WO1999067539A1 - Oscillator fin as a novel heat transfer augmentation device - Google Patents

Abstract

An oscillator fin comprising: two members, said two members of an elliptical cross-section and placed transversely across a flow passage, wherein a major axis of said elliptical cross-section parallel to a direction of said flow passage and wherein said two members form a tapering nozzle to create a jet between said two members; and a third member to receive said jet from said nozzle, said third member having a U-shaped geometry.

Description

OSCILLATOR FIN AS A NOVEL HEAT TRANSFER AUGMENTATION DEVICE

Chapter 1

INTRODUCTION

In order to increase the efficiency of gas turbine engines, effective cooling of high pressure turbine blades is necessary. The enhancement of the heat transfer in internal coolant passages of gas turbine blades can be achieved by increasing the turbulence levels and unsteadiness of the coolant flow while keeping the pressure losses as low as possible. The devices used in internal coolant passages to increase turbulence levels and unsteadiness come with various geometrical sizes and shapes. The most common ones are pin fins and ribs (trip strips).

The trip strips work by tripping the boundary layer periodically and causing a repeating flow pattern within the passage which leads to high turbulence levels in the core flow. Boyle (1984), Han (1988), Abuaf and Kercher (1994), Ekkad and Han (1997) investigated the heat transfer and friction characteristics of channels with ribbed turbulators. Different rib shapes and orientations are investigated by Chandra et al. (1988), Han et al. (1991), Taslim et al. (1996) and Liou et al. (1996). Various rib types like perforated ribs (Hwang and Liou, 1995; Kukreja and Lau, 1996), ribbed-grooved wall combinations (Zhang et al., 1994), rib- vortex generator combinations (Myrum et al., 1996) have also been investigated.

Pin fin banks are arrays of short cylinders and they are used as heat transfer augmentation devices by increasing the internal wetted surface and the passage flow turbulence. In-line and staggered arrays of pin fins are generally used in flow passages. Considerable amount of study has been done on pin fin research. The effects of various parameters on heat transfer and pressure loss has been investigated. Different geometrical parameters as pin height and pin spacing (Van Fossen. 1982), the local and array averaged heat transfer (Simoneau and Van Fossen. 1984, Metzger et al. 1986), pin fin channels with trailing edge ejection holes (Lau et al., 1989), wall contribution to heat transfer (Al Dabagh and Andrews, 1992), perpendicular flow entry (Chyu and Natarajan, 1992) are some of the research topics in the previous years. The heat transfer characteristics of split pin fin arrays are also investigated by Mwangi and Kim (1994).

Other than pin-fins and trip strips, some other heat transfer augmentation devices like hemispherical cavities (Schukin et al., 1995), baffles (Habib et al., 1994) and vortex chambers (Glezer et al., 1996) are also investigated during the past years.

The objective of this study is to introduce a new concept for turbulent heat transfer augmentation in gas turbine blades. This new cooling component is called an "oscillator fin" and is based on using a fluidic oscillator instead of conventional cylindrical pin fins. Fluidic oscillators have been used for mass flow rate measurements (Bauer 1980, Bauer 1981). However their application as a turbulent heat transfer augmentation device has never been investigated before. Therefore an extensive research program is initiated for the complete analysis of the heat transfer and fluid mechanics characteristics of the oscillator fin. This program includes computational simulations of the flow field as well as detailed experiments designed using the predictions from the computational simulations for a thorough study of the oscillator fin. The heat transfer and pressure loss characteristics of the oscillator fin will be compared to those of conventional cylindrical pin fins.

The impinging jet oscillation on a concave wall concept can also find many other applications such as aircraft wing de-icing applications (Piccolo Tube), electronic cooling of microprocessors, jet impingement cooling in gas turbine blades, etc. In other words this concept can be used in all areas where an impinging jet is utilized to enhance transport mechanisms.

The geometry of the oscillator fin and the jet oscillation mechanism inside it is explained in Chapter 2. The computational approach which is used for the visualization of the flow field and for the understanding of the jet oscillation mechanism inside the chamber and the wake characteristics of the oscillator fin is explained in Chapter 3. Chapter 4 explains the experimental plan which is going to be employed for the investigation of the oscillator fin. Chapter 5 has the conclusion of this part of study and the plans for upcoming research to be completed.

Chapter 2

OSCILLATOR FIN CONCEPT

Oscillatory motion of an impinging jet over a concave wall is the main physical phenomenon in many past flowmeter designs. The present study incorporates this known fluid instability into the proposed oscillator fin designed for gas turbine heat transfer augmentation. The device consists of three separate members (Figure 2.1). Two of the members which are of elliptical cross-section are placed transversely

Figure 2.1 Oscillator Fin Geometry

across the passage with the major axis of the ellipse parallel to the flow direction. These two members form a tapering nozzle which is used to create a jet between them. The downstream ends of the members are defined as downstream facing cusps which will be used for directing the oscillating jet into the flow. The third member which receives the jet from the nozzle is called the oscillation chamber and has an upstream facing U shaped geometry. The relative dimensions of the oscillator fin are also given in Figure 2.1

During the operation of the oscillator fin, the jet coming from the nozzle impinges against the all of the oscillation chamber and splits into two oppositely directed flows while generating two counter rotating vortices with equal magnitude of vorticity (Figure 2.2a). At the very first instant the flow field inside the oscillation chamber is symmetrical. The oppositely directed flows on the upper and lower side of the jet have the same amount of mass flow rate and they exit from the upper and lower output passages, respectively. In addition the static pressure levels inside the upper and lower vortices are also equal. However this symmetrical layout is very unstable resulting the deflection of the jet towards one of the sides (upper or lower) and therefore destroying the symmetry (Figure 2.2b). This deflection of the jet produces an imbalance in the mass flow rates of the upper and lower flows. Due to the concavity of the wall, when the jet is deflected upward, the mass flow rate of the lower flow becomes greater and the upper becomes less than the values they have when the jet is not deflected and the flow field is symmetrical. The opposite happens when the jet is deflected downward. This imbalance in the mass flow rates of the upper and lower flows pushes the jet further away from the symmetry line towards the lower mass flow rate side. As the jet is being pushed, the mass flow rate of the higher mass flow rate side keeps increasing and that of the lower mass flow rate side keeps decreasing until the jet reaches its maximum deflection point. Furthermore, while the jet is being pushed towards the maximum deflection, the vortex between the jet and the higher mass flow rate side gets bigger and bigger (keeping the same vorticity magnitude) and moves to the center of the oscillation chamber. The vortex at the lower mass flow rate side get smaller and smaller (also keeping the same vorticity magnitude) and is pushed towards the output passage. When the jet is at its maximum deflection point, the smaller vortex now blocks the passage and most of the incoming flow exits from the opposite output passage. At this instant the layout of the flow field is similar to Figure 2.2c and can be summarized as follows:

b.

Figure 2.2 Jet Oscillation Mechanism inside the Oscillation Chamber • The jet is at its maximum deflection point impinging upon the horizontal sidewall of the oscillation chamber.

• Most of the incoming flow is going out from the higher mass flow rate side output passage (lower passage in Figure 2.2c).

. Two vortices are located as shown in Figure 2.2c having the same vorticity magnitude.

At this stage, since the jet is now impinging upon the horizontal sidewall of the chamber, not on the concave wall, the imbalance in the mass flow rates is no longer capable of pushing the jet further. Additionally, the velocity induced by the bigger vortex just under the jet is much higher than the velocity induced by the smaller vortex just over the jet due to the difference between the radii of the two vortices which have the same vorticity magnitude. As a result the static pressure inside the bigger vortex drops down and a pressure gradient across the jet is created. This pressure gradient moves the jet toward the bigger vortex and eventually the jet returns to the symmetrical position completing the cycle. This mechanism repeats itself continuously and causes the jet to oscillate inside the oscillation chamber.

Figure 2.3 Visualization of the Jet Oscillation inside the Oscillation Chamber

As the jet created between the two front members is swept back and forth inside the oscillation chamber by the mechanism explained above, alternating flow pulses are formed and directed by cusps into the main flow. The effect of mixing of these alternating and periodic flow pulses coming from the oscillator fin with the main flow and with the vortices shed from the afterbody is expected to increase the turbulence levels, mixing and unsteadiness in the wake region which will in turn increase the heat transfer. The effect of increased heat transfer due to increased unsteadiness created by the vortex shedding from an immersed body in a channel flow has been studied by Suzuki and Suzuki (1994) and Valencia (1995). Xie and Wroblewski (1997) investigated the effect of vortex shedding from a cylinder on heat transfer in a turbulent boundary layer and concluded that the large scale periodic fluctuations may contribute to the mixing and wall heat transfer enhancement in the wake region of the circular cylinder. Furthermore, due to the specific geometry of the oscillator fin, the wetted area is also increased. This increase in the wetted area and the periodic sweeping of the jet inside the oscillation chamber are also expected to increase the heat transfer on the oscillator fin itself.

Consequently, in this study, the turbulence levels, pressure loss levels, the vortex shedding mechanism and the modification of the vortex shedding mechanism due to the periodic flow pulses in the wake region and the heat transfer characteristics of an oscillator fin will be analyzed both with solution of the governing flow equations and with detailed experimental investigations. The heat transfer and pressure loss characteristics of the oscillator fin will be compared to those of a conventional cylindrical pin fin.

Chapter 3

COMPUTATIONAL ANALYSIS

In order to understand the physics of the jet oscillation mechanism inside the chamber and for the prediction of the wake characteristics of the oscillator fin and also for qualitative flow visualization purposes, a computational study is performed. The simulations of the flow fields for the oscillator fin and for the pin fin cylinder are obtained by solving two dimensional and incompressible solutions of Reynolds Averaged Navier-Stokes equations. A standard k-ε turbulence model coupled with an Algebraic Reynolds Stress Model is used for the simulation of the turbulent flow field.

3.1 Governing Equations

The computational simulations of the flow fields for the oscillator fin and the pin fin cylinder are obtained by solving two dimensional and incompressible solutions of Reynolds Averaged Navier-Stokes equations. Both transient and steady solutions of the flow fields are obtained. A two equation standard k-ε turbulence model is used for the simulation of the turbulent flow field. Hence the governing equations for the flow field are,

"ύ = 0 (1)

du,

T ^{+ U}KJ = -P, ⁺ T t^* fe ⁺ "Λ. )1, (2) dt Re

For the calculation of the Reynolds stresses, instead of using Boussinesq's well established eddy viscosity model which lacks the ability to predict the anisotropic structure of turbulence, the eddy viscosity model proposed by Launder (1993) is used. This model represents the Reynolds stress tensor as a cubic function of the strain rate tensor and this provides the necessary mechanism for predicting turbulence anisotropy effects. This modified model is needed in order to accurately capture the turbulent structure of the complex wakes of the cylinder and the oscillator fin.

3.2 Solution Method

A finite element based fluid dynamics analysis package FLDAP (1993) is used to solve the governing equations. The flow domain is discretized by using nine-node quadrilateral elements which give a biquadratic velocity and bilinear pressure variation within each element.

Implicit backward Euler temporal formulation with a fixed time increment is used for time integration for transient simulations. At each time step a segregated solver is used to solve the non-linear system of equations. This implicit solver avoids the direct formation of a global system matrix which includes all the unknown degrees of freedom associated with the discretized problem as in fully coupled solvers. Instead it decomposes this matrix into smaller sub-matrices each governing the nodal unknowns associated with only one conservation equation. These smaller matrices are then solved in a sequential manner using different schemes. The use of the segregated solver is preferred because the storage requirements are substantially reduced compared to a fully coupled solver.

3.3 Boundary and Initial Conditions

The computations are performed for Re = 30000 based on the diameter (or oscillator fin width) and the inlet velocity. Velocity components are specified as zero on the walls and on the bodies in order to satisfy the no-slip condition. At the inlet the x component of the velocity is specified as a uniform steady profile and the y component is specified as zero. Values for the turbulent kinetic energy and for the dissipation rate of turbulent kinetic energy corresponding to a 0.1 % turbulence intensity level are also specified at the inlet. A low inlet turbulence level was chosen to illuminate the main unsteady fluid mechanics and turbulence generation character of the flow field. No boundary conditions are explicitly imposed for velocity components, turbulent kinetic energy and the dissipation rate of turbulent kinetic energy at the outflow boundary. The specific form of the finite element solution procedure results in zero streamwise gradients for these variables at the exit plane. The unsteady solutions for the cylinder and for the oscillator fin are started from initial flow fields obtained by a steady solution of the governing equations.

3.4 Simulation Results

3.4.1 Transient Simulations

3.4.1.1 Physical Interpretation of Flow Field for the Cylinder

The transient simulation of the flow field around the cylinder is performed for a Reynolds number of 30000 which is based on the inlet velocity and the cylinder diameter. Figure 3.1 shows the computational domain which starts at 5 diameters upstream and goes up to 8 diameters downstream of the cylinder. The channel walls are 2.5 diameter away from the centerline of the channel.

Figure 3.1 Computational Domain Definition - Cylinder

Figure 3.2 Computational Mesh - Cylinder

Nine-node quadrilateral elements are used to discretize the domain. For the cylinder case 3744 second order finite elements are created which resulted in 14424 number of nodes. The computational mesh is illustrated in Figure 3.2.

Figure 3.3 shows the velocity vectors in the near wake region of the cylinder at different time steps. The periodic vortex shedding process is clearly seen from these figures. Alternating vortices are generated from the separation points on the upper and lower sides of the cylinder and convected downstream inside the wake region.

a. t* = 5.0 b. t* = 5.8

c. t* = 6.6 d. t* = 7.4

e. t* = 8.2 Figure 3.3 Vortex Shedding from the Cylinder

Time history of the static pressure in the wake region at one diameter downstream of the cylinder is shown in Figure 3.4. The periodic variation due to the periodic vortex shedding can be seen from the figure. The Fast Fourier transform is applied to obtain the frequency content of this variation and the result is presented in Figure 3.5 as a power spectrum plot. The value of the dominant non-dimensional frequency, or the Strouhal Number, is found to be 0.27. The experimental Strouhal number for a circular cylinder and for a Reynolds number of 30000 is known to be around 0.2 (Schlichting, 1955).

Figure 3.4 Time History of Static Pressure

Strouhal Number

Figure 3.5 Power Spectrum of Static Pressure

3.4.1.2 Physical Interpretation of Flow Field for the Oscillator Fin

The transient solution of the governing equations for the flow field around the oscillator fin is also performed for a Reynolds number of 30000 which is based on the width of the oscillator fin and the inlet velocity. The width of the oscillator fin is the same as the diameter of the cylinder. The computational domain (Figure 3.7) is also the same as in the cylinder case which starts at 5D upstream and ends at 8D downstream of the oscillator fin The domain is discretized by using nine-node second order quadrilateral elements and 3258 elements are created as a result of the discretization process (Figure 3.8). Total number of nodes is 12200.

Figure 3.7 Computational Domain Definition - Oscillator Fin

t =5.0

t =5.8

t =6.6

t =7.4

Speed Pressure

Figure 3.6 Speed and Pressure Contours for the Cylinder

Figure 3.8 Computational Mesh - Oscillator Fin

The results of the transient runs for the oscillator fin are presented in Figures 3.9 through 3.11. Although the overall features of the flow field are visualized with these runs, it was not possible to capture a full period of the jet oscillation inside the oscillation chamber, which is physically present. In each case, the jet starting from the initial flow field, obtained from the steady solution of the governing equations, deflected towards one of the edges of the oscillation chamber and kept impinging on that side for the rest of the simulation. Therefore it was not possible to obtain any detailed information about the jet oscillation mechanism inside the chamber from the transient simulations. However, the features of the flow field in the wake of the oscillator fin as the jet inside the oscillation chamber is deflected towards one side of the chamber could be observed. Hence the results presented here for the oscillator fin are the results between the time at which the jet impinging on the concave wall of the oscillation chamber is not deflected (symmetrical with respect to the centerline) and the time at which the jet has its maximum deflection upwards. Figure 3.9 shows the jet deflection starting from the centerline and deflecting towards the upper lip of the oscillation chamber. The generation of the vortices inside the chamber and their respective movements can be seen from the figure. As the jet moves upwards the lower vortex (L) gets bigger and situates at the center position while the upper vortex (U) is pushed towards the upper output passage and blocks the passage. In the mean time the jet coming from the nozzle is deflected upwards between these two vortices and most of the incoming flow is going out through the lower output passage when the jet is at its maximum deflected position.

t* = 2.2 t* = 3.4

4.2 t* = 5.0

t* = 5.8 t* = 6.6

Figure 3.9 Jet Oscillation inside the Oscillation Chamber

a. t* = 2.2 b. t* = 3.4

c. t* = 4.2 d. t* = 5.0

e. t* = 5.8 f. t* = 6.6

g. t* = 7.5 h. t* = 8.3

Figure 3.10 Vortex Shedding from the Oscillator Fin Figure 3.10 shows the vortex shedding from the downstream part of the oscillation chamber as the jet in the oscillation chamber is deflected from centerline towards the upper lip. When the jet is at the symmetrical position, the separation points on the afterbody are almost symmetrical. While alternating vortices are shed from the chamber and convected downstream (Figures 3.10a-3.10d), the jet inside the chamber is being deflected upwards and the momentum of the flow coming from the lower output passage of the oscillator fin is slowly increasing. That's due to the fact that the upper flow passage is blocked by the weaker vortex and the stronger vortex delivers the incoming jet through the lower output passage. As a result, the lower separation point is slowly pushed further downstream and at the same time the upper separation point is pulled towards the upper output passage. The lower vortex which would be created and shed if the jet was symmetrical, is now swept away by the flow coming from the lower output passage and mixes with the flow. At the same time, another big vortex is now being formed, again on the upper side, due to very early separation and is about to be convected downstream (Figures 3.10e-3.10h). When the jet inside the oscillation chamber starts to return to its original position, the upper and lower separation points once again will start to move and eventually they will return their original symmetrical position. As soon as the jet starts to deflect downwards, this time the separation points will start to move in the opposite way that they did before. Namely, the upper separation point will be pushed backwards now and the lower separation point will be pulled towards the lower output passage. The speed and pressure distribution predictions of the flow field are also presented in Figure 3.11.

3.4.1.3 Comparison of the Flow Fields of the Cylinder and the Oscillator Fin

The turbulent kinetic energy level in the flow domain is an indication of the generated turbulence which in turn determines the heat transfer characteristics of the system. Therefore an increase in the turbulence level will directly affect the heat transfer rate. However an increase in the turbulence level is generally accompanied with an increase in total pressure loss level. For these reasons the turbulent kinetic energy and the total pressure loss levels for the cylinder and for the oscillator fin are compared.

t =5.0

t =5.8

t =6.6

t =7.4

Speed Pressure

Figure 3.1 1 Speed and Pressure Contours for the Oscillator Fin In order to compare the turbulent kinetic energy level in the flow domain, an integrated mean value for the whole domain is obtained using,

k dA k V = ^■ (5) dA

where A is the area of the computational domain. The time history of the mean turbulent kinetic energy is presented in Figure 3.12. It can be seen that the mean turbulent kinetic energy almost remains constant as time progresses both for the cylinder and for the

-oscillator fin - cylinder

t*

Figure 3.12 Time History of the Mean Turbulent Kinetic Energy over the Whole Domain

oscillator fin. However the turbulent kinetic energy level of the oscillator fin is almost 65% higher than that of the cylinder. This increase in the turbulent kinetic energy level may be due to the mixing of the free stream with the highly unsteady flow coming out of the upper and lower output passages creating continuously changing shear layers and velocity gradients in the flow domain. The turbulent kinetic energy contours for the whole domain both for the cylinder and the oscillator fin are also shown in Figure 3.13 for various time steps. Unsteady pulsating motion of the jets coming out of the output passages interact with the core flow between the oscillator fin and sidewalls and wake flow downstream of the afterbody. Because the streamwise momentum of the unsteady jets from the output passages varies in time significantly, the interaction of the core flow with the wake flow is very strong. Local turbulence enhancements are also carried into a wider downstream area via unsteady sweeping nature of the present flow field. The major turbulence enhancement area occupies a much longer region downstream of the oscillator fin as indicated by red, yellow and green zones in Figure 3.13.

The distribution of the non-dimensional total pressure loss at the exit plane for various time steps is given in Figure 3.14 for the cylinder and Figure 3.15 for the oscillator fin. The total pressure contours for the whole computational domain are presented in Figure 3.16 for the same time steps. The qualitative numerical results show that the aerodynamic penalty level is at the same order of magnitude both for the oscillator fin and the cylinder. Δp_t* values shown in Figure 3.17 are area averaged only at the exit plane for comparison.

The results of the transient simulations were useful in terms of observing the overall features of the flow fields for the oscillator fin and the pin fin cylinder, e.g. the vortex shedding processes, turbulent kinetic energy generation processes and the total pressure loss characteristics. These results reveal the potential in using the oscillator fin for turbulence enhancement without significant aerodynamic penalty. However detailed experimental investigation of the two geometries in order to get some quantitative results and to understand the physics of the flow field is necessary.

t=5.0

t =5.8

t =6.6

t=7.4

Figure 3.13 Turbulent Kinetic Energy Contours, k

y D

Figure 3.14 Non-dimensional Total Pressure Loss Distribution for Various Time Steps at the Exit Plane for Cylinder

Figure 3.15 Non-dimensional Total Pressure Loss Distribution for Various Time Steps at the Exit Plane for Oscillator Fin

t=5.0

t =5.8

t =6.6

t=7.4

Figure 3.16 Total Pressure Coefficient Contours, p^

- oscillator fin -cylinder

Figure 3.17. Time History of the Area Averaged Non-Dimensional Total Pressure

Loss at the Exit Plane

3.4.2 Quasi-Steady Simulations

Since a full period of the jet oscillation inside the chamber could not be captured with the transient simulations, it was not possible to get enough information about the jet oscillation mechanism inside the oscillation chamber. For this reason, instead of simulating the whole periodic process with transient simulations, some steady simulations are performed for the same Reynolds number and for different instants of the process. In other words, the steady form of the governing equations are solved for different values of the jet deflection angle, θ. Therefore θ is imposed as a boundary condition at the jet exit plane. The computational domain for the steady simulations is shown in Figure 3.18 and the definition of the jet deflection angle is illustrated in Figure 3.19.

Figure 3.18 Computational Domain for Steady Simulations

Figure 3.19 Jet Deflection Angle Definition The domain is discretized using nine-node quadrilateral elements and there are 6207 second order elements and 23600 number of nodes. Figure 3.20 shows the velocity vectors and the static pressure contours inside the oscillation chamber for different jet deflection angles. When θ = 0° the flow field is symmetrical, the jet impinges upon the concave surface of the chamber, splits into two oppositely directed flows which have the same mass flow rate and these flows exit from the upper and lower output passages of the oscillator fin. Furthermore, two symmetrical and counter-rotating vortices with the same magnitude of vorticity are created between the incoming jet and the two oppositely directed flows. Now if the deflection angle is changed either in the positive or negative direction, the mass flow rate of the one of the two oppositely directed flows will increase while that of the other will decrease. In order to make this point more clear, we can choose a direction and observe the flow. Starting from θ = 0° (Figure 3.20d) and going in the positive direction (Figures 3.20e-3.20g),

θ = 0°

Symmetrical flow field as explained above

0 = 15°

The incoming jet is deflected upwards and still impinges upon the concave surface of the oscillation chamber. The lower vortex gets bigger and the upper vortex gets smaller both keeping the same vorticity. The mass flow rate exiting the lower output passage is now higher than the mass flow rate at the upper output passage. The static pressure inside the lower vortex is decreasing.

θ = 30°

The impingement point is still on the concave surface of the chamber. The lower vortex is even bigger now and getting closer to the center of the chamber while the upper vortex is pushed further away from the center. The mass flow rate of the lower output passage keeps increasing while the upper output passage is decreasing. The static pressure inside the lower vortex is even less now.

a. θ = -45^c

b. θ = -30°

c.θ = -15°

d.9 = 0°

e.9=15°

f. θ = 30°

g. θ = 45° Figure 3.20 Velocity Vectors and Static Pressure Contours for Different Jet Orientations

9 = 45°

The jet now impinges upon the sidewall of the chamber. The lower vortex is almost at the center and its size is at its maximum. The upper vortex is away from the center and almost blocks the upper output passage. Most of the incoming flow exits from the lower output passage following the contour of the chamber. The static pressure inside the lower vortex is now at its lowest.

When the flow field is not symmetrical (θ ≠ 0°) and the jet impingement point is on the concave surface of the chamber, the mass flow rate imbalance on either side of the impingement point which is due to the concavity of the wall creates a momentum imbalance on the jet. This momentum imbalance pushes the jet further away towards the lower mass flow rate side until the jet impinges upon the sidewall where the impingement point is no longer on the concave surface. At this point further deflection of the jet is restricted by the sidewall. Additionally at this instant, a pressure gradient across the jet exists which is created as the jet is deflected towards the sidewall. This pressure gradient is a result of the static pressure drop inside the bigger vortex as it situates itself at the center of the oscillation chamber. Since the jet can not be pushed further away, this pressure gradient causes the jet to return to its original position. This unsteady process continuously repeats itself resulting the jet oscillation between the upper and lower sidewalls and on the concave surface of the oscillation chamber.

Figure 3.21 shows the turbulent kinetic energy contours in the flow domain. It can be seen that when the jet deflection angle is at its maximum, one of the output passages is blocked. Therefore a high shear region is created between this passage and the main flow resulting in a high turbulent kinetic energy production from this location. As the jet is oscillating inside the oscillation chamber, this high shear region will alternate between the upper and lower output passages creating an unsteady turbulence production mechanism. This is the most important feature of the oscillator fin that will be used for heat transfer enhancement purposes.

θ = -45° 9 = -30°

θ = -15^c 9 = 0°

θ = 15^c 9 = 30°

9 = 45°

Figure 3.21 Turbulent Kinetic Energy Contours at Different Jet Orientations Chapter 4

EXPERIMENTAL PLAN

Predictions from the computational analysis reveal the potential in using the oscillator fin for heat transfer enhancement purposes. Therefore detailed investigation of the fluid mechanics and heat transfer characteristics of the oscillator fin is necessary. For this reason an experimental setup is designed which is currently under construction. Extensive and detailed experiments will be conducted both for a pin fin cylinder and for an oscillator fin in order to be able to compare the heat transfer enhancement and pressure loss characteristics of those devices.

4.1 Experimental Facility

The experimental facility is an open loop wind tunnel which consists of an axial air blower, a diffuser with multiple screens, a plenum chamber, a high area ratio circular nozzle, a circular to rectangular transition duct, a converging nozzle, the test section, a diverging nozzle and a diffuser. The schematic of the facility is shown in Figure 4.1.

An axial flow fan is used to draw the ambient air into the facility. A 66cm x 66cm x 38.7 cm filter box encloses the inlet of the axial fan. A 7.5 kW electric motor drives the 45.7 cm tip diameter fan which has a potential to provide a pressure differential of 15 cm of water over a range of flow rates. The speed of the electric motor is controlled by using a Dynamatic® adjustable frequency AC drive which gives the ability to control the air speed through the facility between 0 and 30 m/s. Figure 4.2 shows the change in air speed at the exit of the transition duct as the frequency of the electric motor is varied using the AC drive.

After the fan the air blows through a series of screens and enters a 1.73 m³ plenum chamber. Downstream of the plenum the air accelerates through a circular nozzle of area ratio 8.65 then transitions to a 36.67 cm x 15.24 cm rectangular cross-section by a Electric Motor and Fan

Filter Box Plenum Chamber

Figure 4.1 Experimental Facility

c 10 20 30 40 50 60 70

Frequency (Hz)

Figure 4.2 Frequency-Speed Calibration Curve for the AC Drive 137 cm long duct. The cross-section is further reduced to 36.67 cm x 7.62 cm by a converging nozzle (Figure 4.3) which is 50.8 cm long and also has a rectangular cross- section.

Figure 4.3 Converging Nozzle

Figure 4.4 Converging Nozzle Profile (Dimensions in cm) After the converging nozzle there is the test section which is 127 cm long straight rectangular duct. It has a 36.67 cm x 7.62 cm cross-section and is illustrated in Figure 4.5.

Figure 4.5 Test Section Isometric View

The test object, i.e. the pin fin cylinder or the oscillator fin, will be placed approximately 4D downstream of the entrance of the test section. The duct continues up to 10D downstream after the test object. Here D is the diameter of the pin fin cylinder (or the width of the oscillator fin). This diameter will be equal to the channel width in order to obtain a height to diameter ratio (WD) of 1 which is a typical value for turbine blade cooling applications. The pin fins commonly used in turbine cooling have pin H/D ratios between Vz and 4 due to blade size and manufacturing constraints. The distance between the sides of the object and the top and bottom surfaces of the duct will be 2D which is also a typical value for the vertical distance between pin fins in a pin fin bank. One side of the channel walls will have a flat surface and it is goina; to be used as an endwall heat transfer test surface. This surface will be coated with chiral nematic encapsulated liquid crystals and will be used to determine and compare the heat transfer capabilities of the two bodies. For the opposite side two surfaces will be manufactured, one flat surface and one with probe access slots. Only one of them will be used during a test depending on the purpose of that specific test. The flat one will be used when liquid crystal thermography measurements are taken because of the necessity to have an optical access. This one is also going to be used when LDV measurements are performed. The other surface will be a slotted surface and will have probe access slots at various upstream and downstream locations relative to the test object (Figure 4.6). These slots will provide necessary access

Mow

Figure 4.6 Slotted Sidewall (Dimensions in cm)

for the wake surveys of the two bodies using the hotwire anemometry and for the pitot- static probe measurements.

After the test section there is the diverging nozzle which is used to diffuse the flow before discharging into the atmosphere. This part will be the same as the converging nozzle (Figure 4.7). Another diffuser with a higher area ratio will be used to further diffuse the flow. All parts except for the final diffuser will be constructed of 1.27 cm thick clear acrylic.

Figure 4.7 Diverging Nozzle

Figure 4.8 Converging Nozzle, Test Section and Diverging Nozzle (Top View)

Figure 4.9 Converging Nozzle, Test Section and Diverging Nozzle (Isometric View) 4.2 Instrumentation

During the experimental investigations of the oscillator fin and the cylinder several types of measurement devices will be utilized for different purposes. Liquid crystal thermography will be used for determining the heat transfer characteristics of the two bodies. Hotwire Anemometry and Laser Doppler Velocimetry will be used for instantaneous velocity and turbulence measurements in the wakes of the two bodies. Pitot-static probe measurements will also be accomplished for mean flow velocity measurements.

4.2.1 Laser Doppler Velocimetry

The LDV system is an Aerometrics three component fiber-optic system which is composed of mainly five units: laser, fiber drive, transmitting and receiving optics, photodetector unit and the Doppler Signal Analyzer (DSA) with the computer data acquisition and analysis system.

Figure 4.10 Laser Doppler Velocimetry System Setup 4.2.1.1 Laser

The laser is a 4 Watt argon-ion continuous wave laser manufactured by Laser Ionics Inc. It is water cooled and uses a separately housed power supply with power monitors and controls. It has a glass tube filled with argon gas that is stimulated by a high voltage to emit light photons. Water must be running through the laser and the power supply during laser use. The tube within the laser must warm up for at least 15 minutes before the laser beam will be ready for experimental use. The rear mirror controls at the rear side of the laser are used to maximize the output power of the beam after the laser warm up.

4.2.1.2 Fiber Drive

The fiber drive is the most important component of the system and it is responsible for color separation and direction of the beams that will be used in the LDV. The laser beam enters the unit and passes through a Bragg cell which gives a series of overlapping frequency shifted beams. The beam then proceeds along the complete length of the fiber drive where it encounters a mirror which turns the beam down and into a prism. The prism splits the original beam and the shifted beam into several beams of varying wavelengths. The prism is positioned such that the beams run parallel to the entering beam. These beams encounter another mirror which separates the shifted beams from the unshifted beams by reflecting them to opposite sides of the fiber drive. The different wavelength beams are at various heights when reflected, green (514.5 nm) is lowest in height, blue (488 nm) is next in height and violet (476.5 nm) is highest. The beams each encounter a mirror at a corresponding height which turns the beam into a fiber coupler. The green beam is reflected first, while the others pass above the mirror until they reach their corresponding mirrors. This occurs with two different sets of mirrors, one for the shifted and one for the unshifted beams. The fiber couplers are composed of five lenses which are used to focus the laser beam onto a single-mode fiberoptic cables with a diameter of 5 μm each. Each coupler has three dimensional positioning control, lateral, longitudinal and normal, as well as two tilt controls for precision focusing on the fiber optic cable ends. This focusing is very important in increasing the power levels of the green, blue and violet beams.

Violet

Figure 4.11 Fiber Drive Unit (Side View)

Upper Level

Shifted Beam

Lower Level

Figure 4.12 Fiber Drive Unit (Top View) 4.2.1.3 Transceiver

The green pair and the blue pair are grouped together and brought to the main transceiver unit. The transceivers serve as both transmitter and receiver units when backscatter measurements are done. They contain collimating lenses as well as the focal lenses (Figure 4.13). The beams leave the transceivers and form the probe volume. Velocity measurements are obtained in the planes of the each crossing beam pair. This setup allows two dimensional velocity measurements using green and blue beam pairs which are orthogonal to each other. These all four beams pass through the same focusing lens and therefore all cross at the same location, which is ideal for two-dimensional measurements. Different lenses with different focal lengths can be used on the main transceiver unit.

Figure 4.13 80 mm Fiber-Optic Transceiver Unit 4.2.1.4 Photodetector Unit

The transceiver unit is connected to the photodetector unit through a multi-mode fiber-optic cable. The photodetector unit contains three photomultiplier tubes, one for each color beam. The photomultiplier tube each have an optical band-pass filter on the surface that allows one LDV wavelength to pass while other wavelengths are reflected off the surface. The arrangement of the tubes allows the light from any one of the three fiber ends to be reflected or passed into the photomultiplier tube of the allowed wavelength. Preamplifiers are connected to the photomultiplier tubes to enhance the signal which is sent via a coaxial cable to the Doppler Signal Analyzer (DSA). The DSA is also connected to the photodetector unit with a cable that supplies voltage to each photomultiplier tube.

4.2.1.5 Doppler Signal Analyzer

The Doppler Signal Analyzer (DSA) is a frequency domain signal processor for determining the frequency of the LDV burst signals which uses high speed analog to

Figure 4.14 Doppler Signal Analyzer digital converters to record the signal and Fourier transform to determine the frequency of the signal. The DSA is composed of four different boards. The controller board is used to set the instrument functions via the computer interface. The sampling board houses the analog to digital converters and continuously samples the signal from the optics, but the data are only stored when a Doppler signal is detected. The oscillator board has a 160 MHz crystal oscillator from which all of the sampling and mixer frequencies are derived. The analog board serves as the direct link to each component of the LDV system. This board controls quadrature downmixing, log amplification of the downmixed signal, d.c. offset adjustments to the raw signal, burst detection, peak detection and low pass filtering. The LDV data acquisition, setup, analysis and presentation are completely controlled by the DSA software.

4.2.1.6 Free Jet Measurements - Setup

In order to test the LDV system introduced above, a free jet flow experiment is conducted. The jet is a circular round jet coming out of a 4 cm diameter pipe. The experimental setup used for the jet measurements is shown in Figures 4.15 and 4.16. The measurements are taken at two diameter (D) downstream of the jet exit plane. Two- dimensional data are obtained (u and v components of the velocity vector) by using the green and blue components of the LDV system and by traversing across the jet in z direction. The system is run in the backscatter mode. Therefore the transmitter is used both for transmitting the beams and collecting the Doppler bursts. A lens with 500 mm focal distance is used on the transceiver. The beam separations are 19.5 mm for the green component and 19.7 mm for the blue component. This setup resulted in probe volumes being ellipsoids with long diameters of 8.4 mm, 7.89 mm and short diameters of 0.164 mm, 0.155 mm for the green and blue components, respectively. Also the fringe spacings are found to be 0.0132 mm and 0.0124 mm with 12 fringes for each component. A Bragg Cell frequency of 40 MHz is used for resolving the directional information. The flow is seeded using oil panicles atomized by a TSI Model 9302 atomizer.

Figure 4.15 Jet Setup (Top View)

Figure 4.16 Jet Setup (Side View)

Figure 4.17 Transceiver, Jet Exit and the Traverse

4.2.1.7 Free Jet Measurements - Results

During the free jet measurements the mean and the fluctuating components of the axial component of the velocity vector (u) and one of the transverse components of it (v) are measured. These measurements are accomplished by making traverses in the direction of the third velocity component (w) which is z. The definition of these directions are illustrated in Figures 4.15 and 4.16 before.

The most important challenge during the experiments was the seeding of the flow in high shear regions. It was very difficult to obtain enough seed density to collect the LDV data without special treatment for seeding. Mean velocity data are also obtained by traversing a pitot-static probe at the same location. Figure 4.18 shows the mean axial velocity profile data obtained by both the pitot-static probe and the LDV system. As it can be seen from the figure, the LDV data could be taken only in the core flow region where the seed density is the highest. However the agreement between the data obtained is satisfactory.

Since the traverse is made at two diameter downstream of the jet exit, the potential core region is still dominating and it is the cause of the almost flat profile in the core region. There is a slight asymmetry in the jet profile captured both by the pitot-static probe and the LDV. This asymmetry is also seen in the measurements taken by the LDV when a special treatment for seeding is applied. It is probably due to some imperfections in the jet facility used in this experiment.

Figure 4.18 Mean Axial Velocity Comparison

Although the comparison between the LDV and the pitot-static probe data is made only in the core region, it is still possible to collect data by properly seeding the shear flow regions. For this purpose the jet exit pipe is enclosed inside a box and the enclosed region is seeded and filled with oil particles from outside the jet, not from inside as in the previous case, during shear flow measurements. Therefore the jet is expected to entrain enough particles to collect LDV data. This modified setup is shown in Figure 4.19.

Using the modified setup for the seeding of the high shear regions helped in collecting data from those regions. The mean profile of the axial velocity component is given in Figure 4.20 and asymmetry of the jet can also be seen from this data. Being able to seed the high shear regions, the turbulent kinetic energy distribution could also be obtained and the peaks occurring in the high shear regions are captured.

Figure 4.19 Modified Jet Setup for Shear Region Seeding

Figure 4.20 Non-dimensionalized mean axial velocity distribution Chapter 5

CONCLUSIONS AND FUTURE RESEARCH

Oscillator Fin is introduced as a novel turbulent heat transfer augmentation device in the coolant passages of gas turbine blades. This part of the research has mainly the computational simulation results which are performed as an initial step of an extensive research program to reveal the potential in using the oscillator fin. Additionally the experimental analysis plan is also explained which is going to be the next part of this research program.

The flow field for the oscillator fin is analyzed by solving the governing equations and the results are compared with the flow field of an equivalent conventional cylindrical pin fin. Preliminary results show that the oscillator fin has a great potential in terms of increasing the turbulent kinetic energy levels in the flow domain while keeping the total pressure loss levels almost at the same order of magnitude with that of the pin fin. Furthermore the increased unsteadiness in the wake of the oscillator fin due to the alternating flow pulses coming from the output passages is expected to enhance the heat transfer characteristics of the oscillator fin over the cylindrical pin fin.

The jet oscillation mechanism inside the oscillator fin is also analyzed using the computational simulations. It is seen that the jet oscillation on a concave wall is mainly a geometry driven phenomenon. The concavity of the wall causes a mass flow rate imbalance around the jet impingement point when the jet deflection angle is different than zero and this imposes a momentum imbalance on the jet. This momentum imbalance together with the periodic variation of the static pressure gradients across the jet are the main driving mechanisms of the jet oscillation inside the oscillation chamber. The pressure gradients are created by the vortices on either side of the jet when they change their size while keeping the same vorticity.

The computational simulations are invaluable tools in terms of predicting the flow fields and for flow visualization purposes. Nevertheless an in-depth experimental investigation of the characteristics of the oscillator fin is necessary for the validation of the oscillator fin potential and for the determination of the oscillator fin performance. For this purpose a new experimental facility is designed and is currently under construction. This facility will be used for extensive experimental investigation of the oscillator fin which will be the next part of this research program. The heat transfer enhancement characteristics of the oscillator fin will be directly analyzed using Liquid Crystal Thermography and the results will be compared with those of the cylindrical pin fin. Laser Doppler Velocimetry and Hot Wire Anemometry will extensively be used for analyzing the turbulent wakes of the two bodies. Different oscillator fin geometries will also be investigated as the one shown in Figure 5.1 in which the jet oscillation on a concave wall concept is embedded inside a cylinder with output passages inclined from the flow direction.

Figure 5.1 Pac Fin Geometry

The potential of using the jet oscillation on a concave wall concept is not limited to only replacing the pin fins with the oscillator fins in gas turbine cooling passages. The impinging jet cooling of the leading edges of the turbine blades can also be modified by the proper application of this concept. Furthermore this concept can be used in different places such as aircraft wing de-icing applications or in electronic cooling systems. Basically, it can be utilized in every field where an impinging jet is used for enhancing the transport mechanisms. Using as a turbulent mixing enhancement device is also one of the possibilities.

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Claims

We Claim:

An oscillator fin comprising:

two members, said two members of an elliptical cross-section and placed transversely across a flow passage, wherein a major axis of said elliptical cross- section parallel to a direction of said flow passage and wherein said two members form a tapering nozzle to create a jet between said two members; and

a third member to receive said jet from said nozzle, said third member having a U-shaped geometry.