Lian Duan

Direct numerical simulation of hypersonic turbulent boundary layers. Part 3. Effect of Mach number

In this paper, we perform direct numerical simulations (DNS) of turbulent boundary layers with nominal free-stream Mach number ranging from 0.3 to 12. The main objective is to assess the scalings with respect to the mean and turbulence behaviours as well as the possible breakdown of the weak compressibility hypothesis for turbulent boundary layers at high Mach numbers ( M > 5). We find that many of the scaling relations, such as the van Driest transformation for mean velocity, Walzs relation, Morkovins scaling and the strong Reynolds analogy, which are derived based on the weak compressibility hypothesis, remain valid for the range of free-stream Mach numbers considered. The explicit dilatation terms such as pressure dilatation and dilatational dissipation remain small for the present Mach number range, and the pressure–strain correlation and the anisotropy of the Reynolds stress tensor are insensitive to the free-stream Mach number. The possible effects of intrinsic compressibility are reflected by the increase in the fluctuations of thermodynamic quantities ( p ′ rms / p w , ρ′ rms / ρ , T ′ rms / T ) and turbulence Mach numbers ( M t , M ′ rms ), the existence of shocklets, the modification of turbulence structures (near-wall streaks and large-scale motions) and the variation in the onset of intermittency.

Direct numerical simulation of hypersonic turbulent boundary layers . Part 2 . Effect of wall temperature

In this paper, we perform direct numerical simulation (DNS) of turbulent boundary layers at Mach 5 with the ratio of wall-to-edge temperature T w / T δ from 1.0 to 5.4 (Cases M5T1 to M5T5). The influence of wall cooling on Morkovins scaling, Walzs equation, the standard and modified strong Reynolds analogies, turbulent kinetic energy budgets, compressibility effects and near-wall coherent structures is assessed. We find that many of the scaling relations used to express adiabatic compressible boundary-layer statistics in terms of incompressible boundary layers also hold for non-adiabatic cases. Compressibility effects are enhanced by wall cooling but remain insignificant, and the turbulence dissipation remains primarily solenoidal. Moreover, the variation of near-wall streaks, iso-surface of the swirl strength and hairpin packets with wall temperature demonstrates that cooling the wall increases the coherency of turbulent structures. We present the mechanism by which wall cooling enhances the coherence of turbulence structures, and we provide an explanation of why this mechanism does not represent an exception to the weakly compressible hypothesis.

Direct Detection of NO Produced by High-Temperature Surface-Catalyzed Atom Recombination

The surface-catalytic recombination of oxygen and nitrogen atoms to form nitric oxide was confirmed by the direct detection of product NO molecules, using single-photon laser-induced fluorescence spectroscopy. Experiments were performed from room temperature to 1200 K in a quartz diffusion-tube sidearm reactor enclosed in a high-temperature tube furnace. Atomic nitrogen was generated using a microwave discharge, and atomic oxygen was produced via the rapid gas-phase titration reaction N + NO → O + N 2 . The use of isotopically labeled titration gases 15 N 16 O and 15 N 18 O allowed for the unambiguous identification of nitric oxide produced by the O + N surface reaction. The absolute number densities of surface-produced NO were determined from separate calibration experiments using 14 N 16 O. Observed variations of the NO number density with temperature and varying O/N atomic ratios at the sidearm entrance are generally consistent with the predictions of a simple reaction-diffusion model of the sidearm reactor that includes surface-catalyzed NO production as a species boundary condition.

Procedure to Validate Direct Numerical Simulations of Wall- Bounded Turbulence Including Finite-Rate Reactions

procedure to test the validity of the simulations by dividing the whole problem into differentcomponents andtesting each component separately. Namely, comparisons against similarity solutions and other established hypersonic boundary-layer solutions are used to test the validity of laminar mean flow with and without gas-phase chemical reactions; comparisons against the analytic solution for the one-dimensional diffusion equation are used to test the validity of the surface catalysis boundary condition; and comparisons against empirical predictions, detailed experimental data and linear stability theory are used to test the validity of turbulent boundary-layer solutions.

Assessment of Turbulence-Chemistry Interaction in Hypersonic Turbulent Boundary Layers

Cp = heat capacity at constant pressure, J= K kg Cv = heat capacity at constant volume, J= K kg c = concentration, mol=m E = total energy, J=m H = shape factor, = , dimensionless h = specific enthalpy, J=kg h = heat of formation, J=kg J = diffusive mass flux, kg=m s Keq = equilibrium constant k = reaction rate coefficient Le = Lewis number, dimensionless M = Mach number, dimensionless ns = total number of species, dimensionless p = pressure, P s s R=Ms T, Pa q = turbulent kinetic energy, u02 v02 w02 =2, m=s qj = heat flux, @T=@xj , J= m s Re = Reynolds number, u = , dimensionless Re 2 = Reynolds number, u = w, dimensionless Re = Reynolds number, wu = w, dimensionless Sij = strain rate tensor, 1 2 @ui=@xj @uj=@xi , s 1 T = temperature, K Ta = activation temperature Tr = recovery temperature, T 1 0:9 1 =2 M , K u = friction velocity, m=s W = molecular weight, kg=mol w = chemical production rate, kg=m s Y = species mass fraction, dimensionless = specific heat ratio, Cp=Cv, dimensionless = boundary-layer thickness, mm = displacement thickness, mm = momentum thickness, mm = mixture thermal conductivity, J= K m s = mixture viscosity, kg= m s = stoichiometric coefficient, dimensionless = density, kg=m ij = shear stress tensor, 2 Sij 23 ijSkk, Pa

Numerical Study of Pressure Fluctuations due to a Mach 6 Turbulent Boundary Layer

Direct numerical simulations (DNS) are used to examine the pressure fluctuations generated by a Mach 6 turbulent boundary layer with nominal freestream Mach number of 6 and Reynolds number of Re? ≈ 464. The emphasis is on comparing the primarily vortical pressure signal at the wall with the acoustic freestream signal under higher Mach number conditions. Moreover, the Mach-number dependence of pressure signals is demonstrated by comparing the current results with those of a supersonic boundary layer at Mach 2.5 and Re? ≈ 510. It is found that the freestream pressure intensity exhibits a strong Mach number dependence, irrespective of whether it is normalized by the mean wall shear stress or by the mean pressure, with the normalized fluctuation amplitude being significantly larger for the Mach 6 case. Spectral analysis shows that both the wall and freestream pressure fluctuations of the Mach 6 boundary layer have enhanced energy content at high frequencies, with the peak of the premultiplied frequency spectrum of freestream pressure fluctuations being at a frequency of !±/U1 ≈ 3.1, which is more than twice the corresponding frequency in the Mach 2.5 case. The space-time correlations indicate that the pressure-carrying eddies for the higher Mach number case are of smaller size, less elongated in the spanwise direction, and convect with higher convection speeds relative to the Mach 2.5 case. The demonstrated Mach-number dependence of the pressure field, including radiation intensity, directionality, and convection speed, is consistent with the trend exhibited in experimental data and can be qualitatively explained by the notion of ‘eddy Mach wave’ radiation.

Study of Emission Turbulence-Radiation Interaction in Hypersonic Boundary Layers

Direct numerical simulations are conducted to study the effects of emission turbulence-radiation interaction in hypersonic turbulent boundary layers, representative of the Orion Crew Exploration Vehicle at peak-heating condition during reentry. A nondimensional governing parameter to measure the significance of emission turbulence-radiation interaction is proposed, and the direct numerical simulation fields with and without emission coupling are used to assess emission turbulence-radiation interaction. Both the uncoupled and coupled results show that there is no sizable interaction between turbulence and emission at the hypersonic environment under investigation. An explanation of why the intensity of emission turbulence-radiation interaction in the hypersonic boundary layer is smaller than that in many combustion flows is provided.

Direct Numerical Simulation of Transition in a Swept-Wing Boundary Layer

Direct numerical simulation (DNS) is performed to examine laminar to turbulent transition due to high-frequency secondary instability of stationary crossflow vortices in a subsonic swept-wing boundary layer for a realistic natural-laminar-flow airfoil configuration. The secondary instability is introduced via inflow forcing derived from a two-dimensional, partial-differential-equation based eigenvalue computation; and the mode selected for forcing corresponds to the most amplified secondary instability mode which, in this case, derives a majority of its growth from energy production mechanisms associated with the wall-normal shear of the stationary basic state. Both the growth of the secondary instability wave and the resulting onset of laminar-turbulent transition are captured within the DNS computations. The growth of the secondary instability wave in the DNS solution compares well with linear secondary instability theory when the amplitude is small; the linear growth is followed by a region of reduced growth resulting from nonlinear effects before an explosive onset of laminar breakdown to turbulence. The peak fluctuations are concentrated near the boundary layer edge during the initial stage of transition, but rapidly propagates towards the surface during the process of laminar breakdown. Both time-averaged statistics and flow visualization based on the DNS reveal a sawtooth transition pattern that is analogous to previously documented surface flow visualizations of transition due to stationary crossflow instability. The memory of the stationary crossflow vortex is found to persist through the transition zone and well beyond the location of the maximum skin friction.

Towards Bridging the Gaps in Holistic Transition Prediction via Numerical Simulations

The economic and environmental benefits of laminar flow technology via reduced fuel burn of subsonic and supersonic aircraft cannot be realized without minimizing the uncertainty in drag prediction in general and transition prediction in particular. Transition research under NASAs Aeronautical Sciences Project seeks to develop a validated set of variable fidelity prediction tools with known strengths and limitations, so as to enable sufficiently accurate transition prediction and practical transition control for future vehicle concepts. This paper provides a summary of selected research activities targeting the current gaps in high-fidelity transition prediction, specifically those related to the receptivity and laminar breakdown phases of crossflow induced transition in a subsonic swept-wing boundary layer. The results of direct numerical simulations are used to obtain an enhanced understanding of the laminar breakdown region as well as to validate reduced order prediction methods.

Effects of Riblets on Skin Friction and Heat Transfer in High-Speed Turbulent Boundary Layers

Direct numerical simulations of spatially developing turbulent boundary layers over riblets are conducted to examine the effects of riblets on skin friction and heat transfer at high speeds. Zero-pressure gradient boundary layers under two flow conditions (Mach 2.5 with Tw/Tr = 1 and Mach 7.2 with Tw/Tr = 0.5) are considered. Simulations are conducted for boundary-layer flows over a clean surface and symmetric V-groove riblets. The DNS results at Mach 2.5 confirm the few existing experimental observations and show that a drag reduction of approximately 7% can be achieved for riblets with proper spacing. The comparisons in turbulence statistics and flow visualizations between a drag-reducing configuration (s + � 20) and a drag-increasing configuration (s + � 40) demonstrate that drag reduction mechanisms proposed for incompressible flows can still apply for highspeed boundary layers. DNS studies at Mach 7.2 further show that riblets remain effective in reducing drag in the hypersonic regime. The Reynolds analogy holds with 2Cf/Ch approximately equal to that of flat plates for the drag-reducing configuration.