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PRESSURE DROP OF PIPE FLOW IN A MANIFOLD BLOCK

Osamu ABE*, Tetsuhiro TSUKIJI*, Takeshi HARA*, and Kazutoshi YASUNAGA**

* Faculty of Science and Technology Sophia University

7-1 Kioi-cho, Chiyoda-ku, Tokyo, 102-8554 Japan (E-mail: t-tukiji@sophia.ac.jp)

** TOKYO KEIKI INC.

ABSTRACT

We deal with a solid manifold block and a laminated manifold block that are used for connecting hydraulic components. They are useful for reducing the space and weight of hydraulic systems. We investigate pressure drops of their pipe flow with computational fluid dynamics (CFD) and compare those of two types. The majority of all pressure drops in both types is pressure drop at corners. In solid type, pressure drop is affected by the distance between two corners and angle of corner against upstream corner. Solid type has round sectional area ,but laminated type has a square one. So, pressure drop of laminated type is smaller than that of solid type. By experiment of visualization with an acrylic manifold block and comparison of pressure drop of CFD results with experimental results, the validity of CFD results is proved unless heavy cavitation occurs.

KEY WORDS

Manifold block, Pressure drop, CFD, Pipe flow

NOMENCLATURE

ρ : Density ν : Kinetic viscosity Q : Volumetric flow rate p : Pressure pe : Pressure at exit θ : Angle L : Length ζ : Pressure loss coefficient pall : All pressure loss pA : Pressure loss at corner A pB : Pressure loss at corner B pf : Friction loss of pipe flow u : Flow velocity d : Pipe diameter

INTRODUCTION

Hydraulic machines have many valves and piping parts. So there are problems that much space is needed and plumbing is more troublesome. Recently, as one of the methods to reduce the space and piping parts, manifold system is developed. This system is the method of connecting valves and actuators by using steel blocks that have pipelines inside. These blocks are called 'Manifold Block'. It is said that pressure drop of pipe flow in the block because it has many curved section. However, pipe flow in the block has hardly been researched ever though curved pipe flow such as bend or elbow is researched by many workers. Manifold block is generally classified into two types by way of machining. One is a solid manifold block (solid type) that has some holes by drilling as shown in figure 1.

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The other is a laminated manifold block (laminated type) that is composed of some blocks grooved and drilled in advance. In solid type, design of pipeline is relatively simple since its pipeline only connects some holes, but it is impossible to design pipeline freely. On the other hand, in laminated type, it is possible to design pipeline freely because it has pipes of rectangular groove, but it is difficult to weld blocks. So it takes much time to manufacture laminated type.

Figure 1 Solid manifold blocks This study focuses on estimating pressure drop of pipe flow in two types as follows with CFD. And by using these results, we aim obtainment of guidelines for pipeline design in a manifold block. Furthermore, we also verify the validity of the CFD results by comparison of CFD results with pressure measurement. In this paper, however, we deal with a manifold block as port converter in case of substituting a valve as shown in figure 2(a) for another valve as shown in figure 2(b) when we compare two types.

(a) One port of valve (b) Another port of valve

Figure 2 Port standard of valves

NUMERICAL ANALYSIS

Objects of Analysis Figure 3 shows a port converter of solid type. And figures 4(a), (b) show flow channels in the block connecting T1 with T2 (solid-T) and P1 with P2 (solid-P). These channels go around because they must avoid tapped holes for attachment and other channels. Pipe diameter is 6[mm], partially 10[mm]. Red arrows in figures show flow direction. Figure 5(a) shows a port

converter of laminated type (laminated 1). This is composed of three blocks shown in figure 5(b). In the same, figures 6(a), (b) show flow channels in the block (laminated 1-T and laminated 1-P, respectively). Unlike solid type, it is possible to connect ports by curved channel. To compare with solid type, we deal with flow channels that are the same length as solid type channel as shown in figures 7(a), (b) (laminated 2-T and laminated 2-P, respectively). Cross section of groove is 6[mm] square.

Figure 3 Port converter of solid manifold block

(a) Solid-T (b) Solid-P

Figure 4 Flow channels in solid manifold block

(a) Block after attached

(b) Three blocks before attached

Figure 5 Port converter of laminated manifold block

(laminated 1)

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(a) Laminated 1-T (b) Laminated 1-P

Figure 6 Flow channels in laminated 1

(a) Laminated 2-T (b) Laminated 2-P

Figure 7 Flow channels in laminated 2

(like solid type) Analysis objects are the above six flow channels. In this paper, we analyze them by FLUENT6.3. SST k-ω model is used for turbulence model along the lines of the study in last year [1]. Inflow boundary condition is set to velocity inlet (uniform flow), and outflow boundary condition is set to pressure outlet (0[MPa]). Those flow channels contain tetrahedral and hexahedral cells. Properties of working fluid is ρ=870[kg/m3], and ν is =32[mm2/s] where T=317[K] (40 degrees). Results of Analysis Figures 8 (a), (b) show pressure on central axis of flow channel in Q=50[L/min]. The vertical axis shows the remainder of pressure (p) on central axis and outlet pressure (pe). Central axis of solid type is shown in figures 9 (a), (b). From figures, pressure drop at corners is the majority of pressure drop of flow channel in all types. Pressure drop of solid type at corners is different from each other, so it is found that the distance to previous corner and the bend angle of previous corner affect pressure drop in solid type. Laminated 1 and 2 have less pressure drop than solid type. When laminated 2 is compared with solid type, pressure drops of laminated 2 at corners are smaller than that of solid type. This is because laminated type has lager sectional area than solid type even if their flow channels have the same width.

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Figure 8 Pressure on central axis of flow channels

(a) solid-T (b) solid-P

Figure 9 Central axis of solid type Figures 10 (a), (b) show velocity vectors of entire flow channels of solid type in Q=50[L/min]. Figures 11 (a), (b) show velocity vectors on cross sections of corner d and e in figure 10 (a). Figures.12 (a), (b) also show velocity vectors on cross sections of corner b and d in figure 10 (b).

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(a) Velocity vectors of solid-T

(b) Velocity vectors of solid-P

Figure 10 Velocity vectors of solid type

(a) Cross section b (b) Cross section d

Figure 11 Velocity vectors on cross section of solid-T

(a) Cross section P1 (b) Cross section P2

Figure 12 Velocity vectors on cross section of solid-P

It is found that there are regions of large velocity (red regions in figures) after corners from figure 10, and velocity vectors like vortex are seen in figure 11 (a), figure 12 (a), but not seen in figure 11 (b), figure 12 (b). This is because the distance from corner c to d is shorter than the distance from corner d to e in Solid-T, and the bend angle of upstream corner is different from each other in corners b and d of Solid-P. Influence of the upstream corner on pressure drop at the downstream To investigate the influence of the upstream corner on flow pattern described above, we propose three flow channels as shown in figure 13. These channels have two corners. In this paper, the upstream corner is named corner A and the downstream corner is named corner B. They are different from the angle θ between inlet and outlet pipeline. Moreover, by varying the length L between corner A and B, we examine the influence of θ and L on pressure drop at corner B, where volumetric flow rate is Q=50[L/min] and all pipe diameter is d=6[mm].

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(a) θ=0°

(b) θ=90°

(c) θ=180°

Figure 13 Flow channels with two corners

To evaluate the influence of θ and L on pressure drop, pressure drop at corner B pB is defined as follows. pB=pall-(pA+pf) (1) where pall is the pressure loss of all pipeline, pA is the pressure loss at corner A, pB is the pressure loss at corner B, and pf is the friction loss of pipeline. Furthermore, pressure loss coefficient ζ, which is dimensionless quantity, is defined as follows. ζ=pB/{(1/2)ρu2} (2)

where ρ is the density of fluid (oil), u is the mean flow velocity, and u=29.47[m/s] for volumetric flow rate Q=50[L/min] and pipe diameter d=6[mm].

Figure 14 Relations between ζ and L/d for each θ The results is shown in figure 14. Horizontal axis L/d shows ratio between L and d. From figure 14, it is found that the transition of ζ differ by θ, especially in case of L/d<5,and ζ approach a constant value for L/d>13 in any θ. In case of θ=90° and 180°, ζ is minimized for L/d≈6, while, in case of θ=0°, the smaller L/d is, the smaller ζ is.

EXPERIMENT Experimental Apparatus and Method We manufacture port converter of manifold blocks (test piece) that have the same flow channel that is used in CFD analysis, and prepare experimental apparatus for measuring pressure shown in figures.15 (a), (b). These manifold blocks are attached to blocks for connecting electronic pressure sensors, a block for returning oil flow from B to T or from P to A, electronic pressure sensors, A/D converter, and 24 [V] power supply. Data of voltage are transmitted from pressure sensor to A/D converter and converted to pressure data. In this paper, pressure drop of each flow channel is defined as the pressure gap of upstream data and downstream data. By comparing with experimental results, we verify the validity of the CFD results. Temperature of working oil is about 40 degree to fit condition of CFD analysis.

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(a) Pressure measurement of flow channels of T

(b) Pressure measurement of flow channels of P

Figure 15 Experimental apparatus for measuring pressure Comparison of Analysis with Experiment Figures 16 (a), (b) show the relations between volumetric flow rate and pressure drop of solid type. Figures 16 (c), (d) show the relations between flow rate and pressure drop of laminated type. In solid type, there is a tendency that experimental values are about 15 percent smaller than CFD results from 20[L/min] (Reynolds number is about 2,200) to 70[L/min] (Reynolds number is about 7,700). Reynolds number is based on pipe diameter, the mean velocity of flow, and kinetic viscosity. So it is found that it is possible to regard pipe flow in solid type as turbulent flow even if Reynolds number is small in case flow channel has many corners. In laminated type, experimental values show good agreement with CFD results except laminated 1-T. In laminated 1-T, the more the flow rate increase, the larger the error between experimental values and CFD results.

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Figure 16 Relations between flow rate and pressure drop

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So when we manufacture an acrylic test piece of laminated 1 and observe oil flow in laminated 1 to investigate factors, luminescence by heavy cavitation [2] is seen at a red circle in figures 17(a), (b) in case of more than 50[L/min]. This is the factor of the error. Figure 17 (a) shows a direction for visualization of laminated 1-T. A picture of cavitation is shown in figure 17 (b).

(a) Direction for visualization of laminated 1-T

(b) Picture of cavitation

Figure 17 Luminescence by heavy cavitation

CONCLUSIONS This paper focuses on estimation of pressure drop of pipe flow in two types of manifold block with CFD analysis, verification of the validity of CFD results by comparison with experimental results, and obtainment of guidelines for pipeline design in a manifold block. Also, we investigate pipe flow from velocity vectors, pressure distribution, and pressure drop. The conclusions of this paper are as given below. (1) Pressure drop at corners is the majority of pressure

drop of pipe flow in manifold block. (2) At corners of solid type, pipe flow pattern is varied

by the distance L and the angle θ, which affect pressure drop at corners.

(3) Pressure drop of laminated type is smaller than that of solid type because laminated type has lager sectional area than solid type even if their flow channels have the same width.

(4) Unless heavy cavitation occurs, it is proved that

estimate of pressure drop with CFD is valid by comparison with experimental results.

REFERENCES

1. Takeshi Hara, Research on pipe flow in a manifold block, The Proceedings on Spring Conference of Fluid Power System Society, 2010, pp 4-6. 2. T. G.LEIGHTON, M.FARHAT, J. E.FIELD and F.AVELLAN, Cavitation luminescence from flow over a hydrofoil in a cavitation tunnel, Journal of Fluid Mechanics, No.480, pp.43-60 (2003)

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