INVESTIGATION OF SHELL AND TUBE HEAT …264346/UQ264346_OA.pdf · Engineering Applications of Computational Fluid Mechanics Vol. 5, ... computational fluid dynamics, heat exchangers,

Engineering Applications of Computational Fluid Mechanics Vol. 5, No. 4, pp. 566–578 (2011)

Received: 19 Nov. 2010; Revised: 11 Jul. 2011; Accepted: 13 Jul. 2011

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INVESTIGATION OF SHELL AND TUBE HEAT EXCHANGER TUBE INLET WEAR BY COMPUTATIONAL FLUID DYNAMICS

Klaus Bremhorst * and Matthew Brennan **

* JK Tech Pty Ltd, 40 Isles Rd, Indooroopilly, Queensland, 4068, Australia ** The Julius Kruttschnitt Mineral Research Centre, The University Of Queensland, 40 Isles Rd,

Indooroopilly, Queensland, 4068, Australia E-Mail: [email protected] (Corresponding Author)

ABSTRACT: Computational fluid mechanics is still a developing art in the prediction of erosion/corrosion often due to lack of suitable mathematical models to represent physical processes. In the present work, new flow modelling strategies have been developed for flow simulation in the inlet header of side entry shell and tube heat exchangers used in alumina plants and minerals processing plants for heat recovery. The traditional approach of treating the tube bundle as a porous plug observing Darcy’s friction law has been replaced by modelling of all tubes individually and application of an inertial model for flow resistance. This better reflects the much higher velocities for the approach into the tube bundle as only about one third of the tube sheet is open area. It also includes the effect of flow separation within the inlet to some tubes which is a flow feature not able to be simulated with the porous plug approach. The traditional use of symmetry for the inlet geometry has been found to suppress the inherent asymmetry found in this flow associated with the large flow expansion from the inlet nozzle to the inlet header space. The results indicate that tube inlet wear is spread across the tube sheet more extensively than indicated by porous plug modelling. The asymmetry of flow uncovered by the new modelling technique leads to less regular wear patterns which may help to explain the difficulty of recognizing clear cut patterns of wear in processing plants. Areas of high angle of flow into tubes, variations of mass flow distributions across tube sheets and a flow component across the geometrical symmetry plane are identified. High flow angles have been found to correlate well with flow separation inside tube entrances where previous studies have shown excessive tube wear to occur. Regions where flow separation within tubes occurs have also been found to correlate well with low static pressure within the tubes downstream of the tube entrances.

Keywords: computational fluid dynamics, heat exchangers, erosion, corrosion

1. INTRODUCTION

Production of alumina from bauxite generally uses the Bayer process, which involves dissolving the aluminium present in bauxite in a hot caustic solution. Considerable heat recovery is achieved where flash steam from the digester product is used to pre-heat the feed. Shell and tube heat exchangers, typically constructed to TEMA (Tubular Exchanger Manufacturers Association) standards with side entry and of mild steel, are commonly used. Due to the build up of scale, regular descaling with an acid wash is undertaken in order to restore good heat transfer. During acid cleaning, the protective oxide layer on the mild steel is removed thus leading to enhanced metal loss until the protective layer is restored. Damage caused is illustrated in Fig. 1 and has been examined from a flow point of view by Bremhorst and Lai (1979) and Lai and Bremhorst (1979). The electrochemical flow processes involved are not well understood and the concern in existing alumina plants is what happens if throughput is

Fig. 1 First pass inlet of four pass shell and tube heat

exchanger.

increased to give a higher yield. While mass transfer processes are often flow Reynolds number dependent with higher Reynolds numbers leading to higher metal loss (flow accelerated corrosion), little evidence exists in support of such a hypothesis in the present application. As corrosion is an electrochemical process, it should be possible to reduce it by chemical means. The use of liquor aeration or even oxygenation has been examined in the laboratory (Kear and

Metal loss through full tube thickness

Engineering Applications of Computational Fluid Mechanics Vol. 5, No.4 (2011)

567

Fig. 2 Flow separation at tube inlet.

Bremhorst, 2008a and 2008b) but found to be beneficial only under limited conditions which may not be met in an alumina plant. However, the dominant factor isolated so far which affects metal loss at tube inlets is the pattern of flow into tubes. Maximum metal loss generally occurs where flow into tubes is at a large angle to the tube axis leading to possible flow separation as shown in Fig. 2 (Elvery and Bremhorst, 1996). Few predictive models exist for the electrochemical processes (Nešić, 2006) thus leaving the most promising line of enquiry to be the search for flow arrangements that lead to flow angles into tubes being as near to axial as possible (Bremhorst and Lai, 1979 and Lai and Bremhorst, 1979). Flow modifiers proposed by these authors have had extensive testing in the plant environment with dramatic improvement in tube life provided that flow angles relative to the tube axis were kept below 30. The area of concern for the present study is the inlet header as already discussed above in the context of the studies by Bremhorst and Lai (1979) and Lai and Bremhorst (1979). Advances in computational resources since the 1970s and the development of reliable turbulence models has allowed the replacement of experimental work in the search for ideal flow patterns applying to this particular geometry of heat exchanger (Bremhorst and Flint, 1988, 1989 and 1991; Nešić, 2006; López del Prá et al., 2010). The modelling approaches used by Bremhorst and Flint (1988, 1989 and 1991) arose from the early limitations of computational resources necessitating the representation of the tube bundle by a porous plug with a resistance given by Darcy’s law and use of symmetry to reduce the number of computational nodes. Although the porous plug modelling results were generally quite representative, the opportunity now exists to refine modelling by including flow features within tube inlets thus leading to a better understanding of the flow processes with better predictability of where rapid tube wear is likely to occur. The review of turbulence models by López del Prá et al. (2010)

concluded that the simpler models were insufficient to give the best available flow predictions, with the SST-k-ω model attributable to Menter (1992), likely to give best performance under the variety of flow geometries encountered in a shell and tube heat exchanger. Limited experimental data were used to support their numerical predictions. Recent experimental studies of a step expansion flow between infinite parallel plates (Escudier et al., 2002; Sugawara et al., 2005; Duwig et al., 2008; Drikakis, 1997) have shown that the flow does not expand symmetrically and attaches preferentially to one side of the expansion, with the data suggesting that a flow switching from one side of the line of symmetry to the other may even occur. In the side entry parallel pass header, the flow expands rapidly from the inlet nozzle into a space which is not axisymmetric. It is untested whether or not a symmetrically expanding flow results. Experimental data of Bremhorst and Lai (1979) certainly lack perfect symmetry which so far has been attributed to experimental variability but in light of these recent observations with the step parallel plate expansions, the asymmetry may in fact be a real flow characteristic. Consequently, symmetry of the inlet channel geometry was not used in the present study in case this forces flow symmetry. Whilst the main focus of this work was to investigate the hydrodynamics of heaters used in the Bayer alumina process, the results from the investigation have application in many other processing plants where heat exchangers of this type are used with corrosive/erosive materials and where the dominant mechanism of metal loss is associated with regions of flow separation.

2. MODEL DESCRIPTION

2.1 Physical model and grid generation

The simulations reported here are of a side entry, parallel pass geometry shown in Fig. 3(a) and (b). A single phase liquor feed rate of 1640 m3h-1 with density 1410 kg.m-3 (equivalent to 10% by volume of alumina) and dynamic viscosity of 0.005 kg.m-1s-1 was assumed. This is the rated feed flow rate of the heater. The first pass geometry is completed by addition of the tube zone for which different modelling approaches are discussed below. Tubes are flush with the tubesheet in order to limit the number of computational nodes. Initially the tube zone was represented by a porous plug extension to the header ("porous

Flow separation


568

600 300

Fluid Region

Porous Region

274 tubes x 33 ID 47.62 pitch

Pressure Outlet Each

Tube

1040 66

Heater ID

543.5

600

Feed 467 ID

Header

Fig. 3 Dimensioned and meshed geometry for inlet

header – dimensions are in mm.

plug" approach) with a Darcy’s law resistance (resistance proportional to velocity) and a one directional diffusion coefficient to give a pressure drop of some 46 kPa (similar to plant values for the tube bundle). Subsequently, the geometry was modified so that the tube sheet and the first 0.9 m of each tube in the tube bundle were simulated (the “with tubes” approach). In the "with tubes" approach the first 600 mm from the tubesheet of each tube was simulated as a region of turbulent pipe flow and the last 300 mm was set up as a porous zone, where the porosity was adjusted so that the effective overall tube pressure drop was the same as that of the entire tube bundle in the pass. This approach permits a numerically economic simulation where the flow behaviour in the tube entrances and flow development in the first 0.9 m of each tube are simulated properly without resorting to simulating the entire tube bundle. Initially the porous zone in each tube of the "with tubes" approach used the Darcy's law resistance. However the tube resistance is in reality proportional to the square of tube flow velocity (given by Eq. (1)) and this relationship is available as a porous zone option (known as the

"inertial model") in FLUENT. The "inertial model" was tested for effects on flow distribution across the tube sheet face relative to that predicted by the Darcy law model and is the porous zone model used in the "with tubes" approach.

1

2x x xp C u u

(1)

The “with tubes” approach introduces several important differences and enhances the modelling. Firstly the tube sheet has been introduced into the simulation as a wall boundary condition and the momentum transfer by shear to the tube sheet between tubes is simulated, which is not possible with the "porous plug" approach. Secondly flow separation within individual tube entrances and flow mal-distribution down particular tubes due to the hydrodynamic effects in the header can now be modelled. Finally in the “porous plug” approach, the axial velocity which determines the pressure drop is determined by the product of the flow velocity magnitude and its angle relative to the tube axis. With the “with tubes” approach, a given axial velocity (which again determines the pressure drop) is a function of flow velocity magnitude, its angle relative to the tube axis, whether or not flow separation occurs at the tube inlet and the azimuthal angle of the velocity vector because the tube array about a given tube is not axi-symmetric. The grids with both "porous plug" and "with tubes" approaches were generated with Gambit and with both approaches the domain of the header fluid space was meshed using the unstructured tetrahedral mesh option. With the unstructured tetrahedral mesh, the size of the volume mesh is ultimately derived from the size of the edge meshes and the mesher auto-grades the mesh when a finer edge mesh is used in one part of the domain. The grids were further refined in FLUENT using the "Adapt to boundary" option to improve grid resolution around the tube plate. The grids using the "porous plug" approach used a 20 mm unstructured tetrahedral mesh with refinement in FLUENT to 5mm in the region of the tube plate and a total of 6.3x105 nodes. The grids and the grid dependence on the "with tubes" approach is discussed in more detail in Appendix A; The results reported in the main section of this paper with the "with tubes" approach used Grid C which had 1.2x106 nodes. The flow domain with Grid C was meshed with a 10 mm unstructured tetrahedral mesh in the header space. (see Fig. 3) The face of the tube plate and each face on the tube inlet were meshed


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with a 7.5 mm tri paved mesh which was then refined in FLUENT to a 3.75mm mesh around the tube plate. A 600 mm length of the inlet pipe to the header was meshed with a 10 mm Cooper mesh using the tri face mesh at the boundary between the pipe and the header as the projecting mesh. Each tube was meshed with the Cooper mesh using the inlet face as the projecting face mesh. The first 600 mm of each tube used a graded axial mesh from 5 to 120 mm. The last 300 mm of each tube needed to be a separate fluid zone and used a 120 mm axial mesh.

2.2 Flow modelling

Continuity and momentum equations were Reynolds averaged (RANS modelling), Eqs. (2) and (3), and the SST-k-ω turbulence model of Menter (1992) and Wilcox (1998) was used, Eqs. (4) to (6). The time dependent form was retained to help with the solution process. Results are for the final steady state solution. The simulation approach is discussed further in the Numerical Details section below.

0i

i

u

x

(2)

1(2( ) )i i

j t ji ij i j

u u pu S g

t x x x

(3)

/t k (4)

' ' *

*

ij i j

j j

tj j

uk u k u u k

t x x

kx x

(5)

' ' 2ij i j

j j

tj j

uu u u

t x k x

x x

(6)

where 13

25

’

* 1

2

’

9 1 70125 1 80

2*

2

1 6809 9for 0, otherwise =

100 1 400 100k

kk

3

1k

j j

k

x x

and

39( )100

ij jk kiS

The header and inlet nozzle geometry are symmetric about a plane perpendicular to the pass separation. Previous CFD studies have assumed that the flow is symmetric about this plane and computed only one half of the inlet pass to minimise the computation. However in this work the full inlet header geometry has been simulated, because simulation of only one half of the header forces symmetry of the flow which may not occur in reality. A seventh power velocity profile as given in Eq. (7) was applied to the inlet pipe of the header (Bird et al., 1960). Sensitivity of results to changes in assumed velocity profiles in the inlet nozzle was tested but found to be only minor when changing from a uniform (top hat) profile to a seventh power law turbulent one.

1/7

max

1p

u r ru R

(7)

2.3 Numerical details

The cases were solved with FLUENT Version 6.3.26. High order discretization of the equations was used; PRESTO (PREssure STaggering Option) was used for pressure, 3rd order MUSCL (Monotone Upstream-Centered Schemes for Conservation Laws) for all other equations and SIMPLE was used for the pressure-velocity coupling. A velocity inlet boundary condition was used at the inlet pipe boundary with a Seventh power profile for the velocity (see above) and the turbulent intensity was set at 10% and the length scale was set to 0.4m. An outflow boundary condition was used at the header outlet with the “porous plug” model. Pressure outlet boundary conditions were used on tube outlets in the “with tubes” model. The cases were initialized and solved using the steady segregated solver for approximately 4000 iterations, after which the unsteady solver was enabled and the case was integrated over time with a time step of 0.05s. Solution using the unsteady solver from initialization was found to converge on identical results but took longer. The criterion used for convergence was not just minimum residuals (which were set at 10-5), but that the flow field reached a steady flow, as evidenced by unchanging angles of attack at the tube sheet. Steady flow was generally achieved after 50s of simulation time. The simulations were run on an 8 core Xeon workstation running Windows XP64 and 8 Gbytes of RAM. The multi-core functionality was used primarily to run a large number of


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Fig. 4 Contours of velocity magnitude at tube sheet,

"porous plug" case at rated feed flow rate of 1640 m3hr-1.

Fig. 5 Contours of flow angle relative to tube axis at

tube sheet, "porous plug" case at rated feed flow rate of 1640 m3.hr-1.

Fig. 6 Contours of vorticity aligned with tube axis,

"porous plug" case at rated feed flow rate of 1640 m3.hr-1.

parametric cases and simulations were typically only run with 1 core. Exact timing of the simulations was not collected as the small increase in solution times experienced was far outweighed by the very substantial cost of plant failure and associated down time. Simulations using the "with tubes" approach took longer to converge than the porous plug approach, but reached convergence on an overnight run with only 1 core.

3. RESULTS

3.1 “Porous plug” approximation for tubes – inlet header

Figures 4-6 show contours of flow conditions at the tube sheet for the “porous plug” approximation. Contours of velocity magnitude, Fig. 4, are relevant to impact effects of flows if particles are present in the flow while contours of flow angle relative to the tube axis, Fig. 5, give an indication of likelihood of flow separation inside tube inlets. Velocity magnitude and angle determine flow velocity through the tubes and hence mass flow distribution across the tube sheet. Contours of the component of vorticity aligned with the tube axis, Fig. 6, give insight into the flow structure which is seen to consist of two major vortices.

3.2 “With tubes” approximation for tubes

The “with tubes” approach used the geometry of Fig. 3 with the tube zone represented by an array of 274 tubes of 33 mm ID and 0.9 m in length and on a 47.625 mm triangular pitch. As described earlier the last 0.3 m of each tube was modelled as a porous zone with the porosity adjusted to give an overall pressure drop of 46 kPa. Flow quantities are displayed 10 mm upstream of the tube sheet in order to reduce the variability of results due to mass flow variations between tubes. The results reported here used the Grid C referred to in Appendix A. The tube Reynolds number at rated feed flow rate is around 19000, which is turbulent. The tube porous zone is positioned 18 tube diameters from the tube entrance. Although 30 diameters would be preferred to achieve full flow development (Mulley, 2004), it was found that radial distributions of velocities at 300 and 500 mm from the tube plate were nearly equal thus indicating that the velocity profiles had approached a sufficiently fully developed profile for present purposes. Furthermore, since the pressure field develops more quickly, the shorter entrance length was preferred. The velocity angle of the flow in a plane 10 mm upstream from the tube sheet is used in this study as the criterion of the quality of the flow. This is defined as the angle of the velocity vector relative to the axis of the heater, which is the x axis and has been calculated in a custom field function, Eq. (8). Typical results for velocity magnitude and velocity angle are shown in Fig.7 and Fig. 8.


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Fig. 7 Velocity magnitude “with tubes” case, 10 mm upstream of tube sheet at rated feed flow rate of 1640 m3.hr-1.

Fig. 8 Flow angle relative to tube axis “with tubes”

case, 10 mm upstream of tube sheet at rated feed flow rate of 1640 m3.hr-1 (Grid C).

Fig. 9 Path lines “with tubes” case.

Fig. 10 Pathlines “with tubes” case as seen through

the shell from the inlet nozzle on the right.

1 2 2180)/ | |y zsin u u

u

(8)

Comparison of Fig. 4 with Fig. 7 and Fig. 5 with Fig. 8 shows that there is a significant asymmetry in the flow simulated by the “with tubes” case and which is not seen in the “porous plug” case. Considerable effort has gone into ensuring that this is not a convergence or grid problem. In the “with tubes” case higher velocity magnitudes are predicted, Fig. 7, because the space between tubes does not carry mass flow as is the case with the “porous plug” approach. Flow angles are also larger in the “with tubes” case, Fig. 8 The reason for this increased angle is due to the fact that with tubes, flow occurs along the tube sheet between tubes and this then turns sharply into the tubes, Fig. 9. Fig. 10 shows that the lack of symmetry is due to a cross-flow from one half of the inlet header to the other half. This cross-flow is suppressed when using only one half of the flow segment for simulations. In Fig. 9 it can also be seen that there is a strong cross flow down the shell on each side of the header. These two cross flows collide at the plane of header symmetry (z=0). At the point where these two flows meet at the tube sheet, instability exists thus leading to the asymmetry observed across the tube sheet. As Eqs. (3), (5) and (6) are time dependent, unsteady RANS solutions are obtained where the time varying flow variables can be viewed as representative of the larger flow structures which vary with time while the finer structures are modelled by the turbulence model. As the time element has been retained in the equations in order to assist convergence, if large scale structures exist, instantaneous solutions will continue to vary about the steady state means where the latter are obtained by sufficiently long averaging times. Consequently, an indication of the fuller extent of regions of high flow angle or low tube inlet velocity becomes evident. The solutions obtained are not unique and depending on the manner in which solutions were commenced, a mirror image solution has been obtained. This is to be expected as there is no asymmetric feature in the inlet flow or the geometry or the solution process which might favour one solution over another. Even longer solution times did not alter the resultant average flow field thus leading the authors to term this a meta-stable solution for which correct time averages have been obtained based on a particular set of initial conditions. Application of results obtained must, therefore, be interpreted by including the mirror image about the line of

Sharp turn of flow into tubes

Path lines show cross-flow from top half to lower half of header


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Fig. 11 Contours of axial velocity (m.s-1) for 1st 9

tubes from LHS of header at a y elevation of 0.42m at feed flow rate of 1640 m3.hr-1.

Fig. 12 Regions of flow separation within tubes at 20

mm from tube entrance - black denotes regions of negative axial velocity in the tubes which indicate the presence of a flow separation bubble at this axial position.

Fig. 13 Contours of velocity angle 10 mm upstream

of tube sheet at 67% rated feed flow rate.

Fig. 14 Contours of velocity angle 10 mm upstream

of tube sheet 130% rated feed flow rate.

geometric symmetry as well as solutions obtained from different starting conditions. A more accurate approach is to apply a large eddy simulation which is given below. Fig. 11 shows the contours of axial velocity at an elevation of 0.42m, which intersects the fourth row of tubes for this same simulation and near the position shown by the arrow on Fig. 8. These tubes are in a region where Fig. 8 suggests the angles of attack are large. As can be seen from Fig. 11 flow separation is predicted, with a recirculation bubble forming within the tubes, as evidenced by a negative axial velocity on the right hand side of each of the 4th through 9th tubes. There is also evidence of a recirculation bubble on the left hand side of the first tube in this row. Fig. 12 identifies tubes with negative tube velocities (flow reversal) which are associated with flow separation. A comparison with flow angle, Fig. 8 shows a high correlation between large flow angle and tubes with flow separation. For the present geometry and flow parameters, a flow angle of greater than 50 degrees is associated with flow separation within the tube inlet. However, this figure will be somewhat different for different distances from the tube entrance as there is a wide spread of lengths of separation regions within tubes.

3.3 Results at different feed flow rates

Simulations at feed flow rates of 67% and 130% of rated flow were generated (1099 m3.hr-1 & 2130 m3.hr-1). The contours of velocity angle show that the velocity angles increase when the feed flow rate is reduced (Fig. 13, 67% rated flow) and decrease somewhat when the feed flow rate is increased (Fig. 14, 130% rated flow). The decrease in flow angle with increased feed flow rate is also shown graphically in Fig. 15 where the flow angles are plotted across the tube sheet at a distance of 0.274m from the pass baffle. The axial velocities at y=0.42m (Fig. 16, 67% rated flow and Fig. 17, 130% rated flow)) show that flow separation within the tubes also occurs for these feed flow rates.

3.4 Static pressure drops

“With tubes” simulations also yield the static pressure profile within tubes, Fig. 18. It should be noted that the tube porous zone exists only to give the same overall pressure drop for the pass without having to simulate the entire length of the tubes. Hence the pressure is only plotted in the fluid zone of the tubes (not the porous zone) on Fig. 18. Due to varying angles of approach of the


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Fig. 15 Velocity angles 10 mm upstream of tube sheet and across tube sheet at 0.27m from pass baffle at 67%, 100% and 130% of rated flow (=1640 m3.hr-1).

Fig. 16 Contours of axial velocity (m.s.-1) for 1st 9

tubes from LHS of header at a y elevation 0.42m at 67% rated feed flow rate.

Fig. 17 Contours of axial velocity (m.s.-1) for 1st 9

tubes from LHS of header at a y elevation of 0.42m at 130% rated feed flow rate.

Fig. 18 Simulated pressure drop along central tube to

the beginning of tube porous zone (at y=0.294m, z= 0.0 m) from "with tubes" simulation at rated flow. Tube entrance is at the tube sheet position of 0 m.

flow into the tubes, entry losses vary across the tube sheet from 11 kPa down to only 3 kPa as seen from Fig. 19, for a header pressure of around 46 kPa. Two “with tubes” simulations were conducted where the overall tube pressure drop was reduced to 27 kPa and 16 kPa. Table 1 shows the dependence of tube mass flow rate on overall tube pressure drop for these cases and the original case at 46 kPa. The ratio of minimum to maximum mass flow rate in the tubes varies across the tube sheet with the highest tube pressure drop giving the least variation. In view of the significant dependence of mass flow variation across the tube sheet on overall pressure drop or mean mass flow rate, simulations were performed with the inertial model instead of Darcy’s law. This led to higher pressure drops and less variation of tube mass flows across the tube sheet as seen from Fig. 20. The flow cross-sections of Fig. 11, Fig. 16 and Fig. 17 show evidence of flow separation within the tube entrance for some tubes but not for others depending on flow angle and flow velocity. Such separation bubbles are not static in a turbulent flow. They have reattachment points or lines the position of which varies with time but have a well defined steady state or time averaged value. This

Fig. 19 Static pressure inside tubes 30 mm from tube

entry.

Fig. 20 Ratio of minimum to maximum tube mass

flow rate at 1640 m3.hr-1 where Darcy and Inertial resistances were adjusted to give header pressure drops of 16, 27 and 45 kPa.


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Table 1 Dependence of tube mass flow rate on pass pressure drop - average tube mass flow rate = 2.344 kg.s-1.

Pressure drop across first

pass kPa

Ratio of minimum to

maximum tube mass flow rate

Standard deviation on average tube

mass flow rate16 0.659 0.205 27 0.772 0.125 46 0.864 0.08

unsteadiness is a flow feature not simulated by the porous plug approach. As it is an unsteady phenomenon, and also inherently unstable when neighbouring tube flows act in a coordinated manner, flow patterns as a whole across the tube sheet are affected. When viewed in the context of the static pressure data of Fig. 19, significant variability across the tube sheet exists. As there is no flow feature linking the two quadrants making up the tube sheet sector analysed, it follows that the two quadrants do not have to be mirror images of each other thus accounting for the asymmetrical patterns of velocity, velocity angle and vorticity across the tubesheet of the inlet sector. Similar asymmetry is not observed with the porous plug simulations and can be attributed to the absence of flow separation within the tube inlets represented by a porous plug. It is not surprising, therefore, that turbulent kinetic energy levels for the “with tubes” simulations are higher than for the porous plug case, Fig. 21 and Fig. 22. Fig. 23 shows the predicted axial velocity within the tube at 30mm from its entrance. Comparison with static pressure at the same location, Fig. 19, shows that a good correlation exists between tubes with low static pressure and tubes within which flow separation (negative axial velocity) occurs.

3.5 Large eddy simulations

A concern with unexpected simulation results is that they may simply be a manifestation of the particular modelling technique. Consequently, large eddy simulation was employed to test outcomes. Using the same grids as for the “with tubes” RANS simulations, large eddy simulations with the dynamic subgrid scale eddy viscosity model of Germano et al (1991) were performed (time-step = 1.0 x 10-4s). Mean flow angles from the LES after 3s of simulation and then over a subsequent 2s of averaging are shown in Fig. 24. Asymmetry of flow distributions noted in the above RANS modelling data was again seen but with variations from the RANS modelling results.

Fig. 21 Turbulent kinetic energy 10 mm from tube

entrance, "with tubes" simulations at rated feed flow rate.

Fig. 22 Turbulent kinetic energy 10 mm from tube

entrance, "porous plug" simulations at rated feed flow rate.

Fig. 23 Axial velocity inside tubes at 30 mm from entrance. Negative velocities indicate reverse flow due to flow separation.

Fig. 24 Time averaged flow angle relative to tube axis,

10 mm upstream of tube-sheet for LES at rate flow.


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However, the general features of the flows are the same as for the RANS simulations. LES is arguably the better technique, but is much more numerically intensive even when used on the same grids as used for the RANS simulations. This is because LES requires much shorter time steps and needs to be run for a significant number of iterations to obtain time averages. The grids used for the RANS simulations have a wall y+ of around 100 in the header, which is too coarse for LES if accurate wall shear stresses are to be computed. In the present case the law of the wall approximation within FLUENT was used thus allowing the first near wall grid point to be at y+ = 100 or even larger. Vector contours shown on Fig. 25 give a clearer view of the major vortices generated by the side entry of flow. The correlation with flow angle of entry to tubes, Fig. 5 and Fig. 8, is quite high in the region of the major vortices. The high angles around the outer shell are seen not to be associated with these vortices but are the result of flow along the shell towards the tube sheet and then turning sharply into the nearby tubes. Distributions of mean and instantaneous vorticity components along the tube axis, Fig. 26 and Fig. 27, show the large vortices that were seen in the RANS simulations and the widespread of vorticity from one tube to the next. The significance of the instantaneous vorticity component is that it can show up as localized tube damage at inlets with a spread far larger than suggested from the mean vorticity distributions.

4. CONCLUSIONS

Modelling of side entry shell and tube heat exchanger flow was undertaken by modelling each individual tube rather than treating the tube bundle as a porous plug as done in previous studies and not making use of geometric symmetries of the header. This revealed the existence of asymmetric flow distributions similar in nature to asymmetries noticed in plane expansion flows and as observed in earlier experimental work. The “with tubes” approach models the flow separation occurring at some tube inlets, which is an aspect not revealed by previous “porous plug” modelling which, therefore, excluded any flow unsteadiness associated with the flow separation bubbles inside some of the tubes. It was found that areas with a high flow angle correlated well with areas where tubes showed flow separation inside the inlet. Using flow angle is, therefore, seen to be a reliable and simple method of predicting areas of

Fig. 25 Velocity vectors 10 mm upstream of tube-

sheet for LES at rated flow.

Fig. 26 Mean vorticity component in direction of tube

axis, 10 mm from tube sheet for LES at rated flow.

Fig. 27 Instantaneous vorticity component in

direction of tube axis, 10 mm from tube sheet for LES at rated flow.

high corrosion in flows where flow separation is known to coincide with higher metal loss. The “with tubes” approach also better reflects the higher tube inlet velocities due to the fact that only about one third of the tube sheet area is free flow area (tube area). Simulations using the inertial pressure drop relationship rather than Darcy’s law were found to predict more uniform flow distributions across the inlet header tube sheet. Static pressure distributions were also found to correlate well with flow reversal and hence flow separation. Simulations using LES confirmed the RANS modelling results and


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extended data by showing that flow vortices are spread widely over the tube sheet and are not simply restricted to the two large vortices generated by the flow off the heat exchanger shell. Although only one solution of asymmetric flow patterns is shown, mirror imaged solutions must exist as there is no flow feature which forces one solution in preference to the mirror imaged one. As operating plants go through cycles of different mass flows and will also suffer blockages of some tubes, a range of asymmetric flow patterns will result, that is, there is no uniqueness of flow patterns. This variation in flow behaviour may well explain the difficulty of indentifying clear evidence of preferred areas of wear/metal loss thus leaving the technique of reducing flow angle into tubes as the most promising means of reducing flow related wear.

NOMENCLATURE

Cx constant in Darcy law g gravitational constant k turbulent kinetic energy p pressure Sij mean strain rate tensor ui , uj mean velocity in tensor notation ux mean velocity in the direction of the

tube axis ' 'i juu temporal average of fluctuating

velocities xi , xj coordinates in tensor form x, y, z in direction of tube axis, normal to tube

axis and pass separation baffle, normal to tube axis and parallel topass separation baffle

density dynamic viscosity ν, νt molecular and turbulent kinematic

viscosities specific dissipation rate ij mean vorticity tensor

REFERENCES

1. Bird RB, Stewert WE, Lightfoot EN (1960). Transport Phenomena. Wiley, New York, 5:154-155.

2. Bremhorst K, Lai JCS (1979). The role of flow characteristics in corrosion-erosion of tube inlets in the inlet channel of shell and tube heat exchangers. Wear 54(1):87,100.

3. Bremhorst K, Flint PJ (1988). A decade of progress in computational fluid mechanics for solution of industrial problems. Proceedings

Mech 88-Thermodynamics Conference, I.E. Aust., Brisbane, 8-13 May.

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APPENDIX

GRID REFINEMENT "WITH TUBES" SIMULATIONS

In this Appendix a summary of the main results for three grids using the "with tubes" approach is reported. The characteristics of the three grids are shown in Table 2. Grids A and B were generated directly in Gambit, whilst Grid C was generated from Grid B by refining the grid 0.24m upstream and 1.16m downstream of the tube sheet.

Table 2 Grids investigated for "with tubes" simulations.

Grid Nodes (number)

Header (mm)

Tube sheet

surface (mm)

Tube Axial(mm)

A 2.48 x 105 20 7.5 10

B 4.45 x 105 10 7.5 10

C 1.2 x 106 10 3.75 5

Fig. 28 shows contours for flow angle 10 mm upstream of the tube sheet for Grids A, B and C. As can be seen all grids show the main aspects of flow at the tube sheet, but there is a change with Grid B and Grid C. Grid C uses a finer grid around the tube sheet and in the tube entrances and this finer grid shows a better resolution of the very high flow angles on the tube sheet itself. Fig. 29 shows graphically the flow angles 10 mm upstream of the tube sheet and across the tube sheet at 0.278 m from pass baffle. The distance from the pass baffle to the shell at the centre of

the header is 0.556m, so this is halfway or between tube rows 6 and 7. The results for all grids are very similar, but Grids A and B show more scatter than Grid C. Fig. 30 shows the static pressure along the header axis at approximately the header centre line. The pressures from Grids A, B and C are similar. These results would suggest that all grids are resolving the asymmettry in the flow, but Grid C is the better grid and in this work, the “with tubes” simulations used grid C.

Grid A

Grid B

Grid C

Fig. 28 Flow angle relative to tube axis “with tubes” case, 10 mm upstream of tube sheet at rated feed flow rate of 1640 m3.hr-1.


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Fig. 29 Flow angle relative to tube axis “with tubes”

case, 10 mm upstream of tube sheet, 0.278mm from pass baffle and across the tube sheet at rated feed flow rate of 1640 m3.hr-1.

Fig. 30 Static pressure along header axis and at a distance of 0.278mm from pass baffle at rated feed flow rate of 1640 m3.hr-1.

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