Ross Wagnild

Mach 10 Boundary Layer Transition Experiments on Sharp and Blunted Cones (Invited)

Boundary-layer transition and stability data were obtained at Mach 10 in the Arnold Engineering Development Complex (AEDC) Hypervelocity Wind Tunnel 9 on a 1.5-m long, 7-deg cone at unit Reynolds numbers between 1.8 and 31 million per meter. A total of 24 runs were performed at angles-of-attack between 0 and 10-deg on sharp and blunted cones with nose radii between 5.1 and 50.8-mm. The transition location was determined with coaxial thermocouples and temperature sensitive paint while stability measurements were obtained using high-frequency response pressure sensors. Mean flow and boundary layer-stability computations were also conducted and compared with the experiment. The effect of angle-of-attack and bluntness on the transition location displays similar trends compared to historical hypersonic wind tunnel data at similar Mach and Reynolds numbers. The N factor at start of transition on sharp cones increases with unit Reynolds number. Values between 4 and 7 were observed. The N factor at start of transition significantly decreases as bluntness increases and is successfully correlated with the ratio of transition location to entropy layer swallowing length. Good agreement between the computed and measured spatial amplification rates and most amplified 2 mode frequencies are obtained for sharp and moderately blunted cones. For large bluntness, where the ratio of transition to entropy swallowing length is below 0.1, 2 mode waves were not observed before the start of transition on the frustum.

Transition delay in hypervelocity boundary layers by means of CO 2 /acoustic instability interactions

A novel method to delay transition in hypervelocity flows over slender bodies by injecting CO2 into the boundary layer of interest is investigated. The results presented here consist of both experimental and computational data. The experimental data was obtained at Caltech’s T5 reflected shock tunnel, while the computational data was obtained at the University of Minnesota. The experimental model was a 5 degree sharp cone, chosen because of its relevance to axisymmetric hypersonic vehicle designs and the wealth of experimental and numerical data available for this geometry. The model was instrumented with thermocouples, providing heat transfer measurements from which transition locations were determined and the efficacy of adding CO2 in delaying transition was gauged. For CO2/N2 freestream blends without injection, the transition Reynolds number more than doubled for mixtures with 40% CO2 mole fraction compared to the case of 100% N2. For the cases with injection, shadowgraph visualizations were obtained, allowing verification of the injection timing. The computations provide encouraging results that for the injection schemes proposed CO2 is reaching high enough temperatures to excite vibrational modes and thus delay transition.

Carbon Dioxide Injection for Hypervelocity Boundary Layer Stability

An approach for introducing carbon dioxide as a means of stabilizing a hypervelocity boundary layer over a slender bodied vehicle is investigated through the use of numerical simulations. In the current study, two different test bodies are examined. The first is a fivedegree-half-angle cone currently under research at the GALCIT T5 Shock Tunnel with a 4 cm porous wall insert used to transpire gas into the boundary layer. The second test body is a similar cone with a porous wall over a majority of cone surface. Computationally, the transpiration is performed using an axi-symmetric flow simulation with wall-normal blowing. The effect of the injection and the transition location are gauged by solving the parabolized stability equations and using the semi-empirical e N method. The results show transition due to the injection for the first test body and a delay in the transition location for the second test body as compared to a cone without injection under the same flight conditions. The mechanism for the stabilizing effect of carbon dioxide is also explored through selectively applying non-equilibrium processes to the stability analysis. The results show that vibrational non-equilibrium plays a role in reducing disturbance amplification; however, other factors also contribute.

Transition within a hypervelocity boundary layer on a 5-degree half-angle cone in air/CO2 mixtures

Laminar to turbulent transition on a smooth 5-degree half angle cone at zero angle of attack is investigated computationally and experimentally in hypervelocity flows of air, carbon dioxide, and a mixture of 50% air and carbon dioxide by mass. Transition N factors above 10 are observed for air flows. At comparable reservoir enthalpy and pressure, flows containing carbon dioxide are found to transition up to 30% further downstream on the cone than flows in pure air in terms of x-displacement, and up to 38% and 140%, respectively, in terms of the Reynolds numbers calculated at edge and reference conditions.

Simultaneous Pressure Measurements and High-Speed Schlieren Imaging of Disturbances in a Transitional Hypersonic Boundary Layer.

High-frequency pressure sensors were used in conjunction with a high-speed schlieren system to study the growth and breakdown of boundary-layer disturbances into turbulent spots on a 7◦ cone in the Sandia Hypersonic Wind Tunnel. At Mach 5, intermittent low-frequency disturbances were observed in the schlieren videos. High-frequency secondmode wave packets would develop within these low-frequency disturbances and break down into isolated turbulent spots surrounded by an otherwise smooth, laminar boundary layer. Spanwise pressure measurements showed that these packets have a narrow spanwise extent before they break down. The resulting turbulent fluctuations still had a streaky structure reminiscent of the wave packets. At Mach 8, the boundary layer was dominated by secondmode instabilities that extended much further in the spanwise direction before breaking down into regions of turbulence. The amplitude of the turbulent pressure fluctuations was much lower than those within the second-mode waves. These turbulent patches were surrounded by waves as opposed to the smooth laminar flow seen at Mach 5. At Mach 14, second-mode instability wave packets were also observed. Theses waves had a much lower frequency and larger spanwise extent compared to lower Mach numbers. Only low freestream Reynolds numbers could be obtained, so these waves did not break down into turbulence.

Vibrational relaxation effects on acoustic disturbances in a hypersonic boundary layer over a cone

The effect of adding a vibrational mode to gas in hypersonic flow over a cone is studied through the use of direct numerical simulations (DNS) and stability analyses using the linear parabolized stability equations (PSE). A brief review of linear acoustic theory demonstrates the importance of energy capacity and energy transfer rate on a gas’s ability to damp acoustic waves. After validating the computational fluid dynamics (CFD) solver for acoustic wave simulations, acoustic disturbances are introduced into a Mach 12 flow around a 7 half-angle, sharp-nosed cone. Results show good agreement between DNS and PSE on the predicted wall pressure disturbance amplification. The effects of acoustic damping are investigated, however, results for the current freestream conditions show that the vibrational temperature disturbance is largely driven by the mean flow, rather than acoustic damping effects. The current simulations are made possible using a recently developed low dissipation flux scheme for the finite volume method.

Computational Verification of Acoustic Damping in High-Enthalpy Environments

T HE motivation for studying acoustic propagation in highenthalpy environments lies partially in the role that acoustics play in promoting laminar–turbulent boundary-layer transition. At high speeds, boundary-layer transition on slender-body vehicles is primarily due to Mack’s second-mode instability [1]. These secondmode disturbances are associated with acoustic waves that become trapped in the boundary layer flowing over the vehicle. Thus, the interaction of an acoustic wave with the boundary layer can either promote or inhibit the growth of second-mode disturbances [2–5]. If the growth of disturbances is sufficiently reduced, then laminar– turbulent boundary-layer transition could be delayed or prevented. In many cases, maintaining laminar flow over a high-speed vehicle is beneficial because a laminar boundary layer exerts significantly less heating and shear forces on the vehicle than a turbulent boundary layer.Accurately capturing the physics of transitionwould allow for a more precise prediction of the transition location. Less uncertainty in the transition location would then allow for optimization of thermal protection systems and design of high-speed vehicles. Thus, it is important to understand the interaction of an acoustic wave with a high-enthalpy flow environment. It has long been postulated that internal molecular relaxation processes can damp acoustic waves. Griffith [6] stated that Jeans [7] first proposed the idea of a lagging internal energy mode due to changes in the gas state. The first experimental evidence of acoustic damping was shown by Pierce [8], who studied the speed of highfrequency sound through various gases. The theoretical modeling of the acoustic damping and dispersion process due to molecular vibration was first formulated a few years later by Herzfeld and Rice [9]. Lighthill [10] performed an analysis similar to Herzfeld and Rice [9], showing the dependency of acoustic damping on the bulk viscosity response of a gas. Vincenti and Kruger [11] also analyzed several aspects of a single internal energy mode on acoustic waves propagating through a gas in equilibrium and found the damping to be greatest when the frequency of sound is near the relaxation rate of the internal mode. Clarke and McChesney [12] performed a similar analysis of the acoustic response to a single chemical reaction. Fujii and Hornung [2,13,14] were able to improve on the modeling of acoustic damping by including several relaxation modes. In doing this, they were able tomodel realisticmixtures of gases in equilibrium. Fujii and Hornung found that various gases had similar damping properties at different equilibrium states and frequencies, meaning that all of thesegases tested couldbe used in acoustic damping applications. A sample plot of Fujii and Hornung’s work is included in Fig. 1a and shows the variation in damping properties based on the temperature range and frequency. Fujii and Hornung showed that the results of the boundary-layer stability calculations by Johnson et al. [15] were due to carbon dioxide’s ability to damp the acoustic frequencies associated with second-mode transition. As demonstrated in Fig. 1b, carbon dioxide proves to be very effective at the temperatures and pressures considered in the experiment and computation. For the current study, we seek to verify our computational solver against an extension of the acoustic damping theory given by Fujii and Hornung [2,13,14] as well as investigate the various features of acoustic waves propagating through high-temperature gases. First, we highlight the generic formula to calculate the optimum damping frequency for an internal molecular process. Next, we introduce the dispersion relation for an acousticwave traveling through a gaswith a mean flow velocity. Based on this dispersion relation, we determine the variation of the optimum damping frequency with the mean flow Mach number. We then use a computational fluid dynamics (CFD) solver to simulate the propagation of slow and fast acoustic waves through carbon dioxide. We compare the acoustic damping rate as calculated from the simulation to the damping rate based on theory. We end with a brief investigation of the physical differences between the disturbance quantities of fast acoustic waves and those of slow acoustic waves.

Compilation and Analysis of Second Mode Amplitudes on Sharp Cones in Hypersonic Wind Tunnels

This research effort coordinated by the NATO AVT-240 specialists’ group compiles and analyzes second-mode amplitudes on sharp slender cones at 0 degrees angle of attack. The analysis focuses on pressure fluctuations measured with piezoelectric sensors in 11 hypersonic wind tunnels operated by 9 organizations located in 3 NATO countries (Belgium, Germany, and USA) and Japan. The measurements are at freestream Mach numbers between 5 and 14, unit Reynolds numbers Re/m between 1.5 and 16 million per meter, and wall-to total temperature ratios between 0.1 and 0.8. The study shows that second-mode growth rates can be predicted with Parabolized Stability Equations (PSE) over the wide range of conditions. The maximum second-mode amplitudes vary weakly at edge Mach number Me greater than ~5.8, but significantly decrease at lower Me. The maximum N factor envelope from PSE and the measured amplitudes are used to estimate the initial amplitudes A0. At each Mach number, A0 varies approximately as Re/m^(-1). This leads to transition N factors that increase with Re/m. This behavior is consistent with the results from Marineau (AIAA Journal, Vol. 55, No. 2, 2017).

Code to code comparison on hypersonic high enthalpy transitional boundary layers

In the present study three boundary layer stability codes are compared based on hypersonic high enthalpy boundary layer flows around a 7° blunted cone. The code to code comparison is conducted between the following codes: the NOnLocal Transition analysis code (NOLOT) of the German Aerospace Center (DLR), the Stability and Transition Analysis for hypersonic Boundary Layers code (STABL) of University of Minnesota and the VKI Extensible Stability and Transition Analysis code (VESTA) of the von Karman Institute. The comparison focuses on the role of real gas effects on the second mode instability, in particular the disturbance frequency. The experimental test cases for the code to code comparison are provided by the DLR High Enthalpy Shock Tunnel Gottingen (HEG) and the JAXA High Enthalpy Shock tunnel (HIEST).

Direct numerical simulation of transient growth on a flat plate at Mach 3

The transient growth phenomenon in three dimensional shear flows has been shown to account for large disturbance growth in cases where traditional stability analyses show limited or no growth. For this reason, transient growth has been put forward as a potential cause of bypass transition. The purpose of the current study is to investigate the presence of non-linear eects as the energy of disturbances increases and their potential role in boundary layer transition on a flat plate in supersonic, compressible flow. An optimal disturbance solver based on linear theory was created and is validated against previously published data. The disturbances generated by this solver are input into a computational fluid dynamics (CFD) solver to model the disturbance evolution in three dimensions. The results from the CFD solver are compared with linear theory to ensure accuracy in the full three-dimensional simulations. Finally, the input energies are increased to investigate the eects of non-linear terms in the governing equations. Results show that a non-dimensional input energy of Ein = 3:024 10 3 is required for a departure from linear behavior for the mean flow conditions considered.