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A novel approach for heat transfer enhancement in composite fins
International Journal of Heat and Mass Transfer 130 (2019) 650–659
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
A novel approach for heat transfer enhancement in composite fins Cosimo Buffone Tianjin Key Lab of Refrigeration Technology, Tianjin University of Commerce, Tianjin City 300134, PR China
a r t i c l e
i n f o
Article history: Received 24 April 2018 Received in revised form 23 October 2018 Accepted 27 October 2018
Keywords: Composite fins Vanes Heat transfer rate Thermal conductivity
a b s t r a c t This paper main goal is aimed at a paradigm shift in the enhancement of heat transfer rate between finned surfaces and surrounding fluid by presenting a novel approach in composite fins. This approach consists in using high thermally conductive coatings on top of the finned substrate in order to increase the local temperature along the fin washed surface. In the present paper a high thermal conductivity coating has been applied to an aeroengine vane of different shape and dimensions subject to icing conditions at high Reynolds numbers and where the main aim was to keep the vane warm as to avoid icing in aerospace applications. Numerical simulations have been carried out to ascertain the range of thickness of the coatings to be used to maximise the wanted effect. Both short Engine Section Stator (ESS) and longer fan Outlet Guide Vane (OGV) have been modelled, having different final goals. In the case of longer OGV, an additional novel design modification has been suggested to enhance further the heat transfer along the vane length by the use of the internal webs. The experimental validation also carried out at much higher Reynolds numbers than that reported in Buffone et al. (2005), demonstrate that the novel concept of heat transfer enhancement in composite fins is a simple and yet powerful strategy in a wide range of Reynolds numbers. A fin analysis has been performed of both the present ESS vane the fins tested in Buffone et al. (2005) at much lower Reynolds numbers and shows that the improvement obtained with the coated fins tested in Buffone et al. (2005) is much larger than the coated ESS vanes investigated in the present study. This said, the present study demonstrates that the use of high conductive coatings in composite fins can keep the ESS vanes ice free, something that was not possible with uncoated vanes. It is important to note that the actual optimal thickness of the thermally conductive coatings is a function of Biot number, fin shape, dimensions and thermal conductivities of fin substrate and coating; depending on the application, a proper design of the fin substrate and coating should be carried out. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction The convective heat transfer between solids and fluids depends on heat transfer coefficient and surface area as well as temperature difference between solid and fluid. Enhancing heat transfer rate between solid and fluid is typically done by improving the heat transfer coefficient and/or increasing the contact surface area. Both these strategies come with a penalty which is increased pressure drop that many times is prohibitive. The task of the heat transfer designer is trying to improve heat transfer rate without a large penalty on pressure drop. The improvement in surface area is typically done by the use of finned surfaces, which are protrusions of the basic contact surface area inside the fluid flow. Fins are employed in both the case where the fluid is cooler than the surface and in the opposite case where the fluid is hotter than the surface; their role is to increase heat transfer rate between solid surface and the adjacent fluid. Cooling fins are found more often E-mail address: [email protected] https://doi.org/10.1016/j.ijheatmasstransfer.2018.10.124 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.
in applications such as electronic cooling [1,2], refrigeration and air-conditioning [3], vehicle thermal management [4]. Fins are not only used by engineers but also by animals. Animals use fins to manoeuvre their movement inside a fluid; fish do this more smoothly and effectively in water than aeroplanes do it in the air with wings, stabilizer and rudder. Animals also deploy fins for deterring attacks from predators by appearing bigger than they actually are. And there are animals like elephants [5] with a body having small surface to volume ratio which need big ears to dissipate heat. Animals like elephants use fins also for their thermoregulation, which is the ability to keep their body temperature within certain limits even though the ambient temperature is different. Stegosaurus and crocodiles had/have dermal plates not attached to the skeleton, but with blood vessels running through them with the aim of cooling the blood by losing heat to ambient. It is also believed that these two last animals used/use these plates as fins when they needed/need to gain heat from the ambient. When air is the heat transfer medium, it is an accepted fact that over 85% of the thermal resistance of a cooling unit is concentrated
C. Buffone / International Journal of Heat and Mass Transfer 130 (2019) 650–659
651
Nomenclature A Bi Cp E ESS f g Gr h k L Nu OGV p p Pr Q Re t t
fin cross section area (m2) Biot number specific heat capacity (J/kg/°C) rate of strain tensor (1/s) Engine Section Stator body forces per unit volume (kg/m3) gravity acceleration (m/s2) Grashof number heat transfer coefficient (W/m2/°C) fin thermal conductivity (W/m/°C) fin length (m) Nusselt number Outlet Guide Vane fluid pressure (N/m2) fin perimeter (m) Prandtl number heat generation per unit volume (W/m3) Reynolds number time (s) fin or coating thickness (m)
at the airside [6], because air is such a poor heat transfer fluid. In a typical car radiator using water and air as heat transfer media on the opposite sides, only the airside has fins; there is no need of fins on the water side. For this reason, extended surfaces are the basic mean to enhance heat transfer from solid surfaces at the airside. Therefore, over the years many different extended surfaces have been investigated. Researchers have concentrated their efforts on fin shapes [7] with 15–20% improvement on heat transfer and a considerable increase in pressure drop; fin spatial arrangement [8] with unsteadiness in the boundary layer region close to the surface that results in a 15% enhancement in heat transfer and an associated increased pressure drop of hundred times; surface roughness [9,10]; and, on the promotion of mixing by turbulence generated because of surface modifications [11] where winglet type vortex generator were used in fully developed laminar channel flow with good improvement of heat transfer and some important pressure drop penalty. Huisseune et al. [12] conducted a numerical study of combined louvered fin heat exchanger with delta winglets as vortex generators which produces heat transfer enhancement because of thinning of the boundary layer due to induced normal flow and the wake size behind the tubes is reduced which produces a reduction of form drag; however, increased friction and flow blockage from the delta winglets result in an increase in net core pressure drop. Wu and Tao [13] numerically and then Wu et al. [3] experimentally proposed a design modification of fin-tube heat exchangers with punched vortex generators only present near the first row of tubes of reduced diameter. Wu et al. [3] for an airspeed of 4 m/s report that for vortex generator in ‘‘common flow up” configuration there is an increase of heat transfer coefficient of around 16% and a corresponding reduction of pressure drop of around 10%, whereas for ‘‘common flow down” configuration there is a 28% increase of heat transfer coefficient and a minor decrease of pressure drop compared with a baseline fin and tube heat exchanger with staggered tubes of same diameter. The proposition of Wu and Tao [13] and Wu et al. [3] shows that particular configurations can bring heat transfer enhancement and either limited pressure drop penalty or even deliver small gains at the expenses of complications in manufacturing and assembling of such heat exchangers design. We will apply a different method to enhance the heat transfer between a finned surface and the surrounding air. This method
T T u
temperature (°C) total stress tensor (N/m2) fluid velocity vector (m/s)
Greek symbols b coefficient of thermal expansion (1/°C) e fin effectiveness turbulent energy dissipation (m2/s3) k fluid thermal conductivity (W/m/°C) j turbulent kinetic energy (m2/s2) m kinematic viscosity (m2/s) l fluid dynamic viscosity (Pa s) q fluid density (kg/m3) Subscripts AV average c coating s substrate 1 undisturbed flow
considers composite fins in which thermally conductive coatings are deposited on a less conductive substrate with the aim to enhance heat transfer by increasing locally the temperature of the washed fin surface in contact with air. The composite fin concept will be applied to aeroengine slender surfaces where Reynolds numbers are relatively high, in order to prove that the air speed range of this concept is quite wide. 1.1. Published work on composite fins Modifying the airside by either trying to increase the air heat transfer coefficient or increasing the washed surface area typically carry an important penalty. A different approach was presented for the first time in [1] for low Reynolds numbers where surface coatings having very high thermal conductivity were suggested as an effective way to enhance the heat transfer rate. A finned heat pipe assembly was used where the aluminium fins were coated with either Diamond Like Carbon (DLC) material or diamond industrial particles. The authors demonstrated that there was no noticeable difference in surface roughness between the three surfaces (basic aluminium, aluminium coated with DLC and aluminium coated with diamond industrial particles). Buffone et al. [1] reported an increase of 30% in the overall heat transfer coefficient for the aluminium fin stack with DLC coating or industrial diamond particles with no penalty on the pressure drop. Buffone et al. [1] introduced a simplified analysis of their heat transfer enhancement concept and estimating the fin effectiveness [14] they found it increased of 29% in the case of aluminium with DLC coated fins compared to the bare aluminium fins; this estimate was found very close to their experimental evidence. This noticeable heat transfer enhancement does not come from either an increase of heat transfer coefficient or an increase in fin surface area at the airside. It is well known [14] that a fin becomes less and less effective along its length because the fin surface temperature decreases along the fin as the fin loses heat to the air. If the fin surface temperature could be kept at the same value as that of the fin’s base, then the fin could be infinitively long. It is actually not strictly necessary that the whole fin cross section is at a temperature close to its base value; the sufficient condition is that the temperature of the fin washed surface is kept as close as possible to the base value. And this is what actually happens with the thermally conductive coatings
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tested in the composite fins of Buffone et al. [1] getting locally higher temperature than the basic aluminium material would have because of preferential conduction along the thin and highly conductive layer of the coating. The basic concept is that a coated fin would behave thermally as if it were entirely made of a highly thermal conductive material. The concept of coated fins (also known as composite fins) is not new. Barker [15] studied constant thickness straight and pin composite fins and concluded that for a sufficiently small Biot number, these fins are equivalent to the 1D treatment with a cross-sectional area average of the thermal conductivities of the basic fin material and the coating. Lalot et al. [16] looked at the same problem of composite annular metallic fins with average thickness between 0.2 and 1 mm, coating thickness between 50 and 150 lm, conductivity ratio around 2, convection heat transfer coefficient ranging between 25 and 150 W/(m2 K). They found the same conclusion of Barker [15]: the composite fin can be treated as ordinary fin of same material with a crosssectional area average thermal conductivity. For a composite fin, a similar fin efficiency can be defined [17] which depends on Biot number, ratio of total half fin thickness to length, ratio of coating to fin thickness, and ratio of coating to fin thermal conductivity. In Cortes et al. [17] it is shown, as per 1D approximation, that the composite fin efficiency reduces to the same expression for an ordinary single-material fin with an averaged thermal length and a cross-sectional area average thermal conductivity. The Biot number is defined with the total half-thickness and cross-sectional area average thermal conductivity. However, coatings are typically used to protect the fin substrate from the ambient and they typically are of lower thermal conductivity than the fin substrate. The types of fins investigated by Cortes et al. [17] are metallic with a ratio of coating to substrate thermal conductivity ranging from 0.04 to 13.6, substrate half-thickness between 0.1 and 0.5 mm, coating thickness between 30 and 80 lm, and fin length ranging from 5 to 40 mm. In the case of Buffone et al. [1] the ratio of coating to substrate thermal conductivity was above 30; the substrate halfthickness was 0.2 mm and the coating between 1 and 5 lm; the fins were almost twice as long as the ones in Cortes et al. [17]. The estimated Biot number for the cases presented in Buffone et al. [1] is almost an order of magnitude less than the range given in Cortes et al. [17]. Coatings are typically used to protect the substrate of fins from wear, oxidation and corrosion, and are also used as thermal barrier. Coatings are also employed as anti-fouling and anti-icing to mitigate the detrimental effects of these conditions on heat transfer and/or lift generating capabilities or even for safety reasons. These are all reasons why coatings are also applied in the compressor, combustor and turbine sectors of a gas turbine Rhys-Jones [18]. The patent by Knott et al. [19] describes the use of surface coatings as an anti-icing approach. The Engine Section Stators (ESS) vanes in
Fan OGVs in typical turbofan engine
an aeroengine are usually made of aluminium or titanium, the latter being not a very good heat conductor. In aerospace as well as wind turbine applications, there are different strategies to deal with the risks posed by ice formation and accretion. The two main strategies are anti-icing and de-icing. Flexible pneumatic air-boots, spraying of anti-icing chemicals, bleed of hot air from engine core, electrothermal systems [20] have been developed for large surfaces such as aeroplane wings and nacelle leading edges as well as in wind turbines [21]. But these strategies are not technically feasible for small vanes inside the engine core, like ESS vanes. The ESS vane is normally heated at the bottom with hot engine oil. The ESS is washed by an air stream with speed ranging between 50 and 100 m/s at a temperature (when the engine flies in freezing conditions) of around 20 °C; In these conditions it is found experimentally that over 1/3 of the ESS length towards the tip is frozen, despite the heating by engine oil at the vane’s base. Ice accretion on cold parts of an aeroengine can pose a serious threat to the engine integrity. In fact, pieces of ice could dislodge from the surfaces and get ingested inside the engine where they could impact violently onto subsequent rotor blades and stator vanes breaking them; solid parts of broken blades/vanes can have the potential to wreck whole parts of the engine and in severe cases put into question the operability of the engine itself, not to mention the risks posed to the airplane and the passengers with crew inside. To solve this issue, in Knott et al. [19] the authors propose the use of high conductivity coating which can be made of graphite, Carbon Nanotubes (CNT) or Diamond Like Carbon (DLC) deposited on the heated ESS. This coating of high thermal conductivity material would transport heat more effectively from the base along the ESS length. Knott et al. [19] introduced this concept but did not give any indications of the thickness of the coatings compared to the dimensions of the vane. 1.2. Goals of the paper This paper presents the numerical simulations performed with COMSOL Multiphysics commercial software of a short ESS and a long fan OGV vanes coated with a thermal conductive layer. Fig. 1 shows schematically where these vanes are located inside the engine. ESS are the first set of short vanes at the entrance of the core compressor and fan OGV are just outside the engine core and in the nacelle duct between the front fan and the exit nozzle. OGV vanes are typically made of aluminium alloys or even composite as they do not carry any load, only the air pressure forces acting on the airfoils. ESS are much shorter vanes than OGV and are typically made of aluminium or titanium alloys. The CFD study conducted on ESS vanes shows how effective is increasing the thickness of the high conductivity coatings. The numerical study is validated by an experimental investigation where coated and
Location of OGV and ESS behind the front engine fan
Fig. 1. Location of fan OGV and ESS inside a typical turbofan engine.
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C. Buffone / International Journal of Heat and Mass Transfer 130 (2019) 650–659
bare stator vanes are actually tested in a laboratory wind tunnel. The concept proposed in this paper of composite fins with specific thermally conductive coatings is far less complex and costly to achieve from an operational point of view than all other suggestions to improve heat transfer between solid and fluid which have been made in the past decades and which always result in quite severe penalties. For this reason, attempting to increase heat transfer rate by the use of composite fins, when finned surfaces are employed, should become the first approach to be investigated. The key is to find the right combination of material and thickness for the substrate and the coating of the fin. 2. Numerical model In this paper we solved the numerical problem of heat transfer from an extended surface such as a fin in the shape of a vane to the airflow by the use of COMSOL Multiphysics commercial CFD package. COMSOL uses the Finite Element Method (FEM) to approximate a set of Partial Differential Equations (PDE) having a finite number of unknown parameters: it performs a discretization of the original problem on an unstructured grid.
Defining another parameter as Pj ¼ lT
@u þ u ru ¼ rp þ r T þ f @t
ð1Þ
where u is flow velocity, q is fluid density, p is pressure, T is component of total stress tensor and f represents body forces (per unit volume) acting on the fluid. The Navier-Stokes equations are strictly a statement of the conservation of momentum. In order to fully describe the fluid flow, more information is needed. A statement of the conservation of mass is generally necessary. This is achieved through the mass continuity equation, in our case given in its form as:
r ðquÞ ¼ 0
qjr u we can finally also write the equations that relate j and :
qðu rÞj ¼ r qðu rÞ ¼ r
lþ
lT rk þ P j q rj
lþ
lT 2 r þ C 1 P j C 2 q r k j
2 1 l j ¼ u2 and ¼ ðru þ ðruÞT Þ
ð3Þ
2
where l is dynamic viscosity. Defining also the parameter lT as lT ¼ qC l j2 with C l a constant and assuming the fluid to be isotro-
pic, we can write the component of total stress tensor in the equation of fluid motion as follows:
1 T ¼ 2ðl þ lT Þ E DI 3
ð4Þ
where D ¼ r u is the rate of expansion of the flow and E ¼ 12 ðruÞ þ 12 ðruÞT is the rate of strain tensor. If we write the pressure as p þ 23 qj and limiting our study to a stationary problem, the Navier-Stokes equation become:
ð6Þ
ð7Þ
with C 1 and C 2 constants. So, summing up the model j- to describe turbulent flow, the whole set of fluid flow equations to be solved are: 8 > qðurÞu ¼ r½pI þ ðl þ lT Þðru þ ðruÞT Þ 23 ðl þ lT Þðr uÞI 23 qjI þ f > > > > > r ðquÞ ¼ 0 > > h i > > > > q ðu r Þ j ¼ r ðl þ rljT Þrj þ Pj q > < h i > qðu rÞ ¼ r ðl þ lrT Þr þ C 1 k Pj C 2 q j > > > > > > > lT ¼ qC l j2 > > h i > > ru > : P j ¼ lT ðruþðruÞT Þ 23 ðr uÞ2 23 qjr u
Now an equation describing the heat transfer in the fluid is needed. The fundamental law governing all heat transfer is the first law of thermodynamics, commonly referred to as the principle of conservation of energy. If we write this principle of conservation of energy in terms of temperature (T), the resulting equation, ignoring viscous heating and pressure work, is:
qC P
@T þ qC P u rT ¼ r ðkTÞ þ Q @t
ð9Þ
where C P is specific heat capacity at constant pressure and k in thermal conductivity. This equation also assumes that mass is always conserved and implies Fourier’s law of conduction which states that the conductive heat flux q is proportional to the temperature gradient:
q ¼ krT
ð10Þ
In our case, seeking a stationary solution, the final energy equation becomes:
qC P u rT ¼ r ðkrTÞ þ Q
ð11Þ
ð2Þ
j- models use the turbulent kinetic energy (j) and the rate of turbulent energy dissipation () defined as follow: 2
i 23 ðr uÞ2
ð8Þ
Because of the high airspeed (65 m/s) and the consequent high Reynolds number of the present cases (around 430,000 for ESS vanes), in COMSOL the turbulent flow is simulated solving the three-dimensional steady Navier-Stokes equations using the Reynolds-Averaged Navier–Stokes (RANS) approach, supplemented with a j- turbulence model. The general form of the Navier–Stokes equations of fluid motion solved in COMSOL is:
ru ðruþðruÞT Þ
2 3
2.1. Basic equations
q
h
2 3
2 3
qðurÞu ¼ r pI þ ðl þ lT Þðru þ ðruÞT Þ ðl þ lT Þðr uÞI qjI þ f ð5Þ
2.2. Grid independency validation The grid sensitivity analysis is performed only on the ESS tapered but not twisted vane. Typically, rotor blades and stator vanes are both twisted and tapered [22] and their shape and dimensions vary along the axial length of the engine because air velocity decreases and pressure increases as work is done by the compressor on air. The modelled ESS vane simplified shape can be seen in Fig. 2 where the important dimensions are reported. It should not be considered as a typical design of an ESS vane; it is rather a simple CAD generated model that can be imported and simulated in COMSOL. Fig. 3 reports the Coarse (left) and Extra Fine (right) unstructured meshes as automatically defined by the grid generator of COMSOL for the problem solved here in the case of an aluminium ESS vane. Table 1 reports details of the tetrahedral mesh elements number, the number of iterations to reach steady state (with a residual of 104) and the calculated DT along the vane (the percentage difference is between the DT of the actual and previous cases). As shown in Table 1, there is a large DT variation between Normal and Fine meshes after which a further mesh refinement has little impact on the accuracy of the result. There-
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C. Buffone / International Journal of Heat and Mass Transfer 130 (2019) 650–659
Isometric view of ESS vane
Top view of ESS vane
Fig. 2. Shape and dimensions of modelled ESS tapered vane.
“Coarse” mesh with 34,344 elements
“Extra fine” mesh with 673,075 elements
Fig. 3. Details of ‘‘coarse” and ‘‘extra fine” unstructured meshes. The blue region is the ESS vane. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 1 Mesh sensitivity analysis for meshes automatically defined in COMSOL grid generator. MESH
N. of elements
N. of iterations to reach steady state
DT (°C)
DT percentage difference (%)
Coarse Normal Fine Extra Fine
34,344 69,435 395,704 673,075
40 42 46 54
17.07 16.71 13.42 13.04
– 2.1 19.7 2.8
fore, a Fine mesh as generate by COMSOL grid generator of almost 400,000 elements is enough to capture the physics of this problem.
3. Numerical results First the results of the simulations of the ESS vane will be given followed by different ones performed on the fan OGV vane. The chosen value of airspeed in the simulations is due to the upper limit of the AEROLAB wind tunnel employed in the validation tests (as described further below). The vane substrate material used in the simulations for ESS is aluminium and the effect of two coatings have been investigated. Being aluminium’s thermal conductivity almost an order of magnitude higher than titanium, then the composite fins with high thermal conductivity coatings are more effective if the vanes are made of titanium than the results presented in the simulations below [16]. The coatings are assumed to have isotropic thermal conductivities; the literature reports that the thermal conductivity value varies widely especially for CNT, depending on the fabrication method. In our calculations we assume a thermal conductivity of 6000 and 2500 W/(m K) for DLC [1] and CNT [23] respectively. Fig. 4 reproduces the temperature profiles along the outmost surface of the aluminium ESS vane without any coating and with
DLC or CNT coatings. In the present study, we keep constant the fin substrate thickness; Lalot et al. [16] demonstrated that for coatings between 50 and 150 lm, the thicker the fin substrate, the lower the improvement of fin efficiency. The different graphs of Fig. 4 show the important effect of the coating thickness. From the graphs of Fig. 4 it is clear that the simulations show little difference between the DLC and CNT coatings; most likely because of the high convective heat transfer coefficient value of this application and the ESS vane dimensions (especially the thickness ratio between coating and substrate). However, DLC is a more mature commercial available product since many years now and therefore might be the preferred option to designers. The other important factor revealed by Fig. 4 (where the temperature profiles along the ESS vane have been normalised) is that the thickness of the coating plays a very important role even for high Reynolds numbers as those of the present study. In particular, it is shown that for coatings up to tens of microns and for such high Reynolds number there is no appreciable heat conducted along the length of the vane compared with the bare aluminium vane. This is due to the fact that there is no much material in the coating to transport a sensible amount of heat along the length of the vane. As soon as the coating becomes of the order of 100 µm (Fig. 4c) there is a noticeable conduction of heat along the vane length. DLC coatings have superior hardness, low friction and excellent corrosion resis-
C. Buffone / International Journal of Heat and Mass Transfer 130 (2019) 650–659
(a) Coating thickness of 1 mm.
(b) Coating thickness of 0.5 mm.
(c) Coating thickness of 0.1 mm.
(d) Coating thickness of 0.01 mm.
655
(e) Coating thickness of 0.001 mm. Fig. 4. Normalised temperature profile along the aluminium ESS vane without and with different high conductivity coatings. (a)–(e) represent different coating thickness.
tance [24]; however, the poor adhesion due to internal stresses limits the thickness to less than 3–5 µm. Recently, there have been cases in which DLC coatings as thick as 37 µm have been made [25]
reaching even 50 µm as reported by Liu et al. [24]. Composite coatings of Al/CNT with thickness of 150 µm have been bonded on Al substrates as shown in Khasenova et al. [26]. These are thickness
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C. Buffone / International Journal of Heat and Mass Transfer 130 (2019) 650–659
not far off from the thickness range of around 100 µm (Fig. 4c) at which a noticeable heat conduction along the coating takes place for the ESS vane modelled in the present paper for high Reynolds numbers. For a ESS vane subject to icing conditions this would mean that a much shorter length of the vane confined at the vane tip is interested by ice formation. These numerical results for high Reynolds numbers are basically a further confirmation of the analytical simplified model developed in Buffone et al. [1] for much lower Reynolds numbers, where it was argued that the heat conduction along the base material of the fin and the coating follows a parallel thermal resistance network and therefore the heat, in certain ratio of thickness to thermal conductivity between coating and fin, would be conducted preferably along the coating rather than along the substrate material of the fin. Fan OGV vanes are much bigger and longer than ESS. They are housed between the engine core and the nacelle and their main purpose is to remove the swirl in the airflow impressed by the front fan of the engine [27]. Again, in our simulations we consider only a tapered OGV without twist along its length. In reality, fan OGV are twisted and tapered. Fan OGVs have been also proposed recently [28] as a means of cooling aeroengine oil. However, this approach carries its own risks and complexity to do with creating networks of passages in the shrouds and inside the multitude of vanes usually employed (usually more than 20 and sometimes up to 50 for aeroengines with high bypass ratio [29]) and possible oil leaks from all the joints and connectors necessary for such design. In the present paper engine oil will only be taken at the root of the fan OVG vanes and a novel strategy will also be employed to limit drastically the heat losses from the heated vane to the cold airstream flowing around it. Typically, large vanes have internal webs for structural reasons that make them light (because the skin is thin) and at the same time strong. For this reason, we suggest to modify the web structure inside the vane and have larger contact surface area between the webs and skin of the vane around the root and tip of the vane and much less contact area in the middle of the vane where the heat losses between the vane skin and the cold airflow should be limited in order for the heat to reach the vanes’ tip. OGVs can be made of aluminium or also of composite materials to reduce engine weight and therefore we will also consider as substrate for our modelling a composite material as well as aluminium. For the OGV vane simulations we have chosen Graphene (with chosen thermal conductivity of 2000 W/(m K) [30]) as coating to show that any other high thermal conductivity material similar to DLC and CNT would deliver the same heat
Surface temperature for OGV skin
transfer enhancement sought compared to the fin substrate. The length of the simulated OGV vanes is 420 mm and the width at the base is 250 mm. Fig. 5 reports the temperature plots from COMSOL of the simulated OGV with aluminium vane core and Graphene coating. Only the temperature on the solid surfaces is shown. On the left frame the skin temperature of the OGV is reported and on the right frame the internal web temperature is reported. From the right frame of Fig. 5 the proposed shape of the web can clearly be seen, which has larger contact area with the OGV skin at the base and tip regions and much reduced contact area in the middle section where heat losses to the airstream should be limited. The adoption of the conductive webs inside the vane would allow to transport heat much further along the vanes in conjunction with the high thermal conductive coating on the outside of the vane and this strategy could also be adopted for anti-icing of propeller blades not contained within the engine nacelle. Finally, Fig. 6 shows the temperature profiles of the modelled fan OGV geometry with internal webs for different substrate and coating materials. The aluminium-Graphene and composite-
Fig. 6. Temperature profiles along the modelled fan OGV with different materials for the substrate and coating.
Surface temperature for OGV internal webs
Fig. 5. Surface temperature for fan OGV tapered vane. Temperature plot of OGV skin (felt) and internal web (right).
C. Buffone / International Journal of Heat and Mass Transfer 130 (2019) 650–659
Graphene cases have Graphene as coating with a thickness of 100 lm. Clearly, for single-material aluminium or composite vanes, there is between 30 and almost 40% of the OGV which is below the freezing point (set at 0 °C and shown in Fig. 6 with the dashed horizontal line) and the temperature variation between base and tip of the vane is very large, which might provoke extra unwanted stresses in the material. When Graphene is added as a coating, all the length of the vane is outside the freezing point and the temperature variation along the length of the vane is much more limited.
4. Experimental validation A ESS vane like the one modelled has been made and tested in similar conditions to those investigated numerically. Three thermocouples were located at the root, mid-span and tip of the ESS vane and with these thermocouples we estimated how much heat is lost along the length of the vane and by comparing the bare and coated vane we can estimate the transfer enhancement brought by the coating (in the same spirit reported in Buffone et al. [1]). An AEROLAB educational wind tunnel was employed with a top airspeed of 65 m/s, test section of 305 305 610 mm, a turbulence level of 0.2% and a top Reynolds number of around 430,000 based on the ESS vane width of 100 mm. The maximum airspeed of the tunnel is lower than the top 100 m/s of the real aeroengine applications in icing conditions, whereas the vane dimensions and orientation with respect to the airflow were the same as those of the simulations. The only difference is that the education wind tunnel runs the tests at ambient temperature and not at freezing temperature as those encountered in real icing conditions. However, this is not an important limitation because as also stated in Cortes et al. [17], this heat transfer problem is homogeneous and therefore specific temperature values do not have any substantial influence on the results. We tested a bare ESS vane and one completely coated with 10 or 100 µm thick DLC. The wind tunnel tests could not show any noticeable improvement at 10 µm thick DLC, presumably because as also the simulation clearly show with graph d of Fig. 4, there is little material in the coating to transfer any sensible amount of hear at such high Reynolds numbers. The fin loses heat to the surrounding airstream and its temperature decreases along the length. Following the pragmatic approach described in Buffone et al. [1], if we monitor the temperature of the fin at any location (base or even tip), we should be able to appreciate any improvement brought by the coating of the composite fin. In the present study, by measuring the temperature at the vane’s tip an improvement of between 4 and 5% for 100 µm thick DLC coating have been measured in the experiments. These values are quite close to the 4.5% predicted by the simulations presented in graph c of Fig. 4. However, these values are well below the enhancement of heat transfer rate of approximately 30% reported in Buffone et al. [1] estimated by monitoring the temperature of the heat pipe condenser from where the fin stack stem from; this is due most likely because at these much higher Reynolds numbers (above 430,000) the heat transfer coefficient at the air side is considerably higher than for Reynolds numbers ranging between 500 and 1500 as in Buffone et al. [1]. After all, this is the reason why fins are more effective in applications involving low convection heat transfer coefficients [31]. The experimental and numerical results of the present study and those of Buffone et al. [1] are in line with the mathematical prediction of Lalot et al. [16], albeit the latter authors were considering different ratios of thickness and thermal conductivity for substrate and coatings of the fins; additionally, the coatings that were proposed by Lalot et al. [16] albeit slightly more conductive than the substrate of the fin, they were mainly used for corrosion resistance purpose.
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Instead, in the present work and in Buffone et al. [1], the main purpose of the coating is to enhance heat transfer. These very high thermal conductive coatings can also offer excellent corrosion and impact resistance and some of them very low friction as well. The results of the present work agree also with the mathematical prediction of Lalot et al. [1] which says that for a coating more conductive than the substrate, the thicker the coating the more efficient the heat transfer from the composite fin. For all these reasons, the basic concept of enhancing heat transfer from a fin by the use of conductive coatings demonstrated in the present work, originally presented in Buffone et al. [1] and later adapted in Knott et al. [19] for a different application, has indeed merit and should be investigated before any other approach aimed at improving the heat transfer from finned surfaces. This is especially advantageous because fins are coated anyway for protection of the substrate. 5. Analysis In this section we are going to perform a simplified analysis of the composite fins following the method developed in Lalot et al. [16] and Cortes et al. [17]. Because the applications are different, we are also going to compare the composite fins of Buffone et al. [1] with the present ones, albeit the fins of the present study are relatively thick vanes, i.e. hollow inside. The first check we need to carry out is that we can assume a one-directional approximation of the heat transfer within the fin. For this we need to evaluate the average thermal conductivity of the composite fin or ESS vane and then estimate the Biot number of the composite fin, both of which are given by [17]:
kAV ¼
ks As þ kc Ac As þ Ac
ð12Þ
hðts tc Þ kAV
ð13Þ
BiAV ¼
where the subscript s stands for fin substrate and c stands for coating. The Biot number varies from 2 105 for the bare aluminium fin to 105 for the composite fin of Buffone et al. [1]. For the present ESS vane, the same Biot number varies between 2 103 and 2 105. Therefore, we can reasonably assume that the temperature within the fin changes only along the fin length (onedirectional approximation). The second thing that we need to ascertain is the flow regime. In both cases, the heat transfer problem is a combination of natural and forced convection. In particular, the direction of the forced convection is transverse with direction of the buoyancy induced natural convection because of the spatial disposition of the fins/vane [31]. Therefore, we need to evaluate the Grashof number and then compare it with the Reynolds number. For the two cases (Buffone et al. [1] and present study), we have a maximum temperature difference between fins and surrounding air of around 45 °C and a maximum characteristic length of 0.1 m. The estimated Grashof number is:
Gr ¼
gbðT s T 1 ÞL3
v2
¼ 9 106
ð14Þ
For Buffone et al. [1] the Reynolds number ranges between almost 500 and almost 1500, therefore we have the following bounds for the ratio:
4<
Gr Re2
< 36
ð15Þ
which suggests that forced convection effects are negligible compared with those of natural convection in the case of composite fins for electronic cooling applications of Buffone et al. [1].
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For the case of vanes at high Reynolds number the estimation of the same ratio gives Gr/Re2 = 5 105 which instead suggests that forced convection forces dominate on buoyancy ones. So, the flow regimes of the two examined cases are completely different. Estimating the Nusselt number is straightforward for the composite fins of Buffone et al. [1] and leads to an approximate value of around 7 which obeys to the one of fully developed laminar flow between close plates [31]. A bit more complex is the estimation of Nusselt number for the kind of flow present for the ESS vanes; in fact, there is laminar flow for a good portion of the vane’s width near the leading edge and then turbulent flow sets in on the rest of the vane‘s width. According to the suggestion in Çengel and Turner [31], we define and evaluate the average Nusselt number as follows:
Nu ¼
hL 1=3 ffi 282 ¼ ð0:037Re0:8 L 871ÞPr k
ð16Þ
This Nusselt value is around 40 times bigger than the one for composite fins of Buffone et al. [1], which adjusted for the differences in characteristic lengths and air thermal conductivity because of different free airstream temperatures, one gets that the estimated heat transfer coefficient for the ESS vanes is more than 6 times larger than that of the composite fins of Buffone et al. [1]. We will calculate now the fin effectiveness which is defined [31] as the ratio of heat transfer rate of the actual fin with the heat transfer rate if no-fin at all is present. Fin effectiveness should be sufficiently larger than 1 to justify the need for fins. It can be shown that for a sufficiently long composite fin, the fin effectiveness can be estimated as:
e¼
rffiffiffiffiffiffiffiffiffiffi kAV p hA
ð17Þ
where kAV is the equivalent thermal conductivity of the composite fin, p is the fin perimeter, h is the convective heat transfer coefficient, and A is the cross-sectional area of the composite fin. The estimated fin effectiveness is between one and two orders of magnitude higher for the fins of Buffone et al. [1] than for the present case; this is due to smaller convective heat transfer coefficient at the airside and thinner fins. To ascertain what is the effect of the coatings, we calculate the fin effectiveness ratio defined as the composite fin effectiveness divided by the bare fin effectiveness. For the fins of Buffone et al. [1] this ratio yields 3.4. Instead, for the present case of a ESS vane the estimated fin effectiveness ratio yields 1.2. For thin coatings this result could be directly obtained from the above fin effectiveness relation as a ratio of the thermal conductivities of composite to bare fin. It should be mentioned that for the fins tested in Buffone et al. [1] and the present ESS vanes, the averqffiffiffiffiffiffiffi hp age thermal length mAV L ¼ kAV L with the coating ranges A between 0.8 and 1.2, which suggests that the fin length (L) are near the optimal value. It is accepted that a good compromise between heat transfer performance and fin cost usually limits mAV L to around 1 [31]. 6. Conclusions In this paper a novel approach is proposed aimed at enhancing the heat transfer between finned surfaces and surrounding fluid. This approach consists in using high thermally conductive coatings on top of the fin substrate in order to increase the local temperature along the fin washed surface in comparison with the bare fin. This strategy is somewhat different from the usually studied cases of fins coated for corrosion or temperature protection, mainly done by low thermal conductivity coatings. The proposed approach is highly effective as it does not have any detrimental effect such as
increased pressure drop, which usually comes with other strategies aimed at enhancing heat transfer rate. The new proposed solution was first tested successfully on an aluminium finned stack for electronic cooling application [1] for low Reynolds numbers. In the present paper a similar strategy has been applied to an aeroengine vane subject to icing conditions at much higher Reynolds numbers. Numerical simulations were carried out to ascertain the range of thickness of the coatings to be used in order to maximise the wanted effect. Both short ESS and longer fan OGV vanes were modelled having different design objectives. In the case of fan OGV vanes, an additional innovative design modification was suggested to enhance further the heat transfer along the vane length by the use of the internal webs which typically are present to strengthen the long, slim and thin vanes. The experimental validation carried out in the present paper at much higher Reynolds numbers than that reported in Buffone et al. [1], demonstrate that the novel concept of heat transfer enhancement by the use of thermally conductive coatings is robust and it is worth exploring further. We have performed a fin analysis of the present ESS vane and compared it with the fins tested in Buffone et al. [1] at much lower Reynolds numbers. We concluded that the fins tested in Buffone et al. [1] have higher fin effectiveness because of much lower convective heat transfer coefficient and much thinner fins. Even the ratio of fin effectiveness between composite and bare fin shows that the improvement obtained with the coated fins tested in Buffone et al. [1] is much larger than the one obtained with the coated ESS vanes. The average thermal length of the composite fins is near the optimal suggested value of 1 for both studies. It is worth mentioning that the actual thickness of the thermally conductive coatings is a function of the Biot number, fin shape, dimensions and thermal conductivity ratios of fin substrate and coating; proper design of the bare vane and coating should be carried out for each application. Conflict of interest None declared. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.ijheatmasstransfer. 2018.10.124. References [1] C. Buffone, K. Sefiane, L. Buffone, S. Lin, Heat transfer enhancement in heat pipe applications using surface coating, J. Enhanced Heat Transf. 12 (1) (2005) 21– 35. [2] D. Reay, P. Kew, Heat Pipes: Theory, Design and Applications, fifth ed., Elsevier, Oxford, 2006. [3] J.M. Wu, H. Zhang, C.H. Yan, Y. Wang, Experimental study on the performance of a novel fin-tube air heat exchanger with punched longitudinal vortex generator, Energy Convers. Manage. 57 (2012) 42–48. [4] B. Torregrosa-Jaime, J.M. Corberan, J. Paya, J.L. Delamarche, Thermal characterization of compact heat exchangers for air heating and cooling in electric vehicles, Appl. Therm. Eng. 115 (2017) 774–781. [5] J. Hamzelou, Jumbo challenge: how elephants keep their cool, NewScientist 218 (2922) (2013) 46–47. [6] C. Lyman, R.A. Stephan, K.A. Thole, L.W. Zhang, S.B. Memory, Scaling of heat transfer coefficient along louvered fins, Exp. Therm. Fluid Sci. 26 (2002) 547– 563. [7] O. Leon, G. De Mey, E. Dick, Study of the optimal layout of cooling fins in forced convection cooling, in: Proceeding of the 8th International Workshop on Thermal Investigation of ICs and Systems, Madrid, Spain, 2002, pp. 260–265. [8] N.C. DeJong, A.M. Jacobi, Flow, heat transfer, and pressure drop in the nearwall region of louvered-fin arrays, Exp. Therm Fluid Sci. 27 (2003) 237–250. [9] F.J. Rowley, S.V. Patankar, Analysis of laminar flow and heat transfer in tubes with internal circumferential fins, Int. J. Heat Mass Transf. 27 (4) (1984) 553– 560.
C. Buffone / International Journal of Heat and Mass Transfer 130 (2019) 650–659 [10] R.C. Henry, R.J. Hansman, K.S. Breuer, Heat transfer variation on protuberances and surface roughness elements, J. Thermophys. Heat Transf. 9 (1) (1995) 175– 180. [11] G. Biswas, K. Torii, D. Fujii, K. Nishino, Numerical and experimental determination of flow structure and heat transfer effects of longitudinal vortices in a channel flow, Int. J. Heat Mass Transf. 139 (16) (1996) 3441–3451. [12] H. Huisseune, C. T’Joen, P. De Jaeger, B. Ameel, S. De Schampheleire, M. De Paepe, Performance enhancement of a louvered fin heat exchanger by using delta winglet vortex generators, Int. J. Heat Mass Transf. 56 (2013) 475–487. [13] J.M. Wu, W.Q. Tao, Impact of delta winglet vortex generators on the performance of a novel fin-tube surface with two rows of tubes in different diameters, Energy Convers. Manage. 52 (2011) 2895–2901. [14] F.P. Incropera, D.P. DeWitt, Fundamentals of Heat and Mass Transfer, fourth ed., John Wiley, New York, 1996. [15] J.J. Barker, The efficiency of composite fins, Nucl. Sci. Technol. 3 (1958) 300– 312. [16] S. Lalot, C. Tournier, M. Jensen, Fin efficiency of annular fins made of two materials, Int. J. Heat Mass Transf. 42 (1999) 3461–3467. [17] C. Cortes, L.I. Diez, A. Campo, Efficiency of composite fins of variable thickness, Int. J. Heat Mass Transf. 51 (2008) 2153–2166. [18] T.N. Rhys-Jones, The use of thermally sprayed coatings for compressor and turbine applications in aero engines, Surf. Coat. Technol. 42 (1990) 1–11. [19] D.S. Knott, A. Lambourne, A.M. Rolt, C. Buffone, Heat transfer arrangement for fluid-washed surfaces, US Patent US2011/0296811 A1, 2011. [20] G.C. Botura, D. Sweet, Concept development of low power electrothermal deicing system, AIAA (2006) 864. [21] O. Parent, A. Ilinca, Anti-icing and de-icing techniques for wind turbines: critical review, Cold Reg. Sci. Technol. 65 (2011) 88–96.
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[22] H. Kou, J. Lin, J. Zhang, X. Fu, Dynamic and fatigue compressor blade characteristic during fluid-structure interaction: Part I-Blade modelling and vibration analysis, Eng. Fail. Anal. 76 (2017) 80–98. [23] C. Diao, Y. Dong, J. Lin, Reactive force field simulation on thermal conductivities of carbon nanotubes and graphene, Int. J. Heat Mass Transf. 112 (2017) 903–912. [24] L. Liu, Z. Wu, X. An, S. Xiao, S. Cui, H. Lin, R.K.Y. Fu, X. Tian, R. Wei, P.K. Chu, F. Pan, Excellent adhered thick diamond-like carbon coatings by optimizing hetero-interfaces with sequential highly energetic Cr and C ion treatment, J. Alloy. Compd. 375 (2018) 155–162. [25] E.L. Dalibon, L. Escalada, S. Simison, C. Forsich, D. Heim, S.P. Bruhl, Mechanical and corrosion behavior of thick and soft DLC coatings, Surf. Coat. Technol. 312 (2017) 101–109. [26] R.S. Khasenova, S.V. Komarov, V.Yu. Zadorozhnyy, Mechanical plating of Al/ CNT composite coatings on aluminium substrates, J. Alloy. Compd. 707 (2017) 238–244. [27] R. Gustavsson, Design Study of Advanced Metallic Structural Integrated Fan Outlet Guide Vanes in Civil Jet Engines, Master Thesis, Lulea University of Technology, Sweden, ISSN, 1402-1617, 2006. [28] M. El Achin Sennoun, OGV heat exchangers networked in parallel and in serial flow, European Patent EP20160200675, 25 November 2016. [29] H. Posson, S. Moreau, M. Roger, Broadband noise prediction of a fan outlet guide vane using a cascade response function, J. Sound Vib. 330 (2011) 6153–6183. [30] G. Xin, H. Sun, T. Hu, H.R. Fard, X. Sun, N. Koratkar, T. Borca-Tasciuc, J. Lian, Large-area freestanding graphene paper for superior thermal management, Adv. Mater. 26 (2014) 4521–4526. [31] Y.A. Çengel, R.H. Turner, Fundamentals of thermal-fluid sciences, second ed., McGraw-Hill, New York, 2005.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
A novel approach for heat transfer enhancement in composite fins Cosimo Buffone Tianjin Key Lab of Refrigeration Technology, Tianjin University of Commerce, Tianjin City 300134, PR China
a r t i c l e
i n f o
Article history: Received 24 April 2018 Received in revised form 23 October 2018 Accepted 27 October 2018
Keywords: Composite fins Vanes Heat transfer rate Thermal conductivity
a b s t r a c t This paper main goal is aimed at a paradigm shift in the enhancement of heat transfer rate between finned surfaces and surrounding fluid by presenting a novel approach in composite fins. This approach consists in using high thermally conductive coatings on top of the finned substrate in order to increase the local temperature along the fin washed surface. In the present paper a high thermal conductivity coating has been applied to an aeroengine vane of different shape and dimensions subject to icing conditions at high Reynolds numbers and where the main aim was to keep the vane warm as to avoid icing in aerospace applications. Numerical simulations have been carried out to ascertain the range of thickness of the coatings to be used to maximise the wanted effect. Both short Engine Section Stator (ESS) and longer fan Outlet Guide Vane (OGV) have been modelled, having different final goals. In the case of longer OGV, an additional novel design modification has been suggested to enhance further the heat transfer along the vane length by the use of the internal webs. The experimental validation also carried out at much higher Reynolds numbers than that reported in Buffone et al. (2005), demonstrate that the novel concept of heat transfer enhancement in composite fins is a simple and yet powerful strategy in a wide range of Reynolds numbers. A fin analysis has been performed of both the present ESS vane the fins tested in Buffone et al. (2005) at much lower Reynolds numbers and shows that the improvement obtained with the coated fins tested in Buffone et al. (2005) is much larger than the coated ESS vanes investigated in the present study. This said, the present study demonstrates that the use of high conductive coatings in composite fins can keep the ESS vanes ice free, something that was not possible with uncoated vanes. It is important to note that the actual optimal thickness of the thermally conductive coatings is a function of Biot number, fin shape, dimensions and thermal conductivities of fin substrate and coating; depending on the application, a proper design of the fin substrate and coating should be carried out. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction The convective heat transfer between solids and fluids depends on heat transfer coefficient and surface area as well as temperature difference between solid and fluid. Enhancing heat transfer rate between solid and fluid is typically done by improving the heat transfer coefficient and/or increasing the contact surface area. Both these strategies come with a penalty which is increased pressure drop that many times is prohibitive. The task of the heat transfer designer is trying to improve heat transfer rate without a large penalty on pressure drop. The improvement in surface area is typically done by the use of finned surfaces, which are protrusions of the basic contact surface area inside the fluid flow. Fins are employed in both the case where the fluid is cooler than the surface and in the opposite case where the fluid is hotter than the surface; their role is to increase heat transfer rate between solid surface and the adjacent fluid. Cooling fins are found more often E-mail address: [email protected] https://doi.org/10.1016/j.ijheatmasstransfer.2018.10.124 0017-9310/Ó 2018 Elsevier Ltd. All rights reserved.
in applications such as electronic cooling [1,2], refrigeration and air-conditioning [3], vehicle thermal management [4]. Fins are not only used by engineers but also by animals. Animals use fins to manoeuvre their movement inside a fluid; fish do this more smoothly and effectively in water than aeroplanes do it in the air with wings, stabilizer and rudder. Animals also deploy fins for deterring attacks from predators by appearing bigger than they actually are. And there are animals like elephants [5] with a body having small surface to volume ratio which need big ears to dissipate heat. Animals like elephants use fins also for their thermoregulation, which is the ability to keep their body temperature within certain limits even though the ambient temperature is different. Stegosaurus and crocodiles had/have dermal plates not attached to the skeleton, but with blood vessels running through them with the aim of cooling the blood by losing heat to ambient. It is also believed that these two last animals used/use these plates as fins when they needed/need to gain heat from the ambient. When air is the heat transfer medium, it is an accepted fact that over 85% of the thermal resistance of a cooling unit is concentrated
C. Buffone / International Journal of Heat and Mass Transfer 130 (2019) 650–659
651
Nomenclature A Bi Cp E ESS f g Gr h k L Nu OGV p p Pr Q Re t t
fin cross section area (m2) Biot number specific heat capacity (J/kg/°C) rate of strain tensor (1/s) Engine Section Stator body forces per unit volume (kg/m3) gravity acceleration (m/s2) Grashof number heat transfer coefficient (W/m2/°C) fin thermal conductivity (W/m/°C) fin length (m) Nusselt number Outlet Guide Vane fluid pressure (N/m2) fin perimeter (m) Prandtl number heat generation per unit volume (W/m3) Reynolds number time (s) fin or coating thickness (m)
at the airside [6], because air is such a poor heat transfer fluid. In a typical car radiator using water and air as heat transfer media on the opposite sides, only the airside has fins; there is no need of fins on the water side. For this reason, extended surfaces are the basic mean to enhance heat transfer from solid surfaces at the airside. Therefore, over the years many different extended surfaces have been investigated. Researchers have concentrated their efforts on fin shapes [7] with 15–20% improvement on heat transfer and a considerable increase in pressure drop; fin spatial arrangement [8] with unsteadiness in the boundary layer region close to the surface that results in a 15% enhancement in heat transfer and an associated increased pressure drop of hundred times; surface roughness [9,10]; and, on the promotion of mixing by turbulence generated because of surface modifications [11] where winglet type vortex generator were used in fully developed laminar channel flow with good improvement of heat transfer and some important pressure drop penalty. Huisseune et al. [12] conducted a numerical study of combined louvered fin heat exchanger with delta winglets as vortex generators which produces heat transfer enhancement because of thinning of the boundary layer due to induced normal flow and the wake size behind the tubes is reduced which produces a reduction of form drag; however, increased friction and flow blockage from the delta winglets result in an increase in net core pressure drop. Wu and Tao [13] numerically and then Wu et al. [3] experimentally proposed a design modification of fin-tube heat exchangers with punched vortex generators only present near the first row of tubes of reduced diameter. Wu et al. [3] for an airspeed of 4 m/s report that for vortex generator in ‘‘common flow up” configuration there is an increase of heat transfer coefficient of around 16% and a corresponding reduction of pressure drop of around 10%, whereas for ‘‘common flow down” configuration there is a 28% increase of heat transfer coefficient and a minor decrease of pressure drop compared with a baseline fin and tube heat exchanger with staggered tubes of same diameter. The proposition of Wu and Tao [13] and Wu et al. [3] shows that particular configurations can bring heat transfer enhancement and either limited pressure drop penalty or even deliver small gains at the expenses of complications in manufacturing and assembling of such heat exchangers design. We will apply a different method to enhance the heat transfer between a finned surface and the surrounding air. This method
T T u
temperature (°C) total stress tensor (N/m2) fluid velocity vector (m/s)
Greek symbols b coefficient of thermal expansion (1/°C) e fin effectiveness turbulent energy dissipation (m2/s3) k fluid thermal conductivity (W/m/°C) j turbulent kinetic energy (m2/s2) m kinematic viscosity (m2/s) l fluid dynamic viscosity (Pa s) q fluid density (kg/m3) Subscripts AV average c coating s substrate 1 undisturbed flow
considers composite fins in which thermally conductive coatings are deposited on a less conductive substrate with the aim to enhance heat transfer by increasing locally the temperature of the washed fin surface in contact with air. The composite fin concept will be applied to aeroengine slender surfaces where Reynolds numbers are relatively high, in order to prove that the air speed range of this concept is quite wide. 1.1. Published work on composite fins Modifying the airside by either trying to increase the air heat transfer coefficient or increasing the washed surface area typically carry an important penalty. A different approach was presented for the first time in [1] for low Reynolds numbers where surface coatings having very high thermal conductivity were suggested as an effective way to enhance the heat transfer rate. A finned heat pipe assembly was used where the aluminium fins were coated with either Diamond Like Carbon (DLC) material or diamond industrial particles. The authors demonstrated that there was no noticeable difference in surface roughness between the three surfaces (basic aluminium, aluminium coated with DLC and aluminium coated with diamond industrial particles). Buffone et al. [1] reported an increase of 30% in the overall heat transfer coefficient for the aluminium fin stack with DLC coating or industrial diamond particles with no penalty on the pressure drop. Buffone et al. [1] introduced a simplified analysis of their heat transfer enhancement concept and estimating the fin effectiveness [14] they found it increased of 29% in the case of aluminium with DLC coated fins compared to the bare aluminium fins; this estimate was found very close to their experimental evidence. This noticeable heat transfer enhancement does not come from either an increase of heat transfer coefficient or an increase in fin surface area at the airside. It is well known [14] that a fin becomes less and less effective along its length because the fin surface temperature decreases along the fin as the fin loses heat to the air. If the fin surface temperature could be kept at the same value as that of the fin’s base, then the fin could be infinitively long. It is actually not strictly necessary that the whole fin cross section is at a temperature close to its base value; the sufficient condition is that the temperature of the fin washed surface is kept as close as possible to the base value. And this is what actually happens with the thermally conductive coatings
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tested in the composite fins of Buffone et al. [1] getting locally higher temperature than the basic aluminium material would have because of preferential conduction along the thin and highly conductive layer of the coating. The basic concept is that a coated fin would behave thermally as if it were entirely made of a highly thermal conductive material. The concept of coated fins (also known as composite fins) is not new. Barker [15] studied constant thickness straight and pin composite fins and concluded that for a sufficiently small Biot number, these fins are equivalent to the 1D treatment with a cross-sectional area average of the thermal conductivities of the basic fin material and the coating. Lalot et al. [16] looked at the same problem of composite annular metallic fins with average thickness between 0.2 and 1 mm, coating thickness between 50 and 150 lm, conductivity ratio around 2, convection heat transfer coefficient ranging between 25 and 150 W/(m2 K). They found the same conclusion of Barker [15]: the composite fin can be treated as ordinary fin of same material with a crosssectional area average thermal conductivity. For a composite fin, a similar fin efficiency can be defined [17] which depends on Biot number, ratio of total half fin thickness to length, ratio of coating to fin thickness, and ratio of coating to fin thermal conductivity. In Cortes et al. [17] it is shown, as per 1D approximation, that the composite fin efficiency reduces to the same expression for an ordinary single-material fin with an averaged thermal length and a cross-sectional area average thermal conductivity. The Biot number is defined with the total half-thickness and cross-sectional area average thermal conductivity. However, coatings are typically used to protect the fin substrate from the ambient and they typically are of lower thermal conductivity than the fin substrate. The types of fins investigated by Cortes et al. [17] are metallic with a ratio of coating to substrate thermal conductivity ranging from 0.04 to 13.6, substrate half-thickness between 0.1 and 0.5 mm, coating thickness between 30 and 80 lm, and fin length ranging from 5 to 40 mm. In the case of Buffone et al. [1] the ratio of coating to substrate thermal conductivity was above 30; the substrate halfthickness was 0.2 mm and the coating between 1 and 5 lm; the fins were almost twice as long as the ones in Cortes et al. [17]. The estimated Biot number for the cases presented in Buffone et al. [1] is almost an order of magnitude less than the range given in Cortes et al. [17]. Coatings are typically used to protect the substrate of fins from wear, oxidation and corrosion, and are also used as thermal barrier. Coatings are also employed as anti-fouling and anti-icing to mitigate the detrimental effects of these conditions on heat transfer and/or lift generating capabilities or even for safety reasons. These are all reasons why coatings are also applied in the compressor, combustor and turbine sectors of a gas turbine Rhys-Jones [18]. The patent by Knott et al. [19] describes the use of surface coatings as an anti-icing approach. The Engine Section Stators (ESS) vanes in
Fan OGVs in typical turbofan engine
an aeroengine are usually made of aluminium or titanium, the latter being not a very good heat conductor. In aerospace as well as wind turbine applications, there are different strategies to deal with the risks posed by ice formation and accretion. The two main strategies are anti-icing and de-icing. Flexible pneumatic air-boots, spraying of anti-icing chemicals, bleed of hot air from engine core, electrothermal systems [20] have been developed for large surfaces such as aeroplane wings and nacelle leading edges as well as in wind turbines [21]. But these strategies are not technically feasible for small vanes inside the engine core, like ESS vanes. The ESS vane is normally heated at the bottom with hot engine oil. The ESS is washed by an air stream with speed ranging between 50 and 100 m/s at a temperature (when the engine flies in freezing conditions) of around 20 °C; In these conditions it is found experimentally that over 1/3 of the ESS length towards the tip is frozen, despite the heating by engine oil at the vane’s base. Ice accretion on cold parts of an aeroengine can pose a serious threat to the engine integrity. In fact, pieces of ice could dislodge from the surfaces and get ingested inside the engine where they could impact violently onto subsequent rotor blades and stator vanes breaking them; solid parts of broken blades/vanes can have the potential to wreck whole parts of the engine and in severe cases put into question the operability of the engine itself, not to mention the risks posed to the airplane and the passengers with crew inside. To solve this issue, in Knott et al. [19] the authors propose the use of high conductivity coating which can be made of graphite, Carbon Nanotubes (CNT) or Diamond Like Carbon (DLC) deposited on the heated ESS. This coating of high thermal conductivity material would transport heat more effectively from the base along the ESS length. Knott et al. [19] introduced this concept but did not give any indications of the thickness of the coatings compared to the dimensions of the vane. 1.2. Goals of the paper This paper presents the numerical simulations performed with COMSOL Multiphysics commercial software of a short ESS and a long fan OGV vanes coated with a thermal conductive layer. Fig. 1 shows schematically where these vanes are located inside the engine. ESS are the first set of short vanes at the entrance of the core compressor and fan OGV are just outside the engine core and in the nacelle duct between the front fan and the exit nozzle. OGV vanes are typically made of aluminium alloys or even composite as they do not carry any load, only the air pressure forces acting on the airfoils. ESS are much shorter vanes than OGV and are typically made of aluminium or titanium alloys. The CFD study conducted on ESS vanes shows how effective is increasing the thickness of the high conductivity coatings. The numerical study is validated by an experimental investigation where coated and
Location of OGV and ESS behind the front engine fan
Fig. 1. Location of fan OGV and ESS inside a typical turbofan engine.
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C. Buffone / International Journal of Heat and Mass Transfer 130 (2019) 650–659
bare stator vanes are actually tested in a laboratory wind tunnel. The concept proposed in this paper of composite fins with specific thermally conductive coatings is far less complex and costly to achieve from an operational point of view than all other suggestions to improve heat transfer between solid and fluid which have been made in the past decades and which always result in quite severe penalties. For this reason, attempting to increase heat transfer rate by the use of composite fins, when finned surfaces are employed, should become the first approach to be investigated. The key is to find the right combination of material and thickness for the substrate and the coating of the fin. 2. Numerical model In this paper we solved the numerical problem of heat transfer from an extended surface such as a fin in the shape of a vane to the airflow by the use of COMSOL Multiphysics commercial CFD package. COMSOL uses the Finite Element Method (FEM) to approximate a set of Partial Differential Equations (PDE) having a finite number of unknown parameters: it performs a discretization of the original problem on an unstructured grid.
Defining another parameter as Pj ¼ lT
@u þ u ru ¼ rp þ r T þ f @t
ð1Þ
where u is flow velocity, q is fluid density, p is pressure, T is component of total stress tensor and f represents body forces (per unit volume) acting on the fluid. The Navier-Stokes equations are strictly a statement of the conservation of momentum. In order to fully describe the fluid flow, more information is needed. A statement of the conservation of mass is generally necessary. This is achieved through the mass continuity equation, in our case given in its form as:
r ðquÞ ¼ 0
qjr u we can finally also write the equations that relate j and :
qðu rÞj ¼ r qðu rÞ ¼ r
lþ
lT rk þ P j q rj
lþ
lT 2 r þ C 1 P j C 2 q r k j
2 1 l j ¼ u2 and ¼ ðru þ ðruÞT Þ
ð3Þ
2
where l is dynamic viscosity. Defining also the parameter lT as lT ¼ qC l j2 with C l a constant and assuming the fluid to be isotro-
pic, we can write the component of total stress tensor in the equation of fluid motion as follows:
1 T ¼ 2ðl þ lT Þ E DI 3
ð4Þ
where D ¼ r u is the rate of expansion of the flow and E ¼ 12 ðruÞ þ 12 ðruÞT is the rate of strain tensor. If we write the pressure as p þ 23 qj and limiting our study to a stationary problem, the Navier-Stokes equation become:
ð6Þ
ð7Þ
with C 1 and C 2 constants. So, summing up the model j- to describe turbulent flow, the whole set of fluid flow equations to be solved are: 8 > qðurÞu ¼ r½pI þ ðl þ lT Þðru þ ðruÞT Þ 23 ðl þ lT Þðr uÞI 23 qjI þ f > > > > > r ðquÞ ¼ 0 > > h i > > > > q ðu r Þ j ¼ r ðl þ rljT Þrj þ Pj q > < h i > qðu rÞ ¼ r ðl þ lrT Þr þ C 1 k Pj C 2 q j > > > > > > > lT ¼ qC l j2 > > h i > > ru > : P j ¼ lT ðruþðruÞT Þ 23 ðr uÞ2 23 qjr u
Now an equation describing the heat transfer in the fluid is needed. The fundamental law governing all heat transfer is the first law of thermodynamics, commonly referred to as the principle of conservation of energy. If we write this principle of conservation of energy in terms of temperature (T), the resulting equation, ignoring viscous heating and pressure work, is:
qC P
@T þ qC P u rT ¼ r ðkTÞ þ Q @t
ð9Þ
where C P is specific heat capacity at constant pressure and k in thermal conductivity. This equation also assumes that mass is always conserved and implies Fourier’s law of conduction which states that the conductive heat flux q is proportional to the temperature gradient:
q ¼ krT
ð10Þ
In our case, seeking a stationary solution, the final energy equation becomes:
qC P u rT ¼ r ðkrTÞ þ Q
ð11Þ
ð2Þ
j- models use the turbulent kinetic energy (j) and the rate of turbulent energy dissipation () defined as follow: 2
i 23 ðr uÞ2
ð8Þ
Because of the high airspeed (65 m/s) and the consequent high Reynolds number of the present cases (around 430,000 for ESS vanes), in COMSOL the turbulent flow is simulated solving the three-dimensional steady Navier-Stokes equations using the Reynolds-Averaged Navier–Stokes (RANS) approach, supplemented with a j- turbulence model. The general form of the Navier–Stokes equations of fluid motion solved in COMSOL is:
ru ðruþðruÞT Þ
2 3
2.1. Basic equations
q
h
2 3
2 3
qðurÞu ¼ r pI þ ðl þ lT Þðru þ ðruÞT Þ ðl þ lT Þðr uÞI qjI þ f ð5Þ
2.2. Grid independency validation The grid sensitivity analysis is performed only on the ESS tapered but not twisted vane. Typically, rotor blades and stator vanes are both twisted and tapered [22] and their shape and dimensions vary along the axial length of the engine because air velocity decreases and pressure increases as work is done by the compressor on air. The modelled ESS vane simplified shape can be seen in Fig. 2 where the important dimensions are reported. It should not be considered as a typical design of an ESS vane; it is rather a simple CAD generated model that can be imported and simulated in COMSOL. Fig. 3 reports the Coarse (left) and Extra Fine (right) unstructured meshes as automatically defined by the grid generator of COMSOL for the problem solved here in the case of an aluminium ESS vane. Table 1 reports details of the tetrahedral mesh elements number, the number of iterations to reach steady state (with a residual of 104) and the calculated DT along the vane (the percentage difference is between the DT of the actual and previous cases). As shown in Table 1, there is a large DT variation between Normal and Fine meshes after which a further mesh refinement has little impact on the accuracy of the result. There-
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C. Buffone / International Journal of Heat and Mass Transfer 130 (2019) 650–659
Isometric view of ESS vane
Top view of ESS vane
Fig. 2. Shape and dimensions of modelled ESS tapered vane.
“Coarse” mesh with 34,344 elements
“Extra fine” mesh with 673,075 elements
Fig. 3. Details of ‘‘coarse” and ‘‘extra fine” unstructured meshes. The blue region is the ESS vane. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Table 1 Mesh sensitivity analysis for meshes automatically defined in COMSOL grid generator. MESH
N. of elements
N. of iterations to reach steady state
DT (°C)
DT percentage difference (%)
Coarse Normal Fine Extra Fine
34,344 69,435 395,704 673,075
40 42 46 54
17.07 16.71 13.42 13.04
– 2.1 19.7 2.8
fore, a Fine mesh as generate by COMSOL grid generator of almost 400,000 elements is enough to capture the physics of this problem.
3. Numerical results First the results of the simulations of the ESS vane will be given followed by different ones performed on the fan OGV vane. The chosen value of airspeed in the simulations is due to the upper limit of the AEROLAB wind tunnel employed in the validation tests (as described further below). The vane substrate material used in the simulations for ESS is aluminium and the effect of two coatings have been investigated. Being aluminium’s thermal conductivity almost an order of magnitude higher than titanium, then the composite fins with high thermal conductivity coatings are more effective if the vanes are made of titanium than the results presented in the simulations below [16]. The coatings are assumed to have isotropic thermal conductivities; the literature reports that the thermal conductivity value varies widely especially for CNT, depending on the fabrication method. In our calculations we assume a thermal conductivity of 6000 and 2500 W/(m K) for DLC [1] and CNT [23] respectively. Fig. 4 reproduces the temperature profiles along the outmost surface of the aluminium ESS vane without any coating and with
DLC or CNT coatings. In the present study, we keep constant the fin substrate thickness; Lalot et al. [16] demonstrated that for coatings between 50 and 150 lm, the thicker the fin substrate, the lower the improvement of fin efficiency. The different graphs of Fig. 4 show the important effect of the coating thickness. From the graphs of Fig. 4 it is clear that the simulations show little difference between the DLC and CNT coatings; most likely because of the high convective heat transfer coefficient value of this application and the ESS vane dimensions (especially the thickness ratio between coating and substrate). However, DLC is a more mature commercial available product since many years now and therefore might be the preferred option to designers. The other important factor revealed by Fig. 4 (where the temperature profiles along the ESS vane have been normalised) is that the thickness of the coating plays a very important role even for high Reynolds numbers as those of the present study. In particular, it is shown that for coatings up to tens of microns and for such high Reynolds number there is no appreciable heat conducted along the length of the vane compared with the bare aluminium vane. This is due to the fact that there is no much material in the coating to transport a sensible amount of heat along the length of the vane. As soon as the coating becomes of the order of 100 µm (Fig. 4c) there is a noticeable conduction of heat along the vane length. DLC coatings have superior hardness, low friction and excellent corrosion resis-
C. Buffone / International Journal of Heat and Mass Transfer 130 (2019) 650–659
(a) Coating thickness of 1 mm.
(b) Coating thickness of 0.5 mm.
(c) Coating thickness of 0.1 mm.
(d) Coating thickness of 0.01 mm.
655
(e) Coating thickness of 0.001 mm. Fig. 4. Normalised temperature profile along the aluminium ESS vane without and with different high conductivity coatings. (a)–(e) represent different coating thickness.
tance [24]; however, the poor adhesion due to internal stresses limits the thickness to less than 3–5 µm. Recently, there have been cases in which DLC coatings as thick as 37 µm have been made [25]
reaching even 50 µm as reported by Liu et al. [24]. Composite coatings of Al/CNT with thickness of 150 µm have been bonded on Al substrates as shown in Khasenova et al. [26]. These are thickness
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C. Buffone / International Journal of Heat and Mass Transfer 130 (2019) 650–659
not far off from the thickness range of around 100 µm (Fig. 4c) at which a noticeable heat conduction along the coating takes place for the ESS vane modelled in the present paper for high Reynolds numbers. For a ESS vane subject to icing conditions this would mean that a much shorter length of the vane confined at the vane tip is interested by ice formation. These numerical results for high Reynolds numbers are basically a further confirmation of the analytical simplified model developed in Buffone et al. [1] for much lower Reynolds numbers, where it was argued that the heat conduction along the base material of the fin and the coating follows a parallel thermal resistance network and therefore the heat, in certain ratio of thickness to thermal conductivity between coating and fin, would be conducted preferably along the coating rather than along the substrate material of the fin. Fan OGV vanes are much bigger and longer than ESS. They are housed between the engine core and the nacelle and their main purpose is to remove the swirl in the airflow impressed by the front fan of the engine [27]. Again, in our simulations we consider only a tapered OGV without twist along its length. In reality, fan OGV are twisted and tapered. Fan OGVs have been also proposed recently [28] as a means of cooling aeroengine oil. However, this approach carries its own risks and complexity to do with creating networks of passages in the shrouds and inside the multitude of vanes usually employed (usually more than 20 and sometimes up to 50 for aeroengines with high bypass ratio [29]) and possible oil leaks from all the joints and connectors necessary for such design. In the present paper engine oil will only be taken at the root of the fan OVG vanes and a novel strategy will also be employed to limit drastically the heat losses from the heated vane to the cold airstream flowing around it. Typically, large vanes have internal webs for structural reasons that make them light (because the skin is thin) and at the same time strong. For this reason, we suggest to modify the web structure inside the vane and have larger contact surface area between the webs and skin of the vane around the root and tip of the vane and much less contact area in the middle of the vane where the heat losses between the vane skin and the cold airflow should be limited in order for the heat to reach the vanes’ tip. OGVs can be made of aluminium or also of composite materials to reduce engine weight and therefore we will also consider as substrate for our modelling a composite material as well as aluminium. For the OGV vane simulations we have chosen Graphene (with chosen thermal conductivity of 2000 W/(m K) [30]) as coating to show that any other high thermal conductivity material similar to DLC and CNT would deliver the same heat
Surface temperature for OGV skin
transfer enhancement sought compared to the fin substrate. The length of the simulated OGV vanes is 420 mm and the width at the base is 250 mm. Fig. 5 reports the temperature plots from COMSOL of the simulated OGV with aluminium vane core and Graphene coating. Only the temperature on the solid surfaces is shown. On the left frame the skin temperature of the OGV is reported and on the right frame the internal web temperature is reported. From the right frame of Fig. 5 the proposed shape of the web can clearly be seen, which has larger contact area with the OGV skin at the base and tip regions and much reduced contact area in the middle section where heat losses to the airstream should be limited. The adoption of the conductive webs inside the vane would allow to transport heat much further along the vanes in conjunction with the high thermal conductive coating on the outside of the vane and this strategy could also be adopted for anti-icing of propeller blades not contained within the engine nacelle. Finally, Fig. 6 shows the temperature profiles of the modelled fan OGV geometry with internal webs for different substrate and coating materials. The aluminium-Graphene and composite-
Fig. 6. Temperature profiles along the modelled fan OGV with different materials for the substrate and coating.
Surface temperature for OGV internal webs
Fig. 5. Surface temperature for fan OGV tapered vane. Temperature plot of OGV skin (felt) and internal web (right).
C. Buffone / International Journal of Heat and Mass Transfer 130 (2019) 650–659
Graphene cases have Graphene as coating with a thickness of 100 lm. Clearly, for single-material aluminium or composite vanes, there is between 30 and almost 40% of the OGV which is below the freezing point (set at 0 °C and shown in Fig. 6 with the dashed horizontal line) and the temperature variation between base and tip of the vane is very large, which might provoke extra unwanted stresses in the material. When Graphene is added as a coating, all the length of the vane is outside the freezing point and the temperature variation along the length of the vane is much more limited.
4. Experimental validation A ESS vane like the one modelled has been made and tested in similar conditions to those investigated numerically. Three thermocouples were located at the root, mid-span and tip of the ESS vane and with these thermocouples we estimated how much heat is lost along the length of the vane and by comparing the bare and coated vane we can estimate the transfer enhancement brought by the coating (in the same spirit reported in Buffone et al. [1]). An AEROLAB educational wind tunnel was employed with a top airspeed of 65 m/s, test section of 305 305 610 mm, a turbulence level of 0.2% and a top Reynolds number of around 430,000 based on the ESS vane width of 100 mm. The maximum airspeed of the tunnel is lower than the top 100 m/s of the real aeroengine applications in icing conditions, whereas the vane dimensions and orientation with respect to the airflow were the same as those of the simulations. The only difference is that the education wind tunnel runs the tests at ambient temperature and not at freezing temperature as those encountered in real icing conditions. However, this is not an important limitation because as also stated in Cortes et al. [17], this heat transfer problem is homogeneous and therefore specific temperature values do not have any substantial influence on the results. We tested a bare ESS vane and one completely coated with 10 or 100 µm thick DLC. The wind tunnel tests could not show any noticeable improvement at 10 µm thick DLC, presumably because as also the simulation clearly show with graph d of Fig. 4, there is little material in the coating to transfer any sensible amount of hear at such high Reynolds numbers. The fin loses heat to the surrounding airstream and its temperature decreases along the length. Following the pragmatic approach described in Buffone et al. [1], if we monitor the temperature of the fin at any location (base or even tip), we should be able to appreciate any improvement brought by the coating of the composite fin. In the present study, by measuring the temperature at the vane’s tip an improvement of between 4 and 5% for 100 µm thick DLC coating have been measured in the experiments. These values are quite close to the 4.5% predicted by the simulations presented in graph c of Fig. 4. However, these values are well below the enhancement of heat transfer rate of approximately 30% reported in Buffone et al. [1] estimated by monitoring the temperature of the heat pipe condenser from where the fin stack stem from; this is due most likely because at these much higher Reynolds numbers (above 430,000) the heat transfer coefficient at the air side is considerably higher than for Reynolds numbers ranging between 500 and 1500 as in Buffone et al. [1]. After all, this is the reason why fins are more effective in applications involving low convection heat transfer coefficients [31]. The experimental and numerical results of the present study and those of Buffone et al. [1] are in line with the mathematical prediction of Lalot et al. [16], albeit the latter authors were considering different ratios of thickness and thermal conductivity for substrate and coatings of the fins; additionally, the coatings that were proposed by Lalot et al. [16] albeit slightly more conductive than the substrate of the fin, they were mainly used for corrosion resistance purpose.
657
Instead, in the present work and in Buffone et al. [1], the main purpose of the coating is to enhance heat transfer. These very high thermal conductive coatings can also offer excellent corrosion and impact resistance and some of them very low friction as well. The results of the present work agree also with the mathematical prediction of Lalot et al. [1] which says that for a coating more conductive than the substrate, the thicker the coating the more efficient the heat transfer from the composite fin. For all these reasons, the basic concept of enhancing heat transfer from a fin by the use of conductive coatings demonstrated in the present work, originally presented in Buffone et al. [1] and later adapted in Knott et al. [19] for a different application, has indeed merit and should be investigated before any other approach aimed at improving the heat transfer from finned surfaces. This is especially advantageous because fins are coated anyway for protection of the substrate. 5. Analysis In this section we are going to perform a simplified analysis of the composite fins following the method developed in Lalot et al. [16] and Cortes et al. [17]. Because the applications are different, we are also going to compare the composite fins of Buffone et al. [1] with the present ones, albeit the fins of the present study are relatively thick vanes, i.e. hollow inside. The first check we need to carry out is that we can assume a one-directional approximation of the heat transfer within the fin. For this we need to evaluate the average thermal conductivity of the composite fin or ESS vane and then estimate the Biot number of the composite fin, both of which are given by [17]:
kAV ¼
ks As þ kc Ac As þ Ac
ð12Þ
hðts tc Þ kAV
ð13Þ
BiAV ¼
where the subscript s stands for fin substrate and c stands for coating. The Biot number varies from 2 105 for the bare aluminium fin to 105 for the composite fin of Buffone et al. [1]. For the present ESS vane, the same Biot number varies between 2 103 and 2 105. Therefore, we can reasonably assume that the temperature within the fin changes only along the fin length (onedirectional approximation). The second thing that we need to ascertain is the flow regime. In both cases, the heat transfer problem is a combination of natural and forced convection. In particular, the direction of the forced convection is transverse with direction of the buoyancy induced natural convection because of the spatial disposition of the fins/vane [31]. Therefore, we need to evaluate the Grashof number and then compare it with the Reynolds number. For the two cases (Buffone et al. [1] and present study), we have a maximum temperature difference between fins and surrounding air of around 45 °C and a maximum characteristic length of 0.1 m. The estimated Grashof number is:
Gr ¼
gbðT s T 1 ÞL3
v2
¼ 9 106
ð14Þ
For Buffone et al. [1] the Reynolds number ranges between almost 500 and almost 1500, therefore we have the following bounds for the ratio:
4<
Gr Re2
< 36
ð15Þ
which suggests that forced convection effects are negligible compared with those of natural convection in the case of composite fins for electronic cooling applications of Buffone et al. [1].
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C. Buffone / International Journal of Heat and Mass Transfer 130 (2019) 650–659
For the case of vanes at high Reynolds number the estimation of the same ratio gives Gr/Re2 = 5 105 which instead suggests that forced convection forces dominate on buoyancy ones. So, the flow regimes of the two examined cases are completely different. Estimating the Nusselt number is straightforward for the composite fins of Buffone et al. [1] and leads to an approximate value of around 7 which obeys to the one of fully developed laminar flow between close plates [31]. A bit more complex is the estimation of Nusselt number for the kind of flow present for the ESS vanes; in fact, there is laminar flow for a good portion of the vane’s width near the leading edge and then turbulent flow sets in on the rest of the vane‘s width. According to the suggestion in Çengel and Turner [31], we define and evaluate the average Nusselt number as follows:
Nu ¼
hL 1=3 ffi 282 ¼ ð0:037Re0:8 L 871ÞPr k
ð16Þ
This Nusselt value is around 40 times bigger than the one for composite fins of Buffone et al. [1], which adjusted for the differences in characteristic lengths and air thermal conductivity because of different free airstream temperatures, one gets that the estimated heat transfer coefficient for the ESS vanes is more than 6 times larger than that of the composite fins of Buffone et al. [1]. We will calculate now the fin effectiveness which is defined [31] as the ratio of heat transfer rate of the actual fin with the heat transfer rate if no-fin at all is present. Fin effectiveness should be sufficiently larger than 1 to justify the need for fins. It can be shown that for a sufficiently long composite fin, the fin effectiveness can be estimated as:
e¼
rffiffiffiffiffiffiffiffiffiffi kAV p hA
ð17Þ
where kAV is the equivalent thermal conductivity of the composite fin, p is the fin perimeter, h is the convective heat transfer coefficient, and A is the cross-sectional area of the composite fin. The estimated fin effectiveness is between one and two orders of magnitude higher for the fins of Buffone et al. [1] than for the present case; this is due to smaller convective heat transfer coefficient at the airside and thinner fins. To ascertain what is the effect of the coatings, we calculate the fin effectiveness ratio defined as the composite fin effectiveness divided by the bare fin effectiveness. For the fins of Buffone et al. [1] this ratio yields 3.4. Instead, for the present case of a ESS vane the estimated fin effectiveness ratio yields 1.2. For thin coatings this result could be directly obtained from the above fin effectiveness relation as a ratio of the thermal conductivities of composite to bare fin. It should be mentioned that for the fins tested in Buffone et al. [1] and the present ESS vanes, the averqffiffiffiffiffiffiffi hp age thermal length mAV L ¼ kAV L with the coating ranges A between 0.8 and 1.2, which suggests that the fin length (L) are near the optimal value. It is accepted that a good compromise between heat transfer performance and fin cost usually limits mAV L to around 1 [31]. 6. Conclusions In this paper a novel approach is proposed aimed at enhancing the heat transfer between finned surfaces and surrounding fluid. This approach consists in using high thermally conductive coatings on top of the fin substrate in order to increase the local temperature along the fin washed surface in comparison with the bare fin. This strategy is somewhat different from the usually studied cases of fins coated for corrosion or temperature protection, mainly done by low thermal conductivity coatings. The proposed approach is highly effective as it does not have any detrimental effect such as
increased pressure drop, which usually comes with other strategies aimed at enhancing heat transfer rate. The new proposed solution was first tested successfully on an aluminium finned stack for electronic cooling application [1] for low Reynolds numbers. In the present paper a similar strategy has been applied to an aeroengine vane subject to icing conditions at much higher Reynolds numbers. Numerical simulations were carried out to ascertain the range of thickness of the coatings to be used in order to maximise the wanted effect. Both short ESS and longer fan OGV vanes were modelled having different design objectives. In the case of fan OGV vanes, an additional innovative design modification was suggested to enhance further the heat transfer along the vane length by the use of the internal webs which typically are present to strengthen the long, slim and thin vanes. The experimental validation carried out in the present paper at much higher Reynolds numbers than that reported in Buffone et al. [1], demonstrate that the novel concept of heat transfer enhancement by the use of thermally conductive coatings is robust and it is worth exploring further. We have performed a fin analysis of the present ESS vane and compared it with the fins tested in Buffone et al. [1] at much lower Reynolds numbers. We concluded that the fins tested in Buffone et al. [1] have higher fin effectiveness because of much lower convective heat transfer coefficient and much thinner fins. Even the ratio of fin effectiveness between composite and bare fin shows that the improvement obtained with the coated fins tested in Buffone et al. [1] is much larger than the one obtained with the coated ESS vanes. The average thermal length of the composite fins is near the optimal suggested value of 1 for both studies. It is worth mentioning that the actual thickness of the thermally conductive coatings is a function of the Biot number, fin shape, dimensions and thermal conductivity ratios of fin substrate and coating; proper design of the bare vane and coating should be carried out for each application. Conflict of interest None declared. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.ijheatmasstransfer. 2018.10.124. References [1] C. Buffone, K. Sefiane, L. Buffone, S. Lin, Heat transfer enhancement in heat pipe applications using surface coating, J. Enhanced Heat Transf. 12 (1) (2005) 21– 35. [2] D. Reay, P. Kew, Heat Pipes: Theory, Design and Applications, fifth ed., Elsevier, Oxford, 2006. [3] J.M. Wu, H. Zhang, C.H. Yan, Y. Wang, Experimental study on the performance of a novel fin-tube air heat exchanger with punched longitudinal vortex generator, Energy Convers. Manage. 57 (2012) 42–48. [4] B. Torregrosa-Jaime, J.M. Corberan, J. Paya, J.L. Delamarche, Thermal characterization of compact heat exchangers for air heating and cooling in electric vehicles, Appl. Therm. Eng. 115 (2017) 774–781. [5] J. Hamzelou, Jumbo challenge: how elephants keep their cool, NewScientist 218 (2922) (2013) 46–47. [6] C. Lyman, R.A. Stephan, K.A. Thole, L.W. Zhang, S.B. Memory, Scaling of heat transfer coefficient along louvered fins, Exp. Therm. Fluid Sci. 26 (2002) 547– 563. [7] O. Leon, G. De Mey, E. Dick, Study of the optimal layout of cooling fins in forced convection cooling, in: Proceeding of the 8th International Workshop on Thermal Investigation of ICs and Systems, Madrid, Spain, 2002, pp. 260–265. [8] N.C. DeJong, A.M. Jacobi, Flow, heat transfer, and pressure drop in the nearwall region of louvered-fin arrays, Exp. Therm Fluid Sci. 27 (2003) 237–250. [9] F.J. Rowley, S.V. Patankar, Analysis of laminar flow and heat transfer in tubes with internal circumferential fins, Int. J. Heat Mass Transf. 27 (4) (1984) 553– 560.
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