Thermal stratification in solar storage tanks

Ph.D. Course

Literature study: Tank Inlets

David Blandin

Centre Scientifique et Technique du Bâtiment

Renewable Energy CSTB – ESE –DE

Route des Lucioles – BP 209

06904 Sophia Antipolis Cedex, France Tel. +33 (0)4 93 95 64 43 ; Fax +33 (0)4 93 95 64 31 david.blandin@cstb.fr

Table of Content

Introduction .......................................................... 3

1- Technical Tank Inlets solutions .................................. 4

a) Inlets to support thermal stratification............................................................................. 4

b) Inlets to maintain stratification ........................................................................................ 6

2- Tank inlet modelling ............................................ 10

a) One-dimensional methods of modelling ....................................................................... 10

b) CFD methods of modelling ........................................................................................... 12

c) Future work: integrating tank inlets in a zonal model ................................................... 14

Conclusion ........................................................... 16

References .......................................................... 17

INTRODUCTION

A “stratified” tank is characterized by a thermocline - the zone of steepest temperature

gradient separating the hot and cold fluid zones in the tank. The thickness of the thermocline

zone is an important indicator of how well the stratified tank is designed. Several parameters

play a role in this stratification quality. Amongst them, a large ratio H/D is essential to obtain

a good stratification. Literatures advice a ratio H/D between 3 and 4 in order to enhance

storage tank performance (Lavan and Thompson 1977). Nevertheless, the Richardson number

[see the nomenclature for its formula], measuring the ratio of buoyancy forces compared with

mixing forces, is the more representative parameter during the dynamic charging and

discharging process of the storage tank (Hahne and Chen 1998). A small Richardson number

means that the storage tank is mixed whereas a bigger Richardson number indicates the

storage tank is stratified. As far as this number is concerned, the difference between inlet and

tank temperature is the most important factor (Hahne and Chen 1998). In practice, we will

reach a good thermal stratification by a charge via the top of the tank with an inlet

temperature much higher than the temperature of the surrounding water (>20°C). Moreover,

we will inject a low flow in order not to disturb the low part of the store. During the dynamic

phases, stratification is influenced by the geometry of the tank, its internal equipment and its

various charge and discharge loops which condition the heat exchange that occurs:

inputs/outputs flows, water and envelope conduction, convective exchange (water/envelope,

envelope/surrounding) and radiative exchange (external envelope/walls).

We propose to focus on flows introduced to the tank. Tank inlets can be defined as direct or

indirect (via a heat exchanger) tank charge. We first describe tank inlets available in current

stock and then we will describe the different ways of modeling tank inlets.

1- TECHNICAL TANK INLETS SOLUTIONS

To have a stratified tank, we are faced with a double challenge. First, we should provide a

high level of stratification and then limit destratification in order to maintain the level of

stratification.

a) Inlets to support thermal stratification

Various techniques make it possible to

support stratification during the solar tank

charge. In the first family, three-way valves

function in “all-or-nothing” and are

controlled according to the outlet solar

collector temperature. The fluid is then

injected at various tank levels according to its

temperature. The number of injections is

generally lower or equal to three because of

the valve cost. Some manufacturers choose

the use of a double solar heat exchanger: the

primary fluid always goes through the lower

heat exchanger but goes through the higher

heat exchanger only if it is justified by the

levels of temperature.

Other manufacturers choose the direct

charge/discharge at various levels in the store

with an external heat exchanger associated

with an adapted regulation.

Figure 1- two solar heat-exchangers regulated by a

three way valve

Moreover, the use of three-way valves can be

associated to a mantle heat exchanger into

which the fluid is injected at the correct level.

Knudsen and Furbo (2004) advise, for this

configuration, the use of a top inlet position

for high temperatures and an intermediate

height position for moderate inlet

temperatures.

Figure 2- inlet heights in mantle tank regulated by

three way valves

To support thermal stratification, a

stratification device makes it possible to

distribute heat at the correct level by natural

convection. The fluid goes up and exits the

unit at approximately the same temperature

in the store, thus maximizing stratification

(figure 1). The importance of “non-return

valves” has been demonstrated (Shah et al.)

by comparison with a stratifier without flaps

which actually works more like a “mixing

device” than a stratifying one because cold

tank water is sucked into the stratifier.

Moreover, it has been found that the stratifier

is the most efficient for flow rates between

5L/min and 8L/min. As the investigated

stratifiers are often used for volume flow

rates much less than 5L/min, it has been

concluded that there is still a need for further

development of these stratifier designs.

Figure 3- charge via a stratification device

Andersen et al. (2007) investigate a number

of different fabric stratification pipes

compared to a rigid inlet stratifier. The

investigation shows that the performance of

fabric stratification pipes can be improved

significantly by using two fabric layers with

a distance of about 10 mm between each

fabric layer instead of using one fabric layer.

The biggest drawback of fabric stratification

pipes is the high horizontal heat transfer

through the very thin fabric. Thus, when hot

water enters a cold tank from the bottom to

the top of the fabric stratification pipe, rigid

stratifier has an advantage because of the low

horizontal heat transfer through the pipe wall.

For the cooling test, fabric layer stratification

pipe performs better than the rigid stratifier,

while the two fabric layer stratification pipe

and the rigid stratifier perform identical

during stratified heating tests.

The advantage of the double fabric layer pipe

over the solid inlet stratifier is that it

maintains stratification better for high flow

rates.

Figure 4- Picture of the double fabric layer pipe

during a heating experiment. Upper right corner:

cross section of the extended fabric pipe where

water leaves the pipe. Lower corner: cross section

of the collapsed pipe

b) Inlets to maintain stratification

In order to limit the mixing during discharge, other technologies are used. Domestic hot water

draw-offs lead to the injection of a cold water jet into the tank bottom. To limit stratification

degradation, a cold water inlet device can be used or the fluid can be instilled in the bottom of

the tank. The results of the impact of the influence of a cold water inlet device on thermal

stratification (Shah and Furbo 2003) show that entropy and exergy variations are influenced

by the Richardson number, draw-off volumes and initial conditions.

The degree of mixing produced by three

different side-inlet geometry (wedged,

perforated and slotted pipe-inlets) is found to

have an impact on the performance (Hegazy,

2007). The slotted inlet is found to be the

more efficient. The performance difference

between the different inlets is more obvious

with high flow rate.

Figure 5- side-inlet geometries tested by Hegazy

Among the three different inlets from figure 7,

half ball baffle inlet allows better stratification in

the tank.

However, large flat baffle plate above the inlet

shows the best thermal stratification in the

tank.according to figure 20. A larger half ball

baffle inlet should thus be a better inlet cold

device.

Figure 6- Model outline of the tank with the three

different inlets

Figure 7- efficiency of three different inlet cold device

Figure 8- different inlet designs for circulation pipe

Figure 9- amount of mixing for a 2,0 m3 vertical

tank with a diameter of 1,25m

Even if there is still little mixing for each

of these inlets configuration, the table

shows which configuration give the best

thermal stratification in the tank.

CFD on parallel plates (Johanes et al.) shows the improvement of stratification in comparison

with a standard inlet. It is shown that parallel plates with different geometries (square plate

above a disk one) leads to better thermal stratification.

Figure 10- temperature fields results obtained by CFD inside a solar tank with three different inlets and

two different flow rates

The ratio of Reynolds to Richardson numbers

seems to be the parameter governing the

performance (Zurigat et al. ,1988). For higher

values of Re/Ri, differences in performance

of the inlet diffusers will occur. This is

expected, because at high Re/Ri, turbulent

mixing at the inlet is dominant while at low

Re/Ri, high buoyancy forces inhibit mixing

at the inlet region.

Perforated diffuser gives the thinnest

thermocline in the tank among the three

radial diffusers tested.

Figure 11- Types of inlet configuration tested

Characterization of the mixing introduced by

these inlets was carried out using an inlet

mixing parameter introduced in a one-

dimensionnal flow model (Zurigat et al., 1991).

Impingement inlet shows to mix less the tank

than the other inlets. (see figure part 2)

Figure 12- side inlet, impingement inlet and

perforated baffle experimentally tested by Zurigat

Numerical simulations show that cold water

inlet device modify the flow inside the tank in

order to decrease the mixing inlet region.

Figure 13- inlet cold device geometry

Effect of using different obstacles on

thermal stratification in a cylindrical

hot water tank is analyzed numerically

(Altuntop et al., 2004). Amongst 12

different obstacles, the obstacle types

having gap in the center provides better

thermal stratification.

Figure 14- different obstacles geometries tested

Figure 15- temperature fields obtained by CFD for no obstacles, and obstacles having a gap in the center

Rather than injecting a cold jet directly

into the store, we can use a DHW quasi-

instantaneous heat exchanger or a smaller

tank inside a bigger one (“tank in tank”

solution). This will then make it possible

to eliminate mixing by the injection from

the cold jet. By this process, the DHW

does not remain stagnant in the bottom of

the tank: this avoids the proliferation of

legionella.

Figure 16- Limitation of mixing by good jet orientation (left)

or “tank in tank” solution (right)

On an other hand, the performance of a tank in tank solution might be not so good because of

the heat transfer from the heat exchanger to the biger tank. This solution avoids mixing by

mass transfer but might increase the one by convection. More investigations are needed to

know what is the pat of each heat transfer.

2- TANK INLET MODELLING

a) One-dimensional methods of modelling

In one-dimensional models, the turbulent mixing was accounted for by introducing an

effective diffusivity factor, effε who can be described according to Zurigat et al (1988) by the

knowledge of effinε . Despite its artificial nature, the effective diffusivity factor can represent

the modifying effect of turbulence caused by the inlet flow. Hence, this factor may be used to

characterize the inlet geometry and identify the best inlets. The variation of the inlet effective

diffusivity factor as a function of the flow parameters is shown in figure17 for three different

inlet configurations. Here, Re is based on the inlet port diameter, while Ri is based on the

height of the tank, and both are based on the inlet port flow velocity. The three inlets used are

the side inlet, the perforated inlet, and the impingement inlet (figure 12).

894.0)(Re/344.0 Rieff

in =ε for the side inlet 586.0)(Re/54.3 Rieff

in =ε for the perforated inlet 522.0)(Re/75.4 Rieff

in =ε for the impingement inlet

Figure 17- inlet effective diffusivity factor variation with Re/Ri

The localized mixing as used by Wildin and Trulan (1985) and Greatarsson et al. (1994) was

also used in a different way by Nakahara et al. (1988), who assumed that the tank consist of

two regions: a fully mixed region which increases as filling proceeds, and a plug flow region

spanning the rest of the tank. The extent of the fully mixed region was expressed in terms of a

dimensionless depth H

XR = , where H is the tank height and X is the depth. R was assumed

to vary linearly with the dimensionless filling time t* ( t

* = Vt / H ) as:

*

0 tRRR k+=

Where R0 and Rk are empirical constants. Rk was taken to be 0.4 under all conditions

whereas correlations for R0 in terms of Richardson number and the inlet length scale were

given for two different inlet types: a pipe inlet and a slot inlet. For a pipe inlet tank:

The tank solution over the time interval DT becomes:

We can also use Hollands and Lighstone who give correlation about the height L* of the inlet

mixing region in fonction of Richardson.

Figure 18- Flow in the jet mixing region ( adapted from Baines)

Figure 19- Plot of L*/L vs Richardson number. measured by Sliwinski.

)/(7.0 0

5.0

0 LdRiR−=

[ ]VR

tQ

tinintt eTTTT

∆−

∆+ −−= ).(

b) CFD methods of modelling

CFD Modeling, in addition to the possibility of simulating new cases, make it possible to

describe the near reality of the physical phenomena and thus to understand the flows inside

solar tanks better. In comparison with one-dimensional modeling, CFD modeling involves

less assumptions and empiricism, and thus is more realistic and accurate. A wider range of

flow thermal and hydrodynamic conditions as well as complex tank geometric parameters

may be modeled. Oliveski and al. (2005) use a two-dimensional method with finished

volumes, experimentally validated, to show stratification with an area at a constant

temperature in the higher area of the tank. It is checked numerically with conditions of natural

convection that two areas of opposite convective flows appear during the tank cooling

(Oliveski et al. 2005): an area of flow going down by thermal boundary along the wall is

opposed to the relatively slow ascending convective flow in the tank central part. The

numerical simulation then makes it possible to represent the evolution of stratification in a

more realistic way. We initially decided to reproduce a simulation met in the literature (Shah

and Furbo 2003).

Figure 20- Temperature distribution in the tank centre plane after 5 min of 10 l/min inlet flow and further

a 30 s´ stand still period. Left: the pipe inlet. Centre: the Metro inlet. Right: The plate inlet

The validation of three-dimensional modeling with the assumption of Boussinesq is carried

out via Fluent. We obtained the same temperature repartition than the published results of

Shah and Furbo for the 2 different inlets, we also noticed a higher hot volume for the tank

with an inlet cold device. This allows us to validate our assumptions and then simulate new

configurations. With this assumption, we simulated a relatively simple configuration of a load

of 60°C to fixed height of a commercial 750-liter tank with a 1m3/h inlet flow. This

corresponds in practice to the reheating top of the tank via a boiler at the time of an

insufficient solar sunning. This situation is selected, because easily reproducible in

experiments and by other types of simulations. Dynamic simulation (0.5s fixed time step) uses

the k-ε model of turbulence by informing the hydraulic diameter of 52mm and the intensity of

turbulence (Fluent User’s guide 1995) of 5.32% calculated according to the Reynolds number.

We selected an inlet of 0.13m/s at 60°C and benefited from the tank symmetry plane to

simulate only a half of its. Moreover, we selected thermal transfer on the walls corresponding

to a 2mm tank thickness, followed by 10cm polyurethane with hdown=6 W/(m2.K), hup=7.5

W/(m2.K) and hside=8.5 W/(m

2.K) as thermal transfer coefficients to the bottom, top and the

side of the solar storage.

Figure 21- 3D visualisation of a 60°C charge at t=20min from a 20°C initial tank

Figure 22- Dynamic temperature evolution from a direct 60°C charge

Dynamic simulation of this configuration enables us to visualize the evolution of the jet

trajectory (figure 5): initially ascending because of strong difference between its inlet

temperature and the tank temperature, the jet will gradually become horizontal when its

temperature is equal to the temperature of the surrounding tank fluid. In addition to this

evolution of the jet, simulation informs us of the dynamics of the load: the effect of the piston

is quite real but the different horizontal layers are not at a uniform temperature (figure 4).

Johannes and al. (2005) compare CFD results with those obtained by multi-layer models: the

60 and 140 Types used in TRNSYS environment predict a temperature lower than CFD

simulation. This is mainly due to the fact that a layer is actually not at a uniform temperature.

An isothermal zone is influenced by the dominant flows (jet, boundary layers) but also by the

presence of obstacles (Altuntop et al. 2005) in the store (heat exchangers, inlet device, etc.).

However, CFD simulations take a considerable computing time (around 5 days for one

physical hour of simulation presented), making annual performance prediction impossible.

The main conclusion of the multi-layer models and CFD comparison with experiments

(Johannes et al. 2005) is the need to develop a zonal model, which is a compromise between a

reasonable calculation and the accuracy of the results.

c) Future work: integrating tank inlets in a zonal model

Because tank inlets effect thermal

stratification inside the tank we must

integrate a good model of them when

considered for zonal modeling. If we don´t

take into account the dynamic of the jet, flow

rate will go from the inlet zone to the

adjacent zone. In airflow pressure zonal

modeling, the jet can be taken into account as

shown in figure 23.

There is then different ways to account for

this jet. Experimental validation can be a way

to find a fitting coefficient Cflow. CFD

simulations provide a suitable way of

determining this coefficient. As this method

is proven to work for air jets in building

simulation, the transfer of this method to

water jets could also prove successful - as

long as it takes into account the inlet velocity

and the effective inlet cross section.

Figure 23- jet with entrainement into airflow zonal model

Here we present another method from work done by Bejan on round jets.

Figure 24- The large-scale instantaneous structure of a two-dimensional turbulent jet, and the constant-

angle shape of the time averaged flow region

Navier stokes time-averaged simplification give us:

0)(1

=∂

∂+

∂

∂

r

vr

rx

u

∂

∂

∂

∂=

∂

∂+

∂

∂

r

ur

rrr

uv

x

uu m

1ε

where mε is the momentum eddy viscosity. The jet strength is defined as:

²²4

²2 000

DUrdruKπ

π == ∫∞

−=

2

35.9expx

ruu c

( )

−−=− ∞∞

2

expT

cb

rTTTT

With Tb the transversal lenght scale experimentally given by Fisher et al.

( )x

DTTTTc

0065.5 ∞∞

−≅−

Figure 25- Temperature and velocity evolutions for 0T =60°C, 0U =0.13m/s , ∞T =20°C , ∞U =0m/s

CONCLUSION

We notice that there are lots of different inlet configurations on the market. For a

charge we should observe the Richardson number and thus the difference in inlet temperature.

Stratifier inlets are a good way to support thermal stratification in tanks, avoiding the mixing

associated with common heat exchangers. For a discharge cold inlets have to go towards the

bottom of the tank with a low velocity. Different cold inlet devices operate with varying

degrees in efficiency.

Tank inlets are not easy characterize. CFD simulations can help us to better understand

their performance but takes a lot of computing time. Integrating tank inlets into the zonal

modelling will not be an easy task and further investigations are needed to find a simple way

to model tank inlets.

REFERENCES

Altuntop N., Arslan M., Ozceyhan V., and Kanoglu M. 2005. “Effect of obstacles on thermal stratification in hot

water storage tanks,” Applied Thermal Engineering 25, pp. 2285-2298, (2005).

Andersen, E. et al., “Multilayer fabric stratification pipes for solar tanks”, Sol. Energy (2007,

doi:10.1016/j.solener.2007.01.008

Bejan A. “Convection Heat Transfer”. Second edition, John Wiley & Sons, New York, USA, 1995, pp 379-397

Dincer I. and Rosen M.A. “Thermal Energy Storage: Systems and applications”,, 2002, pp 259-301

Drück H. and Pauschinger T. 2000. “Multiport store –model for TRNSYS, Type 140,” Institut für

Thermodynamik und Wärmetechnik, Universität Stuttgart, Stuttgart, Germany.

Fluent User’s Guide, Fluent Inc., USA, (1995).

Gretarsson S.P., Pedersen C.O. and Strand R.K. 1994 “Development of a fundamentally based stratified thermal

storage tank for energy analysis calculations, ASHRAE Transactions 100, 1213-1220

Hahne E. and Chen Y. 1998. “Numerical study of flow and heat transfer characteristics in hot water stores,”

Solar Energy 64-1, pp. 9-18.

Hegazy AA, Effect of inlet design performance of storage-type domestic electrical water heaters, Appl Energ

(2007), doi:10.1016/j.apenergy.2006.09.014

Hollands K.G.T. and Lightstone M.F. 1989. “A review of low-flow stratified-tank solar water heating systems,”

Solar Energy 43-2, pp. 97-105.

Johannes K. Fraisse G., Achard G. and Rusaouen G. 2005. “Comparaison of solar water tank storage modelling

solutions,” Solar Energy 79, pp. 216-218.

Klein S.A., Beckman W.A., Mitchell J. W., Duffie J.A., Freeman T.L., Mitchell J.C., Braun J.E., Evans B.L.,

Kummer J.P., Urban R.E., Fiksel A., Thorton J.W., and Blair N.J. 2000. TRNSYS 15 Reference Manual,

Solar Energy Laboratory, University of Wisconsin, Madison, USA.

Knudsen S. and Furbo S. 2004. “Thermal stratification in vertical mantle heat-exchangers with application to

solar domestic hot-water systems,” Applied Energy 78, pp. 257-272.

Lavan Z. and Thompson J. 1977. “Experimental study of thermally stratified hot water storage tanks,” Solar

Energy 19, pp. 519-524.

Nakahara N., Sagara K. and Tsujimoto M. 1988. Water thermal storage tank: Part 2-mixing model and storage

model estimation for temperature stratified tanks, ASHRAE Transactions 94, Part 2, 371-394

Oliveski R.D.C., Macagnan M.H., Copetti J. B. and Petroll A.M. 2005. “Natural convection in a tank of oil :

experimental validation of a numerical code with prescribed boundary condition,” Experimental Thermal

and Fluid Science 29, pp. 671-680.

Shah L.J., Andersen E. and Furbo S. 2005. “Theorical and experimental investigations of inlet stratifiers for solar

storage tanks,” Applied Thermal Engineering 25, pp. 2086-2099.

Shah L.J. and Furbo S. 2003. “Entrance effects in solar storage tanks,” Solar Energy 75, pp. 337-348.

Wildin M.W. and Truman C.R. 1985 “Evaluation of stratified Chilled Water Storage Technique” EPRI Report

EM-4352, December

Zurigat Y.H., Ghajar A.J. and Moretti P.M. 1988 “Stratified thermal energy storage tank inlet mixing

characterization” Applied Energy 30, 99-111

Zurigat Y.H., Liche P.R. and Ghajar A.J. 1991 “Influence of inlet geometry on mixing in thermocline thermal

energy storage” International Journal of Heat and Mass Transfer 34, 115-125