Suresh Menon

Georgia Institute of Technology, Atlanta, Georgia

Large-Eddy/Lattice Boltzmann Simulations of

Micro-Blowing Strategies for Subsonic and

Supersonic Drag Control

NASA/CR—2003-212196

March 2003

CCL–02–004
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Suresh Menon

Georgia Institute of Technology, Atlanta, Georgia

Large-Eddy/Lattice Boltzmann Simulations of

Micro-Blowing Strategies for Subsonic and

Supersonic Drag Control

NASA/CR—2003-212196

March 2003

National Aeronautics and

Space Administration

Glenn Research Center

Prepared under Grant NAG3–2653

CCL–02–004
Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

The Propulsion and Power Program at

NASA Glenn Research Center sponsored this work.

Available electronically at http://gltrs.grc.nasa.gov
NASA/CRó2003-212196 1 

Large-Eddy/Lattice Boltzmann Simulations of Micro-Blowing/Suction 

Strategies For Subsonic and Supersonic Drag Control 

Suresh Menon 

Georgia Institute of Technology 

Atlanta, Georgia 30332

1. Introduction

In recent years, a novel drag reduction method in turbulent boundary layers has 

been demonstrated using a micro-blowing technique (MBT) at NASA GRC (Hwang [1], 

Hwang and Biesiaday [2]; Hwang, 1998 [3], Tillman and Hwang, 1999 [4], Welch et al., 

[5]). Key features of this technique (in contrast to earlier more conventional blowing 

method) are the low effective roughness for the porous skin (achieved due to the use of 

micro holes) and the minimal amount of injection flow rate needed to achieve drag 

control. Results under laboratory and full-scale operating conditions show that large skin 

friction drag reduction (as much as 50 to 70 percent) can be achieved using MBT. 

Application of MBT to turbulent supersonic boundary layers has also shown that even 

higher drag reduction can be achieved. Furthermore, a reduction of noise was also 

observed in the supersonic case. Interesting observations in subsonic flow are that drag 

can be controlled by adjusting the injection flow rate and that the maximum drag 

reduction appears to occur within regions of adverse pressure gradient. However, more 

recent results in strongly adverse pressure gradient flow on a strut suggest that microblowing can lead to increased boundary layer and wake thickness [5] which can result in 

an increase in pressure drag for external flows. Thus, there are still many unresolved 

questions regarding the underlying physics of drag reduction as achieved by the MBT 

and how this blowing process impacts the larger-scale flow features. Furthermore, the 

experimental data suggests that the injection system (and the injected airflow) couple 

strongly with the outer (primary) flow especially in adverse pressure gradient flow. This 

makes the optimization of the design of this device problematic and parametric study 

using primarily an experimental approach is not a cost-effective approach.

Numerical studies of the MBT in subsonic turbulent boundary layers have also 

been recently reported [6] in which a steady-state 3D code was used. Both the micro 

holes and the cross-stream boundary layer were numerically modeled using a low 

Reynolds number turbulence closure. Results showed that for all the simulated cases, 

micro-blowing can potentially lead to unsteadiness due to the formation of vortices. 

However, due to the steady-state model employed this feature could not be studied. A 

recent study (Menon [7]; Cammarato and Menon [8]) studied Micro-Electro-Mechanical 

System (MEMS) based micro-scale blowing/suction devices in a supersonic boundary 

layer using direct numerical simulation (DNS). Significant unsteadiness is shown to be 

associated with the interaction between the injected fluid and the supersonic boundary 

layer. Vortex shedding and even pairing occurs in the near field of the injected fluid in 

the boundary layer. By combining blowing and suction it was further shown that not only 

drag can be reduced but also that it can be increased at specific location. 
NASA/CRó2003-212196 2 

It is clear that DNS of 3D high Reynolds number turbulent boundary layer with 

proper resolution of the micro holes is beyond the current and perhaps future 

computational capability. An alternate method that has the potential for such a study is 

based on large-eddy simulations (LES). In LES, all scales larger than the grid are 

resolved in a space and time accurate manner and only the scales smaller than the grid are 

modeled using a subgrid model. We have developed an advanced localized dynamic 

model based on the subgrid kinetic energy (Menon et al. [9ñ12]) that has shown to be 

very accurate even when relatively coarse grid is employed. This ability has some 

significant implications when high Reynolds number flows have to be simulated, as 

required under this project. 

Although LES looks promising, it has a serious problem in near-wall flows. To 

properly resolve the small-scale dynamics in the log layer, the wall normal resolution has 

to be close to the DNS requirement. This implies that the computational cost will be 

unacceptable. Clearly, an alternate method is required. 

In another recent study (Menon [13ñ15]; Menon and Wang [16]), a simulation 

methodology based on the Lattice Boltzmann Equation (LBE) was developed and 

demonstrated for the study of synthetic MEMS jets (e.g., Smith and Glezer [17]) 

embedded inside typical fuel jets. Both the synthetic jet cavity and the fuel jet are 

modeled using the same solver and thus, no specific imposition of boundary conditions at 

the synthetic jet exit (as done in the past) is required. The unique feature of the LBE 

approach is that it solves the Boltzmann equation (which, in the continuum limit recovers 

the Navier-Stokes equation). Since the Boltzmann equation is a single scalar equation, it 

is computationally very efficient (in fact, orders of magnitude faster than conventional 

FV algorithm). Thus, very high resolution (in fact, DNS-like resolution) can be use in the 

LBE model without paying a price in terms of computational cost. 

In the present study, the LBE model is being developed for use primarily to 

resolve the flow field inside the air injectors while the conventional FV-LES model is 

being used to simulate the boundary layer flow. This approach takes the best of both 

worlds and couples them together within a single formulation. The LBE solver is fully 

coupled to the LES solver and interacts across block structured grid domains. Thus, in the 

injection/suction port regions and in the near wall region (e.g., below y+ <200), a high 

(DNS-like) resolution will be used and the flow field simulated (without requiring any 

modeling, and this is important!!) using the LBE model, while in regions away from the 

wall, a conventional FV LES code will be employed. 

This report summarizes the work accomplished over the period of January 2002 to 

September 2002 under this project. Significant accomplishments have been achieved over 

the last 8 months. 
NASA/CRó2003-212196 3 

2. Technical Objectives

This project has the following overall technical objectives for the 3-year project: 

1. Demonstrate the LES-LBE model for simulation of the turbulent boundary layer and 

the micro-scale blowing system in a seamless coupled manner. 

This is the primary objective of the present yearís effort. The focus so far has 

been on developing a baseline LBE model for a single injection system and then to 

scale it to simulate multiple injection ports. Effort has also focused on setting up a FV 

LES solver to simulate the subsonic boundary layer currently being investigated 

experimentally at NASA GRC 

2. Apply the LES-LBE solver to flows identified by NASA GRC in order to validate the 

methodology and to understand the physics of the interaction process. 

The exact configuration and test conditions to be used for validation has been 

chosen in collaboration with researchers at NASA GRC. Initially, we are studying 

micro-blowing in a Mach 0.4 subsonic turbulent boundary layers. Subsequently, 

micro-blowing in supersonic flow will be considered in the second and third years. 

3. Employ the LES-LBE model to study new strategies and to provide researchers at 

NASA with more detailed information on the dynamical processes that are occurring 

during micro-blowing and/or suction. 

Once the baseline code has been validated, we plan to simulate additional 

scenarios that may or may not have been experimentally evaluated. The choice of 

conditions (e.g., steady or unsteady) and geometry to be simulated will be determined 

in close collaboration with NASA GRC research team. The primary objectives here 

are to determine if the simulation tool can be used to fine-tune and optimize existing 

setups that have already been experimentally evaluated at NASA GRC, and then to 

use the tool to investigate new conceptual designs. Once a representative new 

configuration is determined, experimental evaluation of the design will be addressed. 

We expect this effort to be on-going during this research program. 

4. Further demonstrate the ability of the LES-LBE solver to study more complex microblowing/suction strategies for drag control. 

Although the experiments at NASA GRC have primarily evaluated microblowing techniques, combined blowing and suction could also be a method for drag 

control. Simulation of combined blowing and suction using the LES-LBE technique 

will be considered in the latter half of the second year. This may lead to a new 

capability to study drag control (i.e., increase or decrease drag on-demand). 

5. Carry out a focused set of experimental studies (in Georgia Techís Mach 2.5, 8 cm x 

10 cm test section boundary layer facility) of micro-scale blowing/suction in a 

supersonic boundary layer to obtain data LES validation. 

We have a supersonic test facility at Georgia Tech (Fernando and Menon [18]) 

that will be used in the second year to obtain some baseline data for LES validation in 

the supersonic regime. Detailed measurements using LDV, pressure pitot probes and 

PLIF are planned. All capabilities are currently operational in our lab. 
NASA/CRó2003-212196 4 

3. Summary of Accomplishments To-Date 

This project actually started in late January 2002 at Georgia Tech and the 

highlights noted below are for the first 8 months of this research. 

[1] 3D LBE-LES solver for simulating injection developed and validated. 

This is a key objective since in the present study, the injection port all the 

way to the upstream controller will have to be simulated because the flow in the 

vicinity of the port hole cannot be prescribed a priori due to complex interactions. 

Furthermore, the flow field in this vicinity has to be relatively well resolved. 

Therefore, a new 3D LBE-LES approach has been developed to simulate the flow 

inside the injection port. In order to ensure its accuracy, simulations were carried 

out for a single port injection into a cross-stream. Results have been compared to 

experimental data and very good agreement has been obtained (in fact, superior to 

RANS two-equation and Reynolds-Stress closure models). These results have 

established the accuracy of the 3D LBE model as implemented in the LES mode. 

[2] LES of Incompressible and Compressible Channel Flows 

 This is another critical objective since we need to demonstrate the 

accuracy of the LES solver to capture the baseline boundary layer in the 

experimental studies at NASA GRC. Since the flow is at a Mach number of 0.4, 

fully compressible LES solver has been developed for this purpose. Again, to this 

validation phase, we are simulating two test cases: (a) LES of an incompressible 

channel flow for which detailed DNS data is available (Moser et al. [19]), and (b) 

LES of a compressible channel flow with parameters that match the experimental 

set up of NASA GRC. The former test case will address the resolution and 

accuracy of the code against a well-documented database. However, this DNS 

database is at a relatively low Re (Re = 590 based on wall units) and therefore, the 

second task is focusing on the actual experimental condition, which is at a very 

high Re. Since there are only limited measurements, we are using the DNS data to 

validate the base code. The comparisons obtained so far show that our LES code 

is quite accurate and sufficient to ensure accuracy of the flow physics of interest. 

This task and the task of LES of the experimental flow case are both underway 

and final results are expected in the near future. It is, however, anticipated the 

validation of the LES solver for flows of current interest will be accomplished 

within the next 2 to 3 months. 

[3] New Near-Wall and Injection Port Subgrid Modeling

In parallel to above studies, a new effort is being initiated that leverages 

on the recent development of a new near-wall model for LES (funded by Office of 

Naval Research). In this approach, the region near the wall and the small-scale 

turbulence field are simulated in another embedded locally 1D grid that retains 

DNS-level accuracy but is computationally much cheaper. This approach 

therefore, employs a grid-within-grid approach whereby the large-scales are 

simulated using conventional LES while the small-scales are simulated using 

local 1D grids. Preliminary results for channel flow have been obtained with very 
NASA/CRó2003-212196 5 

good accuracy. The idea here is to implement this local 1D model in the injection 

port all the way to the upstream controller. This approach differs from the LBE 

approach (see [1] above) in that, the LBE approach is fully 3D but in phase space 

whereas this subgrid 1D approach is implemented completely in physical space 

and is coupled directly to the LES solver. 

It is worth noting that this approach is very new and still needs some 

major development (some of which is currently being carried out in a parallel 

ONR project) but has the potential to capture the physics all within a single LES 

formulation. 

[4] Methodology to simulate a large-number of injection ports simultaneously

Finally, since the goal is to simulate 100 to 10000 holes simultaneously 

without specifying boundary condition at the injection port, some new issues need 

to be explored. We have begun this effort and have developed the basic 

framework for simulating many ports simultaneously. Both locally 1D (using the 

approach noted in [3]) and fully 3D (using LBE) are being setup. We expect to get 

some preliminary results within the next 2 months using both these methods after 

which one of them will be chosen for more careful simulations. 

4. Numerical Tools 

 For completeness we are summarizing the key codes being used in the present 

effort. 

4.1 Finite-Volume LES Solver 

 A fully compressible, unsteady, finite-volume LES solver that is second-order 

accurate in time and fourth-order accurate in space is employed for all the simulations of 

the boundary layer flow. This code has been extensively employed to study turbulent 

flows, fuel-air mixing, premixed, non-premixed and spray combustion in complex 

domains as in full-scale gas turbine and internal engine combustors. The code has been 

highly optimized for parallel processing. To simulate flows with shock waves, a second 

order flux vector splitting scheme is also implemented in the code. A localized dynamic 

subgrid model based on the transport model for the subgrid kinetic energy is used to close 

the LES subgrid terms. Details are given in cited references [10, 12, 20]. The key 

advantage of this closure model is that since the subgrid velocity scale is explicitly 

computed (the length scale is still approximated based on the grid scale), the assumption 

of local equilibrium between subgrid kinetic energy production and dissipation (that is 

inherent in algebraic subgrid eddy viscosity models) does not have to be imposed. As a 

direct result, this subgrid model allows simulation high-Re flows using relatively coarse 

grids without compromising the accuracy of the prediction of the large-scale processes 

since the non-equilibrium effects in the small-scales are incorporated within the subgrid 

model. Finally, the dynamic evaluation used in this model employs a scale-similarity 

approach, which avoids the limitations of the Germanoís dynamic closure and thus, is 

more robust and applicable in complex flows without requiring ad hoc averaging or 

smoothing. 
NASA/CRó2003-212196 6 

4.2 LES-LBE Solver 

 Since the LES-LBE model is a relatively new development it is described in some 

detail below. LBE method originates from a Boolean fluid model known as the lattice gas 

automata (LGA) which simulates the viscous fluid flow by tracing the fluid motion 

through advection of fluid particles and particle collision on a regular lattice. LBE is an 

improvement over LGA in which the Boolean fluid model is replaced by a single 

continuous particle distribution, which is analogous to the particle distribution function in 

kinetic theory. This replacement eliminates the intrinsic noise inherent in LGA schemes 

and overcomes the shortcomings of a limited transport coefficient. The introduction of 

the BGK single relaxation time model for the collisional operator further simplifies the 

algorithm and eliminates the lack of Galilean invariance and the dependence of pressure 

on velocity [21, 22]. This model assumes that the particle distribution function relaxes to 

its equilibrium state at a constant rate, and the collision operator is similar to the classical 

BGK Boltzmann operator (Bhatnager et al. [23]). 

Whereas conventional Navier-Stokes schemes solve the macroscopic properties of the 

fluid explicitly, LBE method solves the Boltzmann equation by tracking the evolution of 

the microscopic particle distribution of the fluid. The conserved variables of the fluid 

(density and momentum) are obtained indirectly by local integration of the particle 

distribution. The incompressible Navier-Stokes is recovered in the nearly incompressible 

limit of LBE using the Chapman-Enskog expansion. Solving the lattice Boltzmann 

equation instead of the Navier-Stokes equation provides three distinct advantages. First, 

due to the kinetic nature of the LBE method, the convection operator is linear. Simple 

convection in conjunction with a collision process allows the recovery of the nonlinear 

macroscopic advection through multi-scale expansions. Second, since the macroscopic 

properties of the flow field are not solved directly, LBE method avoids solving the 

Poisson equation, which proves to be numerically difficult in most finite difference 

methods. Third, the macroscopic properties are obtained from the microscopic particle 

distributions through simple arithmetic integration. More details are given in a recent 

review (Chen and Doolen [24]). 

4.2.1 The Lattice Boltzmann Equation Model 

LBE method consists of two primary steps. The particles first stream to its next 

nearest neighbor in the direction of its prescribed velocity. Subsequently, particles of 

different velocity arriving at the same node interacts with each other by relaxing to its 

local equilibrium values which are formulated specifically to recover the low Mach 

number limit of the Navier-Stokes equation. The evolution of the distribution function 

αf is thus govern by: 

( ) ( ) [ ] ( ) , ( ) , ],, 0,1, ,18 1+ , + − , = − α = L τ α αδ δ α α α f x e t f x t f x t f x t eq (1) 
NASA/CRó2003-212196 7 

where τ is the relaxation time, eq fα is the equilibrium distribution function and α e is the 

particle speed in α direction. The characteristic speed is thus αδ δ α c = e = e . Rest 

particles of type 0 with 0 e0 = are also allowed. Note that the time step and the lattice 

spacing each have equal spacing of unity. Thus, δ = 1 in the above formulation. 

In principle, there are an infinite number of possible velocity directions in the 3D 

velocity space. Discretizing these infinite number of velocity directions into a fixed set 

of velocity directions inevitably introduces discretization errors to the solution. As a 

general rule, the accuracy of the model to simulate Navier-Stokes flow comes at the 

expense of increasing computational cost resulting from the number of discrete velocities 

used in the model. Frisch et al. (1986) have shown that the Navier-Stokes equation 

cannot be recovered unless sufficient discrete velocities are used to ensure lattice 

symmetry. 

There are various 3D cubic lattice models developed, most notably the 15-bit 

(D315), 19-bit (D3Q19), and 27-bit (D3Q27) model [26]. Here, using common notations 

in scientific literatures, D is the number of dimensions and Q is the number of discrete 

velocities. In previous numerical simulations of a square duct, a lid-driven cavity and a 

circular pipe [27] no significant improvement in accuracy is observed when the D3Q27 

model was used over the D3Q19 model and thus, the latter model is assumed to be 

sufficient for the current purpose. 

The 19-bit velocity field is given as: 

( )

( ) ( ) ( ) ( ))

( ) ( ) ( ) ( )) 









± ± ± ± ± ± =

± ± ± =

=

=

c class II links

c class I links

rest particle

e

1, 1,0 , 0, 1, 1 , 1,0, 1 2 7,8, ,18,

1,0,0 , 0, 1,0 , 0,0, 1 1,2, ,6,

0,0,0 0,

L

L

α

α

α

α (2) 

Here, eq fα is given by the following form: 

( ) ( ) , 2

. 3

2

3 . 9 1 2

2

4

2

2















 = + + − c

u

c

e u

c

e u f w eq α α

α α ρ (3) 

where 



















=

=

=

=

7,8, ,18

36

1

1,2, ,6

18

1

0

3

1

L

L

α

α

α

wα
NASA/CRó2003-212196 8 

The macroscopic properties of the flow field can be obtained by integrating the 

distribution functions over the velocity space: 

= ∑αρ α f (4) 

= ∑ = αρ u eα fα α 0,1,L,18 (5) 

Here, ρ is the density and u is the velocity. 

The Navier-Stokes mass and momentum equations obtained using the BGK single 

relaxation time model by employing Chapman-Enskog on Eq.(1) are: 

= 0

∂

∂

+

∂

∂

α

ρ ρ α

x

u

t (6) 

( ) ( ) ( ) ( )

β

αβ

β α

ρ α ρ α β ρ νρ

x

S

x

c

x

u u

t

u s

∂

∂

+

∂

∂ = ∂

∂

+

∂

∂ 2 2

 (7) 

Here, repeated indices indicate summation and ( ) αβ α β β α S = ∂ u + ∂ u

2

1 is the 

strain-rate tensor. The pressure is given by the constant temperature ideal gas equation of 

state ρ2

s p = c where s c is the speed of sound with (c c 3) s = , and ν = [ ] (2τ −1) 6 is 

the kinematics viscosity. 

4.2.2 Subgrid Scale Modeling in LBE Formulation 

Since our eventual interest is in the application of the LBE model within the LES 

approach, the above formulation needs to be extended to LES. Spatial filtering reduces 

the high wave number Fourier components of the particle distribution and separates the 

resolved scale parts from the unresolved scales. For high Reynolds flow, LES-LBE 

formulation results in the ``filtered'' form of the LBE equation (LES-LBE): 

( ) ( ) [ ] ( ) , ( ) , ],, 0,1, ,18 1

+ , + − , = − α = L τ α αδ δ α α α f x e t f x t f x t f x t eq

sgs

 (8) 

Here, the distribution function αf represents only those of the resolved scales. The effect 

of the unresolved scale motion is modeled through an effective collision term: 

6

2 −1

+ = sgs τ

ν ν τ (9) 
NASA/CRó2003-212196 9 

The eddy viscosity ν τ represents the effect of dissipation by the unresolved scales and 

must be modeled. In the present effort, we have investigated the application of a simple 

algebraic model based on the classical Smagorinskyís model: 

C S

2 ν τ = ν∆ (10) 

where Cν is the Smagorinsky constant, ( )3

1

∆ = ∆x∆y∆z is the associated length scale 

derived from the local volume of the lattice and ( )

1 2

S = 2Sij Sij is the characteristic 

filtered rate of strain. 

The constant in Eq. 10 is unknown and cannot be prescribed a priori. Therefore, a 

localized dynamic method (LDM) [10, 12] is used to compute this ìconstantî locally as a 

function of space and time. The LDM is formulated based on the assumption of scale 

similarity in the inertial subrange and provided that enough of the inertial subrange is 

resolved, stresses at the cutoff (i.e., the grid size) can be related to stresses at say, twice 

the cutoff (i.e., the test filter width). This then defines a scale level where explicit 

filtering is required. The test-scale field is constructed from the grid-scale field by 

applying a test filter, which is characterized by ∆à (typically, ∆à = 2∆ and ∆ is the 

characteristic grid size). Thus, the application of the test filter on a variable φ is denoted 

by φ

à and the test-scale Favre-filtered variable is denoted by φ ρφ ρà / à = and Cν is 

obtained using the relation (see Kim and Menon [10] for more details) 

ij ij

ij ij

M M

L M

C

2

′

ν = (11) 

Equation (11) is an overdetermined system and is solved using a least-square 

method. In the above equation, ij

test

ij ij L L ρàk δ

3

2 ′ = − , 



 



 = − ∆ ij − kk ij

test Mij ρ k S S δ ~

3

~ 1 à à , 

and ( ) ij i j i j L u u u u à ~ ~ ~ ~ = ρ − is the Leonard stress tensor. Also, 

( ) 2 ρà ~ ~ ~ ~ 1

2

1 kk

i j i j

test L k = u u − u u = is the resolved kinetic energy at the test-filter level 

and 















∂

∂

+

∂

∂ =

i

j

j

i

ij x

u

x

u S

2

~ 1 is the resolved-scale rate-of-strain tensor. 

4.2.3 Boundary Conditions 

The most commonly used method to apply a no-slip boundary condition is the 

particle bounce-back scheme: the particles arriving at the stationary wall are reflected 

back in the direction it came from. Although easy to implement, the exact location of the 

no-slip wall is in question. The bounce-back scheme exhibited second order accuracy 

when the no-slip wall is places at exactly halfway between the boundary node and the 
NASA/CRó2003-212196 10 

first fluid node in numerical simulations of Poiseuille flow using the D2Q9 and D3Q15 

models (Zou and Hem[28]). Thus, the 3D adaptation of this bounce-back boundary 

condition from the D2Q6 model [29] to the present D3Q19 model [30] used for this study 

is assumed to be adequately accurate. It has been noted that certain wall geometries (e.g. 

convex edge and convex corner) cannot satisfy the no-slip condition under this scheme 

because there are insufficient unknown populations to define such a condition, resulting 

in curved instead of sharp-edged boundary. 

For orifice boundaries, a new treatment is proposed whereby, the no-slip wall is 

embedded within the grid and the unknown population of the inward pointing link with 

vector α e is computed prior to streaming by: 

( ) ( ) ( ) ( ) α χ α χ α α ρ α uω e

c

f xb t f x f t f xb t w . 3 , 1 , , 2 2

* = − + + (12) 

Here, subscripts b, f and w denote the boundary node, fluid node and the 

embedded wall, respectively, and α denotes the opposite outward pointing link (i.e. 

α α e = −e ). Here, *αf is an extrapolated population defined by: 

( ) ( ) 



 



 = f + bf + f − uf u f c

e u

c

e u

c

f x t . 2

3 . 2

9 . 3 , 1 2

2

2 4

*

α ωα ρ α α (13) 

where, 

1 2

1 2

2 1

2

3

2

3 1 ∆ ≥

+

∆ − = ∆

+ 



 





∆

u = − u u and for bf f w τ

χ (14) 

( ) 1 2

2

2 1 , ∆ p −∆ − u = u = u x + e t and = for bf ff f f τ αδ χ (15) 

Here, ∆ is the fraction of an intersected link in the fluid region. More details are 

given elsewhere. 
NASA/CRó2003-212196 11 

5. Progress to Date 

 In this section, we present our recent results and progress in this project. The 

progress in each of the topics highlighted in Section 3 is discussed in separate sections. 

As noted earlier, these results have been obtained over the first 8 months of the first year. 

5.1 LES-LBE Studies of Jet in Cross-flow 

In order to validate the sub-grid model a square jet in cross-flow has been 

simulated. The experiment of Ajresch et al. [31] 

is chosen as the benchmark case for validation studies and the dimensions of the 

computational domain is shown in Fig. 1. The simulation is carried out at Reynolds 

number of 4700 based on the jet velocity and the nozzle width D and at jet-cross-flow 

velocity ratio of 0.5. The crossflow velocity profile is initialized with a boundary layer 

thickness of 2D. The computational domain is resolved using 200×50×100 for the crossflow domain and 50×50×100 for jet section. The simulation required approximately 

1.84GB of memory and 1500 single processor hours on SGI O2000. Note that to do this 

simulation using conventional FV scheme the computational cost will easily exceed this 

number by more than an order of magnitude. Periodic boundaries are used in the crossstream boundaries of the cross-flow domain to simulate a single square jet out of a row of 

six used in the experiment. On the top surface free slip and for exit surface, outflow 

conditions have been implemented. 

The incoming pipe velocity profile with constant value is prescribed in the pipe at 

a distance of 10D below the flat plate allowing the flow to develop naturally as the jet 

merges into the cross-flow. This is a key requirement for the present project. The mean 

velocity profile comparisons are presented at various streamwise stations x D along the 

jet center plane y D = 0 and along the edge of the jet y D = -0.5 in Figs. 2 and 3. Results 

obtained earlier using the standard k − ε model (Lam and Bremhorst [32]), and more 

complex Reynolds-stress closure [33, 34] are also included for comparison. It can be 

clearly seen that the present LBE results are considerably superior to these earlier 

attempts for this flow. 

Figure 1. Geometry and computational domain employed in this study 
NASA/CRó2003-212196 12 

Figure 4a shows the iso-surface of vorticity structures in vertical, spanwise and 

streamwise direction. The green isosurface marks regions in the flow where ω x = 0.003, 

the blue surface marks the same magnitude for ω y and the red surface marks the same 

magnitude for ω z . These structures have been called hanging vortices ( ) ω x , spanwise 

rollers ( ) ω y and vertical streaks ( ) ω z [35] due to their distinctive characteristics. The 

hanging vortices are tube-like structures that begin directly above the exit on the lateral 

edges of the jet and then extend around the jet body and then up along the backside of the 

jet roughly matching the jet trajectory. Thus, these tubes mark the location where the jet 

shear layer rolls up into a vortex tubes and eventually contribute to the circulation of the 

counter-rotating vortex pair (CVP). Directly above the jet exit in Fig. 4 two vertical 

structures are clearly evident. One begins directly at the exit on the lateral edge of the jet 

and extends up and around the jet body while the second is located downstream above the 

first and extends horizontally along the lateral edge of the jet. Hanging vortices provides 

a path downstream for the jet fluid. 

Figure 4b shows two sets of instantaneous streamlines. One set originates within 

the jet, and the second set originates from the crossflow boundary layer upstream of the 

jet exit. These lines also collect in the hanging vortex. The vorticity carried by the 

hanging vortex provides the circulation necessary to create CVP. The CVP changes 

position and strength with time and streamwise location. 

Vertical streak forms when the irregularities in the rollers are stretched vertically 

by the local strain field. The majority of the production of vertical streaks occurs in the 

upstream rollers. The vorticity magnitude and streamlines are shown in Figs. 6a and 6b. It 

can be seen that the complex vortex pattern form downstream of the jet as it turns 

towards the direction of the flow. 

The present simulation of jet in crossflow has shown good agreement with 

experiments. Furthermore, the ability of the LES-LBE approach is observed to be 

superior to the previous RANS studies. In addition, the LES-LBE simulation also 

provides a means to study the unsteady dynamics of the mixing process. A movie Is 

attached to this report that shows this complex unsteady dynamics. 

The baseline study has established the ability and accuracy of the LES-LBE 

approach. Therefore, we are now ready to implement this model within conventional LES 

to simulate the multiple injection port. Note that for this coupled effort we are interested 

in only simulating the injection region with LBE. Also, the resolution requirement within 

the injection port does not have to be as high as in the present study since the scale of the 

injection hole is much smaller than the square port simulated here. Also, we have 

extended this LBE model to simulate circular and elliptical shaped holes as well. 

Therefore, all elements are ready for coupling to the LES code and will be the focus of 

the last quarter of this yearís effort. 

However, before attempting the fully coupled simulation, it is also necessary to 

demonstrate the accuracy of the LES solver for this type of flow. To do this we have 

carried out controlled LES of turbulent channel flows, both for a case for which DNS 

detailed data is available and another case which corresponds identically to the test case 

being measured at NASA GRC. These studies are discussed in the next section. 
NASA/CRó2003-212196 13 

Figure 2. Comparison of LES-LBE predictions of velocity profiles with past RANS 

results and experimental data at jet centerline. Figures (a) and (b): U/W_ref at 

x D =0 and 1, (c) and (d): W/W_ref at x D =0 and 1. 

Figure 3. Comparison of LES-LBE predictions of velocity profiles with past RANS 

results and experimental data at jet edge. Figures (a) and (b): U/W_ref at x D =0 and 

1, (c) and (d): W/W_ref at x D =0 and 1. 

(a) (b) 

(c) (d) 

(a) (b) 

(c) (d) 
NASA/CRó2003-212196 14 

 

Figure 4. Characteristics flow pattern in jet in cross-flow. (a) Vorticity contours showing 

the various components, (b) Streamline pattern from the free stream and the injected jet. 

Figure 5. Instantaneous vorticity and streakline patterns in the jet in cross-flow. Vortex 

rollup and breakdown, followed by the formation of the kidney-shaped structure in the 

downstream side is clearly seen. Recirculating flow in the wake of the jet is also clearly 

seen. All observations are in good agreement with experimental observation. 

(a) (b) 

(a) (b) 
NASA/CRó2003-212196 15 

5.2 3D Channel Flow for LES Validation 

In order to validate the LES code, numerical simulations of channel flow for 

Re = 590 τ were performed. This test case was chosen since a detailed DNS analysis has 

been carried out in the past [19] and therefore, detailed database is available for 

validation. This test case is for low-speed incompressible flow but our compressible code 

can handle this limit and therefore, this test case was chosen for code validation. Figure 6 

shows the configuration and dimensions that have been used for this simulation. Periodic 

boundary conditions are applied in the stream-wise (x) and span-wise directions. The 

inflow velocity of 19.68 with 01 δ = 0. was considered for this case. The computational 

domain is resolved using 64×128×64 point in x, y and z directions for the current 

dynamic LES studies. In contrast, the DNS studies of Moser et al. [19] employed a 

resolution of 387×256×256. 

The profile of the mean velocity normalized by the wall-shear velocity is shown 

in Fig. 7. Within the sub-layer (y

+

<5) the computational results follow the linear law 

(U+

=y+) of the wall and in the logarithmic region, the log law holds. Turbulence 

intensities normalized by the wall-shear velocity are shown in Fig. 8. This simulation is 

still underway but preliminary comparison looks very good. More detailed comparison 

will be carried in the near future but results show far show that the current LES model is 

accurate enough to be applied to the micro-blowing study. 

2πδ πδ

2δ

Figure 6. Dimensions and boundary conditions used for channel flow Periodic Periodic 

No-slip 

No-slip x 

y 

z 

Periodic 

Periodic 

y 

Figure 7. Mean velocity profile in wall unit Figure 8. Root-mean square velocity 

fluctuations normalized by the wall 

 shear velocity 

+

rms u

+ wrms

+

rms v

y /δ
NASA/CRó2003-212196 16 

5.3 LES of subsonic boundary layer on a flat plate (NASA GRC experiment) 

The study in Section 5.2 has established the baseline code but it was for a low 

speed (incompressible) flow condition. We have also set up the NASA GRC test case for 

validation as well. However, since very limited data is available only integrated 

parameters will be compared. Although it is believed that the present code is accurate 

enough to capture the dynamics of the high Re flat plate boundary layer simulated in the 

experimental study we still need to establish this prior to the micro-blowing simulations. 

Air flow past the flat plate with temperature of 284 K, pressure of 27068 Pa and an 

inflow velocity is 145.3 m/s (M=0.3). Figure 9 shows the geometry of this simulation. 

The boundary layer thickness is 3.5 cm and a 128×256×128 grid has been used for the 

present study. The grid is highly stretched near the wall to resolve the near wall region. 

This simulation is still underway but the results are expected within the next 

month. Note that our code is highly optimized for parallel simulation. However, we do 

not have access to NASA parallel machines for these studies. We are currently using a 

32-processor cluster in our lab for this simulation. We are also testing a new 64-processor 

PC (Intel Pentium IV Xeon) cluster in our lab. This cluster has been built with this 

project in mind. Once this machine is on-line we hope to speed up the calculations.

(a) 

(b) 

δ

Figure 9. Schematic of the computational domain used to model the experimental 

setup at NASA GRC. Figure below show a preliminary flow pattern in the channel. 

πδ

No slip 

2πδ
NASA/CRó2003-212196 17 

5.4 Simulation Methodology to Simulate Micro blowing 

Given that the LBE approach and the LES solver are operational, the next step is 

to determine how to simulate 100 to 1000 of injection micro-holes within a single 

simulation. Such a study has never been attempted in the past and it offers some 

interesting challenges. Some important conditions have to be maintained and these are 

discussed (along with method of study) in the following. 

All the injection holes have to be simulated simultaneously, as in the real 

experiment. This is schematically shown in Figure 10. In the experiments, an extremely 

small amount of air is blown vertically through these very small holes. However, the flow 

condition is determined by the upstream stagnation or control condition. In order to 

capture the proper dynamics in the boundary layer region, it is necessary to simulate from 

the upstream condition and also through the injection tubes. We plan to investigate two 

approaches that do NOT compromise or drastically increase the computational cost. The 

first approach is the method based on the LBE model discussed above. The second 

approach is more innovative but is also a new approach that was recently developed 

under a ONR project for high Re boundary layer flows but still needs to be evaluated for 

the present application in highly compressible flow. The second approach is discussed 

briefly in the next section. 

To simulate the multi-port blowing section two methods are being investigated. A 

schematic diagram of micro-blowing simulation is shown in Fig. 11. The issue here is to 

ensure that all the ports are resolved reasonably well and also that upstream conditions 

Figure 10. Micro-Blowing configuration in the experiment 
NASA/CRó2003-212196 18 

can be prescribed on all ports as done in the experiment. The two approaches being 

implemented are (a) the LBE approach discussed in section 5.1 and the new locally 1D 

approach (discussed below in the next section). The LBE approach is mature and 

therefore, can be considered for implementation at this stage. However, the subgrid 1D 

approach will require more development (some of which is still underway in the ONR 

project), especially for highly compressible flow. However, we will look at both 

approaches in some detail. 

Cross Flow 

Solved with LES 

Cross Flow 

Solved with LES 

Jet section 

Solved with 3.D. LBE 

Jet section 

Solved with 1D N.S. 

Figure 11. Schematic of two possible approaches to simulate the multi-port injection 

strategy. (a) Application of locally 1-D Navier-Stokes solver within each port, (b) 

Application of fully 3D LBE-LES model within each port. In both cases, the flow in 

the channel will be simulated by the 3D LES solver. 
NASA/CRó2003-212196 19 

5.5 LES Method for Near-Wall and Multi-Port Injection Modeling 

A new approach for high Re flows that departs significantly from conventional 

LES methodology has been developed. In conventional LES, the spatially filtered 

equations are solved on a ``resolved'' grid with a subgrid model for the small-scale 

motion. Current subgrid models specify the grid scale as the characteristic length scale 

and differ primarily in the specification of the velocity scale. The algebraic eddy viscosity 

subgrid model (Smagorinsky, 1963) and the one-equation model for the subgrid kinetic 

energy (Schumann, 1975) are two popular models. Dynamic variants of these models 

[10] have also been developed. In a recent study, a new two-level simulation (TLS) 

methodology has been developed that does not employ LES grid (or test) filtering, and in 

which both large- and small-scale fields are simulated simultaneously. The large-scale 

field is simulated on a conventional 3D grid while the small-scale motion evolves 

concurrently on a finer grid that is locally one-dimensional. The ability of this TLS 

approach in high-Re channel flows is evaluated so far and the results show the unique 

potential of this new approach. Further details are given elsewhere (Kemenov and Menon 

[36, 37]). 

5.5.1 Key Features and Highlights of TLS studies

The following features distinguish TLS from LES: 

1. TLS is not LES in the conventional sense since no grid or test filtering is carried 

out. Thus, TLS does not depend on the grid topology and hence, both structured 

and unstructured solvers can be used to resolve the large scales. 

2. TLS simulates both the large-scale and the "un-resolved" small-scale fields 

simultaneously. The large scales evolve on a 3D grid, whereas the small-scales 

evolve on another (finer) grid that is embedded within the larger 3D grid. 

3. The grid resolution for the small-scale field is fine enough to resolve the 

Kolmogorov scale. However, in order to reduce computational cost, the smallscale field is simulated on 3 1D orthogonal lines that are embedded within the 3D 

grid domain. This reduces the computational cost considerably. 

4. Both large and small-scale fields are obtained by solving the 3D Navier-Stokes 

equations (without any explicit grid or test filtering). On the 3D grid, the flow 

equations contain terms that represent the contribution of the small scales. In the 

small-scale domain, a truncated 1D form of the Navier-Stokes equations is solved 

along the three 1D lines. These equations also contain terms that represent the 

effect of the resolved 3D field projected onto to the 1D lines. Thus, both largeand small-scale fields are fully coupled and evolve together. 

5.5.2 Key Advantages of TLS over LES

The following key points identify the unique advantages of the TLS over LES. 

1. TLS approach is not restricted by the high-resolution near-wall requirement in 

LES since in TLS the near-wall region is well resolved. Thus, TLS has potential 

for application to very high Re flows. 

2. TLS is a small-scale simulation approach whereas conventional LES employs ad 

hoc subgrid models to represent the unresolved motion on the resolved field. As a 

consequence, all LES subgrid models have adjustable constants. Note that, the 

dynamic models which computes the constants using test filtering, assumes scale 
NASA/CRó2003-212196 20 

similarity between the resolved and unresolved scales. This approach will become 

highly questionable or even unstable when very high Re flows have to be 

simulated using relatively coarse grid. 

3. Since the small-scales are simulated, there is additional information on how the 

small-scale fields evolve in the flow. Such information is non-existent in LES. 

4. The reduction of the small-scale domain into 3 1D lines reduces the form of the 

equations. In the TLS approach, the applicability and the validity of the local 1D 

approach depends upon the existence of a well-resolved inertial range. Thus, the 

TLS formulation becomes more accurate as the Reynolds number increases for 

given 3D grid resolution whereas conventional LES does not. 

5. Although TLS is computationally expensive it is highly parallel and is 

considerably cheaper than LES with DNS-level near-wall resolution. 

5.5.3 TLS studies of 3D Channel Flow

The TLS approach has been used to study relatively high Re = 560 3D channel 

flow. We chose this case since DNS data is available for direct comparison. The 

resolution used for DNS was relatively very high (384×384×384) where as the TLS 

studies were conducted using 32×32×32 3D grid with 512 1D grid points within each 1D 

line. The results are summarized below. However, some key observations to note are that 

(a) the TLS approach allows the 3D grid size to be increased so that the near-wall region 

is no longer the constraint for the time-step, (b) the large and small-scale flow fields 

evolve in a consistent manner with the higher frequency scales of motion well resolved in 

the 1D grid, and (c) although some fine-tuning is needed, the results so far suggest that 

the TLS approach is a viable method for high Re flows without resorting to very high 3D 

grid resolution as in classical LES. 

We present some preliminary results from a simulation of a relatively high Re 

channel flow for a Re = 590. The DNS study of this field was carried out earlier by 

Moser et al. [19] using a 384×257×384 grid. Here, we attempt to recover the flow field 

properties (mean and rms velocity fields) using a 32×32×32 large-scale grid and using 

512 points along each 1D lines. Figures 12a and 12b show respectively, the instantaneous 

total streamwise velocity and the small-scale streamwise velocity in the wall normal 

direction. As expected, fine scale fluctuations are captured on the 1D line. Figures 13 and 

14 show the comparison of the DNS results (solid lines) with the TLS predictions. 

Although there are some disagreements between the two results, it is clear that TLS 

approach is able to capture the essential features of the flow field even with a very coarse 

large-scale grid. Note that the peak in the velocity fluctuation occurs inside the first cell 

in the large-scale grid and is resolved by the 1D line. Further studies are still needed to 

refine this approach and also to evaluate its capability over wide range of high-Re flows. 

Additional research is still needed to determine this methodís applicability to highly 

compressible flows and also for flows with multi-port injection. However, the base 

features of this approach are such that it can (at least theoretically) deal with complex 

flows. In any case, the TLS approach as implemented within the injection port holes will 

have to be modified for compatibility with the LES solver for the rest of the flow. This is 

an area of study at this time. 
NASA/CRó2003-212196 21 

 Figure 12. The two-level grid system. The resolved grid is 3D whereas the small-scale 

grid is 1D lines in each coordinate direction 

Figure 13. Two instantaneous snapshots of the flow field. (a) The total velocity field on 

the resolved grid, and (b) The small-scale field along wall-normal 1D lines (vertically 

shifted for visualization). 

Figure 14. (a) The mean velocity profile in wall units. Line: DNS, Symbols: TLS, (b) The 

turbulent fluctuating velocities in descending order: streamwise, spanwise and wall 

normal components. 
NASA/CRó2003-212196 22 

6. Conclusions and Future Plans 

This report summarizes the progress made in the first 8 to 9 months of this 

research. As reported above, substantial progress has been made in all the proposed tasks. 

The LBE methodology for LES of microblowing has been validated using a jet-incrossflow test configuration. In this study, the flow in the intake is also simulated to 

allow the interaction to occur naturally. As shown above, the LBELES approach is 

capable of capturing not only the flow features associated with this flow, such as hairpin 

vortices and recirculation behind the jet, but also is able to show better agreement with 

experiments when compared to previous RANS predictions. The LBELES is shown to be 

computationally very efficient and therefore, a viable method for simulating the injection 

process. This LBELES methodology will be further developed for the present application 

in the next phase of this research. 

 Another study has focused on validating the LES method for the flow in the 

experimental test channel. Preliminary validation for a low Reynolds number channel 

flow is shown for which there is DNS data for comparison. Comparison shows that LES 

method is able to capture the flow physics quite well. 

 Finally, two strategies have been developed to simulate multi-hole injection 

process as in the experiment. In order to allow natural interaction between the injected 

fluid and the primary stream the flow intake for all the holes have to be simulated. The 

LBE method is computationally efficient but is still 3D in nature and therefore, there may 

be some computational penalty in the long run. In order to study a large number of holes, 

a new 1D subgrid model has been developed that will simulate a reduced form of the 

Navier-Stokes equation in these holes. Preliminary validation for channel flow under 

another (ONR) project has shown the potential of this model for such simulations. 

 Future studies in the next quarter of the first year and in the subsequent second 

year will focus on the multi-port injection study of the experimental test case for Mach 

0.4. Comparison with experimental data will be carried out. The goal of this phase will be 

to investigate how the near field flow in the boundary layer is being modified during this 

injection process. Additional simulations will be carried out in investigate if a 

combination of blowing and suction can be used to manipulate the over drag of the flow 

over the flat plate. Finally, a extension of this approach to even high Mach numbers: 0.8 

to 1.9 will be developed during this second year. 

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30

Large-Eddy/Lattice Boltzmann Simulations of Micro-Blowing Strategies for

Subsonic and Supersonic Drag Control

Suresh Menon

Micro-blowing technique; Drag control; Large-Eddy/Lattice Boltzmann Simulations

Unclassified -Unlimited

Subject Category: 02 Distribution: Nonstandard

Computational Combustion Laboratory

School of Aerospace Engineering

Georgia Institute of Technology

Atlanta, Georgia 30332–0150

Project Manager, Danny P. Hwang, Turbomachinery and Propulsion Systems Division, NASA Glenn Research Center,

organization code 5850, 216–433–2187.

This report summarizes the progress made in the first 8 to 9 months of this research. The LBE methodology for LES of

microblowing has been validated using a jet-in-crossflow test configuration. In this study, the flow intake is also

simulated to allow the interaction to occur naturally. The LBELES approach is capable of capturing not only the flow

features associated with the flow, such as hairpin vortices and recirculation behind the jet, but also is able to show better

agreement with experiments when compared to previous RANS predictions. The LBELES is shown to be

computationally very efficient and therefore, a viable method for simulating the injection process. Two strategies have

been developed to simulate multi-hole injection process as in the experiment. In order to allow natural interaction

between the injected fluid and the primary stream, the flow intakes for all the holes have to be simulated. The LBE

method is computationally efficient but is still 3D in nature and therefore, there may be some computational penalty. In

order to study a large number or holes, a new 1D subgrid model has been developed that will simulate a reduced form of

the Navier-Stokes equation in these holes.