ANALYICAL AND CFD VISUALIZATION STUDIES OF COANDĂ MAV

Harijono Djojodihardjo1, Riyadh I. Ahmed, A.R. Abu-Talib, A.S. Mohd-Rafie, 2015

ANALYICAL AND CFD VISUALIZATION STUDIES OF COANDĂ MAV

Harijono Djojodihardjo1, Riyadh I. Ahmed, A.R. Abu-Talib, A.S. Mohd-Rafie

Department of Aerospace Engineering, Faculty of Engineering, Universiti Putra Malaysia,

43400 Serdang, Selangor Darul Ehsan, Malaysia

Abstract. To meet the desired mission and design requirements, the basic working relation-

ships between various relevant variables and parameters governing the aerodynamics forces in the

design of a Coandă MAV should be established. To that end, several tools can be utilized. The first

is the analytical tool, which capitalizes on the basic fundamental principles. The second is the utili-

zation of Computational Fluid Dynamics (CFD), to provide visualization and significant insight in

identifying the relevant problem. Theoretical analysis, and CFD computational and visualization

studies will be useful in the preliminary study stage, as well as in designing specific experiments in

the conceptual and prototype design stages. Various CFD studies have also indicated that there are

still significant discrepancies between CFD and experimental studies, which necessitate the estab-

lishment of specific baseline configurations for validation purposes. The present work carries out

analysis and CFD visualization studies on the spherical and cylindrical Coandă MAV's.

Introduction. Coandă effect and Coandă jet have found many applications in engineering,

among others in aircraft and vehicle technology [1-5], as well as wind-turbines [6-7]. In particular,

Coandă MAV' share in active developments, and various configurations have been proposed and

developed. For the purpose of designing a Coandă MAV which could meet the desired mission and

design requirements, it is mandatory to establish the basic working relationships between various

relevant variables and parameters governing the aerodynamics forces. To assist the analysis, design

and developments of Coandă MAV's, several tools can be resorted to. The first is the analytical tool,

which capitalizes on the basic fundamental principles. The second is the utilization of Computation-

al Fluid Dynamics, (CFD) which has the advantage of providing visualization for significant insight

and identification to the problem at hand, which then can be utilized in enhancing the analysis and

identifying specific details. Experimental tools can benefit from the insight gained by analysis, CFD

computational and visualization studies, in the preliminary study stage by designing specific exper-

iments as well as in the conceptual and prototype design stages. Various CFD studies have also in-

dicated that there are still significant discrepancies between CFD and experimental studies [6],

which necessitate the existence of specific baseline configurations for validation purposes. Coandă

MAV is expected to be capable of maneuvering as illustrated in Figs. 1 (a) and (b), and the analysis

carried out here is associated with hovering condition, which should give further insight into its

hovering performance.

Fig.1: a. An impression of the possible Coandă MAV qualitative performance in comparison to other flight vehicles

(adapted from [9]), b. Flight Manoeuvring Structure (adapted from [10]) .

1 Corresponding Author


In the study of Coandă MAV, it is desired that the Coandă propulsion system will be able to

provide both an efficient cruise phase as well as hover capability, by using Coandă jet blanket (for

semi-spherical Coandă MAV which is deflected downward using a curved surface. Thus lift will be

generated, first to hover and later for propulsion as well. Such Coandă jet has been utilized for cir-

culation enhancement [3][4][5][7][8] for fixed wing aircraft and turbine blades in forward flight and

movement. By referring to Fig. 1a, adapted from Schroijen and van Toren [9], it would be of inter-

est to investigate the principle of Coandă MAV Lift generation as well as its performance in hover

and forward flight. The latter will not be discussed in the present paper. Furthermore, the control

scheme to allow flight-maneuvering structure as depicted in Fig. 1b could be kept as an overall ob-

jective of flight vehicle control system, for later considerations in the design. All of these necessi-

tates a sound bases for the analysis as considered in the present work.

For designing an MAV that could meet the desired missions and the preliminary design re-

quirements, it is mandatory to set the foundation for the basic working relationships between vari-

ous relevant variables and parameters governing the aerodynamic performance parameters. It is

with such motivation that the present work elaborates CFD visualization studies to gain further un-

derstanding as also associated with the authors' previous analysis on two Coandă MAV configura-

tions as baseline. The latter are the spherical and cylindrical Coandă MAV's, as further defined and

elaborated.

Referring to the authors' earlier work on Coandă effect MAV [11][12], a physical and mathe-

matical model has been developed to describe the physical phenomena of the flow field related to

the relevant surfaces influenced by the Coandă effect jet sheets and to gain better insight on the re-

lationship between relevant parameters to the lift.

Baseline Analytical Development.

a. Semi-spherical Coandă MAV: Earlier development elaborated in [10][11] have produced

the relationship between the lift produced and the relevant parameters of the Coandă MAV. The lat-

ter are the characteristic dimension of the MAV, represented by its outer radius R, the input mo-

mentum or energy, as appropriate, of the Coandă jet, represented by its mass flow rate ṁ and inlet

velocity Vj-in and the surrounding atmosphere, represented by the ambient pressure pa. As elaborated

in [11][12][13], the Coandă effect contribution to the generation of lift capability of Coandă MAV

is analyzed by applying the fundamental conservation analysis on the control volume CV. For con-

ceptual development, and referring to Fig.2, the radial flow for Coandă jet blanket on the surface of

the body can be introduced at the symmetry plane. Momentum analysis is carried out in order to

identify the Coandă effect related aerodynamic forces and the Coandă MAV performance parame-

ters.

For the baseline Spherical Coandă MAV, and referring to Fig.2, the Lift produced can be ex-

pressed by [11][12]:

Total Lift force Lift due to Vertical component of momentum Lift due to Pressure difference on the = +

due to Coandă Blanket balance due to Coandă Blanket body of MAV subject to Coandă Bl

0 2

2 2 2 2

- 02 sin 2

1

2

i

pressur

Coanda jet Blanket i i j in i a ainduced pressure difference j R

j in j inCoandablanket contribution

anket

h mLift R h V R R p p πR d

R 2πρRh

m V mV

edifferencecontribution

(1)


where i is the general location of the Coandă injection and 0 the location where the Coandă blan-

ket leaves the surface of the semi-spherical MAV, as elaborated in [12][13]. Equation (1) simplifies

further to:

3 3

2 2 Coanda jet Blanket j in in

induced pressuredifference

Lift m V rateof momentum (2)

Fig. 2.(a) Semi-Spherical Coandă MAV for baseline analysis; (b) Dashed circle indicating the part for which an

appropriate control volume for analysis will be defined

This equation and various aspects leading to its derivation has been verified in [11][12] with

analytical, experimental and CFD results from the literature as elaborated there. Equation (2) is sim-

ilar to that obtained by Schroijen and van Tooren [9] for cylindrical MAV, with the addition of

pressure difference between the lower and upper surfaces due to the presence of Coandă blanket

[9][11]. Such notion can also be concluded from equation (1). In the present work, further insight to

the significance of equations (1) and (2) will be further elaborated using CFD simulation.

Performance measures to evaluate the aerodynamic performance for Coandă MAV system can

then be defined by assessing the output lift as compared to the input momentum rate to the defined

control volume, which is dimensionless and given by

jet+ induce pressure difference 3Performance Measure PM1

Momentum In 2

coandaLift

Coanda Jet (3)

The second performance measure can be defined by comparing the Lift produced by the Coandă

MAV due to Coandă effect and the inlet velocity, which has dimensions, and is given by

jet+ induce pressure difference

0 0

3Performance Measure PM2 3

2 coanda

j in

liftR h V m

Jet Inlet velocity (4)

or a third Performance measure may be defined based on the Coandă jet rate of momentum influx

per unit Coandă jet kinetic energy input (dimensional):

jet+ induce pressure difference 0_2

0

3Performance Measure PM3 3

2

coanda

MAV base

j in

lift h mA

Jet Inlet velocity R V

(5)

Where

2

0_ MAV baseA R

(6)

b. Cylindrical Coandă MAV: Similar analysis can be made for cylindrically shaped MAV.

The analysis can be carried out following the same procedure above, assuming incompressible 2-D

flow. In the following analysis, the cylindrically shaped Coandă MAV is idealized as depicted in

Fig.3 (a) and (b), with the cylindrically shaped upper surface to have a radius of R and depth of l.

The Coandă jet flowing over it is assumed to be a thin jet sheet of thickness h (h<<R); the pressure


gradient (dP/dR) across the jet sheet is assumed to be negligible. Hence, the resultant forces that

contribute the lift are given by: 22

2

j

1

2Total in j in

h hF lift V l V Rl

t t

(7)

The performance measure given by equations (3) to (5) can readily be obtained for the same flow

conditions.

a b

Fig. 3. (a) Schematic of 2D cylindrical Coandă MAV, (b) Pressure forces acting vertically on control volume of Coandă

surface.

CFD Analysis and simulation. The foundation of computational fluid dynamics (CFD) is the

fundamental governing equations of fluid dynamics, i.e. the continuity, momentum and energy

equations. It is basically the conservation principles of physics expressed in the mathematical

statements of three fundamental physical principles upon which all of fluid dynamics is based; these

are the principle of mass conservation, Newton’s second law, and the principle of conservation of

energy. For CFD, the use of these equations in one particular form may lead to success, whereas the

use of an alternate form may result in oscillations (wiggles) in the numerical results, or even

instability (Bakker, [14]). The fluid flow equations obtained by applying the fundamental physical

principles to a finite control volume are in integral form, which can be manipulated to indirectly

obtain partial differential equations. The equations so obtained from the finite control volume fixed

in space in either integral or partial differential form are called the conservation form of the

governing equations. The equations obtained from the finite control volume moving with the fluid,

in either integral or partial differential form, are called the non-conservation form of the governing

equations. This finite volume methods (FVMs) are based on a discretization of the integrals forms

of the conservation equations. The solution domain is subdivided into a finite number of contiguous

control volumes (CVs) and the conservation equations are applied to each CV. An advantage of the

FVM is that it is easily formulated to allow for unstructured meshes. For complex geometries, the

structured approach is however inadequate.

The basis of the computational approach in the present work is the Reynolds averaged Navier–

Stokes (RANS) equation and its implementation into the CFD equation. When pursuing further the

numerical solution of dynamic fluid flow using CFD techniques, in order to arrive at accurate solu-

tion, at least two aspects should be given careful attention, with due consideration of computational

uncertainties. The first is the grid generation, and the second is the turbulence modelling of the par-

ticular flow (Djojodihardjo, [8]). The governing Reynolds averaged Navier–Stokes (RANS) equa-

tion is given by (steady state and ignoring body forces):


____ji i

j ij i j

j j j i

uu uu p u 'u '

x x x x

(8)

i

j

u 0

x

(9)

Care should be exercised to simulate Coandă flows over curved surfaces using Computational Fluid

Dynamics as stipulated by Bakker [14], due to the fact that using the conventional RANS models

appropriate turbulence model has to be chosen, in particular to accurately predict the y+ value and

flow separation points. For this purpose, taking note the suggestions implied by Djojodihardjo [8],

Bakker [14] and Menter [15], in the present CFD simulation k-omega SST turbulence model is

applied.The CFD model of the semi-spherical Coandă MAV is depicted in Fig.4.

a a b

c d

Fig. 4. (a) control volume utilized for the CFD analysis and simulation for the symmetrical half of the semi-spherical

Coandă MAV; (b) Associated CFD Velocity contour; (c) and (d) similar to (a) and (b) for the entire axi-symmetric

plane of the semi-spherical Coandă MAV.

Results and assessment. The analytical performance measures results were compared with

those from the CFD analysis and with pre-assumption for the outlet velocity as a function of the

body radius and as shown in the Fig. 5 and Fig. 6 below for uniform jet inlet velocity of 20m/s.

The CFD computational simulation for the Coandă jet of the semi-spherically shaped MAV

exhibited in Fig. 1 and Fig. 4 is first used to verify the results of the analytical predictions as given

by equations (1) to (5) representing the influence of the Coandă effect in generating lift for Coandă

fitted MAV. The formula given by these equations were derived for semi-spherically shaped

Coandă MAV. The control volume utilized for the CFD analysis and simulation for the symmetrical

half of the semi-spherical Coandă MAV is shown in Fig. 4 (a), while for the entire axi-symmetric

plane of the semi-spherical Coandă MAV is depicted by Fig. 4 (c). Fig. 4 (b) and (d) exhibit the

CFD Velocity contours associated with Figs. 4 (a) and (c), respectively.

Normal stress Reynolds stress Viscous stress Change in mean

momentum of fluid

element


Performance measure PM1 indicates that the Coandă effect for such semi-spherical air vehicle

produces a gain of 150% from the input momentum, which could be verified with the CFD simula-

tion as shown in Fig. 5. Figure 5 exhibits the comparison of the analytical and CFD Performance

measure for spherical Coandă MAV for various Jet slot thickness, with and without actuator Disk.

Fig. 6 shows the comparison of the Analytical and CFD Performance measure PM3 for spherical

Coandă MAV for various Jet slot thickness.

h/R=1%

h/R=2%

h/R=2.5%

h/R=5%

h/R=7.5%

h/R=10%

Fig. 5. Performance measure for symmetrical semi spherical Coandă MAV with various Jet slot thickness

Fig. 6 Comparison of the Analytical and CFD Performance measure PM3 for spherical Coandă MAV for various Jet

slot thickness.

It is noted that the CFD analysis takes into account the viscous flow nature of the flow, while

the theoretical analysis is based on potential flow. Therefore, the present theoretical analysis should

give conservative results. Such situation is exhibited by Fig. 5, 6 and 8, which show that qualitative-


ly the theoretical analysis has qualitative agreement with the CFD analysis, while quantitatively the

CFD analysis should provide lower lift as well as other performance measures, as elaborated subse-

quently. Nevertheless, comparison of both results may serve to confirm the theoretical prediction

for preliminary design purposes.

Another significant comparison can be made for an MAV configuration with a propeller to

produce vertical thrust as illustrated in Fig. 7. In addition to providing thrust (in the vertical direc-

tion, or lift like in helicopter or hovercraft during hover), a small percentage of the airflow induced

by the propeller provides bleed air for the radial Coandă jet along the spherical surface of the MAV.

The vertical thrust (lift) generated by the propeller can be calculated using actuator disk theory (see

Fig. 7, elaborated by Ahmed et al[8] and Djojodihardjo and Ahmed [9] );

2 2 2

actuator I in out actuator

2 2

I in actuator

Lift = ρπ R U -U

8 ρπ R U

9

(10)

Fig. 8 indicates the lift of the MAV due to combined actuator disk (eq.(10) and the Coandă ef-

fect lift (2); here the actuator disk (cylindrical part) is assumed to have a radius RI. Taking into ac-

count the Betz limit, the maximum efficiency of the actuator disk is then η ≈ 59%, which is taken

into account in obtaining the combined lift.

Fig. 7. Semi-Spherical Coandă MAV integrates Coandă effect and actuator effect.

Fig. 8. Analytical and CFD Performance measure for spherical Coandă MAV for various Jet slot thickness, with and

without actuator Disk.

Such configuration is then simulated using CFD as exhibited in Fig. 8. More information could be

obtained from the CFD simulation on the pressure along the Coandă surface and how it varies with

the MAV upper surface radius. For the semi-spherical Coandă jet MAV without actuator, the CFD

simulation and visualization results are exhibited in Fig. 9, while for the cylindrical Coandă jet


MAV in Fig. 10. Figure 9 exhibits the pressure contours along semi-spherical Coandă MAV surface

body obtained by CFD simulation results (left), and the associated static pressure color-coded con-

tour (right). Following similar procedure, the result shown in Fig. 10 exhibits the jet velocity along

the cylindrical MAV surface for two different jet slot thicknesses

Fig. 9. Comparison between the CFD simulation and plot for pressure contours along semi-spherical Coandă MAV sur-

face.

Conclusion: The most promising route to break through the conventional aerodynamic design

limit and bring dramatic performance improvement to aircraft can be found in the use of flow con-

trol, and in the present case, the use of Coandă Effect. However, the main objectives of this paper

are to utilize the benefits of CFD analysis in two aspects; first to obtain some information on the

flow situation, if some assumptions have to be made in the analytical approach, and second, to veri-

fythe validity of the theoretical results subject to the theoretical assumptions.

Fig. 10.The jet velocity along the cylindrical shape surface for different jet slot thickness


Such comparison serve to assess the uncertainties and accuracy of the theoretical approach. In

addition, the CFD computational and visualization studies, can provide further insight in revealing

other characteristics of the flow field, and can assist further in-depth analysis, as well as in the de-

sign of experiments to that end. For example, to find out, under what conditions the effect of viscos-

ity may cause the Coandă jet to separate. In summary, two types of Coandă MAV configurations

have been analyzed in great detail, i.e. the semi-spherical and the cylindrical MAV. CFD visualiza-

tion has certainly assist us in assessing the application of fundamental conservation principle in con-

tinuum mechanics in the present analysis on Coandă jet configured MAV to provide a comprehen-

sive account on the lift generation due to Coandă jet effect.

ACKNOWLEDGEMENT

The authors would like to thank Universiti Putra Malaysia (UPM) for granting Research University

Grant Scheme (RUGS) No.9378200, and the ministry of higher education ERGS: 5527088 ;

FRGS:5524250 under which the present research is carried out.

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ANALYICAL AND CFD VISUALIZATION STUDIES OF COANDĂ MAV

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