# An Efficient Fluid-Dynamic Analysis to Improve Industrial Quenching Systems

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{s}(martensite start temperature). The specific volume of martensite is ~3.5% higher than the corresponding value of austenite, which may lead to an adverse effect during non-uniform cooling. The internal stresses in the solid that are generated from this phase transformation combine with stresses promoted by thermal gradients, and the result may produce disastrous consequences in terms of distortion and/or crack formation in the product. Furthermore, spot areas where the stable vapor film remained for a long time would probably lead to low spotty hardness as result of an insufficient cooling rate to generate the desired solid-phase transformation.

## 2. Materials and Methods

#### 2.1. Materials Properties

^{®}software data base (Version 9, Sente Software Ltd., Surrey Technology Center, Guildford, UK, 2016) using the chemical composition of steel and an austenitic grain size of ASTM 9. These property values were determined considering the cooling of austenite to form martensite. The leaf springs are quenched at rates of cooling that essentially produce only martensite throughout their whole cross section area. The table shows the density; viscosity; boiling point, T

_{sat}; and temperatures for the start of martensite formation, M

_{s}, and 50% and 90% of martensite formation, M

_{50}and M

_{90}, respectively.

_{s}= 288 °C. Density decreases, while thermal conductivity and heat capacity increase. This later property includes the latent heat of solid-phase transformation from austenite to martensite.

#### 2.2. Plant Temperature Measurements

#### 2.2.1. The Quenching System

#### 2.2.2. Diagnostic Thermal Analysis

#### 2.3. Laboratory Temperature Measurements

_{I}, was corrected for the gravity acceleration, g, because the flow is upward. The expression was obtained from Bernoulli’s equation and is given by,

_{N}is the oil velocity at the exit of the nozzle (=Q/A

_{N}) which depends on the oil flowrate, Q, and the cross section area of the nozzle, A

_{N}; and h is the distance between the nozzle exit and the impact surface.

#### 2.4. Connection between Fluid Flow and Heat Transfer

_{f}, C

_{p}and T

_{f}are fluid magnitudes: density, bulk velocity, heat capacity and bulk temperature, respectively; while q

_{w}, τ

_{w}and T

_{w}are the heat flux, shear stress and temperature at the wall. In this analogy, the shear stress is unrelated to heat transfer, that means it can be computed from isothermal fluid flow. The use of this analogy to approach boiling heat transfer in quenching tanks has not been reported before, at least according with the best knowledge of the authors. In this paper, it is proposed an efficient analysis aimed to elucidate the fluid flow field and the rate of heat flux removed from steel pieces quenched in long standing tanks. The isothermal fluid flow calculations predicted detailed shear stress distributions on the surface of leaf springs, while the analyses of heat fluxes determined from plant and laboratory data were used to propose an empirical equation based on the Reynolds-Colburn analogy.

## 3. Formulation of the Model

#### 3.1. Governing Differential Equations

_{ij}is the Reynolds stress tensor; x is the coordinate position; ρ, μ, and υ are the density, viscosity, and kinematic viscosity of the fluid, respectively; and G is the rate of generation of turbulence kinetic energy due to the mean velocity gradients and is defined together with other quantities in Table 6. The oil properties are included in Table 3.

_{ij}is the Kronecker delta (=0 for i ≠ j) and (=1 for i = j). Turbulence viscosity, μ

_{t}, was determined from the following equation:

_{μ}is not a constant but is a function of the main strain and rotation rates and the angular velocity of the system rotation and the turbulence fields, k and ε [24]. Neither the standard model nor the RNG (ReNormalization Groups) model is realizable. This model has been extensively validated for a wide range of flows [25,26], including rotating homogeneous shear flows, free flows including jets and mixing layers, channel and boundary layer flows, and separated flows. For all these cases, the performance of the model has been found to be substantially better than that of the standard k-ε model. Especially noteworthy is the fact that the realizable model resolves the round-jet anomaly; that is, it predicts the spreading rate for axisymmetric jets and that for planar jets. This is particularly useful in our case to obtain a realistic flow field in the immersed oil jets coming from multiple nozzles.

_{s}= 0, and default roughness constant C

_{s}= 0.5 that had no effect in the computation. These coefficients are defined for the Law-of-the Wall Modified for Roughness [27].

#### 3.2. Solution Method

^{TM}(version 16, ANSYS Inc., Canonsburg, PA, USA, 2015), code. Every subdomain was divided into several regions to reduce skewness, improving mesh quality. The underrelaxation factor was manually changed throughout the solution process to reduce the ‘scaled’ residuals for mass, momentum and turbulence equations [28] to values that were less than 10

^{−3}.

## 4. Results and Discussion

#### 4.1. Laboratory Thermal Analysis

_{j}are equal to 0.1, 0.2, 0.4, 0.2 and 0.1 for j = i − 2, i − 1, i, i + 1 and i + 2, respectively. After 12 smoothing sweeps, the temperature curves did not change appreciably but the cooling rate curves improved substantially, by minimizing their numerical noise. The cooling rate was estimated from the temperature smoothed data using central finite differences and no further smoothing was applied to these curves. Temperature curves for all replicas were smoothed and then they were averaged; a 95% confidence interval was computed based on standard deviation and a t-student distribution. Figure 6 shows the average temperature-time curve together with its 95% confidence interval. The limits (average ± σ) are indicated by the upper and lower curves. These results correspond to an oil impact velocity and temperature of 0.9 m/s and 60 °C, respectively, and with initial steel temperature of 850 °C. The figure shows that temperature decreases very fast until it reaches ~300 °C. This is expected since the oil boiling temperature is 290 °C. Below this temperature, boiling stops and cooling proceeds by one-phase convection. The corresponding cooling rate curves are also shown in the figure. They reach a maximum value at a high temperature. The early shoulder formed before the peak is attributed to a brief film boiling regime. Notice that uncertainty for the cooling rate is larger at temperatures above 700 °C, at which the cooling rate reaches its maximum value.

^{2}at a surface temperature of 500 °C and decreases with this temperature. It is seen in all plots of Figure 8 that heat fluxes are ~100 kW/m

^{2}at a surface temperature of 150 °C. Therefore, the heat flux that may cross through non-active surfaces is negligible.

#### 4.2. Plant versus Laboratory Thermal Analyses

_{s}and M

_{90}, respectively. In the figure, it is seen that plant temperatures barely reach the end of martensite formation after 180 s. In contrast, laboratory temperatures decrease well below their plant counterparts after only 100 s. This is attributed to the oil velocity: In laboratory tests, the oil impact velocity is constant during the whole test; but in plant tests the oil velocity changes depending upon the leaf position in the tank, as it will be shown in the next section. To properly compare the previous results, the corresponding boiling curves were determined using the solution of the IHCP as before. Figure 9b shows the heat flux as a function of the computed surface temperature for all plant measurements and for the lowest and highest oil velocity laboratory cases. The major difference between these results is at high temperatures. The magnitude and dispersion of plant heat fluxes are much larger than the corresponding values for laboratory tests. The center section had maximum heat fluxes as low as 1200 kW/m

^{2}while loose section heat fluxes almost reach 2800 kW/m

^{2}. These results contrast with maximum heat fluxes between 1400 kW/m

^{2}and 1550 kW/m

^{2}obtained in laboratory tests. On the other hand, at surface temperatures below 300 °C the laboratory heat fluxes surpass the corresponding plant values. There is only some heat flux perturbation that was found in thermocouples T

_{4}loose section and T

_{2}fixed section. Analyzing the oil velocity in both systems, laboratory test should have had larger heat fluxes, at least for the impact velocity of 2.0 m/s. In plant, the oil mean velocity at the exit of the nozzles is only 1.67 m/s as it can be estimated from data from Table 4 and recalling that input oil velocity is 0.5 m/s. Once the oil enters the tank its velocity decreases very fast with distance, as it will be shown in the next section. The authors attribute these larger heat flux values to the Taylor wavelength. This concept explains the difference of heat fluxes based on the surface area size of the samples. During the transitional boiling regime (at temperatures above those for maximum heat flux) the hot solid surface is almost blanketed with vapor. The vapor tries to buoy up, and it does in big slugs forming unstable columns or vapor jets that form and collapse intermittently under the liquid pressure. The Taylor instability is the collapse process of these emerging jets and the corresponding Taylor wavelength is the distance between jets that for a one-dimensional wave is given by the following equation [31]:

_{f}= 827 kg/m

^{3}and ρ

_{g}= 4.3 kg/m

^{3}. The Taylor wavelength was calculated as 2.2 cm. This means that the laboratory sample, 2.54 cm diameter, was only 1.2 times larger than λ. We can imagine that there will only be one single vapor jet detaching from the surface. In contrast, the leaf spring was 7.5 cm wide, considering its shortest dimension. This accommodates for more than 3 times the value of λ. Therefore, several vapor jets would be forming in the plant sample, improving heat transfer.

_{a}≤ T ≤ T

_{max},

_{b}≥ T > T

_{max},

_{max}is the temperature at the peak heat flux, q

_{orig}and q

_{corr}are the original and corrected heat fluxes, respectively; T

_{a}and T

_{b}are the lowest and highest temperatures where correction applies. In our case, they were taken as 350 °C and the initial sample temperature, respectively. The exponents ma and mb were both fit equal to 1/3. The proposed empirical equations multiply only the peak heat flux by a factor of 2 and modify the rest of the curve by a smaller factor that decreases in proportion to the temperature difference, |T − T

_{max}|, reminding a level rule. Figure 9c shows the data of Figure 9b but with corrected laboratory heat fluxes. The magnitude of heat flux is now above the corresponding plant values, as it is expected from the low oil velocities in most of the tank. The maxima heat fluxes in plant are shifted towards lower temperatures. This is a result of the observed large initial slopes in the temperature-time curves and their abrupt change just below 400 °C, see Figure 9a. Further research is required to elucidate this behavior.

#### 4.3. Fluid Flow Analysis

#### 4.3.1. Mesh Quality

#### 4.3.2. Choice of Virtual Box Size

#### 4.3.3. Fluid Flow Maps for Original Case

#### 4.3.4. Effect of Oil Flowrate

#### 4.3.5. Effect of Baffles at Carousel Periphery

#### 4.3.6. Effect of Tank Depth

#### 4.3.7. Effect of Nozzle Direction

#### 4.4. Isothermal Fluid Flow and Heat Flux

_{I}, is to displace the heat flux curve as it was shown in Figure 8c, we use the following expression for ${q}_{\mathrm{w}}^{1}$:

_{w}. Of course, the same will be true for q

_{w}. Equation (16) together with Equations (17) and (18) represent a relationship between the computed isothermal wall shear stress and the expected heat flux. Application of this equation to the production tank requires that the laboratory heat flux curve should also be corrected for the Taylor wavelength according with Equation (13).

## 5. Summary and Conclusions

## Acknowledgments

^{TM}.

## Author Contributions

## Conflicts of Interest

## References

- Canale, L.D.C.F.; Totten, G.E. Quenching technology: A selected overview of the current state-of-the-art. Mater. Res.
**2005**, 8, 461–467. [Google Scholar] [CrossRef] - Totten, G.E. Quench Process Sensors. In ASM Handbook; Dossett, J., Totten, G.E., Eds.; ASM International: Materials Park, OH, USA, 2013; pp. 192–197. [Google Scholar]
- Gür, C.H.; Şimşir, C. Simulation of quenching: A review. Mater. Perform. Charact.
**2012**, 1, 1–37. [Google Scholar] [CrossRef] - Totten, G.E.; Bates, C.E.; Clinton, N.A. Handbook of Quenchants and Quenching Technology; ASM International: Materials Park, OH, USA, 1993; pp. 339–411. [Google Scholar]
- Garwood, D.R.; Lucas, J.D.; Wallis, R.A.; Ward, J. Modeling of the flow distribution in an oil quench tank. J. Mater. Eng. Perform.
**1992**, 1, 781–787. [Google Scholar] [CrossRef] - Halva, J.; Volný, J. Modeling the flow in a quench bath. Hut. Listy
**1993**, 48, 30–34. [Google Scholar] - Bogh, N. Quench Tank Agitation Design Using Flow Modeling. In Proceedings of the International Heat Treating Conference: Equipment and Processes, Schaumburg, IL, USA, 18–20 April 1994; Totten, G.E., Wallis, R.A., Eds.; ASM International: Materials Park, OH, USA, 1994; pp. 51–54. [Google Scholar]
- Kernazhitskiy, S.L. Numerical Modeling of a Flow in a Quench Tank. Master’s Thesis, Portland State University, Portland, OR, USA, 2003. [Google Scholar]
- Kumar, A.; Metwally, H.; Paingankar, S.; MacKenzie, D.S. Evaluation of Flow Uniformity around Automotive Pinion Gears during Quenching. In Proceedings of the 5th International Conference on Quenching and Control Distortion at 2007 European Conference on Heat Treatment, Berlin, Germany, 25–27 April 2007; International Federation for Heat Treatment and Surface Engineering: Berlin, Germany, 2007; pp. 1–8. [Google Scholar]
- Romão-Bineli, A.R.; Rocha-Barbosa, M.I.; Luiz-Jardini, A.; Maciel-Filho, R. Simulation to Analyze Two Models of Agitation System in Quench Process. In Proceedings of the 20th European Symposium on Computer Aided Process Engineering, Naples, Italy, 6–9 June 2010; Pierucci, S., Ferraris, G.B., Eds.; Elsevier B.V.: Naples, Italy, 2010; pp. 1–6. [Google Scholar]
- Krause, F.; Schüttenberg, S.; Fritsching, U. Modelling and simulation of flow boiling heat transfer. Int. J. Numer. Methods Heat Fluid Flow
**2010**, 20, 312–331. [Google Scholar] [CrossRef] - Srinivasan, V.; Moon, K.-M.; Greif, D.; Wang, D.; Kim, M.-H. Numerical simulation of immersion quench cooling process using an Eulerian multi-fluid approach. Appl. Therm. Eng.
**2010**, 30, 499–509. [Google Scholar] [CrossRef] - Gao, W.-M.; Fabijanic, D.; Hilditch, T.; Kong, L.-X. Integrated fluid-thermal-structural numerical analysis for the quenching of metallic components. J. Shanghai Jiaotong Univ. Sci.
**2011**, 16, 137–140. [Google Scholar] [CrossRef] - Ricci, M.G.; Santin, G.; Cascariglia, F.; Scimiterna, E.; Parrabbi, A.; Carpinelli, A. Numerical analysis applied to thermal and fluid-dynamic quenching simulation of large high quality forgings. La Metall. Italiana
**2011**, 9, 3–10. [Google Scholar] - El Kosseifi, N. Numerical Simulation of Boiling for Industrial Quenching Processes. Ph.D. Thesis, Paris National School of Mines, Paris, France, 2012. [Google Scholar]
- Ko, D.-H.; Ko, D.-C.; Lim, H.-J.; Kim, B.-M. Application of QFA coupled with CFD analysis to predict the hardness of T6 heat treated A16061 cylinder. J. Mech. Sci. Technol.
**2013**, 27, 2839–2844. [Google Scholar] [CrossRef] - Kopun, R.; Škerget, L.; Hriberšek, M.; Zhang, D.; Edelbauer, W. Numerical investigations of quenching cooling processes for different cast aluminum parts. J. Mech. Eng.
**2014**, 60, 571–580. [Google Scholar] [CrossRef] - Passarella, D.N.; L-Cancelos, R.; Vieitez, I.; Varas, F.; Martín, E.B. Thermo-fluid-dynamics quenching model: Effect on material properties. Blutcher Mech. Eng.
**2012**, 1, 3625–3644. [Google Scholar] - Yang, X.-W.; Zhu, J.-C.; He, D.; Lai, Z.-H.; Nong, Z.-S.; Liu, Y. Optimum design of flow distribution in quenching tank for heat treatment of A357 aluminum alloy large complicated thin-wall workpieces by CFD simulation and ANN approach. Trans. Nonferr. Met. Soc. China
**2013**, 23, 1442–1451. [Google Scholar] [CrossRef] - Banka, A.L.; Ferguson, B.L.; MacKenzie, D.S. Evaluation of flow fields and orientation effects around ring geometries during quenching. J. Mater. Eng. Perform.
**2013**, 22, 1816–1825. [Google Scholar] [CrossRef] - López-García, R.D.; García-Pastor, F.A.; Castro-Román, M.J.; Alfaro-López, E.; Acosta-González, F.A. Effect of immersion routes on the quenching distortion of a long steel component using a finite element model. Trans. Indian Inst. Met.
**2016**, 69, 1645–1656. [Google Scholar] [CrossRef] - Standard Test Methods for Determining Hardenability of Steel; ASTM International: West Conshohocken, PA, USA, 2007; pp. 18–26.
- The Reynolds Analogy. Available online: http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node122.html (accessed on 20 March 2017).
- Ansys Fluent Theory Guide, Release 15.0; ANSYS, Inc.: Canonsburg, PA, USA, 2013; pp. 39–55.
- Shih, T.-H.; Liou, W.W.; Shabbir, A.; Yang, Z.; Zhu, J. A new k-ε eddy-viscosity model for high reynolds number turbulent flows. Comput. Fluids
**1995**, 24, 227–238. [Google Scholar] [CrossRef] - Kim, S.-E.; Choudhury, D.; Patel, B. Computations of Complex Turbulent Flows Using the Commercial Code ANSYS Fluent. In Proceedings of the ICASE/LaRC/AFOSR Symposium on Modeling Complex Turbulent Flows, Hampton, VA, USA, 11–13 August 1997. [Google Scholar]
- Ansys Fluent User’s Guide. Release 12.0; ANSYS, Inc.: Canonsburg, PA, USA, 2009; pp. 7-128–7-130.
- Patankar, S.V. Numerical Heat Transfer and Fluid Flow; CRC Press: Boca Raton, FL, USA, 1980. [Google Scholar]
- Beck, J.V. User’s Manual for CONTA: Program for Calculating Surface Heat Fluxes from Transient Temperatures Inside Solids; Michigan State University: East Lansing, MI, USA, 1983. [Google Scholar]
- Liscic, B.; Tensi, H.M.; Canale, L.C.F.; Totten, G.E. Quenching Theory and Technology, 2nd ed.; CRC Press: Boca Raton, FL, USA, 2011. [Google Scholar]
- Lienhard IV, J.H.; Lienhard V, J.H. A Heat Transfer Textbook, 3rd ed.; Phlogiston Press: Cambridge, MA, USA, 2001; pp. 436–445. [Google Scholar]
- Bradshaw, P.; Love, E.M. The Normal Impingement of a Circular Air Jet on a Flat Surface; Her Majesty’s Stationary Office: London, UK, 1959; pp. 1–8. [Google Scholar]

**Figure 1.**Thermophysical properties of steel DIN 51CrV4 estimated from JMatPro

^{®}software for a cooling rate of 56 °C/s from austenizing to ambient temperature. Notice how properties change abruptly at temperature of martensite start, M

_{s}= 288 °C. Heat capacity considers the solid-phase transformation latent heat.

**Figure 2.**(

**a**) Schematic representation of the oil quenching tank. Carousel is fed with leaf springs at position 9. (

**b**) Sequence for shaping a leaf spring before immersion in the tank.

**Figure 3.**(

**a**) Schematic representation of sectioned leaf spring indicating thermocouple locations in millimeters, and photographs of (

**b**) preheated fixed section being placed in shaper table and (

**c**) loose section being preheated in a muffle.

**Figure 4.**(

**a**) Schematic representation of laboratory oil closed-loop for determination of the rate of heat removal during oil-quenching steel samples; (

**b**) detailed view of the probe that holds a steel disc (marron color) and with sub-superficial thermocouple (black color). Dimensions are in mm.

**Figure 5.**Subdomains and boundary conditions: (

**a**) discretized feeder, (

**b**) discretized tank, and (

**c**) discretized virtual box, all with cut view planes. The footprint of shaper table, downholders and leaf spring is shown.

**Figure 6.**Average thermal evolution and its corresponding cooling rate obtained from oil-quenching laboratory experiments. Impact oil velocity and oil temperature were 0.9 m/s and 60 °C, respectively. A 95% confidence interval is indicated for both curves, temperature and cooling rate.

**Figure 7.**Effect of jet impact velocity on the average thermal evolution and corresponding 95% confidence interval.

**Figure 8.**Boiling curves obtained from laboratory data, effect of: (

**a**) impact jet velocity, (

**b**) oil temperature and (

**c**) initial steel temperature.

**Figure 9.**Comparison of plant and laboratory results: (

**a**) measured temperature evolution, (

**b**) boiling curves and (

**c**) boiling curves with Taylor wavelength correction.

**Figure 10.**Sensitivity analysis in terms of computed percent of total oil flowrate through feeder and tank. The number of used elements is indicated in every point. Refined mesh at feeder inlet and nozzle outlets improved calculations accuracy.

**Figure 11.**(

**a**) Comparison of computed wall shear stress maps on the leaf spring surfaces for the first carousel position, with small, selected, and large virtual boxes. (

**b**) Average wall shear stress per face for three box sizes and (

**c**) average pressure per face for three box sizes. L1 = Leaf 1, L2 = Leaf 2, box size 1 = small, 2 = selected, 3 = large.

**Figure 12.**Computed wall shear stress maps on the leaf spring surfaces for the first carousel position in the original quench system using (

**a**) “cascade” and (

**b**) full system methods. Comparison of wall shear stress cell frequency for (

**c**) first carousel position, box 1 and (

**d**) second carousel position, box 2. One class number is equivalent to 0.01 Pa.

**Figure 13.**Computed velocity maps at frontal face areas of virtual boxes. Original system operating at inlet oil velocity of (

**a**) 0.5 m/s, (

**b**) 1 m/s and (

**c**) 5 m/s.

**Figure 14.**Computed velocity maps at frontal face areas of virtual boxes. (

**a**) Original case and (

**b**) Carousel with baffles installed through its perimeter to block the oil flow. Inlet oil velocity was 0.5 m/s.

**Figure 15.**Computed velocity maps at frontal face areas of virtual boxes. (

**a**) Original case and (

**b**) Tank with shortened depth. Inlet oil velocity was 0.5 m/s.

**Figure 16.**Computed oil velocity distribution at nozzle exit for: (

**a**) Original case, (

**b**) nozzle rows at 90° between them. Computed velocity maps at frontal face areas of virtual boxes for (

**c**) Original case, (

**d**) nozzle rows at 90°.

**Figure 17.**Computed velocity maps at face areas but in perspective view for: (

**a**) Original case and (

**b**) nozzle rows at 90°. Inlet oil velocity was 0.5 m/s. Comparison of average wall shear stress in (

**c**) box 1 and (

**d**) box 2 computed in each leaf surface face, 1 = front, 2 = inferior, 3 = superior and 4 = back.

Author (s), Year | CFD | Heat Conduction | Solid-Phase Transformation | Residual Stress and Distortion |
---|---|---|---|---|

Totten et al., 1993 | Isothermal fluid flow | - | - | - |

Garwood et al., 1992 | - | - | - | |

Halva and Volny, 1993 | - | - | - | |

Bogh, 1994 | - | - | - | |

Kernazhitskiy, 2003 | - | - | - | |

Kumar et al., 2007 | - | - | - | |

R.-Bineli et al., 2010 | Non-isothermal but no-boiling flow | Non-isothermal solid | - | - |

Krause et al., 2010 | Mixed fluids | Isothermal and non-isothermal solids | - | - |

Srinivasan et al., 2010 | Non-isothermal solid | - | - | |

Gao et al., 2011 | yes | yes | ||

Ricci et al., 2011 | Computed interface, VOF | yes | - | |

El-Kosseifi, 2012 | Computed interface, LS | Non-isothermal solid | - | - |

Yang et al., 2013 | Isothermal flow | - | - | - |

Banka et al., 2013 | Non-isothermal solid | yes | yes | |

Ko et al., 2013 | Mixed fluids | Non-isothermal solid | - | Hardness prediction using Quenching Factor Analysis (QFA) |

Kopun et al., 2014 | - | - | ||

Passarella et al., 2014 | yes | yes |

Chemical Composition | C | Si | Mn | P | S | Cr | V | Sum of Others ^{1} |
---|---|---|---|---|---|---|---|---|

Mass % | 0.50 | 0.24 | 0.97 | 0.04 | 0.008 | 1.04 | 0.14 | <0.281 |

^{1}Analyzed impurity elements are: Cu (0.14), Ni, Mo, Al (0.07), N, O, Ti, and Nb. Balance is Fe.

Material | k_{t} (W/m·K) | ρ (kg/m^{3}) | C_{p} (J/kg·K) | μ (mPa·s) | T_{sat} (°C) | M_{s} (°C) | M_{50} (°C) | M_{90} (°C) |
---|---|---|---|---|---|---|---|---|

Steel: 51CrV4 | k(T) | ρ(T) | C_{p}(T) | - | - | 288 | 251 | 166 |

Oil: FTR (Equiquench 770) Houghto-Quench^{®} | - | 827 at 60 °C | - | 7.3 at 60 °C | 290 | - | - | - |

Tank Component | Length (m) | Width (m) | Height (m) | Diameter (m) |
---|---|---|---|---|

Feeder, tube | - | - | - | 0.197 |

Feeder, hexahedron | 1.78 | 0.20 | 0.16 | - |

Nozzle | 0.045 | - | - | 0.0254 |

Tank (main body) | 2.96 | 2.11 | 2.74 | - |

Virtual box | 0.22 (thickness) | 1.46 | 0.57 | - |

Tank exit orifice | - | - | - | 0.250 |

Initial Temperature T_{I} (°C) | Impact Velocity V_{I} (m/s) | Oil Temperature T_{f} (°C) |
---|---|---|

800 | 0.9 | 60 |

850 | ||

880 | ||

900 | ||

850 | 0.4 | 60 |

0.9 | ||

1.3 | ||

2.0 | ||

850 | 0.9 | 50 |

60 |

**Table 6.**Variables and constants appearing in turbulence equations [24].

C_{1} | C_{2} | G | η | S | S_{ij} | σ_{k} | σ_{ε} |
---|---|---|---|---|---|---|---|

$\mathrm{max}\left[0.43,\frac{\mathsf{\eta}}{\text{}\mathsf{\eta}\text{}+\text{}5}\right]$ | 1.9 | ${\mathsf{\mu}}_{t}{S}^{2}$ | $S\frac{k}{\mathsf{\epsilon}}$ | $\sqrt{2{S}_{ij}{S}_{ij}}$ | $\frac{1}{2}\left(\frac{\partial {u}_{j}}{\partial {x}_{i}}+\frac{\partial {u}_{i}}{\partial {x}_{j}}\right)$ | 1 | 1.2 |

Case | Characteristics |
---|---|

Original | Feeder with two rows of nozzles pointing upward. Oil average velocity at feeder tube, 0.5 m/s. |

Higher flowrate | Original feeder. Oil average velocity at feeder tube, 1 and 5 m/s. |

Baffles installed around carousel | Original feeder and oil velocity at feeder tube, 0.5 m/s. |

Shallow tank | Original feeder and oil velocity at feeder tube, 0.5 m/s. Depth of tank in carousel area, 1.73 m. |

Nozzle rows at 90° | Feeder with nozzle rows at 90° from each other. Oil average velocity at feeder tube, 0.5 m/s. |

**Table 8.**Number of elements and computing time for fluid flow simulation in a quench tank using “cascade” calculations versus full system calculations. Computer runs were carried out on an 8-core microprocessor Intel Xeon ESG45, 2.4 GHz and 32 GB of RAM.

Subdomain | Millions of Elements | Running Time—“Cascade” (h) | Millions of Elements | Running Time—Full System (h) |
---|---|---|---|---|

Feeder | 1.4 | 1.1 | 48.6 | 168 |

Tank | 6.6 | 12.2 | ||

Box 1 | 3.4 | 1.9 | ||

Box 2 | 3.4 | 1.4 | ||

Box 3 | 3.4 | 1.6 | ||

Box 4 | 3.4 | 1.7 | ||

Box 5 | 3.4 | 1.8 |

Impact Velocity, V_{I} (m/s) | Average Wall Shear Stress, τ_{max}/2 (Pa) | ${\mathit{q}}_{\mathbf{w}}{/\mathit{q}}_{\mathbf{w}}^{1}$ | n |
---|---|---|---|

0.4 | 0.2 | 0.903 | 0.06 |

0.9 | 1.0 | 1 | - |

1.3 | 2.1 | 1.452 | 0.503 |

2.0 | 4.96 | 1.935 | 0.412 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Barrena-Rodríguez, M.D.J.; González-Melo, M.A.; Acosta-González, F.A.; Alfaro-López, E.; García-Pastor, F.A.
An Efficient Fluid-Dynamic Analysis to Improve Industrial Quenching Systems. *Metals* **2017**, *7*, 190.
https://doi.org/10.3390/met7060190

**AMA Style**

Barrena-Rodríguez MDJ, González-Melo MA, Acosta-González FA, Alfaro-López E, García-Pastor FA.
An Efficient Fluid-Dynamic Analysis to Improve Industrial Quenching Systems. *Metals*. 2017; 7(6):190.
https://doi.org/10.3390/met7060190

**Chicago/Turabian Style**

Barrena-Rodríguez, Manuel De J., Marco A. González-Melo, Francisco A. Acosta-González, Eddy Alfaro-López, and Francisco A. García-Pastor.
2017. "An Efficient Fluid-Dynamic Analysis to Improve Industrial Quenching Systems" *Metals* 7, no. 6: 190.
https://doi.org/10.3390/met7060190