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Theoretical and experimental modelling of a heat pipe heat exchanger for high temperature nuclear reactor technology
Applied Thermal Engineering 61 (2013) 259e267
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Theoretical and experimental modelling of a heat pipe heat exchanger for high temperature nuclear reactor technology Ryno Laubscher, Robert T. Dobson* University of Stellenbosch, Department Mechanical Engineering, Banhoek Rd, Stellenbosch 7602, South Africa
h i g h l i g h t s A natural circulation thermosyphon-type heat pipe heat exchanger is considered. Useful in high temperature nuclear reactor technology. Tritium diffusion resistant high temperature heat exchanger. No high pressure shell heat exchanger, pipework and pump needed. A theoretical model is experimentally validated.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 February 2013 Accepted 30 June 2013 Available online 11 July 2013
High temperature heat sources are becoming an ever-increasing imperative in the processing industries for the production of various plastics, fertilisers, coal-to-liquid fuel and hydrogen generation. Current high temperature reactor technology is capable of producing reactor coolant temperatures in excess of 950 C. At these temperatures, tritium which is a radioactive contaminant found in the reactor coolant stream, is able to contaminate the secondary stream by diffusing through the steel retaining wall of the heat exchanger between the reactor coolant and secondary process coolant stream. Current regulations therefore require an extra intermediate heat transfer loop to ensure no cross contamination. A novel heat pipe heat exchanger design is presented which circumvents the need for an intermediate coolant loop. This is done by physically separating the reactor coolant and secondary coolant by two pipe walls and a vapour section and a liquid section. A theoretical transient heat transfer model of such a device is presented. The model uses separate hot gas heating fluid and cold water cooling fluid control volumes, and for the internal working fluid a control volume consisting of a liquid and its vapour in equilibrium with each other. A 2 kW rated experimental model was constructed and tested, using Dowtherm-A as working fluid, to validate the heat pipe heat exchanger theoretical model and design. By determining the boiling heat transfer coefficient through the use of an experimentally formulated correlation it was shown that the theoretical model is indeed able to simulate the characteristic chaotic behaviour, due to the boiling and condensation processes, of the device to within a reasonable level of accuracy. It is concluded that the theoretical simulation model can be used to predict the performance of a higher temperature sodium-charged heat pipe heat exchanger, provided suitable boiling and condensation heat transfer coefficients are used. Ó 2013 Published by Elsevier Ltd.
Keywords: Heat pipe heat exchanger Tritium contamination barrier Dowtherm-A Sodium Theoretical modelling Transient heat transfer
1. Introduction Very high temperature gas-cooled nuclear reactors are expected to operating at reactor coolant temperatures in excess of 950 C and at these temperatures occurrence of tritium in the reactor coolant stream becomes a concern. At these high
* Corresponding author. Tel.: þ27 21 8084268. E-mail address: [email protected] (R.T. Dobson). 1359-4311/$ e see front matter Ó 2013 Published by Elsevier Ltd. http://dx.doi.org/10.1016/j.applthermaleng.2013.06.063
temperatures tritium (H3) has a particularly high diffusion rate through steel [1]. In order to circumvent any possibility of tritium thus finding its way into the secondary stream and ultimately into a consumer product, current nuclear regulatory bodies require an intermediate heat exchanger loop to act as a tritium diffusion barrier between the reactor coolant and secondary coolant streams as shown in Fig. 1(a). This extra heat exchange loop requires additional pumping costs of the intermediate coolant stream, an additional circulating and piping system and an extra heat exchanger all of which significantly increases the
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Nomenclature A cp cv D d E g H h h hfg i k Lc _ m N Nu P Pr Q_ q R Re r R2 T t
area, m2 specific heat at constant pressure, J/kg K specific heat at constant volume, J/kg K diameter, m diameter, m energy, J acceleration due to gravity, m/s2 total enthalpy, J heat transfer coefficient, W/m2 K specific enthalpy, J/kg enthalpy of vaporisation, J/kg K index thermal conductivity, W/m K characteristic length, m mass flow rate, kg/s arbitrary number, number of tubes Nusselt number, Nu ¼ hLc/k pressure, Pa Prandtl number, Pr ¼ cpml/kl heat transfer rate, W heat flux, W/m2 thermal resistance, C/W Reynolds number, Re ¼ rvLc/m radius, m coefficient of determination temperature, C time, s (or min)
initial and operating costs of the power cycle and also results in a larger exergy destruction. A concept design of such a single vessel and single pool and vapour space thermosyphon-type heat pipe heat exchanger (HPHE) is shown in Fig. 2 [2]; it also
Reactor
Single phase shell-and-tube heat exchangers
U u V v x
total internal energy, J specific internal energy, J/kg volume, m3 velocity, m/s direction of flow, distance
Greek symbols r density, kg/m3 m dynamic viscosity, kg/m s D finite difference Subscripts b boiling cond condensation c cold, condenser D diameter evap evaporation h hot int internal (working fluid) l liquid s surface sat saturated v vapour Abbreviations CV control volume HPHE heat pipe heat exchanger HTR high temperature (nuclear) reactor
circumvents the need for the intermediate heat exchange loop and extra heat exchanger. The novel HPHE physically separates the reactor coolant (hot stream) and secondary coolant (cold stream) by two pipe walls and a single pool liquid and vapourspace section as shown in Fig. 1(b). To investigate this HPHE a theoretical model was constructed and its validity established by constructing and testing an experimental HPHE operating at an intermediate temperature of about 230 C, and the feasibility of using this novel concept is analysed in terms of the theoretical and experimental results. In this paper the following areas pertaining to the simulation, design, testing and evaluation of this high temperature heat pipe heat exchanger (HPHE) concept will be considered:
Secondary coolant
(a)
Reactor
Novel heat pipe heat exchanger
Secondary coolant
(b) Fig. 1. Nuclear heat source with a secondary loop (a), and a heat pipe heat exchanger (HPHE) (b).
Fig. 2. Concept drawing of a heat pipe heat exchanger.
R. Laubscher, R.T. Dobson / Applied Thermal Engineering 61 (2013) 259e267 Table 1 Thermal properties of Dowtherm-A (Dow Chemical Company, 1997 [5]). Property
Value
Units
Freezing point Boiling point at atmospheric pressure Flash point Fire point Auto-ignition point Density at 20 C Critical temperature Critical pressure Heat of combustion Latent heat at 100 C Dynamic viscosity at 25 C Thermal conductivity of vapour at 25 C Thermal conductivity of liquid at 25 C Saturated temperature at 50 kPa
12 257.1 113 118 599 1056 497 313.4 30,053 345 3.71 0.0081 0.1379 226.67
C C C C C kg/m3 C kPa kJ/kg kJ/kg mPa s W/m C W/m C C
A literature review/study wherein the design aspects of the HPHE will be highlighted and discussed, and the boiling and condensation heat transfer coefficients correlations used in the theoretical modelling presented and the applicable equations of change considered. The theoretical modelling whereby the conservation of energy equation is applied to control volumes, in order to formulate the equations needed to numerically model the HPHE. The experimental work undertaken, including the experimental setup, instrumentation and operating procedures. The results of the experimental work and the theoretical model, and finally, A brief discussion leading to definite conclusions. 2. Literature review/study and applicable background theory A heat pipe is a closed system containing both the liquid and vapour phases of a working fluid. The one end is heated and the other end cooled. At the so-called evaporator section heat is applied and boiling occurs, at the other end where heat is extracted, the socalled condenser section, the vapour condenses. The condensate flows in the heat pipe under the influence of gravity, or where this is not possible by a capillary structure, back to the evaporator and in this way the heat transfer cycle is completed without the need for any mechanical moving parts and active control devices. If the condensate is returned by gravity only, the heat pipe is often termed a closed two-phase thermosyphon-type heat pipe [3]. The working fluid choice depends on the operating temperature of the HPHE; as a rule of thumb a fluid should be chosen such that, at its desired operating temperature, the corresponding saturation pressure should be between 0.1 and 20 bar [3]. By so doing highvacuum equipment and the possibility of over-pressurisation and rupture are avoided. Another factor determining the choice of a working fluid is that the material of the heat exchanger and the fluid should not react directly with each and neither should the heat exchanger material act as a catalyst resulting in the decomposition of the working fluid. Meeting these requirements is sodium which has a useful temperature range of 600e1200 C. It is generally used for high temperature heat transport due to its desirable low surface tension, high heat transfer coefficient for both boiling and condensation, high latent heat of vaporization, high boiling point, low melting point and high thermal conductivity [4]. Although sodium is thus an excellent choice of working fluid to use in high temperature nuclear reactor heat exchanger applications, in this study however Dowtherm-A, a registered trade name of the Dow Chemical Company [6], a eutectic mixture of 26.5% diphenyl and 73.5% diphenyl oxide, was used as working fluid. Dowtherm-A
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is thermally stable and has a high boiling point at relatively low pressures; its thermal properties are summarised in Table 1. The proposed heat exchanger uses boiling on submerged horizontal tubes in the working fluid liquid and condensation of the thus-formed vapour on the higher set of horizontal tubes as shown in Fig. 2. Heat from the hot stream is transferred by means of internal forced convection to the evaporator pipe wall and by conduction through the pipe wall. Nucleate boiling heat transfer occurs on the evaporator pipe wall and the vapour moves upward, due to the naturally induced pressure difference as a result of condensation on the external surface of the condenser pipe walls through which the colder fluid stream is moving. The heat is then transferred by conduction through the condenser pipe wall and hence by forced convection to the cold stream. The condensate formed then drops back naturally under the influence of gravity into the condensate liquid-pool. This heat transfer process is reminiscent of a conventional wickless gravity assisted heat pipe (or as is often termed a thermosyphon or a two-phase closed thermosyphon). It is also similar to the Perkin’s tube [6]. Heat is transferred in this way through an additional steel barrier and additional liquid and vapour layers, at a relatively low pressure, without the need for an additional high-pressure shell and tube heat exchanger, circulating loop and pump and associated active control systems and with a minimum loss in exergy [7]. The relatively high pressure streams (9 MPa helium and up to 25 MPa water) are conveniently contained in pipes and the need for high pressure large diameter shells obviated. However, should tritium ultimately find its way into the working fluid contained in the HPHE, it being non-condensable, would naturally find its way to the upper-most region of the container where provision can be provided to extract any gas contaminants [2]. When evaluating the thermal characteristics of a new type of HPHE, it is important to consider the boiling and condensation heat transfer coefficients. The boiling heat transfer coefficients can be determined either experimentally or modelled mathematically. The chaotic behaviour of the liquid working fluid within the heat exchanger, due to the boiling of the nucleate and induced bubble flow, so-called bubble pumping [8], makes the modelling of the boiling heat transfer coefficients difficult and hence designers use experimental data to determine the correct heat transfer coefficients for such cases. Boiling has different regimes that depend on the temperature difference between the heating surface and the liquid temperature. Four different boiling regimes are normally defined, namely natural convective boiling, nucleate boiling, transition boiling and film boiling. Nucleate boiling is the most desirable boiling regime in practice because high heat transfer rates can be achieved in this regime with a relatively small temperature difference between the heater surface and liquid [9]. For nucleate boiling, the heat flux is the dominant factor influencing the heat transfer coefficient. Heat transfer rate is also influenced by the physical properties of the boiling fluid, which may even vary along the axial length of the heat exchanger. In general, nucleate boiling heat transfer coefficient correlations contain a wall heat flux, a temperature term to capture the fluid pressure and density and a fluid property dependent factor, such as the fluid Prandtl number, to capture the effect of thermal conductivity, surface tension and heat capacity [8]. Using this logic the correlation for the DowthermA charged HPHE that best simulated the experimentally determined boiling heat transfer coefficients was determined using multivariable linear regression, with a coefficient of determination of R2 ¼ 0.831, is given by Equation (1). Although the Mostinskii, Rohsenow, Kutateladze, StephaneAdelsalam and Gorenflo boiling correlations were also considered as potential candidates in theoretically predicting the experimentally-obtained heat transfer rates none of them gave nearly as good a match as Equation (1) [2].
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3. Theoretical modelling
Fig. 3. Discretisation of heat exchanger into a series of elements, each element consisting of a hot heating, two-phase and a colding control volume, as shown in Fig. 4.
0:07675 0:485 104 Ts evap Tint fluid Cpl ml 0:6857 3:291 0:9287 Tsat kl
The HPHE shown in Fig. 2 consists of a housing or container that is charged with the working fluid, and a hot stream section and cold stream section. The discretisation of this heat exchanger system into numerical control elements, labelled 1, 2, 3, 4, ., i., N 1, N, is seen in Fig. 3. Each vertical element, in turn, consists of three onedimensional control volumes, the hot stream, two-phase working fluid and cold stream control volumes as shown in Fig. 4. The energy equation, neglecting potential and kinetic energy, is given by,
DE _ in ðmhÞ _ out þ Q_ in Q_ out ¼ ðmhÞ Dt
(9)
(1)
Equation (9) is applied to each of the three separate control volumes in each of the i ¼ 1eN elements shown in Fig. 3. In applying the conservation of energy however a number of assumptions are needed, namely:
Condensation of vapour will occur when the temperature of the vapour is reduced to below its saturation temperature. This is done by bringing the hot vapour into contact with a surface that is at a lower temperature than the saturation temperature of the vapour. At the condenser section of the HPHE, condensate wets the surface of the tube(s) and forms a liquid film on the surface that flows down the curvature of the tube under the influence of gravity. This is called laminar film-wise condensation, and as originally formulated by Nusselt, takes on the form (Mills, 1995).
the vapour is assumed to flow uniformly upwards, the condensate drops vertically downwards in each control volume with essentially no axially orientated flow between adjacent working fluid control volumes, there is no interfacial thermal resistance between the liquid and vapour, in each vertical element the entire liquid and vapour volumes are at the same (saturated) temperature and the pressure of the hot gas and cooling water is constant.
hb ¼
hc ¼ 0:728
ðrl rv Þghfg k3l Nðm=rl ÞdðTsat Ts Þ
(2)
For the experimentally tested Dowtherm-A charged HPHE however a correlation better simulating the experimentally determined condensation heat transfer coefficients is better correlated in terms of a film Reynolds number and temperature with a coefficient of determination of R2 ¼ 0.927 as Ref. [2]. 4:30 hc ¼ 0:01074Re2:667 Tsat
Applying the conservation of energy, as given by Equation (9), to each of the three control volumes in the ith element;
DH Dt
for the Evaporator
_ i hot in ðmhÞ _ i hot out Q_ i evap ¼ ðmhÞ (10)
for thecondenser
DH Dt
i cold
_ i cold in ðmhÞ _ i cold out þ Q_ i cond ¼ ðmhÞ
(3)
(11)
Where the film Reynolds number was given by Ref. [8] as,
" #1=3 4 2kl Tint fluid TS cond d 4ðrl rv Þg Re ¼ 2:5872 mhfg 3 3rl ðm=rl Þ2
i hot
and for the working fluid (4)
DU Dt
i int fluid
¼ Q_ i evap Q_ i cond Q_ i loss (12)
The thermal resistances can be defined as follows:
X
X
Revap ¼
1 lnðd0 =di Þ 1 þ ¼ hh Ah 2pkDx hb Ab
(5)
Rcond ¼
1 lnðd0 =di Þ 1 þ ¼ hc Ac 2pkDx hc Ac
(6)
where the internal pipe heat transfer coefficients are calculated using the Gnielinski correlation and Petukhov friction factor as given in Equations (7) and (8), respectively, as Ref. [8]
f ¼ ð0:79ln ReD 1:64DÞ0:2 hD ¼
k ðf =8ÞðReD 1000ÞPr D 1 þ 12:7ðf =8Þ1=2 Pr2=3 1
and where the heat transfer area are given by A ¼ pdDx.
(7)
(8) Fig. 4. Depiction of three control volumes constituting the i-th element in the heat pipe heat exchanger.
R. Laubscher, R.T. Dobson / Applied Thermal Engineering 61 (2013) 259e267
where Q_ i loss represents the heat loss to the environment through the working fluid container and the insulation. Using a fully explicit time-stepping upwind finite difference numerical formulation method Equations (10)e(12) are rewritten as Equations (13)e(14), respectively as:
it h Dt ¼ H t _ _ _ Hitþhot i hot þ Dt ðmhÞi hot in ðmhÞi hot out Q i evap
(13)
it h Dt ¼ H t _ _ _ Hitþ i cold þ Dt ðmhÞi cold in ðmhÞi cold out þ Q i cond cold
(14)
it h Dt ¼ Uit int fluid þ Dt Q_ i evap Q_ i cond Q_ i loss Uitþint fluid
(15)
_ ¼ where Dt denotes the time step, H ¼ rADxh, A ¼ pri2 , h ¼ cpT, m rvA and U ¼ rVcvT. Assuming that cp, cv and r are constant for each element and dividing Equation (13) by ri hotADxcp i hot and Equation (14) by ri coldADxcp i cold and Equation (15) by ri int fluidVcv i int fluid and after rearrangement into a form suitable for computer program solution, Equations (13)e(15) become, respectively, as, Dt ¼ Titþ hot
rcp T t
rcp
!
tþDt
þ i hot
Dt rADxcp
rvAcp T i hot out Dt Titþ cold
¼
rcp T t rcp
tþDt
i cold
Dt rADxcp
rvAcp T i cold out Dt Titþ int fluid
¼
rcv T t ðrcv ÞtþDt
h
rvAcp T
i hot in
i hot it _ Q i evap
! þ
tþDt
þ
Q_ i cond Q_ i loss
tþDt
h
rvAcp T
i cold in
i cold it _ Q i evap
! i int fluid
(16)
it
Dt
(17) h D
t ðrADxcv Þtþ i int fluid
Q_ i evap (18)
Equations (16)e(18) are numerically stable provided the time step is less than Dt < Dx/v; namely provided that a fluid particle does not move a distance greater than the control volume Dx. Note that the density and specific heats at time step t þ Dt and rtþDt ¼ rt þ ðDr=DtÞtDt=2 Dt and ctþDt ¼ ct þ ðDc=DtÞtDt=2 Dt, respectively. The heat transfer rates Q_ i from the heating gas to the working fluid and from the working fluid to the cooling liquid are given by Equation (19) to Equation (20), respectively as:
T T Q_ i evap ¼ i hotP i int fluid Revap
(19)
T fluid T i cold Q_ i cond ¼ i int P Rcond
(20)
where T i hot and T i cold are the average hot stream and cold stream control volume temperatures, and assuming a linear temperature distribution along each control volume, the average heating fluid and cooling fluid temperatures are given, respectively as T i hot ¼ ðTi hot in þ Ti hot out Þ=2 and T i cold ¼ ðTi cold in þ Ti cold out Þ=2, and Ti int fluid is the internal fluid control volume temperature. The thermal resistances for the P P evaporator, Revap and the condenser, Rcond are given by Equations (5) and (6).
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4. Experimental set-up and procedure A special heat pipe heat exchanger with a large glass flanged window in the front and back was designed, built and installed as shown in Fig. 5 and insulated with 50 mm thick ceramic wool. The windows allowed for the visual observation of the detailed twophase flow behaviour during operation. The diameter of the hot gas pipe submerged in the liquid is 101.6 mm, whilst that of the cold water pipe in the vapour space is 21.8 mm; this was done to take into account the lower gas heat transfer coefficient compared with the higher waterside heat transfer coefficient. Single hot pipe and a single cold water pipe was used to eliminate the effect of the pipes on each other; this was done to more confidently compare experimentally determined heat transfer coefficients with published single tube heat transfer coefficients. The applicable parameters for the as-designed experimental HPHE are shown in Table 2. Fig. 6a shows a photograph of the as-built HPHE without the insulation, Fig. 6b shows the burner and installed HPHE and Fig. 6c the HPHE with the insulation applied to the vessel. K-type thermocouples were used for all the temperature measurements. Each and every thermocouple and its specific instrumentation measurement and data capture channel was individually calibrated against a 100 U platinum resistance substandard thermometer which had previously been calibrated by an accredited calibration laboratory. As such all the temperature channel measurements are within 0.1 C, relative to the substandard instrument. The thermocouple junctions were positioned at four vertical-plane locations (0.058, 0.248, 0.428 and 0.618 m from the hot stream inlet side) along the axial length of the pipes. The sensor locations for one such vertically orientated plane is shown in Fig. 7. For each vertical plane three temperature measurements were taken around the periphery of the heat exchange pipes, in the liquid next to and just above the evaporator pipe, and two above each other in the vapour space; giving a total of 44. Four thermocouples were used to measure the inlet and outlet temperatures of the heating gas and cooling water. The temperature in the laboratory was also recorded. Mass flow rate of the gas was determined using a bell-mouth located at the gas-burner inlet to which the liquefied petroleum gas (LPG) fuel was added and its mass flow rate measured using an orifice-plate type flow meter. The mass flow rate of the cold water stream (from a constant head tank) was determined by using a measuring cylinder and stopwatch. Before the HPHE can be operated properly and repeatedly all the non-condensable gasses trapped in the container during the charging procedure needs to be removed. The HPHE container is evacuated at room temperature to an absolute pressure of about 25 kPa, using a two-stage dry vacuum pump. The remaining traces of non-condensable gas are then removed by heating the working fluid using the hot-gas heated evaporator pipe until vigorous boiling occurs. During this phase non-condensable gas tends to collect in the top of the container vapour space and its presence is readily detected by noting whether the top temperature in the container is less than or equal to the boiling liquid temperature. Should the top temperature be less than the liquid temperature the valve to the already running vacuum pump is slightly opened for a short while and the non-condensable gas that has collected in the top of the container is allowed to escape, together with a little vapour; and the valve is then closed. This process is repeated until the vapour temperature just below the top plate corresponds to the temperature of the boiling liquid. Once all the non-condensable gasses have been eliminated from the HPHE container the hot gas heating of the evaporator pipe continues, but with the condenser cooling water turned off, in this way the heating-up process is expedited. During this heating-up
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Fig. 5. Schematic layout of the experimental setup of the heat pipe heat exchanger (HPHE) shown in Fig. 6.
phase temperature readings are taken at regular intervals. Once the internal working fluid reaches the desired temperature the condenser cooling water is turned on and the HPHE is allowed to attain steady-state conditions. The cooling water is then turned off and the working fluid allowed to increase to yet a higher temperature, the cooling water again turned on and temperatures logged and operated until a steady-state condition is again obtained. This process is repeated a few times until the maximum design operating temperature of the working fluid has been reached. One such a heating and cooling procedure, for three heating repetitions is shown in Fig. 8 for a position 0.248 m from the hot gas inlet.
Table 2 Design parameters of experimental model. Working fluid
Dowtherm-A
Inlet hot stream temperature Inlet cold stream temperature Outlet cold temperature Hot stream mass flow Cold stream mass flow HPHE core length Evaporator tube outside diameter Condenser tube outside diameter Heat transfer rate Working fluid temperature
550e650 C 14e18 C 50e90 C 0.045 kg/s 0.02 kg/s 0.67 m 0.1016 m 0.0218 m 1500 to 1800 W 215e230 C
Finally the heating and cooling streams are turned off and the system allowed to cool back to room temperature. During this cooling phase the temperatures are recorded every 10 min. Knowing the mass of working fluid in the container, an idea of the heat loss through the insulation surrounding the HPHE and the pipes and support structures from the working fluid to the environment, as a function of the temperature difference between the working fluid and the laboratory room, can be obtained. 5. Results and discussion Fig. 8 shows the working fluid liquid and vapour temperature as a function of time at a vertical distance 0.248 m from the hot gas inlet and on a vertical plane at a position as indicated in Fig. 7. The objective of showing Fig. 8 is to show how non-condensable gasses can be removed from the working fluid container by so-called “burping”. This is done by increasing the internal pressure of the working fluid container to a pressure above the ambient pressure (by heating the working fluid but without any cooling fluid flow). Provided the internal pressure is higher than atmospheric pressure by opening an escape valve momentarily, valve V-3 in Fig. 5, noncondensable gasses together with a little vapour is expelled out from the top of the container and into the sump. For this figure however the maximum temperature is only 223 C and the saturation pressure corresponding to this pressure is only 45 kPa, well below atmospheric pressure. In this case thus the vacuum pump
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Fig. 6. a. Photograph of experimental heat pipe heat exchanger set-up (without its insulation). The dimensions of the container are (excluding the flanged instrumentation and observation platforms) 596 mm high, 671 mm wide and 516 mm deep. b. Photograph of the heat pipe heat exchanger and hot gas supply burner in the laboratory. c. Experimental heat exchanger with its thermal insulation (ceramic wool), but with the front insulation removed.
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Fig. 9. Energy balance of experimental heat pipe heat exchanger.
Fig. 7. Relative positions of the thermocouples junctions located on one of the four vertical planes along the length of the length of the HPHE located in a vertical plane.
had already been switched on and burping achieved by momentarily opening and then closing valve V-2 in Fig. 5. It is seen that up to about 180 min that the liquid temperature is significantly higher that the vapour temperature, thus indicating the presence of noncondensable gas in the top of the container. At about 180 min the container is “burped” and the temperature of the liquid tends to drop slightly (due to evaporative and adiabatic cooling). The temperature as measured in the vapour space then rises quickly and significantly until both temperatures equalise. Shortly thereafter the temperature of the vapour falls below that of the liquid. At about 260 min burping was again initiated, and so on for several times until the vapour and liquid temperatures remain equal. The HPHE is now ready for normal operation. Very similar curves were obtained at the other three vertical positions along the heat exchanger thereby indicating that the temperature gradient along the axial length along the tubes is small, and thus indicating there is relatively little axial heat transfer between adjacent working fluid control volumes; and thus validating the assumption that the heat transfer is essential one-dimensional and orientated more-or-less vertically upwards.
Fig. 8. Working fluid temperature readings on a vertical plane at a distance 0.248 m from the hot gas inlet side as a function of time during a typical procedure whereby the non-condensable gas is eliminated from the container.
To add credibility to the experimental results the energy needs be accounted for by showing a balance between the evaporator heat input and the heat removed by the condenser, plus the heat losses through the insulation and support structures. Fig. 9 shows such an energy reconciliation for the HPHE in which the data points are scattered more or less uniformly about the diagonal and more or less all within 40%. This relatively wide spread in the results is typical in heat pipes due to the complex and vigorous and chaotic nature of the nucleate boiling process and the seemingly random formation of condensate droplets on the condenser tube and thermocouple probe tips and then their dropping down into the liquid pool, rather than the smooth film-wise flow as suggested by Nusselt film-wise condensation theory. The heat loss was determined experimentally as a function of the temperature difference, and to a coefficient of determination R2 ¼ 0.948, as
Q_ loss ¼ 4:105 Ti int fluid Tambient 177:4
(21)
Fig. 10 gives a depiction of the experimentally measured and theoretically predicted temperatures of working fluid as a function of time at a distance 0.248 m from the hot gas inlet side. The only noticeable discrepancy between the experimental and simulated results is at time 260 min and 320 min. This is when the vacuum pump was switched on during the experiment and the pressure
Fig. 10. Experimentally measured and theoretically predicted temperature of working fluid as a function of time at a distance 0.248 m from the hot gas inlet side.
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Table 3 Heat transfer and pressure comparison between the numerical and experimental results. Parameter
Computer program
Experimental
_h m _c m Q_ loss Q_ in Q_
0.045694 kg/s 0.019 kg/s 537.363 W 1305.626 W 1034.193 W 41.39 kPa
0.045278 kg/s 0.026 kg/s 714.95 W 1388.247 W 1047.746 W 43 kPa
out
Pinternal
was dropped forcibly. The computer program could not accurately simulate this process. Therefore the simulation was setup to run from 190 min to 260 min, at which point the internal temperature of the heat exchanger in the computer program was assigned a lower value to simulate the pressure drop. The lower temperature value was taken from the experimental data and the program was then allowed to continue its calculations. The same process was followed at 320 min. After investigation of the graphs it can be deduced that the theoretical and transient simulation produces accurate results, and can be used to predict the heating time of a heat pipe heat exchanger with relative confidence. A comparison of the numerical computer program simulation and the experimental results is given in Table 3 [2]. At time 330 min in Fig. 8 a steady-state was reached for the experimental model and these results have been reflected in Fig. 11 in vertical planes in the HPHE at the four positions from the hot gas inlet. It is seen that the theoretical model accurately simulates the experimental working fluid and cooling water temperatures, but that the hot gas temperatures are slightly over predicted. This could be due to uncertainties in the exact amount and characteristics of the gasses of combustion from the burner.
6. Conclusions A heat pipe heat exchanger (HPHE) concept was presented that circumvents the need for a secondary pumped heat exchange loop in very high temperature nuclear reactor technology, and that also reduces the likelihood of tritium finding its way into the process heat stream. A transient heat transfer theoretical simulation model was developed and an experimental Dowtherm-A charged model tested at a working fluid temperature of about 220 C. It was found that the theoretical heat transfer model was able to predict the experimentally determined results to within a reasonable degree of accuracy.
Fig. 11. Temperature profiles of the hot stream, cold stream and working fluid for the numerical simulation and the experimental heat exchanger along the length of the evaporator tube (with experimental points as marked).
Dowtherm-A-specific boiling and condensation heat transfer coefficient correlations were specially developed, as generally applicable existing correlations proved to give unsatisfactory results. Having built and tested a 220 C system the detailed design of a more technically challenging 800 C sodium charged experimental model can commence with more confidence. References [1] A. Jousse, Tritium Transport in Very High Temperature Reactors for Hydrogen Production. Report number UCBTH07-005, Department of Nuclear Engineering, University of California at Berkeley, August 31, 2007. Also available: at, http:// pb-ahtr.nuc.berkeley.edu/papers/07-005_Tritium_Report_B.pdf. [2] R. Laubscher, Development Aspects of a High Temperature Heat Pipe Heat Exchanger for High Temperature Gas-cooled Nuclear Reactor Systems. Masters thesis, University of Stellenbosch, Stellenbosch, South Africa, 2013. [3] A. Faghri, Heat Pipe Science and Technology, Taylor and Francis, 1995. [4] G.P. Sabharwall, Theoretical design of thermosyphon for process heat transfer from NGNP to hydrogen plant, in: Proceedings of HTR-2008, ASME 4th International Topical Meeting on High Temperature Reactor Technology, September 28eOctober 1, 2008. Paper number HTR2008-58199, Washington, D.C., USA. [5] The Dow Chemical Company, Dowtherm a Heat Transfer Fluid: Product Technical Data, 1997 (Online) Available at: http://msdssearch.dow.com/ PublishedLiteratureDOWCOM/dh_0030/0901b803800303cd.pdf?filepath¼/ heattrans/pdfs/noreg/176-01337.pdf&fromPage¼GetDoc. [6] D.A. Reay, P.A. Kew, Heat Pipes, Theory Design and Applications, fifth ed., Butterworth-Heinemann, 2006. [7] Y. Cengel, M.A. Boles, Thermodynamics an Engineering Approach, McGraw Hill, 2006. [8] A.F. Mills, Heat Transfer, second ed., Prentice Hall, 1999. [9] Y. Cengel, Heat and Mass Transfer, Fundamentals and Applications, fourth ed., McGraw Hill, 2006 in S.I. units.
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Theoretical and experimental modelling of a heat pipe heat exchanger for high temperature nuclear reactor technology Ryno Laubscher, Robert T. Dobson* University of Stellenbosch, Department Mechanical Engineering, Banhoek Rd, Stellenbosch 7602, South Africa
h i g h l i g h t s A natural circulation thermosyphon-type heat pipe heat exchanger is considered. Useful in high temperature nuclear reactor technology. Tritium diffusion resistant high temperature heat exchanger. No high pressure shell heat exchanger, pipework and pump needed. A theoretical model is experimentally validated.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 February 2013 Accepted 30 June 2013 Available online 11 July 2013
High temperature heat sources are becoming an ever-increasing imperative in the processing industries for the production of various plastics, fertilisers, coal-to-liquid fuel and hydrogen generation. Current high temperature reactor technology is capable of producing reactor coolant temperatures in excess of 950 C. At these temperatures, tritium which is a radioactive contaminant found in the reactor coolant stream, is able to contaminate the secondary stream by diffusing through the steel retaining wall of the heat exchanger between the reactor coolant and secondary process coolant stream. Current regulations therefore require an extra intermediate heat transfer loop to ensure no cross contamination. A novel heat pipe heat exchanger design is presented which circumvents the need for an intermediate coolant loop. This is done by physically separating the reactor coolant and secondary coolant by two pipe walls and a vapour section and a liquid section. A theoretical transient heat transfer model of such a device is presented. The model uses separate hot gas heating fluid and cold water cooling fluid control volumes, and for the internal working fluid a control volume consisting of a liquid and its vapour in equilibrium with each other. A 2 kW rated experimental model was constructed and tested, using Dowtherm-A as working fluid, to validate the heat pipe heat exchanger theoretical model and design. By determining the boiling heat transfer coefficient through the use of an experimentally formulated correlation it was shown that the theoretical model is indeed able to simulate the characteristic chaotic behaviour, due to the boiling and condensation processes, of the device to within a reasonable level of accuracy. It is concluded that the theoretical simulation model can be used to predict the performance of a higher temperature sodium-charged heat pipe heat exchanger, provided suitable boiling and condensation heat transfer coefficients are used. Ó 2013 Published by Elsevier Ltd.
Keywords: Heat pipe heat exchanger Tritium contamination barrier Dowtherm-A Sodium Theoretical modelling Transient heat transfer
1. Introduction Very high temperature gas-cooled nuclear reactors are expected to operating at reactor coolant temperatures in excess of 950 C and at these temperatures occurrence of tritium in the reactor coolant stream becomes a concern. At these high
* Corresponding author. Tel.: þ27 21 8084268. E-mail address: [email protected] (R.T. Dobson). 1359-4311/$ e see front matter Ó 2013 Published by Elsevier Ltd. http://dx.doi.org/10.1016/j.applthermaleng.2013.06.063
temperatures tritium (H3) has a particularly high diffusion rate through steel [1]. In order to circumvent any possibility of tritium thus finding its way into the secondary stream and ultimately into a consumer product, current nuclear regulatory bodies require an intermediate heat exchanger loop to act as a tritium diffusion barrier between the reactor coolant and secondary coolant streams as shown in Fig. 1(a). This extra heat exchange loop requires additional pumping costs of the intermediate coolant stream, an additional circulating and piping system and an extra heat exchanger all of which significantly increases the
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Nomenclature A cp cv D d E g H h h hfg i k Lc _ m N Nu P Pr Q_ q R Re r R2 T t
area, m2 specific heat at constant pressure, J/kg K specific heat at constant volume, J/kg K diameter, m diameter, m energy, J acceleration due to gravity, m/s2 total enthalpy, J heat transfer coefficient, W/m2 K specific enthalpy, J/kg enthalpy of vaporisation, J/kg K index thermal conductivity, W/m K characteristic length, m mass flow rate, kg/s arbitrary number, number of tubes Nusselt number, Nu ¼ hLc/k pressure, Pa Prandtl number, Pr ¼ cpml/kl heat transfer rate, W heat flux, W/m2 thermal resistance, C/W Reynolds number, Re ¼ rvLc/m radius, m coefficient of determination temperature, C time, s (or min)
initial and operating costs of the power cycle and also results in a larger exergy destruction. A concept design of such a single vessel and single pool and vapour space thermosyphon-type heat pipe heat exchanger (HPHE) is shown in Fig. 2 [2]; it also
Reactor
Single phase shell-and-tube heat exchangers
U u V v x
total internal energy, J specific internal energy, J/kg volume, m3 velocity, m/s direction of flow, distance
Greek symbols r density, kg/m3 m dynamic viscosity, kg/m s D finite difference Subscripts b boiling cond condensation c cold, condenser D diameter evap evaporation h hot int internal (working fluid) l liquid s surface sat saturated v vapour Abbreviations CV control volume HPHE heat pipe heat exchanger HTR high temperature (nuclear) reactor
circumvents the need for the intermediate heat exchange loop and extra heat exchanger. The novel HPHE physically separates the reactor coolant (hot stream) and secondary coolant (cold stream) by two pipe walls and a single pool liquid and vapourspace section as shown in Fig. 1(b). To investigate this HPHE a theoretical model was constructed and its validity established by constructing and testing an experimental HPHE operating at an intermediate temperature of about 230 C, and the feasibility of using this novel concept is analysed in terms of the theoretical and experimental results. In this paper the following areas pertaining to the simulation, design, testing and evaluation of this high temperature heat pipe heat exchanger (HPHE) concept will be considered:
Secondary coolant
(a)
Reactor
Novel heat pipe heat exchanger
Secondary coolant
(b) Fig. 1. Nuclear heat source with a secondary loop (a), and a heat pipe heat exchanger (HPHE) (b).
Fig. 2. Concept drawing of a heat pipe heat exchanger.
R. Laubscher, R.T. Dobson / Applied Thermal Engineering 61 (2013) 259e267 Table 1 Thermal properties of Dowtherm-A (Dow Chemical Company, 1997 [5]). Property
Value
Units
Freezing point Boiling point at atmospheric pressure Flash point Fire point Auto-ignition point Density at 20 C Critical temperature Critical pressure Heat of combustion Latent heat at 100 C Dynamic viscosity at 25 C Thermal conductivity of vapour at 25 C Thermal conductivity of liquid at 25 C Saturated temperature at 50 kPa
12 257.1 113 118 599 1056 497 313.4 30,053 345 3.71 0.0081 0.1379 226.67
C C C C C kg/m3 C kPa kJ/kg kJ/kg mPa s W/m C W/m C C
A literature review/study wherein the design aspects of the HPHE will be highlighted and discussed, and the boiling and condensation heat transfer coefficients correlations used in the theoretical modelling presented and the applicable equations of change considered. The theoretical modelling whereby the conservation of energy equation is applied to control volumes, in order to formulate the equations needed to numerically model the HPHE. The experimental work undertaken, including the experimental setup, instrumentation and operating procedures. The results of the experimental work and the theoretical model, and finally, A brief discussion leading to definite conclusions. 2. Literature review/study and applicable background theory A heat pipe is a closed system containing both the liquid and vapour phases of a working fluid. The one end is heated and the other end cooled. At the so-called evaporator section heat is applied and boiling occurs, at the other end where heat is extracted, the socalled condenser section, the vapour condenses. The condensate flows in the heat pipe under the influence of gravity, or where this is not possible by a capillary structure, back to the evaporator and in this way the heat transfer cycle is completed without the need for any mechanical moving parts and active control devices. If the condensate is returned by gravity only, the heat pipe is often termed a closed two-phase thermosyphon-type heat pipe [3]. The working fluid choice depends on the operating temperature of the HPHE; as a rule of thumb a fluid should be chosen such that, at its desired operating temperature, the corresponding saturation pressure should be between 0.1 and 20 bar [3]. By so doing highvacuum equipment and the possibility of over-pressurisation and rupture are avoided. Another factor determining the choice of a working fluid is that the material of the heat exchanger and the fluid should not react directly with each and neither should the heat exchanger material act as a catalyst resulting in the decomposition of the working fluid. Meeting these requirements is sodium which has a useful temperature range of 600e1200 C. It is generally used for high temperature heat transport due to its desirable low surface tension, high heat transfer coefficient for both boiling and condensation, high latent heat of vaporization, high boiling point, low melting point and high thermal conductivity [4]. Although sodium is thus an excellent choice of working fluid to use in high temperature nuclear reactor heat exchanger applications, in this study however Dowtherm-A, a registered trade name of the Dow Chemical Company [6], a eutectic mixture of 26.5% diphenyl and 73.5% diphenyl oxide, was used as working fluid. Dowtherm-A
261
is thermally stable and has a high boiling point at relatively low pressures; its thermal properties are summarised in Table 1. The proposed heat exchanger uses boiling on submerged horizontal tubes in the working fluid liquid and condensation of the thus-formed vapour on the higher set of horizontal tubes as shown in Fig. 2. Heat from the hot stream is transferred by means of internal forced convection to the evaporator pipe wall and by conduction through the pipe wall. Nucleate boiling heat transfer occurs on the evaporator pipe wall and the vapour moves upward, due to the naturally induced pressure difference as a result of condensation on the external surface of the condenser pipe walls through which the colder fluid stream is moving. The heat is then transferred by conduction through the condenser pipe wall and hence by forced convection to the cold stream. The condensate formed then drops back naturally under the influence of gravity into the condensate liquid-pool. This heat transfer process is reminiscent of a conventional wickless gravity assisted heat pipe (or as is often termed a thermosyphon or a two-phase closed thermosyphon). It is also similar to the Perkin’s tube [6]. Heat is transferred in this way through an additional steel barrier and additional liquid and vapour layers, at a relatively low pressure, without the need for an additional high-pressure shell and tube heat exchanger, circulating loop and pump and associated active control systems and with a minimum loss in exergy [7]. The relatively high pressure streams (9 MPa helium and up to 25 MPa water) are conveniently contained in pipes and the need for high pressure large diameter shells obviated. However, should tritium ultimately find its way into the working fluid contained in the HPHE, it being non-condensable, would naturally find its way to the upper-most region of the container where provision can be provided to extract any gas contaminants [2]. When evaluating the thermal characteristics of a new type of HPHE, it is important to consider the boiling and condensation heat transfer coefficients. The boiling heat transfer coefficients can be determined either experimentally or modelled mathematically. The chaotic behaviour of the liquid working fluid within the heat exchanger, due to the boiling of the nucleate and induced bubble flow, so-called bubble pumping [8], makes the modelling of the boiling heat transfer coefficients difficult and hence designers use experimental data to determine the correct heat transfer coefficients for such cases. Boiling has different regimes that depend on the temperature difference between the heating surface and the liquid temperature. Four different boiling regimes are normally defined, namely natural convective boiling, nucleate boiling, transition boiling and film boiling. Nucleate boiling is the most desirable boiling regime in practice because high heat transfer rates can be achieved in this regime with a relatively small temperature difference between the heater surface and liquid [9]. For nucleate boiling, the heat flux is the dominant factor influencing the heat transfer coefficient. Heat transfer rate is also influenced by the physical properties of the boiling fluid, which may even vary along the axial length of the heat exchanger. In general, nucleate boiling heat transfer coefficient correlations contain a wall heat flux, a temperature term to capture the fluid pressure and density and a fluid property dependent factor, such as the fluid Prandtl number, to capture the effect of thermal conductivity, surface tension and heat capacity [8]. Using this logic the correlation for the DowthermA charged HPHE that best simulated the experimentally determined boiling heat transfer coefficients was determined using multivariable linear regression, with a coefficient of determination of R2 ¼ 0.831, is given by Equation (1). Although the Mostinskii, Rohsenow, Kutateladze, StephaneAdelsalam and Gorenflo boiling correlations were also considered as potential candidates in theoretically predicting the experimentally-obtained heat transfer rates none of them gave nearly as good a match as Equation (1) [2].
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3. Theoretical modelling
Fig. 3. Discretisation of heat exchanger into a series of elements, each element consisting of a hot heating, two-phase and a colding control volume, as shown in Fig. 4.
0:07675 0:485 104 Ts evap Tint fluid Cpl ml 0:6857 3:291 0:9287 Tsat kl
The HPHE shown in Fig. 2 consists of a housing or container that is charged with the working fluid, and a hot stream section and cold stream section. The discretisation of this heat exchanger system into numerical control elements, labelled 1, 2, 3, 4, ., i., N 1, N, is seen in Fig. 3. Each vertical element, in turn, consists of three onedimensional control volumes, the hot stream, two-phase working fluid and cold stream control volumes as shown in Fig. 4. The energy equation, neglecting potential and kinetic energy, is given by,
DE _ in ðmhÞ _ out þ Q_ in Q_ out ¼ ðmhÞ Dt
(9)
(1)
Equation (9) is applied to each of the three separate control volumes in each of the i ¼ 1eN elements shown in Fig. 3. In applying the conservation of energy however a number of assumptions are needed, namely:
Condensation of vapour will occur when the temperature of the vapour is reduced to below its saturation temperature. This is done by bringing the hot vapour into contact with a surface that is at a lower temperature than the saturation temperature of the vapour. At the condenser section of the HPHE, condensate wets the surface of the tube(s) and forms a liquid film on the surface that flows down the curvature of the tube under the influence of gravity. This is called laminar film-wise condensation, and as originally formulated by Nusselt, takes on the form (Mills, 1995).
the vapour is assumed to flow uniformly upwards, the condensate drops vertically downwards in each control volume with essentially no axially orientated flow between adjacent working fluid control volumes, there is no interfacial thermal resistance between the liquid and vapour, in each vertical element the entire liquid and vapour volumes are at the same (saturated) temperature and the pressure of the hot gas and cooling water is constant.
hb ¼
hc ¼ 0:728
ðrl rv Þghfg k3l Nðm=rl ÞdðTsat Ts Þ
(2)
For the experimentally tested Dowtherm-A charged HPHE however a correlation better simulating the experimentally determined condensation heat transfer coefficients is better correlated in terms of a film Reynolds number and temperature with a coefficient of determination of R2 ¼ 0.927 as Ref. [2]. 4:30 hc ¼ 0:01074Re2:667 Tsat
Applying the conservation of energy, as given by Equation (9), to each of the three control volumes in the ith element;
DH Dt
for the Evaporator
_ i hot in ðmhÞ _ i hot out Q_ i evap ¼ ðmhÞ (10)
for thecondenser
DH Dt
i cold
_ i cold in ðmhÞ _ i cold out þ Q_ i cond ¼ ðmhÞ
(3)
(11)
Where the film Reynolds number was given by Ref. [8] as,
" #1=3 4 2kl Tint fluid TS cond d 4ðrl rv Þg Re ¼ 2:5872 mhfg 3 3rl ðm=rl Þ2
i hot
and for the working fluid (4)
DU Dt
i int fluid
¼ Q_ i evap Q_ i cond Q_ i loss (12)
The thermal resistances can be defined as follows:
X
X
Revap ¼
1 lnðd0 =di Þ 1 þ ¼ hh Ah 2pkDx hb Ab
(5)
Rcond ¼
1 lnðd0 =di Þ 1 þ ¼ hc Ac 2pkDx hc Ac
(6)
where the internal pipe heat transfer coefficients are calculated using the Gnielinski correlation and Petukhov friction factor as given in Equations (7) and (8), respectively, as Ref. [8]
f ¼ ð0:79ln ReD 1:64DÞ0:2 hD ¼
k ðf =8ÞðReD 1000ÞPr D 1 þ 12:7ðf =8Þ1=2 Pr2=3 1
and where the heat transfer area are given by A ¼ pdDx.
(7)
(8) Fig. 4. Depiction of three control volumes constituting the i-th element in the heat pipe heat exchanger.
R. Laubscher, R.T. Dobson / Applied Thermal Engineering 61 (2013) 259e267
where Q_ i loss represents the heat loss to the environment through the working fluid container and the insulation. Using a fully explicit time-stepping upwind finite difference numerical formulation method Equations (10)e(12) are rewritten as Equations (13)e(14), respectively as:
it h Dt ¼ H t _ _ _ Hitþhot i hot þ Dt ðmhÞi hot in ðmhÞi hot out Q i evap
(13)
it h Dt ¼ H t _ _ _ Hitþ i cold þ Dt ðmhÞi cold in ðmhÞi cold out þ Q i cond cold
(14)
it h Dt ¼ Uit int fluid þ Dt Q_ i evap Q_ i cond Q_ i loss Uitþint fluid
(15)
_ ¼ where Dt denotes the time step, H ¼ rADxh, A ¼ pri2 , h ¼ cpT, m rvA and U ¼ rVcvT. Assuming that cp, cv and r are constant for each element and dividing Equation (13) by ri hotADxcp i hot and Equation (14) by ri coldADxcp i cold and Equation (15) by ri int fluidVcv i int fluid and after rearrangement into a form suitable for computer program solution, Equations (13)e(15) become, respectively, as, Dt ¼ Titþ hot
rcp T t
rcp
!
tþDt
þ i hot
Dt rADxcp
rvAcp T i hot out Dt Titþ cold
¼
rcp T t rcp
tþDt
i cold
Dt rADxcp
rvAcp T i cold out Dt Titþ int fluid
¼
rcv T t ðrcv ÞtþDt
h
rvAcp T
i hot in
i hot it _ Q i evap
! þ
tþDt
þ
Q_ i cond Q_ i loss
tþDt
h
rvAcp T
i cold in
i cold it _ Q i evap
! i int fluid
(16)
it
Dt
(17) h D
t ðrADxcv Þtþ i int fluid
Q_ i evap (18)
Equations (16)e(18) are numerically stable provided the time step is less than Dt < Dx/v; namely provided that a fluid particle does not move a distance greater than the control volume Dx. Note that the density and specific heats at time step t þ Dt and rtþDt ¼ rt þ ðDr=DtÞtDt=2 Dt and ctþDt ¼ ct þ ðDc=DtÞtDt=2 Dt, respectively. The heat transfer rates Q_ i from the heating gas to the working fluid and from the working fluid to the cooling liquid are given by Equation (19) to Equation (20), respectively as:
T T Q_ i evap ¼ i hotP i int fluid Revap
(19)
T fluid T i cold Q_ i cond ¼ i int P Rcond
(20)
where T i hot and T i cold are the average hot stream and cold stream control volume temperatures, and assuming a linear temperature distribution along each control volume, the average heating fluid and cooling fluid temperatures are given, respectively as T i hot ¼ ðTi hot in þ Ti hot out Þ=2 and T i cold ¼ ðTi cold in þ Ti cold out Þ=2, and Ti int fluid is the internal fluid control volume temperature. The thermal resistances for the P P evaporator, Revap and the condenser, Rcond are given by Equations (5) and (6).
263
4. Experimental set-up and procedure A special heat pipe heat exchanger with a large glass flanged window in the front and back was designed, built and installed as shown in Fig. 5 and insulated with 50 mm thick ceramic wool. The windows allowed for the visual observation of the detailed twophase flow behaviour during operation. The diameter of the hot gas pipe submerged in the liquid is 101.6 mm, whilst that of the cold water pipe in the vapour space is 21.8 mm; this was done to take into account the lower gas heat transfer coefficient compared with the higher waterside heat transfer coefficient. Single hot pipe and a single cold water pipe was used to eliminate the effect of the pipes on each other; this was done to more confidently compare experimentally determined heat transfer coefficients with published single tube heat transfer coefficients. The applicable parameters for the as-designed experimental HPHE are shown in Table 2. Fig. 6a shows a photograph of the as-built HPHE without the insulation, Fig. 6b shows the burner and installed HPHE and Fig. 6c the HPHE with the insulation applied to the vessel. K-type thermocouples were used for all the temperature measurements. Each and every thermocouple and its specific instrumentation measurement and data capture channel was individually calibrated against a 100 U platinum resistance substandard thermometer which had previously been calibrated by an accredited calibration laboratory. As such all the temperature channel measurements are within 0.1 C, relative to the substandard instrument. The thermocouple junctions were positioned at four vertical-plane locations (0.058, 0.248, 0.428 and 0.618 m from the hot stream inlet side) along the axial length of the pipes. The sensor locations for one such vertically orientated plane is shown in Fig. 7. For each vertical plane three temperature measurements were taken around the periphery of the heat exchange pipes, in the liquid next to and just above the evaporator pipe, and two above each other in the vapour space; giving a total of 44. Four thermocouples were used to measure the inlet and outlet temperatures of the heating gas and cooling water. The temperature in the laboratory was also recorded. Mass flow rate of the gas was determined using a bell-mouth located at the gas-burner inlet to which the liquefied petroleum gas (LPG) fuel was added and its mass flow rate measured using an orifice-plate type flow meter. The mass flow rate of the cold water stream (from a constant head tank) was determined by using a measuring cylinder and stopwatch. Before the HPHE can be operated properly and repeatedly all the non-condensable gasses trapped in the container during the charging procedure needs to be removed. The HPHE container is evacuated at room temperature to an absolute pressure of about 25 kPa, using a two-stage dry vacuum pump. The remaining traces of non-condensable gas are then removed by heating the working fluid using the hot-gas heated evaporator pipe until vigorous boiling occurs. During this phase non-condensable gas tends to collect in the top of the container vapour space and its presence is readily detected by noting whether the top temperature in the container is less than or equal to the boiling liquid temperature. Should the top temperature be less than the liquid temperature the valve to the already running vacuum pump is slightly opened for a short while and the non-condensable gas that has collected in the top of the container is allowed to escape, together with a little vapour; and the valve is then closed. This process is repeated until the vapour temperature just below the top plate corresponds to the temperature of the boiling liquid. Once all the non-condensable gasses have been eliminated from the HPHE container the hot gas heating of the evaporator pipe continues, but with the condenser cooling water turned off, in this way the heating-up process is expedited. During this heating-up
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Fig. 5. Schematic layout of the experimental setup of the heat pipe heat exchanger (HPHE) shown in Fig. 6.
phase temperature readings are taken at regular intervals. Once the internal working fluid reaches the desired temperature the condenser cooling water is turned on and the HPHE is allowed to attain steady-state conditions. The cooling water is then turned off and the working fluid allowed to increase to yet a higher temperature, the cooling water again turned on and temperatures logged and operated until a steady-state condition is again obtained. This process is repeated a few times until the maximum design operating temperature of the working fluid has been reached. One such a heating and cooling procedure, for three heating repetitions is shown in Fig. 8 for a position 0.248 m from the hot gas inlet.
Table 2 Design parameters of experimental model. Working fluid
Dowtherm-A
Inlet hot stream temperature Inlet cold stream temperature Outlet cold temperature Hot stream mass flow Cold stream mass flow HPHE core length Evaporator tube outside diameter Condenser tube outside diameter Heat transfer rate Working fluid temperature
550e650 C 14e18 C 50e90 C 0.045 kg/s 0.02 kg/s 0.67 m 0.1016 m 0.0218 m 1500 to 1800 W 215e230 C
Finally the heating and cooling streams are turned off and the system allowed to cool back to room temperature. During this cooling phase the temperatures are recorded every 10 min. Knowing the mass of working fluid in the container, an idea of the heat loss through the insulation surrounding the HPHE and the pipes and support structures from the working fluid to the environment, as a function of the temperature difference between the working fluid and the laboratory room, can be obtained. 5. Results and discussion Fig. 8 shows the working fluid liquid and vapour temperature as a function of time at a vertical distance 0.248 m from the hot gas inlet and on a vertical plane at a position as indicated in Fig. 7. The objective of showing Fig. 8 is to show how non-condensable gasses can be removed from the working fluid container by so-called “burping”. This is done by increasing the internal pressure of the working fluid container to a pressure above the ambient pressure (by heating the working fluid but without any cooling fluid flow). Provided the internal pressure is higher than atmospheric pressure by opening an escape valve momentarily, valve V-3 in Fig. 5, noncondensable gasses together with a little vapour is expelled out from the top of the container and into the sump. For this figure however the maximum temperature is only 223 C and the saturation pressure corresponding to this pressure is only 45 kPa, well below atmospheric pressure. In this case thus the vacuum pump
R. Laubscher, R.T. Dobson / Applied Thermal Engineering 61 (2013) 259e267
265
Fig. 6. a. Photograph of experimental heat pipe heat exchanger set-up (without its insulation). The dimensions of the container are (excluding the flanged instrumentation and observation platforms) 596 mm high, 671 mm wide and 516 mm deep. b. Photograph of the heat pipe heat exchanger and hot gas supply burner in the laboratory. c. Experimental heat exchanger with its thermal insulation (ceramic wool), but with the front insulation removed.
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Fig. 9. Energy balance of experimental heat pipe heat exchanger.
Fig. 7. Relative positions of the thermocouples junctions located on one of the four vertical planes along the length of the length of the HPHE located in a vertical plane.
had already been switched on and burping achieved by momentarily opening and then closing valve V-2 in Fig. 5. It is seen that up to about 180 min that the liquid temperature is significantly higher that the vapour temperature, thus indicating the presence of noncondensable gas in the top of the container. At about 180 min the container is “burped” and the temperature of the liquid tends to drop slightly (due to evaporative and adiabatic cooling). The temperature as measured in the vapour space then rises quickly and significantly until both temperatures equalise. Shortly thereafter the temperature of the vapour falls below that of the liquid. At about 260 min burping was again initiated, and so on for several times until the vapour and liquid temperatures remain equal. The HPHE is now ready for normal operation. Very similar curves were obtained at the other three vertical positions along the heat exchanger thereby indicating that the temperature gradient along the axial length along the tubes is small, and thus indicating there is relatively little axial heat transfer between adjacent working fluid control volumes; and thus validating the assumption that the heat transfer is essential one-dimensional and orientated more-or-less vertically upwards.
Fig. 8. Working fluid temperature readings on a vertical plane at a distance 0.248 m from the hot gas inlet side as a function of time during a typical procedure whereby the non-condensable gas is eliminated from the container.
To add credibility to the experimental results the energy needs be accounted for by showing a balance between the evaporator heat input and the heat removed by the condenser, plus the heat losses through the insulation and support structures. Fig. 9 shows such an energy reconciliation for the HPHE in which the data points are scattered more or less uniformly about the diagonal and more or less all within 40%. This relatively wide spread in the results is typical in heat pipes due to the complex and vigorous and chaotic nature of the nucleate boiling process and the seemingly random formation of condensate droplets on the condenser tube and thermocouple probe tips and then their dropping down into the liquid pool, rather than the smooth film-wise flow as suggested by Nusselt film-wise condensation theory. The heat loss was determined experimentally as a function of the temperature difference, and to a coefficient of determination R2 ¼ 0.948, as
Q_ loss ¼ 4:105 Ti int fluid Tambient 177:4
(21)
Fig. 10 gives a depiction of the experimentally measured and theoretically predicted temperatures of working fluid as a function of time at a distance 0.248 m from the hot gas inlet side. The only noticeable discrepancy between the experimental and simulated results is at time 260 min and 320 min. This is when the vacuum pump was switched on during the experiment and the pressure
Fig. 10. Experimentally measured and theoretically predicted temperature of working fluid as a function of time at a distance 0.248 m from the hot gas inlet side.
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Table 3 Heat transfer and pressure comparison between the numerical and experimental results. Parameter
Computer program
Experimental
_h m _c m Q_ loss Q_ in Q_
0.045694 kg/s 0.019 kg/s 537.363 W 1305.626 W 1034.193 W 41.39 kPa
0.045278 kg/s 0.026 kg/s 714.95 W 1388.247 W 1047.746 W 43 kPa
out
Pinternal
was dropped forcibly. The computer program could not accurately simulate this process. Therefore the simulation was setup to run from 190 min to 260 min, at which point the internal temperature of the heat exchanger in the computer program was assigned a lower value to simulate the pressure drop. The lower temperature value was taken from the experimental data and the program was then allowed to continue its calculations. The same process was followed at 320 min. After investigation of the graphs it can be deduced that the theoretical and transient simulation produces accurate results, and can be used to predict the heating time of a heat pipe heat exchanger with relative confidence. A comparison of the numerical computer program simulation and the experimental results is given in Table 3 [2]. At time 330 min in Fig. 8 a steady-state was reached for the experimental model and these results have been reflected in Fig. 11 in vertical planes in the HPHE at the four positions from the hot gas inlet. It is seen that the theoretical model accurately simulates the experimental working fluid and cooling water temperatures, but that the hot gas temperatures are slightly over predicted. This could be due to uncertainties in the exact amount and characteristics of the gasses of combustion from the burner.
6. Conclusions A heat pipe heat exchanger (HPHE) concept was presented that circumvents the need for a secondary pumped heat exchange loop in very high temperature nuclear reactor technology, and that also reduces the likelihood of tritium finding its way into the process heat stream. A transient heat transfer theoretical simulation model was developed and an experimental Dowtherm-A charged model tested at a working fluid temperature of about 220 C. It was found that the theoretical heat transfer model was able to predict the experimentally determined results to within a reasonable degree of accuracy.
Fig. 11. Temperature profiles of the hot stream, cold stream and working fluid for the numerical simulation and the experimental heat exchanger along the length of the evaporator tube (with experimental points as marked).
Dowtherm-A-specific boiling and condensation heat transfer coefficient correlations were specially developed, as generally applicable existing correlations proved to give unsatisfactory results. Having built and tested a 220 C system the detailed design of a more technically challenging 800 C sodium charged experimental model can commence with more confidence. References [1] A. Jousse, Tritium Transport in Very High Temperature Reactors for Hydrogen Production. Report number UCBTH07-005, Department of Nuclear Engineering, University of California at Berkeley, August 31, 2007. Also available: at, http:// pb-ahtr.nuc.berkeley.edu/papers/07-005_Tritium_Report_B.pdf. [2] R. Laubscher, Development Aspects of a High Temperature Heat Pipe Heat Exchanger for High Temperature Gas-cooled Nuclear Reactor Systems. Masters thesis, University of Stellenbosch, Stellenbosch, South Africa, 2013. [3] A. Faghri, Heat Pipe Science and Technology, Taylor and Francis, 1995. [4] G.P. Sabharwall, Theoretical design of thermosyphon for process heat transfer from NGNP to hydrogen plant, in: Proceedings of HTR-2008, ASME 4th International Topical Meeting on High Temperature Reactor Technology, September 28eOctober 1, 2008. Paper number HTR2008-58199, Washington, D.C., USA. [5] The Dow Chemical Company, Dowtherm a Heat Transfer Fluid: Product Technical Data, 1997 (Online) Available at: http://msdssearch.dow.com/ PublishedLiteratureDOWCOM/dh_0030/0901b803800303cd.pdf?filepath¼/ heattrans/pdfs/noreg/176-01337.pdf&fromPage¼GetDoc. [6] D.A. Reay, P.A. Kew, Heat Pipes, Theory Design and Applications, fifth ed., Butterworth-Heinemann, 2006. [7] Y. Cengel, M.A. Boles, Thermodynamics an Engineering Approach, McGraw Hill, 2006. [8] A.F. Mills, Heat Transfer, second ed., Prentice Hall, 1999. [9] Y. Cengel, Heat and Mass Transfer, Fundamentals and Applications, fourth ed., McGraw Hill, 2006 in S.I. units.