Numerical Investigation of a Supersonic Wind Tunnel Diffuser Optimization

Abstract

The objective of this study is to enhance the methodology for the design of a supersonic wind tunnel, improving the process with advanced computational techniques. The supersonic wind tunnel is intended to operate within a flight envelope of Mach 2.5 to 4 and altitudes between 18 and 20 km; this study focuses on the operative condition of Mach 3.5. The research is based on computational fluid dynamics, enabling a deeper understanding of fluid flow phenomena that can deteriorate the operability of the wind tunnel. Additionally, a detailed mesh independence study has been conducted to ensure the reliability and robustness of the computational results. These new analyses allowed for a more comprehensive optimization in the state of the art of tunnel geometry and operational conditions, further enhancing the ability to sustain supersonic flow for extended durations. Particular attention was given to the second throat, which plays a crucial role in the overall performance of the facility, especially during the start-up process. Its design has been refined to improve efficiency by reducing the minimum starting pressure.

1. Introduction

Supersonic blowdown wind tunnels are fundamental tools in the development and testing of aerospace vehicles operating at high speeds. These facilities enable the reproduction of realistic flight conditions by channeling high-pressure air through a convergent–divergent nozzle, generating supersonic or even hypersonic flows within a test section. The flow properties in the test section, such as Mach number, static pressure, and temperature, are calculated using isentropic relations and depend on the stagnation conditions in the settling chamber:

$$M=\sqrt{{\displaystyle \frac{2}{\gamma -1}}\left[{\left({\displaystyle \frac{p_0}{p}}\right)}^{{\displaystyle \frac{\gamma -1}{\gamma }}}-1\right]}$$

(1)

$${\displaystyle \frac{A}{A^{\ast }}}={\displaystyle \frac{1}{M}}{\left[{\displaystyle \frac{2}{\gamma +1}}\left(1+{\displaystyle \frac{\gamma -1}{2}}{M}^2\right)\right]}^{{\displaystyle \frac{\gamma +1}{2(\gamma -1)}}}$$

(2)

where $\gamma$ is the specific heat ratio, $p_0$ is the stagnation pressure, p is the static pressure, M is the Mach number, and $A/A^{\ast }$ is the area ratio relative to the throat.

Over the years, supersonic wind tunnels have been extensively used to support research on airbreathing propulsion systems (e.g., ramjets and scramjets), supersonic aircraft, and re-entry vehicles. However, the design and operation of these tunnels present several challenges. One of the most critical is minimizing the required stagnation pressure while achieving the desired test section conditions. This is essential to reduce the size and cost of the facility, particularly the storage tanks and pressurization systems. Furthermore, preventing shock-induced flow separation and managing start-up transients remain significant engineering difficulties.

One of the key aspects in the development of a wind tunnel is the proper design of the nozzle, as it significantly influences the flow characteristics. Several techniques have been proposed in the literature to optimize nozzle design, including contour shaping methods, boundary layer bleed systems, and adjustable throat geometries [1,2]. Nonetheless, many conventional designs still rely on simplified assumptions that may not fully capture the complex flow features in the nozzle and test section, especially during start-up and unsteady conditions. However, in this study, the focus is placed on the optimization of the second throat. In this context, a specific research gap exists in the state of the art for the accurate design and optimization of the so-called second throat, a geometric constriction placed downstream of the test section or within the diffuser. Its role is critical for improving flow stability, reducing starting loads, and lowering the required stagnation pressure. However, its design is often based on empirical rules or iterative trial-and-error approaches rather than systematic optimization.

The present study addresses this gap by proposing a novel methodology for the optimization of the second throat geometry in supersonic blowdown wind tunnels. The main objective is to minimize the required inlet pressure while maintaining the desired flow characteristics in the test section. This is achieved through a combination of mission analysis, analytical calculations, and computational fluid dynamics (CFD) simulations. The results provide design guidelines that improve efficiency and reduce operational costs, contributing to the advancement of experimental capabilities for future aerospace applications.

1.1. Test Conditions

The wind tunnel is designed to reproduce flight environments corresponding to different points in a vehicle’s trajectory, considering varying altitudes and Mach numbers. To generate supersonic flow in the test section, the total pressure and temperature in the settling chamber must align with the requirements listed in

Table 1. Target test section values [3].

M	Altitude [m]	P0 [Bar]	T0 [K]	PTEST [Bar]	TTEST [K]
2.5	18,368	1.2	488	0.0708	216.6
3.0	19,135	2.3	606	0.0628	216.6
3.5	20,031	4.2	747	0.0547	216.6
4.0	21,370	6.7	916	0.0441	218.0
2.5	15,000	2.0	487	0.1204	216.6
3.0	15,000	4.4	606	0.1204	216.6
3.5	15,000	9.2	747	0.1204	216.6
4.0	15,000	18.3	910	0.1204	216.6

. The optimization discussed in subsequent sections focuses on the operative condition of Mach 3.5 with an altitude of 15 km to enable a more detailed analysis.

1.2. General Layout

The schematic of a typical blowdown supersonic wind tunnel is shown in Figure 1. Key components include a dry air storage tank, pressure regulator, settling chamber, a nozzle, a test section, a second throat, and a diffuser. To achieve flight-like conditions, a pressurized heat storage unit ensures proper temperature and pressure control upstream of the nozzle.

This work focuses on the right-hand side of Figure 1, from the nozzle to the diffuser exit. This section is the most critical part of the system, as it determines the desired flow conditions and manages potential instabilities, ensuring that the test section operates reliably and under controlled conditions.

Considering a wind tunnel with a test section of 30 cm in diameter and an operational Mach number of 3.5, the characteristic Reynolds number for the test section is calculated to be

$$R{e}_{TS}=4.26\ast {10}^6$$

This value is pivotal for assessing the flow behavior within the test section. It serves as a key indicator of the flow regime—whether laminar or turbulent—and directly impacts the aerodynamic performance of the models being tested, influencing both heat transfer and drag characteristics.

1.3. General Scheme

This study focuses exclusively on the diffuser section of the supersonic wind tunnel. For a comprehensive theoretical design of the upstream components—including the gas tanks, settling chamber, first nozzle, and test section—the reader is encouraged to consult our previous work [4]. In that study, we employed a combination of classical design methodologies, computational fluid dynamics (CFD), and empirical guidelines to establish a baseline configuration for Mach 3.5 operations. Key considerations in the prior design process included the following:

• Gas Supply and Testing Time: Analytical and empirical methods were used to calculate the required gas tank volume and ensure sufficient mass flow rates for stable operation during the blowdown phase.
• Settling Chamber and First Nozzle: The settling chamber was equipped with honeycomb screens to linearize the flow, followed by a first nozzle designed using the Method of Characteristics (MOC) to minimize disturbances in the test section.
• Test Section Sizing: The test section was dimensioned to avoid shock wave reflections interfering with the test model, based on guidelines and equations provided by Pope and Goin [5]. Notably, the sizing is strongly influenced by the operational Mach number. At near-transonic conditions, the test section diameter typically needs to be an order of magnitude larger than the model diameter—approximately 10 times—to minimize flow disturbances. Conversely, at higher Mach numbers, the Mach cone becomes narrower, allowing for a more compact test section with a diameter approximately 4 to 5 times larger than the model.
• Second Throat Design: A theoretical second throat was sized to ensure start-up capability at Mach 3.5, considering the relationship between total pressure and throat geometry, as derived in [4].

These preliminary designs provided a solid foundation for evaluating the tunnel’s overall performance.

1.4. Diffuser Design

In transonic wind tunnels, the section located directly downstream of the test section typically has a slightly larger cross-sectional area compared to the test section itself. This configuration allows the air exiting the test section at low supersonic speeds to expand, creating a suction effect that aids in drawing air from the plenum chamber. The diffuser is generally connected to a conical divergent section with a maximum included angle of 7.5 degrees. For supersonic wind tunnels, however, Pope and Goin [5] observed that the diffuser requires a throat with a cross-sectional area smaller than that of the test section. Despite this observation, the ideal design for the diffuser remains an open topic. Various studies have explored ways to optimize the diffuser geometry, testing included angles of up to 30 degrees or more, as well as second throat lengths ranging from zero to ten times the length of the test section. Beyond the second throat, the divergent diffuser should follow design principles similar to those for transonic tunnels, ensuring that the angle between opposing walls does not exceed 12 degrees.

2. Numerical Methodology

The CFD model used to analyze supersonic flow in the wind tunnel employs a density-based solver and the Shear Stress Transport (SST) k-$\omega$ turbulence model, which is widely used for high-speed compressible flows [6]. Using this model, Chaffin [7] conducted a study comparing CFD simulations with experimental data from a supersonic wind tunnel at California State Polytechnic University, Pomona, focusing on different geometries such as cone, ogive, and double-wedge airfoils at various Mach numbers. The study found a good agreement between CFD and experimental results, particularly for the cone and ogive geometries. In general, CFD simulations demonstrated the ability to predict shock wave structures and pressure distributions with reasonable accuracy. The results were also in good agreement with analytical predictions. However, some discrepancies were observed between the CFD and experimental results, which may be attributed to slight manufacturing defects in the components used for the experiments.

In [4], a significant dependency of the simulation results on both the quality of the computational mesh and the numerical scheme used for solving the governing equations was identified. At that stage, the upwind scheme employed was of the first order, which is known to introduce higher numerical dissipation and potentially obscure critical flow features, particularly in high-gradient regions. This limitation raised concerns about the accuracy and robustness of the results, motivating a more comprehensive investigation into these aspects in the present study.

To better understand the impact of these factors, an extensive mesh refinement study was carried out to evaluate how changes in mesh resolution affect the key flow characteristics and convergence behavior. Simultaneously, the numerical scheme was upgraded to a second-order central-upwind method, which is inherently less dissipative and better suited for capturing complex flow phenomena with higher fidelity. By combining these two improvements, a more reliable and accurate representation of the physical problem was sought, reducing the uncertainties associated with numerical errors and mesh-induced artifacts. This systematic approach not only enhances the credibility of the results but also provides valuable insights into the interplay between numerical resolution and solution accuracy, particularly in the context of supersonic flow simulations.

2.1. Governing Equations and Numerical Scheme

The theoretical geometry (Figure 2) was analyzed using a density-based compressible flow solver, rhoCentralFoam, available within the OpenFOAM framework [6]. The governing equations are the RANS equations for compressible flow:

$${\displaystyle \frac{\partial \rho }{\partial t}}+\nabla ·\left(\mathbf{u}\rho \right)=0,$$

(3)

$${\displaystyle \frac{\partial \left(\rho \mathbf{u}\right)}{\partial t}}+\nabla ·\left(\mathbf{u}\left(\rho \mathbf{u}\right)\right)+\nabla P+\nabla ·\mathbf{T}=0,$$

(4)

$${\displaystyle \frac{\partial \left(\rho E\right)}{\partial t}}+\nabla ·\left(\mathbf{u}\left(\rho E\right)\right)+\nabla ·\left(\mathbf{u}P\right)+\nabla ·(\mathbf{T}·\mathbf{u})+\nabla ·\mathbf{j}=0,$$

(5)

where Equations (1)–(3) are the equations of conservation of mass, conservation of momentum (neglecting body forces), and conservation of total energy, respectively. $\rho$ is the density, u is the velocity, P is the pressure, E is the total energy, $\mathbf{j}$ is the diffusive heat flux, and $\mathbf{T}$ is the viscous stress tensor, which can be represented using Newton’s law. The diffusive heat flux can be represented using Fourier’s law, and the dynamic viscosity is obtained using Sutherland’s law [8]. For the convective flux scheme, the second-order central-upwind Kurganov–Noelle–Petrova (KNP) scheme [9] is used. Face interpolations are based on a limiter introduced by Minmod [10], and the time derivatives are discretized using the first-order Euler scheme. The turbulence flow is modeled using Menter’s k-$\omega$ SST two-equation model [11]. The objective was to emulate flow at Mach 3.5 and 15 km altitude (static pressure 0.12 bar) to accurately reflect the dynamics in the test section under such conditions.

2.2. Wind Tunnel Geometry and Boundary Condition

A total pressure of 9 bar was specified at the inlet, with a total temperature of 747 K and 1 bar at the outlet, representing wind tunnel blowdown conditions. No-slip and adiabatic conditions were applied to the walls. To reduce computation time, the axial symmetry of the tunnel was leveraged by performing a 2D-axisymmetric analysis. The rotation axis and a schematic representation of the theoretical wind tunnel design are depicted in Figure 2. All grids were generated as two-dimensional axisymmetric structured grids. Grids on the wall were all set to satisfy $y^{+}<1$.

2.3. Grid Independence

Figure 3 illustrates the computational domain, and the number of cells is 140,000. A grid independence test was conducted using three sets of wind tunnel grids. The total inlet pressure was set to 9 bar. The number of cells in the test section and the diffuser in the flow direction was varied while keeping the number of cells perpendicular to the wall constant. The number of cells for each case is as follows: 113,000, 140,000, and 174,000. Figure 4 shows the wall pressure distribution from the first nozzle throat to the diffuser and the Mach number distribution along the axis. All three results show good agreement, which confirms that the numerical solution of the present study for 140,000 is grid-independent.

2.4. Theoretical Geometry CFD Results

The results in Figure 5a,b demonstrate that this tunnel configuration does not achieve start-up. Although the second throat was analytically sized correctly, the effects of the boundary layer were neglected, leading to inadequate mass flow discharge from the first nozzle. Additionally, the calculation of the second throat area only accounted for the total pressure loss due to a normal shock in the design Mach number. The authors suggest that additional pressure losses caused by the Fanno flow, viscosity, and thickness of the boundary layer in the test section are substantial and cannot be overlooked. The result is the formation of a shock upstream of the test section, which causes a static pressure plug and a total pressure loss, using the same boundary conditions as defined in Section 2.2. Subsequently, due to friction and the geometry of the second convergent section, the flow accelerates again, leading to the emergence of a second shock in the divergent part of the diffuser as highlighted in the circled area A of Figure 5a.

3. CFD Design Optimization

As it has been demonstrated, the wind tunnel is highly sensitive to its diffuser design [3], to the point where it may not even achieve proper start. One of the most critical parameter is the diameter of the second throat, as the other design elements have already been optimized in previous studies [4].

3.1. Second Throat Diameter

The diameter of the second throat must exceed that of the first throat to ensure proper mass flow through it. In fact, the theoretical value does not consider the pressure losses that may influence the correct start-up, and for this reason, a diameter scaling analysis in percentage steps is performed. The simulations investigated various second throat radii, incrementally increasing from the theoretical value (119.5 mm) by 2.5%, 5%, 10%, 15%, and considered the scenario without a second throat. Other parameters, such as convergent angle and throat length, remained constant.

As illustrated in Figure 6, a diffuser with a second throat radius that increased by 2.5% fails to initiate within the studied stagnation pressure range (3–60 bar). This aligns with theoretical expectations, as a too-small second throat prevents the diffuser from accommodating the full mass flow rate, leading to the terminal normal shock being trapped inside the test section and disrupting the required test conditions. Increasing the second throat radius by 10% allows the diffuser to initiate the wind tunnel at a minimum inlet total pressure of 4.8 bar. Below this pressure, the wind tunnel will not start. Further enlarging the second throat radius, while maintaining the same mass flow rate, results in a higher starting total pressure, with this trend continuing until the second throat becomes ineffective. In this study, it was found that a diffuser without a second throat initiates at a stagnation pressure of 5.2 bar, whereas a diffuser with a second throat can start at a lower pressure, depending on the second throat diameter. A lower starting pressure is beneficial as it helps prevent backflow earlier during the transient start-up phase.

The numerical results have been reported in Figure 7. This shows that there is an optimal second throat diameter that minimizes the stagnation pressure required for starting the diffuser.

In this study, the best configuration was found by increasing the second throat radius by 10%. This shows that when designing a wind tunnel, having a larger second throat helps in lowering the starting stagnation pressure, making it easier to start the tunnel.

Compared to the previous results [4], all wind tunnel configurations can be started up at lower inlet total pressures. In terms of accuracy of convective flux scheme, the first-order upwind scheme used in previous studies produces more diffusive solutions than the second-order central-upwind scheme employed in this study, as it struggles to represent discontinuous flow phenomena such as shock waves. Additionally, while the previous studies used around 43,000 grids, the present results were obtained using approximately 140,000 grids. Fine grids are necessary to represent flow structures near the wall, such as the boundary layer and flow separation. The lower accuracy of numerical schemes and use of coarser grids indicate higher numerical dissipation, leading to lower Mach numbers and total pressure outputs. Therefore, it is presumed that the previous results show a higher minimum starting pressure because they overestimated total pressure loss compared to the results of this study. However, the wind tunnel configuration with a 10% increase in the second throat radius remained the optimal design, consistent with the present findings.

3.2. Start Efficiency

The impact of the starting stagnation pressure at the wind tunnel inlet has been examined while maintaining constant backpressure at the outlet (atmospheric pressure). As the stagnation pressure increases, the static pressure in the test chamber rises, thereby reducing the risk of flow detachment caused by a high test-to-atmospheric pressure ratio. However, when simulating high-altitude conditions, where the test section requires low static pressure, the risk of flow detachment increases. Therefore, the static pressure (and thus, the corresponding stagnation pressure) must exceed a critical value to ensure proper wind tunnel start-up. Above this threshold, the test chamber pressure remains uniform. Consequently, for testing that requires a lower starting pressure, a vacuum chamber is necessary. The results of this study are summarized in Figure 8.

At lower stagnation pressures, the flow is unable to push the shock wave out of the nozzle, leading to flow separation within the test chamber. This condition allows for the backflow of atmospheric pressure into the test chamber, disrupting the desired test conditions. Conversely, as the stagnation pressure increases, the air enters the second nozzle, preventing flow separation. This results in the formation of a series of oblique shocks, which act as a plug or isolator, shielding the test chamber from external pressure and effectively preventing backflow. These oblique shocks also facilitate a gradual reduction in stagnation pressure after the start-up phase, as visible in Figure 9, enabling the simulation of higher altitude conditions within the test section.

It is important to note that for the diffuser to operate effectively, the Mach number at its inlet must be supersonic, which is achieved when the stagnation pressure exceeds a critical threshold. At lower stagnation pressures, flow separation occurs, leading to reverse flow near the nozzle walls and resulting in backflow into the test chamber [12].

4. Transient Study for the Optimized Design

While the steady-state analysis provides valuable insights into the final operating conditions of the wind tunnel, a transient simulation is essential for capturing the dynamic evolution of the flow during start-up. Findings from previous chapters have demonstrated that widening the second throat can lower the minimum starting pressure required for the wind tunnel. Analyzing the transient behavior during start-up offers a deeper understanding of the mechanisms responsible for this effect and their influence on the overall operation of the facility. This study provides crucial insights into the underlying flow dynamics, reinforcing the advantages of the optimized design and improving the comprehension of the wind tunnel’s functionality.

After identifying the optimal configuration, it is employed as the geometry for a transient CFD axisymmetric simulation. This method provides several critical insights: it deepens the understanding of flow dynamics during the wind tunnel’s start-up phase, estimates the time required to achieve steady operational conditions, and validates the proposed design. If the results of the transient simulation align with the steady-state analysis, this consistency confirms the validity of the chosen solution. The transient evolution of the Mach number and total pressure during the start-up phase of the wind tunnel is illustrated in Figure 10 and Figure 11.

The numerical simulations were conducted using a variable timestep approach, controlled by maintaining a CFL number of 0.4. On average, the timestep was approximately $3.8\times {10}^{-8}$ s. To ensure numerical accuracy and stability, the solver tolerance was set to $1\times {10}^{-14}$. Consequently, the number of iterations per timestep was not fixed but varied dynamically according to the flow conditions to meet the convergence requirements.

During the start-up phase of a wind tunnel, the state-of-the-art suggests that a normal shock initially forms in the test section and is subsequently displaced downstream by the total pressure at the inlet. Consistent with these findings, our numerical simulations reveal that a normal shock emerges in the test section and remains stationary until a second shock forms in the diffuser. Once the second shock appears, the first shock moves downstream through the test section, while the second shock oscillates in the diffuser’s diverging section until it stabilizes temporarily. This process continues until the first shock reaches the second throat. At this stage, oblique shocks form across the second throat, establishing a new stability where a single normal shock remains at the start of the diffuser’s diverging section.

The Mach number distribution within the blowdown supersonic wind tunnel at various timesteps, presented in Figure 10, corroborates the findings of M. Rabani [13]. During the transient phase, several flow phenomena are observed. Initially, a normal shock forms in the first nozzle but does not propagate to the tunnel’s exit. As the flow reaches the end of the wind tunnel, the system’s inertia initiates a transient phase.

In this phase, the flow accelerates through the second throat until it becomes sonic. As the pressure rises, further acceleration occurs in the diffuser’s divergent section. When the supersonic flow exits the diffuser, the atmospheric pressure exerts a counteracting force, causing a second shock wave to form in the diffuser’s divergent section (Figure 10b). At this point, the test section flow is primarily influenced by the pressure upstream of the second shock rather than directly by the atmospheric pressure. If atmospheric disturbances shift the second shock upstream, it relocates within the diffuser, reducing the Mach number and total pressure loss. To maintain the constant exit pressure, the upstream pressure before the second shock decreases, modifying the pressure ratio across the system. Consequently, the first shock moves downstream, eventually reaching the nozzle’s diverging section (Figure 10c,d). During this unstable phase, the second shock oscillates cyclically in an attempt to stabilize. Finally, as the first shock reaches the diffuser, the flow in the test section becomes fully established, characterized by oblique shocks forming at the second throat. These oblique shocks interact with and merge into the second shock, stabilizing the system. Overall, the results of the present study show that the wind tunnel start-up process progresses more quickly over time compared to previous results [4]. As explained earlier, in the previous results, lower Mach number and pressure were calculated due to numerical diffusion resulting in greater total pressure loss. As a result, the second shock wave generated in the diffuser exits more slowly due to the higher total pressure loss, which appears to lead to a longer time required for the flow to stabilize.

Based on the transient CFD results, it has been determined that the positions of the first and second normal shocks are closely linked, and the formation of these shocks is characteristic of the start-up phase. Furthermore, it has been hypothesized that this behavior is associated with total pressure losses within the wind tunnel and can therefore be described using isentropic relations, Rankine–Hugoniot equations, and Fanno flow theory. Building on these findings, an analytical approach is introduced to establish a correlation between the two shocks. The following analysis aims to provide a theoretical description of this behavior and verify its consistency with the CFD results:

• The first shock’s position in the test section is estimated, and the corresponding total pressure drop is calculated using normal shock theory. The input Mach number, determined from isentropic equations, varies with the shock’s location. For instance, when the shock is positioned within the nozzle’s diverging section, the expansion ratio decreases.
• Downstream of the first shock, the subsonic flow accelerates, experiencing a total pressure loss described by Fanno flow theory in the test section.
• In the convergent section of the second throat, the subsonic flow expands following isentropic relationships.
• At the second throat, the flow undergoes additional total pressure losses. Here, near-sonic conditions $(M\approx 1)$ prevail. If the flow is supersonic, it decelerates under the influence of the convergent geometry, while subsonic flow accelerates.
• After passing through the second throat, the flow expands isentropically until reaching a critical static pressure. According to the “Summerfield criteria” [14], flow separation occurs in a rocket nozzle when the exit pressure lies between 0.25 and 0.4 times the atmospheric pressure.

The analytical and CFD solutions are compared in Figure 12. The x-axis represents the first shock’s position in the test section, normalized by the total wind tunnel length, while the y-axis indicates the second shock’s position in the diffuser, similarly normalized. The two black lines in Figure 12 represent the analytical solutions when the exit pressure is 0.25 times and 0.4 times the atmospheric pressure, respectively. The region between these two lines is referred to as the Sutherland range. The results of the red line indicate the measured position of the oblique shock wave occurring at the wall, while the results of the blue line indicate the measured position of the normal shock wave occurring at the symmetry plane.

The CFD solutions show that the position of the first shock deviates from the analytical solution’s Sutherland range in the early stages. However, the two solutions converge towards the end, satisfying the Sutherland range. This trend is similar to previous CFD result [4], but it is more stably positioned within the Sutherland range compared to the previous CFD results. The authors attribute the initial discrepancy to instability during the early start-up phase. Notably, the CFD solution captures the oscillatory behavior of the second shock, which is absent in the MATLAB R2024-based analytical model. As the inlet total pressure stabilizes, both approaches exhibit near-identical shock behavior. The clear trend in shock motion observed in both methods supports the reliability of using value between 0.25 and 0.4 as the Summerfield factor, aligning with theoretical expectations. Future research should focus on incorporating boundary layer effects to enhance the match between the CFD and analytical solutions. This refinement could resolve transient discrepancies and improve the overall correlation between the two models.

5. Conclusions and Future Work

This research aimed to optimize the geometry of a supersonic wind tunnel to achieve reliable start-up while minimizing the total inlet pressure required. The primary objective was to develop a design capable of ensuring consistent start-up performance and efficient operation at lower inlet pressures, enabling Mach numbers and static pressures suitable for high-speed testing. Key parameters influencing wind tunnel performance were analyzed in depth through CFD simulations. The findings revealed that after the wind tunnel initiates start-up, the total inlet pressure can drop below the previously assumed threshold due to the flow dynamics in the second throat. This section effectively behaves like a plug, maintaining low static pressures in the test section despite the higher external atmospheric pressure. The optimal configuration identified includes a second throat radius increased by 10% compared to the theoretical design. This adjustment compensates for additional total pressure losses caused by Fanno flow in the test section, where the flow chokes in the converging section before reaching the second throat. Among the design parameters, the second throat diameter emerged as the most sensitive and critical factor for ensuring proper wind tunnel operation. While the angle of the converging section between the test section and the second throat also influences start-up performance, its impact is less significant compared to the second throat diameter. Other parameters, such as the length of the second throat and the diffuser’s angle and length, were found to have negligible effects on start-up success.

Beyond the specific geometric optimization, this 2D numerical study provides valuable insights for both researchers and practitioners in the field of supersonic wind tunnel design. The parametric analysis clarifies why relying solely on theoretical correlations from the literature may lead to unsuccessful start-up conditions, offering practical guidelines to avoid common design pitfalls. These findings will support future experimental campaigns by highlighting the key role of total pressure losses and flow choking mechanisms in the test section.

While the current analysis is limited to two-dimensional axisymmetric simulations, the results remain representative for the early design phase of axially symmetric wind tunnels. However, it is acknowledged that three-dimensional effects—particularly in separation zones—may become significant once non-axisymmetric features are introduced. These include optical windows for schlieren imaging, the model support strut, and the test model itself, all of which could interact with the flow, potentially affecting start-up behavior and overall tunnel performance.

To further refine wind tunnel design and performance, apart from a dedicated three-dimensional study, it is recommended in future work to fully capture these effects and refine the design accordingly. The following areas of investigation are recommended:

• CFD Analysis with Models Inside: Conduct additional simulations incorporating models within the tunnel to better understand their influence on flow behavior and overall performance
• Enhanced Analytical Methods: Improve analytical approaches to account for total pressure losses and boundary layer effects, providing more accurate design tools.

Such future studies would contribute to the development of a more comprehensive framework for supersonic wind tunnel design, ensuring both efficient start-up and sustained performance under various operational conditions.