COMPUTATIONAL STUDY ON FLOW CONTROL IN S-SHAPED DUCT OF AN AIRCRAFT WITH PLASMA JET USING ANSYS-FLUENT AND COMSOL-MULTIPHYSICS SOFTWARE

REPORT

SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR

AWARD OF THE DEGREE OF

BACHELOR OF TECHNOLOGY

(Mechanical Engineering)

SUBMITTED BY

Priyanshu Kumar Singh – 20143084

Rachit Agarwal – 20143040

Nikhil Sharma – 20143048

Ashish Kumar Verma – 20143100

Mechanical Engineering Department

MOTILAL NEHRU NATIONAL INSTITUTE OF TECHNOLOGY

ALLAHABAD, INDIA

COMPUTATIONAL STUDY ON FLOW CONTROL IN S-SHAPED DUCT OF AN AIRCRAFT WITH PLASMA JET USING ANSYS-FLUENT AND COMSOL-MULTIPHYSICS SOFTWARE

REPORT

SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR

AWARD OF THE DEGREE OF

BACHELOR OF TECHNOLOGY

(Mechanical Engineering)

SUBMITTED BY

Priyanshu Kumar Singh – 20143084

Rachit Agarwal – 20143040

Nikhil Sharma – 20143048

Ashish Kumar Verma – 20143100

Mechanical Engineering Department

MOTILAL NEHRU NATIONAL INSTITUTE OF TECHNOLOGY

ALLAHABAD, INDIA

CANDIDATE’S DECLARATION

We hereby certify that the work which is being presented in the project report entitled “COMPUTATIONAL STUDY ON FLOW CONTROL IN S-SHAPED DUCT OF AN AIRCRAFT WITH PLASMA JET USING ANSYS-FLUENT AND COMSOL MULTIPHYSIC SOFTWARE” in partial fulfillment of requirements for the award of degree of Bachelor of Technology in Mechanical Engineering at MOTILAL NEHRU NATIONAL INSTITUTE OF TECHNOLOGY, ALLAHABAD is an authentic record of our work carried out during a period from July 2017 to April 2018 under the supervision of Prof. A R Paul. The matter embodied in the thesis has not been submitted to any other University / Institute for the award of any degree.

Signature of the Students

This is to certify that the above statement made by the candidates is correct to the best of my knowledge.

Signature of Supervisor (s)

Abstract

Flow control techniques are important while considering the impact of an aerodynamic load or off design conditions on mechanical parts like compressor and turbine blades or aerodynamic efficiency. Flow control can be classified in several ways.

There can be a number of active flow control techniques like Introduction of Synthetic jets, diaphragm, plasma actuators, unsteady suction or blowing, as air injection through micro jets etc. while passive flow control includes a fixed modification to the flow such as vane or fin-type vortex generators. Passive methods are fixed changes in a geometry driven by a known condition (golf ball dimples, fairings, streaks, etc.). Closed loop flow control means that the flow control can respond to changes in the flow through a feedback loop which provides information on the flow in real time. The one that will have lesser inertia, lesser moving parts along with faster response time apart from obviously having a simple integration into the existing system, will be considered best.

In the light of above few, Plasma actuators are a unique active flow control technique due to their fast response time, lack of moving parts, low mass, purely electric nature and simple integration into many geometries. Plasma actuator are basically boundary layer energizing technique which add momentum to the boundary layer from ionized plasma acting as a body force on the neutral air, resulting in different flow structures. Overall, the flow control has been found to be extremely beneficial in improving the operating range of a compression system for the same inlet duct without flow control.

ACKNOWLEDGEMENTS

The authors are highly grateful to the Director, Motilal Nehru National Institute of Technology (MNNIT), Allahabad for providing this opportunity to carry out the present project work. We avail this opportunity to extend our hearty indebtedness to our guide Prof. A R Paul for his invaluable guidance, untiring efforts and meticulous attention at all stages during my course of work. I would also like to convey my deep regards to our Senior Research Scholar Mr. Krishna Kumar Yadav for his patience, constant motivation and regular monitoring of the work and inputs for which this work has come to fruition. We express our gratitude to Prof. A. D. Bhatt, Head of the Department and Prof. Vinod Yadav, Ex-Head of the Department for providing me the necessary facilities in the department.

Last but not least, our sincere thanks to all who have patiently extended all sorts of help for accomplishing this undertaking.

Priyanshu Kumar Singh

Rachit Agarwal

Nikhil Sharrma

Ashish Kumar Verma

Table of Contents

Abstract……………………………………………………………………………….3 Acknowledgement……………………………………………………………………………………………….4 Table of Contents………………………………………………………………………………….5List of Figures………………………………………………………………………………………7

List of Tables……………………………………………………………………………………….7

1. Introduction…………………………………………………………………………………….82. Literature Review……………………………………………………………………………102.1. Serpentine Ducts …………………………………………………………………………12

2.2.. Plasma actuator…………………………………………………………132.3. Flow Control …………………………………………………………………………………13 2.4. Factors Affecting Engine Performance………………………………………………14

3.0. Project Work………………………………………………………………16

3.1. COMSOL Analysis………………………………………………………..17

3.1.1. Computational Study of Plasma Actuator………………………………17

3.1.2. Background of Fluid Mechanics………………………………………..18

3.1.3. Plasma Discharge Physics……………………………………………….19

3.1.4. Parameters affecting Plasma Discharge…………………………………22

3.1.5. Details of Geometry…………………………………………………….22

3.1.6. Boundary Conditions……………………………………………………23

3.1.7. Mesh Statistics………………………………………………………….24

3.1.8. Solver Details……………………………………………………………25

3.1.9. Method and Termination…………………………………………………..25

3.1.10. Results…………………………………………………………………25

3.1.11. Variation of Electric Potential in Domain……………………………..26

3.1.12. Variation of X-Component of Electric field in Domain……………….26

3.1.13. Variation of X-Component of Body Force in Domain……………………27

3.1.14. Span of Plasma…………………………………………………………29

3.1.15. Average Body Force of Plasma…………………………………………32

3.1.16. Validation of above work and next steps……………………………….33

3.2. Ansys-Fluent Work…………………………………………………………34

3.2.1. Geometry…………………………………………………………………………34

3.2.2. Mesh………………………………………………………………………35

3.2.3. Turbulence Model…………………………………………………………35

3.2.4. Solution Scheme………………………………………………………….36

3.2.5. Boundary Condition………………………………………………………36

3.2.6. Validation of CFD Model…………………………………………………..36

3.2.7 Ansys Fluent- Uncontrolled Flow in S-Duct…………………………………40

3.2.8 Details of geometry…………………………………………………………42

3.2.9 Meshes Used ………………………………………………………………44

3.2.10 Model and Solving Schemes ………………………………………………44.

3.2.11.Boundary condition………………………………………………………..44.

3.2.12 Result ………………………………………………………………………44

3.3.1 Ansys Fluent- Plasma Jet controlled (Constant force field) flow in S-Duct….45

3.3.2 Result (Constant force field) …………………………………………………46

3.3.3 Ansys Fluent -Plasma Jet controlled (Pulsating force field of 20KHz) flow in S- Duct………………………………………………………………………………47

3.3.4 Result (Pulsating force field of 20kHz) ………………………………………47

3.3.5 Ansys Fluent- Plasma Jet controlled (pulsating force field of 2.5KHz) flow in S-Duct …………………………………………………………………………..48

3.3.6. Result (pulsating force field of 2.5Hz) ………………………………………48

4. Discussion

5.Conclusion and future scope……………………………………………………………………..49

REFERENCES……………………………………………………………….50

List of Figures

Fig. 1: Representative S-Duct with Common Terminology

Fig. 2: Layout of Project Work

Fig. 3: Single Dielectric Barrier Discharge Layout

Fig. 4: Details of Geometry of Electrode

Fig. 5: Mesh in Comsol – Multiphysics

Fig. 6: Electric Potential Distribution

Fig. 7: Variation of x Component of Electric Field

Fig. 8: Variation of x component of Body Force

Fig. 9: Regions of Negative Body Force

Fig. 10: Plot of x component of Body Force with x Coordinate

Fig. 11: Plot of x component of Body Force with y Coordinate

Fig. 12: Geometry

Fig. 13: Mesh in Ansys

Fig. 14: Velocity Contours

Fig.15: Geometry

Fig16: 2d geometry of S-Duct

Fig17: meshed geometry of S-Duct

Fig18: Zoomed view of mesh

Fig19: Uncontrolled Result Contour

Fig20: Controlled (constant case) result Contour

Fig21: controlled (20Hz case) result contour

Fig22: controlled (2.5Hz case) result contour

List of Tables

Table 1: Mesh Statistics in Comsol-Multiphysics

Table 2: Mesh Statistics in Ansys-Fluent

Table 3: Mesh Statistics S-Duct

Introduction

1.0.1. Background and Motivation

As aircraft continue to evolve, the requirements for their development are becoming more and more stringent. For military applications, the overall thrust to weight ratio requirement is increasing, demanding either lighter aircraft through length reductions or lighter materials, or more powerful engines which have a disadvantage of adding weight. By reducing the overall aircraft length, large weight savings may be realized with an increase in overall thrust to weight ratio for the same engines.Apart from these, reduction in radar cross-section is another area of design focus where by developing an inlet duct that is offset so that there is no direct line of sight from the entrance of the inlet duct to the engine fan face. This prevents a direct path for radar beams to strike the engine fan face and return to the receiver.

With regards to propulsion, this need for stealth capabilities has led to the development of serpentine inlet ducts. Serpentine inlet ducts have been in existence for some time and can be found in many of today’s commercial and military aircraft including the Boeing 727, F-16 and F-117. Commercial aircraft use serpentine ducts to allow the thrust vector from rear mounted engines to be aligned with the axis of the aircraft.

The developments in technology and reduction in radar cross section requirements are leading to serpentine inlet ducts that are shorter and have larger height offsets throughout the duct. To improve aircraft thrust to weight ratio, the serpentine shape of the inlet duct is becoming more aggressive as an ultra-compact and highly offset and diffusing inlet duct.

These off design conditions pose a significant design challenge. The serpentine inlet duct creates distortion at the aerodynamic interface plane (AIP), where the exit of the inlet duct meets the engine fan face, which will be ingested into the propulsion system following the inlet duct.

The more aggressive inlet ducts result in increased turning which in turn produces secondary flow within the duct. The compact nature of the duct limits the length for diffusion and dissipation of these secondary flows and leads to greater distortion levels at the engine fan face. Inlet distortion can result in high cycle fatigue, which may lead to catastrophic loss of compressor blades, loss of aircraft operability, and increased maintenance costs. The benefits of reduction in aircraft weight and size is proved more beneficial for UAV which offer lesser size and design constraints as opposed to manned aircrafts which have to accommodate for cockpit and support system.

1.1. Literature Review

The various attempts to control the flow within a diffusing serpentine inlet duct will be reviewed. The flow exiting the inlet duct will enter the gas turbine engine. A great deal of literature is available detailing the flow within ducts. As the design of the duct becomes more complex, there is less literature available, and the flow is not as well understood.

Rowe (1970) reported on flow in 45o/45o S-duct. He described the counter-rotating vortices formed in turning ducts. The ducts he investigated were all of circular cross section and therefore produced vortices at the center of the inside turn. In the S-duct tested by Rowe, the second turn of the S-duct tends to dissipate the effect of the first turn. In addition, in the S-duct, the flow is turned only 45 degrees at a time.

In a separate study, by Sullivan et al (1982), the S-duct under investigation involved two 45 degree turns. In this case flow separating vortex pairs were produced at the bottom (inside) of the first turn and the top (inside) of the second turn. This process was documented through dye injection in a water tunnel, and the results show the importance of the severity of the turn in producing secondary flow fields.

Bansod and Bradshaw (1972) examined the flow in several different S-shaped ducts to determine the effect of different radii of curvature of the first and second turns. This study found it was beneficial to have a smaller R/D at the first turn. The shorter intake was found to have better total pressure recovery which indicates that lengthening the turns will allow more distortion to form rather than providing an opportunity for greater dissipation. However, the differences in the various inlet ducts were rather small.

Vakili et al (1983) performed a detailed study on a 30o/30o circular cross section S-duct. They took five-port cone probe measurements at various cross sections along the duct, including the entrance and exit of the duct. This study found that the secondary flow development generated at the first turn was convected throughout the duct with additional vorticity generated at the second turn, in the opposite sense.

Vakili et al (1985) examined a 30o-30o circular cross section S-duct, with an area ratio of 1.51. Here the flow was found to separate in the first turn in the form of a vortex, and did not reattach within the duct.

Povinelli and Towne (1986) examined inlet ducts to determine the main cause of distortion generation. They looked at transitioning cross section (with constant cross sectional area) in combination with centerline curvature. In this portion of the study, the centerline curvature was found to have the largest effect on the distortion generated by the inlet duct.

Thus we see that much of the literature on serpentine or S ducts is for circular cross-section ducts with two equal turns, in opposite directions, bending the flow and then exiting the flow axially. These ducts are often diffusing ducts, with increasing area stream wise along the duct and are being tested with aircraft intake duct applications.

The flow distortion requires correction prior to entering the gas turbine engine. For this reason, flow control techniques have been studied in order to improve the flow uniformity at the exit of the inlet duct.

Flow non uniformity at this stage can decrease engine performance in several ways. This will be discussed in order to understand the importance of improving the flow uniformity at the exit of the inlet duct.

1.1.1 Serpentine Ducts

A representative serpentine or S-duct inlet is shown in Figure 1 along with a graphical representation of common terminology.

Fig.1: Representative S duct with common terminology

1.1.2. Plasma Actuator:

Calculations of Vidmar and Stalder indicate that we should expect a plasma lifetime on the order of 10-8s for our atmospheric-pressure plasma this helps us to assume that the recombination time of the plasma is short compared to the timescale of the discharge.

Shyy, W., Jayaraman, B., and Andersson show different parameters affecting plasma body force magnitude and gave body force values for different voltage input in DBD plasma generation.

First flow separation control on external bluff body using plasma actuator was done by cory stack and he found plasma actuator considerably delayed flow separation.

Plasma actuator not yet been used for internal flow it made us very curious to use.

1.2. Flow Control

In order to combat the effects of secondary flow within the serpentine inlet duct, several attempts to control the flow within the duct and improve exit flow uniformity have been demonstrated. Vortex generators can be designed to direct high energy flow into the low momentum region to re-energize flow near the wall. This approach does not generally reduce secondary flow in the duct and does not always reduce total pressure distortion at the exit of the inlet duct.

Current approaches focus on the source of secondary flow within the duct, that is, the turning of the duct, which creates a series of adverse and favorable pressure gradients. An adverse pressure gradient is associated with the inside of a turn in the duct. The adverse pressure gradient at each turn leads to flow separation along the wall in a pair of counter-rotating vortices.

The flow control technique for the current research involves the use of plasma as a source to delay the flow separation.

1.3. Factors Affecting Engine Performance

As per the above literature review, the flow within a serpentine inlet duct is affected by the centerline curvature, diffusing cross section and transitioning cross section. The flow distortion produced by these design elements varies based on the design. However, all of these factors contribute to inlet. Other forms of inlet distortion that have been studied include total temperature distortion, planar waves and inlet flow angularity or swirl. Total pressure distortion is perhaps the most well-studied and well-documented form of inlet distortion. Total pressure distortion will be used throughout the current research as a measure of inlet distortion due to the well. Total pressure distortion is directly generated by the serpentine shape of the inlet duct in addition to the flow disturbances generated by the presence of a diffusing inlet duct or one with transitioning cross-sectional shape.

1.4. Objective and scope

Our project is based on performing the computational analysis of flow control in S-shaped duct during which we have

to study and Compute the Magnetic Force Field.

To study Complex Duct Geometry and its Flow Behavior.

To analyse Air flow in the complex duct applying Plasma jet in it.

To analyze Aerodynamics Performance of the complex duct without and with Plasma Jets.

Now scopes are:

Flow quality entering the Gas turbine engine can be improved using flow control.

Flow control can decrease the unbalanced forces acting on Compressor blades.

Complex duct can Prevent the detection of rotary parts by enemy radar, thereby increase its stealth.

2.0. Project Work

The project work was divided into subcategories for efficient division of work and maintaining optimum accuracy with minimum time requirement for the completion of individual task. The different steps involved in a successful CFD simulation is described below

Fig.2: Layout of project work

2.1 COMSOL ANALYSIS:

2.1.1. Computational Study of Plasma Actuator

Under certain conditions, the wake of bluff bodies can shed von Kármán and Kelvin-Helmholtz vortices. This shedding creates a periodic, unsteady force from pressure variations in the wake which vibrate the body and can lead to resonance and structural failure.

To control vortex shedding, either passive or active flow control methods can be used. Passive methods are fixed changes in a geometry driven by a known condition (golf ball dimples, fairings, streaks, etc.) while active methods involve a response to an existing condition (jet actuators, deployable fins, etc.). In this case, the plasma actuators are single dielectric barrier discharge (SDBD) plasma actuators. SDBD actuators comprise of two electrodes (one covered and one exposed electrode) separated by a dielectric material as in Fig.3. When sufficient voltage is applied between the electrodes, plasma is formed. The ionized plasma acts as a body force by interacting with the neutral air molecules, creating a wall jet effect and influencing vortex shedding.

The uniqueness of a SDBD separates itself from other flow active control techniques; it has no moving parts, is purely electronic, with fast response time, low mass and can be adhered to nearly any geometry without significant aerodynamic side-effects.

Fig.3: Single dielectric barrier discharge

2.1.2. Background of Fluid Mechanics

Using a cylinder to study and model flow control using plasma actuation is convenient, as the fluid mechanics of a cylinder in a cross flow are well understood. From the frontal stagnation point, the fluid accelerates under a favorable pressure gradient. When the fluid reaches 90 degrees from the frontal stagnation location, the pressure will reach a minimum and the velocity will reach a maximum. After this point the flow faces an adverse pressure gradient and begins to decelerate. Once the fluid experiences a velocity gradient such that (del u/del y)y=0 =0, the flow separates from the surface. This location is the separation point, and is the result of the fluid near the cylinder surface lacking sufficient momentum to overcome the adverse pressure gradient. The flow then detaches from the surface and a wake forms downstream of the cylinder. Low pressure flow within the wake is comprised of von Kármán and Kelvin-Helmholtz vortices which periodically alternate shedding parcels of fluid as time lapses. Generally, SDBDs are placed near the separation point, giving the boundary layer additional momentum to overcome the adverse pressure gradient while moving the flow separation location and possibly eliminating vortex shedding.

2.1.3. Plasma Discharge Physics

When the magnitude of the electric field is large enough, it will cause a Townsend discharge to occur followed by streamer formation. Streamers are small filament discharges that have lives on the order of nanoseconds, and efficiently transfer electric charge from the exposed electrode to the plasma volume above the dielectric due to their high electrical conductivity. For a sinusoidally driven SDBD, the temperature of the plasma rises only slightly due to the added

electrical energy being primarily used to generate energetic electrons.

Plasma is a system of charged particles in electric field, hence the four fundamental Maxwell’s Equations completely represent the phenomena.

…. (2.1)

…. (2.2)

…. (2.3)

…. (2.4)

Where H represents Magnetic field strength, B is magnetic induction, j is current density, D is electric displacement vector, E is electric field and L is curve of circulation. As we are concerned with times scales of fluid response, it is irrelevant to go in details of charge distribution phenomena. Hence we assume all charges have enough time to distribute themselves and situations get settled up, that is, we here assume that the system is quasi-static. density all to zero. Hence simply time derivatives of This assumption sets magnetic field intensity, induction and current electric displacement and magnetic field induction also are zero and we are left only with the Guass Law part of Maxwell’s Equation-

…. (2.5)

but, …..(2.6)

And from the definition of electric potential, we have

Electric potential = negative gradient of the electric field vector

….(2.7)

Therefore,

.…(2.8)

If the system is assumed to be at steady state with negligible velocity gradient and negligible diffusion process the result of applying mechanical force balance (Newton’s 2nd law) we get

…. (2.9)

Where, q is charge, n is the number of such charged particles and p is pressure.

Using Boltzmann’s law and Isothermal gas relations we get-

QUOTE …. (2.10)

Combining we get-

QUOTE …. (2.11)

Solving for this system (q=e) and using the Boltzmann’s relation we get-

QUOTE …. (2.12)

Where QUOTE = number of atoms separated into ions and electrons.

Ti and Te are ion and electron temperatures which can be related to the Debye length using a handy relation.

In terms of the Debye length

QUOTE …. (2.13)

And the volumetric charge density

QUOTE – QUOTE ….(2.14)

Where QUOTE is the Debye length of the plasma, which is the distance till which the shielding effect is felt. And generally has value 0.00016 m. We will be using this value in our simulation.

The charge builds up of the electrons on the dielectric surface causes plasma actuator to be self limiting (Debye length concept.) In case of applied source is AC, in the first half cycle electrons drift from exposed electrode to the encapsulated electrode and accumulate on the surface of dielectric and in negative half cycle these return to the exposed electrode. The effect can be viewed as localised pulsating body force. The body force in other half cycles can be neglected. This encouraged us to compare the AC waves to a saw-tooth waveform with negative cycle neglected (step). Thus the actuator induces a pulsed velocity with frequency equal to the frequency of AC.

Due to accumulation of charges on the dielectric surface above the encapsulated electrode a charge density needs to be given on the electrode. According to Adil et.al the value of this is-

… (2.15)

Where,

…(2.16)

G(x) is half Gaussian function, value of QUOTE is so chosen to exactly mimic the real charge density on the dielectric. Adil et.al reports a value of QUOTE , where L is the length of encapsulated electrode.

The effect of plasma is a pulsating localised body force. Described as-

QUOTE … (2.17)

The solution of electrostatic problem is the potential function. Using which all others can be calculated.

The y component of body force does mainly the job of sucking the flow to the actuator, while the acceleration in flow along the stream is generated by x component, which is mainly responsible for the flow control characteristics of the actuator. Hence we here will be only considering the x-component of body force QUOTE .

2.1.4. Parameters Affecting the Plasma Discharge

The major factors that affect the plasma discharge are the lower electrode size, magnitude of applied voltage, species composition of the plasma, frequency, waveform, and dielectric material. It has been shown by that for a given voltage magnitude the dielectric area above the lower electrode can only absorb a finite charge before becoming saturated. With all other parameters constant, as the lower electrode size increases the force generation increases until an asymptote is reached. This is due to a larger surface discharge generation on the dielectric surface implying that the dielectric area can be too small to take full advantage of the applied voltage.

2.1.5. Details of geometry

Here we present details of the electrode geometry. Geometry is assumed 2D for minimising computational time. Steady Electrostatics is used Note that some of the parameters are arbitrarily chosen and will be later varied in a parametric study, aiming at search of an optimum value.

For sake of simplicity the electrodes are also given material air. As the equation that COMSOL solves only focusses on permittivity and not on conductivity, also the potential can only be given at the edges, it would make a little difference.

Fig. 4: Details of Geometry of electrode

Length of live and ground electrodes is kept 10mm.

On outer boundaries V=0, ?=0

l gap between the electrodes is kept 0.3mm

Horizontal gap is set to be 0.5mm.

Kapton Film is used as dielectric medium with dielectric constant 3.5

Whole electrode is kept in a 100mm x100mm air domain, as shown-

2.1.6. Boundary conditions-

Basic equation of the electrostatic is applied in entire domain (including charge conservation). Exposed electrode is set at 10kV (will be varied later), encapsulated electrode is set as ground electrode (0 V). Outer boundaries of the domain are assumed to be at infinity, hence zero electric potential is assumed there. Additionally, these outer boundaries are also assumed not to carry any charged particles. Note that all maximum possible values (in a duty cycle of AC) are given. That is this model simulates the maximum values of body force produced in a duty cycle. The accumulation of charged particles at the surface of the dielectric (above the encapsulated) is modelled by half Gaussian function.

2.1.7. Mesh Statistics

Mesh here is not user controlled but physics controlled, category is extremely fine. Effect of mesh on convergence is not very marked and an automatically generated physics controlled mesh does the work.

Fig.5 Mesh in Comsol Multiphysics

Description Value

Minimum element quality 0.5403

Average element quality 0.9362

Triangular elements 3758

Edge elements 284

Vertex elements 16

Table 1: Mesh Statistics

2.1.8. Solver Details

Steady state solver is used. MUMPS solver is used with a tolerance of 0.001

2.1.9. Method and termination

Non-linear method used is Newton (Automatic) with initial damping factor vector 1 this changes during study with minimum value attained = 0.0001 (recovery damping factor = 0.75).

Termination technique is tolerance based with tolerance factor 1.

Termination criteria is solution or residuals (residual factor being 1000).

2.1.10. RESULTS

As already stated the solution to electrostatic problem is the electric potential function distribution.

Which can later be processed to extract various information including Electric field, body force field distribution, variation of electric field with x and y co-ordinates etc.

2.1.11. Variation of electric potential in the domain

Fig.6: Electric Potential Distribution

2.1.12. Variation of x component of electric field in the domain

Fig.7: Variation of X component of Electric field

2.1.13. Variation of x component of body force

Fig.8: Variation of x component of body force

Regions of negative body force-

Simulation captured regions having appreciable values of negative body force, these could act as deceleration sites for the fluid.

It is important to precisely know the positions where such regions produce negative force in sufficient magnitude.

These negative force regions occur as an obvious solution of Maxwell’s Equation but important point is that they are not everywhere significant, they become significant only near the edge of the live electrode as shown in following figures. It is important to mention here that such region occur only near the live electrode.

Regions of negative body force

Ground electrode

Live (Exposed) electrode

Fig.9: Regions of Negative Body Force

Extracting meaningful information from the body force field:

We in this section introduce a very computationally efficient method to incorporate the effect of plasma in flow control.

We shall first find a rough span of plasma and an approximate value of average body force produced by the plasma discharge.

In a nut shell what we are going to do here is that first we will find an approximate rectangular region in which all plasma body force will be assumed to act secondly we will find average body force in that region. This will give us a ready-made value of body force at particular V and geometry.

2.1.14. Span of Plasma

Span of plasma is a very important parameter, as we will discuss in flow-control study, altering span of plasma could result in a very dramatic change of circumstances, and the plasma which was working as flow control agent, could itself upset the flow.

This sort of assumption is previously made by some authors. But the reason of assumption of specified dimensions was not made clear. Here we present a satisfying way to do so. We shall traverse horizontal and vertical directions from the actuator and study the pattern of drop in values of certain quantities and then specify the dimensions. Here we assume an even more simplified model, which is not different from the previous. COMSOL Multiphysics allows values of potential to be given at edges, so to minimise the effect of electrode as a separate body during traversing (while calculating the drop in values), we approximate the electrodes to lines. Now we mark lines along which study will be done, this involves two sets –

Horizontal lines

Vertical lines

Horizontal Lines

We plotted value of x component of body force vs x coordinate at various values of y with a step of 0.1mm, with aim of capturing the span of effect of the plasma.

Fig.10(a): Plot of X component of body force with X co-ordinate

Range of y is kept from just surface of upper (exposed) electrode to 2mm with a gap of 0.1mm (till 0.8mm and a directly to 2mm thereafter).

It is clear that effect of plasma falls quiet rapidly as one moves away in x direction, this is extremely fast when we are measuring very close to actuator (black line y=0). As one moves away (wrt y) this drop goes blunt with very little variation at (say) 2mm. (dotted black line) From this graph x wise span of plasma can be determined.

Things become clearer with a close view, as shown below-

Fig.10(b): Plot of x component of body force with X co-ordinate

We can see the effective x wise length of plasma (at this Voltage and geometry) can be assumed to be = 2mm (approx.)

This result matches well with the findings of Cory Stack.

Vertical Lines

Now in this section we measure the drop of body force along a vertical line starting from the right edge of exposed electrode.

It is to note that due to our simplification of the model (approximating the electrodes to edges) an error equal to height of the electrode is bound to creep in (= 0.2mm), but the advantage is that this assumption will certainly simplify the variation which would have otherwise been quiet complex for such simple configuration.

This study will specify the y wise span of plasma.

Fig.11: Plot of x component of body force with Y co-ordinate

From curve it is quite clear that effective y wise span of plasma (at this Voltage and geometry) can be assumed to be = 1mm (approx.) It is to note that Cory Stack also assumed this y wise length of plasma. Now we have a rectangular domain of 2mm X 1mm in which the plasma body force is assumed to be concentrated.

Now we move towards calculating the average body force in that domain.

2.1.15. Average body force of plasma

We assume a rectangular domain near the exposed electrode’s right edge. The dimensions of the domain are as fixed from above discussion 2mm x 1mm.

Average x-body force calculated = 2.5713×105 N/m3.

This value too agrees with the value used by Cory Stack.

2.1.16. Validation of above work and next step

So far we have generated plasma jet at 8000V.The average value of body force is found to be 2.5713×105 N/m3 which too agrees with the one found in Cory stack paper. The next step will be to use this force field as a body force in Navier-stokes equation in Ansys Fluent. But before that, we have to learn the Ansys fluent interface which we did by performing the external flow over a cylinder, first without plasma force field and then with force field i.e., a pulsed source affecting external flow over a cylinder.

2.2. Ansys- Fluent work

We have run 5 simulations in ANSYS FLUENT by varying various control authorities which are discussed one by one in detail.

Ansys Fluent- Flow past Cylinder

Ansys Fluent- Uncontrolled flow in S-Duct

Ansys Fluent- Plasma Jet controlled ( Constant force field) flow in S-Duct

Ansys Fluent -Plasma Jet controlled ( pulsating force field of 20KHz) flow in S-Duct

Ansys Fluent- Plasma Jet controlled (pulsating force field of 2.5KHz) flow in S-Duct

In general, performing any study in Ansys -Fluent requires following steps to be taken:

2.2.1-Geometry

2.2.2-Mesh

2.2.3-Turbulence Model

2.2.4- Solution Scheme

2.2.5-Boundary Condition

2.2.6-Validation of CFD Model

Description of all the above steps is given under:

Ansys Fluent- Flow past Cylinder

2.2.1 Details of geometry

Geometry consists of a 2D view of a cylinder kept in a rectangular air domain. A rectangular domain has been used for this simulation. The outer boundary will be set to be 500*300mm^2 in contrast to cylinder diameter 25.4mm

D 25.4 mm

150 mm

200 mm

500 mm

Fig.12: Geometry

2.2.2 Meshes Used

Fig.13: Mesh in Ansys

Nodes 31644

Elements 38354

Element Type Linear Triangular Element

Inflation 20 Layers

Table 2: Mesh Statistics

2.2.3 Turbulence Model

Spalart–Allmaras model is to be used as it gives better result for bluff bodies The Spalart–Allmaras model is a one-equation model that solves a modelled transport equation for the kinematic eddy turbulent viscosity. The Spalart–Allmaras model was designed specifically for aerospace applications involving wall-bounded flows and has been shown to give good results for boundary layers subjected to adverse pressure gradients.

2.2.4 Solving Schemes

Finite volume method (FVM) based CFD solver-Ansys Fluent 16.0 is used for the simulation of flow field over cylinder. Second-order upwind scheme is used for all equations for achieving higher accuracy. SIMPLE algorithm is used for coupling pressure and velocity. Under-relaxation factors are used for all equations to achieve higher accuracy. Residual monitoring is set to a value of 10^-4 for all equations. Fixed time step method is used for computing unsteady state simulation with a time-step size of 0.001 s and the maximum number of iterations per time step is 25.

2.2.5 Boundary condition

Inlet is velocity inlet with magnitude of 3 m/s. Outlet is pressure outlet with zero-gauge pressure. Wall is specified shear with zero shear stress so that effect of wall should not affect the conditions at cylinder.

2.2.6 Validation of CFD Model

Extensive CFD simulation over flow past a cylinder were carried out by Cory Stack (2014) and the computational model was satisfactorily validated with experimental results. Same CFD model is used in the present study.

The following snapshot sequences demonstrate the development of the von Kármán and Kelvin-Helmholtz vortices. Contour sequences of velocity magnitude, vorticity magnitude are observed to analyze the transient flow characteristics.

t = 0.01 s

t = 0.01 s

t = 0.025 s

t = 0.025 s

t=0.05 s

t = 0.05 s

Cory Stack B) Present

Fig. 14: Velocity Magnitude Contour

Velocity magnitude contours from Fig.14(b) with upper limit 5.227m/s and lower limit 0 m/s demonstrate the transient velocity profile. Upon startup of the simulation at t=.025s, two symmetric vortices are formed in the wake. At t=.05s the first major pressure difference between the top half and the bottom half of the cylinder occurs indicated by the larger region of low velocity in the bottom half of the wake.

3.0 Ansys Fluent- Uncontrolled Flow in S-Duct

3.0.1 Details of geometry

Geometry consists of a 3D view of a duct kept in air domain. A rectangular domain has been used for this simulation in 2D. The duct is of diffused shape with inlet as elliptical cross section of major axis 254mm and minor axis as 68mm. The outlet cross section is circular with diameter 260mm.The total curvilinear length of duct is 1000mm and it best fits in the cuboid of dimensions 800x260x600.

Fig.15: Geometry

The geometry looks like this in 2D.

Fig16: 2d geometry of S-Duct

3.0.2 Meshes Used

Fig17: meshed geometry of S-Duct

Fig18: Zoomed view of mesh

Mesh Statistics are as follows

Table 3: Mesh Statistics S-Duct

3.0.3 Model and Solving Schemes

Model used is Viscous Transient SST (4 eqn.) because it has been shown to give good results for boundary layers subjected to adverse pressure gradients, aerodynamic applications. Pressure and velocity is monitored to calculate coefficient of Pressure recovery(CPR).

3.0.4 Boundary condition

Inlet is velocity inlet with magnitude of 20 m/s. Outlet is pressure outlet with zero-gauge pressure. Wall is specified with No slip condition. The air of density 1.225kg/m3 and dynamic viscosity 1.986 x10^(-5) is flown inside the duct.

3.0.5 Result

Fig19 : Uncontrolled Result Contour

Coefficient of Pressure Recovery was monitored and at outlet it was found to be 0.448 which shows significant loss of pressure at the outlet. So to enhance the performance of Jet engine, we need to achieve increment in value of CPR.

Given result is of Velocity Contour with velocity ranges from 0.0 to 22.1m/s. On the same contour, the velocity profiles were drawn at various planes and flow separation was seen to occur at 280mm along the curvilinear length of duct.

To achieve enhancement in the values of CPR, we now applied a plasma jet which is discussed in next section.

3.0.6 Symbols And Formulae

Pi = Inlet Pressure

Vi = Inlet Velocity

P = Pressure at any plane x

V = Velocity at any plane x

Dynamic Pressure = QUOTE

Cumulative Pressure = P-Pi

CPR = Coefficient of Pressure Recovery = P-Pi

QUOTE

Total Pressure = Static Pressure + Dynamic Pressure = P + QUOTE

Pressure Difference =Total pressure at inlet – Total Pressure at any plane x

Pressure Loss coefficient = Pressure Difference

QUOTE

4. Ansys Fluent- Plasma Jet controlled (Constant force field) flow in S-Duct

In this simulation, the plasma jet is applied at 0.205mm from origin (arrow shown in the 2d view of geometry) with the user defined function at constant force field of 500000 N/m^3 on the same geometry and meshed file keeping the same solver settings with same boundary conditions.

4.1 Result (Constant force field)

Fig20: Controlled (constant case) result Contour

Coefficient of Pressure Recovery was monitored and at outlet it was found to be 0.5103 which shows very less recovery at the outlet and also a lot of energy is getting wasted. So to enhance the performance of Jet engine, we need to achieve increment in value of CPR. We do this by using plasma of pulsating nature.

Given result is again, of Velocity Contour with velocity ranges from 0.0 to 22.1m/s. On the same contour, the velocity profiles were drawn at various planes and flow separation was seen to occur at 287mm along the curvilinear length of duct.

To achieve enhancement in the values of CPR, we now applied a plasma jet of pulsating nature which is discussed in next section.

5. Ansys Fluent -Plasma Jet controlled (Pulsating force field of 20KHz) flow in S-Duct

In this simulation, the plasma jet is applied at 0.205mm from origin (arrow shown in the 2d view of geometry) with the user defined function at pulsating force field of 500000 N/m^3 at 20KHz frequency and of 75% duty cycle of discrete in nature on the same geometry and meshed file keeping the same solver settings with same boundary conditions.

5.1 Result (Pulsating force field of 20kHz)

Fig21 : controlled (20Hz case) result contour

Given result is again, of Velocity Contour with velocity ranges from 0.0 to 22.1m/s. On the same contour, the velocity profiles were drawn at various planes and flow separation was seen to occur at 271mm along the curvilinear length of duct. Thus we see that this result is worse than previous one.

Coefficient of Pressure Recovery was monitored and at outlet it was found to be 0.370 which shows BOUNDARY BLOWN OFF CONDITION. It is because we have given too much energy to the air that entire boundary layer got blown off.

It means that we need to reduce the pulsating frequency of the applied plasma source.

6. Ansys Fluent- Plasma Jet controlled (pulsating force field of 2.5KHz) flow in S-Duct

In this simulation, the plasma jet is applied at 0.205mm from origin (arrow shown in the 2d view of geometry) with the user defined function at pulsating force field of 500000 N/m^3 at 2.5KHz and of 75% duty cycle of discrete in nature on the same geometry and meshed file keeping the same solver settings with same boundary conditions.

6.1 Result (pulsating force field of 2.5Hz)

Fig22: controlled (2.5Hz case) result contour

Given result is again, of Velocity Contour with velocity ranges from 0.0 to 21.92m/s. On the same contour, the velocity profiles were drawn at various planes and flow separation was seen to occur at 310 mm along the curvilinear length of duct. Thus we see that this result is best so far.

Coefficient of Pressure Recovery was monitored and at outlet it was found to be 0.520.

7. Summary

So far we have successfully completed the divided project work of this semester Now the next Semester task will be to design the S-Duct geometry in CATIA and importing the STEP/IGES file in ICEM platform of Ansys software, which is generally used for meshing.

Now the meshed structure will be imported to Ansys-Fluent for the analysis of uncontrolled flow in S-Duct to figure out at what positions the flow separation occurs. After that slots will be provided at strategic positions at the duct to place the plasma generator. Then, analysis of controlled air flow with the help of Plasma jet will be done and finally we will study the aerodynamic performances of jet engines before and after applying Plasma jet.

8. REFERENCES

1 COMSOL libraries, documentation. Version 5.0

2 Bouchmal, A., March 2011,” Modelling of Dielectric-Barrier Discharge Actuator Implementation, validation and generalization of an electrostatic model”, M.Sc. Thesis, Faculty of Aerospace Engineering, Delft University of Technology.

3 Enloe, L., McLaughlin, T., VanDyken, Kachner, Jumper, E., and Corke, T. Mechanisms and responses of a single-dielectric barrier plasma actuator: Plasma morphology. AIAA 42 (2004), 589

4. Enloe, L., McLaughlin, T., VanDyken, Kachner, Jumper, E., Corke, T., Post, M., Haddad, O., 2004,” Mechanisms and responses of a single-dielectric barrier plasma actuator: Geometric effects”. AIAA 42.

5 Landau, L. D., and Lifshitz, E. Electrodynamics of continuous media. Pergamon, 1984.

6 Roth, J., Sherman, D., and Wilkinson, S. Electro hydrodynamic flow control with a glow-discharge surface plasma. AIAA Journal 38 (2000).

7 Shyy, W., Jayaraman, B., and Andersson, A. Modelling of glow discharge-induced fluid dynamics. Journal of applied physics 92 (2002).

8 D.M. Orlov and T.C. Corke. Electric circuit model for aerodynamic plasma actuator. AIAA Aerospace Sciences Meeting and Exhibit, 44, 2006.

9 C. L. Enloe, Thomas E. McLaughlin, Robert D. VanDyken, and John C. Fischer. Mechanisms and responses of a single dielectric barrier plasma actuator: Geometric effects. 42nd AIAA Aerospace Sciences Meeting and Exhibit, 2004.

10 B. Jayaraman and W. Shyy. Modelling of dielectric barrier discharge-induced fluid dynamics and heat transfer. Progress in Aerospace Sciences, 44:139{191, 2008.

11 Suzen, Y. B., Huang, P. G., and Jacob, J. D., “Numerical Simulations of Plasma Based Flow Control Applications,” AIAA-Paper 2005-4630, 35th AIAA Fluid Dynamics Conference and Exhibit, Toronto, Ontario Canada.

12 Aholt, J., and Finaish F., “Active Flow Control Strategy of Laminar Separation Bubbles Developed over Subsonic Aerofoils at Low Reynolds Numbers,” AIAA Paper 2011-733, 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Orlando, Florida

13 Visbal, M. R., Gaitonde, D. V., and Roy, S., “Control of Transitional and Turbulent Flows Using Plasma-Based Actuators,” AIAA-Paper 2006-3230, AIAA Fluid Dynamics and Flow Control Conference, San Francisco, California.

14 Tsubakino, D., Tanaka, Y., and Fujii, K., “Effective Layout of Plasma Actuators for a Flow Separation Control on a Wing,” AIAA-Paper 2007-474, 45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada

15 Corke, T. C., Post, M. L., and Orlov, D. M., “SDBD plasma enhanced aerodynamics: concepts, optimization and applications,” Computers ; Fluid, Vol.43, 2007

16 Cory Stack, Simulating the Effect of Plasma Actuators on the Three-Dimensionality of the Wake of a Cylinder in a Crossflow, Undergraduate Research Thesis, the Ohio state university- department of aerospace/ mechanical engineering, May 2014.

Sample Sheet-References

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