Heat Mass Transfer https://doi.org/10.1007/s00231-017-2210-5
ORIGINAL
Influence of different heating types on the pumping performance of a bubble pump Bernd Bierling 1 & Fabian Schmid 1 & Klaus Spindler 1
Received: 26 September 2016 / Accepted: 24 October 2017 # Springer-Verlag GmbH Germany 2017
Abstract This study presents an experimental investigation of the influence of different heating types on the pumping performance of a bubble pump. A test rig was set up at the Institute of Thermodynamics and Thermal Engineering (ITW), University of Stuttgart. The vertical lift tube is made of copper with an inner diameter of 8 mm and a length of 1.91 m. The working fluid is demineralized water. The test rig offers the possibility to vary the supplied heat flow (0 W − 750 W), the resulting supplied heat flux and the location of the heating. Investigations were carried out using spot heating, partial-length heating and fulllength heating. A Coriolis mass flowmeter was successfully implemented which measures the vapor mass flow rate continuously. The improvement of the vapor mass flow rate measurement by using the continuous measurement method compared to a discontinuous one is discussed. Furthermore, the influence of an unstable inlet temperature of the working fluid entering the lift tube on the pumping performance is investigated. The focus of this publication lies on the build-up of the test rig with the measurement setup and the analysis of the pumping performance for the three heating types. The measurement results show a big influence of the heating type on the pumping performance. The lower the relative length of the heating, the higher is the pumping ratio which is defined as the lifted liquid mass flow rate in relation to the generated vapor mass flow rate.
* Bernd Bierling
[email protected]
1
Institute of Thermodynamics and Thermal Engineering (ITW), University of Stuttgart, Pfaffenwaldring 6, 70569 Stuttgart, Germany
Abbreviations A Amperemeter d Downwards DAR Diffusion absorption refrigerator u Upwards V Voltmeter Latin symbols A Cross sectional area (m2) b Pumping ratio (−) cp Specific heat capacity at constant pressure (kJ kg−1 K−1) D Diameter (m) g Gravitational acceleration (m s−2) ΔH Height (m) Δhv Specific enthalpy of evaporation (kJ kg−1) L Length (m) M˙ Mass flow rate (kg s−1) P Power (W) Δp Relative pressure (bar) Q˙ Heat flow (W) ˙ Heat flux (W m−2) q S Slip ratio (−) SR Submergence ratio (−) t Time (min) V˙ Volumetric flow rate (m3 h−1) w Velocity (m s−1) x Coordinate in flow direction (m) Greek symbols ϑ Celsius temperature (°C) ϑs Boiling temperature (°C) λ Thermal conductivity (W m−1 K−1) ρ Density (kg m−3) ρ Mean density over length (kg m−3) φ Relative length of heating (−)
Heat Mass Transfer
Subscripts amb Ambient cartr Cartridges disc Discontinuous el Electric evap Evaporation ext External f Friction FDR Friction dominant regime GDR Gravity dominant regime heat Supplied heat flow HX2 Double-pipe heat exchanger 2 in At the inlet L Liquid LT Lift tube m Mean mass Related to the mass max Maximum min Minimum out At the outlet part Partial preheat Preheating rel Relative res Reservoir TP Two-phase V Vapor vol Related to the volume
1 Introduction 1.1 Overview Bubble pumps are most frequently used in electric drip coffee makers or coffee percolators. The supplied heat flow causes the water to heat up inside a lift tube to its boiling temperature first and to partially vaporize afterwards. As a result, steam bubbles occur and lift the hot water. The bubble pump principle also occurs in thermally driven two-phase natural circulation loops or closed loop two-phase thermosyphons. Fields of application for two-phase natural circulation loops are nuclear steam generators, thermosyphon boilers or boilers in fossil fuelled power plants [1]. Closed loop two-phase thermosyphons include for example solar water heaters, geothermal systems, cooling systems in nuclear reactors, electronic device cooling or thermoelectric refrigeration cooling [2]. Another important field of application for bubble pumps is the diffusion absorption refrigerator (DAR), which belongs to the group of thermally driven absorption chillers. The most common working pair of a DAR is ammonia (NH3) and water (H2O). The auxiliary gas is either helium (He) or hydrogen (H2). The bubble pump lifts the liquid solution in the lift tube
due to generated refrigerant vapor bubbles caused by a supplied heat flow and operates simultaneously as the generator of the process. In the commercial field, DAR systems are widely spread as minibars in hotel rooms or refrigerators in caravans. Dometic, one of the manufacturers, has sold more than ten million DAR systems until 2011 [3]. The required heat flow to run the process is either supplied by a gas burner or electrically by a heating cartridge in the lower third of the lift tube, so that the bubble pump is partial-length heated. The diffusion absorption process is also subject in the field of research. A directly solar thermal heated diffusion absorption chiller with a cooling capacity of approximately 400 W has been developed at the Institute of Thermodynamics and Thermal Engineering (ITW) [4]. The lift tubes are full-length heated due to the fact, that the bubble pump is directly integrated into a solar collector [5]. Within the scope of investigations, it was shown that the type of heating, correspondingly the location of the supplied heat flow, has a great influence on the cooling performance of a diffusion absorption chiller. 1.2 Fundamentals of the bubble pump In general, there are two types of the thermosiphon principle, the single-phase and the two-phase principle. Both principles are based on changes in the fluid density. In the following, only the two-phase thermosiphon principle will be discussed since it is the working principle of bubble pumps. Liquid fluid is partially vaporized and the resulting vapor bubbles lift the liquid. The basic principle of a bubble pump is presented schematically in Fig. 1. Two vertical columns (reservoir and lift tube) with a horizontal connection build the bubble pump configuration. Liquid working fluid is inside the reservoir with a given reservoir level ΔHres. The supplied heat flow Q˙ heat causes a partial vaporization of the working fluid. A two-phase mixture consisting of vapor bubbles and liquid occurs in the lift tube with a low mean density ρTP;LT along the lift tube length LLT. Depending on the type of heating, the heat flux, the gradient in density and the flow pattern in the lift tube differ. Fig. 1 shows the difference between the mentioned aspects at spot heating (a), partial-length heating (b) and full-length heating (c). Assuming that the supplied heat flow Q˙ heat is the same, the lowest heat flux is achieved at full-length heating because of the largest heat transfer area. Correspondingly, the highest heat flux is achieved at spot heating and the highest temperature of the thermal input is needed. The mean density of the twophase mixture along the lift tube ρTP;LT is defined as follows: ρTP;LT ¼
1 LLT ∫0 ρðxÞdx LLT
ð1Þ
Spot heating causes the generation of all vapor at the bottom of the lift tube. The density drops almost abruptly to its
Heat Mass Transfer
Fig. 1 Schematic of the bubble pump configuration, hydrodynamic and density distribution: a spot heating; b partial-length heating; c full-length heating
lowest value in the entire lift tube. In comparison to the fulllength and partial-length heating, the mean density along the lift tube length at spot heating is the lowest. The density distribution of all three heating types is also illustrated in Fig. 1. The influence of the mean density of the two-phase mixture along the lift tube ρTP;LT onto the pumping performance is shown in the following equations. First, Bernoulli’s equation for incompressible flow is used to determine the condition of the liquid working fluid at the inlet of the lift tube. Bernoulli’s equation from the reservoir level to the inlet of the lift tube is as follows: pamb þ ρL;res g ΔH res ¼ pLT;in þ
1 ρ wL;LT;in 2 þ Δpf 2 L;LT;in ð2Þ
The static head of liquid inside the reservoir ΔHres, the ambient pressure pamb, the mean density of the liquid along the height of the reservoir ρL;res and the density of the liquid at the lift tube inlet ρL,LT,in in Eq. (2) are known or can be measured. The frictional pressure drop Δpf is neglected. The flow behavior from the inlet to the outlet of the lift tube is represented by the conservation of momentum due to the occurrence of the compressible two-phase mixture. In the following, a stable flow and homogenous mixture consisting of vapor and liquid is estimated with a slip ratio of S = 1 (velocity ratio of the vapor phase to the liquid phase). With the cross sectional areas ALT = ALT,in = ALT,out it results: pLT ;in − pamb − ρTP;LT g LLT − Δpf ;LT ¼ ρTP;LT ;out wTP;LT ;out 2 −ρL;LT ;in wL;LT ;in 2
ð3Þ
The length of the lift tube LLT is known. The inlet conditions of the lift tube (pLT,in and wL,LT,in) result from Eq. (2). From the connection of Eqs. (2) and (3) follows that the
submergence ratio SR (ΔHres in relation to LLT) has a big influence on the pumping performance of a bubble pump. The influence of the mean density of the two-phase mixture along the length of the lift tube ρTP;LT on the liquid mass flow rate at the outlet M˙ L;out will be discussed. It is assumed that the value of the density of the two-phase mixture at the outlet of the lift tube ρTP,LT,out is equal at each heating type (compare Fig. 1). The pressure drop Δpf, LT caused by acceleration and wall friction is not considered in detail. However, as a general principle it is assumed that the higher M˙ L;out the higher Δpf,LT. In consequence of this correlation as well as Eqs. (2) and (3), the following relation results: the lower ρTP;LT , the higher wTP,LT,out. Related to the mass flow rate of the two-phase mixture at the outlet of the lift tube, the equation M˙ TP;out ¼ ρTP;LT;out wTP;LT;out ALT
ð4Þ
shows that the higher wTP, LT, out, the higher is M˙ TP;out . The estimation M˙ TP;out ≈ M˙ L;out is a consequence of M˙ TP;out ¼ M˙ L;out þ M˙ V and M˙ L;out ≫ M˙ V . According to Eqs. (3) and (4) it is obvious that the lower the mean density along the length of the lift tube ρTP;LT , the higher is the lifted liquid mass flow rate M˙ L;out . The slip ratio depends on the flow regime in the lift tube and affects the pumping performance of a bubble pump. In general, the flow regime with the highest efficiency is slug flow [6]. Generated vapor bubbles merge into vapor slugs (Taylor bubbles). A Taylor bubble occupies almost the whole diameter of the lift tube and lifts the overlying liquid into the separator. Thus, the slug flow is desirable for the bubble pump operation to succeed in high pumping ratios. Considering slug flow, at ideal spot heating the vapor slugs occur directly at the location of the supplied heat flow. However, at partial-length
Heat Mass Transfer
or full-length heating the vapor slugs do not occur before the end of the supplied heat flow (compare Fig. 1). A leading valuation parameter of the pumping performance or the efficiency of a bubble pump is the pumping ratio b [6]. In general, the pumping ratio is defined as the ratio of the volumetric flow rate of the lifted liquid V˙ L;out (output) to the vapor volumetric flow rate V˙ V (input): bvol ¼
V˙ L;out M˙ L;out ρV ¼ V˙ V M˙ V ρL;out
ð5Þ
With the assumption of constant vapor and liquid densities along the length of the lift tube, the pumping ratio can also be referred to the mass flow rates: bvol ∽
M˙ L;out ¼ bmass M˙ V
ð6Þ
1.3 State of the art There is a wide field of research about bubble pumps as well as air-lift pumps. Due to a different operating principle of airlift pumps (air injection) and bubble pumps (partial vaporization), the pumping behavior is incomparable. Air-lift pumps work quasi-stationary whereas the pumping performance of bubble pumps is transient. Air-lift pumps with the air injection at the bottom of the lift tube are not comparable to bubble pumps with partial-length and full-length heating. They are at most comparable to bubble pumps with spot heating, but the transient working principle is most pronounced at spot heating. Therefore, the following state of the art considers only bubble pumps. The pumping performance of a bubble pump in a vertical tube has already been investigated experimentally in 1935 by Cattaneo [6]. Investigations with water as the working fluid and almost full-length heating of the lift tube by using a heating fluid resulted in a general description of the bubble pump behavior and its physical interpretation. Within these investigations, the pumping ratio of the bubble pump was determined depending on different influencing parameters on the pumping performance. The lift tube length LLT, the submergence ratio SR, the inner lift tube diameter DLT, the Table 1 Literature survey of influencing parameters on a bubble pump
supplied heat flow Q˙ heat and the inlet temperature of the working fluid into the lift tube ϑLT, in are parameters influencing the pumping performance of bubble pumps using one working fluid. These values are independent of each other [6]. The lifted liquid mass flow rate M˙ L;out increases with a smaller value of DLT and higher values of Q˙ heat , ϑLT, in and SR. Furthermore, the thermophysical properties of the working fluid, the system pressure and the surface condition of the lift tube influence the pumping performance. Table 1 gives an overview of experiments varying the mentioned influencing parameters on the pumping performance of a bubble pump. All investigations are made using water as the working fluid. Delano [7] designed a bubble pump with the aim to implement it into the Einstein-Szilard refrigeration cycle. Experiments were made varying the supplied heat flow to adapt it to his analytical model. Therefore, a stainless steel lift tube was heated at the bottom by an electric heater clamped on the lift tube. Brendel also investigated the pumping performance of a bubble pump experimentally [8]. The heat flow was supplied interiorly at the bottom of the lift tube by an integrated electrical heating cartridge. The lift tube diameter and the submergence ratio were varied. Similar to that, Shihab [9] investigated the influence of the lift tube diameter and the submergence ratio onto the pumping performance of the bubble pump as well. The heat flow of the electric heating was also supplied at the bottom of the lift tube, but in contrast to Brendel from the exterior. The results of Delano, Brendel and Shihab show that there is always an optimal supplied heat flow for each set-up that corresponds to the maximum liquid mass flow rate. Vicatos and Bennett investigated the influence of multiple lift tubes on the pumping performance and compared the results with a single lift tube. One electrical heating cartridge was placed interiorly at the bottom of the single lift tube and likewise at the bottom of the multiple lift tubes [10]. The obtained data showed that a bubble pump with multiple lift tubes has a higher lifted liquid mass flow rate compared to the supplied heat flow than a bubble pump with only a single lift tube. Chan and McCulloch [11] investigated a bubble pump with a partiallength heated lift tube to validate their theoretical model. An electrical heating coil was located in the center of the lift tube. Rattner and Garimella [12] investigated a full-length heated bubble pump with the aim of using low-grade thermal energy to run
Reference
SR [−]
DLT [mm]
LLT [mm]
˙ Q heat ½W
Delano [7] Brendel [8] Shihab [9] Vicatos and Bennett [10] Chan and McCulloch [11] Rattner and Garimella [12]
0.2 0.2 – 0.33 0.2 – 0.6 0.2 0.5 – 0.8 0.2 – 0.4
7.62 6 – 10 8 – 12 6 6 – 12 7.8
736 2000 1340 445 470 1700
20 – 200 50 – 750 60 – 700 500 – 1300 25 – 160 25 – 200
Heat Mass Transfer
a diffusion absorption chiller. The lift tube is the inner tube of a counter flow double-pipe heat exchanger where the heating fluid is circulated around the lift tube. The supplied heat flow can be used on a lower temperature level due to a larger heat transfer area. The supplied heat flux compared to spot heated bubble pumps is lower. The lowest temperature level of the heating fluid at the entry of the double-pipe heat exchanger was about 11 K above boiling temperature. 1.4 Aim of the current research There is extensive literature dealing with the pumping performance of bubble pumps. Different authors made parameter variations of influencing parameters on the pumping performance. However, the results are hardly comparable due to dissimilar test facilities and procedures. Especially the influence of the heating type on the pumping performance has not been investigated sufficiently. Moreover, the supplied heat flow, the heat flux, the heating length or the location of the heating at the lift tube is often characterized insufficiently. The main objective of the current research is to investigate the influence of different heating types on the pumping performance of a bubble pump. Therefore, the lift tube with its respective heating type is the only component of the test rig being exchanged. The investigations distinguish between spot heating, partial-length heating and full-length heating of the Fig. 2 Measurement setup of the bubble pump test rig
lift tube made of copper with water as the working fluid. The lift tube length LLT, the submergence ratio SR, the inner lift tube diameter DLT and the inlet temperature of the working fluid into the lift tube ϑLT, in as influencing parameters onto the pumping performance remain unchanged. The supplied heat flow Q˙ heat is varied in a range that enables the comparison of the mentioned heating types. Additionally, the importance of a stable inlet temperature of the working fluid into the lift tube ϑLT, in is shown, because unstable inlet temperatures at different temperature levels have an impact on the comparability of the pumping ratio using the different heating types.
2 Buildup of the test rig The buildup of the test rig is presented in detail based on the measurement setup shown in Fig. 2. The lift tube can be replaced easily due to screw connections to install different heating types. The temperatures ϑ1 to ϑ5 are measured with thermocouples (see Fig. 2). Demineralized water as the working fluid flows in a closed circuit which is open to the atmosphere. Accordingly, the system pressure is equal to the ambient pressure pamb. The working fluid flows in liquid state from the reservoir (I) through two double-pipe heat exchangers to the lift tube (III). Both
Heat Mass Transfer
double-pipe heat exchangers and a heating cord mounted to the reservoir are supposed to control the temperature of the working fluid. The heating cord (Pel,cord,max = 142 W) is controlled by a two-position controller with hysteresis with the aim to adjust the temperature at the reservoir outlet ϑres, out (ϑ1 in Fig. 2) to a desired value. This allows a fine adjustment in the following two double-pipe heat exchangers. Thereby, the inlet temperature of the liquid into the lift tube ϑLT, in (ϑ3 in Fig. 2) can be adjusted close to boiling temperature (compare chapter 3). A high precision pressure transducer placed at the deepest point below the reservoir, which is equivalent to the entry of the horizontal connecting tube (II), measures the relative pressure Δprel against ambient pressure pamb. The ambient pressure is measured by a capacitive pressure transmitter. Due to the fact that the test rig is open to the atmosphere, the measured relative pressure corresponds to the hydrostatic pressure difference (Δprel = Δpres) caused by the head of liquid in the reservoir ΔHres during standstill of the bubble pump. The hydrostatic pressure difference is connected with the head of liquid in the reservoir as follows:
Δpres ¼ ρL;res ϑm;res g ΔH res
Coriolis mass flowmeter as well. Despite very low mass flow rates of the condensate, a suitable Coriolis mass flowmeter was found with an acceptable measuring accuracy. The possible measuring range of the flowmeter is from 0 kg h−1 to 30 kg h−1 in total. The highest mass flow rate of the condensate measured at the highest supplied heat flow is approximately M˙ V;max ¼ 1 kg h−1. The pressure drop caused by the flowmeter and the resulting water column at M˙ V ¼ 1 kg h−1 is still beneath the maximum possible hydrostatic pressure due to the given height of the test rig (compare ΔH4 in Fig. 2). A major and very important advantage of a continuous measurement of M˙ V compared to a discontinuous one are always steady-state conditions. The influencing parameters ΔHres and ϑ LT,in on the pumping performance are constant. Additionally, a measurement series can be completed faster. The influence of a discontinuous measurement method of M˙ V on the pumping performance is discussed in chapter 3.4. Assuming no heat losses along the lift tube and boiling temperature at the inlet (ϑLT, in = ϑs,LT, in), the following applies with ϑs,LT,in ≈ ϑs,LT,out ≈ ϑs: Q˙ heat ≈ M˙ V Δhv ðϑs Þ → Q˙ heat ∼ M˙ V
ð8Þ
ð7Þ
The mean density of the liquid along the height of the reservoir ρL;res ϑm;res is determined by the arithmetic mean temperature of the liquid reservoir level and the inlet of the horizontal connecting tube ϑm,res = (ϑ1 + ϑ2)/2 [13]. During the operation of the bubble pump, the static and dynamic pressure are superimposed. Fig. 2 shows an example of partial-length heating in the lower part of the lift tube using an electric heating element. The two-phase mixture flows upwards into the separator where it is separated into the liquid and vapor state. The lift tube is insulated with a microporous thermal insulating material based on fumed silica (Contherm MP 1000; λ = 0.02 W m−1 K−1 at ϑ = 100 °C) to minimize heat loss. The liquid flows from the lower outlet of the separator (IV) through a Coriolis mass flowmeter back to the reservoir (VII). The mass flowmeter measures the liquid mass flow rate M˙ L;out continuously. A condensation of the vapor in the separator and resulting measurement inaccuracies have to be avoided. Therefore, a heating cord which is mounted underneath the heat insulation directly onto the separator guarantees saturation temperature inside. If the vapor condensates after the highest point of the test rig (VI), there are no measurement inaccuracies due to an inclined tube connected afterwards. The vapor leaving the separator at the upper outlet (V) condenses in the condenser and the liquid flows back into the reservoir (VII). The mass flow rate of the condensate M˙ V , which is equivalent to the mass flow rate of the vapor due to conservation of mass, is continuously measured with a
2.1 Investigated heating types Fig. 3 shows the investigated heating types with an overview of the test conditions. In all cases, the heat flow is supplied from the exterior and the geometrical design of the lift tube inlet is similar. The temperature of the working fluid at the inlet of the lift tube ϑLT, in is kept close to boiling temperature ϑs. The lowest measured temperature entering the lift tube ϑLT, in concerning all heating types is 5.15 K below boiling temperature. 99 % of all the measured values accomplish ϑs − ϑLT, in < 3.9 K. To be able to compare the different heating types, the relative length of heating φ is used, which is defined as follows: φ¼
Ltype LLT
ð9Þ
With the constant lift tube length of LLT = 1910 mm, the relative length of spot heating results with Ltype = Lblock to φblock = 5.5 %, of partial-length heating with Ltype = Lcoil to φcoil = 15.7 % and of full-length heating with Ltype = Ltape to φtape = 92.1 %. At spot heating, a copper block with four blind holes was designed to integrate heating cartridges (press fits) with an electric power of 250 W each (Mickenhagen; ∅10 mm; length 100 mm). The spot heated lift tube realized by the copper block with integrated heating cartridges is shown in Fig. 4. The maximum possible power of all four heating cartridges is Pel,cartr,max = 1000 W (VIII(a); IX(a)). The maximum
Heat Mass Transfer Fig. 3 Investigated heating types and test conditions
supplied heat flux at the inner surface of the lift tube at spot heating regarding the maximum set power of 700 W is q˙ block;max ¼ 278:5 kW m−2 . To ensure the heat transfer and to avoid overheating of the heating cartridges, a metallic thermal paste with a thermal conductivity of λpaste = 80 W m−1K−1 [14] is added between the lift tube and the copper block. Additionally, the temperature inside the copper block is monitored during the measurements. The partial-length heating of the lift tube is realized by a heating coil (Mickenhagen; inner ∅10 mm; wounded length 300 mm) with a maximum electric power of Pel,coil,max = 750 W (VIII (b); IX (b)). The full-length heating is realized by a high temperature heating tape with glass fibre fabric (Hillesheim; type HBS; length 2 m) with a maximum electric power of Pel,tape,max = 500 W (VIII (c); IX (c)). 2.2 Uncertainty analysis
Fig. 4 Spot heated lift tube by use of heating cartridges integrated in a copper block
All temperatures are measured with type K sheath thermocouples using iced water as the reference junction. The entire measurement chain consisting of the thermocouple, the
Heat Mass Transfer
transition point and the data acquisition module was calibrated as a unity between −10 °C and 140 °C. The maximum measuring error is ±0.06 K at 140 °C (compare Table 2). The error results from the inaccuracy of the calibration bath in addition to the polynomial error. A data acquisition module from Agilent-Technologies (34970A) measures the voltage every 30 s. The thermocouples are affixed by through bolt joints at the measuring points to ensure direct contact of the working fluid and the measurement tips. The measured values of both the liquid and the vapor mass flow rate are logged with a data acquisition from Meier-NT (ADL-MX; ±4 μA uncertainty) every 1 s. The liquid mass flow rate is measured continuously by a Coriolis mass flowmeter (Promass 63A – DN4). Including the error of the data logger, the maximum relative error of M˙ L;out of the entire measuring chain lies between 0.17 % and 0.62 %. Likewise, the mass flow rate of the condensate is measured continuously by a Coriolis mass flowmeter (Sitrans FC Mass 2100 – DI1.5). The maximum relative error of M˙ V considering the combined error of the entire measuring chain, lies between 0.16 % to 4.43 % (see Table 2). The relative pressure (Δpres) is measured with a high precision pressure transducer (8267 EN; accuracy < 0.1 % of reading). The measurement values are logged at highfrequency every 0.2 s. The data acquisition module is the same as mentioned before from Agilent-Technologies (34970A; ±[0.0035 % · U reading + 0.0005 % · U range ] uncertainty). Exemplarily, the combined maximum relative error of the measured relative pressure during standstill of the test rig amounts to 0.104 % (Δpres,standstill = [68 ± 0.07] mbar). The electrical heating power (Pel), which is converted into the supplied heat flow (Q˙ heat ), is measured with a wattmeter (PA4400A; ±[0.1 % · Preading + 0.1 % · Prange + 2 mW] uncertainty).
3 Experimental results and discussion The three different heating types are investigated experimentally. The electric power of the four heating cartridges in total Table 2
Pel,cartr (spot heating) was set from 53 W to 700 W. The electric power using the heating coil (partial-length heating) is between 49 W ≤ Pel,coil ≤ 750 W. The range of the electric power of the heating tape Pel,tape (full-length heating) was set from 56 W to 502 W. All measurement results are based on the test conditions listed in Fig. 3 with a lift tube made of copper and demineralized water as the working fluid. The room temperature is controlled to ϑamb = 24 °C. To obtain repeatable and comparable measurement results of the pumping performance, the inlet temperature of the working fluid into the lift tube ϑLT, in must be kept constant at a defined value over the entire measurement range. ϑLT, in depends on the inlet temperature of the external circuit of double-pipe heat exchanger 2 ϑHX2,ext,in and on the outlet temperature of the reservoir ϑres, out. The objective is to control ϑLT, in close to boiling temperature at the inlet of the lift tube ϑs,LT,in. However, bubble generation at preheating has to be avoided. Therefore, ϑres,out = 95 °C and ϑHX2,ext,in = 99 °C is set. The lowest outlet temperature of the reservoir under consideration of all three heating types is ϑres,out,min = 94,45 °C. The importance to avoid subcooled working fluid entering the lift tube is also discussed in the following. This is exemplified by the pumping ratio at full-length heating. 3.1 Influence of the heating type on the pumping ratio The lifted liquid mass flow rate M˙ L;out (output) over the generated vapor mass flow rate M˙ V (input) at spot heating, partiallength heating and full-length heating is shown in Fig. 5. Both an upward (u) measurement series with an increasing supplied heat flow and a downward (d) measurement series with a decreasing supplied heat flow were made at each heating type (see Fig. 5). The upward measurement series starts at the lowest electric power Pel whereas the downward series starts at the highest. Pel is gradually raised or lowered in increments of approximately 12.5 W. At each stage it was waited until steady-state conditions are reached. The measured data of M˙ V and M˙ L;out are averaged according to the measurement
Specifications of the measurement devices
Measurement devices
Measured range
Max. error of the measuring chain at the defined value
Output signal
Type
Thermocouple (ϑ1 − ϑ5)
−10 °C 140 °C 5 kg h−1 45 kg h−1
±0.02 K ±0.06 K ±0.03 kg h−1 (±0.62 %) ±0.08 kg h−1 (±0.17 %) ±0.0009 kg h−1 (±4.43 %) ±0.0016 kg h−1 (±0.16 %) ±0.052 mbar (±0.105 %) ±0.104 mbar (±0.104 %) ±1.31 W (±2.62 %) ±2.01 W (±0.268 %)
Voltage
Rössel; type K; ø 1.5 mm; class 1
Current
Endress + Hauser; Promass 63A - DN4
Current
Siemens; Sitrans FC Mass 2100 – DI1.5
Voltage
Burster; 8267 EN
Digital
Powertek; PA4400A AV Power
Coriolis mass flowmeter (M˙ L;out) Coriolis mass flowmeter (M˙ V) Pressure transducer (Δpres) Wattmeter (Pel)
0.02 kg h−1 1 kg h−1 50 mbar 100 mbar 50 W 750 W
Heat Mass Transfer Fig. 5 Characteristics of the lifted liquid mass flow rate at spot, partial-length and full-length heating
time of Δt = 60 min during steady-state conditions at the respective stage. Fig. 5 shows that liquid is lifted due to the generated vapor over the entire range of the electric power at each heating type. The good reproducibility between the upward and the downward measurement series can be seen. The deviation is determined by use of spline interpolation with increments of ΔM˙ V ¼ 0:001 kg h−1 . The maximum absolute deviation of M˙ L;out as well as the mean deviation between two series results as follows: & & &
spot heating: ΔM˙ L;out;spot;max ¼ 1:74 kg h−1 ; ΔM˙ L;out;spot;m ¼ 0:36 kg h−1 partial-length heating: ΔM˙ L;out;part;max ¼ 4:20 kg h−1 ; ΔM˙ L;out;part;m ¼ 1:39 kg h−1 f u l l - l e n g t h h e a t i n g : ΔM˙ L;out;full;max ¼ 1:22 kg h−1 ; ΔM˙ L;out;full;m ¼ 0:60 kg h−1
This shows a high reproducibility of the measured data. A hysteresis effect between the increasing and the decreasing supplied heat flow is not observed. Thus, it is sufficient to analyze only the downward measurement series of the respective heating type hereafter in this subchapter. The characteristic curves of the lifted liquid mass flow rate M˙ L;out over the generated vapor mass flow rate M˙ V using different heating types vary significantly. The lifted liquid mass flow rate at spot-heating lies between 5:79 kg h−1 ≤ M˙ L;out;spot ≤ 42:15 kg h−1 . M˙ L;out;spot shows an untypical curve progression due to the occurrence
of a local maximum. Increasing M˙ V causes a linear increase of M˙ L;out;spot at the beginning until the local maximum is reached. With further increases of M˙ V a decrease of M˙ L;out;spot occurs followed by a linear increase. Then the gradient is reduced to an angular point (absolute maximum) which is reached with M˙ L;out;spot;max ¼ 42:15 kg h−1 at M˙ V ¼ 0:56 kg h−1 . Beyond the absolute maximum, M˙ L;out;spot decreases again. The progression of M˙ L;out at full-length heating fundamentally differs from the one at spot heating and is substantially less. The lifted liquid mass flow rate at full-length heating lies within 0:85 kg h−1 ≤ M˙ L;out;full ≤ 11:17 kg h−1 . M˙ L;out;full increases steadily linear over the measured range of M˙ V . The characteristic curve of M˙ L;out at partial-length heating proceeds always between the values measured at spot and full-length heating (M˙ L;out;full < M˙ L;out;part < M˙ L;out;spot ). This was expected due to Eqs. (3) and (4). The pumped liquid mass flow rate lies within 5:18 kg h−1 ≤ M˙ L;out;part ≤ 37:47 kg h−1 . The curve proceeds logarithmic up to the limit of M˙ L;out;part ¼ 33:86 kg h−1 and rises rapidly by ΔM˙ L;out;part ≈ 4 kg h−1 at M˙ V ¼ 0:80 kg h−1 . Then the lifted liquid mass flow rate reaches the absolute maximum at M˙ V ¼ 0:87 kg h−1 and decreases afterwards. Flow instabilities might be the reason for the unstable behavior of the lifted liquid mass flow rate at high vapor mass flow rates. Ambient influences like an unstable room temperature (22.0 °C ≤ ϑamb ≤ 25.4 °C), an unstable ambient pressure (0.956 bar ≤ pamb ≤ 0.964 bar), the relative humidity and vibrations are parameters which can release the instabilities.
Heat Mass Transfer
The measurement results imply that the absolute maximum of M˙ L;out shifts towards higher values of M˙ V , if the relative length of heating φ increases. The results also show that the lower φ is, the higher is the pumping ratio bmass. Despite the highest pumping ratio at spot heating, the highest reproducibility between the upward and the downward measurement series is reached (ΔM˙ L;out;spot;m ¼ 0:36 kg h−1). 3.2 Pumping characteristics at spot heating In general, the increase of M˙ V with a resulting increase of M˙ L;out up to the absolute maximum is the gravity dominant regime (GDR). Increasing M˙ V leads to a higher void fraction, a lower density and consequently to a higher buoyancy force. With a further increase of M˙ V beyond the absolute maximum of M˙ L;out , frictional forces predominate and cause the decrease of M˙ L;out in the friction dominant regime (FDR). Decisive for the position of both the local and the absolute maximum is the flow pattern, which depends on the void fraction. The characteristic local maximum occurs presumably due to a transition of the flow pattern. The measurement data at spot heating are examined in detail to investigate the progression of M˙ L;out . Fig. 6 demonstrates the relative pressure below the reservoir Δpres, the temperature of the working fluid at the internal inlet of the double-pipe heat exchanger 2 ϑHX2,int,in (equal to ϑ2 in Fig. 2) and the lifted liquid mass flow rate M˙ L;out over the duration of the upward measurement series. The periodic pumping of the working fluid is characteristic for the bubble pump. This pumping behavior is shown in Fig. 6. M˙ L;out fluctuates, but the measurement data are smoothed due to the pressure drop in the Coriolis mass flowmeter. The relative pressure Δpres fluctuates around the measured mean value at Fig. 6 Detailed pumping performance of the bubble pump at spot heating
the stage of the lowest supplied heat flow at Pel, cartr = 53 W (dashed line). This arithmetic mean value of the relative pressure corresponds to the relative pressure at a standstill of the test rig (Δpres;53W ≈ Δpres;standstill ≈ 65 mbar). Three different sections can be recognized referred to Δpres and ϑHX2,int,in: (A) periodic fluctuations of Δpres and a low fluctuation range of ϑHX2,int,in (B) chaotic fluctuations of Δpres and a high fluctuation range of ϑHX2,int,in (C) periodic fluctuations of Δpres and a low fluctuation range of ϑHX2,int,in In section B, the temperature at the internal inlet of doublepipe heat exchanger 2 sometimes reaches values above ϑHX2,int,in = 99°C. However, the highest possible temperature is the set temperature of the external inlet at the double-pipe heat exchanger 2 with ϑHX2,ext,in = 99 °C. Thus, there has to be a high return flow of the working fluid coming from the inlet of the lift tube towards the reservoir. The boiling of the working fluid due to the supplied heat flow produces a pressure wave which passes through the working fluid against the flow direction. This causes the chaotic fluctuations of Δpres and ϑHX2,int,in between the local and the absolute maximum in section B. The chaotic fluctuations might indicate that there is a transition of the flow patterns between section A and B as well as between B and C.
3.3 Influence of an unstable inlet temperature into the lift tube on the pumping ratio at full-length heating The adjustment of the inlet temperature of the liquid into the lift tube ϑLT, in (ϑ3 in Fig. 2) is crucial for the avoidance
Heat Mass Transfer
of this parameter influencing the pumping performance. Assuming quasi-stationary working conditions and ϑs,LT,in ≈ ϑs, LT, out ≈ ϑs, the supplied heat flow Q˙ heat is calculated as follows: ˙ ˙ ˙ Q˙ heat ¼ Q preheat þ Qevap þ Qloss ¼ M˙ L;out þ M˙ V cp ϑLT;in ϑs − ϑLT;in
ð10Þ
þ M˙ V Δhv ðϑs Þ þ Q˙ loss Q˙ heat is the sum of the heat flow to preheat the working fluid up to the boiling temperature (Q˙ preheat ), the heat flow to evaporate the working fluid (Q˙ evap) and the heat losses (Q˙ loss). According to Eq. (10), the lower ϑLT, in the higher is Q˙ preheat and the lower is Q˙ evap at constant heat losses. The adjustment of ϑLT, in is not quite easy. Oscillations of the working fluid and changing mass flow rates with different heat losses lead to fluctuations of ϑLT, in instead of constant values. Due to this fact, the preheating of the working fluid is not reproducible ˙ and Q evap fluctuates. Therefore, it is important to plot the lifted liquid mass flow rate M˙ L;out against the generated vapor mass flow rate M˙ V and not against Q˙ heat to obtain comparable and repeatable results. Depending on the heating type, changing inlet temperatures ϑLT, in have different impacts on the pumping ratio. The influence of ϑLT, in on the pumping ratio is considered at downward measurement series at full-length heating (see Fig. 7). Full-length heating is chosen to investigate the influence of ϑLT, in since high return flows in some cases at spot and partial-length heating (compare chapter 3.2) make an investigation more difficult. Furthermore, the
Fig. 7 Influence of the inlet temperature into the lift tube on the lifted liquid mass flow rate at full-length heating
impact of ϑLT, in on the pumping ratio is most distinct at full-length heating. Three different cases are set to investigate the influence of ϑLT, in (Fig. 7): (a) ϑLT,in,(a) results from the adjustment of ϑres, out = 95 °C and ϑHX2,ext,in = 99°C; the fluctuation range of ϑLT, in, (a) is within 0.6 K (b) ϑLT, in,(b) results from the adjustment of ϑres, out = 92 °C and ϑHX2,ext,in = 96 °C; the fluctuation range of ϑLT, in,(b) is within 1.1 K (c) ϑ LT, i n , ( c ) results only from the adjustment of ϑHX2,ext,in = 99 °C; the fluctuation range of ϑLT, in,(c) is within 2.8 K The objective of case (a) is to control the liquid entering the lift tube close to boiling temperature. It is achieved that the range of ϑLT, in,(a) is within a small fluctuation range of only 0.6 K at 2.9 K to 3.5 K below boiling temperature (100.3 °C ≤ ϑs, LT, in ≤ 100.5 °C). The settings of case (b) have the objective to measure the pumping ratio with subcooled liquid entering the lift tube. The comparison of graph (a) and (b) shows the influence of ϑLT, in on M˙ L;out at full-length heating with two important effects. The lower ϑLT, in, the lower is the generated vapor mass flow rate at a constant heat flow stage (compare Eq. (10) and exemplarily M˙ V;ðbÞ < M˙ V;ðaÞ at Pel = 502 W in Fig. 7). Besides that, also M˙ L;out;ðbÞ is always lower than M˙ L;out;ðaÞ . The linear interpolations of (a) and (b) show a parallel translation along the ordinate by an absolute value of M˙ L;out ¼ 1: 5 kg h−1 at a difference in ϑLT, in of approximately 2.5 K in average. The reason for this effect is that the location of the
Heat Mass Transfer
first bubble formation in the lift tube rises when ϑLT, in is lower. Graph (c) shows the measurement results without preheating the returning liquid already inside the reservoir. ϑLT, in,(c) ranges within 2.8 K from 93.8 °C to 96.6 °C and therefore the progression of curve (c) can be divided into the sections I, II and III. In section I, curve (a) and (c) overlay which means that ϑLT, in, (a) and ϑLT, in, (c) have the same order of magnitude. Section II represents the transition band where curve (c) drifts in the direction of curve (b). Both double-pipe heat exchangers by themselves are not sufficient to control the working fluid at a desired temperature due to an increasing total mass flow rate. In section III, curve (c) lies on curve (b) which means that ϑLT, in, (b) and ϑLT, in,(c) are in the same order of magnitude. A preheating of the working fluid inside the reservoir even before the preheating in the two double-pipe heat exchangers is essential to obtain a small fluctuation range of ϑLT, in and especially values close to the boiling temperature. It is shown that the characteristic curve of M˙ L;out over M˙ V depends on ϑLT, in, especially at full-length and partiallength heating. Thus, measuring data are only repeatable and comparable if ϑLT, in is stable and within a small and similar value range. 3.4 Improvement of the vapor mass flow rate measurement by using a Coriolis mass flowmeter The influence of a discontinuous measurement method of M˙ V on the pumping performance compared to a continuous method using a Coriolis mass flowmeter is investigated. The
Fig. 8 Influence of the discontinuous measurement method of the vapor mass flow rate on the pumping performance
measurement setup of the discontinuous method consists of a constant filling volume, an optoelectronic sensor and an electrically actuated ball valve. As soon as the volume is filled with condensate, the optoelectronic sensor causes the ball valve to open for Δt = 15 s. M˙ V;disc is then calculated using the measured filling time, the known volume and the density of the condensate. A comparison of the two different measurement methods is possible due to a series connection. M˙ V is measured by the Coriolis mass flowmeter (compare chapter 2) which is mounted in series to the discontinuous measurement setup. The condensate flows through the Coriolis mass flowmeter first. The influence of the discontinuous measurement method on M˙ V , M˙ V;disc , M˙ L;out and ϑHX2,int,in is shown in Fig. 8. The drain of the condensate affects directly ΔHres and ϑHX2,int,in after the opening of the valve. The collected condensate flows at a low temperature level into the reservoir and the two double-pipe heat exchangers. The preheating of the working fluid is insufficient so that ϑHX2,int,in as well. As a result, also M˙ V and M˙ L;out decrease (see chapter 3.3). During closed position of the ball valve, ϑHX2,int,in, M˙ V and M˙ L;out increase again up to the previous value. Additionally, ΔHres fluctuates more strongly than during the continuous measurement method. Thus, there are no steady-state conditions during the use of the discontinuous measurement method. During the continuous mode, where the valve is open and only the Coriolis mass flowmeter is measuring, ΔHres and ϑLT, in as influencing parameters on the pumping performance are more constant. Fig. 8 shows that M˙ V and M˙ L;out are much more stable and even on a different value range.
Heat Mass Transfer
4 Conclusions and outlook The paper presents an experimental investigation of the influence of the heating type on the pumping performance of a bubble pump. Detailed measurements series were conducted using spot heating, partial-length heating and full-length heating. An improvement of the generated vapor mass flow rate measurement was reached. A Coriolis mass flowmeter enables a continuous measuring of the vapor mass flow rate. Furthermore, it has been shown that an unstable inlet temperature of the working fluid entering the lift tube ϑLT, in influences the pumping performance. A test rig was build-up by which steady-state conditions and a stable inlet temperature into the lift tube close to boiling temperature was reached. Thus, reproducible and comparable measurement results can be generated. The measurement results imply a big influence of the heating type on the pumping performance. The results show that the lower the relative length of heating φ is, the higher is the pumping ratio bmass which is defined as the ratio of the lifted liquid mass flow rate and the generated vapor mass flow rate. The main aim of this paper is the investigation of the influence of different heating types on the pumping performance of a bubble pump under the same boundary conditions. In future, the work will be extended to working conditions of diffusion absorption chillers. A new heating method will be investigated with ethanol-water as working pair and a pressure system to gain information for a pressurized binary mixture system. From this, it follows the transferability to diffusion absorption chillers. Acknowledgements This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. Compliance with ethical standards Conflict of interest On behalf of all authors, the corresponding author states that there is no conflict of interest.
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