Supervisors:
Candidate:
Prof. Paolo Di Marco
Giacomo Manfredini
Dr. Alekos I. Garivalis
Sessione autunnale
Anno Accademico 2018/2019
chf enhancement in microgravity
in presence of microstructured
surface and electric field
Master Thesis in Mechanical Engineering
Università di Pisa
Scuola di Ingegneria
Sessione autunnale
Anno Accademico 2018/2019
Pool boiling heat transfer is used in many industrial processes, including electronics cool-ing, power generation, and two-phase thermal management in space stations and nuclear plants. Critical Heat Flux (CHF) is an important performance limiting condition. In particular, in micro-g, CHF encounters a drastic reduction. Thus, it is important to understand the mechanisms that lead to this and identify ways to enhance it. In this work, we explored the possibility to enhance CHF combining engineered surfaces (passive technique) and electric field (active technique). In normal gravity, it has been demon-strated that CHF is enhanced with microstructures; this is thanks to rewetting due to sloshing and imbibition, which is independent of gravity. Moreover, electric field creates a driving force able to remove vapor from the surface. Their combined application appears an effective way to prevent dryout, even if the two effects influence each other. Experi-ments were run during the 71th PFC held by ESA. A dedicated apparatus was built and operated with bare and microstructured surfaces, using subcooled FC72 at 1 bar. A DC electric field was applied via a metal grid laid 6 mm over the surface. Results showed that CHF reduced in micro-g, but these enhancement techniques are able to deal with this reduction: respected to standard g, electric field effects are more effective, working as buoyancy, while microstructures enhancement decreases due to the lack of sloshing, dependent on gravity.
1.1 Nukiyama Experiment and Boiling Curve . . . 15
1.2 Bubbles Development Mechanisms . . . 17
1.2.1 Metastable equilibrium of bubbles . . . 17
1.2.2 Bubble nucleation-Hsu’s Theory . . . 20
1.2.3 Bubble growth . . . 22
1.2.4 Bubble detachment . . . 24
1.3 Nucleate Boiling. . . 27
1.3.1 Heat transfer contributes . . . 27
1.3.2 Rohsenow Correlation . . . 28
1.3.3 Other Correlations . . . 29
1.3.4 Single bubbles-Slugs transition correlation . . . 30
1.4 Critical Heat Flux . . . 30
1.4.1 Hydrodynamic model of CHF . . . 31
1.4.2 Macrolayer and Hot spot theories . . . 34
1.4.3 Short considerations about CHF theories . . . 35
1.5 Post-CHF regimes. . . 37
1.5.1 Transition boiling and Minimum Heat Flux . . . 37
1.5.2 Film Boiling . . . 38
2 Critical Heat Flux Enhancement 40 2.1 Parametric effects in boiling . . . 40
2.1.1 Pressure . . . 40 2.1.2 Liquid Subcooling . . . 40 2.1.3 Dissolved Gas . . . 42 2.1.4 Surface properties . . . 42 2.1.5 Heater features . . . 43 2.1.6 Gravity . . . 44
2.2 Electric field effects . . . 47
2.2.1 Electric Force in a Continuum . . . 47
2.2.2 Bubble shape and Momentum balance with electric field . . . 48
2.2.3 Effects in Nucleate boiling and CHF . . . 50
2.3 Microstructured Surfaces effects . . . 51
2.3.1 General behaviour of microstructured surfaces . . . 51
2.3.2 Microtexture imbibition model . . . 52
2.3.3 Improvement of imbibition model: RAMBO Project . . . 55
2.3.4 Short considerations about microstructures enhancement model . . 56
3 Experimental design and setup 59 3.1 Parabolic Flight experiment . . . 59
3.2 Microstructured Heaters . . . 60
3.2.1 Geometrical Characteristics . . . 60
3.2.2 Machining process . . . 61
3.3 Test Design . . . 64
3.3.1 Test Cell . . . 66
3.3.2 Heaters Test Section . . . 67
3.3.3 Bellows . . . 68
3.3.4 Cooling system . . . 69
3.3.5 Other apparatus systems . . . 71
3.4 Control and software systems . . . 71
3.5 Other apparatus images . . . 75
4 Postprocessing and Results 77 4.1 Data Setting. . . 77
4.2 Data Analysis . . . 79
4.2.1 Data collecting . . . 79
4.2.2 Heat-transfer problem numerical analysis . . . 80
4.2.3 Boiling curves generation . . . 81
4.3 Results . . . 82
4.3.1 Temperature and Heat flux distribution. . . 82
4.3.2 Electric field effects in pool boiling curves . . . 83
4.3.3 Microstructures effects in pool boiling curves . . . 85
4.3.4 Short considerations in Earth gravity . . . 89
4.3.5 Effects of weightlessness . . . 89
4.3.6 Short considerations in hypergravity . . . 94
4.3.7 CHF enhancement contributes . . . 95
4.3.8 Model validation . . . 100
Conclusions 102 A Heaters Results 104 A.1 Results Plots . . . 105
A.1.1 Bare Heater 1g . . . 105
A.1.2 Bare Heater 0g . . . 106
A.1.3 Heater8 1g . . . 107 A.1.4 Heater 8 0g . . . 108 A.1.5 Heater 14 1g . . . 109 A.1.6 Heater 14 0g . . . 110 A.1.7 Heater 9 1g . . . 111 Bibliography 112
Nomenclature αM Void fraction
β Active cavity angle rad
Sd Fluid Stress Tensor Pa
E Electric field N/C
fe Electric surface stress N/m2
n normal unit vector
vm Liquid medium velocity m/s
v = ρq00
ghlg Vapor superficial velocity m/s
∆E Energy J
∆Tw = (Tw − Tsat) Wall Superheat °C
∆Tnucl Wall superheat at Onset of Boiling °C
∆V Voltage V
δM Liquid Macrolayer thickness m
δt Superheat boundary layer thickness m
0 Vacuum dielectric permittivity F/m
R Relative dielectric permittivity F/m
λh Helmholtz wavelength m
λd,1 Taylor one-dimensional wavelength m
λd,2 Taylor bi-dimensional wavelength m
µ Dynamic viscosity Pa s
ρ Density kg/m3
a Pillar size µm Ac Cross-sectional wicking area m2
Ah heater-jet cross section m2
Aj Jets cross section m2
b Pillar spacing s b = ρ ∂R ∂ρ T electrostriction coefficient Bo = lL L Bond Number
Cg Gas concentration mol/mol
cp Specific heat at constant pressure J/kgK
Csf Rohsenow coefficient
D Diameter m
Dd Fritz bubble diameter m
Enh Enhancement %
f frequency Hz
f1, f2 Hsu’s factors
Fe Electric Force N
Fw, Fp, Fq VDI adimensional factors
Ftr Transition factors
g Gravity acceleration m/s2
Gr Grashof Number
H Heater thickness mm
H(T ) Henry’s constant mol/molkPa hc0 VDI reference heat transfer coefficient W/m2K
hc,rad Radiation Heat transfer coefficient W/m2K
hlg Latent heat of evaporation J/kg
I Current A J a = ρlcp,l[T∞−Tsat] ρghlg Jacob Number k Curvature mm−1 kT Thermal conductivity W/mK Kv Viscous permeability m2 lL= q σ (ρl−ρg)g Laplace length m
M Molcular weigth g/mol
n Nucleation Sites Denisty 1/m2
N u = hcD/kT Nusselt Number p Pressure Pa pc Capillary pressure Pa pv Viscous stress Pa P r = cp,lµl kT Prandtl Number q00 Heat flux W/m2
qmin00 Minimum heat Flux W/m2
qtr00 Nucleate boiling transition heat flux W/m2
R Radius m Rc Cavity radius m Rp Surface roughness µm Re Reynolds Number t Time s Tf = Tw+T2 ∞ Film Temperaure °C th Heating time s Tw Wall Temperature °C
V Volume m3 v Specific volume m3/kg y Vertical Cordinate m Suffixes ∞ bulk fluid b of the bubble
CHF at Critical Heat Flux crit Critical
EF in presence of electric field g Vapor
imb due to imbibition l Liquid
M P in presence of micropillars s of the solid
sat At Saturation slo due to sloshing sub subcooled fluid
1.1 Nukiyama’s Test Section(Picture by [2]) . . . 15
1.2 Nukiyama’s Boiling Curve(Picture by [3]) . . . 16
1.3 Pool boiling regimes observed during the 71th ESA Parabolic Flight Cam-paign in Bordeaux(FR) . . . 18
1.4 p-v diagram for metastable fluid . . . 19
1.5 p-v diagram for metastable fluid (Picture by [2]) . . . 19
1.6 Type of surface related to contact angle. . . 20
1.7 Hsu’s Theory of nucleation (Picture by [5]) . . . 21
1.8 Hsu’s Diagram Rc vs ∆Tw for saturated water at atmospheric pressure, fixed δt (Picture by [8]). . . 22
1.9 Bubble equilibrium (Picture from [3]) . . . 25
1.10 Experimental results for detaching diameter for different values of gravity field(Picture by [10]) . . . 26
1.11 Bubble detaching mechanism (Picture by [5]) . . . 27
1.12 DX: Heat transfer contributes behavoiur; SX: heat transfer contributes (Picture by Khalik,1983 ) . . . 28
1.13 Rohsenow correlation applied to data for water boiling on 0.61mm diameter platinum wire(Picture by [2]) . . . 29
1.14 The array of vapor jets as seen on an infinite horizontal heater surface, as predicted by Taylor theory (Picture by [2]) . . . 31
1.15 Helmholtz instability of vapor jets (Picture by [2]) . . . 32
1.16 CHF for different geometries; correction factors by [21] (Picture by [2]) . . 34
1.17 Macrolayer theory by Katto . . . 35
1.18 Schematic drawing of a dry spot forming on the surface;in the diagram and in the optical/infrared visualization by Dhillon[37], we can notice the trend of the temperature in the centre of the spot: at the beginning, there’s a little drop due to evaporation of the liquid inside, and then it rises until the collapse. . . 36
1.19 Influence of surface condition on transition boiling; experimental data by Berenson[24] . . . 37
1.20 Di Marco et al.(2004) results for film boiling; fluid:FC72, saturated, p=115kPa, D=0.2mm . . . 38
2.1 Effects of pressure in nucleate boiling: enhancement of normalized heat transfer coefficient versus reduced pressure(Picture by [32]) . . . 41
2.2 The influence of subcooling on the boiling curve (Picture by [2]) . . . 41
2.8 SX: Nucleate boiling curve on a flat plate 20x20 mm (fluid:FC-72) in normal gravity-diamonds- and microgravity -circles-. DX: Pool boiling curve on a
0.2 mm wire in normal gravity and sounding rocket experiment, 10−4g,
fluid: R113, pressure: 1 bar (Picture by [34]) . . . 46
2.9 The influence of gravity in bubble shape. (Picture by [3]) . . . 47
2.10 The influence of gravity in bubble dimensions, observed during 71th Parabolic Flight Campaign. You notice the increase of bubble’s dimensions in
micro-gravity. . . 47
2.11 The influence of electric field in bubble shape (Picture by [3]) . . . 49
2.12 Electric field effects observed during 71th Parabolic Flight Campaign;
ef-fects caught during 0g parabola . . . 51
2.13 Electric field effects on boiling curve observed during sounding rockets tests by DiMarco and Grassi in 2002: with EF(DX), without EF(SX) (Picture
by [10]) . . . 51
2.14 Electric field effects on hcin terrestrial and microgravity conditions (ARIEL
results): we can notice that 10 kV-green triangles-restores boiling
perfor-mance in standard conditions-purple triangles-(Picture by [35]). . . 52
2.15 Unit cell (Picture by [37]) . . . 52
2.16 Imbibition contributes during rewetting process; notice that λ ≡ lL ≡ Db,
i.e. dry spot radius is equal to average bubble diameter (Picture by [37]) . 53
2.17 Dhillon results and model (Picture by [37]) . . . 55
2.18 Evaluation of cross-sectional area . . . 56
2.19 CHF enhancement due to microstructures from RAMBO model, assuming
Kv and pc from Dhillon and θ = 0. The blue line represents the locus of
CHF enhancement maxima as a function of the pillar dimension a . . . 57
2.20 CHF enhancement due to microstructures from RAMBO model, by
chi-anging pillars’ height . . . 58
2.21 Comparison between Dhillon, Rambo and Dhillon test results(Picture by [43]) . . . 58
3.1 Parabolic flight trajectory (Picture from [44]) . . . 60
3.2 Sketch of the heater. SX: Top surface with micropillars; DX: Bottom surface 61
3.3 SEM images of micropillars . . . 63
3.4 Schematic and real image of test apparatus . . . 65
3.5 Test rack. . . 65
3.6 Test cell schematic(Top), Cell(Left-bottom) and Pad-Heaters(Right-bottom)
. . . 66
3.7 Test section 3D CAD model . . . 67
3.9 Bellows schematic and technical section . . . 69
3.10 Bellows pressurizer system . . . 69
3.11 Cooling loop schematic . . . 70
3.12 Top and lateral view of Cooling Loop . . . 71
3.13 Apparatus subsystems . . . 72
3.14 Labview interfaces: Control(Top) and Acquisition(Bottom) . . . 73
3.15 Arduino control systems . . . 74
3.16 Errors chain example for measured values. . . 74
3.17 Cooling loop Peltier(Top) and Pad-Heaters(Bottom) . . . 75
3.18 Apparatus overview . . . 76
3.19 Acquisition systems . . . 76
4.1 Experimental procedure (Bare heater test) . . . 79
4.2 Examples of data collecting process: standard conditions(SX), boiling cri-sis(DX) . . . 80
4.3 Boundary condition(Top)and simply schematic of the heat-transfer prob-lem(Bottom). . . 81
4.4 Temperature distribution inside the heater . . . 83
4.5 Heat flux streamlines . . . 83
4.6 Electric field behaviour; examples with bare heater(SX) and Heater14(DX), in Earth gravity(Top) and in Zero-g(Bottom). . . 84
4.7 Electric field behaviour in heat transfer coefficient curves of Bare Heater(SX) and Heater14(DX): you can notice no differences between blue and red series. 85 4.8 Micropillars effect on Nukiyama and hc curves for Heater8(5x10) in 1g; comparison with Bare heater . . . 86
4.9 Micropillars effect on Nukiyama and hc curves for Heater14(10x15) in 1g; comparison with Bare heater . . . 87
4.10 Micropillars effect on Nukiyama and hc curves in Heater9(5x20) in 1g; comparison with Bare heater . . . 88
4.11 Residual convection on bare heater(Bottom,SX) and Heater9(Bottom,DX) 89 4.12 Effects of capillary forces on liquid phase in the bottom camera, during zero gravity and observed heater temperature drop . . . 90
4.13 Nukiyama and hc curves of Bare Heater in Earth gravity and Zero-g . . . . 91
4.14 Nukiyama and hc curves of Heater8 in Earth gravity and Zero-g . . . 92
4.15 Nukiyama and hc curves of Heater14 in Earth gravity and Zero-g . . . 93
4.16 Effects of hypergravity on Nukiyama boiling curve and heat transfer coef-ficient correlation on bare heater(Top) and Heater14 (Bottom) . . . 94
4.17 CHF contributes of micropillars and electric field in 1g . . . 97
4.18 CHF contributes of micropillars and electric field in 0g . . . 97
4.19 CHF enhancements in 1g . . . 98
4.20 CHF enhancements in 0g . . . 98
4.21 Effect of restoring due to micropillars and electric field in zero-g on Heater 8 99 4.22 Effect of restoring due to micropillars and electric field in zero-g on Heater 14 . . . 100
4.23 Enhancement model, function of texture geometry . . . 101
A.10 Heater14(10x15) heat transfer coefficient curve; 1g-0kV,15kV . . . 109
A.11 Heater14(10x15) boiling curve; 0g-0kV,15kV . . . 110
A.12 Heater14(10x15) heat transfer coefficient curve; 0g-0kV,15kV . . . 110
A.13 Heater9(5x20) boiling curve; 1g-0kV,15kV . . . 111
3.1 Main characteristics of microgravity experiments . . . 61
3.2 Test Cell components . . . 67
3.3 Test Section components . . . 68
3.4 Bellows components. . . 70
3.5 Cooling Loop components . . . 70
3.6 Acquisition system components . . . 74
4.1 Nominal dimensions of heaters tested . . . 77
4.2 FC72 properties at saturation and silicon properties . . . 78
4.3 CHF comparisons . . . 96
4.4 Model validation . . . 101
face characteristic of liquid and vapor (including surface tension). Furthermore, the flow structure that creates over the surface is very difficult to model and predict. Because of this fact, neither general equations describing the boiling process nor general correlations of boiling heat transfer data are available.
Taking into consideration boiling in stagnant fluids, it is of fundamental importance the analysis of the phenomenon and the description of every parameter that plays a role in it; in particular, many discussions are related to the nucleate boiling regime and how bubble development influences it.
The main focus concerns the critical heat flux (CHF), i.e. the maximum heat flux that the system can provide before the formation of a stable film vapor over the surface, with the subsequent strong reduction of heat transfer coefficient and increasing of wall tem-perature. It is therefore important not only the understanding of this mechanism, which has different nature (hydrodynamic, thermal, fluid-surface interactions), but also the de-velopment of different ways to prevent it.
This work wants to analyze two different enhancement techniques, one active and one pas-sive: external electric field and microstructures on heated surface. It is well-known that electric field can improve buoyancy on bare surface, creating an additional volume force on bubbles, that superimposes to buoyancy. At the same time, microstructures work on surface wettability, preventing the formation of the vapor film. Recent studies have been demonstrated that not structures density plays a minor role with respect to the geometric characteristic of the texture and contact angle are responsible for the imbibition of the path; this with sloshing flow due to gravity strongly enhance CHF.
In particular, the aim of this work is to understand why and how these two methods improve boiling performances, speculate about combined effects, and how microgravity modifies their behaviors. At the same time, a validation analysis of a new prediction model of the microstructures contribute has been carried out, developed by DESTec and MIT, started from Dhillon studies of structures wickability. Experiments were performed during 71th Parabolic Flight Campaign by ESA on Airbus A310-ZeroG on four small silicon heater 15x20x0.7mm, one smooth and the others with a 1cm2 structured area,
each one with different geometric parameters (size and spacing). Experimental tests have been conducted in heat flux control mode, imposing the electric heating power with two
wires connected to a titanium layer on the bottom side of the heater. FC72 has been chosen as working fluid, controlling its pressure and dilatation with a bellows and the bulk temperature with a cooling system. Electric field has been applied with a metal grid placed 6mm above the heated surface, with a DC voltage equal to 15kV. Measurements in different gravity field conditions, with and without electric field, have been collected in order to obtain boiling curves and heat transfer coefficient correlations. Concerning this aim, a Matlab code has been realized, able to collect data and solve the 3D conduction problem, imposing heat power on the bottom surface and converging on its temperature value.
Results confirms previous experiments in normal gravity with micro-structures and electric field, and suggest an interaction between them. Moreover, investigations in microgravity have highlighted the relationship between gravity field and enhancement value due to these two techniques. Contemporary, model predictions are comparable with results in standard gravity, confirming the good quality of the model itself, but fail in weightlessness, so leading to future new theories of pool boiling in zero-g.
particular attention has to be paid to maximum heat flux values and the critical conditions of this phenomenon.
There are two distinct boiling configurations: 1. pool boiling
2. forced convection boiling
In this work, we are going to focus on the first one, i.e. boiling in a stagnant mass of fluid.
1.1
Nukiyama Experiment and Boiling Curve
In 1934, Shiro Nukiyama performed a pioneristic experiment [1], schematized in Figure
1.1, consisting in heating a thin wire of platinum in a large pool of liquid saturated water (and subcooled in another test) at atmospheric pressure. As long as temperature of the
Figure 1.1: Nukiyama’s Test Section(Picture by [2])
surface does not exceed the boiling point by more than a few degrees, heat is transferred 15
by natural convection; so bubbles are not present yet.
As the temperature of the heater is increased, we have the formation of isolated bubbles, that escape from the heated surface in certain places known as nucleation sites: these zones are very small inclusions in the surface, and they are present mainly due to man-ufacturing process. At first, the vapor bubbles are few and small, but as the surface temperature is raised further, they become many and larger.
This trend continues until a particular high value of heat flux, in which temperature sud-denly increases; at this moment, a vapor layer covers the surface and the heat transfer mechanism changes to film boiling, degrading heat transfer coefficient.
Observing and analyzing his tests, Nukiyama derived the so called Boiling Curve, shown in Figure 1.2. The curve plots heat flux (q00) as function of the difference between the
Figure 1.2: Nukiyama’s Boiling Curve(Picture by [3])
surface temperature, commonly called Wall Temperature (Tw), and liquid saturation
tem-perature (Tsat). As we can see, the behavior can be divided in 4 Regions, described
below:
• Natural Convection: This is characterized by single-phase natural convection from the hot surface to the saturation liquid without formation of bubbles. This behavior can be easily studied with the classical correlations of natural convection. • Nucleate Boiling: In this regime, which begins at the transition point called Onset of Boiling (point A of the curve), bubbles appear and there’s a two-phase natural convection process in which bubbles nucleate, grow, and depart from the heated surface. The heat flux increases rapidly with increasing wall temperature.
This region is also divided in two different sub-regimes:
1. Isolated bubbles regime: bubbles rise from isolated nucleation sites; as q00
and sensible increment of Tw (so ∆Tw). This famous transition point is known as
Boiling Crisis or Critical Heat Flux (CHF). We will call this value q00 CHF.
• Transition Boiling: After the q00
CHF is reached, the number of vapor slugs increase.
In this region, vapor convection and boiling heat transfer coexists until the film vapor becomes stable and covers all the heating surface.
Actually, in this region one of two situations can occur, depending on the control method:
1. Heat flux Control: the process progresses on a horizontal line of constant heat flux so that the wall superheat jumps to point E. In this case, it is possible to compromise the heater surface due to burnout.
2. Wall Temperature Control: q00 decreases until he reaches his minimum value q00 min
(point D). In this case, the process oscillates between nucleate boiling and film boiling, where each mode may coexist on the heated surface or may alternate at the same location on the surface. [5]
• Film Boiling: In this regime, a stable vapor film blankets the entire surface; the heat transfer coefficients are much lower because heat must be conducted through a vapor film instead of through a liquid film.
1.2
Bubbles Development Mechanisms
In order to understand pool boiling’s particular behavior, we want to analyze mechanisms that permit bubbles to nucleate, grow and finally detach.
1.2.1
Metastable equilibrium of bubbles
As it’s shown in Figure 1.4, we have to study the boiling fluid as a mixture of liquid and vapor in metastable equilibrium: line BC represents the superheated liquid, which is in metastable equilibrium at a pressure lower than its saturation one; the line EF is supersaturated vapor (p ≥ psat). The maxima and minima of the isotherms are joined
by the so-called spinodal curve, which bound the metastable regions. Taking this into account, we can determine bubble’ s shape and size, imposing mechanical and thermal equilibrium:
thermal equilibrium requires the same temperature outside and inside the bubble, i.e saturation temperature; assuming spherical bubble, force balance can be obtained by the
Figure 1.3: Pool boiling regimes observed during the 71th ESA Parabolic Flight Campaign in Bordeaux(FR)
equilibrium of spherical shells. So, neglecting normal viscous stress, bubble radius Rb is
equal to: Rb = 2σ pg − pl (1.1) where: σ: surface tension (N
m). It’s a substance’s characteristic and depends on saturation
tem-perature and critical temtem-perature(Some correlations are discussed in [6]) pg: vapor pressure(inside bubble)1
pl: liquid pressure(outside bubble)
Observing the p-v diagram in Figure 1.5, it can be shown that[2], because of the over-pressure ∆p = pg−pl(= 2σRb)due to bubble surface tension, the external liquid surrounding
the bubble is superheated; so bubble may exist in equilibrium only into super-heated liquid (the smaller the bubble radius, the higher the pressure inside, the higher
1There is an effect of the curvature of the interface that lower the pressure in the vapor nucleus
calculated on a simply planar interface. This correction has been shown by Lord Kelvin, and depends on molecular weight and specific volumes of vapor and liquid. For more details, refer to [2]
Figure 1.4: p-v diagram for metastable fluid
Figure 1.5: p-v diagram for metastable fluid (Picture by [2])
the superheat requested). The estimate of this value can be evaluate by the classical Clausius-Clapeyron equation: dT dp sat = Tsat(vg− vl) hlg (1.2) where:
vl: specific volume of liquid
hlg: latent heat of evaporation
Assuming finite difference and substituting eq.1.1, we obtain: Nucleation Superheat ∆Tnucl = (Tw− Tsat)ON B ≈ vgTsat hlg 2σ Rb (1.3)
It is easy to see that bubble’s equilibrium is unstable: in fact, fixed ∆Tnucl, if Rbis less than
the value calculated with eq1.1, vapor inside will condense and the bubble disappears; on the contrary, liquid at the interface will evaporate and the bubble will begin to grow. Thus, as the heater surface temperature increases, bubble radius becomes smaller, and so smaller nucleation sites are activated. We have also to clarify that this analysis is just for degassed fluid: if air is trapped in nucleus with vapor, the ∆Tnucl required reduces,
because partial pressure must be taken into account [5].
1.2.2
Bubble nucleation-Hsu’s Theory
There are two different types of nucleation:
1. Homogeneous nucleation: nucleation occurring in a perfectly clean and super-heated liquid. A simple «Rule of Thumb» says that at any pressure, the minimum superheat is around 80 − 90% of the critical temperature.
2. Heterogeneous nucleation: nucleation at the interface between fluid and solid surface, due to achievement of the free energy of formation in a cavity.
The second mechanism is the most common, and we are going to discuss it.
It’s easy to see that contact angle2 plays a fundamental role in this process; its value
can be calculated by Young’s equation:
cos θ = σsg− σsl
σlg (1.4)
where σ are surface tensions between solid, liquid and vapor.
The lower θ, the more the liquid is wetting the surface: surfaces with θ ≤ 90° are called Hydrophilic, whereas they are Hydrophobic or Superhydrophobic if θ is over 150°. The free
Figure 1.6: Type of surface related to contact angle
energy required for the nucleation is less in cavities than on a perfect planar surface; in
2Actually, contact angle is not properly a real concept, but it represents a microscopic region(also
called evaporation microlayer )where some important phenomena that determinate the shape of interface occur; many articles define it as "apparent"contact angle; for more details, refer to [?]
Figure 1.7: Hsu’s Theory of nucleation (Picture by [5])
active nucleation site’s size (Figure1.7). He speculated that in the superheated boundary layer of thickness δt the temperature varies linearly as:
T (y) − Tsat = ∆Tw(1 −
y δt
) (1.5)
Defined Rcas the cavity radius and hb as the bubble’s height(yb in the picture), he assumed
Rb = f1Rc
and hb = f2Rc
where f1 and f2 are two factors function of contact angle very close to one. Equating1.5
with 1.3 for y = hb, we obtain:
Critical active cavity radius Rc,crit =
4σTsat
f1ρghlg∆Tw
Observing the figure, we obtain this value when the two curves of ∆Tw and boundary
temperature are tangent. Increasing the heat flux, we find two points of intersection, which means the minimum and the maximum value of Rc, so they identify the range of
active nucleation sites.
We can also derive a new relation between boundary thickness and ∆Tnucl; so, fixed δt,
we can evaluate the minimum superheat in order to have active nucleation sites:
∆Tnucl,crit=
8σTsat
ρghlgδt
(1.7)
Hsu’s theory is not the perfect theory about nucleation, but underlines some main
fea-Figure 1.8: Hsu’s Diagram Rc vs ∆Tw for saturated water at atmospheric pressure, fixed
δt (Picture by [8])
tures:
• A minimum value of surface superheat is necessary to start boiling • Very large cavities are useless as very small ones
• the more the wall superheat, the more active nucleation sites
Other theories were developed during years (Benjamin and Balakhrisnan, Klausner ecc..) in order to correlate active sites with roughness or fluid and wall properties.
1.2.3
Bubble growth
The bubble growth process can be distinct basically in two process:
1. Inertia-controlled: it occurs in the initial stage; the heat transfer is very rapid through the microlayer between bubble and hot surface, and the growth is limited by how fast the bubble can push back the surrounding liquid
Rayleigh-Plesset Equation (pg− p∞)/ρl = Rb d2R b dt2 + 3 2 dRb dt 2 + 2σ ρlRb +4vl Rb dRb dt (1.8) Neglecting surface tension and viscosity, and comparing the overpressure with Clausius-Clapeyron equation, we have:
Rb(t) = t s 2 3 ρghlg[Tb − Tsat(p∞)] ρlTsat(p∞) (1.9)
where T∞ and p∞ are temperature and pressure of the Bulk Liquid(the liquid far from
the hot surface) and Tb is the temperature inside the bubble, i.e. Tsat(pg). We can easily
note that the radius increases linearly with time t and (obviously) the volume of the bubble increases as t3.
As growth continues, pressure an liquid inertia forces become smaller, surface tension tends to pull the bubble into a more spherical shape and the process becomes heat transfer-controlled. The process is ruled by Fourier’s Equation, considering the thermal energy balance of the bubble (heat flux at wall = evaporated fluid)[10]; solution has been found by Scriven-Plesset(1959) and Zwick(1954).
Rb(t) = s 12 π kTt ρlcp,l J a (1.10) where: kT: thermal conductivity
cp,l: liquid specific heat
J a: Jakob Number
J a = ρlcp,l[T∞− Tsat] ρghlg
As we can see, in heat flux-controlled process Rb increases as t0.5.
In literature, many expressions of Rb(t) are discussed; in particular, we mention
Mi-kic(1970), who combined 1.9 and 1.10 in a single equation and Van Stralen(1975), who developed a more complex model that takes into consideration both contributes of evap-oration and relaxation microlayer. More recently, many numerical approaches have been presented (e.g Dhir, Stephan, Fujita).
Another important aspect of bubble growing is bubble shape; it lets us know mechanical forces on bubble interfaces. In order to estimate it, we have to consider mass and momen-tum balance on a generic liquid-vapor interface of curvature k (expressions are available in [10] or [40]).
Combining them, after some math calculations, we obtain the local equilibrium:
m00(vl− vg) = n(pl− pg) + n(Sd,l− Sd,g) − ∇sσ − 2σnk (1.11)
where:
Sd: Stress tensor in fluids
∇sσ: Marangoni contributes
It is important to underline that 2.7 includes static and dynamic actions, and is ab-solutely general.
In static conditions and neglecting viscosity, mass transfer and Marangoni contributes,
2.7 along normal direction n becomes:
(pl− pg) = 2σk (1.12)
(This is the classical Laplace Shell Equation). Taking into consideration Stevin Law:
pl(y) = pl(0) + ρlgy
pg(y) = pg(0) + ρggy
where y=0 refers to bubble apex. Finally, considering that in the apex ?? is
pl(0) − pg(0) =
2σ Rb(0)
due to axialsymmetry, we obtain: Bubble Shape Equation
σ(k1+ k2) =
2σ Rb(0)
− (ρl− ρg)gy (1.13)
In Eq.1.13, only hydraulic head is responsible of deviation of the bubble from spherical shape: in fact, in the absence of external force fields, bubbles grow as perfect spheres in microgravity[40].
1.2.4
Bubble detachment
For what concern the last mechanism of bubble development, we have now to calculate the momentum balance in a control volume surrounding the bubble; neglecting dynamical and mass transfer, integration gives a balance of buoyancy, excess of internal pressure and surface tension at bubble neck[10]:
Vb(ρl− ρg)g +
πD2 b
4 (ρg− ρlghb) = πDbσ sin θ (1.14) Actually, other forces act in this process, someone quite difficult to estimate or don’t play a leading role:
Figure 1.9: Bubble equilibrium (Picture from [3])
• Liquid Inertia
• Marangoni convection • Drag
• Vapor recoil
• Lift of preceeding bubble
There are many models for estimate detachment bubble diameter that takes into account more forces contributes and consider more or less one force rather than another; more details are presented in [5] or [10]. Anyway, bubble detachment occurs when force balance is no longer possible.
One of the most famous formula was obtained by Fritz in 1935, equating surface tension at bubble neck with buoyancy[11]:
Fritz Detachment Diameter
Dd= Cbθ
r σ
(ρl− ρg)g (1.15)
Cb is a constant, usually taken as 0.0208;
q σ
(ρl−ρg)g is usually known as Laplace lenght or Capillary lenght lL and it appears
in many expressions concerning pool boiling.
Observing 1.15, we can notice that gravity plays an important role (Dd ≈ Kg−0.5) and
above all doesn’t allow detachment if gravity field is equal to zero. This last implication doesn’t agree with many pool boiling experiments performed in microgravity; so, some empirical correlations were developed, most of them based on this relation:
Dd Dd,1g = g gground −m
In Figure 1.10 some experimental results in variable gravity are shown: it can be noted that experimental values of m are generally around 0.5 for vapor bubbles detaching from a boiling surface and gravity acceleration larger than 0.07 gE; a comparison with some correlations from literature is also shown. On the contrary, for bubbles detaching from orifices, where the contact line is pinned to the orifice rim, the values are smaller, around 0.35.
Another important aspect of detachment is the departure frequency. Paying attention
Figure 1.10: Experimental results for detaching diameter for different values of gravity field(Picture by [10])
at Figure1.11, it can be calculated as:
fb =
1
tgr+ twait (1.16)
where:
tgr: Bubble Growth Time: it can be obtained by calculating Ddusing1.15 and solving for
time t Rayleigh-Plesset equation(1.8).
twait: Waiting Time: time necessary for rewetting the hot surface with cooler fluid from
bulk and reheating it.
In 1971, Malenkov proposed another formula in order to calculate bubble frequency:
fb = 1 πDd 1 + q 00 ρghlgw ! w , w = s Ddg 2 + 2σ Ddρl (1.17)
Looking at this equation, we are able to make some conclusions: • if Dd is large, fbD 1/2 d ≈ constant ≈ g 1/2 • if Dd is small, fbD 3/2 d ≈ constant
• if Dd is in a intermediate region, fbDd ≈ constant; in particular, fb decrease in
microgravity, fixed Dd
Known fb and Dd, it is easy to calculate the volumetric flow rate per unit area (Volume x
frequency x nucleation site density), and hence latent heat transport. However, Malenkov theory doesn’t concern the effects of neighboring bubbles and the subcooling degree.
Figure 1.11: Bubble detaching mechanism (Picture by [5])
1.3
Nucleate Boiling
We are going to talk about the main mechanism of pool boiling heat transfer; it refers to the second region of Nukiyama Curve. This process is still unresolved, because of the difficulty in predicting nucleation site density, thermal boundary layer, interactions between neighboring boiling sites and bubbles; however, some correlations have been proposed, based on experimental data, in order to predict this particular regime.
1.3.1
Heat transfer contributes
During this process, three main contributes of heat transfer are present:
1. Single phase convection/Bubble agitation: the motion of growing and departing bub-bles agitates the fluid, transforming natural convection into a localized forced con-vection
2. Boundary layer stripping/Enhanced convection: departing bubbles remove part of the boundary layer and bring "cooler liquid" to the hot surface in order to cool the wall. 3. Evaporation: Heat is conducted into the thermal boundary layer and then to the
bubble interface, where is converted to latent heat [5]
The first two mechanisms refer to the so called sensible heat and contrary to first evidence, it may be dominant, as shown in Figure1.12in the first sub regime; but at high flux (Slug regime) latent heat contribution begins to increase.
Figure 1.12: DX: Heat transfer contributes behavoiur; SX: heat transfer contributes (Pic-ture by Khalik,1983)
1.3.2
Rohsenow Correlation
First experiments on pool boiling revealed that: q00 ∝ ∆Ta wn
b (1.18)
where n is the nucleation site density, and a e b are specific coefficients approximately equal to 1.2 and 1.3. This empirical relation is the basis for every correlation explained below.
In 1952 Rohsenow assumed the boiling process is dominated by bubble agitation; so nucleate boiling was quite similar to standard single-phase forced convection [13][5].
N u = CRexP ry
In pool boiling, these three adimensional number have this form:
N ub = hcDd kT = q 00 ∆TwkT CbθlL (1.19)
obtained substituting1.15 in Dd and hc= q00/∆Tw.
Reb = ρgvDd µl = CbθlLq 00 µlhlg (1.20) obtained defining v = q00
ρghlg as vapor superficial velocity.
P r = cp,lµl kT
s: 1 for water, 1.7 for other fluids
Csf = Cbθ/C: empirical coefficient depends on surface-fluid coupling, geometry and
sur-face finish. Some values are visible in [2],[14],[4]; there are all between 0.002 and 0.02. Rohsenow correlation(which results can be visible in Figure1.13) doesn’t distinguish the two sub-regimes of Nucleate boiling, and it is not very accurate because it has nothing to say about nucleation site density.
Figure 1.13: Rohsenow correlation applied to data for water boiling on 0.61mm diameter platinum wire(Picture by [2])
1.3.3
Other Correlations
Cooper[5][10] hc= Cc p pcrit !0.12−0.091 ln (Rp0Rp) −0.4343 ln p pcrit −0.55 M−0.5q000.67 (1.23) where:Rp: surface roughness
Rp0: 1µm
M: molecular weight of the fluid
VDI 2010[32][10]
This recent correlation correctly predicts the trend of hc vs q00; it permits to estimate the
heat transfer coefficient with three non-dimensional factors: hc hc0 = FwFqFp (1.24) Fw = Rp Rp,Cu 2/15 (k Tρcp)w (kTρcp)Cu 0.25 Fp = 0.7p0.2rid+ 4prid+ 1.4prid 1 − prid , prid = p pcrit Fq = q00 q000 0.9−0.3p0.15rid
and hc0 and q000can be evaluated with experimental reference datas or correlations
pro-vided. For specific expressions and values of coefficients refers to [32]
More recent correlations are available in literature, most of all based on many experi-mental data. For all the relations, q00 is proportional to ∆Tm
w with m ≈3-4 and they have
better ability in predicting T rather than q00. Currently, mechanistic models of boiling still
have empirical parameters inside (mainly due to surface properties, bubble detachment frequency and most of all nucleation sites) and we are still far from model fully based on first principles.
1.3.4
Single bubbles-Slugs transition correlation
All the expressions analyzed before don’t concern the transition between the two sub-regimes of the nucleate boiling explained in section 1.1.
According to Moissis and Berenson[15], the transition is located at
qtr00 = 0.11ρghlgθ0.5
σg ρl− ρg
!0.25
(1.25)
1.4
Critical Heat Flux
The most important aspect of the boiling process is the boiling crisis. It occurs when the surfaces of the heater is suddenly blanketed by a continuous layer of vapor. Several theories have been proposed for CHF: the basic idea is that at high vapor flow rates liquid is prevented to reach and rewet the heated surface; the most famous classical theories are: 1. Hydrodynamic theory: First shown by Zuber in 1958, it proposes that the rising bubble coalesce into slugs and jets, which become unstable due to fluid instabilities and collapse as the vapor rate is increased.
1.4.1
Hydrodynamic model of CHF
In order to understand hydrodynamic mechanisms involving the boiling crisis, we must contend with the unstable configuration of a liquid on top of a vapor.
In two-phase fluid the heavy one collapses at one node of a wave and the light one rises into the other node; this process is called Taylor instability and the Taylor Wavelength λd is the length of the wave that grows fastest and therefore predominates during the
collapse of an infinite plane horizontal interface[2].
Bellman, Pennington and Sernas, using the adimensional analysis, derived the relation
Figure 1.14: The array of vapor jets as seen on an infinite horizontal heater surface, as predicted by Taylor theory (Picture by [2])
that ties λd and Laplace length:
λd
lL
= (
2π√3, for one-dimensional waves
2π√6, for two-dimensional waves (1.26) This behaviour is better shown in Figure1.14.
Another important mechanism is the Helmholtz instability(shown in Figure 1.15): this phenomenon causes the vapor jets to cave in when the vapor velocity in them reaches a critical value[2]; so we have high pressure zones where velocity is law, and low pressure where velocity is high, i.e a wave with wavelength λh.
Considering the fact that there’s surface tension in jet walls, which tends to balance the flow-induced pressure forces that bring about collapse, velocity critic value has been
evaluated[16]: ug = s 2πσ ρgλh (1.27)
Keeping in mind hydrodynamic behaviour of the fluid, a non-dimensional analysis
(Buck-Figure 1.15: Helmholtz instability of vapor jets (Picture by [2])
ingham Theorem) was performed in order to estimate the maximum heat flux value. Ku-tateladze in 1948[18] and Zuber in 1958[17] obtained almost the same correlation; so we are going to speak about the Zuber-Kutateladze CHF Correlation:
Zuber-Kutateladze Correlation
qCHF00 = Kρ0.5g hlg[σg(ρl− ρg)]0.25 (1.28)
where:
• KZuber = 0.1309
• KKutateladze = 0.16
According to their experiments results, K values are in a range of 0.119-0.157(27% range).
Taking into account energy balance between the heat flux carried away from the heated surface and the latent heat for saturating liquid, we can write:
q00 = ρghlgug
Aj
Ah
Aj is the cross-sectional area of a jet and Ah is the area of the square portion of the heater
that feeds the jet.
So, for any heater configuration, two things must be determined: the square ratio Aj/Ah
Another important CHF correlations was proposed by Griffith and Rohsenow in 1956[25]: they postulated that increased packing of the heating surface with bubbles at higher heat fluxes inhibited the flow of liquid to the heating surface; plotting their experimental re-sults, they obtained the following expression:
Griffith Correlation qCHF00 = CGrhlgρg g gs 0.25 ρ l− ρg ρg 0.6 (1.30)
where CGr = 0.0068m/sand gs is the standard gravity acceleration on ground.
These three expressions are acceptable provided that the heater size is larger than Laplace length. For small heaters, a new dimensionless parameter must be added; according to Lienhard and Dhir[21], this parameter is taken as:
L0 =√Bo = L
lL (1.31)
where Bo is the Bond Number, which is used to compare buoyant force with capillary force and L is a characteristic length of the heater(diameter,heigth,length ecc..). Consequently, predictions and correlations of q00
CHF have been made for several finite geometries in the
form:
q00CHF q00
CHF,Zuber
= f (L0)
Values of f(L0)are available in plots and tables shown in Figure1.16, with a claimed
accu-racy of ±20%(which is very little more than the inherent scatter of q00
CHF data. However,
they are subject to some restrictions: 1. Bulk liquid must be saturated 2. There are not surface imperfections 3. There isn’t forced convection
4. if L0 < 0.15the process becomes completely dominated by capillary force and
Taylor-Helmholtz instabilities; the boiling curve becomes monotonic and we reach imme-diately film boiling.
Figure 1.16: CHF for different geometries; correction factors by [21] (Picture by [2])
1.4.2
Macrolayer and Hot spot theories
This model was originally proposed by Katto and Haramura[22]: they supposed that in proximity of CHF the heated surface is wet by tiny liquid film of thickness δM, called
per-qCHF00 = hlgρ0.5g [σg(ρl− ρg)]0.25α 5/8 M π4 211· 32 161 (1 − αM) 5 16 ρl ρg + 1 / 11 16 ρl ρg + 1 35165 (1.32) Obviously, the key paramters are δM and αM: setting these properly, it is possible to have
similar results with the classical correlation of Zuber-Kutateladze; many assumptions have been done during years; for example[22], δM = λH/4and αM = 0.058(
ρg
ρl)
1/5 (which ones
were used in1.32), but the postulated values are often in disagreement with measurements. A different approach about macrolayer theory is the analysis of the so called dry spots,
Figure 1.17: Macrolayer theory by Katto
formed under the bubbles: many researhers obsverved[37] that these hot spot spread and envelop the entire heated surface, forming the vapor film. Most of the evaporation into vapor occurs from the vapor-liquid interface near the heater surface (in accordance with microlayer theory of the classic theory); this evaporation results in the motion of the interface away from the centre of the dry spot, becuase of mass and momentum conservation.[37]. During nucleate boiling bulk liquid is able to rewet the surface thanks to gravitational and capillary forces, while near the crisis the surrounding liquid is unable to wet the dry spot because of a competition with high rates of evaporation precipitated by elevated temperatures inside the dry spot.
1.4.3
Short considerations about CHF theories
• Surface properties don’t play a role int the hydrodynamic theory, but keeping in mind that thermal conductance and capacitance influence the local
ther-Figure 1.18: Schematic drawing of a dry spot forming on the surface;in the diagram and in the optical/infrared visualization by Dhillon[37], we can notice the trend of the temperature in the centre of the spot: at the beginning, there’s a little drop due to evaporation of the liquid inside, and then it rises until the collapse.
mal transient in the wall. In the last few years, many models were developed that take into account surface roughness and (expecially) surface contact angle; exper-iments by Kandlikar cofirmed that CHF increases with lower contact angle. For more details, refer to [26].
• The void fraction αM decreases in proximity of the surface. Conversely, a region of
constant void fraction is predicted if the flow pattern is as depicted by the hydro-dynamic theory[10]
• Researchers use to debate about the coexistence of more different mechanisms during the boiling crisis; according to many of them, however, the hydrodynamic limit is the main one.
any other pool boiling regime[24]. Transition boiling can be modeled as the superposition of heat transfer to liquid and to vapor, corrected by weight factors[27]:
q00 = Ftrql00+ (1 − Ftr)qg00 Where: Ftr = exp −2.2 ∆Tw ∆Tw(CHF ) + 2
Heat flow contributes q00
l and q 00
g can be evaluated by a sort of linear interpolation with
experimental data of CHF and Minimum heat flux[5]. Some experiment performed by Witte and Lienhard[28] have identified two sub-regions, one ruled by nucleation, the other one by film boiling, often connected by abrupt jumps.
Regarding the Minimum heat flux q00
min, Zuber[17] and later Berenson[24] provided a
Figure 1.19: Influence of surface condition on transition boiling; experimental data by Berenson[24]
prediction, assuming that as ∆T is reduced in the film boiling regime, the rate of vapor generation eventually becomes too small to sustain Taylor’s wave action that characterizes film boiling[2]. For flat horizontal heaters, Zuber proposes:
qmin00 = Cminρghlg
σg(ρl− ρg)
(ρl+ ρg)2
!0.25
Cmin = 0.09
The problem with this expression is that some contact frequently occurs with liquid and heated surface; when it happens, boiling curve deviates above film boiling curve and finds an higher minimum than that reported above.[2]
1.5.2
Film Boiling
In film boiling, a stable layer of vapor covers the heater surface and the interface oscillates with Taylor wavelength, giving origin to bubbles detaching regularly. Since film boiling can be easily compared with film condensation, Bromley in 1950 proposed a correlation for horizontal cylinders in order to estimate Nusselt number[29]:
N u = 0.62 GrP r Sp !0.25 = 0.62 " (ρl− ρg)gh0lgD3 υgkT ,g(Tw− Tsat) #0.25 (1.34) h0lg = hlg[1 + (0.968 − 0.163/P r)J a] where:
υg: kinematic viscosity of gas.
D: tube diameter
The second expression was proposed by Sadasivan and Lienhard[30].
All the liquid and vapor properties should be evaluated at the Film Temperature, i.e Tf = (Tw+ T∞)/2.
Several models , all based on Bromley works, were presented over the years, in order to predict film boiling coefficient for other heater’s geometries(e.g Sakurai, Westwater, Chang), but the comparison of the predictions of all these models evdences big discrep-ances. The preceeding expressions take into account only the convective heat flux, but
Figure 1.20: Di Marco et al.(2004) results for film boiling; fluid:FC72, saturated, p=115kPa, D=0.2mm
All these consideration of film boiling are based on the analogy with film condensation; this hypothesis failed in some occasions, such as vertical surface and small curved bodies; for these cases, some corrections must be included.
Critical Heat Flux Enhancement
The main purpose of this work is to investigate the mechanisms that lead to the boiling crisis, but also to explore and identify ways to enhance it. Many works have been presented that focus on active or passive techniques; in particular, after a brief analysis of the effects of the main parameters, we are going to discuss two relevant enhancement factors:
1. Electric Fields (Active technique)
2. Microstructured Surfaces (Passive technique)
In addition to this, space applications require the understanding of the behaviour of these phenomena in micro and hyper gravity, and how gravity field, electric forces and micro textures interact each other.
2.1
Parametric effects in boiling
2.1.1
Pressure
It is well-known that nucleate boiling heat transfer coefficient improves with pres-sure. Many correlations that take into account system pressure were already submitted in paragraph1.3.3(see equation1.24); a typical trend on heat transfer coefficient function of reduced pressure is shown in Figure2.1
2.1.2
Liquid Subcooling
One of the most important parameter in pool boiling is subcooling. Working with a T∞< Tsat considerably modifies Nukiyama Curve, as it shows in Figure 2.2. The
modifi-cation of natural convection is mainly due to the increase of ∆Tw ( in laminar convection
∆T1.25, in turbulent ∆T1.33); the effects in nucleate boiling are almost inexistent. How-ever, CHF and Minimum Heat Flux are strongly increased by subcooling; Ivey and Morris also proposed a simply correlation in order to estimate the value of this en-hancement:
Ivey-Morris Subcooling factor qCHF,sub00 q00CHF,sat = 1 + 0.1J a ρl ρg 0.75 (2.1) 40
Figure 2.1: Effects of pressure in nucleate boiling: enhancement of normalized heat trans-fer coefficient versus reduced pressure(Picture by [32])
Figure 2.2: The influence of subcooling on the boiling curve (Picture by [2])
Concerning Transition boiling, the effects are not well documented, but it is expected to have an increase too; film boiling enhances rather strongly, especially at lower heat fluxes. Many experiments confirm these behaviours in subcooled fluids[35][36]; in particular, ob-serving Figure2.3, we can easily assume that subcooling has no effects in nucleate boiling (heat transfer coefficient doesn’t change with ∆Tsub).
Figure 2.3: ARIEL results in 1g: no influences of subcooling in boiling heat transfer coefficient (Picture by [35])
2.1.3
Dissolved Gas
Highly wetting dielectric fluids present a vary high gas solubility; so, the presence of incon-densable gas could result in decrease of saturation temperature, called gassy subcooling: when a saturated fluid is in equilibrium with vapor and gas, we have
pT OT = pvap+ pgas, pgas = Cg/H(T )
Tl = Tsat(pvap) < Tsat
where
Cg: gas concentration
H(T ): Henry’s constant
Many experiments1 have highlighted that:
• The overshoot at the Onset of Boiling is reduced at high dissolved gas content • Nucleate boiling is enhanced
• CHF is increased in accordance with Ivey-Morris subcooling correlation
2.1.4
Surface properties
As we observed in the previous chapter (see paragraph1.5.1), surface characteristics play a crucial role. In particular, contamination influences q00
min and it doesn’t take part in
nucleate boiling (see Figure 1.19), while roughness promotes nucleate boiling and
1We have to consider the fact that as boiling progresses, dissolved gas are eliminated and this might
Unlike the expectations, qCHF is less sensitive to surface finishing, while it
de-creases with aging; this last sentence is not easy to justify and it’s thought to be due to physicochemical changes of the surface induced by deposition of inert matter and chemical reactions with the liquid[10].
It is important to underline that film boiling is not affected by this parameter because liquid is no longer in contact with the surface.
Figure 2.4: The influence of roughness on the boiling curve (Picture by [2])
2.1.5
Heater features
It is well-known that heater structural properties severely affect pool boiling. Of course, the most important features are size and geometries, on which we have already dis-cussed in paragraph 1.4.1).
Another important aspect is thickness: boiling crisis occurs first on thin heater, approaching an asymptotic value when thickness is tenths of a millimeter; many studies (Choen and McNeil, Carvalho and Berges, Guglielmini) have observed that this behaviour is ruled by the thermal effusivity of the heated surface.
others have underlined that pool boiling is improved only in isolated bubble regime; this particular behaviour is thought to be due to bubble sliding, i.e. bubbles adhere to the surface and sweep it, improving disruption of the boundary layer and evaporation in the liquid film.
Figure 2.5: The influence of orientation in nucleate boiling: the enhancement is only in isolated regime,i.e. for low fluxes (Picture by [33])
In the end, cooling system applications also take into account the role of the fluid con-finement2: very recent works[31] found out that increasing the confinement, at low wall superheat pool boiling improves, whereas at high one it slightly decreases (see Figure2.6), as vapor escape and fresh liquid supply are impaired. However, confinement always deteriorates CHF: exstimating confinement with Bond number, it was observed that his damaging effects on q00
CHF decline for Bo > 4.
2.1.6
Gravity
One of the most important parameter in boiling is the gravity field: in fact, gravity influences most of the pool boiling correlations described so far. It’s easy to notice that all of these expressions (from Zuber 1.28 to Lienhard 1.29) predict q00
CHF = 0 for g = 0,
contrary to experimental evidences; therefore, many studies propose simple corrections, all of them related to heat transfer coefficient as:
hc hc,1g = g gground m (2.2) m = −0.4 ÷ −0.5
This correction-factor is very similar to the correction of bubble detaching diameter shown in paragraph1.2.4: in fact, reduction of gravity field strongly modifies boiling mechanisms, depending on liquid subcooling:
Figure 2.6: The influence of confinement in boiling curve (Picture by [31])
• Saturated liquid: a large bubble forms by coalescence, engulfing all the others until it detaches; during this process, liquid is supplied from lateral sides of the slug. Some-times bubble is not able to detached and CHF (or dryout) unpredictably occurs. • Subcooled liquid: especially if we have high subcooling, attached bubbles expand
and collapse without detachment (a sort of cavitation similar to what happend in pumps)
Completely different behaviour is expected in hyper gravity: bubble detachment is pro-moted, and bubbles are smaller and many nucleation sites are activated compared to standard gravity tests. Observing Figure 2.7, we can see that a sudden heat flux degra-dation takes place below a certain threshold of gravity, associated by a change in flow pattern. This rules out the possibility to adopt a simple scaling criterion like equation
2.2.
Low gravity experiments on plates and wires (parabolic flight and sounding rocket) by Di Marco, Grassi and Kim [35][34][36] have highlighted that:
• Nucleate boiling degrades in microgravity; degradation is showed to be closely linked to the boiling pattern, and in particular to the presence and evolution of the big mass of vapor over the heater, originated by bubble coalescence and due to the fact that bubbles become bigger than in standard gravity. This last sentence is correlated with test results; moreover, wall temperature seems to increase(and so hc decreases) in micro-g and constantly fluctuates.
• Critical heat flux strongly decreases in micro-g. Despite the fact we have few data of boiling crisis in weightlessness, all tests results has shown significant reduction in q00
CHF; in ARIEL tests [35], no sharp CHF transition was identified
Figure 2.7: The influence of gravity in pool boiling: evidence of threshold of gravity due to flow pattern change (Picture by [34])
Fig. 2.8) which coincided with the formation of a stable coalesced bubble over the heater.
Figure 2.8: SX: Nucleate boiling curve on a flat plate 20x20 mm (fluid:FC-72) in normal gravity-diamonds- and microgravity -circles-. DX: Pool boiling curve on a 0.2 mm wire in normal gravity and sounding rocket experiment, 10−4g, fluid: R113, pressure: 1 bar
Figure 2.9: The influence of gravity in bubble shape. (Picture by [3])
Figure 2.10: The influence of gravity in bubble dimensions, observed during 71th Parabolic Flight Campaign. You notice the increase of bubble’s dimensions in microgravity.
2.2
Electric field effects
Pool boiling mechanisms, as we see in previous section, are strongly affected by buoyancy, despite other forces, as capillary ones, come into play.
Weightlessness can result in a drastic reduction of heat transfer coefficient, and so in an anticipated dryout of heating surfaces. The application of an electric field may provide an additional volume force able to replace buoyancy, to reduce the size of detaching bubbles and to lead them away of the surface, restoring efficient heat transfer conditions. The effectiveness of this technique was already demonstrated by several experiments carried out in microgravity[40].
2.2.1
Electric Force in a Continuum
The most generally accepted expression for the volumic electric force has been provided by Landau and Lifšitz in 1984[41]:
fe = ρeE − 0E2 2 ∇R+ 1 20∇(beE 2 ), be = ρ ∂R ∂ρ T (2.3)
where:
be: electrostriction coefficient
ρe: electric charge density[C/m3]
E: electric field[N/C]
0: vacuum dielectric permittivity[F/m]
R: relative dielectric permittivity[F/m]
The first term is the classical Coulomb’s force, and it’s the only one that depends on the sign of the electric field; it is present whenever free charge buildup occurs, and in such cases it generally predominates over the other electrical forces.
The remaining two terms are dielectrophoresis and electrostriction: the first one is a body force due to non-homogeneities of the electric permittivity, whereas the second one is due to non-uniformities in the electric field distribution; however, each of them depend on the magnitude of E2, thus they are independent of the field polarity.
A particular attention deserved by the evaluation of be: for non-polar fluids, it is given
by the Clausius-Mossotti law:
be=
(R− 1)(R+ 2)
3 (2.4)
whereas, for polar fluids, many expressions have been proposed, e.g. Zahn correlation; for more details, refer to [40].
According to continuum mechanics, the volumic force can be reformulated as the diver-gence of a stress tensor; in particular, the expression2.3can be easily related to Maxwell’s Stress Tensor.
fe = divTe
Using this approach allows calculating stress and force only from knowledge of the electric field, so without determining charge density distribution or dealing with discontinuities at liquid-vapor interfaces.[40]
Expression of Te components can be written as:
teik = 0rEiEk−
0E2
2 (R− be)δik (2.5) Taking into account 2.5, electric boundary conditions of the surfaces:
(
0(R,lEn,l− R,gEn,g) = σe
Et,l = Et,g
Considering the fact that be,g ≈ 0 and R,g ≈1, guessing σe = 0 we can write:
fe,n = 0 2[(1 − R,l)(R,lE 2 n,l+ E 2 t,l) + be,lEl2] (2.6) fe,t = 0
2.2.2
Bubble shape and Momentum balance with electric field
Electric field forces have to be taken into account because they play a fundamental role in bubble shape during its growth. The local equilibrium of a curve surface, described in
where:
fe,n = n(Te,l· n Keeping in mind same steps described in paragraph1.2.3, bubble shape
equation becomes:
Bubble Shape Equation with Electric field
σ(k1+ k2) = 2σ Rb(0) + (fe,n− fe,n(0)) + 0be,l 2 (E 2 (0) − E2) − (ρl− ρg)gy (2.9)
This last relation clarifies that electric forces contributes depends on field configuration, i.e. electric field can affect bubble shape: in particular, it stretches bubbles along its direction and reduces top bubble radius.
Accounting for bubble equilibrium 1.14, we have to include another term, i.e. electric
Figure 2.11: The influence of electric field in bubble shape (Picture by [3]) force contribute: Vb(ρl− ρg)g + πDb2 4 (ρg− ρlghb) − πDbσ sin θ − Z S ˆ k · Te,l· ndS − Z A ˆ k · Te,g· ndS = 0 (2.10)
where S and A are the bubble surfaces (refer to Figure1.9).
Observing this last expressions and considering the changing of bubble shape, we can affirm that both internal pressure and surface tension increase due the presence of electric field; however, pressure promotes detachment, while surface forces contrast it. Despite the fact that the resulting electric forces of the bubble shell could promote or contrast the detachment, they are generally weak for an attached bubble, compared to the changes in
internal pressure[40]; so, despite the fact that the resulting electric force is pressing the bubble towards the surface, the increase in internal pressure, due to bubble elongation, always contrasts this trend.
Finally, in the absence of free charge, and in the limiting assumptions outlined later, the net force acting on a gas bubble in a fluid can be expressed as[41]:
Fe = π 6D 3 b R,g− R,l n1R,g+ (1 − n1)R,l 0R,l∇E2 (2.11)
The constant n1, which can be calculated with an elliptic integral related to the
eccen-tricity of the bubble, is equal to 1/3 for a perfect sphere, while n1 > 1/3 for an oblate
ellipsoid.
This last equation has some restrictions:
• Dielectric must be isotropically, linearly and homogeneously polarizable
• Bubbles must be small enough to obtain the amount of polarization by approximat-ing the field as locally uniform.
• Theoretically, a uniform electric field produces no net force on a bubble immersed in it. However, even a small asymmetry in bubble shape or in bubble position within the electrodes is enough to break the symmetry of the field and to generate a net force on the bubble: the presence of bubbles itself may substantially alter the local electric field distribution with respect to the one in the absence of bubbles.
2.2.3
Effects in Nucleate boiling and CHF
Electric field benefits have been proved both theoretically and experimentally.[35][40][3] The application of an electric field creates an additional pressure drop across the bubble interface that alters the bubble shape, as it’s shown in Figure 2.11: increasing applied voltage, bubble’s top radius decreases. For a bubble attached to the wall, the electric pressure promotes an additional contact force, changing the contact angle. Both these effects promote bubble detachment.
This force has generally a little magnitude; however, in the absence of buoyancy it might be an important tool for phase separation.
This analysis on bubble dynamics is strongly linked with the macroscopic effects that electric force has on boiling; in particular, an external electric field:
• moves and spreads bubbles on the heated surface
• increases the number of bubbles by breaking up large bubbles (see Figure2.12) • improves the transitional and minimum film boiling conditions by destabilizing the
blanketing vapor film
• introduces the waves and perturbations at the surface of a boiling liquid, due to the instability of the vapour-liquid interface
These considerations result in an enhancement of hc and qCHF00 : this contribute is
quite high in standard gravity, especially for low fluxes in nucleate boiling region, but in micro-g, at the highest value of the applied electric field, bubbles are easily removed from the surface, and boiling performance are quite similar to terrestrial one;in some instances boiling crisis limits in standard conditions are restored.
Figure 2.12: Electric field effects observed during 71th Parabolic Flight Campaign; effects caught during 0g parabola
Figure 2.13: Electric field effects on boiling curve observed during sounding rockets tests by DiMarco and Grassi in 2002: with EF(DX), without EF(SX) (Picture by [10])
2.3
Microstructured Surfaces effects
2.3.1
General behaviour of microstructured surfaces
A number of methods to modify surfaces for nucleate boiling have been investigated since pool boiling crisis was studied; in fact, many researchers observed that surfaces characteristics could enhance q00
CHF value until almost 4 times. Most famous works regard:
• Roughness • Porosity • Nanofluids
• Surface wettability
Many experiments, especially nanocoating and porosity, confirm a substantial increase of boiling performances and critical heat flux; despite that, physical mechanisms governing
Figure 2.14: Electric field effects on hcin terrestrial and microgravity conditions (ARIEL
results): we can notice that 10 kV-green triangles-restores boiling performance in standard conditions-purple triangles-(Picture by [35])
the phenomenon remain largely unclear. Many recent tests, in particular Dhillon et al. works, have demonstrated that wettability plays a crucial role in enhancing CHF, while roughness is responsible only for nucleate regime; CHF models based on it fail in capturing trends of boiling crisis, since they predict a monotonic increase with roughness which has been experimentally disproved[37][39]. The probable reason of this particular behaviour is related to an observed strong correlation between CHF and the so called wickability, i.e. liquid imbibition in textured surfaces, that is function of fluid and surface properties, as well as geometrical parameters of the textures.
2.3.2
Microtexture imbibition model
In 2015, Dhillon proposed a new model[37] based on the balance between capillary pressure and viscous forces in the presence of micro pillars on a silicon surface.
Taking into account dry spot model previously described in Chapter 1, it is clear that the
Figure 2.15: Unit cell (Picture by [37])
