Research Article
Investigation of ShockBoundary Layer Interaction in a Ramp Flow with MVG Under Different Turbulent Inflows
Yonghua Yan^{2}, Caixia Chen^{1}*, Fan Yang^{3} and Herious A Cotton^{2}
^{1}Tougaloo College, USA
^{2}Jackson State University, USA
^{3}Department of Mechanical Engineering, Omdurman Islamic University, Sudan
Caixia Chen, Tougaloo College, 500 West County Line Road, Tougaloo, MS, 39174, USA.
Received Date: September 05, 2018; Published Date: September 25, 2018
Abstract
MVG (micro vortex generator) is a potentially new device which can alleviate or overcome the adverse effects of SBLI (Shockboundary layer interaction) and improve the “health” of the boundary layer. In this paper, the SBLI in a ramp flow with MVG under different inflow conditions is investigated by LES (large eddy simulation). Three turbulent inflows with different boundary layer thickness are generated based on turbulent profiles obtained from DNS (Direct numerical simulation) of transition. The numerical results show that the interaction between ringlike vortices generated by MVG and the ramp shock is influenced by these different inflow conditions. With lower boundary layer thickness, the ringlike vortices are less distorted and thus more stronger when they travel to the ramp corner. The more regular and stronger ringlike vortices have more capability to eliminate or distort the strong ramp shock wave. Moreover, it confirms that ringlike vortices generated by MVG, and not the lower turbulent boundary layer, is dominant in flow separation reduction.
Keywords: LES, MVG, Flow control, Turbulence, SBLI
Abbreviations: MVG: Micro Vortex Generator; SBLI: ShockBoundary Layer Interaction; DNS: Direct Numerical Simulation; M: Mach Number; Re: Reynolds Number Based on Momentum Thickness; H: Micro Ramp Height; : Incompressible BoundaryLayer Nominal Thickness; X, Y, Z: Spanwise, Normal and Streamwise Coordinate Axes; u, v, w: Spanwise, Normal and Streamwise Velocity
Introduction
Shockboundary layer interactions (SBLI) in highspeed flows can significantly reduce the quality of the flow field by inducing large flow separation, causing flow unsteadiness and total pressure loss. The performance and the overall propulsive efficiency of the engine of a highspeed vehicle will be degraded [13].
MVG is a potentially new device which can alleviate or overcome the adverse effects of SBLI and, therefore, to improve the “health” of the boundary layer [49]. The height of MVGs are usually less than the boundary layer thickness (2090% of the boundary layer thickness). The small size of the MVGs allows them to be embedded inside the boundary layer, hence reducing the parasitic drag relative to the conventional full size vortex generator. The improved physical understanding of how MVGs reduce shockinduced boundary layer separation will add significantly to the understanding of SBLI that dominate highspeed aerodynamics. In addition, optimized MVG configurations that destabilize the wake and improve the “health” of the boundary layer more efficiently should be studied [1012].
In previous work [1315], we performed numerical simulations of supersonic ramp flow with MVG control at M=2.5 and Re=5760 to understand the flow structures, especially the 3D vortex structures, behind the MVG. The flow field around the MVG and surrounding areas have been studied in detail. According to the analysis, a dynamic vortex model was provided. The results of our LES also showed that there exist a series of ringlike (or Ω shaped) vortices [13,14,16] which are formed behind MVG and then travel downstream. Furthermore, it is pointed out that the shock waves at the ramp corner are weaken substantially under the interaction of boundary layer contains ringlike vortices at the upper bound [17].
To confirm that the series of ringlike vortices generated by MVG is the major mechanism of flow separation reduction at the ramp corner, the influence on SBLI under turbulent inflows with different boundary layer thickness (or different relative heights between the MVG and the inlet turbulent boundary layer) are studied. The rest of the paper is organized as follows: In Sec.2, the numerical methods we used are briefly introduced. In Sec. 3, the flow structures especially the ringlike vortices are introduced. The influence on the ringlike vortical structure with different inlet flows are discussed; in Sec. 4. The special SBLI between the ringlike vortices and ramp shock wave under different inlet flows are studied; in Sec. 5. A summary of the present study is provided.
Numerical Methods, Grids and Turbulent Inflows
To reveal the mechanism and get deep understanding of the mechanism of MVG, high order DNS/LES is necessary. Our LES solved the unfiltered form of the NavierStokes equations with the 5th order bandwidthoptimized WENO scheme at M=2.5 and Re=5760.
The governing equations are the nondimensional Navier Stokes equations in conservative form as follows:
where
in which p denotes the pressure, e is the inner energy and T represents the temperature. The dynamic viscosity is given by Sutherland’s equation [19].
Nondimensional variables are defined as follows:
where the variables with ‘∼’ are the dimensional counterparts.
Since the domain is not regular, the NavierStokes equations in curvilinear coordinate system are actually solved. Considering the following grid transformation,
the NavierStokes equations can be transformed in generalized coordinates
where and
etc., are grid metrics , etc.
The domain of the fluid flow with the MVG is illustrated in Figure 1. The grid numbers for the whole system is 137(spanwise) × 192(normal) × 1600(streamwise). Parallel computing is used for this 3D LES [20]. Detail configurations of MVG and the grids can be found in [13].
The adiabatic, zerogradient of pressure and nonslipping conditions are adopted at the wall. To avoid possible wave reflection, the nonreflecting boundary conditions are used on the upper boundary. The boundary conditions at the front and back boundary surfaces in the spanwise direction are treated as the periodic condition. The outflow boundary conditions are specified as a kind of characteristicbased condition, which can handle the outgoing flow without reflection.
To generate the true turbulent inlet, turbulent profiles are obtained from previous DNS simulation and used as the time dependent inflow [21]. After a short range of development, the inflows generated in the upstream of the MVG are fully developed turbulent flows.
The parallel computation is accomplished through the Message Passing Interface (MPI) together with domain decomposition in the streamwise direction (Figure 2).
RingLike Vortices Generated by MVG
In the downstream, there exists a chain of ringlike vortices behind the trailingedge of MVG. The mechanism of these ringlike vortices was investigated both numerically and analytically [14,15]. The boundary layer shed from the MVG causes momentum deficit. The momentum deficit forms a cylindrical highshear (HS) layer behind the MVG. The HS layer has inflection surfaces which cause KelvinHelmholtz (KH) like instability which generates the ringlike vortices [15]. The existence of the ringlike vortices was verified by Lu’s and Sun’s experiments [13] recently.
In this work, three simulations are conducted with the different turbulent inflows described above. The boundary layer thicknesses of the inflows obtained in this study are given in Table 1. The shape factors of the boundary layers in front of MVG are 1.33, 1.42, 1.46 respectively, which indicate that the inflows evolve to fully developed turbulent flows. The vortex structures around the MVG in all the three cases are given in Figure 3. Ringlike vortical structure is observed in all cases.
Table 1: flow parameters of the three inlet flows (h is the height of MVG).
To visualize the vortex structures in the field, the λ_{2} method [22,23] is used to capture the isosurfaces of vortices. In this method, λ_{2} is the second eigenvalue of the 3 × 3 matrix comprised of velocity gradient, i.e.,
where the 3 × 3 tensors
Once the ringlike vortices are generated, they will be continuously distorted and enlarged due to complicated interaction within the boundary layer. Although the difference among the turbulent inflows does not give different mechanisms on the generation of the ringlike vortices [16], the ringlike vortex structures are significantly influenced when they travel to the ramp corner. Figure 3 shows the ringlike vortex structures at the ramp’s corner in the three cases. It shows that the ringlike vortices line up regularly when the boundary layer thickness of inflow is smaller. With smaller inflow boundary layer thickness, there is less distortion applied on the vortex structure so that the ringlike vortices are relatively regular.
Figure 4 also shows that the ringlike vortices are much stronger when they travel to the ramp corner where involves the interaction with the ramp shock. It is normal since less interaction with the lower boundary layer has made the ringlike vortices in case 3 less distorted and remain more stronger. In [12] we already showed that when strong ringlike vortex penetrate the shock wave, the shock wave will be cut off at the location where it meets the ringlike vortex. Although the heights of the ringlike vortices in the three cases are almost the same at the ramp corner, the more regular and stronger ringlike vortices have more ability to reduce the ramp shock.
Analysis on SBLI
When the ringlike vortices travel downstream, they will eventually interact with the ramp shock wave. The influence of interaction on ringlike vortices and ramp shock wave were investigated carefully. In the three cases, the ringlike vortical structures are quite robust. They never break down during the interaction. Moreover, they are influenced marginally by the strong shock wave. The interaction is a smooth process to the ringlike vortex structure which is generated by MVG.
However, the 3D ramp shock wave in every case is blurred at the ramp corner substantially. During the interaction with ringlike vortices, the ramp shock wave is badly distorted. In Figure 5, we can see that the quantity of the shock wave is reduced substantially at the region where the interaction happens. The upper part of the shock wave keeps well in the shape. However, the bottom part suffers severe interaction. With the existence of ringlike vortices at upper boundary layer, the separation is reduced due to the interaction.
The different turbulent inflows with different boundary layer thickness do bring difference on the interaction between the ringlike vortices and the ramp shock. With lower inflow boundary layer thickness (or relative higher MVG), the ramp shock wave is more reduced by the ringlike vortices. In Figure 6, the time averaged spanwise vorticity distributions and the contour of pressure gradient on the central spanwise plane(x=0) from all the 3 cases are given. The ramp shock wave can be captured by those contour lines of pressure gradient. It can be found that in case 3, the shock wave is almost eliminated at the corner. As a result, there will be less resistance to the separation induced by the ramp shock and the separation zone at the ramp’s corner in case 3 is reduced the most.
Figure 7 gives the isosurface of pressure at p=2.2 from the time averaged data of the cases. In Figure 6a, it shows clearly that the ramp’s shock wave is badly distorted and reduced where the interaction with ringlike vortices happens. Furthermore, when the boundary layer thickness of the inflow is lower, the ramp shock wave is more distorted and weakened.
For comparison, time averaged spanwise vorticity distributions and contour of pressure gradient on the streamwise plane beside the ringlike vortices (see Figure 8, the plane in green) of case 1 and case 3 are given in Figure 9. On this streamwise plane, without the interaction between ringlike vortices and shock wave, the shock wave in case 3 is less distorted and the separation zone becomes larger than that in case 1. It’s normal for the larger separation zone in case 3 on that plane since the inlet turbulence intensity is lower. However, it strongly emphasized the role of ringlike vortices on the flow separation reduction in the MVG controlled supersonic ramp flow. With lower inflow boundary layer thickness, the ringlike vortices will be less distorted and thus become stronger when they travel to the ramp corner. The stronger and more regular ringlike vortices have more potential to eliminate the ramp shock wave and reduce the corresponding flow separation induced by the shock wave.
Conclusion
LES (large eddy simulation) is conducted on the MVG controlled supersonic ramp flow under the influence of different inflow conditions. Three turbulent inflows with different boundary layer thickness are generated in front of the MVG. The different inflow conditions do not influence the mechanism of the generation of vortical structures in downstream of MVG but have significant influences on the topology and intensity of the ringlike vortical structure generated by MVG. More important, it is found that the interaction between ringlike vortices and the shock wave at the ramp corner which controls the boundary layer separation is also influenced. With lower boundary layer, the ringlike vortices are less distorted and remain stronger when they propagate to the ramp shock wave. The stronger ringlike vortices thus have more capability to eliminate or distort the strong ramp shock wave. Accordingly, the induced separation zone is more reduced.
Acknowledgement
This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI1548562.
Conflict of Interests
The authors declare that they have no conflict of interest.
References
 in JC (2002) Review of Research on LowProfile Vortex Generators to Control BoundaryLayer Separation. Progress in Aerospace Sciences 38(45): 389420.
 Ashill PR, Fulker JL, Hackett KC (2005) A Review of Recent Developments in Flow Control. The Aeronautical Journal 109(1095): 205232.
 Dussauge JP, Dupont P, Debieve JF (2006) Unsteadiness in Shock Wave Boundary Layer Interaction with Separation. Aerospace Science and Technology 10(2): 8591.
 Estruch Samper D, Vanstone L, Hillier R, Ganapathisubramani B (2015) Micro vortex generator control of axisymmetric highspeed laminar boundary layer separation. Shock Waves 25(5): 521533.
 Babinsky H, Li Y, Ford CWP (2009) Microramp Control of Supersonic Oblique ShockWave/BoundaryLayer Interactions. AIAA J 47(3): 668 675.
 Zhang B, Zhao Q, Xiang X, Xu J (2015) An improved microvortex generator in supersonic flows. Aerospace Science and Technology 47: 210–215.
 Saad MR, Zare Behtash H, Che Idris A, Kontis K (2012) MicroRamps for Hypersonic Flow Control. Micromachines 3(2): 364378.
 Jeong J, Hussain F (2006) On the identification of a vortex. Journal of Fluid Mechanics 285: 6994.
 Tufo HM, Fischer PF, Papka ME, Blom K (1999) Numerical simulation and immersive visualization of hairpin vortices. (Argonne National Lab, IL (US).
 Li Q, liu C (2010) in 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. Aerospace Sciences Meetings (American Institute of Aeronautics and Astronautics).
 Heinbockel JH (1996) Introduction to Tensor Calculus and Continuum Mechanics.
 Luo H, Bewley TR (2004) On the contravariant form of the Navier–Stokes equations in timedependent curvilinear coordinate systems. Journal of Computational Physics 199: 355375.
 Yonghua Yan, Qin li, Chaoqun Liu, Adam Pierce, Frank Lu (2012) Numerical Discovery and Experimental Confirmation of Vortex Ring Generation by Microramp Vortex Generator. Applied Mathematical Modelling 36(11): 5700–5708.
 Yan Y, Liu C (2013) Study on the Initial Evolution of Ringlike Vortices Generated by MVG. CEAS Aeronautical Journal 4(4): 433442.
 Yan Y, Liu C (2013) Shear Layer Stability Analysis in Boundary Layer Transition and MVG controlled Ramp Flow. AIAA paper, pp. 112.
 Yan Y, Liu C (2014) Study on the Ringlike Vortical Structure in MVG Controlled Supersonic Ramp Flow with Different Inflow Conditions. Aerospace Science and Technology 35: 106115.
 Yonghua Yan, Caixia Chen, Ping Lu, Chaoqun Liu (2013) Study on Shock WaveVortex Ring Interaction by the Micro Vortex Generator Controlled Ramp Flow with Turbulent Inflow. Aerospace Science and Technology 30(1): 226–231.
 Weirs VG, Candler GV (1997) Optimization of weighted ENO schemes for DNS of compressible turbulence. AIAA Paper, pp. 528538.
 Sutherland W (1893) LII. The viscosity of gases and molecular force. The London, Edinburgh, and Dublin Philosophical Magazin and Journal of Science 36(223): 507531.
 John Towns, Timothy Cockerill, Maytal Dhana, Ian Foster, Kelly Gaither et al. (2014) XSEDE: Accelerating Scientific Discovery. Computing in Science & Engineering 16(5): 6274.
 Yonghua Yan, Jie Tang, Chaoqun Liu, Fan Yang (2016) DNS Study on the Formation of Lambda Rotational Core and the Role of TS Wave in Boundary Layer Transition. Journal of Turbulence 17(6): 572601.
 Guarini SE, Moser RD, Shariff K, Wray A (2000) Direct numerical simulation of a supersonic turbulent boundary layer at Mach 2.5. Journal of Fluid Mechanics 414(1): 133.
 Yinlin Dong, Yonghua Yan, Chaoqun Liu (2016) New visualization method for vortex structure in turbulence by lambda2 and vortex filaments. Applied Mathematical Modelling 40(1): 500–509.

Yonghua Yan, Caixia Chen, Fan Yang, Herious A Cotton. Investigation of ShockBoundary Layer Interaction in a Ramp Flow with MVG Under Different Turbulent Inflows. Glob J Eng Sci. 1(2): 2018. GJES.MS.ID.000506.

ShockBoundary Layer Interaction, Ramp Flow, MVG, Turbulent Inflows, LES, Flow control, Turbulence, SBLI, DNS, Mach Number, Reynolds Number, Micro Ramp Height, Incompressible BoundaryLayer Nominal Thickness, Spanwise, Normal and Streamwise Coordinate Axes, Spanwise, Normal and Streamwise Velocity, Numerical Methods, Grids, Vortex

This work is licensed under a Creative Commons AttributionNonCommercial 4.0 International License.