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Diese Studie untersucht die experimentelle Erzeugung ungleicher Oberflächentemperaturverteilungen im Hochgeschwindigkeitsfluss, wobei der Schwerpunkt auf der Kontrolle des Grenzschichtübergangs in Hyperschallfahrzeugen liegt. Die Forschung zeigt eine passive Methode, bei der Materialien mit kontrastierenden thermischen Diffusitäten wie Kupfer und MACOR verwendet werden, um signifikante Temperaturschwankungen zu erzeugen. Die Studie umfasst die Erprobung eines flachen Plattenmodells in einem Überschall-Windkanal und den Einsatz von Infrarot-Thermographie zur Validierung der Temperaturverteilungen. Zur Vorhersage der Reaktion auf die Oberflächentemperatur wird ein physikalisch fundiertes Wärmemodell entwickelt, das eine hervorragende Übereinstimmung mit experimentellen Daten aufweist. Die Ergebnisse bestätigen die Realisierbarkeit einer quantitativen Vorhersage des Oberflächentemperaturverhaltens unter starken konvektiven Bedingungen. Die Studie unterstreicht auch die Bedeutung der Erholungstemperatur bei der Bestimmung der Richtung und des Ausmaßes des Wärmetransfers an die Oberfläche. Die nächsten Schritte umfassen die Beurteilung der Amplituden der Geschwindigkeitsstreifen, die durch diese Temperaturprofile erzeugt werden, und die Durchführung einer speziellen Hyperschall-Windkanal-Kampagne, um die Fähigkeit der Methode zu überprüfen, den Übergang zu verzögern.
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Abstract
This study presents prediction and experimental measurement of non-uniform surface temperature distributions on a flat plate test article for a flow control method. The test article features strips of materials (copper and MACOR) with dissimilar thermal properties interacting with a developing boundary layer to establish a passively controlled, non-uniform temperature profile. Experiments with a pre-heated model are conducted within the Imperial College supersonic wind tunnel at Mach 2.75. Infrared thermography is used for surface temperature measurements. Results from the experiments confirm the passive surface temperature control, demonstrating temperature variations between the strips. Furthermore, the physics-informed thermal model, with boundary conditions derived from actual wind tunnel conditions, predicts non-uniform surface temperature distributions that quantitatively align with the experimental results. Higher temperature differences between the strips of dissimilar materials can be achieved by increasing the difference between the recovery temperature and the initial temperature. These results validate the proposed actuation method’s ability to generate significant spanwise surface temperature variations. This validation of the actuation method serves as a prerequisite for future experimental campaigns, which will focus on measuring the induced velocity streaks and assessing their efficacy for boundary layer transition delay in hypersonic environments.
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1 Introduction
Significant frictional drag and aerodynamic heating on hypersonic vehicles are caused by boundary layer transition, often triggered by second-mode instability, which impacts not only aerodynamic performance but also thermal protection system design. Therefore, controlling the onset of boundary layer transition is desirable to enhance vehicles’ performance.
The transition of a hypersonic boundary layer from laminar to turbulent is a complex process influenced by freestream disturbances and various instability mechanisms. At lower Mach numbers (below 4), transition is typically driven by the first Mack mode instability, while at higher Mach numbers, the dominant instability is the second Mack mode, characterized by the amplification of planar acoustic waves. Nonlinear interactions of these instabilities lead to turbulence onset, which is influenced by the disturbance spectrum (Morkovin 1994; Fedorov 2011; Mack 19874).
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Previous research has demonstrated that stationary velocity streaks within the boundary layer possess significant potential to suppress the onset of transition in hypersonic flows (Ren et al. 2016; Paredes et al. 2016). These streaks, characterized by alternating regions of low and high velocity, modify the instability characteristics of the second mode, thereby contributing to transition delay (Paredes et al. 2019). Studies have shown that when the amplitude of these streaks is sufficiently low, they can effectively reduce the amplification of disturbances associated with the second Mack mode (Paredes et al. 2016). Stronger streaks may also suppress the growth of the second Mack mode, but may simultaneously destabilize the oblique sinuous first mode, creating a tradeoff in their effectiveness. Despite this, an optimal streak amplitude has been identified that can delay the onset of transition by simultaneously suppressing both the first mode and the Mack mode, highlighting the potential of velocity streaks as a flow control mechanism in hypersonic boundary layers (Ren et al. 2016; Paredes et al. 2019).
To generate stationary velocity streaks in hypersonic boundary layers, specific actuation methodologies are required. Among these, roughness elements have been extensively investigated for their potential to produce streaks in hypersonic flows (James 1959; Fujii 2006; Chang and Choudhari 2011; Taylor 2018). These physical protuberances, attached to the surface, alter the downstream flow path and can delay transition depending on their height, spacing and shape. Similarly, vortex generators (VGs) produce streaks that can delay transition, with their shape optimized for improved performance (Fiala et al. 2006, 2014; Schneider 2008; Taylor 2018; Jahanbakhshi and Zaki 2023; Paredes et al. 2018; Pederson et al. 2020). However, both methods are limited by specific conditions—roughness elements and VGs can inadvertently promote early transition depending on disturbance levels and may pose challenges due to their reliance on convex geometries, which are prone to failure from excessive aerodynamic heating and increased drag at off-design conditions. Given these limitations, a more robust and adaptable method is needed to generate streaks effectively for transition control, while addressing practical concerns such as aerodynamic heating and drag.
To overcome the limitations of existing flow control methods, a novel approach has been proposed that uses non-uniform surface temperature distributions (Ozawa et al. 2023, 2025; Ozawa and Bruce 2025; Boscagli et al. 2025). This method generates streaks by imposing different spanwise temperatures at the wall to introduce different thermal boundary layers, as illustrated in Fig. 1. Unlike traditional convex geometries, such as roughness elements or vortex generators, this approach offers significant potential to enhance the feasibility and durability of hypersonic vehicles, particularly under the extreme aerodynamic heating encountered during real-world operations, including off-design conditions. The effectiveness of this method has been demonstrated through Direct Numerical Simulations (DNS) conducted by Ozawa et al. (2023, 2025) and Boscagli et al. (2025), which showed that non-uniform temperature distributions can delay the onset of transition by generating stabilizing streaks. To further validate this concept, prototype actuation methods have been proposed for ground testing (Ozawa et al. 2025). One approach involves combining dissimilar thermal materials with varying thermal diffusivity and non-uniform spanwise thickness distributions to control the wall surface temperature. Another method utilizes a single material with a non-uniform spanwise thickness to manipulate the heat flux path via internal wall geometry, enabling precise control of surface temperature.
This study focuses on the design and experimental characterization of the actuation method. This work represents the validation phase of the research program: Following conceptual studies by simulations (Ozawa et al. 2023, 2025; Boscagli et al. 2025), it aims to demonstrate that the dissimilar material approach can effectively establish controlled non-uniform surface temperature distributions in a wind tunnel environment. Given that the heat transfer mechanisms governing surface temperature evolution are analogous in supersonic and hypersonic regimes, these actuation tests are conducted in a supersonic wind tunnel. The test article comprises alternating strips of MACOR (a ceramic insulator) and copper (a thermal conductor), with a steel leading edge for mechanical integrity. Infrared thermography (IRT) is employed to capture the surface temperature evolution, and a physics-informed thermal model is developed to predict the response. This experimental validation of the thermal actuation authority is a necessary prerequisite for future work, which will focus on the assessment of the generated velocity streaks and their subsequent impact on boundary layer transition.
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Section 2 outlines the experimental facility, the design of the flat plate test article and the implementation of IRT measurements. Section 3 describes the thermal modeling setup and the boundary conditions used. Section 4 presents a comprehensive analysis of the measured results and thermal modeling predictions. Finally, Sect. 5 summarizes the key findings of the paper.
Fig. 1
Non-uniform temperature distributions on the wall and boundary layer modulation by streaks (Ozawa et al. 2025)
This section details the experimental methodology employed to validate the passive thermal actuation concept. First, the supersonic wind tunnel facility and flow conditions are described. Second, the design and fabrication of the flat plate test article, utilizing the dissimilar material approach, are presented. The operational procedure is then outlined, specifically the pre-heating system required to establish the thermal gradient and the surface coating applied to ensure uniform emissivity. Finally, the infrared thermography setup and calibration process for surface temperature measurement are detailed.
2.1 Imperial College supersonic wind tunnel
Experiments were conducted in the Imperial College supersonic wind tunnel. This cold supersonic wind tunnel operates as a blow-down facility. The freestream in the wind tunnel reaches Mach 2.75, while the working section maintains a constant square cross section with dimensions of 150 mm \(\times\) 150 mm. The wind tunnel provides a run time of approximately 20 s, and Table 1 summarizes the freestream conditions used in the experiment. Upon reaching the target pressure ratio, the freestream is assumed to be uniform. This assumption is supported by previous work, which identified a freestream variation of 1.3 % at Mach 2 in this facility (Threadgill and Bruce 2020). A similar level of uniformity is assumed for the Mach 2.75 conditions.
Table 1
Freestream and post-shock flow configurations
M
Re (m\(^{-1}\))
\(T_{\infty }\,(\textrm{K})\)
\(p_{\infty }\,(\textrm{Pa})\)
\(T_{r}\) (K)
Shock angle \(\beta\) (deg.)
Freestream
2.75
\(3.5\times 10^7\)
116.7
15910.7
274.1
–
Post-shock
2.61
–
124.0
19663.3
274.9
23.5
2.2 Flat plate test article
To achieve non-uniform surface temperature distributions, the implementation of dissimilar materials or single material with non-uniform spanwise thickness is crucial, as emphasized by Ozawa et al. (2025). These approaches regulate heat flux by manipulating material characteristics or the internal wall heat transfer to locally increase or decrease surface temperatures. This behavior can be described by the transient heat transfer equation
where T, t, \(\alpha\), \(\rho\), c, \(\kappa\), x, y and z represent temperature, time, thermal conductivity, density, specific heat, thermal diffusivity and spatial directions, respectively. Ozawa et al. demonstrated through thermal modeling that the dissimilar material approach results in a higher temperature difference between insulating and conducting regions compared to the single material with non-uniform spanwise thickness (Ozawa et al. 2025). Additionally, they proposed a practical arrangement for bonding two dissimilar materials using tooth-shaped slots to enhance structural integrity and thermal performance. In this study, the practical arrangement of two dissimilar materials is selected for implementation. This choice is based on its ability to achieve significant temperature variations and its potential feasibility for real-world applications, as validated by prior thermal modeling and design considerations.
Fig. 2
Photograph of the assembled flat plate test article, including steel leading edge, MACOR and copper strips with the diagram of heating system
Prototype fabrication of MACOR–copper interface. Two slot configurations in the copper base: one empty and one fitted with a coated MACOR strip, used to validate fit and surface treatment
Figure 2 presents the fully assembled test article, comprising copper and MACOR strips embedded into a copper base, with a sharp steel leading edge. The test surface measures 270 mm in the streamwise direction and 138 mm in the spanwise direction, and the plate includes a 12-degree beveled leading edge made of steel for robustness and sharpness. To generate spanwise surface temperature variations passively, materials with contrasting thermal properties are selected: MACOR, a machinable glass–ceramic, is employed as the insulating material due to its low thermal diffusivity, high strength and ease of precision fabrication (Ozawa et al. 2025); copper is selected as the conducting material for its high thermal diffusivity and heat capacity.
The surface features three MACOR strips alternating with two copper segments, arranged in a spanwise pattern. Each MACOR strip is fabricated from five 50-mm-long pieces. The strips are embedded into the copper base using a tooth-slot configuration, where each tooth is 3 mm wide and 3 mm deep on both sides, forming a symmetric interlock. The dimensional tolerance between the MACOR teeth and the copper slots is maintained within \(\pm 0.05\) mm to ensure a snug fit and reliable thermal contact. All inserts are 6 mm thick and assembled flush with the copper surface. After integration, the entire surface is machined and polished together to ensure smoothness across interfaces and to minimize aerodynamic disturbance. A prototype assembly, shown in Fig. 3, is first manufactured to verify the slot geometry, confirm coating behavior and evaluate the assembly process.
The flat plate was installed in the wind tunnel test section (Fig. 4) at a \(3^\circ\) incident angle to prevent blockage (Ozawa et al. 2023), secured by two bolts on each side. The resulting \(3^\circ\) incident angle generates an attached oblique shock wave at the leading edge with \(\beta = 23.5^\circ\). The flow conditions downstream of this oblique shock are detailed in Table 1.
Fig. 4
The test article with coating (etch primer and heat resistant paint) installed in the supersonic wind tunnel test section, secured by bolts and set at a \(3^\circ\) incidence angle
The recovery temperature plays a pivotal role in facilitating heat transfer between the test surface and the surrounding flow, enabling the establishment of non-uniform surface temperature distributions. In hypersonic free-flight conditions, the recovery temperature is high, which naturally promotes heat transfer to the surface. Consequently, the surface heats up naturally, and the difference in material properties passively controls local heating rates to achieve non-uniform surface temperature distributions. However, in conventional low-enthalpy wind tunnels, such as the current experimental setup, the recovery temperature is much lower and acts as a cooling mechanism for the plate. Despite this difference, the behavior of the plate can be assumed to be analogous to hypersonic free-flight conditions as long as heat transfer occurs on the surface. To achieve non-uniform surface temperature distributions, it is essential to create a significant temperature difference between the initial surface temperature and the recovery temperature. This is accomplished by preheating the plate before each experiment. In this configuration, the recovery temperature effectively cools the plate, while the preheating process establishes the necessary thermal conditions for heat transfer. A key distinction arises in the behavior of the insulator and conductor strips. Unlike the assumption made by Ozawa et al. (2025), where the insulator strips are heated by the flow to temperatures relatively higher than the surrounding thermally conducting surface, the present experimental setup exhibits surface cooling of the insulator strips due to their low thermal diffusivity. In contrast, the conductor strips, with their high thermal conductivity and heat capacity, are expected to maintain a hotter surface during wind tunnel operation.
Preheating was achieved through the use of two 600-W heating elements controlled by a Proportional-Integral-Derivative (PID) controller. To monitor the bulk temperature, three Type-K thermocouples are embedded within the copper base along one side at streamwise intervals of 67.5 mm. The heating system maintained the flat plate at temperatures of 323, 373 and 423 K, corresponding to 50, 100 and 150 \(^\circ\)C, respectively, prior to experiments. During the heating process, the test article was thermally isolated using a 6-mm-thick rigid insulation board made of alumina–silica ceramic fiber, as shown in Fig. 5. The board covers both the test surface side and the bottom side of the plate to suppress heat loss to the surrounding environment. This material is chosen due to its low thermal conductivity (0.13 W/m\(\cdot\)K at 1100 K), high temperature resistance (up to 1700 K) and cost-effectiveness. These properties help maintain a uniform thermal boundary condition at the surface before the experiment. Once the PID system achieves the target temperature, the heating is sustained for 5 min to ensure uniform temperature throughout the entire test article. The insulation board is manually removed immediately prior to sealing the wind tunnel test section. To mitigate any potential damage to the wind tunnel walls, a 6-mm air gap is maintained between both sides of the article, shown in Fig. 4.
Fig. 5
Photograph of the test article covered with the insulator on the test surface side and bottom side to maintain uniform thermal conditions before the wind tunnel run
The surface coating plays a critical role in ensuring both a smooth surface and consistent surface emissivity for accurate measurements. When copper strips are exposed to the atmosphere, they undergo an inevitable oxidation process, which intensifies after heating the plate. This oxidation results in the formation of cupric oxide (CuO) and cuprous oxide (Cu\(_2\)O), significantly altering the emissivity of the surface. Additionally, determining the emissivity of polished copper surfaces at low temperatures is challenging due to their inherently low emissivity, which further changes as oxidation progresses during measurements.
To address these challenges and ensure uniform high emissivity, surface coating is essential. Two primary techniques can achieve this: oxidation coating and spray coating. Oxidation coating involves forming a CuO layer on the copper surface by initially oxidizing (Cu\(_2\)O) at temperatures above 573 K (Unutulmazsoy et al. 2020). This process creates a nanometer-thick CuO layer with an emissivity of approximately 0.87, significantly higher than that of polished copper, which has an emissivity of around 0.03 (Honkanen et al. 2007). However, the CuO layer is fragile and difficult to control, as its properties are highly sensitive to heat temperature and exposure time (Castrejón-Sánchez et al. 2019). This fragility makes oxidation coating unsuitable for supersonic testing, as the coating may degrade or fail under such conditions.
In contrast, thermal spray paint coating is a more reliable and practical solution. It provides a smooth surface with uniform emissivity not only for copper but also for MACOR and steel leading edge surfaces. The process involves applying an etch primer paint, capable of withstanding temperatures up to 660 K, to enhance adhesion. This is followed by a heat-resistant paint that can endure temperatures up to 970 K. After application, the surface is polished to achieve a smooth finish, as illustrated in Fig. 4. The thickness of the paint layers is measured to be approximately 20 \(\mu\)m using a micrometer.
2.5 Infrared thermography calibration and measurement
Surface temperature measurement can be achieved through contact or non-contact methods. While contact methods, such as thermocouples and thin-film gauges, offer high durability and accuracy, they physically cover the surface and disrupt heat convection from the boundary layer’s recovery temperature. This makes them unsuitable for assessing surface temperature distributions. Therefore, non-contact temperature measurement methods are preferred to avoid interference with heat transfer. Infrared thermography (IRT) is a non-intrusive, high-resolution technique for measuring surface temperature and offers advantages in calibration simplicity compared to methods like temperature-sensitive paint (TSP) (Ozawa et al. 2015). IRT has been widely used for intuitive surface temperature measurements in various applications. For instance, Avallone et al. employed IRT to measure the surface temperature of a flat plate at Mach 7.5 (Avallone et al. 2015), while Cardone et al. used it to measure the complex surface temperature distribution of a double-cone geometry (Cardone et al. 2012). These studies demonstrate the versatility and reliability of IRT for temperature measurement in aerodynamic testing.
Fig. 6
Schematic representation of the experimental setup for IRT measurements, showing the aerodynamic test surface and optical access via a zinc selenide window (\(D=70\) mm)
In this study, an infrared thermography system was used to measure the surface temperature of the test plate. The system consists of a FLIR A655SC camera equipped with a 25 \(^\circ\) field-of-view (FOV) lens, positioned such that the viewing angle ranges from 75 to 81 \(^\circ\) (Fig. 6). The camera observed the test surface through a Zinc-Selenide (ZnSe) window (\(D=70\) mm) installed in the test section. The camera features an uncooled microbolometer detector array with a resolution of 640 by 480 pixels, a frame rate of 50 Hz and a spectral response range of 7.5–14.0 \(\mu\)m, providing a spatial resolution of approximately 6 px/mm. For in situ IRT calibration, a portable infrared calibrator (Fluke 9132) with a quasi-black-body target (\(\epsilon = 0.95\)) was used. The calibration data were obtained by measuring the calibrator installed in the wind tunnel’s test section through the Zinc-Selenide window (Carlomagno and Cardone 2010). The total radiant intensity detected by the camera, \(I_D\), can be expressed as follows, accounting for the effect of the window
where \(\epsilon\), \(T_{obj}\), and \(T_{amb}\) denote the target emissivity, the object temperature and the ambient environmental temperature, respectively, while R, B, F and C represent coefficients of radiation and a constant. During the calibration process, the camera recorded the signal of the calibration target at 22 temperature points ranging from 303.3 K to 633.2 K. Collecting data from the calibration target took several hours, as the target requires several minutes to stabilize at each temperature. The average signal value at each temperature point was recorded. The Levenberg–Marquardt nonlinear least squares algorithm was used to calculate the calibration coefficients R, B, F and C, as described in Eq. 2. The resulting calibration curve is presented in Fig. 7, and the calibration parameters, including the coefficient of determination and the root-mean-square (RMS) error, are summarized in Table 2.
Summary of the infrared \(\textrm{camera}\) calibration
Parameter
Value
R
14794
B
1500
F
1.0
C
35.7
Coefficient
of determination
0.9999
RMS error
3.27
Following the in situ calibration with the calibrator, an objective signal from the painted test surface was measured after heating to a known temperature. This objective signal was compared to the signal from the calibrator, and the surface emissivity was determined to be \(\epsilon = 0.84\), with observed local variations of approximately \(\pm 5\) % across the measurement area. These variations were found to be systematic: The central area of the measurement data contains a slightly higher signal due to reflections between the IRT lens and the window. Additionally, the outer regions of the image captured by the infrared camera result in lower emissivity values due to the oblique angle from the lens. To overcome these problems, an in situ calibration using the coated test surface was conducted to account for lens reflection and directional emissivity at each pixel. The emissivity value for each pixel was determined by analyzing the object signal emitted from the coated test surface.
Spatial calibration was performed using a thin steel plate with 5-mm holes at 10-mm intervals. Placed directly over the coated test surface, this plate allows for the adjustment of the camera’s focus and scale by using the perforations as reference locations, a technique similar to that described by Cardone et al. (2012). Figure 8 shows the calibration plate and a corresponding raw IRT image. The image clearly resolves the reference holes while also showing minor artifacts, such as a central reflection from the IRT lens and the visible edges of the ZnSe window.
Fig. 9
a The thermal model domain showing the alternating conductor–insulator geometry and the convective heat flux boundary condition (Q) applied to the aerodynamic test and rear surfaces. b The unstructured mesh discretization used for the thermal modeling
A thermal model is employed to estimate the surface temperature response of the flat plate under convective heat transfer from the boundary layer, based on previous approaches (Gramola et al. 2021, 2021; Ozawa et al. 2023; Ozawa and Bruce 2025; Ozawa et al. 2025). To compute the convective heat flux, the heat transfer coefficient h between the surface and the post-shock recovery temperature \(T_r\) is a critical parameter in this model. Here, \(T_r\) is assumed to be constant during the wind tunnel operation. The Chilton–Colburn analogy is employed to determine the local Stanton number \(St_x\) from the local Reynolds number \(Re_x\) and the Prandtl number Pr (White and Majdalani 2006):
The relation assumes a turbulent friction coefficient consistent with a turbulent boundary layer under the experimental condition. The local heat transfer coefficient h is then calculated as
In this equation, \(\rho _{ref}\) and \(U_\infty\) are the reference density and freestream velocity, respectively, determined using the Meador–Smart method (Meador and Smart 2005), which accounts for boundary layer thermal conditions. The specific heat capacity at constant pressure is assumed to be \(C_p = 1010\) J/(kgK), and the viscosity is estimated using Sutherland’s law.
3.2 Thermal model
Heat transfer calculations are carried out using the MATLAB Partial Differential Equation Toolbox, which solves a parabolic differential equation. The flat plate geometry is illustrated in Fig. 9(a), exported from 3D CAD software. An unstructured mesh with a resolution of 5 mm is employed, as shown in Fig. 9(b). Each component is assigned specific material properties: The leading edge is modeled with steel properties, the insulator is characterized by MACOR properties, and the connector is defined with copper properties (Table 3). Due to difficulties encountered in accurately resolving the two cylindrical slots for the heating element, the model adopts a simplified representation wherein the slots are geometrically defined as rectangular shapes with equivalent volumes to the original cylinders. The 20-\(\mu\)m-thick thermal paint layer on the test article’s surface is not explicitly included in the thermal modeling. Due to its minimal thickness, both its thermal resistance and thermal mass are deemed negligible.
The local heat transfer coefficient based on the local Stanton number is calculated using Eq. 4 at the aerodynamic test surface and backside surface, while other surfaces are considered adiabatic walls. The initial temperature is set as the target temperature, obtained through pre-heating before each experiment. The time step used in the calculation is 0.1 s, and the calculation is performed for the experimental duration of 15 s. A mesh independence study was conducted to ensure grid convergence and minimize numerical errors.
Table 3
List of model components and material properties
Component
Material
Conductivity
Specific heat
Density
(W/m\(\cdot\)K)
(J/kg\(\cdot\)K)
(kg/m\(^{3}\))
Leading edge
Steel
45
466
7900
Conductor
Copper
386
389
8960
Insulator
MACOR
1.43
777
2520
Fig. 10
Time history of estimated Mach number (left axis) and total pressure ratio (right axis) for three individual runs (dashed lines) and their average (solid line) in Case 1. Operating conditions are listed in Table. 4
3.3 Experimental freestream data for thermal boundary condition estimation
To calculate the time-varying convective heat transfer coefficient h (Eq. 4), the thermal model requires the freestream flow properties: density, velocity, recovery temperature and viscosity. Although these are assumed to be constant during the steady-state period of each test, they will vary significantly during wind tunnel start-up. To quantify these variations, pressure tapping data synchronized with the wind tunnel operation are recorded and analyzed. Figure 10 shows the three-run wind tunnel log for Case 1, along with its averaged configuration over time, as referenced in Table 4. The left axis presents the estimated Mach number in the test section, obtained from a wall pressure tap located upstream of the model using isentropic relations. The right axis indicates the total pressure measured in the settling chamber upstream of the nozzle. Data are recorded at a temporal resolution of 0.1 s. Once the Mach number is estimated, the freestream temperature is computed using isentropic flow relations. The freestream velocity \(U_{\infty }\) is then calculated based on this temperature and Mach number, accounting for the 3 \(^\circ\) incidence angle and the resulting oblique shock. During the tunnel start-up phase, the total pressure ratio (\(P_0/P_{atm}\)) initially overshoots the target due to limitations in PID control. The flow stabilized approximately 5 s after initiation, reaching Mach 2.75. Consequently, this physics-informed thermal model integrates experimental wind tunnel data, ensemble-averaged across runs with a 0.1-s temporal resolution, to provide synchronized boundary conditions for quasi-one-dimensional heat flux computations.
Fig. 11
Initial surface temperature (\(T_i\)) distribution for Case 2 from the IRT measurement, overlaid on the test article outline. Inset: Pixel count histogram for Window 2 (Case 2) showing distinct temperature peaks for insulator (359.7 K) and conductor (364.8 K) regions
4.1.1 Initial temperature of the aerodynamic test surface
The study involves three primary test conditions, Cases 1, 2 and 3, with nominal target initial surface temperatures of 50, 100 and 150,\(^\circ\)C, respectively, as summarized in Table 4. Due to the limited optical access of the observation window (\(D=70\) mm), multiple wind tunnel runs were conducted with the model positioned at different streamwise locations to construct the comprehensive surface temperature map. Specifically, the plate was moved 45 mm upstream from its Window 1 measurement position to acquire data for Window 2. For Window 3 measurements (where applicable), the model is shifted an additional 45 mm upstream from the Window 2 position. Consequently, Cases 1 and 2 include temperature measurements across three observation windows, while Case 3 is limited to Windows 1 and 2 due to a failure in the model’s mounting system during testing.
The surface temperature at \(t = 0.1\) s post-initiation of the datalogging is defined as the initial surface temperature \(T_i\). Figure 11 presents this \(T_i\) distribution for Case 2 as a representative example, rendered as a composite image from the individual measurements across the observation windows. This composite image is generated by spatially arranging the individual IRT recordings and, in areas where measurement windows overlapped, trimming each adjacent recording at the centerline of the shared region before stitching them together. To preserve the full contrast of local temperature variations, the raw IRT data are presented directly without any filtering or smoothing. The measurement area in the streamwise direction (x) spans approximately 20 to 180 mm for Cases 1 and 2 and 20 to 140 mm for Case 3. In the spanwise direction (y), measurements extend from 40 to 100 mm, covering three insulator (MACOR) strips, two conductor (copper) strips and a portion of the leading edge.
A consistent experimental challenge is an unavoidable drop in the plate’s surface temperature prior to the wind tunnel run. This occurs because the preparation for each test, which includes removing an insulating heat shield and securing the wind tunnel door, takes several minutes. Active reheating during this interval is avoided, as heating without the insulation board would induce localized hot spots and degrade the thermal uniformity of the initial condition. During this period, the insulator strips typically exhibit slightly lower temperatures than the conductor strips due to their lower thermal diffusivity. This thermal distinction is quantified in the inset of Fig. 11, which shows a pixel count histogram for Window 2 of Case 2. The histogram reveals two distinct temperature peaks: \(T_{i,ins}\)=359.7 K for the insulator material and \(T_{i,cond}\)=364.8 K for the conductor, resulting in a spanwise temperature difference (\(\Delta T_{i,stp}\)) of 5.1 K for this specific window. Across Windows 1 and 3 of Case 2, this \(\Delta T_{i,stp}\) ranges between 2 and 5 K. The average spanwise temperature difference for Case 2, \(\Delta \overline{T}_{i,stp}\), is 3.8 K. This difference corresponds to approximately 5 % of the intended temperature elevation of the plate above ambient laboratory conditions (i.e., 5 % of \(T_{t}-T_{atm}\)). The mean initial surface temperature for Case 2 is \(\overline{T_i}\)=362.1 K. This value represents a reduction from the target temperature, equivalent to 14 % of the intended temperature elevation (\(T_{t}-T_{atm}\)). Across all test cases, the measured initial surface temperatures show a consistent reduction of 12–14 % relative to this target elevation. Similarly, spanwise temperature differences between the conductor and insulator strips are consistently in the range of 5–6 % of the target elevation. These observations confirm that the initial thermal conditions are established with reasonable consistency across the different measurement windows and that similar temperature drop trends are present in all cases.
Figure 12 presents the surface temperature distributions at the steady-state condition (\(t=15\) s) for all cases. The experimental results are overlaid onto the thermal modeling predictions. A distinct temperature contrast between the different material strips is evident across the test article. The copper conductor strips consistently maintain an elevated temperature close to the initial pre-heated condition, while the MACOR insulator strips and the leading edge cool toward the aerodynamic recovery temperature.
This result successfully demonstrates the efficacy of using a dissimilar materials approach for the passive control of local surface temperature. The thermal contrast becomes significantly more pronounced as the initial plate temperature increases from Case 1 through Case 3 (Fig. 12(b) and (c)).
The numerical predictions accurately capture the key thermal phenomena observed in the experiments. A strong correlation is evident, particularly for the copper conductor strips and the leading edge, where the predicted temperatures align closely with the IRT measurements. The model also accurately captures the sharp temperature gradients at the material interfaces, indicating a robust representation of the thermal junctions between the MACOR and copper. While minor discrepancies exist within the insulator regions (discussed in Sec. 4.2), the overall cooling trend and the magnitude of the temperatures are predicted quantitatively.
Fig. 13
Spanwise normalized temperature profiles at \(t=15\) s at streamwise locations \(x = 15\) (black), 50 (red) and 100 mm (blue). Experimental results (dashed lines) are compared with thermal modeling predictions (solid lines) for a Case 1, b Case 2 and c Case 3
Figure 13 presents the spanwise surface temperature distributions at \(t=15\) s for each case, extracted at streamwise locations of \(x=15\), 50 and 100 mm. The temperature is normalized by the post-shock freestream temperature \(T_{\infty }\) to yield the non-dimensional temperature, \(\Theta = T_w/T_\infty\). The primary goal of this comparison is to assess the model’s ability to predict the sharp thermal contrast, which is the key feature of this passive thermal control method.
Overall, the thermal model demonstrates qualitative agreement with the experimental spanwise profiles, successfully capturing the characteristic ‘step-like’ structure of the temperature field. At the established downstream locations (\(x=50\) and 100 mm), a distinct thermal contrast is achieved between the strips, clearly distinguishing the conducting and insulating regions. Within the leading edge region (\(0< x < 20\) mm) at \(x=15\) mm, both the experiment and model show how lateral conduction creates a mild distortion in the profile, with temperatures slightly elevated in regions adjacent to the conductors. Further downstream, the distinction between the materials becomes more defined. The model accurately reproduces the uniform spanwise temperature across the copper conductor strips, a direct result of the material’s high thermal diffusivity that eradicates local gradients. Minor localized temperature peaks are observed near the corners of the conductor strips at \(x=100\) mm (see Fig. 13(b)); these are likely attributable to localized edge effects at the material interface not fully resolved by the thermal model. In contrast, the MACOR insulator regions exhibit a more complex, concave temperature profile, which is also well-replicated by the model in terms of its characteristic shape. However, while the profile shape is quantitatively matched, a consistent underprediction of the insulator’s absolute temperature magnitude is observed. For example, in Case 2, the measured \(\Theta\) is higher than the model’s prediction by approximately 0.1 at \(x=50\) mm (2.7 measured vs. 2.6 predicted) and by 0.05 at \(x=100\) mm. This deviation is more pronounced in Case 3, where the measured temperature is higher than the prediction by 0.18 at \(x=50\) mm and 0.11 at \(x=100\) mm. This discrepancy is further analyzed in Sec. 4.2.3 by correlating the transient temperature data with the wind tunnel start-up phase captured by Schlieren visualization.
Despite the quantitative offset in the insulator regions, the model demonstrates a robust capability to predict the fundamental features of the spanwise thermal profile. It accurately predicts the magnitude and uniformity of the conductor temperatures and captures the fundamental shape of the insulator profiles. Most importantly, it validates the model’s ability to reliably predict the sharp thermal gradients and overall temperature contrast at the material boundaries, which is the critical performance metric for this system.
Fig. 14
Streamwise normalized temperature profiles at \(t=15\) s for a Case 1, b Case 2 and c Case 3. Thermal model predictions (solid lines) are compared with experimental results (dashed lines) for the center insulator (blue) and conductor (red)
The streamwise surface temperature profiles along the centerline of the central insulator strip and a conductor strip (\(y=54\) mm) are presented in Fig. 14 for all three cases at \(t=15\) s. For the copper conductor strips, the model exhibits excellent quantitative agreement with the experimental data across all cases. The profiles are characterized by a slight temperature dip at the leading edge followed by a nearly uniform temperature distribution downstream. This leading edge cooling (\(x < 20\) mm) is primarily attributed to the high local Stanton number \(\overline{St}_x\) in the region of low local Reynolds number \(Re_x\), which results in a significantly elevated convective heat transfer rate. Downstream, the flat temperature profile, accurately captured by the model, reflects the high thermal diffusivity of copper, which effectively resists convective cooling and smooths spatial gradients, even under complex flow conditions.
In contrast, while the model successfully reproduces the general cooling trend of the MACOR insulator strips, a quantitative discrepancy is apparent. For Case 1, the agreement is close; however, for Cases 2 and 3, the model consistently overpredicts the rate of cooling. Furthermore, the experimental profiles exhibit distinct, localized temperature fluctuations that are absent from the smooth model predictions. These sharp drops align with the physical gaps between the five separate insulator pieces (refer to Fig. 12). These gaps likely disturb the turbulent boundary layer, locally enhancing the convective heat transfer rate. The low thermal diffusivity of MACOR makes its surface temperature highly sensitive to these local disturbances, effectively imprinting a thermal signature of the assembly geometry.
The origin of the broader discrepancy in the cooling rate (the offset between model and experiment) likely lies in the fundamental assumption used to define the model’s freestream conditions. The thermal model incorporates a time-varying freestream condition calculated from pressure data measured at the nozzle exit every 0.1 s, assuming these conditions uniformly describe the flow over the test article. However, the Schlieren visualizations presented in Fig. 15 reveal that this assumption is invalid during the highly dynamic wind tunnel start-up. The images show that the actual flow field is dominated by unsteady, structured shock waves interacting directly with the plate’s surface. This complex aerodynamic environment dictates the true convective heating history, which is not captured by the nozzle exit pressure data. The low thermal diffusivity of the MACOR makes it extremely sensitive to this actual heating history, effectively imprinting a thermal signature from the start-up phase that persists into the steady-state measurement period. This likely explains the discrepancy between the measured temperature and the model’s prediction. Besides, the sharp, localized temperature drops seen experimentally also align with the physical gaps between the five separate insulator pieces. Ultimately, the model’s limitation is its inability to account for the complex, localized flow structures that differ significantly from the simplified freestream conditions derived from upstream measurements.
A key practical insight also emerges from these streamwise profiles. Figure 14 clearly shows that the significant temperature difference between the conductor and insulator strips is established almost immediately downstream of the leading edge and is then robustly sustained along the test article’s length. This indicates that the desired thermal contrast for flow control applications does not require a long development section, providing valuable guidance for the placement of such material strips in future hypersonic experiment designs.
Fig. 15
Schlieren visualization of the flow field during wind tunnel start-up. The images show the evolution of shock structures at a\(t=4.0\) s and b\(t=4.3\) s during the initial acceleration phase and c the final steady-state flow at \(t=5.0\) s
Transient temperature evolution at \(x=100\) mm during wind tunnel operation for a Case 1, b Case 2 and c Case 3. Comparison between experimental results (dashed lines) and thermal modeling predictions (solid lines) for the insulator and conductor
The transient temperature evolution at a downstream location of \(x=100\) mm is presented in Fig. 16 for all three cases, directly comparing the experimental IRT measurements with the thermal modeling predictions. This temporal analysis provides critical insight into the system’s response during the wind tunnel start-up phase and the subsequent approach to the steady state. Across all cases, a consistent trend is observed in the initial five seconds. The copper conductor cools gradually, whereas the MACOR insulator exhibits a much sharper and more immediate drop in temperature. This initial phase is punctuated by a distinct and sudden temperature decrease in the experimental insulator data around \(t=4\) s. This event corresponds precisely with a documented overshoot in the wind tunnel’s PID-controlled pressure ramp (Fig. 10), which temporarily enhances convective cooling and disproportionately affects the thermally sensitive MACOR surface.
The thermal model, which incorporates the measured pressure data as a boundary condition, successfully captures the timing and qualitative effect of this pressure spike. However, consistent with the analysis in the previous section, the model overpredicts the overall cooling rate for the insulator during this 0-5 s start-up period. This confirms the hypothesis that the simplified freestream conditions in the model do not fully account for the complex, unsteady shock phenomena that dictate the true convective environment during start-up. Beyond \(t=5\) s, as the wind tunnel flow stabilizes, the system transitions to the steady state. In this phase, the model and experimental data show excellent agreement. Both datasets show the conductor maintaining a stable temperature due to copper’s high thermal inertia, while the insulator’s cooling rate slows considerably as it asymptotically approaches the recovery temperature. The quantitative match in the cooling rates for both strips after the start-up phase is particularly notable. It demonstrates that the model accurately captures the fundamental heat transfer physics on the test surface once a steady aerodynamic state is achieved, reinforcing that the observed temperature offset on the insulator is a thermal artifact imprinted during the initial, complex transient phase.
Fig. 17
Normalized temperature profiles of the insulator and conductor at \(x = 100\) mm at \(t=15\) s comparing the thermal model and the experimental results across different initial temperatures of the test article
4.2.4 Characterization of the temperature difference with initial temperature
Figure 17 presents the normalized surface temperature profiles for both the insulator and conductor materials at \(x=100\) mm and \(t=15\) s, across the range of initial model temperatures investigated. The thermal model simulations cover a broad range of nondimensional initial temperatures, \(\Theta _{i}\), from 1.8 to 4.2 (corresponding to absolute temperatures from 123 to 573 K), while the experimental cases span \(\Theta _{i}\)=2.6 to 3.3 (Cases 1–3). The plot effectively demonstrates how the thermal model successfully captures the underlying physics of surface temperature evolution. The linear decrease in normalized surface temperature for both materials as \(\Theta\) approaches unity, i.e., as the initial model temperature approaches the recovery temperature \(T_r\). This linearity highlights that the final surface temperature difference directly scales with the initial thermal offset relative to \(T_r\). The results reinforce the principle that the surface temperature difference is primarily driven by the thermal contrast between the wall and the recovery temperature: When the initial temperature exceeds \(T_r\), the surface cools, and conversely, when it is below \(T_r\), the boundary layer heats the surface. This behavior illustrates the importance of the recovery temperature in dictating the direction and magnitude of heat transfer to the surface. Furthermore, this parameter study is crucial as the magnitude of the surface temperature difference significantly impacts the generation and characteristics of velocity streaks within the boundary layer. For experimental control over streak intensity—for instance, to achieve greater streak prominence—it is necessary to either maximize the relative difference between the initial temperature and the recovery temperature or increase the convective heat transfer coefficient, such as under high-enthalpy flow conditions.
5 Conclusion
This study demonstrates a passive method for generating non-uniform surface temperature distributions in a hypersonic environment by leveraging materials with contrasting thermal diffusivities. A flat plate model composed of copper and MACOR strips is uniformly pre-heated and tested at Mach 2.75 in the Imperial College supersonic wind tunnel. Infrared thermography (IRT) confirms that significant spanwise temperature variations developed shortly after flow onset, with greater variations observed at higher initial surface temperatures. A physics-informed thermal model, considering wind tunnel start-up behavior and preheating conditions, accurately predicts the measured temperature fields. The agreement between the model and experiment across multiple initial temperatures confirms the feasibility of quantitatively predicting surface temperature behavior under strong convective conditions. This work establishes the foundation for a passive thermal actuation method to generate non-uniform surface temperature distributions. The next steps involve assessing the amplitudes of the velocity streaks generated by these temperature profiles. Ultimately, this work paves the way for a dedicated hypersonic wind tunnel campaign to experimentally verify the method’s capability to delay transition.
Acknowledgements
KO acknowledges the support from the NAKAJIMA Foundation and the Department of Aeronautics at Imperial College London. The authors wish to thank Mark Grant, Ian Pardew and Franco Giammaria for their extensive assistance with the model design, manufacture and heating system. The authors also wish to thank Ian James for assistance with tunnel operations.
Declarations
Conflict of interest
The authors declare no conflict of interest.
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