 3 Weight error K of connection type II

Three-factor and three-level response surface test was carried out by selecting connection type, cavity diameter and cavity length-diameter ratio as the independent variables with the total pressure loss coefficient as the response value. Table 4 shows the range and levels of the three variables coded by S, D and N. The total pressure loss coefficient C_{p, t} is defined as follows:

                        (9)

In the definition, P_total represents the mass- weighted total pressure of inlet; P_local represents the local total pressure;represents the mass- weighted density of outlet, and represents the mass-weighted velocity of outlet.

Table 4 Range and level of variables

4.2 Results and variance analysis

BBD (Box-Benhnken Design) is a response surface model that uses experimental design theory to test the specified set of design points and obtains the objective and constraint functions necessary to predict the response value of non-test points [19]. Table 5 shows the result of 17 simulations with different design parameters gathered in Design Expert 8.0.7 software.

Multiple regression analysis was performed using the BBD model in Design Expert. The total pressure loss coefficient C_p,t was obtained for the two multiple regression equations of the experimental factors as follow:

C_p,t=2.97+4.911E–004S–1.55D–0.057N+3.96E–003SD–0.042SN+0.017DN+0.17S²+0.84D²+0.071N²

Table 6 shows the quadratic model results of analysis of variance [20, 21]. The sum of “squares”, ‘‘mean square” and ‘‘F value” were used to estimate the square of the deviation from the grand mean, to divide the sum of squares by the degrees of freedom, and to check the accuracy of the model, respectively. The factors are significant if the p-values are less than 0.05. The calculation of the p value of the model at less than 0.0001 yielded a rejection of the null hypothesis, indicating that the model is significant statistically. ‘Lack of fit’ greater than 0.05 was not significant representing that there was little difference between the model prediction and simulation value.

Table 5 Response surface test design and results

Table 6 Quadratic model results of analysis of variance

In this study, the Adj R-Squared was 0.9992 indicating that the model can explain 99.92% of the change in response value. The correlation coefficient of R-squared was 0.9997 means that the model fitting degree is good, and the regression equation can substitute for simulation results. The F and p values of each factor in the table indicate that the diameter of the flow passage showed the greatest influence on the total pressure loss coefficient, followed by cavity length-diameter ratio and connection type of flow passage.

4.3 Parameters optimization

According to response surface test results, the optimal factor level of the flow passage occurs at connection type II, diameter of 14.64 mm and length-diameter ratio of 67.53% with a predicted minimum total pressure loss coefficient of 2.260. It means that the length-diameter ratio is not the shorter the better as we thought before. The results predicted by three-dimensional numerical simulation with these factor levels in ANSYS FLUENT 12.0 code differed by only about 2.54%.

Table 7 presents the optimal factor level of the right-angled flow passage under several inlet flow rates. It shows that there is similar result between the optimal factors at different flow rates which occurs at connection type II, flow passage diameter within the range of 14 to 15 mm and ratio of cavity length-diameter within the range of 60% to 70%. This indicates that the optimal level is relatively stable and does not change with working conditions.

Table 7 Optimal factor level at different inlet velocities

Figure 9 shows the calculation results of streamline and total pressure loss coefficient under the best factor level of connection type II (Figure 9(a)) and the most unfavorable factor level of connection type III (Figure 9(b)), with the diameter of 14.64 mm and cavity length-diameter ratio of zero. An arc transition flow passage numerical model with a turning radius of 20 mm,which can be made by additive manufacturing, was built as an ideal model for comparison against the models above.

Figure 9 Streamline and C_p,t distribution of different right-angled turn channel:

The streamline of arc transition flow passage was smooth and without any obvious vortex, and the total pressure loss coefficient was only 0.920– the smallest among all three types shown in Figure 9. The flow separation range and high total pressure loss area were the largest in the flow passage under the most unfavorable factors with a total pressure loss coefficient of 2.610. The total pressure loss coefficient of the optimal factor level of connection type II fell between the above two cases. After optimization, the total pressure loss of the best factor level was reduced by 11.15%, and if the arc transition flow passage is applied to the right-angled flow passage, the total pressure loss can be reduced by 64.75%.

5 Conclusions

In this study, the flow field of six kinds of right-angled flow passage were measured by PIV technique and found that two vortices, A and B, generated in the cavity and after the right-angle bend, respectively. The relative position of the cavity for the inlet and outlet cannot affect the basic flow features of the right-angled flow passage but do affect the vortex formation and its scale.

The flow field of right-angled flow passage was simulated via seven different turbulence models respectively. Each model can capture the main flow characteristics of the right-angled flow passage, but the prediction accuracy of the vortex core position differed among them. The S–A model was selected as the optimal turbulence model by defining the weighted error function K and considering the balance between prediction accuracy and calculation cost.

Multiple regression analysis was performed using the BBD model with a good fitting degree. The influence order of the factors was cavity diameter, cavity length-diameter ratio and connection type. The optimal factor level of the right-angled flow passage studied in this paper was identified at connection type II, diameter of 14.64 mm and length-diameter ratio of 67.53%, and these parameters yielded similar results at different inlet flow rates. The total pressure loss of the right-angled flow passage under these parameters can be reduced by 11.15% compared to the least favorable parameters. If an arc transition right-angled flow passage is used, the total pressure loss can be reduced by 64.75% indicating a new direction for the optimization design of right-angled flow passage in hydraulic manifold blocks.

Nomenclature

A

Defined as vortex A

B

Defined as vortex B

L

Cavity length

k_p

Density ratio

k_v

Velocity ratio

k_l

Length ratio

k_μ

Viscosity ratio

K

Weighted error function

C_p,t

Total pressure loss coefficient

P_total

Total pressure of inlet

P_local

Local total pressure

Average density of outlet

Average velocity of outlet

S

Flow passage connection type

D

Diameter of flow passage

N

Cavity length-diameter ratio

T

Temperature

Greek letter

ρ

Density of fluid, kg/m³

l

Characteristic length of flow passage, m

μ

Dynamic viscosity of fluid, Pa·s

References

[1] YOO Geun-jong, CHOI Hoon-ki, KIM Chul-hwan. Characteristics of turbulent flow distribution in branch piping system [J]. Journal of Central South University, 2012, 19(11): 3208-3214. DOI: 10.1007/s11771-012-1397-3.

[2] GUO Kai, LI Qi, LIU Bo-tan, LIU Hui, LIU Chun-jiang. A novel design method based on flow pattern construction for flow passage with low drag and pressure drop [J]. Chemical Engineering Science, 2015, 135: 89–99.

[3] HANSPAL N S, WAGHODE B, NASSEHI V, WAKEMAN R J. Development of a predictive mathematical model for coupled stokes/Darcy flows in cross-flow membrane filtration [J]. Chemical Engineering Journal, 2009, 149: 132–142. DOI: 10.1016/ j.cej.2008.10.012.

[4] WU D Z, JIANG X K, CHU N, WU P, WANG L Q. Numerical simulation on rotordynamic characteristics of annular seal under uniform and non-uniform flows [J]. Journal Central South University, 2017, 24: 1889-1897. DOI: https://doi.org/10.1007/s11771-017-3596-4.

[5] KAMISLI, FETHI. Second law analysis of a disturbed flow in a thin slit with wall suction and injection [J]. International Journal of Heat and Mass Transfer, 2008, 51(15, 16): 3985–4001. DOI: 10.1016/j.ijheatmasstransfer.2007.10. 038.

[6] FARZANE N S, ELHAM O A. Numerical study on the flow distribution uniformity in angled and curved manifolds [J]. Microsystem Technologies-Micro- and Nanosystems- Information Storage and Processing Systems, 2018, 24(4): 1891–1898. DOI: 10.1007 /s00542-017-3572-9.

[7] MIAO Zheng-qi, XU Tong-mo. Single phase flow characteristics in the headers and connecting tube of parallel tube platen systems [J]. Applied Thermal Engineering, 2006, 26(4): 396–402. DOI: 10.1016/j.applthermaleng.2005.06. 013.

[8] LU Li-peng, ZHONG Lu-yang, LIU Yang-wei. Turbulence models assessment for separated flows in a rectangular asymmetric three-dimensional diffuser [J]. Engineering Computations, 2016, 33(9): 978–994. DOI: 10.1108/EC-05- 2015-0112.

[9] CHOU H T, LEI H C. Outflow uniformity along a continuous manifold [J]. Journal of Hydraulic Engineering, 2008, 134(9): 1383–1388.

[10] SAYED-HOSSEIN S, PETERS T. Adjusted friction correction factors for center-pivots with an end-gun [J]. Irrigation Science, 2103, 31(3): 351–358. DOI: 10.10077/S00271-011-0307-Z.

[11] ALAZBA A A, ASCE M, MATTAR M A, EINESR M N, AMIN M T. Field Assessment of friction head loss and friction correction factor equations [J]. Journal of Irrigation and Drainage Engineering, 2012, 31(2): 166–176. DOI: 10.1061/(ASCE)IR.1943-4774.0000387.

[12] TOMOR A, KRISTOF G. Junction losses for arbitrary flow directions [J]. Journal of Fluids Engineering-Transactions of the ASME, 2017, 140(4): 041104. DOI: 10.1115/1. 4038395.

[13] ABE O, TSUKIJI T, HARA T, YASUNAGA K. Flow analysis in pipe of a manifold block [J]. International Journal of Abrasive Technology, 2012, 6: 494–501.

[14] WANG Jun-ye. Theory of flow distribution in manifolds [J]. Chemical Engineering Journal, 2011, 168(3): 1331–1345. DOI:10.1016/ j.cej.2011.02.050.

[15] MURAKAMI M, SHIMIZU Y, S HIRAGAMI H. Studies on fluid flow in three-dimensional bend conduits [J]. Bull JSME, 1969, 12: 1369–1379.

[16] IDELCHIK I E. Handbook of hydraulic resistance [M]. 2nd ed. London, UK: Hemisphere Publishing Corp., 1986.

[17] TIWARI P, ANTAL S P, PODOWSKI M Z. Three- dimensional fluid mechanics of particulate two-phase flows in U-bend and helical conduits [J]. Physics of Fluids, 2006, 18(4): 043304. DOI: 10.1063/1.2189212.

[18] HU Jian-jun, KONG Xiang-dong, LI Zhi-xian, ZHANG Yong-gui, XU Jin-liang. Experimental investigation of aerodynamic interaction between tip leakage flow and spontaneous tip injection flow using 2D-PIV [J]. Experimental thermal and Fluid Science, 2014, 54: 127–135. DOI: 10.1016/j.expthermflusci.2014.02.014.

[19] SHOKUFAR A, KHALILI S M R, GHASSEMI A F. Analysis and optimization of smart hybrid composite plates subjected to low-velocity impact using the response surface methodology (RSM) [J]. Thin-Walled Structures, 2008, 46(11): 1204–1212. DOI: 10.1016/j.tws.2008.02. 007.

[20] BOX G E P, WILSON K B. On the experimental attainment of optimum conditions [M]. KOTZ S, JOHNSON N L Eds. Breakthroughs in Statistics. New York: Springer-Verlag Inc., 1992: 270–310.

[21] YANG Peng, LIU Ying-wen, ZHONG Ge-yu. Prediction and parametric analysis of acoustic streaming in a thermo acoustic Sterling heat engine with a jet pump using response surface methodology [J]. Applied Thermal Engineering, 2016, 10: 1004–1013.

(Edited by HE Yun-bin)

中文导读

液压集成块直角转弯流道的流动测量及参数优化

摘要：本文研究了典型液压集成块中具有不同刀尖角容腔的直角流道的流场特征。搭建了低速可视化试验台，采用2D-PIV技术测量了具有不同刀尖角容腔结构的直角流道流场。建立了全三维数值模型并开展数值模拟研究，通过与粒子图像测量(PIV)测量结果进行比较，比较了七种湍流模型在流场预测中的准确性。通过定义权重误差函数K，筛选出S–A模型作为合适的湍流模型。通过3因素3水平响应面数值试验，研究了流道连接类型、容腔直径和容腔长径比对压力损失的影响。结果表明，Box-Benhnken Design(BBD)模型可以准确预测总压力损失。最优模型是II型流道连接，直径为14.64 mm，容腔长径比为67.53%，总压力损失相对于最差模型可下降11.15%。如能进一步采用圆弧型直角转弯流道，总压力损失可降低64.75%，这为液压集成块流道优化设计提供了新的方向。

关键词：流量测量；粒子图像测量(PIV)；直角流道；参数优化

Foundation item: Projects(51705446, 51890881) supported by the National Natural Science Foundation of China

Received date: 2018-04-25; Accepted date: 2018-11-01

Corresponding author: HU Jian-jun, PhD, Associate Professor; Tel: +86-335-8074618; E-mail: kewei729@163.com; ORCID: 0000-0001-7491-7899