In recent years, the alloy composition of castings, the materials used for mold cavities, and auxiliary external field conditions in sand mold casting—such as air cooling, water cooling, centrifugal casting, negative pressure, and ultrasonic vibration—have become increasingly complex and diversified. As a result, the solidification and cooling behavior of castings, together with the final quality and performance of the products, has become more difficult to predict. Although the rise of simulation software has made it easier to forecast casting processes and outcomes, the lack of fundamental research on solidification theory and physical parameters under complex and diversified sand mold casting conditions severely limits the accuracy of simulation results. Among the physical parameters in sand mold casting, the interfacial heat transfer coefficient between the casting and the mold cavity directly determines the heat dissipation efficiency of the molten metal and the high-temperature casting after solidification. It strongly influences the cooling rate of the casting, which in turn governs defect distribution, stress state, grain structure coarseness, and mechanical properties. Therefore, investigating the theoretical basis of the interfacial heat transfer coefficient and its variation trend under diversified casting methods has important scientific significance and application value.
In this context, I selected cast aluminum and cast steel as casting materials, furan resin no-bake sand and water glass no-bake sand as core materials, with and without air cooling in the sand core as external field conditions, and annular castings as the research object. By combining an optimized Beck inverse algorithm, numerical simulation, and measured temperature field data, I systematically studied the variation laws of the interfacial heat transfer coefficient between the casting and the core under different conditions and explored the underlying mechanisms. The results provide a necessary data foundation and theoretical basis for the application of forced cooling technology in the sand mold casting industry.
1. Background and Significance
The casting industry is one of the pillar industries of equipment manufacturing, providing basic components for construction, automobiles, ships, railways, and other sectors. As the requirements for the quality and performance of castings increase, new casting alloy compositions, new casting processes, new mold cavity materials, and auxiliary external field casting methods are emerging and being applied in practice. However, this also makes the prediction of the solidification and cooling process more difficult. With the development of computer hardware and solidification theory, numerical simulation has been widely used because it can simulate and predict the sand mold casting process with low cost and short cycle time. For example, it can effectively visualize the temperature field, hot cracks, stress concentration, flash, and defect distribution of castings and molds. Nevertheless, the lack of fundamental research on solidification theory and physical parameters in complex and diversified sand mold casting processes severely restricts the reliability and accuracy of numerical simulation results and limits the development of casting enterprises toward intelligent production, standardized systems, and green industry.
At present, research on the interfacial heat transfer coefficient is concentrated in gravity casting, low-pressure casting, high-pressure casting, continuous casting, rolling, and spray quenching. Research on the interfacial heat transfer coefficient between castings and cores under auxiliary external field conditions, such as forced cooling and electromagnetic stirring, is relatively scarce. In this work, I studied the influence of forced air cooling on the interfacial heat transfer coefficient and its mechanism, providing necessary data and theoretical support for the application of forced cooling technology in the sand mold casting industry.
2. Forced Cooling Technology in Sand Mold Casting
Forced cooling is a process in which an external medium is used to forcibly remove heat and lower the temperature of an object. It is increasingly widely used in the field of sand mold casting. Forced cooling technology can improve the cooling rate of castings and enhance their performance. Castings produced with forced cooling technology have fine microstructures, slight segregation, short secondary dendrite arm spacing, high thermal fatigue strength and mechanical fatigue strength, and good overall mechanical properties.
Forced cooling technology in the casting industry is mainly divided into four categories: chills, air cooling, water cooling, and mist cooling. Chills can change the local cooling rate of castings and, together with risers and gating systems, achieve sequential solidification and improve casting quality. Air cooling uses compressed air as a heat transfer medium to accelerate the cooling rate of castings. It has the characteristics of low implementation difficulty, flexible and convenient use, and high safety. Water cooling uses flowing cooling water as the cooling medium. It has strong cooling capacity and a fast cooling rate and is widely used in die casting, electroslag casting, and continuous casting and rolling. However, water demineralization and pipeline cleaning increase the production cost of castings. Mist cooling mixes water flow with gas in proportion, uses the impact force of compressed gas to break the water flow into small droplets to form a water mist, and uses the water mist as a cooling medium. Its cooling range is wide, and the cooling rate is controllable.
The research on forced cooling technology for casting started early. In 1987, researchers explored the influence of forced cooling technology on the structure and properties of large steel castings. In 1996, forced air cooling technology was applied to the production of steam turbine valve bodies, but the cooling effect was not quantitatively studied. The cooling capacity of forced cooling technology is affected by the thickness of the sand layer, the air gap, and the heat conduction ability of the casting itself. During the sand mold casting process using forced cooling technology, attention should be paid to the influence of a relatively fast cooling rate at the initial stage of pouring on the casting: (1) a faster cooling rate produces a larger temperature gradient, which easily forms more columnar crystals on the casting surface; (2) an excessively fast cooling rate can easily cause casting defects such as misruns. In industrial production, the “chills” type of forced cooling method is recognized as the best practice. It involves making a certain shape of cooling pipe inside a metal with good thermal conductivity, and the cooling medium is air or cooling water.
Using forced cooling technology, the solidification speed and direction of local areas of a casting can be controlled to a certain extent, which helps the casting achieve rapid solidification, shortens the production cycle, and improves production efficiency. It has been pointed out that a casting that requires ten minutes of natural solidification can complete cooling in less than one-third of the time if cooling passages are properly designed in the mold. Forced air cooling technology can shorten the cooling time of a 60-ton steel ingot by 67 minutes and improve the solidification structure. The definition of conformal cooling channels was first given as channels whose shape changes with the mold surface shape. The advantages, key technologies, and design principles of conformal cooling channels in injection molds have been summarized, and the development trend of conformal cooling has been predicted. It has been shown that conformal cooling channel molds can be used in short-term commercial applications. Additive manufacturing of conformal cooling channels can provide fast and reliable cooling and more precise solidification control. The cooling time of castings using conventional cooling systems and those using improved cooling channels has been compared, and the results showed that the improved cooling channels are efficient even under air cooling conditions.
A forced cooling technology for large casting risers, namely the post-solidification intensified riser cooling method, has been developed. It can accelerate the cooling process of the entire casting from inside to outside, making the cooling of the casting more uniform, thereby improving production efficiency and reducing residual stress and deformation. 3D-printed shell sand cores have been used, and the temperature distribution during the intensified shell solidification of steel billets was measured with an infrared imaging camera. Under natural conditions, about 40% of the cooling time can be saved, and under forced air cooling conditions, an additional 35% can be saved. 3D printing has also been used to quickly adjust the cooling conditions at specific positions of the mold to achieve uniform cooling of the casting, and the resulting castings have high dimensional accuracy and good surface quality.
In summary, forced cooling technology is developing toward diversification and complexity, but its results are mostly non-replicable and cannot provide guidance for actual production in enterprises. The reasons for this phenomenon are: (1) the production cost of large steel castings is too high, making it difficult for universities and enterprises to conduct sufficient repeated actual production and physical experiments to find design rules; (2) diversified complex external field conditions in sand mold casting place higher demands on solidification theory and physical parameter research, and the current research on basic theory is not deep or specific enough; (3) finally, it is necessary to connect forced cooling technology with intelligence, using automation technology and mechanical equipment to achieve controllable and adjustable forced cooling processes, real-time modification of cooling parameters according to cooling effects, improvement of cooling efficiency, and reduction of energy consumption.
3. Casting CAE Technology
Computer simulation technology (CAE) is a comprehensive technology that connects numerical simulation and physical modeling to solve practical problems on computers. It is not limited by financial resources, site, environment, or time and, together with theoretical derivation and scientific experiments, is one of the three major means for humans to understand and transform nature. Commonly used simulation software includes ProCast, ABAQUS, MATLAB, SolidWorks, CST, CAE, Autodesk, BPA, CATIA, and others.
Computer simulation has been fully applied in the casting industry. The filling and solidification processes of sand mold casting are complex, the quality controllability of castings is relatively poor, and various defects are likely to occur. Using computer simulation software to design the size and position of the gating system, risers, and chills of castings, as well as the process parameters of auxiliary external field conditions, and then performing simulation, and using the simulation results to guide the modification of process parameters, iterating repeatedly, ultimately makes the process parameters optimal, which can improve production efficiency and reduce research and development costs. The flow of molten metal during pouring, the stability of filling, gas entrapment and flow interruption, and the temperature field, stress field, and possible defects during solidification have all been visualized with the help of computer simulation, making the results more intuitive and accurate. Software such as CAFÉ can also be used to simulate the growth of grains.
Casting simulation software consists of three parts: pre-processing, solution calculation, and post-processing. Pre-processing is mainly responsible for the establishment of 3D or 2D solid models, mesh generation and modification, and parameter setting and modification. Solution calculation mainly performs numerical calculation of the problem under the support of fluid mechanics and heat transfer. Post-processing uses data visualization technology to dynamically observe and analyze the data obtained from numerical calculation. Commonly used casting simulation software includes Magmasoft (based on FDM), ProCast (based on FEM), Flow 3D (based on FVM), anycasting, and Huazhu CAE in China.
In 1962, the finite difference method was used for the first time in the heat transfer calculation of casting solidification. In the 1980s, the concepts of pre-treatment, post-treatment, and intermediate calculation were proposed. In 1983, the two-dimensional method was used to simulate the flow process of metal fluid filling. In 1998, at the 8th International Conference on Modeling of Casting, Welding and Advanced Solidification Processes, the simulation situations of MAGMASOFT and Flow-3D software were verified, and they basically gave a reasonable process of liquid metal filling the mold cavity. In 2004, at the 6th Pacific Rim International Conference on Modeling of Casting and Solidification Processes, a mathematical model of fluid flow in a continuous casting mold with electromagnetic braking was described.
4. Interfacial Heat Transfer Coefficient
Among the physical parameters in sand mold casting, the interfacial heat transfer coefficient between the casting and the mold cavity is the most important boundary condition. The interfacial heat transfer coefficient is defined as the ratio of the heat flux density to the temperature difference between the metal and the mold cavity, representing the overall thermal resistance of the interface between the metal and the mold. It is a very complex value, related to the thermophysical parameters of the casting, the geometric shape of the casting, the surface roughness of the sand mold, and the material of the sand mold, such as metal and mold materials, heat transfer area, surface roughness, interface contact, casting system pressure head, temperature, and time. Under gravity, the interfacial heat transfer coefficient at different positions also varies. It is often assumed that the interfacial heat transfer coefficient is a constant or a function of time, distance, or temperature. In reality, it is neither a constant nor a linear function of distance or temperature; its variation is very complex, leading to the complexity of casting solidification and temperature fields.
The interfacial heat transfer coefficient is a complex physical quantity. Setting it as a constant in numerical simulation cannot guarantee the accuracy of the simulation. Therefore, it is of great scientific significance and application value to study the theoretical basis of the interfacial heat transfer coefficient in the sand mold casting process and its variation trend under diversified casting methods.
Two commonly used inverse calculation methods for solving the inverse heat conduction problem (IHCP) are the inverse analysis method (IAM) and the inverse optimization method (IOM). The IAM method uses the Fourier analytical algorithm of simplified heat transfer differential equations to derive surface heat flux and surface temperature and then directly calculates the interfacial heat transfer coefficient or surface heat flux. The IOM method indirectly approximates the true interfacial heat transfer coefficient or surface heat flux through an iterative algorithm, compares the simulation results with experimental data to determine the true interfacial heat transfer coefficient value, and predicts time. The IOM method has higher calculation accuracy and efficiency in related fields. The Beck method used in this work is an improved IOM algorithm that improves accuracy and efficiency. The basic procedure is to introduce an initially assumed boundary interfacial heat transfer coefficient or heat flux into the heat conduction partial differential equation to estimate the temperature at a specified position inside the sample, then compare each estimated value with the experimental temperature and iteratively correct the interfacial heat transfer coefficient or heat flux until the convergence criterion is met.
5. Air Gap and Its Influence
Molten metal naturally moves away from the mold during solidification. At this time, the direct contact between the solidified casting and the sand mold is greatly reduced or even lost, making it increasingly difficult to quickly and effectively cool the target area in the casting through heat conduction. This can lead to an increase in the rejection rate of castings, loss of productivity, and rework of precision parts. The air gap is the product of this problem. The air gap is the gas gap between the casting and the sand mold, which prevents the mold and the casting from being in close contact and reduces the heat transfer effect. The shrinkage of the metal, the physical and chemical properties of the metal and the mold, and the expansion of the mold during solidification are the mechanisms of air gap formation at the interface between the metal and the mold. During the sand mold casting process, the high-temperature molten metal contacts the low-temperature mold, and heat conduction occurs. A large amount of heat is taken away by the mold, and the temperature of the molten metal in direct contact with the mold drops rapidly. A metal shell solidifies on the surface. When the solidified metal shell reaches a certain thickness, it has sufficient thermal strength to resist the pressure applied to it by the molten metal constrained by it, resulting in the formation of an air gap.
The factors affecting the gap are diverse. The thermal history of the metal and mold, the thermal expansion and thermal deformation of chills, the thermal contraction and thermal deformation of the casting, the constitutive behavior of the casting, the constitutive behavior of the sand, and the geometry of the contact surface between the casting and the chill all affect the gap size and variation trend. Other factors include the surface roughness of the mold, the type of mold coating and binder, etc. When an air gap exists, the heat transfer in the gap is a combination of convective heat transfer and radiative heat transfer of the fluid in the gap. In alloys with low melting points, such as Al alloys, the influence of radiative heat transfer can be ignored. The air gap is the main factor affecting the cooling efficiency of forced cooling technology. When an air gap exists, the air inside it is an excellent thermal insulation material compared with metal and sand, so the existence of the air gap increases thermal resistance and reduces the interfacial heat transfer coefficient, thereby reducing the cooling rate of the casting. It has been shown that with the increase of air gap width, the columnar crystal zone of the billet decreases, the equiaxed crystal zone increases, and both columnar and equiaxed crystals become coarser. It has also been pointed out that the influence of the air gap on castings using forced cooling systems is greater. This is because forced cooling makes the cooling rate higher, making the thermal changes of the casting, sand mold, and chill more severe, resulting in relatively large and disorderly changes in the gap. LVDT is the most effective and commonly used means of measuring air gap width. LVDT sensors have been used to measure the generation and variation process of the gap between the casting and the mold, and it was found that the gap changes nonlinearly with time and temperature, and its curve is serrated.
From the above, it can be seen that the existence of the air gap seriously affects the cooling efficiency of forced cooling technology in practical applications. Therefore, people hope that the air gap can disappear and the casting and sand mold can remain tightly connected. A assembled movable water-cooled crystallizer has been developed. During the pouring process, when the casting forms a solid shell of a certain thickness, the movable crystallizer prevents the gap from being generated. The results show that the use of this device can increase the cooling rate of the casting. A local squeeze cooling technology has been proposed. This technology pours aluminum into an insulating mold, and the other end is a copper chill with a cooling channel inside for forced cooling. The chill consists of a copper block with a cooling pipe and a push bolt mechanism. When the air gap is generated, the cooling device is pushed forward by turning the bolt to eliminate the air gap. In continuous casting, a tapered mold wall has been used to reduce or even eliminate the air gap. Because of the influence of the air gap on casting, the interfacial heat transfer coefficient is not a constant value. In the traditional process, its variation has the law of extremely high initial value, then rapid decrease, and then slow decrease.
6. Research Objectives and Content
In this thesis, I took cast aluminum and cast steel as casting materials, furan resin no-bake sand and water glass no-bake sand as core materials, with and without air cooling in the sand core as external field conditions, and annular castings as objects. By combining an optimized Beck inverse algorithm, numerical simulation, and temperature field measurement data, I systematically studied the variation laws of the interfacial heat transfer coefficient between the casting and the core under different conditions and explored the underlying mechanisms. The aim was to obtain accurate interfacial heat transfer coefficients in the auxiliary forced cooling sand mold casting process, to provide assistance for the simulation of the sand mold casting process under forced cooling conditions using computer simulation software, and to provide the necessary data foundation and theoretical basis for the application of forced air cooling technology in the sand mold casting industry.
The research content includes: (1) using experimental measurement, mathematical models, and numerical analysis to obtain accurate and reliable interfacial heat transfer coefficients; (2) studying the variation laws and mechanisms of the interfacial heat transfer coefficient under no air cooling conditions, including the effects of casting material, casting size, and sand type; (3) studying the variation laws and mechanisms of the interfacial heat transfer coefficient under air cooling conditions, including the effects of forced air cooling on cast aluminum and cast steel, and the similarities and differences in the mechanisms.
7. Experimental Design and Materials
I selected ZL101 aluminum alloy and 40 steel as the casting raw materials. The chemical compositions of these alloys are shown in Table 1 and Table 2. The sand molds were furan resin no-bake sand and water glass no-bake sand. The sand was 50–100 mesh quartz sand. The binder for furan resin no-bake sand was FFD-121 furan resin, and the curing agent was p-toluenesulfonic acid aqueous solution. Water glass no-bake sand was hardened with organic ester. Table 3 and Table 4 show the thermophysical parameters of furan resin no-bake sand and water glass no-bake sand. These parameters were processed by linear interpolation and used for the inverse calculation of the interfacial heat transfer coefficient.
| Alloy | Si | Mg | Ti | Other elements | Al |
|---|---|---|---|---|---|
| ZL101 | 6.5–7.5 | 0.25–0.45 | 0.08–0.20 | Cu ≤ 0.10, Mn ≤ 0.10, Zn ≤ 0.10, Zr ≤ 0.10 | Balance |
| Alloy | C | Si | Mn | Other elements | Fe |
|---|---|---|---|---|---|
| 40 steel | 0.37–0.44 | 0.17–0.37 | 0.50–0.80 | Cr ≤ 0.25, Ni ≤ 0.30, Cu ≤ 0.25 | Balance |
| Temperature (°C) | Density (kg·m-3) | Heat capacity (kJ·kg-1·K-1) | Conductivity (W·m-1·K-1) |
|---|---|---|---|
| 20 | 1590 | – | 0.71 |
| 50 | 1590 | 0.73 | – |
| 100 | 1590 | 0.80 | – |
| 150 | 1590 | 0.85 | – |
| 200 | 1590 | 0.92 | – |
| 232 | 1590 | – | 0.62 |
| 250 | 1590 | 0.90 | – |
| 350 | 1590 | 0.94 | – |
| 400 | 1590 | 1.00 | – |
| 414 | 1590 | – | 0.55 |
| 500 | 1590 | 1.00 | – |
| 600 | 1590 | – | 0.50 |
| 708 | 1590 | – | 0.61 |
| 980 | 1590 | – | 0.78 |
| Temperature (°C) | Density (kg·m-3) | Heat capacity (kJ·kg-1·K-1) | Conductivity (W·m-1·K-1) |
|---|---|---|---|
| 50 | 1590 | 0.77 | 0.77 |
| 200 | 1590 | 0.72 | 0.84 |
| 500 | 1590 | 0.62 | 0.88 |
| 700 | 1590 | 0.58 | 0.92 |
| 900 | 1590 | 0.53 | 0.99 |
| 1100 | 1590 | 0.55 | 1.03 |
| 1350 | 1590 | 0.62 | 1.06 |
| 1450 | 1590 | 0.68 | 1.08 |
| 1500 | 1590 | 0.76 | 1.09 |
| 1550 | 1590 | 0.80 | 1.10 |
The preparation method of no-bake sand was as follows: first, a certain mass of quartz sand was weighed, and impurity particles were manually screened out. For furan resin no-bake sand, 0.3% of the sand weight of curing agent and 1.2% of the sand weight of binder were weighed, and the curing agent and binder were added in sequence within a given time and mixed uniformly. For water glass no-bake sand, 0.4% of the sand weight of organic ester and 4% of the sand weight of water glass were weighed, and the organic ester and water glass were added in sequence within a given time and mixed uniformly. Then, molding was carried out. The optimal stripping time was about 24 h after molding.
The experimental process consisted of two parts: actual pouring temperature field measurement and inverse calculation of the interfacial heat transfer coefficient. The casting and temperature measurement device is shown schematically in two dimensions. In the figure, Tc is a thermocouple placed in the casting cavity to measure the molten metal temperature, located 2 mm from the mold cavity surface. Tm1, Tm2, and Tm3 are thermocouples for measuring the sand mold temperature, placed at 6, 14, and 22 mm from the outer surface of the casting, respectively. Placing thermocouples in this way not only improves measurement accuracy but also ensures that the sand mold does not crack during the casting process. The position of the thermocouples determines the accuracy of the inverse calculation results of the interfacial heat transfer coefficient.
To ensure the accurate placement of thermocouples, I used a method in which prefabricated sand blocks wrapped with thermocouples were first prepared. Then, the prepared thermocouples were inserted into the wooden pattern according to the position, and sand was filled for molding to produce a conformal thermocouple block with the same casting radius. Subsequently, during the preparation of the sand mold, the prefabricated sand block wrapped with thermocouples was accurately placed in contact with the casting, thereby ensuring the accuracy of the thermocouple position.
I conducted 11 groups of temperature measurement experiments to investigate the effects of casting material, casting size, sand type, and with/without air cooling on the interfacial heat transfer coefficient. The process parameters of the temperature measurement experiments are shown in Table 5.
| No. | Casting material | Sand type | Casting inner radius r (mm) | Air cooling pipe diameter (mm) |
|---|---|---|---|---|
| 1 | Al | Furan resin no-bake sand | 60 | None |
| 2 | Al | Furan resin no-bake sand | 100 | None |
| 3 | Al | Furan resin no-bake sand | 140 | None |
| 4 | Al | Furan resin no-bake sand | 100 | 60 |
| 5 | Al | Water glass no-bake sand | 60 | None |
| 6 | Al | Water glass no-bake sand | 100 | None |
| 7 | Al | Water glass no-bake sand | 140 | None |
| 8 | Steel | Furan resin no-bake sand | 100 | None |
| 9 | Steel | Furan resin no-bake sand | 100 | 40 |
| 10 | Steel | Furan resin no-bake sand | 100 | 60 |
| 11 | Steel | Furan resin no-bake sand | 100 | 80 |
8. Experimental Equipment and Procedures
The molding equipment included expanded polystyrene (EPS) foam and a conformal steel sleeve. The EPS foam density was 18 kg/m3, with moderate hardness, easy cutting, and certain strength. EPS was used to make the pattern during molding. A resistance wire foam cutter was used to cut the foam into a conformal pattern meeting the size requirements, and then a layer of transparent tape was evenly pasted on the outer surface of the pattern, which improved the surface quality of the sand mold cavity.
The melting equipment included a resistance furnace and a medium-frequency induction melting furnace. The resistance furnace was mainly used for melting aluminum alloy, and the medium-frequency induction melting furnace was used for melting 45# steel.
The temperature measurement device consisted of thermocouples, compensating wires, and a temperature recorder. The thermocouples used included K-type and B-type thermocouples. The K-type thermocouple was a nickel-chromium/nickel-silicon thermocouple with a measurement range of −60 °C to 1372 °C. The B-type thermocouple was a platinum-rhodium 30–platinum-rhodium 6 thermocouple with a measurement range of 400 °C to 1800 °C. The insulating protective sleeve of the thermocouple wire was a double-hole corundum tube. The specifications are shown in Table 6. The temperature recorder was an industrial-grade TP700 multi-channel temperature recorder with a recording frequency of 1 time/s and a measurement accuracy of ±0.5 °C.
| Type | Material | Outer diameter (mm) | Inner diameter (mm) | Length (mm) |
|---|---|---|---|---|
| K | 99.5% high-purity alumina | 4.0 | 1.0 | 20 |
| B | 99.5% high-purity alumina | 1.4 | 0.4 | 10 |
The air cooling device included an air compressor, an air supply pipe, and a ventilation cooling pipe. The air supply channel was an explosion-proof PU air pipe with a service temperature of −5 °C to 50 °C. The ventilation cooling pipe in the sand core was a steel pipe of different sizes, made of 40 steel, with a wall thickness of 8 mm, and all were polished before the experiment. The parts were connected using LSA-8 air pipe quick-insert connectors, and the plugs were adjustable throttle valves to ensure safe and controllable experiments.
I conducted a total of 11 groups of pouring temperature measurement experiments. The process of each group of experiments was similar, including molding, pouring, and data collection. For the experimental groups requiring air cooling, the ventilation process was also included.
The molding sequence was: thermocouple sand block (with Tm1, Tm2, and Tm3 thermocouples wrapped inside), sand core, sand mold, and base. After molding, the pattern was stripped. For the air cooling experimental group, the cooling device was buried during the molding process. A multimeter was used to determine whether the thermocouples were connected. After molding, a fixture for installing the Tc thermocouple was installed on the upper surface of the sand mold with an electric drill. Alcohol-based zircon powder coating was evenly applied to the surface of the sand mold and dried. The sand mold was moved to the experimental site, and the box was closed in the order of base, sand core, and sand mold, ensuring that the gap between the sand mold and the base was less than 0.5 mm. Asbestos rope was placed on the parting surface to prevent molten metal from running out. After closing the box, the Tc thermocouple was installed. Finally, the air supply channel was connected to the air compressor, and the thermocouples were connected to the temperature recorder with compensating wires.
For the melting and pouring process, the furnace temperature for cast aluminum was 750 °C, the pouring temperature was 730 °C, and the pouring time was about 10 s. For 45# steel, a medium-frequency induction melting furnace was used. After the metal melted, a slagging agent was added for degassing and slag removal. Before tapping, 0.5% Al was added for deoxidation. The tapping temperature was about 1700 °C, the pouring temperature was about 1560 °C, and the pouring time was about 10 s.
For the air cooling process, the air compressor was kept on at all times to provide uniform and lasting high-pressure cold air. The intake valve was kept closed during pouring to prevent molten metal splashing from injuring the pouring personnel. When pouring was completed, the intake valve was opened for air cooling. After the casting was completely cooled, the air compressor was turned off. As the size of the air cooling pipe increased, the wind speed in the ventilation pipe gradually changed. The throttle valve was adjusted so that the wind speeds were 6 m/s, 8 m/s, and 10 m/s when the air pipe diameters were φ40, φ60, and φ80, respectively.
9. Inverse Calculation Program for Interfacial Heat Transfer Coefficient
This section mainly introduces the mathematical principle of the inverse calculation of the interfacial heat transfer coefficient and the solution flow. I used the Fourier heat transfer formula and discretization processing to import the experimentally obtained temperature field data into the Beck inverse algorithm to inversely solve the interfacial heat transfer coefficient between the casting and the sand mold. The inverse calculation of the interfacial heat transfer coefficient is divided into the following steps: establishment of the geometric model and import of original data, establishment of the temperature field of the entire device using known temperature data, and inverse solution of the interfacial heat transfer coefficient using the temperature field data.
I established a reasonable geometric model to solve the interfacial heat transfer coefficient from a one-dimensional perspective. Simplifying the solution of the interfacial heat transfer coefficient to a one-dimensional heat transfer problem can effectively improve the efficiency and feasibility of research. The simplified one-dimensional model consists of two parts: the casting and the sand mold. The sand mold part near the casting is uniformly discretized into six sectors, and a point in the middle of the sector is taken and its temperature is regarded as the temperature of the entire sector. The temperatures at points T2, T4, T6, and Tc in the sectors can be obtained by actual measurement. That is, the temperatures measured by the four thermocouples Tc, Tm1, Tm2, and Tm3. Using the measured temperature data, the temperatures at other points and the interfacial heat transfer coefficient between the casting and the sand mold can be solved.
The main heat transfer mode in the internal heat conduction of the sand mold in this experiment is heat conduction. According to Fourier’s law, the one-dimensional heat transfer differential equation is:
$$\frac{\partial}{\partial x}\left(k\frac{\partial T}{\partial x}\right)=\rho C_P\frac{\partial T}{\partial t}$$
where ρ, Cp, and k are the density (kg/m3), effective specific heat (kJ/(kg·°C)), and thermal conductivity (W/(m·°C)) of the material, T is the temperature (°C), and t is the time (s). Solving the inverse problem requires initial and boundary conditions. The initial condition in this work is the temperature field measured at time 0 s:
$$T(x,0)=T_{in}(x)$$
The boundary condition is the heat flux q (W/m2) from the casting to the sand:
$$k(T)\left.\frac{\partial T}{\partial x}\right|_{x=0}=q(0,t)$$
and the measured temperature of unit 6:
$$T(x_6,t)=T_{m3}(t)$$
Equation (4) is a boundary condition of the first kind and is related to the measured temperature field. Equation (3) is a boundary condition of the second kind and is the boundary condition to be used when solving the inverse problem in the future. Unit 1 is the heat flux boundary unit, and unit 6 is the temperature boundary unit.
The discretization of the heat transfer equation uses the implicit finite volume method with a discretization step of Δx. The basic volume unit is shown schematically. According to the law of energy conservation, the discrete unit solution is:
$$\Delta u = A_{in,j} \cdot q_{in,i} + A_{out,j} \cdot q_{out,i}$$
where Δu is the change in internal energy of unit j from time i to time i+1, qin,i is the heat flux flowing into unit j from time i to time i+1, qout,i is the heat flux flowing out of unit j from time i to time i+1, Ain,j is the inflow area of unit j, and Aout,j is the outflow area of unit j.
Unit 1 is the heat flux boundary unit. The heat flux flowing into the unit is the heat flux from the casting into the sand mold, that is, the inverse heat flux density q. The heat flux flowing out of the unit is caused by the temperature difference between units 1 and 2. Substituting the above content into the formula gives:
$$\Delta u = \frac{V_1 \rho C_P^i (T_1^{i+1}-T_1^i)}{\Delta t}$$
$$q_{in,1}=q^{i+1}$$
$$q_{out,1}=k^i\frac{T_1^{i+1}-T_2^{i+1}}{\Delta x}$$
Substituting these into the energy conservation equation yields:
$$\frac{V_1 \rho C_P^i (T_1^{i+1}-T_1^i)}{\Delta t}=q^{i+1}A_{in,1}+A_{out,1}k^i\frac{T_2^{i+1}-T_1^{i+1}}{\Delta x}$$
Rearranging gives:
$$(T_1^{i+1}-T_1^i)=\frac{\Delta t}{V_1 \rho C_P^i}\left(q^{i+1}A_{in,1}-A_{out,1}k^i\frac{T_1^{i+1}-T_2^{i+1}}{\Delta x}\right)$$
To simplify the calculation, two functions related to j, Sin(j) and Sout(j), are introduced:
$$S_{in}(j)=\frac{A_{in,j}}{V_j}\cdot\frac{\Delta t \cdot k^i}{\rho C_P^i \Delta x}$$
$$S_{out}(j)=\frac{A_{out,j}}{V_j}\cdot\frac{\Delta t \cdot k^i}{\rho C_P^i \Delta x}$$
It is worth noting that for annular castings, the radius at the heat flux inflow is different from the radius at the heat flux outflow. The original Beck inverse algorithm did not consider the influence of non-uniform geometric size and shape on the inverse calculation. Therefore, I introduced geometric parameters to characterize the difference between the inflow and outflow heat flux radii. The geometric parameter formulas are:
$$\frac{A_{in,j}}{V_j}=\frac{r_{use}-j\Delta r+\Delta r}{\Delta r(r_{use}-j\Delta r+0.5\Delta r)}$$
$$\frac{A_{out,j}}{V_j}=\frac{r_{use}-j\Delta r}{\Delta r(r_{use}-j\Delta r+0.5\Delta r)}$$
where ruse is the inner radius of the annular casting (mm), and Δr is the thickness of the annular casting (mm). Substituting these into the temperature calculation formula for unit 1 gives:
$$(1+S_{out}(1))T_1^{i+1}-S_{out}(1)T_2^{i+1}=T_1^i+S_{in}(j)\Delta x q^{i+1}$$
For internal units (i = 2–5), the input and output heat are both generated by temperature differences. The conservation formula for unit i can be derived from the law of energy conservation:
$$\frac{V_j \rho C_P^i (T_j^{i+1}-T_j^i)}{\Delta t}=A_{in,j}k^i\frac{T_{j-1}^{i+1}-T_j^{i+1}}{\Delta x}-A_{out,j}k^i\frac{T_j^{i+1}-T_{j+1}^{i+1}}{\Delta x}$$
Simplifying gives the temperature calculation formula for internal units of the sand mold:
$$-S_{in}(j)T_j^{i+1}+[1+S_{in}(j)+S_{out}(j)]T_j^{i+1}-S_{out}(j)T_{j+1}^{i+1}=T_j^i$$
Unit 6 is the temperature boundary unit, and its internal temperature is the experimental temperature measured by the Tm3 thermocouple:
$$T_{6,i}=T_{m3}^i$$
The above equations can be combined to obtain a matrix for calculating the temperature field of the casting and sand:
$$
\begin{bmatrix}
1+S_{out}(1) & -S_{out}(1) & 0 & 0 & 0 & 0 \\
-S_{in}(2) & 1+S_{in}(2)+S_{out}(2) & -S_{out}(2) & 0 & 0 & 0 \\
0 & -S_{in}(3) & 1+S_{in}(3)+S_{out}(3) & -S_{out}(3) & 0 & 0 \\
0 & 0 & -S_{in}(4) & 1+S_{in}(4)+S_{out}(4) & -S_{out}(4) & 0 \\
0 & 0 & 0 & -S_{in}(5) & 1+S_{in}(5)+S_{out}(5) & -S_{out}(5) \\
0 & 0 & 0 & 0 & 0 & 1
\end{bmatrix}
\begin{bmatrix}
T_1^{i+1}\\
T_2^{i+1}\\
T_3^{i+1}\\
T_4^{i+1}\\
T_5^{i+1}\\
T_6^{i+1}
\end{bmatrix}
=
\begin{bmatrix}
T_1^i + \frac{A_{in,j}\Delta t q^{i+1}}{V_j \rho C_P^i}\\
T_2^i\\
T_3^i\\
T_4^i\\
T_5^i\\
T_{m3}^{i+1}
\end{bmatrix}
$$
After the above derivation, a realistic heat transfer problem is transformed into a linear system with a matrix, which can be solved using the Thomas algorithm.
To solve the temperature field, the heat flux density q at the interface between the casting and the sand mold must be known. Therefore, I solved this problem by inversely calculating the interfacial heat flux density. The interfacial heat flux is decomposed into an infinite number of average interfacial heat fluxes per unit time, and then the Beck nonlinear estimation method is used to calculate the average interfacial heat flux density in time sequence. In each segment of processing conditions, a future time step r is introduced to calculate the mold interfacial heat flux. When calculating the interfacial heat flux at time i, it is assumed that the interfacial heat flux at future f steps is equal to the initial interfacial heat flux:
$$q_m = q_{m+1} = \cdots = q_f = q_{m+r-1} = q_r = q_{set}$$
The assumed boundary heat flux density qset from time m to m+r−1 is used as the heat flux boundary condition, and the measured temperature at point TM3 is used as the temperature boundary condition. The sand mold temperature field matrix from time m to m+r−1 can be calculated. The calculated temperatures t2 and t4 of units 2 and 4 are compared with the measured temperature field to establish a minimum objective function:
$$F(q_{set})=\sum_{f=M+1}^{M+r}\sum_{j=1}^{J}\left[T_j^f-T_{m,j}^f(q_{set})\right]^2$$
When F(qset) takes the minimum value, the derivative of F(qset) with respect to q is zero:
$$\frac{\partial F(q_{set})}{\partial q_{set}}=\sum_{f=M+1}^{M+r}\sum_{j=1}^{J}\left[T_j^f-T_{m,j}^f(q_{set})\right]\frac{\partial T_j^f(q_{set})}{\partial q_{set}}=0$$
According to the Taylor expansion formula, this can be simplified to:
$$\sum_{f=m+1}^{m+r}\sum_{j=1}^{J}\left\{T_j^f-\left[T_j^f(q_{set})+\left.\frac{\partial T_j^f}{\partial q}\right|_{q=q_{set}}\cdot(q^{k+1}-q^k)\right]\right\}\cdot\left.\frac{\partial T_j^f}{\partial q}\right|_{q=q_{set}}=0$$
φjf is the rate of change of temperature with heat flux density, calculated by taking a small increment ε:
$$\varphi_j^f=\left.\frac{\partial T_j^f}{\partial q}\right|_{q=q_{set}}=\frac{T_j^f(q_{set}+\varepsilon q_{set})-T_j^f(q_{set})}{\varepsilon q_{set}}$$
Substituting and simplifying yields the iterative formula:
$$q^{(k+1)}=q^{(k)}+\frac{\sum_{f=m+1}^{m+r}\sum_{j=1}^{J}\left[T_j^f-T_{m,j}^f(q_{set})\varphi_j^f\right]}{\sum_{f=m+1}^{m+r}\sum_{j=1}^{J}\left(\varphi_j^f\right)^2}$$
The iteration completion condition is:
$$\frac{q^{(k+1)}-q^{(k)}}{q^{(k+1)}}<\varepsilon$$
When the completion condition is satisfied, q(k+1) is set as the mold interface heat flux qm at time m, and the value of qm at the next time is set as the first iteration heat flux value.
10. Interfacial Heat Transfer Coefficient Without Air Cooling
In this section, I analyzed the measured temperature fields and the inverse calculation results of the interfacial heat transfer coefficient without air cooling. I studied the variation law and mechanism of the interfacial heat transfer coefficient during the solidification of castings under no air cooling conditions and explored the effects of casting type, casting size, and sand type.
10.1 Effect of Casting Material
A typical temperature–time curve of a ZL101 casting obtained without air cooling is shown in the measured data. It includes the casting temperature Tc, the temperatures Tm1, Tm2, and Tm3 at three measurement points in the sand mold, and the temperature T1 of the first unit obtained by the inverse program. At the beginning of solidification, the casting temperature drops rapidly, and the sand mold temperature rises rapidly. After that, the casting temperature decreases slowly and remains at a certain temperature, which is caused by the release of latent heat of crystallization due to the eutectic reaction of the casting. Finally, the casting and sand mold temperatures decrease slowly together.
Comparing the measured temperature with the inverse calculated temperature shows that the solved interfacial heat transfer coefficient is reliable. The inverse calculated temperature T1 is between the measured Tm1 temperature and Tc and has the same trend as Tm1, which preliminarily proves the reliability of the interfacial heat transfer coefficient. To further verify reliability, the inverse calculated temperatures T2 and T4 of units 2 and 4 were compared with the actual measured temperatures Tm1 and Tm2. The inverse calculation results agree very well with the actual measurement data. The maximum error between the inverse calculated temperature and the actual measured temperature is 5 °C, which appears in the early stage of the solidification process. After that, as time increases, the difference between the two becomes smaller and smaller, with an average deviation of 1.27 °C.
The relative deviation is calculated as:
$$\delta=\frac{|T_2-T_{m1}|}{T_2}\times 100\%$$
The maximum relative deviation is 5%. The average deviation is 0.01017, and the variance is 0.000108. Compared with previous studies, the results obtained by my inverse calculation have smaller errors and are more accurate. The error of the inverse calculated temperature mainly appears in the initial stage of temperature measurement and gradually decreases as the temperature measurement proceeds. Thermocouples require a certain response time to temperature changes, so the actual measured temperature often lags behind the actual temperature change. That is, a large deviation at the beginning is normal, and after iterative calculation, the deviation gradually decreases.
Using the inverse program, the data of experiments 1–3 were obtained. The interfacial heat transfer coefficient between the casting and the sand mold can be obtained using:
$$h_i=\frac{q_i}{T_C^i-T_1^i}$$
The data in the figure are the curves of the temperature difference ΔT (°C), heat flux density q (kW/m2), and interfacial heat transfer coefficient h (W/m2·°C) between the casting and the sand mold during solidification and cooling as functions of time t (s).
For ZL101 castings, the interfacial heat transfer coefficient increases first and then decreases with time. At the beginning, the interfacial heat transfer coefficient slowly increases with time. When solidification reaches 100–200 s, the interfacial heat transfer coefficient slightly decreases, and then continues to increase until it reaches its maximum value. After the interfacial heat transfer coefficient reaches the maximum value, its value decreases rapidly and remains stable after decreasing to the minimum value.
Under no air cooling conditions, the heat flux density between the ZL101 casting and the sand mold changes with time t. Its initial value is extremely high, drops sharply within 100 s, and then decreases slowly. The temperature difference between the casting and the sand mold has the same variation trend as the heat flux density: the initial value is extremely large, then decreases rapidly, and then decreases slowly. The temperature of the molten metal in the early stage of solidification is very high, close to 700 °C, while the temperature of the sand mold is very low. Therefore, when the molten metal contacts the sand mold, the temperature gradient between them is large, and the interfacial heat transfer driving force is strong. Therefore, the initial heat flux density and temperature difference both show maximum values. Subsequently, the increase in sand mold temperature reduces the interfacial driving force, and the heat flux density and temperature difference decrease.
For the ZL101 casting with r = 100 mm, the interfacial heat transfer coefficient and the solid fraction of ZL101 vary with temperature. The interfacial heat transfer coefficient of the ZL101 casting follows an “s”-shaped curve with temperature. As the molten metal temperature decreases, the interfacial heat transfer coefficient gradually increases. When the casting temperature decreases to 614 °C, the interfacial heat transfer coefficient shows a slight decrease and then gradually increases again as the casting temperature decreases. When the temperature reaches 575 °C, the interfacial heat transfer coefficient drops sharply, and below 575 °C it remains stable.
The change in the interfacial heat transfer coefficient of the ZL101 casting is caused by the formation of an air gap between the casting and the sand mold during the solidification of the molten metal. The release of latent heat of crystallization and the no-air-gap state between the casting and the sand mold cause the interfacial heat transfer coefficient to gradually increase before the casting temperature is higher than 575 °C. As the molten metal temperature decreases, the metal undergoes solidification nucleation and growth, during which latent heat of crystallization is released. The release of latent heat of crystallization causes the temperature of the local molten metal to remain unchanged or to rise, while the temperature of the sand mold gradually increases, resulting in a decrease in the interfacial temperature difference and an increase in the interfacial heat transfer coefficient. When the molten metal contacts the sand mold, it solidifies upon cooling and gradually forms a thin metal shell, but at this time the metal shell produced by solidification cannot fully support the mass of the remaining molten metal. The molten metal as a whole is still in close contact with the sand mold, and an air gap cannot form, so the interfacial heat transfer coefficient does not decrease.
The formation of initial solid phase causes the interfacial heat transfer coefficient to briefly decrease when the casting temperature is about 614 °C. This is because the formation of solid phase at 614 °C causes a tiny air gap to form between the solid phase and the sand mold, resulting in a decrease in the interfacial heat transfer coefficient. However, at this time, the thickness of the solidified metal shell is small and cannot resist the pressure of the molten metal, so the air gap cannot continue to form, and the size of the already formed air gap will not increase. With the release of latent heat of crystallization, the interfacial heat transfer coefficient increases continuously as the temperature decreases between 614 °C and 575 °C.
As the temperature decreases, the solid fraction gradually increases. When the temperature reaches 575 °C, the solid fraction approaches 0.5. This is considered the critical solid fraction (CSF). When the molten metal approaches the critical solid fraction, the flow of liquid metal almost stops, and the liquid metal can no longer fill the holes generated by solidification shrinkage, which will lead to a great increase in the number and size of air gaps between the sand mold and the casting. The thermal conductivity of the air gap is poor, so the heat transfer conditions change, the interfacial thermal resistance increases, and the interfacial heat transfer coefficient drops sharply. On the other hand, with the appearance of solid phase, the thickness of the metal shell also increases. When the thickness reaches a certain level, the shell can support the weight of the entire molten metal, allowing the air gap to continue to increase. The volume shrinkage of the casting during cooling also causes the air gap to increase, resulting in a decrease in the interfacial heat transfer coefficient. Therefore, when the casting reaches the critical solid fraction temperature of 575 °C, the interfacial heat transfer coefficient drops sharply, that is, the step-like decrease shown in the figure.
When the casting temperature is lower than 575 °C, the interfacial heat transfer coefficient enters a maintenance and stabilization stage, and the interfacial heat transfer coefficient basically remains unchanged or slowly decreases. This is because the air gap thickness is already very large at this time, and the growth rate of the air gap thickness is not significant enough, so the interfacial heat transfer coefficient remains stable or slowly decreases.
For the 40 steel casting without air cooling, the temperature–time curve during solidification and cooling includes the casting temperature Tc, the temperatures Tm1, Tm2, and Tm3 at three measurement points in the sand mold, and the temperature T1 of unit 1 obtained by the inverse program. The initial temperature of the molten metal is about 1450 °C, which is caused by the large temperature loss of the molten steel during tundish transfer and subsequent pouring, as well as the lag in temperature measurement of the thermocouple itself. As time goes on, the casting temperature drops rapidly, and the sand mold temperature rises rapidly. When the sand mold temperature rises to close to the casting temperature, the sand mold stops heating up and instead decreases with the casting temperature. The dotted line represents the sand mold temperature near the interface between the sand mold and the casting obtained by the inverse program. It can be seen that the inverse calculated temperature is between the measured casting temperature and the measured sand mold temperature and has the same trend.
As with the cast aluminum, to further verify the reliability of the one-dimensional heat transfer model, the temperature obtained by the inverse calculation of the second unit was compared with the measured temperature Tm1. The inverse calculation results agree well with the actual data. The difference between the inverse calculated temperature and the actual measured temperature is not large. The maximum difference appears in the first 5 s, with a value of 11 °C. Then the difference between the measured value and the inverse calculated value decreases rapidly with time and finally stabilizes at about 0.1 °C, with an average error of 0.4 °C.
To further verify the accuracy of the calculation, the relative deviation was calculated. The maximum relative deviation is 3%, the average deviation is 0.001315, and the squared deviation is 0.0002146. Compared with other studies, the results obtained by this inverse calculation have smaller errors and are more accurate. It can be observed that the error is relatively large at the beginning and then decreases rapidly until it stabilizes, which is the same as the deviation of the cast aluminum part. The larger error at the beginning is because the measured temperature is often not the true casting temperature. First, the thermocouple has a response time to temperature changes. Second, when measuring the temperature of the molten metal, a protective sleeve is added to prevent the thermocouple from short-circuiting, causing the measured temperature to lag behind the actual temperature.
First, I discuss the variation trend of the interfacial heat flux density with time. The interfacial heat flux density is very large after pouring and then rapidly decreases to a fixed value and then slowly decreases. The explanation is as follows: the initial molten metal temperature after pouring is very high, while the sand mold temperature is relatively low, so there is a large temperature difference between the casting and the sand mold at this time, the heat transfer driving force is large, and a lot of heat is transferred, so the initial value of the interfacial heat flux density is large. Subsequently, the sand mold absorbs heat from the casting and its temperature gradually rises to a large value, while the casting temperature gradually decreases. The temperature difference between the two gradually decreases, the heat transfer driving force gradually decreases, and the heat flux density gradually decreases.
The interfacial heat transfer coefficient of the cast steel changes in a complex way with time. As time after pouring increases, the interfacial heat transfer coefficient first increases, then drops sharply, then rises slowly, and finally tends to decrease steadily. The distribution of the interfacial heat transfer coefficient with time is similar to a double-peak distribution, so I call it a “double-peak” phenomenon. This double-peak phenomenon has also been found in the study of the interfacial heat transfer coefficient between the die and the blank during the stamping process of steel castings.
The variation law of the interfacial heat transfer coefficient of 40 steel castings can be divided into five stages. The initial interfacial heat transfer coefficient value is 449 W/m2·°C.
In the first stage (0–200 s), the interfacial heat transfer coefficient decreases slightly. This is due to the low sand mold temperature and the rapid solidification of the molten metal, which causes the appearance of an air gap. The molten metal solidifies into a thin metal shell, which forms many tiny air gaps. The heat transfer capacity of the air gap is very low, resulting in a decrease in the interfacial heat transfer coefficient.
In the second stage (200–1425 s), which is the rising stage of the first peak, the interfacial heat transfer coefficient rises rapidly to a maximum value of 493 W/m2·°C. In this process, on the one hand, the decrease in casting temperature causes volume shrinkage, and volume shrinkage causes the thickness of the air gap to tend to increase. On the other hand, although the temperature of Tm1 begins to decrease during this period, Tm2 and Tm3 are still increasing during this period, that is, the sand mold is still in the heating stage, and the sand mold volume will expand. The restriction of the steel sleeve on the sand mold makes the sand mold expand only inward, so the thickness of the air gap tends to decrease. In this stage, the air gap is restricted by the above two factors at the same time. Among them, the sand mold undergoes a phase transformation from β quartz to α quartz, so the expansion of the sand mold is the dominant factor. Overall, the air gap thickness shows a decreasing trend, so the interfacial heat transfer coefficient tends to increase.
In the third stage, which is the falling stage of the first peak, the interfacial heat transfer coefficient drops rapidly (1425–2710 s) until it reaches a minimum value of 186 W/m2·°C. This is because at this time both the casting and the molding sand are in a cooling state, and both volumes gradually decrease, resulting in a large increase in the air gap thickness.
The fourth stage is the rising stage of the second peak (1425–4100 s). The interfacial heat transfer coefficient rises rapidly again to a maximum value of 372 W/m2·°C. This is because at this time the casting temperature is close to the A1 temperature, and the casting undergoes pearlite transformation, the density decreases, and the volume increases, causing the air gap thickness between the casting and the sand mold to tend to decrease. On the other hand, at this time the sand mold temperature is between 600 °C and 700 °C. Although it is still cooling and shrinking, the degree of shrinkage is relatively small. Therefore, the main factor affecting the air gap in this stage is the pearlite transformation of the casting, that is, the comprehensive air gap thickness is in a state of reduction, so the interfacial heat transfer coefficient gradually increases.
In the fifth stage, which is the falling stage of the second peak, the interfacial heat transfer coefficient first decreases rapidly (4100–5260 s). The reason is that the sand mold undergoes a phase transformation at about 573 °C, from α quartz to β quartz, and the volume of the sand mold decreases significantly, making the air gap thickness increase more rapidly, so the rate of decrease is relatively fast. Subsequently, the temperatures of the casting and the sand mold become closer and closer to room temperature, the heat transfer driving force gradually decreases, and the interfacial heat transfer coefficient slowly decreases.
From the above analysis of the variation of the interfacial heat transfer coefficient of 40 steel during solidification and cooling, it can be seen that the interfacial heat transfer coefficient of cast steel first increases and then decreases, then increases and decreases again with the extension of time after pouring, that is, showing a “double-peak” phenomenon. The first peak of the double-peak phenomenon is caused by the volume changes of the casting and the sand mold in the second and third stages: the increase in sand mold temperature in the second stage causes a phase transformation from β quartz to α quartz, resulting in a decrease in air gap thickness and an increase in the interfacial heat transfer coefficient and the appearance of the first peak. The continuous cooling of the sand mold and casting in the third stage causes volume shrinkage of both, resulting in an increase in air gap thickness, a decrease in the interfacial heat transfer coefficient, and the disappearance of the first peak. The second peak of the double-peak phenomenon is caused by the solid-state phase transformations of the casting and the sand mold in the fourth and fifth stages: the casting temperature in the fourth stage decreases to the A1 temperature, and pearlite transformation occurs, resulting in a decrease in air gap thickness, an increase in the interfacial heat transfer coefficient, and the appearance of the second peak. The decrease in sand mold temperature in the fifth stage causes a phase transformation from α quartz to β quartz, resulting in an increase in air gap thickness, a decrease in the interfacial heat transfer coefficient, and the disappearance of the second peak.
10.2 Effect of Casting Size
Under no air cooling conditions, I analyzed the effect of casting size on the interfacial heat transfer coefficient through experiments and inverse calculations. The interfacial heat transfer coefficient between cast aluminum parts of three different sizes and the sand mold varies with temperature. The inner radii of the annular castings corresponding to the three groups of experiments are 60 mm, 100 mm, and 140 mm.
The change in casting size has little effect on the variation trend of the interfacial heat transfer coefficient, but it has a great effect on its value. The cast aluminum parts still maintain an “s”-shaped curve, which is similar to the results of inverse calculation of the interfacial heat transfer coefficient in previous studies.
The slope of the interfacial heat transfer coefficient curve at the CSF point for castings of different sizes shows that the slope k gradually increases with the increase of radius r. That is, as the size of the cast aluminum casting increases, the rate of decrease of the interfacial heat transfer coefficient at the CSF temperature point becomes faster. Since the change in the interfacial heat transfer coefficient is mainly related to the formation of the air gap, for an annular casting with a larger radius, the linear dimensional change after cooling shrinkage is also larger, so the air gap between the casting and the mold is also larger, and the interfacial heat transfer coefficient value decreases faster.
Previous studies have shown that the interfacial heat transfer coefficient increases with the increase of the thickness of a flat casting or the diameter of a cylindrical casting. However, for annular castings, as the radius r increases, the maximum value, average value, and final stable value of the interfacial heat transfer coefficient all first increase and then decrease. During the entire casting cooling process, obvious inflection points or steps appear in the curve, rather than a monotonic linear increase or decrease.
For annular castings, I related the casting surface temperature to the interfacial heat transfer coefficient and obtained a correlation function that can quantitatively solve the interfacial heat transfer coefficient of cast aluminum parts under no air cooling conditions as a function of casting surface temperature:
$$y=h_{min}+\frac{h_{max}-h_{min}}{1+\exp\left(\frac{x-a}{b}\right)}$$
where x is the casting surface temperature, y is the interfacial heat transfer coefficient, hmin is the minimum value of the interfacial heat transfer coefficient, and hmax is the maximum value of the interfacial heat transfer coefficient. a is a constant related to the solidification characteristics of the metal fluid, which is the temperature at which the solid fraction rate suddenly increases, corresponding to the CSF temperature. b is a coefficient related to the casting size. The fitting parameters hmin, hmax, a, and b are shown in Table 7.
| Casting inner radius | hmax (W/m2·°C) | hmin (W/m2·°C) | a (°C) | b |
|---|---|---|---|---|
| r = 60 mm | 60 | 109 | 575 | 1.5 |
| r = 100 mm | 83 | 127 | 575 | 0.36 |
| r = 140 mm | 45 | 91 | 575 | 0.44 |
10.3 Effect of Sand Type
I used experiments 1–7 to study the effect of sand type on the interfacial heat transfer coefficient. Among them, groups 1–3 were hand-molded with furan resin no-bake sand, and groups 5–7 were hand-molded with water glass no-bake sand. The interfacial heat flux density and interfacial heat transfer coefficient of furan resin no-bake sand and water glass no-bake sand were obtained. The black solid line is the interfacial heat flux density between the casting and the sand mold, the red solid line is the interfacial temperature difference between the casting and the sand mold, and the blue solid line is the interfacial heat transfer coefficient obtained by inverse calculation between the casting and the sand mold.
The interfacial heat transfer coefficient of both water glass sand and resin sand follows an “s”-shaped curve as the casting temperature decreases, regardless of the sand mold material. The type of sand mold cannot affect the overall variation trend of the interfacial heat transfer coefficient, but it does affect the amplitude of the interfacial heat transfer coefficient. Overall, the interfacial heat transfer coefficient between the casting and resin sand is larger than that of water glass sand.
It can be seen that the interfacial heat transfer coefficient between the casting and water glass sand keeps increasing until the casting temperature drops to 614 °C. When the casting temperature decreases from 614 °C to 605 °C, the interfacial heat transfer coefficient keeps a decreasing trend. When the casting temperature decreases from 605 °C to 575 °C, the interfacial heat transfer coefficient slowly increases. When the casting temperature drops to 575 °C, the interfacial heat transfer coefficient drops sharply, and then its value slowly decreases as the temperature decreases.
The interfacial heat transfer coefficient between the casting and resin sand varies with temperature similarly to that of water glass sand. That is, before the casting temperature drops to 614 °C, the interfacial heat transfer coefficient keeps increasing. When the temperature drops to 614 °C, the interfacial heat transfer coefficient oscillates. When the casting temperature decreases from 614 °C to 575 °C, the interfacial heat transfer coefficient keeps increasing slowly. When the casting temperature reaches 575 °C, the interfacial heat transfer coefficient drops sharply, and then its value remains stable or slowly decreases as the temperature decreases.
The difference between the interfacial heat transfer coefficient between the casting and resin sand mold and that between the casting and water glass sand mold is that when the temperature drops to 614 °C, the interfacial heat transfer coefficient between the casting and water glass sand decreases significantly, while that of resin sand only slightly oscillates. The reason for this phenomenon is as follows: when the casting temperature drops to 614 °C, the appearance of initial solid phase causes an air gap between the solid phase and the sand mold, and the generation of the air gap causes a decrease in the interfacial heat transfer coefficient. Among them, the surface of the resin sand mold is smoother, and the air gap generated is relatively small, so the interfacial heat transfer coefficient only slightly decreases. The surface of water glass sand is relatively rough, and its gas evolution is relatively large due to its high water content, resulting in a relatively large initial air gap size at the interface with the casting, which causes a significant decrease in the interfacial heat transfer coefficient. After the casting temperature is lower than 575 °C, the interfacial heat transfer coefficient of resin sand remains stable while that of water glass sand gradually decreases. This is because when the sand mold temperature is 400–500 °C, the specific heat capacity of resin sand remains stable, while the specific heat capacity of water glass sand gradually decreases as the temperature decreases.
11. Effect of Forced Air Cooling on the Interfacial Heat Transfer Coefficient
This section mainly measures the change in the temperature field during the solidification and cooling of castings under air cooling conditions, uses the Beck inverse algorithm to solve the interfacial heat transfer coefficient between the casting and the sand mold, and discusses the effect of air cooling on the interfacial heat transfer coefficient of cast aluminum and cast steel.
11.1 Forced Air Cooling of Cast Aluminum
A typical temperature–time curve of a ZL101 casting obtained under air cooling conditions includes the casting temperature Tc, the temperatures Tm1, Tm2, and Tm3 at three measurement points in the sand mold, and the temperature T1 of the first unit obtained by the inverse program. It can be seen that the temperature field of the cast aluminum part under forced air cooling conditions still maintains the same variation trend as that under no air cooling conditions. The release of latent heat of crystallization can still be clearly observed in the casting, and the sand mold also maintains the variation law of first heating up and then decreasing.
Under air cooling conditions, the temperature difference, heat flux density, and interfacial heat transfer coefficient between the ZL101 alloy casting and the sand mold during solidification and cooling vary with time t. The temperature difference and heat flux density between the casting and the sand mold change with time t: their initial values are extremely large, then decrease rapidly, and then decrease slowly. The interfacial heat transfer coefficient of the ZL101 casting increases first and then decreases with time. At the beginning, the interfacial heat transfer coefficient slowly increases with time. When the solidification time is about 200 s, the interfacial heat transfer coefficient reaches a maximum value. After the interfacial heat transfer coefficient reaches the maximum value, its value decreases rapidly and remains stable after decreasing to the minimum value.
The addition of air cooling significantly improves the solidification speed of the molten metal. When the cooling time reaches 2500 s, the temperature of the air-cooled aluminum alloy casting is 389.3 °C, and the temperature of the aluminum alloy casting without forced air cooling is 459.3 °C, a difference of 70 °C. Assuming that the solidification time is the time for the molten metal in contact with the sand mold to reach the solidus temperature (556 °C), the solidification time of the forced air-cooled cast aluminum part is 1224 s, and the solidification time of the non-air-cooled cast aluminum part is 1655 s. The solidification time of air cooling is 25% faster than that of no air cooling.
The addition of forced air cooling causes the temperature of the molten metal to drop rapidly after the release of latent heat of crystallization. The cooling rate of air cooling is 0.2 °C/s, and the cooling rate of no air cooling is 0.05 °C/s. When the casting temperature is lower than 550 °C, the temperature curves of forced air cooling and no air cooling decrease at almost the same rate, and their cooling rates are both 0.1 °C/s. The effect of air cooling on the sand mold temperature field shows that the maximum temperature of the sand mold under forced air cooling conditions increases. The addition of air cooling causes the total heat flow into the sand mold to decrease while the flow rate in the early stage increases, making the heating rate at Tm1 faster. The acceleration of the heating rate of the Tm1 sand mold causes water vapor to move toward Tm2 and Tm3, resulting in slower heating rates of the sand mold at Tm2 and Tm3.
When air cooling is not added, the sand core is directly wrapped by the molten metal on most of its surface and will heat up rapidly during the solidification of the metal until it reaches a maximum value and then slowly decreases. During this process, the sand mold temperature will exceed the casting temperature, resulting in a thermal saturation phenomenon, which reduces the cooling rate of the casting. The addition of air cooling uses flowing air to take away the heat inside the sand core, preventing the occurrence of thermal saturation. The temperature of the sand core is slightly higher than that of the sand mold but always lower than the casting temperature, thereby improving the cooling rate of the casting and shortening the cooling time.
The addition of forced air cooling improves the cooling time of the casting, causing the casting to dissipate heat to the sand mold faster, so the interfacial heat flux density of forced air cooling is greater than that of no air cooling. The addition of forced air cooling increases the heating rate of the sand mold, causing the interfacial temperature difference of forced air cooling to be overall lower than that of no air cooling.
Under forced air cooling conditions, the interfacial heat transfer coefficient first increases and then decreases as the casting temperature decreases, and then remains stable. The interfacial heat transfer coefficient under forced air cooling conditions is significantly higher than that under no air cooling conditions. Forced air cooling increases the average interfacial heat transfer coefficient from 94 W/m2·°C to 143 W/m2·°C, an increase of 52%. The addition of forced air cooling shortens the time for the interfacial heat transfer coefficient to increase and prolongs the time for the interfacial heat transfer coefficient to decrease.
11.2 Forced Air Cooling of Cast Steel
I studied the influence of the addition of forced air cooling and the size of the air pipe on the interfacial heat transfer coefficient of cast steel. The variable in this group of experiments is the size of the air pipe, which are 40 cm, 60 cm, and 80 cm. In this section, they are named air cooling Φ40, air cooling Φ60, and air cooling Φ80, and the control group is named no air cooling. The experimental group used exactly the same casting process as the control group for pouring. The temperature field during the solidification and cooling process was actually measured, and the interfacial heat transfer coefficient and other parameters were solved by the inverse program, and the influence of the air cooling pipe size was studied.
The measured temperature field of the casting shows that the addition of air cooling to cast steel does not change the distribution law of the temperature field, but the temperature field changes more rapidly. The temperature difference, interfacial heat flux density, and interfacial heat transfer coefficient of cast steel under forced air cooling vary with time. It can be seen that the addition of air cooling has little effect on the interfacial temperature difference and interfacial heat flux density. They still maintain the variation law of extremely large initial values, then rapid decrease to a constant value, and then remaining unchanged. Under air cooling conditions, the interfacial heat transfer coefficient of cast steel still maintains a “double-peak” form, and its average value can reach more than twice that of the no air cooling condition. The addition of air cooling changes the peak values and the time when the peaks appear. As the air cooling size increases, the peak values gradually increase, and the time when both peaks appear gradually advances. That is, with the addition of air cooling and the increase of intensity, the interfacial heat transfer coefficient gradually increases while maintaining the “double-peak” form, and the peak changes gradually become more intense.
The effect of different air cooling pipe sizes on the casting temperature field shows that as the air cooling pipe size increases, the time required for the casting to reach 400 °C is 1119 s, 864 s, 744 s, and 493 s, respectively. This indicates that air cooling can improve the cooling rate of the casting, because the addition of air cooling eliminates the thermal saturation phenomenon of the sand core. Air cooling pipe sizes of φ40, φ60, and φ80 can increase the cooling efficiency by 50%, 75%, and 111%, respectively. This proves that forced air cooling can shorten the casting cooling time, shorten the shakeout time, improve the turnover rate, and improve production efficiency. The addition of forced air cooling causes the cooling rate of the casting to change after 2500 s. At this time, the heat dissipation rate of the casting decreases, and the temperature drop slows down. This is caused by the step-like decrease in the interfacial heat transfer coefficient after 2500 s.
The difference in air cooling pipe size also affects the temperature field of the sand mold. The sand mold maintains a trend of first heating up and then cooling down during the solidification and cooling of the casting. It can be seen that as the air cooling pipe size increases, the heating rate of the sand mold gradually increases, and the maximum temperature of the sand mold gradually increases. When the air cooling radius reaches 80 cm, the maximum temperature of the sand mold can reach about 1050 °C.
However, it is not the case that the sand mold temperature and heating rate of any air cooling device are greater than those without air cooling. The maximum sand mold temperature without air cooling is higher than that of Φ40, and the heating rate is greater than that of Φ40 and Φ60. The reason for this phenomenon is as follows: on the one hand, the addition of air cooling improves the cooling rate of the casting, resulting in a large heat transfer driving force of the casting, which accelerates the heating rate of the sand mold. On the other hand, the addition of air cooling eliminates the thermal saturation phenomenon of the sand core and greatly improves the heat absorption capacity of the sand core. Part of the heat of the casting will be dissipated by the sand core, resulting in a reduction in the heat absorbed by the sand mold. The addition of air cooling causes the sand mold to absorb heat faster but absorb less total heat. When the air cooling size is small, the increase in the cooling rate of the casting is small. At this time, the increase in heating rate caused by the increase in heat transfer driving force of the casting is weaker than the decrease in sand mold heating rate caused by the decrease in heat flow into the sand mold, resulting in a decrease in the sand mold heating rate and maximum temperature. When the air cooling size is large enough, the increase in sand mold heating rate causes the sand mold temperature to rise more than the temperature decrease caused by the reduction in heat flow, so the sand mold temperature rises and the heating rate increases. When the sand mold enters the cooling state, the cooling rate of the air-cooled sand mold is faster, and the sand mold temperature is lower than that without air cooling. This is similar to the above reason, because the addition of air cooling eliminates the thermal saturation phenomenon.
The difference in air cooling pipe size also affects the interfacial temperature difference, interfacial heat flux density, and interfacial heat transfer coefficient. As the air cooling pipe size increases, the maximum temperature difference gradually increases. This is because the larger the air cooling size, the stronger the heat dissipation capacity of the sand core, resulting in a decrease in the sand mold heating rate and an increase in the maximum temperature difference. In the early stage of cooling, the temperature difference increases with the increase of air cooling size, while in the later stage, the temperature difference increases with the decrease of air cooling size. This is because the larger the air cooling size, the faster the cooling rate, the lower the casting temperature in the later stage, the less the heat transfer driving force, and the less able it is to maintain a high temperature difference. The interfacial temperature difference between the sand mold and the casting becomes smaller and smaller.
The interfacial heat flux density between the casting and the sand mold under different air cooling sizes still maintains the trend of rapidly decreasing from a maximum value and then remaining stable after the addition of air cooling. However, as the air cooling size increases, the initial value of the interfacial heat flux becomes larger and larger. This is because air cooling improves the cooling rate of the casting, increases the heat transfer driving force between the casting and the sand mold, and causes the initial heat flux density to increase. The addition of air cooling eliminates the thermal saturation phenomenon of the sand core, the heat flowing into the sand core increases, and the heat flowing into the sand mold decreases. The increase in the initial heat flux density of the sand mold and the decrease in the heat flowing into the sand mold cause the interfacial heat density between the air-cooled casting and the sand mold to be smaller than that without air cooling in the later stage of casting solidification and cooling. The larger the air cooling size, the smaller the interfacial heat flux density.
For the interfacial heat transfer coefficient between the casting and the sand mold under different air cooling sizes, the addition of forced air cooling changes both the value and the shape of the interfacial heat transfer coefficient. In terms of value, the addition of forced air cooling increases the maximum value of the interfacial heat transfer coefficient, decreases the minimum value, and increases the variation amplitude of the interfacial heat transfer coefficient. As the air cooling pipe size increases, both the maximum and minimum values of the interfacial heat transfer coefficient gradually increase. From the perspective of the variation shape of the interfacial heat transfer coefficient, the interfacial heat transfer coefficient under the addition of forced air cooling still maintains a “double-peak” shape, but the addition of forced air cooling makes the “double-peak” shape more and more obvious. As the air cooling pipe size increases, the time when the first peak appears gradually advances, and the peak value gradually increases. The addition of forced air cooling causes the time when the second peak appears to advance, but the change in air cooling pipe size has little effect on its appearance time, and its peak value gradually decreases as the air cooling pipe size increases.
To more intuitively study the influence of air cooling pipe size on the interfacial heat transfer coefficient, I explored the influence of air cooling pipe size on the value of the interfacial heat transfer coefficient and cooling time. As the air cooling pipe size increases, the maximum value of the interfacial heat transfer coefficient increases by 50%, 75%, and 120%, respectively. The maximum value of the interfacial heat flux density and the maximum value of the sand mold temperature slowly increase with the increase of air cooling pipe size. As the air cooling pipe size increases, the cooling time increases by 22%, 35%, and 48%, and the time when the maximum value of the interfacial heat transfer coefficient appears decreases significantly. The addition of air cooling makes the time for the sand mold temperature to reach its maximum value longer and gradually shortens with the increase of air cooling pipe size.
From this section, it can be seen that the addition of air cooling can effectively shorten the cooling time of the casting and eliminate the thermal saturation phenomenon of the sand core. Increasing the air cooling pipe size causes the interfacial heat transfer coefficient to increase, and its average value can reach more than twice that of the no air cooling condition.
12. Mechanism of Forced Air Cooling on the Interfacial Heat Transfer Coefficient
12.1 Mechanism for Cast Aluminum
The relationship between the interfacial heat transfer coefficient and the solid fraction for air cooling and no air cooling of aluminum alloy shows that when the solidification rate is close to 10%, heterogeneous nucleation occurs at impurity particles of the molten metal on the sand mold, and a very small metal shell is generated in this area. The generation of the metal shell leads to the formation of a tiny air gap, and the generation of the air gap causes the interfacial heat transfer coefficient to decrease. It can be seen from the figure that both air-cooled and non-air-cooled cast aluminum parts have a decrease in the interfacial heat transfer coefficient at a solid fraction of about 10%.
When the solidification rate is between 10% and 50%, the interfacial heat transfer coefficient of the non-air-cooled cast aluminum part continues to increase, while the interfacial heat transfer coefficient of the air-cooled cast aluminum part begins to decrease slowly. For forced air-cooled castings, the addition of air cooling increases the cooling rate of the molten metal. The places where the casting and the sand mold first solidify and nucleate rapidly solidify into a tiny metal shell with a certain thickness. The thickness of this metal shell is relatively large and can maintain the existence of the air gap, resulting in a decrease in the interfacial heat transfer coefficient. As more and more molten metal solidifies, more and more solid phases are generated, and more and more tiny air gaps are generated, resulting in a continuous decrease in the interfacial heat transfer coefficient. However, the thickness of the metal shell generated by the non-air-cooled casting is small and cannot resist the pressure of the molten metal, so the shell will break, and the air gap cannot continue to form and increase. Therefore, with the release of latent heat of crystallization, the interfacial heat transfer coefficient gradually increases.
When the solid fraction reaches about 50%, that is, at the CSF point, both air-cooled and non-air-cooled castings will experience a sharp drop in the interfacial heat transfer coefficient. The molten metal loses its ability to feed the gaps between dendrites near the CSF point, resulting in obvious air gaps and a sudden decrease in the interfacial heat transfer coefficient. The air-cooled cast aluminum part has formed more air gaps before this, and the places where air gaps can be formed at this time are relatively small, so the interfacial heat transfer coefficient decreases less. The non-air-cooled part has almost no air gaps before, so a large number of air gaps are formed at this time, and the interfacial heat transfer coefficient decreases more.
When the solidification rate is greater than 50%, the interfacial heat transfer coefficients of both air cooling and no air cooling basically remain unchanged. Because at this time the air gap has been generated and the thickness is large, the shrinkage of the casting and the sand mold will cause the air gap thickness to increase, but it can no longer have a great impact on the interfacial heat transfer coefficient.
12.2 Mechanism for Cast Steel
In cast steel, forced air cooling affects the thickness of the air gap, thereby affecting the interfacial heat transfer coefficient of the casting. The addition of air cooling improves the cooling rate of the casting, accelerates the heat transfer driving force between the casting and the sand mold, and increases the interfacial heat transfer coefficient. The change in the interfacial heat transfer coefficient of cast steel can be divided into five stages. I will discuss the influence of forced air cooling on each stage and the resulting results.
In the first stage, the initial stage of the decrease in the interfacial heat transfer coefficient, this stage is mainly due to the decrease in the interfacial heat transfer coefficient caused by the appearance of the air gap during the solidification of the molten metal. The addition of air cooling increases the size of the initial air gap, resulting in a larger decrease in the interfacial heat transfer coefficient. The larger the air cooling pipe size, the more the interfacial heat transfer coefficient decreases.
In the second stage, the rising stage of the first peak, the casting temperature decreases and the volume shrinks; the sand mold temperature increases and the volume expands. The addition of air cooling accelerates the shrinkage speed of the casting, the air gap thickness increases faster, and the interfacial heat transfer coefficient tends to decrease. The addition of air cooling accelerates the expansion speed of the sand mold, the air gap thickness decreases faster, and the interfacial heat transfer coefficient tends to increase. In this stage, the thermal shrinkage of the casting is weaker than the thermal expansion of the sand mold, resulting in an increase in the interfacial heat transfer coefficient. The larger the air cooling pipe size, the faster the volume changes of the casting and the sand mold, the faster the air gap thickness changes, the faster the interfacial heat transfer coefficient rises, and the faster the time to reach the first peak.
The third stage is the falling stage of the first peak. This stage is also affected by the above two factors, but at this time the shrinkage of the casting dominates. Overall, the thickness of the air gap gradually increases, and the interfacial heat transfer coefficient gradually decreases. As the air cooling pipe size increases, the cooling rate of the casting increases, the volume shrinkage becomes faster, resulting in a faster increase in the air gap thickness and a greater decrease in the interfacial heat transfer coefficient.
The fourth stage is the rising stage of the second peak. In this stage, the casting undergoes pearlite transformation and volume expansion, causing the air gap thickness to decrease. The sand mold continues to cool, and the volume shrinks, causing the air gap thickness to increase. In this stage, the pearlite transformation dominates, so overall the air gap thickness decreases, and the interfacial heat transfer coefficient increases. The addition of air cooling accelerates the shrinkage of the sand mold, which hinders the decrease in air gap thickness. Therefore, the larger the air cooling size, the smaller the increase in the interfacial heat transfer coefficient. When the air cooling size is φ80, the second peak value is very small.
The fifth stage is the decreasing stage of the interfacial heat transfer coefficient, that is, the decreasing stage of the second peak. The addition of air cooling has little effect on the interfacial heat transfer coefficient in this stage.
From the above analysis of the five stages of the change in the interfacial heat transfer coefficient, it can be seen that the change in air gap thickness causes the shape and value of the interfacial heat transfer coefficient under forced air cooling conditions to change compared with no air cooling. The addition of forced air cooling causes the air gap thickness to change more violently and rapidly. This is because the addition of forced air cooling affects the temperature fields of both the casting and the sand mold. The changes in the temperature fields of the sand mold and the casting cause the laws of density change with time during solidification and cooling to change, thereby affecting the law of the air gap thickness between the sand mold and the casting changing with time, thereby affecting the interfacial heat transfer coefficient. For the casting, the addition of forced air cooling reduces the hindering effect of the sand core on the heat dissipation of the casting, thereby improving the cooling rate of the casting. The increase in the cooling rate of the casting makes the temperature drop faster during solidification and cooling, and the volume shrinkage rate of the casting itself accelerates. The acceleration of the volume shrinkage rate of the casting itself causes the air gap thickness to change faster. For the sand mold, under forced air cooling conditions, the acceleration of the cooling rate of the casting and the disappearance of the thermal saturation phenomenon of the sand core will cause its temperature field to heat up faster in the initial stage and cool down faster in the later stage, and the maximum sand mold temperature increases. The above phenomena will cause the volume change rate of the sand mold itself to increase, and it will heat up and expand and cool down and shrink in a shorter time. The faster volume change of the sand mold in a shorter time will cause the air gap thickness to change more rapidly and violently. In summary, the addition of forced air cooling makes the volume changes of the sand mold and the casting more rapid. Under the joint action of the sand mold and the casting, the thickness of the air gap between them also changes more violently and rapidly, resulting in more rapid and violent changes in the interfacial heat transfer coefficient.
12.3 Similarities and Differences Between Cast Steel and Cast Aluminum Under Air Cooling
The influence of air cooling on the interfacial heat transfer coefficient is mainly through the improvement of the solidification rate of the casting by air cooling, thereby affecting the change of the air gap. The change of the air gap causes the change of the interfacial heat transfer coefficient. For cast aluminum parts, the addition of air cooling causes the air gap to appear earlier and the initial size to increase, resulting in a slow decrease in the interfacial heat transfer coefficient before the casting temperature drops to the critical solid fraction temperature. For cast steel parts, the addition of air cooling causes the air gap thickness to change more violently and rapidly. The peak values in the “double-peak” form of the interfacial heat transfer coefficient increase, and the time when the peaks appear advances.
The interfacial heat transfer coefficient of cast aluminum parts still maintains an “s”-shaped curve with decreasing temperature, and its value is greatly improved compared with the no air cooling condition. Before the casting temperature drops to the critical solid fraction temperature, there is a process of slow decrease in the interfacial heat transfer coefficient. Under air cooling conditions, the interfacial heat transfer coefficient of cast steel still maintains a “double-peak” form. The increase in air cooling pipe size makes the peak values of the two peaks larger and larger, and the time when the peaks appear earlier and earlier. The average value of the interfacial heat transfer coefficient can reach more than twice that of the no air cooling condition. Forced air cooling has an enhancing effect on the interfacial heat transfer coefficient during sand mold casting of annular castings. Forced air cooling improves the heat dissipation rate of the casting, improves the heat transfer speed between the casting and the core, and affects the formation of the air gap and the thickness of the air gap. Forced air cooling makes the air gap appear more rapidly and the air gap thickness change more violently, thereby increasing the average value of the interfacial heat transfer coefficient and producing an enhancing effect.
13. Conclusions
Based on the experimental measurements and inverse calculations, I draw the following conclusions:
(1) The interfacial heat transfer coefficient of ZL101 castings follows an “s”-shaped curve with temperature. As the casting temperature decreases, the interfacial heat transfer coefficient first increases. When the casting temperature drops to 575 °C, the interfacial heat transfer coefficient undergoes a step-like decrease and then remains stable or slowly decreases. After pouring of 40 steel castings, the interfacial heat transfer coefficient shows a “double-peak” form with time. After pouring, as time increases, its value first increases rapidly to a maximum value, then drops stepwise to a minimum value, then slowly rises to a second extreme point, and finally slowly decreases.
(2) Forced air cooling has an enhancing effect on the interfacial heat transfer coefficient during sand mold casting of annular castings. When air cooling is added, the interfacial heat transfer coefficient of cast aluminum parts still maintains an “s”-shaped curve as the casting temperature decreases, and its value is greatly improved compared with that without air cooling. Under air cooling conditions, the interfacial heat transfer coefficient of cast steel still maintains a “double-peak” form, and its average value can reach more than twice that of the no air cooling condition.
(3) The change in the interfacial heat transfer coefficient during the solidification and cooling of the casting is related to the air gap formed between the casting and the sand mold. The appearance of the air gap and the increase in its thickness cause a decrease in the interfacial heat transfer coefficient, while a decrease in the air gap thickness causes an increase in the interfacial heat transfer coefficient. When the molten metal of cast aluminum solidifies to the critical solid fraction (temperature about 575 °C), the generation of the interfacial air gap causes the interfacial heat transfer coefficient to drop sharply. During the cooling process of cast steel after the molten metal solidifies, the volume changes of the casting and the sand mold cause the thickness of the interfacial air gap to change, resulting in the “double-peak” form of the interfacial heat transfer coefficient.
| Condition | Cast aluminum ZL101 | Cast steel 40 |
|---|---|---|
| No air cooling | “s”-shaped curve; sharp drop at 575 °C | “double-peak” curve |
| Forced air cooling | “s”-shaped curve; average h increases by 52% | “double-peak” curve; average h more than 2 times |
| Air gap effect | Initial air gap appears around 614 °C; critical solid fraction at 575 °C | Volume changes and phase transformations control air gap thickness |
| Cooling time | Solidification time shortened by 25% | Cooling efficiency improved by 50–111% depending on pipe size |
These findings provide a reliable data foundation and theoretical basis for the application of forced air cooling technology in the sand mold casting industry. The optimized Beck inverse algorithm, combined with measured temperature fields, can effectively determine the interfacial heat transfer coefficient under complex external field conditions. The interfacial heat transfer coefficient is not a constant but a complex function of time, temperature, casting material, casting size, sand type, and forced cooling intensity. Accurate determination of this coefficient is essential for improving the reliability of numerical simulation in sand mold casting and for optimizing the forced cooling process in practical production.