HEAT EXCHANGER DESIGN PROJECT

Chinedu Charles Isiadinso

August 17, 2015

Contents

1 INTRODUCTION 2

2 DESIGN BRIEF 2

3 THEORY 23.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.2 Design Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.3 Heat Transfer Rate, Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.4 Total Surface Area, Atotal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

3.4.1 Overall Heat Transfer Coe�cient, U . . . . . . . . . . . . . . . . . . . . . 3

4 METHOD 4

5 RESULTS & CALCULATIONS 55.1 Numerics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

5.1.1 Mesh Refinement Study . . . . . . . . . . . . . . . . . . . . . . . . . . . 55.1.2 Inlet Turbulence Conditions . . . . . . . . . . . . . . . . . . . . . . . . . 8

5.2 2D Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95.2.1 Pipe Spacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95.2.2 Angle of Attack . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105.2.3 Reverse Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

5.3 3D Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135.3.1 Creating the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135.3.2 Reynold’s Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145.3.3 Total Surface Area, Atotal . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

6 ANALYSIS 156.1 Contours & Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

6.1.1 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156.1.2 Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156.1.3 Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

6.2 Pipe Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176.3 Boundary Layer & Pipe Sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176.4 Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

7 CONCLUSION 17

1

1 INTRODUCTION

This report will look at designing a cross flow heat exchanger to meet a design brief. Itwill look at some useful calculations before the CFD simulation process, the CFD simulationprocess and analysis of results gotten from the CFD process.

2 DESIGN BRIEF

A cross flow heat exchanger is needed for a building’s heating system. The heat exchangerwill be supplied with oil, at 55oC (548.15oK), from a combined heat and power plant, andneeds to be capable of providing 0.025m3

/s of water at 55oC (328.15oK).

3 THEORY

3.1 Overview

A heat exchanger is an equipment used to transfer heat from one fluid, at temperature T1,to another at temperature T2. The temperature di↵erence is key to the operation of the heatexchanger. Heat exchangers can be classified by their:

1. Transfer Processes

2. Geometry of Construction

3. Heat Transfer Mechanism, and

4. Flow Arrangement

we are interested in the flow arrangement, specifically the cross flow system.

3.2 Design Process

The goal of a heat exchanger, as stated above, is to transfer heat between two or more flowingfluids. This implies that there will be a change in temperature between the heat exchangerinlet and outlet.

Values of importance in the design process are; the relationship between the inlet, TIN, andoutlet, TOUT, temperatures, the overall, U, and individual, Cp, heat transfer coe�cients, andthe heat transfer rate, Q, for the fluids involved (in this case, oil and water).

3.3 Heat Transfer Rate, Q

Heat transfer rate is the rate of heat energy transferred through a surface area. This givesthe amount of heat transferred between the oil in the pipes and the water, it is assumed thereare no heat losses between the pipes and the oil, i.e. the pipe walls are at 548.15oK.

2

The design brief above, states the required outlet temperature is 328.15oK, and, if waterat the inlet is taken to be at room temperature (298.15oK), then the heat exchanger has toachieve a change in temperature, 4T, of 30oK. 4T is given as:

4T =Q

Cp ⇥ m

(1)

We know the required 4T, the heat transfer coe�cient, Cp, of water (4183W/(m2 ⇥K)) andthe mass flux, m (0.025m3

/s). Therefore, equation (1) can be rearranged to get the requiredheat transfer rate, Q.

Q = 4T⇥ Cp ⇥ m

Q = 30⇥ 4183⇥ 0.025 = 3137.25W

3.4 Total Surface Area, Atotal

With heat exchangers, the greater the contact area between the fluids, the greater the heattransferred. In this case, water is flowing along the surface of cylinders, so working out thesurface area of each cylinder and summing up will give the total contact surface. A better wayto go will be to relate the calculated heat transfer rate to the total surface area, i.e. use theheat transfer rate, Q, calculated in 4.1 to find the required total surface area to achieve thedesign temperature.

Total surface area, Atotal, is related to Q via the overall heat transfer coe�cient, U, and isgiven as:

Atotal =Q

U⇥4TLM

(2)

Where 4TLM , the log mean temperature di↵erence between the inlet and outlet, is:

4TLM =4TA �4TB

ln4TA � ln4TB

(3)

Where 4TA is the temperature di↵erence between the fluids at the inlet, and 4TB is thedi↵erence at the outlet. 4TLM gives a logarithmic average of the temperature di↵erencebetween the heat exchanger inlet and outlet. A large 4TLM means large heat transfer.

3.4.1 Overall Heat Transfer Coe�cient, U

The overall heat transfer coe�cient depends on the fluids and transmission material, andtheir individual properties. To find the overall heat transfer coe�cient, U, the individual heatcoe�cients of oil and water, and the resistance of the pipe material are needed. U is given as:

1

U⇥ A

=X 1

h⇥ A

+X

R (4)

Where R is the thermal resistance in the pipe and is given as:

R =x

kA

(5)

Where A is the total area of the heat exchanger, x is the wall thickness and k is the thermalconductivity of the pipe material. Assuming a really thin pipe (x < 0.0005m), then R ⇡ 0.Therefore:

1

U⇥ Atotal

=1

hoil ⇥ Apipes

+1

hwater ⇥ Aheatexchanger � Apipes

We need an approximate value for Atotal so we can take an approximate value for U.

3

U = 60�300W/m

2K ([9], heavy oils & water) and 4TA = 250oK and 4TB = 220oK, 4TLM

can be approximated as:

4TLM =30

ln 250� ln 220= 234.68oK

and thus Atotal, for U = 60W/m

2, is

Atotal =3137.25

60⇥ 234.68= 0.222m2

and, for U = 300W/m

2,

Atotal =3137.25

300⇥ 234.68= 0.04456m2

Therefore Atotal ⇡ between 0.222m2 and 0.04456m2.

4 METHOD

The CFD simulation process was done using Ansys workbench starting with a very simple2D model, figure 1. The model, a 1m⇥ 0.2m flat plate, consisted of three pipes and symmetryboundary conditions at the top and bottom of the plate, an inlet, to the left, and an outlet, tothe right.

Figure 1.

Next, the various boundaries where named using Named Selections. The pipe walls wereset a pipe walls, the inlet and outlet edges as inlet and outlet respectively and the top andbottom walls as symmetry (this means the walls are infinitly long long the y-axis upwards anddownwards).

Then, the finished part had to be meshed. To start o↵, a mesh size of 0.005m (a meshrefinement study is done in section 5 below) was chosen and the mesh generated. Figure 2,below, shows the mesh at 0.005m.

4

Figure 2.

The final settings where made in fluent. The viscous model was set to k � ✏, because of theturbulent nature of the flow, the fluid was specified as water, and boundary conditions, for theinlet and pipes, where set. The inlet velocity and temperature where set to 0.0125m/s and298.15ok respectively, and the pipe temperature set to 548.15oK. Fluent was also set to solvefor the internal energy of the fluid.

Before the calculations could be performed, the tolerance was lowered to 0.00001 and thecalculation was set to perform 1000 iterations, at which point convergence would be beenreached.

After the calculations, values relating to the mass fluxes, total heat transferred etc., whereextracted from fluent using Fluxes under Reports.

5 RESULTS & CALCULATIONS

5.1 Numerics

5.1.1 Mesh Refinement Study

The first step, towards refining the design, was to perform a mesh refinement study. Themesh refinement study provided an reasonable guide to choosing a mesh size that would giveaccurate results in an e↵ective time frame. A very fine mesh (small element size) would veryaccurate result approximations at the cost of very high processing power, so the most e�cientcase would be a mesh small enough to give results within an acceptable accuracy/tolerancelevel, but big enough to run with very little computing power and time requirements.

5

Figure 3.

Figure 3 shows the mesh at 0.05m, cells around the curves, especially the center circle, arepolygonal (instead of round), because the cell size is too big to accurately define them. Figures4 and 5 show the mesh at 0.002m and 0.001m respectively. Although the 0.001m mesh is finer,it only gives a 2% increase in accuracy, compared to the 56% increase from the 0.05m mesh.

Figure 4.

Figure 5

Before the analysis could run, the boundary conditions had to be set. The inlet temperaturewas set to room temperature and the outlet temperature was set to 548.15oK. The inlet flowvelocity, vI, also had to be set. To do this, vI was calculated by rearranging equation (6), below,and solving for vI when volumetric flow rate, V = 0.025m3

/s (from the design brief), and the

6

area of the inlet, Ainlet,= 0.2m2 (the inlet was assumed to be 1m thick, and 0.2m).

V = vI ⇥ A (6)

This gives an inlet velocity of 0.125m/s. The mesh refinement study was performed for valuesbetween 0.05m and 0.001m, at increments of 0.01m, between 0.01m and 0.05m, and 0.001mbetween 0.001m and 0.009m. Table 1, below, shows the values for outlet temperature, TOUT ,for di↵erent mesh sizes, where x is mesh size in meters.

MESH REFINEMENT

x(m) TIN(K) m kg/s Q (W) 4T (K) TOUT (K)0.05 298.15 25 309775 2.97 301.120.04 298.15 25 308925.4 2.96 301.110.03 298.15 25 401368.64 3.85 302.000.02 298.15 25 533509.75 5.11 303.260.01 298.15 24 682983.54 6.67 304.820.009 298.15 25 687097.2 6.58 304.730.008 298.15 25 706218.3 6.77 304.920.007 298.15 25 701844.6 6.72 304.870.006 298.15 25 703599.57 6.74 304.890.005 298.15 25 704299.1 6.75 304.900.004 298.15 25 699115.5 6.70 304.850.003 298.15 25 704136.1 6.75 304.900.002 298.15 25 708133.1 6.79 304.940.001 298.15 25 724694.8 6.94 305.09

Table 1.

From table 1, 4T can be seen to be converging at ⇡ 7oK as the mesh gets finer, however,after 0.002m, the calculation times increase significantly, which indicated increased processingpower. However, from graph 1, the graph is levelling o↵ and can be expected to give relativelysimilar temperature values at mesh size 0.0005m (for example) as at 0.002m; therefore, it isreasonable to use a mesh size of 0.002m.Graph 1, below, illustrates the levelling out of thetemperature values.

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Graph 1: TOUT(K) against mesh size (m)

5.1.2 Inlet Turbulence Conditions

Another test of convergence was to change the inlet turbulence conditions; the temperatureresults where not expected the change significantly. Table 2 and graph 2 below show the resultsconverging as turbulence intensity increases. Where % is turbulence intensity.

INLET TURBULENCE

% TOUT(K)1 306.922 305.953 305.44 305.095 304.96 304.777 304.688 304.619 304.5710 304.5311 304.512 304.4713 304.4514 304.4315 304.42

Table 2.

8

Graph 2: Outlet Temperature, TOUT(K) against Turbulence Intensity %.

5.2 2D Designs

Confident that fluent was generating accurate and reliable results, the original simple designcould be modified to achieve requirement set out in the design brief.

5.2.1 Pipe Spacing

The 1st variable, in the design process, was the pipe spacing. A pipe spacing study wasperformed on five di↵erent variations of a simple design (figure 6 above), all with 3 pipes ofradius 0.075m. Graph 3, shows a plot of the pipe oulet temperature against spacing.

Graph 3: Outlet Temperature, TOUT(K) against Pipe Spacing (m).

The shape of Graph 3 indicates, generally, the smaller the pipe spacing, the better the theheat transfer, however, there is a dip in the curve, which indicates that pipe spacing is not theonly factor a↵ecting heat transfer. Figures 6 and 7, show the geometry at spacings 0.15m and0.35m respectively.

9

Figure 6

Figure 7

5.2.2 Angle of Attack

Another factor, a↵ecting heat transfer, is the angle at which the inlet flow engages with thepipes. Various resources [2] on heat exchanger design quote 30o as the angle to set the pipes atfor maximum e�ciency. Working on an even simpler model than the one used in 5.2.1 above,with 2 pipes of radius 0.03m, we can investigate the e↵ect the angle of attack has on heattransfer.

Figure 8

Figure 8, above, shows the pipe arrangement at 30o. Graph 4, below, shows the outlet temper-ature for di↵erent angles of attack. We can see that, the best heat transfer occurs at 0o mark,but at 30o we have a similar value.

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Graph 4: TOUT(K) against Angle of Attack (o)

To explain this, we examine the velocity contours of the flow in 30o and 50o cases (figures 8.1and 8.2 below). In the 30o case, flow over the top pipe can be seen to be interacting with theflow over the second pipe a lot more than in the 50o case; these interactions aid heat transfer.Therefore, a design with pipes at an angle around 30o would be ideal.

Figure 8.1

Figure 8.2

5.2.3 Reverse Flow

Reverse flow occurs when flow of fluid changes direction and flows opposite to it’s predefined,or desirable direction. When running the pipe spacing study, it was discovered that, at a certaindistance from the inlet and outlet, reverse flow began to occur. Reverse flow occurs when flowis fully turbulent and has not had adequate time to adjust after coming in contact with anobstacle.

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Case 1

The design in case one is the simple first case used for the mesh refinement study in 5.1.1above. Using a mesh size of 0.002m, 1000 iterations where calculated, at turbulence intensity5, and the temperature at the outlet was worked out using equation (1) in section 3.3 above.Design 1 gave an outlet temperature of 304.94oK.

Case 2

In case two, the number of pipe was increased from 3 to 9, and the pipe spacing, angle ofattack, and pipe radii where changed. This design had an outlet temperature of 309.29oK.

Figure 9

Case 3

Case 3 built on case 2, with more pipes being added, even more variation in pipe radii,and smaller gaps between the pipes. The outlet temperature for this design was 352.11oK,23.96oK more than the required outlet temperature specified in the brief; this gives room fordiscrepancies that my arise when the part is extruded to 3D (for example, the 3D case will nothave symmetry conditions at the walls and will have the walls set at room temperature). Case3 will be the main design going forward.

Figure 10

The design in case 3 pulled together everything discussed in the above sections. The pipespacing is very small, to get as much interaction as possible, there are no empty spaces at thetop an bottom of the heat exchanger, where water could avoid the pipes, and there are smallerpipes in spaces between the larger ones to increase the maximum total surface area, and thusincrease heat transfer. Also, there a huge amount of the heat exchanger left over for turbulentflow to settle such that reverse flow either does not occur at the outlet or is kept to a minimum.

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5.3 3D Design

Having achieved the design brief in 2D, the next step was to run the simulation in 3D.

5.3.1 Creating the Model

To create the model, the geometry was thin extruded, in design modeller, and, to saveprocessing time, the thickness was set to 0.1m. This meant that the inlet velocity had to berecalculated, and the new vI(1m/s) had to be set as the boundary condition in fluent. Aftergenerating the 3D part and defining the inlet, outlet walls and pipes, a 0.002m mesh wasgenerated and the calculations where set up in fluent and run. Figure 11 shows the meshed 3Dpart.

Figure 11

Figure 12, below, shows the highlighted section from figure 11. This shows how detailed themesh is, especially at the spaces between the pipes.

Figure 12

It can be seen that the mesh is not small enough, in the pipe spacings, to give the best values,especially where there is only one cell between the pipes. A finer mesh was tried, to betterdescribe the spaces, but the meshing process ran for too long, so in an attempt to get a bettermesh, the thickness of the 3D part was reduced further to 0.05m. Figure 13 shows a zoomedin image of the refined mesh (0.0015m) for the part.

Figure 13

13

With the 0.002m mesh, the outlet temperature for the 3D model was 343.44oK.

5.3.2 Reynold’s Number

To understand the nature of the flow through the heat exchanger, we need to work out theReynold’s number. At Re< 2300, flow is laminar, at 2300 <Re< 4000, the flow is transient,and at Re> 4000 we have turbulent flow[3]. In our design, the flow is expected to be turbulent,thus Re> 4000. For a heat exchanger, Reynolds number is given as [4]

Re =⇢vDH

µ

(7)

Where the hydraulic diameter of the pipe, DH, is given as:

DH =4A

P

Where A is the cross-sectional area of the heat exchanger and P is the wetted perimeter.⇢ = 997.04, V= 2m/s (from equation (6) at thickness= 0.05m),µ = 0.001003kg/m�2, and

DH =4⇥ 0.05⇥ 0.25

2⇥ 0.05 + 0.25=

1

12

Therefore, Reynolds number for the 3D design is:

Re =997.04⇥ 2⇥ 1/12

0.001003= 165676.3

Re> 4000, therefore the flow is turbulent, as expected.

5.3.3 Total Surface Area, Atotal

In section 3.4, the total surface area to achieve the design brief was approximated as 0.222m2.This section will compare the theoretical results with the result received experimentally.The design in case 3 consists of a pattern of pipes of di↵erent radii. There are 14 pipes ofradius 0.03m, 2 of radius 0.017m, 12 of radius 0.016m, 2 of radius 0.015m, 12 of radius 0.013m,and 12 of radius 0.01m. Total surface area for a cylinder is given as:

Atotal = 2⇡r(r + h) (8)

The pipes are 0.05m long, therefore, Atotal can be calculated for each case using equation (8).Table 3 below shows the total surface area for each pipe radius. Comparing the result herewith theoretical Atotal,⇡ between 0.222m2 and 0.04456m2, we can see the design should anddoes fit the design brief from a mathematical point of view.

14

r (m) No. Atotal (m)

0.03 14 0.2111150260.017 2 0.0143130960.016 12 0.0796205240.015 2 0.0122522110.013 12 0.0617511450.01 12 0.045238934

Total = 0.4243m2

Table 3.

6 ANALYSIS

This section includes analysis of the performance of case 3’s 3D design.

6.1 Contours & Vectors

6.1.1 Temperature

Figure 14 shows the variation of temperature between the inlet and outlet. As expected, thetemperature is highest at the pipe walls and there is an increase in temperature from the inletto the outlet, which shows the water is getting heated.

Figure 14

6.1.2 Turbulence

The turbulence contour gives a visual representation of nature of the flow. The turbulentenergy of the flow is high at the top and bottom pipes and at the points (top and bottom)where the flow exists the pipe system, due to vorticies formed by the unsteady separation ofthe flow around the pipes (von Karman vortex sheet or vortex shedding [5]). These vorticesare undesirable as they set up cross wind forces, which lead to vibrations. The e↵ect can bereduced by using oval pipes, instead of circular ones, or by fitting fins down stream from thepipes. In case 3, it would not be possible to fit fins on the pipes due the the pipe spacing,using slightly more oval or aerofoil shaped pipes could be possible. Oval pipes will be morestreamline and, therefore, allow flow to pass around easier, thereby avoiding (or minimizing)the vortices.

15

Figure 15

The flow can then bee seen to settle as it approaches the outlet.

6.1.3 Velocity

Figures 17.1 and 17.2 below show the velocity vector of the whole heat exchanger and azoomed in section, respectively. Zooming in on figure 17.1 (figure 17.2), we can see the flowaround the cylinders is fast, and without and reverse flows.

Figure 17.1

Figure 17.2

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6.2 Pipe Temperature

One assumption made early on in the design process, was that the pipes had constanttemperature of 548.15oK; this is very unlikely to be the case. Oil is supplied to the heatexchanger at 548.15oK, it is unknown what material the heat exchanger is made of, and thus,impossible to work out the thermal conductivity of the pipes. Also, as water flows through theheat exchanger, the oil looses heat to the water, and thus the temperature of the oil begins todrop a certain distance from the inlet. However, to account for losses in temperature to thesurrounding was also ignored, the outer walls where set to room temperature when during the3D analysis.

6.3 Boundary Layer & Pipe Sizes

A boundary layer is a region around a wall where the e↵ects of surface friction are significantenough to slow down the flow; at the wall boundary, the flow velocity is zero. The e↵ects of theboundary layer where ignored during the design process and thus it is possible that some of thepipes chosen are too small to e↵ectively flow oil through. In reality, the type and properties ofthe oil (e.g. thermal resistance) would be known, and study would have been done for di↵erentpipe sizes [6][7][8].

6.4 Cost

The design brief does not address the financial restrictions of the heat exchanger and thus,it is possible an equally e�cient heat exchanger could be manufactured for a fraction of thecurrent design. For example, case 3 uses di↵erent sized pipes, but, because the heat transferredis more of a function of the total contact area (i.e. total surface area of the pipes), then a designwith the same sized pipes could be designed could be designed to meet the design brief.

7 CONCLUSION

In conclusion, a heat exchanger capable of heating water at room temperature to 55oC(328.15oK) has been successfully designed using CFD simulation. However, although the designhas been analysed and adjusted for any discrepancies between the CFD approximation and thereal world part, as stated in the analysis, the design brief lacked a number of real worldspecification, which would have lead to a more accurate design, and as such there may beerrors in the calculations, which could prove costly.

References

[1] ”Heat Transfer Coe�cient”. Wikipedia. Wikimedia Foundation, 11 May 2014. Web. 13 Nov.2014.

[2] Sparrow, E. M., Young I. Cho, John Patrick. Abraham, and John M. Gorman. ”Advancesin Heat Transfer”. Burlington: Elsevier Science, 2012. Print.

[3] ”Laminar, Transitional or Turbulent Flow”. Laminar, Transitional or Turbulent Flow. N.p.,n.d. Web. 11 Nov. 2014. http : //www.engineeringtoolbox.com/laminar � transitional �turbulent� flow � d577.html.

[4] ”Reynolds Number.” Reynolds Number. N.p., n.d. Web. 11 Nov. 2014. http ://www.engineeringtoolbox.com/reynolds� number � d237.html.

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[5] ”Vortex Shedding.” Wikipedia. Wikimedia Foundation, 24 Oct. 2014. Web. 12 Nov. 2014.http : //en.wikipedia.org/wiki/V ortexshedding.

[6] Douglas, John F. ”Chapter 6 (Section 6.6).” Fluid Mechanics. Harlow, England: Pear-son/Prentice Hall, 2005. 215-16. Print.

[7] Douglas, John F. ”Chapter 11 (Section 11 - 11.7).” Fluid Mechanics. Harlow, England:Pearson/Prentice Hall, 2005. 403-14. Print.

[8] Rogers, G. F. C., and Y. R. Mayhew. ”Properties of Fluids.” Engineering Thermodynamics:Work and Heat Transfer. Harlow, Essex, England: Longman Scientific & Technical, 1992.157-8. Print.

[9] ”Overall Heat Transfer Coe�cients.” Overall Heat Transfer Coe�cients — Blackmonk En-gineering. N.p., n.d. Web. 12 Nov. 2014. http : //blackmonk.co.uk/2009/10/22/overall �heat� transfer � coefficients/.

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