2019:688 Influence on tip leakage flow in a compressor cascade with plasma actuation Haotian Wang Approved Date 2019‐10‐30 Examiner Björn Laumert Supervisor Nenad Glodic Commissioner Contact person
Abstract
As one of the key components of aero engines, compressor is required to endure higher pressure, possess higher efficiency and wider operating range. Intensive studies have been made on tip leakage flow and researchers find that by reasonably organizing tip leakage flow, aero engines are more likely to achieve better performance and reliability. Conventional flow controlling methods like casing treatment and micro jet could substantially modify tip leakage flow, unfortunately with a price of additional loss, not to mention the difficulty in manufacturing such structure. Whereas plasma actuation flow control method uses plasma actuators, such equipment is easy to build, responses fast and has a wide excitation bandwidth. This method has become a new trend in internal flow active control field.In this research, a phenomenological model is adopted to simulate DBD plasma actuation in the flow field inside a compressor cascade. The aim is to find out how plasma actuation will influence tip leakage flow. Meanwhile possible means to improve plasma actuation performance are discussed.
circumferential shearing.
4. Casing movement has little influence on total pressure field concerning absolute pressure value. While total pressure loss does reduce slightly with increasing moving speed of shroud. 5. Vorticity transport from tip clearance into passage may be contributing significantly to
generation of tip leakage vortex inner core.
Secondly, a simplified model of DBD plasma actuation based on literature [1] is derived and applied through UDF function of commercial software Fluent into the flow field. Different actuation positions, voltages and frequencies are applied in simulation and compared. After that casing movement is included. Main conclusions are as follow:
6. Plasma actuation shows significant suppressing effect on tip leakage vortex on both size, trajectory and strength. 7. The suppressing effect on tip leakage vortex grows stronger as actuator moves towards leading edge. 8. Increasing actuation voltage results in stronger suppressing effect on tip leakage vortex. 9. Plasma actuation can effectively improve total pressure loss situation near shroud region with increasing actuation power. 10. Increasing actuation frequency results in stronger suppressing effect on tip leakage vortex as well. Additionally, frequency performs slightly better than voltage.
11. Casing movement tends to weaken suppressing effect of tip leakage vortex by plasma actuation. More actuation power is needed to achieve sufficient suppressing effect in real compressors.
Keywords: Flow control, DBD Plasma actuation, phenomenological model, numerical simulation, tip leakage flow, compressor cascade.
Sammanfattning
Som en av de viktigaste komponenterna i flygmotorer krävs det att kompressorn utsätts för högre tryck, har högre effektivitet och större driftsintervall. Intensiva studier har gjorts om skovlarnas toppspel läckageflöde och man anser att det är mer sannolikt att flygmotorer uppnår bättre prestanda och tillförlitlighet genom att på ett rimligt sätt reglera läckageflödet i toppspelet. Konventionella metoder för reglering av flödet, som behandling av “casing” och mikrojet, skulle kunna ändra läckageflödet avsevärt, men medför tyvärr ytterligare förlust, för att inte tala om svårigheten att tillverka en sådan struktur. Samtidig flödeskontroll med hjälp av plasma aktuatorer som är relativt lätta att bygga, reagerar snabbt och har en bred excitationsbandvid. Denna metod har blivit en ny trend inom det interna flödesaktiva kontrollområdet.
I denna forskning antas en modell för att simulera plasmaaktivering av DBD i flödesfältet i en kompressorskaskad. Man försöker ta reda på hur plasmaaktivering påverkar läckageflödet. Möjliga sätt att förbättra effekten av plasmaaktivering diskuteras.
För det första genomförs numerisk simulering av flödet i en kompressorskaskad utan plasmaaktivering för att validera noggrannheten i den numeriska metoden. Därefter undersöks i detalj vilken inverkan den relativa rörelsen av ”casing” har på läckageflödet genom toppspelet och mekanismen för toppspelsvirvel analyseras. Resultaten visar: 1. Startposition för läckagevirveln rör sig mot skovelns framkant när man introducerar och ökar den relativa hastigheten för ”casing”. 2. I takt med att den relativa hastigheten ökar, kretsbanan för läckage virveln rör sig bort från skovelns sugsida och närmare mot ”casing”.
3. Den relativa rörelsen tenderar att omvandla virveln från cirkulär till oval form på grund av skjuvkrafter. 4. Den relativa rörelsen av ”casing” påverkar inte det totala tryckfältet när det gäller det absoluta tryckvärdet. Samtidigt som den totala tryckförlusten minskar något med ökad hastighet. 5. Virveltransport från toppspelet till huvudkanalen kan på ett betydande sätt bidra till att skapa virvelns inre kärna. I senare delen av arbetet utvecklas och tillämpas en förenklad modell för plasmaaktivering av DBD baserad på litteratur [1], genom att använda UDF‐funktionen i kommersiell CFD programvara Fluent. Olika aktuatorläge, spänningar och frekvenser prövas i simuleringen och jämförs. De viktigaste slutsatserna är följande:
6. Aktuering av plasma visar en betydande dämpningseffekt på läckagevirveln i toppspelet både va det gäller dess storlek, bana och styrka.
7. Den dämpande effekten på läckagevirveln blir starkare när aktuator monteras närmare skovelns framkant.
8. Ökad aktuatorspänning leder till en starkare dämpande effekt på läckagevirveln.
10. Den relativa rörelsen av ”casing” försvagar effekten av plasmaaktuering. För att uppnå tillräcklig dämpningseffekt i riktiga kompressorer krävs mer effekt till aktuatorn.
Nyckelord: Flödesreglering, DBD Plasma‐aktuator, numerisk simulering, toppspelsflöde,
Figures
Figure 1 Classification of flow control strategies ... 14 Figure 2 Classification of active control strategies ... 14 Figure 3 Typical DBD plasma actuator structure ... 16 Figure 4 Illustration of a working DBD plasma actuator and the micro discharge process ... 16 Figure 5 Classification of plasma ... 17 Figure 6 Comparison of different dielectric materials ... 17 Figure 7 Flow field with different actuation voltage phases ... 18 Figure 8 Orlov's numerical model of DBD plasma actuation ... 18 Figure 9 Paraelectric plasma actuators' effect on leading edge separation ... 19 Figure 10 Lift‐drag ratio increase by plasma actuation ... 19 Figure 11 Effect of different DBD setup on delta wing with different sweep back angle... 20Figure 12 Suppression effect of DBD actuation on leading edge separation with different excitation voltage and duty cycle ... 20 Figure 13 Influence of DBD plasma actuation on separation in a low pressure turbine ... 20 Figure 14 Comparison of different actuation frequencies on tip leakage flow ... 21 Figure 15 Stall suppression effect in axial compressor with different actuation positions ... 21 Figure 16 Suppressing effect of plasma actuation on tip leakage flow ... 22 Figure 17 Working process of UDF within Fluent ... 23 Figure 18 Illustration of electric field distribution of plasma area ... 24 Figure 19 Illustration of compressor cascade passage and measuring positions ... 27 Figure 20 Comparison of pressure coefficient for different turbulent models at 98.5% span 28 Figure 21 Comparison of axial velocity with different turbulent models at 55% chord, 97% span ... 29 Figure 22 Illustration of medium mesh ... 30
Figure 23 Circumferential averaged pressure at trailing edge plane for different meshing proposals ... 30
Figure 24 Total pressure of tip leakage vortex core at different axial planes with different meshing ... 31
Figure 25 Pressure contour on shroud for different casing moving speed(unit/Pa) ... 32
Figure 26 Distance of TLV core from shroud for different casing moving speed ... 33
Figure 27 Distance of TLV core from blade suction side ... 33
Figure 28 Q contour of multiple traverse planes for different casing moving speed ... 34
Figure 36 Zoom‐in contour of z vorticity contour near tip clearance exit for stationary and moving casing at 10% chord ... 39 Figure 37 Tip leakage vortex illustration for stationary casing and moving casing ... 40 Figure 38 Illustration of different actuation positions ... 42 Figure 39 Pressure contour of shroud for different actuation positions(unit/Pa) ... 43 Figure 40 Q contour for multiple traverse planes with and without plasma actuation ... 43 Figure 41 Zoom‐in view of Q contour at 70% chord for position 1 and position 3 ... 44 Figure 42 Streamtraces of tip leakage vortex with and without plasma actuation ... 44
Figure 43 Z‐vorticity contour inside tip clearance at 10% chord with and without plasma actuation ... 45 Figure 44 Shroud pressure contour with different actuation voltages(unit/Pa) ... 46 Figure 45 Q contour at multiple traverse planes for different actuation voltages ... 47 Figure 46 Zoom‐in view of Q contour at 70% chord for different actuation voltage ... 47 Figure 47 Z‐vorticity contour inside tip clearance at 10% chord for different actuation voltages ... 47
Figure 48 A certain set of streamtraces for different actuation voltages and leakage flow illustration with 9000 volts actuation ... 48 Figure 49 Total pressure contour with different actuation voltages(unit/Pa) ... 49 Figure 50 Mass‐averaged total pressure loss coefficient at different axial planes for different actuation voltages ... 49 Figure 51 Shroud pressure contour with different actuation frequencies(unit/Pa) ... 50 Figure 52 Comparison of shroud pressure contour for 9000 V case and 9000 Hz case(unit/Pa) ... 51 Figure 53 Q contour at multiple traverse planes for different actuation frequencies ... 52 Figure 54 Q contour at 70% chord for 9000V case and 9000Hz case ... 52 Figure 55 Z‐vorticity contour inside tip clearance at 10%chord for 9000 V case and 9000 Hz case ... 52 Figure 56 Tip leakage vortex structure for 9000 V case and 9000 Hz case ... 53
Figure 57 Shroud pressure contour with casing movement for different actuation frequencies(unit/Pa) ... 54
Figure 58 Q contour with casing movement for different actuation frequencies ... 55
Figure 59 Z‐vorticity contour inside tip clearance at 10% chord with and without casing movement for 3000 Hz and 9000 Hz actuation ... 56
Figure 60 A certain set of streamtraces with and without casing movement for 3000 Hz and 9000 Hz actuation ... 57
RSM Reynolds stress model
TLV Tip leakage vortex
1 Introduction
1.1 Background
Flow control methods consist of active control method and passive control method, as shown in figure 1. Passive control method has been widely used on airfoil and aero engines. This kind of method modifies flow field through a set of mechanical structures and is predesigned. Which means when engines work at off design conditions, best performance could not be achieved. However, active control method tends to be more flexible. It achieves effective flow modification locally or globally by inputting local energy. The excitation time and position can be adjusted to a certain extent [2]. In recent years, much attention has been paid to active control method, especially on the field of aerodynamic designing.
Figure 1 Classification of flow control strategies
There are numerous kinds of active control methods, a detailed classification has been made by Louis. N [3], as shown in figure 2. Most commonly used method is fluidic method, namely jet flow, including micro blowing and zero net mass flux. Another method is moving object/surface method. It provides flow field with steady or periodic or pulse momentum input through certain parts moving, rotating or transforming. However, both methods require introducing complex mechanical devices. Additionally, such methods cannot respond fast enough due to mechanical limits. The advantages and disadvantages of these active control strategies are listed in table 1.
Table 1 Advantages and disadvantages of commonly used active control strategies
Figure 3 Typical DBD plasma actuator structure
Figure 4 Illustration of a working DBD plasma actuator and the micro discharge process
1.2 Fundamentals of Dielectric barrier discharge control
technology
Figure 5 Classification of plasma Device for dielectric barrier discharge is usually relatively easy to build. In addition, unwanted heat can be dissipated through metal electrode. The barrier is capable of preventing electric spark or arc discharge. Normally the discharge process is steady under atmospheric pressure.
Discharge will influence the flow field in two ways. First one is through plasma’s collision with surrounding air particles. Plasma accelerates in the electric field, then inevitably collides with other air particles. Whether the collisions are elastic or inelastic, energy is transferred to the flow field. Secondly, a part of the electric energy turns into heat and dissipated into the flow field, causing the temperature near the electrode to change.
1.3 Overview for development of DBD plasma actuation
Roth and Sherman investigated boundary layer control with uniform glow discharge plasma and came up with the plasma momentum transfer theory and found out the best dielectric materials were Teflon and quartz [7], as shown in figure 6. Post and Corke adopted PIV and Pitot tube and collected abundant experimental data with different voltage phases for plasma actuator [8], as shown in figure 7. Estevadeordal and Gogineni divided the induced flow field into three parts, reversed flow region upstream of the exposed electrode, wall jet region downstream of the buried electrode and the in between region [9]. Whalley studied DBD induced vortex and arrived at similar conclusion with Corke and Estevadeordal [10]. Erfani found that the temperature of dielectric barrier surface had great influence on plasma induced velocity [11].Figure 7 Flow field with different actuation voltage phases
Based on rich experimental data, researchers started to work on computational model to accurately simulate DBD plasma actuation. One of the earliest models was proposed by Roy and Gaionde. This model mainly focused on resolving transport equation to obtain reduced body force. However, it took huge calculating resource and time [12]. Then Shyy came up with a model that was more suitable for engineering application. It assumes body force is linearized, which turned out to be feasible compared with experimental results [1]. A number of researchers had applied this model and verified its reliability [14, 15]. Suzen proposed a more complicated model which resolved Maxwell equation and charge density equation to achieve distribution of electrical field and charges, thus achieving body force [13]. Liang Hua did some related research using this model [16]. Orlov and Corke treated plasma actuator as a lumped circuit model. They tried to acquire body force by resolving this lumped circuit [17], as shown in figure 8. Figure 8 Orlov's numerical model of DBD plasma actuation
Figure 9 Paraelectric plasma actuators' effect on leading edge separation
Corke studied NACA 663 and NACA0015 airfoils under different working conditions [19]. He found that although induced velocity by one actuator was small, the leverage effect could increase control range. Also, critical angle of attack would increase with plasma actuation. Patel investigated aerodynamic control of plasma actuation on an unmanned air vehicle and came to conclusion that plasma actuation could reduce drag and increase effective lift‐drag ratio [20], as shown in figure 10.
Figure 10 Lift-drag ratio increase by plasma actuation
Figure 11 Effect of different DBD setup on delta wing with different sweep back angle Li Yinghong studied suppression effect of DBD actuation on leading edge separation with different excitation voltage, location and duty cycle, as shown in figure 12. Data indicated that best location for DBD actuation was the separation starting point. With larger inlet velocity and more severe separation situation, higher voltage should be provided. Plasma actuation could improve critical angle of attack and lift for NACA0015 airfoil [27]. Figure 12 Suppression effect of DBD actuation on leading edge separation with different
excitation voltage and duty cycle
DBD plasma actuation has been applied on turbomachinery as well. Huang Junhui applied plasma actuation on low pressure turbine to study its influence on separation, as shown in figure 13. He came to conclusion that plasma actuation was able to make the reattachment happen. The reattachment point shifted upstream with plasma actuation [22].
flow with passive casing treatment and active plasma actuation. Results showed plasma actuation decreased total pressure loss by 12 percent and plasma actuation affected the flow field less than casing treatment [24]. Travis D found out that plasma actuation could influence tip leakage flow more with high frequency [23], as shown in figure 14.
Figure 14 Comparison of different actuation frequencies on tip leakage flow Huu investigated stall suppression effect in axial compressor with plasma actuation. The research indicated that when actuator was placed near leading edge and tip clearance, an effective control could be achieved, as shown if figure 15.
Figure 15 Stall suppression effect in axial compressor with different actuation positions
Figure 16 Suppressing effect of plasma actuation on tip leakage flow
1.4 Objective and contents of this dissertation
Main objective of this dissertation is to investigate how could plasma actuation influence tip leakage flow in a compressor cascade. Methods to enhance its influence are also to be explored so that loss reduction and better performance can be achieved. Contents for each chapter are presented below. Chapter one is an introduction to this research work. Background information is provided. Basic knowledge about DBD plasma actuation is given. An overview of DBD plasma actuation technology is presented. Chapter two is about methodology adopted, including numerical software for both meshing and calculating. More importantly, the phenomenological model used to simulate DBD plasma actuation is explained in detail. A piece of code is created to link the model with the numerical software.
In chapter three, geometry detail of the compressor for this research is described. Several turbulent models as well as meshing arrangements are tested to determine an approach that best simulates the flow field in the compressor cascade. Flow field without plasma actuation is compared with experimental data for accuracy verification. Meanwhile influence of casing movement on tip leakage flow is investigated. Possible mechanism on tip leakage vortex core generation is discussed. In chapter four, influence of plasma actuation on tip leakage flow with different actuation locations, different voltages and different frequencies are discussed in detail. Casing movement is included afterwards to simulate a more real compressor working condition.
Chapter five is a summary for the research work. Improvements needed for future work are pointed out.
2 Methodology
2.1 Introduction of numerical tools
Since 1960s, computational fluid dynamics has been rising rapidly along with development of computers and numerical algorithms. Researchers are able to conduct thorough analysis on fluid dynamics, heat transfer and combustion with help of numerical simulation and visualization technique. After decades’ development and improvement, numerical simulation has become essential and widely used in the field of fluid dynamics.
of its own. A UDF program can be interpreted or compiled. Interpreted UDF program is easy to use, but has calculating speed limitation. Compiled UDF program does not have such problems, but has some setup difficulties. UDF can be used to define boundary conditions, material properties, add source term to transport equations, initialize cases and modify models. In this research plasma actuation body force is added into the flow field as source term.
2.2 Phenomenological model for plasma actuation simulation
The phenomenological model created by Shyy [1] is adopted in this research. This model is based on sufficient experimental and theoretical analysis. It focuses on dominating factors to simulate plasma actuation while neglects some relatively minor factors. Though this model cannot simulate the interaction between plasma and air particles one hundred accurately, it can capture core structure of plasma. This model is relatively easy to build, plus it does not consume huge amount of calculating resource. All of the above make this model a perfect choice for preliminary studies for complex flow.
Figure 18 Illustration of electric field distribution of plasma area
Figure 18 shows the simplified illustration of electric field of plasma actuator. Shyy assumes a linear distribution for the electric field. Electric field strength decreases away from point O, electric strength can be derived as: |𝐸| 𝐸 𝑘 𝑥 𝑘 𝑦 (1) 𝐸 represents electric strength of point O, namely the strongest electric strength, it is calculated by: 𝐸 (2) Where d represents the distance between exposed electrode and buried electrode.
𝐷 0 𝐹 𝐹 0 (14) Where u, v are velocity components. 𝜌, p, t represent density, static pressure and time. 𝜏 is shear stress and k is heat transfer coefficient. 𝐹 and 𝐹 are linearly distributed in certain region and turn zero outside this region. Induced body force and electric field strength are:
𝐹 𝜗𝛼𝜌 𝑒 Δ𝑡𝐸𝛿 (15) 𝐸 , (16)
3 Result and analysis on tip leakage flow with casing
movement
3.1 Compressor cascade description
A compressor cascade with NACA65‐1810 blades at design condition is selected for this research. S. Kang and C. Hirsch have conducted experimental study on this cascade [33,34]. Rich experimental data and detailed analysis on velocity, pressure and tip leakage vortex are accessible. Geometry detail of the compressor blade is listed below in table 2 and an illustration of the blade passage is shown in figure 19.
Table 2 Compressor Blade Geometry
Figure 19 Illustration of compressor cascade passage and measuring positions
Gas inside this cascade can be regarded as ideal incompressible air due to its low velocity. S. Kang provided velocity boundary condition at 40 percent chord upstream of leading edge. But 40 percent chord upstream of leading edge may not be sufficient. Thus, boundary condition 100 percent chord upstream of leading edge is derived, plus inlet flow angle to be the inlet velocity boundary condition. Outlet boundary is pressure boundary. No slip condition is selected for the walls. Periodic condition is set for the two boundaries circumferentially. Second Order Upwind SIMPLE algorithm is adopted for the solution. For reference, X Y Z represent spanwise, circumferential and axial direction respectively.
3.2 Turbulent model choice
There are mainly three kinds of numerical simulation methods for complex flow, namely direct numerical simulation, large eddy simulation and Reynolds averaged Navier Stokes equations simulation. DNS and LES methods are limited by current calculating technology and are difficult to apply on engineering problems since they consume huge calculating resources. Currently, they can only be used on basic flow simulation research. However, RANS method requires much less calculating resource and it is able to acquire sufficient solution for engineering applications. One of the key elements influencing accuracy for RANS method is turbulent model selection.
energy transfer but is limited by isotropic assumption of turbulent viscous coefficient. RSM model is the most accurate model among the above models. It abandons isotropic assumption and strictly considers streamline bending, swirling and tension changing. Thus, RSM model achieves better accuracy for complex flow. But it adds seven equations into three‐dimensional flow field and significantly increases calculating resource. Plus, good convergence is hard to achieve with RSM model than with SA or k‐𝜀 model.
In this research, Spalart‐Allmaras model, k‐𝜀 model, k‐𝜔 model and Reynolds stress model are all applied and compared with each other in order to find out suitable model for better simulation of tip leakage flow. Tip clearance is set as 4mm (2% chord) with no casing movement. Figure 20 shows comparison of static pressure coefficient with different turbulent models at 98.5% span. Static pressure coefficient is calculated by: 𝐶 (17) Reference parameters are obtained from 50% span of inlet plane as mentioned in literature [33]. Difference exists for all models compared with experimental data. This is acceptable since no turbulent model predicts flow field one hundred percent accurate. The lowest pressure position is generally believed to be closely related with generation of tip leakage vortex. It is seen that all models predict this position nearer leading edge than experimental value. Apart from this, distinction between different models seems little. Near trailing edge on suction side, two k‐𝜀 models share same predicted value with RSM model. While two k‐𝜔 models seem a bit off from experimental value. SA model prediction is somewhere between k‐𝜀 and k‐𝜔 predictions.
Figure 20 Comparison of pressure coefficient for different turbulent models at 98.5% span
Figure 21 is comparison of axial velocity distribution along circumferential direction with different turbulent models at 55%chord, 97%span. All models have captured the low velocity zone
distribution the most. Again, two k‐𝜀 models do not exhibit much difference.
Figure 21 Comparison of axial velocity with different turbulent models at 55% chord, 97% span Based on the above discussion, for flow field near blade tip region and suction side of the blade, RSM model does not perform better than other models even at a cost of much more calculating resource. Additionally, according to common experience it is hard to achieve well convergent results for RSM model than other models. S‐A model does not acquire better predicted results than k‐𝜀 model either due to its excessive simplification. Taking everything into consideration, k‐ 𝜀 standard model is to be employed for this research.
3.3 Meshing arrangements
Generating fine mesh is a significant step to achieve accurate simulating results, especially for tip leakage flow study. Auto grid5 provides structural O‐4H grid. Connections between different partitions are completely matched, thus interpolation error is avoided. In this study, three meshing plans are proposed. Medium mesh has 1.2 times of grid points along three directions than coarse mesh, while fine mesh has 1.5 times of grid points than coarse. Tip clearance is set 4mm (2% chord) with no casing movement. Figure 22 is an illustration of the mesh quality for medium mesh proposal. Details for three meshing proposals are listed in table 3. The aim is to dig out how fine the meshing should be to achieve sufficiently accurate results which are independent of meshing.Medium Mesh 77 29 94 131 64 94 29 <1.35 1267411 Fine mesh 93 33 111 152 80 111 33 <1.38 1895560 Figure 22 Illustration of medium mesh
Figure 23 is circumferential averaged pressure on trailing edge plane for different meshes. It can be clearly seen that medium mesh and fine mesh obtain same results while coarse mesh prediction seems a bit lower than these two. For reference, actual pressure minus 1 atm equals the pressure values in this research. Total pressure value of tip leakage vortex core at different axial planes for these meshing proposals is also acquired, as illustrated in figure 24. Q criterion is adopted to identify vortex in this research. Similar conclusion can be drawn that coarse mesh does not predict the flow field well enough compared with medium and fine mesh. In the meantime, fine mesh seems to be taking up unnecessary calculating resource than needed. Overall, medium mesh is selected for better sufficient simulation results.
Figure 23 Circumferential averaged pressure at trailing edge plane for different meshing proposals
Figure 26 Distance of TLV core from shroud for different casing moving speed
Figure 29 Total pressure contour of traverse axial planes for different casing moving speed(unit/Pa)
Figure 30 Mass-averaged total pressure loss coefficient at different axial planes for different casing moving speed
25m/s
3.5 Discussion on tip leakage vortex roll‐up mechanism
In this part, possible roll‐up mechanisms for tip leakage vortex are discussed with different tip clearances and with different casing moving speed. Flow field is analyzed in detail with streamtraces inside the blade passage in three dimensions. A commonly known explanation for roll‐up of tip leakage vortex is shearing between passage flow and leakage flow. This mechanism may not work for all cases. 1% chord clearance is selected as a comparison. Figure 31 shows a set of streamtraces passing near leading edge and blade tip for two tip clearances. For 1% chord clearance, shearing between passage flow and leakage flow is not observed. Instead, all streamtraces are pushed under bottom tip leakage flow and do not roll around outer side of tip leakage vortex until far downstream of trailing edge. This is a good indicator of the blockage effect for tip leakage flow. However, for 2% chord clearance, situation seems obviously different. Majority of streamtraces are still pushed under tip leakage flow inside the passage which is similar with 1% chord clearance case. Some of the streamtraces are involved into tip leakage vortex before trailing edge.
But the swirling direction is opposite to that of tip leakage vortex. These streamtraces are likely to resist being involved into tip leakage vortex and end up under bottom of the tip leakage vortex. They will join the blockage flow mentioned above and roll around outer side of tip leakage vortex gradually after downstream of trailing edge. Third type of streamtraces pass through tip clearance after 50% chord axially. Normally these streamtraces tend to roll up into tip leakage vortex as a group and form the outer part of tip leakage vortex in a tube shape. Whether passing near blade tip or passing near shroud does not make a big difference any more. They just roll up an existing core generated from first half chord. Overall, streamtraces that pass through tip clearance near blade tip are likely to join tip leakage vortex faster than others.
Figure 33 z vorticity contour at 10% chord inside tip clearance for 1% chord clearance case
A conclusion can be drawn that for small tip clearance situation, transport of vorticity from tip clearance to blade passage is leading mechanism for tip leakage vortex core roll‐up. As for large tip clearance situation, conventional explanation of shearing between tip leakage flow and passage flow may be playing vital role. While for medium tip clearance, tip leakage vortex core roll‐up may be related with both mechanisms. However, results presented above does not represent real flow condition since casing movement is not included. In the following part, influence of casing movement on tip leakage vortex core roll‐up is to be investigated. With shroud moving, its shearing on leakage flow should be acting to enhance leakage flow as well as tip leakage vortex. Figure 34 shows a set of streamtraces passing near leading edge and blade tip for stationary casing and moving casing with speed of 25m/s. Obvious difference is shown between two cases. Instead of being pushed under tip leakage flow, almost all streamtraces are involved into tip leakage vortex within blade passage. However, most of the streamtraces roll around tip leakage vortex after 50%chord axially. Which means these streamtraces do not constitute tip leakage vortex core. This will lead to the fact that vorticity transport may still be significant concerning generation of tip leakage vortex core. Figure 34 Streamtraces passing near blade tip and leading edge for different casing moving speed
Near exit
Stationary
moving casing in figure 35. For stationary casing, tip leakage flow shearing with blade tip results in positive vorticity while shearing with shroud results in negative vorticity as already discussed previously. Thickness of positive and negative vorticity region are symmetric inside tip clearance. However, for moving casing, negative vorticity zone is no longer observed. If a closer look at the thickness of the positive vorticity zone is taken, it also increases with moving casing as shown in figure 36. With increased boundary layer thickness, more fluid rather than that very close to the blade tip will pass through tip clearance and roll into tip leakage vortex. Which means more vorticity is transported out of tip clearance, thus a larger tip leakage vortex is to be generated. Figure 35 Z vorticity contour inside tip clearance at 10% chord for stationary and moving casing
Figure 36 Zoom-in contour of z vorticity contour near tip clearance exit for stationary and moving
Figure 37 Tip leakage vortex illustration for stationary casing and moving casing
3.6 Summary
Compressor cascade together with blade geometry is described in detail. Commonly used turbulent models are applied in this study and k‐𝜀 standard is adopted after weighing various factors comprehensively. Three meshing structures are proposed with increasing mesh number and medium mesh proposal is sufficient for this research. Influence of casing movement on tip leakage flow is investigated with speed of 0 m/s, 15 m/s and 25 m/s separately. Main conclusions are as follow: 1. Generating position of tip leakage vortex moves towards leading edge with increasing moving speed of shroud. 2. As shroud moving speed increases, trajectory of tip leakage vortex moves away from suction side of blade and closely towards shroud.
3. Casing movement tends to transform tip leakage vortex from circular to oval shape due to circumferential shearing.
4. Casing movement has little influence on total pressure field concerning absolute pressure value. While total pressure loss does reduce slightly with increasing moving speed of shroud. 5. Vorticity transport from tip clearance into passage may be contributing significantly to
generation of tip leakage vortex inner core.
4 Influence of plasma actuation on tip leakage flow
Modern aero engine compressor is required to possess high pressure ratio, which is a conflict with wide and stable operation range. When aero engine works at off‐design condition, compressor is likely to enter unstable working condition such as rotating stall and surge which may lead to major accident. In order to effectively widen stall margin, study on instability mechanism is inevitable. Abundant experimental and numerical research has indicated that rotating stall is closely related with tip leakage flow [38,39,40].
Plasma actuation, as an active flow control method, can adjust actuation strength according to operating condition without efficiency reduction. A great deal of numerical research has been conducted concerning plasma actuation. Vo introduced plasma actuation into N‐S equations as body force and studied its suppression effect on rotating stall [41]. Whereas experimental work that has been conducted concerning plasma actuation application in turbomachinery is not as much.
In this chapter, as a first step before experimental research on casing treatment, numerical simulation is conducted on a compressor cascade to investigate influence of plasma actuation on tip leakage flow with different actuation parameters.
Figure 39 Pressure contour of shroud for different actuation positions(unit/Pa) Next, Q contours for multiple traverse planes are to be investigated to study influence of different actuation positions on tip leakage vortex strength. Figure40 shows clearly that tip leakage vortex is retained right adjacent to blade suction side with a much smaller area with plasma actuation. Plasma actuation exhibits great suppressing effect on development of tip leakage vortex. Figure 41 shows zoom‐in Q contour comparison between position 1 and position 3 at 70% chord. The vorticity of actuation position 3 is obviously stronger than of actuation position 1. Which coincides with the shroud pressure contour discussion that further away from leading edge of plasma actuation results in stronger tip leakage vortex. Figure 40 Q contour for multiple traverse planes with and without plasma actuation
Without plasma
Position 3 Position 2
Figure 41 Zoom-in view of Q contour at 70% chord for position 1 and position 3
Figure 43 Z-vorticity contour inside tip clearance at 10% chord with and without plasma
Figure 45 Q contour at multiple traverse planes for different actuation voltages
Figure 46 Zoom-in view of Q contour at 70% chord for different actuation voltage
through tip clearance. While most of them are blown into the passage flow with an axial direction. The shear layer of plasma induced jet flow not only reduces leakage flow through tip clearance, but also obstructs leakage flow by forcing it towards axial direction so that tip clearance flow exits tip clearance further downstream. On the other hand, due to this axial change of direction caused by shearing of induced flow, some streamtraces which used to travel along blade pressure side are now pushed into tip clearance. This clearance flow coming in from blade pressure side, together with leakage flow form a small vortex with weak strength, as shown in the fourth picture of figure 48.
Figure 48 A certain set of streamtraces for different actuation voltages and leakage flow illustration with 9000 volts actuation
Figure 49 Total pressure contour with different actuation voltages(unit/Pa)
Figure 50 Mass-averaged total pressure loss coefficient at different axial planes for different actuation voltages
Mass‐averaged total pressure loss coefficient at different axial planes for different actuation voltages is collected and compared in figure 50. It can be seen that with increasing actuation
for fluid near tip region. Total pressure for that part of fluid is enhanced accordingly. An approximately linear relation between actuation power and decreasing total pressure loss is observed.
4.3 Influence of different actuation frequency on tip leakage
flow
In this section, actuation voltage is fixed at 3000 volts while actuation frequency varies with 3000 Hz, 6000 Hz and 9000 Hz separately with tip clearance of 4mm (2% chord). The aim is to investigate influence of actuation frequency on tip leakage vortex behavior. Meanwhile, the suppressing effect for tip leakage vortex with actuation voltage and actuation frequency is to be compared and discussed to find out which parameter performs better at suppressing tip leakage flow.
Figure 51 shows shroud pressure contour for different actuation frequencies. Results seem similar with those of last section. Low pressure zone related with tip leakage vortex is located at about same position for three cases at 70% chord. While pressure value of the low‐pressure zone increases with increasing actuation frequency. Which represents stronger suppressing effect for tip leakage vortex with stronger actuation.
Figure 51 Shroud pressure contour with different actuation frequencies(unit/Pa)
3000Hz 6000Hz
value is observed, as shown in figure 52. The darker color of blue means stronger influence of tip leakage vortex on pressure distribution in tip region. Which may mean tip leakage vortex with 9000 volts actuation is stronger than that of 9000 Hz actuation. And actuation frequency may be more influential on suppressing tip leakage vortex than actuation voltage. More evidence is needed before this conclusion can be drawn.
Figure 53 Q contour at multiple traverse planes for different actuation frequencies
Figure 54 Q contour at 70% chord for 9000V case and 9000Hz case
Figure 55 Z-vorticity contour inside tip clearance at 10%chord for 9000 V case and 9000 Hz case
9000V 9000Hz
Figure 56 Tip leakage vortex structure for 9000 V case and 9000 Hz case
Figure 54 shows Q value at 70% chord position where tip leakage vortex is generated. Size of tip leakage vortex tends to be a bit bigger for 9000 volts case than 9000 Hz case. Z‐vorticity contour inside tip clearance for both cases are also compared, as shown in figure 55. Thickness of positive vorticity zone on blade tip is a bit bigger for 9000 volts case than 9000 Hz case. Meanwhile the length of negative vorticity coming inside tip clearance is shorter for 9000 volts case than 9000 Hz case. Which indicates less obstruction for 9000 volts case. It can be inferred from both phenomena that tip leakage vortex of 9000 volts case should be stronger than that of 9000 Hz case. Streamtraces are generated and compared to provide us a clearer view of the tip leakage vortex structure for both cases, as shown in figure 56. Result agrees with the theory above that tip leakage vortex of 9000 volts case is larger and stronger than that of 9000 Hz case. Which answers the question at the beginning of this section. Compared with actuation voltage, the actuation frequency tends to be more influential suppressing tip leakage vortex.
It should be noted that both voltage increase and frequency increase eventually come down to power increase. With increasing energy added into tip region of compressor, tip leakage vortex is more efficiently suppressed. Which results in compressor performance and efficiency improvement.
Shroud pressure contour is compared first between two 3000 Hz actuation cases with and without casing movement, as shown in figure 57. From chapter 3 it is learnt that casing movement enhances tip leakage vortex with a shearing layer of same direction with leakage flow. Darker blue in low‐pressure region caused by tip leakage vortex is clearly seen with casing movement that agrees with this discussion. Casing movement acts to weaken the tip leakage vortex suppressing effect of plasma actuation. Then as actuation frequency increases, pressure value rises again. Figure 57 Shroud pressure contour with casing movement for different actuation
Figure 59 Z-vorticity contour inside tip clearance at 10% chord with and without casing
movement for 3000 Hz and 9000 Hz actuation
9000Hz (stationary) 9000Hz (moving)
Figure 60 A certain set of streamtraces with and without casing movement for 3000 Hz and 9000
Hz actuation A same set of streamtraces is generated for comparison with and without casing movement for 3000 Hz and 9000 Hz actuation, as shown in figure 60. Detachment of tip leakage vortex from blade suction side with casing movement is clearly seen for 3000 Hz actuation. Here two streamtraces are picked out as a representative of the shearing effect with casing movement. The streamtrace labeled in red shows a change in direction towards direction of leakage flow. The streamtrace labeled in green which used to travel near trailing edge is now forced to join leakage flow. This also reveals an increase in leakage flow caused by casing movement. The plasma induced jet flow obstructs tip leakage flow with a shearing layer in axial direction while casing movement enhances tip leakage flow with a shearing layer in circumferential direction. In this study, rotational speed is relatively low. Thus, enhancing effect of tip leakage vortex is not so severe, but still worth noticing. It is reasonable to believe that in a real compressor with high rotational speed, higher actuation power will be needed to achieve substantial suppressing effect. Which will in return result in higher requirements for the plasma actuator.
4.5 Summary
Different actuation positions, different actuation voltages and different actuation frequencies are applied to investigate influence of plasma actuation on tip leakage flow. Major conclusions are as follow:actuation. More actuation power is needed to achieve sufficient suppressing effect in real compressors.
5 Conclusions
In this research, a 3‐D numerical simulation of flow field inside a compressor cascade is conducted. A numerical model is adopted to simulate plasma actuation. This model is added into flow field with UDF function of commercial software Fluent. The focus is on influence of plasma actuation on tip leakage flow.Firstly, numerical simulation without plasma actuation is conducted to validate accuracy of the numerical methodology and then determine one scheme that satisfies specific needs sufficiently. Meanwhile, influence of casing movement on tip leakage flow as well as mechanism of tip leakage vortex core generation is studied in detail. Major conclusions are as follow: 1. Generating position of tip leakage vortex moves towards leading edge with increasing moving speed of shroud. 2. As shroud moving speed increases, trajectory of tip leakage vortex moves away from suction side of blade and closely towards shroud.
3. Casing movement tends to transform tip leakage vortex from circular to oval shape due to circumferential shearing.
4. Casing movement has little influence on total pressure field concerning absolute pressure value. While total pressure loss does reduce slightly with increasing moving speed of shroud. 5. Vorticity transport from tip clearance into passage may be contributing significantly to
generation of tip leakage vortex inner core. Secondly, numerical simulation with plasma actuation is conducted. Different actuation positions, voltages and frequencies are applied and investigated. Then casing movement is included in the simulation. The main conclusions are as follow:
6. Plasma actuation shows significant suppressing effect on tip leakage vortex on both size, trajectory and strength. 7. The suppressing effect on tip leakage vortex grows stronger as actuator moves towards leading edge. 8. Increasing actuation voltage results in stronger suppressing effect on tip leakage vortex. 9. Plasma actuation can effectively improve total pressure loss situation near shroud region with increasing actuation power. 10. Increasing actuation frequency results in stronger suppressing effect on tip leakage vortex as well. Additionally, frequency performs slightly better than voltage.
11. Casing movement tends to weaken suppressing effect of tip leakage vortex by plasma actuation. More actuation power is needed to achieve sufficient suppressing effect in real compressors.
6 Future Plan of improvement
Plasma actuation is in fact a very complicated process which involves multiple subjects. Instead of empirical estimation, a finer mathematical model is desperately needed which considers chemical reaction, collision effect, temperature rise and other related process.
In this research, only steady simulation is conducted due to calculating resource limitation. Unsteady actuation may suppress tip leakage flow even better with less power consumption. This area is worth noticing.
The suppressing effect of plasma actuation on tip leakage flow is quite well in this study. This is due to strong plasma actuation power provided. However, this kind of actuation strength is practically very difficult to achieve. In experiments, strong actuation is generated with multiple actuators working together. But there is a strict limitation on the number for actuators working together because casing may be easily broken with high actuation power. Therefore, there is still a long way to go before applying satisfying plasma actuation control in real turbomachinery.
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