Sabersky RH, Hauptmann EG, Forced convection heat transfer to carbon dioxide near the critical point, International Journal of Heat and Mass Transfer, Vol.10, pp. 1499-1508, 1967

AbstractSabersky et al. investigated the convective heat transfer from a flat plate in CO2 near the critical point. The main objective was the visualisation of the heated flow. The experimentally determined heat transfer coefficient became large when approaching the pseudo-critical temperature, but no significant changes in the flow field were observed. So, in contrast with free convection of CO2 around a cylinder and to nucleate boiling, no disturbance was observed of the gross flow. Above the pseudo-critical point the heat transfer coefficient decreased again. The high heat transfer coefficients were assigned due to the large values of thermodynamic and transport properties occurring near the critical point and also to minor modifications of the turbulent motion.

Heat transfer from a plate Most tests in the supercritical state Principal objective direct visual observation of the heated field

o High speed movie with Schlieren apparatuso Hot wire probe measurements of velocity fluctuations (measures fluctuations of wire

current).o Objectives was not to give quantitative predictions of supercritical heat transfer

rates, but to help in the selection of realistic models of the heat transfer mechanism in future theoretical studies.

Experimental apparatus and procedure Test setup see paper Pressure: 72.4, 75.8 and 82.7 bar Fixed fluid temperature: 24.9, 25.6 and 40.5°C Surface temperature plate: from free stream to free stream + 500° Maximum heat flux: 77000 Bti/h ft² F Free stream velocity: up to a maximum of 1,5ft/s

General trends in experimentsHeat transfer measurements

Free stream: supercritical pressure + below pseudo-critical temperature.

o HTC shows a peak (no abrupt changes)o HTC increases smoothly for increasing surface temperatureo HTC is larger for high velocity

Free stream: supercritical pressure + above pseudo-critical temperature

o HTC decreases slightly with increasing surface temperatureo No peak noticeableo HTC is larger for high velocity

HTC dependence on free stream temperature (cte flow rate and heat flux)

o T<Tpc HTC extremely dependent on heat transfer rate Q (and thus of Twall) HTC high for T slightly < Tpc and Twall slightly > Tpc (thus small heat rate) As heat rate Q increases the peak was smaller (HTC smaller) For a very large heat rate Q no peak in HTC near pc-point

o Above Tpc HTC was reduced compared to far below Tpc For the HTC in subcritical CO2 very sharp rise of HTC at the beginning of nucleate boiling.

Flow field observations

Low heat transfer rate Twall<Tpc

o Flow field appears to be like that of a constant property turbulent flowo Small amount of fluid motion normal to the heated surface due to free convection

Twall = Tpc + 2° and free stream/surface = 2.5

o Near the peak of HTCo Small regions of rapid change in densityo Flow appears still similar to a normal turbulent forced flow field

For Twall > >Tpc

o Regions of differing density increase in sizeo Free convection motion becomes superimposed on the basic forced flow through a

large portion of the boundary layer

For subcritical

o Stable film boiling appearso Large vapour clusters break away and rise into the free stream

Comparing the turbulence level between a subcritical and supercritical flow, it was noticeable that the turbulence level shows a sharp and abrupt increase at the start of nucleate boiling for subcritical, while for supercritical the turbulence level increases slow and smoothly and no sharp or discontinuous increase was noted. The turbulence level at the peak HTC was not grossly different from those occurring in normal turbulent flows.

Discussion Low heat transfer rate (q) Maximum of HTC at Tb slightly lower than Tpc Higher heat transfer rates (q) HTC has a sharp drop when Tb exceeds Tpc

o Resulting low value of HTC = MINIMUMo Both MAXIMA and MINIMA in HTC may occur depending on “q” and bulk fluid

properties.o This explains conflicting results about occurring maxima and minima near C.P.

Conclusions Experimentally determined HTC became large when the temperature approached the

pseudo-critical temperature, above this point the HTC decreased again. The magnitude of the HTC-peak = f(free stream pressure, temperature and velocity)

o Pressure near critical pressure high HTC

o For cte pressure, high HTC as free stream temperature approaches the pseudo-critical temperature.

No significant change in the flow field was observed when approaching the pseudo-critical temperature. It looked like normal forced turbulent convection for all regions in this study.

o No “bubble-like” phenomena (break-up phenomena as in nucleate boiling)o In contrast with free convection of CO2 around a cylinder and to nucleate boiling, no

disturbance was observed of the gross flow. High heat transfer coefficients were assigned due to the large values of thermodynamic and

transport properties occurring near the critical point and also to minor modifications of the turbulent motion.

Hot wire studies showed no grossly different turbulence levels at the peak of HTC compared to normal turbulent flows. BUT, some modifications in the spectrum and intensity of the turbulent motion probably did occur.

Bourke PJ, Pulling DJ, Gill LE, Denton WH, Forced convective heat transfer to turbulent CO2 in the supercritical region, International Journal of Heat and Mass Transfer, Vol.13, pp. 1339-1348, 1970

AbstractBourke et al. investigated the heat transfer to turbulent flow of CO2 at supercritical pressure for both a vertically downward and upward flow to determine the effect of changing the direction of flow relative to the buoyancy forces. From the experiments performed, it was concluded that at low heat fluxes, heat transfer across the critical region shows an order of magnitude enhancement compared to well sub- or supercritical temperatures, independent of the direction of flow. On the contrary, at high heat fluxes, heat transfer deteriorations occurred, which was noticed by the local increase of wall temperature at the beginning of the heated region. This was only observed when the flow was upwards and when there were large radial changes in density and viscosity, assumed to be caused by the effects of buoyancy. For low flow rates, double peaks were observed in the wall temperature at intermediate heat flux and these disappeared by increasing the flux, suggesting that the buoyancy effect is unstable. As the pressure increases above the critical pressure, all these effect are less severe and become insignificant at p = 1.5 pcrit. This strengthens the assumption that these effects are caused by the rapid property variations near critical point.

Experimental apparatus and procedure Measurements of Twall Vertical tube of 4.56m long, 2.28 cm diameter and 1.27 mm thickness Test section: stainless steel Electrically isolated from the rest of the closed loop Pressure: 7.44MPa 10.32MPa q: 0.8x104 35x104 W/m² by alternating current (150 kW power supply) mass flow: 0.127 0.695 kg/s 50 thermocouples clipped to the tube along the length and around T_wall,out

o Calibrated by passing wet steam under isothermal conditionso T_wall,in via T_wall, out and thermal conductivity, assuming UNIFORM heating

Thermocouples measuring T_bulk at in- and outlet in mixing boxes. Safety: bursting discs for pressure and thermocouples for temperature connected to

automatic power cut-out CO2 cooler counter-current with water and cooling tower

o Automatic controller for water flow rate to keep T_cond,CO2, out at 15°C B.S. 1042 flow measuring orifice behind cooler Pump Pre-heater before test section (max 30kW) setting inlet temperature test section

o 15-35°C Electro-manometer at test section inlet Flow upwards and downwards

General trends in experiments Variations dependent variables

o T_bulk,out: 18-70°Co T_wall: 20-300°Co Re_entry: (0.09-0.57)x106

o Re_out: (0.3-1.65)x106

For each test: comparison between (electrical input)/(heating of CO2)o Heating of CO2 = flow rate x enthalpy difference (Tb,in and Tb,out)o Problem: near the critical region accuracy dropped due to the variations in

enthalpy with temperature Calculation bulk enthalpy along the section via;

o Uniform wall heat flux so heat flux between 0 and x: q_x= q.x/Lo Flow rateo Enthalpy at inlet or outlet bulk temperature (choose the one further from C.P.)o h_bulk,x = (q_x/mass flow)+h_bulk_in or h_bulk, out - (q_x/mass flow)o T_bulk,x via h_bulk,x and pressure and tables

T_wall and T_bulk as function of bulk enthalpy for ≠ q

Dashed lines = HTC and T_wall calculated via Colburn single-phase HT correlation (30-40°C from the critical region)

[1]

For Tw/TB (kelvin) >1.1 (gaseous conditions with high heat flux) Nu x (Tw/TB)-0.27 to allow for small variations in physical properties [2]

Mass flow of 0.127 kg/s UPWARD at 7.44 x 106 N/m2

Mass flow of 0.504 kg/s UPWARD at 7.44 x 106 N/m2

Mass flow of 0.504 kg/s DOWNWARD at 7.44 x 106 N/m2

Mass flow of 0.504 kg/s UPWARD at 10.32x 106 N/m2

Heat-transfer coefficient vs. bulk temperature for ≠ q Mass flow 0.695 kg/s UPWARD at 7.44MPa

Mass flow 0.127 kg/s UPWARD at 7.56MPa

Discussions

Effect of heat flux q and inlet enthalpy Fig 2: UPWARD, slightly supercritical pressure

For low heat flux, the Colburn correlation predicts well the T_wall far from critical region. For high heat flux, the prediction is below the experiments. But the difference reducing with higher T_bulk

Fig5: Critical region, low heat flux HTC improvement over the entire length of the tube (broad range of inlet enthalpy)

Increasing heat flux 2 effectso Broad improvement disappearso Local peak of T_wall along a short length (0.3-0.6 m)

Bigger as heat flux increases

Conditions for occurrence of this peak not simply defined Peak develops near the start of the heated tube It appears to be an entry effect, independent of local bulk enthalpy Downstream of these peaks: T_wall again dependent of heat flux and local

bulk enthalpy

Effect of mass flow For all mass flows, the variation in T_wall with q was similar Except at lowest mass flow (fig1): T_wall behaviour was different

o HT improvement at low heat flux still present, but at intermediate flux 2 peaks, with second much broader

o Further increase in flux, both peaks disappearo But at higher flow rates the single peaks becomes more pronounced as the heat flux

increases.

Effect of flow direction Upward flow: peaks at T_wall Downward flow: no peaks At low heat fluxes: HT improvements and independent of direction of flow

Effect of pressure Fig 2 and 4: Upward

o Reduced peak in HT and T_wall for low heat flux Unusual HT effects are greatest at slightly supercritical pressure and become negligible at

±1.5 pcrit This confirms that the behaviour is caused by the variation in thermophysical properties,

because the variation is similarly related to the pressure.

Comparison with other data Jackson Fig 6

o J. D. JACKSON and K. EVANS-LUTERODT, Impairment of turbulent forced convective heat transfer to supercritical CO2, Simon Engineering Lab. Report N.E.2. Manchester University (1968).

o Satisfactory agreement: HT improvement for LOW heat flux Independently of flow direction Intermediate heat flux 2 maxima in HTC for UPWARD flow Higher heat flux NO maxima suggested caused by unstable effect

which can collapse and re-establish itself. Sabersky and Hauptmann

o Sabersky RH, Hauptmann EG, Forced convection heat transfer to carbon dioxide near the critical point, International Journal of Heat and Mass Transfer, Vol.10, pp. 1499-1508, 1967

o HTC for low heat flux show same variation with T_bulk as in Fig 5 of Saberskyo Improved HT

Flow in boundary layer was not much changed from that for constant property fluids improvement mainly due to property variation on HTC

o Higher heat flux reduced HTC observed thickening of the boundary layer and increased turbulence near its outer edge These changes were attributed to the large difference in density between T_wall and T_bulk

o Here: improvement up and down deterioration only up caused by changes in flow due to buoyancy

Shitsman

oo Water in vertical tubeso Deterioration when flow is upward over a wide range of bulk enthalpyo Deterioration due to large differences in viscosity between T_wall and T_bulk

Here these changes are also present when deteriorations occurs CONTRADICTION!!

Shitsman: due to laminarization of boundary layers Here: Increased turbulence with HTD

o Fit data of CO2 to correlation of water from Shitsman Poor correlation for HTD Failed correlation for HTI

o Conclusion: changes in density and viscosity through the fluid flow and flow pattern are relevant!!

Hall and Jacksono W. B. HALL and J. D. JACKSON, Laminarization of turbulent pipe flow by buoyancy

forces, A.S.MG. Paper 69-HT-55.o THEORETICAL ANALYSISo Mechanism for HTD due to the local suppression of turbulence in the boundary layer

Caused by reduction of shear stress in upward flow by buoyancy forces acting on a thin layer of low density fluid near the wall.

+ Changes in density and viscosity through the fluid flow.

Conclusions Low heat flux HTI in the critical region, better than at well sub- and well supercritical

temperatures, Independently of the flow direction High heat flux Peak in T_wall T between wall and bulk in the BEGINNING of the

heating region. ONLY for UPWARD flow + when there are large radial changes in density and viscosity suggesting caused by effects of buoyancy on turbulence in the flow

Low flow rate double peaks in T_wall at intermediate heat flux + disappear at higher heat flux showing buoyancy effect is UNSTABLE

All effect decrease with increasing supercritical pressure insignificant at 1.5 p_crit suggesting caused by rapid near critical variation in physical properties.

Tanaka H, Nishiwaki N, Hirata M, Tsuge A, Forced convection heat transfer to fluid near critical point flowing in circular tube, International Journal of Heat and Mass Transfer, Vol.14, pp. 739-750, 1971

AbstractTanaka et al. performed experimental measurements under high heat fluxes to supercritical CO2 in a circular tube. The phenomena of heat transfer deterioration near the pseudo-critical point were investigated. Tanaka states that the forced convection heart transfer to supercritical fluid is not a new type of heat transfer problem, but that it is an extension of the usual turbulent convection heat transfer of fluid with constant physical properties, without significant changes in the theory. They also investigated the effect of surface roughness on the heat transfer.

Theoretical considerations Physical HTI for low heat fluxes due to increase in in c_p near T_pc increase turbulent

thermal conductivity .c_p._t !o When T_pc is located in the buffer zone of the turbulent boundary layer, the

temperature drop across the boundary layer decreases HT increases! Decrease of HTC for very high heat flux ( low heat flux): increase in heat flux increase

temperature gradient proportion of thickness occupied by the T_pc zone (where c_p is great) in the boundary layer decreases.

o effect of increase in c_p loses its meaning and the flow DIVIDES into virtually 2 phases.

Gas-like fluid layer in the neighbourhood of the wall surface Liquid-like fluid flow near the centre of the tube

o When the fluid is heated up from an entrance bulk temperature << T_pc the thin layer of gas-like fluid on the wall surface appears first. Then the temperature drop across this gas-like fluid layer increases rapidly in the early stage HTC decreases rapidly. But the bulk temperature will also increase mean velocity of flow also increases and the HTC rises. Especially when the temperature near the center of the tube exceeds the T_pc v_mean ↑↑ HTC ↑↑

FURTHER INFO ABOUT TURBULENCE AND BOUNDARY LAYERS IN PAPER

Experimental apparatus and procedure CO2: 78,48 bar UPWARDS flow Circular tube:

o 6mm ID; 8mm OD and 1000mm longo Smooth tube: 0.2 micron roughnesso Rough tube: 14 micron roughness

Heating by AC passing through the tube

Precision pressure gauge Gear pump Flow rates via orifice and water-CO2 manometer Thermocouples t_in and t_out at inlet and outlet test section

o Fluid temperatures along test section interpolated T_wall at 9 points by thermocouples attached to the outer surface of the tube – 100mm

apart T_wall_inside via T_wall_outside and assuming uniform heat generation in the tube

General trends in experiments

Smooth tubes Various inlet enthalpies, various flow rates and constant heat flux value

o (5.5 and 4.2) x105 kcal/m²ho T_wall rises to a maximum after the inleto The bulk enthalpy for maximum T_wall shifts to a higher value as inlet enthalpy

increaseso Besides pure entrance effects, buoyancy effects take place due to the large density

variation especially at low flow rate hot spots in T_wall

Rough tubes q=6.0x105 kcal/m²h

Higher heat flux than smoother tubes lower T_wall due to HT improvement due to roughness.

Adebiyi GA, Hall WB, Experimental investigation of heat transfer to supercritical pressure carbon dioxide in a horizontal tube, International Journal of Heat and Mass Transfer, Vol.19, pp. 715-720, 1976

AbstractAdebiyi investigated heat transfer to supercritical and subcritical pressure CO2 flowing in a uniformly heated 22.14 mm diameter horizontal pipe. The influence of buoyancy is observed by measurement of the circumferential temperature variations. It was observed that buoyancy reduced the heat transfer at the top of the pipe and enhanced it at the bottom, when the values were compared with data in which buoyancy effect were neglected. Jackson and Petukhov both proposed a criterion to indicate the conditions under which buoyancy effects begin to occur. In the experiments it was observed that buoyancy was still not fully developed 100 diameters after the inlet section. However for lower mass flow and higher heat flux buoyancy appeared fully developed and the heat transfer coefficient was established.

IntroductionThe influence of buoyancy in a horizontal flow has not been properly investigated. The extent of the peripheral and axial temperature variation depends in part on the material and the thickness of the pipe.

Data on supercritical water flowing in horizontal pipes:

Shitsman: 16 mm ID pipe significant difference between temperature at the top and bottom

Yamagata: 7.5 and 10 mm ID pipe difference between top and bottom T_wall as T_bulk approaches T_pc

Dickenson and Welch: 7.62 mm ID

Schmidt: 5 an 8 mm ID pipe

Vikrev and Lokshin: 6 mm ID pipe HT poorer at upper surface than lower surface (qualitatively)

Data in supercritical CO2 in horizontal tubes

Schnurr: 2.6mm ID differences between top and bottom T_wall

Koppel: 4.93 mm (USELESS, no direction, no indication of peripheral temperature variation)

Experimental apparatus and procedure 22.14mm ID horizontal; 25.4mm OD (1inch); 1.63 mm (0.064 inch) thickness Stainless steel tube Heated length 2.44 m (= 110 dia) Unheated length before of 1.22m (55 dia) Uniform heat flux: 5kW/m² 40 kW/m² (T_max test section <100°C) Electrically heated by AC current through the tube Rest flexible hoses easy for assembling rest of the loop and allow for thermal expansion of

the tube 76 bar T_inlet: 10-31°C T_pc = 32°C at 75.86 bar Mass flow 0.035 0.15 kg/s Centrifugal pump Parallel pre-heater and pre-cooler vary inlet temperature After cooler Orifice plate for flow rate measurements T_bulk at inlet unheated section 5 chromel/alumel thermocouples immersed in the fluid 8 thermocouples welded on outer surface of unheated section 196 chromel/alumel thermocouples welded on test section outer surface

o Every 3in (76.2mm) at 0°, 90°, 180° and 270°o Every 6in (152.4mm) at 45°, 135°, 225° and 315°

Thermal insulation on test section: layer of woven glass tape (held also thermocouple wires on tube) + 50 mm glass wool

o Heat losses measured as first experiment <2% of heat input Set of 5 thermocouples T_bulk after test section Mixer

General results Experimental conditions

Independent parameters: mass flow, T_bulk_inlet, wall heat flux Temperature profiles

Discussion

Comparison with existing data Similar trends with the data of Shitsman and Miropolsky (water) T_wall_lower <<

T_wall_upper Comparison in axial temperature distributions for horizontal and vertical flow (similar

conditions [Weinberg])

The HT is worse for the top surface of the horizontal flow compared to vertical flow V2 buoyancy peaks at higher heat flux in vertical upward flow CONCLUSION: a serious reduction in HT at the top occurs for horizontal flow at LOWER

heat flux, than that required to induce buoyancy peaks with vertical upward flow.

Comparison with data obtained in absence of buoyancy forces Vertical tube fairly precise criterion for the absence of buoyancy:

Upward flow buoyancy peaks (V2 FIG7)o When this condition is not satisfied

Downward flow improved HT when this criterion is satisfied Correlation for water and CO2 with absence of buoyancy

o Application of this correlation to the present conditions give T_wall between upper and lower surface (FIG3)

o T_wall for x/D = 100 for zero buoyancy and the test data

o CONCLUSION: Buoyancy in horizontal flow Decreases HT at the top Increases HT at the bottom REMARK: RESULTS FOR UNIFORM WALL HEAT FLUX

Criteria for buoyancy effect in horizontal flows Jackson: ABSENCE of buoyancy - Horizontal

o Criterion believed to be too conservative Petukhov: ABSENCE of buoyancy - Horizontal

Conclusion Criterion of Jackson: indication of the conditions of which buoyancy effects begin to occur

effect of x/D is necessary Criterion of Petukhov: based on “fully developed” solution of mixed convection problem

x/D not important anymore Buoyancy effect still developing after 100xdia

Confusion between the usual entry length and the length required to develop the temperature distribution characteristic of buoyancy effects

Liao SM, Zhao TS, An experimental investigation of convection heat transfer to supercritical carbon dioxide in miniature tubes, International Journal of Heat and Mass Transfer 45 (2002) 5025–5034

AbstractLiao et al. investigated convection heat transfer to supercritical CO2 in heated horizontal and vertical miniature stainless steel circular tubes (0.70, 1.40 and 2.16 mm). Buoyancy effects are significant for all flow directions even for high Reynolds numbers. Severe heat transfer deterioration occurred for a downward flow in the pseudo-critical region; however heat transfer enhancement occurred for the upward and horizontal flow. Thus in the downward flow, the heat transfer coefficients near the pseudo-critical point were much lower than those in horizontal flow, upward flow, and for constant property fluid flow. As the tube diameter reduces below 1.0mm, the Nusselt numbers decreases and this for all flow directions. They also developed correlations for the axially-averaged Nusselt numbers of forced convection heat transfer to supercritical carbon dioxide in horizontal, upward and downward flow in miniature heated tubes. The results of this study are of significance to the design of compact heat exchangers of supercritical fluids.

For a horizontal flow:

For an upward vertical flow:

For a downward vertical flow:

Experimental apparatus and procedure CO2 Circular microchannels

o 0.70/1.10; 1.40/3.18 and 2.16/3.18mm IDo Stainless steel AINSI 304

Pressure: 75120 bar Temperatures: 20110°C

o Compressed CO2 cylindero High-pressure CO2 pump: model P-200 Thar designs

Input pressure 57 bar Discharge pressure 680 bar Max flow rate 0.020.2 kg/min Controllable based on feedback from pressure sensor or flow rate

o Filtero Coriolis-type Micro motion mass flow meter: model CFM-010M, with IFT9701

transmitter Nominal range: 0-1.37 kg/min (accuracy <0.2%)

o Pre-heater to regulate T_in test sectiono Test sectiono After-coolero High-pressure fittings and valveso Pressure gauge transducer static pressure at inlet test section

Model 3051CG5, Rosemounto Differential pressure transducer at both ends test section

Model 3051CD3, Rosemounto Pressure transducers calibrated with pressure calibrator (acc ±0.2%)o Onboard microprocessor monitored flow meter, calculated flow rate and sent

feedback to the pumpo Portable chiller for cooling pump and after-coolero Electrical heater: 1042x105W/m²

Detail test section

Test tube tight in a Cu cylinder 25mm OD and 110 mm lengtho Electrical resistance wire around cylinder to heat test tube, electrically isolated from

Cu with isinglass and thermally from the ambient air with fiber glass wool Thermally insulated length of 110mm preceeds the heated length + thermally insulated exit

of 40mm Between test tube and Cu cylinder thin layer of metal oxide filled silicone oil paste (Heat

Sink Compound Plus, RS) to reduce contact thermal resistance 6 uniformly spaced T-type thermocouples T_wall_outer T_in and T_out measured with 2 armored T-type thermocouples All thermocouples calibrated in a cte temperature bath acc ±0.2%

Data reduction

Heat transfer from tube wall to CO2 steady state energy balance o m = Mass flowo i_in and i_out = enthalpy in and outlet test sectiono compare with electrical heating power current and voltage

difference within 12% for all data heat addition: heating outer Cu cylinder which enhanced axial heat conduction

boundary condition for test tube = ± constant temperature condition, rather than constant heat flux condition

Outer wall mean temperature 6 thermocouples Inner wall mean temperature T_w T_w_mean_outer, wall thickness and heating power LMTD of test tube

o Near the pseudo-critical point T_out-T_in very small due to high c_p (2°C)o Far from pseudo-critical point large differences (12°C)

Here c_p nearly constant This justifies the use of LMTD

Average HTC over entire length

o A = inner surface Nusselt number

o d = tube diametero k = thermal conductivity CO2o subscript b = properties evaluated at bulk mean temp T_b

Physical properties refprop Remark:

The uncertainties in the experimental data were evaluated according to the methods introduced in NIST Technical Note 1297 [14]. Since near the pseudocritical temperature Tpc, the thermal properties become rather sensitive to temperature, a small error in temperature measurements will cause a large uncertainty in the Nusselt numbers. For this reason, the uncertainty of the Nusselt number Nub near the pseudocritical temperature (Tpc ± 3°C) could be up to 30%. Except for the measuring points near the pseudocritical temperature, it is estimated that the relative standard uncertainty of the Nusselt numbers Nub and Nuw was within 8%.

Results and discussion Variation HTC with T_b_mean - HORIZONTAL

o Peak at T_B_mean near T_pc indicates HT enhancement near the pseudocritical region in horizontal tubes, mainly due to the fact of sililar behaviour of c_p near pseudocritical region

o Peak decreases as static pressure increases (similar for c_p) Variation HTC for different flow direction

o Downward flow HTC decreases passing through T_pco For T_b > T_pc: HTC downward generally lower than horizontal and upwardo Similar for larger diameter

CONCLUSION: Buoyancy still has an effect for HT in smaller diameters at high Re (105) MIXED TURBULENT CONVECTION in LARGE tube:

o Buoyancy enhancement HT in DOWNWARD flow (BUOYANCY-OPPOSED FLOW)o UPWARD flow HT impairment or enhancement depending on strength free

convection (BUOYANCY-AIDED flow) HERE: MINIATURE TUBES

o Results did not reached the same conclusion of previous investigations on mixed turbulent convection in LARGE vertical tubes

o The results suggest that the HT for turbulent convection in miniature vertical tubes agree UNDER SOME CONDITIONS with the theory of LAMINAR MIXED CONVECTION IN VERTICAL TUBES

Effect of tube diameter on Nu_b (for a fixed ratio of mass flow and diameter, to keep the Re_b and Pr_b constant in the 3 tubes)

o For comparison: Dittus-Boelter equation for cte property heating

o Most of the data for the larger diameters are favourably in agreement with the Dittus-Boelter eq.

o Nu-numbers depend very much on tube diameter near T_pc and dropped substantially as tube diameter was reduced!

o One of the major reasons for the behaviour in relation to tube diameter might be the effect of buoyancy

HORIZONTAL FLOW effect of buoyancy-induced secondary flow becomes negligible for

o For the larger tubes the ratio was exceeds the criterion for T_b/T_pc <1.01 buoyancy effects important at low temperatures

o For d=0.70mm according to criterion no effect of buoyancyo As tube diameter Decreases ration Decreases

Buoyancy less important for small diameters VERTICAL FLOW

o Influence of buoyancy on HT more complex PREVIOUS STUDIES for LARGE diameter

Buoyancy enhancement HT in DOWNWARD flow (BUOYANCY-OPPOSED FLOW)

UPWARD flow HT impairment or enhancement depending on strength free convection (BUOYANCY-AIDED flow)

Approximate analysis (Jackson) no deterioration due to buoyancy for:

o Present data

All values lower than then criterion Results didn’t have significant HT impairment Even for very small values of the criterion, there was still a big difference

between upward and downward flow due to buoyancy effects The results are INCONSISTENT with the previous works (and suggested

criterion) for turbulent mixed convection in LARGE vertical tubes where in downward flow HT enhancement was found due to buoyancy

o UPWARD flow here compared with Dittus-Boelter

When , the Nu_b was much lower than the Dittus-Boelter correlation

buoyancy-induced impairment of HT cannot be neglected for upward flow

o ~d0.3 buoyancy is one of the main reasons of the size effect on the Nu-number

But as d Decreases Nu-number for UP-and DOWNward flow Decreases besides buoyancy, there must be another physical mechanisms leading to smaller Nu-values for vertical tubes

Effect heat flux on HTo DOWNWARD FLOW

o Heat flux important influence different heat fluxes gives different velocity and temperature profiles HT deterioration for T_b/T_pc ≈ 1, compard to constant property fluids

o For HT correlations, the influence of the heat flux is usually take into account ysing

appropriate property parameter groups: with

HT correlations for miniature tubes Heat flux AND buoyancy IMPORTANT

Buoyancy effects accounted by the parameters

o ~d

o ~d0.3

o Effect of diameter is included by this in the correlation HORIZONTAL FLOW

o

o o MAXIMUM REL ERROR = 21.8%, MEAN REL ERROR 13.5%

VERTICAL UPWARD FLOW

oo MAXIMUM REL ERROR = 18.6%, MEAN REL ERROR 12.3%

VERTICAL DOWNWARD FLOW

oo MAXIMUM REL ERROR = 22.4%, MEAN REL ERROR 15.6%

CORRELATIONS VALID FOR:

Conclusions Buoyancy effect still important even for high Re-numbers Downward flow

o HTC near ps-point lower than horizontal and upward flowo Results are INCONSISTENT with the data in literature for LARGE tubes

Nu-number ↓ with d↓

Duffey RB, Pioro IL, Experimental heat transfer of supercritical carbon dioxide flowing inside channels (survey), Nuclear Engineering and Design 235 (2005) 913–924

AbstractDuffey et al. investigated the heat transfer and pressure drop at supercritical conditions using carbon dioxide. Their literature study showed that the majority of experimental data were obtained for heat transfer in vertical tubes, some data in horizontal tubes and just a few in other flow geometries. Three modes of heat transfer at supercritical pressures have been recorded, the so-called normal heat transfer, the improved heat transfer, characterized by higher-than-expected heat transfer coefficient (HTC) values than in the normal heat transfer regime and the deteriorated heat transfer, characterized by lower-than-expected HTC values than in the normal heat transfer regime. The deteriorated heat transfer usually appears at higher heat fluxes and lower mass fluxes. This phenomenon can be suppressed or significantly delayed by increasing the turbulence level with flow obstructions and other heat transfer enhancing devices. Heat transfer at supercritical pressures is affected with flow orientation (upward, downward and horizontal). Horizontal flows show non-uniform cross-section temperature profile with higher temperature and therefore, lower HTC values, at the top of a channel.

Junghui Chen, Kuan-Po Wang, Ming-Tsai Liang, Predictions of heat transfer coefficients of supercritical carbon dioxide using the overlapped type of local neural network, International Journal of Heat and Mass Transfer 48 (2005) 2483–2492

AbstractChen J et al. proposes an overlapped type of local neural network to improve the accuracy of the heat transfer coefficient estimation of supercritical CO2. The main idea is to use the network to estimate the heat transfer coefficient for which there is no accurate correlation model due to the complexity of the thermo-physical properties around the critical region. Unlike the global approximation network (e.g. backpropagation network) and the local approximation network (e.g. the radial basis function network), the proposed network allows us to match the quick changes in the near-critical local region where the rate of heat transfer is significantly increased and to construct the global smooth perspective far away from that local region. Based on the experimental data for carbon dioxide flowing inside a heated tube at the supercritical condition, the proposed network significantly outperformed some the conventional correlation method and the traditional network models. The alterative neural network design procedure, MRBFN, offers a systematical framework for constructing and training network. For practical use, the overlapped and localization property of the proposed network brings the benefits of the fast convergence and easy training. Compared with the other two existing and popular networks (RBFN and BPN) in this study, the proposed network which includes the features of the overlapped local regions can achieves better estimations. Although the supercritical CO2 is used in this paper, a proposed model can be easily extended to predict the heat transfer coefficient when any supercritical fluid is applied to a heat exchanger.

Introduction Empirical equations for heat transfer exist and even modifications for when the fluid is near

the critical point Traditionally dimensionless analysis is used to reduce the number of variables Due to the strong dependence on temperature of the thermophysical properties procedure

to design correlations become very complex and potentially lose their generality Complex heat transfer + large number of variables

o Most of the models rely on assumptions and simplifications that disagree at the real operating conditions

ALTERNATIVE APPROACH NEURAL NETWORK TECHNIQUEo = method used to predict the response of a physical system that cannot be easily

modelled mathematically.o They have demonstrated the strong capability of learning non-linear and complex

relationships between process variables WITHOUT any prior knowledge of system behaviours

o Since the highly complex behaviour of heat transfer systems in the near critical region is presently ahead of the theoretical method from a fundamental physical

standpoint, the network is derived from the data presented instead of the exact form of the analytical function on which the model should be built.

o By training the net to reduce the difference between the neural network output and the actual experimental values, each neural network represents a non-linear or complex behavior for the output that it learned.

o The neural network is ideally suited for the heat transfer process problem mainly because of the derivation from the data presented instead of the exact form of the heat transfer on which the model should be built. Many researchers have focused on the neural network approach to heat transfer modeling.

o In recent years, the number of applications of neural networks to heat transfer process has increased dramatically. Research shows that neural network models exhibit superior predictive abilities over traditional statistical methods and require less experimental training data.

o Literature that deals with the use of neural networks to the heat transfer problems includes:

the prediction of the heat transfer coefficient [7],

Nusselt number [8,9],

heat transfer rates [10,11],

the simulation of a liquid-saturated steam heat exchanger [12] and so on.

o Advantages: Neural network approach safe time and money It learns and extracts the process behaviour from the past operating

information

Can be used for process optimization and designo BPN = Backpropagation neural network

Often used But a large amount of data points needed to cover the whole design range

for training a healthy neural network model Not applicable to process design, since only the data located at some local

design regions is critical to building the neural network model. The structure of the locally tuned and overlapping receptive field has been

widely applied in the region of the cerebral cortex, the visual cortex, etc.o RBFN = the radial basis function network (RBFN) [14] with the property of the local

function is proposed to eliminate unnecessary and extrapolation errors.

The non-linear mapping is used to transfer the inputs into the intermediate outputs covered at some local regions. Due to the local structure, the curse problem, which refers to the exponential increase in the number of hidden neurons with the increase of the input space dimensions, still exists.

o This paper neural network with the overlap structure, the modified RBFN (MRBFN), is proposed to improve the modelling the heat transfer coefficient for supercritical CO2 in the heat exchanger system.

It has not only the valid smooth approximation in the design space but also the fine and variation approximation in several local neighbourhoods. It provides a systematic modelling procedure based on the input–output data with the desired accuracy. The comparisons with the conventional correlation method and the model based on BPN and RBFN are also made.

Experimental data Data from Olson and Allen for horizontal CO2 flow

Duffey RB, Pioro IL, Experimental heat transfer of supercritical carbon dioxide flowing inside channels (survey), Nuclear Engineering and Design 235 (2005) 913–924

AbstractDuffey et al. investigated the heat transfer and pressure drop at supercritical conditions using carbon dioxide. Their literature study showed that the majority of experimental data were obtained for heat transfer in vertical tubes, some data in horizontal tubes and just a few in other flow geometries. Three modes of heat transfer at supercritical pressures have been recorded, the so-called normal heat transfer, the improved heat transfer, characterized by higher-than-expected heat transfer coefficient (HTC) values than in the normal heat transfer regime and the deteriorated heat transfer, characterized by lower-than-expected HTC values than in the normal heat transfer regime. The deteriorated heat transfer usually appears at higher heat fluxes and lower mass fluxes. This phenomenon can be suppressed or significantly delayed by increasing the turbulence level with flow obstructions and other heat transfer enhancing devices. Heat transfer at supercritical pressures is affected with flow orientation (upward, downward and horizontal). Horizontal flows show non-uniform cross-section temperature profile with higher temperature and therefore, lower HTC values, at the top of a channel.

Jiang P.X., Shi R.F., Xu Y.J, He S., Jackson J.D., Experimental investigation of flow resistance and convection heat transfer of CO2 at supercritical pressures in a vertical porous tube, Journal of Supercritical Fluids 38 (2006) 339-346

Experimental setup and data reduction

Local tube T_wall with 8 copper-constantan thermocouples Mixers installed before and after test section T_in and T_out with accurate platinum thermal resistance thermometers RTD All calibrated with constant temperature oil bath Inlet pressure pressure gauge tranducer Model EJA430A (until 12MPa) Pressure drop differential pressure transducer Model EJA110A (until 500kPa) Mass flow rate Coriolis-type mass flowmeter Model MASS2100/MASS6000, MASSFLO,

Danflos (0-65 kg/h) Accumulator for flow rate variations Steady state after 50-120min!!

o Steady state if variations in T_wall, T_in and T_out are within ±0.1°Co Variation flow rate and inlet pressure ± 0.2% for at least 10min

Experimental uncertainty of heat balance was ±5% The experimental uncertainty of the convection heat transfer coefficients was mainly caused

by experimental errors in the heat balance, axial thermal conduction in the test section, temperature measurement errors and the calculation of the heat transfer surface temperature.

The root-mean-square experimental uncertainty of the convection heat transfer coefficient was estimated to be 15.8%. The experimental uncertainties in the inlet pressures were estimated to be ±0.09%.

T_wall_in via T_wall_out and assuming one-dimensional steady state conduction in the

wall

Local HTC at each axial location

Local fluid bulk temperature via local fluid bulk enthalpy

Kim JK, Jeon HK, Lee JS, Wall temperature measurement and heat transfer correlation of turbulent supercritical carbon dioxide flow in vertical circular/non-circular tubes, Nuclear Engineering and Design 237 (2007) 1795–1802

AbstractKim JK et al. presented experimental data for turbulent supercritical carbon dioxide in vertical tubes with circular, triangular and square cross-sections. Based on the wall temperature measurements, an improved heat transfer correlation is proposed which is applicable for both forced convection and mixed convection regimes, and was compared with previous correlations. The proposed correlation predicts the averaged Nusselt number within 20% accuracy for the 90% of the present experimental data for circular and non-circular tubes.

Experimental setup

Main loop for CO2 and secondary for cooling water Pressurizing of CO2 via air-driven booster pump + accumulator Magnetic gear pump Mass flow rate via rpm pump and Coriolis type flow meter Electric pre-heater set T_in test section Bypass line to adjust flow rate or stabilize system 2 S&T coolers Chiller for chilled cooling water Tubes Inconel 625 Vertical test tube DC heating for uniform heat flux

T_wall_outer chromel-alumel sheath type thermocoupleso Thermocouples electrically isolatedo 41 thermocouples silver-soldered to the wall at every 30mm from starting point

heating regiono Extra 20 thermocouples for non-circular tubes

Outer wall thermally isolated by ceramic wool for high-temperature insulation + ceramic tape

Measure conduction to non-heating region of the test tube 2 thermocouples in upstream of the starting position of the test tube

T_in and T_out same kind of thermocoupleso T_bulk_out in outlet mixing chamber

Thermocouples calibrated with RTD (resistance temperature detector)

h_bulk_x energy balance based on T_bulk_in, mass flow, heat fluxo T_bulk_x h_bulk_x and property tableso NIST Chemistry Web Book and NIST Refrigerant Properties Database 6.0

Nu Near pseudo-critical point small variation in T large deviation in enthalpy

uncertainty via method of Holman 2001 Holman, J.P., 2001. Experimental Methods for Engineers, 7th ed. McGraw-Hill (Chapter 3).

Uncertainty of the measured T_wall estimated by considering thermocouple conduction (Schneider 1955) Schneider, P.J., 1955. Conduction Heat Transfer. Addison-Wesley Publishing Company Inc (Chapter 8).

Results When the bulk fluid temperature at the outlet mixing chamber becomes the pseudocritical

temperature violent oscillations of the wall and outlet bulk fluid temperatures are observed. This phenomenon has also been found by the numerical simulation of Koshizuka et al. (1995).

The bulk fluid in the tube core region is near the pseudocritical temperature whose properties vary nonlinearly with temperature. During the interaction with the boundary layer flow, it makes the temperature in the boundary layer collapse and grow in a repeated manner. On that score, the heat transfer is enhanced and impaired, resulting in the wall temperature oscillation.

Jiang P.X., Zhang Y., Zhao C.R., Shi R.F., Convection heat transfer of CO2 at supercritical pressures in a vertical mini tube at relatively low reynolds numbers, Experimental Thermal and fluid science 32 (2008) 1628-1637

Abstract

[1] A. P. COLBURN. A method of correlating forced convective heat transfer data, Trans. Am. Soc. Mech. Engrs. 29, 174-188 (1933).

[2] A. R. Pickering, Turbulent heat transfer to fluids with variable physical properties, A.E.E.W. R.290 (1964).