We perform a systematic study of the thermal shock experienced by the alumina during quenching by cold water droplet impingement with heated surface temperature ranging from 125°C to 475°C for Weber number ≈32. We explore the effect of surface heat transfer mode on the thermal shock experienced by the material. It is found that the variation of residual strength translates into the mode of boiling heat transfer, hence surface heat flux. The material remembers the degree of thermal shock; the heat transfer foot print is embedded in the residual strength. This finding speaks to a possibility of developing a ceramic detector for heat transfer modes in extreme environments. This study finds that superior thermal shock tolerance can be achieved by removing the heat transfer footprint with reduced heat flux. By promoting the film boiling with nano-fractal hydrophobic surface, we achieved superior thermal shock tolerance for alumina substrates. This is a novel approach to reduce thermal shock by controlling the heat transfer with surface modification, different from conventional, yet expensive, method of improving the bulk material properties.

Ceramics has been extensively used in extreme environments due to their high melting points and chemical stability. Poor resistance to thermal shock is one of the major limiting factors of the ceramic material. Most past efforts for improvements of thermal shock tolerance focused on increasing material strength, and material thermal conductivity, which assure structural robustness, and uniform temperature fields of the material thereby reducing thermal stresses, respectively.1–5 As much as the material aspect of thermal shock tolerance is concerned, convective heat transfer is the other critical component for thermal shock tolerance, as it determines non-uniform temperature fields from which thermal stresses originate. The boiling phenomena of liquid drop with a superheated wall in various spray cooling6–8 can be divided into four distinct regimes: single phase convection, nucleate boiling, transition boiling and film boiling9–11 and two critical and limiting points namely critical heat flux (CHF) and Leidenfrost point. However, relatively less attention has been given to the influence of the boiling heat transfer rate on the thermal shock tolerance of a material.12,13 Hence, in this study, we decided to (1) explore the crucial influence of surface heat transfer modes on thermal shock tolerance of ceramic materials by conducting water droplet impingement experiments, and (2) demonstrate the concept of achieving ultra-thermal shock tolerance of materials by controlling surface heat transfer.

Firstly, we explore the effect of heat transfer modes during an impinging droplet on the residual strength of ceramics. The substrate is heated to desired temperature and a droplet of deionized water is allowed to fall under the influence of gravity from the suspended syringe. The impact velocity (vdrop), droplet diameter (ddrop) are kept constant by fixing the height of the suspended needle and gauge of the needle. The initial temperature of the droplet (Tf,i = 30 ± 5°C) is also kept constant while the temperature of the substrate (Tw) is varied. The impact velocity and droplet diameter are measured using high speed video recordings to be 0.95m/s and 2.52mm with standard deviation of 0.0078 and 0.042 respectively. The Weber number (We=ρfvdrop2ddrop/σ where ρfis the density of the liquid) and Reynolds Number (Re = (ρfddropvdrop)/μ where μ is the dynamic viscosity of the liquid) are 32 and 2992 with standard deviation of 0.8 and 59.8 respectively. High speed video camera is used to record the hydrodynamics of the droplet impingement, from which heat transfer modes can be inferred. The schematic of experimental setup is shown in Fig. S1 in the supplementary material. Alumina coupon (32mm x 20mm x 15mm) was used as the substrate. The measured contact angle of as-received alumina was 60°. The residual strength of the material is determined using three-point flexural bending test.

The time evolution of droplet dynamics impinged on to a heated hydrophilic alumina surface at temperature of Tw with impact velocity of 0.95m/s is shown in Fig. 1. For Tw = 125°C, the subcooled droplet reaches saturation temperature on contact with the wall during the spreading of the droplet and then nucleate boiling occurs characterized by the wetted radius being equal to the spreading radius14 and bubbly boiling.15 The droplet spread is almost constant after the initial impact. We also observe similar characteristics of droplet behavior at Tw = 150°C with increase in intensity of bubbly boiling.

FIG. 1.

Hydrodynamic evolution of the droplet impingement at different wall temperatures mentioned on the left with time shown at top for hydrophilic surface (top section) and hydrophobic surface (bottom section).

FIG. 1.

Hydrodynamic evolution of the droplet impingement at different wall temperatures mentioned on the left with time shown at top for hydrophilic surface (top section) and hydrophobic surface (bottom section).

Close modal

For 150°C < Tw< 250°C, we find the first sign of droplet recoil after the initial impact with further increased intensity of the bubbly boiling. Recoil phenomena occurs when the vapor layer formation starts. The contact area during the recoil stage of the droplet decreases faster with increase in wall temperature and eventually the tornado lift-off of the droplet occurs at Tw = 175°C. We observe intermittent outburst upon landing of the droplet. This happens as the film thickness is big and rate of heat transfer is not sufficient for the formation of sustainable vapor film. We know that the number of active nucleation site increases exponentially with increase in surface temperature for smooth surface16–18 and rough surface has much more nucleation sites compared to the smooth surface. So, we see first sign of initial ejection of tiny droplets through the lamella starting at Tw = 225°C known as ‘atomization’. Number and intensity of the initial ejection of the tiny droplets increases with increase in surface temperature due to higher active nucleation sites and increasing rate of formation and growth of the vapor bubbles and decrease in lamella thickness. We also observe the vapor cutback phenomena in which the end of the lamella is lifted off.19,20 At Tw = 250°C, we see the jet ejection at t = 3ms with increase in intensity of atomization as shown in Fig.1. The liftoff of the droplet happens with reduced tornado formation. The intermittent outburst is no longer observed on landing of the droplet. We believe this is the static Leidenfrost point for the surface. The intensity of jet intensity increases with increase in wall temperature until Tw = 300°C shown in Fig. 1 and after this the jet ejection is reduced with increase in atomization. As evident from Fig. 1, we see a drastic change at Tw = 325°C, where the jet ejection is minimized with highest intensity of atomization. We believe, this is the critical heat flux point where we have the largest heat flux.19 With further increase in temperature, the intensity of the atomization decreases and jet ejection is no longer observed as shown in Fig. 1 for Tw = 350°C, 475°C. The recoiling and bouncing of the droplet is more lucid.

The observed heat transfer modes allow us to understand the relative size of thermal stresses for tested specimens. The thermal stress is directly related to the temperature gradient (∇T) seen by the material, which is directly proportional to the surface heat flux as qs=kT. The surface heat flux (qs) is determined by both the heat transfer coefficient (h) and temperature difference between the surface (Tw) and bulk fluid (T), as qs=h(TwT). While we progressively increased Ts with the fixed T in the conducted experiments, h decreased with an appreciable departure from the bubbly boiling mode due to the formation of thicker vapor sublayer with the pronounced Leidenfrost effect. This speaks to the inflected behavior of qs with respect to increasing surface temperature (as shown in the boiling curve) hence the resulting ∇T and thermal stresses.

We use the residual strength of ceramics to explore these ‘heat transfer footprints’ left in the material. The residual strength physically represents materials’ ability to withstand loads after cracks propagated by thermal shock. As higher stresses lead to higher propagated crack densities, the peak thermal stress experienced by ceramics is inversely related to the residual strength. Hence, measuring the residual strength serves as a direct indicator for the materials’ thermal shock tolerance. The variation of residual strength of as-received Alumina with wall temperature is shown in Fig. 2(a). We can see that the residual strength decreases with increase in degree of superheat defined as (ΔTsat=TwTsat) where Tsat is the saturated temperature of the water, and then increases for Tw > 325°C. The early moments of droplet interaction is relevant to peak heat flux that materials experience.20 The inflection point of the residual strength shown by the lowest point of the residual strength curve (② in Fig.2(a)) corresponds to the maximum thermal stress with the highest heat flux. Before the inflection point, pronounced jet heat transfer mode (① in Fig.2(a)), which is evidence of high heat flux, is observed. After the inflection point, appreciable jet or atomization (③ in Fig.2(a)) disappears, demonstrating that the surface heat flux is suppressed with the appreciable formation of vapor sublayer. This match between the residual strength and heat transfer modes demonstrates the heat transfer foot print left on the residual strength of the material. That is, the material remembers the degree of thermal shock; the heat transfer foot print is embedded in the residual strength.

FIG. 2.

(a) Residual strength variation with wall temperature. Strength was normalized with the unquenched strength. The inset figures (left to right) are for Tw = 300°C, 325°C and 350°C at t=3ms, showing the evidence of changes in heat flux shown by variations in jet and atomization (Error bars represent the standard deviation of obtained residual strength); (b) Schematic variation of the residual strength (σresidual) and surface heat flux for pool boiling21 (q) with wall superheat.

FIG. 2.

(a) Residual strength variation with wall temperature. Strength was normalized with the unquenched strength. The inset figures (left to right) are for Tw = 300°C, 325°C and 350°C at t=3ms, showing the evidence of changes in heat flux shown by variations in jet and atomization (Error bars represent the standard deviation of obtained residual strength); (b) Schematic variation of the residual strength (σresidual) and surface heat flux for pool boiling21 (q) with wall superheat.

Close modal

The heat transfer footprint on the residual strength can be further evidenced by the functional similarity between the residual strength and heat flux. We correlated the residual strength of the material with degree of superheat of the substrate by ΔTsatn for different regimes namely nucleate boiling, and transition boiling regime. For the nucleate, and transition boiling regimes, the residual strength behaves ∼ ΔTsat3.04 (R2=0.78), and ∼ΔTsat1.0 (R2=0.8577), respectively. This functional behavior gives the mirror image of the heat flux which is known to behave as ΔTsat3 for the nucleate boiling regime, and ΔTsat1 for the transition boiling regime,21 as illustrated in Fig 2(b). There are regions where the strength does not change (outside of the observable heat transfer footprint regime in Fig. 2(b)). These regions correspond to the case where induced thermal stresses were not big enough to cause crack propagation in the material.

We observe that the heat transfer footprint translates into degree of thermal shock experienced by the material. This implies that superior thermal shock tolerance can be achieved by removing the heat transfer footprint with reduced heat flux. One way of doing this is promoting film boiling. Studies have indicated that the hydrophobic surface promotes film boiling22 due to the fractal nature of the surface containing air pockets. Hence, we coat the surface with Glaco Mirror Coat ‘Zero’ solution containing organic hydrophobidizing agents to reduce surface energy and creating fractal surface structure with self assembly of silica nanoparticles to further enhance the hydrophobicity as evident from Fig. 3(c), (d). Compared to the as-received surface (Fig. 3(a), (b)), wettability of the nano-fractal surface is significantly reduced (θcontact changed from 60o to 145o).

FIG. 3.

(a) (b) The SEM and AFM image of as-received Alumina sample showing absence of fractal structure, respectively. Contact angle is ∼60o; (c) (d) SEM and AFM image of coated samples showing silica nanoparticles of size 40-60nm with fractal structure. Contact angle is ∼145o.

FIG. 3.

(a) (b) The SEM and AFM image of as-received Alumina sample showing absence of fractal structure, respectively. Contact angle is ∼60o; (c) (d) SEM and AFM image of coated samples showing silica nanoparticles of size 40-60nm with fractal structure. Contact angle is ∼145o.

Close modal

The surface-treated Alumina specimen was thermal shocked with an impinged droplet under the identical conditions for the as-received surfaces, and its heat transfer mode was recorded with a high-speed video camera, as shown in Fig. 1. The hydrodynamic analysis of the recorded video reveals that there is no sign of nucleate boiling, jet formation, and atomization as observed in the previous case. We observe elastic bouncing of the drop at all tested temperatures which are obvious signs of film boiling with the reduced Leidenfrost point. Surface heat flux is inversely proportional to the thermal resistance. We observe that the heat flows through the material to the surface, from surface to the vapor layer and vapor layer to the water droplet upon impingement. As per thermal boundary layer analysis shown in supplementary material, one dimensional heat transfer can be assumed. Hence, we can describe the total resistance of the system as resistances connected in series consisting of material resistance (RM), surface resistance (RS), vapor layer resistance (RVL) and resistance inside water droplet (Rf) shown schematically in Fig. S2 in the supplementary material. The controlling resistance will dictate the surface heat flux during the impingement process. While RM is same, RVL depends on thickness of vapor sublayer for both cases. RS is only considered for the hydrophobic specimen due to coating. It is takes into account the areal fraction of non-wetting air pockets and wetted material on the surface. The antiwetting pressure due to capillarity (PC) and wetting pressure during to impingement (PEWH) and droplet spreading (PD) are calculated using model developed by Varanasi et. al.23 to be ≈825kPa, ≈286kPa and ≈0.451kPa respectively. This suggests Cassie Baxter model24 can be used to calculate the areal fraction of wetting and non-wetting area using equation cos θCB = −1 + fM(cos θE + 1) where fM is the areal fraction of the solid in contact with the liquid, θCB and θE are the contact angle of the coated and uncoated sample respectively, fM ≈ 0.1347. So, the areal fraction of the air space on the surface, fv = 1 − fM ≈ 0.8653.

The resistance of the material layer, RM = LM/kM = 2.278 x 10−5(m2K/W) where LM = 0.638x10−3m is the characteristic length given by ratio of volume to surface area and kM is the thermal conductivity of Alumina. The resistance of the surface layer is a composite resistance of air gap and material surface and is given by RS = fV(1/hA) + fM(L/kM) = 0.8652 (m2K/W) where hA ≈ 1W/m2K is the natural convection coefficient25 of air trapped in the surface micro/nanostructure and L = 300nm is the height of the microstructure. The resistance due to convection in water drop RW = 1/(fMhW) = 7.4x10−4m2K/W where hW is the forced convection coefficient of water and is of the order of 10-4 W/m2K.25,26 Vapor layer thickness is of the order of few microns,20,27 thus we calculate the resistance of the vapor layer at vapor thickness of 1μm and 10μm. Vapor Layer resistance is given by RVL=δkV. The maximum vapor layer resistance is calculated to be RVL,max = 4.06 × 10−4m2K/W. Hence, we see that the air gap is the controlling resistance and is at least 2 orders of magnitude higher. In case of hydrophilic surface, controlling resistance is combined effect RVL and RW depending on the development of vapor layer. Therefore, we observed only film boiling mode on hydrophobic surface while all the three modes can be observed for hydrophilic surface resulting in reduced thermal shock for hydrophobic specimen. Similar observation has been found by Vakarelski et al. for hydrophobic surfaces with contact angle greater than 140°.22 

Due to the reduction in surface heat flux, the material is anticipated to experience less thermal shock. Similar to previous case, we perform the 3 point bending test and find that the residual strength remains almost constant with increase of surface temperature within the tested range as shown in Fig. 4(a). The hydrodynamics at t = 3ms and residual strengths at points ①, ② and ③ in Fig.4(a) are similar, which demonstrates removal of heat transfer foot print. Although the surface heat flux increases gradually due to the increased temperature difference between the droplet and the specimen, the residual strength remains constant as the increased qs is not sufficient to cause crack propagation in the material schematically shown in Fig. 4(b).

FIG. 4.

(a) Residual strength variation with wall temperature for hydrophobic surface. Strength was normalized with the unquenched strength. The inset figures (left to right) are for Tw = 125°C, 200°C, and 350°C, showing the evidence of low heat flux by the absence of jet and atomization (Error bars represent the standard deviation of obtained residual strength); (b) Schematic variation of the residual strength(red line) and surface heat flux(black line)22 for hydrophobic surface with wall superheat.

FIG. 4.

(a) Residual strength variation with wall temperature for hydrophobic surface. Strength was normalized with the unquenched strength. The inset figures (left to right) are for Tw = 125°C, 200°C, and 350°C, showing the evidence of low heat flux by the absence of jet and atomization (Error bars represent the standard deviation of obtained residual strength); (b) Schematic variation of the residual strength(red line) and surface heat flux(black line)22 for hydrophobic surface with wall superheat.

Close modal

The demonstrated method may be applicable for applications lower than ∼350oC. This implies a wide range of low pressure applications One of the application is lowering thermal stress of steam turbine blades upon droplet impingement.

We observe notable changes in droplet impingement dynamics and heat transfer mode with increase in surface temperature for hydrophilic specimen characterized by nucleate boiling, jet formation, atomization and elastic bounce while only elastic bounce is observed for hydrophobic surface for all surface temperatures. The mode of surface heat transfer determines the size of thermal stress experienced by the material. The heat transfer footprint embedded into the materials is reflected in the residual strength curve and governs the thermal shock tolerance of the material. This finding speaks to a possibility of developing a ceramic detector for heat transfer modes in extreme environments. By promoting the film boiling with hydrophobic surface, we demonstrated superior thermal shock tolerance can be achieved by thermally insulating the material. This is a novel approach to reduce thermal shock by controlling the heat transfer with surface modification, different from conventional, yet expensive, method of improving the bulk material properties.

See supplementary material for the detailed experimental setup, calculation steps, and video images of droplet impingements.

We thank Prof. Bhaskar Majumdar of New Mexico Tech for lending of his MTS machine and Prof. Mehran Tehrani for lending of Romulus machine to perform the mechanical testing. We thank Dr. Ying-Bing Jiang of University of New Mexico for his guidance to get better SEM images.

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Supplementary Material