Airflow resistance analysis of wire screens used in waste heat recovery systems

Wire screens are widely used in electronics, refrigeration, insect screens, food processing, filtration, oil refinery, agricultural, and other applications. For instance, these wire screens are used as heat exchange materials in regenerators due to higher surface area density. Heat transmission can typically be enhanced by increasing the surface area density of wire screens, however flow obstruction is a possibility. As a result, this wire screen analysis is necessary not only to estimate the heat transfer rate but also to assess the airflow obstruction. This extensive study investigates the role of wire screens in a wind tunnel on the different velocities of air moving through them in order to compute the pressure drop. Six wire screens were examined as part of this investigation, and the experimental results were utilised to derive the coefficients of second order polynomials (a,b, and c). Permeability and inertial factor were calculated using this second order polynomial and Forchheimer’s equations. Second-order polynomial equations were found to be the best fit for the permeability versus porosity ratio and the inertial factor versus porosity ratio.


Introduction
Fluid flow through wire screens is important in many industrial and domestic applications, including paper industry design, pharmaceuticals, and filtration, among others.There are numerous benefits to using porous media to improve the rate of heat and mass transfer in energy systems.Many researchers concentrated on analysing the fluid flow performance of a wire screen using different wire densities, wire diameters, weaving structures, and materials.The study's goal was to demonstrate that pressure drop for various types of screen weaves can be predicted.Armour and Canon [1] investigated the flow of Newtonian fluids through the wire screen to predict the pressure drop in a packed system of various weave screens.The method for collecting pressure drop-velocity data for the flow of nitrogen and helium through various types of weaves is described.Xu et al [2] studied the brazed woven screen's pressure drop and heat transfer rate.They calculated the impact of different wire screen configurations.It was also discovered that the porosity is near 0.81, indicating maximum heat dissipation.Tian et al [3] estimated the fluid flow and heat transfer rate between copper wire screens and opened cell copper foams through experimentation.The copper wire screen meshes were discovered to be good due to their low pumping power when compared to metal foams.Furthermore, wire screens have a higher thermal performance than copper foams.Hellstrom and Lundström [4] performed the simulations in fluid flow between parallel cylinders, and the simulation results were validated using a grid refinement study.According to the simulation results, inertia effects should be considered up to Re 10.Furthermore, the Ergun equation is suitable for simulating fluid flow through porous media up to Re 20.
Miguel et al [5] conducted experiments and analyses to investigate the airflow properties of some commonly used greenhouse screens.The Forchheimer equation was used to define the airflow properties of nine different thermal, shading, and insect screens in terms of permeability and porosity.The performance of a moving bed regenerator was investigated by Almendros-Ibanez et al [6].The pressure drop and heat dissipation in the inside moving bed was calculated.Additionally, the length and width of the regenerator were tested, as well as the velocity and flow rate.Okolo et al [7] introduced a novel method for identifying and differentiating fluid flow regions upstream, downstream, and within wire screen pores, showing areas of velocity change as well as turbulence quantity changes.As aircraft landing gear noise reduction treatments, wire screens have been proposed.
Sayed et al [8] investigated experimentally a cross-flow regenerator with three different types of wire screens.Plain copper tubes and wire screens in various positions were compared, and the results indicated that the heat transfer rate could be increased by up to 114%.Pamuk and Ozdemir [9] investigated the oscillating and steady flow of water in the packed steel balls.The permeability and inertial factor of oscillating flows were found to be higher than those of steady flows of water through packed balls.For steady flow, the inertial coefficient is 0.598, while for oscillating flow, it is 0.758.Furthermore, the friction factor in a steady flow of water is lower than that in an oscillating flow.
Dierickx [10] tested synthetic screens in both water and airflow equipment to determine their flow reduction coefficient.Because water and uncompressed air flow obey the same laws, similar results were obtained.In addition, a relationship between the open area of the fabrics and the flow reduction coefficient was discovered.Sung and Liu [11] investigated heat transfer in a rectangular pipe with many air jets experimentally.The channel was filled with wire screens.The porous filling ratio and jet Reynolds number were investigated.Porous material has obstructed airflow and reduced the surface Nusselt number.Moreover, the Nusselt number was lower in the filled channel than in the unfilled channel.The porous material also changed the flow pattern and affected the flow of the jet core.Defraeye et al [12] studied the convective drying of the porous flat plate.The drying behaviour was predicted by the conjugate model and also verified with porous modelling using convective transfer coefficients.It was found that the spatial and temporal constant convective transfer coefficients have a good impact on the drying behaviour.Dehghan and Aliparast [13] numerically studied laminar forced convection in a porous channel.It was discovered that larger particle diameters provide better heat transfer performance than smaller particle diameters.Fluid flow in a porous channel with slots was calculated using the Brinkman-Forchheimer equation.
Shuangtao et al [14] performed simulations for the design and heat flow analysis of a wire screen.The effectiveness-NTU method was used to validate the numerical model, which was then compared to experimental results.The effectiveness was increased by increasing the length of the wire screen with a high flow rate.Haji-Sheikh and Vafai [15] investigated the heat transfer rate to the flow of fluid passing through a porous medium channel.In addition, the modified Graetz problem in rectangular pipes and circular tubes was considered.
Krishnakumar and Anjan [16] used transient testing methods to investigate steel and galvanized iron wire mesh regenerators and determined the Colburn factor and fanning friction factor.As a result of higher thermal diffusivity, the Colburn factor for galvanized iron wire mesh regenerator was found to be high.Dyga and Placzek [17] studied heat exchange and pressure drop in a channel with and without wire mesh packing.The air in the channel with wire mesh was heated more, and the flux of heat exchange was greater than in an empty channel.Muralidar and Suzuki [18] examined the movement of gas in the screens as a non-Darcy flow and nonequilibrium heat exchange in a wire-screen regenerator.Peng et al [19] conducted experimental research on the internal flow patterns of woven wire mesh with varying porosity.The permeability and inertial factor of woven wire screens of various diameters were investigated, and the results revealed that the larger wire diameter structure provides better penetrating quality.
Teruel and Rizwan-uddin [20] demonstrated a large number of microflow modelling in the Representative Elementary Volume (REV) of a porous medium made up of staggered square cylinders.The permeability of the porous medium is calculated using these microscopic results, and a porosity-dependent relation for this macroscopic measurement is developed.Liu et al [21] studied fluid flow and heat transfer characteristics to estimate the flow pattern of sintered metal wire mesh structures, and a new empirical friction factor equation was proposed.Sodre and Parise [22] investigated fluid flow through finite woven screens to predict the friction factor.Based on screen dimensions and layer count, an expression for measuring the porosity of plain square wire-mesh woven-screen beds has been developed.
Costa et al [23] performed a numerical analysis of the pressure drop in a stirling regenerator made of woven wire screens.New correlations for various flow configurations were developed to describe the pressure drop friction coefficient.Alejandro Lopez Martinez et al [24] investigated the use of insect proof screens with optimised porosity to improve greenhouse ventilation while also preventing pest entry.Sabri Ergun [25] studied fluid flow through granular solids beds and discovered that simultaneous kinetic and viscous losses affect pressure losses.Trilok G et al [26] investigated the temperature and flow properties of such a substrate, numerically simulating a vertical tube housing the specified wire-mesh porous media.The expressions proposed in this study are intended to be useful in the numerical modelling of flow and heat transfer in porous media with varying morphological parameters.Meir Teitel [27] examined how insect-proof screens affected roof apertures.Screens that produced a larger pressure drop for a given air velocity in wind tunnel testing have been demonstrated by experiments in a greenhouse with leeward roof openings where screens were installed.
In the current investigation, the various wire screens were tested in the wind tunnel experimental setup, which allows a flow of forced air through the porous medium.The results of this study can be utilised to compute the permeability and inertial factor by evaluating the airflow performance through wire screens.The permeability of a porous substance is an estimate of the degree to which a fluid can flow through it.Inertial effects are identified using the Ergun coefficient and the kinetic energy of the fluid.

Darcy-forchheimer equation
The frictional pressure loss through a porous medium, which is brought on by a combination of pressure and shear forces, can be calculated empirically using the Darcy-Forchheimer equation.Although Darcy's law was discovered by experimentation, it has subsequently been obtained by homogenization techniques from the Navier-Stokes equations.It is used to describe the movement of gas, water, and oil through petroleum reservoirs, as well as the flow of water through an aquifer.
The motion of viscous fluid materials is described by the partial differential equations known as the Navier-Stokes equations.The momentum balance for Newtonian fluids and the application of mass conservation are mathematically expressed by the Navier-Stokes equations.An equation of state connecting pressure, temperature, and density may occasionally be included with them.
The instantaneous flux through a porous medium, the permeability, the fluid's dynamic viscosity, and the pressure drop over a given distance in a homogeneously permeable material have a simple proportionality relationship as follows: The Darcy law's integral form is given by: The flow velocity (u) is related to the flux (q) by the porosity (ε), which has the following form: ( ) e = u q 3 Forchheimer described fluid flow across porous medium and suggested modifying Darcy's Law:

Theoretical background
The Darcy's law is applied to the study of creeping fluid flow (Re«1) through a porous medium [5].It depicts the connection between flow rate and pressure drop.The pressure gradient with velocity through the wire screens is expressed as follows, The Forchheimer equation ( ) Where β is the Forchheimer coefficient, C E is the Ergun constant, and it accounts for inertial effects.A modified Forchheimer's equation [24] can be used to define air flow through the highly porous material, as shown equation (5); Bernoulli's equation is also used to investigate fluid flow resistance through porous materials [5].The discharge coefficient is used to calculate the airflow pressure drop through the wire mesh when the Reynolds number is greater than 150 [24].The flow is not controlled by the first term in (5), so it can be eliminated, yielding the Bernoulli equation as follows,

Experiments in a wind tunnel
Wire screens are frequently used as heat exchange materials in regenerators because of their greater surface area density.The function of such stacked wire meshes in a regenerator is highlighted in our research.In the wire screen analysis, the resistance to airflow is determined using a wind tunnel experimental setup that transfers forced air through the porous materials (figure 1).
Its goal is to study different wire screen densities and wire diameters in order to examine fluid flow performance.The permeability and inertial factor are also used in this analysis to determine the airflow properties of wire screens.
The experiment was carried out in a suction type low velocity subsonic wind tunnel with a length of 6470 mm, a test section cross-section of 300 mm square, and a length of 1500 mm (figure 2).The contraction length is 1150 mm, and the diffuser length is 2000 mm.The maximum airflow velocity that this wind tunnel can provide is 60 m s −1 .
Some commercial stainless steel wire screen meshes were tested for wire screen function in a low velocity subsonic wind tunnel at various air velocities to calculate pressure drop (figure 3).The porosity in the table above is computed as the ratio of screen void volume to total screen volume.In the contraction, the cone has transferred the airflow with proper velocity and pressure of air to the test section.The design of this cone is critical because it has the potential to influence airflow properties.Also, the length of the tunnel is an important parameter that affects the constant speed profile.The axial fan is used to supply the air with a maximum speed of 1500 rpm.The fan speed was controlled by an inverter.
The performance of wire screens was determined using the tunnel's test section size of 300 × 300 × 1500 mm.The wire screens were placed in the centre of the test section.The airflow velocity was controlled by an alternating current inverter.The constant current inputs have a linear relationship with the inverter response and range from 0 to 10 volts and the inverter frequency range from 0 to 50 hertz.An electronic circuit with a microprocessor that receives instructions from a computer monitored the inputs.The pressure variations were measured with two pitot tubes placed 40 cm from the center of the test section.The airflow velocity was   measured using a Scanivalve-Miniature pressure scanner (MPS4262) with a sampling frequency of 850 Hz (samples/channel/second), 64 channels, 0.06% full-scale long-term accuracy, and a pressure range of 0-50psi.

Results and discussion
The experiment was carried out to investigate the function of wire screens in the wind tunnel at various velocities of air passing through them in order to calculate the pressure drop.The coefficients a, b, and c of the second order polynomial as well as the coefficient of determination R2 are provided in table 1 for the six different types of wire mesh.Table 2 shows the pressure drop measured in the wind tunnel with varying upstream velocity through wire mesh 20.Six different types of wire screens were tested (table 3).
As shown in figure 4, the pressure drop through the wire screen increases as velocity increases.The experimental results were displayed as pressure drop versus velocity for each test sample, as shown in figures 5 and 6.
According to Miguel et al [5], it was predicted that a second-order polynomial could be used to fit the experimental results when analysing the pressure drop through the porous medium.The curves measured in all wire screen samples appeared to be best fit by a second order polynomial equation.
Equating the firstand second-order terms of Forchheimer's equation (5) with the above polynomial's firstand second-order terms yields: A porous material's permeability is a measure of how easily a fluid can flow through it; the greater the permeability, the higher the flow rate for a given fluid pressure gradient.Inertial effects are observed by the Ergun coefficient and the fluid's kinetic energy.The high velocity flow regime coefficient should be adjusted to allow for the experimental inertial effects.The permeability, K, and inertial factor, Y can be calculated using equation (8) if the fluid propertiesμ, ρ and screen thickness, Δx are known.Fitting a polynomial equation to experimental pressure drop versus air velocity results yielded the permeability and inertial factor for all tested wire screens.
For all of the wire screen samples examined, equation (5) fit the data well.If the best fit coefficients for the second-order polynomial are found, the permeability K and inertial factor Y can be calculated using equation (8).The results are displayed in table 4. Figure 7 shows the wire screens permeability versus porosity and inertial factor versus porosity.The permeability of the wire screen increases as its porosity increases.Furthermore, the inertial factor decreases as the porosity of the wire screen increases.The best-fitting equations with experimental data are listed below,    The expressions for permeability and inertial factor have been obtained, indicating that the geometrical properties of the mesh have little influence on the values of parameters.The results demonstrated that second-order polynomial equations were best suited for fitting the permeability versus porosity ratio and the inertial factor versus porosity ratio.For the porosity range of 0.67 to 0.86, the best fit equation described by the relationship between permeability, inertial factor, and porosity of the wire screen is a second order polynomial.

Conclusion
The airflow resistance of six wire screens was tested in this experiment.A detailed study was carried out to determine the impact of wire screens on various air velocities in a wind tunnel in order to estimate the pressure drop.Pressure drop versus velocity pairs for wire screens can be fitted to a second-order polynomial with a high coefficient of determination (R2) using the Forchheimer equation.Permeability and inertial factor for wire screens have been computed based on these fittings.With just a little amount of influence from the values of permeability (K) and inertial factor (Y) as a function of porosity, the geometric parameters of the wire screens were determined.The second order polynomials that describe the relationship between the permeability and inertial factor of the wire screens with respect to porosity provide the best fit equations for the porosity range of 0.67 to 0.86.According to the results, it is possible to use the current analysis to look at how changing wire screen geometrical characteristics can enhance regenerator performance.The performance of wire screens with regard to heat transmission will be assessed in my further study.

[ 5 ]
can be used to describe steady-state fluid flow at high velocity through a porous medium (Re >1).It discovers that as flow velocity increases, inertial effects dominate the flow.Attempting to account for high velocity inertial effects in the Darcy equation by incorporating an inertial term representing the fluid's kinetic energy.The vector form of the aforementioned equation with the Ergun constant [25] is shown equation (3); the coefficient is theoretically challenging to figure out.This value is derived from experiments with real-world applications.

Figure 2 .
Figure 2. (a) A low velocity subsonic wind tunnel test rig, (b) Wire screens are placed on the test section.

Figure 7 .
Figure 7. (a) Permeability of wire screen versus porosity, (b) Inertial factor of wire screen versus porosity.

Table 1 .
Stainless Steel Wire screen specifications and best fit equation for second order polynomial (Δp = au 2 +bu+c ).

Table 2 .
Mesh 20was tested for pressure drop and velocity in a wind tunnel.

Table 3 .
Six wire screens were tested in a wind tunnel for pressure drop and velocity.

Table 4 .
Permeability and inertial factor calculated for six wire screen meshes.porosity.