PIV measurements and a CFD benchmark study of a screen under fan-induced swirl conditions

International Journal of Heat and Fluid Flow 46 (2014) 43–60

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PIV measurements and a CFD benchmark study of a screen under fan-induced swirl conditions Asier Bengoechea ⇑, Raúl Antón, Gorka S. Larraona, Alejandro Rivas, Juan Carlos Ramos, Yunesky Masip Thermal and Fluids Engineering Division, Mechanical Engineering Department, Tecnun (University of Navarra), Manuel de Lardizábal 13, 20018 San Sebastián, Spain

a r t i c l e

i n f o

Article history: Received 6 August 2013 Received in revised form 5 December 2013 Accepted 20 December 2013 Available online 21 January 2014 Keywords: Swirl flow Push cooling Perforated plate Particle Image Velocimetry Pressure drop Turbulence modelling

a b s t r a c t A perforated plate placed behind an axial fan (push cooling) is a common assembly in electronic systems. The flow approaching the screen will have a swirling component, and therefore, there is uncertainty in the prediction of the flow pattern at the outlet of the screen and the pressure drop through the screen. Correctly predicting the flow field is important in order to properly place the electronic components. This work tries to give some insight into these issues. A wind tunnel was manufactured in order to produce the typical flow field at the outlet of an axial fan and to measure the field at the inlet and at the outlet of the perforated plate using the Particle Image Velocimetry (PIV) technique; the pressure drop through the screen was also measured. The velocity contours measured at the screen inlet were used as boundary conditions for computational fluid dynamics (CFD) simulations. Several turbulence models (k–e, k–x and RSTM) and their variations were used for the simulations and the results at the outlet of the perforated plate are compared with the Particle Image Velocimetry results. Two screens with very different geometrical characteristics were used. Results show that if k–e models are used a significant error is made in the prediction of the velocity field and in the pressure drop. Although the k–x models predicted better than the k–e models, the RSTM were shown to be the most reliable. Ó 2014 Elsevier Inc. All rights reserved.

1. Introduction Thermal management has become a major issue when designing electronic equipment. Nowadays, due to customer demand, electronic devices have to be smaller while also having larger data processing speed. This trend involves increasing the number of transistors in the devices. This factor, along with others, results in greater heat generation per unit of volume. It is normal to set electronic equipment in an electronic cabinet or rack, and given that each rack has several sub-racks, it means that each sub-rack has several PCBs (Printed Circuit Boards). The heat generated by the PCBs must be removed from each of these levels via an appropriate cooling strategy, e.g. liquid cooling, air cooling, etc. There is interest in extending the limits of air cooling by using, for example, a cross flow and jet impingement Masip et al. (2012). For some special cases where there is an extremely high heat flux, liquid cooling must be used (see for example studies with spray cooling Martínez-Galván et al. (2013a,b). However, the most common technique used at the sub-rack level is still air cooling due to safety and availability. An electromagnetic compatibility (EMC) screen placed behind an axial fan (push cooling) is a common assembly in electronic systems. This screen is placed in a device in order to meet ⇑ Corresponding author. Tel.: +34 943 219 877; fax: +34 943 311 442. E-mail address: [email protected] (A. Bengoechea). 0142-727X/$ - see front matter Ó 2014 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.ijheatfluidflow.2013.12.007

electromagnetic compatibility requirements, and its design must provide a sufficient free area ratio to tolerate a correct airflow for refrigeration purposes. Furthermore, the holes of the screen must be small enough to block electromagnetic radiation. According to Ott (1988), the maximum aperture size should be less than 1/20th of the source wavelength. Different solutions for this problem (free area ratio versus electromagnetic radiation) are being studied, as described by Siebert (2006). The configuration of the cabinets has evolved over the years. Several years ago, one fan tray was placed at the bottom part of the cabinet in such a way that the flow went through all the subracks and it was rejected at the top of the cabinet. Later on, the power dissipation from the electronics increased to the extent that it was necessary to use a fan tray for each of the sub-racks. Nowadays, this is not sufficient for some applications, and a pull–push configuration is used for each of the sub-racks (two fan trays placed either from bottom-to-top or side-to-side). In this way, a correct airflow rate is achieved. In order to know the airflow rate that the fans provide to the system, the operating point must be obtained. This point is the result of the intersection between the hydraulic resistance curve of the system (this curve is influenced by many parameters, as shown by Auld (2004)) and the characteristic curve of the fan (static pressure versus volumetric flow rate). Placing the screen very close to the fan could affect the characteristic curve of the fan hydraulically. This effect has been studied by Hill (1990), Grimes

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et al. (2001), Lin and Chou (2004), Swim (2005) and Antón et al. (2012), among others. The pressure drop in a screen is important in order to know the hydraulic resistance of the system. The pressure loss coefficients that define the pressure drop through a screen when the flow is perpendicular to the perforated plate can be found in several handbooks, such as the one by Idelchik (2003). The problem is that these handbooks are not able to give pressure loss coefficients when the flow is more complex, like in a fan-induced flow. Brundrett (1993) introduced the effect of an inclined flow in the pressure drop through a screen, he concluded that if the velocity magnitude remains constant, the pressure drop is proportional to the square of the velocity component perpendicular to the thin screen. Bejan et al. (1995) applied the intersection-of-asymptotes method to the cooling of stacks of plates shielded by screens, though in that case the airflow was perpendicular to the screens. Antón et al. (2007a,b) in two publications implemented some correlations that provide the pressure drop and flow pattern after a screen in a sub-rack with a 90-degree pull configuration (air inlet is perpendicular to the flow over the PCBs). Furthermore, another important issue is to predict the flow field after the screen. From this point of view, a pull configuration is normally not complex due to the flow at the inlet of the screen that is perpendicular to it. However, a push configuration is complex (see Fig. 1). This configuration produces a non-even axial velocity profile together with a non-even tangential or rotational velocity profile. In front of the slots where the PCBs are placed, an EMC is normally placed as explained above (sometimes there is just a fan-tray guard and this is to a certain extent a similar scenario: a flow obstruction). Antón et al. (2007a,b) analysed the influence that a screen (in a push configuration) has both on the flow pattern and on the pressure drop. The screen will straighten the flow to a certain unknown extent. Knowing to what extent the perforated plate modifies this swirling component is important in order to predict a correct velocity field in the system. This issue has been studied for telecommunications cabinets where air is sucked

Fig. 1. Scheme of push configuration.

through an inlet slot and then it turns 90-degrees and flows into the PCB slots, as was reported in Antón et al. (2007a,b) It is shown that more than one pressure loss coefficient is needed to model a screen in order to predict the change in the flow pattern when the approaching flow is not perpendicular. Kordyban (2000) compared a planar resistance (one pressure loss coefficient) with a volumetric resistance (more than one pressure loss coefficient). They concluded that the flow pattern will not be correctly predicted using a planar resistance if the flow is not perpendicular to the screen, although a correct pressure drop could be obtained. However, in none of these studies is the approaching flow to the screen created by an axial fan. These articles tried to explain this effect since it is very important to know the velocity field at the outlet of a screen in cases like those in Fig. 1. This importance is because of the high correlation that always exists between the air velocity magnitude and the heat transfer coefficient. The flow in each of the slots in the figure will be affected by the screen, and it may be different for each of the slots. Since it is a 3D phenomenon, the use of CFD is required. Furthermore, the flow that is produced by a fan is turbulent and this implies a need for a benchmark of turbulent models. This benchmark requires a reference, namely an experimental validation. A fast design time is one of the most important issues in today’s market, and the thermal designer does not have time to run the required simulations or even do the modelling. The goal of this article is not only to carry out the analysis that has been introduced but also to be the foundation of a future CFD compact model. The EMC screen in the present article has been modelled in detail, and therefore the CFD mesh is very dense. A future work will be to develop a compact model using a porous media approach that requires a low number of elements but that is able to obtain the same results as the present detailed model.

2. Test rig description The experiments were performed in a test rig that was designed and manufactured to measure the average velocity field at a certain distance from both the inlet and the outlet of a screen. Fig. 2 schematically illustrates the test bench. The centrifugal fan is placed at the beginning of the tunnel, which produces a sufficient jump in pressure to overcome the pressure losses of the tunnel. Just in front of the fan is a honeycomb that removes the rotational component produced by the fan. Right after the honeycomb, the oil that is needed for the PIV measurement is seeded in the wind tunnel to ensure that is correctly homogenized with the flow when it approaches the test section. The next adjacent piece is a geometry reduction. This piece shortens the geometry from the size of the chamber where the oil is introduced (160  160 mm2) to the size of the test section (40  40 mm2), which is the next piece. The test section was manufactured in methacrylate in order to have visual access into the test section. Two pieces are placed in the test section (Fig. 3a). The first one is a piece (a fan dummy) that is used to produce axial and tangential velocity profiles like those at the outlet of a fan. The flow that is obtained is similar to the one produced by a fan that is similar to the one shown in Nevelsteen et al. (2006) and Yen and Lin (2006). The main characteristic of this kind of flow is that both axial and tangential profiles have an annulus shape and the flow mainly goes through the annulus. In order to generate that kind of flow, the dummy fan has to be added. The rotational component of the flow is controlled by the pitch of the helices of the dummy blades and by the annulus shape with the diameter of the cylinder assembled at the outlet of the blades (see Fig. 3a). Just at the outlet of the blades the flow is not homogeneous as it is at the outlet of a fan. At this point the flow has passed through the number of helicoidal holes that the dummy

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45

Fig. 2. Scheme of the test rig.

Fig. 3. Test section.

piece has in order to mimic blades, and thus the flow has the same number of jets as helicoidal holes. With the cylinder of the figure a homogeneous flow is achieved without jets since along the cylinder the jets have mixed together but they have maintained the annulus shape. The end of this cylinder is what is considered the outlet of the dummy fan and the distance to the screen (‘‘a’’) is represented in Fig. 3b. The second piece in the test section is the EMC screen. This screen has been placed (‘‘a’’) at 25 mm or 15 mm from the outlet of the dummy fan. The test section also has pressure taps in order to measure the pressure drop in the screen. Just after the test section, there is a transition piece that changes the cross section to the size of the filter. This filter is important in order to remove the oil from the flow before entering the Laminar Flow Element (LFE), which measures the volumetric flow rate. The humidity, atmospheric pressure and ambient temperature were also measured in order to correct the flow-rate reading according to the manufacturer. After the air exits the LFE it is expelled into the atmosphere. In order to control and monitor the different variables through the test rig, a computer application was developed in Labview 8. With the aim of measuring the velocity field at the inlet and at the outlet of the screen, the PIV technique was used. The characteristics of the PIV equipment and of the different components of the test rig are schematized in Table 1.

3. Test procedure 3.1. Cases of study The geometrical and physical parameters of the experiments are summarized in Table 2. The first parameter, ‘‘D’’, is the diameter of the dummy fan in the test section. The test section

(40  40 mm2) has the same internal dimensions as the diameter: 40 mm. ‘‘Dh/D’’ is the relation between the hub of the fan and the external diameter. ‘‘a’’ is the distance between the outlet of the dummy fan and the inlet of the perforated plate represented in Fig. 3b. The porosity of the screen is ‘‘e’’ and is defined as the ratio between the open area and the total area. The next parameter ‘‘n’’ is the ratio between the lateral area of the walls of the pores and the area of the test channel (40  40 mm2). The last two parameters are the thickness of screen ‘‘t’’ and the mean velocity in the channel ‘‘V’’, which is related to the Reynolds number ‘‘Re’’. The Reynolds number is calculated based on the hydraulic diameter of the test section and its mean axial velocity. In order to evaluate how the different turbulence models respond to parameter changes, two cases that have very different values for several of these parameters will be used as reference. In Fig. 4 the geometry of the screens is shown in mm. The large difference in porosity (open area ratio) between the screen in experiment 1 (75%) and the screen in experiment 2 (30%) must be highlighted.

3.2. Measurements methodology 3.2.1. PIV measurements In order to measure the velocity fields in planes parallel to the screen (both at the inlet and at the outlet) two configurations of the camera and laser were needed. These configurations are presented in Fig. 5, where each of the configurations in the picture represents the components that are measured as well as the coordinate system used. Thanks to both set-ups, it is possible to obtain the three velocity components and five of the six Reynolds stresses that are needed to define the inlet turbulence boundary conditions. From the first disposition two velocity components and three Reynolds stresses are

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Table 1 Equipment data. Equipment

Manufacturer

Model and characteristics

Centrifugal fan

SODECA

Model Sodeca CMA-531-2T-3

Honeycombs

Liming Honeycomb Composites Inc.

Microcell CS 1/160 0 -3003 Aluminium foil 0.04 mm (porosity of 0.8 and ratio between the thickness and Dh 0.8)

Air filter

CAMFIL Inc.

Efficiency of 99%

LFE

Meriam Instruments Inc.

Accuracy of ±0.87% of the reading

Pressure transducer

TESTO

An accuracy of ±0.7 Pa

Oil injector

TSI Inc.

Model 9307 that uses a system of Lazkin nozzles to produce particles with a mean diameter of 1 lm

Illumination source of the laser

Big Sky Lasers Inc.

A dual-head Nd:Yag Ultra PIV-120 with a pulse energy of 120 mJ at a wavelength of 532 nm (green), a pulse frequency of 15 Hz and an exit beam of 5.3 mm

Camera

TSI Inc.

CCD camera Power View 4MP with 2048  2048 pixels of resolution and an individual pixel size of 7.4 lm squares

Lens

Nikon

105 mm Focal length

Synchronizer

TSI Inc.

610035 Model with 1 ns of resolution

Software

TSI Inc.

Insight 3G in order to calibrate the equipment, capture and process the data

Traverse system

Dantec Dynamics

Three dimensional accurate movement system

Articulated arm

TSI

TSI LaserPulseTM Light Arm

Table 2 Summary of the parameters of the experiments. Parameters

D (mm)

Dh/D

a (mm)

e (%)

n

t (mm)

V (m/s)

Re

Exp. 1 Exp. 2

40 40

0.55 0.55

25 15

75 30

0.37 0.25

2.5 2.5

2.5 1

6293 2517

Fig. 4. Geometry of the screens used in the experiments.

obtained and the remaining velocity component and two Reynolds stresses are obtained from the second configuration. In order to obtain the velocity fields with these dispositions, a scan has been done for each configuration. Thus, by giving a spacing of 1 mm between two consecutive measurement planes, the 40 mm of the test section are covered. Through this procedure the spatial resolution with which the ‘‘x’’ and ‘‘z’’ components are obtained is 120  41 (120 due to the PIV resolution and 41 due to the scan spacing). In contrast, the ‘‘y’’ velocity component (along with the ‘‘z’’, since this is also measured in the second setup but not used) is obtained is the transpose of the previous one, i.e. 41  120. In order to obtain the tangential velocity field the same spatial resolution of points is needed for the ‘‘x’’ and ‘‘y’’ velocity components. Therefore, the zeroth-order interpolation method has been used to achieve these velocity fields. The u0 v 0 Reynolds stress cannot be measured with the presented setups as the u and v components are not measured at the same time in any of the layouts. Since this Reynolds stress is not in the

main flow direction, it is expected to be small. An estimation of its value was made, and it was verified that its influence in the prediction of both the velocity pattern after the screen and the pressure drop was small. The difference that was found when using the estimation of the sixth Reynolds stress in the velocity peaks of the velocity profile, both axial and tangential, in a line (x = 0) of a cross section at 20 mm from the screen outlet had variations of less than 1%. Therefore, we will report and use for boundary conditions the five Reynolds stresses that can be properly measured. In order to carry out the experiments, a 45  45 mm2 FOV was established, so the entire width of the test section could be taken in the measurement. A Dt of 5 ls was chosen due to the rules recommended by Keane and Adrian (1990). With the aim of deciding on an appropriate number of frames (or sample size), the procedure proposed by Uzol and Camci (2001) and Ullum et al. (1988) was followed. For two lines (x = 0) that belong to two different cross sections (one at 8 mm from the inlet and the second one at 20 mm from the outlet of the screen), the velocity and the Reynolds stresses profiles were measured using a different number of frames (50, 100, 200, 300, 400, 500 and 1000 frames). For each sample size an rms-value of the scatter was obtained. 400 Pairs of images were used because it is beyond 400 pair of images where the rsm-scatter value has no significant variation. Using 400 image pairs at the inlet, the non-dimensional rms scatters were between 0.1% and 4.5% for velocities and between 0.1% and 5% for Reynolds stresses. At the outlet, the non-dimensional rms scatters for velocities were between 0.1–2.5% and 0.1–3.5% for the Reynolds stresses. When increasing the number or pairs of images to 1000, the values at the inlet improved to 2%. This does not justify the use of 1000 images, however, since it increases both the experimental and processing time by a large amount. The uncertainties of the velocity measurements for the experiments were calculated with the guidelines proposed by ITTC (2008). The different sources of uncertainties presented by ITTC were considered. This results in a total uncertainty, with respect

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47

Fig. 5. Scheme of the camera and laser layout in both setups.

to the mean channel velocity of the respective case study, of 2.5% for the first experiment and 4.5% for the second. The LFE measurements were used in order to ascertain the reliability of the PIV measurements. The LFE measurements were actually inside the PIV uncertainty. 3.2.2. Pressure drop measurements The pressure drop measurements have been measured with the pressure transducer and were carried out simultaneously with the PIV measurements. Different pressure taps are installed around the test section (Fig. 6) in order to measure the pressure drop. Each of the measured values is the average of ten measurements spaced two seconds apart. And each of these ten values is the result of the average of 8000 samplings at a sample rate of 1 kHz. These values have been decided on in order to reduce the uncertainties associated with the variation of the physical magnitudes. The total uncertainty of the pressure drop measurements is obtained by calculating the square root of the sum of the squares between the equipment uncertainty and the uncertainty of the measurements. Thus, the uncertainty for the measurements is between 0.7 Pa and 0.86 Pa. 4. Numerical model 4.1. Flow domain 3D perforated plates with squared holes were modelled in detail for each of the cases studied. The geometrical parameters of the models and of the screens are the same as for the experiments described in Table 2. A scheme of the domain is shown in Fig. 7 where the origin of the coordinate system is also shown to be placed at the centre of the cross section placed at the outlet of

the screen (z = 0). The tangential velocity is defined as having an origin around the x = 0 and y = 0 point. The channel length before the screen is 8 mm, since it is the distance where PIV measurements were taken in order to be used as boundary conditions for the numerical simulation. The channel length after the screen is 60 mm, since this distance was verified as being long enough to avoid any reversed flow at the outlet cross-section. 4.2. Governing equations and turbulence modelling The experimental measurements confirmed that the flow is fully turbulent throughout the domain considered. Since the present study is focused on an electronics cooling application, it should be pointed out that it is mainly concerned with the prediction of mean axial and tangential velocities after the perforated plate. Therefore, the Reynolds Averaged Navier–Stokes (RANS) approach has been adopted for the numerical simulation of the flow. Therefore, the mean flow has been calculated by solving the equations:

@U i ¼0 @xi @ @P @ ðqU i U j Þ ¼  þ @xj @xi @xj

ð1Þ     @U i @U j  qu0i u0j l þ @xj @xi

ð2Þ

Different turbulence models have been considered in order to calculate the Reynolds stresses (qu0i u0j ) and thus close the system of Eqs. (1) and (2). In this regard, it has to be highlighted that the induced swirl is expected to produce complex flow features, such as secondary shear stress, streamline curvature, strong departure from local equilibrium and turbulence anisotropy, that invalidate some of the assumptions on which simple turbulence models are based (Jakirlic et al., 2002). Eddy Viscosity Models (EVM) are known to perform worse than Reynolds Stress Transport Models (RSTM) in predicting confined swirling flows, but the former are

Fig. 6. Scheme of pressure taps in Experiment 1 and 2. Bracketed distances correspond to Experiment 2.

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Fig. 7. Scheme of the domain and boundary conditions.

more robust and cost-effective. Moreover, it has been reported that, regardless of their limitations, EVM are often capable of predicting mean velocities correctly in flows with significant swirl (Khademi Shamami and Birouk, 2008; Yajun et al., 2011). Thus, both EVM and RSTM models have been considered in this study.

Table 3 Terms and coefficients of the two k–e turbulence models employed in the study.

Ck

4.2.1. Eddy Viscosity Models Four different EVM have been employed for the simulation of the flow, namely the Standard, and Realizable k–e models, and the Standard and Shear Stress Transport (SST) k–x models. With these models the Reynolds stresses are calculated by means of the Boussinesq hypothesis.

  @U i @U j 2 þ qkdij qu0i u0j ¼ lt þ 3 @xj @xi



@ @ @k þ Pk  Dk ðqU i kÞ ¼ Ck @xi @xj @xj

ð4Þ

  @ @ @e þ P e  De ðqU i eÞ ¼ Ce @xi @xj @xj

ð5Þ

The exact definitions of each term are depicted in Table 3 for the standard and realizable k–e models. The turbulent viscosity is calculated with both models as

lt ¼ q C l

k

2

e

ð6Þ

with the coefficient Cl, which is a constant in the standard k–e model (Cl = 0.09) but a function of different flow characteristics in the realizable k–e model. The standard k–e model (Launder and Spalding, 1974) does not have any term of its transport equations sensitized to rotation or streamline curvature effects, so it is usually unable to provide accurate predictions of the mean velocities in confined swirling flows (Jones and Pascau, 1989). On the other hand, the transport equations of the realizable k–e model do include terms that are affected by streamline curvature and thus typically predict the velocities better than the standard model in flows with a significant swirl component (Khademi Shamami and Birouk, 2008). The realizable k–e model from Shih et al. (1995) ensures realizability, i.e. the positivity of normal Reynolds stresses and the Schwarz inequality for shear Reynolds stresses, by calculating the Cl coefficient as

Realizable k–e

l þ rlkt l þ rlet

l þ rlkt l þ rlet ltS2 qe C1qSe 2 ffi C 2 q kþepffiffiffi me

Pk Dk Pe De

ltS2 qe

Coeff.

rk = 1.0; re = 1.3

C 1e ke P k 2

C 2e q ek

ð3Þ

So that the Reynolds stress tensor is to be aligned with the mean strain-rate tensor (Sij). The turbulence anisotropy promoted by swirl makes this linearity far from realistic and this fact is often argued as the main reason for which EVMs are not capable of predicting Reynolds stresses accurately in flows with significant swirl. The k–e models consist of two transport equations for both the turbulent kinetic energy (k) and its dissipation rate (e), which can be expressed in a compact way as



Ce

Standard k–e

Cl ¼

C1e = 1.44

rk = 1.0; re = 1.2 h i g C 1 ¼ max 0:43; gþ5

C2e = 1.92

C2 = 1.9

1 A0 þ AS U  ke

ð7Þ

with the parameters U and AS and the coefficient A0 defined as

U 

pffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Sij Sij þ Xij Xij ; AS ¼ 6cos/; A0 ¼ 4:04 pffiffiffi S S S / ¼ 13 cos1 ð 6WÞ; W ¼ ij Sjk3 ki

ð8Þ

This dependence of the Cl coefficient on the mean strain-rate (Sij), the mean rate-of-rotation (Xij) and the turbulent time scale (k/e) allows the realizable k–e model to provide good predictions of mean velocities in flows with significant rotation or streamline curvature effects. In this regard, it is likely that the specific features of the transport equation for e in this model (realizable), e.g. the dependence of the coefficient C1 on the scale ratio g (see Table 3), would also contribute to the improved predictions. Two examples in which the realizable k–e model is shown to successfully reproduce the measured mean velocities are presented by Wang et al. (2009) and Yajun et al. (2011) for a swirling flow in a combustor. The k–x models, on the other hand, consist of two transport equations for both the turbulent kinetic energy (k) and its specific dissipation rate (x). The equation for k can be expressed in the same compact way as Eq. (4), whereas the equation for x can be written as

  @ @ @x þ Px þ CDx  Dx ðqU i xÞ ¼ Cx @xi @xj @xj

ð9Þ

The exact definitions of each term for the standard k–x (Wilcox, 1998) and SST k–x (Menter, 1994) models are depicted in Table 4. The turbulent viscosity is calculated with both models as

lt ¼ a q

k

x

ð10Þ

where the coefficient a is constant (a = 1) in the standard k–x model, but it is calculated as

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a ¼

1

ð11Þ

max½1; aSF1 x2 

in the SST k–x model. In the latter equation a1 is a constant (a1 = 0.31) and F2 is a blending function

"

# pffiffiffi k 500l U2 ¼ max 2 ; 0:09xy qy2 x

2 2 Þ;

F 2 ¼ tanhðU

ð12Þ

where y is the distance to the closest wall. One on the main features of the SST k–x model is that it effectively blends the formulation of the k–x and k–e models by means of the blending function.

F 1 ¼ tanhðU41 Þ; "

U1

! # pffiffiffi 500l 4qk k ¼ min max ; ; 0:09xy qy2 x rx;2 CDþx y2

ð13Þ

which is applied to the cross-diffusion hterm (CDx, see Tablei 4). In10 1 1 @k @ x is the deed, in the latter equation CDþ x ¼ max 2q rx;2 x @xj @xj ; 10 positive portion of the cross-diffusion term. Neither the Standard nor the SST k–x models have a term in their transport equations that is sensitized to rotation or streamline curvature effects. Indeed, their performance in confined swirling flows has not been as widely assessed as for the k–e models. The SST k–x model has been reported to provide good predictions of mean velocities for a swirling flow in a can-combustor (Khademi Shamami and Birouk, 2008) as well as giving quite poor results for a combustor consisting of an annular swirling stream that is concentric with a non-swirling jet (Yaras and Grosvenor, 2003). The standard k–x model, formulated in an older version (Wilcox, 1988), was shown to perform successfully in the simulation of the flow in a centrifugal air separator (Shvab et al., 2010). 4.2.2. Reynolds Stress Transport Model The Reynolds Stress Transport Models, like the one employed in this study, involve six transport equations for the independent stresses u0i u0j and a scale-determining equation, which is usually a transport equation for the turbulent dissipation rate (e). In a general form, the six equations for the Reynolds stresses may be written as

@ ðqU k u0i u0j Þ ¼ dij þ Pij þ Pij  eij @xk

ð14Þ

in which the terms on the right hand side represent diffusion (dij), production (Pij), redistribution (Pij) and dissipation (eij) of Reynolds

stresses. A significant feature of the latter equations is that the production of Reynolds stresses is calculated exactly as

Pij ¼ qu0i u0k

@U j @U i  qu0j u0k @xk @xk

ð15Þ

So that the direct effects of strain field, body forces and convective transport on the Reynolds stresses appear directly in the equations. This is the main reason for which RSTM models have greater capacity than EVM models for capturing the influence of rotation and streamline curvature on turbulence (Hanjalic and Launder, 2011). In this regard, there are many studies about confined swirling flows in which the improved performance of RSTM models over EVM models is clearly demonstrated—see, for example, Jones and Pascau (1989) and Jakirlic et al. (2002). In the RSTM employed in the present study, the diffusion of the Reynolds stresses was approximated by a simple gradient model.

dij ¼

@ @xk

"

lþ

 lt @u0i u0j rs @xk

# ð16Þ

where rs = 0.82, as proposed by Lien and Leschziner (1994). On the other hand, the dissipation of the Reynolds stresses was modelled by assuming the local isotropy hypothesis eij ¼ 23 qedij and calculating e from the corresponding equation of the standard k–e model. Finally, stress redistribution was modelled by considering four contributions, namely the slow pressure-strain (Pij,1), the rapid pressure-strain (Pij,2) and the corresponding wall-reflection effects w (Pw ij;1 and (Pij;2 ):

Pij ¼ Pij;1 þ Pij;2 þ Pwij;1 þ Pwij;2

ð17Þ

Each contribution has been modelled following the proposal of Launder and Shima (1989), with the exception of the rapid pressure-strain, which incorporates the isotropization of convection as suggested by Fu et al. (1987):



Pij;2 ¼ C 2 Pij  Cij 

dij ðPkk  Ckk Þ 3

 ð18Þ

In the latter equation Cij is the convection term, i.e. the left hand side of the Reynolds stress transport Eq. (16), and C2 is the coefficient proposed by Launder and Shima (1989) for the rapid pressure-strain contribution. The inclusion of the isotropization of convection improves the RSTM’s predictions in confined swirling flows as was shown by Fu et al. (1987) and Ohtsuka (1995).

Table 4 Terms and coefficients of the two k–x turbulence models employed in the study. Standard k–x

SST k–x

Pk Dk Px

l þ rlkt l þ rlxt ltS2 qb fb kx a xk Pk

l þ rlkt l þ rlxt min(ltS2, 10qbkx)

CDx

–

@k @ x 2ð1  F 1 Þq xr1x;2 @x j @xj

Dx

qbfbx2

qbx2

Coeff.

rk = 2.0; rx = 2.0

1 rk ¼ F 1 =rk;1 þð1F 1 Þ=rk;2 1 rx ¼ F 1 =rx;1 þð1F 1 Þ=rx;2

Ck Cx

qbkx q lat Pk

a = 0.52; b = 0.072; b = 0.09 ( fb  ¼

1 1þ680v2k 1þ400v2k

vk 6 0 1 @k @ x vk > 0 ;vk ¼ x3 @xj @xj

  X X S  1þ70v fb ¼ 1þ80vx ; vx ¼  ij  jk 3ki  x

ðb

xÞ

rk,1 = 1.176; rk,2 = 1.0 rx,1 = 2.0; rx,2 = 1.168

a = F1a1 + (1  F1)a2 b = F1b1 + (1  F1)b2 a1 = 0.553; a2 = 0.44 b1 = 0.075; b2 = 0.0828; b = 0.09

4.2.3. Near-wall treatment of turbulence models The k–e models employed in the study, as have been formulated above, are not suitable for correctly predict flow characteristics very close to solid walls, where viscous effects are pervasive. Thus, the k–e models were combined with the low-Reynolds-number model from Wolfshtein (1969), following the two-layer approach of Chen and Patel (1988). In this method, the different turbulent viscosity and dissipation rates calculated with each of the two models were blended by the procedure proposed by Jongen and Marx (1997). In contrast to the k–e models, both the Standard and the SST k–x models can be integrated through the viscous sublayer and do not need any special near-wall treatment. In the case of the RSTM employed, the transport equations for the Reynolds stresses can be effectively integrated down to solid walls, since they model the effect of viscosity and wall blockage on the turbulence. The turbulent dissipation rate, however, was calculated with the same two-layer approach applied to the k–e models.

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4.3. Boundary conditions

that 60 mm was enough to use this boundary condition. Finally the non-slip condition was used as boundary condition for walls.

The scheme of the boundary conditions is shown in Fig. 7. Fig. 8 shows the mean velocity field obtained from PIV measurements in each experiment that is used as boundary condition. It is clear that the produced flow is similar to a fan-induced flow: an annular axial and tangential flow with a low velocity zone due to the fan hub. The inlet turbulence boundary conditions have been defined from the experimentally measured Reynolds stresses. It must be highlighted that the turbulent intensity obtained through the Reynolds stresses are 42% for the first case and 73% for the second one. Thus, the Reynolds stresses were directly used when using the RSTM, whereas k was calculated for the Eddy Viscosity Models using the following expression.

k¼

1 0 0 ðu u þ þv 0 v 0 þ w0 w0 Þ 2

ð19Þ

The values for e and x were obtained through expressions (20) and (21).

e ¼ C 3=4 l x¼

k

e kC l

3=2

l

ð20Þ

ð21Þ

where the turbulence length scale (l) is 0.07 times the hydraulic diameter (0.04 mm). An outflow condition has been imposed at the outlet. Different lengths of the outlet channel were simulated in order to ensure

5. Numerical simulation of the model 5.1. Geometry meshing In order to achieve a perfect value of skewness (i.e. all the angles of an element are 90°), the meshing strategy shown in Fig. 9 has been used. At first the pore (a) is divided into square shapes (b) in order to mesh the whole pore with squared shaped elements (c). In order to capture the existing gradients of velocity near the walls, several rows of small elements are placed their size increasing as they move away from the walls. The velocity field at the screen holes changes abruptly, since the flow collides with the internal faces of the holes and is slightly straightened. That is why there is a need to have fine mesh within the screen holes and in the proximity of the screen if it is necessary to correctly capture this sudden change in direction. Taking into account that the elements near the walls must be small enough to capture the velocity gradients next to the walls (the first element size is 0.04 mm, which produces the highest value of y+ of 2.5), the only thing left to do is to evaluate what the size of the other elements would be (both in the flow and in the perpendicular direction of the flow). Different internal meshes were built with several interval sizes (IS) of the elements (0.25, 0.4, 0.55, 0.7, 0.85 and 1, all of them in mm) for the core of the model (outside the near wall region). Each case of IS has been simulated

Fig. 8. Velocity fields measured with PIV at 8 mm from the inlet of the screen.

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with the explained boundary conditions (the same y+) using the Reynolds Stress Transport Model (RSTM) as the turbulence model. The difference between the model using an IS of 0.25 and 0.4 was very small (i.e. less than 1.2% in the peak either for velocities or for Reynolds stresses at the centreline of the cross section) and therefore an IS of 0.4 mm was chosen as the mesh resolution for the core of the model. This results in a total number of 6.5 million elements for experiment 1 and 8.7 million elements for the experiment 2.

provided by the different turbulence models with those obtained experimentally. These parameters must be such that when comparing two cases that have similar parameters, the flow patterns should be also similar. In other words, the parameters should be a good and quantitative representation of the flow pattern. The parameters that are defined for a given cross section perpendicular to the flow are the following: the area weighted average of the tangential velocity (V t ), the ratio between the minimum and the max min imum axial velocity values VVmax and the swirl number (S, Beér ax

5.2. Numerical procedure The finite volume method implemented in Ansys Fluent 13.0 was used as the numerical discretization method. The equations of the mathematical models were solved with a segregated scheme using a second-order centred scheme for the diffusion terms. The convection terms of the RANS equations and of the transport equations for the turbulence quantities k, e and x were discretized with a second-order upwind scheme. The convection terms for the Reynolds stresses, however, had to be discretized with a first-order upwind scheme due to the severe stability problems that higherorder schemes produced in the calculations. Nevertheless, this fact should not degrade the numerical accuracy in the prediction of mean flow quantities (Roache, 1998). The SIMPLE pressure–velocity–coupling algorithm was used to solve the continuity equation by employing a momentum interpolation method to calculate velocities at cell faces. 5.3. Convergence criterion and computational time The guidelines proposed by the ‘‘European Research Community On Flow, Turbulence And Combustion’’ (ERCOFTAC, 2000) in order to establish a good level of convergence have been followed. 35,000 Iterations are necessary in order to reach a convergence in the simulations with k–e, 43,000 with k–x and 51,000 with RSTM. The scaled residuals of all the variables were always less than 1.1  105. When checking the convergence on global balances like mass flow balance at inlet and outlet, the residual of the balance is about 1  1015 kg/s for the simulations. The tangential velocity in a cross section at 20 mm from the outlet has been monitored and checked to be constant (no variations in the 4th decimal) when stopping the simulations. The required simulation time using a server with 32 processors (2.8 GHz each) was the following: 66, 18 and 24 h when using RSTM, k–e and k–x models, respectively. 6. Results and discussion 6.1. Flow characteristics It is very important for a thermal designer to know the velocity profile at the outlet of a screen. Some parameters have to be defined in order to quantitatively compare the velocity profiles

and Chigier, 1983), which gives us an idea of the rotational component of the velocity and is defined as:

RR S¼

q  V a  V t  r  dA RR Lc  A q  V 2a  dA A

ð22Þ

where ‘‘Lc’’ is a characteristic length that has been established to be the half of the test section edge (20 mm), ‘‘q’’ is the density of the air, ‘‘r’’ is the radial coordinate and ‘‘Va’’ and ‘‘Vt’’ are the local axial and tangential averaged velocities, respectively. The experimental values of these parameters are shown at the inlet and at 20 mm from the outlet of the screen in Tables 5 and 6 for experiments 1 and 2. From both tables it can be concluded that the screen destroys part of the rotational component of the flow, as was expected. The percentage of variation in the swirl number from the inlet to the outlet, as expected, is larger for the second experiment since the porosity of the screen is smaller. If the ratio between the minimum and maximum axial velocities is compared, in Experiment 1 this ratio increased whereas in Experiment 2 it decreased considerably. In order to explain this effect, it is important to note that the biggest part of the flow in both experiments goes through the outer side (a kind of annular shape) as was previously shown in Fig. 8. On the other hand, the pressure drop through an obstacle is obtained through (23).

1 DP ¼ n   q  v 2 2

ð23Þ

where n is the pressure loss coefficient of the obstacle. Since most of the flow goes through the outer or annular side of the screen, the local static pressure drop is larger through the annular side than through the central side of the screen. Finally, this means that right after the screen, in the central side the static pressure will be higher than right after the screen in the annular side. This pressure difference produces a recirculation. It is important to keep this phenomenon in mind when placing electronics components on a PCB. In Fig. 10 the static pressure drop (Pa) between two lines (x = 0) at two different cross sections parallel to the screen (3 mm from the inlet and 5 mm from the outlet) and obtained with CFD is shown for both experiments. It is clear that the pressure drop is greater in the annulus than in the central side. The recirculation can be also observed for the flow patterns of a middle longitudinal section of the domain (x = 0), which are shown in Fig. 11.

Fig. 9. Meshing strategy for a pore.

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Table 5 Parameter variation between inlet and outlet in Experiment 1. Vt Inlet Outlet |% Of variation|

2.80 1.41 49.64





V min V max ax

0.1435 0.0816 43.13

S 0.76 0.35 53.94

Table 6 Parameter variation between inlet and outlet in Experiment 2. Vt Inlet Outlet |% Of variation|

2.11 0.55 73.93





V min V max ax

0.0091 0.3676 3939.56

S 1.09 0.22 79.81

Fig. 10. Numerical static pressure difference (Pa) for both cases between two lines (x = 0) at different two cross sections.

6.2. Turbulence models benchmark 6.2.1. Velocity fields 6.2.1.1. Experiment 1. In this section a comparison between the results measured with PIV and those predicted by the numerical simulations at a distance of 20 mm after the screen is presented for both experiments. That distance is used as the uncertainty due to the number of frames that has been verified as being small at that distance where the jets produced by the holes have almost disappeared. The employed turbulence models for the benchmark are the standard and realizable k–e, standard and SST k–x and RSTM. The mean velocity fields for experiment 1 at 20 mm from the outlet are presented in Fig. 12 (axial velocity) and Fig. 13 (tangential velocity). Fig. 12 shows that for the axial PIV measurements at 20 mm from the outlet of the screen there is a difference in velocity magnitudes between the annulus and the hub zones. There is a low velocity zone in the hub, whereas at the annulus the maximum velocities are located mainly in the corners. The low velocity zone belongs to a recirculation that is caused by the static pressure differences between the annulus and the hub zones as was previously explained. If the PIV results in Fig. 12 are compared with those predicted by the different k–e models, it is evident that although the shape of the flow is well predicted, the magnitudes of the negative velocities are far from the results obtained with PIV. Nevertheless, the improvements (in the calculation of the turbulent viscosity and in the transport equations as explained in a previous chapter on ‘‘Governing equations and turbulence modelling’’) introduced from the standard k–e to the realizable one (Table 3) can be also observed in Fig. 14, where the velocity profile at one centreline of a

cross section at 20 mm after the screen is depicted for the k–e variations. Although there is improvement in the maximum axial velocities, it is marginal from the standard to the realizable. The figure shows that the realizable k–e predicts negative velocity values when the standard one does not predict negative axial velocities. In comparing the velocity fields provided by the k–e models with the other employed turbulence models, it can be concluded that the recirculation zone shown in Fig. 12 is better predicted with both k–x (standard and SST)and the RSTM models. Fig. 15 compares the experimental width of the recirculation zone along the distance after the screen for the predictions of the k–e standard and realizable, the k–x standard and SST and the RSTM for a longitudinal centre plane (x = 0). The recirculation zone width is defined as the diameter of the zone with negative values for the axial velocities around the centre of the section; the width of the recirculation provided by the k–x SST and the RSTM are very close to the real one. From the tangential velocity point of view the results in Fig. 13 show that for this experiment there is not a large difference in the results provided by each of the turbulence models. This is reflected in Table 7, where the comparison parameters of the experimental results at the cross section 20 mm after the screen are compared with those obtained numerically. There is not a big difference in the swirl number and tangential velocity parameters between the models. The modifications made to the k–e standard do not improve the results from the realizable one much. The k–x SST and the RSTM give better values for tangential velocities, as shown in Fig. 13. Thus, it can be said that both are the models that better adjusts to the experimental results from the tangential point of view. In order to better show the adjustment between the RSTM, the k–x SST and the experimental results, some velocity profiles for the lines shown in Fig. 16 are presented in Fig. 17 (at the cross section located 20 mm after the perforated plate). The results in Fig. 17 are for experiment 1. Fig. 17 shows that the low velocity zone with both models is accurately predicted for the first experiment, as can be concluded from the axial velocity profiles. The maximum axial velocity values also fit to the experimental ones. In the tangential velocity profiles it is seen that the rotational component of the problem is also well predicted using these turbulence models, especially in lines 1 and 2, both of which are the centrelines of the employed cross section. It is clear that for Experiment 1, either the k–x SST or the RSTM are the turbulence models that best predicts the flow pattern after the screen. 6.2.1.2. Experiment 2. It is important to highlight that this second experiment has some geometrical characteristics that very different from Experiment 1, as can be seen in Table 2. Figs. 18 and 19 show the mean axial and tangential velocity fields obtained with PIV and those obtained numerically with the different turbulence models for Experiment 2. One thing that is immediately clear is that the standard k–x, although converged, does not provide good results for this experiment, as is shown in Figs. 18 and 19. Neither flow shape is well predicted by this model for the established conditions. In Figs. 18 and 19, it can be seen that the k–e models present a worse fit to the experimental results than for experiment 1. k–e Models tend to homogenize the flow too much. On the other hand, the k–x SST model tends to exaggerate the value of maximum and minimum axial velocities. As Fig. 18 shows, the minimum and maximum axial velocities for the SST are out of the range established for the rest of the models. In fact, the maximum value is 5.45, which is clearly higher than the one measured for PIV, which is 3.49. In Table 8 the comparison parameters are presented for both the PIV results and the numerical results. Neither the

A. Bengoechea et al. / International Journal of Heat and Fluid Flow 46 (2014) 43–60

53

Fig. 11. Axial velocity fields (m/s) with CFD for a centre cross section (x = 0) after the screen: (a) Experiment 1 and (b) Experiment 2.

Fig. 12. Mean axial velocity fields (m/s) for the experiment 1 at 20 mm from the outlet of the screen: PIV and different turbulence models predictions.

Fig. 13. Mean tangential velocity fields (m/s) for the Experiment 1 at 20 mm from the outlet of the screen: PIV and different turbulence models predictions.

tangential velocity destruction by the screen nor the ratio between the minimum and maximum axial velocities is well predicted by any one of the variations of the k–e model.

Comparing the results obtained with the k–x SST and the RSTM, in Experiment 2 the RSTM better predicts the maximum velocity values as well as the ratio between the axial velocities. Because

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A. Bengoechea et al. / International Journal of Heat and Fluid Flow 46 (2014) 43–60

Fig. 14. Axial velocities in a line (x = 0) at 20 mm from the outlet of the screen.

Fig. 15. Evolution of the recirculation width (mm) in a centre line (x = 0) along the flow direction for the first experiment.

Table 7 Comparison parameters in Experiment 1. Comparison parameters Vt S 

PIV 1.41



V min V max ax

0.3475 0.0816

k–e Std 1.37 0.3653 0.0016

k–e Realizable

k–x Std

k–x SST

1.34

1.29

1.47

1.37

0.3582 0.0754

0.3153 0.1120

0.3582 0.087

0.3485 0.0970

RSTM

experiment, more distance is needed than in the previous case in order to homogenize the static pressure distribution at the outlet of the screen. This distance is different for each of the models. The k–x SST is the model that needs more distance as it predicts a larger recirculation zone (Fig. 20). Therefore, the RSTM seems to result in a better overall prediction since the comparison parameters (see Table 8) are a bit closer to the experimental ones than for the other models. From the tangential point of view the k–e models give values that are far from the real ones according to the comparison parameters (see Fig. 19). With the SST model the S number is completely incorrectly predicted, whereas for the tangential velocity parameter it makes the best prediction. In Fig. 21 the adjustment between the k–x SST, RSTM and experimental results is shown for the same lines previously used in a cross section at 20 mm after the screen. It is seen that the RSTM better adjust to the experimental values, as the k–x SST overestimate both the maximum and minimum values of the axial velocity. It is surprising that the k–x SST results are much worse when comparing them with those for the first experiment, whereas the RSTM again provides quite good results. One of the possible reasons could be due to the prediction of the Reynolds stresses. The k–x SST and the k–e models, as previously explained, assume the Boussinesq hypothesis. However, they could make as good a prediction as the RSTM, as was the case in Khademi Shamami and Birouk (2008). However, as Figs. 22 and 23 show, this does not happen. From these figures it should be noted that the difference in the number of points for the different lines in the experimental measurements is due to the spatial resolution that each of the layouts shown in Fig. 5 has in each direction. The Reynolds stress for the main direction of the flow (w0 w0 ) is clearly better predicted with the RSTM. As shown in the plots in Fig. 22, the general tendency with the EVM is to underestimate the value of this Reynolds stress in all the lines represented in the figure, whereas the RSTM presents a better adjustment to the PIV measurements. The same conclusion can be drawn from Fig. 23, although for certain zones the models using the Boussinesq hypothesis do not make as a bad prediction as for the previous Reynolds stress. In this case, for the centrelines of the cross section (lines 1 and 2) the RSTM continues working better, but for the outer lines there are zones where the EVM fit correctly to the experimental values. The adjustment between the models with the measurements for (u0 u0 are not shown as the same behaviour as (v 0 v 0 is observed when analyzing the results. Having presented the results obtained with the different turbulence models for both experiments, it can be said that the RSTM is the best choice in order to predict the velocity fields in this kind of swirling flow. In Experiment 1, both the SST k–x and the RSTM clearly work better than the other employed turbulence models, and in Experiment 2 the RSTM is presented as performing the best. Therefore, it should be highlighted that the RSTM is reliable in both experiments. Thus, the RSTM is presented as the best choice in order to predict the velocity fields at the outlet of a screen with this kind of swirling flow approaching the screen.

Fig. 16. Scheme of lines used for the comparison.

of the overestimation of the axial velocities with the k–x SST, even though the ratio of Table 8 is more or less well estimated (0.2564), it is not reliable because of the incorrect values of the other two comparison parameters. The recirculation zone across the outlet duct as seen in Fig. 20 is also better predicted with the RSTM. Given that the porosity of the screen is smaller in this

6.2.2. Pressure drop In this section the pressure drop at some locations outlined in Fig. 6 are compared by using the analysed turbulence models and the experimentally obtained values. First it is necessary to point out that because the pressure drop values obtained in the screens are not very high, the uncertainties presented for the pressure drop measurements could play a role in the analysis of the results. For the first experiment, the uncertainty is 8% of the

A. Bengoechea et al. / International Journal of Heat and Fluid Flow 46 (2014) 43–60

Fig. 17. PIV, k–x SST and RSTM velocity profiles for Experiment 1 at 20 mm from the outlet of the screen.

55

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Fig. 18. Mean axial velocity fields (m/s) for the Experiment 2 at 20 mm from the outlet of the screen: PIV and different turbulence models predictions.

Fig. 19. Mean tangential velocity fields (m/s) for the Experiment 2 at 20 mm from the outlet of the screen: PIV and different turbulence models predictions.

Table 8 Comparison parameters in Experiment 2. Comparison parameters Vt S 



V min V max ax

PIV

k–e Std

k–e Realizable

k–x SST

RSTM

0.58

0.40

0.38

0.62

0.44

0.2545 0.3676

0.2453 0.0922

0.2368 0.1183

0.1465 0.2564

0.2417 0.3092

measurements, and for the second one it is 4.2%. The results are presented in Table 9 for the first experiment. Looking at Table 9, some conclusions can be drawn about the first experiment. The k–e models tend to underpredict the pressure drop by around 18%. The pressure drop between taps 1 and 2 is poorly predicted; however, the prediction is improved for taps 1–3 and 1–4.

Fig. 20. Evolution of the recirculation width (mm) in a centre line (x = 0) across the flow direction for the second experiment.

The standard k–x model does not accurately predict the pressure drop and what happens is the opposite of the k–e models as

A. Bengoechea et al. / International Journal of Heat and Fluid Flow 46 (2014) 43–60

Fig. 21. PIV, k–x SST and RSTM velocity profiles for Experiment 2 at 20 mm from the outlet of the screen.

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Fig. 22. Experimental and different turbulence models w0 w0 Reynolds stress in a cross section at 20 mm from the outlet of the screen.

Fig. 23. Experimental and different turbulence models

v0v0

Reynolds stress in a cross section at 20 mm from the outlet of the screen.

the pressure drop is overrated. On average, the k–x SST model makes a similar percentage difference (to the experimental values) than the difference obtained with the RSTM model. The difference is around 7.7% (below the measurement uncertainty for this experiment). Therefore, these two models predict the pressure for Experiment 1 very well. The pressure drop calculated by using a handbook (Idelchik) for a flow perpendicular to a perforated plate with the same porosity is not the correct one. This is logical since our flow is not perpendicular to the screen and therefore the pressure loss coefficients from a handbook cannot be used. Furthermore, the pressure loss from the handbook is between two

locations that are sufficiently far apart such that there is no dynamic pressure drop. Although the value from the handbook cannot be properly compared, it is included in the table since its use is ordinary practice in thermal design. Table 10 shows the pressure drops for Experiment 2, which has some geometrical characteristics that are very different than those in Experiment 1. The pressure drop predictions are underestimated by all the turbulence models. The larger underestimation is once again made by the k–e models. Of the k–x models, the standard one gives values that are closer to the measured ones. Nevertheless, it should be noted that the shape of the velocity field was poorly predicted (see

A. Bengoechea et al. / International Journal of Heat and Fluid Flow 46 (2014) 43–60 Table 9 Static pressure drop for Experiment 1: experimental, numerical and Idelchik values. Experiment 1

Experimental values

Standard k–e

Realizable k–e

Standard k–x

SST k–x

RSTM

Idelchik

2

X X X

X

X X X

X

X X X

X

X X X

X

X X X

X

X X X

X

3

–

X

20.50 – 16.94 – 15.46 –

38.41

X

11.12 45.75 10.73 36.65 10.38 32.85

38.43

X

11.02 46.20 10.79 36.26 10.38 32.84

21.26

X

14.80 27.80 14.57 13.99 12.06 21.99

22.71

Acknowledgements

X

14.86 27.51 14.03 17.17 11.83 23.47

28.62

X

14.55 29.02 11.97 29.33 11.20 27.51

X

11.06 28.46

28.46

|%| Of difference relative to the measurement

Average % of difference

– – –

–

X

10.64 7.54 7.73

25.93 13.79 13.58

17.76

X

7.88 6.50 6.68

21.89 10.21 10.47

14.19

X

8.31 6.77 6.92

23.77 30.23 24.96

26.32

X

13.17 9.82 9.66

9.30 8.35 5.43

7.69

X

11.63 8.17 8.15

9.02 5.03 1.68

5.24

X

11.60 7.92 7.60

X

2.85

63.13

63.13

4

X

X

X

X

X

X

X

Table 10 Static pressure drop for Experiment 2: experimental, numerical and Idelchik values. Experiment 2

Pressure tap number 1

2

Experimental values X X X

X

Standard k–e

X X X

X

X X X

X

X X X

X

X X X

X

X X X

X

Realizable k–e

Standard k–x

SST k–x

RSTM

Idelchik

X

3

7. Conclusions The flow pattern that is produced at the outlet of a screen with an approaching flow like those produced by axial fans is presented. A recirculation zone is produced at the outlet of the screen. The tangential velocity decrease through the screen depends strongly on the screen porosity. The lower the screen porosity is, the larger the reduction in the tangential velocity. Experimental measurements with PIV have been made and used in order to make a benchmark study between different turbulence models: standard and realizable k–e models, the Standard and Shear Stress Transport (SST) k–x models, and the Reynolds Stress Transport Models (RSTM). The performance for swirling flow prediction has been reviewed for all the turbulence models from a modelling point of view. The velocity fields at the inlet and at the outlet and the pressure drop in a screen for two cases with very different geometrical characteristics have been experimentally measured. For the cross sections presented in this work (20 mm from the outlets of the screens in each experiment), even though the influence of the jets is negligible, the flow is shown to be non-uniform for both the axial and tangential components of the velocity. It is important to know this non-uniformity since the flow through the slots (between PCBs) depends strongly on this non-uniformity. Three parameters that together correctly define the shape of the flow have been presented and used to quantitatively compare the numerical predictions and the experimental measurements. A benchmark of turbulence models using two very different study cases has concluded that the model that best predicts the flow pattern and pressure drop from an overall point of view is the RSTM model, and the k–x SST model has been shown to be the best model among the EVT models when the screen has a high porosity value. As expected, k–e models are not able to make accurate predictions both from the flow pattern and pressure drop point of views. Although the RSTM model has performed best in this benchmark, it is also the most CPU-time consuming model. From a thermal designer point of view, it is not feasible to use such a large amount of time, which is why the importance of a compact model has been introduced in order to help thermal designers save time without losing accuracy.

DP s (Pa)

Pressure tap number 1

59

DP s (Pa) 4

X

X

X

X

X

X

|%| Of difference Average % of difference relative to the measurement

This research was funded by Eusko Jaurlaritza-Gobierno Vasco, Spain through Proyecto PI2011-30. The support of Cátedra Fundación Antonio Aranzábal – Universidad de Navarra is also gratefully acknowledged. References

Fig. 18) using the standard k–x model. Therefore, although the predicted values are close to the measured values, they may not be reliable. The models that give the best predictions are the k–x SST and the RSTM. However, both models underestimate the pressure drop by around 25%. Since the porosity in Experiment 2 is very low, the flow through the holes is forced to be more perpendicular (Vt decreases a lot after the screen) and it seems that prediction using a handbook for flows perpendicular to a screen (and therefore different than a fan-induced approaching flow) under predicts the pressure drop to the same extent that the RSTM model does for Experiment 2. Having analysed the results in both experiments, it can be concluded that the k–x SST predicts the pressure drops slightly better than the RSTM model.

Antón, R., Jonsson, H., Moshfegh, B., 2007a. Compact CFD modelling of EMC screen for radio base stations: a porous media approach and a correlation for the directional loss coefficients. IEEE Trans. Compon. Packag. Technol. 30 (4), 875– 885. Antón, R., Jonsson, H., Moshfegh, B., 2007b. Detailed CFD modelling of EMC screen for radio base stations, a benchmark study. IEEE Trans. Compon. Electron. Packag. 30 (4), 754–763. Antón, R., Bengoechea, A., Rivas, A., Ramos, J.C., Larraona, G.S., 2012. Performance of axial fans in close proximity to the electromagnetic compatibility screens. J. Electron. Packag. 134, 011004. Auld, G., 2004. An estimation of fan performance for leaky ventilation ducts. Tunn. Undergr. Space Technol. 19, 539–549. Beér, J., Chigier, N., 1983. Combustion Aerodynamics. Robert E. Krieger Publishing Company Inc.. Bejan, A., Kim, S.J., Morega, A.I.M., Lee, S.W., 1995. Cooling of stacks of plates shielded by porous screens. Int. J. Heat Fluid Flow 16, 16–24. Best Practice Guidelines, 2000. European Research Community On Flow, Turbulence And Combustion, Version 1.0.

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