“…swept airfoil experiments of Radeztsky et al 5 are shown (black diamond symbols) in Figure 3. The effect of surface roughness on transition momentum thickness Reynolds number is very evident from the Highly Polished (h = 0.25 μm), Polished (h=0.5 μm) and Painted (h = 3.3 μm) data at various Reynolds numbers.…”
Section: New Empirical Correlation For Stationary Crossflow Transmentioning
confidence: 98%
“…For low freestream turbulence environments, experiments show that stationary crossflow modes are the main crossflow instability mechanisms on swept airfoils 4,5 . Stationary crossflow transition is strongly influenced by the surface roughness as shown in Fig.…”
Section: Introductionmentioning
confidence: 99%
“…Stationary CrossFlow (SCF) instability N-factor with surface roughness level based on NLF(2)-0415 airfoil experiments of Radeztsky et al5 .Figure reproducedwith permission from Ref [4]…”
The correlation-based γ-Re θt transition model has been extended to include crossflow transition effects. This paper will detail a new empirical correlation for stationary crossflow transition based strictly on local flow quantities and the implementation into the γ-Re θt model. This new correlation for crossflow is based on the well known 45° swept NLF(2)-0415 airfoil experiment including surface roughness effects. Linear-stability predictions were also used to augment the new correlation to account for variations in the sweep angle and crossflow strength. The improved transition model has shown encouraging results for transitional flows dominated by crossflow and a number of validation test cases will be shown in this paper. Most importantly, the model maintains its compatibility and ease of implementation with modern CFD techniques such as unstructured grids and massively parallel execution. There is a strong potential that this improved transtion model will allow the 1 st order effects of transition, including crossflow, to be included in everyday industrial CFD simulations.
NomenclatureAoA = Angle of attach (deg.) C f = skin friction coefficient, τ/(0.5ρU ref 2 ) dU/ds = acceleration along the streamline direction FSTI = freestream turbulence intensity (percent), 100(2k/3) 1/2 /U ref h rms = Surface roughness height (rms) k = turbulent kinetic energy Re x = Reynolds number, ρLU ref /μ Re θ = momentum thickness Reynolds number, ρθU 0 /μ Re θt = transition onset momentum thickness Reynolds number (based on freestream conditions), ρθ t U 0 /μ t e R = local transition onset momentum thickness Reynolds number (obtained from a transport equation) R T = viscosity ratio R y = wall-distance based turbulent Reynolds number R v = vorticity Reynolds number S = absolute value of strain rate, (2S ij S ij ) 1/2 S ij = strain rate tensor, 0.5(∂u i /∂x j + ∂u j /∂x i ) Tu = turbulence intensity, 100(2k/3) 1/2 /U U = local velocity U o = local freestream velocity U ref = inlet reference velocity = unit velocity vector u' = local fluctuating streamwise velocity x/C = axial distance over axial chord 1 Senior Engineer, Flight Sciences, Boeing Commercial Airplanes -Seattle, WA, USA, and AIAA member.2 y = distance to nearest wall y + = distance in wall coordinates, ρyμ τ /μ δ = boundary layer thickness θ = momentum thickness λ θ = pressure gradient parameter, (ρθ 2 /μ)(dU/ds) μ = molecular viscosity μ t = eddy viscosity ρ = density τ = wall shear stress Ω = absolute value of vorticity, (2Ω ij Ω ij ) 1/2 Ω ij = vorticity tensor, 0.5(∂u i /∂x j -∂u j /∂x i ) = vorticity vector, = specific turbulence dissipation rate Subscripts t = transition onset s = streamline
“…swept airfoil experiments of Radeztsky et al 5 are shown (black diamond symbols) in Figure 3. The effect of surface roughness on transition momentum thickness Reynolds number is very evident from the Highly Polished (h = 0.25 μm), Polished (h=0.5 μm) and Painted (h = 3.3 μm) data at various Reynolds numbers.…”
Section: New Empirical Correlation For Stationary Crossflow Transmentioning
confidence: 98%
“…For low freestream turbulence environments, experiments show that stationary crossflow modes are the main crossflow instability mechanisms on swept airfoils 4,5 . Stationary crossflow transition is strongly influenced by the surface roughness as shown in Fig.…”
Section: Introductionmentioning
confidence: 99%
“…Stationary CrossFlow (SCF) instability N-factor with surface roughness level based on NLF(2)-0415 airfoil experiments of Radeztsky et al5 .Figure reproducedwith permission from Ref [4]…”
The correlation-based γ-Re θt transition model has been extended to include crossflow transition effects. This paper will detail a new empirical correlation for stationary crossflow transition based strictly on local flow quantities and the implementation into the γ-Re θt model. This new correlation for crossflow is based on the well known 45° swept NLF(2)-0415 airfoil experiment including surface roughness effects. Linear-stability predictions were also used to augment the new correlation to account for variations in the sweep angle and crossflow strength. The improved transition model has shown encouraging results for transitional flows dominated by crossflow and a number of validation test cases will be shown in this paper. Most importantly, the model maintains its compatibility and ease of implementation with modern CFD techniques such as unstructured grids and massively parallel execution. There is a strong potential that this improved transtion model will allow the 1 st order effects of transition, including crossflow, to be included in everyday industrial CFD simulations.
NomenclatureAoA = Angle of attach (deg.) C f = skin friction coefficient, τ/(0.5ρU ref 2 ) dU/ds = acceleration along the streamline direction FSTI = freestream turbulence intensity (percent), 100(2k/3) 1/2 /U ref h rms = Surface roughness height (rms) k = turbulent kinetic energy Re x = Reynolds number, ρLU ref /μ Re θ = momentum thickness Reynolds number, ρθU 0 /μ Re θt = transition onset momentum thickness Reynolds number (based on freestream conditions), ρθ t U 0 /μ t e R = local transition onset momentum thickness Reynolds number (obtained from a transport equation) R T = viscosity ratio R y = wall-distance based turbulent Reynolds number R v = vorticity Reynolds number S = absolute value of strain rate, (2S ij S ij ) 1/2 S ij = strain rate tensor, 0.5(∂u i /∂x j + ∂u j /∂x i ) Tu = turbulence intensity, 100(2k/3) 1/2 /U U = local velocity U o = local freestream velocity U ref = inlet reference velocity = unit velocity vector u' = local fluctuating streamwise velocity x/C = axial distance over axial chord 1 Senior Engineer, Flight Sciences, Boeing Commercial Airplanes -Seattle, WA, USA, and AIAA member.2 y = distance to nearest wall y + = distance in wall coordinates, ρyμ τ /μ δ = boundary layer thickness θ = momentum thickness λ θ = pressure gradient parameter, (ρθ 2 /μ)(dU/ds) μ = molecular viscosity μ t = eddy viscosity ρ = density τ = wall shear stress Ω = absolute value of vorticity, (2Ω ij Ω ij ) 1/2 Ω ij = vorticity tensor, 0.5(∂u i /∂x j -∂u j /∂x i ) = vorticity vector, = specific turbulence dissipation rate Subscripts t = transition onset s = streamline
“…These properties are still valid for supersonic flows but there are extended to the generalized inflexion point (GIP) defined as the value of z where the quantity micron-sized roughness elements (i.e. surface polishing) at the location where the vortices start to be amplified [17], typically between 1% and 5% chord on a swept wing. It follows that improving surface polishing of the leading edge decreases the initial amplitude of the vortices and delays transition.…”
“…For Case 1, the amplitudes of both modes are around 2% of U ∞ , while the amplitude of the mode in Case 2 is roughly 6% of U ∞ . Typically, in stationary crossflow dominated flows, stationary crossflow amplitudes are nearly 10-20% of U ∞ at transition [14][15][16] . The dynamic hotwire data were investigated further to determine the cause of the seemingly early transition.…”
Experimental evidence indicates the presence of a triad resonance interaction between traveling crossflow modes in a swept wing flow. Results indicate that this interaction occurs when the stationary and traveling crossflow modes have similar and relatively low amplitudes (~1% to 6% of the total freestream velocity). The resonant interaction occurs at instability amplitudes well below those typically known to cause transition, yet transition is observed to occur just downstream of the resonance. In each case, two primary linearly unstable traveling crossflow modes are nonlinearly coupled to a higher frequency linearly stable mode at the sum of their frequencies. The higher-frequency mode is linearly stable and presumed to exist as a consequence of the interaction of the two primary modes. Autoand cross-bicoherence are used to determine the extent of phase-matching between the modes, and wavenumber matching confirms the triad resonant nature of the interaction.
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