Three-Dimensional Thermocline Dynamics In Thermal Storage Tanks

S. S. Ratnu and K. V. Manu / JAFM, Vol. 14, No. 5, pp. 1483-1495, 2021. 0.079 0 t 0.25 sVd t 0.25 s 02.2 Initial and boundary conditionsThe velocity boundary condition is applied at theinlet and the outlet of the TES as in the twodimensional simulations of (Tinaikar et al. 2016).Adiabatic thermal condition is applied for the storagetank walls by setting a zero heat flux at the wallsurface. At side walls, top plane and bottom plane(except inlet and outlet of domains) no-slip andadiabatic conditions are assigned. 610 KTd 651K0s t 0.25 st 0.25 s(9)(10)The disturbance velocity and temperature at inlet areas follow; for medium disturbance: 0.079 0s t 0.50 sVd t 0.50 s 0 610 KTd 6510s t 0.50 st 0.50 s(11)(12)The disturbance velocity and temperature at inlet areas follows; for strong disturbance: 0.079 0 s t 0.75 sVd t 0.75 s 0 610 KTd 6510s t 0.75 st 0.75 s(13)(14)The following definitions are used to define Atwoodnumber ( A ), Reynolds number(Re) and circulationbased Reynolds number.A Fig. 3. Non-dimensional temperature profileprofile (sigmoid function). c h c h(15) dVd d(16) 2 (17)Re Temperature profile is initialized by the followingsigmoid profile as shown in Fig. 3. This distributionof temperature at the end of the charging process canbe represented by the sigmoid profile as shown invarious studies (Zachar et al. 2003; Flueckiger et al.2013).T Tc Th Tc1 e m( y n)Rev Here, is the circulation strength.Here, in Eq. 16 the diameter of the pipe is selectedas one of the length scales to define Reynoldsnumber asduring in many vortex-ring-inducedstratified mixing studies Shy (1995), Olsthoorn andDalziel (2017). However, in the present case, theinlet flow is discontinuous as evident in Eq. 9. Hencea better way to calculate the ratio of inertia andviscous force is to use circulation-based Reynoldsnumber which is used in vorticity dominated flows.This alternate definition allows us to include theeffect of flow duration as shown in many otherexperimental and numerical works Dahm et al.(1989), Orlandi et al. (1998). The followingdefinitions are used to define Richardson number,Richardson number based of circulation and Froudenumber.(8)Here, m represents the shape parameter whichdetermines the thermocline thickness and ndesignates the axial location of the thermocline. Thethickness of thermocline calculated using thefollowing expression Th TcHere, Th is the lowest y value at which thetemperature reached 0.99 Th and Th is the largestvalue at which the temperature attains a value of 1.01Tc . Here, the values of Th and Tc are 651K and563K. Disturbances were introduced by adding thecolder fluid at inlet through a port with a 7.5 mm( d ) with Velocity Vd and temperature Td into thestable thermocline which is maintained at the centerof the tank. The temperature ( Td 610 ) hastemperature higher than cold fluid temperature andlower than hot fluid temperature( Tc Td Th ).Ri g ( c h )d hVd2Riv AR(18)(19)where, R a3 g / 2Fr The disturbance velocity and temperature at inlet areas follows; for weak disturbance:1486VdNd(20)

S. S. Ratnu and K. V. Manu / JAFM, Vol. 14, No. 5, pp. 1483-1495, 2021.Table 1 Simulation details.Caseτd(s)ReRiδ/hARRiv 20.068915.4510.581where, N and 0 g ( y ) 0 y3. RESULTSThe two-dimensional view of the instantaneous non T Tc dimensional temperature plots T * atTh Tc variousnon-dimensionalized timeinstance* tVd(t ) of weak disturbance cases (SC1, MC1hand LC1) are shown in Figs. 5 (a), (b) and (c). Theevolution of the flow disturbance inside the TEShappens in three distinct phases: the initial roll-up,vortex-thermocline interaction and recovery phase.During the initial phase, the added disturbance fluid h c2Here, a is the distance between two vortex centre.The non-dimensional numbers along with otherparameters are tabulated in table 1.2.3. Mesh Independent AnalysisA mesh independent analysis is conducted todetermine the optimum grid to capture the flowphysics. Initially, three types of meshes of sizes254 600 254 (Fine mesh), 127 300 127(medium mesh) and 64 150 64 (coarse mesh)were considered for the simulations. Figure 4 showsthe effect of grid resolution on temperature atrolls- up near the inlet port region ( t * 0.47 ). Theinterface is unaffected by the added perturbationduring the initial phase. Subsequently, in the secondphase ( 0.47 t * 1.89 ) the rolled up flow structurepenetrates the lighter hot-fluid and impinges on thethermocline region.t * 0.47 . The difference between fine grid andmedium grid is negligible. Here, the maximumdifference in velocity and temperature are 1.2\% and3.00\% respectively. Hence to reduce computationalcost and time, grid 127 300 127 (medium mesh)is considered for further simulations.Depending upon the interface thickness and strengthof the disturbance, a wide gamut of flow patterns areformed near the thermocline region. This interactionmechanisms are analogous to the vortex ring- densityinteraction interaction experiments of (Linden1973;Dahm et al. 1989; Orlandi et al. 1998; Advaithet al. 2017) and various two dimensional simulations(Manu et al. 2015; Manu et al. 2016;Tinaikar et al.2016).Unfortunately, to our knowledge noexperimental data is available for direct comparisonwith Molten salt based TES.In Fig. 6 the numerical simulations results arecompared with the visualization experiments of(Dahm et al. 1989). As shown in the Fig.6 for similarAR value ( AR 0.1 ) the flow features are similarwith the the experimental observations of (Dahm etal. 1989). This interaction causes oscillation ofthermocline region. Finally, during the recoveryphase ( t * 1.89 ), thermocline oscillations areobserved and a new thermocline with increasedthickness is established.Fig. 4. Mesh independent analysis.1487

S. S. Ratnu and K. V. Manu / JAFM, Vol. 14, No. 5, pp. 1483-1495, 2021.Fig. 5. Temperature contour at different flow instances; case SC1.ring detachment phenomena was not observed asdepicted in Fig.7 (c). In this case, the disturbancefluid propagates as a jet-like structure rather than avortex ring as observed in the other two cases.A close up view of the vortex ring structure formednear the inlet port is shown in Fig. 8. The vortex ringdisplays as a vortex pair in the side view as observedin the two-dimensional simulations. The downwardpropagating vortex ring interacts with thermoclinewhich is kept at the center of the TES.Fig. 6. Qualitative comparison with theexperiments of Dahm et al.3.2 Second phase: Impingement of coherentstructures3. 1 First Phase: Vortex formationIn order to effectively understand the vortex ringthermocline interaction mechanism, the collision ofthe coherent structures with three differentstratification levels (different thermocline thickness)are systematically analysed.The initial development of three-dimensional vortexstructures for three opening duration at various nondimensionalized time instance ( t * tVd / h ) isdepicted in fig.7. Soon after the injection, therelatively cold fluid rolls-up and coherent vorticalstructures are formed near the inlet section. Theevolution of three types of disturbances are analysed v uby plotting the contour of z vortcity ( z ) x yas shown in Fig.7.3. 2. 1 Evolution of weak disturbanceThe interface dynamics of weak disturbance withsharp, moderate and large interface are depicted inFig.9. The injected vortex ring propagates towardsthe thermocline and touches the upper layer ofthermocline at t * 1.42 . In case of sharp interface(SC1) the vortex ring barely penetrates the upperlayer of the thermocline (Fig. 9 (a)). In this case thevortex ring thermocline interaction is analogous tovortex ring-wall interactions. With increase in flowtime, the vortex ring spreads in the radial directionsas shown in Fig. 9 (b).In case of relatively short opening duration, (weak disturbance) two isolated vortex rings are formed asshown in Fig. 7 (a). For medium disturbances, a shorttail is formed behind the downward propagatingprimary vortex ring Fig. 7 (b). In case of largeopening duration, (strong disturbance) the vortex1488

S. S. Ratnu and K. V. Manu / JAFM, Vol. 14, No. 5, pp. 1483-1495, 2021.Fig. 7. Vorticity iso-surfaces at selected time instant ( z 1.5s -1 ).Fig. 8. Vortex ring (a) Isometric view, (b) Front View, (c) side view d) top view.In the case of moderate interface, (MC1) the vortexring partially penetrate the interface as shown inFigs. 9 (c) and (d).Here, a part of the vortex ring penetrates through thethermocline while the remainder recoils upwardforming a plume structure (Figs. 9(e) and (f)) as inthe experimental study of Advaith et al. (2017).Subsequently, the vortex ring shrinks in size andfinally diffuses in the interface region. At later flowtime, after a few rebounds, a new thermocline isestablished with increased thickness.In the case of large interface, (LC1) the vortex ringpenetrates into thermocline cause oscillations inaxial and radial directions. Baroclinic production ofopposite signed vortices are observed in this case.1489

S. S. Ratnu and K. V. Manu / JAFM, Vol. 14, No. 5, pp. 1483-1495, 2021.Fig. 9. Iso-surfaces of vorticity at two time instance: (a), (b) sharp interface; (c), (d) moderate interface;(e) and (f) large interface.Fig. 10. Temperature and Velocity profile at center line at selected time instant a)T (y) for sharpinterface b)v (y) for sharp interface c)T (y) for medium interface d)v (y) for medium interface e)T (y)for strong interface f)v (y) for strong interface.Figure 10 shows the variation of temperature andvelocity in axial direction at four time instants (at thecenter of the tank). The propagation of weakdisturbance in the axial direction are evident in thetemperature and velocity plots (Figs. 10 (a) and (b)respectively).the disturbance propagates downstream which altersthe temperature and velocity profiles. Here, in thecase of sharp interface, the disturbance is not strongto penetrate the top part of the interface. This isevident in the velocity profile graphs Fig. 10 (b). Theaxial profiles of temperature and velocity formoderate interface thickness case (MC1) are shownin Fig. 10 (c) and (d) respectively. Due to the additionof flow perturbations, the temperature profiles areinitially distorted near the inlet and this distortionmigrates downwards with increase in flow time.Distortions inside the thermocline region are evidentThe upper part of of the sigmoid profile is distortedby the flow disturbance. During initial stages(t * 0.23) the bulk of the inserted cold fluid(formed coherent structure) is at the top part of TES(0.8 h* 1) which causes inflections intemperature and velocity profiles. At later flow timein this case ( t * 1.9 ).1490

S. S. Ratnu and K. V. Manu / JAFM, Vol. 14, No. 5, pp. 1483-1495, 2021.Fig. 11. Iso-surfaces of vorticity (ωz 1.5s 1) at two time instance (a) sharp interface, (b) Mediuminterface, (c) Large interface.The velocity profiles (Fig.10 (d)) are qualitativelysimilar to SC1 case. In the case of large interface(LC1), some difference in the interaction mechanismare evident in the temperature and axial velocityprofiles (Figs.10 (e) and (f)). Inflections inside thethermocline regions are observed in the case of largeinterface thickness (Fig. 10(e)). Positive values ofaxial velocity are observed in this case. This isrelated to the upward propagation of baroclinicallygenerated plume- like structures.profiles are quantitatively similar to weakdisturbance cases as shown in Fig. 12 (d)). In the caseof large interface thickness, the sigmoid profile issignificantly disturbed by the impingement ofvertical structure as shown in Fig. 12 (e)). Here, thecomplex interactions inside the thermocline createsmultiple inflectional points in the velocity profiles(Fig. 12 (f)).3. 2. 2 Evolution of medium disturbanceHere, the outer surface removal of the jet-likestructure is reminiscent to the banana peeling processas observed in experimental study of Shy (1995).Typical interface dynamics of medium disturbancewith sharp, moderate and large interface are shownin Fig. 11. In the case of medium disturbances (SC2,MC2 and LC2) the interface dynamics isAnother important aspect of strong disturbance is theoscillations observed during the recovery phase (postimpingement period) which will be discussed in thesection 3.4.complicated by the tail of the coherent structures. ForSc2 (sharp interface case), the vortex ring hardlypenetrates and the interface remains flat after theimpingement as shown in Fig. 11 (a). At later flowtime, the disturbance propagates in the radialdirection (Fig. 11 (b)). In the case of moderateinterface thickness (MC2), multiple small scalestructures are observed to orbit around the primaryvortex ring near the interface as region as shown inFigs. 11 (c) and (d). Here, the spreading of thevorticity in the radial direction is less compared withSC2. In the case of large interface (LC2), the vortexring -thermocline interaction creates a crater insidethe thermocline region as shown in Fig. 11 (e) . Thecold fluid stored in bottom half splashes upwardsbecause of this interaction. Complex small scalestructures are formed in the interface region due tothe baroclinc generation of vorticity (Fig. 11 (f)).Vorticity contour of strong disturbance with differentinterfaces are shown in Fig. 13. The temperatureprofiles shows negligible penetration for SC3 case(Fig. 14 (a)). For SC3 case increase in magnitude ofvelocity component is associated increase in theduration of flow disturbance (Fig. 14 (b)). Upwardpropagation of vortical structures are observed in theinterface region for all the cases as evidenced in Figs.14 (b) (d) and (f). In the case of moderate and largeinterface thickness (MC3 and LC3) a significantalteration in the sigmoid profiles are observed duringthe interaction period (Figs. 14 (c) and (e)).3. 3 Third phase: Thermocline oscillations andSpectraDuring the post-impingement period (recoveryphase), continuous damping oscillations ofthermocline are observed in the simulation.Thermocline oscillations are observed for all thesimulation cases. However, the amplitude ofoscillations is highest for strong disturbances cases.In the case of moderate interface thickness, thepartial penetration of disturbance is evident in thetemperature profiles (Fig. 12 (c)). The velocity1491

S. S. Ratnu and K. V. Manu / JAFM, Vol. 14, No. 5, pp. 1483-1495, 2021.Fig. 12. Temperature and Velocity profile at center line at selected time instant (a) T (y) for sharpinterface, (b)v (y) for sharp interface, (c) T (y) for medium interface, (d) v (y) for medium interface,(e) T (y) for strong.Fig. 13. Iso-surfaces of vorticity(ωz 1.5s 1) at two time instance a) sharp interface b)Mediuminterface c)Large interface.In order to quantify the nature of oscillationstemporal variation of axial and radial velocity and thecorresponding spectra at the center of thethermocline are plotted in Figs. 15 and 16. Here, theamplitude of oscillations decreases with increase inthermocline thickness as shown in Fig. 15. Theobtained peak frequency from the FFT analysisscales with the buoyancy frequency (Brunt-Vä isä läfrequency). Brunt-Vä isä lä frequency is tabulated intable 2.In order to understand the flow dynamics during thethermocline oscillations phase, the vorticity plotduring one cycle is plotted in Fig. 17. Here, thethermocline oscillations near the thermocline regionis connected with the generation of baroclinicvorticity. Figure 17 indicates that the oscillations atthe inferface are through the successive generation ofcountersign vorticity which retards/suppresses thepropagation of the disturbance.1492

S. S. Ratnu and K. V. Manu / JAFM, Vol. 14, No. 5, pp. 1483-1495, 2021.Fig. 14. Temperature and Velocity profile at center line at selected time instant (a) T (y) for sharpinterface, (b) v (y) for sharp interface, (c)T (y) for medium interface, (d)v (y) for medium interface, (e)T (y) for strong interface, (f) v (y) for strong interface.Fig. 15. Temporal variation of axial velocity and spectra.Fig. 16. Temporal variation of radial velocity and spectra.1493

S. S. Ratnu and K. V. Manu / JAFM, Vol. 14, No. 5, pp. 1483-1495, 2021.REFERENCESAdvaith, S., K. Manu, A. Tinaikar, U. K. Chetia andS. Basu (2017). Interaction of vortex ring witha stratified finite thickness interface. Physics ofFluids 29(9), 093602.Advaith, S., D. R. Parida, K. Aswathi, N. Dani, U. K.Chetia, K. Chattopadhyay and S. Basu (2021).Experimental investigation on single-mediumstratified thermal energy storage system.Renewable Energy 164, 146–155.Fig. 17. Vorticity production at the interface.Table 2 Parameters of under- dampedoscillations induced by flow disturbance at r* 0,h* 0.5CaseBrunt-V𝑎̈ is𝑎̈ l𝑎̈ frequencyPeak hm, W., C. Scheil and G. Tryggvason (1989).Dynamics of vortex interaction with a densityinterface. Journal of Fluid Mechanics 205, 1–43.Flueckiger, S. M., Z. Yang and S. V. Garimella(2013). Review of molten-salt thermocline tankmodeling for solar thermal energy storage. HeatTransfer Engineering 34(10), 787–800.Gil, A., M. Medrano, I. Martorell, A. Lázaro, P.Dolado, B. Zalba and L. F. Cabeza (2010). Stateof the art on high temperature thermal energystorage for power generation. part 1concepts,materials and modellization. Renewable andSustainable Energy Reviews 14(1), 31–55.For large interface case the internal waves aregenerated by the periodic array of vortices whichgenerates a standing wave pattern near the BruntVä isä lä frequency.Gonzál

instabilities that occurred in two dimensional and three dimensional simulations are performed by Van Berkel et al. (2002) in a thermocline based water storage tank. In two-dimensional simulations the entrainment velocity was 40% higher than that found in the corresponding three dimensional simulations.