International Journal of Aerospace Engineering

Volume 2017 (2017), Article ID 4012731, 15 pages

https://doi.org/10.1155/2017/4012731

## CFD Simulations of a Finned Projectile with Microflaps for Flow Control

U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005, USA

Correspondence should be addressed to Jubaraj Sahu; lim.liam@vic.uhas.jarabuj

Received 9 September 2016; Revised 10 November 2016; Accepted 27 November 2016; Published 19 January 2017

Academic Editor: Antonio Ficarella

Copyright © 2017 Jubaraj Sahu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This research describes a computational study undertaken to determine the effect of a flow control mechanism and its associated aerodynamics for a finned projectile. The flow control system consists of small microflaps located between the rear fins of the projectile. These small microflaps alter the flow field in the aft finned region of the projectile, create asymmetric pressure distributions, and thus produce aerodynamic control forces and moments. A number of different geometric parameters, microflap locations, and the number of microflaps were varied in an attempt to maximize the control authority generated by the flaps. Steady-state Navier-Stokes computations were performed to obtain the control aerodynamic forces and moments associated with the microflaps. These results were used to optimize the control authority at a supersonic speed, . Computed results showed not only the microflaps to be effective at this speed, but also configurations with 6 and 8 microflaps were found to generate 25%–50% more control force than a baseline 4-flap configuration. These results led to a new optimized 8-flap configuration that was further investigated for a range of Mach numbers from to and was found to be a viable configuration effective in providing control at all of these speeds.

#### 1. Introduction

The prediction of aerodynamic coefficients for projectile configurations is essential in assessing the performance of new designs. Accurate determination of aerodynamics and flight dynamics is thus critical to the low-cost development of new advanced munitions. Various techniques such as the semiempirical [1, 2], wind tunnel [3, 4], free-flight [5–8], and computational fluid dynamics (CFD) [9–11] are used routinely for aerodynamic characterization of projectiles without any flow control. The flow fields associated with munitions can be complex at high angles of attack and even at low angles of attack for complex configurations. Body and wing vortices [12, 13] can dominate the flow field and interact with one another resulting in a very complex flow field even for simple geometries. With active or passive flow control, the flow fields are generally more complex which in turn makes determination of aerodynamics more challenging and difficult. This is true even for simple base flow control [14, 15] used for reduction in base drag and especially true for forebody flow control of asymmetric vortices at high angles of attack [16–18].

Active flow control [19, 20] involves flow actuators; some examples include fluidic [21, 22], synthetic jet [23, 24], and plasma jet [25, 26] actuation. Passive flow control, on the other hand, usually involves geometrical modifications, such as vortex generators [27] on a wing, or strakes [28–30] on a body, or other protuberances [31, 32] that are used for flow control applications. For projectile and missile applications, both types of active and passive flow control mechanisms are used to provide aerodynamic control. For a guided munition, aerodynamic control provides the required control force and moment that are then used to maneuver or alter its trajectory as needed. The flow fields associated with these control mechanisms for munitions are complex, involving three-dimensional (3D) shock-boundary layer interactions, jet interaction with the free-stream flow, and highly viscous-dominated separated flow regions.

Traditionally, fins, canards, and other control surfaces are often used to provide the required passive control for maneuvering projectiles and missiles. A major concern, especially when adding moveable aerodynamic surfaces (e.g., canards) [33, 34], upstream of the body or stabilizing fins, is flow interaction. The motion of upstream control surfaces at various aerodynamic angles of attack and Mach numbers greatly influences the pressure distribution on downstream surfaces. Even for unguided flights, these flow interactions exist and must therefore be accurately taken into account in the design analysis for both uncontrolled and controlled flights. Canard control is a preferred way to provide control force and moment required for maneuvering munitions and is effective at both low (subsonic) and high (supersonic) speeds. However, adverse flow interactions downstream can occur on the afterbody at certain flow conditions (speeds and angles of attack) and again must be taken into account in the aerodynamic analysis.

Traditionally, supersonic jets are used for active flow control for high speed projectile and missile applications. Activation of a jet generates a control forces and thus provides the control authority needed to maneuver the flight vehicle. The resulting flow field is highly three-dimensional, unsteady, and very complex with shock structures and separated flow regions even at small angles of attack. This is especially true at high angles of attack where the flow field is complex even without jet interaction. Slender bodies at high angle of attack exhibit complicated flow structures such as asymmetric vortex shedding which induce nonlinear side forces and side moments [12]. One must take into account the jet interaction effects to be able to predict the overall aerodynamic forces and moments acting on the projectile at low to high angles of attack. Accurate numerical modeling of the unsteady aerodynamics can be challenging and generally requires the use of advanced time-accurate CFD solution techniques. Examples of experimental and numerical studies of lateral jet interaction on a finned projectile include both steady-state jets and transient pulse jets [11, 35–38]. Recently, time-accurate CFD was used in case of a pulse jet [39].

Other researchers have looked at other means to provide aerodynamic control with control devices located either in the nose area (nose control) [40–42] or in the afterbody region (rear control) [43]. The nose of the body is often deflected or bent [40, 41] creating flow asymmetry resulting in aerodynamic control force and moment. Other nontraditional means include optically generated air channels [44] and electromagnetic aerodynamic control [45].

Recently, many new weapon control mechanisms such as plasma jets [47, 48], deployable pins [49, 50], microflaps [46, 51–53], and microjets [24, 54–56] have been investigated for their feasibility for providing sufficient control forces and moments for projectile control and other applications. These control mechanisms result in highly complex unsteady flow interactions and must be taken into account properly for accurate prediction of aerodynamics. Clearly, some of these new flow control mechanisms are unconventional and more research is needed to fully understand the flow interaction effects and accurately predict the aerodynamics and flight dynamics and hence overall guided flight performance. From a computational standpoint, accurate modeling of the critical flow interaction phenomena during guided flight control is a major challenge in terms of both numerical solution techniques and computing resources required. Fortunately, improved computer technology and state-of-the-art numerical procedures now enable solutions to complex 3D problems associated with projectile and missile aerodynamics both without and with flow control. CFD thus offers a viable approach for obtaining aerodynamics of projectiles with traditional or new flow control mechanisms.

Recently, a number of studies, both experimental and computational, have been conducted in exploring these flow control mechanisms for projectile control. Massey et al. [49] studied the effect of pin-based actuators for control of a projectile at supersonic speeds. Later, the projectile was flight tested [50] to determine the feasibility of these actuators for projectile control. These studies have indicated some potential of the pin-based actuators for projectile control at supersonic speeds. Another control mechanism that is similar to the pin-based actuator consists of a set of small microflaps [46, 51–53]. This new flow control mechanism has recently been investigated for feasibility of providing adequate aerodynamic control and is also used in the present research. In this case, the flow control is achieved by locating the small microflaps between rear fins of the finned projectile. The rear location of the microflaps offers an advantage in that one does not need to worry about any adverse flow interaction effects commonly associated with canards and jets because of their upstream location. At supersonic speeds these microflaps alter the flow field in the finned region of the projectile due to shock wave interactions between the body, fins, and microflaps. These flow interactions result in asymmetric pressure distribution over the rear finned section and thus produce control forces and moments. Cler et al. [51] and Dykes et al. [52] used a flat-plate fin interaction design of experiments model to examine the level of control authority at Mach 1.7 and obtained an optimized layout with 4 microflaps. Sahu and Heavey [46] computationally studied the effect of microflaps on the aerodynamics of a finned projectile using the same set of 4 flaps. Computed results indicated that the microflaps were effective at supersonic speeds and not effective at transonic speeds. The aerodynamic characterization work reported by Scheuermann et al. [53] contained both computational and flight test results. Resulting aerodynamic models were found to be in generally good agreement and continued to show promise for microflaps as a viable control mechanism at supersonic speeds (2 < < 3). These previous studies using microflaps were largely based on the 4-flap configurations; the effect of the number of flaps was not investigated. Also, earlier optimization that led to the 4-flap configuration did not include the actual finned projectile geometry and was done on a flat plate [52]. Some preliminary results were reported by Sahu [57] with optimization performed on an actual finned configuration.

In the present study, the focus is again on generation of maximum control authority on a real finned projectile configuration. This detailed study now includes a number of different geometric parameters, microflap locations, and numbers of microflaps that are used to maximize the control authority generated by the flaps. In addition, the present study investigates the flow control performance of the optimized configuration at various speeds from subsonic to supersonic ( = 0.8 to 5.0). Computed results obtained are compared with that of the baseline configuration with 4 microflaps. In all cases, steady-state CFD is used to investigate the level of control forces and moments due to the interaction of body, fins, and microflaps flow fields. Computed control forces and moments generated by the microflaps are also currently being used in a six-degree-of-freedom (6DOF) flight dynamic analysis to demonstrate cross-range control of the finned projectile.

#### 2. Computational Methodology

The CFD capability used here solves the full three-dimensional (3D) Navier-Stokes equations in a time-dependent manner for simulations of projectile flow fields. A commercially available Navier-Stokes flow solver, CFD++ [58–60], is used in the present work. The basic numerical framework in the solver contains unified-grid, unified-physics, and unified-computing features. Details of the basic numerical framework can be found in [58, 59]. Here, only a brief synopsis of this framework and methodology is given. A finite volume method is used to solve the 3D time-dependent Reynolds-Averaged Navier-Stokes (RANS) equationsHere, is the vector of conservative variables, and are the inviscid and viscous flux vectors, respectively, is the vector of source terms, is the cell volume, and is the surface area of the cell face.

Implicit local time-stepping and relaxation techniques were used to achieve faster convergence. Use of an implicit scheme circumvents the stringent stability limits encountered by their explicit counterparts, and successive relaxation allows update of cells as information becomes available and thus aids convergence. CFD++ uses an algebraic multigrid approach as the means to efficiently solve the linear algebra problem that results in applying an implicit scheme to both steady-state and unsteady modes of operation. In the present work, only steady-state solutions have been obtained.

The governing RANS equations (1) were marched in time using a point-implicit time integration scheme with local time-stepping, defined by the Courant-Friedrichs-Lewy (CFL) number until solutions converged. Initially, the flow solution started with free-stream conditions in the entire domain. For supersonic flow cases, CFL number was ramped from 1 to 40 over the first 100 iterations and then remained unchanged until converged solutions were obtained. At transonic and subsonic speeds, the maximum CFD number was set at 100. Five orders of magnitude reduction in the residuals of the RANS equations was achieved within 1000–1500 iterations and within 3000–4000 iterations at supersonic and subsonic speeds, respectively. Additionally, the total aerodynamic forces and moments were monitored and found to converge a lot faster, usually within 500 iterations.

Second-order discretization was used for the flow variables and turbulent viscosity equations. The spatial discretization was a second-order, upwind scheme and used a Harten-Lax-van Leer-Contact (HLLC) Riemann solver in conjunction with a multidimensional Total-Variation-Diminishing (TVD) flux limiter. Supersonic flow cases required the use of a first-order discretization over the first 200 iterations. A blending function was used to transition from first- to second-order discretization over the next 100 iterations.

For computation of turbulent flows that are of interest here, a realizable* k*-*ε* model [61] provided the turbulence closure. This two-equation turbulence model solves two transport equations, one for the turbulent kinetic energy () and the other for the turbulent dissipation rate (). These two turbulence variables are then used to obtain the turbulent eddy viscosity using Boussinesq assumption. This turbulence model has been successfully and routinely used in a number of projectile and other aerodynamics applications. The turbulence equations were fully solved all the way to the wall of the projectile and required high resolution meshes near the projectile surface wall (nondimensional wall distance, + ≤ 1.0). Free-stream values of and *ε* were obtained using a free-stream turbulence intensity of 2% and a turbulent-to-laminar viscosity ratio of 50.

#### 3. Model Geometries and Computational Grids

The projectile modeled in this study is the Basic Finner, a cone-cylinder-finned configuration [3]. A schematic diagram of the Basic Finner shape is shown in Figure 1. The length of the projectile is 10 cal. and the diameter is 30 mm. The conical nose is 2.84 cal. long and is followed by a 7.16 cal. cylindrical section. Four rectangular fins are located on the back end of the projectile. Each fin is 1 cal. long, has a sharp leading edge, and is 0.08 cal. thick at the trailing edge. The center of gravity is located 5.5 cal. from the nose of the finned projectile.