Numerical Analysis of Active Flow Control using Unsteady ...

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14th International Conference on Wind Engineering – Porto Alegre, Brazil – June 21-26, 2015

Numerical Analysis of Active Flow Control using Unsteady Jets

Applied to a Square Prism in Turbulent Flow R. Cummings

1, C. Letchford

2, O. Sahni

3

1Scientific Computation Research Center, Postdoctoral Research Associate, Rensselaer Polytechnic Institute, Troy, New York

2Department of Civil and Environnemental Eng., Department Chair, Rensselaer Polytechnic Institute, Troy, New York

3Department of Mechanical, Aerospace, and Nuclear Eng., Assistant Professor, Rensselaer Polytechnic Institute, Troy, New

York

email: [email protected], [email protected], [email protected]

ABSTRACT: Wind induced vibration is a major concern in the design of tall buildings. Auxiliary dampers or modifications to

the building shape are typically applied to tall buildings to mitigate these vibrations. This study proposes an alternative, Fluid

Aerodynamic Modification (FAM), in which jets are located on the building and eject air out of the building into the

surrounding flow. These jets then change the flow field around the building and reduce the vibrations due to the wind forcing.

This study conducted several numerical simulations of unsteady jets on a square prism with smooth and turbulent inflow

conditions to examine if flow control on bluff bodies in turbulent flow was possible. Numerical analysis was first conducted on

the square prism without the jets to validate the model. It was found that the numerical model was able to predict the mean and

fluctuating forces on the square prism with good accuracy. Then unsteady jets were activated on the prism’s windward wall. The

jets were seen to increase the curvature of the shear layers, similar to the effect of additional freestream turbulence. Additionally,

the vortex formation region was seen to move further downstream. These two actions significantly reduced the mean drag and

fluctuating lift forces on the square prism for smooth and turbulent inflow conditions.

KEY WORDS: CFD, Active Flow Control, Square Prism, Fluctuating Lift, Turbulence

1 INTRODUCTION

Structures experience oscillatory forces from alternating vortices that are shed in a building’s wake. These forces led to

vortex-induced vibrations, which can cause major disruption for occupants including; headaches, nausea and even absenteeism

[1]. To prevent these disturbances, tall buildings must be designed for wind serviceability requirements rather than purely for

ultimate strength capacity, as is the case in earthquake design. Multiple flow control techniques have been tested and

implemented in tall buildings to reduce wind-induced vibrations [2]. These techniques include physical modifications such as

auxiliary damping, increased lateral stiffness, and cross-section shape modifications, which may be grouped under the category

of Geometric Aerodynamic Modification (GAM).

An alternative to physical modifications is Fluidic Aerodynamic Modification (FAM) where flow is ejected from the building

to modify the surrounding flow field. Fluidic Aerodynamic Modifications have been extensively tested and implemented in

aerodynamic applications to reattach separated flow or change the virtual shape of an airfoil [3] [4]. Using unsteady forcing on

the flow has been shown to be much more efficient at enhancing flow control versus steady forcing [3] [5]. Unsteady forcing has

the capability of exciting features in the flow at their natural frequency. This creates a type of resonance in the flow that allows a

small energy input to cause large global changes to the flow field.

The aim of this study is to demonstrate the feasibility of FAM on bluff bodies in turbulent inflow (the built environment). This

study investigates the significant cause of wind induced building vibrations, namely vortex shedding, by numerically analyzing

the flow around a square prism with smooth and turbulent inflow conditions. Vortex shedding about rectangular prisms has been

extensively researched in physical wind tunnel testing [6] [7] [8] [9] [10] and has provided insight into the casual mechanisms.

Sharp corners of rectangular prisms cause the boundary layer on the windward face of the prism to separate and become free

shear layers and large velocity gradients create significant vorticity in the shear layers. In the wake these shear layers under the

right conditions alternatively “roll-up” into discrete wake vortices. The strength of these vortices is determined by the vorticity

supplied from the shear layers. Additionally the location of the vortex formation region dictates the effects the vortices’ suction

pressure has on the prism, (e.g. vortices closer to the prism exert greater suction than vortices further away).

The effects of wake vortices on a rectangular prism are dependent on the rectangles afterbody length and the presence of

freestream turbulence.

The longer the afterbody length, the more the side walls of the prism interact with the shear layer. Flat plates, perpendicular to

the flow (with no side wall length) have no interaction with the shear layers which separate from the windward face and “roll-

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up” in the wake unperturbed. As the afterbody length increases, the sidewall interactions remain small and the vortex formation

region remains in much the same location. However the leeward wall of the prism is moving closer to the vortices and

consequently it experience increased suction resulting in increased mean drag on the prism. This process continues until an

aspect ratio (D/B where D is the along wind depth and B is the cross-stream breadth) of 0.6 where the drag reaches a maximum

[9]. Beyond this aspect ratio the side wall interactions with the shear layers becomes more significant. A separation or

recirculation bubble forms on the side wall reducing the vorticity of shear layer and thus reducing the strength of the wake

vortices. As the afterbody length continues to increase partial flow reattachment is observed on the side wall. This allows for

pressure recovery on the sidewall, and moves the vortex formation region further downstream of the leeward wall thus reducing

the strength of the wake vortices and their effect on the prism. For aspect ratios above 3 the shear layers are able to fully reattach

to the sidewalls. This greatly reduces the drag and fluctuating forces on the prism.

Inflow turbulence intensity is another key factor influencing vortex shedding. The small scale vortical structures in the inflow

turbulence are entrained into the shear layer causing diffusion of the shear layer, and an increase the shear layer curvature [11].

The change in shear layer curvature causes partial and full reattachment to occur at lower aspect ratios [12]. Therefore inflow

turbulence can be thought of as increasing the effective aspect ratio [6]. As the shear layer diffuses, the supply of vorticity to

wake vortex formation is disrupted, causing wake vortices to be weaker and exert less force on the rectangular prism. The

diffusion of the shear layer inhibits shear layer interactions in the wake which further weakens the wake vortices and increases

the formation length (the distance from the vortex formation to the leeward wall).

This study aims to implement unsteady jets near the corners of the prism to disrupt the shear layers, in hopes that the

fluctuations from the jets can interact with the shear layers in a manner similar to that of freestream turbulence, and hence

reduce the mean drag force coefficient (CD), and more importantly the root mean square (rms) of the lift force coefficient (CL).

Of particular interest for this research was to investigate the effects of the unsteady jets in the presence of freestream turbulence

to determine if unsteady jets can augment the load reductions seen in the presence of freestream turbulence.

2 SIMULATION PROCEDURE

The effects of unsteady jets on the flow around a square prism were tested with smooth and turbulent inflow. First the

generated inflow turbulence was simulated in an empty fetch to measure the turbulence properties at the proposed square prism

location (see Section 2.4). Next a square prism with no flow control was tested in smooth and turbulent flow conditions to

validate the numerical model (see Section 3). These simulations also served as a baseline reference. The final simulations

consisted of activating the unsteady jets on the square prism for both the smooth and turbulent inflow conditions. These jet cases

were then compared to the baseline cases to measure the effects of the jets on the mean and fluctuating forces on the square

prism.

Domain and boundary conditions 2.1

All simulations were completed using similar geometry and boundary conditions. Figure 1 illustrates the domain used in the

simulations. To adequately capture the three-dimensionality of turbulent flow, a three-dimensional computational domain was

used. The height of this domain was set large enough to resolve the vortical structures in the flow without any interference from

the top and bottom boundaries. The domain height was verified as large enough by examining the correlation in the wind speeds

along the z direction. The top and the bottom boundaries were setup as periodic boundary conditions. Periodic boundary

conditions enforce that the velocity and pressure at a location (x,y) on one surface is equal to the velocity and pressure on the

other surface at the same location (x,y). This effectively makes an infinite domain along the prism’s height. Additionally the

sides of the domain were set to periodic to preserve the turbulent structures of the inflow near the walls. The inflow conditions

were defined through specifying all three components of the velocity along with the eddy viscosity. This allowed for smooth

flow or turbulent flow to be specified at the inflow. The method for creating the turbulent inflow and its validation is detailed in

Section 2.4. The outflow was prescribed to the reference pressure.

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(a) (b)

Figure 1 - (a) Domain and boundary conditions for the baseline and jet case, (b) jet configurations on the square prism

Mesh 2.2

An unstructured mesh, consisting of 4-noded, linear tetrahedral elements was used (see Figure 2). Mesh refinement zones

were placed around the square prism to capture the boundary layer on the windward face, the shear layers and the wake vortices.

The mesh was further refined in front of the jets with 20 nodes along the jet face to ensure the jet velocity profiles were fully

specified. For the turbulent inflow case additional refinement zones were placed between the inflow and the square prism to

resolve the turbulent eddy structures from the inflow conditions. A boundary layer mesh was used on solid surfaces of any

object to ensure that the first layer height in wall units was less than 1, i.e., 𝛥𝑦0+ =

𝑢∗𝑦0

𝜈≤ 1, where 𝑢∗ is the wall friction

velocity, 𝑦0is the height of the element on the surface and 𝜈 is the kinematic viscosity of air. The mesh contained approximately

of 2.6M nodes and 16M elements for the smooth cases and 8.5M nodes and 50M elements for the turbulent cases.

(a) (b)

Figure 2 - Cross-sectional mesh view of (a) the entire domain, and (b) upstream mesh refinement region for the turbulent inflow

case

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Simulations 2.3

All simulations in this study were carried out using the AcuSolve ™ flow analysis package provided by Altair Engineering,

Inc. under Altair Hyperworks. AcuSolve ™ uses the finite element method to solve the Navier-Stokes flow equations. It

employs the Galerkin least-squares stabilization methodology [13] and the second-order generalized-alpha implicit time

integration scheme [14]. Delayed detached eddy simulation (DDES) turbulence model was used for out for all cases. DDES is a

hybrid turbulence model which uses Large Eddy Simulation (LES) away from wall boundaries in separated regions and

Unsteady Reynolds Averaged Navier-Stokes (URANS) close to wall boundaries in attached flow regions [15]. The Spalart-

Allmaras turbulence model was used for the URANS portion of flow. DDES allows for the large, energy carrying eddies in the

flow to be resolved while saving computational time by modeling the fine-scale eddies near the wall. All cases where run until

the mean drag and root mean square (rms) lift converged. The smooth baseline case was run for a longer duration to examine the

effects of the averaging period.

Inflow Conditions 2.4

The inflow turbulence boundary condition was created using the Divergence-Free Synthetic Eddy Method (DFSEM) first

proposed by Jarrin [16] and modified by Poletto [17]. The DFSEM computes the fluctuating velocity components through a sum

of synthetic eddies with random position and intensity.

The inflow turbulent velocity field was generated to be isotropic and homogeneous, which is the typical condition for grid-

generated turbulence in wind tunnel testing [18]. The turbulence intensity (TI) in each direction at the inflow was set to 12% and

the stream-wise turbulence length (Lu) was set as 0.5D (see Table 1). The length scales in the cross-stream (Lv) and span-wise

(Lw) directions were set to Lu/2 to match homogeneous, isotropic conditions [18].

An isotropic turbulence spectrum was the inflow target in accordance with Equation 1 [18].

𝑆𝑢(𝑓) ∙ 𝑓

𝜎𝑢2

=(

4𝑓𝐿𝑢

𝑈∞)

1 + (2𝜋𝑓𝐿𝑢

𝑈∞)

2 (1)

The generated turbulent velocities were simulated in an empty fetch to measure the turbulence properties at the model

location. As seen in Table 1 the turbulence intensities decay to approximately 8% at the square prism location, while the

turbulence length scale remains almost constant.

Table 1 - Inflow turbulence properties

Inflow Model Location

u v w u v w

𝑼𝒊 (m/s) 15.15 -0.12 0.00 15.25 -0.21 0.02

TI=(𝒖𝒊

′

𝑼𝒊) 12.0% 11.9% 12.1% 8.1% 9.4% 8.5%

Li/D 0.52 0.28 0.26 0.50 0.28 0.29

As seen in Figure 3(a) the along wind turbulence spectrum generated at the inflow agrees with the target spectrum, especially

in the lower frequency range. Towards the higher frequency the spectrum diverges slightly. As seen in Figure 3(b) the spectrum

at the model location has a reasonable match at the middle frequency range as compared to the target spectrum. The spectrum

significantly deviates at higher frequency range due to mesh size not being small enough to adequately resolve the fine-scale

eddies in the inflow. These creates a high frequency cut-off, which is seen by the dramatic decline in the spectrum at fLu/U∞ = 1.

The undulations in the lower frequency range are most likely due to a short sample time for this simulation which consisted of

1.6 seconds or about 60 vortex shedding cycles.

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Figure 3 - Turbulence spectrum at (a) inflow (──) and (b) 5D downstream for the generated turbulence (model location) (──)

versus ideal isotropic homogeneous turbulence spectrum (-∙-)

Jet Parameters 2.5

Unsteady jets are flow actuating systems that pulse air in and out of an orifice at a specified velocity and frequency. Unsteady

jets were implemented in the simulations through specifying the stream-wise and cross-stream velocity components on the jet

surface at the prism face. The jet velocity profile was assumed to be parabolic in space, which approximates a laminar jet

profile, and sinusoidal in time (see Equations 3 and 4).

𝑢𝑗𝑒𝑡(𝑎, 𝑡) = 𝑈𝑗𝑒𝑡𝑚𝑎𝑥 (1 −𝑎2

(4𝐿𝑗𝑒𝑡)2) sin(2𝜋𝑓𝑗𝑒𝑡𝑡) cos 𝛼 (2)

𝑣𝑗𝑒𝑡(𝑎, 𝑡) = 𝑈𝑗𝑒𝑡𝑚𝑎𝑥 (1 −𝑎2

(4𝐿𝑗𝑒𝑡)2) sin(2𝜋𝑓𝑗𝑒𝑡𝑡) sin 𝛼 (3)

where 𝑢𝑗𝑒𝑡 is the stream-wise jet velocity, 𝑣𝑗𝑒𝑡 is the cross-stream jet velocity, 𝑈𝑗𝑒𝑡𝑚𝑎𝑥 is the maximum jet velocity at the jet

center, a is the local coordinate on the jet surface, 𝐿𝑗𝑒𝑡 is the length of the jet slot opening, 𝑓𝑗𝑒𝑡 is the jet frequency and α is the

jet angle (see Figure 1(b)).

The unsteady jets were located on the windward wall to influence the flow prior to separation. The jet angle (α) was set to 45° based on a previous parameter study of the effect of jet angle [5]. The blowing ratio (𝑈𝑗𝑒𝑡

/𝑈∞) of the jet has been found to be

directly proportional to the reduction in drag and fluctuating lift [5]. The maximum jet velocity (𝑈𝑗𝑒𝑡𝑚𝑎𝑥) was set based upon a

target blowing ratio of 0.33, which was expected to produce large force reductions. Previous studies have shown that unsteady

jets are most effective when actuated at the shear layer frequency [19]. Therefore the natural frequency of the shear layer for the

baseline cases was calculated, to determine the pulsing frequency for the jets. The mean velocity profiles of the shear layers, at a

location of x/D of 0.25, are shown in Figure 4. The baseline cases for the numerical model compared relatively well with wind

tunnel data and were used to determine the natural frequency of the shear layer. Through stability analysis, and wind tunnel

testing Michalke [20] found the natural frequency of a shear layer (𝑓𝑠ℎ𝑒𝑎𝑟) to be:

𝑓𝑠ℎ𝑒𝑎𝑟 = 0.0018𝑈0𝜃 (4)

where θ is the shear layer momentum thickness, and U0 is the maximum velocity in the shear layer.

With the mean velocity profiles of the shear layer, and the momentum thickness, the shear layer frequency was computed. The

jet's frequency (𝑓𝑗𝑒𝑡) was then set to the natural frequency of the shear layer. This corresponded to an F+ (𝑓𝑗𝑒𝑡/𝑓𝑠ℎ𝑒𝑑 , where 𝑓𝑠ℎ𝑒𝑑

is the shedding frequency of square prism) of 10 for both smooth and turbulent flow cases.

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Figure 4 - Time-averaged velocity profiles of the shear layers at x/D=0.25 for smooth base case (──), the turbulent base

case (──), and wind tunnel testing smooth baseline [21] (▷)

3 NUMERICAL VALIDATION

The smooth and turbulent baseline cases were run first to compare these simulations with previous published wind tunnel

studies. As seen in Figure 5(a) the time-averaged pressure around the circumference of the square prism agrees reasonably well

with the wind tunnel data. The suction peak on the side wall is slightly overestimated for both the smooth and turbulent cases,

however, the location of the peak suction occurs at the same location for both the numerical and wind tunnel data for each flow

type. With freestream turbulence the suction peak on the sidewall moves closer to the windward edge, an indication of the

increased curvature of the shear layers. Downstream of the suction peak the pressure recovers. Since the pressure peak with

freestream turbulence occurs farther upwind a greater amount of pressure recovery is possible thus increasing (less negative) the

base pressure, and hence reducing the mean drag. The smooth numerical results underestimate the base pressure which leads to

an overestimation of the drag. For the turbulent inflow case the model predicts a pressure recovery to occur faster than the wind

tunnel results leading to nearly identical base pressure and mean drag force.

Figure 5(b) shows the smooth baseline case where the pressure standard deviation is slightly underestimated as compared to

the wind tunnel data. However, the trend is the same with a large increase in fluctuating pressure occurring in the same location

for the numerical results and experimental. This peak occurs at the same location as the mean pressure peak suggesting it is due

to the flow trying to partially reattach to the surface.

(a) (b)

Figure 5 - (a) Time averaged surface pressure coefficient for the current study smooth baseline case (──), wind tunnel smooth

inflow [7] (▪), current study turbulent baseline case (──), wind tunnel turbulent inflow [7] (+), and (b) fluctuating surface

pressure coefficient for the current study smooth baseline case (──), turbulent baseline case (──), and wind tunnel smooth case

[22] (*)

The increased curvature of the shear layers in the turbulent inflow case, compared to the smooth flow case leads to a reduction

in the mean drag, and fluctuating lift on the square prism [9]. As seen in Figure 6 the numerical model does a good job of

predicting the rms of the lift for the smooth and turbulent inflow cases compared to wind tunnel studies [7] [8]. The numerical

model slightly overestimates the mean drag for the smooth inflow case but the turbulent inflow case is in good agreement.

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(a) (b)

Figure 6 - The (a) mean drag and (b) fluctuating lift component on a square prism versus turbulence intensity for current study

baseline cases (■), current study jet cases (⧫), Vickery’s wind tunnel on square prism [8] (○), and Lee’s wind tunnel on a square

prism [7] (△)

4 RESULTS

Next the simulations were run with the unsteady jets activated. When the jets are activated, a large reduction (40%) in the rms

of the lift coefficient can be seen in both the smooth and turbulent inflow cases (see Figure 6 and Table 2). The drag in the

smooth inflow case also sees large reduction whereas the drag in the turbulent case undergoes a much smaller reduction. It is

surprising to see that the jets lead to a lower mean drag in the smooth inflow case compared to the turbulent case. This suggests

that the inflow turbulence is interfering with the mechanism that reduce the mean drag, or a plateau is being reached, in which it

is not possible to further decrease the drag utilizing unsteady jets.

Table 2 - The mean and fluctuating forces on the baseline and actuated cases for smooth and turbulent inflow conditions

Inflow Smooth Turbulent

Case Base Jet Base Jet

CD 2.25 1.62 1.81 1.67

% change - -27.0% - -7.7%

CL′ 1.39 0.84 0.93 0.48

% change - -40.2% - -47%

Pressure Distributions 4.1

It is suggested that the unsteady jets on the square prism are effective at reducing the mean drag by increasing curvature of the

shear layers. This increases the partial reattachment on the side walls of the prism, in a manner similar to that caused by

freestream turbulence. This phenomenon is evident in the mean and fluctuating surface pressure distributions shown in Figure 7.

In the jet case with smooth inflow the mean suction peak and the fluctuating pressure peak on the side wall both move toward

the windward edge (Figure 7(a) and (b), indicated by the arrows). This indicates that partial reattachment is occurring on the

square prism further upwind for the unsteady jet case leading to a large pressure recovery on the sidewall. The pressure recovery

causes less suction on the leeward wall and a reduction in drag. Additionally there is a 15% reduction of sidewall pressure

fluctuation while leeward wall fluctuations remain constant. As expected the jets increase the fluctuating pressure on the

windward face due to their orientation and unsteady nature. A similar trend is seen for the turbulent inflow case (Figure 7(c)

and (d)). The maximum suction peak is slightly reduced by the jets and occurs further upwind on the side wall (indicated by the

arrow in Figure 7(c)). This allows for greater pressure recovery on the side wall and thus higher (less negative) base pressure.

The peak pressure fluctuation is also seen moving further upwind in the jet case (indicated by the arrow in Figure 7(d)).

However the peak value is seen to increase with the addition of the jets. Since the rms of the lift is seen to decrease, it is likely

that interaction between the separated shear layers in the wake is diminished and they are acting less coherently. It is worth

noting that the mean pressure coefficients for the jets in smooth flow (Figure 7(a)) are very similar to the turbulent flow case

(Figure 7(c)) suggesting that the shear layer curvature is near its maximum, and drag cannot be decreased much more.

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(a) (b)

(c) (d)

Figure 7 - (a) Mean surface pressure coefficients and (b) fluctuating surface pressure coefficients for the current study smooth

baseline case (──), current study smooth jet case (──)and (c) mean surface pressure coefficient and (d) fluctuating surface

pressure coefficient for the turbulent baseline case (──) , and the turbulent jet case (─ ─) with arrows indicating the trend of

the maximum suction and fluctuation peaks

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Flow fields 4.2

The complete flow fields for the time averaged velocities can be seen in Figure 8 for all the cases. The time averaged velocity

shows that the shear layers for the jet cases and the turbulent baseline case move closer to the square prism, and the wake

narrows. The jets in turbulent inflow case are seen to significantly elongate the wake.

(a) (b)

(c) (d)

Figure 8 - Time averaged velocity fields for baseline cases with (a) smooth inflow, and (b) turbulent inflow, and jet cases with

(c) smooth inflow and (d) turbulent inflow

The fluctuating stream-wise velocities (𝑢′) flowfields are shown in Figure 9 and the cross-stream fluctuating (𝑣′ ) flowfields

can be seen in Figure 10. Additional time-averaging is needed for the turbulent cases for the fluctuating velocities to fully

converge, but significant trends can still be observed.

For the smooth baseline case (Figure 9(a)) there are large stream-wise velocity fluctuations (𝑢′) throughout the shear layer and

the wake. The fluctuations in the shear layers are due to the shear layer moving vertically (y-direction) throughout the shedding

cycle. The fluctuations in the wake are due to the shear layers interacting with each other. For the smooth cases there is nothing

to prohibit shear layer interaction so when one vortex is “rolling-up” it is drawing vorticity from the opposite shear layer into the

vortex, therefore creating a very strong vortex. The addition of freestream turbulence (Figure 9(b)) inhibits this interaction as

indicated by the reduction in 𝑢′ near the wake centerline, thus limiting the growth of the wake vortices and their force on the

prism. The jets can be seen to have the same effect, where for the smooth inflow case (Figure 9(c)) a large reduction in the 𝑢′

near the wake centerline is observed, indicating less shear layer wake interaction. A similar trend is seen in the turbulent case

however to a lesser extent (Figure 9(d)). Additionally, the 𝑢′ in the shear layers is decreased for the jet cases. This indicates a

reduction in the flapping of the shear layers on the sides and accounts for some of the reduction in the rms of the lift, and the

weakened wake interactions of the shear layers.

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(a) (b)

(c) (d)

Figure 9 - Stream-wise fluctuation plots (𝑢′) for baseline cases with (a) smooth inflow, and (b) turbulent inflow, and jet cases

with (c) smooth inflow and (d) turbulent inflow

The jets cause three major changes in the 𝑣′ flow fields (shown in Figure 10) that play a role in reducing the fluctuating

forces. Firstly, it is seen in the jet cases an increase in the 𝑣′ in the shear layers. This indicates that the shear layers are diffusing

before they reach the wake. The diffusing of the shear layers restricts the shear layer vorticity from being carried across the

wake [23]. This limits the shear layer interactions and the strength of the wake vortices. Secondly, an overall decrease in the

fluctuation magnitudes in the wake indicates that the strength of the wake vortices has been reduced by the jets. This is seen

through the limiting of shear layer interactions due to partial flow reattachment and shear layer diffusion. Thirdly, it is seen in

the near wake, directly behind the leeward wall, a drastic reduction in the cross stream velocities (shown by the dashed

rectangle). This area is named the “recirculation free zone” [24]. This zone pushes the vortex formation region further

downstream, as indicated by the peak 𝑣′ regions for smooth inflow moving from x/D = 2 for the baseline case to x/D = 3.25 for

the jet case. For the turbulence inflow the peaks move from x/D = 2.5 to x/D = 3. This combination of weaker wake vortices

and the vortex formation region being pushed downstream reduces both the fluctuating lift and drag forces on the prism.

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(a) (b)

(c) (d)

Figure 10 - Cross-stream fluctuation plots (𝑣′) for baseline cases with (a) smooth inflow, and (b) turbulent inflow, and jet cases

with (c) smooth inflow and (d) turbulent inflow with the recirculation free-zone indicated by the dashed rectangle box.

Velocity Profiles 4.3

The flow fields presented in Figure 8, Figure 9, and Figure 10 give a global summary of the flow characteristics. In this section

a detailed examination of the average and fluctuating velocities will be undertaken.

4.3.1 Smooth Inflow Cases

For the smooth inflow case (Figure 11) the mean stream-wise velocity profiles (U) of the shear layers show that the shear

layer moves closer to the side for the jet case (as indicated with an arrow). The biggest difference between the baseline and jet

case can be seen in the fluctuating velocity profiles. For the smooth baseline case the stream-wise fluctuations are due to the

coherent vertical motion (flapping) of the shear layers [21] (i.e. a point at y/D=0.75 moves in and out of the shear layer, thus has

a large variations in velocity). When the jet is applied the fluctuations dramatically decrease. The jets are causing the shear

layers to intermittently reattach to the sidewalls, which is dramatically reducing the flapping of the shear layer, and the 𝑢′ in the

shear layers. The cross-stream fluctuating velocity (𝑣′) increases with the addition of the jets. This is due to the shear layer

diffusing creating more random motions in the vertical direction.

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Figure 11 - Mean and fluctuating velocity profiles for the shear layer at different x/D locations for the baseline (──) and jet case

(─ ─) with smooth inflow conditions

The shear layers then move into the wake where their velocity profiles are plotted in Figure 12 and Figure 13. The mean

velocity profiles show that the wake recovers more quickly in the presence jets. This is seen in slightly narrower stream-wise

velocity profiles (Figure 12), and wider cross-stream velocity (V) from momentum being brought into the wake to recuperate the

deficit. Along the centerline (Figure 13) the mean stream-wise velocity profile can be seen to have a slightly more negative

minimum, but then recovers faster than the baseline case. This indicates that the wake vortices are further downstream for the jet

case, thus exerting less force on the prism. This is corroborated by the fluctuating cross-stream velocity (𝑣′) profile in which the

peak fluctuations occur further downstream. The wake vortices are pushed downstream inhibiting shear layer interaction from

partial flow reattachment and increased shear layer diffusion. The shear layers act independently in the near wake, as happens

with splitter plates, dividing the wake and preventing interaction altogether [25]. Additionally both stream-wise and cross-

stream velocities significantly decrease in magnitude from the addition of the jets, indicating a weakening of the wake vortices.

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Figure 12 - Mean and fluctuating velocity profiles in the wake at different x/D locations for the baseline (──) and jet case (─ ─)

with smooth inflow conditions

Figure 13 - Mean and fluctuating velocity profiles at the wake centerline for the baseline (──) and jet case (─ ─) with smooth

inflow conditions with the change in the magnitude and location of the fluctuating velocity peaks shown with arrows

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4.3.2 Turbulent Inflow

The presence of freestream turbulence causes similar effects on the flow field as the unsteady jets (Figure 14). This is seen in the

baseline turbulent case profiles which have a lower 𝑢′ peak and greater 𝑣′ peak than the smooth baseline case. Therefore, the

effects of the unsteady jets on the square prism are not as pronounced in the turbulent case compared to the smooth flow cases.

The mean stream-wise profiles for the baseline and jet case are very similar. There is a slight decrease in the 𝑢′, indicating a

reduction in the shear layer flapping from the jet. Additionally there is an increase in the 𝑣′ profiles, especially for x/D<0.5,

suggesting the shear layers are undergoing even more diffusions.

Figure 14 - Mean and fluctuating velocity profiles for the shear layer at different x/D locations for the baseline (──) and jet case

(─ ─) with turbulent inflow conditions

The jets elongate the wake, as seen by the minimum stream-wise velocity (U) in the wake centerline occurring at x/D=1.75

compared to 1.5 for the baseline case (Figure 16). Additionally the stream-wise velocity takes longer to recover for the jet case.

The cross-stream velocity (V) profiles vary significantly as well between the baseline and jet case (Figure 15). For the jet case

the peak cross-stream velocity is lower than the baseline case and is located further away from the prism in the y-direction. This

is due to the recirculation free zone preventing flow from entering the near wake. Further downstream the cross-stream velocity

increases and the peak moves towards the centerline indicating the vortex formation region has moved further downstream, thus

the wake vortices are exerting less influence on the prism. The fluctuating stream-wise velocity profile peak starts further away

in the y-direction, indicating that near the recirculation free zone the shear layers act independently of each other as if there was

still a body separating them. As the flow continues downstream (~x/D=2.5) the 𝑢′ profile maxima move towards the centerline

and reach a global peak value, indicating that wake vortices are forming. This global peak is less for the jet case than the

baseline case, indicating weaker vortices are forming. Away from the centerline the cross-stream fluctuation profile are similar;

however near the centerline the fluctuations are reduced. The centerline 𝑣′ profiles show the near wake fluctuation reduced, and

the peak fluctuation occurring further away from the leeward wall, which is additional evidence of the wake vortex formation

region being pushed downstream due to the jets (Figure 16).

15


Figure 15 - Mean and fluctuating velocity profiles in the wake at different x/D locations for the baseline (──) and jet case (─ ─)

with turbulent inflow conditions

Figure 16 - Mean and fluctuating velocity profiles at the wake centerline for the baseline (──) and jet case (─ ─) with turbulent

inflow conditions

16


5 CONCLUSIONS

The first part of this study was able to validate the DDES turbulence model as suitable to capture turbulent flow around a bluff

square cylinder. The mean and fluctuating forces on the square prism agreed well with published wind tunnel data. The mean

and fluctuating surface pressure around the prism captured the same trends as the wind tunnel data, however slightly over

predicted the mean pressure, and slightly underestimated the fluctuating pressure. Activating unsteady jets on the front face of

the prism modulated at 10 times the natural frequency of the vortex shedding led to various changes in the flow field, surface

pressures and overall forces. The jets were seen to increase the curvature of the shear layers, similar to the addition of freestream

turbulence. This induces partial flow reattachment on the sidewalls and moves the peak surface pressure on the sidewall towards

the windward edge. This allows for more pressure recovery on the sidewall, which increases the base pressure, thus reducing the

mean drag force on the square prism. The jets also diffused the shear layers, thus reducing the vorticity supply to the wake

vortices and reducing their strength. The combination of intermittent reattachment and increased diffusion restricted the shear

layer interactions in the wake leading to a recirculation free zone. This pushed the vortex formation region further downstream

and reduced the effects the vortices have on the prism.

6. ACKNOWLEDGEMENTS

This study was partially funded from NSF grant CMMI-1200987.

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