Section 1 Semi Solid Casting

## **Chapter 1**

## Slope Casting Process: A Review

*Mukkollu Sambasiva Rao and Amitesh Kumar*

## **Abstract**

Semi solid processing is a near net shape casting process and one of the promising techniques to obtain dendritic free structure of metals. Semi solid casting gives numerous advantages than solid processing and liquid processing. Semi solid casting process gives, Laminar flow filling of die without turbulence, Lower metal temperature, Less shrinkage, Less porosity, Higher mechanical properties. Semi solid casting process is industrially successful, producing a variety of products with good quality. Slope Casting process is a simple technique to produce semi solid feed-stoke with globular microstructure and dendrite free structure castings. Slope casting process depends on different process parameters like slope length, slope angle, pouring temperature etc. The present study mainly focuses on review of various explorations made by researchers with different process parameters of the Slope casting process and explain the mechanisms that lead to microstructural changes which leads to good mechanical properties.

**Keywords:** semi-solid process, thixo casting, Rheo casting, slope casting, aluminum alloys, non dendritic structure, slope length, slope angle, slope plate temperature, slope vibration

## **1. Introduction**

Semi-solid processing as the name suggests is the processing of non-dendritic material between its liquidus and solidus temperatures. In recent years, much work has been conducted in exploring this field with respect to understanding the mechanisms involved. The inherent properties of semi-solid materials at the semi-solid processing temperature such as lower heat content, relatively higher viscosity comparable to liquids and low flow stresses, enables the semi-solid process to show distinct advantages over fully liquid and/or fully solid-state processes. Some of the important benefits of this technique are low mold erosion, low energy consumption, improved die filling, less gas entrapment, lower solidification shrinkage, reduced macro-segregation and fine microstructure. Therefore, this process is rapidly gaining commercial importance [1–3]; A non-dendritic microstructure can be obtained by stirring, either mechanically or electro-magnetically; grain refining; low superheat melt processing; solid state mechanical treatment and reheating [4–7]; The manufacturing industries widely focused on the semi solid routes to produce components with superior mechanical and metallurgical properties. Slope casting process is one of the simplest techniques to produce semi solid slurry [8]. Slope cating process is pouring of molten metal through a slope channel into a mold. This slope channel help as a site for nucleation and

fragmentation of dendrites due to shearing force between different layers of flowing stream [9]. Slope casting process depends on different process parameters like slope length, slope angle, pouring temperature etc. [10–14]. In recent years Aluminum alloys are using mostly in the automotive industries. Among the Aluminum alloys, the Al-Si alloys have good casting characteristics like high fluidity and good cast-ability which makes them advantageous for both small and complicated castings. Every year lakhs of Aluminum alloy components are produced through semi solid processing route. The present study mainly focuses on review of various explorations made by researchers with different process parameters of the Slope casting process and explain the mechanisms that lead to microstructural changes which leads to good mechanical properties.

## **2. Semi-solid casting**

The processing of alloy between liquidus and solidus (mushy zone) range is known as the semi solid process, it was first discovered in 1970s, by spancer at Massachusetts Institute of Technology (MIT); found that at semi solid range of alloy behaves thixotropically (Decreases in viscosity if it is sheared but it will thicken again if it is allowed to stand)and by applying continuous stirring on the semi solid state produced no dendritic and spheroidal microstructure [15–19]. The semi solid casting route gives enormous advantages like dendritic free structure leads to globular structure as seen in **Figure 1**, less defects such as porosity, shrinkage, gas entrapment and macro-segregation. Better advantages than conventional casting that superior quality, low forming temperature, superior mechanical properties with microstructural refinement. The semi-solid process results in a non-dendritic microstructure due to forming at a temperature between solidus and liquidus temperature as shown in phase diagram, **Figure 2**. In semi solid process, temperature has a pivotal role on the resultant microstructure like orientation of grain, morphology of grain during solidification of alloys [22–24]. Semi-solid processing is used for all the shape forming processes which take advantage of the semi-solid range of the alloys for processing. Rheology and Thixotropy, two basic phenomena play a major role, In semi-solid processing. The apparent viscosity of a material in the liquid state varies with change in shear rate In Rheology. This gives the liquid like slurry to be processed even at sufficiently high solid fraction [25]. Thixotropy, is the ability of a material to Decreases

**Figure 1.** *Using semi solid process technique dendritic structure changes to globular [20].*

**Figure 2.** *Phase diagram of Al-Si alloy [21].*

in viscosity if it is sheared but it will thicken again if it is allowed to stand [26]; A material with a non-dendritic structure is the best suitable material for semi-solid processing. it is believed that, in the semi-solid state, the non-dendritic equiaxed grains easily slide/glide on each other on the application of a shear force [27].

Thixotropy behavior can be define as when the material state is partially solid with 40–50% solid fraction and is sheared applied by external force, then its viscosity will decrease due to the break/detachment of the coalescence material, and it will flow like a liquid, for a certain time if it is allowed to stand, equiaxed coalescence will increase the viscosity of the material, by that it being able to support its own weight in the same way as if it was solid [28].

## **2.1 The mechanism of non-dendritic structure**

To describe mechanism for non-dendritic structure in semi solid process many theories have been proposed. These mechanisms include dendrite arm fragmentation, dendrite arm root re-melting, and growth control mechanism. Hv Atikson et al. [20], Vogel et al. [29]; proposed that under shearing forces dendrite arms bends due to its plasticity, which introduce large misorientations inside the dendrite arms and dislocations introduced; rearrangements of dislocations occur to form grain boundaries at the melting temperature. The energy of the grain boundaries becomes more than twice the liquid/solid interfacial energy when the misorientations between grain boundaries are more than 20°, then separation of the dendritic arms observes due to wetting of the grain boundaries by liquid metal. Schematically illustrated in **Figure 3**.

Hellawell et al. [30]; proposed grain multiplication theory, Thermal convention and shearing force have a direct effect at the roots of secondary dendrite arms, melting off rather than breaking off secondary arms observed, and grain multiplication, schematically illustrated in **Figure 4**. Evolution of structure during solidification with shear force depends on the cooling rate and shear rate, with increase in shear and cooling rate gives non dendritic/globular structure that that the particle shape and size vary irreversibly with shear and colling rate. Illustrate in **Figure 5**.

#### **Figure 3.**

*Schematic illustration of the steps of the mechanism of dendrite fragmentation: (a) undeformed dendrite; (b) after bending; (c) formation of high-angle boundary; and (d) fragmentation through wetting of grain boundary by liquid metal [22].*

**Figure 4.** *Schematic diagram of dendrite multiplication theory [22].*

### **2.2 Classification of semi solid process**

The semi solid casting process mainly classified into the thixo casting and rheo casting and these processes are farther divided into many process techniques show in below (**Figure 6**).

*Slope Casting Process: A Review DOI: http://dx.doi.org/10.5772/intechopen.102742*

#### **Figure 5.**

*Evolution of structure during solidification with shear force: (a) initial dendritic fragment; (b) dendritic growth; (c) rosette; (d) ripened rosette; and (e) spheroid [20].*

#### **Figure 6.**

*Classification of semi solid processes [31].*

#### *2.2.1 Thixo casting*

Thixo casting mainly consists of three separate stages the production of a pre-cast billet having the special equiaxed microstructure, the re heating of these billets to the semi-solid temperature and the casting of the components 3. Illustrated in **Figure 7**.


## *2.2.2 Rheo-casting*

Rheo-casting is single step process to produce semi solid alloy start with liquid alloy, introduced directly into a mold without any intermediate solidification step. The semisolid slurry produced by means of different process like slope casting, new rheo casting etc. and directly introduced into a die. While thixo-forming is a route consists of reheating and forming process (**Figure 8**).

**Figure 8.** *Rheo casting process [2].*

## **3. Slope casting process**

Slope casting process is a rheo casting process used for the produce semi solid slurry, it consists with simple equipment and operation technique, the process carried out by pouring molten metal through channel with certain angle into a die where subsequent solidification takes place [32]. The solidification of molten alloy along a slope channel involves heat transfer, fluid flow, adhesion behavior. When the molten metal flowing through the slope channel with an angle and length [33–37], heat transfer takes between the slope channel wall and melt in contact, where generation of nuclei takes places, due to the effect of gravitation force and flow of stream the nuclei produced on slope wall are detached from the slope plate and subsequently flow through the melt stream, solid fraction of metal(semi solid slurry) observed at end of slope channel [38–42]. shear stress acting on the slurry layers and melt flow inertia restricted dendritic growth usually observed in conventional casting alloys. Illustrated in **Figure 9**. Slope casting process is a simple technique, but it can be prone to gas pick up and oxide formation which will impact negatively on mechanical properties [44, 45].

**Figure 9.** *Line illustration of slope casting process [43].*

## **3.1 Mechanisms involved in slope casting process**

Two mechanisms have been suggested to explain the formation of non-dendritic microstructure during flow along slope casting process. According to Haga and Kapranos et al. [46, 47], dendritic fragmentation mechanism plays an important role in slope casting process during microstructural evolution. The fragmentation of weak dendritic arms observed when the partially solidified melt collides under gravitational forces on the inclined/slope channel. Motegi et al. [48] proposed, crystal separation theory, where granular crystals nucleate and grow on the slope wall and are washed away from the wall by fluid motion illustrated in **Figure 10**.

The shear force is main factor for dendritic arm fragmentation but its effect is related to the velocity boundary layer [21] as shown in **Figure 11**.

## **3.2 Parameters effect the slope casting process**

The process parameters in the slope casting of semisolid slurry preparation are [21, 31, 43–49]:

• Pouring temperature,


#### **Figure 10.**

*Crystal separation theory (a). The generation of nuclei at slope plate wall (b). Segregation of granular crystal (c) flow through the melt [30].*

#### **Figure 11.**

*Schematic diagram of the shear stress variation and velocity distribution inside the boundary layer during the flow of melt in cooling slope casting process [38].*

## *3.2.1 Effect of pouring temperature*

It is the most influencing parameter in slope casting process, T hogo et al. [36] investigated the effect of melt temperature and mold material found that pouring temperature have the great effect on the microstructure and it accounts nearly 35% of the total effect. Y Birol et al. [37] investigated the effect of pouring temperature and slope length, reported that the melt superheat required longer cooling lengths for higher pouring temperatures. Pouring with lower temperature causes formation of solid shell (formation of a thin layer of metal due to the primary nuclei that stick to the slope channel that reduces the effectiveness of the slope channel in generating nuclei) and pouring with the super-heated temperature may not get sufficient time to cool to range to produce solid nuclei on the slope plate, the main reason is that each parameter corelate each. Similar observation reported by Wen Liu et al. [39], if pouring temperature is too high a small number of primary α-aluminum phase will precipitate and some coarse primary α-aluminum phase. If the pouring temperature is too low the melt will cool rapidly and solidify. P. das et al., the temperature of the cooling plate has no prominent effect on microstructure, nevertheless a slurry with approximately 10% fraction solid can easily be obtained at the end of the plate.

## *3.2.2 Effect of slope length*

Most of studies, slope length ranges from 200 to 800 mm, H. bidhiman et al. [41]. reported that increase in slope length that means melt flow time through channel increases it may cause the temperature drop and formation of the oxidation and solid shell as we above discussed it causes decrease in rate of heat transfer which leads to the decrease of the nucleation rate of primary solid phase, too short length does not give the proper nuclei formation and the time for the dendritic fragmentation. Slope length and slope angle are interrelated. If slope angle high need slope length should be more otherwise melt does not get sufficient time for shearing. The slope length effect on final microstructure accounts nearly 30% from studies. P. das et al. [40].

## *3.2.3 Effect of the slope angle*

Most studies the angle ranges from 15 to 60°, the small angle is unable to give the melt to flow and shear effect on the slope plate will be less and the higher angle may cause the high velocity which does not give time to melt formation semi solid slurry and dendritic fragmentation. Farshid Taghavi and Ghassemi [42] reported the angle of slope channel had remarkable effects on the size and morphology of α-Al phase. By increasing the angle of the slope channel, the effect of shear stress and the rate of heat transfer increase. As a result, more solid particles are detached from the layer of slope channel. On the other part, duration time of shear stress and heat transfer between the melt and surface of inclined plate decrease by increase in the angle. As we above discussed in 3.2.2. the slope length and slope angle corelated to each other.

## *3.2.4 Effect of the slope vibration*

Very few studies on effect of vibration slope on microstructural changes. Slope vibration frequency ranges from 10 to 60 Hz. Studies by Shaya Safari et al. [44],

Wen Liu et al. [39] conclude that There was no solid shell formation on the surface of slope channel by using slope vibration. The combine effect of vibration and slope channel causes increase in the amount of nucleation and nuclei due to uniform cooling rate. The mechanism in vibration slope channel is proposed that vibrating force and gravity result in Bending stress introduced in between the growing dendritic and liquid. Because of the viscous resistance of liquid, with respect to the dendritic particles and liquid phase there is a difference of the transport velocity, which causes crash among the grains and the scrub of the liquid on dendritic particles. The weak dendrite arms breakoff and form fine grains. Vibration helps the heat transfer mechanism in possible direction. The stirring caused by vibration gives rise to local temperature fluctuation of liquid phase around the primary α-al phase and Re melting of dendritic arms at the necks occurs. Which favorable to form short and homogenous small primary dendrites, equiaxed and rosette non dendritic grains.

## *3.2.5 Heat treatment by reheating*

Researchers extended work on Slope casting process by subsequent heat treatment of casts after slope casting for better mechanical properties through spheroidization of grains and removal of defects like internal stress and porosity. Yucel Birol et al. [37] worked on the cooling slope casting and thixo forming of hypereutectic A390 alloy. Reported that The thixoformed part after slope casting process was metallurgically sound, free from porosity and revealed a uniform dispersion of fine Si particles in a homogeneous matrix. Increase mechanical properties observed. Nursen Saklakoglu et al. [33]: investigated on the microstructural evolution of ETIAL 160 aluminum feed stock produced by the cooling slope casting process experiments done with pouring temperatures of 605 and 615°C respectively subsequent isotheral heating at 565°C at 5 and 10 mins respectively, slope casting process results the primary α-aluminum dendrites has changed into α-aluminum rosette. Subsequent heat treatment helps to modify the rosette to globular structure. P das et al. [40]; too long a heating time will cause structural coarsening, while too short a heating time will lead to incomplete spheroidization of solid particles. Thus, there is a need to get optimum reheating parameters of the semi-solid alloys processed via slope casting.

## **3.3 Composites by slope casting**

Composite materials produced using slope casting technique were reported by researchers. P. Das, [40] has studied about the semi solid microstructure of Mg2 Si/Al composite by cooling slope casting process, reported that, the morphology of primary Mg2Si obtained non-dendritic and size of α Al was changed to 10 from 200 μm, Toshio Haga et al. [36]. Reported that slope casting has a significant influence on the shape and grain morphology of the Metal matrix composites (MMCs). The properties of the MMCs produced by slope casting were found to be higher than those of the MMCs produced by using conventional stirring.

Distinguished the literature into table according to the optimum process parameters used in Slope Casting Process of Semi-Solid Alloys and Composites shown in **Table 1** and post parameters in **Table 2**.


## *Slope Casting Process: A Review DOI: http://dx.doi.org/10.5772/intechopen.102742*


#### *Casting Processes*


*Slope Casting Process: A Review DOI: http://dx.doi.org/10.5772/intechopen.102742*


**Table 1.** *Process parameters.*

#### *Casting Processes*

## *Slope Casting Process: A Review DOI: http://dx.doi.org/10.5772/intechopen.102742*



#### **Table 2.**

*Post process parameters.*

## **4. Conclusions**

A considerable review of the literature on slope casting of semisolid Aluminum alloys suggest the following:


## **Author details**

Mukkollu Sambasiva Rao\* and Amitesh Kumar National Institute of Advanced Manufacturing Technology, Ranchi, India

\*Address all correspondence to: samba.siva129@gmail.com

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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## **Chapter 2**

## Squeeze Casting Process: Trends and Opportunities

*Adeolu Adesoji Adediran, A. Babafemi Ogunkola, Francis Odikpo Edoziuno, Olanrewaju Seun Adesina, M. Saravana Kumar and Osueke Christian Okechukwu*

## **Abstract**

This chapter introduces the importance of casting process, particularly in ferrous foundries. It opens with a high level functional classification of casting processes, with focus on squeeze casting, and its application in the design of metal matrix composites. To lay a suitable foundation on the subject, detailed discussions on the process parameters, process sequence, cost effectiveness, factors governing the selection of the process, associated casting defects, merits and demerits of the process are included. Special emphasis is given to discussions on the casting defects remedial measures and casting quality, types of squeeze casting processes, differences between them, area of application and components that can be manufactured using squeeze casting. The chapter closes with a brief discussion on the future trends and opportunities for improving the squeeze casting process.

**Keywords:** casting process, surface finish, squeeze casting, mold and foundry

## **1. Introduction**

Metal matrix composites (MMCs) are frequently produced through squeeze casting. Because of their superior stiffness and strength than homogenous materials, MMCs are frequently used to replace engineered materials. MMCs have been used in aeronautical, automotive, and defense engineering structural applications. MMCs are typically made in industries using squeeze casting, stir casting, infiltration, and spray deposition techniques [1]. It is particularly well-known in the automotive industry for the production of diesel engine pistons. This chapter describes the process, parameters, applications and casting flaws that occurs during squeeze casting of metal matrix composites [2]. The mechanism of the defects creation is examined, as well as its implications for squeeze casting's future.

## **2. Casting processes**

Molten materials, usually metals and their alloys, are used in casting operations. After that, the molten material is poured into a mold cavity, which takes the shape of the finished part. The molten material then cools until it solidifies into the required shape, with heat being extracted and conducted mostly through the mold. Despite the fact that the above represents a reasonably straightforward operation, casting is inherently a difficult process due to the metallurgy of working with molten metal [3].

## **2.1 Classification of casting processes**

Casting techniques can be divided into two categories based on the type of mold.

## **2.2 Materials**


The molds are destroyed in expendable mold operations in order to remove the casting. Sand, plaster, and ceramics mixed with a bonding agent are common mold materials. Permanent mold procedures, on the other hand, require the mold to be created in such a way that the casting may be easily removed. Permanent molds are typically formed of metals that keep strength at high temperatures.

Various casting procedures can be used, as shown in **Figure 1**. The majority of them can handle complex geometries in a variety of weights and sizes. Overall, these casting procedures are utilized, because:


## **Figure 1.**

*General classification of casting processes [4].*


Other factors are considered while determining the suitability of distinct casting techniques for a given part. Under the category of general qualities, these are discussed. Finally, casting processes are used to classify a variety of plastic processing techniques [5].

## *2.2.1 Importance of casting processes in ferrous foundries*


## **3. Squeeze casting**

Because of its ability to mass produce, simpler process parameter control, improvements in wettability of the reinforcements by the liquid metal, better metallurgical quality of matrix alloys due to solidification under pressure, and the ability to reinforce only selected regions of components, squeeze casting is the preferred metal matrix composite manufacturing process for a wide range of commercial applications [6].

Squeeze casting is a hybrid of casting and forging in which molten metal is injected into a warmed die and the upper die is closed after solidification to form the mold cavity. Squeeze casting causes the metal to completely fill the cavity due to the pressure produced by the higher die, resulting in a good surface quality and low shrinkage.

Both ferrous and non-ferrous alloys can be squeeze cast, however aluminum and magnesium alloys are the most frequent due to their lower melting temperatures. Parts for automobiles are a popular use [7].

The liquid metal is forced against the die walls, preventing air gaps from forming at the casting–die interface. Because pressure is applied, defects such as porosity and shrinkage are minimized, allowing for the production of finer grain castings with higher strength [8].

Preheating the die containing the preform to 300–400°C is the first step in the casting process. The punch is then driven into the die cavity at a constant ram speed of around 10 m/s after the molten metal has been injected into the die. In most circumstances, a pressure of 20–30 MPa is ideal. During solidification and a subsequent cooling time of 5–10 min, the pressure is maintained [9]. After then, the ram is removed and the composite is ejected. Squeeze casting enables for the elimination, or at least reduction, of not just gas porosity, but also flaws caused by solidification shrinkage. The origins of squeeze casting can be traced back to squeeze forming, which is a three-phased process:


A schematic of a squeeze casting procedure is shown in **Figure 2**.

## **3.1 Types of squeeze casting process**

The two basic forms of squeeze casting process may be distinguished, depending on the natural pressure applied as shown in **Figure 3**.


**Figure 2.**

*Schematic representative of a typical squeeze casting machine [10].*

*Squeeze Casting Process: Trends and Opportunities DOI: http://dx.doi.org/10.5772/intechopen.103764*

**Figure 3.** *Direct and indirect squeeze casting [11].*

## • **Direct squeeze Casting**

Direct squeeze casting (DSC) is also known as liquid metal forging. The DSC method involves Pouring liquid metal into a warmed, lubricated die and forging it while it solidifies [12]. The pressure is applied shortly after the metal begins to freeze and maintained until the entire casting has solidified. Casting ejection and handling are identical to closed die forging ejection and handling.

## • **Indirect Squeeze Casting**

Direct squeeze casting (DSC) is often performed on a vertical machine (akin to a forging press), whereas indirect squeeze casting (ISC) is performed on both vertical and horizontal machines. During indirect squeeze casting, molten metal is fed to the shot sleeve and then injected into the die cavity through relatively large gates and at a low velocity (usually less than 0.5 m/s). The plunger applies high pressure "indirectly" through the huge gating system to solidify the melt in the die cavity. **Figure 4** compares the metal flow in a typical die casting method to an indirect squeeze casting method [12].

#### **Figure 4.**

*Schematic illustration of metal flow in (a) conventional die casting; and (b) indirect squeeze casting process [12].*


#### **Table 1.**

*Differences between direct squeeze casting method and indirect squeeze casting method [13].*

The slower injection speed of the ISC method supports planar filling of the metal face within the die cavity, removing trapped gases from the castings (**Table 1**).

#### **3.2 Reasons for squeeze casting**

There has been a continuing need and necessity to make automobiles lighter and more fuel efficient while also improving passenger comfort. Automobile makers have been looking for solutions to keep or reduce vehicle mass. Dies have prompted die casting producers to develop new parts that were formerly iron castings or stamped steel assemblies, as well as stronger die castings that can be welded and painted. Because it gives characteristics to the metal that are difficult to accomplish with GPM casting and standard die casting, squeeze casting is typically referred to as a 'high integrity' method. Reduced porosity in the metal matrix, improved mechanical capabilities, and increased wear resistance are among the improved qualities. Squeeze castings can also be heated-treated, which is not possible with traditional die castings. In comparison to traditional die castings, thicker runner systems and, in particular, massive in-gates are utilized. The casting can be solidified under sufficient pressure to avoid practically all shrinkage by properly positioning the in-gates and maintaining high pressure on the molten alloys, as well as the use of pressure pins (if needed) during solidification. The high pressure used during solidification retains the molten metal in direct contact with the die surface, resulting in castings that are faithful to the die dimensions. Because the filling rates, also known as in-gate velocities, are low, entrapped gas in the casting is usually prevented with correct venting. As a result, the part is pore-free or substantially pore-free. Squeeze casting is a procedure that combines the benefits of both casting and forging into a single operation. The process's main selling points are the possible cost savings compared to forging and the metallurgical advantages compared to alternative manufacturing techniques. It has been demonstrated that the squeeze casting technique can generate sound and fine equiaxed grain structures in most commonly used cast alloys even some that are generally only employed in wrought form. This sound cast structure is bound to give the material isotropic properties. With excellent dimensional accuracy and repeatability, the squeeze casting technique may produce complex shapes. This allows designers to construct near-net shapes, reducing the need for further machining. Automobiles are subjected to extensive research and development in order to increase their efficiency and functionality. These enhancements frequently result in increased vehicle weight

*Squeeze Casting Process: Trends and Opportunities DOI: http://dx.doi.org/10.5772/intechopen.103764*

and decreased engine performance, resulting in poor fuel efficiency. Meanwhile, in order to address global environmental challenges, the desire for automobiles that are lighter and consume less gasoline is increasing. One viable option for addressing these criteria is to replace steel with aluminum. Engine blocks and gearbox cases are two examples of structural parts made from aluminum die casting. Die casting goods are currently being used in important safety elements such as suspension and space frames, which demand a high degree of strength, elongation, and yield strength.

## **3.3 Application of squeeze casting in the design of metal matrix composites (MMC)**

Depending on the type of hardening particles used and the intended application condition, metal matrix composite materials are made via casting or powder metallurgy. Aluminum, magnesium, copper, titanium alloys, and super alloys are the most frequent metal matrixes [14]. Graphite, carbon, oxides, carbides, boron, molybdenum, and tungsten are common hardening particle or fiber materials. Casting route is used to make the majority of reinforced aluminum. Depending on the composition of the aluminum alloys, several casting procedures are used. The most common casting methods are gravity, vacuum, rotary centrifugal, squeeze, and extrusion casting. In some cases, an automatic bottom pouring stir casting furnace (**Figure 5**) for melting aluminum and/or magnesium metals and alloys is provided, along with the various casting methods. The bottom pouring stir casting furnace has a bottom furnace that pours molten metal composites directly into the casting equipment by activating a single mechanism while the stirring process continues [16].

As a result, new casting procedures have been developed to minimize these flaws. Squeeze casting, out of all the current casting processes, offers the greatest potential

#### **Figure 5.** *Bottom type stir casting set up with squeeze casting attachment [15].*

## **Figure 6.**

*A micrograph of (a) squeeze casting and (b) conventional casting [17].*


## **Table 2.**

*Squeeze casting factors that have an impact on part quality [9].*

for producing fewer defective cast components. **Figure 6** shows the micrograph of a) squeeze casting and b) conventional casting (**Table 2**).

## **3.4 Squeeze casting process sequence**


The squeeze casting sequence of operation is schematically illustrated in **Figure 7.**

*Squeeze Casting Process: Trends and Opportunities DOI: http://dx.doi.org/10.5772/intechopen.103764*

#### **Figure 7.**

*Schematic illustrating squeeze casting process sequence of operations. (a) Melt charge, preheat, and lubricate tooling. (b) Transfer of melts into die cavity. (c) Close tooling, solidify melt under pressure. (d) Eject casting, clean dies, charge melt stock [18].*

### **3.5 Process parameters**

The primary process parameters during squeeze casting are as follows:


Process parameters: a number of parameters that can affect the casting quality for both direct and indirect Squeeze casting are explained below;


Squeeze casting is simple and low-cost, makes good use of raw materials, and has a lot of potential for automation at high speeds. The technique produces cast products with the best mechanical qualities possible. A fluid metal is solidified under pressure during solidification in the squeeze casting process, resulting in a high cooling rate and temperature gradient. Squeeze casting has a lot of advantages, including low porosity density, heat treatability, consistency, and good mechanical qualities [11].

*Squeeze Casting Process: Trends and Opportunities DOI: http://dx.doi.org/10.5772/intechopen.103764*

## **3.6 Merits and demerits of squeeze casting**

## **Merits**


## **Demerits**


## **3.7 Associated casting defects**

I.**Oxide inclusions:** Failure to maintain clean melt-handling and melt-transfer systems is the cause of oxide inclusions. Filters should be included in the melttransfer system, or molten metal turbulence should be controlled when filling the die cavity, to reduce the chances of introducing metallic inclusions. It's also a good idea to keep foreign materials out of open dies.

The image below represents oxide inclusion (**Figure 8**).

**Figure 8.** *Oxide inclusion on materials [19].*


**Figure 9.** *Porosity on cast materials [20].*

**Figure 10.** *Image of segregation on cast materials [21].*

more concentrated. Such flaws can be eliminated by increasing die temperature, reducing die closure time, or choosing a different alloy (**Figure 11**) [18].

V.**Blistering:** During turbulent die filling, trapped air or gas from the melt generates blisters on the cast surface when the pressure is released or during subsequent solution heat treatments. Degassing the melt and preheating the handling transfer equipment, utilizing a slower die closing speed, increasing the die and punch venting, and lowering the pouring temperature are all ways to avoid such problems (**Figure 12**).

**Figure 11.** *Optical image of centerline segregation [22].*

**Figure 12.** *Image of blistering on metal [23].*


**Figure 13.** *Image of cold lapping of a metal represented below [24].*

**Figure 14.** *Hot tearing shown on a cast metal [25].*

*Squeeze Casting Process: Trends and Opportunities DOI: http://dx.doi.org/10.5772/intechopen.103764*

**Figure 15.** *Image of stcking [26].*


**Figure 16.**

*Image of extrusion on a metal [27].*

IX.**Extrusion debonding** When the metal sits in the open die for a long time before being extruded to fill the die cavity, this happens. After the melt has been extruded around the partially hardened crust in the die, the oxide remains there, resulting in the absence of a metal-to-metal link at oxide stringer positions. Increase the tooling or pouring temperatures to prevent extrusion debonding. The production of oxide on the semi-liquid metal in the die can be reduced by reducing the die closure time (**Figure 16**) [28].

## **4. Future trends and oppportunities for improving squeeze casting process**

The introduction of squeeze casting as a production technique has provided a solution to these criteria, with the present emphasis on lowering materials use through near-net shape processing and the necessity for both higher strength and high ductility parts. Squeeze casting has been used in manufacturing in the United States, the United Kingdom, and Japan in recent years. Squeeze casting is gaining

popularity in the industry. Squeeze casting was first advertised as a solution for components that had difficulty with traditional castings. This could have been due to design constraints, new applications resulting in higher loads, increasing pressure tightness requirements, or a desire to improve customer reliability. Following this initial surge in the industry, replacements for aluminum forgings and conversions from ferrous castings, such as ductile iron, were the following growth areas. While smaller tonnage machines are frequently utilized in Japan, where customers are more diverse, squeeze castings are mostly used in the automotive industry in the United States. These uses are driven by the need to reduce vehicle weight. This necessitates the conversion of iron to aluminum, as well as the requirement for cost savings, which necessitates the conversion of existing processes such as forging and permanent mold to new ones. The majority of the automotive items are steering and suspension components, such as steering knuckles and control arms, as well as air conditioning components. Squeeze casting is the recommended method when fatigue and ductility are critical component qualities. There is a significant chance for squeeze castings to flourish as industry expertise with squeeze casting is combined with technical understanding. In the past, the method has been used on defective parts or poorly designed designs, with disastrous outcomes. However, when a deeper understanding of the process' capabilities is gained, and technically competent models and algorithms for squeeze casting optimization are established, new applications will consistently meet or surpass expectations. Squeeze casting parts and components can be used to replace cast iron and pressed steel parts in automobiles. Furthermore, when the pressure increases, structural improvements occur, allowing the tensile characteristics to be comparable to wrought aluminum [29].

## **4.1 Some components produced by squeeze casting**

The squeeze casting process has a number of applications which include; Dome, blades, disks, automotive wheels, pistons, gears, hydraulic brake valve, Brake master cylinder, steering knuckles, control arms.

## **5. Conclusion**

The process sequence, parameters and properties of squeeze casting operation with the attendant technical advantages over other conventional casting production techniques have been discussed in the foregoing sections. Squeeze casting of metal matrix composites is amenable to mass production, especially in the automotive industry. The process and production sequences can be subjected to automatic process control with the gains of consistent high casting quality and production rates. There exist a plethora of opportunities for future improvement and optimization of squeeze casting process parameters as researches and development efforts in the automobile industry and metal matrix composites is intensified.

*Squeeze Casting Process: Trends and Opportunities DOI: http://dx.doi.org/10.5772/intechopen.103764*

## **Author details**

Adeolu Adesoji Adediran1 , A. Babafemi Ogunkola1 \*, Francis Odikpo Edoziuno2 , Olanrewaju Seun Adesina3 , M. Saravana Kumar4 and Osueke Christian Okechukwu3

1 Department of Mechanical Engineering, Landmark University, Omu-Aran, Kwara State, Nigeria

2 Department of Metallurgical Engineering, Delta State Polytechnic, Ogwashi-Uku, Nigeria

3 Department of Mechatronics, Bowen University, Osun State, Nigeria

4 Department of Production Engineering, National Institute of Technology, Tiruchirappalli, Tamil Nadu, India

\*Address all correspondence to: ogunkolababafemi111@gmail.com

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

## **References**

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[8] Chelladurai SJS, Arthanari R, Nithyanandam N, Rajendran K, Radhakrishnan KK. Investigation of mechanical properties and dry sliding wear behaviour of squeeze cast LM6 aluminium alloy reinforced with copper coated short steel fibers. Transactions of the Indian Institute of Metals. 2018;**71**(4):813-822. DOI: 10.1007/ s12666-017-1258-8

[9] "lectureofsqueezecastingosama2 (1)"

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[12] Vinarcik EJ. Understanding defects in high integrity die castings. SAE Transactions. 2003;**112**:405-413

[13] Kwok TWJ, Zhai W, Peh WY, Gupta M, Fu MW, Chua BW. Squeeze casting for the production of metallic parts and structures. Encyclopedia of Materials: Metals and Alloy. 2021:87-99. DOI: 10.1016/ B978-0-12-819726-4.00038-7

[14] Kapranos P, Carney C, Pola A, Jolly M. Advanced casting methodologies: Investment casting, centrifugal casting,

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squeeze casting, metal spinning, and batch casting. Comprehensive Materials Processing. 2014;**5**:39-67. DOI: 10.1016/ B978-0-08-096532-1.00539-2

[15] Kannan C, Ramanujam R. Comparative study on the mechanical and microstructural characterisation of AA 7075 nano and hybrid nanocomposites produced by stir and squeeze casting. Journal of Advanced Research. 2017;**8**(4):309-319. DOI: 10.1016/j.jare.2017.02.005

[16] Bottom Pouring Type Stir Casting Furnace to form Metal Matrix. Available from: https://www.quickcompany.in/ patents/bottom-pouring-type-stircasting-furnace-to-form-metal-matrixcomposite-using-aluminium-magnesium [Accessed: January 25, 2022]

[17] Verma SK, Dorcic JL. Squeeze casting process for metal-ceramic composites. SAE Transactions. 1987;**96**:143-154

[18] Squeeze casting process: Part One: Total Materia Article. Avialble from: https://www.totalmateria.com/page.asp x?ID=CheckArticle&site=ktn&LN=TH &NM=172 [Accessed: January 25, 2022]

[19] Oxide Inclusion. Available from: https://www.giessereilexikon.com/en/ foundry-lexicon/Encyclopedia/show/ oxide-inclusion-3936/?cHash=ade0f107 20424c9d84b2636a8006a316 [Accessed: February 05, 2022]

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[29] Iyer A. Squeeze casting: The future. International Specifications of Ski Instructions. 2011:1-48

Section 2

## Green Sand Molding and Molten Metal Flow in Molds

## **Chapter 3**

## Methods to Determine, Influence and Improve the Flowability of Sand Mixtures

*Vincent Haanappel*

## **Abstract**

Due to increasing environmental awareness, more and more foundries started to replace the organic binders with an environment-friendly binder system based on inorganics. However, inorganic binder systems can only replace the conventional organic binders if all requirements, set by the foundry industry are being fulfilled. One of these is the production of high-quality cores, indicative of good compaction, no surface defects, and high surface smoothness. Such types of cores can only be manufactured when the sand mixture shows sufficient flowability. This chapter presents a study on the flowability of various types of sand mixtures all including inorganic binder systems finally to be used for the production of sand cores for the foundry industry. Results have shown that the flowability of sand mixtures can be modified and improved by (1) the addition of small amounts of surface-active agents and/or (2) well-chosen additives characterized by micro-sized spherical particles. The addition of only a few amounts of surface-active agents resulted in a significant improvement of flowability and thus of core quality. Similar results were achieved with the use of small concentrations of spherical micro-sized particles.

**Keywords:** flowability, sand mixture, inorganic binder, alkali silicate, surfactant, surface tension, additive, spherical particles, powder flow tester, cores

## **1. Introduction**

Environment-friendly binder systems for molds and cores are generally based on the use of a 2-component inorganic binder system consisting of a liquid alkali silicate and a powder-like solid consisting of various minerals. Since environmental awareness receives today more and more attention, the replacement of organic by inorganic binders result can be considered in this, resulting in a significant reduction of dirty smell and toxic emissions. This means that the introduction of the so-called inorganic binder system needs many research and development activities before it can replace the old-fashion organic binder systems. In this context, with the existing technology to heat cure the cores, high strength can be achieved, comparable with that obtained with the existing organic binders.

The new environment-friendly binder system SOLOSIL TX developed by Foseco, Vesuvius, is an inorganic thermosetting core binder, which combines the advantages of the organic binder regarding strength and productivity with environmental friendliness [1].

Achieving high-quality castings with the use of cores including the abovementioned inorganic binder systems depend not only on the casting process itself and their processing parameters, but also on the quality of these cores. Use of cores with insufficient strength or with locally low compaction results in lower surface smoothness and often in defects of the casting surface. The main requirements to achieve high-quality cores and received from the foundry industry are:


It is not the aim of this chapter to highlight and/or to discuss all parameters affecting the manufactured castings; this contribution is dealing with only one aspect: how to produce good quality cores (read: high compaction, no surface defects and high surface smoothness) with quartz sand as the filling material and well-chosen inorganic binder systems, the latter to achieve an environment-friendly working area.

High-quality cores can only be produced when the flowability of the sand mixture is such that the core box is filled completely. This means that the surface friction between individual sand grains and the wall friction, meaning the friction between the sand mixture and the surface of the core box, should be sufficiently low. **Figure 1** shows a small part of two types of cores, one (left picture) with insufficient compaction due to low flowability, and the other (right picture) with high compaction—high flowability of the sand mixture.

Flowability of sand mixtures depends on various parameters: the nature and amount of the liquid binder, the nature and amount of the optional additive(s), and the type of the filling material. Regarding the additive and filling material, the flow properties of these components depend on several parameters, such as particle size distribution, particle shape, chemical composition, moisture and temperature [2].

*Methods to Determine, Influence and Improve the Flowability of Sand Mixtures DOI: http://dx.doi.org/10.5772/intechopen.102017*

**Figure 1.**

*Left: core with locally insufficient compaction (low flowability of the sand mixture); right: core with high compaction (high flowability of the sand mixture). Both cores were manufactured with inorganic binder systems.*

Generally, the filling material is a given since foundries obtained their sand from local sand quarries. This means that only the nature and properties of the liquid binder and/or additive are (is) accessible for modification.

The objective of this chapter is to highlight some methods to determine, to influence and to optimize the physical and chemical properties of inorganic binder systems aiming at high flowability of the sand mixture.

## **2. Experimental**

## **2.1 Equipment**

### *2.1.1 Attension optical tensiometer*

With the Attension optical tensiometer surface tension of liquids can be analyzed following the pendant drop method. Since the drop shape is partly related to the surface tension of the liquid, the captured image will be analyzed with a drop profile fitting method calculating the surface tension. This instrument has already shown its high accuracy and fast sampling rate, so results can be obtained within a few seconds. **Figure 2** shows some pictures of this tensiometer.

## *2.1.2 PFT powder flow tester*

The powder flow tester was initially developed to characterize the flow behavior of solid powder material with particle sizes up to a maximum of about 1 mm. Since there was also a need to determine and to define the flowability of sand mixtures with a relatively small amount of a liquid, it was considered to use the PFT also for these applications. To compare different types of sand mixtures, results will be published by a so-called "flow function" plot. This flow function plot shows the flowability of various types of samples over so-called different "consolidation stresses", the latter being considered as compressive stress. This plot shows various regions starting from free-flowing, to easy flowing, cohesive, very cohesive to non-flowing. The lower the curve the higher the measured flowability. **Figure 3** shows the PFT Brookfield powder

**Figure 2.** *Attension optical tensiometer.*

**Figure 3.** *PFT powder flow tester to measure flowability of powders and sand mixtures.*

flow tester. About this equipment, the weight of the sand mixture placed in the sample holder, can also be an indirect indication of the flowability. In this case, the Hausner ratio (Eq. (1)) [3] can be used to obtain a more quantitative value of the flowability:

$$\mathbf{H} = \mathfrak{p}\_{\mathrm{T}} / \mathfrak{p}\_{\mathrm{B}} \tag{1}$$

where ρ<sup>T</sup> can be considered as the bulk density under pressure and ρ<sup>B</sup> the freely settled bulk density of the mix. The Hausner ratio is not an absolute value for flowability but gives only a quantitative approach. The higher the Hausner ratio, the lower the flowability. In the industry, also the Carr index C (Eq. (2)) [4] is sometimes used, which is another value of flowability but related to the Hausner ratio:

$$\mathbf{C} = \mathbf{100} - \mathbf{100}/\mathbf{H} \tag{2}$$

where H is the Hausner ratio. The lower the C value, the higher the flowability.

*Methods to Determine, Influence and Improve the Flowability of Sand Mixtures DOI: http://dx.doi.org/10.5772/intechopen.102017*

## *2.1.3 Special types of core boxes*

Besides the use of the PFT, also various types of test core boxes were developed to obtain more information on the flowability of sand mixtures based on inorganic binder systems (see **Figure 4**). These core boxes were manufactured aiming to measure/visualize the amount of sand mixture blown into the open space of the core box.

## *2.1.4 Core weight*

another approach to obtain indirect data related to the flowability of sand mixtures is to measure the core weight. From a general point of view, it is suggested that the higher the core weight, the higher the compaction. Compaction, which can be given as weight per core or by density, is related to flowability. In case the flowability of a sand mixture is low, core box filling is a severe issue finally resulting in a non-complete filling of the core box resulting in low(er) density of the produced cores.

## *2.1.5 Core shooter*

The core shooter being used during this project is a Laempe L1. This core shooter is often used to produce transverse bars but also other types of cores can be manufactured with the Laempe laboratory machine type L1 being developed for manufacturing testing cores in heated and non-heated tooling, using gas hardening processes like CO2, cold box and hot box. The sand mixture is automatically injected into the core box, which is clamped between the side presses, and heated at various temperatures. The release of high-pressured air blows the sand from the sand storage bunker into the core box at high speed. The total elapsed shooting time for transverse bars was set at 1 s and with a shooting pressure of 4 bar. In case of producing cores, these were purged with heated air for 60 (bars) or 120 (cylinders) s and at 120°C. The

#### **Figure 4.**

*Various types of core boxes with different complexities to measure flowability of different sand mixture compositions.*

core box temperature was set at 140°C. However, deviations from these processing parameters are always possible since other types of cores need lower or higher shooting times and shooting pressures, shorter or longer purging times, lower or higher core box temperature, etc. In the case special types of core boxes are used to measure flowability, no curing step is considered. Pictures of this type of core blower are shown in **Figure 5**.

## **2.2 Various types of sand mixtures**

The various types of sand mixtures can be characterized by the nature of the filling material, the type of the liquid inorganic binder and the type of additive.

## *2.2.1 Type of sand*

In the case of sand, the most important structural parameters influencing the flowability of the sand mixtures, are the average grain size, the grain size distribution and shape. Generally, foundries will use that type of sand that is available from a local quarry near the production site, so to reduce transport costs. This means that the type of sand is a given parameter that can hardly be replaced by another type of sand. Tests presented in this contribution are mainly based on the use of H32 or H33 (Quarzwerke, Germany). These types of sand showed medium sphericity of the individual sand grains including a sub-rounded to a rounded shape. **Figure 6** shows various types of sand grains with various shapes from very angular to well-rounded and from low sphericity to high sphericity. Macrographs of quartz sand type H32 and H33 are depicted in **Figure 7**.

## *2.2.2 Inorganic liquid binder*

Not only the type of sand, but also the type of liquid binder affects the flowability of the sand mixture. In case the viscosity of the liquid binder is relatively high, it will have a detrimental impact on flowability. Viscosity can be modified by adding solvents with specific rheological properties, or by diluting the binder easily by adding a

**Figure 5.** *Laempe L1—1-liter core blower.*

*Methods to Determine, Influence and Improve the Flowability of Sand Mixtures DOI: http://dx.doi.org/10.5772/intechopen.102017*

**Figure 6.**

*Sand with various shapes from very angular to well-rounded and from low sphericity to high sphericity [5].*

**Figure 7.** *Macrographs of sand type H32 (left) and H33 (right).*

small amount of water. Adding a small amount of water of 5 wt% already lowered the kinematic viscosity by 50%.

Next to modifying or adapting viscosity, also the surface tension of the liquid can play a significant role of importance. In case the surface tension (mN/m) is rather high, it will be difficult to produce new surfaces because this is energetically unfavorable. This is the case during core manufacturing when sand is blowing into the core box. Many times, individual sand grains will be separated from each other creating new surfaces (higher state of energy). This means that it is more difficult to separate two individual sand grains from each other when surrounded by a thin liquid film of the binder with high surface energy. So, it is expected that the lower the surface energy of the binder, the better the flowability. One of the means to modify surface tension is the use of a small amount of a so-called surfactant or surface-active agent. The lowest surface tension is achieved when the CMC (critical micelle concentration) is reached, generally the addition of a few tens of percent based on the liquid binder. Once the surface area is fully occupied, the addition of more surfactant will not further reduce the surface tension of the liquid.

## *2.2.3 Additives to improve flowability*

Special types of additives can be considered to further improve specific properties of the sand mixture as well as of the produced cores. Irregular shapes resulted generally in low flowability whereas on the other hand, spherical particles improved flowability. Often discussed in papers and patents, the use of a small amount of fly ash indeed improved flowability, which can be considered as a suitable fully inorganic mineral. Improved flowability will directly affect the bending strength due to improved compaction. Some results with various types of additives can be found in Ref. [1]. **Figure 8** shows a macro- and micrograph of a certain type of fly ash. Also appointed is the use of graphite flakes which can modify flowability, see also **Figure 9**. The presence of platelets can improve tribological properties, so these particles can also be considered as an additive of sand mixtures with inorganic binder systems. In the following, only spherical particles being used as inorganic additives will be discussed in more detail.

#### **Figure 8.**

*Macrograph (left) and micrograph (right) of fly ash. Interesting to note is the spherical shape of the individual fly ash particles.*

#### **Figure 9.**

*Macrograph (left) and micrograph (right) of graphite. Interesting to note is the platelet/flaky structure of the individual graphite particles.*

*Methods to Determine, Influence and Improve the Flowability of Sand Mixtures DOI: http://dx.doi.org/10.5772/intechopen.102017*

## **3. Results and discussion**

### **3.1 On the influence of the surfactant concentration**

First series of tests were done with one type of the inorganic binder and with various concentrations of three types of surfactants, A, B and C. **Figure 10** shows the surface tension as a function of the concentrations of the surfactants. Measurements with the Theta Attension optical tensiometer showed that the surface tension of the liquid inorganic binder was about 53 mN/m. The addition of 0.25 wt% bob (based on binder) surfactant type C to the liquid binder resulted already in a significant decrease of the surface tension to values of 20 mN/m. A further increase in the concentration did not result anymore in a further obvious decrease of the surface tension, since the CMC (critical micelle concentration) was already achieved. In case of surfactant type A or B, the decrease in surface tension was less pronounced.

With the use of the PFT powder flow tester, more information was obtained on the flowability properties of sand mixtures including various concentrations of the surfactant type C. Here, quartz sand type H33 was used. No additives were taken into consideration, only one type of liquid inorganic binder type. **Figure 11** shows the unconfined failure strength as a function of the applied compressive stress. This failure strength is related to the cohesive behavior of the sand mixture, and as such, it can be used to evaluate quantitative flowability. This figure shows clearly that up to about 0.2 wt% bob surfactant type C, the increase in flowability was significant. Higher concentrations showed only a further small improvement of flowability. Another approach is to calculate the Hausner ratio and the Carr index. **Table 1** shows the indices as a function of the concentration of the surfactant type C.

From **Table 1** it is clear that the Hausner, as well as the Carr index, decreased with higher concentrations of the surfactant. This relationship indicates that the flowability of the sand mixture improved with the presence of the surfactant type C, whereas with a further increase in surfactant concentration (>0.2 wt% bob) the change in these values was much less.

#### **Figure 10.**

*Surface tension of a sodium silicate binder with various concentrations (bob: based on binder) of surfactants type A, B and C.*


#### **Table 1.**

*Hausner ratio (H) and Carr index (C) as a function of the surfactant concentration (wt%—bob).*

#### **Figure 11.**

*Unconfined failure strength versus major principal consolidating stress as a function of the concentration of a surfactant type C.*

## **3.2 On the influence of the type of surfactant**

Not only the amount of added surfactant does influence the flowability of the sand mixture, but also the chemical composition can have an impact on this. Another series of tests were dealing with various types of surfactants. Results obtained with the PFT powder flow tester are depicted in **Figure 12**. This figure shows that the lowest flowability was achieved with the surfactant type F, and the highest with type D. In addition to these tests, flowability was also determined using a special type of core box for flowability measurements, as shown in **Figure 13**.

Based on these results, it can be concluded that the higher filling of the core box is thus related to a higher flowability as measured by the PFT (**Figure 14**).

In addition to the special type of core box, depicted in **Figure 13**, where only the weight of the sand could be measured, the one shown in **Figure 15** will also visualize the filling rate. Also here, it is clear that the presence of a surfactant resulted in higher flowability.

As already shown, the addition of a small amount of a well-chosen surfactant indeed improved the flowability of the sand mixture. This was approved and confirmed by various testing methods including powder flow tester PFT, various types of core boxes, and by calculating the Hauser ratio and Carr index. Based on these results, a series of transverse bars were manufactured with the Laempe core shooter L1.

*Methods to Determine, Influence and Improve the Flowability of Sand Mixtures DOI: http://dx.doi.org/10.5772/intechopen.102017*

**Figure 12.** *Unconfined failure strength versus major principal consolidating stress as a function of the type of surfactant.*

**Figure 13.** *Special type of core box for flowability measurements.*

The outcome of these tests was that the bending strength, as shown in **Figure 16**, significantly improved with even a very low addition level of 0.05 wt% bob of the surfactant. The strength stabilized at concentration levels of 0.10 wt% bob or higher. Furthermore, also the sample weight (see also **Figure 16**) increased with the presence of a small amount of surfactant. Due to the higher compaction of the cores, the strength values were also higher, since higher compaction is directly related to a higher number of contact points (bonding bridges) between individual sand grains.

In addition to the use of surfactants, which lower the surface tension of the liquid binder and as such improve flowability, also the viscosity and the type of the liquid inorganic binder can play a significant role in the production of high-quality cores. The viscosity can be lowered by adding a small amount of water, thus reducing the solid content of the binder. Due to a lower viscosity, a more homogeneous sand mixture can be achieved. This means a more homogeneous distribution of the binder

#### **Figure 14.**

*Filling (weight of the sand blown into the core box) of a special type of core box as a function of the various sand mixtures.*

**Figure 15.** *An example of the filling with a sand mixture without surfactant (left) and with surfactant (right).*

#### **Figure 16.**

*Bending strength values (sample weight on top of the individual bars (in g)) as a function of the amount of surfactant added to the inorganic liquid binder (wt% bob). In this case, 1.0 wt% bos additive type A01 was also present in the sand mixture.*

### *Methods to Determine, Influence and Improve the Flowability of Sand Mixtures DOI: http://dx.doi.org/10.5772/intechopen.102017*

around the individual sand grains, which probably can result in a net lower amount of binder to achieve similar strength and surface quality. Another approach is the use of lithium—or potassium silicate, next to sodium silicate. It is well-known that the viscosity of potassium silicate is lower than that of sodium silicate, however, care must be taken since differences in strength can occur.

This means that aiming high-quality cores can be rather complex, since the various chemical and physical parameters can play a role into this. The chemical structure and the concentration of the surfactant, the viscosity and chemical composition of the liquid binder (solid content and type and modulus of the silicate) and the amount or concentration of liquid binder based on the filling material will have an impact on the flowability of the sand mixture and thus directly on core quality (compaction, surface defects, surface friability and surface smoothness).

### **3.3 Use of additives to improve core quality**

The addition of powder-like inorganic compounds, also called core additives, to sand mixtures is at present indispensable. Since the requirements from the foundry industry are continuously growing and more demanding, sand with only a liquid inorganic binder cannot fulfill anymore all requirements. Research and development on a new generation of inorganic additives are continuing, aiming to further improve the casting process. First of all, it needs to improve the surface quality of the core, indicative of high surface smoothness. Another advantage can be improved flowability which makes cores denser. In addition to this, it will support to fill complex core boxes, such as those being used to produce complex-shaped water jackets. A well-chosen core additive can also induce higher strength values, which helps to reduce the amount of binder to be added to the sand mixture. Thus, less water is present in the sand mixture and as such, the total cycling time (read: purging time with hot air) can be further reduced. On the other hand, the casting quality is also related to the amount and type of the core additive. A non-well-chosen additive can result in amongst others, metal penetration, gas defects, low de-coring properties and sand adhesion. As already mentioned, core additives are also added to improve flowability and thus compaction and strength of the cores.

A small addition of 0.6 wt% bos of the additive type A01 resulted in an obvious improvement of flowability of the sand mixture (see **Figure 17**). However, a further increase of the concentration level resulted in over-saturation inducing lower flowability. The addition of 1.8 wt% bos type A01 (spherical particles) resulted in an even lower flowability than adding 1.2 wt% bos. A similar approach was obtained by measuring the bending strength of transverse bars including the various concentrations of the additive. These results are shown in **Figure 18**. Here, it is clear that up to about 0.3 wt% bos additive type A01 strength values increased from about 350 to 480 N/cm<sup>2</sup> , thus an increase in strength of about 30%. Starting from 0.3 up to about 1.2 wt% bos, strength values stabilized around values between 450 and 480 N/cm<sup>2</sup> . Higher concentrations of the additive resulted in the decrease of the bending strength.

#### **3.4 On the influence of micro- and nano-sized spherical particles**

It is well-known that the grain size (distribution) of sand being used for cores and molds can strongly influence the surface morphology of castings. Relatively large grains result in large pores allowing penetration of the liquid metal, finally resulting in

#### **Figure 17.**

*Unconfined failure strength (kPa) as a function of the major principal consolidating stress (kPa) and the amount of additive type A01 (wt%—based on sand (bos)).*

#### **Figure 18.**

*Bending strength as a function of the additive concentration type A01. The liquid inorganic binder was set at 2.1 wt% (bos).*

the undesired surface finish of the product. To improve the surface finish, finer grains can be chosen to suppress or inhibit metal penetration during the casting process.

However, not only the grain size distribution but also properties like the geometry and shape of the chosen sand are important. The grain shape is defined in terms of angularity and sphericity. More information concerning this can be found in the Foseco Non-Ferrous Foundryman's Handbook [6]. It is mentioned that grains with medium to high sphericity give good flowability, whereas more angular and lower sphericity of sand grains will result in low flowability, finally resulting in relatively low compactness (packing density of the sand grains).

To move individual sand grains independently of each other, relatively high friction forces Fw have to overcome. A schematic view of individual sand grains with medium to low sphericity is depicted in **Figure 19**.

*Methods to Determine, Influence and Improve the Flowability of Sand Mixtures DOI: http://dx.doi.org/10.5772/intechopen.102017*

#### **Figure 19.** *Individual sand grains characterized by medium to low sphericity.*

To enhance the flowability of such a type of quartz sand, one possibility is to add micro-sized spherical particles covering the outer surface of the sand grains in such a way that contact between the sand grains is obviously suppressed or even prevented. These particles will act as so-called "spacers" lowering the overall friction forces between the individual grains. In the case of inorganic additives, spherical micro-silica particles are often chosen to improve the flowability of the sand mixture. More information on flowability can be found in various references [7–12]. A micrograph of such a type of micro-silica is shown in **Figure 20**. Under the most ideal conditions, it can be expected that the relatively small particles of micro-silica cover the large sand grains by a uniform distribution.

A minimum number of these small spherical particles will be needed to achieve non-contact between the individual sand grains.

A schematic view of sand grains with the addition of micro-silica is shown in **Figure 21**. A common average diameter of quartz sand lies between 200 and 400 μm.

**Figure 20.** *Spherical micro-silica particles.*

**Figure 21.** *Individual sand grains with the addition of micro-silica particles to ensure non-contact between the host particles.*

The specific diameter of spherical particles of micro-silica is between 0.1 and 2.0 μm, significantly smaller than the sand grains. If the amount of added micro-silica is insufficient, the flowability of the sand mixture is far from the optimum, and sufficient compactness of the core and/or mold is difficult to guarantee. With the addition of a sufficient amount of micro-silica, flowability was significantly improved resulting in cores with good quality: sufficient packing density and smooth surface finish.

Based on these results, it was considered to improve further the flowability of such systems. Focusing on the guest particles, it was obvious that these were significantly smaller than the host (sand) particles. A similar model can be considered to design the mechanistic aspects of two spherical micro-silica particles. If a critical number of very small spherical particles (nano range) can be added in such a way that this cover

*Individual micro-particles (micro-silica) with the addition of nano-silica particles to ensure non-contact between the micro-silica particles.*

## *Methods to Determine, Influence and Improve the Flowability of Sand Mixtures DOI: http://dx.doi.org/10.5772/intechopen.102017*

(uniformly distributed) the outer surface, a similar configuration can be expected as that with the sand grains (see **Figure 22**). Probably due to this modified configuration, the flowability of the sand mixture systems can be improved further. However, this theory can still be discussed. A micrograph of micro-silica particles covered with nano-particles is shown in **Figure 23**. First results have indeed shown that a small increase in flowability and bending strength was achieved with the addition of a small amount of nano-particles, in this case 0.05 wt% bos.

Based on these experimental data, the following model, as depicted in **Figure 24**, can be proposed, related to an improved flowability resulting in higher compactness of the core material, and as a consequence, higher bending strength.

Besides the use of micro- and nano-spheres to improve flowability, also other compounds/components are needed to meet all requirements related to high-quality casting surfaces. It is beyond the scope of this contribution to discuss all requirements,

**Figure 23.** *Spherical micro-silica particles covered with nano-silica.*

but it shows that a well-balanced inorganic binder system is highly complex. In addition to high-quality cores, cold and hot strength, resistance against hot distortion, no interaction with the liquid metal, no metal penetration, good de-coring properties, etc. and finally re-use of core residue should be considered too.

## **4. Conclusions**

Before inorganic binder systems can be considered to replace the existing organic binder systems, the combination of a liquid inorganic binder and an inorganic additive has to meet the requirements set by the foundry industry. Such a system can be extremely complex and one of the main requirements is to produce high-quality cores with sufficient compaction and with high surface smoothness. This can only be achieved when the flowability of the sand mixture is sufficient. In the case of optimizing only the flowability of the sand mixture, the liquid inorganic binder, as well as the inorganic additive, can play a significant role in this.

Results have shown that in the case of the liquid binder, various parameters can affect flowability, in particular, the presence of a small amount of a surfactant. The lower the surface tension, the higher the flowability. Also, the chemical composition of the surfactant (an-ionic, cat-ionic, or non-ionic) influences flowability.

Besides a modification of the liquid binder, also the additive can play a significant role. The size and shape of the individual particles of the additive, and also its addition rate to the sand, play also a significant role of importance. Flowability tests with the powder flow tester have clearly shown that spherical particles with specific (average) grain size with well-chosen addition rates can improve flowability finally resulting in sufficient compaction of cores and completely filling of core boxes being used for complex-shaped cores such as water jackets for cylinder heads.

The newly developed inorganic binder SOLOSIL TX by Foseco, the Netherlands, can be adapted in such a way that all requirements set by each individual foundry are met. For more complex applications, such as the production of water jackets, high flowability is needed, whereas high-quality less-complex cores can already be achieved with sand mixtures including lower flowability. In addition to flowability, also other properties of the sand mixtures and cores can be adjusted by a small modification of the environment-friendly inorganic binder system SOLOSIL TX.

## **Acknowledgements**

The authors wish to thank all colleagues of the mold and core (M&C) team of the R&D Global Research Centre of Vesuvius, Enschede, the Netherlands, for their help and support.

## **Conflict of interest**

The authors declare no conflict of interest.

*Methods to Determine, Influence and Improve the Flowability of Sand Mixtures DOI: http://dx.doi.org/10.5772/intechopen.102017*

## **Author details**

Vincent Haanappel Foundry Global R&D Centre of Vesuvius, Foseco, Enschede, The Netherlands

\*Address all correspondence to: vincent.haanappel@vesuvius.com

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

## **References**

[1] Schrey A. The new environmentfriendly binder system SOLOSIL TX for core making for the mass production of complex cast components. Foundry Practice, The Authoritative Magazine for Foundry Engineers. 2015;**263**:15-23

[2] Schulze D. Powders and Bulk Solids— Behavior, Characterization, Storage and Flow. Berlin, Heidelberg, Germany: Springer-Verlag; 2008. DOI: 10.1007/ 978-3-540-73768-1. Available from: https://www.dietmar-schulze.de/pdf/ flowproperties.pdf

[3] Riley RE, Hausner HH. Effect of particle size distribution on the friction in a powder mass. International Journal of Powder Metallurgy. 1970;**6**(1):17-22

[4] Cain J. An alternative technique for determining ANSI/CEMA standard 550 flowability ratings for granular materials. Powder Handling and Processing. 2002;**14**(3):218-220

[5] Turkeli A. Sand, Sand Additives, Sand Properties, and Sand Reclamation. Available from: https://mimoza. marmara.edu.tr/altan.turkeli/files/cpt-2-sand\_sand.pdf

[6] Brown JR. Foseco Non-Ferrous Foundryman's Handbook. Linacre House, Jordan Hill, Oxford OX2 8DP, United Kingdom: Butterworth/ Heinemann; 1999

[7] Xin F, Son L, Li Y. Modification of inorganic binder used for sand coremaking in foundry practice. China Foundry. 2020;**17**:341-346. DOI: 10.1007/s41230-020-0018-2

[8] Zaretskiy L. Microsilica in sodium silicate bonded sands. International Journal of Metalcasting. 2019;**13**:58-73. DOI: 10.1007/s40962-018-0247-y

[9] Ng Y, Ng P, Wong H, Kwan A. Roles of silica fume and fly ash in improving flowability, segregation stability and passing ability of self-consolidating concrete. In: Proceedings of the 9th CANMET/ACI International Conference on Fly Ash, Silica Fume, Slag and Natural Pozzolans in Concrete; Warsaw, Poland; 20–25 May 2007. Michigan: American Concrete Institute; 2007. pp. 109-123

[10] Chang Y, Hocheng H. The flowability of bentonite bonded green molding sand. Journal of Materials Processing Technology. 2001;**113**: 238-244

[11] Ni C, Lu G, Jing T, Wu J. Influence of core sand properties on flow dynamics of core shooting process based on experiment and multiphase simulation. Research and Development, China Foundry. 2017;**14**(2):121-127. DOI: 10.1007/s41230-017-6118-y

[12] Anwar N, Sappinen T, Jalava K, Orkas J. Comparative experimental study of sand and binder for flowability and casting mold quality. Advanced Powder Technology. 2021;**32**(6):1902-1910. DOI: 10.1016/j.apt.2021.03.040

## **Chapter 4**

## Novel Physical Modelling under Multiple Dimensionless Numbers Similitudes for Precise Representation of Molten Metal Flow

*Yuichi Tsukaguchi, Kodai Fujita, Hideki Murakami and Roderick I.L. Guthrie*

## **Abstract**

Physical model experiments, together with numerical model calculations, are essential for scientific investigations such as molten metal flow in casting processes. Considering the physical modelling of flow phenomena, a common method is used to construct a physical model with a reduced scale ratio and then, experiment is carried out under one or two dimensionless number(s) similitude(s). It is an ideal condition of the experiment to establish the simultaneous similitude of multiple dimensionless numbers (SMDN) concerned with the objective flow phenomena but was considered difficult or impossible to realize in practice. This chapter presents a breakthrough in this matter. A simple relationship between the physical properties of fluids and the scale ratio of the physical model is clearly expressed for the simultaneous similitude of the Froude, Reynolds, Weber, Galilei, capillary, Eötvös and Morton numbers. For establishing the physical modelling to represent molten Fe flow phenomena under the SMDN condition, the physical properties of some molten metals can be demonstrated to meet the required relationships. Furthermore, this novel concept is also applicable for other combinations of molten metals. Precise, safe, and easy physical model experiments will be conducted under the SMDN condition that exactly mimics industrial casting operations in higher-temperature systems.

**Keywords:** physical modelling, physical model experiment, similitude, similarity, viscosity, surface tension, density, Reynolds number, froude number, weber number, flow phenomena in mould

## **1. Introduction**

Molten metal flow in casting mould has great influence on the productivity and quality of the cast products. **Figure 1** shows an image of flow phenomena in a continuous casting (CC) mould of steel production. There are various flow phenomena described in **Figure 1**; closed channel flow contains small vortex in submerged entry nozzle (SEN), injected argon (Ar) behaviour, free-surface flow, viscous bulk flow, and so on. It is difficult to observe or measure the velocity of high-temperature opaque molten metal flow. Consequently, physical model experiments, as well as numerical simulations, are widely carried out to estimate the flow phenomena in the mould.

As for physical modelling, similitude is an essential matter for accurate representation. Prior dimensionless numbers to represent flow phenomena in the continuous casting mould are Froude number (Fr), Reynolds number (Re), and Weber number (We) [1–4]. However, the simultaneous similitude of these three dimensionless numbers has been recognised as being difficult or impossible to realise [5–7]. As a matter of record, there has been no concept previously proposed for similitudes of multiple dimensionless numbers in physical modelling [2–36].

Standing on this point of view, physical modelling condition of simultaneous similitude of multiple dimensionless numbers (SMDN) has been studied and then

**Figure 1.** *Image of molten steel flow in CC mould.*

*Novel Physical Modelling under Multiple Dimensionless Numbers Similitudes for Precise… DOI: http://dx.doi.org/10.5772/intechopen.102655*

established [37, 38] for the precise representation of the real flow phenomena with an appropriate relationship of scale ratio and physical properties of liquids.

## **2. Physical modelling condition to satisfy simultaneous similitude of multiple dimensionless numbers**

Bulk flow is governed by inertial, gravitational, and viscous forces. Consequently, dimensionless numbers must correspond with are the Fr and the Re to represent the bulk flow. In addition, the We is important for the precise representation of the surface flow phenomena, such as droplet/bubble formations or ripple waves.

These three dimensionless numbers are defined in Eqs. (1), (2), and (3) [39], where the Fr is defined as the square root of (inertial force/gravitational force), the Re is defined as (inertial force/viscous force), and the We is defined as the square root of (inertial force/surface-tension force). Alternative definitions for the Fr (inertial force/ gravitational force) and We (inertial force/surface-tension force) attain the same result.

$$\text{Fr} = \frac{V}{\sqrt{\mathbf{g} \bullet L}} \tag{1}$$

$$\text{Re} = \frac{\rho \bullet V \bullet L}{\eta} \tag{2}$$

$$\text{We} = V \sqrt{\frac{\rho \bullet L}{\sigma}} \tag{3}$$

where *V* is characteristic velocity of fluid, *L* is characteristic length, *g* is gravitational acceleration, *ρ* is density of fluid, *η* is viscosity of fluid, and *σ* is surface tension of fluid.

Describing the prototype with subscript *0*, flow velocity *V* in the physical model is expressed as Eq. (4) in the case of the Fr similitude (∵*Fr* <sup>¼</sup> *<sup>V</sup>*<sup>0</sup> ffiffiffiffiffiffiffiffi *g* ∙ *L*<sup>0</sup> <sup>p</sup> <sup>¼</sup> *<sup>V</sup>*ffiffiffiffiffiffi *<sup>g</sup>* <sup>∙</sup> *<sup>L</sup>* <sup>p</sup> <sup>¼</sup> *<sup>V</sup>*ffiffiffiffiffiffiffiffiffiffiffi *g* ∙ *λ* ∙ *L*<sup>0</sup> p ) [8].

$$V = \sqrt{\lambda} \bullet V\_0 \tag{4}$$

where *λ* is scale ratio of the physical model.

Coincidence of the Re between a physical model and the prototype are expressed as Eq. (5).

$$\text{Re } = \frac{\rho\_0 \bullet V\_0 \bullet L\_0}{\eta\_0} = \frac{\rho \bullet V \bullet L}{\eta} = \frac{\rho \bullet V \bullet \lambda \bullet L\_0}{\eta} \tag{5}$$

In the same manner, coincidence of the We between a physical model and the prototype is expressed as Eq. (6).

$$\mathbf{V}\mathbf{e} = \mathbf{V}\_0 \sqrt{\frac{\rho\_0 \bullet L\_0}{\sigma\_0}} = \mathbf{V} \sqrt{\frac{\rho \bullet L}{\sigma}} = \mathbf{V} \sqrt{\frac{\rho \bullet \lambda \bullet L\_0}{\sigma}} \tag{6}$$

Scale ratio *λ* for the Fr and Re similitudes obtained by substituting Eq. (4) into Eq. (5) and scale ratio *λ* for the Fr and We similitudes obtained by substituting Eq. (4) into Eq. (6) should be equal in the condition of the Fr, Re, and We similitudes [37, 38]. Subsequently, Eq. (7) is obtained to express a relationship of physical properties for the simultaneous similitude of multiple dimensionless numbers (SMDN).

$$\lambda = \left(\frac{\eta/\rho}{\eta\_0/\rho\_0}\right)^{\frac{2}{7}} = \left(\frac{\sigma/\rho}{\sigma\_0/\rho\_0}\right)^{\frac{1}{7}}\tag{7}$$

Eq. (7) can be rearranged to Eq. (8) by applying kinematic viscosity *ν* ¼ *η=ρ* and a new parameter of *ι* ¼ *σ=ρ*. *ι* <sup>1</sup>*=*2*=ν*2*=*<sup>3</sup> in Eq. (8) is a parameter (named the S-parameter) to indicate satisfaction of the SMDN condition [37]. Precise physical model experiments will be carried out employing fluids that satisfy the relationship of physical properties described in Eq. (8) with the appropriate scale ratio shown in Eq. (7).

$$\frac{\nu^{1/2}}{\nu^{2/3}} = \frac{\nu\_0^{1/2}}{\nu\_0^{2/3}}\tag{8}$$

As a result of the Fr, Re, and We similitudes satisfying Eqs. (7) and (8), the similitude conditions of Eötvös number (Eö) and the Morton number (Mo) are also established as described below.

As shown in Clift, Grace, and Weber's chart that classifies the shape of the rising bubble [40], the Eö and Mo have a dominant influence on the bubble shape and the bubble rising velocity.

The Eö described in Eq. (9) [40], represents buoyancy force/surface-tension force. If the density of the gas is sufficiently smaller than that of the surrounding liquid, Eq. (9) can be converted to Eq. (10). Where subscript *b* is for the gas phase of the bubble.

The rearranged right side of Eq. (10) as shown in Eq. (11) indicates that the Eö similitude is established under the condition of the Fr and We similitudes [37, 38]. Here, the value of *db/L* in Eq. (10) is same for the prototype and the physical model (∵*db=<sup>L</sup>* ¼ *<sup>λ</sup>db*<sup>0</sup>*=<sup>λ</sup>L*<sup>0</sup> ¼ *db*<sup>0</sup>*=<sup>L</sup>*0).

$$\mathbf{E}\ddot{\mathbf{o}} = \frac{\mathbf{g}(\rho - \rho\_b) \bullet d\_b^{\;>}}{\sigma} \tag{9}$$

$$\mathsf{E}\ddot{\mathsf{o}} \approx \frac{\mathsf{g} \bullet \rho \bullet d\_b}{\sigma} \tag{10}$$

$$\frac{\text{g}\cdot\rho\bullet d\_b}{\sigma} = \frac{V^2\bullet\rho\bullet L}{\sigma}\bullet\frac{\text{g}\bullet L}{V^2}\bullet\left(\frac{d\_b}{L}\right)^2 = \left(\frac{\text{We}}{\text{Fr}}\bullet\frac{d\_b}{L}\right)^2\tag{11}$$

Provided that the density of the bubble is quite little compared with that of the surrounding fluid, Mo described in Eq. (12) [1, 41] consists of gravitational acceleration *g* and the physical properties of the fluid. Accordingly, the Mo similitude is undoubtedly established in the case that the physical model employs the same fluid as in the prototype. In contrast, the physical properties should satisfy a strict relationship for the Mo similitude in the case that the fluids are different for the physical model and the prototype. As described in Eq. (13), Mo is comprised of three dimensionless numbers; Fr, Re, and We [1, 41]. As such, Mo similitude is always established under the SMDN condition for the case of simultaneous dimensionless numbers equalities for the Fr, Re, and We.

$$\text{Mo} = \frac{\text{g} \bullet \eta^4}{\rho \bullet \sigma^3} \tag{12}$$

*Novel Physical Modelling under Multiple Dimensionless Numbers Similitudes for Precise… DOI: http://dx.doi.org/10.5772/intechopen.102655*

$$\frac{\text{We}^6}{\text{Re}^4 \bullet \text{Fr}^2} = \frac{V^6 \bullet \rho^3 \bullet L^3}{\sigma^3} \bullet \frac{\eta^4}{\rho^4 \bullet V^4 \bullet L^4} \bullet \frac{\text{g} \bullet L}{V^2} = \text{Mo} \tag{13}$$

Similarly, any other combinations of inertial, gravitational, viscous, and surface tension forces, such as gravitational/viscous forces (Galilei number) and viscous/ surface tension forces (the capillary number), are identical for the physical model and the prototype, under the above mentioned SMDN condition.

## **3. Physical properties of molten metals and water**

Precise physical model experiment to represent flow phenomena under the SMDN (similitude of multiple dimensionless numbers) condition could be realised in the case that physical properties of molten metal in the prototype and experimental fluid satisfy the strict relationship described in Eq. (8).

**Table 1** shows the physical properties of molten metals and water reported by many researchers and scientists [42–54]. Where "Sn-40Bi" in **Table 1** means 60mass % Sn – 40mass% Bi alloy.

These physical properties listed in **Table 1** are plotted in **Figure 2**, where the abscissa X (horizontal)-axis and the ordinate Y (vertical)-axis are the denominator and numerator of the S-parameter (*ι* <sup>1</sup>*=*<sup>2</sup>*=ν*<sup>2</sup>*<sup>=</sup>*3), respectively. This *ν*<sup>2</sup>*=*<sup>3</sup> versus *ι* <sup>1</sup>*=*<sup>2</sup> chart has been named the SMDN chart. The SMDN chart indicates whether a combination of two liquids satisfies the relation in Eq. (8), or not. As indicated in **Figure 2**, Fe at 1575°C, Cu (1085–1185°C, closely at 1145°C), and Sn (232–332°C, closely at 288°C) are all located on the same S-parameter line of *ι* <sup>1</sup>*=*<sup>2</sup>*=ν*<sup>2</sup>*=*<sup>3</sup> <sup>¼</sup> 211. This indicates that the SMDN condition is established between these three molten metals at the appropriate temperatures and scale ratios.


#### **Table 1.**

*Physical properties of molten metals and water for Figure 2.*

**Figure 2.** *Physical properties of molten metals and water plotted on SMDN chart.*

Scale ratios to satisfy the SMDN conditions are also indicated in the SMDN chart. For example, the ratio of the distance between the origin point and the Ga plot to the distance between the origin point and the Al plot is 0.57, as shown in **Figure 3**. As is obvious from Eq. (7), this value of 0.57 is the scale ratio of molten Ga models needed to represent molten Al flow satisfying the SMDN condition. In the same manner, molten Sn-40Bi models with a scale ratio of 0.71 can represent molten Zn flow under the SMDN condition. Naturally, the same rule is applicable for molten Fe, Cu, and Sn.

In the case only the Fr and Re similitudes are required to represent the bulk flow, water models could represent flow phenomena of molten Fe, Cu, Sn, Al, Ga, Zn, Sn-40Bi, Bi, and Hg with proper scale ratios according to the ratios of *<sup>ν</sup>*<sup>2</sup>*=*<sup>3</sup> <sup>¼</sup> ð Þ *<sup>η</sup>=<sup>ρ</sup>* 2*=*3 , as shown in Eq. (7). Please note that kinematic-viscosity *ν* of water has a large temperature-dependency, as shown in **Figure 2**. Therefore, temperature of the water should be carefully considered to determine the scale ratio.

Moreover, the physical modelling concept of the SMDN is applicable not only for molten metal systems described in this chapter but also for many types of liquids [37]. *Novel Physical Modelling under Multiple Dimensionless Numbers Similitudes for Precise… DOI: http://dx.doi.org/10.5772/intechopen.102655*

## **4. Applications of physical modelling under multiple dimensionless numbers similitudes**

As described above, the physical modelling concept of SMDN is applicable for flow phenomena influenced by followed four forces—inertial, gravitational, viscous, and surface tension forces. Some examples of flow phenomena representations under the SMDN condition are shown in this section.

#### **4.1. Injected bubble size**

In the case of bubble formation during gentle gas injection, three forces—gravity, surface tension, and buoyancy forces, are dominant to determine the bubble diameter *Db*, and thus *Db* can be calculated using Eq. (14) [55], provided that the density of the gas bubble is negligibly small compared with that of the surrounding fluid.

$$D\_b = \sqrt[3]{\frac{\mathbf{6} \bullet D\_n \bullet \sigma}{\rho \bullet \mathbf{g}}} \tag{14}$$

where *Dn* is the internal diameter of the gas injection nozzle.

**Table 2** shows the parameters of physical properties (*ν* and *ι*), the S-parameters described in Eq. (8), and the adequate scale ratios obtained by Eq. (7) for several molten metals. The physical properties of these molten metals are shown in **Table 1**. As is obvious in **Table 2**, there are three groups with similar S-parameters—molten Al and Ga for the S-parameter of 287, molten Fe, Cu, and Sn for the S-parameter of 211, and molten Zn and Sn-40Bi for the S-parameter of 177. Scale ratios shown in **Table 2** are defined against "BASE" molten metals for each S-parameter group. The "BASE" metals are—molten Al for the group of S-parameter = 287, molten Fe for the group of S-parameter = 211, and molten Zn for the group of S-parameter = 177.

Bubble diameters formed by injected inert gas under those conditions calculated by Eq. (14) for various nozzle diameters are shown in **Figure 4**. The abscissa X (horizontal)-axis of **Figure 4** shows equivalent bubble diameters considering the scale ratios. As is clear from **Figure 4**, equivalent bubble diameters are plotted on the same point under the conditions with the same S-parameters. This is a simple comparative case to show the availability of physical model experiments respecting the SMDN condition.

#### **4.2. Rising velocity of bubbles**

Inert gas injection is widely applied to casting processes to remove non-metallic inclusions. Meanwhile, it causes bubble defects of the cast products. Consequently, it is valuable to represent the two-phase flow of bubbles and molten metals in physical model experiments.

Complicated demeanour of the rising bubble is dominated by two dimensionless numbers—the Eö and Mo. They have dominant influences on the bubble shape as well as the bubble rising velocity [40]. Therefore, physical models under the concept of SMDN will accurately represent bubble rising demeanour.

In connection with the bubble deformation, the drag coefficient of a rising bubble changes in value complicatedly, which has been investigated by many researchers. Eq. (15) shows Tomiyama's Equation [56], one of the trustworthy equations to express


#### **Table 2.**

*Physical properties and S-parameters for various molten metals.*

**Figure 3.** *Proper scale ratios indicated on SMDN chart.*

the drag coefficient of rising bubbles. However, this equation was obtained by the experiments with water and some organic liquids, so it should be confirmed if this equation could be applied to the molten metal systems or not.

*Novel Physical Modelling under Multiple Dimensionless Numbers Similitudes for Precise… DOI: http://dx.doi.org/10.5772/intechopen.102655*

**Figure 4.** *Generated bubble sizes for various S-parameter groups.*

$$\mathbf{C}\_{D} = \max\left[\min\left\{\frac{24}{\mathrm{Re}\_{b}}\left(1 + 0.15\,\mathrm{Re}\_{b}{}^{0.685}\right), \frac{72}{\mathrm{Re}\_{b}}\right\}, \frac{8}{3}\,\frac{\mathrm{E\ddot{o}}}{\mathrm{E\ddot{o}} + 4}\right] \tag{15}$$

Therefore, data of investigated terminal velocity of rising bubble in molten metals of reliable researches [38, 57] were compared with Tomiyama's equation. As shown in **Figure 5**, Tomiyama's equation well represents the bubble terminal velocity in molten Sn and Hg. The result shows that Tomiyama's equation can be extensively applied to molten metal systems.

Accordingly, bubble rising velocity in molten metals could be calculated by Tomiyama's equation. Before comparing the bubble rising velocity, it should be noted that in the case of the Fr similitude with the scale ratio of physical modelling, flow velocity is described in Eq. (4; *<sup>V</sup>* <sup>¼</sup> ffiffi *λ* <sup>p</sup> <sup>∙</sup>*V*0). Consequently, time progression in the physical model will expand or contract as expressed in Eq. (16) [38]. For example, in the case of scale ratio *<sup>λ</sup>* <sup>¼</sup> <sup>0</sup>*:*5, time progression in the physical model will shrink ffiffiffiffiffiffi <sup>0</sup>*:*<sup>5</sup> <sup>p</sup> <sup>≈</sup> <sup>0</sup>*:*71 times as compared with the real-time progression. For example, in the case of the physical models under the Fr similitude and the scale ratio of 0.5, real flow phenomena generated in 100 seconds will be represented in 71 seconds.

$$t = \frac{L}{V} = \frac{\lambda \bullet L\_0}{V\_0 \sqrt{\lambda}} = \sqrt{\lambda} \bullet t\_0 \tag{16}$$

**Figure 6** shows the relationship between equivalent bubble diameter in molten Fe and relative rising velocity (*RRV*) of bubbles under variable similitude conditions. *RRV* is (rising velocity of the bubble in physical model experiment considering the scale ratio/rising velocity of the bubble in prototype) as expressed in Eq. (17). The time progression described in Eq. (16) is also taken into account in Eq. (17). Here, *U*<sup>0</sup> is bubble rising velocity in the prototype (in molten Fe), *U* is bubble rising velocity in

**Figure 5.** *Comparison of terminal velocity of rising bubbles in molten metals.*

the physical model experiment. Please note that the bubble diameter *db* for *U* and bubble diameter *db*<sup>0</sup> for *U*<sup>0</sup> are not same (*db* ¼ *λ* ∙ *db*0).

$$RRV = \begin{pmatrix} \frac{U}{\sqrt{\lambda}} \zeta\_{U\_0} \end{pmatrix} \sqrt{\lambda} = \frac{U}{U\_0 \bullet \sqrt{\lambda}} \tag{17}$$

As shown in **Figure 6**, rising velocity of bubbles in molten Sn or molten Cu under the SMDN condition precisely represents rising velocity of bubbles in molten Fe. On the other hand, rising velocity of bubbles in water under the Fr and Re similitudes condition (*λ* ¼ 1*:*0) corresponds to that in molten Fe only in the region of the small bubble diameters. In contrast, rising velocity of bubbles in water under the Fr and We similitudes condition (*λ* ¼ 0*:*52) correspond to that in molten Fe only in the region of the large bubble diameters. The reason can be read from Eq. (15). Drag coefficient of bubbles are dominated by the Re in the region of the small bubble diameters, consequently, the water model under the Fr and Re similitudes condition is enough to represent the small-bubble rising velocity. In the region of the large bubble diameters, drag coefficient of bubbles is dominated by the Eö, and the Eö similitude is established under the Fr and We similitudes as described in Eqs. (10) and (11). Consequently, the water model under the Fr and We similitudes condition is adequate to represent the large-bubble rising velocity.

## **4.3. Other applications of physical modelling under multiple dimensionless numbers similitudes**

Other applications of the SMDN concept include the following examples—in the case of the Mesler entrainment of a liquid drop to produce many fine bubbles, threedimensionless numbers, the We, Fr, and capillary numbers, describe the entrainment phenomenon [58]. Consequently, physical model experiments under the SMDN condition will precisely represent the bubble sizes formed by the Mesler entrainment. *Novel Physical Modelling under Multiple Dimensionless Numbers Similitudes for Precise… DOI: http://dx.doi.org/10.5772/intechopen.102655*

**Figure 6.**

*Comparison of relative terminal velocity of rising bubbles under a variety of similitude conditions.*

As expressed in the above examples, the SMDN concept of the physical modelling is applicable for the precise representation of all the flow phenomena dominantly affected by four forces—inertial force, gravitational force, viscous force, and surfacetension force. However, physical models under the SMDN condition could not precisely represent flow phenomena affected by other forces or flow phenomena of other types of fluids. For example, flow phenomena of compressible fluid flow, two-phase flow with solid-particles and liquid are outside the SMDN concept region in this chapter.

As for the representation of the thermal convection flow, the similitude of the Rayleigh number (Ra), shown in Eq. (18) for both the prototype and the physical model [59], is required.

$$\text{Ra} = \frac{\text{g} \bullet \beta\_0 \bullet \Delta T\_0 \bullet L\_0^{\text{\textdegree}}}{\nu\_0 \bullet a\_0} = \frac{\text{g} \bullet \beta \bullet \Delta T \bullet L^{\text{\textdegree}}}{\nu \bullet a} \tag{18}$$

where *α* is thermal diffusivity, *β* is thermal expansion coefficient, and Δ*T* is temperature drop across the convection layer.

The thermal convection flow phenomena will also be represented under the SMDM condition in the case that Δ*T* was controlled to make the Rayleigh numbers equal expressed in Eq. (18).

Eq. (18) can be rearranged to Eq. (19) by substituting *L* ¼ *λ* ∙ *L*0, Eq. (7) that expresses the scale ratio of the SMDN condition and kinematic viscosity *ν* ¼ *η=ρ*. Then theΔ*T* ratio to satisfy the Rayleigh number similitude under the SMDN condition is obtained, as shown in Eq. (20) [37]. It should be noted that if the Δ*T* ratio calculated by Eq. (20) was large, thermal effects on the physical properties of the experimental liquid could not be negligible. If temperature dependencies of the physical properties of two liquids for the prototype and the physical model are similar, a large Δ*T*<sup>0</sup> itself will not induce a lower accuracy in the experimental results.

$$\text{Ra} = \frac{\text{g} \bullet \beta\_0 \bullet \Delta T\_0 \bullet L\_0^{\text{3}}}{\nu\_0 \bullet a\_0} = \frac{\text{g} \bullet \beta \bullet \Delta T \bullet \left(\lambda \bullet L\_0\right)^{\text{3}}}{\nu \bullet a} = \frac{\text{g} \bullet \beta \bullet \Delta T \bullet \left(\nu\_{\nu\_0}\right)^2 \bullet L\_0^{\text{3}}}{\nu \bullet a} \tag{19}$$

$$\frac{\Delta T}{\Delta T\_0} = \frac{a \bullet \beta\_0 \bullet \nu\_0}{a\_0 \bullet \beta \bullet \nu} \tag{20}$$

Naturally, the SMDN concept of physical modelling is applicable to represent the turbulent flow. Minutes of turbulent flow, such as small eddies, vortexes, and swirls, will be precisely represented since such flow phenomena are governed by inertial, gravitational, and viscous forces. It should be noted that the thermal effects on the physical properties should be considered under heavy turbulent flows with the rising temperature of the experimental fluid. Besides, the wettability between the fluid and the wall of the flow channel will affect the result.

## **5. Conclusion**

The novel physical modelling concept, involving the simultaneous similitude of multiple dimensionless numbers, the Froude, Reynolds, Weber, Galilei, capillary, Eötvös, and Morton numbers, have been proposed in this chapter indicating a simple relationship among density, viscosity, surface tension of fluids, and the scale ratio of physical model. This concept has been named SMDN (similitude of multiple dimensionless numbers). Subsequently, it was shown that some combinations of molten metals, such as Fe & Sn, Cu & Sn, Al & Ga, and Zn & Sn-Bi, could satisfy the strict relationship of physical properties required for the SMDN condition. As a matter of record, no one except for us has made the specific proposal of the multiple dimensionless numbers similitudes in the physical modelling of flow phenomena.

Physical modelling satisfying the SMDN condition can represent many kinds of flow phenomena influenced by inertial, gravitational, viscous, and surface tension forces as some examples of applications were shown in this chapter. This novel concept of physical modelling will enable precise, safe, and easy physical model experiments using low-temperature fluids to exactly represent flow phenomena in various high-temperature liquid operations within the pyro-metallurgical industries.

## **Nomenclature**


*Novel Physical Modelling under Multiple Dimensionless Numbers Similitudes for Precise… DOI: http://dx.doi.org/10.5772/intechopen.102655*


## **Author details**

Yuichi Tsukaguchi<sup>1</sup> \*, Kodai Fujita1 , Hideki Murakami<sup>2</sup> and Roderick I.L. Guthrie<sup>3</sup>

1 Steelmaking Research Lab., R&D Laboratories, Nippon Steel Corporation, Kamisu-City, Japan

2 R&D Laboratories, Nippon Steel Corporation, Futtsu-City, Japan

3 McGill Metal Processing Centre, McGill University, Montreal, QC, Canada

\*Address all correspondence to: tsukaguchi.6fk.yuichi@jp.nipponsteel.com

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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