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MIXED CONVECTION IN A NARROW RECTANGULAR CAVITY WITH APPLICATION

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MIXED CONVECTION IN A NARROW RECTANGULAR CAVITY WITH APPLICATION Powered By Docstoc
					 The Eleventh International Symposium on Transport Phenomena                                                                         No. 20
 ISTP-11, Hsinchu, Taiwan, November 29 - December 3, 1998




                MIXED CONVECTION IN A NARROW RECTANGULAR CAVITY WITH
                  APPLICATION TO HORIZONTAL MANTLE HEAT EXCHANGERS



                               Gary Rosengarten, Graham L. Morrison and Masud Behnia
                                   School of Mechanical and Manufacturing Engineering
                                            The University of New South Wales
                                             Sydney NSW, 2052, AUSTRALIA
                             Facsimile: 61 2 9663 1222, Email: z2202633@student.unsw.edu.au




KEY WORDS: Mantle heat exchanger, solar water heater, PIV, CFD



ABSTRACT                                                                  The mantle heat exchanger is the most effective of the three
  The heat transfer process in horizontal mantle heat exchangers       types as it combines low manufacturing costs with high heat
used in solar water heaters has been investigated using a              transfer rates; leading to high system efficiencies (Furbo, 1993).
rectangular cavity as a simplified geometry. Using particle            The horizontal mantle heat exchanger, coupled to a
image velocimetry (PTV) the flow field in the centre-plane of          thermosyphon driven flat plate collector, is the preferred design
the rectangular cavity has been visualised Three dimensional           for domestic solar water heaters in many countries (e.g.
flow simulations were performed using a commercial CFD                 Australia, Greece, Korea). The inlet to the mantle is located at
package. The impinging jet formed by the inlet flow directed           the bottom of the tank to avoid reverse circulation at night
towards the back wall was found to produce localised                       Unlike conventional heat exchangers, the performance of a
turbulence in the cavity, with an inlet Reynolds number as low         mantle heat exchanger must be quantified in two ways. The
as 360. This turbulence was found to effect the flow field and         first, as for any other heat exchanger, is the amount of heat that
heat transfer in the cavity when the inlet Reynolds number was         is transferred into the tank. The second is the vertical position in
above 1200. It is shown that, with the boundary conditions used        the tank where the heat is transferred, as the efficiency of a
in this study, most of the heat transferred was in the bottom half     SDHW system is affected by stratification in the tank (Sharp,
of the cavity. This is not the ideal situation for optimisation of     1979).
solar water heating systems.                                              In order to optimise the system in terms of these two factors,
                                                                       an understanding of the flow field in the mantle is needed. The
                                                                       flow into the mantle is normal to the tank wall and thus forms a
INTRODUCTION                                                           low Reynolds number, submerged impinging jet (Webb and
  The most common design for domestic solar water heaters              Ma, 1995). The flow inside the mantle is affected by a
(SDHWs) involves the use of a heat exchanger to transfer heat          combination of forced flow from the collector fluid and
from the hot collector fluid to the water in the storage tank. If      buoyancy-induced flow arising from the temperature difference
the collector fluid is separated from the potable water in the         between the inlet fluid and the tank wall. The combination of
storage tank, and freeze and anti rust components can be added         mixed convection in the mantle, the stratification in the tank,
to the collector circuit As well as this, the collector loop           and the geometry, makes it impossible to analytically solve the
doesn't have to comply with the pressure design restrictions to        problem.
which the storage tank is subject.                                        Currently, it is impractical to model the entire mantle heat
  Currently there are three categories of heat exchangers used in      exchanger numerically. It is extremely computationally
SDHWs.                                                                 expensive to take into account the time dependant nature of both
1. Immersed coil or immersed tubes that have the heat                  the flow in the annulus and the natural convection in the tank. In
     exchanger installed inside the storage tank (Mertol et al,
     1981).
2. External shell and tube heat exchanger with collector fluid
     pumped though the tubes, and the tank water (driven by                                      Storage
     natural convection) flowing through the shell (Dahl and                                     tank
     Davidson, 1997).
3. The mantle heat exchanger - in either its vertical form
     (Shah and Furbo, 1997) or the horizontal form (Morrison et
                                                                           Potable
                                                                           water
                                                                                       JTo
                                                                                                                     ^
                                                                                                               Prom Man tie heat
                                                                                     collector                collector
     al, 1997) - consists of a narrow annular jacket around the
     storage tank in which the collector fluid flows (see Fig. 1).                   Figure 1: Schematic of mantle heat exchanger.



                                                                     126
this study we model only the flow in the annulus, with wall              camera and down-loaded to a PC using a Scion LG3 capture
boundary conditions corresponding to the stratified tank                 card and Scion Image software. The image software's particle
temperature distribution. This will allow us to understand what          centre finding utility was used to find the particle centres and a
affects the flow and heat transfer in the tank under a wide              C program was used to trace particles and find velocities.
variety of conditions.
  Due to large ratio of tank diameter to mantle gap width the
effect of wall curvature is minimal. Therefore the flow and heat        NUMERICAL MODEL
transfer in the annulus can be approximated to that in a                  The commercial CFD package Fluent V4.4 was used to
rectangular cavity by assuming that there is a vertical plane of        simulate the flow and heat transfer. The Boussinesq
symmetry through the cylinder Nasr et al (1997). Half of the            approximated equations were used in the comparison with
annulus is then effectively unwrapped to form a rectangular             experiments. Both laminar and turbulent flows were simulated.
cavity whose height is equal to half the mean circumference of          The RNG k-e model, with no wall function, was used to
the annulus. The advantage of this is that it is easier to visualise    simulate turbulent flow. The standard k-e model tends to
the flow experimentally, and a rectangular geometry is simpler          overestimate the turbulence in high gradient areas like
to model numerically.                                                   stagnation points (Fluent, 1997). As the mantle flow involves an
  In this paper we compare numerical simulations of flow and            impinging jet, the RNG k-e model was used instead For low
heat transfer in the rectangular cavity with experimental data          Reynolds number flows, like those that occur in the gap
obtained using particle image velocimetry (PIV).                The     (mantle), a wall function is inadequate. Instead the grid was
comparisons allow us to determine the validity of the numerical         made very fine near the walls and the equations were solved all
model that is used to assess the efficiency of the mantle heat          the way into the viscous sublayer, ie the two-layer model. The
exchanger.                                                              two-layer model divides the computational domain into two
                                                                        distinct regions, a fully turbulent region and a near wall
                                                                        viscosity-affected region, based on the turbulent Reynolds
EXPERIMENTAL SETUP                                                      number. For the lower two flow rates examined in this study,
  The rectangular cavity (0.48x0.23m) used in the experiments           the whole flow domain was in the viscous effected region due to
consists of 10mm thick Plexiglas front and sidewalls, and a             the low turbulence levels combined with the narrow gap. The y*
copper back wall (Fig. 2). The gap width was 10mm and the               values for the cell closest to the walls were less than 2 for most
inlet and outlet diameters were both 15mm. The temperature of           of the cavity.
the back wall was controlled by the flow of temperature                   The numerical boundary conditions consisted of an inlet
controlled water through two independent channels connected             temperature and velocity obtained from experiments, a
to the back of the wall. Twenty-seven calibrated type T                 temperature distribution on the back wall obtained from
thermocouples were embedded in the wall with their tips                 experiments, with all the other walls considered adiabatic. It is
approximately 2mm from the front surface. A thermocouple                estimated that losses to the environment are less than 2% of the
was installed at the centre of both the inlet and outlet pipes,         total heat transfer. The inlet turbulence was set to 0.5%
about 20mm from the front wall of the cavity. Temperatures              considering the low velocity, laminar inlet conditions.
were electronically recorded on a PC via a YEW hybrid
recorder.
  Inlet water was supplied from a pumped, temperature-                   RESULTS
controlled, closed loop water source, so that flow rate and inlet        Numerical validation
temperature into the channel could be controlled The flow rate             The effect of the grid and the use of the turbulence model on
was measured by a calibrated turbine flow meter and recorded             the outlet temperature at the centre of the outlet pipe are shown
on a PC.                                                                 in Fig. 3. The grids had varying resolution, bunching and
  The PTV (Dahl et al, 1995) measurements used a light sheet             skewness. The difference between the laminar and the turbulent
that was produced by a 22mW HeNe laser and a cylindrical                 models is decreased as the grid is improved. Solving the
lens. The front of the cavity was divided into four quarters for         equations on grid A, which had regions of high skewness,
PTV measurements. This viewing size allowed reasonable                   produced an anomaly. The turbulence changed the flow field to
resolution of the seed particles and adequate illumination from          such an extent that the overall heat transfer was greater for the
the light sheet. Plastic seed particles with diameters in the range      laminar flow case. The final grid used, grid E, shown in Fig. 4,
of 100-200nm, and specific gravity at 20°C of 0.99, were used.
Images were recorded with a Panasonic EZ1 digital video                        60
                                                                               5.8
                                                                               3.6                                   •   Laminar
                                                                               5.4
                                                                                                                     •   Turbulent
  Thermccotples
                                                                             ^ 5.2
                                                                             O



Temperature                                      Temperature
cortrolled                                       controlled water              48
water baths                                      source to simulate
                                  _5,.-.Teet     solar Ic                      4.4-


                                                                               4.2-


                                                                               4.0
                                                                                        Zl'41'71   15'32'53
                                                                                                      B
   Water
Cu plate
                           "Plexiglas front                                                                   Grid
                                    'Plexiglas spacer
                                                                                      Figure 3: Grid dependence for inlet Re = 1210.
           Figure 2: Schematic of experimental set up.


                                                                       127
                                                                                  o.tt
                                                                                  0.10

                                                                                  0.08

                                                                                  O.OB
                                                                                                                                          Lamninar
                                                                                  0.07                                              -•--- Laminar Boussinesq
                                                                              £. 0.06                                              -•••• Turbulent
                                                                              f > ° 05
                                                                                                                                   -•—Turbulent Boussinesq

                                                                              I 0.04

                                                                                  0.03

                                                                                  0.02
   Inlet                                                           Outlet         0.01
           Figure 4: The computational grid, E (front view).
                                                                                             3200    3400    3600     3800     4000    4200   4400    4600   4800
                                                                                                                    Heat Flux (W/ma)
was chosen as there was minimal change, in the outlet
                                                                              Figure 6: Heat flux as a function of height for inlet Re =1210,
temperature and in the heat flux as a function of height for both
                                                                              using different models.
the Re=1210 and Re=360 cases, relative to the previous grid.
  Points to note about this grid are; the higher density near the
inlet (left side) relative to the outlet; and the fact that the
maximum skewness (about 10°) is about half way between the                   numerical results show' that the flow in the outlet pipe is
inlet and outlet, where the gradients are very small.                        stratified and the stratification increases with increasing Re. The
  The effect of flow rate is examined in this paper for a 30°C               position of the thermocouple in the outlet pipe is known only to
inlet flow, and a stratified back wall from 20°C to 30°C. An                 about ±lmm, which accounts for about ±0.5°C uncertainty. The
example of a typical back wall temperature distribution                      error bars on the graph do not take this into account Future
measured from experiment is shown in Fig. 5. The mean                        experiments will incorporate an outlet mixer so that mean
distribution, averaged over the three vertical distributions, was            temperatures can be compared.
used as the wall boundary condition for the numerical
simulations.                                                                 PIV Measurements
  The effect of using the Boussinesq approximation on the heat                  The PIV procedure allows the determination of velocity
transfer is shown in Fig. 6. Although using the Boussinesq                   vectors and streaklines, as shown in Fig. 8. The streaklines were
approximation tends to over predict the heat transfer by, on                 obtained by averaging 60 frames at sampling intervals that
average about 2%, there is effectively no effect on the flow                 depend on the flow rate. For example, the top left part of Fig. 8
field. This means that the comparing important results - the                 used 3 frames a second while the corresponding section in Fig.
distribution of heat flux as a function of height - will be                  9 used 6 frames a second.
unaltered                                                                       Figure 8 shows the experimental and numerical flow field in
  Figure 7 shows how the net heat transfer rate varies as a                  the mid-plane of the gap for an inlet Reynolds number of 360.
function of the inlet Re. Heat transfer was calculated using the             The results from the laminar simulation are displayed, as there
mass flow rate and the temperature difference between the inlet              was negligible difference between the solutions with and
and the outlet water. A least squares second order curve is fitted           without turbulence. The flow direction and magnitude of the
to the data and the three numerical cases are also plotted. The              numerical results are in close agreement to the experimental
data show proportionality with Re0"3, which is the standard Re               results. There are no experimental velocity vectors in the top
proportionality in forced convective heat transfer.                          right hand corner as a minimal amount of the inlet flow entered
  The slight deviation of the numerical data from the                        the region.
experimentally measured data is most probably due to the
uncertainty in the position of the outlet thermocouple. The

                                                                                  250         D     Measurements
   225                                                                                        •     Numerical
                                                                                                    Least squares quadratic fit to meatun
   200-
                                                                                  200-
    175-

    1SO-

 fua
 — too-
                                                                                  100-
 1 7S :
    50-

    25-                                                                            50-

                                        —T—
                       22   23     24    25   2«    27   28   21   30
                                 Temperature (°C)
                                                                                         0          200       400            600      800      1000      1200
                                                                                                                        Re (inlat)
Figure 5: Typical temperature distributions in the back wall
measured experimentally. The inlet, outlet and middle correspond
to columns of 9 thermocouples in line with the inlet, outlet and              Figure 7: Heat transfer as a function of inlet Re, stratified 20-
middle of the wall respectively.                                                           30°C tank wall and 30°C inlet flow.



                                                                            128
                                                                             250




   0     50    100   150   200   250       300   350   400   450   5
                                                                                      50   100   150   200   250   300   350   400   450




                                                                                                               1    1 1 1
                                       I    3 5 3




                                                                             Figure 9: Flow in the mid plane and heat transfer for inlet
Figure 8: Flow in the mid plane and heat transfer for inlet                  Re=715, Tin=31°C and back wall stratified from 20-30°C.
Re=360, Tin=30°C and back wall stratified from 20-30°C.                      From top to bottom; a) streak lines obtained by averaging 60
From top to bottom; a) streak lines obtained by averaging 60                 video frames, b) velocity vectors obtained by using HV. c)
video frames, b) velocity vectors obtained by using PIV. c)                  velocity vectors obtained from turbulent numerical model, d)
velocity vectors obtained from numerical model, d) heat flux                 heat flux (W/m2) into the back wall obtained from numerical
(W/m ) into the back wall obtained from numerical model.                     model.



                                                                         Figure 9 shows that the inlet flow stream splits up just above the
  The main characteristics of the cavity flow are the entrapment         inlet Most rises to the top then slowly makes its way down to
of the inlet flow up the sidewall followed by the rapid fall of the      the outlet, while there is a lower recirculation zone that draws
flow until it reaches its thermal equilibrium level. As the              water in from the bottom left hand region of the tank. The
momentum of the flow takes the water above its thermal                   streaklines of Fig. 9 show that the turbulent region around the
equilibrium level, heat is lost from the upper level of the wall         inlet has increased relative to the Re=360 case. For this flow
above the inlet. This explains the negative heat flux in Fig 8d.         rate the laminar and turbulent heat flux values were within -1%
Also, even though the inlet flow is laminar, the jet impingement         of each other.
causes a small region of turbulence that is rapidly dissipated             Increasing the flow to 44 1/hr, the typical maximum flow rates
around the inlet. The turbulence is made visible by the smooth           in thermosyphon collector loops, the turbulence produced by the
streamlines being replaced by a speckled pattern near the inlet.         laminar impinging jet at the inlet becomes significant The
This localised turbulence was also noticed by using dye                  streaklines in Fig. 10 indicate a reasonably extensive region of
injection (Rosengarten et al, 1997).                                     turbulence around the inlet The two numerical velocity vector
  As the inlet flow rate is increased the flow tends to rise             plots show that there is a difference in the flow when a
rapidly to the top, not losing as much heat as the previous case.        turbulence model is used. In fact the laminar simulation docs



                                                                       129
                                                                                                                                                 T

                                                                            250 -i




                                                                                 0   SO   100   150   200   250   300   350    0
                                                                                                                              40     450   500




   Figure 10: Flow in the mid plane and heat transfer for inlet Re=1210, Tin=32°C and bade wall stratified from 20-30°C. From top to
   bottom (left to right);
        a) Streak lines obtained by averaging 60 video frames.
        b) Velocity vectors obtain by using P1V.
        c) Velocity vectors obtained from numerical model (laminar).
        d) Velocity vectors obtained from numerical model (turbulent).
        e) Heat flux (W/m2) into the back wall from laminar numerical model.
        f) Heat flux (W/m2) into the back wall from turbulent numerical model.



not capture the cavity flow features properly, as it indicates a        the three inlet flow rates. The heat flux for the Re= 360 and 710
region of slower moving water between the wall-bounded flow             cases showed negligible difference between the turbulent and
and the flow that picks up some of the recirculation. The centre        laminar models. Both the laminar and turbulent heat flux curves
of the recirculation zone in the laminar model is 0.123m from           are plotted for the Re=1210. These plots indicate a difference in
the left wall while in the turbulent model it is 0.085m. The            heat flux of up to about 5% at a height of 0.065m, even though
experiments indicate 0.08810.005.                                       the total heat transfer varies by less than 2%.
  Most studies of impinging jets have concentrated on the effect          The general trend of these plots is similar. Most of the heat
on local heat transfer, generally for cooling (see for example          transfer takes place in the bottom half of the cavity, which is not
Web and Ma, 1997). In the mantle, however, the impinging jet            ideal as it will degrade stratification in the storage tank. Ideally
forms a part of a larger flow field that is of interest The laminar     the inlet should be located at the top, but in practice this is not
inlet flow becomes turbulent near the inlet due to, most                used in thermosyphon systems as reverse circulation then occurs
probably, the effect of jet impingement. This localised                 at night An optimum location for the inlet needs to be
turbulence changes the heat transfer characteristics of the             investigated.
mantle heat exchanger. A numerical turbulence model is thus
needed to accurately predict the flow and heat transfer when the
inlet Reynolds number is in the order of 1200 or above.                 CONCLUSION
  As mentioned previously, the defining quantity for mantle               A rectangular cavity has been used to simulate the flow in a
heat exchangers is the heat transfer as a function of height. Fig.      mantle heat exchanger used in SDHWs. A combination of
 11 shows the heat transfer as a function of height obtained by         numerical modelling and experiments has allowed the
averaging the heat flux along the length of the cavity for each         determination of the flow field and heat flux in the rectangular
horizontal grid line on the back wall. Results are displayed for        cavity. Using PIV measurements, the flow field in the mid-




                                                                      130
                                                                                                          Re=360
                                                                                                          Re=710
                                                                                                            =1210 (Laminar)
                                                                                                          Re=1210 (Turbulent)
      500




                  .S> 0.10 -4
                   <D
                  IE 0.08 -J




                            -500
                                                500       1000      1500         2000    2500      3000     3500      4000      4500     5000
                                                                   Heat Flux (W/m2)
                                           Figure 11: Heat flux as a function of height for different Reynolds numbers.



              plane of a rectangular cavity has been determined for an inlet
                                                                                         Furbo, S. (1993) Optimum design of small DHW low flow
              flow temperature equal to the top temperature of a stratified
  to          back wall.                                                               solar systems, ISES Solar World Congress, 1993, Budapest,
                                                                                      Hungary.
                It was shown that turbulence production due to inlet jet                 Fluent Inc. (1997), Fluent 4.4 User's guide Volume 4.
             impingement onto the back wall of the cavity effected the flow
                                                                                         Mortal, A., Place W., Webster, T. and Greif, R.(1981)
             and heat transfer when the Reynolds number was 1210. For the             Detailed loop model analysis of liquid solar thermosiphons with
             lower Reynolds number flows (Re=360 & 710) the effect of the             heat exchangers, Solar Energy, vol. 27, pp. 367-386.
             turbulence was minimal.
                                                                                         Morrison G. L., Nasr, A., Behnia, M. and Rosengarten, G.
                The important quantity to measure in mantle heat exchangers           (1997) Performance of Horizontal Mantle Heat Exchangers for
             is the heat flux as a function of height. It has been shown that         Solar Water Healing Systems, presented at ISES 1997 Solar
             most of the heat is transferred in the bottom half of the tank,          World Congress, Taejon, Korea
             which is not ideal for solar water heaters.
                                                                                        Nasr, A. Morrison G. L and Behnia M. (1997).
  0             The next stage of this study will involve the determination of       Computational Study of How and Heat Transfer Characteristics
 id         a correlation for the heat flux as a function of height, that may        of Annular and Vertical Cavities. CASCM'97, Procs of 2"
 -s         be used in solar heating system simulations like TRNSYS.                 Sypm on Comp. Mcch.
 in         Further investigations will look at means of controlling the heat           Rosengarten, G., Morrison, G. and Behnia, M., Understanding
            flux distribution in the mantle to better promote stratification in      Mantle Heat Exchangers used in Solar Water Heaters, presented
            the storage tank.
                                                                                     at Solar 97, 35* Annual Conference of Australian and New
 at                                                                                  Zealand Solar Energy Society, Paper 101, Ed. T. Lee.
 3t                                                                                     Shah, L S. and Furbo S. (1997) Correlation of experimental
            REFERENCES
 iy                                                                                  and theoretical data for mantle tanks used in low flow SDHW
ot            Dahl, J., Hermansson, R.., Tiberg ,S. E. and Veber P. (1995)          system, presented at ISES 1997 World Congress, Taejon, Korea
            Use of Video-based Particle Image Velocimetry techniques for                Sharp, M. K. and Loehrke, R. L (1979). Stratified Thermal
            studies of velocity fields in a water heat storage. Experiments in      Storage in Residential Solar Energy Applications. Journal of
            Fluids, vol. 18, pp. 385-388.                                           Energy, vol. 3(2), pp. 106-113.
              Dahl, S.D. and Davidson, J. H. (1997). Performance and                   Webb, B. W. and Ma, C. F. (1995). Single phase liquid jet
            Modeling of Thermosyphon Heat Exchangers for Solar Water                impingement heat transfer. Advances in Heat Transfer, vol. 26,
            Heaters, J. Solar Energy Engineering, vol. 119, pp. 193-200.            pp.105-217.
  a
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