A Similarity-Based Scaling Methodology for the Thermal-Hydraulic Design of Dual Fluid Reactor Demonstrators

Abstract

The Dual Fluid Reactor (DFR) is a Generation IV concept that relies on a phased development pathway using a low-temperature microdemonstrator ($\mu$DEMO) and a high-temperature minidemonstrator (mDEMO). A rigorous methodology is required to scale experimental data between these facilities to ensure the reliable design of the final reactor. This paper establishes such a methodology grounded in Similarity Theory. The Cathare-2 system code was used to perform a parametric study on a simplified model of the demonstrators, which use lead–bismuth eutectic and pure liquid lead, respectively. This study focused on identifying the specific operating conditions required to match key “defining” dimensionless numbers—the Reynolds number (Re) for dynamic similarity and the Peclet number (Pe_h) for thermal similarity. The analysis successfully identified and presented the distinct operating ranges of fluid velocity and mass flow required to achieve either state. Results show that matching the Reynolds number allows for the dimensionless pressure drop to be scaled with a deviation below 0.2%, while matching the Peclet number allows for the dimensionless temperature profile to be scaled with a deviation under 2.5%. The central finding is that dynamic and thermal similarity cannot be achieved simultaneously due to the different working fluids and temperatures of the demonstrators. This forces a strategic choice in experimental design, where an experiment must be tailored to investigate either fluid dynamics or heat transfer. This work provides the foundational “rulebook” for designing these crucial experiments, ensuring that data from the DFR demonstrator program is both reliable and scalable.

1. Introduction

The Dual Fluid Reactor (DFR) is an innovative Generation IV nuclear reactor concept based on the principle of separating the fuel and cooling functions into two independent liquid circuits. This design, which can use either molten salt [1] or a liquid metal alloy as fuel and liquid lead as a coolant, allows for the independent optimization of each loop [2]. The DFR diagram is shown in the Figure 1. The technology is a combination of the Molten Salt Reactor (MSR) [3] and the Lead Fast Reactor (LFR) [4,5].

A distinction is made between the DFR(m), which uses liquid metal fuel, and the DFR(s), which uses molten salts [6,7]. The DFR is characterized by very high operating temperatures (1000–1300 °C for fuel and 800 °C for coolant), which necessitates a coolant with a very high heat capacity, such as liquid metals [8,9].

Because the DFR(m) is a new reactor concept, simplified models must first be established to allow for tests and experiments to be conducted under safe, controlled conditions. These test systems, known as demonstrators, are designed to perform thermal-fluid experiments [10]. The purpose of this work is to select appropriate dimensionless numbers to compare these demonstrators. This will create a methodology to predict the operating parameters of a larger minidemonstrator—and eventually the final DFR—based on data obtained from a smaller microdemonstrator.

The purpose of the work was to select appropriate dimensionless numbers, with which to compare demonstrators among themselves. This solution would allow us, based on the data from the microdemonstrator, to predict the operating parameters for the minidemonstrator and then for the conceptual DFR reactor. Specifically, applying fundamentals of the Similarity Theorem, experimental data gathared from micro-, mini- and other demonstrators will provide detailed knowledge of actual and potential flow patterns and heat transfer parameters.

The fundamental design of the Dual Fluid Reactor is elegantly captured in its two-circuit system, which efficiently separates the nuclear and thermal functions of the plant [11]. The first circuit, the Fuel Loop, circulates the liquid fuel through the reactor core, where fission takes place. This loop also contains a Pyroprocessing Unit (PPU) for continuous, online removal of fission products and an MHD (magnetohydrodynamic) pump to maintain circulation. The second circuit, the Coolant Loop, pumps liquid lead through the reactor core to absorb the intense heat generated in the Fuel Loop. This heat is then transported via another MHD pump to a heat exchanger (HEX), where it is transferred to a conventional power conversion system to generate electricity [11]. DFR flow parameters are presented in

Table 1. Operating flow parameters of the DFR concept.

Parameter	Value	Unit
General
Operating Power	250	$\mathrm{M}\mathrm{W}$
Fuel Loop (Uranium-Chromium Eutectic)
Mass Flow Rate	6476	$\mathrm{k}\mathrm{g}{\mathrm{s}}^{-1}$
Temperature Range	1000 °C to 1200 °C
Density	15,634	$\mathrm{k}\mathrm{g}{\mathrm{m}}^{-3}$
Velocity	0.5	$\mathrm{m}{\mathrm{s}}^{-1}$
Coolant Loop (Liquid Lead)
Mass Flow Rate	7540	$\mathrm{k}\mathrm{g}{\mathrm{s}}^{-1}$
Temperature Range	800 °C to 1100 °C
Density	984	$\mathrm{k}\mathrm{g}{\mathrm{m}}^{-3}$
Velocity	1.0	$\mathrm{m}{\mathrm{s}}^{-1}$

.

Demonstrators

The DFR concept is a very complicated device in many aspects, and before a full-scale Dual Fluid Reactor can be constructed, a strategic, phased approach using demonstrators is essential. These demonstrators serve as proof-of-concept and first-of-a-kind facilities, allowing for a plethora of experiments on key technologies under safe, controlled conditions. This pathway involves building systems with gradually increasing fidelity and operating temperatures, mitigating risks and validating the design at each stage.

The demonstrator pathway is shown in table [12] and begins with the microdemonstrator (µDEMO), a small-scale facility operating at lower temperatures (200–400 °C) with lead–bismuth eutectic. This facility will have similar velocities as the actual concept of the DFR. It then progresses to the minidemonstrator (mDEMO) [10], which uses liquid lead at higher temperatures (800–1000 °C) [13]. This progression allows for critical experiments on phenomena concerning liquid metal thermal hydraulics (studying the unique flow and heat transfer characteristics of liquid metals), materials science and engineering (testing the performance and corrosion resistance of advanced piping and heat exchanger materials when exposed to high-temperature, corrosive fluids), and pumping solutions (validating and optimizing novel pumping solutions, such as magnetohydrodynamic (MHD) pumps, which are necessary because conventional pumps cannot handle the high-temperature liquid metals). The micro- and minidemonstrator diagram is shown in Figure 2.

On the other hand, the minidemonstrator will share similar operating medium, velocities, and temperatures as the DFR concept. Data gathered from these demonstrators is invaluable for validating computational models, refining component design, designing following stages of demonstrators, and ultimately ensuring the safety and reliability of the final DFR.

2. Theoretical Framework

The theoretical framework for scaling the experimental data between the DFR demonstrators is grounded in the Similarity Theorem. This theorem is the cornerstone of thermal-hydraulic scaling, providing a rigorous method to ensure that a small-scale model accurately represents the phenomena of a full-scale prototype. Its application relies on the use of dimensionless numbers to characterize the physical system, making the results independent of the absolute size or operating conditions.

Similarity numbers (or dimensionless numbers) are ratios that help engineers and physicists understand how a system behaves without getting bogged down by specific units or sizes. They are essential for scaling experiments, like predicting the behavior of a large reactor based on a small model, which is the core issue discussed in the paper. Three key theorems from Similarity Theory together form the rulebook for scaling phenomena [14].

• Newton’s Theorem (The Principle): This is the basic idea. It states that if two physical phenomena are truly similar, then their corresponding similarity numbers must be identical. For example, if a small model of a pump is dynamically similar to its full-size version, their Reynolds numbers (a similarity number for fluid flow) will be the same [15].
• Buckingham’s $\pi$ Theorem (The Method): This theorem provides a method for finding the similarity numbers in the first place. This shows that all physical variables describing the phenomenon (like velocity, density, viscosity, and pipe diameter) can be grouped into a smaller, basic set of dimensionless similarity numbers. This drastically simplifies the problem [15].
• Kirpichev–Guchman Theorem (The Condition) [15]: This is the most critical theorem for practical application. It states that to guarantee two phenomena are similar, two conditions must be met as follows:

  (a)

  The “uniqueness conditions” (geometry, material properties, and initial and boundary conditions) must be similar.

  (b)

  The “defining” similarity numbers must be equal.

Defining numbers (the “Inputs” or Criteria) are constructed from the parameters that can be controlled or that define the system’s setup (the “uniqueness conditions”). To achieve similarity between two systems, these numbers must be deliberately aligned. This approach is essential for the DFR’s phased development, as it provides a scientifically sound basis for extrapolating findings from the low-temperature microdemonstrator to the high-temperature minidemonstrator.

Defining numbers, such as the Reynolds number (Re) and the Peclet number (Pe), are constructed from controllable “inputs” like fluid velocity, geometry, and inherent material properties [16]. To achieve true similarity, the primary objective is to match these defining numbers between the two demonstrators, ensuring that the fundamental physical ratios—such as inertial to viscous forces (Re) and convective to conductive heat transfer (Pe)—are identical [17]. In contrast, non-defining numbers, like the Nusselt number (Nu), are “outputs” because they include a resulting quantity like the heat transfer coefficient (h). The correct application of the theorem dictates that if the defining numbers are matched, the non-defining numbers will also match as a direct consequence of the established physical similarity [18].

The application of this theorem is central to the validation of computational tools like the Cathare-2 code. By carefully designing experiments where the microdemonstrator’s operating conditions are adjusted to match the defining numbers (Re and Pe) of a target scenario in the minidemonstrator, a “similarity zone” is created. Experimental data gathered from the microdemonstrator within this zone provide a direct, one-to-one benchmark for validating the code’s predictive accuracy. This process ensures that the computational models are not just theoretically sound but are also anchored by real-world data from a physically analogous system.

Equally important is the theorem’s role in guiding experiments that fall outside the scope of direct similarity. The framework can identify conditions where the demonstrators are fundamentally different, such as operating in vastly different turbulence regimes. Intentionally performing experiments in these “out-of-similarity” zones is crucial for building a broader, more comprehensive database on liquid metal interactions, flow mechanics, and heat transfer. This expands the overall engineering knowledge base, ensuring the final DFR design is robust and safe across its entire operational envelope, not just under the limited conditions where direct scaling is possible.

To ensure that the experimental data from the micro- and minidemonstrators can be accurately compared and scaled, it is essential to use a theoretical framework that can describe the complex physical phenomena independently of the system’s size or temperature. This is achieved using a specific set of defining dimensionless numbers that characterize the dominant transport mechanisms at play. For the DFR, the three most critical phenomena are the transport of momentum (fluid flow), heat (energy extraction), and mass (fission product movement). Each of these is best described by a corresponding dimensionless number, making them the most suitable for identifying similarities between the demonstrators.

The two defining numbers are the Reynolds number (Re) and the Peclet number for heat transfer (Pe_h). Reynolds number characterizes the fluid dynamics by describing the ratio of inertial forces to viscous forces. Matching the Reynolds number ensures that the flow regimes (e.g., laminar or turbulent) are similar in both the micro- and minidemonstrator, which is fundamental to achieving any further similarity. This number is expressed by the following equation:

$$Re={\displaystyle \frac{v{D}_h\rho }{\mu }},$$

(1)

where, v, $D_h$, $\rho$, and $\mu$ are velocity, hydraulic diameter, fluid density, and dynamic viscosity.

Peclet number for heat transfer (Peheat) describes the ratio of convective heat transport (heat carried by the fluid’s motion) to conductive heat transport (heat spreading through the fluid). For liquid metals, which have very high thermal conductivity, the Peclet number is the most accurate defining number for thermal similarity, as it captures the dominant heat transfer mechanisms more effectively than other numbers. It is expressed by the following equation:

$$P{e}_h=Re·Pr,$$

(2)

where $Pr$ is a Prandtl number which is the ratio of momentum diffusivity to thermal diffusivity. In simpler terms, it compares how quickly momentum (velocity changes) spreads through a fluid versus how quickly heat spreads through it. It is a fundamental property of the fluid itself and is critical for understanding heat transfer. A low Prandtl number ($Pr$ ≪ 1), like that of liquid metals, means that heat diffuses much faster than momentum. This results in the thermal boundary layer being much thicker than the velocity boundary layer. Conversely, a high Prandtl number ($Pr$ ≫ 1), like that of oils, means momentum diffuses faster than heat, leading to a thermal boundary layer that is thinner than the velocity boundary layer. It is defined as

$$Pr={\displaystyle \frac{c_p·\mu }{k}},$$

(3)

where $c_p$ and k are specific heat and thermal conductivity.

3. Reference Calculations

To provide a reliable benchmark for the subsequent scaling analysis, referential calculations for the heat exchangers of both the micro- and minidemonstrators are necessary. For this purpose, the Cathare-2 computer code was selected, as it is capable of providing high-fidelity values for fluid velocities and temperatures. As a well-established thermal-hydraulic software based on a robust six-equation, two-phase model, its suitability for high-temperature modeling has been demonstrated in its application to gas-cooled reactors. Critically, the code has been specifically validated for liquid metal systems, including a liquid sodium loop experiment with satisfactory results, and its library includes the necessary working fluids for both demonstrators by default.

CATHARE [19] (Code for Analysis of THermalhydraulics during an Accident of Reactor and safety Evaluation) is a two-phase thermal-hydraulic software developed since 1979 at CEA-Grenoble under an agreement between CEA, EDF, AREVA, and IRSN. The software is based on a two-phase model with six equations (conservation of mass, moments, and energy for both phases). This software’s modular structure can operate in 0D, 1D, or 3D and is capable of modeling any type of reactor. The native support for liquid metals in Cathare-2 is essential for accurately modeling the DFR demonstrator systems [20]. After simplification and reorganization, the momentum balance which is used to calculate pressure drop is as follows:

$$A{\rho }_L\left[{\displaystyle \frac{\partial V_L}{\partial t}}+V_L{\displaystyle \frac{\partial V_L}{\partial z}}\right]+A{\displaystyle \frac{\partial P}{\partial z}}=-{\chi }_f{C}_L{\displaystyle \frac{{\rho }_L}{2}}{V}_L|V_L|-A{\displaystyle \frac{K}{2\Delta Z}}{\rho }_L{V}_L\left|V_L\right|+A{\rho }_L{g}_z+S{M}_L$$

(4)

where

• ${\displaystyle A{\rho }_L\left[\frac{\partial V_L}{\partial t}+V_L\frac{\partial V_L}{\partial z}\right]}$ represents the inertia (temporal and convective acceleration).
• ${\displaystyle A\frac{\partial P}{\partial z}}$ is the pressure gradient.
• ${\displaystyle -{\chi }_f{C}_L\frac{{\rho }_L}{2}{V}_L\left|V_L\right|}$ is the distributed wall friction term. $C_L$ includes the single-phase friction factor $f_L$.
• ${\displaystyle -A\frac{K}{2\Delta Z}{\rho }_L{V}_L\left|V_L\right|}$ represents the localized singular pressure loss (form loss) over a length $\Delta Z$. K is the singular pressure drop coefficient.
• ${\displaystyle A{\rho }_L{g}_z}$ is the gravitational force term.
• ${\displaystyle S{M}_L}$ represents external momentum sources or sinks per unit volume.

This equation is the standard form of the one-dimensional momentum balance for a single-phase, incompressible or compressible fluid.

For the heat transfer law, for high Reynolds number liquid heat transfer a Dittus–Boelter correlation is applied as follows:

$$H_{turb}=0.023·R{e}_L^{0.8}·P{r}_L^{0.4}·{\displaystyle \frac{{\lambda }_L}{D_{hL}}}$$

(5)

where

• $H_{turb}$ is the turbulent forced convection heat transfer coefficient ($\mathrm{W}{\mathrm{m}}^{-2}{\mathrm{K}}^{-1}$).
• $R{e}_L$ is the Reynolds number for the liquid phase.
• $P{r}_L$ is the Prandtl number for the liquid phase.
• ${\lambda }_L$ is the thermal conductivity of the liquid ($\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$).
• $D_{hL}$ is the hydraulic diameter associated with the liquid phase ($\mathrm{m}$).

3.1. Cathare-2 Model Setup

The simulations were performed using the Cathare-2 V2.5_3mod9.1 system code [19], which employs a two-fluid, six-equation model [21]. Both the µDEMO and mDEMO were represented using a simplified 1D counter-flow tube-in-tube heat exchanger geometry to serve as a consistent basis for scaling analysis. The inner tube had an inner diameter of $0.0465$ $\mathrm{m}$ and a thickness of $0.002$ $\mathrm{m}$, while the outer tube had an inner diameter of $0.08$ $\mathrm{m}$. The heated length for both models was $0.5$ $\mathrm{m}$. The µDEMO tube material was INOX317 stainless steel, whereas the mDEMO used a Titanium–Zirconium–Molybdenum (TZM) alloy. Axial nodalization comprised 50 nodes ( $0.01$ $\mathrm{m}$ each), with 10 radial nodes for wall conduction. Temperature-dependent thermophysical properties for lead–bismuth eutectic (LBE) and pure lead (Pb), sourced from the Cathare-2 library, were used as defined in

Table 2. Material properties for lead–bismuth eutectic and pure lead implemented in Cathare-2 code [21,22].

Parameter	Lead–Bismuth	Lead
Density $\left[{\displaystyle \frac{\mathrm{kg}}{{\mathrm{m}}^3}}\right]$	$\rho =11065-1.293·T$	$\rho =11441-1.2795·T$
Dynamic viscosity $\left[\mathrm{Pa}·\mathrm{s}\right]$	$\eta =4.94\times {10}^{-4}·exp(754.1/T)$	$\eta =4.55\times {10}^{-4}·exp(1069/T)$
Specific heat $\left[{\displaystyle \frac{\mathrm{J}}{\mathrm{kg}·\mathrm{K}}}\right]$	$c_p=164.8-3.94\times {10}^{-2}·T+$ $1.25\times {10}^{-6}·T^2-4.56\times {10}^5·T^{-2}$	$c_p=176.2-4.923\times {10}^{-2}·T+$ $1.544\times {10}^{-6}·T^2-1.524\times {10}^6·T^{-2}$
Thermal conductivity $\left[{\displaystyle \frac{\mathrm{W}}{\mathrm{m}·\mathrm{K}}}\right]$	$\lambda =3.284+1.617\times {10}^{-2}·T+$ $-2.305\times {10}^{-6}·T^2$	$\lambda =9.2+0.011·T$

.

3.2. Results

While the Cathare-2 models for the micro- and minidemonstrator share an identical core geometry to provide a consistent basis for comparison (Figure 3), they differ fundamentally in three key areas. The primary differences are the operating media (lead–bismuth eutectic vs. pure liquid lead), the operating conditions of these fluids, which result in distinct densities and viscosities, and the heat exchanger materials required to withstand the vastly different temperature ranges. Consequently, even with the same geometry, the resulting dimensionless numbers for each system will differ, requiring a scaling analysis to bridge the gap between their performance. The fluid properties are presented in Table 2, where T, in all equations, must be in Kelvin (K). The validity of these formulas has been checked and confirmed using a build-in CATHARE-2 post-processor.

Boundary conditions for the reference calculations are shown in

Table 3. Boundary conditions for micro- and minidemonstrator simulations.

	Microdemonstrator (µDEMO)		Minidemonstrator (mDEMO)
Parameter	Fuel Loop	Coolant Loop	Fuel Loop	Coolant Loop
Mass Flow Rate [kg/s]	2.5	3.48	1.741	1.786
Inlet Temperature [°C]	400.0	200.0	1000.0	800.0
Velocity [m/s]	0.144	0.100	0.104	0.053
Reynolds Number [-]	45,220	14,410	45,248	14,594

. The core that is depicted in Figure 3 is simplified to a tube in a heat exchanger with an inner diameter of 0.0465 m, inner tube thickness of 0.002 m, and outer tube inner diameter of 0.08 m. The temperatures are imposed in the inlets in Figure 3. However, the values of velocities and Reynolds numbers are checked at the core inlet. For the microdemonstrator, the heat exchanger has been designed with INOX317 stainless steel, since it operates at lower temperatures and for minidemonstrator, the heat exchanger is made of Titanium–Zirconium–Molybdenum alloy [23] to withstand high temperatures [24,25]. The height of both heat exchangers is 0.5 m. The nodalization for calculations for both models is presented in

Table 4. Nodalization for µDEMO and mDEMO Cathare-2 models.

Nodalization
	Microdemonstrator	Minidemonstrator
Axial nodalization:	50	50
Axial length	0.5 m	0.5 m
Axial nodalization length	0.01 m	0.01 m
Wall nodalization	10	10
Wall thickness	0.002 m	0.002 m

.

For such defined reference operating conditions, the temperatures of both fluids are depicted in Figure 4.

For such defined reference operating conditions, the heat flux of both fluids are depicted in Figure 5.

Lastly, the comparison of Reynolds and Peclet numbers is presented in Figure 6. In this figure, on the left, one can observe a comparison of Reynolds numbers ratios for fuel and coolant between micro- and minidemonstrators defined as

$$R{e}_{ratio}={\displaystyle \frac{R{e}_{micro}}{R{e}_{mini}}}$$

(6)

4. Achieving Similarity Between Demonstrators

This section presents the Cathare-2 simulation results for the micro- and minidemonstrators, focusing on the specific operating conditions required to achieve similarity in their dimensionless numbers. The analysis is presented in two main cases: one targeting dynamic similarity (matching Reynolds numbers) and the other targeting thermal similarity (matching Peclet numbers). The criterion established in the article regarding the similarity of dimensionless numbers is that the relative difference between them cannot exceed 10%. The results demonstrate that the conditions required to satisfy each similarity case are distinct.

4.1. Dynamic Similarity

This subsection details the analysis performed to achieve dynamic similarity between the micro- and minidemonstrator. The primary objective was to identify the operating conditions that result in an identical Reynolds number ($Re$) in both systems. Matching this key defining number is the foundation of a valid scaling experiment, as it ensures that the fundamental fluid dynamics—including the flow regime and turbulence characteristics—are directly comparable. To find these conditions, numerous calculations were performed in a systematic parametric study. For a given fluid velocity in the microdemonstrator, the Reynolds number similarity equation was solved to determine the precise corresponding velocity required in the minidemonstrator to yield the same $Re$ value. This process was iterated across a wide spectrum of initial velocities for both the lead–bismuth eutectic and liquid lead, effectively mapping the operational relationship between the two systems.

A critical constraint on this study was to keep the results within realistic operational limits. The calculations were bounded by velocities that represent real-life values for magnetohydrodynamic pumps to avoid scenarios that would lead to excessive material erosion or impractical power requirements. This constrained approach successfully identified the ranges of applicability-specific, paired velocity ranges for each demonstrator, within which dynamic similarity can be confidently achieved, thus defining the precise conditions for valid experimental comparison.

From the

Table 5. Operating conditions ranges for dynamic similiarity.

	Reynolds Number		Mass Flow [kg/s]		Velocity [m/s]
Loop	µDEMO	mDEMO	µDEMO	mDEMO	µDEMO	mDEMO
Fuel	45,204	45,238	2.50	1.74	0.144	0.104
	159,045	159,316	8.79	6.13	0.507	0.366
Coolant	14,410	14,595	3.48	1.79	0.100	0.053
	275,762	278,319	66.66	34.09	1.912	1.014

above, it is important to note that as long as fuel velocity in the minidemonstrator is slower than fuel velocity in the microdemonstrator by exactly $1.386$ times, the dynamic similarity will be achieved between system. For the coolant case, the ratio of micro-D coolant velocity to mini-D coolant velocity must be equal to $1.88$. Both values are estimated from the definition of the Reynolds number.

$$R{e}_{micro,f}=R{e}_{mini,f}={\displaystyle \frac{V_{micro,f}·{\rho }_{LBU}}{{\mu }_{LBU}}}={\displaystyle \frac{V_{mini,f}·{\rho }_{Pb}}{{\mu }_{Pb}}}$$

(7)

which can be re-arranged into the following:

$${\displaystyle \frac{V_{micro,f}}{V_{mini,f}}}={\displaystyle \frac{{\rho }_{Pb}·{\mu }_{LBU}}{{\rho }_{LBU}·{\mu }_{Pb}}}$$

(8)

Substituting actual properties of fuel and coolant to Equation (8), we receive confirmation of the velocities ratio from Table 5.

Finally, matching dynamic similarity, we achieve that the deviation of dimensionless pressure drop, defined in Equation (9), between micro- and minidemonstrators, is lower than 2%—as depicted in Figure 7.

$${\theta }_p={\displaystyle \frac{P\left(z\right)-P_{inlet}}{P_{outlet}-P_{inlet}}}$$

(9)

4.2. Thermal Similarity

This subsection focuses on achieving thermal similarity by identifying the operating conditions that yield an identical Peclet number for heat transfer ($P{e}_{heat}$) in both the micro- and minidemonstrator. Matching the Peclet number is paramount for scaling heat transfer experiments in liquid metals, as it ensures the fundamental ratio of convective to conductive heat transport is the same in both systems. This provides a valid basis for comparing and extrapolating thermal performance from the low-temperature model to the high-temperature prototype.

To determine these conditions, a comprehensive parametric study involving numerous calculations was performed. For a given fluid velocity within the microdemonstrator’s model, the Peclet number similarity equation was solved to find the precise corresponding velocity needed in the minidemonstrator to achieve an equal $Pe$ value. This iterative process was repeated across a broad spectrum of initial velocities, allowing for a complete mapping of the operational relationship between the two systems (

Table 6. Operating conditions ranges for thermal similarity (Peclet number matching).

	Power [kW]		Peclet Number [-]		Mass Flow Rate [kg/s]		Velocity [m/s]
Loop	µDEMO	mDEMO	µDEMO	mDEMO	µDEMO	mDEMO	µDEMO	mDEMO
Fuel	12 30	25 62	520.58 1437.83	511.94 1415.49	1.66 4.61	0.523 0.525	0.096 0.266	0.183 0.507
Coolant			253.80 4313.53	255.83 4325.89	1.85 30.37	0.456 0.463	0.053 0.871	0.115 1.912

).

The entire study was constrained by velocities that represent real-life values for magnetohydrodynamic pumps, ensuring the findings are applicable to a practical engineering design and avoiding scenarios that would lead to excessive material erosion or impractical power requirements. This constrained approach allowed for the clear identification of the ranges of applicability—the specific, paired velocity ranges for each demonstrator—within which thermal similarity can be confidently achieved. It is important to note that these conditions for thermal similarity are distinct from those required to achieve dynamic similarity, a key finding that will be discussed further.

Finally, matching thermal similarity, we achieve that the deviation of dimensionless temperature, defined in Equation (10), between micro- and minidemonstrators, is lower than 3%—as depicted in Figure 8.

$${\theta }_T={\displaystyle \frac{T\left(z\right)-T_{inlet}}{T_{outlet}-T_{inlet}}}$$

(10)

5. Discussion

The primary objective of this work was to establish a scaling methodology for thermal-hydraulic phenomena between a low-temperature microdemonstrator ($\mu$DEMO) and a high-temperature minidemonstrator (mDEMO). A parametric study successfully identified the operating ranges required to achieve either dynamic similarity, by matching the Reynolds number ($Re$), or thermal similarity, by matching the Peclet number ($P{e}_h$).

The central finding from the parametric study is the critical conflict inherent to scaling these systems: dynamic and thermal similarity cannot be achieved simultaneously. This challenge stems from the physical relationship $P{e}_h=Re·Pr$. The two demonstrators use different liquid metals at vastly different operating temperatures (200 °C to 400 °C for the $\mu$DEMO vs. 1000 °C to 1200 °C for the mDEMO), resulting in significantly different Prandtl numbers ($Pr$). Because the Prandtl number is an intrinsic and unequal property between the two systems, it is impossible to satisfy the conditions for both similarities at once. If fluid velocities are adjusted to make the Reynolds numbers equal ($R{e}_{\mathrm{\mu }\mathrm{DEMO}}=R{e}_{\mathrm{mDEMO}}$), the differing Prandtl numbers ensure the Peclet numbers will not match.

6. Conclusions

This paper establishes a cornerstone methodology for the design and validation of the Dual Fluid Reactor’s technology demonstrators. The core contribution is the creation of a clear pathway to align the working conditions of these disparate systems for meaningful scientific investigation. By conducting a systematic parametric study, this analysis has successfully identified the precise, actionable operational ranges required to achieve either dynamic or thermal similarity. Using Cathare-2 simulations, this study produced the following key quantitative results. The specific operating ranges (velocities and mass flow rates) required to achieve dynamic similarity (matching $Re$) were identified (Table 5). Achieving this similarity allows the dimensionless pressure drop (${\theta }_p$, Equation (9)) to be scaled between demonstrators with a maximum deviation below 0.2%. Distinct operating ranges necessary for achieving thermal similarity (matching $P{e}_h$) were also successfully identified (Table 6). Under these conditions, the dimensionless temperature profile (${\theta }_T$, Equation (10)) can be scaled with a maximum deviation below 2.5%.

The critical finding that these two similarity states are mutually exclusive provides an essential guiding principle that directly impacts the designing aspects of potential demonstrators. This forces engineers to make a deliberate choice: is the primary goal of a given experimental facility to validate hydrodynamic models (requiring dynamic similarity) or to confirm thermal performance (requiring thermal similarity)? This decision directly informs the engineering specifications of key components—such as the required flow rates for the MHD pumps—and the necessary experimental instrumentation.

Furthermore, this scaling methodology is not limited to the micro- and minidemonstrators; its principles can be extrapolated to bridge the gap between each successive demonstrator stage and, ultimately, to the full-scale Dual Fluid Reactor itself. Therefore, the presented methodology is a foundational tool that provides the essential “rulebook” for ensuring the entire DFR demonstrator pathway is built on a foundation of reliable, scalable, and physically meaningful data, paving the way for the safe and successful development of the final reactor.