N

November 2014

NASA/TM–2014-218551 

Delay of Transition Using Forced Damping 

Reginald J. Exton 

Langley Research Center, Hampton, Virginia 
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 N

November 2014

NASA/TM–2014-218551 

Delay of Transition Using Forced Damping 

Reginald J. Exton 

Langley Research Center, Hampton, Virginia 
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757-5802 
 

 Delay of Transition Using Forced Damping 

 Reginald J. Exton 

 Advanced Measurements and Data Systems Branch 

 Research Directorate 

 N.A.S.A. Langley Research Center 

 Hampton, Virginia 23681-2199

 

Abstract: 

Several experiments which have reported a delay of transition are analyzed in terms of the 

frequencies of the induced disturbances generated by different flow control elements. Two of 

the experiments employed passive stabilizers in the boundary layer, one leading-edge 

bluntness, and one employed an active spark discharge in the boundary layer. It is found that 

the frequencies generated by the various elements lie in the damping region of the associated 

stability curve. It is concluded that the creation of strong disturbances in the damping region 

stabilizes the boundary-layer and delays the transition from laminar to turbulent flow. 

 

Symbols: 

St Strouhal number 

St Stanton number 

U velocity (in the boundary-layer) at the effective diameter of an isolated trip 

u velocity (in the boundary-layer) at the top of a corrugation 

s distance between corrugation peaks 

αi imaginary part of the disturbance wave number 

αr real part of the disturbance wave number 

b bluntness of leading-edge 

d effective diameter of isolated trip 

δ boundary-layer thickness 

δ* boundary-layer displacement thickness 

M Mach number 

Ro Free-Stream Unit Reynolds number 

Rc Cone Transition Reynolds number 

Rp Planar Transition Reynolds number 

Rδ* Reynolds number based on boundary-layer displacement thickness 

k trip height 

f dimensional frequency 

fC corrugation frequency 

fVS vortex shedding frequency 

F dimensionless frequency parameter 

1
Introduction: 

The design of aircraft is highly dependent on the dynamics of the fluid flow around the craft. 

For 100 years, it has been recognized that the flow in a thin boundary layer on the surface is 

critical to the efficient design of the aircraft. The flow in the boundary layer is initially laminar, 

but at some point transitions to a turbulent flow increasing the drag (and heat transfer) on the 

vehicle. As a result, research on methods to reduce the skin friction drag through laminar flow 

control is a major objective of aerodynamic research. The amplification of instabilities in the 

boundary layer is thought to be the dominant effect leading to turbulence. The instabilities may 

be generated directly from elements within the boundary layer or imposed from external 

sources and usually result in an advance of transition. An early review of the receptivity of the 

boundary layer to various on-board as well as off-board disturbances is outlined by 

Reshotko[1]. A more recent review of stability and transition in boundary layers is given by Saric 

et al. [2].

Occasionally, experiments report a delay of transition as a result of surface modifications. The 

objective of this paper is to analyze several of these experiments in terms of the frequency of 

the induced disturbances brought about by these modifications. The disturbances are 

generated in the boundary layer by several different methods. The frequencies of the various 

induced disturbances are calculated to be in the damping region of the associated stability 

curve. This results in stabilization of the boundary layer and to a delay of the transition from 

laminar to turbulent flow. 

 

Boundary-Layer Flow Control Mechanisms: 

Decades of research in aerodynamics have shown little progress in delaying transition. Many 

attempts to modify the boundary-layer flow have been tried, but most lead to an advance of 

transition. Some small encouraging success has been observed, but it has been difficult to 

identify the critical elements of the process in order to be able to develop a given technique to 

a practical level. A few of the techniques investigated thus far are listed below: 

1) Distributed Roughness: Early attempts included very thin modifications of the surface 

such as the addition of sandpaper, scotch tape, or flapping layers. 

2) Riblets: These are long grooves machined into the surface and aligned along the streamwise direction of the flow. Walsh [3]. 

3) Blowing/Suction: Although structurally demanding, this technique has been employed 

to an advantage in special locations. 

4) Cooling: Cooling of the surface appears to exhibit an advantage in delaying transition, 

but has not been demonstrated to be a practical method. Potter [4]. 

5) Isolated Roughness Elements (Trips): Physical trips have been tried in a variety of 

shapes, sizes, and configurations with some success. In most of the experiments, the 

height of the trip, k, is a small fraction of the boundary-layer thickness, {k / δ << 1}. Saric 

et al. [5]. 

2
6) Bluntness: Leading-edge bluntness on slender models can often bring about a delay in 

transition, but is not a practical solution for shaped wings. Brinich and Sands [6], Potter 

and Whitfield [7]. 

7) DBD’s (Dielectric Barrier Discharges): These surface plasma discharges have been shown 

to successfully modify flow, but on a very small scale. The small scale is a result of the 

weak momentum transfer from the plasma to the flow, making it difficult to envision 

their use in a full scale environment. T. C. Corke et al. [8]. 

8) Forced Streaks: Delay of transition has been observed in the presence of streamwise 

forced streaks at low velocities (5 m/sec). The delay has been ascribed to the stabilizing 

action of the streaks on low amplitude TS waves in the boundary layer. 

J. H. M. Fransson et al. [9].

Stability Theory and Transition: 

A stability theory has been developed by Mack [10] to calculate the conditions for a boundarylayer to transition from laminar to turbulent flow. The theory is based on individual oscillatory 

vorticity waves, (the Tollmien-Schlichting, or TS, waves), and calculates for a given wave 

frequency and Reynolds number, where the wave will be damped, neutral, or amplified. The 

amplitude of the waves is assumed to be weak initially so that a linear theory can be used. 

Ultimately, when the wave amplitude becomes large enough, nonlinear processes take over, 

triggering the laminar to turbulent transition. The theory is developed using a series expansion 

which leads to an infinite sequence of terms which are denoted modes. Mode 1 describes the 

TS waves just mentioned. Mode 2 exhibits order of magnitude higher frequencies than mode 1, 

and experiments have shown them to be in resonance with the boundary layer (i.e. λ ≈ 2 δ),

identifying them as an acoustical mode. Mode 2 has been observed mainly in blowdown 

facilities in which high pressure air is forced thru a small nozzle in order to generate high 

velocities. This process generates high frequency sound waves, which are then captured in the 

boundary-layer of the tunnel walls, before impinging on the model itself. Many attempts have 

been made to reduce this effect, resulting in “quiet” tunnels. 

Arnal [11] has computed detailed stability diagrams for two-dimensional waves (adiabatic wall) 

for Mach numbers 0, 1.3, 2.2, 3, 4.5, 4.8, 5.8, 7, and 10. Cebeci and Cousteix [12] show 

additional results obtained by Arnal for Mach numbers 0.6, 0.9, and 1.1. For stability diagrams 

up to Mach 3.0, only mode 1 instabilities are indicated, while above Mach 3, the higher 

frequency mode 2 appears and begins to be blended with mode 1. An example of a stability 

diagram is shown in figure 1 as computed by Arnal [11] for an adiabatic, flat-plate (planar) 

geometry at Mach 2.2. It shows the range of instabilities versus the Reynolds number, Rδ*. It 

must be recognized that the stability diagrams as calculated are for ideal flat-plate conditions, 

and can change for other configurations and practical applications. 

3
A vertical cut thru figure 1 at Rδ* = 3 x 103

 is shown in figure 2 which displays the amplification 

rate as a function of the dimensional frequency for this particular Reynolds number.

Experimental measurements have verified this general form in the amplification region (above 

zero). The dotted segments are extrapolations into the damping region (below zero). Very few 

experimental rate measurements have been made in the damping region. Between the 

frequencies A and B, fluctuations are amplified (an unstable flow), ultimately resulting in the 

transition of laminar to turbulent flow. Fluctuations exhibiting frequencies lower than A, or 

above B, are expected to be damped and to stabilize the flow. 

Induced Disturbances and Delay of Transition: 

The following experimental observations of the delay of transition result from the generation of 

strong disturbances in the flow at specific frequencies (repetition rates). These frequencies lie 

in the damping region of the associated amplification rate curve. With the exception of the 

leading-edge bluntness experiment, the disturbances are generated in the boundary-layer thru 

passive or active stabilizers on the surface of the model. The passive stabilizers generate the 

specific frequency by having a particular geometry and dimensions. They exhibit a significant 

height, k, but less than the boundary layer thickness, {k / δ < 1}. The active stabilizers are spark 

discharges that are initiated on the surface of a flat-plate model. 

1) Passive Spherical Trips 

Holloway and Sterrett [13] employed a single row of spherical trips of various sizes on a flatplate model to study boundary-layer transition and heat transfer at Mach numbers of 4.8 and 

6.0. Heat transfer was determined by a line of thermocouples aligned along the model length. 

Spheres with a trip height, k, larger than the boundary-layer thickness, δ, generated an advance 

of transition; whereas spheres with a trip height smaller than δ led to a delay of transition. 

Figure 3 {figure 6(a) in Holloway and Sterrett} shows heating rates at Mach 6 for two of the

sizes, k/δ = 1.85, and k/δ = 0.76, to illustrate the effect. The no trip condition is designated as 

k/δ = 0. Figure 4 shows the size and height of the spherical trips described in figure 3 relative to 

the boundary-layer thickness, δ. The larger trip, with k/δ = 1.85, protrudes through the 

boundary layer generating turbulence and advancing transition. The smaller trip, with k/δ = 

0.76, is embedded in the boundary layer and involves more subtle effects. The vortex shedding 

frequency, fVS, of this trip is given by, 

 fVS = St [U / d] (1) 

 

where St is the Strouhal number, d is the effective diameter of the truncated sphere, 

and U is the velocity in the boundary-layer at the height of the effective diameter. 

The smaller trip is a truncated sphere with an effective diameter, d, of 0.00256 ft 

0.78 mm), at a point in the boundary layer where the velocity, U, is 704 ft/sec 

214 m/sec). The Strouhal number is assumed to be 0.18 for a vortex shedding frequency. 

The smaller trip would, therefore, exhibit a flow-induced shedding frequency of 

4
50.1 kHz in the boundary layer. This vortex shedding frequency is shown in figure 5 and 

lies in the damping region for a Mach 5.8 flow as computed by Arnal [11]. Thus, by generating a 

strong instability in this frequency region, the row of smaller trips act as a boundary layer 

stabilizer and delays the transition to turbulent flow as was seen in the heating rate data of 

figure 3. An extension of this technique for a practical, full scale, geometry might be to employ 

tandem rows of trips. 

2) Passive Wavy Wall Trips 

In another passive trip experiment, Fujii [14,15] has extended the tandem row of trips idea, by 

employing either a wavy wall or a sequential series of wires. Similar results are observed for 

each, but the wavy wall configuration will be considered here since it would appear to be the 

easiest to implement. The wavy wall consisted of 5 individual grooves located approximately 

200 mm from the apex of a 5-degree half-angle cone model. Each groove has a trapezoidal 

cross-section of height 0.5 mm and the spacing between the grooves is 2 mm. The wavy-wall 

thus exhibits a cross between surface trips and surface cavities. The experiments were 

conducted in a pebble heated blowdown facility at Mach 7.1. Transition was detected by 

measuring heat transfer distributions using infrared (IR) thermography. Figure 6 shows the 

result of an experiment at 1000 K and 6 MPa {Figure 8(c) in Fujii [14, 15]}, in which the wavy 

configuration, with only 5 grooves, has a weak, but discernible effect in delaying transition. 

 Comparison of these results on a cone with the planar computations of Arnal [11] requires that 

they be made for the same Reynolds number based on the thickness of the boundary layer. 

Battin and Lin [16]. As a first step in the comparison, figure 7 shows a planar equivalent to the 

cone experiment with estimated flow patterns interacting with a trip/cavity configuration. The 

figure also illustrates the significant height of the trips relative to the boundary layer thickness, 

δp, a counter-intuitive development to traditional concepts using thin surface modifications. 

The interaction of the flow with the wavy wall (trip/cavity) configuration leads to the definition 

of a corrugation frequency, fc, given by 

 fc = u / s (2) 

where the velocity, u, is effectively determined at the top of the grooves within the boundary 

layer (not the edge velocity), and, s, is the spacing of the peaks in the corrugation. For the 

6 MPa experiment, u = 345 m/sec. Using this velocity and the separation of 2mm, results in a 

corrugation frequency, fc = 173 kHz. 

The second step in comparing with the planar calculations of Arnal [11] is to determine Rδ* for 

use in the Mach 7 amplification rate curve. For this purpose, it is necessary to employ the coneto-planar transition Reynolds number ratio, Rc / Rp . Although this ratio has been determined 

originally from purely geometric considerations, experiments have shown that the ratio is a 

function of the facility size and on the unit Reynolds number. It is speculated that facility noise, 

originating on the turbulent walls of a particular facility, is the major cause of this effect. Pate 

[17] has evaluated the ratio for a number of facilities and has found that it decreases from 2.2 

5
to 1 over the Mach number range from 3 to 8. For the Fujii experiment at Mach 7.1, this ratio is 

1.23. Figure 8 shows the amplification rate for the delay of transition observations shown in 

figure 6 using the Mach 7 computations of Arnal [11] at Rδ* = 0.94 x 104. The wavy wall 

corrugation frequency, fc = 173 kHz, is also shown in figure 8 and lies in the damping region of 

the amplification rate curve. The generation of a strong disturbance by the wavy wall in the 

damping region results in stabilization of the boundary layer flow and a delay of transition. 

The reliance on a significant empirical factor depending on facility size for the cone to planar 

comparison is necessary, but unsettling. The implication of flow contamination from facility 

walls is similar to the mode 2 facility dependence mentioned earlier. These facility effects lead 

to many uncontrollable factors which hinder progress in fluid flow research and point to the 

need for improved ground based flow facilities. 

3) Leading-Edge Bluntness 

A “Reversal of Transition” was observed by Lysenko [18] with increasing leading-edge bluntness 

on a slender, insulated, flat-plate model at Mach 4. The model consisted of a polished steel flat 

plate 450 mm long with a bevel angle of the leading edge of 20 degrees. A sharp leading-edge 

of 0.02 mm bluntness was used as a baseline and is taken to be a direct measurement of the 

amplification rate for this condition. The bluntness, b, was then varied thru seven steps with 

the following values: 0.1, 1, 1.5, 2, 3, 5 and 10 mm. Measurements of transition were made 

using hot-wires and pressure gauges. Figure 9, {figure 13 in Lysenko}, shows an initial advance 

of transition with increasing bluntness Reynolds number and then a delay of transition as the 

bluntness is increased further. The seven numbers along the x-axis in figure 9 have been added 

here to denote the increasing values of bluntness. 

Figure 10, {figure 12 in Lysenko}, shows experimental measurements of amplification rate for 

the baseline sharp leading-edge and two values of bluntness, 3 mm and 5 mm. This is one of 

the few experiments that have made measurements of amplification rate in the damping 

region. The dimensionless frequency parameter, F, employed by Lysenko, is converted to 

dimensional frequency, f, using the equation, [f = (1/2π) R0 V F], where R0 is the associated Unit 

Reynolds number and V is the velocity incident on the leading-edge. Measured data points from 

Lysenko are left off in figure 10 for clarity. 

Vortex shedding generated by the leading edge is assumed to account for the bluntness 

spectra. Using a Strouhal number of 0.18, the 5 mm bluntness and its measured peak 

frequency at 8 kHz predict an incident velocity on the edge of 222 m/sec. Likewise, the 3 mm 

bluntness and its measured peak frequency at 15 kHz would predict an incident velocity of 250 

m/sec. Although there have not been any measurements of velocity in the detached shock 

region, these two velocities are within the range of the subsonic velocities to be expected 

between the sonic lines for this Mach number. The numbers, (5) and (6), along the x-axis and 

the vertical dotted lines in figure 10 show the location of the vortex shedding frequencies for 

the associated values of Strouhal number, bluntness, and velocity which are consistent with the 

peak frequencies measured experimentally. Based on this analysis, the vortex shedding 

6
frequencies due to the blunt edges lie in the damping region defined by the baseline spectrum. 

The measured amplification rates for the 3 mm and 5 mm bluntness’s also extend into the 

damping region for an appreciable range of dimensional frequency. This extension into the 

damping region parallels the observations of Lysenko and Maslow [19] in which it is possible to 

achieve complete stabilization of the flow with the aid of cooling (i.e. the boundary layer will 

only contain damped disturbances and laminar flow is extended). In summary, vortex shedding 

generated by a blunt leading-edge would be expected to stabilize the boundary layer and bring 

about a delay in transition from laminar to turbulent flow.

 

4) Active Spark Discharge 

Using a spark discharge, Klein [20] has demonstrated the equivalence of high repetition rate 

discharges and physical trips to influence flow control. Three flat-plate models were used: 

 

1) No protuberances on the surface, 

2) A Row of Spheres 2.22 cm from the leading edge, 

 3) A Single Spark Discharge 2.22 cm from the leading edge. 

On each model, skin friction measurements were made 14.92 cm downstream of the leadingedge. The spark discharge was run at several set frequencies between 1 and 32 kHz. Each 

model was tested at Mach numbers 1.98, 2.56, 3.53, and 3.88 over a range of free-stream 

Reynolds numbers. Figure 11 shows the size of the spheres (model 2) relative to the boundary 

layer thickness for the Mach 3.53 case. Figure 11 also includes an estimated height for the 

discharges (model 3), inferred from a localized microwave surface plasma generated by the 

author in a static laboratory experiment. Figure 12 {figure 6(c) in Klein} shows the increase in 

the skin-friction coefficient at Mach 3.53 as the frequency of the discharge is increased. The 

figure demonstrates the equivalence of high repetition rate discharges with physical trips (row 

of spheres). The discharge measurements shown represent a matrix of 5 of the frequencies 

employed and 9 values of the Reynolds number. The results for only a single spark discharge 

(model 3) lie in-between the no disturbance condition (model 1) and the level attained by the 

row of 0.8 mm spheres (model 2). The model 2 results agree with the calculated fully turbulent 

level. All of the frequencies employed in the laminar or transition region at Mach 3.53 resulted 

in an advance of transition. Figure 13 shows the amplification rate spectrum for four of these 

Reynolds numbers along with the positions of the discharge frequencies. All of the frequencies 

are in the amplification range for their respective Reynolds number, except for 32 kHz at 5.5 x 

104cm-1 and 6.6 x 104cm-1, which lie in the damping region. Data points for these two 

conditions were not reported {figure 6(c) in Klein [20]}. 

 

 

7
At Mach 2.53, however, Klein indicated, in a brief quote, a reduction of skin-friction coefficients 

using high repetition rate discharges of 6 and 32 kHz {figure 6(b) in Klein [20]}: 

 “At Mach 2.53, it was observed that high frequency spark discharges 

 were able to reduce skin-friction coefficients somewhat at unit Reynolds numbers 

 at which normally turbulent boundary layers resulted at the measuring station.”

This observation of a reduction in skin-friction was not made in a laminar or transitional flow, 

but in a region where the flow had already transitioned to turbulence. In an established 

turbulent flow, the effect of higher frequencies to modify the flow is expected to be a subtle 

one. Figure 14 shows the amplification rate spectrum at Ro = 1.56 x 105cm-1 for Mach 2.56 

(interpolation between Mach 2.2 and Mach 3 from Arnal [11]). In support of the observation of 

the reduction in skin-friction, the discharge frequencies shown in figure 14 are located both 

below (6 kHz) and above (32 kHz) the unstable portion of the amplification rate spectrum. 

The main conclusion to be realized from the Klein experiments is the importance of the 

frequency (repetition rate) of forced plasma disturbances as an active influence on boundary 

layer flow control.

 

Recommendations for Future Research: 

Development of forced damping using passive and active stabilizers in the boundary layer 

should be conducted in subsonic, supersonic and hypersonic ranges, for fuel efficiency, 

increased flow control, and increased range, respectively. In each of the three regimes, there 

will be a need to evaluate the various stabilizer frequencies and strengths. For this measure, the 

height and shape of the stabilizer relative to the boundary-layer thickness and the velocity 

distribution within the boundary-layer will be required. 

The extension of the wavy-wall configuration to the subsonic range, in particular, may have the 

largest payoff thru increased fuel savings for commercial aircraft. The delay of transition using a 

wavy-wall by Fujii [14, 15] was achieved using only 5 grooves and a fixed separation of 

corrugation. In the extended wind tunnel effort, the number of grooves should be increased to 

strengthen and firmly establish the corrugation frequency. Ultimately, the grooves should cover 

the surface. Another interesting variation to the wavy-wall configuration would be to increase 

the separation of the peaks gradually in the downstream direction, hence allowing for a change 

in the Reynolds number. This procedure may allow the transition point to be delayed even 

further, perhaps indefinitely. The experiments should also be conducted on a flat-plate model, 

allowing a better correlation with theoretical calculations. As a starting point, the flat-plate 

stability diagram given by Cebeci and Cousteix [12] for Mach 0.90 is shown in figure 15. This 

Mach number approximates the cruising speed, Mach 0.85, of a commercial airliner. Two 

Reynolds numbers are selected; Rδ* = 1.5x103 for wind tunnel tests, and Rδ* = 5.5x103 for a 

closer simulation to flight. The amplification rate spectra for these two conditions are shown in 

figure 16. For the wind tunnel tests, a corrugation frequency of 2.4 kHz, as shown, would create 

disturbances in the damping region on the low frequency side of the amplification rate 

8
spectrum. This same corrugation frequency would create disturbances in the damping region 

for the flight Reynolds number, but on the higher frequency side of the amplification rate curve. 

 

Active, plasma, stabilizers should also be explored further since they may provide an 

alternative, or supplement, to passive stabilizers. Plasma stabilizers can operate at any desired 

frequency, offer no drag to the flow, and may offer the ultimate in (programmable) boundary 

layer flow control. Only a single active, plasma trip was employed by Klein [20]. Experiments 

with multiple plasma trips, including the use of parasitic trips, should be explored in order to 

increase their effectiveness. Active plasma trips (stabilizers) may be energetically prohibitive for 

application to a large surface area, but may be especially useful in smaller, more difficult to 

access flow regions. 

All of the stabilizers discussed in this report, both passive and active, employed models having a 

simple geometry. Ultimate application to a flight configuration will have to confront many 

different configurations and flow environments. 

Summary and Conclusions: 

1) In the past, most experiments have shown that almost any physical perturbation in the 

boundary layer results in an advance of transition, but a few rare experiments have 

exhibited a delay of transition. 

2) The height of the physical trips in both the Holloway and Sterrett [13] and Fujii [14, 15] 

experiments are a significant fraction of the boundary layer thickness. This observation 

is counter-intuitive to many of the earlier attempts to delay transition through thin 

surface modifications. 

3) The frequency (repetition rate) of the induced disturbance is a key factor in the delay of 

transition and is dependent on the geometry of the trip (stabilizer) and the velocity that 

it encounters in the boundary layer. 

4) The generation of strong disturbances in a laminar boundary-layer with a frequency 

(repetition rate) in the damping region of the associated amplification rate curve 

stabilizes the flow and delays transition. 

5) An alternative to (passive) physical stabilizers would be (active) plasma stabilizers. These 

stabilizers can operate at any desired frequency, offer no drag to the flow, and may 

offer the ultimate in (programmable) boundary layer flow control. 

6) It is anticipated that passive or active perturbations generated on the surface of the 

model will remain in the boundary layer for an appreciable distance downstream. This 

will be important in promulgating the delay effect downstream and the development of 

flow control techniques. 

9
References: 

1

 E. Reshotko, “Boundary-Layer Stability and Transition”, Ann. Rev. Fluid Mech. 8, 311-349 

 (1976). 

2

 W. S. Saric, H. L. Reed, and E. J. Kerschen, “Boundary-Layer Receptivity to Freestream 

 Disturbances”, Ann. Rev. Fluid Mech. 34, 291-319 (2002). 

3

 M. J. Walsh, “Riblets”, AIAA Progress in Aeronautics and Astronautics: Viscous Drag Reduction 

 in Boundary Layers, edited by D. M. Bushnell and J. N. Hefner, Vol. 123, pp. 203-261 (1990). 

4

 J. L. Potter, “Review of the Influence of Cooled Walls on Boundary-Layer Transition”,

 AIAA J. 18 (8) 1010-1012 (1980). 

5

 W. S. Saric, R. B. Carrillo, Jr., and M. S. Reibert, “Leading Edge Roughness as a Transition

 Control Mechanism”, AIAA 98-0781 (1998). 

6

 P. F. Brinich and N. Sands, “Effect of Bluntness on Transition for a Cone and a Hollow Cylinder

 at Mach 3.1”, NACA TN-3979 (1957). 

7 J. L. Potter and J. D. Whitfield, “Effects of Slight Nose Bluntness and Roughness on 

 Boundary-Layer Transition in Supersonic Flows”, J. Fluid Mech. 12, 501-535 (1962).

8

 T. C. Corke, M. L. Post, and D. M. Orlov, “Single Dielectric Barrier Discharge Plasma Enhanced 

 Aerodynamics: Physics, Modeling and Applications”, Exp. Fluids 46, 1-26 (2009). 

9 J. H. M. Fransson, A. Talamelli, L. Brandt, and C. Cossu, “Delaying Transition to Turbulence by

 a Passive Mechanism”, Phys. Rev. Letts. 96, 064501 (2006). 

10 L. Mack “Linear Stability Theory and the Problem of Supersonic and Hypersonic Boundary- 

 Layer Transition”, AIAA J. 13 (3) 278-289 (1975). 

11D. Arnal, “Laminar-Turbulent Transition Problems in Supersonic and Hypersonic Flows”,

 In Special Course on Aerothermodynamics of Hypersonic Vehicles. AGARD-R-761, (1989). 

12 T. Cebeci and J. Cousteix, “Modeling and Computation of Boundary-Layer flows”, Second 

 Edition (2005), Horizons Publishing Inc., Long Beach. 

13 P. F. Holloway and J. R. Sterrett, “Effect of Controlled Surface

 Roughness on Boundary-Layer Transition and Heat Transfer at Mach

 Numbers of 4.8 and 6.0,” NASA TN D-2054, (1964). 

14 K. Fujii, “Experiment of the Two-dimensional Roughness Effect on 

 Hypersonic Boundary-Layer Transition,” J. Spacecraft and Rockets 43, 731 (2006). 

15 K. Fujii, “An Experiment of Two Dimensional Roughness Effect on 

 Hypersonic Boundary-Layer Transition,” AIAA Paper No. 2005-891, (2005). 

16

 R. H. Battin and C. C. Lin, “On the Stability of the Boundary Layer over a Cone”, 

 J. Aeronautical Sciences 17, 453-454 (1950). 

17

 S. R. Pate, “Effects of Wind Tunnel Disturbances on Boundary-Layer Transition with Emphasis 

 on Radiated Noise: A Review”, AIAA 80-0431 (1980). 

18 V. L. Lysenko, “High-Speed Boundary-Layer Stability and Transition,”

 Int. J. Mech. Sci. 35, 921 (1993). 

19 V. L. Lysenko and A. A. Maslov, “The Effect of Cooling on Supersonic Boundary-Layer 

 Stability”, J. Fluid Mech. 147, 39-52 (1984). 

20 E. J. Klein, “Excitation of Boundary-Layer Turbulence Through Spark Discharges,” 

 NASA TN D-6378, (1971). 

10
11
Figure 1: Stability Diagram for Mach 2.2, Arnal [11].

12
Figure 2: Amplification Rate vs. Dimensional Frequency for Mach 2.2 

and Rδ* = 3 x 103

13
Figure 3: Delay and Advance of Transition at Mach 6 [13].

14
Figure 4: Dimensions for the Two Trips Described in Figure 3.

15
Figure 5: Vortex Shedding Frequency Relative to the Amplification Rate 

Spectrum at Mach 5.8 (Approximation to Mach 6).

16
Figure 6: Delay of Transition using a Wavy Wall at Mach 7.1, Fujii [14, 15].

17
Figure 7: Planar Equivalent of Cone Boundary Layer at Mach 7.1

18
Figure 8: Amplification Rate Spectrum for Mach 7 [11]. The Wavy Wall

Corrugation Frequency [fC = 173 kHz] lies in the Damping Region.

19
Figure 9: “Reversal of Transition” as observed by Lysenko [18] at Mach 4.

20
Figure 10: Measurement of Amplification Rates by Lysenko [18].

21
Figure 11: Sphere Size Relative to Boundary Layer Thickness at Mach 3.53, Klein [20]. 

An Estimate for the Size of the Surface Discharges is also shown.

22
Figure 12: Increase in Skin Friction Coefficient at Mach 3.53 with Increasing 

Discharge Frequency, Klein [20]. 

23
Figure 13: Amplification Rate Spectrum for Specific Reynolds 

Numbers at Mach 3.53, Klein [20].

24
Figure 14: Amplification Rate Spectrum for Ro = 1.56 x 105 cm-1 and 

Mach 2.56. Mach 2.56 Interpolated between Mach 2.2 and 

Mach 3, Arnal [11].

25
Figure 15: Stability Diagram for Mach 0.9, Cebeci and Cousteix [12].

26
Figure 16: Amplification Rate Spectrum for Mach 0.9 and Two 

Selected Reynolds numbers.

27
REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

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Technical Memorandum

 4. TITLE AND SUBTITLE

Delay of Transition Using Forced Damping

5a. CONTRACT NUMBER

 6. AUTHOR(S)

Exton, Reginald J.

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NASA Langley Research Center

Hampton, VA 23681-2199

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National Aeronautics and Space Administration

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NASA

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14. ABSTRACT

Several experiments which have reported a delay of transition are analyzed in terms of the frequencies of the induced 

disturbances generated by different flow control elements. Two of the experiments employed passive stabilizers in the 

boundary layer, one leading-edge bluntness, and one employed an active spark discharge in the boundary layer. It is found that 

the frequencies generated by the various elements lie in the damping region of the associated stability curve. It is concluded 

that the creation of strong disturbances in the damping region stabilizes the boundary-layer and delays the transition from 

laminar to turbulent flow. 

15. SUBJECT TERMS

Delay of Transition; Flow Control; Forced Damping; Turbulent Flow

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01- 11 - 2014