VORTEX STRUCTURES AND HEAT TRANSFER INCORRUGATED PLATE HEAT EXCHANGERS

J. Turnow1, R. Kewitz1 and N. Kornev1

1 Institute of Modeling and SimulationDepartment of Mechanical Engineering and Shipbuilding

University of Rostockjohann.turnow@uni-rostock.de

1 AbstractNumerical simulations have been performed using

RANS and hybrid LES-RANS method for turbulentflow through cross-corrugated plates in a new gener-ation of compact plate heat exchangers. The innova-tive circular shape of the corrugated plates has beeninvestigated to ensure flow homogeneity and best per-formance for different Reynolds numbers and corruga-tion profiles. With application of RANS method, thedependencies of local and integral parameters frictionfactor f and Nusselt number Nu have been studied us-ing a simplified corrugated channel. The heat transfermechanisms for the hot and cold fluid side has beenanalyzed using CHT-method. Parallel conducted ex-periments confirm the numerical results. The detailedflow distribution and enhancement of vortex structuresin the recirculation zones are determined using timeresolved hybrid LES-RANS method with applicationof different vortex identifications algorithms.

2 IntroductionPlate heat exchangers (PHE) are widely employed

in many industrial fields due to their compactness, ef-ficiency and flexibility. The corrugated metal platesare packed together to form a series of channels whereboth fluids are running in parallel or in opposite direc-tion. Rectangular corrugated plates are the most fa-vorite design since the flow distribution is nearly ho-mogeneous ensuring the transfer of energy over thewhole plate. However, when a high fluid pressure ispresent, the rectangular plates cannot resist and avoid-ance of leakage cannot be ensured. The new gener-ation of a plate heat exchanger with a circular shapeis designed to overcome this problem for applicationsat high pressure operating points. A single corrugatedchannel including an inlet and outlet is presented inFig. 1.

The circular design ensures an uniform static pres-sure distribution at the surrounding plates whereas forthe rectangular design the strain could exceed the elas-tic limit of the material in the sharp corners. Appear-ance of leaks and deformation of the rectangular ex-changers due to pressure peaks within the system are

Figure 1: Single channel of the circular plate-and-shell heatexchanger.

not rarely observed. For a safe employment, the newPHE design has to be investigated in detail to ensureneeded heat transfer rates and optimal performance.The thermo-hydraulic performance of an plate heat ex-hanger is strongly influenced by the corrugation pro-file, corrugation angle between adjacent plates, sur-face enlargement factor and corrugation height. Thevortex formations, heat transfer area, evolving of re-circulation zones and reattachment of boundary layersare directly related to these geometric parameters. Nu-merous experimental and numerical studies have beenconducted to optimize the surface structure in orderto enhance heat transfer rates while keeping the pres-sure drop at a moderate level. Today most used sur-face geometries within heat exchangers consist of thechevron geometry with a corrugated surface pattern.The plates are assembled in order that they contact incertain points where narrow flow passages are formed.The investigations published in literature point out,that numerical simulations are used more and morewithin the dimensioning process of heat exchangersdue to the development of more powerful and morecost-effective computers. Bhutta et al. [2012] give avery good overview of the published literature in themeans of numerical simulations of heat exchangers. Itis shown that the RANS method is capable of calcu-lating the performance of heat exchangers. In addi-tion, Bhutta et al. [2012] state that the fields of interestcan be divided into four branches: flow maldistribu-

tion, fouling, pressure drop and thermal analysis. Ka-naris et al. [2004] studied the pressure drop, the heattransfer and the fluid flow for a simplified model ofa single channel from a heat exchanger. The channelconsists of only one plate with a wave pattern keep-ing the model fairly simple. The results were in goodcompliance with experimental data and it was shownthat CFD is a powerful tool for the calculation of plateheat exchangers. Despite that, Kanaris et al. [2004]observed that the fluid flow mainly follows the furrowsof the corrugation profile until it is reflected at the sidewalls. This kind of fluid flow was also experimentallyobserved by Focke and Knibbe [1986]. The hydraulicperformance of a real cross-corrugated single channelof a plate heat exchanger were numerically and exper-imentally investigated by Liu and Tsai [2010]. Themain focus of the authors was concentrated on the fluidflow behind the contact points, whereas heat transferwas neglected. They stated that the fluid flow patterndiffers in the developing area close to the ports and thefully developed area in the middle of the channel. Inthe developing area the fluid flow is separated at thecontact points. One part follows the furrows until thenext contact points and the other part is aligned to themain flow direction. On the contrary, the fluid flow fol-lows the main flow direction behind the contact pointswithin the fully-developed region.

Despite the published studies of flow distributionand heat transfer for the rectangular shape, the fluiddynamics and thermophysical properties have not beeninvestigated for the new circular design. One the ba-sis of the above considerations, a detailed numericalresearch of flow distribution, pressure drop and heattransfer has been carried out within this study. TheReynolds number varies from Re=800 up to Re=1400based on the hydraulic diameter Dh. Finding the op-timal corrugation profile, three different corrugationradii have been analyzed. Parallel to the numerical in-vestigations, an experimental testcase of a single chan-nel for validation of the overall pressure drop has beenestablished. Furthermore, one plate has been remanu-factured using acrylic glass for dye injections and ob-servation of local flow distribution.Although it is known, that the chevron geometry in-duces helical fluid flow in the narrow passages and vor-tex flow at the contact points, the influence of the com-plex three-dimensional flow on the heat transfer andthe pressure loss is not well investigated using time re-solved numerical methods. The structure of vorticescreated at the contact points is still an open issue. Theaim of this research is to analyze the fluid flow in-side the narrow passages of a plate heat exchanger us-ing time resolved numerical methods (LES/URANS)and to clarify the generation of vortices at the contactpoints and their influence on heat transfer enhance-ment.

3 Numerical method

The steady simulations based on the Reynolds-averaged-Navier-Stokes equations (RANS) were per-formed using a 3-D finite volume method. The equa-tions are written for an incompressible fluid and steadystate flow. The choice of the k − ω − SST turbulencemodel has been based on the variation of turbulencemodels for the validation test case proposed by Ka-naris et al. [2004]. Heat transfer rates and friction fac-tors at different mesh resolutions are compared to re-sults published by Kanaris et al. [2004]. Due to the lowReynolds number, the standard k−ε-model and k−ω−SST peform poor since the models overestimate heattransfer and flow resistance (not shown here). Also therequired coarse mesh for y+ > 30 is not applicable forthe current configuration including heat transfer. Low-Re formulation by Lam and Bremhorst (LBKE) showsbetter performance, whereas using k − ω − SST writ-ten in low Reynolds form gives slightly better results.Therefore, the k − ω − textnormalSST model isused in the present study.

For calculation of unsteady effects and vortexstructures a hybrid LES-RANS model proposed byKornev et al. [2011] has been applied. The flow istreated fully turbulent in this work since in severalpublications it is stated, that the flow regime in plateheat exchangers is already fully turbulent for Reynoldsnumbers in the range of 200− 650 (Focke and Knibbe[1986], Vlasogiannis et al. [2002], Sha and Wanniarar-chchi [1991]). In the hybrid LES-RANS model thenear wall flow region is treated using RANS, whereasthe far flow regions are treated using LES method.Hence, unsteady effects are taken into account andthe number of grid nodes is lower than in pure LES.For implicit filtering the governing equations have thesame form in unsteady RANS and LES (Kornev et al.[2011]).

∂ui∂t

+∂(uiuj)

∂xj= −∂p

∗

∂xi+∂(τ lij + τ tij)

∂xj(1)

The notation p∗ is used for the pseudo-pressure andτ lij and τ tij for the laminar and turbulent stresses re-spectively. The turbulent stresses are calculated in de-pendency of LES or RANS region. For separation ofboth regions, the fluid domain is dynamically dividedinto the regions depending on the ratio of the integrallength scale L and the extended LES filter ∆. The in-tegral length scale L is defined by Schlichting [2000].

L = 0.168k3/2

ε(2)

The extended LES filter ∆ is slightly modifiedfrom the proposal by Kornev et al. [2011].

∆ =

√d2max + δ2

2(3)

Dmax is the maximal length of the cell edges(max(dx, dy, dz)) and δ is the standard LES filter

width. If L > ∆ the cell is in the LES region andif L < ∆ the cell is in the RANS region, respectively.In Figure 2 the arrangement of the zones can be exem-plary seen for a so called unitary cell of the plate heatexchanger.

Figure 2: Unitary cell of a cross-corrugated pattern. Defini-tion of RANS and LES zones in the hybrid model.

The Reynolds-stress tensor in the RANS region ismodeled using the k − ω − SST model proposed byMenter [1994] whereas the subgrid stress tensor in theLES region is modeled using the dynamic Smagorin-sky model proposed by Germano et al. [1991]. For thediscretization of the governing equations in space andtime a second order limited central difference schemeis used. Further a blending function is applied to en-sure continuous stresses between RANS and LES re-gion.

The conjugate heat transfer (CHT) simulationshave been performed using RANS method for the coldand the fluid side. Simulations confirmed, that the con-ductive thermal resistance of the solid plates betweenadjacent fluid channels can be neglected. For simplic-ity and stability, the temperature is treated as passivescalar variable, since the temperature differences aresmall and its influence on material properties can benegelected. Furthermore, the corrugated plates wereassumed to be free from fouling.

4 Geometry and Computational GridThe geometry of the corrugations is presented in

Fig. 3. For optimization of surface structure, the

top plate

bottom plate

flow area

radii

hs

Figure 3: Cross section of plates with varying curvatureradii.

radii is varied from r = 0.1mm up to r = 1.5mm.The channel height h and corrugation angle θ towardsthe flow direction is assumed to be constant at hs =

5.4mm and θ = 75◦ respectively. The whole circularPHE channel (see Fig. 1) have been calculated to an-alyze the flow distribution in lateral direction for thecircular shape. Investigations of vortex structures andheat transfer have been performed on a channel sec-tion cut out from the original model to save computa-tion time. Mesh generation for PHE requires specialattention to cover the sinusoidal corrugations at thecontact points between the bottom and top plate. Forhigh roundness the angle between the plates becomesfairly small introducing numerical errors and stabil-ity problems. By application of an improved mesh-ing tool snappyHexMesh, a hex dominant unstructuredgrid with prism layers close to the boundary is gen-erated to overcome this problem. Grid independencystudies have been performed to avoid numerical errorsdue to bad mesh quality. Simulations are carried outfor whole model up to 35 mio cells and for channelup to 15mio cells. Grid convergence by calculationof friction factor and heat transfer has been reached at18mio cells for the whole PHE and 8mio cells for thesimplified channel.

5 ResultsFor validation, grid independence and choice of

RANS turbulent model simulations of turbulent flowin a simplified heat exchanger channel were con-ducted. The validation model is represented by a rect-angular channel, comprises of only one corrugatedplate on top and a flat plate on the bottom. Fivedifferent Reynolds numbers within the range 900 <Re < 1400 have been considered, representing theflow regime in plate heat exchangers. Results for Fan-ning friction factor f (Fig. 4) and j-Colburn factor(Fig. 5) show good comparison to experimental andnumerical data published by Kanaris et al. [2004] andVlasogiannis et al. [2002]. The pressure drop can bemade dimensionless by defining the Fanning frictioncoefficient f

f =∆pDh

2ρu2Lp, (4)

where Dh = 4.33 · 10−3m is the hydraulic diam-eter and Lp = 0.216m the effective length of the cir-cular plate respectively. As regards heat transfer, thelocal Nusselt number Nul is defined:

Nul =hDh

λf, (5)

where the heat transfer coefficient h is calculated toh = qw/(Tw − Tf ) and the surface averaged Nusseltnumber Nu as the integral of the heat transfer surface.The j-Colburn factor is defined to:

j =Nu

RePr13

. (6)

0.06

0.08

0.1

0.12

0.14

800 900 1000 1100 1200 1300 1400 1500

Fa

nn

ing

friction

fa

cto

r f

[-]

Re [-]

k-ω-SSTk-ε

realizable-k-εLam-Bremhorst-k-ε

k-ω-SST KanarisExp. Kanaris

Figure 4: Fanning friction factor f for different Reynoldsnumbers and turbulence models compared to ref-erence data published by Kanaris et al. [2004].

0.016

0.018

0.02

0.022

800 900 1000 1100 1200 1300 1400 1500

j C

olb

urn

facto

r [-

]

Re [-]

k-ω-SSTk-ε

realizable-k-εLam-Bremhorst-k-ε

k-ω-SST KanarisExp. Kanaris

Figure 5: j-Colburn factor for different Reynolds numberscompared to reference data published by Kanariset al. [2004] and Vlasogiannis et al. [2002].

The numerical setup has been applied to the actualobject of investigation: the circular PHE.Published results e.g. by Focke and Knibbe [1986] re-veal a nearly homogeneous flow distribution shortlybehind the inlet of the fluid. Numerical simulationsconducted within this study showed that the commonassumption of homogeneous flow distribution can beforwarded to the circular PHE for the turbulent flowregime. The streamlines reveal a separation of the fluidat each contact point of the corrugated plates whereone part follows the main flow direction (see Fig. 9).The other part is directed in lateral direction due to thehigh flow resistance. Hence, zones of nearly zero ora dramatic minimum velocity nearby the outer circu-lar wall could not be observed within the flow fieldsfrom numerical simulations. Only close to the inletand outlet port blind areas with very small velocitiesare emerging due to the high flow rates. The main partof the fluid flow is driven through the narrow passagesbetween the contact points. Numerical results of theFanning friction factor (see Fig. 1) remain nearly con-stant at f = 2.5 for an increasing Reynolds number upto Re=1200. Deviations in comparison to experimentsshow a very good agreement at low Reynolds numberless than 5% where in contrast a difference of 32%for the friction factor at Reynolds number Re=1200 ispresent. The experimental setup is briefly described in

Buscher et al. [2013]. The test section includes twoplates melted together. One plate is made of acrylicglas to visualize flow distribution using dye injections.Actual investigations showed that the plates reveal asmall flexibility and are widen due to the high pres-sure in transversal direction. The emerging leackageand evolving flow channels are responsible for the highdifference of experimental and numerical results athigh mass flow rates. Additional simulations includ-ing leackage channels underlined the observation. Attime, the experimentators are working on strenghtenthe plate material.

According to the constant friction factor in depen-dence to the fluid velocity, the pressure drop dependsquadratically on the Reynolds number pointing to ahigh flow resistance in the channel due to the cross-corrugated pattern. This high resistance leads to ahomogeneous distribution of the fluid over the wholeplate, although the plate is circular. From the pres-sure distribution shown in Fig. 6 it can be seen thatperpendicular direction to the main flow, the pressurevalues are almost constant which leads to the under-standing of a homogeneous distribution of the fluid.Streamline patterns and and experimental dye obser-vations (not shown here) confirmed the homogeneousflow distribution through the channel. Fig. 7 presentsthe velocity vectors near the inlet port which underlinethe homogeneity in lateral direction and the movementof the fluid through the valleys of the corrugations.

Figure 6: Pressure distribution of a plane through the heatexchanger plate at Re=1200.

Parameter variationSince mesh convergence is determined around

18mio cells for the whole model and flow homogene-ity is ensured, the parameter variations of Reynoldsnumber and rounding radius are investigated using asimplified channel. The cut-out channel includes 15sinusoidal waves and about four contact points of bothplates for each corrugation to ensure the developmentand growth of the swirl flow and to avoid strong in-fluence of the symmetric boundary conditions in lat-eral direction. The channels are reconstructed for thehot and cold fluid which are energetic coupled usingCHT method. Temperature fields of heat transfer sur-

Figure 7: Streamlines at the inlet of the circular plate heatexchanger at Re=1200.

faces are linearly interpolated between both sides onlyat the corrugated surface. Both channels are shownin Fig. 8. Three different radii r = 0.1; 0.5, 1.5mm(see Fig. 3) and four different Reynolds numbersRe = 800, 1000, 1200, 1400 have been analyzed. Theintegral results are presented in Tab. 1 and Tab. 2.

Figure 8: Geometry of the simplified channel for parametervariations.

Table 1: Nusselt number Nu and Fanning friction factor ffor different radii at Reynolds number Re= 1000.

radius r = 0.1 r = 0.5 r = 1.5f 0.64 0.56 0.47Nu 11.32 11.02 10.83

The significant influence of the different radii onheat transfer and friction factor is clearly evident. Atthe constant Reynolds number Re = 1000, the flowresistance decreases up to 26.5% for an increasingroundness. It confirms the general assumption, thatNu and f are higher for sharp than for smooth geome-tries (see Zhang and Defu [2011]). The difference ofthe heat transfer in terms of Nu can be neglected withvariation of the radius. A nearly linear dependenceof Nu could be found the selected Reynolds numbers.The heat transfer is almost doubled for the investigated

Table 2: Nusselt number Nu and Fanning friction factor ffor r = 1.5 at different Reynolds numbers.

Re 800 1000 1200 1400f 0.54 0.47 0.40 0.38Nu 8.78 10.83 12.77 15.92

Re range. In contrast, the friction factor is decreasingfrom f = 0.54 down to f = 0.38 at Re = 1400.The deviations of the integral values can be forwardedto the different flow behavior. Defined flow separa-tion behind the contact points is observed at r = 0.1whereas for the smooth surface a deep separation pointcould not be seen in the flow fields. As example, thestreamlines at Re= 1200 and r = 1.5 are presented inFig. 9.

U

Figure 9: Streamline patterns for a rectangular cross-corrugated channel at Re= 1200 and r = 1.5.

Streamlines show the evolving flow channelsthrough the cross-corrugated PHE. The observation oflarge recirculation zones between each stream seemto be negative since the velocities decrease dramati-cally and induce a fairly low heat transfer rates withinthis regions. For heat transfer enhancement a bettermixing of this recirculation zones should be provided.However, the streamline patterns barely depend on theReynolds number. At higher Reynolds numbers the re-circulation zone behind the contact points is more dis-tinct and thus, the rate of the fluid flow following themain stream flow is less. Based on this observation andthe achieved results of RANS for the cut-out channelit can be stated, that at higher Reynolds numbers thefluid becomes better mixed and distributed across thechannel width resulting in higher heat transfer rates.To underline this observation, the temperature field atthe heat exchanger surface is presented in Fig. 10.

The temperature indicates the separated flow chan-nels of the hot and cold fluid side. For the actualconfiguration both streams nearly move next to eachother. Where at one side the fluid velocity remainsfairly high, at the other fluid side it is nearly zero due

Figure 10: Temperature distribution at the heat exchangersurface at Re= 1200 and r = 1.5.

to the remaining contact points. Hence, the highestheat transfer rates can found at the attaching surfaceeach stream. However, for heat transfer enhancementa better mixing behind the contact points should be en-sured with application of special flow regulators. Nu-merical simulations of special designs e.g. dimples arecurrently under investigation.

Vortex structuresUsing hybrid LES-RANS method, the unsteady ef-

fects and vortex structures behind the contact pointscould be visualized using time resolved flow fields.Focke and Knibbe [1986] published flow visualiza-tions in cross channels for different corrugation pro-files. It was shown, that the flow pattern and the vortexstructures strongly depend on the implemented surfaceprofile and on the selected radius. Within this work thecorrugation angle is defined to 75◦ and the surface pro-file is nearly a sinusoidal pattern. For a sinusoidal pro-file and a corrugation angle of 80◦ Focke and Knibbe[1986] reported that the fluid does not only follow onefurrow until it is reflected at the wall and enters thenext furrow, but rather is reflected close to a contactpoint and the fluid is transported at this point fromone furrow to another. These patterns can also be rec-ognized in the time averaged streamline patterns (seeFig. 9) for the rectangular cut out channel of the cir-cular PHE model. Here, a proportion of the fluid fol-lows the furrows and is reflected at the contact pointsas well. Close downstream the contact points a coun-terflow is noticed inducing a relatively stable recircula-tion zone. In the downstream region between two con-tact points the fluid enters from both sides of the nar-row passages from the main flow. Due to the evolvingshear layer between main and recirculation flow vortexstructures are generated. Thus, the the fluid is drivenalong spiral trajectories rotating around an inclinedaxis which drive the hot fluid back to the mean flowenhancing mixing process and heat exchange. Themain part of the fluid ejected from the recirculationzone does not directly enter the following zone down-stream. It is entrained by the main flow and hencebecomes well mixed. A snapshot of the velocity in a

plane through the center of the channel represents theareas of different velocities (Fig. 11).

Figure 11: Velocity distribution at Re= 1200 and r = 1.5 incenter plane perpendicular to the flow direction.

Fig. 12 presents the vortex structures at Re= 1200reconstructed by iso-surfaces using Λ2 criteria whichare colored by the pressure. As it can be seen, thatthe flow in the narrow passages is dominated by smallscale eddies arising at the peaks and valleys of the lat-ter. Whereas, in the region between the contact pointsthe vortices are dominated by tubular and strongerstructures arising at the sharp edges of the contactpoints.

Figure 12: Visualization of vortex structures using λ2-criterion for turbulent flow in a rectangular cross-corrugated channel at Re = 1200. Tubular vor-tex structures between the contact points in thedownstream.

To underline the results gained by numerical sim-ulations, experimental investigations of the flow resis-tance and heat transfer being undertaken at the Tech-nical University of Berlin at the moment. Despite that,first flow visualizations using dye injections under-lined the flow phenomena obtained by the numericalsimulation inside the circular PHE.

6 ConclusionsNumerical simulations for incompressible turbu-

lent flow through circular PHE are obtained to investi-gate flow structures and heat transfer pattern. Usingvalidated k − ω − SST model and carefully gener-ated meshes for the different geometries and Reynoldsnumbers, a detailed overview of certain dependenciesof heat transfer and friction factor is provided. Three-

dimensional simulations for a single corrugated plateof the circular design show a homogeneous flow dis-tribution in lateral direction. The assumption of lowvelocity areas in circular PHE has been disproved. Ap-plication of CHT-method for a selected channel of thecircular PHE a detailed analysis of the local heat trans-fer coefficient shows fairly low values behind the con-tact points and next to the flow passages respectively.The variation of radii and Reynolds number give a de-tailed on heat transfer and friction dependency. Withinthis study a hybrid RANS-LES model by Kornev et al.[2011] is applied to determine vortex structures andunsteady effects of a new designed circular heat ex-changer. It could be shown that the hybrid RANS-LESmodel by Kornev et al. [2011] is a powerful tool topredict vortex structures and unsteady effects withouthigh computational costs. Streamline patterns showedthat the flow in a cross-corrugated channel is charac-terized by large recirculation zones, disruptions andreattachments of boundary layers as well vortex flowgeneration at the contact points which is in accordancewith the experimental investigations e.g. by Focke andKnibbe [1986].

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