# Exploratory study on the impact of evaporative liquid droplet on heated walls of the forged die

S Vignesh

Department of Mechatronics, Bannari Amman Institute of Technology,Sathyamangalam, Erode, Tamil Nadu, India - 638401

Dr Pranab Samanta

Surface Engineering and Tribology Division,Central Mechanical Engineering Research Institute (CSIR-CMERI), Durgapur, West Bengal, India - 713209

## Abstract

One of the manufacturing approaches where the metallic parts are pressed with higher level of pressure is hot forging. In order to enhance the flow of metal, the lubricant is provided to the heated dies. The better understanding on heat transfer and film formation will ensure precise control of lubricant spray, which in turn, helps in lessening the level of energy utilization in hot forging. It is essential to investigate the interaction between droplets of liquid based lubricant and surface of die. The concept of drop impingement has projected various explorations by the scientific community over a lot of decades in search of meticulous consideration of interactions related to heat transfer, mass and momentum. The survey related to the solid objects (high temperature) interacting with evaporative liquid droplets has clearly pointed out the scope for theoretical analysis. The research related to droplet evaporation near Leidenfrost point seems to have good scope in many technical applications. Based on the work carried out in the field of evaporation droplet as reported in literature, the scope for theoretical analysis on various types of droplet impact experiments is identified. The theoretical analysis will help us to investigate the process of evaporation on the liquid drop impacting on heated surface at the Leidenfrost point. The experimental and calculated results can be compared for drawing the relationship between evaporation lifetime, diameter & height of droplet, and thickness of vapor film. Also, the maximum value of contact radius can be determined using theoretical analysis. The research articles related to modeling of evaporative liquid droplet impacted on the surface of die, heated to the temperature beyond Leidenfrost point have been studied and the appropriate derivations were practiced. It was useful to theoretically understand the relationship between evaporation lifetime of droplet and surface temperature using experimental & calculated results.

Keywords: hot forging, liquid droplet, leidenfrost temperature, Inada and Yang correlation, Baumeister correlation, heated walls.

## Abbreviations

Abbreviations
 e Thickness of vapour film D Diameter of droplet h Change of thickness of droplet Tn Dimensionless parameter

## INTRODUCTION

The high strength parts are effectively produced through the process of forging which is one of the manufacturing processes where the metal is said to experience huge pressure. The process of hot forging is usually carried out by preheating the metallic work-piece to an appropriate temperature higher than the recrystallization point. In hot forging, the environment in which the work has been carried out can be enhanced by incorporating the concept of lubrication as a significant factor. The billet is said to get forged only after the lubricant being provided to the die. This is mainly for substantial reduction of friction and wears thereby assisting the release of the finished component at the time of forging. Although, there are many types of lubricants suitable for the work, the largely preferred lubricant is graphite [1]. The usual method of spraying it to dies is carried out through nozzles in the form of droplets. The mode in which it is applied plays a vital role as it tends to influence the lubricant wetting on the die. This leads to understanding of the thermal effects on heated walls of the forged die. The better understanding on heat transfer and film formation will ensure precise control of lubricant spray, which in turn, helps in lessening the level of energy utilization in the hot forging process. This is achieved through enrichment of lubricant wetting with the die with substantial decrease in the billet pre-heat temperature.

## LITERATURE REVIEW

M. S. Lin Yang [1] has carried out physio-thermodynamic investigation of lubricant application to hot die surfaces in his Ph.D. dissertation in the year 2005. His research included several novel theoretical approaches to deal with the concept of drop impingement. The research work carried out by Heng Xie et. al. [2] focused more on developing a model for droplet evaporation near Leidenfrost point. The parameters considered in their work were wettability, initial droplet diameter, initial Weber number and solid surface superheat. They were able to develop a connection for determining evaporation lifetime using the theoretical analysis and experimental results. Gangtao Liang et al. [4] reviewed the research related to the drop impact on heated walls. His research was focused on the drop impact in terms of the mechanisms related to heat transfer. The results focused on the impact process and its inconsistencies. Nagai and Nishio [5] carried out a typical research experiment of acetone droplet impact and analyzed the experimental results with the calculated details. L.H. Wachters et. al. [6] conducted a research on the heat transfer from a hot wall to impinging water drops in the spheroidal state. The theoretical analysis was carried out using the expression suggested by S. Inada et. al. [7] for the film boiling heat transfer of saturated drops impinging on a heated surface.

## METHODOLOGY

The notion of drop impingement is said to exhibit abundant engineering benefits. The importance of this fact has spurred various investigations by researchers in search of meticulous consideration of interactions related to heat transfer, mass and momentum. The survey on solid objects (high temperature) interacting with evaporative liquid droplets has clearly pointed out the scope for theoretical analysis thereby analyzing the effect of significant factors along with their influences, and developing appropriate correlation based on the experimental and theoretical models. The research related to droplet evaporation near Leidenfrost point seems to have good scope in many technical applications, such as, process of rewetting in the case of fuel rod in nuclear reactor, heat treating of metallic alloys at the time of spray cooling, and impingement of oil droplets on turbine engines. Whenever a liquid drop tends to impact against a hot solid surface, it tends to remain on its own surface or rebound based on the situation. It tends to boil rapidly and vanishes after a short period of time. But, if the temperature of hot surface is found to be high enough, the drop tends to avoid the contact with the surface.

## Impact scenario of liquid droplet onto a solid surface

When the liquid drop hits or strikes the solid surface (preferably hot) at the Leidenfrost point, it tends to spread on that surface. Once it has reached the maximum diameter, it tends to produce a vapor film below the drop which is stretched [9]. The stretched drop tends to rise and float on the vapor film. This makes the drop to get transformed into a spherical one through the process of recoiling or rebounding.

Process of liquid droplet hitting the hot solid surface

## Concept of droplet evaporation

The concept of liquid droplet evaporation deals with the formation of vapor film which tends to play a crucial role in the process. Initially, the liquid drop hits the hot solid surface and it tends to spread on the solid surface. It has the potential to stretch itself to the maximum reachable diameter [10]. The vapor film is said to form below the stretched drop which helps in lifting the stretched drop during the process of evaporation. It is said to change its shape gradually into a spherical one. Finally, the liquid droplet is said to disappear at the end of evaporation process.

Evaporation of liquid droplet near Leidenfrost point

## Physical phenomenon of Leidenfrost effect

The concept of Leidenfrost effect deals with the temperature of wall at which the droplet’s whole evaporation time on the heated surface is found to be highest. It is found to be an approach, in which an insulating layer gets formed in order to check the rapid boiling of liquid. The liquid has to be available near the surface which is considerably hotter than the boiling point of liquid.

Liquid droplets at a point closer to the hot solid surface
Liquid droplets at a point of insulating vapor layer

## Conceptual relations involved in theoretical modeling of droplet evaporation

The maximum value of droplet radius has been derived in Eqn. No. 01 by Roisman et al. [3] in which a dimensionless parameter was introduced in Eqn. No. 02. It was also insisted that the contact angle cannot be determined in an accurate manner, when the temperature of the surface is found to be very high. Also, the solid surface temperature tend to increase based on the decrease in the contact angle. After the impact of liquid drop on the hot solid surface, there is a sudden fall in the surface temperature. It is observed for a short period of time and the surface temperature has recovered due to the formation of vapor film.

$R_m=\left[\frac{\overline{D_1}}4+\frac{6A\overline D_1^2}8\sqrt{1-\frac{\cos\varnothing}{W_e}}+\frac{\sqrt6}{48A}\sqrt{\frac{W_e}{1-\cos\varnothing}}\right]D_0$

Here,

$A=\frac1{\sqrt[4]6}\left[\frac1{12}+\frac1{W_e}-\frac1{R_e}\frac1{20\overline h_1^3}+\frac3{5{\overline h}_1}-\frac{D_1^21-\cos\varnothing}{4W_e}-\frac{{\overline D}_1{\overline h}_1}{W_e}\right]^{{}^{-1/2}}$

The mass change of the droplet has been defined similar to that of the heat transfer model suggested by Biance et al. [11] which involves thermal conductivity ‘k’, temperature gradient ‘$\mathrm\Delta\mathrm T$/e’, $\mathrm\Delta\mathrm T$= Surface (plate) temperature – Saturated (boiling) temperature, surface area ‘$\mathrm\pi{\mathrm\lambda}^2$’, mass flow rate ‘$\frac{dm}{dt}$’, and latent heat of evaporation ‘L’. The heat or mass brought to liquid per unit time is defined as${Q}{∝}{{\frac{kΔTπ{{λ}^{2}}}{e}}}$.The height of droplet is expressed as h = [m/ρ1π${\mathrm\lambda}^2$]. Heng Xie et. al. [2] developed a dimensionless parameter (T n) by incorporating the influence of the parameters relating to curvature of drop. The curvature of drop is mainly related to the change of thickness of droplet, diameter of droplet, and thickness of vapor film.

The relationship is expressed in terms of the dimensionless parameter as given in Equation No. 03.

$T_n=\frac{{\mathrm\tau}_1e\mathrm ĥ}{\mathrm D_{\mathrm o}^2}$

The equations derived by Heng Xie et. al. [2] was studied and the mathematical relations were understood.

We know that,

h = [m/ρ1πRm2] &$\frac{dm}{dt}{=}{{\frac{kΔTπ{{λ}^{2}}}{eL}}}$

Substituting the values of h and e in Eqn. No. 03, we get

$T_n=\frac{\tau_1}{D_o^2}\frac{k\Delta T}{\frac{dm}{dt}L}\pi\lambda^2\left(\frac m{\rho_1\pi R_m^2}\right)$

Assume,

$\lambda^2=R_m^2$

dm/dt ≈ Q ≈ m

$T_n=\frac{\tau_1}{D_o^2}\frac{k\Delta T}{mL}\pi\lambda^2\left(\frac m{\rho_1\pi\lambda^2}\right)$
$T_n=\frac{{\mathrm\tau}_1k\mathrm\Delta\mathrm T}{\mathrm L{\mathrm\rho}_1\mathrm D_{\mathrm o}^2}$

Let us assume

Tn = C

A1 = $\frac{k\mathrm\Delta\mathrm T}{\mathrm L{\mathrm\rho}_1}$

A2 = $\frac{{\mathrm\rho}_{\mathrm v}g}{\mathrm\eta}$

From the earlier equation, it was clear that

${\mathrm\tau}_1=\frac{T_n\mathrm L{\mathrm\rho}_1\mathrm D_{\mathrm o}^2}{k\mathrm\Delta\mathrm T}$
${\mathrm\tau}_1=\frac{C\mathrm D_{\mathrm o}^2}{A_1}$

We know that,

$\tau_1=\frac{16R_0^\frac94-R_1^\frac94}{9\frac{k\Delta T}{L\rho_1}^{0.75}\frac{\rho_1g}\eta^{0.25}R_m}$
$\frac{CD_o^2}{A_1}=\frac{16R_0^\frac94-R_1^\frac94}{9\frac{k\Delta T}{L\rho_1}^{0.75}\frac{\rho_1g}\eta^{0.25}R_m}$
$\frac9{16}\frac{CD_o^2}{A_1}A_1^{0.75}A_2^{0.25}R_m=R_0^\frac94-R_1^\frac94$
$\frac9{16}\frac{CD_o^2}{A_1^{0.25}}A_2^{0.25}R_m=\frac{D_0}2^\frac94-R_1^\frac94$
$R_1^\frac94=\frac{D_0}2^\frac94-\frac9{16}\frac{CD_o^2}{A_1^{0.25}}A_2^{0.25}R_m$
$R_1^{\frac94\ast\frac59}=\frac{D_0}2^{\frac94\ast\frac59}-\frac9{16}\frac{CD_o^2}{A_1^{0.25}}A_2^{0.25}R_m^\frac59$
${{{R}_{1}}^{\frac{5}{4}}}{=}{{{{\frac{{D}_{0}}{2}}}}^{\frac{9}{4}{*}\frac{5}{9}}}{-}{{{{\frac{9}{16}\frac{C{{D}_{o}^{2}}}{{A}_{1}^{0.25}}{{A}_{2}^{0.25}}{{R}_{m}}}}}^{\frac{5}{9}}}$

Also,

$\tau_2=\frac{24\frac23^\frac13R_1^{1.25}}{5\frac{k\Delta T}{L\rho_1}^{0.75}\frac{4\rho_vg}{3\eta}^{0.25}}$
$\tau_2=\frac{24\frac23^\frac13R_1^{1.25}}{5A_1^{0.75}A_2^{0.25}}$
${\tau }_{2}=\frac{{R}_{1}^{1.25}}{{A}_{1}^{0.75}{A}_{2}^{0.25}}\frac{24\left[{{\left(2/3\right)}^{\left[\frac{1}{3}\right]}}^{1.25}\right]}{5}$
${\tau }_{2}=\frac{{{R}_{1}}^{1.25}}{{A}_{1}^{0.75}{A}_{2}^{0.25}}\frac{24{{\frac{2}{3}}^{\frac{1}{3}}}^{1.25}}{5}$
$\tau_2=\frac{R_1^\frac54}{A_1^{0.75}A_2^{0.25}}\left(3.76\right)$

Substituting (21) in (16), we get,

$\tau_2=3.76\frac{\frac{D_0}2^{\frac94\ast\frac59}-\frac9{16}\frac{CD_o^2}{A_1^{0.25}}A_2^{0.25}R_m^\frac59}{A_1^{0.75}A_2^{0.25}}$
${\tau }_{2}=\frac{3.76{\frac{{D}_{0}}{2}}^{\frac{9}{4}}-\frac{9}{16}C\frac{{R}_{m}{A}_{2}^{0.25}}{{A}_{1}^{0.25}}{{D}_{o}^{2}}^{\frac{5}{9}}}{{A}_{1}^{0.75}{A}_{2}^{0.25}}$
${\tau }_{2}=\frac{3.76{\frac{{D}_{0}}{2}}^{2.25}-\frac{9}{16}C\frac{{R}_{m}{A}_{2}^{0.25}}{{A}_{1}^{0.25}}{{D}_{o}^{2}}^{\frac{5}{9}}}{{A}_{1}^{0.75}{A}_{2}^{0.25}}$

We know that,
${\mathrm\tau=\mathrm\tau}_1+{\mathrm\tau}_2$

${τ}{=}{{\frac{3.76{{{{{{{{\frac{{D}_{0}}{2}}}}^{2.25}}{-}\frac{9}{16}{C}\frac{{{R}_{m}}{{A}_{2}^{0.25}}}{{A}_{1}^{0.25}}{{D}_{o}^{2}}}}}^{\frac{5}{9}}}}{{{{{A}_{1}^{0.75}}{A}}_{2}^{0.25}}}}}{+}{{\frac{C{{D}_{o}^{2}}}{{A}_{1}}}}$

The results determined by Heng Xie et. al. [2] was studied and a clear understanding has been obtained after solving them on our own. Further, it was evident that the analysis carried out by them paves way for research in the theoretical analysis of liquid droplet [8].

## CONCLUSION

The following points have been concluded from the exploratory investigation carried out by us on the concept of drop impingement.

• The precise control of lubricant spray can be ensured by carrying out a detailed analysis on heat transfer and film formation. This also helps in reducing the amount of energy getting utilized during the process of hot forging.
• The investigation on drop impingement is highly essential to know about the interaction between droplets of liquid based lubricant and surface of die.
• There is a huge necessity to carry out an evaporative liquid droplet analysis which are said to impact the solid objects of high temperature.
• The evaporation of droplet occurring near Leidenfrost point seems to have huge technical applications. They are highly beneficial in the process of re-wetting in the case of fuel rods in nuclear reactor and investigation of heat treatment of metallic alloys at the time of spray cooling.

The evaluation of significant factors and their influences can be investigated by clearly pointing out the relationship between evaporation lifetime, diameter & height of droplet, and thickness of vapor film.

## REFERENCES

[1] M. S. Lin Yang, Physio-thermodynamics of lubricant application to hot die surfaces, Ph.D. dissertation, Industrial and Systems Engineering, The Ohio State University, Columbus, Ohio, 2005.

[2] Heng Xie, Zhiwei Zhou, A model for droplet evaporation near Leidenfrost point, International Journal of Heat and Mass Transfer, 50 (2007) 5328–5333.

[3] I. Roisman, R. Rioboo, C. Tropea, Normal impact of a liquid drop on a dry surface: model for spreading and receding, Proceedings of the Royal Society of London. Series A, 458 (2002) 1411–1430.

[4] Gangtao Liang, Issam Mudawar, Review of drop impact on heated walls, International Journal of Heat and Mass Transfer, 106 (2017) 103-126.

[5] N. Nagai, S. Nishio, Leidenfrost temperature on an extremely smooth surface, Exp. Therm. Fluid Sci. 12 (1996) 373–379.

[6] L.H. Wachters, N.A.J. Westerling, The heat transfer from a hot wall to impinging water drops in the spheroidal state, Chem. Eng. Sci. 21 (1966) 1047–1056.

[7] S. Inada, W.J. Yang, Film boiling heat transfer for saturated drops impinging on a heated surface, Int. J. Heat Mass Transfer 37 (1994) 2588–2591.

[8] K.J. Baumeister, T.D. Hamill, G.J. Schoessow, A generalized correlation of vaporization times of drops in film boiling on a film plate, Proceedings of the Third International Heat Transfer Conference vol. 3 (1966) 66–73.

[9] Y. Takata, S. Hidaka, A. Yamashita, H. Yamamoto, Evaporation of water drop on a plasma-irradiated hydrophilic surface, Int. J. Heat Fluid Flow 25 (2004) 320–328.

[10] S. Chandra, C.T. Avedisian, On the collision of a droplet with a solid surface, Proceedings of the Royal Society of London. Series A, 432 (1991) 13–41.

[11] A. L. Biance, C. Clanet, D. Quere, Leidenfrost drops, Physics of Fluids, 15 (2003) 1632-1637.

## ACKNOWLEDGEMENTS

I greatly acknowledge the opportunity provided by Indian Academy of Sciences to get associated with Dr Pranab Samanta, Senior Scientist, Surface Engineering and Tribology Division, CSIR-CMERI, Durgapur, West Bengal. I also deeply thank the support provided by Dr. Biplab Choudhury, Principal Scientist and Dr. Partha Sarathi Banerjee, Senior Principal Scientist, Skill and Innovation Promotion Group, CSIR-CMERI.

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