Boundary Layer Transition Prediction on Planar Turbine Cascade Using Temperature-Sensitive Paint and Numerical Simulation

Abstract

Advanced measurement technology on boundary layer transition is an effective means to study the flow mechanism and the performance of the cascade. In this research, to investigate the boundary layer transition of transonic VKI-RG turbine cascade, a noncontact measurement technique named temperature-sensitive paint (TSP) that is capable of quantitatively measuring the surface temperature of a model is used. Under the conditions of outlet Mach number (Ma₂) = 0.4, 1.03, and 1.2, the transitional location of a cascade is accurately measured by TSP technique. Moreover, a numerical study on the transitional location of a planar cascade was conducted with the conditions of Mach number (Ma) and attack angle (α). The numerical results show that the transitional location moved forward with the increase in Ma₂ and α at Ma₂ < 1; otherwise, the transitional location moved backward with increasing Ma₂ (Ma₂ > 1). Lastly, a strong adverse pressure gradient was formed behind the shock wave, which led to the beginning of the transition.

1. Introduction

Aeroengines are not only the power source of aircraft, but also an important driving force for the development of the aviation industry. The turbine cascade is a major part of the aeroengine, and its performance directly affects the performance index of the aeroengine. The complex flow field structure and loss mechanism of cascades have become important research content to improve the performance of aeroengines. The state of the boundary layer on the cascade surface and the transitional location are an important basis for describing the flow mechanism of the cascade and analyzing its performance.

Although the basic theory and occurrence mechanism of boundary layer transition are still under research and development, its importance in engineering practice has become increasingly prominent, and has received extensive and sustained attention [1,2,3]. For example, the transitional location and development process have a significant impact on the lift–drag characteristics, boundary layer separation, and surface aerodynamic heating of the aircraft in aerospace engineering [4,5,6]. Some research on the measurement method and numerical method of the transitional location of the cascade boundary layer was carried out, and it is of great value to further understand the flow mechanism of aeroengine cascades and improve the design level of China’s aeroengines.

In recent years, scholars have carried out a lot of work on flow display technology and measurement methods [7,8,9,10,11,12,13]. Hausmann et al. [12] used the hot-film technique to measure the flow separation and transition on the airfoil surface. Halstead et al. [14] also used hot-film technology to detect the boundary layer state of compressor blades. For the particle image velocimetry (PIV) technique [15], Medina et al. [16] investigated the flow mechanism of the pulsating transition jet. Horstmann et al. [17,18] performed transitional measurements on the boundary layer of airfoils with infrared image technology. Holmes et al. [19] confirmed that shear-sensitive liquid crystal technology can be applied well under different wind-tunnel test conditions of airfoils, and Mee et al. [20] accurately measured the boundary layer transition with this technology. Pressure-sensitive paint (PSP) is a well-established optical pressure measurement technique that can provide qualitative and quantitative surface pressure distributions on models with high spatial resolution. Kameda et al. [21], and Gregory et al. [22] have applications in the flow field and acoustic diagnosis. Although the above-mentioned testing techniques have unique advantages in certain scenarios, they are difficult to operate and cost-limited. For example, infrared thermal imaging equipment is expensive, has low spatial resolution, and has a large influence on background radiation signals in a normal temperature environment. Shear-sensitive liquid crystal technology cannot obtain quantitative temperature field data. Therefore, their applications to cascade transitional measurement are still relatively limited. TSP is used as a similar optical measurement technology to PSP by some researchers [23,24], but is relatively rarely used in the boundary layer transition of the cascade. In addition, some researchers [25,26] used numerical methods to predict the transitional location, and their results were in good agreement with the experimental data.

This paper combines the TSP technique, wind tunnel tests, and computational fluid dynamics (CFD) simulation to carry out predictive research on the boundary layer transition of a cascade. First, a TSP measurement method for the boundary layer transition of the cascade was constructed through the TSP technique and wind-tunnel test devices. Second, the wind-tunnel test of the transonic planar cascade turbine was carried out under different inflow conditions, and the transitional location was obtained. Lastly, the boundary layer transition location was verified by comparing the numerical calculation results. To analyze the variation in the transitional location under different inflow conditions, a large number of numerical simulation calculations of a planar cascade were further carried out.

2. Transitional Measurement Experiment on TSP

2.1. TSP Principle

The TSP technique is a modern optical measurement technology for the measurement of the surface temperature field distribution, and its basic principle is the thermal quenching effect of TSP fluorescent probe molecules. TSP uses luminescent molecules as probes that are mixed into suitable polymer coatings and coated on the surface of the aerodynamic model. Luminescent molecules are sensitive to temperature, and luminescent quantum efficiency decreases with increasing temperature. However, the heat transfer coefficients in the laminar boundary layer and the turbulent boundary layer are different, resulting in differences in the temperature distribution in the laminar and turbulent regions.

In this study, the technique was used to spray temperature-sensitive paint on the surface of a cascade, which is produced by ISSI Inc. in the United States. The specific parameters are shown in

Table 1. Parameters of UNT-200 one-component TSP.

Items	Value
Pressure sensitivity	0.0%/kPa
Pressure range	1 kPa~10 MPa
Temperature sensitivity	1.4%/°C
Temperature range	10 °C to 80 °C
Response time	750 ms
Excitation wavelength	400 to 550 nm (peak, 470 nm)
Emission wavelength	600 to 750 nm (peak, 620 nm)
Photodegradation rate	1%/h
Expiration date	12 months

. Laminar and turbulent flow areas showed different luminous characteristics when the light source illuminated the model surface paint. The light-intensity distribution on the surface is captured with a IMPERX B4020 CCD Camera. The camera lens was 50 mm fixed-focus, and a 580 nm high-pass filter was installed in front of the lens to eliminate the influence of excitation light. The light sources were two sets of 400 nm LEDs that were arranged on both sides of the camera. A 400 nm LED light source was used to illuminate the surface of the model sprayed with TSP. At that time, the TSP was excited by the excitation light and emitted red light with a peak wavelength of around 610 nm. Then, a CCD camera was used, and a 580 nm high-pass filter was installed in front of the camera lens to eliminate the influence of excitation light and collect TSP luminous intensity images under different working conditions. The relationship between light intensity I and temperature T can be described by the Arrhenius formula [27]. Using the above collected temperature and light intensity data, the TSP calibration data were fitted on the basis of Equation (1) to obtain the relationship curve between I/I_ref and temperature (T) under different pressure conditions; the calibration curve is shown in Figure 1. Therefore, the light intensity distribution could be converted into temperature distribution, and the transitional location could be observed.

$$\frac{I}{I_{\mathrm{ref}}}=f\left(\frac{T}{T_{\mathrm{ref}}}\right)$$

(1)

where I_ref is light intensity under the normal temperature (T_ref) and pressure.

2.2. Wind-Tunnel Test Device

The TSP transitional test was carried out in the turbine cascade test section of the variable density planar cascade wind tunnel, as shown in Figure 2a, where the test section size (width × height) was 190 × 445 mm. The cascade model was placed in the wind-tunnel test section. The camera and excitation light source were integrated into a specially designed collection box and installed above the back of the test section.

This study takes the transonic VKI-RG turbine blade as the research object, as shown in Figure 2b, and the cascade consisted of seven blades. The distance from the leading edge of the blade to the front of the cascade was 75 mm, the distance from the trailing edge to the rear of the cascade was 43 mm, and its specific parameters are shown in

Table 2. Design parameters of transonic VKI-RG turbine.

Parameters	Value
Inlet flow angle (β)	30°
Blade angle relative to cascade axis (θ)	33.3°
Chord length (c)	95 mm
Ratio of chord length to grating pitch (σ)	1.40845
Aspect ratio (h/c)	2.0
Number of blades in the cascade (N)	7

. The observation blade is a nonmetallic model produced out of epoxy resin material, and the blade surface was sprayed with temperature-sensitive paint. The specific operation was to first clean the surface of the blade with anhydrous alcohol and then spray the primer on the surface of the blade cascade. In order to prevent the induced transition from occurring in advance due to large particles on the surface, the surface was polished with fine sandpaper after the primer had been completely dried and cured, and a luminous topcoat was applied. The schematic diagram of the coating structure is shown in Figure 3a. The excitation light source in the collection box irradiates the temperature-sensitive paint on the blade surface for excitation and then uses a high-speed camera to capture the light intensity. To facilitate the accurate calibration of a transitional location, a schematic diagram of the blade size captured by the high-speed camera is shown in Figure 3b. Lax refers to the length of the blade in the direction perpendicular to the incoming flow when the cascade is set at a position where the vertical line of the forehead line is 30 degrees from the incoming flow.

2.3. Experimental Data Processing and Result Analysis

The wind tunnel test uses a fixed cascade α of 0° to conduct the blowing test, and the inflow conditions include the Ma and Re, whose calculation formula is as follows:

$$Ma=\sqrt{5{\left[\left(\frac{p_{\mathrm{t}1}}{p_{\mathrm{s}1}}\right)-1.0\right]}^{2/7}}$$

(2)

$$Re=0.04766\frac{\left[{\left(1+0.2M{a}^2\right)}^{-1}+\frac{114}{T_{\mathrm{t}1}}\right]Ma}{{\left(1+0.2M{a}^2\right)}^{1.5}{T}_{\mathrm{t}1}}{p}_{\mathrm{t}1}\times {10}^6$$

(3)

where p_t1 is the total pressure of the stable section; p_s1 is the average static pressure; T_t1 is the average total temperature of the stable section.

As shown in

Table 3. Wind-tunnel tests.

Test	pt1	ps1	Ma2	Re1	TIin
1	172 kPa	86.7 kPa	1.03	8.6 × 105	0.3%
2	170 kPa	72.1 kPa	1.2	8.6 × 105	0.3%
3	59.1 kPa	53.1 kPa	0.4	3.1 × 105	0.3%
4	103 kPa	51.1 kPa	1.03	5.1 × 105	0.3%

, four blowing tests were carried out in which specific test parameters such as outlet Mach number (Ma₂) and inlet Reynolds number (Re₁), inlet turbulence intensity (TI_in), and Ma₂ and Re₁ were calculated with Equations (2) and (3), respectively.

The TSP measurement results at different outlet Mach numbers and inlet Reynolds numbers are shown in Figure 4. The temperature ratio (T/T_ref) distribution at both ends of the blade was significantly larger, which was caused by the wall effect. Due to the difference in the heat transfer coefficients of laminar and turbulent flow, there was a significant temperature difference. The slight unevenness of the temperature-sensitive paint spraying on the blade surface and the air flowing through the blade may have been mixed with tiny particles, hitting the blade surface and causing the transition to occur earlier, resulting in a sharp temperature distribution, but the temperature ratio (T/T_ref) distribution on the suction surface of the blade changed significantly as a whole, and the occurrence of the transition could be determined. The transitional location was about 0.63 Lax at Ma₂ = 0.4, Re₁ = 3.1 × 10⁵, as shown in Figure 4a. When Ma₂ and Re₁ increased to 1.03 and 8.6 × 10⁵, respectively, the boundary layer transition occurred at approximately 0.42 Lax, as shown in Figure 4b. However, with the decrease in Re₁, as shown in Figure 4c, the transitional location was moved backward, to about 0.47 Lax. Compared with Figure 4b, the transitional location shifted backward with the increase in Ma₂, which occurred at about 0.49 Lax in Figure 4d.

3. Numerical Prediction of Transition

3.1. Numerical Method and Validation

The geometric model of numerical calculation was the transonic VKI-RG cascade, which is the same as the wind-tunnel test model. Since transitional calculation had a high requirement for the mesh refinement of the normal and tangential directions near the wall, the total number of subsequent meshes increased sharply, and the requirements for computing resources were further increased. In addition, the purpose of this study was mainly to focus on the flow of a single blade, so the cascade composed of seven blades was simplified into a single blade, as shown in Figure 5. The inlet was set at 3c from the leading edge of the blade, and the outlet was set at 8c from the trailing edge to ensure the full development of the wake.

To ensure the accuracy of the subsequent numerical calculations, the structured meshes of the geometric model shown in Figure 5 were generated with ICEM CFD software. The blade-shaped part was divided by an O-shaped mesh, and there were 50 mesh nodes along the circumferential direction near the wall. The first-layer height of the mesh was set to 1 × 10⁻⁶ m, which led to y⁺ < 1 for all test cases. The normal mesh growth ratio is 1.2, and the elements of the 3D computational domain were about 8.01 million. Figure 6 shows the local mesh distribution of the blade cascade. To improve the numerical accuracy of the flow along the flow direction, 240 nodes were arranged along the flow direction, and 120 nodes were arranged along the blade span. Mesh refinement was performed on the trailing part of the edge.

ANSYS CFX software was used to solve the flow field in the computational domain, and all numerical simulations adopted the three-dimensional compressible Reynolds-averaged Navier–Stokes (RANS) equations. The transitional model was the γ-Re_θt model proposed by Langtry [28] based on the SST k-ω turbulence model [29], which considers the natural, bypass, and separation-bubble transitions, and can more accurately predict the transitional location [30,31]. Figure 7 shows the boundary condition settings with total pressure at the inlet and static pressure at the outlet, and the specific boundary conditions and solver settings are shown in

Table 4. Numerical calculation settings.

Item	Setting
Inlet boundary condition	Total pressure
Inlet total temperature	300 K
Inlet turbulence intensity	1%
Outlet boundary condition	Static pressure
Blade wall condition	No-slip wall
Upper and lower surfaces	No-slip wall
Advection scheme	High-resolution
Turbulence numeric	High-resolution
Residual convergence criterion	1 × 10−5

.

The reliability of the numerical method was verified by comparing the experimental results of the isentropic Mach number (Ma_is) and the transitional location on the blade surface. Figure 8 shows the Ma_is distribution on the surface at 50% blade height when the angle of attack was 0° and the outlet Mach number was 0.78. Overall, the numerical results of the Ma_is were in good agreement with the experimental results. Figure 9 is a comparison of the transitional location between numerical simulation and experiment, and the transitional locations were basically the same, about 0.42 Lax.

3.2. Numerical Results

Wall shear and intermittency are more accurate methods to determine the transitional location of the boundary layer. The location where the wall shear begins to increase sharply is the beginning of the transition. Intermittency represents the percentage of time turbulence occurring. When the intermittency is 0, it represents a fully laminar state, and 1 represents a fully turbulent state. The intermittency increases from 0, which represents the beginning of the transition.

3.2.1. Influence of Ma₂

To study the effect of the Ma₂ on the transitional location of the blade boundary layer, numerical calculations were carried out for Ma₂ < 1 and Ma₂ > 1 by adjusting the outlet static pressure. Figure 10 shows the distribution of wall shear and intermittency on the suction side of the blade at Ma₂ < 1, and the transitional location moved forward with the increase in Ma₂. In Figure 10a, the transition occurred at about 60% L_x at Ma₂ = 0.56. The transitional location was significantly moved forward, which occurred at 51%L_x at Ma₂ = 0.78. With the further increase in Ma₂, the transitional location was about 48%L_x at Ma₂ = 0.98. Furthermore, the wall shear in the laminar and turbulent parts increased with increasing Ma₂. The same transitional location and its variation with Ma₂ could be obtained from the intermittency distribution shown in Figure 10b.

Figure 11 is the distribution of wall shear and intermittency on the suction side of the blade at Ma₂ > 1, and the transitional location moved backward with the increase in Ma₂. In Figure 11a, the transition occurred at about 86% L_x at Ma₂ = 1.1. The transitional location was significantly moved backward, which occurred at 88%L_x at Ma₂ = 1.2. As Ma₂ further increased, the transitional location was about 94% L_x at Ma₂ = 1.4. Furthermore, the shear stress in the laminar remained constant, while the wall shear in the turbulent part increased with increasing Ma₂. Figure 10b shows the intermittency distribution with different Ma₂. The variation trend of intermittency was the same as that of the wall shear.

3.2.2. Influence of Attack Angle

Figure 12 shows the distribution of wall shear and intermittency on the suction side of the blade under different attack angles, and the transitional location moved forward with the increase of α. In Figure 12a, the transition occurred at about 54%L_x at α = −10°. The transitional location was significantly moved forward, which occurred at 51%L_x at α = 0°. With a further increase in the angle of attack, the transitional location was about 37%L_x at α = 10°.

In addition, the shear stress in the laminar remained constant, while the wall shear in the turbulent part decreased slightly with an increased attack angle. The same transitional location and its variation trend with α could be obtained from the intermittency distribution in Figure 12b.

3.2.3. Shock-Wave Influence

When the Mach number of the flow field is greater than 1, strong disturbances often occur in flows, such as the sudden compression of supersonic airflow. At that time, sudden changes in flow parameters often occur, that is, shock waves. Figure 13 shows the Mach number distribution of the flow field. The airflow flowed into the leading edge and out of the trailing edge. When flowing through the suction side, it first passed through the expansion wave, which caused the pressure here to drop sharply, and then passed through the shock wave, that is, the compression wave, causing the pressure to increase sharply. Moreover, the wake was formed behind the base pressure of the trailing edge, and interference between shock and wake could be seen.

The wall shear distribution at 50% of the blade height in Figure 14 also shows that an expansion wave was generated near 0.8 L_x. The shear stress dropped sharply at the chord length of 80–83%, and the pressure suddenly increased after the shock wave, resulting in a strong reverse pressure gradient that eventually led to laminar boundary layer separation. The local streamlines of the suction side in Figure 15 show the existence of a separation bubble. The laminar separation trigger transition occurred at 0.85 L_x, and the wall shear increased rapidly at 85% L_x.

4. Conclusions

In this paper, to study the transitional prediction of the planar cascade and the variation law of the transitional location, TSP transitional measurement tests were carried out under the conditions of Ma₂ = 0.4, 1.03, and 1.2. The numerical simulations of plane cascade transition with different Ma₂ (Ma₂ = 0.56, 0.78, 0.98, 1.1, 1.2, 1.4) and α (α = −10°, 0°, 10°) were investigated. The main obtained conclusions are as follows:

(1)

TSP transitional measurement results show that the transitional location was about 0.63 Lax at Ma₂ = 0.4, Re₁ = 3.1 × 10⁵, and transition occurred at approximately 0.42 Lax at Ma₂ = 1.03 Re₁ = 8.6 × 10⁵. As Re₁ decreased, the transitional location moved backward, about 0.47 Lax at Ma₂ = 1.03, Re₁ = 3.1 × 10⁵. The transitional location shifted backward with the increase in Ma₂, occurring at about 0.49 Lax at Ma₂ = 1.2, Re₁ = 8.6 × 10⁵.

(2)

The numerical calculations of the planar cascade with Ma₂ < 1 (Ma₂ = 0.56, 0.78, 0.98) and α (α = −10°, 0°, 10°) were completed. The boundary layer transition of the planar cascade moved forward with the increase in Ma₂ and α.

(3)

Numerical calculations of the planar cascade with Ma₂ > 1 (Ma₂ = 1.1, 1.2, 1.4) were carried out. The transitional location of the boundary layer moved backward with the increase in Ma₂, which was consistent with the experimental results. In addition, the generation of shock waves formed a large adverse pressure gradient that led to the onset of transition.