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Thermostatic Mixing Valves Thermostatic temperature

distribution during various operating conditions

Joakim Wren, Peter Persson and Dan LoydDepartment of Mechanical Engineering

Linkpings universitet, SE 581 83 Linkping, SWEDEN

Abstract: A model of a thermostat used in thermostatic mixing valves (TMVs) has been developed. The model

contains realistic boundary conditions and material properties including the latent heat corresponding to a mixture

of waxes inside the thermostat. The temperature-time characteristics show a relatively slow heating of the thermo-

stat regardless of the flow rate. This implies an improvement potential for the thermostat and thus the entire valve.

KeyWords: Thermostatic mixing valves, Thermostat, heat flux, Modeling and simulation, Phase transition

1 IntroductionThermostatic mixing valves (TMVs) are important

components in many heating, refrigeration and sani-

tary systems. The demands on such systems have in-

creased the last years, for example due to new safety

standards [1]. In this study we look at the temperature

distribution inside the thermostat, which is responsi-

ble for the thermostats function as a combined sen-

sor/actuator. The thermostat contains a specific mix-

ture of waxes and all waxes in the mixture undergo

a phase transition within the working temperature in-

terval of the valve. The thermostat is also influencedby among others the heat flux from the surrounding,

which in turn is affected by e.g. the flow conditions in

the proximity of the thermostat.

In this study a finite element model of the ther-

mostat including the temperature dependent thermal

conductivity, the specific and latent heat of the mix-

ture of waxes and the convective heat transfer. The

results show a temperature distribution that varies

greatly in both axial and radial directions throughout

the response time for the valve for all investigated con-

ditions.

2 Materials and Methods

2.1 The valve and thermostat

A thermostatic mixing valve (TMV) mixes hot and

cold water to a preset mean temperature. The TMV

investigated is ESBE series30 HR valve (ESBE AB,

Reftele, Sweden) which has a short response time and

stable mixed water temperature under varying water

pressure, flow and temperature conditions. The valve

is shown in Fig.1.

Figure 1: The thermostatic mixing valve. Cold water inlet

is at the bottom of the valve, hot water inlet to the left and

mixed water outlet to the right. The height of the valve is

approximately 100 mm.

The valve regulation emerges from a thermo-static element (thermostat) located in the water-stream

inside the valve. The thermostat contains a phase

change material consisting of copper powder and a

specific mixture of waxes, which change its density

upon heating and thereby bring rise to the control.

The wax mixture also contains a significant amount

of copper powder in order to increase the thermal dif-

fusivity and thereby the speed of the thermal response.

The thermostat forces a plastic shuttle to move to-

wards/against a spring feed-back mechanism, which

determine the cold and hot water intake (see Fig.2).

Proceedings of the 2006 WSEAS/IASME International Conference on Heat and Mass Transfer, Miami, Florida, USA, January 18-20, 2006 (pp42-45)

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Thermostat(Probe)

Outlet

Inlets: hotand cold

Shuttle

Spring

Figure 2: Schematic picture of the valve in Fig.1.

2.2 Governing equations and boundary con-

ditions

The heat transport in the thermostat is given by

the heat conduction equation (1), which in axial-

symmetric cylindrical co-ordinates, r and z , is givenby

cT

t =

1

r

r

krr

T

r

+

z

kz

T

z

+ Q (1)

for an isotropic material whereis the density,cis the specific heat capacity,T =Ti(t,r,z)is the tem-perature,t is time,ki is the thermal conductivity (i=randz), and Qis a heat sink or source. All parameterscan vary in both time and space. See e.g. [2].

The equation is used together with a convective(Neumann) boundary condition, see e.g. [2]. In this

case the convective heat flux is descried by equation

(2). The surrounding temperature is given by T,hBis the convective heat transfer coefficient andlrand lzare the direction cosines. All parameters can vary in

both time and space.

krT

rlr+kz

T

zlz+ hB(T T) = 0 (2)

Equation (1) was solved along with appropriate

boundary conditions for the present geometry using

the simulation software Femlab 3i (Comsol AB, Swe-

den), which as the name indicates exhibits simula-

tion capabilities based on the Finite Element Method

(FEM), see e.g. [3].

2.3 Simulation model

The axi-symmetric simulation model (Fig.3) com-

prises the thermostat including the phase-change cop-

per/wax mixture in its surrounding of flowing water at

three flow rates (4, 10 and 20 liters per minute).

Figure 3:The geometry of the thermostat showing its prin-

ciple parts included in the model.

For the copper, brass and rubber of the thermo-

stat, the density was 8850, 8430 and 1100 kg/m3

re-spectively, the specific heat 385, 400 and 2000 J/kgK

respectively, and the thermal conductivity was 230,

110 and 0.24 W/mK respectively; all these are hand-

book values. For the copper/wax mixture, conduc-

tivity measurements were carried out at 20, 35, 43

and 51 C, giving a conductivity of 3.8, 3.0, 2.2 and2.0 W/mK respectively. Interpolation was carried out

along with the simulations. Also measurements of

the combined effect of specific/latent heat of the cop-

per/wax mixture were carried out at discrete tempera-

tures, giving the result shown in Fig.4.

Simulations were carried out for three flowcases, each corresponding to a set of measured [4]

space-dependent convective heat transfer coefficients

(hB). For the lowest flow rate (4 l/min), hB is 4500kW/m2 for the lowest horizontal face of the thermo-

stat, linearly decreasing from 9600 to 6000 for the

long vertical face, 3000 for the upper horizontal face

and 2000 for the vertical curved part. For the other

flow rates, 10 and 20 liters per minute, hB was in-creased by approximately 50 and 90%, respectively.

Further details of the values and measurement ofhBfor the flow cases are found in [4].


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500

1000

1500

2000

2500

20 30 40 50 60

Spec

ificheat[J/kgK]

Temperature [C]

Figure 4: The combined specific/latent heat of the copper

wax mixture measured at discrete temperatures and fitted

by a cubic spline function.

3 Results

The temperature as a function of time for each flow

condition is given in Fig.5 for two locations, both at

a radius of 1 mm and at axial locations 3 and 15 mm

from the bottom of the thermostat. The temperature-

time derivative is slightly larger for the higher bound-

ary heat fluxes. It is also interesting to note that the

curves tend to flatten out at between 30 and 40 C,before their derivative increases again.

20

30

40

50

60

0 1 2 3 4 5

Temperature[C]

Time [s]

Flow 4, AFlow 4, B

Flow 10, A

Flow 10, BFlow 20, AFlow 20, B

Figure 5: Temperature in the copper/wax mixture as a

function of time for the flows 4, 10 and 20 l/min at a radiusof 1 mm and axial locations 3 and 15 mm (A and B respec-

tively) from the bottom of the thermostat. The temperature

decreases from the bottom to the top of the thermostat.

4 Discussion

The temperature distribution inside a thermostat of a

TMV has under various operating conditions been an-

alyzed using modeling and computer simulation. This

is an interesting problem from a thermal point of view,

due to the steep pressure and temperature gradients

present inside the valve [5] as well as the large spa-

tially and temporally dependent convective heat trans-

fer at the boundary of the thermostat [4]. These affect

the valve/thermostat characteristics, which in turn are

responsible for the performance and safety classifica-

tion of the valve. This is among others actualized by

the risk for invasion of Legionellae bacteria [6].The temperature-time plots in Fig.4 show that

the the large difference in heat transfer coefficients

associated with the various flow rates do not have a

substantial impact of the temperature inside the cop-

per/wax mixture. This means that other aspects than

the heat flux over the boundary dominates the situ-

ation. The relatively low thermal conductivity of the

mixture together with the latent heat of the phase tran-

sition in the copper wax mixture decreases the thermal

diffusivity and thus slow down the heating of the mix-

ture. This effect is actually seen in Fig.4 where the

curves tend to flatten out at slightly below 30 C. Onereason is that this temperature coincides with the tem-

perature for which the largest change in specific heat

and thermal conductivity (increase and decrease, re-

spectively) occurs. Another reason is the various tran-

sition temperatures for the wax mixture.

An interesting finding is that after four seconds

after a temperature step, the temperature distribution

inside the thermostat is far from equilibrated. This is

quite unexpected, as the valve is classified as a high

performance valve meeting among others the Asse

(American Society of Sanitary Engineering) no.1016

standard which demands a response time less thanfour seconds. See e.g. [7] for a discussion of response

times.

5 Conclusion

The temperature-time characteristics of the thermostat

show a relatively slow heating regardless of the flow

rate. There is an axial temperature difference inside

the thermostat throughout the simulated time, and the

combined effect of the specific and latent heats can be

seen in the presented graphs. Altogether, this impliesan improvement potential for the thermostat and thus

the entire valve.

Acknowledgement

The author is very grateful to Tech.Lic. Nils Hjelte

and Eng. Dan Bengtsson, both at ESBE AB, for fruit-

ful discussions during this work, and to Res.Eng. Ulf

Bengtsson at Linkping university for accurate design

of the thermostat dummy. The study was supported

by The Swedish Foundation for Strategic Research.


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References:

[1] N. McGrellis, Tmv3 why was it needed,Hospi-

tal Development.

[2] H. S. Carslaw and J. C. Jaeger,Conduction of heat

in solids(Oxford University Press, 1959), 2 edn.

[3] O. C. Zienkiewicz, The Finite Element Method

(McGrawHill, 1977).

[4] J. Wren and P. Persson, Thermostatic mixing

valves a method for non-disturbing intra-valve

heat transfer estimation, Transactions on Fluid

Mechanics, ISSN: 1790-5087.

[5] P. Persson, D. Loyd and J. Wren, A measure-

ment equipment for analyzing control characteris-

tics of thermostatic mixing valves, inProceedings

of the 4th European Thermal Sciences Conference

(Birmingham, UK, 2004).

[6] M. Lacroix, Electric water heater designs for

load shifting and control of bacterial contamina-tion,Energy Conversion and Management, 40(2),

1999, 131340.

[7] J. P. Murray, A study of the prevention of hot tap-

water burns,Burns, 14(3), 1988, 18593.


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