The Influence of Water Temperature Conditions on the Tracer Transport Process in the Tundish Water Model

Abstract

During continuous casting, the flow behavior of liquid steel in the tundish directly affects the temperature distribution of liquid steel, inclusion removal, and billet quality. In tundish-related research, water model experiments remain an intuitive method for investigating the flow process in the tundish. However, water model experiments are often conducted in different seasons, and variations in experimental temperature can change fluid properties such as density and viscosity, thereby affecting flow characteristics and the comparability of experimental results. In this study, a 1:3.57 transparent bare single-strand tundish model made of acrylic was used, and the differences in tracer transport processes at 7 °C and 20 °C, as well as the influence of different tracer dosages on the experimental results, were systematically investigated through flow visualization and stimulus-response experiments. The results showed that, under the 7 °C condition, the upward transport tendency of the pure ink tracer was weakened, the overall flow remained closer to the tundish bottom, the transport speed decreased, and the time required to reach the outlet was significantly prolonged. For the saturated KCl solution tracer, a lower temperature enhanced its transport along the bottom toward the outlet and suppressed its diffusion toward the liquid surface. The RTD results showed that, after the temperature was increased, the curves shifted to the left as a whole, and both the peak time and the mean residence time were shortened. The outflow percentage of tracer results showed that the difference for the 10 mL saturated KCl solution between the 7 °C and 20 °C conditions was the most significant. At 7 °C, the total outflow percentage of the 10 mL salt solution tracer at 1500 s was 76.86%, which was 22.97% lower than that at 20 °C. As the tracer dosage increased, the differences in the transport process, RTD curves, and outflow percentage curves under different temperature conditions gradually decreased, indicating that the effect of dosage on the experimental results gradually became stronger than that of temperature. These results indicate that the combined effects of experimental temperature and tracer dosage cannot be neglected in tundish water model experiments.

1. Introduction

The tundish is an important metallurgical reactor connecting the ladle and the mold, and the flow behavior of liquid steel inside it directly affects the temperature distribution of liquid steel, inclusion removal, and billet quality [1,2,3]. Because liquid steel in an industrial tundish is at high temperature and in an opaque state, its internal flow behavior is difficult to observe directly. Therefore, physical models [4,5,6] and numerical simulations [7,8,9] are usually adopted to investigate the flow-field characteristics in the tundish. Among them, water models are mostly used in physical simulation. Owing to the advantages of convenient operation, relatively low cost, and easy visualization of flow fields, water models have been widely applied in tundish flow studies. Under the premise that geometric similarity and dynamic similarity are satisfied, water model experiments for tundishes are usually conducted by taking advantage of the similarity in kinematic viscosity between water at 20 °C and liquid steel at 1600 °C. In this way, water is used instead of liquid steel to simulate the flow behavior in the tundish, and the flow, mixing, and residence characteristics of the fluid are analyzed by combining the stimulus-response method, flow visualization, and particle image velocimetry [10,11,12]. Because flow-field characteristics in the tundish can be characterized from different perspectives by these methods, they have been widely used in tundish flow studies.

At present, the major international institutions engaged in tundish water model research mainly include McGill University in Canada [13,14], the University of Toronto in Canada [15,16,17], RWTH Aachen University in Germany [18,19,20], KTH Royal Institute of Technology in Sweden [21,22,23], the Indian Institute of Technology in India [24,25,26], Częstochowa University of Technology in Poland [27], Silesian University of Technology in Poland [28], the Instituto Politécnico Nacional in Mexico [29,30,31], the Morelia Institute of Technology in Mexico [32,33,34], the Universidad Nacional Autónoma de México in Mexico [35], Aalto University (Helsinki University of Technology) in Finland [36,37], VSB-Technical University of Ostrava in the Czech Republic [38], and many universities in China, such as the Northeastern University [39,40,41,42,43], the University of Science and Technology Beijing [44,45,46,47,48], Chongqing University [49,50], Shanghai University [51], Central South University [52], Wuhan University of Science and Technology [53,54], Inner Mongolia University of Science and Technology [55,56], University of Science and Technology Liaoning [57,58], Soochow University [59], Taiyuan University of Technology [60,61,62], Jiangxi University of Science and Technology [63] and the Anhui University of Technology [64,65,66]. However, in most existing water model experiments, only limited influence has been assumed for experimental temperature conditions on the experimental results, and systematic attention has not been paid to the differences in flow-field results obtained under different water temperature conditions. In fact, annual temperature varies greatly across different regions.

Table 1. Maximum annual temperature difference in 2025 in the regions where different universities conducting tundish water model research are located [67,68].

University	Country	City	Latitude and Longitude	Annual Maximum Temperature (°C)	Annual Minimum Temperature (°C)	Annual Maximum Temperature Difference (°C)
McGill University	Canada	Montréal	45°30′32″ N, 73°33′15″ W	35	−22	57
University of Toronto	Canada	Toronto	43°39′9″ N, 79°22′54″ W	36	−18	54
RWTH Aachen University	Germany	Aachen	50°46′32″ N, 6°5′1″ E	38	−8	46
KTH Royal Institute of Technology	Sweden	Stockholm	59°19′46″ N, 18°4′7″ E	30	−13	43
Indian Institute of Technology	India	New Delhi	28°36′50.04″ N, 77°12′32.04″ E	43	6	37
Częstochowa University of Technology	Poland	Częstochowa	50°48′0″ N, 19°7′0″ E	33	−15	48
Silesian University of Technology	Poland	Gliwice	50°17′39″ N, 18°39′57″ E	33	−15	48
Instituto Politécnico Nacional	Mexico	Ciudad de México	19°26′0″ N, 99°8′0″ W	32	3	29
Morelia Institute of Technology	Mexico	Morelia	19°46′6″ N, 101°11′22″ W	34	0	34
Universidad Nacional Autónoma de México	Mexico	Mexico City	19°26′0″ N, 99°8′0″ W	32	3	29
Aalto University	Finland	Espoo	60°12′20″ N, 24°39′20″ E	30	−17	47
VSB-Technical University of Ostrava	Czech Republic	Ostrava	49°50′8″ N, 18°17′33″ E	34	−12	46
Northeastern University	China	Shenyang	41°48′9″ N, 123°25′41″ E	36	−30	66
University of Science and Technology Beijing	China	Beijing	39°54′24″ N, 116°23′51″ E	38	−14	52
Chongqing University	China	Chongqing	29°33′49.32″ N, 106°33′1.44″ E	41	2	39
Shanghai University	China	Shanghai	31°13′57″ N, 121°28′9″ E	39	−5	44
Central South University	China	Changsha	28°13′40.8″ N, 112°56′20.4″ E	39	−2	41
Wuhan University of Science and Technology	China	Wuhan	30°35′42″ N, 114°17′51″ E	39	−4	43
Inner Mongolia University of Science and Technology	China	Baotou	40°37′16.68″ N, 109°57′11.52″ E	33	−26	59
University of Science and Technology Liaoning	China	Anshan	41°6′28.8″ N, 122°59′38.4″ E	36	−30	66
Soochow University	China	Suzhou	31°18′0″ N, 120°37′10″ E	39	−5	44
Taiyuan University of Technology	China	Taiyuan	37°52′13.44″ N, 112°32′58.92″ E	38	−17	55
Jiangxi University of Science and Technology	China	Ganzhou	25°49′51.6″ N, 114°55′58.8″ E	39	−4	43
Anhui University of Technology	China	Ma’anshan	31°40′8.4″ N, 118°30′25.2″ E	39	−10	49

summarizes the maximum annual temperature differences in 2025 for the regions where different institutions conducting tundish water model research are located. The city locations of these institutions were taken from Wikipedia [67], and the maximum and minimum temperatures in 2025 were taken from the 2025 historical weather data of Time and Date [68]. The data in Table 1 show that the maximum annual temperature differences for these institutions range from 24 to 66 °C in 2025. Because laboratory environments and water-supply conditions vary, the temperature of the simulated medium often differs by more than ten degrees Celsius between seasons, which may lead to changes in the physical properties of water and may further affect the macroscopic flow behavior in the tundish and the tracer transport results.

Taking the experimental location of this study as an example, the relevant research was carried out in Taiyuan, Shanxi Province, China, which is located at 37°52′13.44″ N, 112°32′58.92″ E [69]. In 2025, the highest air temperature recorded in this region was 38 °C (19 May 2025) [70], whereas the lowest air temperature was −17 °C (7 February 2025) [71]. Therefore, the maximum annual temperature difference reached 55 °C. Experimental measurements show that the water temperature in the tundish is usually 5 to 10 °C in winter, whereas it is 20 to 25 °C in summer. Therefore, 7 °C and 20 °C were selected in this study as two representative experimental temperatures corresponding to the low-temperature season and the commonly used water-model condition, respectively. The purpose of this work was not to establish a continuous temperature-response curve, but to determine whether these two representative conditions would lead to significantly different flow characterization results. The physical properties of liquid steel and water at 7, 15, 20, and 25 °C are listed in

Table 2. Physical properties of liquid steel and water at different temperatures [72,73,74].

	Working Temperature (°C)	Density (kg·m−3)	Dynamic Viscosity (kg·m−3)	Kinematic Viscosity (m2·s−1)	Pr Number
liquid steel	1873.15	7000.00	6.1 × 10−3	0.87 × 10−6
Water	280.15	999.93	1.35 × 10−3	1.45 × 10−6	10.77
	288.15	999.00	1.16 × 10−3	1.16 × 10−6	8.27
	293.15	998.20	1.00 × 10−3	1.01 × 10−6	7.02
	298.15	997.00	9.03 × 10−4	9.06 × 10−7	6.22

. Water density and viscosity data at different temperatures were obtained from the NIST Chemistry WebBook [72] and the IAPWS viscosity formulation [73], while general thermophysical-property reference values were checked against the CRC Handbook of Chemistry and Physics [74]. As shown in Table 2, when the water temperature increases to 25 °C, the similarity in kinematic viscosity between water and liquid steel is further weakened. At 7 °C, although the two values remain within the same order of magnitude, the kinematic viscosity of water is already obviously higher than that at 20 °C. Meanwhile, thermophysical properties such as the density and viscosity of water also vary with temperature, thereby affecting the flow structure, mixing behavior, and tracer transport characteristics in the model. This suggests that additional deviations may exist among water model experimental results obtained in different seasons or under different batches of conditions, thus weakening the comparability of the results. Therefore, the first objective of this paper is to reveal the variation mechanism of fluid flow behavior in the tundish water model under different experimental temperature conditions, to clarify the influence of temperature variation on the macroscopic flow results, and to provide a basis for the reasonable comparison of experimental results obtained in different seasons.

In addition to the influence of experimental temperature on the macroscopic flow in the tundish, the influence of the tracer itself on the results of water model experiments should not be neglected [75,76]. In stimulus-response experiments with tundish water models, KCl and NaCl solutions are mainly used as tracers. Residence time distribution (RTD) curves are obtained by measuring the variation in tracer concentration at the outlet with time, and the flow and mixing characteristics of fluids in the tundish are then analyzed accordingly. As an important flow characterization index, RTD curves [77] are also often used for the validation of CFD models. Jha et al. [78,79], Odenthal et al. [80,81], and Sheng et al. [82] all used a bare single-strand tundish as the research object, and related CFD models were optimized and validated, but certain deviations between simulation results and experimental results are still generally observed. Previous studies have indicated that, when a density difference exists between the tracer and the bulk fluid, even a small amount of tracer addition may alter the local flow state and may further affect the RTD curve and the judgment of the flow field [83]. In previous studies [45,84], the ratio of saturated salt solution dosage to the water volume in the tundish, defined as Dta (i.e., dimensionless tracer amount), varied significantly among different studies, ranging from 0.008 × 10⁻³ to 2.680 × 10⁻³, with the maximum value being 335 times the minimum value. With regard to the volume effect of tracers, the results reported by Chen et al. [22,45,83] and Ding et al. [85,86] show that stronger downward flow appears in the tundish as the tracer volume increases. When the tracer volume is reduced or the concentration is lowered, the disturbance of the flow field caused by the tracer is gradually weakened, and the RTD curves obtained experimentally become closer to those under ideal tracer conditions. However, the tundishes investigated in these studies were all equipped with flow-control devices. In 2025, Wang et al. [84] further used a bare single-strand tundish as the research object, and the results showed that when Dta was lower than 0.375 × 10⁻³, that is, when less than 35 mL of saturated KCl solution was used, only a weak influence of the tracer on the flow field was produced. Beyond this range, strong downward flow, short-circuit flow, and return flow were induced by the tracer. It can therefore be concluded that tracer dosage is an important factor affecting the results of tundish water model experiments. However, existing studies have mainly focused on specific experimental temperature conditions, and insufficient attention has still been paid to the effect of tracer dosage under different experimental temperatures. Therefore, the second objective of this paper is to further investigate the variation law associated with different tracer dosages under different experimental temperature conditions.

In summary, most existing tundish water model studies have assumed that results obtained under different experimental temperature conditions have good comparability. In fact, however, changes in experimental temperature alter the physical properties of water, such as density and viscosity, and may therefore affect the flow behavior of fluids in the model. In addition, variations in tracer dosage may further alter the transport and diffusion characteristics of the tracer, thereby affecting the judgment of macroscopic flow in the tundish. Therefore, whether experimental results obtained under different experimental temperature conditions and different tracer dosages are consistent and comparable still needs to be further investigated.

On this basis, the flow behavior in a bare single-strand tundish water model under different experimental temperature conditions is investigated in this paper. First, the differences in macroscopic flow characteristics in the tundish under 7 and 20 °C conditions are compared, and the influence mechanism of experimental temperature variation on flow-field results is revealed. Second, the influence of different tracer dosages on the macroscopic flow results in the tundish under these two temperature conditions is further analyzed, and the applicability of the recommended tracer dosage determined under the 20 °C condition (less than 35 mL saturated KCl solution, that is, Dta < 0.375 × 10⁻³) at other experimental temperatures is discussed. It is expected that this study will provide a basis for the reasonable comparison of tundish water model experimental results obtained in different seasons and for the optimal selection of tracer dosage.

2. Experimental Principle and Scheme

2.1. Principle of Experiment

This study conducted physical simulation based on the bare single-strand tundish reported by Singh and Koria [87]. Under the premise of ensuring both geometric and dynamic similarity, this study carried out water model experiments with an organic glass model at a model-to-prototype scale ratio of 1:3.57.

Table 3. Size parameters of the industrial prototype and water model [62].

Parameters	Water Model	Industrial Tundish
Volumetric flowrate nozzle (L/min)	9.3	224
Diameter of the outlet nozzle (mm)	25	89.25
Depth of liquid (mm)	280	1000
Diameter of the shroud (mm)	22	78.54
Immerse of shroud depth (mm)	44	157.08

lists the geometric parameters of the industrial tundish and the corresponding water model tundish, and Figure 1 shows the detailed dimensions of the tundish water model.

To ensure compliance with the similarity principle, geometric similarity was first maintained between the model and the prototype. In terms of dynamic similarity, the Reynolds number was used to verify that both the water model and the industrial prototype remained within the same turbulent self-modeling regime, while the Froude number was taken as the main criterion for establishing the flow similarity between the two systems. The corresponding equations are given as follows:

$$\lambda ={\displaystyle \frac{L_{\mathrm{m}}}{L_{\mathrm{p}}}}={\displaystyle \frac{1}{3.57}}=0.28,$$

(1)

$$F{r}_{\mathrm{p}}={\displaystyle \frac{u_{\mathrm{p}}^2}{g{L}_{\mathrm{p}}}}={\displaystyle \frac{u_{\mathrm{m}}^2}{g{L}_{\mathrm{m}}}}=F{r}_{\mathrm{m}},$$

(2)

$${\displaystyle \frac{Q_{\mathrm{m}}}{Q_{\mathrm{p}}}}={\displaystyle \frac{u_{\mathrm{m}}{L}_{\mathrm{m}}^2}{u_{\mathrm{p}}{L}_{\mathrm{p}}^2}}={\lambda }^{{\displaystyle \frac{5}{2}}},$$

(3)

where m and p represent the tundish water model and the industrial prototype, respectively. Fr is the Froude number. u is the outlet velocity, m/s. L is the characteristic length of the tundish, m. g is the gravitational acceleration, m/s². Q is the outlet flow rate of the tundish, m³/h. λ is the scale factor, with a value of 0.28.

2.2. Experimental Scheme

To examine the differences in fluid flow behavior in the tundish water model between winter and summer, this study used pure ink and saturated KCl solution for investigation. In summer, both the water temperature and tracer temperature remained at 20 °C. In winter, both the water temperature and tracer temperature remained at 7 °C. In the two seasons, this study carried out flow visualization experiments using 15 mL of ink and mixtures of ink with 35, 55, and 150 mL of saturated KCl solution, respectively. The details are shown in

Table 4. The scheme for the flow visualization experiments under different experimental temperature conditions.

Schemes	Water Temperature (°C)	Tracer Temperature (°C)	The Types and Volumes of Tracer	Tracer Density (kg/m3)
A1	20	20	15 mL pure ink	1037
A2	7	7		1077
A3	20	20	35 mL Saturated KCl solution+3.5 mL ink	1116
A4			55 mL Saturated KCl solution+5.5 mL ink
A5			150 mL Saturated KCl solution+15 mL ink
A6	7	7	35 mL Saturated KCl solution+3.5 mL ink	1166
A7			55 mL Saturated KCl solution+5.5 mL ink
A8			150 mL Saturated KCl solution+15 mL ink

. In addition, in the two seasons, this study carried out stimulus-response experiments using 10, 35, 55, and 150 mL of saturated KCl solution. The details are shown in

Table 5. The stimulus-response experimental scheme under different experimental temperature conditions.

The Types of Tracer	Water Temperature (°C)	Tracer Temperature (°C)	The Volumes of Tracer (mL)	Tracer Density (kg/m3)
Saturated KCl solution	20	20	10, 35, 55, 150	1119
	7	7	10, 35, 55, 150	1168

. In all experiments, the tracer volume was measured using a graduated cylinder and then introduced into the tundish through the same funnel and following the same injection procedure, so as to ensure consistency and accuracy of tracer addition.

The tracer dosages were selected on the basis of previous studies. In the study by Wang et al. [84], it was found that when the ratio of tracer dosage to the water volume in the tundish (Dta) was lower than 0.375 × 10⁻³, the tracer had almost no influence on the flow field, whereas when Dta was higher than 0.589 × 10⁻³, a strong downward flow was generated in the tundish. Therefore, salt solution tracers with Dta values of 0.107 × 10⁻³, 0.375 × 10⁻³, 0.589 × 10⁻³, and 1.608 × 10⁻³ were selected in the present study to further investigate the effects of different tracer dosages on the macroscopic flow behavior in the tundish under the two temperature conditions. In addition, the applicability of the recommended tracer dosage determined at 20 °C (i.e., Dta < 0.375 × 10⁻³) under other experimental temperature conditions was further evaluated. The ink tracer was mainly selected to investigate the macroscopic flow behavior in the tundish through visualization. As shown in Table 5, the density of ink at both temperatures was close to that of water, and the influence of the density difference on the flow field was small. In addition, to reduce the influence of tracer volume on the flow field in the tundish, the Dta of the ink tracer was controlled at 0.161 × 10⁻³ (i.e., 15 mL).

2.3. Analysis Method

2.3.1. RTD Curve Analysis Method

The Concentration Curve and Effluent Curve were commonly used to analyze the transport process of tracers in the tundish [88]. The C curve was directly obtained from the water model experiments, and it represented a concentration–time curve or a conductivity-time curve. The E curve was the dimensionless form of the C curve, namely, the RTD curve. The E curve was calculated by Equations (4)–(6).

$$E(\theta )=C(\theta )/{\displaystyle {\int }_0^{\infty }C(\theta )}d\theta ,$$

(4)

$$\theta ={\displaystyle \frac{t}{t_{\mathrm{theory}}}},$$

(5)

$$t_{\mathrm{theory}}={\displaystyle \frac{V}{Q_{\mathrm{in}}}},$$

(6)

In the equations, θ represents the dimensionless time. E(θ) denotes the dimensionless concentration at the outlet at time θ. C(θ) is the volume fraction of the tracer at the outlet at time θ. t is the measurement time, with a unit of s. t_theory is the theoretical residence time, with a unit of s. In this study, t_theory is 599.98 s. V refers to the volume of water in the tundish, with a unit of m³. Q_in is the volumetric flow rate at the inlet of the tundish, with a unit of m³/h.

2.3.2. Outflow Percentage Curve Analysis Method

Taking the saturated KCl solution tracer as an example, the outflow percentage analysis method [89,90] initially refers to the calculation of ratio w(t) of mass of the tracer at the outlet during time interval Δt to the total mass of the added tracer, and the ratio W(t) of the accumulated mass of tracer at the outlet at time point t to the total mass of the added tracer. The following formulas could be used:

$$w(t)=m(t)/M,$$

(7)

$$M={\rho }_{\mathrm{tracer}}{Q}_{\mathrm{in}}\Delta t^{\prime },$$

(8)

$$m(t)={\rho }_{\mathrm{tracer}}{Q}_{\mathrm{out}}\omega (t)\Delta t,$$

(9)

$$W(t)={\displaystyle \sum _{t=0}^{t}w(t)},$$

(10)

where m(t) is mass of the tracer flow out from the tundish during time interval Δt, with a unit of kg. M is the total mass of the tracer injected at the inlet, with a unit of kg. ρ_tracer is the density of the added tracer solution, with a unit of kg/m³. In the water model, ρ_tracer is numerically equal to the density of the added saturated KCl solution tracer. Δt′ is the time interval for injection of the tracer at the inlet, with a unit of s. Δt is the data sampling time interval, with a unit of s. Q_in and Q_out are the volume flow rate at the inlet and outlet in the tundish, with a unit of L/s. ω(t) is the volume fraction ratio of the volume of saturated KCl solution with KCl solute of the same mass to the volume of the outflow solution during time interval Δt. In the water model experiment, the real-time conductivity difference at outlet can be converted into the volume fraction ratio of the added tracer by the following formula:

$$\Delta \kappa =A^{\prime }{\displaystyle \frac{V_{\mathrm{tracer}}(t)}{V_{\mathrm{solution}}(t)}}+B=A^{\prime }\omega (t)+B,$$

(11)

where Δκ(t) is the real-time conductivity difference at the tundish outlet, with a unit of S/m. V_tracer(t) is the volume of saturated KCl solution corresponding to the KCl solute contained in the outflowing KCl solution during time interval Δt, with a unit of L. And V_solution(t) is the volume of solution flows out of outlet during time interval Δt, with a unit of L. V_tracer/V_solution is the volume fraction ratio of the volume of saturated KCl solution with KCl solute of the same mass in the diluted solution to the volume of the outflow solution during time interval Δt. Based on the results of the water model experiment, A′ = 520.61467, and B = −0.00433, with a coefficient of determination of R² = 0.9994. The experimental data and fitted result are given in Appendix A.

3. Results and Analysis

In this section, the selected ink transport results were based on the transport of ink to fixed positions in the tundish. The seven subfigures correspond to the following positions, respectively: (1) the moment when the ink had just reached the tundish bottom, (2) the moment when the ink reached 1/3 of the tundish length, (3) the moment when the ink reached 1/2 of the tundish length, (4) the moment when the ink reached a position close to 2/3 of the tundish length, (5) the moment when the ink reached 2/3 of the tundish length, (6) the moment when the ink reached the outlet, and (7) the moment when part of the ink reached the side wall near the outlet. By analyzing the time required for the ink to reach these seven positions, the changes in ink transport at different temperatures were further investigated; that is, the differences in the flow-field structure in the tundish were examined. The red arrows in the figures indicated the diffusion direction of the ink tracer.

3.1. Transport Process of Pure Ink

Figure 2 shows the transport process of 15 mL pure ink at 20 °C (scheme A1). After the pure ink flowed from the shroud to the bottom of the tundish, it was divided into two streams. One stream was transported along the free surface, and the other was transported upward from the bottom of the tundish. The transport of ink at the bottom was slightly faster than that near the liquid surface. At 20 s, the ink dispersed from the bottom reached the central region of the tundish. Between 20 s and 37 s, a clear upward transport trend of the ink tracer was observed, and the leading edge of diffusion was located at half of the liquid level. At 37 s, the ink began to flow out from the outlet and simultaneously diffused into the region above the outlet. However, the diffusion rate in this region, especially near the liquid surface, was very slow. The ink did not gradually diffuse into this region until 72 s, and a long time was still required for it to disperse throughout the entire region.

Figure 3 shows the transport process of 15 mL pure ink at 7 °C (scheme A2). After flowing out from the shroud, the ink was also divided into two streams for transport. Unlike in scheme A1, in scheme A2, the upward transport tendency of the ink from the bottom was slightly weakened. No obvious difference was observed between the transport rate of the ink at the bottom and that near the liquid surface. From 14 s until just before 74 s, the ink was dispersed toward the right region of the tundish in a plug-flow manner. At 74 s, the ink transported along the bottom began to flow out from the outlet, and this stream stagnated on the left side of the outlet. At 93 s, the ink near the liquid surface was further transported toward the right wall of the tundish. Subsequently, the ink in the right region above the outlet mainly originated from this stream. In the region above the outlet and on the right side, a longer time was required for the ink to diffuse. Overall, the ink transport in scheme A2 was slowed down, and some stagnation was observed after 49 s. As a result, the arrival of the ink at the outlet (74 s) was significantly delayed compared with that in scheme A1.

Figure 4 shows the overall transport schematics of pure ink in the tundish for schemes A1 and A2. As shown in Figure 4, in scheme A1, a continuous upward transport trend of the ink was observed. In this scheme, the ink in the right region of the tundish was mainly formed by the diffusion of ink transported upward from the bottom toward the region near the liquid surface. Compared with scheme A1, a lower experimental temperature was used in scheme A2. Under this condition, the upward transport tendency of the ink at the tundish bottom was weakened, and the ink was transported toward the right region of the tundish in the form of “plug flow”. In addition, the ink transported along the bottom stagnated after it reached the outlet. The ink in the right region of the tundish was mainly formed by the diffusion of ink near the liquid surface.

3.2. Transport Process of Saturated KCl Solution at 20 °C

Figure 5 shows the transport process of 35 mL saturated KCl solution at 20 °C in scheme A3. Transport of the tracer along the bottom was clearly strengthened. At 5 s, an upward flow tendency was observed, but the bottom stream then developed strongly, and tracer transport near the liquid surface became very slow. No particularly strong short-circuit flow was observed in the tundish, but less tracer was transported along the liquid surface. Although the stream in the lower half of the tundish still dominated, it gradually shifted downward during transport compared with the ink transport process. The tracer did not reach the outlet region until 32 s, and the tracer diffused slowly. At 76 s, the tracer reached the right wall and then diffused upward along the wall toward the liquid surface. At 107 s, the tracer at the liquid surface had only diffused to one-third of the tundish length. During this process, a large amount of tracer accumulated in the middle region of the tundish and then slowly diffused from this region toward the liquid surface. At 118 s, the tracer still had not completely diffused to the liquid surface.

Figure 6 shows the transport process of 55 mL saturated KCl solution at 20 °C in scheme A4. Similar to scheme A3, transport of the tracer along the bottom was further strengthened. At 22 s, the tracer reached the region near the outlet. At 38 s, the tracer reached the right wall and then diffused upward along the wall toward the liquid surface. At 64 s, the tracer at the liquid surface had diffused to one-half of the tundish length. At 77 s, a transport state similar to that in scheme A3 at 118 s was observed. In other words, a large area near the liquid surface of the tundish still remained undiffused.

Figure 7 shows the transport process of 150 mL saturated KCl solution at 20 °C in scheme A5. Transport of the tracer along the bottom was further strengthened, and a pronounced short-circuit flow was observed in the tundish. At 17 s, the tracer had already reached the tundish outlet. From 30 s to 67 s, two transport paths were clearly observed during the tracer transport process. In one path, the tracer was transported along the right wall to the liquid surface. In the other path, the tracer was transported upward from the middle region of the tundish to the liquid surface. At 152 s, the tracer still had not diffused into the upper right region of the tundish. This result was mainly attributed to the strong short-circuit flow, by which a large amount of tracer was carried out of the tundish. As a result, the tracer concentration in the tundish was reduced, and the tracer diffusion rate was slowed.

Figure 8 shows the overall transport schematics of saturated KCl solution at 20 °C under different dosages. After tracer injection, short-circuit flow was observed in the tundish. In schemes A3, A4, and A5, the tracer reached the tundish outlet at 32 s, 22 s, and 17 s, respectively. Compared with scheme A1 (37 s), the time required for the tracer to reach the tundish outlet was shortened as the dosage of the salt solution tracer was increased in these three schemes. When the dosage of the salt solution tracer was low (35 mL saturated KCl solution, with a Dta value of 0.375 × 10⁻³, scheme A3), its diffusion process remained similar to that in scheme A1, although some changes were observed in the overall flow field and diffusion process. In schemes A4 and A5, the higher dosage of the salt solution tracer altered the flow field in the tundish, and strong downward flow and short-circuit flow were generated. As a result, a large amount of tracer was accumulated at the tundish bottom, and the transport process was significantly changed. As the dosage of the salt solution tracer was increased, tracer diffusion at the tundish bottom was accelerated, but transport toward the liquid surface was suppressed. Therefore, more time was required for the tracer to diffuse throughout the entire tundish.

3.3. Transport Process of Saturated KCl Solution at 7 °C

Figure 9 shows the transport process of 35 mL saturated KCl solution at 7 °C in scheme A6. The overall transport process in this scheme was similar to that in scheme A3 (35 mL saturated KCl solution, 20 °C), but transport of the tracer along the tundish bottom was slightly strengthened, and diffusion toward the liquid surface was slowed. The tracer reached the outlet at 32 s and reached the right wall of the tundish at 76 s. It was then slowly transported along the wall toward the liquid surface. Notably, compared with scheme A3, transport of the tracer toward the liquid surface was slower. In scheme A3, 107 s was required for the tracer to reach the region near the liquid surface, whereas 118 s was required in scheme A6. Thus, the required time was slightly prolonged. At 174 s, a large area near the liquid surface in scheme A6 still remained undiffused, whereas in scheme A3, a similar diffusion state near the liquid surface was reached at 118 s.

Figure 10 shows the transport process of 55 mL saturated KCl solution at 7 °C in scheme A7. Compared with the transport process in scheme A4 (55 mL saturated KCl solution, 20 °C), a marked change in the overall transport behavior was observed in scheme A7, and transport along the bottom was significantly strengthened. Before 18 s, similar times were required in the two schemes for the tracer to reach the same position, but the figure clearly shows that the tracer in scheme A7 was transported closer to the tundish bottom. At 18 s, the tracer in scheme A7 reached the region near the outlet, which was slightly earlier than the 22 s observed in scheme A4. However, after the tracer reached the outlet, transport and diffusion in scheme A7 became clearly slower than those in scheme A4, and the difference between the two became increasingly obvious as transport and diffusion proceeded. At 47 s, the tracer in scheme A7 reached the right wall of the tundish and was then transported along the wall toward the liquid surface. At 72 s, the tracer reached half of the liquid level height. At 159 s, the tracer reached the region near the liquid surface, but a large area still remained undiffused. By contrast, in scheme A4, the diffusion state near the liquid surface at 77 s was already similar to that in scheme A7 at 159 s. In summary, the lower temperature strengthened the downward short-circuit flow in the tundish, shortened the time required for the tracer to reach the outlet, and suppressed diffusion of the tracer toward the liquid surface.

Figure 11 shows the transport process of 150 mL saturated KCl solution at 7 °C in scheme A8. The process from tracer injection through the ladle shroud to its arrival at the tundish outlet was basically consistent with that in scheme A5 (150 mL saturated KCl solution, 20 °C). In scheme A8, the tracer reached the outlet at 18 s and reached the right wall of the tundish at 30 s, where it began to be transported along the wall toward the liquid surface. At this stage, the transport path through which the tracer diffused from the middle region toward the liquid surface still existed. After 30 s, tracer transport was slowed. At 72 s, the tracer reached the region near the liquid surface, which was slightly later than the 67 s observed in scheme A5. At 160 s, the tracer had diffused into most regions of the tundish, but it still had not diffused into the upper right region of the tundish, which was slightly later than the 152 s observed in scheme A5.

Figure 12 shows the overall transport process schematics of saturated KCl solution at 7 °C under different dosages. As the dosage of the salt solution tracer was increased, the downward flow and short-circuit flow in the tundish were strengthened. Compared with the transport behavior at 20 °C, when the dosage of the salt solution tracer was kept the same, a lower experimental temperature (schemes A6 to A8) strengthened the downward flow in the tundish, intensified the short-circuit flow, and caused the tracer to be transported along paths closer to the bottom. When the dosage of the salt solution tracer remained low (35 mL and 55 mL saturated KCl solution, with Dta values of 0.375 × 10⁻³ and 0.589 × 10⁻³, respectively), nearly the same time was required for the tracer to reach the same position during transport toward the tundish outlet at different temperatures. Therefore, during this stage, only a limited effect of lower temperature was exerted on the transport and diffusion rates of the tracer. After the tracer reached the outlet, it began to be transported toward the region near the liquid surface. For these two dosages, the time required for the tracer to diffuse into most regions of the tundish was prolonged by 56 s and 82 s, respectively, compared with the time required at 20 °C to reach the same diffusion state. These results indicated that, when the dosage of the salt solution tracer remained low, the effect of temperature was greater than that of tracer dosage, and the lower temperature suppressed transport and diffusion of the tracer toward the liquid surface. However, when the dosage of the salt solution tracer was increased to 150 mL (schemes A5 and A8), the overall transport and diffusion processes remained basically the same. At this stage, the effect of tracer dosage on the flow field became stronger than that of water temperature.

3.4. Analysis of Tracer Transport Paths

Figure 13 shows the transport path schematics of pure ink in the tundish for schemes A1 and A2. In the figure, the red arrows indicate the main flow stream of the tracer, the black arrows indicate the downward flow induced by the tracer, and the gray arrows indicate the diffusion effect caused by the concentration difference between the tracer and water. For the gray arrows, a darker color indicates a stronger diffusion effect at that position. At an experimental temperature of 20 °C, in scheme A1, because the density difference between the ink and water was small, the ink was mainly transported along the upward main flow stream. When the experimental temperature was decreased to 7 °C, in scheme A2, the ink transport path shifted closer to the tundish bottom, the transport mainly took the form of “plug flow”, and transport near the right wall of the tundish became very slow.

Figure 14 shows the transport path schematics of saturated KCl solution in the tundish for schemes A3 to A8. Because the tracer had a higher density than water, the main flow stream gradually shifted closer to the tundish bottom as the dosage of the salt solution tracer was increased, and short-circuit flow was generated at the same time. Compared with the results at 20 °C, stronger downward flow was observed in the experiments at 7 °C. As a result, the main flow stream was driven closer to the tundish bottom, and the transport and diffusion rates of the tracer near the right wall were reduced. However, compared with the ink transport schemes, no major change was caused in the transport path of saturated KCl solution by the temperature variation. As the dosage of the salt solution tracer was increased, the short-circuit flow became more obvious. The effect of tracer dosage on transport of the salt solution tracer gradually became stronger than that of water temperature, and the differences in tracer transport under different experimental temperatures were reduced. When the dosage of the salt solution tracer remained low (35 mL saturated KCl solution, with a Dta value of 0.375 × 10⁻³), the upward transport tendency of the salt solution tracer was weakened compared with that in the pure ink transport (schemes A1 and A2). After the dosage of the salt solution tracer was increased (55 mL and 150 mL saturated KCl solution, with Dta values of 0.589 × 10⁻³ and 1.608 × 10⁻³, respectively), the main flow stream changed into strong short-circuit flow and downward flow.

3.5. RTD Curves of Saturated KCl Solution

Figure 15 shows the RTD curves obtained after different dosages of saturated KCl solution were injected through the ladle shroud at experimental temperatures of 20 °C and 7 °C, and

Table 6. Characteristic parameters of the average RTD curves of the tracer at different experimental temperatures.

The Volumes of Saturated KCl Solution (mL)	10		35		55		150
parameters	Temperature (°C)
	7	20	7	20	7	20	7	20
Response time (s)	37	35	24	24	26	22	21	16
peak concentration time (s)	215	122	135	111	94	72	48	43
peak concentration	0.95	0.98	1.18	1.24	1.21	1.32	3.09	3.35
Mean residence time (s)	521.33	473.95	438.09	412.5	423.38	415.39	338.86	321.42
Dimensionless concentration at 1500 s	0.059	0.034	0.057	0.016	0.033	0.030	0.027	0.023

lists the characteristic parameters of the average RTD curves for each dosage under different experimental temperatures. As the experimental temperature was increased from 7 °C to 20 °C, a leftward shift in the RTD curves was observed, and the dimensionless concentration of the RTD curves at 2.5 times the theoretical residence time (1500 s) was reduced. Among these results, the RTD curves corresponding to 10 mL saturated KCl solution showed the most significant difference between the two temperatures. As the tracer dosage was increased from 35 mL to 150 mL, the differences in the RTD curves under different temperature conditions were gradually reduced. According to the parameters listed in Table 6, only slight changes were observed in the response time of the RTD curves at each dosage after the temperature was increased, whereas the peak time and mean residence time were obviously shortened. This phenomenon was attributed to the decrease in water viscosity caused by the temperature increase, by which tracer transport was promoted and a large amount of the salt solution tracer was allowed to flow out from the outlet at an earlier time. However, as the dosage of the salt solution tracer was increased from 10 mL to 150 mL, the extent to which the peak time of the RTD curves was shortened at different temperatures was gradually reduced. Under the 10 mL condition, the difference in peak time between 7 °C and 20 °C was 93 s, which was clearly greater than the corresponding values of 24 s, 22 s, and 5 s under the 35 mL, 55 mL, and 150 mL conditions, respectively. This result indicates that, when the dosage of the salt solution tracer exceeded 35 mL (Dta > 0.375 × 10⁻³), the effect of tracer dosage on the transport of the salt solution tracer became stronger than that of water temperature. This conclusion is consistent with the results presented in this paper regarding the effect of experimental temperature on the tracer transport process.

3.6. Outflow Percentage Curves of Saturated KCl Solution

Figure 16 shows the outflow percentage curves [89,90] of saturated KCl solution at experimental temperatures of 20 °C and 7 °C for different dosages and Figure 17 shows the total outflow percentages of saturated KCl solution at 1500 s for the corresponding schemes. It can be seen that the outflow percentage curves of the 10 mL salt solution tracer showed the largest difference at different temperatures. At 7 °C, the total outflow percentage of the 10 mL salt solution tracer at 1500 s was 76.86%, which was 22.97% lower than that at 20 °C, indicating that part of the salt solution tracer had not flowed out from the tundish outlet at that time, and that temperature significantly affected the flow behavior of the low-dosage salt solution tracer in the tundish. In a previous study [84], 35 mL salt solution tracer at 20 °C was identified as the turning point at which tracer dosage affected the tundish flow field. The outflow percentage curves of the 35 mL salt solution tracer at different temperatures were similar, and at 7 °C, its total outflow percentage at 1500 s was 3.40% lower than that at 20 °C. As the tracer dosage was further increased, the total outflow percentages of the 55 mL and 150 mL salt solution tracer at 1500 s were reduced, and the differences between the outflow percentage curves of the tracer at the same dosage under different temperatures were gradually decreased. At 7 °C, the total outflow percentage of the 55 mL salt solution tracer at 1500 s was 87.53%, which was 9.75% lower than that at 20 °C. At 7 °C, the total outflow percentage of the 150 mL salt solution tracer at 1500 s was 73.72%, which was 2.58% lower than that at 20 °C. These results indicate that, as the tracer dosage was increased, the effect of dosage on the experimental results gradually became stronger than that of temperature variation, thereby reducing the differences in the outflow percentage curves of the salt solution tracer at different temperatures.

4. Discussion

In this study, the Dta values corresponding to 10 mL, 35 mL, 55 mL, and 150 mL saturated KCl solution were 0.107 × 10⁻³, 0.375 × 10⁻³, 0.589 × 10⁻³, and 1.608 × 10⁻³, respectively. From the comparison between the 20 °C and 7 °C conditions, it was found that tracer transport and diffusion in the tundish were accelerated at the higher experimental temperature. The diffusion of the tracer toward the region near the liquid surface was also enhanced. In contrast, under the 7 °C condition, the overall tracer transport path remained closer to the tundish bottom, and the upward diffusion rate after the tracer reached the outlet was markedly reduced. For the saturated KCl solution tracer, this “temperature effect” was more significant at low dosage. As the tracer dosage was increased, rapid tracer transport along the bottom toward the outlet became more obvious, whereas the differences in the transport process under different temperature conditions were gradually reduced. It was therefore indicated that the effect of tracer dosage on the flow field and transport path gradually became stronger than that of temperature variation. Therefore, when the tracer dosage was small, special attention needed to be paid to the errors caused by changes in experimental temperature. When the tracer dosage was large, the differences in the experimental results under different temperature conditions became smaller. However, the disturbance of the flow field caused by the tracer itself became significantly stronger, and the accuracy of the experimental results was thereby reduced. Previous studies rarely reported the effect of water temperature on experimental results. This may have been attributed to the relatively large dosage of salt solution tracer used in earlier experiments. Under such conditions, downward flow was dominant, and the effect of temperature variation was relatively weak. However, the original flow field could be significantly disturbed, and the measurement results could be affected by a high dosage of salt solution tracer. Therefore, reduction in the salt solution tracer dosage had already been suggested in recent studies [22,83,85,86].

To further interpret the observed temperature effect from a dimensionless viewpoint, it should be noted that the geometry and flow rate were kept unchanged in the present experiments. Therefore, the Froude number of the tundish system remained essentially unchanged, and the macroscopic inertial-gravity flow pattern was not fundamentally altered by temperature variation. In contrast, the Reynolds number changed with water viscosity. Taking the outlet diameter as the characteristic length, the Reynolds number remained on the order of 10⁴ under both 7 °C and 20 °C conditions, indicating that both cases were still within the turbulent regime, although the 20 °C condition corresponded to a higher Reynolds number and thus stronger convective transport and mixing. This provides one explanation for the faster tracer transport and the shorter peak and mean residence times observed at 20 °C.

In addition, the relative density difference between the tracer and water, defined as (ρ_tracer − ρ_w)/ρ_w, also changed with temperature. At 7 °C, both the pure ink tracer and the saturated KCl solution showed a larger relative density difference with respect to water than at 20 °C. As a result, the tendency of the tracer to remain near the tundish bottom was strengthened, and transport toward the free surface was weakened. For the saturated KCl solution tracer, this effect became more evident as the tracer dosage increased. Therefore, the observed flow behavior can be understood as the combined result of viscosity-dependent transport, temperature-dependent density difference, and dosage-dependent flow disturbance. When the tracer dosage was low, the temperature effect was more clearly reflected in the experimental results; when the tracer dosage was high, the disturbance induced by the tracer itself became dominant, and the difference between 7 °C and 20 °C was correspondingly reduced.

In a previous study [84], it was shown that, at 20 °C, less than 35 mL of saturated KCl solution should be used in experiments with a bare single-strand tundish water model. When the RTD curve results and the outflow percentage curve results obtained in this study were considered together, large differences were observed between the results for 10 mL saturated KCl solution at 7 °C and 20 °C. Compared with the results at 20 °C, under the 7 °C condition, the mean residence time of 10 mL saturated KCl solution was increased by 10%, and the total outflow percentage at 1500 s was reduced from 99.78% to 76.86%, corresponding to a decrease of 22.97%. These results indicated that the transport process of 10 mL saturated KCl solution was strongly affected by temperature. Therefore, when the dosage of the salt solution tracer remained low at 7 °C (Dta < 0.375 × 10⁻³), the experimental results were strongly influenced by water temperature conditions, and particular attention needed to be paid to the errors caused by changes in experimental conditions. When tundish water model experiments were conducted, the effects of season and water temperature conditions needed to be taken into consideration.

5. Conclusions

In this study, the differences in fluid flow behavior in the tundish water model between winter and summer were investigated. The following conclusions were obtained:

(1)

Tracer transport and diffusion behavior in the tundish water model were significantly affected by experimental temperature. Compared with the condition at 20 °C, under the condition at 7 °C, a weaker upward transport tendency was observed for the pure ink tracer. The overall transport path was found to remain closer to the tundish bottom, and “plug flow” characteristics were more easily exhibited. In addition, the overall transport speed was reduced, and the time required for the tracer to reach the outlet was significantly prolonged. These results indicated that changes in the overall experimental temperature significantly affected the macroscopic flow characteristics in the tundish.

(2)

For the saturated KCl solution tracer, transport along the bottom toward the outlet was strengthened and diffusion toward the liquid surface was suppressed at lower experimental temperatures. Under the 7 °C condition, stronger downward flow and short-circuit flow were observed in the tundish, and the tracer was more likely to be transported rapidly toward the outlet along the bottom. Among the tested dosages, the 10 mL saturated KCl solution tracer showed the most obvious differences in the RTD curves and outflow percentage curves between 7 °C and 20 °C. This result indicated that the low-dosage tracer was more sensitive to temperature changes.

(3)

As the dosage of saturated KCl solution was increased, the influence of temperature on the experimental results was gradually weakened, whereas the influence of tracer dosage on the flow field and transport behavior was gradually strengthened. After the experimental temperature was increased, the RTD curves were shifted to the left as a whole, and both the peak time and the mean residence time were shortened. These results indicated that the tracer was transported faster at higher temperatures. At the same time, large differences were observed in the outflow percentage curves of the low-dosage tracer at different temperatures, whereas the differences in the tracer transport process, RTD curves, and outflow percentage curves under different temperature conditions were gradually reduced as the dosage was increased. When the tracer dosage was increased to 150 mL, the influence of tracer dosage on the flow field became clearly stronger than that of temperature variation. These results indicated that, in tundish water model experiments, especially under low-dosage tracer conditions, the errors caused by changes in experimental temperature should be carefully considered.

(4)

In summary, when tundish water model experiments are conducted in different seasons, sufficient attention should be paid to water temperature conditions, and the consistency and comparability of water temperature should be maintained as far as possible. When the water temperature deviates from the commonly used condition of around 20 °C, its influence on flow characterization results and tracer transport behavior should be carefully considered, so as to improve the reliability and practical value of the experimental results.