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Numerical and experimental investigation into hypersonic boundary layer transition induced by roughness elements
Chinese Journal of Aeronautics, (2019), 32(3): 559–567
Chinese Society of Aeronautics and Astronautics & Beihang University
Chinese Journal of Aeronautics [email protected] www.sciencedirect.com
Numerical and experimental investigation into hypersonic boundary layer transition induced by roughness elements Hao DONG a, Shicheng LIU a, Xi GENG a,*, Song LIU a, Liming YANG b, Keming CHENG a a b
Department of Aerodynamics, Nanjing University of Aeronautics and Aeronautics, Nanjing 210016, China Department of Mechanical Engineering, National University of Singapore, Singapore 119260, Singapore
Received 3 July 2018; revised 21 September 2018; accepted 11 November 2018 Available online 3 January 2019
KEYWORDS Boundary layer transition; Hypersonic; Direct numerical simulation (DNS); Oil-film interferometry; Roughness elements
Abstract In this work, the Direct Numerical Simulation (DNS) and Oil-Film Interferometry (OFI) technique are used to investigate the hypersonic boundary layer transition induced by single and double roughness elements at Mach number 5. For single roughness, the DNS results showed that both horseshoe vortices and hairpin vortices caused by shear layer instability can affect the boundary layer instability. The generation of the near-wall unstable structure is the key point of boundary layer transition behind the roughness element. At the downstream of the roughness element, the interaction between horseshoe vortices and hairpin vortices will spread in the spanwise direction. For double roughness elements, the effect of the spacing between roughness elements on the transition is studied. It is found that the case of higher spacing between roughness elements is more effective for inducing transition than the lower one. The interaction between two adjacent roughness elements can suppress the evolution of horseshoe vortices in the downstream and trigger the instability of shear layer. Thus, the transition will be suppressed accordingly. Ó 2019 Chinese Society of Aeronautics and Astronautics. Production and hosting by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction Laminar-to-turbulent transition induced by roughness plays an important role in the design of hypersonic vehicles, espe* Corresponding author. E-mail address: [email protected] (X. GENG). Peer review under responsibility of Editorial Committee of CJA.
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cially for the aerodynamic and thermodynamic performances. On one hand, the skin friction and heat transfer rate of turbulent flow are much higher than those of laminar flow, which makes the Thermal Protection Systems (TPS) design for hypersonic vehicles be quite challenging. But on the other hand, turbulent flow can effectively eliminate the boundary layer separation on the forebody of scramjet vehicles, as well as enhance the mixture of fuel and air in the engine. In the studies of the influence of roughness on hypersonic boundary layer transition, three different types of roughness elements are usually adopted, including 2D roughness step, 3D isolated
https://doi.org/10.1016/j.cja.2018.12.004 1000-9361 Ó 2019 Chinese Society of Aeronautics and Astronautics. Production and hosting by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
560 roughness element, and distributed roughness elements. The height and spacing of the roughness elements are the most important parameters related to the transition progress.1 Many transition experiments have been carried out in wind tunnel over the past 60 years.2 Van Driest3 found that the roughness can trip the boundary layer transition at a certain roughness height. Further increasing the roughness height, resulting in a stronger turbulence, while the position of transition remaining unchanged. Whitehead4 experimentally investigated the geometric shape effect of isolated roughness on hypersonic boundary layer transition at Mach number Ma = 6.8. In their work, the sphere, pin generator, wedge generator, rod, triangular prism, pinhead, and cylinder roughness were studied systemically. They found that the element drag coefficient depends primarily on the geometric shape, the spacing between the elements, and the ratio of the element height to boundary layer height. Berry et al.5 studied the effect of Mach number on the transition with various types of trips and found that the influence of free stream Mach number on forcedtransition is greater than that on natural transition. Tirtey et al.6 studied the transition process in hypersonic flow by using the surface oil visualization technique with various isolated roughness element, such as the cylinder, ramp, square, and half-sphere. He found that different types of roughness elements showed obvious similarities in the generation of streamwise vortices. However, in his work, the mechanism of promoting transition by vortices has not been clearly revealed due to the limitations of the surface oil visualization technique. In the recent ten years, some advanced measurement methods have been used in hypersonic boundary layer transition induced by roughness elements. Danehy et al.7 investigated the hypersonic flow at Ma = 10 over a flat plate with and without a 2 mm radius hemispherical trip by using the Nitric Oxide (NO) Planar Laser-Induced Fluorescence (PLIF) method. In his work, the boundary layer thickness determined by the PLIF image is in line with the result of boundary enthalpy profile computed from the CFD. The experimental results showed that the flow becomes unsteady and tends to be turbulent as the angle of incidence of the plate with respect to the oncoming flow is increased. The first comprehensive experiment of the roughness-induced instability in the laminar boundary for hypersonic flow was conducted by Wheaton and Schneider8 in the Purdue Mach 6 Quiet Tunnel. Pitot probes, hot-wire probes, and wall-mounted pressure sensors were used to detect the instability in the wake of the roughness, and the results indicated that the instability grows to a large amplitude in the downstream of the roughness and is away from the wall, with Root-Mean-Square (RMS) value around 35% of the mean mass flux. Ye et al.9 investigated the transition flow features of the hypersonic boundary in the downstream of a micro-ramp at Ma = 6.5. They found that the maximum streamwise velocity fluctuation gathers around the central low-speed region, which is close to the micro-ramp and in the vicinity of stream vortices. The effects of distributed roughness elements on hypersonic boundary layer transition are complex, difficult to measure and abstruse to be understood.1 For distributed roughness elements, it is often very difficult to distinguish the dominant factor in the transition, since the sources of the disturbance caused by distributed roughness elements are much more than the isolated one. Whitehead4 explored the effect of roughness elements spacing on the transition. It was found that the tran-
H. DONG et al. sition is independent of the element spacing when s/w > 3 (s is the spacing between roughness elements and w is the element width). For s/w < 3, the flow field around the roughness element is influenced significantly by its adjacent elements. When the elements are too close, the vortices interactions would diminish the effectiveness of the element. In addition to experimental investigations, high fidelity computational techniques such as Direct Numerical Simulation (DNS) offer the possibility to characterize the physical mechanism of transition induced by roughness with fine details and to obtain better physical models. Subbareddy et al.10 extensively studied the evolvement of horseshoe vortices and the separated shear layer generated by the roughness element by Dynamic Mode Decomposition (DMD) method. The DMD results showed that the unsteady horseshoe vortices, the harmonic mode of horseshoe vortices wrapped around the cylinder roughness element and the roll-up of the shear layer emerge at the frequencies of 20, 40, 53 kHz respectively. Duan et al.11 investigated the hypersonic boundary layer transition induced by an isolated cylinder roughness element by DNS. The simulation results showed that the flow transition is dominated by the instability of both the horseshoe vortex and the shear layer around the roughness. Duan and Xiao12 also studied the geometrical parameter effects on the hypersonic ramp-induced transition by DNS. Their simulation results indicated that the wake vortices interact with each other in the interval region and the flow transition occurs earlier with decreasing the spacing. Recently, Gao et al.13 experimentally investigated the effects of discrete roughness elements on oscillatory flows at a Mach number 6, and the schlieren results indicated that roughness can suppress external separation effectively. As a summary, a lot of numerical and experimental researches have been conducted in hypersonic boundary layer transition induced by roughness elements. However, the characteristics of multiple instabilities induced by roughness element have not been revealed clearly. In addition, most of them focus on the transition mechanism for a single element and the convincing conclusion for two or more roughness elements is still lacking. In this paper, transition processes induced by a single or the distributed roughness elements in hypersonic flow are studied. The objectives of this work are to obtain the flow structure around and in the downstream of the roughness elements and to figure out the mechanism of transition induced by single and double roughness elements by using DNS method combined with oil-film interferometry measurement technique. In addition, the effect of the spacing between roughness elements on transition is also investigated. As far as we know, this work is the first investigation of the hypersonic boundary layer transition induced by roughness elements by the Oil-film interferometry technique. Moreover, the quantitative comparison will be made between computations and measurements. 2. Numerical simulation The governing equations are the three-dimensional unsteady compressible Navier-Stokes equations with the Stokes hypothesis. The compact upwind Total Variation Diminishing (TVD) scheme is used to reconstruct the numerical convective flux. The viscous flux is discretized by the central difference scheme
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and the time evolution is carried out by the second-order explicit Runge-Kutta method.14 2.1. Governing equation The dimensionless form of Navier-Stokes equations, which are normalized by the reference length, free stream velocity, free stream density and free stream temperature, can be written as ð@U Þ þ ðF FV Þiþ1;j;k ðF FV Þi1;j;k @t i;j;k 2
2
þðG GV Þi;jþ1;k ðG GV Þi;j1;k þ ðH HV Þi;j;kþ1 2
2
2
ð1Þ
ðH HV Þi;j;k1 ¼ 0 2
where U is the conservative flow vector, F, G, H are the convective flux vectors and FV, GV, HV are the viscous terms. The detailed expressions of these vectors can be referred to Refs.15,16 2.2. Numerical scheme The DNS method with high-order accuracy is utilized to solve the governing Eq. (1). The sixth-order compact scheme is used to calculate the spatial derivatives in the streamwise and wallnormal directions.17 In the spanwise direction, the compact scheme is replaced by the spectral method due to the periodic condition. The Fast Fourier Transform (FFT) is employed to calculate the derivatives in the spanwise direction. To eliminate the numerical oscillations, which are commonly observed in the central difference scheme, a sixth-order implicit filtering method is applied for the primitive variables u, v, w, p, and q after certain iteration steps. In this work, the spatial filtering is implemented at every 15 steps. In order to speed up the calculation, the Message Passing Interface (MPI) together with a domain decomposition approach is introduced in the streamwise direction.18
Fig. 1 Sketch of multi-block grid and near-field grids of cylinder-shape roughness.
in wake case, before the roughness element (x/c = 60 mm), it can be observed that the CH, mod values are lower than the laminar theory results during x = [45, 55] mm for experiments and x = [50, 55] mm for DNS. In these regions, the flow will be hindered by the roughness element, forming inverse flow, denoted as ‘‘horseshoe vortices”. It will cause relatively smaller shear stress and heat transfer between the flow and wall than the case without roughens element. After x = 60 mm, the experimental CH, mod values gradually decrease, and reached minimum value at x = 80 mm. After that, it increases and gradually tends to be stable. Similar trend of experimental measurement can be observed in the DNS results. In addition, the fluctuation of CH, mod value after x > 140 mm exists in the DNS results, reflecting the complexity of flow structure in the wake, which is hard to capture in the experiments. Fig. 3
2.3. Validations The present simulation of the transition induced by the cylindrical roughness element will be compared with the experimental results in Ref.6 The flow Mach number in the example is Ma = 6, the unit Reynolds number is Re = 2.6 107/m, and the total pressure is P0 = 3100 kPa. Calculation domain in streamwise is x = [40, 300] mm, in normal direction is y = [0, 6.5] mm, and in spanwise direction is z = [-50, 50] mm. The roughness element is 4 mm in diameter, 0.83 mm in height, and the center of the element is located at 60 mm away from the leading edge of the flat plate. The total number of grid cells are 28566000, and the minimum grid size from the wall is 102 mm. Fig. 1(a) and (b) show the sketch of multiblock grid and near-field grid of the cylinder-shape roughness, respectively. The inlet boundary condition is given by the Blasius similarity solution of 2D flat-plate laminar boundary layer. On the outflow boundaries, the buffer technology is applied. The isothermal wall condition is used, and both sides are set as the exits. The dimensionless time step is taken as dt = 106. Fig. 2 shows the modified Stanton number (CH, mod) measured by Tirtey et al.6 (Fig. 2(a)) and computed by DNS (Fig. 2(b)). For cylinder out wake case, both experimental and DNS results are consistent with laminar theory results. For cylinder
Fig. 2 Modified Stanton number obtained by experimental measurement6 and numerical simulation.
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Fig. 3 Surface heat flux measured by Infra-red6 and numerical simulation.
Fig. 5
Fig. 4 Vortex structures defined by Q-criterion and colored by velocity u.
presents the infrared thermal imaging experimental results6 (Fig. 3(a)) and the numerical simulation result of the surface heat flux (Qw) (Fig. 3(b)). It can be seen from the comparison that good agreement between two results is achieved (in terms of the distribution of heat flux). But the numerical simulation provides more details of flow field, which can distinguish clearly the high and low Qw value regions in the wake. Fig. 4 shows the vortex structures defined by Q-criterion. In this figure, the process of the formation, development, and broken of horseshoe vortices and hairpin vortices caused by roughness element and the whole process of the transition from laminar motion to turbulence are clearly observed. From this test case, the performance of the developed code is well validated.
Sketch and photograph of NHW.
sphere with the volume of 650 m3. The stable runtime of the wind tunnel is greater than 10 s. There are two optical windows (300 mm in the diameter) at each side of the plenum chamber, which can be used for schlieren and PIV measurements. One rectangular window (300 mm 350 mm) at the above the plenum chamber used for optical access of Charge-Coupled Device (CCD) or high-speed camera. For current experiments, the Mach number 5 nozzle is used, and the unit Reynolds number is taken as Re = 4.7 106 m1. 3.2. Test model The model used in this study is a flat plate as shown in Fig. 6. It is made of steel with the surface electroplated by a thin layer of titanium to provide a mirror-smooth surface for the oil-film interferometry skin friction measurement. The length of the flat plate is l = 190 mm and the spanwise length is d = 150 mm, which fits the size of the test section of the wind tunnel. The cylindrical roughness element with the diameter of D = 3 mm and the height of k = 1.6 mm is used in the current study. The roughness element is adhered to the surface of the flat plate at the location of x = 50 mm from the leading edge. During the test, the angle of attack is fixed at a = 0° and the
3. Experimental setup 3.1. Wind tunnel The present experiments are conducted in Nanjing University of Aeronautics Astronautics Hypersonic Wind Tunnel (NHW) as shown in Fig. 5. This is a blow-down and vacuum suction mode wind tunnel with the operating Mach number from 4.0 to 8.0. The air of the wind tunnel is supplied by two storage tanks with the volume of 32 m3 at the pressure of 20 MPa. An interchangeable converging-diverging nozzle with the exit diameter of 500 mm is mounted in the plenum chamber. The test section and diffuser are at the downstream of the nozzle. At the end of the wind tunnel, the air is inhaled into a vacuum
Fig. 6
Sketch of flat plate with isolated roughness element.
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free stream Mach number is retained at Ma = 5. The sketch of the roughness elements is shown in Fig. 7 and Z denotes the spacing between each element. 3.3. Oil-film interferometry skin friction measurement The principle of the Oil-film interferometry skin friction technique is that the oil applied to a surface can move along the surface and become thin due to the shear stress under the friction of the boundary layer. By using the visible monochromatic light, the interference patterns (fringes) will be emerged clearly19–21. The spacing distance between the fringes is related to skin friction, which can be calculated by Cf ¼
2n0 coshr Ds R t 1 ðtÞ Nk t12 qlðtÞ dt
ð2Þ
where n0 is the refractive index of the silicon oil, hr the refracted light angle through the oil, k the wavelength of the light source, N the number of the fringes used in the equation, Ds the total width of N fringes, q1 the dynamic pressure of the free stream, and l the viscosity of the oil; t1 and t2 are the start time and end time to capture the pictures respectively. More details for the derivation of Eq. (2) can be referred to Ref.21 The principle schematic of Oil-film interferometry is depicted in Fig. 8.21 The oil applied in the present test is the silicon oil with the viscosity of 50 centistokes (cSt). The monochrome sodium lamp with the wavelength of 598 nm is used for the illumination. Due to the duration of the wind tunnel, the fringe patterns are captured by the HotShot 1280 cc high speed camera mounted with the lens of Nikkor AF 70–300 mm f/4–5.6D, with the resolution of 1280 1024 pixels (see Fig. 9).
Fig. 8 Principle of oil-film interferometry21 (Ds is the total width of N fringes and h is the height of oil film).
4. Results and discussion In the experiments, the angle of incidence of the flat plate is a = 0°. The Mach number is set at Ma = 5, the free stream total temperature is T0 = 516 K, the free stream total pressure is P0 = 3.909 105 Pa, and the wall temperature is set to be Tw = 300 K. According to the above conditions, the corresponding Reynolds number is about Re = 4.718 106. The simulation condition by DNS is the same as the experimental condition. In addition, the original k-x-SST model is adopted. The turbulence intensity of the incoming flow is 1% according to the experimental conditions, and the lT1 = 0.01 lL1 (turbulent viscosity ratio of is 0.01).
Fig. 9
Experiment apparatus installed in wind tunnel.
4.1. 2D results without roughness elements
Fig. 7
Sketch of roughness elements.
In order to figure out the basic flow field on a flat plate, a twodimensional numerical simulation is conducted first. The 2D grid around the flat plate is shown in Fig. 10. At the same time, oil-film interferometry experiment on the flat plate without roughness element is also performed. Fig. 11 shows the oil-film interferometry patterns on the 2D flat plate without roughness element, and Fig. 12 depicts the distribution of skin friction coefficient along the streamwise of flat plate obtained by numerical simulation and experiment. Clearly, the experimental results agree well with the laminar simulation, which indicates that the Oil-film interferometry
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Fig. 10
Grid of 2D numerical simulation.
Fig. 12 plate.
Simulation and experimental results of Cf on 2D flat
technique is able to effectively measure the Cf on a flat plate in hypersonic flow. In addition, the results shown in Fig. 12 indicate that the flow pattern for this case belongs to the laminar regime since the roughness element has not been mounted on the flat plate. According to the numerical simulation, the displacement thickness (d) of the laminar boundary layer at a distance of 50 mm from the leading edge of the flat plate is about 1.3 mm (99% of the mean flow velocity). Note that, this displacement thickness will be used to determine the height of roughness in the following text. The results of 2D simulation are also taken as the initial condition of 3D simulation for faster convergence. 4.2. Computational grids and boundary conditions for cases with roughness Roughness element with the diameter of D = 3 mm and the height of k = 1.6 mm (k/d = 1.23, which is ‘‘effective”3) is chosen to explore the characteristic of transition progress induced by single roughness element. Fig. 13 shows the overall grid and the near-field grid around a cylindrical roughness element. Computation domain in streamwise is x = [40, 300] mm, in normal direction y = [0, 6.5] mm, and in spanwise direction is z = [50, 50] mm. Grid refinement is performed near the wall surface with a minimum grid spacing of 0.01 mm. The total number of grid cells is 26730000, divided into 185 blocks for parallel calculations. The initial conditions are interpolated from the two-dimensional numerical simulation results. The wall surface is taken as an isothermal and non-slip condition at the temperature of Tw = 300 K. The outlet condition is extrapolated from the inner domain and treated as a buffer layer. The boundary conditions of two sides are set to be periodic.
Fig. 11 Oil-film interferometry patterns on flat plate without roughness element.
Fig. 13 Overall grid and near-field grid around cylindrical roughness element.
4.3. Effect of single roughness element Fig. 14 shows the comparison of Cf on the centerline behind the roughness element between DNS and experimental results. Also displayed in this figure are the results obtained by twodimensional simulation. As is shown, the DNS result is comparable with the laminar result at about x = [30, 40] mm, and then drops to a quite low level due to the effect of the stagnation flow in front of the roughness element. Behind the roughness element, the Cf value is increased with streamwise distance at x = [55, 65] mm, and then keeps constant at x = [65, 100] mm, which is comparable with the laminar results. At the location of x = [100, 137] mm, the Cf value grows gradually and reaches a peak value of 0.0064 at x = 137 mm. Boundary layer transition occurs in this region. After the peak, the Cf value decreases gradually and finally approaches the turbulent results. In addition, the oil-film interferometry experimental results agree well with the numerical simulation at x = [55, 120] mm. Overall, the numerical simulation over predicts the Cf value. This phenomenon is similar to that of Bartkowicz’s22 and Duan’s11 results.
Numerical and experimental investigation into hypersonic boundary layer transition induced by roughness elements
Fig. 14 Comparison of Cf on centerline behind roughness element between DNS and experimental results.
Fig. 15 presents the distribution of the computed density gradient on the z = 0 mm plane for the single element case. On top of the roughness element, bow-shock and expansion shock are observed obviously. Behind the roughness element, a stable shear layer along the streamwise is observed at about x = [55, 80] mm. At the range of x = [80, 110] mm, the instability occurs in the shear layer and some regular structures are formed, which could be the ring-vortex structures in threedimensional space. At the location of x = 110 mm, the secondary instability occurs near the wall within the boundary, which formed another regular structure. As shown in Fig. 14, the Cf value increases rapidly from this position. In addition, the growth, evolution, and distortion of unstable structures occur near the wall at the range of x = [110, 160] mm. The near-wall instability leads the high value of Cf at x = 137 mm. This observation may indicate that the formation of the near-wall unstable structure is the key factor of the transition behind the roughness element. After x > 160 mm, the shear layer structure and near-wall unstable structure interact and blend with each other, resulting in the full turbulence in this range. The distribution of statistical average Cf on y = 0 mm plane computed by DNS is presented in Fig. 16(a) and measured by oil-film interferometry technique is depicted in Fig. 16(b). As shown in Fig. 16(a), the affected region by the roughness element can be divided into two zones at about x = 100 mm. Before x = 100 mm, there are two high Cf value regions in the wake of the roughness element: the upper region (A) and the lower region (B) of the symmetry plane. In the centerline, the Cf value is small at the range of x = [65, 100] mm.
Fig. 15
Distribution of density gradient on z = 0 mm plane.
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After x = 110 mm, the Cf value at regions of A and B decreases, and another high Cf value region (C) emerges at the range of x = [110, 160] mm, which is located in the centerline. At the downstream behind x = 160 mm, the affected region becomes broader, and the distribution of Cf in spanwise becomes more uniform. The oil-film interferometry presents the similar results of the simulation as shown in Fig. 16(b). At the range of x = [60, 90] mm, the oil-film fringe in the upper (regions 1 and 2) and the lower regions is evident, which indicates high Cf value in these regions. At x > 90 mm, the fringe patterns become straight gradually (region 3) and the spacing in the centerline grows slightly (the experimental Cf value in the centerline is shown in Fig. 14). The coherent structures predicted by DNS around and in the wake of the roughness element are presented in Fig. 17. Around the roughness element, several stable horseshoe vortices are observed. At the same time, a strong shear layer right behind the roughness element is formed and it develops to the hairpin vortex structures in the wake. After x = 110 mm, the hairpin vortices break down into many small-scale structures and interact with horseshoe vortices. This phenomenon can be used to explain the appearance of near-wall structure as shown in Fig. 15. In the further downstream of the roughness element, the flow structures become smaller and smaller. This indicates that the interaction between the horseshoe vortices and the shear layer becomes stronger and the flow almost becomes turbulent in the spanwise direction. 4.4. Effect of space between two roughness elements In this section, the effect of the spacing between two roughness elements is investigated numerically. The roughness element taken in this simulation is the same as the previous case. The spacing Z between two roughness elements are set to be 3 mm and 6 mm, which represent to the cases of Z/D = 1 and Z/D = 2 respectively.
Fig. 16 results.
Comparison of simulation results and experimental
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Fig. 17 Coherent structures around and in the wake of roughness element.
Fig. 18 shows the distribution of the skin friction coefficient on the centerline of roughness elements for the cases of Z/ D = 1 and Z/D = 2. Near the position of x = 50 mm, the Cf distributions of these two cases are similar except the slight overstep of the Cf value for the case of Z/D = 2. Behind x = 50 mm, the Cf value grows in both cases, while the growth rate of Z/D = 2 is much higher than that of Z/D = 1. For the case of Z/D = 1, the Cf value reaches its peak value of 0.0017 at about x = 130 mm. This peak value is lower than that of the turbulent case as shown in Fig. 14. After x > 130 mm, the Cf value starts to decrease, which indicates that no transition occurs in this region. For the case of Z/D = 2, the Cf value reaches it speak value of 0.00285 at almost the same position of the case of Z/D = 1and decreases at the downstream, indicating the occurrence of the transition. Fig. 19 shows the distribution of the computed density gradient on the centerline plane behind each element for the cases of Z/D = 1 and Z/D = 2 are shown in. For both cases, the shear layer behind the roughness elements is observed clearly, which is stable at x = [50,130] mm. For the case of Z/D = 2 (Fig. 19(b)), the near-wall instability occurs at about x = 90 mm, but the intensity is lower than single element case and no regular structures are formed near wall until x = 180 mm. After x > 180 mm, slight fluctuations occur at both shear layer and near-wall unstable structure. However, for the case of Z/D = 1 (Fig. 19(a)), the shear layer keeps stable in the whole symmetry plane.
Fig. 18 Distribution of the computed Cf on the centerline for double roughness elements.
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Fig. 19 plane.
Comparison of density gradient magnitude on symmetry
Fig. 20 presents the Cf distribution on the y = 0 mm plane around and in the wake of the roughness elements for the cases of Z/D = 1 and Z/D = 2. In the range of x = [0, 50] mm, the distribution of Cf for the case of Z/D = 1 is uniform in the spanwise direction, and the arched contours before each roughness element combine to wave-shaped curve, which indicates the existence of interactions between each roughness element. In contrast to the case of Z/D = 1, the distribution of Cf for the case of Z/D = 2 is similar to the isolated roughness element mentioned above: Each roughness element is relatively independent and the interactions between two adjacent roughness elements are minor. Around the roughness elements, the characteristics of Cf on the side of roughness element are distinct between two cases as shown in Fig. 20. For the case of Z/D = 1, a break occurs in the high Cf value region, while for the case of Z/D = 2, the region shows continuity. The results of Z/D = 2 are comparable to the single roughness element (Fig. 16(a)). For the case of Z/D = 2, two high Cf regions on the upper and lower sides of each roughness element emerge at about x = [60,100] mm, and then merge gradually into one region in the centerline at about x = 110 mm. However, this kind of merging does not occur in the case of Z/D = 1. These results reveal that the shorter
Fig. 20 Comparison of Cf distribution on y = 0 mm plane around and in the wake of roughness elements.
Numerical and experimental investigation into hypersonic boundary layer transition induced by roughness elements spacing between roughness elements will suppress the evolution of horseshoe vortices and trigger the instability of shear layer at the downstream, leading to the suppression of the transition. 5. Conclusions (1) In this work, the Direct Numerical Simulation (DNS) method is used to study the flow structure and the OilFilm Interferometry (OFI) technique is utilized for characterizing the skin friction coefficient. A quantitative comparison is made between computations and measurements. The numerical simulation results agree well with experimental data. (2) For single roughness, the DNS results show that both horseshoe vortices around the roughness element and hairpin vortices behind the roughness element caused by shear layer instability can affect the boundary layer instability. The generation of the near-wall unstable structure is the key point of boundary layer transition behind the roughness. (3) At the downstream of the roughness element, the interaction between multiple vortices will spread in the spanwise direction. For distributed roughness elements, the higher spacing between two roughness elements is more effective in inducing transition than the lower one. (4) The interaction between two adjacent roughness elements can suppress the evolution of the downstream horseshoe vortices and trigger the instability of shear layer. As a result, the transition will be suppressed at the downstream.
Acknowledgements The authors would like to thank the China Scholarship Council (CSC), the Aeronautics Science Foundation of China (No. 20163252037), the China Postdoctoral Science Foundation (No. 2017M610325), the Natural Science Foundation of Jiangsu Province of China (No. BK20170771), and the Fundamental Research Funds for the Central Universities of China (No. NP2017202) for their support.
References 1. Schneider SP. Effects of roughness on hypersonic boundary-layer transition. J Spacecr Rockets 2008;45(2):193–209. 2. Schneider SP. Hypersonic laminar–turbulent transition on circular cones and scramjet forebodies. Prog Aeosp Sci 2004;40(1–2):1–50. 3. Van Driest ER. The effect of controlled three-dimensional roughness on boundary-layer transition at supersonic speeds. J Aerosp Sci 1960;27(4):261–71.
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4. Whitehead AH. Flow-field and drag characteristics of several boundary-layer tripping elements in hypersonic flow. Washington, D.C.: NASA; 1969. Report No.: NASA-TN-D5454. 5. Berry SA, Auslender AH, Dilley AD, Calleja JF. Hypersonic boundary-layer trip development for Hyper-X. J Spacecr Rockets 2001;38(6):853–64. 6. Tirtey S, Louis W, Olivier C. Characterization of hypersonic roughness induced transition for the EXPERT flight experiment. 16th AIAA/DLR/DGLR international space planes and hypersonic systems and technologies conference. Reston: AIAA; 2009. 7. Danehy PM, Bathel B, Ivey C, Inman JA, Jones SB. NO PLIF study of hypersonic transition over a discrete hemispherical roughness element. 47th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition. Reston: AIAA; 2009. 8. Wheaton BM, Schneider SP. Roughness-induced instability in a hypersonic laminar boundary layer. AIAA J 2012;50(6):1245–56. 9. Ye QQ, Schrijer F, Scarano F. Tomographic PIV measurement of hypersonic boundary layer transition past a micro-ramp. 47th AIAA fluid dynamics conference. Reston: AIAA; 2017. 10. Subbareddy PK, Bartkowicz MD, Candler GV. Direct numerical simulation of high-speed transition due to an isolated roughness element. J Fluid Mech 2014;748:848–78. 11. Duan ZW, Xiao ZX, Fu S. Direct numerical simulation of hypersonic transition induced by an isolated cylindrical roughness element. Sci China-Phys Mech Astron 2014;57(12):2330–45. 12. Duan ZW, Xiao ZX. Direct numerical simulation of geometrical parameter effects on the hypersonic ramp-induced transition. 7th AIAA theoretical fluid mechanics conference. Reston: AIAA; 2014. 13. Gao WZ, Li ZF, Yang JM, Zeng YS. Effects of trips on the oscillatory flow of an axisymmetric hypersonic inlet with downstream throttle. Chin J Aeronaut 2018;31(2):225–36. 14. Shu CW, Osher S. Efficient implementation of essentially nonoscillatory shock-capturing scheme. J Comput Phys 1988;77:39–471. 15. Chen L, Tang DB, Liu XB, Oliveira M, Liu CQ. Evolution of the ring-like vortices and spike structure in transitional boundary layers. Sci China-Phys Mech Astron 2010;53(3):514–20. 16. Chen L, Tang DB, Liu CQ. Numerical studies on evolution of secondary streamwise vortices in transitional boundary layers. Appl Math Mech Engl Ed 2011;32(4):449–58. 17. Lele SK. Compact finite difference schemes with spectral-like resolution. J Comput Phys 1992;103:16–42. 18. Zhu ZB, Yuan XJ, Chen L. Zone decomposition parallel algorithm of high order compact scheme. Chin J Comput Mech 2014;32(6):825–30 [Chinese]. 19. Driver DM. Application of oil-film interferometry skin-friction measurement to large wind tunnels. Exp Fluids 2003;34(6):717–25. 20. Driver DM, Zilliac GG. Oil-film interferometry shear stress measurements in large wind tunnels – technique and applications. 24th AIAA aerodynamic measurement technology and ground testing conference. Reston: AIAA; 2004. 21. Driver DM, Drake A. Skin friction measurements using oil-film interferometry in NASA’s 11-Foot Transonic Wind Tunnel. AIAA J 2008;46(10):2401–7. 22. Bartkowicz MD. Numerical simulations of hypersonic boundary layer transition [dissertation]. Minnesota: University of Minnesota; 2012.
Chinese Society of Aeronautics and Astronautics & Beihang University
Chinese Journal of Aeronautics [email protected] www.sciencedirect.com
Numerical and experimental investigation into hypersonic boundary layer transition induced by roughness elements Hao DONG a, Shicheng LIU a, Xi GENG a,*, Song LIU a, Liming YANG b, Keming CHENG a a b
Department of Aerodynamics, Nanjing University of Aeronautics and Aeronautics, Nanjing 210016, China Department of Mechanical Engineering, National University of Singapore, Singapore 119260, Singapore
Received 3 July 2018; revised 21 September 2018; accepted 11 November 2018 Available online 3 January 2019
KEYWORDS Boundary layer transition; Hypersonic; Direct numerical simulation (DNS); Oil-film interferometry; Roughness elements
Abstract In this work, the Direct Numerical Simulation (DNS) and Oil-Film Interferometry (OFI) technique are used to investigate the hypersonic boundary layer transition induced by single and double roughness elements at Mach number 5. For single roughness, the DNS results showed that both horseshoe vortices and hairpin vortices caused by shear layer instability can affect the boundary layer instability. The generation of the near-wall unstable structure is the key point of boundary layer transition behind the roughness element. At the downstream of the roughness element, the interaction between horseshoe vortices and hairpin vortices will spread in the spanwise direction. For double roughness elements, the effect of the spacing between roughness elements on the transition is studied. It is found that the case of higher spacing between roughness elements is more effective for inducing transition than the lower one. The interaction between two adjacent roughness elements can suppress the evolution of horseshoe vortices in the downstream and trigger the instability of shear layer. Thus, the transition will be suppressed accordingly. Ó 2019 Chinese Society of Aeronautics and Astronautics. Production and hosting by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction Laminar-to-turbulent transition induced by roughness plays an important role in the design of hypersonic vehicles, espe* Corresponding author. E-mail address: [email protected] (X. GENG). Peer review under responsibility of Editorial Committee of CJA.
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cially for the aerodynamic and thermodynamic performances. On one hand, the skin friction and heat transfer rate of turbulent flow are much higher than those of laminar flow, which makes the Thermal Protection Systems (TPS) design for hypersonic vehicles be quite challenging. But on the other hand, turbulent flow can effectively eliminate the boundary layer separation on the forebody of scramjet vehicles, as well as enhance the mixture of fuel and air in the engine. In the studies of the influence of roughness on hypersonic boundary layer transition, three different types of roughness elements are usually adopted, including 2D roughness step, 3D isolated
https://doi.org/10.1016/j.cja.2018.12.004 1000-9361 Ó 2019 Chinese Society of Aeronautics and Astronautics. Production and hosting by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
560 roughness element, and distributed roughness elements. The height and spacing of the roughness elements are the most important parameters related to the transition progress.1 Many transition experiments have been carried out in wind tunnel over the past 60 years.2 Van Driest3 found that the roughness can trip the boundary layer transition at a certain roughness height. Further increasing the roughness height, resulting in a stronger turbulence, while the position of transition remaining unchanged. Whitehead4 experimentally investigated the geometric shape effect of isolated roughness on hypersonic boundary layer transition at Mach number Ma = 6.8. In their work, the sphere, pin generator, wedge generator, rod, triangular prism, pinhead, and cylinder roughness were studied systemically. They found that the element drag coefficient depends primarily on the geometric shape, the spacing between the elements, and the ratio of the element height to boundary layer height. Berry et al.5 studied the effect of Mach number on the transition with various types of trips and found that the influence of free stream Mach number on forcedtransition is greater than that on natural transition. Tirtey et al.6 studied the transition process in hypersonic flow by using the surface oil visualization technique with various isolated roughness element, such as the cylinder, ramp, square, and half-sphere. He found that different types of roughness elements showed obvious similarities in the generation of streamwise vortices. However, in his work, the mechanism of promoting transition by vortices has not been clearly revealed due to the limitations of the surface oil visualization technique. In the recent ten years, some advanced measurement methods have been used in hypersonic boundary layer transition induced by roughness elements. Danehy et al.7 investigated the hypersonic flow at Ma = 10 over a flat plate with and without a 2 mm radius hemispherical trip by using the Nitric Oxide (NO) Planar Laser-Induced Fluorescence (PLIF) method. In his work, the boundary layer thickness determined by the PLIF image is in line with the result of boundary enthalpy profile computed from the CFD. The experimental results showed that the flow becomes unsteady and tends to be turbulent as the angle of incidence of the plate with respect to the oncoming flow is increased. The first comprehensive experiment of the roughness-induced instability in the laminar boundary for hypersonic flow was conducted by Wheaton and Schneider8 in the Purdue Mach 6 Quiet Tunnel. Pitot probes, hot-wire probes, and wall-mounted pressure sensors were used to detect the instability in the wake of the roughness, and the results indicated that the instability grows to a large amplitude in the downstream of the roughness and is away from the wall, with Root-Mean-Square (RMS) value around 35% of the mean mass flux. Ye et al.9 investigated the transition flow features of the hypersonic boundary in the downstream of a micro-ramp at Ma = 6.5. They found that the maximum streamwise velocity fluctuation gathers around the central low-speed region, which is close to the micro-ramp and in the vicinity of stream vortices. The effects of distributed roughness elements on hypersonic boundary layer transition are complex, difficult to measure and abstruse to be understood.1 For distributed roughness elements, it is often very difficult to distinguish the dominant factor in the transition, since the sources of the disturbance caused by distributed roughness elements are much more than the isolated one. Whitehead4 explored the effect of roughness elements spacing on the transition. It was found that the tran-
H. DONG et al. sition is independent of the element spacing when s/w > 3 (s is the spacing between roughness elements and w is the element width). For s/w < 3, the flow field around the roughness element is influenced significantly by its adjacent elements. When the elements are too close, the vortices interactions would diminish the effectiveness of the element. In addition to experimental investigations, high fidelity computational techniques such as Direct Numerical Simulation (DNS) offer the possibility to characterize the physical mechanism of transition induced by roughness with fine details and to obtain better physical models. Subbareddy et al.10 extensively studied the evolvement of horseshoe vortices and the separated shear layer generated by the roughness element by Dynamic Mode Decomposition (DMD) method. The DMD results showed that the unsteady horseshoe vortices, the harmonic mode of horseshoe vortices wrapped around the cylinder roughness element and the roll-up of the shear layer emerge at the frequencies of 20, 40, 53 kHz respectively. Duan et al.11 investigated the hypersonic boundary layer transition induced by an isolated cylinder roughness element by DNS. The simulation results showed that the flow transition is dominated by the instability of both the horseshoe vortex and the shear layer around the roughness. Duan and Xiao12 also studied the geometrical parameter effects on the hypersonic ramp-induced transition by DNS. Their simulation results indicated that the wake vortices interact with each other in the interval region and the flow transition occurs earlier with decreasing the spacing. Recently, Gao et al.13 experimentally investigated the effects of discrete roughness elements on oscillatory flows at a Mach number 6, and the schlieren results indicated that roughness can suppress external separation effectively. As a summary, a lot of numerical and experimental researches have been conducted in hypersonic boundary layer transition induced by roughness elements. However, the characteristics of multiple instabilities induced by roughness element have not been revealed clearly. In addition, most of them focus on the transition mechanism for a single element and the convincing conclusion for two or more roughness elements is still lacking. In this paper, transition processes induced by a single or the distributed roughness elements in hypersonic flow are studied. The objectives of this work are to obtain the flow structure around and in the downstream of the roughness elements and to figure out the mechanism of transition induced by single and double roughness elements by using DNS method combined with oil-film interferometry measurement technique. In addition, the effect of the spacing between roughness elements on transition is also investigated. As far as we know, this work is the first investigation of the hypersonic boundary layer transition induced by roughness elements by the Oil-film interferometry technique. Moreover, the quantitative comparison will be made between computations and measurements. 2. Numerical simulation The governing equations are the three-dimensional unsteady compressible Navier-Stokes equations with the Stokes hypothesis. The compact upwind Total Variation Diminishing (TVD) scheme is used to reconstruct the numerical convective flux. The viscous flux is discretized by the central difference scheme
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and the time evolution is carried out by the second-order explicit Runge-Kutta method.14 2.1. Governing equation The dimensionless form of Navier-Stokes equations, which are normalized by the reference length, free stream velocity, free stream density and free stream temperature, can be written as ð@U Þ þ ðF FV Þiþ1;j;k ðF FV Þi1;j;k @t i;j;k 2
2
þðG GV Þi;jþ1;k ðG GV Þi;j1;k þ ðH HV Þi;j;kþ1 2
2
2
ð1Þ
ðH HV Þi;j;k1 ¼ 0 2
where U is the conservative flow vector, F, G, H are the convective flux vectors and FV, GV, HV are the viscous terms. The detailed expressions of these vectors can be referred to Refs.15,16 2.2. Numerical scheme The DNS method with high-order accuracy is utilized to solve the governing Eq. (1). The sixth-order compact scheme is used to calculate the spatial derivatives in the streamwise and wallnormal directions.17 In the spanwise direction, the compact scheme is replaced by the spectral method due to the periodic condition. The Fast Fourier Transform (FFT) is employed to calculate the derivatives in the spanwise direction. To eliminate the numerical oscillations, which are commonly observed in the central difference scheme, a sixth-order implicit filtering method is applied for the primitive variables u, v, w, p, and q after certain iteration steps. In this work, the spatial filtering is implemented at every 15 steps. In order to speed up the calculation, the Message Passing Interface (MPI) together with a domain decomposition approach is introduced in the streamwise direction.18
Fig. 1 Sketch of multi-block grid and near-field grids of cylinder-shape roughness.
in wake case, before the roughness element (x/c = 60 mm), it can be observed that the CH, mod values are lower than the laminar theory results during x = [45, 55] mm for experiments and x = [50, 55] mm for DNS. In these regions, the flow will be hindered by the roughness element, forming inverse flow, denoted as ‘‘horseshoe vortices”. It will cause relatively smaller shear stress and heat transfer between the flow and wall than the case without roughens element. After x = 60 mm, the experimental CH, mod values gradually decrease, and reached minimum value at x = 80 mm. After that, it increases and gradually tends to be stable. Similar trend of experimental measurement can be observed in the DNS results. In addition, the fluctuation of CH, mod value after x > 140 mm exists in the DNS results, reflecting the complexity of flow structure in the wake, which is hard to capture in the experiments. Fig. 3
2.3. Validations The present simulation of the transition induced by the cylindrical roughness element will be compared with the experimental results in Ref.6 The flow Mach number in the example is Ma = 6, the unit Reynolds number is Re = 2.6 107/m, and the total pressure is P0 = 3100 kPa. Calculation domain in streamwise is x = [40, 300] mm, in normal direction is y = [0, 6.5] mm, and in spanwise direction is z = [-50, 50] mm. The roughness element is 4 mm in diameter, 0.83 mm in height, and the center of the element is located at 60 mm away from the leading edge of the flat plate. The total number of grid cells are 28566000, and the minimum grid size from the wall is 102 mm. Fig. 1(a) and (b) show the sketch of multiblock grid and near-field grid of the cylinder-shape roughness, respectively. The inlet boundary condition is given by the Blasius similarity solution of 2D flat-plate laminar boundary layer. On the outflow boundaries, the buffer technology is applied. The isothermal wall condition is used, and both sides are set as the exits. The dimensionless time step is taken as dt = 106. Fig. 2 shows the modified Stanton number (CH, mod) measured by Tirtey et al.6 (Fig. 2(a)) and computed by DNS (Fig. 2(b)). For cylinder out wake case, both experimental and DNS results are consistent with laminar theory results. For cylinder
Fig. 2 Modified Stanton number obtained by experimental measurement6 and numerical simulation.
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Fig. 3 Surface heat flux measured by Infra-red6 and numerical simulation.
Fig. 5
Fig. 4 Vortex structures defined by Q-criterion and colored by velocity u.
presents the infrared thermal imaging experimental results6 (Fig. 3(a)) and the numerical simulation result of the surface heat flux (Qw) (Fig. 3(b)). It can be seen from the comparison that good agreement between two results is achieved (in terms of the distribution of heat flux). But the numerical simulation provides more details of flow field, which can distinguish clearly the high and low Qw value regions in the wake. Fig. 4 shows the vortex structures defined by Q-criterion. In this figure, the process of the formation, development, and broken of horseshoe vortices and hairpin vortices caused by roughness element and the whole process of the transition from laminar motion to turbulence are clearly observed. From this test case, the performance of the developed code is well validated.
Sketch and photograph of NHW.
sphere with the volume of 650 m3. The stable runtime of the wind tunnel is greater than 10 s. There are two optical windows (300 mm in the diameter) at each side of the plenum chamber, which can be used for schlieren and PIV measurements. One rectangular window (300 mm 350 mm) at the above the plenum chamber used for optical access of Charge-Coupled Device (CCD) or high-speed camera. For current experiments, the Mach number 5 nozzle is used, and the unit Reynolds number is taken as Re = 4.7 106 m1. 3.2. Test model The model used in this study is a flat plate as shown in Fig. 6. It is made of steel with the surface electroplated by a thin layer of titanium to provide a mirror-smooth surface for the oil-film interferometry skin friction measurement. The length of the flat plate is l = 190 mm and the spanwise length is d = 150 mm, which fits the size of the test section of the wind tunnel. The cylindrical roughness element with the diameter of D = 3 mm and the height of k = 1.6 mm is used in the current study. The roughness element is adhered to the surface of the flat plate at the location of x = 50 mm from the leading edge. During the test, the angle of attack is fixed at a = 0° and the
3. Experimental setup 3.1. Wind tunnel The present experiments are conducted in Nanjing University of Aeronautics Astronautics Hypersonic Wind Tunnel (NHW) as shown in Fig. 5. This is a blow-down and vacuum suction mode wind tunnel with the operating Mach number from 4.0 to 8.0. The air of the wind tunnel is supplied by two storage tanks with the volume of 32 m3 at the pressure of 20 MPa. An interchangeable converging-diverging nozzle with the exit diameter of 500 mm is mounted in the plenum chamber. The test section and diffuser are at the downstream of the nozzle. At the end of the wind tunnel, the air is inhaled into a vacuum
Fig. 6
Sketch of flat plate with isolated roughness element.
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free stream Mach number is retained at Ma = 5. The sketch of the roughness elements is shown in Fig. 7 and Z denotes the spacing between each element. 3.3. Oil-film interferometry skin friction measurement The principle of the Oil-film interferometry skin friction technique is that the oil applied to a surface can move along the surface and become thin due to the shear stress under the friction of the boundary layer. By using the visible monochromatic light, the interference patterns (fringes) will be emerged clearly19–21. The spacing distance between the fringes is related to skin friction, which can be calculated by Cf ¼
2n0 coshr Ds R t 1 ðtÞ Nk t12 qlðtÞ dt
ð2Þ
where n0 is the refractive index of the silicon oil, hr the refracted light angle through the oil, k the wavelength of the light source, N the number of the fringes used in the equation, Ds the total width of N fringes, q1 the dynamic pressure of the free stream, and l the viscosity of the oil; t1 and t2 are the start time and end time to capture the pictures respectively. More details for the derivation of Eq. (2) can be referred to Ref.21 The principle schematic of Oil-film interferometry is depicted in Fig. 8.21 The oil applied in the present test is the silicon oil with the viscosity of 50 centistokes (cSt). The monochrome sodium lamp with the wavelength of 598 nm is used for the illumination. Due to the duration of the wind tunnel, the fringe patterns are captured by the HotShot 1280 cc high speed camera mounted with the lens of Nikkor AF 70–300 mm f/4–5.6D, with the resolution of 1280 1024 pixels (see Fig. 9).
Fig. 8 Principle of oil-film interferometry21 (Ds is the total width of N fringes and h is the height of oil film).
4. Results and discussion In the experiments, the angle of incidence of the flat plate is a = 0°. The Mach number is set at Ma = 5, the free stream total temperature is T0 = 516 K, the free stream total pressure is P0 = 3.909 105 Pa, and the wall temperature is set to be Tw = 300 K. According to the above conditions, the corresponding Reynolds number is about Re = 4.718 106. The simulation condition by DNS is the same as the experimental condition. In addition, the original k-x-SST model is adopted. The turbulence intensity of the incoming flow is 1% according to the experimental conditions, and the lT1 = 0.01 lL1 (turbulent viscosity ratio of is 0.01).
Fig. 9
Experiment apparatus installed in wind tunnel.
4.1. 2D results without roughness elements
Fig. 7
Sketch of roughness elements.
In order to figure out the basic flow field on a flat plate, a twodimensional numerical simulation is conducted first. The 2D grid around the flat plate is shown in Fig. 10. At the same time, oil-film interferometry experiment on the flat plate without roughness element is also performed. Fig. 11 shows the oil-film interferometry patterns on the 2D flat plate without roughness element, and Fig. 12 depicts the distribution of skin friction coefficient along the streamwise of flat plate obtained by numerical simulation and experiment. Clearly, the experimental results agree well with the laminar simulation, which indicates that the Oil-film interferometry
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Fig. 10
Grid of 2D numerical simulation.
Fig. 12 plate.
Simulation and experimental results of Cf on 2D flat
technique is able to effectively measure the Cf on a flat plate in hypersonic flow. In addition, the results shown in Fig. 12 indicate that the flow pattern for this case belongs to the laminar regime since the roughness element has not been mounted on the flat plate. According to the numerical simulation, the displacement thickness (d) of the laminar boundary layer at a distance of 50 mm from the leading edge of the flat plate is about 1.3 mm (99% of the mean flow velocity). Note that, this displacement thickness will be used to determine the height of roughness in the following text. The results of 2D simulation are also taken as the initial condition of 3D simulation for faster convergence. 4.2. Computational grids and boundary conditions for cases with roughness Roughness element with the diameter of D = 3 mm and the height of k = 1.6 mm (k/d = 1.23, which is ‘‘effective”3) is chosen to explore the characteristic of transition progress induced by single roughness element. Fig. 13 shows the overall grid and the near-field grid around a cylindrical roughness element. Computation domain in streamwise is x = [40, 300] mm, in normal direction y = [0, 6.5] mm, and in spanwise direction is z = [50, 50] mm. Grid refinement is performed near the wall surface with a minimum grid spacing of 0.01 mm. The total number of grid cells is 26730000, divided into 185 blocks for parallel calculations. The initial conditions are interpolated from the two-dimensional numerical simulation results. The wall surface is taken as an isothermal and non-slip condition at the temperature of Tw = 300 K. The outlet condition is extrapolated from the inner domain and treated as a buffer layer. The boundary conditions of two sides are set to be periodic.
Fig. 11 Oil-film interferometry patterns on flat plate without roughness element.
Fig. 13 Overall grid and near-field grid around cylindrical roughness element.
4.3. Effect of single roughness element Fig. 14 shows the comparison of Cf on the centerline behind the roughness element between DNS and experimental results. Also displayed in this figure are the results obtained by twodimensional simulation. As is shown, the DNS result is comparable with the laminar result at about x = [30, 40] mm, and then drops to a quite low level due to the effect of the stagnation flow in front of the roughness element. Behind the roughness element, the Cf value is increased with streamwise distance at x = [55, 65] mm, and then keeps constant at x = [65, 100] mm, which is comparable with the laminar results. At the location of x = [100, 137] mm, the Cf value grows gradually and reaches a peak value of 0.0064 at x = 137 mm. Boundary layer transition occurs in this region. After the peak, the Cf value decreases gradually and finally approaches the turbulent results. In addition, the oil-film interferometry experimental results agree well with the numerical simulation at x = [55, 120] mm. Overall, the numerical simulation over predicts the Cf value. This phenomenon is similar to that of Bartkowicz’s22 and Duan’s11 results.
Numerical and experimental investigation into hypersonic boundary layer transition induced by roughness elements
Fig. 14 Comparison of Cf on centerline behind roughness element between DNS and experimental results.
Fig. 15 presents the distribution of the computed density gradient on the z = 0 mm plane for the single element case. On top of the roughness element, bow-shock and expansion shock are observed obviously. Behind the roughness element, a stable shear layer along the streamwise is observed at about x = [55, 80] mm. At the range of x = [80, 110] mm, the instability occurs in the shear layer and some regular structures are formed, which could be the ring-vortex structures in threedimensional space. At the location of x = 110 mm, the secondary instability occurs near the wall within the boundary, which formed another regular structure. As shown in Fig. 14, the Cf value increases rapidly from this position. In addition, the growth, evolution, and distortion of unstable structures occur near the wall at the range of x = [110, 160] mm. The near-wall instability leads the high value of Cf at x = 137 mm. This observation may indicate that the formation of the near-wall unstable structure is the key factor of the transition behind the roughness element. After x > 160 mm, the shear layer structure and near-wall unstable structure interact and blend with each other, resulting in the full turbulence in this range. The distribution of statistical average Cf on y = 0 mm plane computed by DNS is presented in Fig. 16(a) and measured by oil-film interferometry technique is depicted in Fig. 16(b). As shown in Fig. 16(a), the affected region by the roughness element can be divided into two zones at about x = 100 mm. Before x = 100 mm, there are two high Cf value regions in the wake of the roughness element: the upper region (A) and the lower region (B) of the symmetry plane. In the centerline, the Cf value is small at the range of x = [65, 100] mm.
Fig. 15
Distribution of density gradient on z = 0 mm plane.
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After x = 110 mm, the Cf value at regions of A and B decreases, and another high Cf value region (C) emerges at the range of x = [110, 160] mm, which is located in the centerline. At the downstream behind x = 160 mm, the affected region becomes broader, and the distribution of Cf in spanwise becomes more uniform. The oil-film interferometry presents the similar results of the simulation as shown in Fig. 16(b). At the range of x = [60, 90] mm, the oil-film fringe in the upper (regions 1 and 2) and the lower regions is evident, which indicates high Cf value in these regions. At x > 90 mm, the fringe patterns become straight gradually (region 3) and the spacing in the centerline grows slightly (the experimental Cf value in the centerline is shown in Fig. 14). The coherent structures predicted by DNS around and in the wake of the roughness element are presented in Fig. 17. Around the roughness element, several stable horseshoe vortices are observed. At the same time, a strong shear layer right behind the roughness element is formed and it develops to the hairpin vortex structures in the wake. After x = 110 mm, the hairpin vortices break down into many small-scale structures and interact with horseshoe vortices. This phenomenon can be used to explain the appearance of near-wall structure as shown in Fig. 15. In the further downstream of the roughness element, the flow structures become smaller and smaller. This indicates that the interaction between the horseshoe vortices and the shear layer becomes stronger and the flow almost becomes turbulent in the spanwise direction. 4.4. Effect of space between two roughness elements In this section, the effect of the spacing between two roughness elements is investigated numerically. The roughness element taken in this simulation is the same as the previous case. The spacing Z between two roughness elements are set to be 3 mm and 6 mm, which represent to the cases of Z/D = 1 and Z/D = 2 respectively.
Fig. 16 results.
Comparison of simulation results and experimental
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Fig. 17 Coherent structures around and in the wake of roughness element.
Fig. 18 shows the distribution of the skin friction coefficient on the centerline of roughness elements for the cases of Z/ D = 1 and Z/D = 2. Near the position of x = 50 mm, the Cf distributions of these two cases are similar except the slight overstep of the Cf value for the case of Z/D = 2. Behind x = 50 mm, the Cf value grows in both cases, while the growth rate of Z/D = 2 is much higher than that of Z/D = 1. For the case of Z/D = 1, the Cf value reaches its peak value of 0.0017 at about x = 130 mm. This peak value is lower than that of the turbulent case as shown in Fig. 14. After x > 130 mm, the Cf value starts to decrease, which indicates that no transition occurs in this region. For the case of Z/D = 2, the Cf value reaches it speak value of 0.00285 at almost the same position of the case of Z/D = 1and decreases at the downstream, indicating the occurrence of the transition. Fig. 19 shows the distribution of the computed density gradient on the centerline plane behind each element for the cases of Z/D = 1 and Z/D = 2 are shown in. For both cases, the shear layer behind the roughness elements is observed clearly, which is stable at x = [50,130] mm. For the case of Z/D = 2 (Fig. 19(b)), the near-wall instability occurs at about x = 90 mm, but the intensity is lower than single element case and no regular structures are formed near wall until x = 180 mm. After x > 180 mm, slight fluctuations occur at both shear layer and near-wall unstable structure. However, for the case of Z/D = 1 (Fig. 19(a)), the shear layer keeps stable in the whole symmetry plane.
Fig. 18 Distribution of the computed Cf on the centerline for double roughness elements.
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Fig. 19 plane.
Comparison of density gradient magnitude on symmetry
Fig. 20 presents the Cf distribution on the y = 0 mm plane around and in the wake of the roughness elements for the cases of Z/D = 1 and Z/D = 2. In the range of x = [0, 50] mm, the distribution of Cf for the case of Z/D = 1 is uniform in the spanwise direction, and the arched contours before each roughness element combine to wave-shaped curve, which indicates the existence of interactions between each roughness element. In contrast to the case of Z/D = 1, the distribution of Cf for the case of Z/D = 2 is similar to the isolated roughness element mentioned above: Each roughness element is relatively independent and the interactions between two adjacent roughness elements are minor. Around the roughness elements, the characteristics of Cf on the side of roughness element are distinct between two cases as shown in Fig. 20. For the case of Z/D = 1, a break occurs in the high Cf value region, while for the case of Z/D = 2, the region shows continuity. The results of Z/D = 2 are comparable to the single roughness element (Fig. 16(a)). For the case of Z/D = 2, two high Cf regions on the upper and lower sides of each roughness element emerge at about x = [60,100] mm, and then merge gradually into one region in the centerline at about x = 110 mm. However, this kind of merging does not occur in the case of Z/D = 1. These results reveal that the shorter
Fig. 20 Comparison of Cf distribution on y = 0 mm plane around and in the wake of roughness elements.
Numerical and experimental investigation into hypersonic boundary layer transition induced by roughness elements spacing between roughness elements will suppress the evolution of horseshoe vortices and trigger the instability of shear layer at the downstream, leading to the suppression of the transition. 5. Conclusions (1) In this work, the Direct Numerical Simulation (DNS) method is used to study the flow structure and the OilFilm Interferometry (OFI) technique is utilized for characterizing the skin friction coefficient. A quantitative comparison is made between computations and measurements. The numerical simulation results agree well with experimental data. (2) For single roughness, the DNS results show that both horseshoe vortices around the roughness element and hairpin vortices behind the roughness element caused by shear layer instability can affect the boundary layer instability. The generation of the near-wall unstable structure is the key point of boundary layer transition behind the roughness. (3) At the downstream of the roughness element, the interaction between multiple vortices will spread in the spanwise direction. For distributed roughness elements, the higher spacing between two roughness elements is more effective in inducing transition than the lower one. (4) The interaction between two adjacent roughness elements can suppress the evolution of the downstream horseshoe vortices and trigger the instability of shear layer. As a result, the transition will be suppressed at the downstream.
Acknowledgements The authors would like to thank the China Scholarship Council (CSC), the Aeronautics Science Foundation of China (No. 20163252037), the China Postdoctoral Science Foundation (No. 2017M610325), the Natural Science Foundation of Jiangsu Province of China (No. BK20170771), and the Fundamental Research Funds for the Central Universities of China (No. NP2017202) for their support.
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