Shock wave–boundary-layer interactions (SBLIs) occur when a shock wave and a boundary layer converge and, since both can be found in almost every supersonic flow, these interactions are commonplace. The most obvious way for them to arise is for an externally generated shock wave to impinge onto a surface on which there is a boundary layer. However, these interactions also can be produced if the slope of the body surface changes in such a way as to produce a sharp compression of the flow near the surface – as occurs, for example, at the beginning of a ramp or a flare, or in front of an isolated object attached to a surface such as a vertical fin. If the flow is supersonic, a compression of this sort usually produces a shock wave that has its origin within the boundary layer. This has the same affect on the viscous flow as an impinging wave coming from an external source. In the transonic regime, shock waves are formed at the downstream edge of an embedded supersonic region; where these shocks come close to the surface, an SBLI is produced.

Introduction to Transonic Interactions

By definition, transonic shock wave–boundary layer interactions (SBLIs) feature extensive regions of supersonic and subsonic flows. Typically, such interactions are characterized by supersonic flow ahead of the shock wave and subsonic flow downstream of it. This mixed nature of the flow has important consequences that make transonic interactions somewhat different from supersonic or hypersonic interactions.

The key difference between transonic interactions and other SBLIs is the presence of subsonic flow behind the shock wave. Steady subsonic flow does not support waves (e.g., shock waves or expansion fans), and any changes of flow conditions are gradual in comparison to supersonic flow. This imposes constraints on the shock structure in the interaction region because the downstream flow conditions can feed forward and affect the strength, shape, and location of the shock wave causing the interaction. The flow surrounding a transonic SBLI must satisfy the supersonic as well as subsonic constraints imposed by the governing equations. The interaction also is sensitive to downstream disturbances propagating upstream in the subsonic regions. In contrast, supersonic interactions are “shielded” from such events by the supersonic outer flow.

Introduction

Some of the most serious and challenging problems encountered by the designers of hypersonic vehicles arise because of the severity of the heating loads and the steepness of the flow gradients that are generated in shock wave–boundary layer interaction (SBLI) regions. The characteristics of these flows are difficult to predict accurately due in no small measure to the significant complexity caused by shear-layer transition, which occurs at very low Reynolds numbers and can lead to enhanced heating loads and large-scale unsteadiness. Even for completely laminar flows, viscous interaction can degrade appreciably the performance of control and propulsion systems. It is interesting that both of the two major problems encountered with the U.S. Space Shuttle program were associated with SBLI. The first was the so-called Shuttle Flap Anomaly that nearly resulted in disaster on the craft's maiden flight due to a failure in the design phases to account correctly for the influence of real-gas effects on the shock-interaction regions over the control surfaces. During the flight, a significantly larger flap deflection was required to stabilize the vehicle than had been determined from ground tests in cold-flow facilities. Miraculously, it was possible to achieve the necessary control, and disaster was narrowly averted. The second problem was the leading-edge structural failure caused by the impact of foam that had been fractured and released from the shuttle tank as a result of the dynamic loads caused by a shock interaction. Figure 6.1 is an example of the shock structures that are generated among the shuttle, the main tank, and the solid reusable boosters. The contour plot illustrates the corresponding computer-predicted pressure distribution. Aerothermal loads generated by shock waves in the region of the bipod that supports the shuttle nose caused the foam glove to be fractured and released. Unfortunately, the damage this caused resulted in a tragic accident.

Introduction

If the shock wave associated with a shock wave–boundary-layer interaction (SBLI) is intense enough to cause separation, flow unsteadiness appears to be the almost-inevitable outcome. This often leads to strong flow oscillations that are experienced far downstream of the interaction and can be so severe in some instances as to inflict damage on an airframe or an engine. This is generally referred to as “breathing” or, simply, “unsteadiness” because it involves very low frequencies, typically at least two orders of magnitude below the energetic eddies in the incoming boundary layer. The existence of these oscillations raises two questions: “What is their cause?” and “Is there a general way in which they can be understood?”

There are several distinct types of SBLIs, depending on the geometry and whether the flow separates, and it is possible that these create fundamentally different types of unsteadiness. An interpretation was proposed by Dussauge [1] and Dussauge and Piponniau [2] using the diagram reproduced in Fig. 9.1. The organization of the diagram requires comment: In the upper branch, unseparated flows are depicted; those that separate are restricted to the lower branch. In both cases, the shock wave divides the flow into two half spaces: the upstream and the downstream layers. Hence, the shock wave can be considered an interface between the two conditions and its position and motion vary accordingly. With these various elements in mind, the shock motion can be analyzed from the perspective of the upstream and downstream conditions. The discussion in this chapter is a commentary about flow organization and other phenomena related to the two branches of the diagram.

Shock Wave–Boundary-Layer Interactions: Why They Are Important

The repercussions of a shock wave–boundary layer interaction (SBLI) occurring within a flow are numerous and frequently can be a critical factor in determining the performance of a vehicle or a propulsion system. SBLIs occur on external or internal surfaces, and their structure is inevitably complex. On the one hand, the boundary layer is subjected to an intense adverse pressure gradient that is imposed by the shock. On the other hand, the shock must propagate through a multilayered viscous and inviscid flow structure. If the flow is not laminar, the production of turbulence is enhanced, which amplifies the viscous dissipation and leads to a substantial rise in the drag of wings or – if it occurs in an engine – a drop in efficiency due to degrading the performance of the blades and increasing the internal flow losses. The adverse pressure gradient distorts the boundary-layer velocity profile, causing it to become less full (i.e., the shape parameter increases). This produces an increase in the displacement effect that influences the neighbouring inviscid flow. The interaction, experienced through a viscous-inviscid coupling, can greatly affect the flow past a transonic airfoil or inside an air-intake. These consequences are exacerbated when the shock is strong enough to separate the boundary layer, which can lead to dramatic changes in the entire flowfield structure with the formation of intense vortices or complex shock patterns that replace a relatively simple, predominantly inviscid, unseparated flow structure. In addition, shock-induced separation may trigger large-scale unsteadiness, leading to buffeting on wings, buzz for air-intakes, or unsteady side loads in nozzles. All of these conditions are likely to limit a vehicle's performance and, if they are strong enough, can cause structural damage.

Introduction

This chapter continues the description of supersonic turbulent shock wave–boundary layer interactions (STBLIs) by examining the flowfield structure of three-dimensional interactions. The capability of modern computational methods to predict the observed details of these flowfields is discussed for several canonical configurations, and the relationships between them and two-dimensional interactions (see Chapter 4) are explored.

Three-Dimensional Turbulent Interactions

To aid in the understanding of three-dimensional STBLIs, we consider a number of fundamental geometries based on the shape of the shock-wave generator – namely, sharp unswept (Fig. 5.1a) and swept (Fig. 5.1b) fins, semicones (Fig. 5.1c), swept compression ramps (SCRs) (Fig. 5.1d), blunt fins (Fig. 5.1e), and double sharp unswept fins (Fig. 5.1f). More complex three-dimensional shock-wave interactions generally contain elements of one or more of these basic categories. The first four types of shock-wave generators are examples of so-called dimensionless interactions [1] (Fig. 5.1a–d). Here, the shock-wave generator has an overall size sufficiently large compared to the boundary-layer thickness δ that any further increase in size does not affect the flow. The blunt-fin case (Fig. 5.1e) is an example of a dimensional interaction characterized by the additional length scale of the shock-wave generator (i.e., the leading-edge thickness). The crossing swept-shock-wave interaction case (Fig. 5.1f) represents a situation with a more complex three-dimensional flow topology. We briefly discuss the most important physical properties of these three-dimensional flows and provide examples of numerical simulations.

Introduction

Effective design of modern supersonic and hypersonic vehicles requires an understanding of the physical flowfield structure of shock wave–boundary layer interactions (SBLIs) and efficient simulation methods for their description (Fig. 4.1). The focus of this chapter is two-dimensional supersonic shock wave–turbulent boundary layer interactions (STBLIs); however, even in nominally two-dimensional/axisymmetric flows, the mean flow statistics may be three-dimensional. The discussion is restricted to ideal, homogeneous gas flow wherein the upstream free-stream conditions are mainly supersonic (1.1 ≤ M∞ ≤ 5.5). Computational fluid dynamics (CFD) simulations of two-dimensional STBLIs are evaluated in parallel with considerations of flowfield structures and physical properties obtained from both experimental data and numerical calculations.

Problems and Directions of Current Research

The main challenges for modeling of and understanding the wide variety of two- and three-dimensional STBLIs include the complexity of the flow topologies and physical properties and the lack of a rigorous theory describing turbulent flows. These problems have been widely discussed during various stages of STBLI research since the 1940s. In accordance with authoritative surveys [1, 2, 3, 4, 5, 6, 7] and monographs [8, 9, 10, 11], progress in understanding STBLIs can be achieved only on the basis of close symbiosis between CFD and detailed physical experiments that focus on simplified configurations (see Fig. 4.1) and that use recent advances in experimental diagnostics (e.g., planar laser scattering [PLS]; particle image velocimetry [PIV]); and turbulence modeling, including Reynolds-averaged Navier-Stokes [RANS], large eddy simulation [LES], and direct numerical simulation [DNS]).

Introduction

Hypersonic flows are synonymous with high-Mach number flows and therefore are characterized by very strong shock waves. Every hypersonic vehicle has a bow shock wave in front of it, which bounds the flow around the vehicle. On the windward side of a vehicle, the bow shock usually is aligned closely with the vehicle surface, and the distance between the surface and the shock wave is usually small relative to the characteristic dimension of the vehicle. Thus, this shock-layer region is usually quite thin. Hypersonic vehicles tend to fly at high altitudes so that convective heating levels can be managed. Thus, the characteristic Reynolds numbers tend to be low and boundary layers are usually thick. In addition, shear heating in hypersonic boundary layers increases the temperature and viscosity, which also increases the thickness. The low Reynolds number and the relative stability of hypersonic boundary layers mean that many practical hypersonic flows are laminar or transitional. If the flow is turbulent, it is often only marginally turbulent. Therefore, hypersonic flows are particularly susceptible to shock wave–boundary-layer interactions (SBLIs).

The field of static aeroelasticity is the study of flight-vehicle phenomena associated with the interaction of aerodynamic loading induced by steady flow and the resulting elastic deformation of the lifting-surface structure. These phenomena are characterized as being insensitive to the rates and accelerations of the structural deflections. There are two classes of design problems that are encountered in this area. The first and most common to all flight vehicles is the effects of elastic deformation on the airloads, as well as effects of airloads on the elastic deformation, associated with normal operating conditions. These effects can have a profound influence on performance, handling qualities, flight stability, structural-load distribution, and control effectiveness. The second class of problems involves the potential for static instability of the lifting-surface structure to result in a catastrophic failure. This instability is often termed “divergence” and it can impose a limit on the flight envelope.

“Aeroelasticity” is the term used to denote the field of study concerned with the interaction between the deformation of an elastic structure in an airstream and the resulting aerodynamic force. The interdisciplinary nature of the field is best illustrated by Fig. 1.1, which originated with Professor A. R. Collar in the 1940s. This triangle depicts interactions among the three disciplines of aerodynamics, dynamics, and elasticity. Classical aerodynamic theories provide a prediction of the forces acting on a body of a given shape. Elasticity provides a prediction of the shape of an elastic body under a given load. Dynamics introduces the effects of inertial forces. With the knowledge of elementary aerodynamics, dynamics, and elasticity, students are in a position to look at problems in which two or more of these phenomena interact. The field of flight mechanics involves the interaction between aerodynamics and dynamics, which most undergraduate students in an aeronautics/aeronautical engineering curriculum have studied in a separate course by their senior year. This text considers the three remaining areas of interaction, as follows:

• between elasticity and dynamics (i.e., structural dynamics)

• between aerodynamics and elasticity (i.e., static aeroelasticity)

• among all three (i.e., dynamic aeroelasticity)

Because of their importance to aerospace system design, these areas are also appropriate for study in an undergraduate aeronautics/aeronautical engineering curriculum. In aeroelasticity, one finds that the loads depend on the deformation (i.e., aerodynamics) and that the deformation depends on the loads (i.e., structural mechanics/dynamics); thus, one has a coupled problem.

The purpose of this chapter is to convey to students a small introductory portion of the theory of structural dynamics. Much of the theory to which the students will be exposed in this treatment was developed by mathematicians during the time between Newton and Rayleigh. The grasp of this mathematical foundation is therefore a goal that is worthwhile in its own right. Moreover, as implied by the da Vinci quotation, a proper use of this foundation enables the advance of technology.

Structural dynamics is a broad subject, encompassing determination of natural frequencies and mode shapes (i.e., the so-called free-vibration problem), response due to initial conditions, forced response in the time domain, and frequency response. In the following discussion, we deal with all except the last category. For response problems, if the loading is at least in part of aerodynamic origin, then the response is said to be aeroelastic. In general, the aerodynamic loading then will depend on the structural deformation, and the deformation will depend on the aerodynamic loading. Linear aeroelastic problems are considered in subsequent chapters, and linear structured dynamics problems are considered in the present chapter. Other important phenomena, such as limit-cycle oscillations of lifting surfaces, must be treated with sophisticated nonlinear-analysis methodology; however, they are beyond the scope of this text.

From First Edition

A senior-level undergraduate course entitled “Vibration and Flutter” was taught for many years at Georgia Tech under the quarter system. This course dealt with elementary topics involving the static and/or dynamic behavior of structural elements, both without and with the influence of a flowing fluid. The course did not discuss the static behavior of structures in the absence of fluid flow because this is typically considered in courses in structural mechanics. Thus, the course essentially dealt with the fields of structural dynamics (when fluid flow is not considered) and aeroelasticity (when it is).

As the name suggests, structural dynamics is concerned with the vibration and dynamic response of structural elements. It can be regarded as a subset of aeroelasticity, the field of study concerned with interaction between the deformation of an elastic structure in an airstream and the resulting aerodynamic force. Aeroelastic phenomena can be observed on a daily basis in nature (e.g., the swaying of trees in the wind and the humming sound that Venetian blinds make in the wind). The most general aeroelastic phenomena include dynamics, but static aeroelastic phenomena are also important. The course was expanded to cover a full semester, and the course title was appropriately changed to “Introduction to Structural Dynamics and Aeroelasticity.”

Aeroelastic and structural-dynamic phenomena can result in dangerous static and dynamic deformations and instabilities and, thus, have important practical consequences in many areas of technology.