Research Papers: Flows in Complex Systems

Pressure Drop in Generating Free-Surface Liquid Microjet Array From Short Cylindrical Orifices

[+] Author and Article Information
Avijit Bhunia

C. L. Chen

 Teledyne Scientific Company, 1049 Camino Dos Rios, Thousand Oaks, CA 91360

J. Fluids Eng 133(6), 061103 (Jun 15, 2011) (8 pages) doi:10.1115/1.4004085 History: Received August 10, 2010; Revised April 22, 2011; Published June 15, 2011; Online June 15, 2011

Liquid microjet arrays have received a lot of research attention in recent years due to its high heat flux cooling capability. The microjets are generated from a jet head cavity with a liquid inlet port on one wall and an array of micro-orifices on another wall. An important, yet relatively less studied aspect of the topic is the pressure (also frequently referred to as the pressure drop) necessary to generate the jets and maintain certain jet velocity. In this study we investigate the pressure drop for17 different array patterns of liquid jet issuing in a surrounding gas (air) medium, i.e., a free surface liquid jet. The number of jets varies from 1 to 126, while the jet diameter ranges from 99 to 208 μm. The current results show more than 200% deviation from the existing correlations in the literature. Through a systematic experimental study we identify the functional dependence of pressure drop on the various geometric parameters. The results uncover the reasons behind the widespread disagreement between the current data and the existing correlations. Pressure drop shows a weak, nonlinear dependence on the orifice wall thickness, compared to the linear dependence used in the existing correlations. Furthermore, the depth of the jet head cavity is shown to be an important parameter dictating pressure drop, unlike the previous studies that inherently assume the cavity to be an infinite reservoir. A new dimensionless pressure drop parameter is proposed and its variation with the jet Reynolds number is correlated. The new correlation predicts all the experimental data within a ± 10% range.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

Schematic of jet head cavity with liquid inlet port (tube of diameter Dt ) and orifice wall with micro-orifices, generating free surface liquid microjet array. Insets: Microscopic image of the orifice wall, and SEM image of a 100 μm diameter orifice.

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Figure 2

Dimensionless pressure drop (f) versus Reynolds number of individual jet (Rej ): Comparison of some of the present experimental data for various jet array configurations with the existing correlations in literature [1,11]. The geometric details of each jet pattern are listed in Table 1.

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Figure 3

The effect of number of jets on pressure drop: Variation of dimensionless pressure drop (f) with individual jet Reynolds number (Rej ) for various number of jets (Nj ). Dimensionless orifice wall thickness (t/Dj ) held constant at 6.4. Data set 1: Dimensionless pitch (Pj /Dj ) and jet head cavity length (Ljh /Dt ) held constant at 22 and 2.4, respectively. Nj  = 21, 50, and 70 for patterns J, K, and F, respectively. Data set 2: Ljh /Dt  = 2.7. Pattern E—Nj  = 90, Pj /Dj  = 18, and pattern D—Nj  = 126, Pj /Dj  = 22.

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Figure 4

The effect of orifice wall thickness (t) on pressure drop (ΔP). (a) Variation of dimensionless pressure drop (f) with individual jet Reynolds number (Rej ) for various dimensionless orifice wall thickness (t/Dj ) conditions. Dimensionless jet head cavity length (Ljh /Dt ) fixed at 2.4 ± 0.03. Pattern A—12 jets, patterns G, B, I, J—21 jets. (b) Variation of f with (t/Dj ) for Rej  > 1200. The y axis is an average f value of the experimentally measured data for Rej  > 1200, termed the “Saturated regime.”

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Figure 5

Numerical simulation of a single jet. Geometric details: cavity size (Ajh ) = 0.01 m × 0.01 m, cavity depth (Ljh ) = 0.006 m, orifice diameter (Dj ) = 150 μm, orifice wall thickness (t/Dj ) = 2.4, and area contraction ratio αj  = 0.0177%, similar to the experimental condition. Jet Reynolds number (Rej ) = 1408. (a) Geometry of the simulation domain—one quarter of the jet head cavity, and the orifice tube; (b) flow pathlines from the jet head cavity into the orifice; (c) z velocity contours inside the orifice tube. Positive z velocity indicates a flow reversal, leading to formation of a recirculation cell.

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Figure 6

The effect of jet head cavity geometry, length (Ljh ), and area (Ajh ) on pressure drop (ΔP). (a) Variation of dimensionless pressure drop (f) with individual jet Reynolds number (Rej ) for various dimensionless cavity length (Ljh /Dt ) conditions. Data set 1: (Ajh /At ) varied between 5.5 in pattern N to 13.8 in pattern A. Orifice wall thickness (t/Dj ) and jet head cavity length (Ljh /Dt ) held constant at 2.6 and 2.4, respectively. Data set 2: Jet head cavity area (Ajh /At ) and orifice wall thickness (t/Dj ) held constant at 5.5 and 2.4, respectively, while jet head cavity depth (Ljh /Dt ) is varied among patterns M, O, and P. (b) Variation of f at the saturated region (Rej  > 1200) with dimensionless jet head cavity depth (Ljh /Dt ). (Ajh /At ) and (t/Dj ) constant at 5.5 and 2.4, respectively.

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Figure 7

Schematic of flow field inside the jet head cavity and close to the orifice inlet for a multijet array

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Figure 8

Proposed new dimensionless pressure drop parameter (Ω), and its variation with jet Reynolds number (Rej )




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