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SOLAR ‘93

THE 1993 AMERICAN SOLAR ENERGY SOCIETY

ANNUAL CONFERENCE

Washington, DC April 22-Z&1993

Editors: S. M. Burley M. E. Arden

American Solar Energy Society U.S. Section of the International Solar Energy Society

2400 Central Avenue, Suite G-1 Boulder, CO 80301

Printed on recycled paper

SIMULATION OF WATER TANKS WITH MANTLE HEAT EXCHANGERS

J&-g M. Baur, Sanford A. Klein, William A. Beckman Solar Energy Laboratory, University of Wisconsin-Madison

Madison, WI 53706, U. S. A

ABSTRACT

A computer program for use in TRNSYS [ 1 ] has been written to simulate a water thermal storage tank with a mantle heat exchanger for use in solar domestic hot water systems. The model is based on the physics of the problem, including convective flows, heat exchange with the environment and the mantle, and conduction between the control volumes. Comparisons of the model results with experimental data show reasonable agreement.

1. INTRODUCTION

A mantle tank is a cylindrical storage tank surrounded by an annulus through which hot liquid from the collector flows thereby transferring energy to the tank contents. The separating wall is the heat exchange surface. Wrap-around coil and tank-in-tank systems are similar in this respect. Wrap-around coil designs usually have a smaller fluid inventory than mantle tanks and operate with higher flow rates to produce turbulent conditions within the coil. Tank- in-tank systems allow the top and bottom of the water storage tank, in addition to the sides, to serve as heat exchanger surface.

Mantle heat exchangers are an interesting alternative to

external heat exchangers because they reduce the complexity

of the system by combining the heat exchanger and the

storage unit in one element. In a mantle heat exchange

system, fluid flow from the heat source does not pass

through the tank. A possible advantage of this flow

configuration is reduced internal tank mixing and, as a

consequence, improved temperature stratification resulting

in higher solar collector efficiency. Mantle heat exchangers

are limited to small-scale solar hot water systems because

the mantle heat transfer area to volume ratio decreases with

increasing storage capacity.

2. EXISTING MODELS

Simulation programs for mantle (or surface) heat exchanger tanks have been developed by Furbo [2,3,4] and by develop-

ers of the WATSUN [S] program. The concepts behind these two models are quite different. The Furbo model uses a finite difference method. The water in the tank, the fluid in the mantle, and the tank walls are divided into elements or nodes. The temperatures of these nodes are calculated by an implicit finite difference formulation. Only thermal conduction is directly considered in the energy balances. Flow streams are accounted for by exchanging entire control volumes. If a temperature inversion occurs, the affected nodes are mixed. Heat and fluid transfer by free convection are considered to be negligible. Heat transfer coefficients between mantle and tank are obtained by a linear curve fit to experimental data. The heat transfer coefficients used during charging periods ranged from 550 to 200 W/m2K from mantle inlet to outlet and were found to be roughly three times greater than the values obtained with correlations for laminar flow between parallel plates with one side insulated

[61.

The model used in WATSUN [5] is based on heat exchanger equations and is applicable to wrap-around coil and mantle systems. This model assumes the storage tank to be fully mixed and the temperature in the mantle (or coil) to change continuously over the height of the mantle. This assumption makes it possible to derive an analytical solution for the mantle outlet temperature. The heat exchanger wall is considered to be at the same temperature as the liquid in the mantle (or coil) at every height. The heat transfer coefficient from the wall to the storage medium is calculated using a correlation for turbulent free convection. A heat exchanger effectiveness is determined every time step based on these calculations.

3. MANTLE HEAT EXCHANGER MODEL

Modeling assumptions affect both the accuracy and the required computational effort. In the model developed here, an attempt was made to apply assumptions which reduce the computational effort while retaining the overall physics of the problem. Liquid in the main tank and mantle is split up into horizontal layers, each of which is assumed to be fully mixed, as in the Furbo model. Temperature changes in the radial direction are neglected.

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Heat transfer from the mantle fluid to the water in the tank can be described with three heat transfer resistances: convection from the hotter fluid to the wall, conduction through the wall, and convection from the wall to the colder fluid. An order of magnitude analysis shows that the conduction resistance through the wall can be neglected. The resistance on the tank side of the wall is modelled with a user-specified constant. The resistance from the mantle fluid to the wall is estimated using an empirical equation for laminar flow between flat plates with one side insulated and constant heat flux on the other side, as detailed in section 3.3.

Situations occur where a node in the middle of the tank is hotter than a node at the top. In this case, it is assumed that the hot water rises and mixes with the colder water above. If the mixed temperature is still higher than the temperature of the node above, this node is also mixed.

Conduction in the axial direction, both through the tank fluid and the tank wall, is considered in the model. However, the energy transfer within the tank as a result of convective mass flow is neglected. Convective energy transfer calculated based on boundary layer theory was found to overpredict experimental heat transfer between tank nodes in times of no4oad flow by two orders of magnitude [7].

3.1 MATHEMATICAL DESCRIPTION OF THE TANK

Equation 1 is an energy balance on an arbitrary tank node i.

dTt,i miCpdt = Ql0ad.i + Qc0nd.i + 0man.i + &ss,i (1)

The rate of convective energy transfer from a node to the load flow stream is

Qload,i = Ti7.LCp(Tt,i+l - Tt,i)

The rate of energy conduction between nodes is

Q (Tt,ii condj =

- Tt,i) + (Tt,i+l - Tt,i)

i-l Ri (3)

where Ri is the heat transfer resistance between nodes i+l and i considering conduction through both the fluid and the tank wall.

The rate of convective heat transfer from the mantle fluid to

the water in the tank is described with Ut-m,iAm. an overall

heat transfer coefficient - area product for each node.

G man, i = Ut-mArn, i CTrn,i - Tt, i) (4)

The rate of heat heat transfer from the environment is

described in a similar manner with an assumed constant

value for Ut-env , the heat transfer coefficient between the

external tank wall and the environment.

O,oss. i = ut-env&nv. i flenv - Tt, i) (3

A maximum of two nodes have a common surface with both the environment and the mantle. For all other nodes, the heat transfer term that doesn’t apply is set to zero.

Equation (1) can be written in the form

dTt i ( = A Tt,i + B dt (6)

where A and B are constants

A=

+ j$y + $ +Ut-m,iAm,i + UtenvAenv,i

mi cp (7)

Tt i-l Tt,i+l

B= inLcpTt,i+~~~+Ut-rn,iAm,iTm.i+Ut-envAenv,iTenv

mi cp (8)

Equation (6) can be solved analytically to obtain the temperature at the end of the time step .

(9)

and the average node temperature during the time step used in the energy balances.

T, I.1 =

The storage tank is broken into n nodes and the mantle into m nodes (m less than or equal to n) so that there are n+m unknown temperatures. Equation (10) provides n equations. The initial temperatures in a time step are set to the final temperatures of the previous time step. The value of B depends on the average temperatures of the nodes above and below as well as the average temperature in the mantle, if the node has contact to the mantle so that an iterative solution is required. The remaining m equations are developed in the next section.

3.2 MANTLE MATHEMATICAL DESCRIPTION

An energy balance yields the following differential equation for an arbitary mantle node temperature.

dTrn i mm,icp,af dt

-z=Q * flow,i - Qman,i + Qloss,i

The rate of energy transfer as a result of the flowing flow

iz * flow, i = mSCp,af (Tm, i-l - Trn, i)

The heat transfer rate from the environment is simply

Q loss, i - - urn-e*~env, i (T,rw - Tm, i)

(12)

The solution of Equation (11) follows the proceedure used for the solution of Equation 1.

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3.3 DETERMINATION OF THIE HEAT TRANSFER COEFFICIENT

The average Nusselt number from location zero to location x is estimated using the empirical equation developed by Mercer et al. [8] for laminar flow between two flat plates with constant heat flux on one side and perfect insulation on the other.

E(x) = 4.9 + O.O606@e Pr Dh/~)t*~

1 + O.O909(Re Pr Dh/x)Oe7 Pro.’ (14)

Reynolds number is defined

. Dh mh

Re=- CL AC,

(1%

and Prandtl number and viscosity are obtained from temperature dependent property data for the mantle fluid [7,

91.

The average Nusselt number for the ith node is obtained from

Nui = Nu(Xj) Xi - Nu(Xi-,) Xi-1

xi - xi-l (16)

and the heat transfer coefficient for node i is determined in terms of the node-average Nusselt number.

-

u - .=c kafNui t-m, I

’ Dh (17)

The correction factor C 1, fitted with experimental data, is introduced to improve equation (17) for application in a mantle heat exchanger.

4. COMPARISON WITH EXPERIMENTAL DATA

Experimental mantle heat exchanger tank performance have been measured by Furbo and Berg [3] at the Thermal Insulation Laboratory in Denmark. Mantle flow rates between 23 and 30 liters per hour were used in their tests resulting in low flow rates in which the mantle fluid required approximately one hour to pass through the mantle.

The experiments did not use solar collectors as the heat source but rather a flow of water at a controlled temperature. Data for three experiments were provided by Furbo: a) tank heating with no load; b) tank heating with a concurrent load; and c) and cooling with no heating or load. All three experiments used a 200 liter tank 1.2 m high and 0.46 m in diameter as displayed in Figure 1. An annulus-shaped mantle is welded around the tank. The mantle covers the tank over a height of 0.91 m positioned 0.1 m from the bottom and 0.19 m from the top. The outer diameter of the mantle is 0.50 m. The material of the wall is plain carbon steel with a conductivity of 60 W/mK. The thickness of the tank wall is 5 mm and the thickness of the mantle wall

288

is 3 mm. The hot liquid enters at the top of the mantle and exits at the bottom on the opposite side of the tank to reduce short circuiting of the hot water in the mantle. The inlet to the storage tank, where the cold water from the mains enters, is in the center of the bottom surface of the tank and the outlet to the load is in the middle of the top surface. The insulation on the tank is such that the heat transfer conductance is 0.89 W/m*K at the sides, 1.79 W/m*K at the top and 2.79 W/m*K at the bottom. Temperatures were measured with thermocouples close to the middle of the tank at the positions indicated by crosses in Figure 1. Water is used for both mantle flow and hot water storage in the tank.

IL-- Fig. 1. Mantle tank showing thermocouple positions

The mantle heat exchanger model utilized tank nodes spaced symmetrically around the thermocouples reaching 2.5 cm (1 in) up and down from the location of the thermocouples. The heat transfer coefficient from the heat exchanger surface to the liquid in the tank was assumed to be 2000 W/m*K which essentially eliminates this heat transfer resistance.

In the heating experiment, the temperatures in the tank are

initially between 27C and 30C. The mantle inlet temperature is fixed at 49.3C, and the mantle flow rate is

approximately 30 liters/hour. During this test there are no

draws from the tank. The experimental tank and mantle

temperatures appear in Figures 2 and 3 along with the

simulation results. A correction factor of Cl=1.8 produced the best matching of the simulated and experimental

temperature curves, and this value of Cl was used in all

simulations of experimental systems. The maximum difference between experiment and simulation results is less

than 1C. The predicted temperatures in most tank nodes and

.-

at the outlet of the mantle are slightly higher than the temperatures obtained in the experiment indicating that the heat loss coefficient to the environment in the experiment was slightly higher than that assumed in the simulation.

calculated temperatures for the third, fourth and fifth nodes are between one and three degrees higher than the measured temperatures. The calculated temperatures for the two bottom nodes are lower for roughly the first half of the time period and then higher. The simulated temperatures of the two bottom nodes show larger temperature drops as a result of the two draws than observed in the experiment. The calculated temperatures are also more sensitive to the change

temperature at time 6.5 than observed in the

i Simulation Results: Dashed Lines

0 5 10 15 20

Time in Hours

Fig. 2, Tank temperatures for heating experiment

50

45

40

35

30

25 0 5 10 15

Time in Hours

20

Fig. 3. Mantle temperatures for heating experiment

The experiment with both mantle heating and load draws is representative of normal operation in a solar domestic hot water system. The temperatures in the tank are initially between 16.5C at the bottom and 19.1C at the top. The mantle flow rate is, with small variations, 23.5 liters/hours. The temperature at the mantle inlet varies over time and is plotted as Tin in Figure 4. The load flow occurs in two 50 liter draws, the first after one hour and the second after 3.5 hours. The mains water temperature is 14.2 C. These draws cause the steep tank temperature drops seen in Figure 5. After 6.5 hours the mantle inlet temperature is lowered to 30C so that most of the tank is cooled as a result of heat transfer to the mantle fluid.

The results of the simulation with a heat transfer correction factor of C1=1.8 are also shown in Figure 4 and 5. The calculated temperature curves for the top two nodes are below the measured values throughout the simulation. The

Time in Hours

Fig. 4. Mantle temperatures for heating and draws

experiment

60 , I

Experimerkal Data: Full Lines Simulation Results: Dashed Lines ;

lo . 1. ” 1. ” ” ” 1” 0 2 4 6 8 10

Time in Hours

Fig. 5. Tank temperatures for heating and draws

experiment

The cooling test investigated the energy loss and decay of thermal stratification over time. The tank was initially stratified with the top half of the tank being at temperatures between 44C and 48C and the bottom half being at temperatures between 19C and 22C. After the initial draw, no additional water is drawn, nor is any water run through the mantle. The top tank nodes cool due to losses to the environment but they also transfer energy to the lower nodes by conduction.

The experimental and simulation results are plotted in Figure 6. The model underpredicts the stratification decay,

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i.e., the hot nodes are calculated to cool too slowly and the cool nodes are calculated to warm too slowly. The stratification decays too slowly in the simulation because fluid movement within the tank as a result of free convection has not been modeled. To improve the model, fluid movement resulting from free convection should be included,but no correlations are known to be applicable for these conditions.

..(..-..- . . . ..-............. Experimental Data: Full Lines . . . . _... Simulation Results: Dashed Lines

I 1” 1

0

Fig.

8 12 16 20 24

Time in Hours

6. Tank temperatures for cooling experiment I

Fig 7 Tank-in-tank system tested by Harrison [lo]

4.2 EXPERIMENTS AT OUEEN’S UNIVERSITY

The experimental performance of the tank-in-tank SDHW system shown in Figure 7 was measured by Harrison and Weir [lo]. The inner tank has a volume of 208 liters and the shell contains 19 liters. The height of the inner tank is 1.48 m, and the total height is 1.54 m. The diameter of the inner tank is 0.44 m. The boundary wall between shell and inner tank is 1.6 mm thick and is undulated to increase the heat transfer coefficient and the heat exchanger surface. Due to the undulation, the smallest distance between the inner and the outer tank wall is 9 mm and the largest distance is 25 mm. The undulations increase the heat transfer area by a factor of 1.2 compared to a flat wall. The outer tank is

insulated with a 30 mm of PVC coated rubber foam. The combined loss coefficient from the outer tank is estimated to be 1.2 W/m*K. Water is drawn to meet a standardized load as shown in Fig. 8.

C .I 60

0 0 4 8

Fig. 8, Load and

12 16 20 24

Time in Hours

leat source flowrates

The mantle is fed with a 60-40 percent water-propylene glycol mixture at a constant flow rate between 8 am and 4 pm. The liquid in the shell is exchanged 4.5 times per hour (compared to once per hour or less in the experiments of Furbo). The experimental mantle inlet and outlet temperatures are plotted in Figure 9. The storage tank is fed at the bottom with replacement water from the mains at a temperature of 18C. The eight thermocouples in the tank are positioned at intervals of 0.2 m with the lowest thermocouple at the bottom of the tank.

60

r.....i.....: .A .I 0 4 8 12 16 20 24

Time in Hours

FiL. 9. Experimental and simulated mantle temperatures

The tank-in-tank system is simulated by using the mantle

heat exchanger model for a mantle which extends from the

shell outlet to the top of the tank. This approximation

introduces an error in the determination of the temperature

in the top node, as only the side walls of the heat transfer

surface at the top node are used for the simulated heat

transfer. The tank model used fifteen nodes. All of the

nodes,except the top and the bottom node, have a thickness

290

of 0.1 m. exchanger.

Experimental and simulated (with C l= 1.8) temperatures for nodes 2, 4, 6, and 8 are shown in Figures 10. The temperature of node 1, the hottest node (not shown), is underpredicted by a maximum of 5C and node 8, the coldest node, is underpredicted by 12C at the worst point. These large differences occur because the mantle heat exchanger model was not specifically developed for tank-in-tank systems and consequently did not account for the heat transferred through the top and the bottom wall of the inner tank. The simulated temperatures in all the other nodes follow the experimental results except for the middle nodes at the end of the experiment.

6. CONCLUSIONS

A model of the performance of a mantle heat#exchanger tank has been developed for use with the TRNSYS program. Experimental data from two sources have been compared with results generated by the model. The calculated and experimental tank and mantle temperatures compare reasonably well while the largest differences occur during load draw periods. Annual simulations of mantle and external heat exchanger SDHW systems show that the two system types perform comparably. Additional experiments are needed to establish general heat transfer relations for use in mantle tank analyses.

60 I I 7. ACKNOWLEDGEMENTS

Experiment; Data: Full Lines Simulation Results: Dashed Lines [ 11 Klein, S.A. et al., TRNSYS, Version 13.1, Solar

10. I 1 I , . Energy Laboratory, University of Wisconsin, Madison, 0 4 8 12 16 20

Time in Hours 1990

Fig. 10. Temperatures in tank nodes 2,4, 6, 8

5. LONG-TERM PERFORMANCE CALCULATIONS

Yearly simulations of a SDHW system have been performed for a base case system with a standard tank and a separate heat exchanger as well as for a tank with mantle heat exchanger. The base case system, located in Sacramento, California, has a 5 m2 single-glazed flat-plate collector with F~(ra)=0.7 and F,U,- -4.17 W/m*-K and a 200 liter

storage tank. The collector flow rate is 150 liters/hour. The mantle volume is 30 liters. Both systems were subjected to daily loads of 200, 400, and 600 liters of water heated from 1OC to 60C. All common simulation

parameters were the same in both cases, including the

division of the tank into ten equal nodes. The effectiveness

of the external heat exchanger was taken to be 1 .O in order to determine an upper bound on the performance of this

system. The mantle tank was simulated using a heat transfer correction factor of C 1=2.0.

The calculated annual solar fractions for the system with the

external heat exchanger were 0.82, 0.60, and 0.43 for daily

water loads of 200, 400, and 600 liters, respectively. The

corresponding solar fractions for the mantle tank were 0.85,

0.60, and 0.42. These results indicate that the performance of a well-designed system with a mantle heat exchanger tank

is comparable to a similar system with an external heat

[2] Furbo, S., Solar Water Heating Systems Using Low Flow Rates - Experimental Investigations, Thermal Insulation Laboratory, Technical University of Denmark, Report No. 89-9, January 1992 [3] Furbo, S. Berg, P., Calculation of the Thermal Performance of Small Hot Water Solar Heating Systems using Low Flow Operation, Thermal Insulation Laboratory, Technical University of Denmark, 1992 [43 Furbo, S., PC Model for Low Flow Solar Heating Systems, Thermal Insulation Laboratory, Technical University of Denmark, January 1992 [5] WATSUN-manual, Watsun Simulation Laboratory, University of Waterloo, Ontario, Canada [6] J. A. Duffie and W. A. Beckman, Solar Engineering of Thermal Processes, 2nd Edition, Wiley & Sons, Inc., 1991 [7] Baur, J.M., Simulation of energy Storage Tanks with Surface Heat Exchanger, M.S. Thesis, Dept. of Mechanical Engineering, University of Wisconsin - Madison, 1992 [8] Mercer, W. E., Pearce, W. M., and Hitckcock, J. E., “Laminar Forced Convection in the Entrance Region Between Parallel Flat Plates”, Trans. ASME, J. Heat Transfer, 89,25 1 ( 1967) [9] Dowfrost, Engineering and Operation Guide for Dowfrost and Dowfrost HD Inhibited Propylene Glycol- based Heat Transfer Fluids, Form No. 180-1286- 1190 AMS, 1990 [lo] Harrison, S. J. and Weir, B., unpublished from the Solar Calorimetry Laboratory, Dept. of Mechanical Engineering, Queen’s University, Kingston, Ontario, Canada k7L 3N6

Financial support for this project was provided by the U.S. Department of Energy and The German Academy for Exchange Services. The authors greatly appreciate the experimental data contributed by Simon Furbo of the Technical University of Denmark and Steve Harrison of Queen’s University in Kingston, Ontario.

8, REFERENCES

291