Journal of Mechanics Engineering and Automation 3 (2013) 29-34

Flow Loss in Screens: A Fresh Look at Old Correlation

Ramakumar Venkata Naga Bommisetty, Dhanvantri Shankarananda Joshi and Vighneswara Rao Kollati Engineering Aerospace, MCOE, Honeywell Technology Solutions Pvt. Ltd., Bangalore 560037, India

Received: December 7, 2012 / Accepted: January 5, 2013 / Published: January 25, 2013.

Abstract: Pressure losses in flow components are generally characterized either by pressure loss coefficients or by discharge coefficients. The pressure drop for incompressible flow across a screen of fractional free area α is often calculated from widely used correlation provided in Perry’s Handbook. This correlation was developed based on experimental work which have covered a wide range of fractional free area (α = 0.14 to 0.79). The present work aims at validation for a flow in plain square mesh screen with a particular fractional free area (porosity, α) of 0.25 using CFD (Computational Fluid Dynamics) approach. The simulations are carried out for wide range of screen Reynolds number (Re = 0.1 to 105) covering both laminar and turbulent flow regimes. Initial simulations are carried out for incompressible fluid (water) and further extended to compressible fluid (air). Discharge coefficients obtained from the simulations are compared with experimental values. Effect of compressibility on discharge coefficients is described. Key words: Pressure loss coefficient, discharge coefficient, screen, fractional free area, CFD (computational fluid dynamics), compressibility.

1. Introduction

Fluid flow through screens takes place in a number of technical areas including filtering, mining and mineral processing, porous beds and a variety of flow straightening and turbulence reduction applications. Information on flow characteristics of these screens is very important factor while selecting the screens for different applications. Several experimental studies were carried out earlier to generate these flow characteristics for general purpose screens. Kays and London [1] did investigation on friction factor for four woven metal screens. Armour and cannon [2] investigated hydraulic resistance of five types of woven metal screens through experiments made in a circular channel with single layer of metal screen. They provided an equation for the calculation of pressure drop based on the flow velocity, the porosity and the geometry of the screen. Brundrett [3] did investigation on the prediction of pressure drop for incompressible

Corresponding author: Ramakumar Venkata Naga

Bommisetty, Ph.D., technology specialist, research fields: turbine cooling, heat transfer and CFD. E-mail: ramakumar.bommisetty@honeywell.com.

flow through screens. They developed a pressure loss correlation which predicts flow through screens for the wire Reynolds number range of 10−4 to 104 using the conventional orthogonal porosity and a function of wire Reynolds number. The correlation was extended by the conventional cosine law to include flow which is not perpendicular to the screen.

Sodré and Parise [4] designed an experimental procedure to investigate the friction factor of plain-square woven metal screen adopted in Stirling engine regenerator. They developed an equation to evaluate the pressure drop in annular bed of screens. Wu et al. [5] conducted experiments to measure pressure drop of the flow through woven metal screens. Four woven metals screens with different porosities of the plain-square type were tested and based on the tested study, an empirical equation was developed for friction factor characteristic of plain square type woven metal screens. They also developed five empirical equations respectively for five types of metal screens (Plain square, fourdrinier, full twill, plain dutch and twilled dutch types). Along with these resources, pressure drop across the screens is widely obtained

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from Perry’s Chemical Engineer’s Handbook [6] in which pressure drop (Δp) across the screens for incompressible fluids (for constant densities) is expressed as

2

2VKp ρ=Δ (1)

where ρ = fluid density, V = superficial velocity based upon the gross area of the screen, K = pressure loss coefficient.

The relation between pressure loss coefficient and discharge coefficients for such screens is obtained by

⎟⎟⎠

⎞⎜⎜⎝

⎛ −⎟⎠⎞

⎜⎝⎛= 2

2

2

11α

αC

K (2)

where C = discharge coefficient and α = the fractional free area or porosity which is defined as surface area of opening to the total area.

The discharge coefficient (C) for the screen with aperture Ds is given as a function of screen Reynolds number, Re = Ds(V/α)ρ/μ in a graphical form. This information is useful for plain square-mesh screens with wide range of porosity, α = 0.14 to 0.79. This graphical curve fits most of the data within ±20 percent. But this information is limited to incompressible flows.

An attempt has been made in this paper to model a screen and generate flow characteristics for a typical screen to cover a wide range of screen Reynolds number (Re = 0.1 to 105) using CFD. Commercial software ANSYS ICEMCFD (version 12.1) [7] is used for model and mesh generation. ANSYS CFX (version 12.1) [8] is used for solving and post processing. The reason for this tool’s selection is its flexibility and robustness for creating unstructured mesh using tetrahedral elements with embedded prism layers at the walls [7] and the solving capability of the tool with great accuracy [8]. All the simulations are performed under steady state conditions with quality and trust regarding grid refinement and iterative errors. Initial simulations are carried out with incompressible fluid (with water) and then extended to compressible fluids (with air). Discharge coefficients are calculated from pressure drop across the screen and are compared with the correlation available [6] for both the

incompressible and compressible flows. Effect of compressibility on discharge coefficient is also explored.

2. Numerical Set-Up

In order to simplify the simulations, a screen with an array of 5 × 5 holes is considered, shown in Fig. 1. As shown, holes are square in section with side of 0.015 mm and the gap between each hole is 0.015 mm. This screen leads to fractional free area (porosity) of 0.25. Screen length of 0.015 mm is considered for present study. This represents a typical screen used for flow straightening application. In order to have some duct length for flow to develop, an entry and exit duct of lengths 1mm each are considered. The full domain considered for the present study is shown in Fig. 2. ANSYS ICEMCFD (version 12.1) is used for model generation and mesh generation. Tetrahedral elements with prism layers are considered for grid generation. For the grid refinement study the grid is refined uniformly (by changing the maximum element size) while the number of nodes have changed by 2-3 times.

Regarding the boundary conditions for the simulations, the top, bottom and side faces (surrounding faces) are considered as walls. Velocity inlet condition is used for domain inlet. Pressure outlet with gage pressure of zero is applied for domain outlet. Simulations are also performed with symmetry boundary condition for surrounding faces and no considerable change is found in pressure drop with change of boundary condition. High resolution scheme is used to solve the continuity, momentum, energy and turbulence equations. The simulations are considered well converged when the monitored properties got stabilized and the RMS residuals has dropped to 1e-4. For the simulations with screen Reynolds number less than 10, flow is considered as laminar [6]. At higher Reynolds number, flow is considered as turbulent and standard k-ε model is used for turbulence closure.

Flow Loss in Screens: A Fresh Look at Old Correlation

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(a) Front view of the screen with an array of 5 × 5

(b) Isometric view of the screen

Fig. 1 Geometric details of the screen.

(a) (b)

(c) (d)

Fig. 2 (a) Mesh for the full domain; (b) Mesh distribution near the screen; (c) Mesh in the fluid domain; (d) Mesh and prism layer distribution in the screen.

3. Results

This part is divided into 3 sections dealing with grid refinement, screen characteristics for incompressible fluids and screen characteristics for compressible fluids.

3.1 Grid Refinement Study

This grid refinement study is performed with Reynolds number of 100 for three meshes. The parameter of interest is static pressure drop across the screen. Simulations are performed with nodes of 0.09M, 0.17M and 0.5M. The difference of static pressure drop across the screen is about 1.2% and the value obtained with 0.17M is closer to the experimental value compared to the other meshes. This accuracy is by all means good enough and since the computational time is reasonable with mesh of 0.17M nodes, this mesh is used for further analysis.

3.2 Screen Characteristics for Incompressible Fluids

As mentioned earlier, simulations are performed with incompressible fluid of water. Seven number of simulations with screen Reynolds number of 0.1, 1, 10, 100, 1000, 10000 and 100000 are performed. Flow with screen Reynolds number up to 10 is considered as Laminar and the simulations with other Reynolds number are treated as turbulent. K-ε turbulence model is used for turbulence closure. For the selected Reynolds numbers, inlet velocity is calculated from screen opening dimension and fractional free area. This value is supplied as the boundary condition at inlet.

Two rating stations, one at upstream of screen and the second one at downstream of screen, are considered for pressure drop calculation. Upstream station is considered at a distance of two hydraulic diameter of screen opening. Downstream rating station is considered at a distance of five hydraulic diameters of channel. Static pressures at these two rating stations are obtained from the converged solutions and discharge coefficients are calculated using Eqs. (1)-(2). Discharge coefficients for various screen Reynolds

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number are compared with the available experimental values [6], shown in Fig. 3. As is shown in Fig. 3, predicted discharge coefficient matches very well with experimental data up to Reynolds number of 10 (i.e., in the laminar region).

For turbulent region, simulations under predicted the discharge coefficients compared to the corresponding experimental data. Discharge coefficient has increased with increase in screen Reynolds number up to the screen Reynolds number of 1000 and there is no change in discharge coefficient with further increase in Reynolds number. Simulations are also able to predict the similar trend but the discharge coefficient got stabilized at 0.92 against the experimental value of 1.4. Discharge coefficients have crossed the value of unity in the experiments which is not observed with the simulations.

Velocity and pressure contours at selected planes along the stream wise direction are shown in Figs. 4a-4b), for screen Reynolds number of 1000. Location of selected planes and stream lines are shown in inset of Fig. 4. Complete mixing and uniform flow is observed on the upstream locations of the screen. As expected, higher velocities are found near the screen regions. Presence of screen is highlighted on the downstream locations. A fully developed profile in velocity is observed at outlet. From the contours of the pressure, it can be noticed that huge pressure drop is required to cross the screen. Pressure drop across the channel as a function of screen Reynolds number is shown in Fig. 5.

Fig. 3 Effect of screen Reynolds number on discharge coefficients.

(a) Velocity contours at selected planes

along the streamwise direction

(b) Pressure contours at selected planes along

the stream wise streamwise direction Fig. 4 Contours of CFD results.

Fig. 5 Pressure drop across the channel for various screen Reynolds numbers.

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The pressure drop across the screen is found to be proportional to the Reynolds number (velocity) for Reynolds number less than 10, and then increased as square of the Reynolds number for Reynolds number greater than 100. These observations are in line with the assumption of laminar flow lower Reynolds number (< 100) and turbulent for higher Reynolds number.

3.3 Screen Characteristics for Compressible Fluids

Simulations with compressible fluid, air, have been carried out to cover the similar range of Reynolds number. Simulations are run with the geometry shown in Fig. 1 up to screen Reynolds number of ~ 100. It is found difficult to get converged solutions for further increase in Reynolds number because of high mach numbers obtained in the screens. Dimensions of the screen are scaled and simulations are performed for further increase in Reynolds number. Using scaling, it has been possible to increase the Reynolds number even with lower mach numbers in the screen. Fig. 6 shows the comparison of predicted discharge coefficients with experimental and incompressible simulations. The maximum Mach number obtained at the entrance of screen in these calculations is 0.4. The maximum density variation across the screen is about 20% (for Reynolds number of 100). With this low Mach number and lower density variation, no considerable differences are observed in the dependence of discharge coefficient on Reynolds number. But slightly lower discharge coefficients are found with compressible fluid compared to incompressible fluids in turbulent region (Reynolds number > 100). Discharge coefficient for compressible fluid became constant at 0.85 against the value of 0.92 for incompressible fluid.

In addition to the aforementioned simulations, few more simulations are also performed in the screen Reynolds number range of 100-1000 with the initial screen dimensions to study the compressibility effects. Mach number in the screen is observed to be transonic

Fig. 6 Effect of compressibility on discharge coefficient.

in these simulations. Huge pressure drop is observed across the screen because of high mach exist in the screen. Variation of discharge coefficient with screen Reynolds number is shown in Fig. 6. As there is a considerable variation of fluid density on upstream and downstream locations, Screen Reynolds number is calculated based on upstream location. Drastic reduction in discharge coefficients is observed in these simulations with increased screen Reynolds number. Compressible effects have shown large impact on discharge coefficients. For the same Reynolds number for 1000, discharge coefficient has reduced from 0.8 to 0.41. It is noted that density variation across the screen plays an important role in discharge coefficients. So, the available correlation is found suitable for density variation below 20%.

4. Conclusions

A numerical study is carried out to find the flow loss in screens. Commercially available CFD code ANSYS CFX 12.1 is used for numerical study. Simulations are performed for both incompressible and compressible fluids. Laminar model is used for screen Re ≤ 10 and Standard k-ε turbulence model for higher screen Reynolds Numbers. Based on the present study, the following conclusions can be derived:

Predicted discharge coefficient values of incompressible fluid matched with the available experimental results up to screen Reynolds number of 10. But for the turbulent region, predicted discharge coefficients are lesser compared to the experimental

Flow Loss in Screens: A Fresh Look at Old Correlation

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values; Discharge coefficient has increased with increase

in Reynolds number up to screen Reynolds number of 1000 and then constant discharge coefficient is obtained with further increase in Reynolds number. The constant discharge coefficient obtained from the simulation is 0.91 against the value of 1.4 in experiments;

For compressible fluids, predicted discharge coefficients are in line with incompressible fluids till the density variation across the screen is about 20%;

Considerable reduction (maximum of 50% reduction) is noticed in discharge coefficient with higher density change for compressible fluids;

Density change of fluid in the screen is found to be stronger influencing parameter for flow loss in screens compared to the screen Reynolds number.

Acknowledgments

The authors are thankful to the management of Honeywell and HTS for permitting them to share the findings.

References

[1] W.M. Kays, A.L. London, Compact Heat Exchangers, McGraw-Hill, 1964.

[2] J.C. Armour, J.N. Cannon, Fluid flow through woven screens, AIChE Journal 14 (3) (1968) 415-420.

[3] E. Brundrett, Prediction of pressure drop for incompressible flow through screens, Journal of Fluids Eng. 115 (2) (1993) 239-241.

[4] J.R. Sodré, J.A.R. Parise, Friction factor determination for flow through finite wire-mesh woven-screen matrices, Journal of Fluids Eng. 119 (1997) 847-851.

[5] W.T. Wu, J.F. Liu, W.J. Li, W.H. Hsieh, Measurement and correlation of hydraulic resistance of flow through woven metal screens, International Journal of Heat and Mass Transfer 48 (2005) 3008-3017.

[6] D.W. Green, R.H. Perry, Perry’s Chemical Engineers Handbook, 8th ed., McGraw-Hill, 2008.

[7] ANSYS, User Manual ANSYS ICEM CFD/AI* Environment Release 12.1, ANSYS, Inc., Southpointe 275 Technology Drive, Canonsburg, PA 15317, November 2009.

[8] ANSYS, User Manual ANSYS CFX Release 12.1, ANSYS, Inc., Southpointe 275 Technology Drive, Canonsburg, PA 15317, November 2009.