Effects of the pocket cavity on heat transfer and fluid flow of the downstream outlet guide vane at different flow attacking angles

A pocket cavity is generated at the junction position of the low pressure turbine (LPT) and the outlet guide vane (OGV) in the rear part of a modern gas turbine jet engine. In the present study, a triangular pocket cavity is placed upstream of an OGV at different distances. The effects of the pocket cavity on heat transfer and fluid flow of the downstream OGV with different flow attack angles are investigated numerically with well validated turbulence models. The flow attack angles are varied as -30°, 0°, and +30° at a constant Reynolds number =160,000. The turbulent flow details are provided by numerical calculations using two turbulence models, the unsteady DES model and the steady k-ω SST model. For different flow attack angles, the high Nusselt number regions around the OGV are changed. The high heat transfer region is really drawn back at a flow attack angle = +30° (Case 2b) compared with Case 2a with a flow attack angle =0°. As the flow attack angle is changed to -30° (Case 2c), the high Nusselt number regions are greatly enlarged not only on the suction side also on the pressure side because of the strengthened flow impingement on the vane surfaces. The pocket cavity weakens the flow impingement on the vane surfaces and the effect is more obvious when the pocket cavity is placed close to the vane. In addition, the heat transfer distribution over the pocket surface is also affected by the location of the vane. When the vane is placed close to the pocket cavity (Case 1), the heat transfer on the pocket edge is increased. In the case with a flow attack angle =0°, the high turbulent kinetic energy region is mainly located near the vane and wake region downstream the vane and recirculating flows can hardly be found.

Outlet guide vanes are placed in the rear part of a gas turbine jet engine to provide support to the main engine case. In addition, it controls the flow ejected from the gas turbine and then affects the propulsion of the engine. In the design of advanced aero engines, the requirements of flow manipulation of the outlet guide vanes (OGVs) have become significantly higher. In the engine of an aircraft, the rear part is often designed as a contracted outlet to increase the ejecting velocity of the exhaust gas. However, a pocket cavity is generated at the junction position of the low pressure turbine (LPT) and the OGV because of the contraction, as shown in Figure 1. The triangular pocket cavities are not designed for heat transfer purposes but they are difficult to avoid in the mechanical assembly. This kind of pocket cavities, due to the high Reynolds number and the specific shapes, are hardly investigated in previous research works [1]. The heat transfer and flow pattern of pocket cavities have significant effects on the incoming flow of the OGVs [2].

PHOTO (COLOR): Figure 1. A pocket cavity formed at the connecting part of Outlet Guide Vane.

As an important heat transfer enhancement method, pockets or grooves are commonly applied in modern heat exchangers and some cooling equipment. In the past decades, researchers have paid much attention to the investigation of rectangular and triangular grooves [,,]. Lorenz et al. [3] measured the distributions of the heat transfer coefficient along a channel wall with periodic transverse grooves for thermal developing and periodic turbulent flows at 104 ≤ Re ≤ l05. The Nusselt number augmentation ratio of the grooved surfaces was about 1.52 ≤ Nu/Nu0 ≤ 1.75 compared to a smooth channel. The combination of grooves and other heat transfer elements is another approach to augment heat transfer [,,,,]. Promvonge [7] investigated the characteristics of turbulent flows in a rib-grooved channel. The rib-groove combined structures were found to enhance the heat transfer rate significantly compared with a smooth duct. Lorenzini-Gutierrez et al. [9] performed a numerical and experimental analysis of heat transfer enhancement in a grooved channel with curved flow deflectors. The main function of the deflectors is to divert a portion of the flow into the space between blocks in order to increase the fluid motion in this area and to remove the trapped fluid in the low heat transfer region. Recently, researchers paid more attention to variously shaped grooves to find optimal configurations with better thermal performance [,,,,,].

The heat transfer and fluid flow on the endwall with an obstacle, such as a bluff body or a vane or combined structures, have received a lot of interest. The 3D vortical structure produced by the obstacle greatly affects heat transfer on the endwall. Wang et al. [17] investigated the endwall heat transfer characteristics of forced flow past bluff bodies using liquid crystal thermography (LCT). The results indicated that due to the formation of horseshoe vortices, the heat transfer of a single bluff body and two bluff bodies arranged in tandem were both enhanced and the power index of Reynolds number was flow dependent. Praisner and Smith [18,19] investigated the endwall heat transfer and vortices formed upstream of an airfoil using simultaneous PIV and LCT. Different cross sections were selected to study the vortical behavior and corresponding endwall heat transfer. Two high heat transfer zones were found upstream of the symmetric airfoil. From the study, angle of incidence was found to play a pivotal role in bringing hydrodynamic instabilities and thereby vortex shedding for such steady mixed convective flows. The effects of the incoming flow characteristics on the endwall heat transfer and turbulent flow of turbine blades have received some interest [,,,,]. Rhee and Cho [20,21] investigated local heat/mass transfer characteristics on a stationary blade for various relative positions of the blade in a low speed wind tunnel with a stationary annular turbine cascade. They found the change in blade position, which causes a different interaction between vane and blade, altered the incoming flow condition. Qureshi et al. [22] investigated the impact of swirl on the aerodynamic and heat transfer characteristics of a high pressure turbine stage using a combustor swirl simulator. Zhang et al. [23] studied the effects of inlet turbulence and end-wall boundary layer on aerothermal performance of a transonic turbine blade. They observed noticeable changes in heat transfer on the suction side near-tip surface due to the different inlet endwall boundary layer profiles. Lynch and Thole [24] compared the 3D boundary layer on flat versus contoured turbine endwalls. They found elevated turbulence levels in the contoured endwall compared to the flat endwall. In the design of advanced aero engines, the requirements of flow manipulation of the OGV become significantly higher and the heat transfer and flow pattern of pocket cavities have significant effects on the incoming flow of the OGV. Therefore, effect of this pocket cavity on the downstream vane needs to be deeply investigated to provide references for the design of gas turbines. Researchers have carried out some investigations on the endwall heat transfer and fluid flow of the OGV [25,26].

Large Eddy simulation (LES) is considered as a relatively accurate method to solve turbulent flows, but it still requires a huge amount of computational efforts, especially dealing with wall bounded flows. In order to obtain results with sufficient accuracy and reduce the computational demand, a method combining the LES model and Reynolds Averaged Navier Stokes (RANS) model has been proposed, namely the so-called detached Eddy Simulation (DES) model [27]. DES models are specifically designed to address wall bounded flows at high Reynolds numbers, where the efforts of the near-wall resolution of LES would be reduced [28]. Further, the Improved Delayed Detached Eddy Simulation (IDDES) model [29,30] was a development of the original model to provide shielding against grid induced separation (GIS), similar to the Delayed Detached Eddy Simulation (DDES) model [31]. The IDDES model modifies the treatment in the GIS for the LES, which may resolve the turbulence activity close to the wall more effectively. Generally, a DES model seems very suitable for dealing with the wall bounded flow in this investigation.

The effect of the pocket cavity on heat transfer and fluid flow of the downstream OGV under different flow attack angles are investigated numerically with well validated and established turbulence models. The turbulent flow details are provided by numerical calculations using two turbulence models, the DES model and the k-ω SST model. The OGV profile is taken from the previous research work in our group and measuremeants by Wang et al. [25]. The turbuluence model is validated by the liquid crystal themography (LCT) experimental results. The flow attack angles are varied between -30°, 0°, and +30° at constant Reynolds number =160,000. The heat transfer field and turbulent flow characteristics are provided and analyzed.

The computational channel is based on the OGV profile with upstream extended and downstream extended channels as shown in Figure 2. The profile is taken from Wang et al. [25] with a chord length of 24.3 cm. The length of the upstream extended channel is 24 cm and the length of the downstream extended channel is 12 cm. The endwall and pocket region are the heated surfaces. The span of the OGV and the pitch are 24 cm. The pocket is placed upstream of the OGV with a certain distance L = 5 cm or 10 cm. The depth of the pocket D is 5 cm with an attack angle of 45° connecting to the adjacent flat surfaces. The fillet radius of the pocket cavity is 2 cm. The flow attack angles α change as -30°, 0°, and +30°. The origin of the axis is set at the stagnation point of the OGV. Based on the above, nine cases are tested with different locations of the pocket cavity and flow attack angles, respectively, Case 0a, Case 0b, Case 0c, Case 1a, Case 1b, Case 1c, Case 2a, Case 2b and Case 2b.

PHOTO (COLOR): Figure 2. Computational domain and related parameters.

The grids of the computational channel are generated using the software package ICEM. Typical grids in the pocket region and the symmetric vane region are shown in Figure 4. In order to obtain acceptable levels of accuracy and computational efficiency, structured grids are employed. In addition, Figure 3 shows that the grids near the boundary are very dense, whereas the grid density is relatively sparse far from the wall boundary. The grid independence study is shown in Table 1. The study is performed based on case 1a at Re =160,000. Four mesh systems are built, respectively, 3.2 M, 4.5 M, 6.1 M, and 7.7 M, are tested. The total area-weighted pressure drop between the inlet and the outlet and averaged Nusselt number on the heated walls are provided and compared. From the figure, all the mesh systems show relatively accurate results besides the 3.2 M case. The errors between the other three mesh systems are <0.5%. Considering accuracy and efficiency, the mesh system of 6.1 M is deemed suitable for the numerical calculations.

PHOTO (COLOR): Figure 3. Computational channel and typical structured grids used in the calculations.

Mesh independence study.

1 Bold values are the chosen or recommended ones.

In the calculation part, two kinds of turbulence models are, respectively, tested and compared. The k-ω SST model is a hybrid turbulence model which takes advantages of both the k-ε model and the k-ω model [32,33]. The solution of the k-ω model shows high accuracy and robustness in the boundary layer region. A DES model is considered suitable for dealing with the wall bounded flow in this investigation. In this study, the IDDES model is applied and the validation of the model is provided below. In the IDDES model, the modified Menters SST two-equation eddy viscosity model is used as the RANS model. It modifies the dissipation-rate term of the turbulent kinetic energy (TKE) transport equation. Hence, the TKE equation for the IDDES model can be written as: where t, k, ρ, uj, μ, μt, τij, and Sij are the time, turbulent kinetic energy, density, velocity, molecular viscosity, turbulent viscosity, stress tensor, and mean strain rate tensor, respectively. The LIDDES is defined as the IDDES length scale [34], given by: where the LIDDES and the LLES are the length scales of the RANS and the LES, respectively. These are defined as: where β* is a constant in the SST k-ω.is the grid scale. Cw is an empirical constant, d is the distance to the nearest wall, and.. More details can be found in Ref. [30].

In this study, the sidewalls and top wall are adiabatic. A constant surface heat flux of 1,000 W/m2 is applied on the endwall and the pocket region. No-slip velocity conditions are applied at all wall surfaces. Uniform velocity and temperature are applied at the channel inlet. The flow attack angle changes from -30° to +30° at a constant Reynolds number =160,000. The turbulence intensity level at the inlet is set 3.5% based on the measurements by Wang et al. [25].

For the k-ω SST model, ANSYS FLUENT 17.0 is employed to solve the governing equations. The Semi-Implicit Method for Pressure Linked Equations Consistent (SIMPLEC) algorithm is chosen for the pressure-velocity coupling. Second order difference formulae are chosen for spatial discretization of TKE, turbulent dissipation rate and energy equations.

For the DES model, the coupled method is chosen for the pressure-velocity coupling. Second order difference formulae are chosen for spatial discretization of TKE, turbulent dissipation rate and energy equations. A bounded central differencing scheme is chosen for the momentum discretization. A second order implicit transient formulation is chosen. The convergence criterion is set as 10−4 at every time step. The time step is set as 0.0001 s. Three channel flowing-through times are recorded to obtain the time-averaged heat transfer and flow field.

The OGV experiments were performed by Wang et al. [25] in a linear cascade test facility. The Nusselt number contours on the endwall with an OGV by the LCT experiments are presented on the left side of Figure 4 for comparisons. The numerical calculation results by Wang et al. are also presented, using standard k-ω model and baseline k-ω model (BSL) by ANSYS CFX, respectively. The numerical results in the present study are, respectively, performed by the two turbulence models, namely the DES model and k-ω SST model. The Nusselt number contours are compared with the previous research work. Compared with previous experimental results, the distributions are considered as acceptable. The distribution of the high heat transfer regions is similar. Compared with previous simulation results, all the results predicted by the different turbulence models have pretty good agreement. Based on the above, the turbulence models applied in the present study have shown relatively good accuracy.

PHOTO (COLOR): Figure 4. Validation of the turbulence models. The experimental results and numerical calculation results are taken from the Wang et al. [ 25].

The Reynolds number is defined as where u is the inlet velocity, Dh is the hydraulic diameter of the computational domain, and ν is the air kinematic viscosity.

The Fanning friction factor f is defined as where Δp is the pressure drop of the middle heated part and L is the length of middle heated part.

The local Nusselt number is defined as where Tf is the inlet middle heated part, and T(i) is the local surface temperature. The overall Nusselt number is obtained by area-averaging the local Nusselt numbers on the heated surfaces.

The Nusselt number distributions on the endwall of the OGV with a pocket cavity (Case 2, L/D = 2) for different flow attack angles at Re =160,000 are provided in Figure 5. In addition, the results of the DES model and k-ω SST model are compared. Three different flow attack angles are applied, respectively, -30°, 0°, and +30°. With different flow attack angles, the high Nusselt number regions around the OGV are changed. From the figure, the high heat transfer region is really drawn back for the flow attack angle = +30° (Case 2b). When the flow attack angle is changed to -30° (Case 2c), the high Nusselt number regions are greatly enlarged not only in the suction side but also on the pressure side. For Case 2c, the flow impingement on the vane surfaces becomes stronger and enhances the flow mixing. In the case of the flow attack angle =0° (case 2a), the Nusselt number distribution is moderate compared to the other two cases. For the results of the k-ω SST model, the high Nusselt number regions are relatively larger than those predicted by the DES model. The DES model can effectively avoid the over production of TKE k compared to the k-ω SST model. The effect of the flow attack angle is similar for both the turbulence models. Because the k-ω SST model is a steady simulation, the unsteady flow characteristics are difficult to be handled on the pressure side of the cane which can be found when flow attackangle is set as -30° (Case 2c). Under this flow attack angle, the vane has a large blocking ratio and cause strong vortex streets. In the simulation of the DES model, the results are time-averaged to provide more reasonable reference for the overall heat transfer characteristics. However, the location of the high Nusselt number region over the pocket surface is also changed for different flow attack angles. Overall, the Nusselt number over the pocket surface is much smaller than in the region near the vane.

PHOTO (COLOR): Figure 5. Nusselt number distributions on the endwall of an OGV with pocket cavity (Case 2) for different flow attack angles. The results of the DES model and k-ω SST model are compared.

The Nusselt number distributions on the endwall of an OGV without a pocket cavity (Case 0) for different flow attack angles at Re =160,000 are presented in Figure 6. Without the pocket cavity, the flow directly impinges on the vane surfaces. The Nusselt number distributions are similar to those of Case 2 for different flow attack angles. It seems that the flow impingement on the vane surfaces becomes stronger without the pocket cavity. The high Nusselt number regions of Case 0 are enlarged on the endwall around the vane surfaces. The Nusselt number distributions on the endwall of an OGV with a pocket cavity (Case 1, L/D = 1) for different flow attack angles are shown in Figure 7. The effects of different flow attack angles are still similar to Case 1. Because of the effect of the pocket cavity, the high Nusselt number region of Case 1 is smaller than that of Case 0 and Case 2. The pocket cavity weakens the flow impingement on the vane surfaces and this effect is more obvious when the pocket cavity is placed close to the vane. In addition, the heat transfer distribution over the pocket surface is also affected by the location of the vane. When the vane is placed close to the pocket cavity (Case 1), the heat transfer on the pocket edge is enlarged. The high heat transfer region is also affected by the flow attack angle. When the flow attack angle is changed from -30° to +30°, the high heat transfer region on the pocket edge is also enlarged. Based on above, the Nusselt number distributions of the vane and the pocket cavity interact with each other.

PHOTO (COLOR): Figure 6. Nusselt number distributions on the endwall of an OGV without pocket cavity (Case 0) for different flow attack angles.

PHOTO (COLOR): Figure 7. Nusselt number distributions on the endwall of an OGV with pocket cavity (Case 1, L/D = 1) for different flow attack angles.

The effect of the pocket cavity on the endwall heat transfer with an OGV for a flow attack angle =0° at Re =160,000 is clearly presented in Figure 8. From this figure, when the pocket cavity is placed in front of the vane, the flow impingement on the vane is weakened and induced decreased heat transfer around the vanes. When the pocket cavity is put close to the vane, the high heat transfer region on the pocket edge is enlarged. However, the high heat transfer region around the vane is decreased when the pocket cavity is placed closer. The averaged Nusselt numbers for all the cases are shown in Table 2. As expected, for the flow attack angle = -30°, the averaged heat transfer is highest, both for the endwall, pocket surface and overall heat transfer values. In addition, when the pocket cavity is placed far away from the vane, i.e., from Case 1 to Case 2, the endwall heat transfer is increased because of the strong flow impingement. For the pocket surface, the heat transfer is greatly decreased as the pocket cavity is placed far away from the vane.

PHOTO (COLOR): Figure 8. Effects of the pocket cavity on the endwall heat transfer with an OGV. The effect of the location of the pocket cavity is investigated in different cases.

Averaged Nusselt number for all the cases.

2 Bold values are the chosen or recommended ones.

The Nusselt number distributions along the centerline for different flow attack angles at Re =160,000 by the DES model are presented in Figure 9. The centerline is marked on the left side of the schematic configuration. There are two peaks to be found in the distribution along the centerline. The first peak is because of the thermal boundary development at the inlet. The second peak is caused by the strong flow impingement on the vane surfaces. There are three peaks in the figure of Case 1 and Case 2. The third peak is located on the downstream edge of the pocket cavity. Low heat transfer can be found in Case 1 and Case 2 which is caused the flow recirculation inside the pocket cavity. It seems that the flow attack angle has a small effect on the centerline distributions of the Nusselt number. All the distribution curves overlap and only small fluctuation can be found near the heat transfer peak region. Obviously, the peak value on the edge of the pocket cavity is much larger when the pocket cavity is placed near the vane especially when the flow attack angle is -30°.

PHOTO (COLOR): Figure 9. Comparisons of Nusselt number distributions along the centerline with different flow attack angles by the DES model.

The Nusselt number distributions along the centerline with different locations of the pocket cavity for the same flow attack angle at Re =160,000 are presented in Figure 10. The effect of the pocket cavity is clearly shown in this figure. The heat transfer peak of the curve clearly shows the location of the pocket cavity. The beginning part and back part of the distribution curves, without the effect of the pocket cavity, overlap very well in this figure. For the cases at flow attack angle = -30°, the distributions in the back part vary between different cases and as the vane is approached. In addition, the Nusselt number of Case 1c, with a relatively small distance between the pocket cavity and the vane, is the highest.

PHOTO (COLOR): Figure 10. Nusselt number distributions along the centerline with different locations of the pocket cavity for the same flow attack angle.

The pressure coefficient distributions on the endwall of the OGV with a pocket cavity (Case 2) for different flow attack angles by the k-ω SST model are presented in Figure 11.

PHOTO (COLOR): Figure 11. Pressure coefficient distributions on the endwall of an OGV with a pocket cavity (Case 2, L/D = 2) for different flow attack angles by the k-ω SST model.

The pressure coefficient distributions greatly depend on the flow attack angles. A high pressure region means usually strong flow impingement. For the flow attacking angle = +30°, all the high pressure regions are located on the pressure side, which means it belongs to on-design working condition. For the flow attack angle = -30°, low pressure regions are located on the pressure side. It is an off-design working condition. The boundary layer transition and separation are affected by the flow attack angles. The flow transition and separation greatly affect the pressure distributions. In the separation region, low pressure is usually observed. For the off-design working condition, flow attack angle = -30°, a large flow separation region at the pressure side can be found.

The streamlines and TKE distributions on the mid-span plane of the OGV with a pocket cavity (Case 2, L/D = 2) for different flow attack angles at Re =160,000 are presented in Figure 12. The streamlines are obtained by averaging large quantities of time steps predicted by the DES model. In the case with the flow attack angle =0°, the high TKE region is mainly located near the vane and wake region downstream the vane. The recirculating flows can hardly be in Case 2a. For the case with the flow attack angle = +30°, the flow separation happens at the suction side and a large area of high TKE can be found around the flow separation. The distributions for the case with the flow attack angle = -30° are similar. The high TKE region is located on the pressure side of the vane. With strong recirculating flows, the high TKE region expands within the pressure side and a large scale high TKE region can be found. The strong separation and recirculating flow regions can also be clearly found in Case 2b and Case 2c.

PHOTO (COLOR): Figure 12. Streamlines and turbulent kinetic energy on the mid-span plane of an OGV with pocket cavity (Case 2, L/D = 2) for different flow attack angles.

The velocity vectors and TKE distributions on the centerline section (x-z) of the OGV with a pocket cavity (Case 2, L/D = 2) under different flow attack angles are displayed in Figure 13. The velocity vectors are also averaged vectors obtained by the DES model. For Case 2 with different flow attack angles, the recirculating flows inside the pocket cavity still exist. For the flow attack angle = -30°, the high TKE region at the pressure side of the endwall is greatly decreased. For different flow attack angles, the stagnation region is changed around the vane. For the flow attack angle =0°, the transverse flows in the waking region of the vane are weakened. However, in the other two cases, the flow disturbances in the wake region are relatively strong because of the strong flow separation.

PHOTO (COLOR): Figure 13. Velocity vectors and turbulent kinetic energy distributions on the centerline section (x-z) of an OGV with pocket cavity (Case 2, L/D = 2) for different flow attack angles.

The effect of the pocket cavity on heat transfer and fluid flow of the downstream OGV for different flow attack angles are investigated numerically with well validated turbulence models. The turbulent flow details are provided by numerical calculations using two turbulence models, the unsteady DES model and the steady k-ω SST model. The flow attack angle is varied as -30°, 0°, and +30° at a constant Reynolds number =160,000. The heat transfer field and turbulent flow characteristics are provided and analyzed.

• With different flow attack angles, the high Nusselt number regions around the OGV are changed. The high heat transfer region is really drawn back for the flow attack angle = +30° (Case 2b) compared with Case 2a for the flow attack angle =0°. When the flow attack angle is changed to -30° (Case 2c), the high Nusselt number regions are greatly enlarged not only in the suction side but also on the pressure side with strengthened flow impingement on the vane surfaces.
• The pocket cavity weakens the flow impingement on the vane surfaces and the effect is more obvious as the pocket cavity is placed close to the vane. In addition, the heat transfer distribution over the pocket surface is also affected by the location of the vane. When the vane is placed close to the pocket cavity (Case 1), the heat transfer over the pocket surface is greatly enlarged.
• In the case with a flow attack angle =0°, the high TKE region is mainly located near the vane and wake region downstream the vane. The recirculating flows can hardly be found in Case 2a. The strong separation and recirculating flow zones can be clearly found in Case 2b and Case 2c.

• Nomenclature

• c

• chord of the OGV (m)

• CP

• pressure coefficient

• Dh

• hydraulic diameter (m)

• D

• depth of the pocket cavity (m)

• H

• channel height (m)

• h

• heat transfer coefficient (W/m2·K)

• k

• turbulent kinetic energy (m2/s2)

• L

• distance between the pocket cavity downstream edge and the OGV (m)

• Ltotal

• total length of the channel (m)
• Lupstream
• length of the upstream extended channel (m)
• Ldownstream
• length of the downstream extended channel (m)

• Nu

• Nusselt number

• Nu0

• Nusselt number of a smooth channel

• p

• pressure (Pa)

• P

• pitch distance (m)

• R

• fillet radius of the OGV (m)

• Re

• Reynolds number

• s

• span of the OGV (m)

• T

• temperature (K)

• Tf

• fluid temperature (K)

• Tw

• wall temperature (K)

• u

• flow velocity (m/s)

• W

• channel width (m)

• x

• streamwise direction (m)

• y

• spanwise direction (m)

• z

• normal direction (m)

• Α

• Greek symbols

• A

• attack angle of the OGV (degree)

• Δp

• pressure drop (Pa)

• Λ

• thermal conductivity (W/m·K)

• μ

• fluid dynamic viscosity (Pa·s)

• ρ

• fluid density (kg/m3)
• Subscripts

• m

• average/overall

• max

• maximum

• w

• wall