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).

Selection of Marine Propulsion Machinery

The selection of propulsion machinery and plant layout will depend on design features such as space, weight and noise levels, together with overall requirements including areas of operation, running costs and maintenance. All of these factors will depend on the ship type, its function and operational patterns.

Propeller Geometry, Coefficients, Characteristics

1. Compactness and weight: Extra deadweight and space. Height may be important in ships such as ferries and offshore supply vessels which require long clear decks.

2. Initial cost.

3. Fuel consumption: Influence on running costs and bunker capacity (deadweight and space).

4. Grade of fuel (lower grade/higher viscosity, cheaper).

5. Level of emission of NOx, SOx and CO2.

6. Noise and vibration levels: Becoming increasingly important.

7. Maintenance requirements/costs, costs of spares.

8. Rotational speed: Lower propeller speed plus larger diameter generally leads to increased efficiency.

Purpose

When making conventional power predictions, no account is usually taken of scale effects on:

1. Hull form effect,

2. Wake and thrust deduction factors,

3. Scale effect on propeller efficiency,

4. Uncertainty of scaling laws for appendage drag.

Experience shows that power predictions can be in error and corrections need to be applied to obtain a realistic trials power estimate. Suitable correction (or correlation) factors have been found using voyage analysis techniques applied to trials data. The errors in predictions are most significant with large, slow-speed, high CB vessels.

Model-ship correlation should not be confused with model-ship extrapolation. The extrapolation process entails extrapolating the model results to full scale to create the ship power prediction. The correlation process compares the full-scale ship power prediction with measured or expected full-scale ship results.

Background

The accurate experimental measurement of ship model resistance components relies on access to high-quality facilities. Typically these include towing tanks, cavitation tunnels, circulating water channels and wind tunnels. Detailed description of appropriate experimental methodology and uncertainty analysis are contained within the procedures and guidance of the International Towing Tank Conference (ITTC) [7.1]. There are two approaches to understanding the resistance of a ship form. The first examines the direct body forces acting on the surface of the hull and the second examines the induced changes to pressure and velocity acting at a distance away from the ship. It is possible to use measurements at model scale to obtain global forces and moments with the use of either approach. This chapter considers experimental methods that can be applied, typically at model scale, to measure pressure, velocity and shear stress. When applied, such measurements should be made in a systematic manner that allows quantification of uncertainty in all stages of the analysis process. Guidance on best practice can be found in the excellent text of Coleman and Steele [7.2], the processes recommended by the International Standards Organisation (ISO) [7.3] or in specific procedures of the ITTC, the main ones of which are identified in Table 7.1.

In general, if the model is made larger (smaller scale factor), the flow will be steadier, and if the experimental facility is made larger, there will be less uncertainty in the experimental measurements. Facilities such as cavitation tunnels, circulating water channels and wind tunnels provide a steady flow regime more suited to measurements at many spatially distributed locations around and on ship hulls. Alternatively, the towing tank provides a straightforward means of obtaining global forces and moments as well as capturing the unsteady interaction of a ship with a head or following sea.

Background

The overall ship powering process is shown in Figure 2.3. A number of worked examples are presented to illustrate typical applications of the resistance and propulsor data and methodologies for estimating ship propulsive power for various ship types and size. The examples are grouped broadly into the estimation of effective power and propeller/propulsor design for large and small displacement ships, semi-displacement ships, planing craft and sailing vessels.

The resistance data are presented in Chapter 10 together with tables of data in Appendix A3. The propeller data are presented in Chapter 16, together with tables of data in Appendix A4.