The coupling of CFD and heat treatment analyses provides a more robust application of computer modeling to predict the latent heat release, distortion, and residual stresses during the quench hardening process.

Today, powertrain development is driven in the direction of weight reduction by replacing heavier components with low-cost or higher strength alloys for industries such as automotive, aerospace, and process engineering. Accurate prediction and optimization of the heat treatment process of metal parts is important to achieve optimum material properties or to increase the magnitude of surface compressive residual stress from local thermal gradients and solid phase transformation timing during hardening processes, thereby extending component life during operation. Among all other heat treatment techniques, the immersion quenching process has long been identified as one of the most important methods to fulfill the aforementioned requirements. In order to achieve the desirable microstructure and mechanical properties of the metal piece, steel components are heated to an austenitization temperature, followed by immediate submerging into quenching media [1]. The common austenitization and soaking temperature of steel gears is approximately above 900°C. The temperature varies based on the steel grade. During quenching hardening of steel components, the latent heat released during solid phase transformations affects the cooling significantly, which needs to be considered in heat treatment process modeling.

The paper features the results of the Eulerian multi-fluid model implemented within the commercial CFD code AVL Fire coupled with DANTE®, using the Abaqus/Standard finite element solver. The coupled modeling is capable of considering the solid phase transformation kinetics, which affects the microstructure, thermal, and mechanical properties. Phase transformation during quench hardening also involves releasing latent heat, which is considered in this study.

In this paper, a test gear component made of Pyrowear® 53 is simulated, and the modeling results include the entire history of the part response during hardening including heating, carburization, and quenching. The temperature gradients predicted by the presented model reproduce the latent heat release during the phase transformation. It is clear that neglecting the additional heat source would result in very different thermal gradients and consequently very different thermal stresses and surface properties of the treated component.

Theoretical Background and Simulation Setup

The Eulerian multi-fluid model considers each phase as interpenetrating continua coexisting in the flow domain, with interfacial transfer terms accounting for phase interactions where conservation laws apply [2]. The averaged continuity, momentum, energy, and boiling models equations are well-described in works of Srinivasan et al. [3] and Greif et al. [4]. The methodology is applied in an industrial environment as described by Jan et al. [5] and Mulayim Kaynar et al. [6].

The gear geometry is shown in Figure 1. The bore diameter of the gear is 48.35 mm, the tip diameter is 106.25 mm, and the total number of teeth is 41.

Figure 1: (a) CAD model and (b) the dimensions of the gear
Figure 2: (a) computational model and (b) coupled solid domain using DANTE and liquid domain using AVL Fire

Figure 2 shows finite element meshing of the computational model. In this coupled model, the fluid and the solid structure are modeled by different computational codes, and their geometries are shown in Figure 2. It is assumed that all the gear teeth behave the same during quenching, so the gear is modeled using a single tooth with cyclic symmetry boundary conditions.

CFD Simulation Results and Discussion

The modeling results shown in Figure 3 are the volumetric fraction of oil to illustrate the boiling process and the temperature distribution of the solid gear at four different time snapshots during quenching. The results are shown on the planar cut through the fluid domain (top row) and on the surface of the structure. The gear temperature prior to quenching is 915°C.

Figure 3: Oil phase volume fractions and solid gear temperature distributions at four different times during quenching: (a) 1.0 second, (b) 5.0 seconds, (c) 15 seconds, and (d) 25 seconds
Figure 4: Surface point and core point selected to study the cooling history of the gear during quenching

Figure 4 shows two points selected to study the cooling history of the gear during quenching. The surface point is located at the bore surface, and the core point is located at approximately the center of the cross-section.

The thermal properties during quenching are affected by the temperature, as well as the phase transformations because different phases have different thermal properties. The overall thermal properties are calculated from the volume fractions of individual phases and their properties. The cooling history of the part is also significantly affected by the latent heat released due to phase transformation. By turning off the latent heat in the quenching model but still including the phase transformations, the effect of latent heat is shown in Figure 5. The bump in the time-temperature profile after 15-20 seconds represents the latent heat release. Slower cooling is clearly visible (yellow and gray profile), thus affecting the local cooling and overall temperature gradients. Orange and blue curves show the case without latent heat consideration.

Figure 5: Temperature profiles at monitored locations

Thermal and Stress Modeling Using DANTE

Prior to quench hardening, the gear tooth is gas carburized with all other surfaces being copper plated. After carburization, the gear is reheated for hardening. It is important to include the carbon distribution profile in the quench hardening model because the carbon content has a significant effect on the phase transformation kinetics. The carbon distribution profile after carburization is shown in Figure 6.

Figure 6: Carbon distribution after the gas carburization process: (a) overall view and (b) magnified view of the tooth section
Figure 7: Temperature, austenite, and circumferential stress of the gear at 673 seconds during heating

The heating process is modeled by applying a uniform heat transfer coefficient on the gear surface with the furnace temperature at 915°C. Figure 7 shows temperature, austenite, and circumferential stress distributions at 673 seconds during heating. The tooth tip has a higher heating rate, and the austenite transformation occurs earlier at the tip.

Figure 8: Temperature, austenite, and radial displacement at 820 seconds during heating

Figure 8 is a snapshot of the gear at 820 seconds during heating. The austenite distribution clearly shows the effect of carbon on the austenite formation. The growth of the gear due to heating is also shown.

At the end of heating, the gear temperature is 915°C, and it is fully austenitic. The radial growth is 0.431 mm.

Figure 9: Temperature, austenite, and radial displacement at the end of heating (3,600 seconds)

Using the predicted temperature from coupled AVL Fire and DANTE thermal model, the stress model of the quenching process is executed. Figure 10 shows the temperature, martensite, and circumferential stress distributions at 3.7 seconds during quenching. When austenite transforms to martensite, the material volume increases because martensite has a lower density. As shown in Figure 10, the region with martensite forming shows a compression stress, and its neighbor is under tension to balance the stress.

Figure 10: Temperature, martensite, and circumferential stress at 3.7 seconds during quenching
Figure 11: Temperature, martensite, and circumferential stress at the end of quenching

At the end of quenching, the volume fraction of martensite and residual stress in the circumferential direction is shown in Figure 10. Pyrowear 53 has high hardenability, and the austenite transforms only to martensite during quenching. The gear tooth is carburized, and the retained austenite at the gear tooth case is about 12 percent due to the lower Ms and Mf temperatures of the high carbon content of the case.


The applied CFD code AVL Fire is coupled with DANTE to predict the latent heat release, distortion, and residual stresses during the quench hardening process. The latent heating release has a significant effect on the temperature distribution during quenching, which will affect the rate of phase transformation, distribution, and residual stresses of the quenched part. The study shows the possibility of coupling CFD transient analysis with the heat treatment model of a solid part, which is valuable in understanding the cooling uniformity around the part and its effect on the part response during liquid quenching processes.


  1. R. Kopun, R., Greif, D., Zhang, D., Stauder, B., Škerget, L., Hriberšek, L., Advances in Numerical Investigation of immersion Quenching at Different Pool temperatures, SAE Brasil under revision.
  2. AVL List GmbH, Fire® CFD Solver, Eulerian Multi-fluid model. Solver Theory Guide. 2013, Graz, Austria.
  3. Srinivasan, V., Greif, D., Basara, B., On the heat and mass transfer modeling to simulate quenching heat treatment process, 6th International Quenching and Control of Distortion Conference, Chicago (2012).
  4. Greif, D., Kovacic, Z., Srinivasan, V., Wang, D.M., Suffa, M., Coupled numerical analysis of quenching process of internal combustion engine cylinder head, BHM Journal, Vol. 154 (2009).
  5. Jan, J., Prabhu, E., Lasecki, J., Weiss, U., Mulayim Kaynar, A., Eroglu, S., Development and Validation of CFD Methodology to Simulate Water Quench, Proceedings of the ASME 2014 International Manufacturing Science and Engineering Conference.
  6. Mulayim Kaynar, A., Eroglu, S., Weiss, U., Prabhu, E., Jan, J., Lasecki, J., Kopun, R., Greif, D., Experimental and Numerical Investigation of Water Quench Cooling of Aluminum Cylinder Heads, 5th International Conference on Thermal Process Modeling and Computer Simulation, June 16-18, 2014, Florida.
Proceedings of the 28th ASM Heat Treating Society Conference. October 20–22, 2015, Detroit, Michigan. Reprinted with permission of ASM International.
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founder and president of DANTE Solutions Inc., received his Ph.D. in materials engineering from Drexel University. He has over 40 years of industrial experience in thermal and mechanical processing of steel parts and has been a leader in the application of mathematical modeling of heat treatment processes.
works as an analysis engineer at AVL-AST in Maribor, Slovenia. He graduated with a B.Sc. degree in Mechanical Engineering from the University of Maribor in 2010 and continued at the same faculty toward his Ph.D. The area of his doctoral thesis was numerical modeling of the immersion quenching process using an Eulerian multi-fluid modeling approach. As analysis engineer, Kopun is responsible for the product AVL Fire, focusing on the multiphase topics.
works as a support engineer at AVL-AST in Maribor, Slovenia. He graduated with a B.Sc. in 2011 and continued toward his M.Sc. degree at the University of Maribor in 2010, which he completed in 2013. The area of his M.Sc. work was spray bomb multi-component CFD simulation of gasoline fuel. Urbas is responsible for the support and services worldwide for the CFD product AVL Fire, focusing on the multiphase topics.
has been an analysis engineer at AVL-AST in Maribor since 1996. He graduated with a B.Sc. degree in Mechanical Engineering from the University of Maribor, Slovenia, in 1980 and obtained his M.Sc. degree from the same university in 1993. He has more than 20 years of experience in the modeling and simulation of combustion engine structures using the Finite Element Analysis method.
is a principal at DANTE Solutions, Inc. where he focuses on DANTE software applications to the heat treat industry. He is a Ph.D. mechanical engineer from Wright State University. His interests center around process modeling of carburizing and quench hardening of steel parts.
is a product manager at AVL-AST in Maribor, Slovenia. He graduated with a B.Sc. degree in Mechanical Engineering from the University of Washington, Seattle, in 1996 and continued toward his M.Sc. degree at the Montana State University, Bozeman, which he completed in 1998. In 2012, he received his Ph.D. from the University of Maribor, Slovenia. The area of his doctoral thesis was numerical modeling of cavitating flows in high pressure injection equipment accounting for cavitation erosion effects. As product manager, Greif is responsible for the CFD product AVL Fire, focusing on the multiphase topics.