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Abstract
This paper presents our recent work on investigating velocity slip boundary conditions’ effects on supersonic flat plate boundary layer flow stability. The velocity-slip boundary conditions are adopted and the flow properties are obtained by solving boundary layer equations. Stability analysis of two such boundary layer flows is performed by using the Linear stability theory. A global method is first utilized to obtain approximate discrete mode values. A local method is then utilized to refine these mode values. All the modes in these two scenarios have been tracked upstream-wisely towards the leading edge and also downstream-wisely. The mode values for the no-slip flows agree well with the corresponding past results in the literature. For flows with slip boundary conditions, a stable and an unstable modes are detected. Mode tracking work is performed and the results illustrate that the resonance phenomenon between the stable and unstable modes is delayed with slip boundary conditions. The enforcement of the slip boundary conditions also shortens the unstable mode region. As to the conventional second mode, flows with slip boundary conditions can be more stable streamwisely when compared with the results for corresponding nonslip flows.
Highlights
Boundary layer (B.L.) flow transitions are important in many engineering fields
Slip boundary condition (B.C.) effects on flow stability have received much attention with new developments and applications in: (1) Micro-Electro-Mechanical System (MEMS) [5,6]; (2) slip flows in porous medium [7,8]; and (3) high speed flights with low air density [9,10]
The numbers and types of identified modes in general agree with the corresponding past results (Figure 6 in [20])
Summary
Boundary layer (B.L.) flow transitions are important in many engineering fields. One example is the prediction of drag and heat transfer rates in the aircraft preliminary design stages [1]. The thickness of a thermal protection layer over a hypersonic re-entry spacecraft is estimated with the surface heat transfer rate which can be several times larger in the turbulent B.L. than a laminar one [2,3,4]. Slip flow models can predict more accurate none-equilibrium regions near interfaces [11]. A more accurate laminar to turbulent transition prediction with considerations of slip B.C.s is desired
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