of which pressure in the downstream region increases. Such disturbance propagates upstream of the compression corner through the subsonic part of the approaching boundary layer. This upstream propagation of disturbance leads to boundary layer thickening which in turn may end in separation.
Compression corner based adverse pressure gradient in the presence of oblique shock remains one of the driving parameters for the possible separation in case of R-SWBLI. However, such local flow separation is not always guaranteed. Separation of the flow in the presence of ramp induced adverse pressure gradient depends on many parameters like Mach number, Reynolds number, ramp angle, wall temperature, boundary layer stability etc. For a given freestream conditions the minimum ramp angle required to initiate the separation is known as incipient separation angle [3]. If the deflection angle is higher than the incipient separation angle, then boundary layer separation takes place at station ‘S’ (shown in figure 1.5), well ahead of the compression corner, depending on the viscous interaction parameter. In such a case, the thick- ened separated boundary layer locally deflects the inviscid freestream over the boundary layer.
Deflection of inviscid flow forms an oblique shock wave known as the separation shock. Reat- tachment of the separated flow takes place at station ‘R’ downstream of the compression corner.
Introduction 7 Such reattachment raises pressure and local heat flux. The closed separated region with sub- sonic recirculation remains isolated from the approximately inviscid supersonic flow above it by a thin mixing layer, called as shear layer. The supersonic flow above the shear layer and below the separation shock gets deflected by the reattachment shock. Therefore prediction of various features of SWBLI becomes a challenging task in the presence of such a complicated flowfield.
1.4 Shock wave boundary layer interaction terminologies
The intensity of SWBLI and its dependence on various parameters can be well understood using different SWBLI features. These characteristic features of SWBLI are clearly shown in figure 1.6. Prior quantification of these SWBLI parameters is extremely necessary for the success- ful design of hypersonic systems involving shock wave boundary layer interactions. Therefore definitions of important SWBLI parameters are discussed here under.
1.4.1 Upstream influence
Presence of ramp can leads to considerable flow alterations, even without separation, in the re- gion, upstream of the interaction. Such upstream flow alteration is generally termed as upstream influence. In case of R-SWBLI, extent/length of upstream influence is defined as the distance from the ramp-foot to the most upstream location, which experiences the influence of ramp based disturbance. Higher the value of extent of upstream influence, higher is the intensity of SWBLI.
1.4.2 Separation bubble size
Separation bubble size is another important terminology. It needs consideration only when flow is separated due to R-SWBLI. However, separation depends on ramp angle, freestream con- ditions and wall specifications. Therefore separation bubble size is also function of these pa- rameters. Here, separation bubble size is defined as the linear or streamwise distance between the separation and reattachment points for the well separated flow. Higher value of separation bubble size indicates high intensity of shock-boundary layer interaction.
Literature review 8
1.4.3 Separation and Plateau pressure
Separation and plateau pressures are important SWBLI parameters, obtained from wall pressure distribution. As their names represent, these two are the pressure values corresponding to sepa- ration point and plateau region of a typical wall pressure distribution in the presence of SWBLI.
Here, plateau pressure is the nearly constant pressure in the separation zone. This pressure remains a clear indicator of separated flowfield.
1.4.4 Peak Stanton number
Peak Stanton number is the non-dimensional value of maximum heatflux on the ramp surface.
Here peak Stanton number is expressed as,
Stpeak = qmax
ρ∞U∞Cp∞(T0−Tw)
This parameter is important for R-SWBLI with separation. In such cases, the reattached bound- ary layer attains minimum thickness downstream of the reattachment point which leads to max- imum local surface heatflux. Beyond this location the Stanton number decreases due to further thickening of the boundary layer. Hence, this parameter helps to quantify the strength of the interaction.
1.5 Literature review
In the past, SWBLI has been investigated by several researchers owing to its growing signifi- cance. Research in this field has been started early in 1950. From this time, many investigations and parametric studies are reported for high speed laminar and turbulent flows. Some of these studies are related to understanding of the SWBLI and its dependence on various influencing parameters. Few researchers have also concentrated on development of correlations for predic- tion of characteristic features of interaction using freestream and geometry conditions. Some findings are related with the control of SWBLI. Experimental, computational and theoretical efforts in this field are summarised in following subsections.
The studies of Chapman et al. [4] can be considered as the oldest one among the available studies related to SWBLIs in high speed flows. Chapman et al. first proposed the free-interaction theory through experimental and theoretical studies. His free-interaction concept is worth noticeable due to its prime importance in explaining the basic physics of SWBLI. This theory has showed the independency of separation point pressure, plateau pressure and extent of first part of sepa- ration on downstream parameters. Subsequently Kuehn [5] continued the shock wave boundary layer interaction studies and focused on identification of incipient separation condition. Here, incipient separation condition was defined as a situation where some portion of the surface skin friction distribution becomes exactly zero. However by considering the difficulty involved in experimental measurement of skin friction distribution, Kuehn proposed an alternative method to predict incipient separation from surface pressure measurements. According to this revised proposition, incipient separation should coincide with the first appearance of three inflection points in the surface pressure distribution. Followed by Kuehn, Needham [6] proposed another methodology to estimate the incipient separation. This criterion was based on the heat transfer measurements, which identifies incipient separation from a rounded minimum heatflux near the interaction region. However both Kuehn’s and Needham’s methods were observed to be failing