Rotating Metal Foam Structures for Performance Enhancement of Double-pipe Heat Exchangers Ahmed Alhusseny 1, 2, *, Ali Turan 1, and Adel Nasser 1

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1 Rotating Metal Foam Structures or Perormance Enhancement o ouble-pipe Heat Echangers Ahmed Alhusseny 1,, *, Ali uran 1, and Adel Nasser 1 1 School o Mechanical, Aerospace and Civil Engineering, he University o Manchester, Manchester, UK Mechanical Engineering epartment, College o Engineering, University o Kua, Naja, Iraq ABSRAC In order to enhance the amount o heat transported in a double-pipe heat echanger, a compound enhancement is proposed incorporating both active and passive methods. he irst one is through introducing secondary lows in the vicinity o the conducting surace using metal oam guiding vanes, which are ied obliquely and rotating coaially to trap luid particles while rotation and then orce them to low over the conducting surace. he other is via covering the conducting surace between the two pipes with a metal oam layer to improve the heat conductance across it. his proposal is eamined numerically by studying the three-dimensional, steady, incompressible, and laminar convective luid low in a counter-low double-pipe heat echanger partially illed with high porosity metal oam and rotating coaially. With regards to the inluence o rotation, both the centriugal buoyancy and Coriolis orces are considered in the current study. he generalised model is used to mathematically simulate the momentum equations in the porous regions. Moreover, thermal dispersion has been taken into account while considering that luid and solid phases are in a local thermal non-equilibrium. Computations are perormed or a wide range o design parameters inluencing the perormance achieved such as the operating conditions, the coniguration o the guiding vanes utilized, and the geometrical and thermal characteristics o the metal oam utilised. he results are presented by means o the heat echanger eectiveness, pressure drop, and the overall system perormance. he current proposed design has eectively proved its potential to enhance the heat transported considerably in view o the signiicant savings in the pumping power required compared to the heat echangers ully illed with metal oams. Furthermore, the data obtained reveal an obvious impact o the design parameters inspected on both the heat echanged and the pressure loss; and hence, the overall perormance obtained. Although the heat echanger eectiveness can be improved considerably by manipulating the design actors, care must be taken to avoid unnecessary epenses resulted rom potential increases in pressure drop. KEYWORS: Heat Echanger, Compound Enhancement, Metal Foams, Rotation, Overall Perormance Nomenclature a s solid-to-luid interacial speciic surace area c p speciic heat o luid phase C c cold stream heat-capacity rate C c = ṁ c c p,c C h cold stream heat-capacity rate C h = ṁ h c p,h C min the smaller o the hot (C h) and the cold (C c) luid-phase heat-capacity rates d iber diameter d p pore diameter a arcy number, a=k / h h hydraulic diameter o the channel i1, i internal and eternal diameters o the inner annular tube o1, o internal and eternal diameters o the outer annular tube F inertial coeicient h s solid-to-luid interacial speciic heat transer coeicient H s dimensionless solid-to-luid interacial speciic heat transer coeicient k thermal conductivity K permeability o the porous medium * address: Ahmed.Alhusseny@manchester.ac.uk 1

2 ṁ luid mass low rate OSP overall system perormance, OSP= 0.5(Q c+q h)/pp p dimensional pressure p r dimensional reduced pressure PP pumping power Pr Prandtl Number, Pr=ν /α e Q c heat rate gained by the colder stream, Q c=c c ( c, c,1) Q h heat rate given by the hotter stream, Q h= C h ( h,1 h,) Q ma optimum heat transported rom hot to cold stream, Q ma=c min ( h,1 c,1) R Ω radial distance to the centreline o the double-pipe heat echanger Ra Ω rotational Rayleigh number, Ra Ω = Ω R Ω β Δ c 3 h /ν α e Re Reynolds number, Re= u in a /ν Re d Reynolds number based on the luid velocity near the iber, Re d= u d /ϕ ν Ro rotation number, Ro= Ω h / u in S hollow ratio dimensional temperature Δ c dimensional characteristic temperature dierence, Δ c= h1- c1 u, v, w dimensional velocity components U, V, W dimensionless velocity components v dimensional velocity vector dimensional position vector, y, z dimensional coordinates X, Y, Z dimensionless coordinates Greek symbols θ dimensionless temperature ρ luid density μ dynamic viscosity ϕ metal oam porosity ε heat echanger eectiveness κ solid to luid-phase thermal conductivity ratio Ω angular velocity β coeicient o thermal epansion ω pore density γ distinguishing parameter between the hollow and porous region Subscripts c, h cold, hot stream d dispersive e eective, s luid, solid phase H hollow region in inlet int interace surace between the hollow and porous region 1, inlet to/out rom the heat echange section Ω rotation Superscripts n Normal to the interace between the hollow and porous region 1. Introduction Improving the perormance o power generation plants while minimising the environmental damage caused by the ecessive use o ossil uels has become a crucial concern recently. o achieve a high thermal eiciency in power generation systems, heat recirculation is applied between the cold intake and hot ehausts to recover a part o its thermal energy instead o releasing it directly to the environment (Alhusseny and uran [1]). Heat recirculation is usually accomplished by means o two options. Either a

3 recuperative or regenerative heat echanger is used, depending respectively on whether the heat echange takes place directly via a thermally conductive surace separating the two streams or through an intermediate storage medium eposed to them alternately (Hewitt et al. []). Enhancing the heat transported in recuperative heat echangers has acquired increasing attention due to their crucial role in many practical applications ound in industry, power plants, and space eploration, as well as many others. Heat transer enhancement techniques can be classiied into active, in which an eternal power is required; passive, which does not require an eternal power input; or compound, where two or more o the aorementioned techniques may be employed simultaneously to achieve a larger enhancement than what can be produced using the individual techniques separately (Bergles [3]). One o the simplest arrangements o recuperators available in industry and practical applications is the double-pipe heat echanger. It is widely utilised in practical applications, and hence, has been the ocus o plenty o studies recently. In the light o economic considerations, many eorts have been made to construct cheaper and smaller but more eective heat echangers. Among these investigations, some have been dedicated to renew the boundary layer developing over the heat echange surace, and hence, enhance the amount o heat transported. For eample, it was ound that placing propellers inside the inner tube leads to enhance the heat echanged by up to 50% and a urther enhancement can be achieved through increasing Reynolds number and/or the number o propellers used [4]. Another passive way is to place a strip turbulator twisted in certain angles to touch the inside wall o the inner pipe [5], where heat transer rate can be improved by 100% or more through increasing the pitch length. Also, it was ound that covering the conducting surace with a porous layer ([6], [7], and [8]) or attaching porous structures to this surace ([9] and [10] can considerably improve the eectiveness achieved. Convective lows in porous materials have been widely investigated or over the last decades and various aspects were considered or dierent applications, where their state o art has been summarised etensively by Nield and Bejan [11] as well as Ingham and Pop [1]. However, most studies have been limited to media having a porosity range o and there are relatively ew studies on convective low phenomena in materials with very high porosity like open-cell metal oams. High porosity metal oams are usually porous media with low density and novel structural and thermal properties (ianjian [13]). hey oer light weight, high rigidity and strength, and high surace area, which make them able to recycle heat eiciently. Also, their open-cell structure makes them less resistant to the luids lowing through them, and hence, pressure drop across them is much less than it in the case o low via packed beds or granular porous media. hereore and due to their ability to meet the highly thermal demands with no ecessive loss in pressure, open-cell metal oams have been utilised in heat echangers [14], [15] besides internal cooling o both turbine blades [16] and the rotor windings o high-capacity electrical generators [17], [18], and [19]. hus, it is not surprising to use them recently in double-pipe heat echangers [0] and [1], where a substantial enhancement in the heat transer perormance has been acquired. With regards to combined luid low and heat transer in rotating porous media, relevant studies have been motivated by its wide range o practical and undamental applications in engineering and geophysics. Chemical processing, materials, and ood industries, in addition to rotating machinery are just a ew eamples o its engineering applications (Vadasz []). Recently, Alhusseny and uran [3] presented a numerical study or Coriolis' eect on combined heat and mass transer in a radially rotating porous channel, where rotation was ound to have a negative impact on heat and mass transport. Utilizing metal oams to improve the internal cooling o turbine blades was eamined eperimentally by zeng et al. [4] through illing a radially rotating serpentine channel with aluminum oam. It was ound that this proposal enhances the amount o heat transported between the solid and luid phases, and hence, improves the overall eiciency o cooling process. More recently, Alhusseny and uran [17] and Alhusseny et al. [18] studied numerically the developing low through a channel rotating in a parallel- 3

4 mode and ully illed with high porosity metal oam, where eects o rotation, geometrical and thermal characteristics o the iber used, channel aspect ratio, and thermal dispersion on heat transer perormance were investigated. espite the act that using porous media, which have high thermal conductivity, improves heat transer considerably, it also results in relatively high pressure losses. hereore, channels partially illed with permeable materials have been proposed as an alternative to avoid unnecessary pressure drop while keeping the heat transer at as high rates as possible. For eample, and in order to improve the overall enhancement achieved, the eect o utilising rotating cooling channels partially illed with open-cell metal oams was numerically investigated by Alhusseny et al. [19]. he current paper is dedicated to present a proposal to improve the perormance o a double-pipe heat echanger. A compound enhancement method is suggested including both passive, i.e. using metal oam structures, and active technique, by subjecting the system to a coaial rotation. he beneit gained rom using such coniguration is checked numerically taking into account the potential losses due to the increase in pressure drop.. Mathematical ormulation wo steady, incompressible, laminar, and counter-lowing streams are carried in a heat echanger rotating coaially and comprised o two annular pipes separated with a mm conducting surace, as shown in Figure 1. he total length o the heat echange section is 400mm, while the internal and eternal diameters o the inner annular tube are i1=0 and i=40mm, respectively, and their values or the outer pipe are o1=44 and o=64mm, respectively. Figure 1- Geometrical shape o the studied problem he porous material is considered isotropic, homogeneous, and rigid metal oam o high porosity ϕ he generalised model is employed to simulate the momentum equations considering both the solid and luid phases to be in local thermal non-equilibrium with each other. In regards to the inluence o rotation, both the centriugal buoyancy and Coriolis orces are taken into account. hus, the dimensional orms o conservation equations o mass, momentum, and energy or both luid and solid-phase as well as the conducting surace are: 4

5 v 0 (1) F ( v ) v p v v v v v r e K K e ( e () ) 0 c ( v ) (1 ) k ( k k ) a h ( ) (3) p e d 0 k a h ( ) (4) se s s s s 0 k w w (5) In Eqs.[(), (3)], γ is a distinguishing parameter equals to either zero or one depending on whether the low takes place in the clear or porous regions, respectively; while the medium porosity ϕ equals to one just in the clear regions. Also, K and F represent the permeability and inertial coeicient o the metal oam, respectively, where their values are computed according to the model proposed by Calmidi [5] as: d K d p (1 ) (6) d p 1.63 d 0.13 F (1 ) (7) d p In addition, ke and kse are the eective thermal conductivity o luid and solid phase, respectively. heir values are computed using the model developed by Boomsma and Poulikakos [6] and then corrected by them [7]. he dispersion conductivity kd, which is assumed to be isotropic, is determined based on the model presented by Hunt and ien [8]: k d C c u K (8) d p Where Cd is the coeicient o thermal dispersion and its value was ound to be 0.06 as proposed by Calmidi and Mahajan [9]. Finally, as and hs are the solid-luid interacial speciic surace area and heat transer coeicient and can be determined using the model suggested by Calmidi and Mahajan [9]. However, the hs value is estimated using the model proposed by Lu et al. [30] due to its generality in not only relying on the oam porosity and iber diameter, but being also a unction to the pore low regime as: Re d Pr, (1 Re d 40) hs d (1 ) 0.04 Nu s 0.5 Re d Pr, (40 Re d 10 ), where; d 1 e d (9) k Re d Pr, (10 Re d 10 ) Although the governing equations o luid low and heat transport either within the metal oams or in the clear zones are not coupled with each other, they are linked together through interace suraces separating them. So, Eqs.[ (1) (4)] need to be closed by means o interacial coupling conditions, where continuity o velocity, shear stress, luid temperature, and heat lu along the luid solid interaces shown in Figure must be ensured to get meaningul physics (Xu et al. [31]). o this end, boundary conditions proposed by Ochoa-apia and Whitaker [3] or the luid-solid interace are used with taking the thermal dispersion into account as detailed in Eqs.(11.a e) mentioned previously by Alhusseny et al. [19]. s s s 5

6 6 Figure - Interaces between the clear and the porous regions he boundary conditions employed to solve the aorementioned governing equations are: 0 0, : ) ( 0, : ; 0 0, : ; 0 0,, : 0 : 0 : ; 0 : 0 : 0,, : 0; 1 1,, ,, 1 n s n o n w w n d e n s se o i n s n i in h s in h o o w o i s i i s o o w o i in c s in c i i w v u k k k k w v u w v u L at w v u u w v u L at w v u w v u u at (10) 3. Solution procedure he governing equations are discretised using the inite volume method. he second-order dierencing scheme is employed to represent the convection terms in the discretised governing equations, while the problem o pressure velocity coupling is resolved using SIMPLE algorithm. A structured grid ormed o heahedral elements was built using Pointwise sotware, where the stationary clear regions are linked to the rotating clear/porous regions through our interace suraces as shown in Figure 3. Steep gradients epected at the boundaries including the walls and the interaces are

7 captured by reining the mesh at these regions. Grid dependency was checked by eamining our sets o grid including the stationary and rotating regions (914,60, 1,,40, 1,541,380, and 1,838,00) at Reinner=Reouter=000, Ω=500rpm, ks=kw, ϕ=0.9, and ω=10ppi. It is noticed that the deviation in the data obtained becomes marginal between the third and ourth grid set and thereater. hus, the mesh size o (1,541,380) can be considered suicient or the accuracy o the current study. Figure 3- he used grid with the interaces linking the stationary clear to the rotating porous regions he SAR CCM+ commercial CF code is utilised to simulate the current problem. However, this sotware does not support using "the local thermal non-equilibrium model" to track the solid-to-luid interstitial heat transport within the porous regions. o overcome this drawback, the porous region was duplicated into two identical zones representing the solid and luid phase individually and then heat can be allowed to transer between the two phases and tracked by creating a heat echanger interace there. Under-relaation technique is used in order to avoid divergence during the iterative process, where under-relaation actors o about ( ) are used or the dependent variables. Convergence is measured in terms o the maimum change in the dierence between the heat transported rom the outer stream to the conducting surace and that transerred rom the conducting surace to the inner stream during any iteration as: Qin, Gained Qout, Lost Err. (11) Q Abs ( Q ) in, Gained out, Lost Where the maimum change allowed or convergence check is ue to the lack o eperiments conducted on heat and luid low in double-pipe heat echangers illed with metal oam, the currently computed data were validated with the numerical data presented by Xu et al. [0] or a stationary heat echanger. he proiles o dimensionless aial velocity at the eit section o each pipe were compared with the corresponding data rom the above mentioned study as shown in Figure 4. Regarding the heat transer problem, the aial development o the cross-sectional mean temperature or the inner luid, conducting wall, and the outer luid was also compared with the corresponding data presented by Xu et al. [0] as shown in Figure 5. Overall, the currently computed results are clearly in ecellent agreement with numerical data presented in the above mentioned study. 7

8 (a) ω=5ppi (b) ω=30ppi Figure 4- Comparing the dimensionless velocity proile at the eit sections o a double pipe heat echanger ully illed with metal oam at Reinner=Reouter=1000, and ϕ=0.9 Figure 5- Aial development o the cross-sectional mean temperature or the inner pipe, conducting wall, and the outer pipe o a double pipe heat echanger ully illed with metal oam at Reinner=Reouter=1000, ϕ=0.9, and ω=10ppi 4. Results he obtained results are presented or a wide range o parameters including the clearance-to-vane size ratio S, oam porosity ϕ, oam thermal conductivity ks, Reynolds number ratio Re *, rotational speed Ω, and characteristic temperature dierence Δc, while the values o pore density, inner inlet temperature, and outer Reynolds number are kept constant at ω=10ppi, inner=30 C, and Reouter=000, respectively. he eiciency o heat echange process is mainly measured in terms o two key design parameters. he irst is the eectiveness o the counter-low heat echanger, which can be computed as: Q Q c Q h ma Q ma (1) Where; 8

9 Q c C ), Q C ( ), Q C ( ) (13) c ( c, c,1 h h h,1 c,1 ma min h,1 c, 1 he other key parameter in assessing the overall perormance is the total pressure loss ΔPt occurring across the heat echanger, which indicates the pumping power required as: PP PP PP t c h V P V c c h P h m c m Pc h P Overall, eamining the practical worth o using a speciic design or low characteristics is essential in designing heat echangers. his can be achieved through introducing a dimensionless perormance measure called the overall system perormance OSP, which is deined as the ratio o the heat echanged to the pumping power required as: Q OSP PP Echanged t his actor can be even used or designing other types o heat echangers, where as long as the OSP value or the ratio o the gain to the cost is higher, the overall perormance is better. h (14) (15) 4.1. Inluence o rotation on luid low and heat transer development Rotation eects on the development o low ield and heat transer are illustrated in Figure 6 or various aial locations at S=, ϕ=0.9, ω=10ppi, ks=kw, Re * =1, Δc =30 C, and Ω=500rpm. When the two counter-lowing streams enter to the rotating heat echange part, the inluence o body orces induced by rotation starts to appear, i.e. Coriolis and centriugal orces, resulting in orming transverse vortices and reorganising the low patterns in a quite dierent way rom the classical low behaviour. As a result o Coriolis orces, a main counter-to-rotation vorte is created at the entrance o each o the inner and outer pipe, i.e. =0.01L and 0.99L, respectively. hereater, this vorte induces urther smaller ones trapped in the clear regions due to the rotating porous vanes, which act as a semi-buer that orces the luid particles to swirl and then low back over the conducting surace through the porous layer covering it. Consequently, the boundary layer in the vicinity o the conducting surace becomes thinner, which leads to reactivating the heat echange surace continually. As the luid lows downstream, however, the secondary lows are alleviated gradually along the main low path until they almost vanish close to the eit o each pipe. his is attributed to the viscous dissipation and the negligibly small vorticity generation close to the ully-developed region, as inerred by Soong and Yan [33]. o justiy this phenomenon, it is better to look closely at the dimensionless orm o the aial vorticity transport equation presented earlier by Soong and Yan [33] but modiied to take into account the oam presence as: 1 U U V W X Y Z X U W U V 1 Y X Z X Re X Y Z a Ro U Ra Y Z X PrRe Z Y Where Ψ is the aial vorticity and is deined as: 9 F V a W V (17) Y Z 1 Re (16)

10 On the right side o Eq.(16), the second term reers to the vorticity dissipation due to porous resistance, while the last two ones stand or the vorticity generation terms by Coriolis inluence and centriugal buoyancy, respectively. As the aial velocity gradient is steep at the entrance regions, which in turn contributes eectively in the vorticity generation due to Coriolis eects; the secondary lows are very strong there. More downstream, however, velocity gradients start to decrease as an outcome o low development, and hence, the decreasing Coriolis generation term cannot make up the dissipation occurred in vorticity due to the oam and viscous resistance. hus, secondary vortices are alleviated gradually until they almost ade away at the ully developed region, where the aial gradients o velocity components become zero. =0.01L =0.1L =0.5L Figure 6- evelopment o transverse velocity vectors in rotating rame (let) and dimensionless temperature contours o luid (middle) and solid-phase (right) at S=, Re * =1, and Ω=500rpm 10

11 =0.5L =0.75L =0.9L =0.99L Figure 6- Continued 4.. Combined eects o operating conditions Inluence o rotation strength o eplain the eects o rotation level on the low and heat transer patterns, the development o transverse velocity vectors are plotted in rotating rame along with the luid temperature contours at S=, ϕ=0.9, ks=kw, Re * =1 or various rotation levels, as illustrated in Figure 7. In general, the stronger 11

12 the rotational speed is applied, the better the heat echange is achieved. Moreover, it is observed that secondary lows in the inner part are enhanced with increasing the rotation rate and sustained or a urther downstream as a result o the increase in vorticity generation by Coriolis inluence. he secondary vortices in the outer pipe, in contrast, look slightly weaker when rotation is enhanced. his is justiied by looking closely at Eq.(16), where the higher temperature dierences ound in the case o lower rotational speeds result in a stronger vorticity generation due to centriugal buoyancy and vice versa, which makes up or neutralises the dissipation along the low path in the outer pipe. Generally, the enhancement in heat transer improves the eectiveness attained as shown in Figure 8. As in most heat echangers, however, such improvement has a price, which is the increase in the pressure drop, and hence, the pumping power required. his is attributed to the augmentation in low resistance due to the enhancement in the swirls generated across the clear and porous regions. In regard to the overall system perormance achieved, it is slightly improved at the lower rotation levels, but then starts to deteriorate. his outcome is due to the act that pressure drop increases marginally at the lower rotational speeds, while thereater its growth becomes considerable causing to augment the pumping power signiicantly. Overall, the negligibly small pumping power required compared to the amount o heat echanged makes the overall perormance o such heat echangers incomparable, i.e. OSP=O(10 ). =0.01L =0.1L =0.5L Figure 7- Velocity vectors in rotating rame and dimensionless luid-phase temperature at S= and Re * =1 or rotational speed: 15rpm (let), 50rpm (middle), and 500rpm (right) 1

13 =0.5L =0.75L =0.9L =0.99L Figure 7- Continued 13

14 Figure 8- Inluence o rotation rate on the eectiveness, total pressure drop, and overall system perormance at Ω0 =50rpm, ε0 =0.615, ΔPt0=38.4Pa, and OSP0= Inluence o luid low strength As eplained earlier, the Reynolds number value is kept constant at the inlet to the outer part. So, the eect o changing the inner low rate, or in other words the value o Re *, is what being discussed herein. hree values o outer-to-inner Reynolds number ratio, i.e. Re * =1,, and 4, are compared by plotting the aial development o transverse velocity vectors and luid temperature contours as shown in Figure 9. In general, the low stream with the smaller heat capacity rate Cmin eperiences a higher temperature change, and consequently, it will be the irst to reach the maimum temperature bounds allowed, at which heat echange comes to a halt (Kays and London [34]). hus, the higher the Re * value, which means the lower Cc /Ch ratio, the higher the eit luid temperature rom the inner pipe. In contrast, increasing the Re * value results in augmenting luid temperature at the eit o the outer pipe. Moreover, as the inner low velocity decreases with increasing the Re * value, the strength and sustainability o inner vortices is reduced as a result o the reduction in Coriolis inluence. By contrast, the secondary lows become stronger and more sustainable in the outer pipe while increasing the Re * value. he reason or this is that vorticity generation by centriugal buoyancy becomes more inluential due to the relatively high temperature gradients ound there. Overall, as the inner heat capacity rates decreases, not only the heat transer eectiveness is signiicantly improved as illustrated in Figure 10, but a considerable saving in pressure drop is attained as well, as shown in Figure 11. However, these two gains are not relected positively on the overall perormance obtained. Instead, it is observed that the overall perormance deteriorates due to the reduction in the amount o heat absorbed by the inner stream. 14

15 =0.01L =0.1L =0.5L =0.5L Figure 9- Velocity vectors in rotating rame and dimensionless luid-phase temperature at S= and Ω=500rpm or Renolds number ratio: Re * =1 (let), (middle), and 4 (right) 15

16 =0.75L =0.9L =0.99L Figure 9- Continued Figure 10- Inluence o outer-to-inner Reynolds number ratio on the eectiveness 16

17 Figure 11- Impact o Re * on the total pressure drop and overall perormance achieved Inluence o characteristic temperature dierence At moderate characteristic temperature dierences, i.e. Δc 30 C, luid and solid thermophysical properties are assumed to be constant everywhere ecept the luid density in the centriugal buoyancy term, which varies according to the Boussinesq approimation. However, as the temperature dierence between the heat echanger terminals increases, it implies signiicant changes in the thermophysical properties. hus, both air viscosity and thermal conductivity are considered variable with the luid-phase temperature depending on Sutherland s law, while the density variation is estimated as a unction to the temperature only using the Equation o State in order to maintain the incompressible low conditions. he inluence o temperature dierence (Δc=h1-c1) on the eectiveness and pressure drop as well as the overall system perormance, or S=, Ω=500rpm, and c1 =0 C, is shown in Figure 1.a,b. In general, the eectiveness is slightly improved with increasing the temperature dierence. However; as both the low velocity and dynamic viscosity increase, which results in augmenting the oams resistance to the luid lowing across it, the pressure loss is augmented considerably. Overall, this etra cost resulting rom the increase in the pumping power required looks quite marginal compared to the considerable enhancement in the amount o heat gained by the inner stream, see Figure 1.b. It is apparent that while increasing the temperature dierence rom 30 to 300 C, the overall perormance achieved can be improved up to % depending on the Re * value. his outcome indicates the promising prospects o utilising the proposed coniguration as a recuperator in gas turbines systems. a) Figure 1- Inluence o Δ c on a) the eectiveness and pressure drop, b) the overall system perormance 17

18 b) Figure 1- Continued 4.3. Inluence o hollow ratio on the luid low and heat transport o demonstrate the inluence o the hollow ratio, or in other words, the clearances-to-vanes size ratio, the development o transverse velocity vectors are plotted in rotating rame along with the luid temperature contours as illustrated in Figure 13. In general, a less heat echange is attained when the size o clearances becomes larger. his is attributed to the reduction occurs in the mass low across the oam region; and hence, decreasing the amount o heat transported due to the low luid heat conductance compared to metal oams as shown in Figure 14. On the other hand, it leads to a signiicant saving in the pressure drop due to the reduction in the volume o the solid matri, which acts as an obstructing or damper to the luid lowing across it as illustrated in Figure 15. However, increasing the rotational speed Ω does not result in the same etent o augmentation in both heat transer and pressure drop. epending upon the hollow ratio S, it is apparent that rotation becomes less inluential at the lower hollow ratios. his is attributed to the act that the oam impact dominates the rotational eects in both transerring heat and resisting the luid low within the pipes more occupied with metal oams. In regard to the overall perormance attained, Figure 15 indicates that reducing the size o clearances improves the overall perormance considerably as a result o the signiicant reduction occurred in the pressure drop, where it is obvious that the perormance achieved in the heat echangers semi/ully illed with metal oam, i.e. S 1, is negligibly small compared to those having larger clearances, i.e. S. 18

19 =0.01L =0.1L =0.5L =0.5L Figure 13- Velocity vectors in rotating rame and dimensionless luid-phase temperature at Re * = and Ω=500rpm or hollow ratio: S=1 (let), (middle), and 4 (right) 19

20 =0.75L =0.9L =0.99L Figure 13- Continued Figure 14- Hollow size inluence on the eectiveness achieved 0

21 (a) (b) Figure 15- Eects o hollow size on both total pressure drop and the overall perormance or: a) Re * =1, and b) Re * = Combined inluence o oam porosity and thermal conductivity Combined eects o oam porosity and thermal conductivity accompanying with rotation on heat transer and the overall perormance achieved are illustrated in Figure 16.a-c. In general, i the oam porosity is ied, the amount o heat echanged is enhanced when the conductivity ratio increases. his is owing to the increase in the oam eective conductivity, which in turn results in augmenting the overall capability o the luid-solid medium to circulate more heat between the two streams. As the eective oam thermal conductivity is improved with decreasing the oam porosity, it seems reasonable at irst glance that heat transer eectiveness will be enhanced as well. Apparently, this is 1

22 true i oams with a relatively low thermal conductivity are used, e.g. stainless steel, where more heat can be echanged, and hence, a better overall system perormance is achieved. For this limited case, it is observed that porosity change becomes more inluential when thinner vanes are utilised. However, this is not the act or the case o low porosity oam ormed rom materials having a relatively high conductivity, i.e. aluminium. Surprisingly, it is noticed that using such sort o oams with a relatively low porosity, ϕ = 0.89, causes deterioration in the eectiveness obtained compared to the corresponding oams having a higher porosity, ϕ = his unepected outcome is attributed to the oam aial thermal conduction, which in particular becomes much stronger in the case o ully/semi illed pipes and/or the low values o inner low rate, leading to a short-circuiting across the heat echanger. So, more heat is conducted away via the outer-pipe outlet rather than being transported to the inner-pipe across the conducting surace separating them. o overcome this drawback, the proposal presented by Wu et al. [35] can be utilised. So, the oams structures can be split into multi-blocks placed alternately along the heat echanger and separated by gaps to reduce the longitudinal thermal conduction between the aially neighbouring oam elements. In general, inluence o the porosity and oam thermal conductivity on both the heat transer and overall system perormance is alleviated with decreasing either the clearances volume or the inner low rate. (a) Figure 16- Eects o oam porosity and thermal conductivity on heat transer eectiveness and overall system perormance or various hollow ratios at a) Re * =1, b) Re * =, c) Re * =4

23 (b) (c) Figure 16- Continued 5. Conclusions In the current study, a compound enhancement or the heat transported in a double-pipe heat echanger is proposed through utilising both active and passive methods. he modiication introduces secondary vortices in the vicinity o the conducting surace using metal oam guiding vanes. he role o these obliquely ied vanes is to trap luid particles while rotation and then orce them to low over the conducting surace. he other enhancement is via covering the conducting surace between the two pipes with a metal oam layer to improve the heat conductance across it. his proposal is eamined numerically by studying the three-dimensional, steady, incompressible, and laminar convective luid low in a counter-low double-pipe heat echanger partially illed with high porosity metal oam and rotating coaially. Computations are perormed or a wide range o design parameters inluencing the perormance achieved such as the operating conditions, the coniguration o the guiding vanes utilized, and the geometrical and thermal characteristics o the metal oam utilised. 3

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