An experimental study has been performed on thermal mixing phenomena in a narrow channel by twin-jetsat different temperatures. Water was used as working fluid and it is supplied by hot and cold taps. The chan-nel has a circular exit hole to supply continuity of mass. An adiabatic square shaped object, which in thethickness of the channel, is inserted into the channel to control thermal mixing as a passive technique.Other parameters in experiments are ratio of flow rate of inlet fluid, inclination angle of the channel, jet di-ameter and jet velocities. Finally, a thermal mixing index was calculated from measured values of tempera-tures for different parameters. Temperature distribution is obtained for whole channel and isotherms areplotted. The obtained results indicated that higher thermal mixing efficiency is observed for ϕ=60o andinserted body can be a control parameter for thermal mixing for the same geometrical parameters.
Mixing processes are very crucial subjects in chemistry, mechani-cal engineering and environmental science. It can be classified in twoseparate groups such as flow mixing and thermal mixing. In flowmixing phenomena, the same fluid/fluids are mixed using mechanicaldevices such as propeller or jet mixing can be used [1]. In this context,jet mixed tanks are very popular due to low energy consuming, lowinvestment and there is no complex mechanical part they have. Thisidea also can be used for thermal mixing process.
Humprey et al. [2] numerically studied the time-dependent mo-tion of a constant property, Newtonian fluid in a counter currentshearing flow configuration. The three-dimensional flow and mixingcharacteristics of multiple and multi-set three dimensional confinedturbulent round opposing jets in a novel in-liner mixer are examinednumerically using the standard k-ε turbulence model by Wang andMujumdar [3]. They indicated that multiple opposing jets achievebetter mixing than single opposing jets in the study. Wang et al. [4]numerically studied the laminar flow in an in-line mixer based on op-posing jet impingement. They found that unequal inlet momenta of
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opposing jets obtained using both equal and unequal slot widthsand the addition of baffles in the exit channel yield better mixingover shorter distances after impact. In their another study, they testedthe effects of type of fluid as using air and water on flow and mixingeffectiveness for various temperature differences between the con-fined opposing jets of different geometries. Beuf et al. [5] studiedthe influence of the geometry of the cell on mixing efficiency usingthree different geometries as circle, square and rectangle. They indi-cated that the flows in Hele–Shaw cells are generally laminar and itcan be in a first approximation considered as quasi-two dimensional.They also showed that the rectangular geometry leads to a bettermixing, but also that the aspect ratio of the rectangle play unexpect-edly no important role on mixing. Walker et al. [6] made both numer-ical and experimental study to carry out mixing of coolant streams ofdifferent temperature in pipe junctions. In this way thermal fatiguemay prevent in the pipe wall. They presented a distribution of timeaveraged mixing scalar for different velocity ratios.
Wang et al. [7] studied jet mixing problem inside a slot experi-mentally. They tested the jet array effect on cooling performance.They also tested effect of orientation angle and H/D ratio. It is foundthat the acceptable uniform flow is observed for shallow as H/D=1.Chang et al. [8] made a numerical analyzes to investigate the thermalmixing efficiency in Y-shaped channel. They solved two dimensionalincompressible, steady state equations using Lattice Boltzmann meth-od. They inserted different types of passive element to improve ther-mal mixing efficiency. It is demonstrated that the enhanced mixingefficiency is result of an increased intersection angle between the ve-locity vector and the temperature gradient within the channel.
D Diameter (mm)ṁc Cold water mass flow (kg/s)ṁh Hot water mass flow (kg/s)MI Mixing indexn Number of jetPE Passive elementSt Standard deviation of fluid temperaturet Time (s)Tavg Average temperature (°C)Tc Cold jet temperature (°C)Th Hot jet temperature (°C)WMI Uncertainty of mixing indexΔT Temperature difference between hot and cold water
(°C)ϕ Inclination angle of the channel
1246 Y. Varol et al. / International Communications in Heat and Mass Transfer 39 (2012) 1245–1252
Thermal mixing is also a very important application for T-junctions asgiven by Naik-Nimbalkar et al. [9]. Hu and Kazimi [10] made a numer-ical simulation on thermal striping for three-dimensional, unsteadyturbulent model. They used two types of mixing tee configurations
Fig. 1. Diagram of exp
and they modeled using commercial CFD code FLUENT. A similarwork has been done by Kamide et al. [11] using water as a numericalwork with finite difference method. They indicated that mixing be-havior in the tee was characterized by the relatively large vortexstructures defined by the diameters and the velocities in the pipes.
Using of jets to enhance thermal mixing efficiency is very usefulway and many of authors are worked on this subject as Shi et al.[12], Lou et al. [13], Chua et al. [14] and Devahastin and Mujumdar[15]. These authors mostly studied the jet mixing phenomena usingnumerical techniques. They observed that thermal mixing is mostlya function of temperature of jets. Sometimes, different shaped passiveelements are used to control flow field, heat transfer and thermalmixing. Shan and Zhang [16] made a numerical calculation to investi-gate the different mixer configuration for an exhaust system ofturbo-fan engine. They observed that the lobed forced mixer can in-crease the mixing efficiency by 65%, decrease the thrust coefficientby 3% only. Turki [17] used square cylinder to make a control mechan-ics for flow mixing numerically. Patil and Tiwari [18] made a numer-ical work to control laminar flow in a channel behind two inclinedsquare cylinders.
The main objective of this study is to understand the phenomena offlow and thermal mixing in a narrow channel with square objectinserted. Twin jets are used at different temperature to supply water
erimental set-up.
1247Y. Varol et al. / International Communications in Heat and Mass Transfer 39 (2012) 1245–1252
into channel. This is good application for some sanitary system andmixture tanks. Based on above literature, there is no experimentalwork on thermal mixing in a narrow channel with passive elementinserted.
2. Experimental set-up
A schematic view of the experimental set-up is presented in Fig. 1with equipment. In this experiment, two circular inlet jets areobtained. The water was used as working fluid. Each jet has differentflow temperature. The temperatures were measured by T-type ther-mocouples located 100 mm distance in vertical and 133 mm dis-tance in horizontal directions as given in Fig. 2 (b). The measuringpoints are named as T1, T2, T3,…..T20. We called station for eachfour thermocouples in a column. Thus, there are 5 stations in the ex-periment from left to right. This figure (Fig. 2 (a)) also shows the
Fig. 2. a) Model of experimental set-up, b) dimensions of exper
model experiment for channel with passive element. The passive el-ement that inserted into the channel is 100×100×30 mm squareadiabatic object. The channel can be an inclined position with incli-nation angle of ϕ. The channel can be seen from the side view inFig. 2 (c). The length of the pipe is chosen to allow the flow to befully developed at both inlet and exit. Hot water is supplied intothe system using an electrical heater. Flowrates of hot and cold wa-ters are measured by two different water rotameters. The inlet andoutlet temperatures of water were also measured at the inlet andoutlet pipe. The channel was insulated using rock wool at 10 cmthickness [19].
3. Definition of mixing index
The definition of themixing index is the key results for this study. It isdefined by Eq. (1) as used by many others earlier [3]. Here as value of
imental set-up and location of thermocouples, c) side view.
Fig. 3. a) Variation of mixing index with X coordinate, b) variation temperature of fluidwith Y coordinate for _mh ¼ 0:05kg=s; _mc ¼ 0:033kg=s and ϕ=0°.
Fig. 5. a) Variation ofmixing indexwith X coordinate, b) variation temperature of fluidwithY coordinate for _mh ¼ 0:05kg=s; _mc ¼ 0:05kg=s, ΔT=15 °C and D=10 mm jet inlet.
Fig. 4. Temperature field for _mh ¼ 0:05kg=s; _mc ¼ 0:033kg=s and ϕ=0°, a) ΔT=15 °C, D=5 mm, b) ΔT=20 °C, D=5 mm, c) ΔT=15 °C, D=10 mm, d) ΔT=20 °C, D=10 mm.
1248 Y. Varol et al. / International Communications in Heat and Mass Transfer 39 (2012) 1245–1252
Fig. 6. Temperature field for _mh ¼ 0:05kg=s; _mc ¼ 0:05kg=s, ΔT=15 °C and D=10 mm jet inlet, a) ϕ=0°, b) ϕ =30°, c) ϕ=60°, d) ϕ=90°.
Fig. 7. a) Variation of mixing index with X coordinate, b) variation temperature of fluidwith Y coordinate, for _mh ¼ 0:05kg=s, ΔT=20 °C, ϕ=60° and D=5 mm jet inlet.
1249Y. Varol et al. / International Communications in Heat and Mass Transfer 39 (2012) 1245–1252
thermalmixing decrease from100% to zero, the thermalmixing efficiencyof hot and cold water get better.
MI ¼ StΔT
� 100 ð1Þ
In this equation, St shows the standard deviation between hot andcold water temperatures. Thus, standard deviation is given by
St ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi∑n
i¼1 Th−Tavg� �2
= n−1ð Þ� �s
ð2Þ
where ΔT is temperature difference between hot and cold water andTavg average temperature.
4. Uncertainties
The independent parameters measured in the experiments: tem-peratures in the channel. To carry out these experiments, accuracyof data logger is 0.001. The Uncertainty in the result having withodds is calculated by
WR ¼ ∂R∂x1
W1
� �2
þ ∂R∂x2
W2
� �2
þ ∂R∂x3
W3
� �2
þ ::::::::::::::∂R∂xn
Wn
� �2" #1=2
ð3Þ
Following Eq. (3), St uncertainty for ΔT can be written as
Tavg ¼ Thot−Tcold2
ð4Þ
WTavg
Tavg¼ WThot
Thot
� �2
þ WTcold
Tcold
� �2" #1=2
ð5Þ
Fig. 8. Temperature field for _mh ¼ 0:05kg=s, ΔT=20 °C, ϕ=60 and D=5 mm jet inlet,a) _mc ¼ 0:033kg=s, b) _mc ¼ 0:042kg=s, c) _mc ¼ 0:05kg=s.
Fig. 9. a) Variation ofmixing indexwith X coordinate, b) variation temperature of fluidwithY coordinate, for _mh ¼ 0:05kg=s; _mc ¼ 0:042kg=s ΔT=15 °C, ϕ=30° and D=5 mm jetinlet.
1250 Y. Varol et al. / International Communications in Heat and Mass Transfer 39 (2012) 1245–1252
St ¼ Thot−Tavg ð6Þ
WStTt
¼ WThotThot
� �2
þWTavg
Tavg
!2" #1=2
ð7Þ
ΔT ¼ T1−T2 ð8Þ
WΔT
ΔT¼ WT1
T1
� �2
þ WT2T2
� �2" #1=2
ð9Þ
WMI
MI¼ WSt
St
� �2þ WΔT
ΔT
� �2" #1=2
ð10Þ
Calculations show that the total uncertainty in calculating for MI;WMI=0.46%.
5. Results and discussion
An experimental study has been performed in this work to see the ef-fects of parameters on thermal and flowmixing under twin-jet flow. Thestudied parameters are inclination angle of the channel, diameters of theinlet jet nozzle, temperature difference between two inlet jets and flowrate of the jets. Finally, mixing index and temperature distribution will
be presented in the next parts of the study. Also temperature distributionis plotted via isotherms for each case.
Fig. 3 (a) and (b) illustrates variation of mixing index (MI) with Xcoordinate and variation of fluid temperature with Y coordinate at thestation 5, respectively. The governing parameters for this figure are_mh ¼ 0:05kg=s; _mc ¼ 0:033kg=s and ϕ=0°. Variation of mixingindex with X coordinates for the indicated parameters is given inFig. 3 (a). This figure is plotted using definition of mixing index whichis calculated from Eq. (1). It is started from a huge value and decreasesalong the channel. An increasing is formed at the location of square ob-ject.MIfluctuating along the channel at the D=10 mm,ΔT=20 °C andD=5 mm, ΔT=20 °C. This mean thermal mixing is better along thechannel at lower temperature difference for these parameters. Also asit is seen from the figure thermal mixing is better at D=5 mm nozzlediameter. Fig. 3 (b) gives variation temperature of fluid with Y coordi-nate with same parameters as Fig. 3 (a). It compares the effect of bothtemperature difference and jet inlet diameters on temperature varia-tion. As seen from Fig. 3 (b), for D=5 mm, ΔT=20 °C, temperaturesvalues are almost constant with Y direction. D=10 mm, ΔT=15 °Cand D=10 mm, ΔT=20 °C exhibit similar trend and a low tempera-ture is formed at Y=0.16 m due to bigger jet diameter. The lowestvalue is formed at this point for D=10 mm, ΔT=15 °C.
Fig. 4 indicates temperature distribution for different studied pa-rameters as Fig. 3. It is noted that these temperatures distributionsare shown for t=450 s which is approximately steady-state regime.Inlet jets and outlet hole are symbolized with different colored ar-rows. Here, blue, red and black arrows are shown cold fluid, hotfluid and output hole, respectively. The left and right columns arepresented the different ΔT values. Thus, effects of ΔT on temperaturevariations can be seen at different jet velocities. As indicated in the
1251Y. Varol et al. / International Communications in Heat and Mass Transfer 39 (2012) 1245–1252
Fig. 4 (a) and (b), hot fluid mostly sits at the right top corner due tohot inlet jet. The fluid impinges onto top corner of passive element(PE) and come back and makes circulation at this point. Thus, hotfluid captured in that area. Due to high jet velocity, cold fluid directlymoves under the PE. For lower jet velocity, above the PE more fluid isheated. In Fig. 4 (c) and (d), the hot fluid deviated from its originalpath after impinging onto PE and in (c) second impingement is oc-curred onto channel boundary. It is an interesting result that highertemperature has disappeared near the exit for ΔT=20 °C and D=10 mm.
Fig. 5 (a) and (b) illustrates the mixing index and temperaturevalues with location for _mh ¼ 0:05kg=s; _mc ¼ 0:05kg=s, ΔT=15 °Cand D=10 mm jet inlet diameter, respectively. In this case, there ishuge difference between ϕ=0° and other inclination angles as seenfrom Fig. 5 (a). A stable variation is formed for ϕ=30°, 60° and 90°. Inother words, values of mixing index goes to zero after x=0.32 m. Itmeans that well thermal mixing is achieved at those inclination angles.In Fig. 5 (b), higher temperature is measured around Y=0.24 m forϕ=0°. At Y=0.32 m, the minimum temperature value is obtained forϕ=30°. The figure also indicated that temperatures at the middlepoints are higher than that of edge nodes except ϕ=30°. In the hori-zontal position of the channel (ϕ=0°), due to oscillation of flow, tem-perature values present zig-zag shaped distribution. For other values
Co
a
Co
b
25 .98 26 .42 26 .86 27 .3 27 .74 28 .18 28 .62
26 .04 26 .4 26 .76 27 .12 27 .48 27 .84 28 .2
28 .74 29.32 29 .9 30.48 31 .06 31 .64 32 .22 Co
c
Fig. 10. Temperature field, a) _mh ¼ 0:05kg=s; _mc ¼ 0:042kg=s ΔT=15 °C, ϕ=0° and D=5inlet, c) _mh ¼ 0:05kg=s; _mc ¼ 0:042kg=s ΔT=20 °C, ϕ=60° and D=5 mm jet inlet.
of inclination angle temperatures are oscillated at low frequency. Itmeans that thermal mixing becomes better.
For this case isotherms are plotted in Fig. 6. Fig. 6 (a) shows that pre-sentation of PE into the channel divides the channel to two parts as hotand cold of fluid. In the middle of the channel values of temperatureequal to arithmetic mean of inlet temperatures. However for othervalues of inclination angles, hot fluid cumulates upstream region ofthe channel. At the exit of the channel flow temperatures are almostequal for other inclination angles. As seen from the figures at differentinclination angles, heatedfluid become lesserwith increasing of inclina-tion angle. As we indicated above that the homogeneity in temperaturedistribution is the most important aim of this work.
In this study, effect of ratio of inlet flowrate is investigated to seethe efficiency on thermal mixing. With this aim flow rate of hot jetis taken as fixed while cold jet changes from _mh ¼ 0:033kg=s to_mc ¼ 0:05kg=s. For this case variation of mixing index with channel
length is presented in Fig. 7 (a) and temperature variation is plottedin Fig. 7 (b). As seen from Fig. 7 (a), MI is lower and more uniformat _mh ¼ 0:05kg=s while other fluctuating, especially around PE. Alsowhen look thermal changes along station 5 at Fig (b), temperatureis nearly constant along the column at _mh ¼ 0:05kg=s. These meanthermal mixing is better in the channel when flow rate between hotand cold jets is lower.
mm jet inlet b) _mh ¼ 0:05kg=s; _mc ¼ 0:042kg=s ΔT=15 °C, ϕ=30° and D=5 mm jet
1252 Y. Varol et al. / International Communications in Heat and Mass Transfer 39 (2012) 1245–1252
Fig. 8 is plotted to show the affect of ratio of inlet flowrate on tem-perature distribution. As seen from the figures well thermal mixing isperformed for _mc ¼ 0:033kg=s in Fig. 8 (a). For increasing of flow rateof cold jet hot fluid locates at the top-left corner due to domination ofcold jet as seen from Fig. 8 (b) and (c).
Finally Fig. 9 (a) and (b) compares the effect of passive element onmixing index and variation temperature of fluid with Y coordinate,respectively. The figures indicate that inserting of passive element(PE) into the channel disturbs the flow and mixing index increasesaround the PE. Near the exit of the channel same mixing indexvalue is performed for both cases. Also, temperatures values are de-creased due to presence of PE. It means that PE can be used as controlelement for flow and thermal mixing.
Fig. 10 (a) to (c) also compares the temperature distributions with(right column) and without (left column) PE. As given in the figurespresence of PE changes the temperature distribution inside the chan-nel for all parameters.
6. Conclusions
An experimental work has been performed in this study for differ-ent parameters such as jet temperatures, jet diameters, temperaturedifference, inclination angle of the channel and flow rates. The mainfindings can be listed as
• Mixing index decreases from inlet of the fluid to exit part of thechannel almost for all cases due to increasing of thermal mixing.
• Thermal mixing is the main function of temperature of inlet jets.• Temperature distribution depends on mainly flowrate inside thechannel.
• Presence of passive element, affects the mixing index. It behaveslike a curtain between hot and cold jet inlets. Thus, mixing indexdecreases around the body. It means that the insertion of the bodycan be used as control parameter for flow and thermal mixing.
• Another effective parameter on thermal mixing is the inclination ofthe channel. It affected from this parameter, higher thermal mixingefficiency is observed for ϕ=60°.
Acknowledgments
Authors thank the Firat University scientific and research fund fortheir valuable financial support with a project number 1747.
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