THERMAL ACCELERATION OF SCW FLOW IN HEAT-GENERATING CHANNELS AS A FACTOR OF HEAT TRANSFER DETERIORATION

Transcription

1 Technical Meeting on Heat Transfer, Thermal-Hydraulics and System Design for Supercritical Water Cooled Reactors 4 August 06 The Diamond, The University of Sheffield Sheffield, United Kingdom THERMAL ACCELERATION OF SCW FLOW IN HEAT-GENERATING CHANNELS AS A FACTOR OF HEAT TRANSFER DETERIORATION V.G. Razumovskiy, E.M. Mayevskiy, E.N. Pis mennyi, A.E. Koloskov National Technical University of Ukraine Kyiv Polytechnic Institute

2 TABLE OF CONTENTS (continued) (continued). INTRODUCTION. FLOW FULL THERMAL ACCELERATION 3.THE EXPERIMENTS: REQUIREMENTS AND PROCEDURE 4. THE RESULTS AND THEIR ANALYSIS 5. CONCLUSIONS

3 . INTRODUCTION Experimental study of heat transfer and pressure drop in smooth tubes cooled by water at supercritical pressure (SCW) revealed that at certain high heat flux rates q/g and a definite range of coolant temperature (from about 340 to 400 o C, i.e., in the region of transition from liquid to gaseous state, when water viscosity is growing with temperature) hydraulic resistance to thermal acceleration of the flow prevails over friction resistance (case of high acceleration s condition). At the temperature below and above this range the pressure drop is a function either of a very strong dependence of coolant s viscosity upon temperature (t f < 50 o C that is a region of viscous flow) or of viscous and inertial forces, if 50 t f 340 o C or t f 400 o C). There is a strong correlation between HTC α and heat flux q, when t w > t m > t f. Namely, under low values of q temperature head corresponds to enhanced heat transfer. Growth in q above certain level results in deterioration of heat transfer (DHT), when t w abruptly rises, sometimes reaching maximum in one or more cross-sections of the channel. In both cases α could by several or even dozen times differs from HTC in normal mode. DHT is dangerous, first of all, not by so high level of channel s wall temperature, as by its high dependence upon even negligible change in operating conditions. The efforts to explain and evaluate DHT are known perhaps since the first description of it was published by Styrikovich et al. in 955 and until now for more than 60 years nothing of the methods to foresee and assess this deterioration, i.e., to find its location and level with accuracy acceptable for practical application was derived. As already known, DHT results from certain set of operating conditions (supercritical pressure, flow rate, heat flux, thermal state of coolant, buoyancy), geometric parameters (heated diameter and length), roughness of heated surface, kind of coolant and its pureness, space orientation and even acoustic features of the channel. There are two main evident reasons why temperature and velocity profiles could be distorted in normal axially symmetric coolant flow: buoyancy and thermal acceleration. In some cases, these forces so strongly change radial heat and mass transfer that it could results in their significant enhancement or deterioration The proposed work is devoted to experimental measurement and analysis of channel (tube of 6.8-mm diameter and 600-mm length) local hydraulic resistance (and of its inertial and frictional components) to water flow accelerated due to thermal expansion under high heat flux. 3

4 . FLOW FULL THERMAL ACCELERATION Prediction of pressure drop due to thermal expansion resulting in flow acceleration by using conventional one-dimensional model of flow profile based on the equation of motion with uniform distribution of fluid velocity and temperature under neglected change in their radial profiles yields P ac = G (V V ), () where V and V are specific volumes of coolant at the outlet and inlet of heated tube. friction resistance, if calculated as P fr = P - P ac following (), could exceed (sometimes by 5 to 30%) the value of isothermal friction P fro. However, as well known, non-isothermal friction P fr at the same flow temperature is always significantly lesser, i.e., P fr / P fro <. It could only mean that P ac is not fully estimated, because radial change of impulse (velocity) profile is not considered in one-dimensional flow model. Developed at the Institute of High Temperatures (Moscow) and tested for supercritical carbon dioxide the so-called method of two pressure drops considered in one-dimensional flow model in brief consists in measurement of pressure drop both at heated section and the next downstream adiabatic section, which minimal length l ad should be enough to restore developed isothermal turbulent flow under constant physical properties, in other words, to return an energy consumed by the flow during its acceleration. Two pressure drops allow considering of the system of two equations: P P P ad fr P P fr. ad ac P P ac. ad P where P aс = I l - I in ; P ac.ad = I ol I l ; I l, I o.in and I ol are flow impulses ( I W RdR S( W ) / ) at heated g section outlet, adiabatic section inlet and outlet, respectively; and ~ Pg gd d l are efficient hydrostatic heads in both sections. g. ad 0 0 () 4

5 (continued) Flow impulse at heated section inlet after the section of hydrodynamic stabilization corresponds to the impulse of stabilized one-dimensional turbulent flow of liquid with constant physical properties I in = S o G /ρ in, (3) where S o const =.0 (at Re > ) is an impulse factor of turbulent isothermal flow (Boussinesq ratio). Fig.. Scheme of experimental section and the results of calibration measurements of adiabatic hydraulic resistance, 6 inlet and outlet thermocouples;, 5 - mixing chambers; 3 channel; 4 current buses; 7 pressure taps; 8 voltage taps; 9 wall thermocouples; h in, kj/kg (t in, o C) : (38.5); 690 (357.8) 5

6 (continued) In two-dimensional model of heated flow real impulse factor S depends upon the degree of velocity profile population and increases from.0 to.3 as the latter decreases (Petukhov and Medvedskaya, 978). In the utmost case of laminar isothermal flow S = S ol =.33, where S ol is a laminar profile impulse factor. Thus, the less velocity profile population (filling), the more incorrect application of the onedimensional model. friction pressure drop in adiabatic section P ad equals to P fr c... ~ l ad Po fr ad, lad ol where: P o.fr.ad is a friction resistance of the adiabatic section under isothermal flow; с is a constant characterizing the restoration curve of velocity isothermal profile (Ankudinov, 98); d is a diameter of tube; ξ l and ξ ol = ξ ad are the friction coefficients at the outlet of the heated and adiabatic sections, ~ l l / d. respectively;. ad At the same time, ξ l /ξ ol could be replaced by mean value of the reduced friction factor at the heated section: ad l ol o l o P fr G l o ~ o dl f. (4). (5) Finally, solution of the system () taking into account (3), (4) and (5) yields P fr P I 0. in I 0l P ol c l ~ l 0 ad ~ 0 / dl G ~ 0 l l l ad c. (6) 6

7 (continued) Series of P i and P i.ad measurements at different heated lengths (0 < l i < l) under the same operational conditions makes possible to obtain a set of equations (), which solution gives distribution of full hydraulic resistance P ~ ~ ~ l and its components P fr l and P ac l along the channel. Local factors of these hydraulic resistances are equal to ~ i dp l i G fr i ac i i dpfr G i di G ~ l ~ l ~ / dl ~ / dl ~ / dl i i i. (7) 7

8 (continued) TABLE. TEST MATRIX n n (h (h in, in, kj/kg) m m q/g, q/g, (400) (400) (600) 33 (800) kj/kg kj/kg p p The tests are numbered as nmp, where n corresponds to the value of inlet enthalpy h in, m is the level of heat flux rate q/g, and p is the number of heated sections by 0-mm length each. For example, number 365 means that the experiment had been conducted at h in = 800 kj/kg (t in = 369 o C), q/g = kj/kg and heated length l = 0 5 = 600 mm. The whole number of nmp experiments equaled 30 that mostly were repeated or 5 times to get reliable averaged data. 8

9 (continued) TABLE. MAXIMUM UNCERTAINTIES OF MEASURED AND CALCULATED PARAMETERS Parameter Maximum uncertainty Measured parameters Inlet pressure ±0.% Bulk-fluid temperatures ±3.4% Wall temperature ±3.% Calculated parameters Mass-flow rate ±.3% Heat flux ±3.5% HTC ±.7% Heat loss 3.4% 9

10 3.THE EXPERIMENTS: REQUIREMENTS AND PROCEDURE ~ l ad Fig.. Wall temperature as a function of heated length. d = 6.8 mm; G, kg/(m s): a 405; b 9 Tests #: 35; 35; 3 353; 4 354; Preliminary tests performed to define the length of adiabatic section ~ had shown that full braking length did not exceed l ad = 50 (Fig. ). These experiments resulted in the diagrams of isothermal profile restoration due to which the constant с = 0 in (4) was chosen. Due to appropriate choice of mass velocity value the impact of up- and down-stream flow patterns was decreased to neglected level (i.e., buoyancy became so neglected that pre- and post-history of the flow did not affect flow pattern at all), when at h in = idem wall temperature along the tube (taking into account accuracy of operation conditions repeatability) does not depend upon its length. The higher flow velocity, the shorter entrance and exit sections of a channel, where hydrodynamic and thermal boundary layers are formed and ruined respectively. As a result, at a certain flow velocity, as seen in Fig., temperature profile t(l) in 0- mm heated section repeats its profile in 40-mm section, while t(l) profile in 40-mm section repeats its profile in 360-mm section and so on. 0

11 (continued),5 0,0 7,5 5,0,5 ΔP, kpa Analogous is the dependence of P upon m (Fig.3). It is worth to note that the curves similar to plotted there could serve as an experimental verification of the reliability of P measurements. All the experiments by the method of two pressure drops were carried out at one mass velocity G = 90 kg/(m s). In this case the criterion of thermal lift that could not be neglected as a factor impacting on heat transfer, according to (Hall and Jackson, 978), is 0, m Gr/Re.7 >. 0-5, (8) or following other also well-known recommendation (Protopopov, 977) Fig.3. Full hydraulic resistance vs. heat flux rate and heated length: h in = 800 kj/kg; q/g, kj/kg: see Table for relevant m from to 8 Gr/Re > 0.0. (9) Due to high coolant mass velocity its value didn t exceed So, it is enough reason to consider thermal acceleration as a single thermal factor affecting the heat transfer.

12 ΔP, kpa 4. THE RESULTS AND THEIR ANALYSIS As seen (Fig.4), raising q/g is followed by increasing share of P ac and decreasing share of P fr (dashed lines) in full hydraulic resistance P (solid lines) until they are equal at a certain boundary (q/g) b. The shorter the section, the higher q/g of P ac = P fr. In further growth of q/g the resistance to thermal acceleration P ac exceeds friction resistance P fr q/g, kj/kg Fig.4. Dependence of full hydraulic resistance and friction resistance upon heat flux rate. h in = 800 kj/kg; l, mm: 0; 40; 3 360; 4 480; 5 600; 6 line of P ac = P fr

13 (continued) Set of the experimental curves plotted as P = f(q/g) b at h in = 400, 600 and 800 kj/kg permitted to lay out the family of the lines (Fig.5) in the coordinates l b = f(q/g) b (l b is a length from tube inlet to the place of deterioration onset) with extrapolation of them to q/g higher than were reached in the experiments. Analysis of temperature and pressure drop measurements shows that the values of (q/g) b corresponding to equality of friction and acceleration forces practically coincide with q/g of transition from normal to deteriorated heat transfer (DHT). It means that transition to flow with domination of acceleration force over friction one is a condition or index of the mentioned transition to DHT, in other words, it takes place, if P aс > P fr or ξ ac /ξ fr >. (0) That is why inequality (0) could be considered as a hydrodynamic condition of DHT at developed turbulent flow in the tubes under weak influence of buoyancy. The family of l b = f(q/g) b (Fig.5) was approximated with ± 5% scattering by correlation (q/g) b = 0.04 (l/d) -0.5 (h m h in ) 0.7, kj/kg () where h m and h in are the enthalpies at the temperature of maximal specific isobaric thermal capacity c pm and at tube inlet temperature, respectively. 3

14 l, mm (continued) ,7 0,9,,3,5,7 q/g, kj/kg Fig.5. Boundary heat flux rate vs. length of channel and inlet enthalpy t in, o C (h in, kj/kg): 369. (800); (600); (400) 3 The zones on the right side of the boundary lines in Fig.5 correspond to the region of DHT. As seen, heat flux rate of DHT beginning, as a function of coolant average enthalpy (inlet enthalpy and relative heated length), varies in a wide range. For example, at l/d 00 (q/g) b in our experiments changed from 0.7 to.3 kj/kg, while in (Vikhrev et al., 97) dangerous temperature regimes would be expected at (q/g) b kj/kg. Proposed in (Petukhov et al., 97) correlation (q/g) b (c p /β p ) m ξ/8 () predicts normal heat transfer at q/g < 0.84 kj/kg, but does not give permissible limit of heat flux. 4

15 (continued) Well-known correlation (q/g) b = 0. G 0., (3) early proposed in (Yamagata et al., 97), and correlation (q/g) b = 0.79(p/p cr ).5, (4) given in (Gabarayev et al., 006) for prediction of DHT conditions correspond to (q/g) b within the range from 0.6 to 0.9 and from 0.8 to. kj/kg, respectively, whereas in our experiments it varied from 0.7 to.55 kj/kg. Measurements of P(l) by the method of two pressure drops allowed to get P fr (l), on the basis of which the coefficients of local full ζ(l), frictional ξ fr (l) and acceleration ξ ac (l) resistances were predicted by (7). Profiles of their values along the tube are plotted in Fig.6. As more illustrative examples the curves of h in = 800 kj/kg are shown. It is seen that ξ fr (l) negligibly varies, i.e., frictional resistance weakly depends upon thermal state of the flow. For estimation of reduced frictional resistance ξ fr /ξ 0 in a channel heated by SCW flow at heat flux rate q/g < 0.5 kj/kg simplex (Tarasova and Leontyev, 968) (μ w /μ f ) 0. (5) and in a channel heated by flow of SC CO simplex (Popov, 964) are proposed. (ρ w /ρ f ) 0.4 (6) 5

16 (continued) Basing on our and mentioned above experiments and analytical studies we can agree with the idea (Kurganov et al., 0) that, when h f is near the enthalpy of the beginning of the zone of high specific isobaric heat capacity (c p > 8 kj/(kg K); 650 < h f < 750 kj/kg) and t w >> t m, inequality ξ ac >> ξ ac (ξ ac is ξ ac corresponding to equation ()) is of high probability, especially under the conditions of progressing DHT. At this stage in gas-like wall layer a significant share of input heat is detained and due to great expansion work this layer forces back flow solid core from the wall thus narrowing cross-section for the main mass flow. It results in a kind of gas nozzle that causes abrupt acceleration of solid core carrying the main share of flow momentum and quick growth of impulse factor S f along the tube that is followed by increasing both of coefficient of inertia (acceleration) resistance ξ ac and gradient p ac / (x/d) with corresponding consequences for turbulent transfer and heat transfer. 6

17 ,5,, ac fr a),0,, ac fr c) (continued),5 fr 0,75,0 ac ac fr 0,5 0,5 500 t, C b) 500 t, C t w d) t w 400 t m 400 t m 350 t f h, kj/kg 350 t f h, kj/kg Fig.6. Local coefficients of hydraulic resistance and longitudinal temperature profiles. h in = 800 kj/kg. (a), (b): q/g = kj/kg; (c), (d): q/g = kj/kg One dimensional model: ) dashed lines - acceleration resistance; ) dot-and-dash lines friction resistance 7

18 Temperature. C α d /α o ,0 0,5 0, ,5,5 q/g, kj/kg Fig.7. Wall temperature (a) and reduced differential heat transfer coefficient (b) vs. heat flux rate. h i, kj/kg: 470; 640; 3 90 a) b) (continued) In Fig.7 wall temperature is plotted as a function of q/g under permanent flow enthalpy (h f = idem). Analysis of dependence t w = t(q/g) shows that the rate of growth in t w as q/g increases changes from typical for normal convective and enhanced heat transfer to one typical for DHT, initial stage of which is characterized by accelerated growth in outlet t w. Therefore, it is easy to analyze temperature regime t w = t(q/g) expressing it as a reduced differential coefficient of heat transfer α /α 0, where α = [ ( t)/ q] - = ( t w / q) -, α 0 coefficient of heat transfer at permanent physical properties, t f is assumed constant (Petukhov et al., 98). The proposed criterion of heat transfer assessment indicates not the heat flux of deterioration beginning, but q/g corresponding to yet developing DHT. Thus, there is a reason to consider parameter (q/g) b rather as the maximal heat flux rate from safe temperature mode point of view than the conventional boundary between normal and deteriorated heat transfer. Insignificant variation in operational parameters, if (q/g) > (q/g) b, able to cause strong oscillations of wall temperature. They negatively impact on reliability of heated surface, despite usually in this case t w is by o C below the temperature permissible by long-term strength conditions, i.e., is far from the level of extreme temperatures in some works resulted in wall burnout. 8

19 Temperature. C (continued) h, kj/kg Fig.8. Dependence of wall temperature upon heat flux rate. h in = 800 kj/kg; q/g, kj/kg: see Table for relevant m from to Wall temperatures along the tube measured in all experiments are shown in Fig.8, for example, at h in = 800 kj/kg. It is worth to note absence of extreme t w values usually indicating heat transfer deterioration. At low q/g the temperature patterns remind boiling under subcritical pressures and correspond to enhanced heat transfer, which.5 to times as high as normal one. At certain higher values of q/g the temperature head increases at the tube end and then this process moves to the tube entrance until horizontal part of the profile disappears. From this moment temperature head curve only increases its slope. In this case, reduced heat transfer coefficient ( = α/α o, where α o corresponds to heat transfer at permanent physical properties of coolant) steadily decreases with growing heat flux asymptotically approaching to some level about 0. to 0.5 depending upon h in. For example, in the experiments performed at h in = 800 kj/kg ~ 0. (Fig.0), at h in = 600 ~ ~ kj/kg 0.3, and at h in = 400 kj/kg 0.4. In these regimes absolute value of heat transfer as well decreases as a strong function of q. Such heat transfer respectively could be called deteriorated. 9

20 Δt w-f, K Δt w-f, K Δt w-f, K c) b) (continued) For more visualization temperature heads (t w t f ) are plotted for all five sections in Fig.9. As seen, they differ with scatter not exceeding 0 to 5 K. This range of scatter at the level of 500 to 600 o C taking into account real mismatch of operational conditions (h in and q/g) under transition from one heated length to another could be considered as quite satisfactory. Under low heat fluxes and wall temperatures above t m the temperature head along the tube practically does not change. Comparison of the results of temperature and hydraulic measurements (for h in = 400 and 800 kj/kg they are partially represented in Fig. 4, 8, 9, and 0) shows that (q/g) b practically coincides with (q/g) corresponding to transition from normal/enhanced heat transfer to deteriorated one. Thus, it means that transition to flow with acceleration force dominating over friction force is a condition or indicator of the mentioned transition to DHT. 80 a) i Fig.9. Temperature head along the tube vs. heat flux rate. h in = 400 kj/kg; q/g, kj/kg: (a) 0.86; (b) 0.950; (c).075. i number of thermocouple. Legend: m =,, 3, 4, 5 0

21 (continued) Briefly summarizing the results of many years investigation of heated channels friction and acceleration resistances we propose to apply somewhat conditional division of the whole range of SCW thermal state into 3 zones: A zone of low enthalpies (h 650 kj/kg), where friction coefficient ξ fr follows correlation reflecting strong dependence of viscosity upon coolant enthalpy (Lafay, 970): ξ fr /ξ 0 = 0.5 ( + X) B lg( + X), (7) where X = (μ f /μ w )( μ f /μ w ) 0.7 ; B = Re + 800/Re. In this zone of practically zero flow acceleration the ratio ξ fr /ξ 0 is a function of not only μ f /μ w but of Re as well (the lesser Re the stronger function). If Re > 0 5, ξ fr /ξ 0 = f(re) 0 and ξ fr /ξ 0 corresponds to equation (3). B zone of viscous-inertial flow zone of high enthalpies of liquid phase (650 h 500 kj/kg) and zone of the enthalpies of gaseous phase (h 550 kj/kg), where (3), derived for q/g 0.5 kj/kg overestimates the result by 5 to 30 and more % for high q/g. It means that in the case of intense heating disturbance of one-dimensional thermal acceleration of SCW flow could be significant and revealed by traditional measurements of pressure drop in heated sections with small l/d. The data array for tubes of d = 3 0 mm at q/g > 0.5 kj/kg was generalized by correlation with a scatter within ± 5%. ξ fr /ξ 0 = [(ρ w /ρ f ) (μ w /μ f )] 0.5 (8)

22 (continued) C intermediate zone of inertial-viscous flow in transition from liquid to gaseous state in the zone of high heat capacities (c p >7 kj/(kg K)), where one-dimensional model of thermal acceleration could cause substantial errors (ξ fr /ξ 0 > ). Zones A and B correspond with normal heat transfer that is quite satisfactorily predicted by correlation (Petukhov and Kirillov, 958) fr /8 Re Pr Nu fr /8 Re f, /3 Pr f (9) Fig.0. Longitudinal profile of reduced heat transfer coefficient vs. heat flux rate. h in = 800 kj/kg; i number of the thermocouple; p = 4 to 7 (Table ) where denominator could be considered as a coefficient of Reynolds analogy characterizing the sum of thermal resistances of viscous wall boundary layer and of turbulent core.

23 In zone C at q/g kj/kg both enhanced and deteriorated heat transfer is 3 or even more times as high and low, respectively, as normal one. Obtained temperature profiles reflecting low reduced heat transfer coefficients and called deteriorated differ from known DHT with extreme, peak change in wall temperature by monotonously accelerating temperature increase along the channel. Such extreme profiles were reached under the impact of considerable buoyancy due to free convection (terms (8, 9)). All the experiments by the method of two pressure drops were conducted at the flow enthalpy within the range from 370 to 80 kj/kg, i.e., they were covered by zone C. 3

24 5. CONCLUSIONS The local hydraulic characteristics of supercritical water upward flow obtained due to the method of two pressure drops allowed correlating wall temperature regime in vertical smooth tube with the ratio of friction and acceleration hydraulic resistances and their dependence upon heat flux rate. Analysis of the obtained experimental data revealed that under negligible effect of buoyancy is the necessary condition of heat transfer deterioration caused by laminarization of boundary layer and resulted in suppression of turbulence. Thus, these data could serve as an additional evidence of crucial effect of thermal acceleration on heat transfer and its deterioration under the conditions of the developed turbulent flow without impact of free convection. The empirical correlation for prediction of boundary heat flux rate corresponding to transition from normal to deteriorated heat transfer based on 0 experimental tests that covered a wide range of q/g is proposed. Unlike existing recommendations it takes into account: (a) an initial thermal state of coolant in relation to it at the point of maximal isobaric specific heat capacity; and (b) the length of heated section from inlet to the point of DHT beginning. As a result, in many cases the DHT boundary could be reasonably almost twice as high as considered so far, thus significantly increasing safe thermal load of a channel. 4

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