Visibility Enhancement in Rotorwash Clouds

Charles C. Ryerson*, Robert B. Haehnel† and George G. Koenig‡

U. S. Army Corps of Engineers Engineer Research and Development Center Cold Regions Research and Engineering Laboratory

Hanover, NH 03755-1290 U.S.A.

and

Marvin A. Moulton§

U.S. Army Aviation and Missile Research, Development and Engineering Center Redstone Arsenal, AL 35898-5000 U.S.A

Enhancing vision in rotorwash dust and snow clouds using remote sensing devices would improve the safety of helicopter operations. Our approach is to simulate remote sensor performance by modeling brownout cloud microphysical conditions. We use computational fluid dynamics techniques to model rotorwash, assuming incompressible and laminar flow, to develop the nearfield and farfield flow around a rotorcraft of given weight and configuration. We are developing two phase flow techniques to incorporate dust particles into the flowfield. Currently, stochastic techniques are being used to simulate particle entrainment in the boundary layer, with ongoing research to model entrainment using more realistic boundary conditions of turbulent flow impinging on a porous, erodible bed. Sensor signal performance is being simulated with MODTRAN, driven by the synthetically created cloud particle size distribution and concentration.

Nomenclature a = weighting coefficients C = entrainment coefficient Cl, Cd = aerodynamic airfoil characteristics ch = blade chord length D = diffusion coefficient e = discretized form of momentum source term F = resultant aerodynamic force vector Fxd = turbulent drag force acting in the x-direction g = gravitational constant K = particle flux coefficient k = turbulent kinetic energy of the flow m = particle mass N = number of rotor blades

iN = total number of particles for the i th component of the particle distribution

( )N r = particle concentration for particles greater than a given radius rp = pressure Qs = particle flux from the bed to the flow

iR = geometric mean radius for the i th component of the particle distribution

* Research Physical Scientist, Snow & Ice Division, 72 Lyme Road, Hanover, NH 03755-1290. † Research Mechanical Engineer, Snow & Ice Division, 72 Lyme Road, Hanover, NH 03755-1290. ‡ Research Physical Scientist, Geophysical Sciences Branch, 72 Lyme Road, Hanover, NH 03755-1290. § Aerospace Engineer, Aviation Engineering Directorate/Aeromechanics, Redstone Arsenal, AL 35898-5000.

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43rd AIAA Aerospace Sciences Meeting and Exhibit10 - 13 January 2005, Reno, Nevada

AIAA 2005-263

This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.

r = particle radius S = momentum source term t = time Uz = velocity at an elevation z above the bed u* = friction velocity u*t = threshold friction velocity u, v, w = flow velocity components in the x-, y- and z-directions respectively u’p, v’p, w’p= fluctuations in the particle velocity components in the three coordinate directions, respectively up, vp, wp = particle velocity components in the three coordinate directions, respectively Vabs = absolute velocity wf = particle fall velocity x, y, z = coordinate directions zo = aerodynamic roughness height α = angle of attack γ = particle concentration γ’ = fluctuations in the particle concentration ζ = a normally distributed random number ∆θ = angular measure of cell width κ = von Karmon’s constant µ = coefficient of viscosity ρ = density

iσ = geometric standard deviation for the i th component of the particle distribution Φ = general variable representing a primitive variable (u,v,w,p) ω = angular velocity of rotor

I. Introduction OTORWASH from Vertical Take Off and Landing (VTOL) and Super Short Take Off and Landing (SSTOL) aircraft in locations with loose dust, sand, or dry snow can cause loss of situational awareness and incidents or

accidents, especially when landing. These problems are due to brownout conditions that occur when visibility is severely reduced due to clouds generated by lofting of dust and sand particles around and above the rotorcraft when it is close to the Earth’s surface. Remote sensing devices, such as infrared or millimeter wave imagers, may enhance vision through rotorwash clouds and improve safety. Assessment of the capability of remote sensing devices to enhance vision in reduced visibility conditions is possible if the lofted dust and snow clouds are characterized in terms of their impact on the remote sensing system performance. Little is known about characteristics of rotorwash (downwash and outwash) created dust and snow clouds and the ability of remote sensing devices to sense through them. Our goal is to model the shape, size, and microphysics of downwash clouds to allow prediction of remote sensing system performance.

R

II. Background Impingement of rotorwash on loose material at landing zones is a cause of several significant helicopter

operational problems. The most significant problem is reduction of visibility during landing. Dust causes loss of situational awareness because the ground and horizon are not visible. The reduced visibility allows collisions with unseen obstructions, landing on terrain unsuited to aircraft stability and unloading operations (e.g. ditches), and lateral drift that causes rotorcraft to roll over upon touching down. Running landings and takeoffs are typically recommended in dusty conditions allowing the aircraft nose to remain ahead of the dust cloud.1 Brownouts may also limit multiple aircraft operations, reducing operational tempo (OPTEMPO), and preventing other helicopters from landing in the vicinity of the lead aircraft. Clearing of a dust cloud can require many minutes if the ambient winds are nearly calm and the dust is fine enough to remain suspended. Brownout conditions also damage hardware, such as causing increased blade erosion and loss of engine power by clogging filters. Dust can accumulate on the aircraft in sufficient quantities that payload capacity is reduced. The fine dust is difficult to remove using traditional washing methods. Finally, brownout clouds announce the presence of helicopters and mark their position for possible hostile activities.

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Existing methodologies for predicting rotorwash include a semi-empirical code called ROTWASH, which was developed by Ferguson.2 By modeling the rotors as wall jets and using similarity curve fits to flight test data, the method is able to predict outwash velocity profiles in the farfield, in this case beyond approximately 1.2 rotor radii. Each flight condition as well as each aircraft configuration requires a new model. Currently, ROTWASH has been validated for single rotor and tiltrotor configurations operating at a number of flight conditions.

Nearfield rotorwash predictions are not amenable to empiricism since the flowfield is highly dependent on the aircraft configuration and is, by definition, unsteady. A higher level of fidelity is required to discern unique characteristics of individual aircraft. This paper uses a Computational Fluid Dynamics (CFD) method to predict both the near and farfield characteristics of the rotorwash.3 It is noteworthy that CFD has the capability to account for most of the deficiencies of ROTWASH.

In the 1960’s there was a considerable effort launched to understand the effects of downwash from VTOL aircraft on particle entrainment.4-7 This effort resulted in the development of a parameterization of the size and shape of the dust or snow cloud based on the geometry of the rotorcraft (e.g. one rotor or two) and the type of material on the ground (e.g. snow, loose sand, sod). However, methodology developed to characterize the particle concentration and size distribution within the cloud was too simplistic to be useful for making any realistic prediction about transmission attenuation through the cloud (i.e. visibility degradation, etc.). This simple parameterization of the cloud geometry was brought forward and included in the ROTWASH computer model.2

A separate effort initiated in the 1980s looked at developing algorithms to model signal attenuation through a snow or dust cloud generated by helicopter downwash. The resulting model, COPTER,8 is part of the Electro-optical Systems Atmospheric Effects Library (EOSAEL) maintained by the Army Research Laboratory (ARL). Transmission predictions made using COPTER are based on the measured visible range through a snow cloud formed by rotorcraft downwash. The visible range is then converted to an extinction coefficient that can be used to predict transmission using the Beer-Bouger Law. Scaling laws are used to determine the transmission at other wavelengths and particle types. However, no attempt is made to characterize the aerosol cloud in terms of particle concentration or size distribution.

In an aerosol-laden atmosphere, Electro-Optical (EO) propagation depends on the characteristics of the Electro-Magnetic (EM) wave and the physical and optical properties of the aerosols. Aerosol scattering is the dominant extinction mechanism, especially in the visible and infrared spectral regions. The aerosol radiative properties depend on the aerosol composition (complex index of refraction), particle size distribution and particle concentration. Desert aerosols with a Aitken or nucleation mode (10-3 < radius < 10-1 µm), large or accumulation mode (10-1 < radius < 1.0 µm), and a giant or coarse mode (radius > 1.0 µm) are modeled using three log normal distributions. The larger size or coarse mode is associated with dust storms and high surface winds. The wind dependent desert aerosol model implemented in LOWTRAN/MODTRAN provides a means for computing spectrally dependent transmission in natural environmental conditions.9-10 As indicated, the desert aerosol model computes aerosol radiative properties for natural environmental conditions. The model must be modified to handle the spatial and temporal variation associated with atmospheric aerosol loading resulting from rotorwash.

Modeling rotorcraft-induced aerosol clouds requires parameterization of flow fields created by the rotorwash, and simulation of particle entrainment as the flow strikes dust, sand, or snow surfaces. In this effort we seek to develop a physics based methodology for determining the particle concentration and size distribution in a dust/snow cloud based on the properties of the particles and the predicted flow field for a specific airframe (e.g. CH-47, CH-60). Then, using this derived three-dimensional cloud, (with varying particle concentration and size distribution throughout the cloud structure) predict transmission for wavelengths of interest.

III. Rotorwash Simulation Our approach is to use ROT3DC – a computational fluid dynamics (CFD) code designed specifically to model

rotorcraft induced flows – to generate a rotorwash flow field.11 ROT3DC was originally developed at Iowa State University and employs a graphical user interface to model either isolated rotors or rotor and fuselage interaction, including ground effects. The model, supported by the Army Aviation & Missile Research, Development, and Engineering Center, solves the Reynolds Averaged Navier-Stokes (RANS) equations on structured grids with a momentum-source representation for the rotor blades.

A. ROT3DC ROT3DC simulates the flowfields for various rotorcraft configurations. For all calculations, flow is assumed to

be incompressible and laminar. For certain calculations the flow is assumed to be steady while for others the inclusion of unsteady terms was crucial for the correct resolution of the flow. For the sake of explaining the overall

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source evaluation procedure, the Cartesian equations for mass and momentum conservation, respectively are quoted below.

mass:

0u v wt x y zρ∂ ∂ ∂ ∂

+ + + =∂ ∂ ∂ ∂

(1)

x-momentum:

2 2 2

2 2 2 xu u u u u u u pu v w St x y z xx y z

ρ µ⎛ ⎞⎛ ⎞∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂

+ + + = + + − +⎜ ⎟⎜ ⎟∂ ∂ ∂ ∂ ∂∂ ∂ ∂⎝ ⎠ ⎝ ⎠ (2)

y-momentum:

2 2 2

2 2 2 yv v v v v v v pu v w St x y z yx y z

ρ µ⎛ ⎞⎛ ⎞∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂

+ + + = + + − +⎜ ⎟⎜ ⎟∂ ∂ ∂ ∂ ∂∂ ∂ ∂⎝ ⎠ ⎝ ⎠ (3)

z-momentum:

2 2 2

2 2 2 zw w w w w w w pu v wt x y z zx y z

ρ µ⎛ ⎞⎛ ⎞∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂

+ + + = + + − +⎜ ⎟⎜ ⎟∂ ∂ ∂ ∂ ∂∂ ∂ ∂⎝ ⎠ ⎝ ⎠S (4)

where µ is the flow viscosity and Sx, Sy and Sz are the time averaged source terms per unit volume due to the rotor’s motion in the coordinate directions, x, y and z, respectively. Sx, Sy and Sz are in addition to other source terms that may exist in the flowfield. The source terms are time-averaged for convenience and are not a requirement of the method itself. These source terms denote the rotor-induced force per unit volume at a point. It is through these terms that the rotor's influence is introduced into the flowfield.

The numerical algorithm for solving the governing equations of the flow is based on Patankar's SIMPLER algorithm.12 In this procedure, the primitive variables, static pressure and the components of velocity are obtained directly by solving the mass and momentum conservation equations.

The flow equations, written in the conservation form, are discretized using the control volume approach in SIMPLER. For a general variable Φ representing any of the primitive variables (u,v,w,p), the discretized equation at a grid point (i,j,k) is found to be

(5) , , , , 1, , 1, , 1, , 1, , , 1, , 1, , 1, , 1,

, , 1 , , 1 , , 1 , , 1 , ,

i j k i j k i j k i j k i j k i j k i j k i j k i j k i j k

i j k i j k i j k i j k i j k

a a a a a

a a e+ + − − + + − −

+ + − −

Φ = Φ + Φ + Φ + Φ

+ Φ + Φ +

where (i,j,k) are the grid indices, the ‘a’ terms are the coefficients that link the neighboring Φ's to Φi,j,k; ei,j,k is the discretized form of the source term that consists of contributions from the specific governing differential equation being discretized, as well as the discretized source terms due to the action of the rotor blades. The discretized equations are solved by a line-by-line method combining the Tri-Diagonal Matrix Algorithm and the Gauss-Seidel method. The rotor source terms (Sx, Sy and Sz) are evaluated in a specific number of computational cells through which the rotor blades pass.

B. Rotor Source Terms As mentioned earlier, the action of the rotor blades is modeled in this formulation through the momentum

equation sources (Sx, Sy and Sz) in the coordinate directions. The strength of the rotor source at a specific location through which the blade is passing is a function of the local flow conditions, the physical location, and the geometric and aerodynamic characteristics of the rotor blades. In functional notation, the discretized source terms can be stated as follows:

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(6) ( , , , , , , , , , , ,α ω ρ= l d absC C V x y z t ch NS S ) where Cl and Cd are airfoil characteristics of the rotor blade; α is the angle between the rotor blade and the

relative velocity vector; Vabs is the absolute velocity of the fluid at the instantaneous blade location (x,y,z,t); ch is the chord of the blade; ρ is the flow density and N is the number of blades. The effects of unsteady fluctuations in angle of attack are not addressed in the investigations presented here. However, these effects can be included, in a limited sense, through the use of a proper dynamic stall model. The influence of viscosity and compressibility on the source terms are considered only through the airfoil aerodynamic characteristics (Cl and Cd) used in the calculations.

In summary, these source terms are not known a priori and are a highly desired result of all rotor solution procedures. For example, their integration along the span of the rotor yields the performance characteristics. Further, it is not related/imposed by any experimentally known quantity, such as a pressure difference across the rotor disk, for this would restrict the analysis to the set of operational conditions for which the experiment was conducted.

Therefore, our aim is to let the source terms develop as part of the overall solution of the entire flowfield. Since the rotating blades can be thought of as a momentum changing device, the source terms in the momentum conservation equations would represent the action of the rotating blades truly when the flowfield is converged. In other words, when there is an overall and local conservation of momentum, the source terms would yield the proper loading on the rotor blades and the associated wake.

C. Time Averaging and Coupling Next, we consider the time averaging procedure used to simplify the analysis. As the blades rotate, they develop

a force distribution along the blades. If F is the resultant aerodynamic force vector on the blade at a given section, then -F is the instantaneous force vector acting on a fluid element at a given location (x,y,z), which must be added to the momentum equation as an external force acting on the fluid. However, for a time averaged solution, only a fraction of this force is to be added at a computational cell. This fraction is determined as follows. The time taken by the center of the blade element, at a rotational speed of ω, to traverse one revolution is

1,2πω

=revt (7)

and the time the center of a blade element spends in a given control volume of width ∆θ radians is

θθ

ω∆

∆=t (8)

Therefore, the fractional time that the blade element spends in a cell is

2fract θπ

∆= (9)

For a rotor with N blades the time averaged source term to be added to the momentum equation is

2

N θπ∆

= −S F (10)

The source terms are grid specific and are calculated from the velocity field of the flow solution. Figure 1

summarizes the coupling of the time-averaged source term computation with the overall solution procedure.

D. Solid Surface Modeling In general, body conforming grids are not used and the difficulties of irregular surfaces are overcome solely by

finely resolving the grid where necessary. All of the control volumes that lie in the solid region are blocked off with zero velocities everywhere. The no-slip viscous boundary condition is applied at all solid surfaces.

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E. Boundary Conditions Far upstream (above the rotor), at the inlet to the computational domain, the flow is considered to be uniform

with a very small velocity. The outlet boundary values are extrapolated from the interior grid points and are adjusted to conserve mass flow through the computational domain.

Figure 1. Flowchart showing the coupling of the momentum source term computation with the flow solver.

So far, we use ROT3DC only to define the flow fields from the rotorwash. Simulations for descent have, thus far, been created by simulating hover at various heights above ground level. However, work is now being conducted to provide an improved maneuver capability that will allow continuous simulation of descents.

IV. Two Phase Flow Modeling the effects of particle drag and momentum requires a two-phase flow model. ROT3DC is presently a

single-phase model and therefore is not capable of modeling dust cloud formation. Rather, we are using the converged flow field obtained using ROT3DC as input to our separate Particle Entrainment and Dispersion (PED) model. As such, entrainment and dispersion are modeled using one-way coupling, that is the momentum exchange from the fluid to the particles is modeled, but the effects of the particle drag on the flow is considered negligible and is ignored. This assumption is generally acceptable for dilute two-phase flows (particle concentrations less than 0.1 percent by volume), which is the case for much of the snow/dust cloud. However, this is not true in the entrainment layer where the particle volume fraction is of the same order of magnitude as the maximum packing density of the particle bed (e.g. particle volume fractions in the flow of 20 percent or higher). Regardless, at this stage in the model

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development we have ignored momentum transfer from the particles to the fluid within the entrainment layer. Furthermore, the entrainment functions used at this stage of PED model development are based on equilibrium entrainment in flow parallel to a packed bed. Using this simplified approach, we have created simulations of cloud density, though they have not been verified by field measurements. Our goal, though not yet realized, is to create a PED model that fully simulates non-equilibrium entrainment in unsteady flow.

V. Particle Entrainment At this stage of model development we have assumed that flow traveling over the surface is predominately

parallel to the packed bed and mechanistically is very similar to blowing sand and snow conditions. In this case particles are removed from the bed due to aerodynamic lift or being knocked loose by other particles impacting the bed, a process known as saltation. Particles are then lifted up out of this saltation layer through turbulent diffusion. The general equation of interest is13

2 2 2

2 2 2

( )' ' ' ' ' 'p p p f

p p p

u v w wD u v w

t x y z x y z x y zγ γ γγ γ γ γ γ γ γ

∂ ∂ ∂ − ⎛ ⎞∂ ∂ ∂ ∂ ∂ ∂ ∂+ + + = + + − − −⎜ ⎟∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂⎝ ⎠

(11)

which takes into account advection and diffusion in three-dimensions. The concentration, γ, varies spatially and temporally. The particle velocity components in the three coordinate directions are up, vp, wp. Gravitational effects are taken into account via the fall velocity of the particles, wf. The Reynolds sediment fluxes in the three directions are ' 'puγ , ' 'pvγ , ' pwγ ' (the overbar notation denotes a mean value is taken). The entrainment from the bed

into the flow is governed by Qs=0

' 'z

wγ=

which is provided as a boundary condition via a suitable “entrainment

function.” For this present work we consider ' 'puγ = ' pvγ ' =0 at the bed surface. We assume the advection terms will dominate since the downwash velocities, in general, are very large making the advection terms much larger than the diffusion contribution. As such we ignore the effects of diffusion (i.e. the diffusion coefficient, D=0). These assumptions greatly simplify Eq. (11) so that the time dependent change in concentration is a function of the particle velocity-concentration gradients in the three coordinate directions accompanied by an appropriate boundary flux condition, Qs.

The key aspect in modeling entrainment is in formulation of this boundary condition. Numerous works have considered particle entrainment due to flow parallel to a packed bed.13-19 In these works both fluvial and eolian flow have been considered. From these studies principally two different expressions have been developed for quantifying the equilibrium mass flux of particles leaving a packed bed, Qs, as a function of a characteristic flow velocity (e.g. friction velocity, u*). Practically speaking both versions of these entrainment functions serve equally well for predicting the entrainment flux, and usage of one over the other really comes as a matter of preference. In this work we use the formulation put forward by Pomeroy and Gray,15 Cao16 and others:

2 2* * *( )s tQ K u u u

gρ

= − (12)

where u*t is the threshold friction velocity, ρ is the fluid density, g is the gravitational constant and K is a coefficient. The value of K varies within the literature; we have adopted the expression for K used by Pomeroy and Gray15:

*2*

tuK Cu

= . (13)

where C=0.68s-1. In Eq. (12) and Eq. (13) the properties of the particle (e.g. density, shape, etc.) are wrapped up in the threshold friction velocity, the minimum velocity at which the particles begin to become entrained by the flow. Thus, the actual entrainment physics is distilled down to the minimum threshold velocity sufficient to pluck particles out of the surface and into the flow. The threshold friction velocity is a function of particle density and size is tabulated in several works. Table 1 gives typical values of u*t.

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Table 1. Typical values of particle density, ρ , particle radius, r, threshold friction velocity, u*t, and aerodynamic roughness height of packed bed, zo.9, 20-21

ρs, kg/m3 r, µm u*t, m/s zo, mm Snow20 700 150 0.3 0.21 Desert Soil9 Sand 2650 10 0.2821 0.0221

Water Soluble 1769 0.029 Carbonate 2000 0.012

To use Eq. (12) to determine the entrainment flux one needs to know the friction velocity acting on the surface. This is done by assuming the flow near the surface follows a logarithmic velocity profile

*

1 lnz

o

U zzu k

⎛= ⎜⎝ ⎠

⎞⎟ (14)

where Uz is the velocity at an elevation, z, above the packed bed, κ =0.4 (von Karman’s constant) and zo is the aerodynamic roughness height of the packed bed (some example values of zo are provided in Table 1). Knowing z and Uz the friction velocity can be readily determined from Eq. (14). Thus, using the flow field created with ROT3DC and Eq. (14) we can determine the friction velocity acting on the ground plane. This is then used to in Eq. (12) to provide the particle flux boundary condition at the ground.

Most production CFD models, including ROT3DC, provide a time-averaged flow field. Yet, rotorcraft flow fields are rarely steady-state, since the most common brownout and whiteout problems occur during a transient flow condition (e.g. descent to landing). Yet, even during hover the flow is turbulent and therefore is constantly changing. Hence, the flow field provided by ROT3DC represents the average taken over a long time and completely removes the fluctuating nature of real turbulent flows. Yet, it is the energy associated with these fluctuations in velocity that are largely responsible for entraining particles into the flow, especially when the mean flow is near threshold conditions. In fact, we were unable to simulate entrainment using the boundary condition presented in Eq. (12) by using the time averaged flow field provided by ROT3DC.

To properly simulate the entrainment process we needed to include the fluctuating component present in the flow field. This could be done by several means, for example:

1. Direct numerical simulation 2. Large-Eddy simulation 3. Stochastic modeling of the turbulence Though the first two methods would work in principle, they are computationally intensive and would require us

to use time series flow fields as inputs to our PED model. The third method allows us to still use the converged flow field obtained from ROT3DC and generate a time varying turbulent flow field for each simulated time step with little additional computational overhead.

The approach in 1-D as follows. The instantaneous velocity component in the x-direction can be written as

'u u u= + (15)

where the overbar denotes a mean value and the primed term is the variance from the mean at any given instant in time (similar expressions can be written for the velocity components in the y- and z-directions, readily extending this approach to 3-D). Since we obtain u from ROT3DC, we need only to determine u’ to determine the instantaneous velocity, u. Since we cannot determine the fluctuating component directly, we model the fluctuating component stochastically.22

2'3ku ς= (16)

where k is the turbulent kinetic energy of the flow and ζ is a normally distributed random number. Using Eq. (16) we generated a fluctuating component field for each of the coordinate directions at each time step and use this in Eq.

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(15) to synthesize a perturbed flow field. This allowed direct use of Eq. (12) to model the entrainment of the particles into the synthesized flow field.

Once the particle flux from the ground plane was determined the lofted particles are mixed into the flow according to Eq. (11). In Eq. (11) we allow for the general condition that up≠u, that is, the particles are not flow following at every instant in time, but are accelerated up to the fluid velocity via drag. The acceleration of a particle in the x-direction is (similar expressions are obtained for the y- and z-directions) 23:

xdpx

Fdu gdt m= − (17)

where Fxd is the turbulent drag force acting on the particle in the x-direction, m is the particle mass, and gx is gravitational acceleration in the x-direction. The drag force is determined in a straightforward manner knowing the coefficient of drag (a function of particle shape and Reynolds number) and the relative velocity of the fluid and particle. At this stage of model development we have assumed that particles are spherical.

The present model formulation ignores affects of flow through the bed, fluidization, and alteration of the bed shape (via erosion and pressure deformation) and how these processes may influence the entrainment flux, Qs. This is an area of active research, the results of which are anticipated to yield a more realistic boundary condition for the case of turbulent flow impinging on a porous, erodible bed. Furthermore, this modeling approach needs to be validated against measured data, also a subject of current research. In future work we will couple the CFD and PED models so that we can model the momentum exchange between the particles and fluid (two-way coupling), particularly in the entrainment layer.

VI. Sensor Signal Simulation Accurate dust cloud modeling provides a three-dimensional matrix of cloud microphysical properties around the

rotorcraft, including particle size distributions and particle concentrations. The impact of desert aerosols on remote sensing systems requires scaling the wavelength dependent extinction coefficients computed using the 30 m/sec wind dependent aerosol model associated with MODTRAN and the rotorwash dust cloud. MODTRAN can also simulate sensor signal interactions with airborne particles. Dust cloud model predictions must be validated using field measurements. The following procedures used to compute the impact of lofted dust on sensor transmission utilize the wind dependent desert aerosol model from MODTRAN.

The desert aerosol model is a three-component aerosol model consisting of carbonaceous, water soluble, and wind dependent sand components. The size distribution of the particles is given as

(18)

( )( ) ( )

( )( )

22,3

1 2 21

logexp

log r 2 log 2 logii

i i i

r RdN r Nd π σ σ=

⎛ ⎞⎡ ⎤⎣ ⎦⎜ ⎟= −⎜ ⎟⎜ ⎟⎝ ⎠∑

where is the particle concentration for particles greater than a given radius r , is the total number of

particles for the distribution ,

( )N r iNi iσ is the geometric standard deviation and iR is the geometric mean radius for

particle distribution i. The wind dependent component particle distribution is calculated for four wind speeds; 0, 10, 20, and 30 m s-1. For this effort we used the distribution associated with the 30 m s-1 (parameters in bold text) wind speed and scaled the extinction coefficient based on the amount of dust lofted by the rotorwash. Table 2 represents the values of the variables used in Eq. (18) for the three component desert aerosol model.

The only parameter missing is . The desert aerosol report provides information on the volume concentration (total aerosol volume) and aerosol mass of each aerosol component per unit volume (Table 3). In addition, Table 4 provides the surface area and volume of each of the desert aerosol components for a single particle. for each aerosol component of the desert aerosol model can be computed by dividing the aerosol volume concentration by the volume obtained from Eq. (18) for equal to 1.0 and the values of the equation variables from Table 2 for each

component. See Table 3 for the computed value for for each aerosol component.

iN

iN

iN

iN

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Table 2. Parameter values used for the desert aerosol model.9

Aerosol Component

Wind speed (m sec-1)

Ri ( )log iσ Radii range (µm)

Carbonaceous 0-30 0.0118 0.301 0.0005-100 Water soluble 0-30 0.0285 0.350 0.0005-100

Sand

0 10 20 30

6.24 7.76 9.28

10.80

0.277 0.331 0.384 0.438

0.05-100 0.05-100 0.05-750

0.05-1000

Table 3. Volume concentration and mass per unit volume.9

Aerosol Component

Aerosol volume concentration

( of air) -3 cm3mµ

Aerosol mass

( of air) -3mgmµiN

( ) 3cm−

Carbonaceous 0.022 0.044 368.51 Water Soluble 6.613 0.0164 3673.89

Sand 0 m/s wind 15.5 41.07 0.0025 Sand 10 m/s wind 395.5 1048.1 0.0149 Sand 20 m/s wind 8029.1 21277.1 0.0717 Sand 30 m/s wind 161353.9 427587.8 0.3390

Table 4. Surface area, volume and computed effective radius for the desert aerosol components.9

Aerosol

Component Surface area (area) (µm2 cm-3 of air)

Volume (vol) (µm3 cm-3 of air)

Carbonaceous 1.14*10-3 5.97*10-5

Water Soluble 9.35*10-3 1.80*10-3

Sand 0 m/s wind 2.76*102 6.30*103

Sand 10 m/s wind 6.04*102 2.66*104

Sand 20 m/s wind 1.29*103 1.12*105

Sand 30 m/s wind 2.78*103 4.76*105

Using Eq. (18), and the appropriate parameters in Tables 2 and 3, the particle distribution can be generated. The resulting plot is presented in Fig. 2.

As an example of calculations using MODTRAN to address the capability of detecting objects through rotorwash dust, a mid-latitude summer atmosphere was used with a desert aerosol and vertical path to simulate a sensor located 100 meters above the ground. The visual range (visual range =1.3*visibility) was varied and the transmission for the 0.4 µm to 0.8 µm and 8 µm to 12 µm wavebands was computed using MODTRAN. In general, if transmission drops below 5% a passive detector cannot detect the ground. If the system is active, such as an infrared laser, two additional factors play a role in the performance of the laser system. The laser uses a two-way path, thus transmission is reduced in both directions, and near field backscatter from the aerosol cloud may swamp the detector and render the system ineffective.

From Table 5 it is evident that a passive infrared system does provide some advantage over the visual wavelengths. However, even when the visual range falls below 100 meters (0.100 km) infrared wavelengths will not allow detection of the ground. We will also assess millimeter wave systems as a potential solution for imaging through dust clouds. Our modeling techniques will allow creation of performance requirements for a prototype system for sensing through aerosol clouds and imaging/detecting the ground surface.

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Desert Aerosol Model

(wind speed = 30 m/sec)

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E-03 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03

Radius (Microns)

Num

ber D

ensi

ty (p

artic

les/

cm3 )

Figure 2. Size distribution versus particle concentration for desert aerosol model. Table 5. Visual range (VR), percent visible transmission, and percent infrared transmission for a 100-m vertical path using dust characteristics presented in bold in Tables 2-4.

VR(km) Visible

Tran(%) IR Tran(%)

10 95.82 95.24 5 91.99 94.81 3 87.14 94.23 2 81.45 93.52 1 66.64 91.43

0.75 58.38 90.09 0.5 44.94 87.48 0.3 26.97 82.62 0.2 14.58 77.11 0.1 2.63 63.67

0.05 0.13 45.67 0.01 0 6.87

0.005 0 0.91 0.001 0 0

VII. Case Study Using ROT3DC and the PED model we simulated the formation of snow and dust clouds created by a UH-60

Blackhawk helicopter during hover. In this report we present only the results for the dust cloud. In this simulation, the rotor is operating at sea level standard pressure approximately 3.5m (0.5 rotor radii) above

the ground. The model includes a fuselage (minus the empennage and tail rotor) for blockage effects and the main rotor operating at 88,960N (20,000 lbs) of thrust.

The soil we simulated was the desert sand given in Table 1. We simulated entrainment and dispersion of all three particle sizes used to characterize this soil. Though the entrainment and dispersion of these three particulate phases were modeled simultaneously, interaction of each of the particulate phases with each other was not modeled, only the interaction between the fluid and the particles.

We did, however, modify the bed response of the water-soluble and carbonate phases slightly by assuming that the larger sand particles would protrude higher into the flow, thus determining the aerodynamic roughness of the bed

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for all three phases. Furthermore, due to the size and density of the sand particles we assumed that they would be entrained into the flow by saltation mechanisms. If the bed were composed only of the smaller sub-micron particles, the threshold velocity would be much higher than that of the sand and these small particles would go directly into turbulent diffusion with no appreciable saltation taking place. Yet, since the carbonate and water-soluble particles are in a mixture with the sand, the most likely response is that the sand particles will be entrained at their threshold velocity and as they saltate along the bed the sand particles will kick sand, carbonate and the water-soluble particles loose . In this manner the presence of the sand will have the net effect of depressing the threshold velocities for the sub-micron particles. So for this simulation we set the values of u*t and zo for all of the particulate phases equal to that of the sand phase.

Figure 3. Simulated dust cloud created by a UH-60 after 0.013 seconds in hover. The cloud is represented by a translucent iso-surface of particle concentration (concentration volume fraction = 4×10-7) to provide an approximate representation of the visible edge of the cloud.

ROT3DC generated the three-dimensional flow field and the PED model simulated entrainment and dispersion

of the dust and sand into the air. Fig. 3 is an image of the simulated dust cloud after 0.013 seconds of simulated time showing roughly the boundary of the visible edge of the composite dust cloud containing all three particle sizes. However, the cloud is primarily submicron particles with the majority of the sand particles confined to a layer close to the ground.

VIII. Discussion and Conclusions Brownouts have significant implications in the helicopter operational environment because they affect landing

safety, multi-ship operations, and overall OPTEMPO. Measurements of rotorcraft brownout conditions are difficult to obtain because of the high cost of obtaining the measurements, and because of the difficulty of locating dust of the proper consistency to represent an OCONUS location faithfully. We have chosen to model brownout clouds to provide the flexibility of simulating its creation and evolution during flight, and for the ability to simulate time-varying cloud microphysical properties anywhere within the cloud. Modeling also allows us to simulate a variety of aircraft types and loading conditions, weather, and flight configurations, and allows simulation of a variety of dust and snow conditions. Most importantly, however, modeling allows simulations of electro-optical paths, using MODTRAN for example, through any variety of cloud conditions.

Our approach, using ROT3DC, allows a generally high definition simulation of flow fields around a rotorcraft in different flight configurations. Though some assumptions are made for computational efficiency, such as the flow around blades being generalized as flow around a disk, the model allows simulation of many types of rotorcraft under a variety of load conditions, Though only steady state simulations of maneuver situations are now represented, full flight simulations may be possible soon allowing dynamic simulations of transitions from cruise, to descent and landing.

Though the effects of particle drag on the fluid (two-way coupling) must be added to the PED model, our primary challenge is to explicitly represent the physics of particle entrainment due to impingement at the soil surface. That work is in progress by one of us (Haehnel) in the doctoral program in the Dartmouth College Thayer School of Engineering. The key to this work is the unsteady flow that occurs as a result of turbulence in the flow field causing localized impingement forces sufficiently large to loft particles from the surface through saltation or direct entrainment.

Though not within our tasking, field verification of the simulation capabilities being developed is necessary. We will be working with Army aviation to develop a field verification program after the modeling is completed.

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Acknowledgments The authors wish to thank Saeid Niazi at Sukra Helitek, Inc. for his help and valuable suggestions with ROT3DC

setup and execution. We also thank Professor R. Ganesh Rajagopalan of Iowa State University for his suggestions with rotorwash modeling. Funding provided by the ERDC Battlespace Terrain Reasoning and Awareness program.

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10 Kneizys, F.X., Shettle, E.P., Gallery, W.O., Chetwynd, J.H., Abreu, L.W., Selby, J.E.A., Clough, S.A., and Fenn, R.W. (1983) , Atmospheric Transmittance/Radiance Computer Code LOWTRAN6, AFGL-TR-83-0187, (NTIS AD A137796).

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236. 17Marticorena, B. Bergametti, G., Gillette, D., and Belnap, J., “Factors Controlling Threshold Friction Velocity in Semiarid

and Arid Areas of the United States,” Journal of Geophysical Research, 102, 1997, 23277-23287. 18Fukushima, Y., Etoh, T., Ishiguro, S., Kosugi, K. and Sato, T., “Flow Analysis of Developing Snowdrifts using a k-ε

turbulence model,” SEPPYO, Journal of the Japanese Society of Snow and Ice, Vol. 63, No. 4 (in Japanese), 2001. 19Doorschot, J.J.J. and M. Lehning, “Equilibrium Saltation: Mass Fluxes, Aerodynamic Entrainment and Dependence on

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Regions Research and Engineering Laboratory, Hanover, NH, 1965. 21Draxler, R.R., Gillette, D.A., Kirkpatrick, J.S. and Heller, J., “Estimating PM10 Air Concentrations from Dust Storms in

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