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Jet quenching phenomena during emergency cooling of high temperature solid surface
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2nd International Conference on Energy and Power, ICEP2018, 13–15 December 2018, 2nd International Conference on Energy and Power, ICEP2018, 13–15 December 2018, Sydney, Australia Sydney, Australia
Jet quenching phenomena during emergency cooling of high The 15th International Symposium District Heatingcooling and Cooling Jet quenching phenomena duringonemergency of high temperature solid surface temperature solid surface Assessing the feasibility of usingMousumi the heatAhmed demand-outdoor Aloke Kumar Mozumder*, Aloke Kumar temperature function for aMozumder*, long-termMousumi districtAhmed heat demand forecast Department of Mechanical Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka-1000, Bangladesh Department of Mechanical Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka-1000, Bangladesh
I. Andrića,b,c*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc
Abstract a IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal Abstract b Veolia Recherche & Innovation, Avenueheat Dreyfous Daniel, Limay, France In the case of loss of coolant accident, LOCA in nuclear291 reactor, removal can78520 be successful only when water rewets the c Département Systèmes Énergétiques et Environnement IMT Atlantique, 4 rue Alfred Kastler, 44300 France surface. Jet ofimpingement is aaccident, highly potential of heatheat removal from temperature solid After the In the case loss of coolant LOCA intechnique nuclear reactor, removal can high be successful onlyNantes, whensurface. water rewets impingement of liquid jet onis hot solid surface it is technique not capableoftoheat wet the surfacefrom immediately, it takes time (wetting delay) to the get surface. Jet impingement a highly potential removal high temperature solid surface. After a favorable condition to wet and itthen propagate thethe surface. of vapor and its (wetting explosiondelay) creates impingement of liquidby jetthe on liquid hot solid surface is not capable over to wet surfaceGeneration immediately, it takes time to the get barrier for the liquid front to liquid move. toAn investigation hassurface. been conducted during sub-cooled jet impingement a favorable condition by the wetexperimental and then propagate over the Generation of vapor and itswater explosion creates the Abstract quenching of three of copper, brass and steel. Theconducted jet velocity variedsub-cooled from 3 to15 m/s,jetjetimpingement sub-cooling barrier for the liquiddifferent front to cylindrical move. Anblocks experimental investigation has been during water was 5-80 Kofand initial block cylindrical temperatureblocks was 250 to 600 ºC. Theand study was conducted to determine the3dominating of quenching three different of copper, brass steel. The jet velocity varied from to15 m/s, jetparameters sub-cooling District heating networks are commonly addressed in the literature as one of the most effective solutions for decreasing the maximum delay, quench front boiling region size and finally developed correlationparameters of maximum was 5-80 Kheat andflux, initialwetting block temperature was 250movement, to 600 ºC. The study was conducted to determine theadominating of greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat heat flux for steel. elapsing wetting delay period, aboiling visible region smallersize boiling region developed was observed to move radially from maximum heat flux,After wetting delay,the quench front movement, and finally a correlation of maximum sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, the impinged centre.After The elapsing leading edge of this boiling region aisvisible designated as the quench front. Theobserved boiling region is radially a vital region heat flux for steel. the wetting delay period, smaller boiling region was to move from prolonging the investment return period. as maximum heatThe fluxleading occurred at this region during cooling. The boiling region increases withboiling the movement the quench thethe impinged centre. edge of this boiling region is designated as the quench front. The region is of a vital region The main scope of this paper is to assess the feasibility of using the heat demand – outdoor temperature function for heat demand front therefore position of at maximum heat flux cooling. moves accordingly. The boiling region increases of with as theand maximum heatthe flux occurred this region during The boiling region increases withwidth the movement thematerial quench forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 conductivity and decreases with liquid sub-cooling velocity. The maximum heat flux increases with jet velocity, liquid front and therefore the position of maximum heatand fluxliquid moves accordingly. The boiling region width increases with material buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district sub-cooling, soliddecreases material with conductivity and it is almost independent solid initial temperature. Wetting delay increasesliquid with conductivity and liquid sub-cooling and liquid velocity. of The maximum heat flux increases with jet velocity, renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were block initial temperature andconductivity decreases with liquid sub-cooling. sub-cooling, solid material andjetit velocity is almostand independent of solid initial temperature. Wetting delay increases with compared with results from a dynamic heat demand model, previously developed and validated by the authors. block initial temperature and decreases with jet velocity and liquid sub-cooling. The results showed that when only weather change is considered, the margin of error could be acceptable for some applications © 2018 The Authors. Published by Elsevier Ltd. (the error inAuthors. annual Published demand was lower than 20% for all weather scenarios considered). However, after introducing renovation © The by Ltd. This is an open accessPublished article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) © 2019 2018 The Authors. by Elsevier Elsevier Ltd. scenarios, the error increased to BY-NC-ND 59.5% (depending the weather and renovation scenarios combination considered). This is an open accessvalue article under theupCC license on (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection under responsibility of the scientific committee of the 2nd International Conference on Energy and This is an and openpeer-review access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection under increased responsibility of the scientific the up 2ndtoInternational Conference on Energytoand The valueand of peer-review slope coefficient on average within thecommittee range of of 3.8% 8% per decade, that corresponds the Power, ICEP2018. Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Energy and Power, ICEP2018. decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and Power, ICEP2018. renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the Keywords: LOCA; jet impingement; quench front; maximum heat flux; rewetting; boiling coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and Keywords: LOCA; jet impingement; quench front; maximum heat flux; rewetting; boiling improve the accuracy of heat demand estimations. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee * Corresponding author. Tel.: +88-02-9665636; fax: +88 02 8613046of The 15th International Symposium on District Heating and Cooling. E-mail address: [email protected] * Corresponding author. Tel.: +88-02-9665636; fax: +88 02 8613046
E-mail address: [email protected] Keywords: Heat Forecast; Climate 1876-6102© 2018demand; The Authors. Published bychange Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) 1876-6102© 2018 The Authors. Published by Elsevier Ltd. Selection under responsibility of the scientific of the 2nd International Conference on Energy and Power, ICEP2018. This is an and openpeer-review access article under the CC BY-NC-ND licensecommittee (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Energy and Power, ICEP2018. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Energy and Power, ICEP2018. 10.1016/j.egypro.2019.02.168
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1. Introduction During the Loss of Coolant Accident (LOCA) in a nuclear reactor, emergency high rate of heat removal is one of the criteria to avoid severe accident. During LOCA, a large amount of heat is accumulated in the component material that needs to be removed immediately. Quenching is a high heat removal technique which removes heat from hot surfaces at a sufficiently high rate by means of sudden contact with a low temperature fluid. This method is also widely employed in heat treatment of metal parts to achieve desired hardness and mechanical properties. Many experimental and analytical works [1-3] on quenching phenomena have been studied during the last few decades. The quench front propagation in the case of water emergency cooling of water cooled fusion nuclear components was studied during the LOCA accident [4]. They found that the quench front propagation depends on the initial wall temperature, coolant flow rate, and heat accumulated in the cooled components. A transient cooling of hot stainless steel surface of 0.25 mm thickness was conducted with round water jet impingement [5]. Initially, the surface was heated up to the temperature of 800 oC before the water was injected through straight tube type nozzle of 2.5 mm diameter and 250 mm length. Rewetting was defined as the onset of transition or unstable boiling in going from stable film boiling to nucleate boiling, and found that it corresponded to the minimum film boiling heat flux on the standard boiling curve [6]. Transient boiling experiments were conducted where a large preheated specimen was quenched by a water wall jet on its top surface [7]. An experimental investigation of quenching for high temperature metal surface using a sub cooled water jet was conducted where they observed that the wetting front becomes stagnant for a certain period of time at a small central region before covering the entire surface and they defined this time as resident time [8]. Maximum heat flux and their propagation also analysed there. Analysis on quenching of carbon steel with water jet impingement was conducted by Mozumder and Ahmed [9] and Ahmed [10], they mainly focused on maximum heat flux and its characteristics on hot surface. Their study revealed that the wetting delay and maximum heat flux are very important in investigating the underlying mechanisms of quenching process. The experiment was actually carried out by Mozumder [8] and Ahmed [10] analysed the data to reveal the quench cooling phenomena on carbon steel surface. The present study is mainly based on the analysis of data conducted by Ahmed [10]. Here, a correlation has proposed for the maximum heat flux of steel surface quenching. The dominating parameters of quench cooling for steel has analysed in this study though it is difficult to have quenching phenomena specially for low conductivity material like steel than copper or brass. Nomenclature d Qmax hfg Ja r rq Tb Tliq Tsat
Jet diameter Maximum heat flux Latent heat of vaporization Jackob Number = (ρlcl∆Tsub)/ρghfg Radial position of the block Radial position at Qmax point Initial block temperature Liquid temperature Saturated liquid temperature
(mm) (MW/m2) (kJ/kg) (-) (mm) (mm) (°C) (°C) (°C)
ΔTsub Liquid subcooling, (Tsat -Tliq) u Jet velocity c Specific heat λ Thermal conductivity ρ Density σ Surface tension Subscripts l liquid s solid
(K) (m/s) (kJ/kgK) (W/m2K) (kg/m3) (N/m)
2. Experiment The experiment was conducted for three different surfaces of metal block made of copper, brass and steel [8]. Hot cylindrical block (94 mm diameter and 59 mm height) as shown in Fig. 1 was quenched by 2 mm diameter subcooled water jet impinged at the centre surface of the block. The jet velocity varied from 3 to15 m/s, jet sub-cooling was 5-80 K and initial block temperature was 250 to 600 oC. The temperature readings from the thermocouples
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Fig. 1. Test section for the experimentation
1. Tested block, 2.Thermocouple wires, 3. Heater, 4. Nozzle, 5.Test surface, 6. High speed video camera recorded by the data acquisition system were used to get the surface parameters i.e. surface temperature and surface heat flux of the heated block. During quenching of hot surfaces the direct measurement of surface heat flux and temperature is very difficult. It is impossible to get the thermal history directly just from the surface at which the jet is impinged without greatly disturbing the flow and boiling phenomena. An inverse heat conduction technique [11] is proved to get the surface heat flux and temperature from knowing the history of temperatures inside the hot solid surface. A high speed video camera was used to capture the visual flow phenomena during quenching. The present study mainly focuses to investigate the quenching phenomena of carbon steel (0.45 % carbon) block under the same experimental conditions as for copper and brass block. 3. Results and Discussions When the liquid jet was first impinged on the hot surface, it remained stagnant at the small impinged region for a certain period of time before start to wet the entire surface, here this time is called resident time. When the water jet impinged on the surface, a vapor explosion occurred and the impinged liquid splashed out from the stagnation region instead of wetting the entire surface. The vapor bubble bursting force and the produced vapor layer made a barrier for the liquid jet to make direct contact with the solid surface. As there is no contact between the hot solid and liquid, no vapor is generated and thus the repulsive force becomes absent which results in solid liquid contact again. As the contact established again, vapor generation and repulsive force acts again. This touching and detouching phenomena continues and consequences less significant local cooling of the hot solid. After a certain period of time (resident time), the solid becomes colder and the liquid side potential becomes dominating over solid and a constant contact is established. This contact ensures starting of the bulk cooling of the solid. The impinged liquid then starts to wet the hot solid surface and moves over the surface instead of bouncing from the impinged surface as it was before the resident time. A visible boiling is seen at the leading region of this moving liquid. The leading edge of this boiling region is defined as the quench front and the trailing region of this quench front is defined as the visible boiling region. The size of the boiling region in radial direction is defined here as boiling width, w. The maximum heat flux for a certain position on the hot surface occurs when the boiling region reaches that position. Actually, when the thermal potential/parameters of that position becomes favourable for boiling, the
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quench front moves and reaches that position. As the boiling region moves towards the circumferential direction, the position of maximum heat flux moves accordingly. The dominating parameters of the boiling width and maximum heat flux will be discussed in this section. 3.1 Maximum heat flux and radial position At initial cooling period (just immediate after the quench front start moving), the heat transfer rate is high due to the higher potential of the solid as its temperature is higher. But, when the quench front reaches the higher radial region, the bulk cooling (cooling of the whole object) is happened to a certain level and resulted in reduction of heat transfer at higher radial position. As shown in Fig. 2, after r = 10 mm, two steps decrease of maximum heat flux, Qmax is occurred. For the radial position, r = 10-20 mm, a gradual decrease of Qmax is observed and r = 20-35 mm, a more steep falling of Qmax is noted. Due to cumulative exhaustion of heat from the solid body, the heat energy content in the solid decreases and consequences a decreases of heat transfer. For the simplification of analysis, the two regions r = 10-20 mm is defined as region-I and r = 20-35 mm is defined as region-II. At region-II, Qmax is relatively a strong function of radial position than region-I. When the quench front reaches at region-II, the bulk cooling of solid is almost completed which consequences sudden drop of maximum heat flux. For the case of low thermal conductivity material like steel, the bulk cooling especially along the direction of the jet inside the solid is not happened so vigorously. Only the local surface cooling allows the quench front to move over the surface. This material effect will be discussed in section. 3.4 . Fig. 2 also reveals that jet velocity influences the value of Qmax. Higher jet velocity means that the mass flow rate of the coolant liquid is high which results in increase of heat extracting potential by the liquid from the solid and ultimately heat flux increases. 3.2 Effect of jet sub-cooling on maximum heat flux During cooling of the solid, a heat energy balancing play the vital role for the overall thermal and hydrodynamic phenomena. Liquid side has a potential to extract heat and on the other hand, solid has the potential to supply. In between, vapor explosion, vapor layer formation and some other physical issue make a barrier to heat transfer between solid and liquid. When the liquid sub-cooling becomes high (i.e. liquid temperature is low), the heat extracting potential of the liquid increases which results increase of heat flux. Fig. 3 shows that with the increase of liquid sub-cooling (from 5K to 80 K), the value of maximum heat flux, Qmax increases gradually. The figure also reveals that this increasing trend remains same for all the radial positions.
region I (10-20)
region II (20-35)
Fig. 2. Maximum heat flux with radial position for different jet velocities (Steel, Tb=300°C, ΔTsub=20K)
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Qmax (MW/m2)
10
1
0.1
r=5 r=12 r=20 r=25 r=35 1
10
100
Tsat-Tliq (K) Fig. 3. Maximum surface heat Flux with liquid sub-cooling (Steel, Tb=250°C, u=03 m/s)
3.3 Effect of surface initial temperature on maximum heat flux The effect of the initial surface temperature on maximum heat flux is not so significant. The maximum heat flux usually occurs when the surface temperature is in the range 120-200 oC [8]. The maximum heat flux situation is established when the surface temperature attains more or less corresponding to the boiling (particularly nucleate boiling) temperature. As the boiling (nucleate boiling) happens within a certain range of temperature, the maximum heat flux occurs for that fixed rage of temperature. Tentatively, it can be said that whatever is the initial temperature, is does not matter for maximum heat flux. For higher initial temperature, it takes long time to cool down the surface temperature to the corresponding range of boiling (nucleate boiling) temperature and the maximum heat flux occurs at that temperature. For this reason initial temperature has less effects on maximum heat flux. 3.4 Effect of solid material property on maximum heat flux The solid material influences strongly the rate of heat transfer. Mozumder [8] experimented on jet impingement quenching of three different block materials (copper, brass and steel) and reported that the maximum heat flux for copper is two times more than steel. The thermal conductivity of copper, brass and steel are 380 W/mK, 112 W/mK and 37.8 W/mK respectively. Therefore, the thermal conductivity of carbon steel is approximates 1/10 times of copper. At first, when the jet is impinged on the central region of the surface, the central impinged region is cooled locally as well as heat is transferred from other region of the solid towards the relatively cold central region. If heat transfer depends only on the local cooling of the central region, it would be very small. But actually the amount of heat energy transfer depends on the central region cooling and significantly on the amount of heat coming from the other region towards the central colder region by the mode of conduction. Therefore, the heat conducting capacity by the solid play the vital role for the amount of heat transfer. For copper or brass, the higher conductivity ensures larger amount of stored heat energy transport through the solid towards the central colder region and results in higher high transfer. In the case of steel, lower conductivity of the material transfers smaller amount of stored heat towards the central colder region which consequences the lower heat flux. As the steel conducts less amount of heat, mostly local surface cooling occurs during quench front propagation. But local cooling is not the requirement for most of the heat transfer processes specially during LOCA instead of bulk cooling. For low conductivity material like steel this is a big challenge for bulk cooling and this makes steel cooling analysis difficult.
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3.5 Visual phenomena during jet cooling Frame by frame analysis of high speed camera recorded video (as shown in Fig. 4) reveals that when the jet first struck the surface, the liquid quickly spread over a small central region about two to four times the jet diameter and it was splashed out from the surface. Fig.4 shows four sequences of video images which presents the quench front propagation during cooling. This quench front should not be thought of a single point or single line but it should be considered that the entire transition boiling region will be in the quench front region. For steel, the material conductivity is low which permits only a small amount heat conduction from other portion of the solid to the impinged region. When the quench front tries to move, only a local surface (at the front region of the quench front) cooling happens immediately because only an insignificant amount of heat is supplied from other portion of the solid to recover the colder region. Less heat energy supply to the surface results it to be remains at a low surface temperature which consequences a faster movement of the quench front. The similar observations were found for all the experimental conditions with steel. For copper or brass, high conductivity results in faster recovery of heat to the impinged region and makes the surface temperature hotter which ultimately makes the quench front movement slower. Fig. 4 shows that it takes 180 sec to move the quench front around 70 % of the block radius; but for copper or brass it may take more than a thousand seconds for the same experimental conditions [8]. As found from the Fig. 4 that the boiling width, w increases from 0.5 mm to 7 mm by a time period of 5 sec to 180 sec for the case of steel. For steel, during the movement of the quench front, heat recovery for the already colder region has not been done significantly by the other hotter portion of the solid. For this reason, the already quenched local surface temperature remains lower but the other surface temperature remains higher which makes the surface temperature gradient high in the radial direction. This high temperature gradient in the radial direction does not allow the quench front to move easily in the radial direction. Only the temperature of a smaller region becomes favourable for boiling which results in smaller size of the boiling width. The boiling width as shown in the Fig. 4 is only 7 mm after 180 sec (covering around 70 % of the radial distance) for steel; for copper or brass for the same quench front position, the boiling width may be around three times [8]. 3.6 Correlation for maximum heat flux of steel Mozumder [8] proposed a correlation of maximum heat flux for copper and brass which agreement is good enough but due to the different behaviour of steel, the same correlation does not agree well for steel. Ahemed [10] included some important parameters in the correlation which has influence on maximum heat flux for steel. The correlations of maximum heat flux have developed for steel for two distinct regions of radial position for 10-20 mm and 20-35 mm. It is considered that the wetting front started to move from the radial position of 10 mm. Therefore the maximum heat flux for the radial positions of less than 10 mm has not been included here. The two regions are distinguished according to their heat transfer rate in the radial direction. It is observed that the maximum heat flux w = 2 mm, t = 15 sec w = 0.5 mm, t = 5 sec
w = 4 mm, t = 60 sec
w = 7 mm, t = 180 sec
Fig. 4: Visual phenomena (quench front movement) during jet cooling (Steel, Tb = 600 oC, ΔTsub = 50 K, u = 5 m/s)
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gradient with the radial position is higher in region II. These correlations have included the terms [(ρcλ)l/(ρcλ)s]0.5, ρlu2(2rq-d)/σ and (1+Ja). The term [(ρcλ)l/(ρcλ)s]0.5 indicates the relative effects of solid and liquid thermal properties. Another non-dimensional group ρlu2(2rq-d)/σ represents the ratio of inertia force to surface tension force. In addition, Jacob number, Ja is considered an important non-dimensional number in subcooled boiling. It is the ratio of the sensible heat for a given volume of liquid to heat through ΔTsub in reaching its saturation temperature, to the latent heat required in evaporating the same volume of vapor. The term (1+Ja) has included in the correlation which has significant effect for region I. It indicates the effect of maximum possible heat transfer into the liquid in relative to the heat required to evaporate the same volume of vapor. The heat removal capacity of liquid decreases with radial position, as the liquid moves over the hot solid it becomes heated and getting closer to its saturation temperature which ultimately reduces its heat extracting potential. The value of ΔTsub (i.e Tsat-Tliq) decreases as the liquid temperature increases with radial position which ultimately decreases the value of maximum heat flux. Analysis also reveals that the effect of (1+Ja) on maximum heat flux is not significant in region II and for this reason it is not included in the correlation of region II, though it is included in region I. Finally, the following two correlations have developed (for Tb = 250-400 oC) for the two distinct regions: For region I (radial position of 10-20mm)
( ρ cλ ) l = 55.119 ρ g h fg u ( ρ cλ ) s
Q max
0.674
ρ l u 2 (2rq − d ) σ
−0.295
(1 + Ja )
0.136
(1)
For region II (radial position of 10-20mm) Q max
ρ g h fg u
= 1.106
( ρ cλ ) l ( ρ cλ ) s
−1.291
ρu l
2
(2 rq − d )
σ
−0.287
(2)
The coefficients of these two correlations are determined by using least square method from the experimental data of maximum heat flux. The experimental data is within ±25% and ±30% for region I and II of the proposed correlations respectively as shown in Fig. 5.
0.5
Q max ρ h u g
fg
exp
Eqn. (1)
0.1
+25%
80k, u=5
80k, u=10
80k, u=15
5k, u=5
50k, u=3
50k, u=5
5k, u=10
50k, u=10
50k, u=15
20k, u=3
20k, u=5
20k, u=10
20k, u=15
5k, u=3
5k, u=15
k is sub-cooling in Kelvin and u is jet velocity
-25%
0.06
80k, u=3
1.0
0.1 ( ρ cλ ) l 55.119 ( ρ cλ ) s
0.674
ρ l u 2 (2rq − d ) σ
−0.295
(1 + Ja )
0.136
Fig. 5. Maximum heat flux, Qmax (Tb = 250-400 oC) with the proposed correlation (for region I)
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4. Conclusions The following conclusions can be drawn from the present study: 1. 2. 3. 4. 5.
Maximum heat flux always occurs at the visible boiling region which is the moving trailing region of the quench front. The size of the visible boiling region (i.e. boiling width) increases with the movement of the quench front and material conductivity and decreases with liquid sub-cooling and liquid velocity. The maximum heat flux increases with jet velocity, liquid sub-cooling, solid material conductivity and it is almost independent of solid initial temperature. Due to the smaller thermal conductivity of steel, liquid jet removes heat locally from the heated surface and as a result the entire body does not feel immediately the quenching effect though the quench front moves over. But in the case of copper and brass, bulk cooling occurs with the quench front movement. Two correlations of maximum heat flux for block initial temperature 250-400 oC have been proposed for steel for region I (10-20mm) and region II (20-35mm) whose agreement is ±25% and ±30% respectively with the experimental data.
Acknowledgements The authors acknowledge their gratefulness to the Department of Mechanical Engineering, Bangladesh University of Engineering and Technology for providing computer laboratory facility. References [1] Karwa N, Stephan P. "Experimental investigation of free-surface jet impingement quenching process." International Journal of Heat and Mass Transfer 64 (2013): 1118-1126 [2] Gopal N, Sahoo PK, Ravi K, Leled HG, Chatterjeed B, Mukhopadhyay D. "Experimental investigation of heat transfer during LOCA with failure of emergency cooling system." 5th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, (2007) Paper number: NG1 [3] Mozumder AK, Monde M, Woodfield PL. "Delay of wetting propagation during jet impingement quenching for a high temperature surface." International Journal of Heat and Mass Transfer 48 (2005): 2877-2888 [4] Jan S, Vaclav B, Vaclav D, Slavomir E. "Effective water cooling of very hot surfaces during the LOCA accident." Fusion Engineering and Design 124 (2017): 1211–1214 [5] Chitranjan A, Ravi K, Akhilesh G, Barun C. "Rewetting and maximum surface heat flux during quenching of hot surface by round water jet impingement." International Journal of Heat and Mass Transfer 55 (2012): 4772-4782 [6] Iloeje OC, Plummer DN, Rohsenow WM, Griffith P. "Effect of mass flux, flow quality, thermal and surface properties of materials on rewet of dispersed flow film boiling." Trans. ASME, Journal of Heat Transfer 104 (1982): 304-308 [7] Filipovic J, Incropera FP, Viskanta R. "Quenching Phenomena Associated with a Water Wall Jet: I. Transient Hydrodynamic and Thermal Conditions." Experimental Heat Transfer 8 (1995): 97-117 [8] Mozumder AK. "Thermal and hydrodynamic characteristics of jet impingement quenching for high temperature surface." Ph.D thesis, Graduate School of Science and Engineering, (2006) Saga University, Japan [9] Mozumder AK, Ahmed M, Monde M. "Carbon steel quenching and maximum heat flux with water jet impingement." Proc. of the International Conference on Mechanical Engineering, (2009) Dhaka, Bangladesh [10] Ahmed M. "Maximum heat flux and wetting delay during quenching of high temperature carbon steel block." M. Sc. Thesis, Dept. of Mechanical Engineering, Bangladesh University of Engineering and Technology, (2008) Dhaka, Bangladesh [11] Monde M, Arima H, Liu W, Mitsutake Y, Hammad JA. "An analytical solution for two-dimensional inverse heat conduction problems using Laplace transform." International Journal of Heat and Mass Transfer 46 (2003): 2135–2148
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2nd International Conference on Energy and Power, ICEP2018, 13–15 December 2018, 2nd International Conference on Energy and Power, ICEP2018, 13–15 December 2018, Sydney, Australia Sydney, Australia
Jet quenching phenomena during emergency cooling of high The 15th International Symposium District Heatingcooling and Cooling Jet quenching phenomena duringonemergency of high temperature solid surface temperature solid surface Assessing the feasibility of usingMousumi the heatAhmed demand-outdoor Aloke Kumar Mozumder*, Aloke Kumar temperature function for aMozumder*, long-termMousumi districtAhmed heat demand forecast Department of Mechanical Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka-1000, Bangladesh Department of Mechanical Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka-1000, Bangladesh
I. Andrića,b,c*, A. Pinaa, P. Ferrãoa, J. Fournierb., B. Lacarrièrec, O. Le Correc
Abstract a IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal Abstract b Veolia Recherche & Innovation, Avenueheat Dreyfous Daniel, Limay, France In the case of loss of coolant accident, LOCA in nuclear291 reactor, removal can78520 be successful only when water rewets the c Département Systèmes Énergétiques et Environnement IMT Atlantique, 4 rue Alfred Kastler, 44300 France surface. Jet ofimpingement is aaccident, highly potential of heatheat removal from temperature solid After the In the case loss of coolant LOCA intechnique nuclear reactor, removal can high be successful onlyNantes, whensurface. water rewets impingement of liquid jet onis hot solid surface it is technique not capableoftoheat wet the surfacefrom immediately, it takes time (wetting delay) to the get surface. Jet impingement a highly potential removal high temperature solid surface. After a favorable condition to wet and itthen propagate thethe surface. of vapor and its (wetting explosiondelay) creates impingement of liquidby jetthe on liquid hot solid surface is not capable over to wet surfaceGeneration immediately, it takes time to the get barrier for the liquid front to liquid move. toAn investigation hassurface. been conducted during sub-cooled jet impingement a favorable condition by the wetexperimental and then propagate over the Generation of vapor and itswater explosion creates the Abstract quenching of three of copper, brass and steel. Theconducted jet velocity variedsub-cooled from 3 to15 m/s,jetjetimpingement sub-cooling barrier for the liquiddifferent front to cylindrical move. Anblocks experimental investigation has been during water was 5-80 Kofand initial block cylindrical temperatureblocks was 250 to 600 ºC. Theand study was conducted to determine the3dominating of quenching three different of copper, brass steel. The jet velocity varied from to15 m/s, jetparameters sub-cooling District heating networks are commonly addressed in the literature as one of the most effective solutions for decreasing the maximum delay, quench front boiling region size and finally developed correlationparameters of maximum was 5-80 Kheat andflux, initialwetting block temperature was 250movement, to 600 ºC. The study was conducted to determine theadominating of greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat heat flux for steel. elapsing wetting delay period, aboiling visible region smallersize boiling region developed was observed to move radially from maximum heat flux,After wetting delay,the quench front movement, and finally a correlation of maximum sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, the impinged centre.After The elapsing leading edge of this boiling region aisvisible designated as the quench front. Theobserved boiling region is radially a vital region heat flux for steel. the wetting delay period, smaller boiling region was to move from prolonging the investment return period. as maximum heatThe fluxleading occurred at this region during cooling. The boiling region increases withboiling the movement the quench thethe impinged centre. edge of this boiling region is designated as the quench front. The region is of a vital region The main scope of this paper is to assess the feasibility of using the heat demand – outdoor temperature function for heat demand front therefore position of at maximum heat flux cooling. moves accordingly. The boiling region increases of with as theand maximum heatthe flux occurred this region during The boiling region increases withwidth the movement thematerial quench forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 conductivity and decreases with liquid sub-cooling velocity. The maximum heat flux increases with jet velocity, liquid front and therefore the position of maximum heatand fluxliquid moves accordingly. The boiling region width increases with material buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district sub-cooling, soliddecreases material with conductivity and it is almost independent solid initial temperature. Wetting delay increasesliquid with conductivity and liquid sub-cooling and liquid velocity. of The maximum heat flux increases with jet velocity, renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were block initial temperature andconductivity decreases with liquid sub-cooling. sub-cooling, solid material andjetit velocity is almostand independent of solid initial temperature. Wetting delay increases with compared with results from a dynamic heat demand model, previously developed and validated by the authors. block initial temperature and decreases with jet velocity and liquid sub-cooling. The results showed that when only weather change is considered, the margin of error could be acceptable for some applications © 2018 The Authors. Published by Elsevier Ltd. (the error inAuthors. annual Published demand was lower than 20% for all weather scenarios considered). However, after introducing renovation © The by Ltd. This is an open accessPublished article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) © 2019 2018 The Authors. by Elsevier Elsevier Ltd. scenarios, the error increased to BY-NC-ND 59.5% (depending the weather and renovation scenarios combination considered). This is an open accessvalue article under theupCC license on (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection under responsibility of the scientific committee of the 2nd International Conference on Energy and This is an and openpeer-review access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection under increased responsibility of the scientific the up 2ndtoInternational Conference on Energytoand The valueand of peer-review slope coefficient on average within thecommittee range of of 3.8% 8% per decade, that corresponds the Power, ICEP2018. Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Energy and Power, ICEP2018. decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and Power, ICEP2018. renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the Keywords: LOCA; jet impingement; quench front; maximum heat flux; rewetting; boiling coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and Keywords: LOCA; jet impingement; quench front; maximum heat flux; rewetting; boiling improve the accuracy of heat demand estimations. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee * Corresponding author. Tel.: +88-02-9665636; fax: +88 02 8613046of The 15th International Symposium on District Heating and Cooling. E-mail address: [email protected] * Corresponding author. Tel.: +88-02-9665636; fax: +88 02 8613046
E-mail address: [email protected] Keywords: Heat Forecast; Climate 1876-6102© 2018demand; The Authors. Published bychange Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) 1876-6102© 2018 The Authors. Published by Elsevier Ltd. Selection under responsibility of the scientific of the 2nd International Conference on Energy and Power, ICEP2018. This is an and openpeer-review access article under the CC BY-NC-ND licensecommittee (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Energy and Power, ICEP2018. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the scientific committee of the 2nd International Conference on Energy and Power, ICEP2018. 10.1016/j.egypro.2019.02.168
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1. Introduction During the Loss of Coolant Accident (LOCA) in a nuclear reactor, emergency high rate of heat removal is one of the criteria to avoid severe accident. During LOCA, a large amount of heat is accumulated in the component material that needs to be removed immediately. Quenching is a high heat removal technique which removes heat from hot surfaces at a sufficiently high rate by means of sudden contact with a low temperature fluid. This method is also widely employed in heat treatment of metal parts to achieve desired hardness and mechanical properties. Many experimental and analytical works [1-3] on quenching phenomena have been studied during the last few decades. The quench front propagation in the case of water emergency cooling of water cooled fusion nuclear components was studied during the LOCA accident [4]. They found that the quench front propagation depends on the initial wall temperature, coolant flow rate, and heat accumulated in the cooled components. A transient cooling of hot stainless steel surface of 0.25 mm thickness was conducted with round water jet impingement [5]. Initially, the surface was heated up to the temperature of 800 oC before the water was injected through straight tube type nozzle of 2.5 mm diameter and 250 mm length. Rewetting was defined as the onset of transition or unstable boiling in going from stable film boiling to nucleate boiling, and found that it corresponded to the minimum film boiling heat flux on the standard boiling curve [6]. Transient boiling experiments were conducted where a large preheated specimen was quenched by a water wall jet on its top surface [7]. An experimental investigation of quenching for high temperature metal surface using a sub cooled water jet was conducted where they observed that the wetting front becomes stagnant for a certain period of time at a small central region before covering the entire surface and they defined this time as resident time [8]. Maximum heat flux and their propagation also analysed there. Analysis on quenching of carbon steel with water jet impingement was conducted by Mozumder and Ahmed [9] and Ahmed [10], they mainly focused on maximum heat flux and its characteristics on hot surface. Their study revealed that the wetting delay and maximum heat flux are very important in investigating the underlying mechanisms of quenching process. The experiment was actually carried out by Mozumder [8] and Ahmed [10] analysed the data to reveal the quench cooling phenomena on carbon steel surface. The present study is mainly based on the analysis of data conducted by Ahmed [10]. Here, a correlation has proposed for the maximum heat flux of steel surface quenching. The dominating parameters of quench cooling for steel has analysed in this study though it is difficult to have quenching phenomena specially for low conductivity material like steel than copper or brass. Nomenclature d Qmax hfg Ja r rq Tb Tliq Tsat
Jet diameter Maximum heat flux Latent heat of vaporization Jackob Number = (ρlcl∆Tsub)/ρghfg Radial position of the block Radial position at Qmax point Initial block temperature Liquid temperature Saturated liquid temperature
(mm) (MW/m2) (kJ/kg) (-) (mm) (mm) (°C) (°C) (°C)
ΔTsub Liquid subcooling, (Tsat -Tliq) u Jet velocity c Specific heat λ Thermal conductivity ρ Density σ Surface tension Subscripts l liquid s solid
(K) (m/s) (kJ/kgK) (W/m2K) (kg/m3) (N/m)
2. Experiment The experiment was conducted for three different surfaces of metal block made of copper, brass and steel [8]. Hot cylindrical block (94 mm diameter and 59 mm height) as shown in Fig. 1 was quenched by 2 mm diameter subcooled water jet impinged at the centre surface of the block. The jet velocity varied from 3 to15 m/s, jet sub-cooling was 5-80 K and initial block temperature was 250 to 600 oC. The temperature readings from the thermocouples
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Fig. 1. Test section for the experimentation
1. Tested block, 2.Thermocouple wires, 3. Heater, 4. Nozzle, 5.Test surface, 6. High speed video camera recorded by the data acquisition system were used to get the surface parameters i.e. surface temperature and surface heat flux of the heated block. During quenching of hot surfaces the direct measurement of surface heat flux and temperature is very difficult. It is impossible to get the thermal history directly just from the surface at which the jet is impinged without greatly disturbing the flow and boiling phenomena. An inverse heat conduction technique [11] is proved to get the surface heat flux and temperature from knowing the history of temperatures inside the hot solid surface. A high speed video camera was used to capture the visual flow phenomena during quenching. The present study mainly focuses to investigate the quenching phenomena of carbon steel (0.45 % carbon) block under the same experimental conditions as for copper and brass block. 3. Results and Discussions When the liquid jet was first impinged on the hot surface, it remained stagnant at the small impinged region for a certain period of time before start to wet the entire surface, here this time is called resident time. When the water jet impinged on the surface, a vapor explosion occurred and the impinged liquid splashed out from the stagnation region instead of wetting the entire surface. The vapor bubble bursting force and the produced vapor layer made a barrier for the liquid jet to make direct contact with the solid surface. As there is no contact between the hot solid and liquid, no vapor is generated and thus the repulsive force becomes absent which results in solid liquid contact again. As the contact established again, vapor generation and repulsive force acts again. This touching and detouching phenomena continues and consequences less significant local cooling of the hot solid. After a certain period of time (resident time), the solid becomes colder and the liquid side potential becomes dominating over solid and a constant contact is established. This contact ensures starting of the bulk cooling of the solid. The impinged liquid then starts to wet the hot solid surface and moves over the surface instead of bouncing from the impinged surface as it was before the resident time. A visible boiling is seen at the leading region of this moving liquid. The leading edge of this boiling region is defined as the quench front and the trailing region of this quench front is defined as the visible boiling region. The size of the boiling region in radial direction is defined here as boiling width, w. The maximum heat flux for a certain position on the hot surface occurs when the boiling region reaches that position. Actually, when the thermal potential/parameters of that position becomes favourable for boiling, the
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quench front moves and reaches that position. As the boiling region moves towards the circumferential direction, the position of maximum heat flux moves accordingly. The dominating parameters of the boiling width and maximum heat flux will be discussed in this section. 3.1 Maximum heat flux and radial position At initial cooling period (just immediate after the quench front start moving), the heat transfer rate is high due to the higher potential of the solid as its temperature is higher. But, when the quench front reaches the higher radial region, the bulk cooling (cooling of the whole object) is happened to a certain level and resulted in reduction of heat transfer at higher radial position. As shown in Fig. 2, after r = 10 mm, two steps decrease of maximum heat flux, Qmax is occurred. For the radial position, r = 10-20 mm, a gradual decrease of Qmax is observed and r = 20-35 mm, a more steep falling of Qmax is noted. Due to cumulative exhaustion of heat from the solid body, the heat energy content in the solid decreases and consequences a decreases of heat transfer. For the simplification of analysis, the two regions r = 10-20 mm is defined as region-I and r = 20-35 mm is defined as region-II. At region-II, Qmax is relatively a strong function of radial position than region-I. When the quench front reaches at region-II, the bulk cooling of solid is almost completed which consequences sudden drop of maximum heat flux. For the case of low thermal conductivity material like steel, the bulk cooling especially along the direction of the jet inside the solid is not happened so vigorously. Only the local surface cooling allows the quench front to move over the surface. This material effect will be discussed in section. 3.4 . Fig. 2 also reveals that jet velocity influences the value of Qmax. Higher jet velocity means that the mass flow rate of the coolant liquid is high which results in increase of heat extracting potential by the liquid from the solid and ultimately heat flux increases. 3.2 Effect of jet sub-cooling on maximum heat flux During cooling of the solid, a heat energy balancing play the vital role for the overall thermal and hydrodynamic phenomena. Liquid side has a potential to extract heat and on the other hand, solid has the potential to supply. In between, vapor explosion, vapor layer formation and some other physical issue make a barrier to heat transfer between solid and liquid. When the liquid sub-cooling becomes high (i.e. liquid temperature is low), the heat extracting potential of the liquid increases which results increase of heat flux. Fig. 3 shows that with the increase of liquid sub-cooling (from 5K to 80 K), the value of maximum heat flux, Qmax increases gradually. The figure also reveals that this increasing trend remains same for all the radial positions.
region I (10-20)
region II (20-35)
Fig. 2. Maximum heat flux with radial position for different jet velocities (Steel, Tb=300°C, ΔTsub=20K)
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Qmax (MW/m2)
10
1
0.1
r=5 r=12 r=20 r=25 r=35 1
10
100
Tsat-Tliq (K) Fig. 3. Maximum surface heat Flux with liquid sub-cooling (Steel, Tb=250°C, u=03 m/s)
3.3 Effect of surface initial temperature on maximum heat flux The effect of the initial surface temperature on maximum heat flux is not so significant. The maximum heat flux usually occurs when the surface temperature is in the range 120-200 oC [8]. The maximum heat flux situation is established when the surface temperature attains more or less corresponding to the boiling (particularly nucleate boiling) temperature. As the boiling (nucleate boiling) happens within a certain range of temperature, the maximum heat flux occurs for that fixed rage of temperature. Tentatively, it can be said that whatever is the initial temperature, is does not matter for maximum heat flux. For higher initial temperature, it takes long time to cool down the surface temperature to the corresponding range of boiling (nucleate boiling) temperature and the maximum heat flux occurs at that temperature. For this reason initial temperature has less effects on maximum heat flux. 3.4 Effect of solid material property on maximum heat flux The solid material influences strongly the rate of heat transfer. Mozumder [8] experimented on jet impingement quenching of three different block materials (copper, brass and steel) and reported that the maximum heat flux for copper is two times more than steel. The thermal conductivity of copper, brass and steel are 380 W/mK, 112 W/mK and 37.8 W/mK respectively. Therefore, the thermal conductivity of carbon steel is approximates 1/10 times of copper. At first, when the jet is impinged on the central region of the surface, the central impinged region is cooled locally as well as heat is transferred from other region of the solid towards the relatively cold central region. If heat transfer depends only on the local cooling of the central region, it would be very small. But actually the amount of heat energy transfer depends on the central region cooling and significantly on the amount of heat coming from the other region towards the central colder region by the mode of conduction. Therefore, the heat conducting capacity by the solid play the vital role for the amount of heat transfer. For copper or brass, the higher conductivity ensures larger amount of stored heat energy transport through the solid towards the central colder region and results in higher high transfer. In the case of steel, lower conductivity of the material transfers smaller amount of stored heat towards the central colder region which consequences the lower heat flux. As the steel conducts less amount of heat, mostly local surface cooling occurs during quench front propagation. But local cooling is not the requirement for most of the heat transfer processes specially during LOCA instead of bulk cooling. For low conductivity material like steel this is a big challenge for bulk cooling and this makes steel cooling analysis difficult.
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3.5 Visual phenomena during jet cooling Frame by frame analysis of high speed camera recorded video (as shown in Fig. 4) reveals that when the jet first struck the surface, the liquid quickly spread over a small central region about two to four times the jet diameter and it was splashed out from the surface. Fig.4 shows four sequences of video images which presents the quench front propagation during cooling. This quench front should not be thought of a single point or single line but it should be considered that the entire transition boiling region will be in the quench front region. For steel, the material conductivity is low which permits only a small amount heat conduction from other portion of the solid to the impinged region. When the quench front tries to move, only a local surface (at the front region of the quench front) cooling happens immediately because only an insignificant amount of heat is supplied from other portion of the solid to recover the colder region. Less heat energy supply to the surface results it to be remains at a low surface temperature which consequences a faster movement of the quench front. The similar observations were found for all the experimental conditions with steel. For copper or brass, high conductivity results in faster recovery of heat to the impinged region and makes the surface temperature hotter which ultimately makes the quench front movement slower. Fig. 4 shows that it takes 180 sec to move the quench front around 70 % of the block radius; but for copper or brass it may take more than a thousand seconds for the same experimental conditions [8]. As found from the Fig. 4 that the boiling width, w increases from 0.5 mm to 7 mm by a time period of 5 sec to 180 sec for the case of steel. For steel, during the movement of the quench front, heat recovery for the already colder region has not been done significantly by the other hotter portion of the solid. For this reason, the already quenched local surface temperature remains lower but the other surface temperature remains higher which makes the surface temperature gradient high in the radial direction. This high temperature gradient in the radial direction does not allow the quench front to move easily in the radial direction. Only the temperature of a smaller region becomes favourable for boiling which results in smaller size of the boiling width. The boiling width as shown in the Fig. 4 is only 7 mm after 180 sec (covering around 70 % of the radial distance) for steel; for copper or brass for the same quench front position, the boiling width may be around three times [8]. 3.6 Correlation for maximum heat flux of steel Mozumder [8] proposed a correlation of maximum heat flux for copper and brass which agreement is good enough but due to the different behaviour of steel, the same correlation does not agree well for steel. Ahemed [10] included some important parameters in the correlation which has influence on maximum heat flux for steel. The correlations of maximum heat flux have developed for steel for two distinct regions of radial position for 10-20 mm and 20-35 mm. It is considered that the wetting front started to move from the radial position of 10 mm. Therefore the maximum heat flux for the radial positions of less than 10 mm has not been included here. The two regions are distinguished according to their heat transfer rate in the radial direction. It is observed that the maximum heat flux w = 2 mm, t = 15 sec w = 0.5 mm, t = 5 sec
w = 4 mm, t = 60 sec
w = 7 mm, t = 180 sec
Fig. 4: Visual phenomena (quench front movement) during jet cooling (Steel, Tb = 600 oC, ΔTsub = 50 K, u = 5 m/s)
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gradient with the radial position is higher in region II. These correlations have included the terms [(ρcλ)l/(ρcλ)s]0.5, ρlu2(2rq-d)/σ and (1+Ja). The term [(ρcλ)l/(ρcλ)s]0.5 indicates the relative effects of solid and liquid thermal properties. Another non-dimensional group ρlu2(2rq-d)/σ represents the ratio of inertia force to surface tension force. In addition, Jacob number, Ja is considered an important non-dimensional number in subcooled boiling. It is the ratio of the sensible heat for a given volume of liquid to heat through ΔTsub in reaching its saturation temperature, to the latent heat required in evaporating the same volume of vapor. The term (1+Ja) has included in the correlation which has significant effect for region I. It indicates the effect of maximum possible heat transfer into the liquid in relative to the heat required to evaporate the same volume of vapor. The heat removal capacity of liquid decreases with radial position, as the liquid moves over the hot solid it becomes heated and getting closer to its saturation temperature which ultimately reduces its heat extracting potential. The value of ΔTsub (i.e Tsat-Tliq) decreases as the liquid temperature increases with radial position which ultimately decreases the value of maximum heat flux. Analysis also reveals that the effect of (1+Ja) on maximum heat flux is not significant in region II and for this reason it is not included in the correlation of region II, though it is included in region I. Finally, the following two correlations have developed (for Tb = 250-400 oC) for the two distinct regions: For region I (radial position of 10-20mm)
( ρ cλ ) l = 55.119 ρ g h fg u ( ρ cλ ) s
Q max
0.674
ρ l u 2 (2rq − d ) σ
−0.295
(1 + Ja )
0.136
(1)
For region II (radial position of 10-20mm) Q max
ρ g h fg u
= 1.106
( ρ cλ ) l ( ρ cλ ) s
−1.291
ρu l
2
(2 rq − d )
σ
−0.287
(2)
The coefficients of these two correlations are determined by using least square method from the experimental data of maximum heat flux. The experimental data is within ±25% and ±30% for region I and II of the proposed correlations respectively as shown in Fig. 5.
0.5
Q max ρ h u g
fg
exp
Eqn. (1)
0.1
+25%
80k, u=5
80k, u=10
80k, u=15
5k, u=5
50k, u=3
50k, u=5
5k, u=10
50k, u=10
50k, u=15
20k, u=3
20k, u=5
20k, u=10
20k, u=15
5k, u=3
5k, u=15
k is sub-cooling in Kelvin and u is jet velocity
-25%
0.06
80k, u=3
1.0
0.1 ( ρ cλ ) l 55.119 ( ρ cλ ) s
0.674
ρ l u 2 (2rq − d ) σ
−0.295
(1 + Ja )
0.136
Fig. 5. Maximum heat flux, Qmax (Tb = 250-400 oC) with the proposed correlation (for region I)
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4. Conclusions The following conclusions can be drawn from the present study: 1. 2. 3. 4. 5.
Maximum heat flux always occurs at the visible boiling region which is the moving trailing region of the quench front. The size of the visible boiling region (i.e. boiling width) increases with the movement of the quench front and material conductivity and decreases with liquid sub-cooling and liquid velocity. The maximum heat flux increases with jet velocity, liquid sub-cooling, solid material conductivity and it is almost independent of solid initial temperature. Due to the smaller thermal conductivity of steel, liquid jet removes heat locally from the heated surface and as a result the entire body does not feel immediately the quenching effect though the quench front moves over. But in the case of copper and brass, bulk cooling occurs with the quench front movement. Two correlations of maximum heat flux for block initial temperature 250-400 oC have been proposed for steel for region I (10-20mm) and region II (20-35mm) whose agreement is ±25% and ±30% respectively with the experimental data.
Acknowledgements The authors acknowledge their gratefulness to the Department of Mechanical Engineering, Bangladesh University of Engineering and Technology for providing computer laboratory facility. References [1] Karwa N, Stephan P. "Experimental investigation of free-surface jet impingement quenching process." International Journal of Heat and Mass Transfer 64 (2013): 1118-1126 [2] Gopal N, Sahoo PK, Ravi K, Leled HG, Chatterjeed B, Mukhopadhyay D. "Experimental investigation of heat transfer during LOCA with failure of emergency cooling system." 5th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, (2007) Paper number: NG1 [3] Mozumder AK, Monde M, Woodfield PL. "Delay of wetting propagation during jet impingement quenching for a high temperature surface." International Journal of Heat and Mass Transfer 48 (2005): 2877-2888 [4] Jan S, Vaclav B, Vaclav D, Slavomir E. "Effective water cooling of very hot surfaces during the LOCA accident." Fusion Engineering and Design 124 (2017): 1211–1214 [5] Chitranjan A, Ravi K, Akhilesh G, Barun C. "Rewetting and maximum surface heat flux during quenching of hot surface by round water jet impingement." International Journal of Heat and Mass Transfer 55 (2012): 4772-4782 [6] Iloeje OC, Plummer DN, Rohsenow WM, Griffith P. "Effect of mass flux, flow quality, thermal and surface properties of materials on rewet of dispersed flow film boiling." Trans. ASME, Journal of Heat Transfer 104 (1982): 304-308 [7] Filipovic J, Incropera FP, Viskanta R. "Quenching Phenomena Associated with a Water Wall Jet: I. Transient Hydrodynamic and Thermal Conditions." Experimental Heat Transfer 8 (1995): 97-117 [8] Mozumder AK. "Thermal and hydrodynamic characteristics of jet impingement quenching for high temperature surface." Ph.D thesis, Graduate School of Science and Engineering, (2006) Saga University, Japan [9] Mozumder AK, Ahmed M, Monde M. "Carbon steel quenching and maximum heat flux with water jet impingement." Proc. of the International Conference on Mechanical Engineering, (2009) Dhaka, Bangladesh [10] Ahmed M. "Maximum heat flux and wetting delay during quenching of high temperature carbon steel block." M. Sc. Thesis, Dept. of Mechanical Engineering, Bangladesh University of Engineering and Technology, (2008) Dhaka, Bangladesh [11] Monde M, Arima H, Liu W, Mitsutake Y, Hammad JA. "An analytical solution for two-dimensional inverse heat conduction problems using Laplace transform." International Journal of Heat and Mass Transfer 46 (2003): 2135–2148