Large eddy simulation of base drag reduction using jet boat tail passive flow control

Large Eddy Simulation of Base Drag Reduction Using Jet Boat Tail Passive Flow Control

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Large Eddy Simulation of Base Drag Reduction Using Jet Boat Tail Passive Flow Control Yunchao Yang, William Bradford Bartow, Gecheng Zha, Heyong Xu, Jianlei Wang PII: DOI: Reference:

S0045-7930(19)30356-1 https://doi.org/10.1016/j.compfluid.2019.104398 CAF 104398

To appear in:

Computers and Fluids

Received date: Revised date: Accepted date:

14 March 2019 11 September 2019 20 November 2019

Please cite this article as: Yunchao Yang, William Bradford Bartow, Gecheng Zha, Heyong Xu, Jianlei Wang, Large Eddy Simulation of Base Drag Reduction Using Jet Boat Tail Passive Flow Control, Computers and Fluids (2019), doi: https://doi.org/10.1016/j.compfluid.2019.104398

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Highlights • Typical base configuration has large coherent structures far downstream, weak entrainment. • Jet boat tail(JBT) flow interacts with shear layer immediately at base surface. • Two primary flow instabilities of the baseline and JBT model identified by spectrum analysis. • JBT creates larger vortex structures enhancing entrainment and energizing base flow. • Energized base flow increases base pressure and reduces drag.

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Large Eddy Simulation of Base Drag Reduction Using Jet Boat Tail Passive Flow Control Yunchao Yang ∗, William Bradford Bartow †, Gecheng Zha ‡, Heyong Xu §, Jianlei Wang

¶

Dept. of Mechanical and Aerospace Engineering University of Miami, Coral Gables, Florida 33124 E-mail: [email protected]

Abstract

This study conducts an implicit large eddy simulation (ILES) of jet boat tail (JBT) flows to investigate its drag reduction mechanism. The concept of JBT passive flow control is to create a circumferential jet around a bluff body toward the center of the base area. It forms a jet cone to have the similar effect of a solid boat tail. The LES is performed for a baseline bluff body and a JBT model modified from the baseline. The LES predicts that the JBT reduces the averaged drag coefficient by 19.3%, a reasonable agreement with the experimental drag reduction of 22.5%. The reduced averaged wake area is also observed for the JBT model, resulting in a decreased drag. In addition, the unsteady flow structures of the baseline and JBT flow are analyzed to study the flow mixing and entrainment mechanism. For the baseline configuration, the coherent vortex structures occur far downstream of the base surface. It hence does not have strong entrainment and energy transfer from freestream to the base area. For the JBT flow, a pulsative jet is induced by the vortex shedding of the shear layer and interacts immediately with the shear layer near the base surface. It generates the small structures that ∗ † ‡ § ¶

Ph.D. student, Current position: Postdoc Associate, University of Florida Master student, Current position: aerodynamic engineer, NASA Ames Professor, ASME fellow, AIAA associate fellow Visiting Scholar, Current position: Professor, Northwestern Polytechnical University, Xi’an, China Visiting Student, Current position: Associate Professor, Northwestern Polytechnical University, Xi’an, China

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are substantially larger than those of the baseline configuration. The larger vortex structures of JBT enhance the flow entrainment and transfer more energy from the freestream to the base area. It results in higher static pressure in the base area that substantially reduces the pressure drag. Proper orthogonal decomposition of flow field reveals the periodic jet pulsation pattern in the azimuthal direction.

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Introduction The aerodynamic drag reduction of bluff bodies has been studied for the past few decades [1, 2, 3]. For the

flow passing a bluff body, a dominant phenomenon is the vortices separated from the base surface, forming a large wake in the base area [4]. The total pressure loss in the base area creates a region with low pressure and low momentum on the base surface that generates a large pressure drag. Bluff bodies flow control hence focuses on minimizing the pressure drag component. The wake flow structures determine the pressure distribution on a bluff body. The flow recirculation in the wake region is enclosed by the shear layers. The high energy loss in the base flow of the bluff bodies is attributed to the flow separation caused by the non-streamlined geometry. The energy loss mechanism is associated with various flow phenomena such as development of separated shear layer, turbulence, and the interaction between the wake flow and freestream flows. Conventional passive flow control drag reduction methods were reviewed by Tanner [1], including the boattailing, base bleed, splitter plates, and trailing edges improvement. Currently, most of the bluff body drag reduction techniques still utilize these passive methods today[5, 6, 7, 8]. The boat-tailing technique utilizes the after-body surfaces attached to the base surface, forming a streamlined trailing edge, delaying or removing separation and thus reducing the wake size [9, 10, 11, 12] . Coon [9] studied the drag reduction effect of planarsided boat-tail plates on the aft-end of a tractor-trailer. A maximum drag reduction of 9% is achieved. However, boat tail devices make loading and unloading inconvenient and create extra weight and space penalty for road vehicles. The base bleed concept [13, 14, 15] creates a flow tunnel from the front stagnation point to the rear base center. Because of the high-energy bleed flow, the vortical flow structures in the base region is altered with increased pressure and the pressure drag is reduced. Falchi et al. [14] performed a study of passive ventilation drag reduction with base bleed. Their numerical results indicate an approximated average drag reduction of 7-8% for the vented body. The drag reduction percentage varies with Reynolds number. However, it is rare to open a bleed duct inside the vehicles without affecting their major functions in their industrial applications. In particular, for some specific applications such as automobile rear-view mirrors, none of the aforementioned passive methods are applicable due to visibility blockage. Active flow control (AFC) provides an alternative approach to mitigate flow separation of bluff bodies, including blowing and suction, unsteady perturbation, and synthetic jet [16, 17, 18, 19, 20, 21, 22]. The AFC

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devices using the Coandaˇ a effect are employed for truck-shaped bluff bodies drag reduction. The wake flow is altered by steady or pulsed blowing jets tangential to the main flow. Seifert et al. [17] studied the add-on AFC devices on the aft-body of bluff body configurations using the TAU-developed Suction and Oscillatory Blowing (SaOB) devices. It indicates that using the optimal arrangement of suction holes, the pulsed AFC devices can reduce the drag by 10% - 20%. Barros et al. [20] investigated the effect of fluidic forcing by pulsing periodic jets. It shows that the unsteady Coandaˇ a blowing exerts unsteady high frequency forcing on the turbulent flow in addition to recovering the base pressure. Bruneau et al. [22] investigated the coupling of active and passive techniques to control the flows past square back bluff bodies. It shows that by coupling the porous layers passive control and AFC, it is possible to achieve a drag reduction of 30%. However, AFC itself requires auxiliary power and may offset the benefit of drag reduction. Furthermore, it is complicated to install and maintain the AFC-related actuators and powered pumping system.

1.1

The Jet Boat-Tail Passive Flow Control

The Jet Boat-Tail (JBT) passive flow control was first proposed by Zha et al. [23, 24, 25, 26, 27, 28, 29]. Fig. 1 shows the JBT principle. Fig. 1 (a) shows a typical bluff body flow of a conventional base configuration. Fig. 1 (b) demonstrates the idea of a JBT configuration, which has an opening in the front as an inlet to introduce flow from free stream, accelerates the flow through the converging inlet duct, and exhausts the flow as a very thin jet surrounding the base surface with an angle toward the base axis. This novel flow control method is named “Jet Boat-Tail”, aiming to achieve base drag reduction using the passive jet to function as a boat tail. The passive jet entrains the energy from freestream and energizes the base flow, which increases the base pressure, and thus achieves the drag reduction for the bluff bodies with the wake size reduced. Wind tunnel experiments [26, 27, 28] demonstrate the above-mentioned drag reduction effect of the JBT method. Parametric study with varied inlet area and outlet jet size are also conducted in[26, 27, 28]. In general, a larger inlet captured area will have a stronger jet, and thus more drag reduction. For numerical simulations, Yang et al. [29] conducted a preliminary large eddy simulation (LES) of the JBT flow without detailed study of the unsteady jet characteristics. Despite of the existing experimental and numerical studies, the underlying mechanism of flow entrainment of the JBT passive flow control still remains unclear. The purpose of this study is to investigate the base drag reduction mechanism of the JBT using high-order implicit large eddy simulations (LES). Specifically, the focus of this study is the turbulent flow structures, which reflect the flow mixing and energy entrainment mechanisms.

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(a) bluff body flow

(b) JBT controlled flow over a bluff body Figure 1: The schematic illustration of flows over a bluff body and a JBT configuration.

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Numerical Algorithms

2.1

Governing Equations

For the large eddy simulation governing equations, the procedure of Knight et al. [30] is adopted to filter the compressible Navier-Stokes(NS) equations. In the Cartesian coordinates the filtered NS equations read 1 ∂R ∂S ∂T ∂Q ∂E ∂F ∂G + + + = ( + + ) ∂t ∂x ∂y ∂z Re ∂x ∂y ∂z where

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(1)

  ρ¯u ˜ ρ ¯       2  ρ¯u   ρ¯u  ˜ + p¯  ˜       Q= ρ¯u ˜v˜  ρ¯v˜  , E =        ρ¯u ˜w ˜ ˜    ρ¯w    (¯ ρe˜ + p¯)˜ u ρ¯e˜ 



0

   τ¯xx + σxx   R=  τ¯xy + σxy    τ¯xz + σxz  Qx







ρ¯v˜



0



      ρ¯v˜u ˜      , F =  ρ¯v˜2 + p¯       ρ¯v˜w ˜     (¯ ρe˜ + p¯)˜ v

     τ¯yx + σyx       , S =  τ¯ + σ yy  yy       τ¯yz + σyz    Qy





ρ¯w ˜

0



      ρ¯w˜ ˜u     ,G =  ρ¯w˜ ˜v       ˜ 2 + p¯  ρ¯w    (¯ ρe˜ + p¯)w ˜ 

     τ¯zx + σzx       , T =  τ¯ + σ zy  zy       τ¯zz + σzz    Qz

           

          

  where, the filtered conservative variables Q = ρ¯, ρ¯u ˜, ρ¯v˜, ρ¯w, ˜ ρ¯e˜ are used. E, F, G are inviscid flux vectors in

x, y and z directions respectively. R, S, T denote viscous flux vectors in the respective x, y and z directions. In all the above equations, ρ denotes fluid density, p is the static pressure, u, v, w are the velocity component

in x, y, z direction respectively, and e is the total energy per unit mass. To treat complex geometries, the Navier-Stokes equations in the Cartesian coordinates expressed in Eq. (1) are transformed and solved in the generalized coordinates (ξ, η, ζ) as described in [31, 32]. The viscous stress tensor τ¯ is calculated by

τ¯ij =

2 ∂u ˜k ∂u ˜i ∂u ˜j µ ˜ δij + µ ˜( + ), i, j = 1, 2, 3 3 ∂xk ∂xj ∂xi

(2)

The subgrid-scale(SGS) stress tensor σ is

σij = −¯ ρ(ug ˜i u ˜j ) i uj − u

(3)

Qi = u ˜j (¯ τij + σij ) − q¯i + Φi

(4)

Φi = −Cp ρ¯(ug ˜i T˜) iT − u

(5)

In the energy equation, the energy flux Qi can be computed using SGS heat flux

where Φ is the subscale heat flux:

The q¯i is the molecular heat flux:

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q¯i = − where a =

2.2

q

µ ˜ ∂a2 (γ − 1)P r ∂xi

γRT˜ is the speed of sound.

Implicit Large Eddy Simulation (ILES)

The in house CFD code FASIP (Flow-Acoustics-Structural Interaction Package) is used for the LES conducted in this research. The implicit LES (ILES) strategy is utilized for the SGS stress tensor and the energy flux closure. The ILES accuracy of the FASIP code is intensively validated with various flows in [31, 32]. In the ILES approach, the Low diffusion E-CUSP scheme (LDE) proposed by Zha et al. [33] is used to calculate the inviscid flux. In the LDE scheme, the inviscid flux E is split into the convective component Ec and the pressure component Ep following characteristic analysis. The pressure flux component is split based on the acoustic waves propagating in each direction at subsonic regime. The convective flux is split in an upwind manner following the LDFSS schemes [34] on the basis of the Mach number. The benefit of LDE scheme is to resolve crisp shock profiles accurately while maintaining the exact contact surfaces with low diffusion. For the high order discretization schemes, the fifth-order finite difference WENO scheme [35, 36, 37] is used to evaluate the inviscid flux, Ei+ 12 = E(QL , QR ) based on the conservative variables QL and QR . The optimum value of  in the WENO scheme is tailored for minimizing numerical dissipation in smooth regions while maintaining the sensitivity to capture non-oscillatory shock. The fourth-order accurate finite central differencing scheme proposed by Shen et al. [36] is used to discretize viscous flux terms. For the unsteady computation, a second-order three-point, backward differencing scheme is employed for the temporal term

∂Q ∂t

discretization. The temporal term

∂Q ∂t

is discretized as

∂Q 3Qn+1 − 4Qn + Qn−1 = , ∂t 2∆t A pseudo-time iterative approach is used within each physical time step with the additional term

(6) ∂Q ∂τ .

To obtain

diagonal dominance of the system, the pseudo temporal term is discretized using first-order Euler scheme [38] ∂Q ∂τ

=

Qm+1 −Qm . ∆τ

With the spatial and temporal discretization, the semi-discretized governing equations (1)

become [(

1 1.5 ∂R n+1,m 3Qn+1,m − 4Qn + Qn−1 + )I − ( ) ]δQn+1,m+1 = Rn+1,m − , ∆τ ∆t ∂Q 2∆t

(7)

where n and m represent the physical time step index and pseudo time iteration index respectively. R represents the net fluxes integrating all the inviscid and viscous fluxes. The solution of the Eq. (7) is obtained using an

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unfactored Gauss-Seidel line relaxation method given in [38]. The implicit algorithm of domain decomposition parallel computing suggested by Wang et al in [39] is adopted.

2.3

Boundary Conditions and Computational Mesh

The present LES calculation uses the bluff body geometry experimentally tested in [40, 26] as the baseline. The baseline model is adopted from an automobile rear view mirror with streamlined front body and an elliptic base surface. The JBT model opens a converging duct from the front stagnation region of the baseline model. The freestream velocity U∞ is 30 m/s. The Reynolds number is 2.55 × 105 and the Mach number is 0.088. A cylindrical computational domain is constructed, extending approximately 40 L∞ upstream of the bluff body (L∞ is the model length.), 80 L∞ downstream, and 40 L∞ to the farfield boundary. The computational domain and boundary setup is shown in Fig. 2. Total pressure, total temperature, and two flow angles are prescribed at the inlet of the far field. For the far field downstream boundary, the static pressure is specified as freestream value to match the intended freestream Mach number. The no-slip adiabatic condition is enforced on the wall boundaries. The wall treatment suggested in [41] to achieve flux conservation by shifting half interval of the mesh on the wall is employed. If the wall surface normal direction is in η-direction, the no slip adiabatic condition is enforced on the surface by computing the wall inviscid flux F1/2 in the following manner: 

 ρV   ρuV + pηx   Fw =   ρvV + pηy    ρwV + pηz  (ρe + p)V



           

w

 0   pηx   =  pηy    pηz  0

           

(8)

w

and a third-order accuracy wall boundary formula is used to evaluate p|w , pw =

1 (11p1 − 7p2 + 2p3 ) 6

(9)

Fig. 3 shows the baseline and JBT model and multi-block structured mesh topologies. The overall base area boundaries of the two models are the same. But the base area of the JBT model is reduced slightly by less than 1% due to the jet slot. The inlet area is 8 times larger than the outlet jet slot area. An O-mesh topology is utilized on the rear surface of the model with refined mesh size to capture the turbulent flow structures in the wake. To simulate the boundary layer correctly, η1+ (η in the generalized coordinates) is mostly less than unity. The nondimensional mesh resolution on the surface in the ξ, η, ζ direction for the baseline mesh is plotted in Fig. 4.

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Figure 2: Schematic description of baseline and JBT computational domain. The characteristic time is normalized by the model length and freestream velocity tc =

L∞ U∞ .

The non-

dimensional time step size is ∆t = 0.02tc . Each calculation is run for 400tc . The simulation results from 200 tc to 400 tc are used for unsteady flow statistics and post-processing.

2.4

Grid sensitivity study

LES lies between direct numerical simulation (DNS) and URANS methods in terms of flow resolution. In an ideal LES, 80% of the total turbulence kinetic energy should be resolved [42]. In this paper, we compare two grid resolution for the baseline and four grid resolution for the JBT mesh. The JBT flow involves the interactions between the internal jet flow and the wake, which creates complicated turbulent flows with eddies. Therefore, to resolve the small-scale eddies, fine mesh size is required to resolve the turbulent flow physics. The mesh sensitivity is conducted with four different sets of mesh (JBTc1, JBTc2, JBTc3, and JBTf) for the JBT model and two sets of meshes (BSc, BSf) for the baseline model. Those meshes have the grid size varied from 15.55 million points to 34.56 million points as shown in Table 1. The mesh refinement study is emphasized on the resolution of shear layer related regions, including wall boundary layer, wake region and the flow channel. Both time-average drag coefficient and lift coefficient are used as grid convergence criteria. The calculation of these flow quantities is based on an average of 200 characteristic time. Table 2 shows the simulation results using different grid resolutions. The results indicate that the fine mesh of the baseline and JBT models are sufficient to obtain grid-independent simulation results. The averaged drag coefficient predicted by the baseline configuration with the BSc and BSf mesh has a variation of 1%. For the JBT configuration, the drag coefficients of the mesh JBTc1, JBTc2, JBTc3 have a deviation of 1%, 5.5%, and 2.1% as compared to the finest mesh JBTf results. The drag variation is within the acceptable range for

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baseline model

JBT model

JBT X-Y plane

JBT X-Z plane

Figure 3: Schematic description of baseline and JBT model and mesh. mesh independence. The fine mesh results for the baseline configuration (BSc, 28.86 million points) and JBT configuration (JBTf, 34.56 million points) are used in this paper.

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Figure 4: Nondimensional grid distance on the surface of the baseline model.

Table 1: Mesh independence study with different grid resolutions Case BSc BSf JBTc1 JBTc2 JBTc3 JBTf

Total cells (×10−6 ) 15.552 28.86 19.12 18.96 24.688 34.56

streamwise 130 130 130 130 130 130

spanwise 320 400 400 240 320 400

wall-normal 80 80 60 80 80 80

wake-wall 320 520 320 520 320 520

Table 2: Mesh independence study with different grid resolutions Case BSc BSf JBTc1 JBTc2 JBTc3 JBTf

< CL > -0.0056 -0.0050 -0.0034 -0.0029 -0.0023 -0.0036

0 CL,rms 0.0141 0.0133 0.0185 0.0167 0.0141 0.0153

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< CD > 0.3312 0.3277 0.2672 0.2805 0.2701 0.2645

wake 200 200 100 200 200 250

channel 60 60 90 90

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Results and Discussion Fig. 5 gives the instantaneous drag coefficient CD of the baseline and JBT. The predicted drag coefficients of

the baseline and JBT models show strong oscillations due to large vortical flow structures of the base flow. The time-averaged results are averaged over the nondimensional time 200 to 400. The LES predicted time-averaged drag coefficient for the JBTf mesh is 0.3277, which is 5.6% higher than the experimental value of 0.31. The drag reduction by the JBT model is 19.3% from the LES calculation, which agrees with the experimental drag reduction of 22.5%. The predicted drag coefficient of the JBT configuration is substantially lower than that of the baseline configuration, which is consistent as the experimental measurement summarized in Table 3. The drag reduction trend predicted by LES is consistent with the experiment, and provides the basis to investigate the qualitative physical mechanism. Since the base area reduction due to the slot size is less than 1%, the large drag reduction is obviously not due to the area reduction, but due to the flow field.

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Figure 5: Instantaneous lift and drag coefficients (CL , CD ) predicted by the LES Table 3: The experiment and LES predicted drag coefficients using the fine mesh. CDExp. CDLES Discrepancy(%)

Baseline 0.31 0.3277 5.6%

JBT 0.24 0.2645 9.3%

Drag Reduction (%) 22.5 % 19.3 % -

The total drag force is calculated by the integration of the surface pressure and friction force over the whole body. The overall drag coefficient on the JBT model consists of pressure drag and friction drag components on

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Table 4: Drag coefficient decomposition for the JBTf results. Subscripts p and f refer to the pressure and friction components, respectively; i and o refer to the inner body and outer surface, respectively. Total CD 0.2645

Inner CDpi CDf i 0.7245 0.0045

Outer CDpo CDf o -0.4732 0.0087

the inner body and outer surface, respectively. The pressure and friction drag coefficient breakdown for the JBT inner body and outer surface is shown in Table 4. It is clear that the total drag is dominated by the pressure components. The JBT duct creates a high pressure drag for the inner body due to the stagnation effect in the duct. On the other hand, the pressure drag on the outer surface is negative, which offset the pressure drag increase of the inner body. The overall drag force is reduced by the increased base pressure of the JBT model. The higher the base pressure, the lower the overall drag.

3.1

Time-averaged flow field

Fig. 6 compares the experimentally measured [40] and LES predicted time-averaged streamlines and streamwise velocity Vx contours in the base flow area. In each of the plots, the top half is the experimental results and the bottom half is the LES results. The LES predicted wake areas are slightly larger than the experiment, reflecting a smaller drag reduction predicted by the LES, but the overall predicted wake recirculation region and velocity profile agree very well with the experiment. Both the experimental and LES predicted wake areas of the JBT (right plot) are smaller than those of the baseline configuration (left plot) as the streamlines converge earlier to the centerline than the baseline model. The recirculation zones of the JBT model measured and simulated are about 10% shorter than those of the baseline.

(a) baseline X-Z midplane

(b) JBT X-Z midplane

Figure 6: Comparison of the experimental and LES time-averaged streamlines and streamwise velocity Vx for the baseline and JBT model.

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(a) baseline X-Z midplane

(b)JBT X-Z midplane

Figure 7: Mean streamwise velocity (Vx ) contours The time-averaged streamwise velocity Vx contour for the baseline and JBT models are presented in Fig. 7. A low momentum region is observed in the wake, which is caused by the counter-rotating vortices enclosed by the shear layers. It is clear that the size of the low momentum region of the JBT model with the negative streamwise velocity is substantially decreased in both the vertical and horizontal direction compared with the baseline model. The aerodynamic principle indicates that the drag of the bluff body is determined by the velocity profile integral across the wake [43] as D=

Z

δ

ρu(u∞ − u)dy

(10)

where δ is the wake width, u is the streamwise velocity component. Eq. (10) indicates that the narrower and shallower of the wake, the smaller the drag is. Fig. 8 compares the wake velocity profile at the locations downstream of the base surface at x/L∞ = 1.5, 2.0, 2.5, which shows that the JBT velocity deficit in the wake region is narrower and shallower, consistent with the results of Fig. 6 and 7. The drag of the JBT would be thus

]

]

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smaller based on Eq. (10).

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(a) x/L∞ = 1.5

9[

(b) x/L∞ = 2.0

9[

(c) x/L∞ = 2.5

Figure 8: Mean streamwise velocity profiles at x/L∞ = 1.5, 2.0, 2.5. Fig. 9 is the static pressure contours of the time-averaged baseline and JBT flow field in the vertical midplane. Note that much higher static pressure is observed in the base region of the JBT model in comparison with the

14

(a) baseline X-Z midplane

(b)JBT X-Z midplane

Figure 9: Mean static pressure contour (Ps ) %6 -%7

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Figure 10: Mean static pressure profile at x/L∞ = 1.5, 2.0, 2.5. baseline. Fig. 10 compares the pressure profile across the wake region for the base line and the JBT configuration at x/L∞ = 1.5, 2, 2.5. The closer to the base surface (x/L∞ =1.0), the higher the static pressure, which decreases the drag. The overall drag force is hence reduced for the JBT model. For the JBT model, the pressure in the front part of the duct is significantly higher than the other region due to ram effect. However, it does not increase the total drag because the increased pressure is offset by the inner wall surfaces of the duct. The flow acceleration inside the inlet duct is induced by low pressure at the base area. The flow on the outside wall surface of the JBT model is also accelerated by the low base pressure as observed in the experiment [40]. The integral of all above pressure forces results in a lower total pressure drag of the JBT model. Fig. 11 shows the total pressure contours, which describes the energy loss in an adiabatic flow system. A much higher total pressure loss is observed in the base area of the baseline than that of the JBT model. The reduced total pressure loss of the JBT configuration is benefited from the passive jet entraining effect, which transfers energy from the freestream to the base region.

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(a) baseline X-Z midplane

(b) JBT X-Z midplane

Figure 11: Time-averaged total pressures (Pt ) contours in the X-Z midplane

3.2

Instantaneous Flow Structures

(a) baseline vortical flow structures

(b) JBT vortical flow structures

Figure 12: The iso-surfaces of vorticity colored by Mach number for the baseline and JBT models To investigate the three-dimensional vortical flow structures, the instantaneous iso-surfaces of vorticity colored by Mach number is shown in Fig. 12. The vortical flow structures of the baseline model is characterized by the detached shear layer traveling downstream the bluff body. Vortex shedding generates a considerable amount of flow instabilities and small vortices in the wake region of the baseline configuration. For the JBT model, the vortical flow is dominated by large-scale structured array of vortex shedding. As reported by Kopp et al. [44], large-scale turbulent bulges, as they travel downstream, is the key contribution in energy entrainment of the ambient fluid. This observation agrees well with the experiment, which also reveals dominant large structures of the JBT flow [40]. As shown by the time-averaged turbulent kinetic energy contours in Fig. 13, the JBT’s larger vortical structures enhance more energy transfer due to entrainment with higher turbulent kinetic energy in the base area. The turbulent kinetic energy in the base area of JBT is enhanced by two order of magnitude. The instantaneous vorticity contours at four time steps are plotted in Fig. 14. The baseline flow shows the

16

(a) baseline

(b) JBT

Figure 13: Time-averaged turbulent kinetic energy contours k =

(a) t¯ = 250.2

(b) t¯ = 250.4

(c) t¯ = 250.6

1 2





(u0 )2 + (v 0 )2 + (w0 )2 .

(d) t¯ = 250.8

Figure 14: Instantaneous vorticity at different time steps for the baseline (top row) and JBT model (bottom row). coherent vortex structures forming from the free shear layer. The JBT flow shows that jet interacts with the shear layer and create a region that flow mixing is enhanced with more energy entrained from the freestream to the base flow. Similar to Fig. 12, the baseline flow field is composed of smaller-scale turbulent flow structures. The JBT flow has larger vortex structures caused by the passive jet at the commencement of the detached shear layer, which corresponds to the strengthened turbulent kinetic energy in Fig. 13. The observations are consistent with the flow structures in the wind tunnel experiment [40]. The jet created by the JBT is exhausted periodically as a pulsing jet and the formation of the jet is displayed in Fig. 15. After the high momentum jet is ejected out, it bifurcates and interacts with the shear layer and wake flow. Further downstream, the bifurcated jet merges and is dissipated. The pulsing jet swings up and down along with the shedding shear layer. The periodical interaction strengthen the mixing between the free stream and wake flow and energize the flow in the base area.

17

Figure 15: Instantaneous velocity contours in X-Z and X-Y midplane of JBT.

Figure 16: Comparison of vortex structures behind the baseline and JBT configurations.The top plots are vorticity contours predicted by LES, the bottom plots are flow visualization in experiment [40]. Fig. 16 shows the comparison of the vortical flow structures of the baseline and JBT model between the LES and experimental flow visualization. The top plots show the LES z-component vorticity ωz contours; and the bottom plots are smoke flow visualization measured in the wind tunnel experiment [40]. For both the baseline and JBT model, the predicted mixing layers show good agreement with the measured flow structures. In the baseline smoke flow visualization, the starting point of large-scale coherent vortices is located at 0.5L∞ downstream of the base surface. The vortices play a significant role in the formation of mixed layers, which are referred as the natural mixing layer of a bluff body. The coherent structures occurring far downstream do not have strong entrainment and energy transfer from freestream to the base area.

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In the JBT configuration, the large vortex structures start at 0.2L∞ downstream of the rear wall, significantly earlier than the 0.5L∞ of the baseline configuration. The pulsative jet interacts immediately with the shear layer and generates flow structures that are substantially larger than the vortex structures of the baseline configuration. The larger vortex structures enhance the flow entrainment and transfer more energy from the freestream to the base area. The pulsative jet interrupts the natural mixing layer and significantly enhances the mixing effect. The jet induced mixing layer can be viewed as a “forced” mixing layer. The vigorous jet is followed by paired vortices as visualized in the experiment (lower right plot) shown in Fig. 16. Because of the forced mixing layer, the energy entrainment effect of JBT model is substantially enhanced.

Proper Orthogonal Decomposition

32' PRGH FRHIILFLHQW

3.3

32' PRGH QXPEHU

Figure 17: POD spectrum of the pressure in the JBT flow. To extract dominant flow structures of the JBT model, Proper orthogonal decomposition (POD) analysis is performed. POD was applied separately to the base pressure and velocity in the wake to extract the dominant coherent structures and their energy content. The variable fluctuation can be represented as set of eigenfunctions φi (x) and corresponding coefficients ai . u0 =

N X

ai φi (x)

(11)

i=1

where, u0 (x, t) and φi (x) are N-dimensional vectors of position. N is total number of grid point that consist of an instantaneous flow field. In this study, the snapshot version of POD [45] is employed, which is based on the cross-correlation between individual snapshots of velocity fluctuations. In the present study, 800 snapshots near

19

Mode 1

Mode 2

Mode 3

Figure 18: First three POD modes of the pressure in the x/L∞ = 1.2 plane for the JBT flow. the wake area are collected with a time step of 10 intervals for the POD analysis. The fractional energy of the first 12 dominant POD modes is plotted in Fig. 17. The mean component of the base pressure is removed from the samples. The fractional energy of the first two modes are dominant, indicating that the major flow pattern is controlled by the first two modes. The first three POD modes in the plane of x/L∞ = 1.2 of the JBT model are shown in Fig. 18. It is clear that the dominant POD modes have a circular periodic pattern. Mode 2 is similar to Mode1 with a phase shift in the azimuthal direction. The fractional energy of Mode 3 is much smaller than the first two modes, which is less energy-containing. Mode 3 has a symmetric flow pattern regarding the long axis of the ellipse. The similar pattern is also observed in the POD mode decomposition of the streamwise velocity as shown in Fig. 19. The azimuthal periodic flow pattern corresponds to the periodically pulsating phenomena in the circumferential direction.

Mode 1

Mode 2

Mode 3

Figure 19: First three POD modes of the streamwise velocity Vx in the x/L∞ = 1.2 plane for the JBT flow.

20

Spectrum Analysis FFT analysis of the drag coefficients

3RZHU 6SHFWUDO 'HQVLW\

3.4.1

3RZHU 6SHFWUDO 'HQVLW\

3.4

IUHTXHQF\ +]

IUHTXHQF\ +]

Figure 20: FFT of CD for the baseline model. Figure 21: FFT of CD for the JBT model. The power spectra analysis is conducted by performing a fast Fourier transformation (FFT) of the unsteady drag coefficients and the streamwise velocity component in the LES. The peak frequency in the power spectra of the drag coefficient can help to identify the major contribution for the drag force. The peak frequency of the velocity power spectra reflects the flow structure containing the majority turbulent energy [46]. Fig. 20 and 21 show the power spectra of the drag coefficients for the baseline and JBT model. The peak frequencies are observed at approximately 50 Hz and 1200 Hz for the baseline configuration. The higher frequency is 24 times of the lower frequency. For the JBT configuration, the 50 Hz is also a lower dominant frequency. The higher dominant frequency is 1000 Hz, which is 20 times of its low frequency and is 17% lower than the higher frequency of the baseline configuration. The peak frequency of 50 Hz corresponds to a Strouhal number StCd = 0.215, which matches the shear layer Strouhal number of bluff body flows at the Reynolds number of roughly 104 [47]. The normalized streamwise velocities (Vx /U∞ ) on probe points are recorded on the X-Y and X-Z midplane. The probe points are indicated in Fig. 22. The probe locations are located in the vicinity of the wall to cover the flow behavior of boundary layer flow, shear layer separation and shear layer/wake interaction. FFT analysis is also conducted on the probed signals to obtain the power spectra.

21

(a) baseline X-Z midplane

(b) JBT X-Z midplane

Figure 22: Probe locations in the baseline and JBT flows

(a) Probe 04 X-Z

(b) Probe 05 X-Z

(c) Probe 06 X-Z

Figure 23: FFT of streamwise velocity at Probe 04, 05, 06 of the baseline model. 3.4.2

FFT analysis of the baseline velocity fluctuation

Fig. 23 shows the spectral analysis on the streamwise velocity at Probe 04, 05, 06 of the baseline model in X-Z midplane. The three probes are located to investigate the response of the flow and the shear layer far upstream of the base surface (Probe 04), immediately upstream of the base surface edge (Probe 05), and immediately downstream of the base surface edge (Probe 06). The shear layer separation starts at Probe 05. Upstream of the base surface (Probe 04), a peak frequency flow fluctuation of 50 Hz is observed. At Probe 05, a secondary peak frequency of 1200 Hz is detected. In the more downstream of the base surface (Probe 06), the velocity fluctuations 50Hz frequency is still dominant with the second slightly lower peak frequency of about 600Hz, which means the high-frequency flow structures are more dissipated in that region. In summary of the baseline configuration flow, a dominant frequency of 50 Hz exists due to the vortex

22

shedding frequencies of bluff bodies in the subcritcal range [48, 47, 22]. In addition, a higher frequency of 1200 Hz, reflecting the small-scale flow instabilities produced by shear layer separation, plays an important role in the shear layer region [49]. Therefore, two peak frequencies indicate the co-existence of vortex shedding and shear layer instabilities, similar to the sphere wake flow structure as reported by Kim and Durbin [50]. The two dominant frequencies captured by the velocity probes are consistent with those obtained from the drag coefficient oscillation shown in Fig. 20.

3.4.3

FFT analysis of the JBT velocity fluctuation

(a) Probe 04 X-Z

(b) Probe 05 X-Z

(c) Probe 06 X-Z

Figure 24: FFT of streamwise velocity at Probe 04, 05, 06 of the JBT model. For the JBT flow, the frequency spectrum of the streamwise velocities at the selected probe positions (Probe 04, 05, 06) are shown in Fig. 24. The three probes are placed at the locations to investigate the response of the jet and the shear layer far upstream of the base surface inside the duct (Probe 04), immediately upstream of the base surface edge inside the duct (Probe 05), and immediately downstream of the base surface edge outside the duct (Probe 06). For Probe 04, two peak frequencies are observed, a lower dominant frequency of approximate 50 Hz and a higher dominant frequencies of approximate 800-1000 Hz. Actually, all the three probes have the similar spectrum pattern with the same peak frequencies. The frequency distribution is similar to the frequency distribution of the drag shown in Fig. 21. The 50-Hz frequency is consistent with the vortex shedding frequency of bluff body configurations at this Reynolds number range. It induces the jet pulsation at the same frequency. The higher dominant frequency of 800-1000 Hz is lower than those of the baseline high frequency of 1200 Hz. It indicates that the jet and shear layer interaction creates larger flow structures than the baseline with enhanced entrainment. The peak frequency patterns reflect the interaction between the pulsed jet, the shear layer, and wake flow.

23

4

Conclusions High order implicit large eddy simulation (ILES) of a bluff body with jet boat tail passive flow control is

conducted to investigate the drag reduction mechanism and its flow characteristics. A baseline model with an elliptic base surface and a JBT configuration modified from the baseline model are numerically investigated. The flow structures and wake size are also compared with the experiment. The predicted averaged drag coefficient is reduced by 19.3%, showing a reasonable agreement with the experimental drag reduction of 22.5%. The predicted averaged wake area is reduced by the JBT model, and is in good agreement with the one measured by PIV in the experiment. POD analysis of the base pressure and velocity is performed. The circular periodic pattern in the azimuthal direction is identified, which corresponds to the periodically pulsating jet. For the baseline configuration flow, two primary flow instabilities are captured: the large-scale vortex shedding structure with a lower peak frequency of 50 Hz and the small-scale shear layer separation with 24 times higher frequency. The baseline flow is characterized by the large coherent structures far downstream of the bluff body. It hence does not have strong entrainment and energy transfer from freestream to the base area. For the JBT flow, a pulsative jet is induced by the vortex shedding of the shear layer also at frequency of 50 Hz. The pulsative jet interacts immediately with the shear layer near the base wall and generates the vortical flow structures that are substantially larger than those of the baseline configuration. The larger vortex structures enhance the flow entrainment and transfer more energy from the freestream to the base area. It results in higher static pressure in the base area that substantially reduces the pressure drag.

5

Acknowledgment The simulation is conducted at the Titan supercomputer of Oak Ridge National Lab, and the Pegasus

supercomputer at the Center of Computational Sciences of the University of Miami.

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