Numerical imulation of supersonic-supersonic shear flow ... · vertically upward into the primary stream. The supersonic flow enters the flow domain from the upper and lower sides

15th International Conference on Fluid Control, Measurements and Visualization 27-30 May 2019, Naples, Italy

Paper ID:180 1

Numerical simulation of supersonic-supersonic shear flow mixing

enhancement based on transverse jet

Liu Yang1, *, Ma Dong1, Yu Xiao-jing2, Chai Ze-xin1

1 Science and Technology on Combustion, Internal Flow and Thermo-structure Laboratory, Northwestern Polytechnical University, Xi’an, CHINA

2 School of Power and Energy, Northwestern Polytechnical University, Xi’an, CHINA *corresponding author: [email protected]

Abstract: The Supersonic - Supersonic shear mixing flow is a typical type of turbulent flow. In the scramjet combustion chamber, the flow between the air flow and the fuel jet flow is a typical Supersonic - Supersonic shear mixing flow. Because of the highly compressible state of the supersonic flow, the mixing efficiency of the two supersonic flows is not high, which directly affects the combustion efficiency and the propulsion system performance. Adding a transverse jet to the supersonic flow, the secondary eject method, is a potential method of controlling flow that enhances the mixing of the supersonic-supersonic shear mixing flow. It is of great significance to study the flow development law and mixing effect of the supersonic-supersonic shear mixing flow enhanced by the secondary eject for revealing its working mechanism and establishing the active flow control method to improve its working performance. In this paper, air is injected into the upstream flow with the higher Mach number and the disturbance is introduced to accelerate the development of turbulence. Large eddy simulation (LES) of the supersonic-supersonic shear mixing flow enhanced by secondary gas ejection with different total temperature, pressure, jet Mach number and jet inlet size was performed to investigate the main flow characteristic, shear layer growth law and the influencing factors of the supersonic-supersonic shear layer mixing based on secondary injection method. A total of 9 sets of numerical simulation were carried out. The jet inlet pressure ranged from 80K to 300KPa, the total jet temperature range was 295-1000K, and the jet Mach number ranged from 0.2-2. The results showed that the introduction of transverse jet can effectively accelerate the turbulent transition and generating the large-scale quasi-ordered structures. The total temperature, pressure and jet Mach number of the transverse jet affected the development of the shear layer. Higher total temperature and pressure can enhance the development of the supersonic-supersonic shear layer. The higher Mach number of supersonic jet flow enhanced the development of the shear layer; however, the higher Mach number of subsonic jet flow suppressed the development of the shear layer. Keywords: Large eddy simulation, Supersonic -supersonic shear mixing flow, Transverse Jet

1 Introduction

The Supersonic - Supersonic shear mixing flow mixed flow refers to a turbulent flow phenomenon in which two different supersonic flows are flowed together in the same direction and mixed with each other. In a scramjet engine, this flow phenomenon is formed between the fuel and the air. Since the airflow has a large absolute speed, the mixing time of the fuel and the air is extremely short. Accelerating the mixing of such flow by intensive mixing methods is of great significance for improving the performance of the scramjet engine.

The principle of most intensive mixing technology is to generate vortices in different ways, increase the contact area between fuel and air and make the molecular diffusion more fully. At present, many flow mixing enhancement methods have been implemented in engineering, but most of the hybrid enhancement technologies are still mostly in the experimental stage. The current study of the Supersonic-Supersonic shear mixing layers is neither able to give a quantitative evaluation of the mixing efficiency nor accurately predict the response of the mixed layer to various disturbances or excitations. Therefore, it is necessary to study the mixing enhancement problem of the flow of the Supersonic-Supersonic shear mixing layers.

In this paper, secondary injection techniques are used to enhance flow mixing. In this paper, a secondary injection technique is used to enhance flow mixing. The entrainment of the secondary jet produces a vortex that dominates the downstream velocity field [1]. The addition of the secondary jet causes a bow shock to occur in one inflow, and a boundary layer separation in the upstream. The obstruction caused by the jet generates a bow shock in the freestream. Although the secondary jet technique promotes disturbances to enhance mixing, it also increases total pressure loss.

Up to now, the study of the influence of the crossflow on the supersonic flow field is as follows. Zukoski (1964) et al. [2] injected gas nitrogen, argon and helium vertically into the supersonic flow to obtain pressure field, concentration field and shock shape information around the secondary jet. Aso (1991) et al. [3] studied


Paper ID:180 2

the complex flow field caused by the secondary jet injected into the supersonic flow, and believed that the interaction between the bow shock and the turbulent boundary layer caused the boundary layer to separate. Later, You (2012) et al. [4] conducted a separation vortex simulation (DES) study of jets with low momentum flux ratios, providing a detailed view of the flow characteristics and finding the interaction between the unstable Kelvin-Helmholtz(K-H) instability and CVP deformation creating an Ω-shaped cortex. Lee (2006) et al. [5] proposed that The flow field of multi-port transverse injection into a supersonic crossflow is more complex than the single injection flow field, and this is due to the strong interactions among the injection flows, various shock wave structures and vertical flows around the injection flows. The numerical simulation method was used by Abdelhafez et al. [6] to compare the relative performance of oblique and transverse injection in a scramjet combustor. It was found that the oblique injection scheme gives higher mixing efficiency.

The purpose of this paper is to study the variation of the Supersonic - Supersonic shear layer strengthening effect with different secondary jet states, and provide an optimized design reference for ramjet systems.

2 Numerical Method

2.1 Physical model

Fig. 1 shows a schematic diagram of the calculation domain which has a streamwise direction of 300mm and a vertical direction of 40mm. The thin plate with a thickness of 0.5 mm divides the left side into two supersonic inlets of the same height. The jet hole on the plate is 10 mm from the inlet and the air is sprayed vertically upward into the primary stream. The supersonic flow enters the flow domain from the upper and lower sides with Ma 1.96 and Ma1.37, and the convection Mach number is 0.2. The specific parameters are shown in Table 1 below.

Fig. 1 Schematic diagram of the computational domain of a supersonic-sonic shear flow with a

transverse jet

Table 1 Supersonic flow parameter P, kPa Ttotal, K U, m/s Ma

Primary flow 46 295 515 1.96 Secondary flow 46 295 404 1.37

The mixing enhancement effect of the secondary jet with different properties on the supersonic-supersonic

mixing flow is studied by changing the total temperature (Tj*), pressure (Pj) and jet Mach number (Maj) of the secondary jet. The secondary jet with Tj*=295K, Pj= 80 kPa, Maj=1 and Lj=1 mm (Lj is the Jet inlet width) was used as a control group, and 9 calculations were performed. The secondary jet parameters of the specific working conditions are shown in table 2.

Table 2 The secondary jet parameters

case Tj*, K Maj Pj , KPa Uj , m.s-1

1 295 1 80 314.75 2 295 1 180 314.75 3 295 1 300 314.75 4 600 1 80 447.29 5 1000 1 80 579.5 6 295 1.5 80 428.74 7 295 2 80 512.22 8 295 0.6 80 200.06


Paper ID:180 3

9 295 0.4 80 155.99 At the free flow inlet, speed, total temperature and static pressure were determined. Random disturbances

were added at the entrance to simulate fully developed turbulence, which is used to shorten the length of the basin and save computing time. The boundary velocity, temperature, and pressure of the right, upper and lower sides of the computational domain were set to zero gradient boundary conditions for simulating the intensive mixing of the supersonic-supersonic shear flow in the open space. The intermediate plate was a wall boundary and was set to a no-slip condition.

2.2 Numerical procedure

The compressible N-S equations can describe the compressible turbulent flow process. The LES (Large

eddy simulation) control equations for compressible turbulent flow can be obtained by using Favre averaging and spatial filtering operations on the equations, as shown below:

!"#!$+ !("#'())

!+)= 0 (1)

.(/#0(1).2

+ .(/#0(10(3).43

= ..435−δ89 + τ;89 − τ<=<> (2)

!5"#?@>!$

+ !!+)

A�̅�ℎE𝑢;G + ℎGHIH + �̅�𝑢GK =

!!+)

A𝑞;M + �̃�MG𝑢;M + 𝜎GHIHK (3)

Where τ;89 = QA.0(1

.4R+ .0(3

.4RKS − T

Uδ89

.0(R

.4R and q;9 = k .X

@

4R.

The sub-lattice term can be expressed as:

𝜏HIH = −2𝜈MG𝑆\MG +]U𝛿MG𝜏__ (4)

Where "-" represents spatial filtering, "~" represents a parameter item larger than the filtering scale after

Favre averaging, and "sgs" represents a sub-grid model parameter item smaller than the filtering scale, 𝑢G is velocity, ρ is density, p is pressure, 𝑇MG represents the stress term, 𝛿MG represents the unit tensor function, and 𝜈$ is the sub-grid viscous term.

Both the Smagorinsky and dynamic Smagorinsky models can solve the shear layer reasonably [7]. The model in this study is Smagorinsky eddy model. The sub-grid scale viscosity can be written as:

𝜈$ = (𝐶HΔ)T52𝑆\MG𝑆\MG>

]/T (5) Where 𝐶H is the Smagorinsky constant. The numerical simulation uses the open source CFD calculation software OpenFOAM (Open Source Field

Operation and Manipulation) computing platform. It uses a finite volume method and has a superior design architecture, a rich physical model library and a numerical solver. The large eddy simulation uses the rhoCentralFoam compressible solver for numerical simulation. The solver is a Compressible Density Solver based on the Kurganov&Tadmor Center Upwind Scheme, which has good adaptability for compressible flow.

2.3 Validations of the numerical procedures

LiuYang et al. [8] used the same numerical calculation method to perform numerical verification on subsonic-supersonic shear mixing flow at normal temperature. The final numerical calculation results are in good agreement with the experimental results, which proved that the numerical calculation method based on OpenFOAM computing platform is suitable for numerical simulation of supersonic-supersonic shear mixing flow.

To determine the accuracy of the calculation program for the secondary jet simulation, the calculation of the secondary jet in the supersonic flow is compared with the experimental data of Aso et al. [3] under the same


Paper ID:180 4

conditions. As shown below, Fig. 2 (a) and (b) show the distribution of 𝑃e 𝑃f⁄ along the wall surface at different 𝑃h 𝑃i⁄ , respectively, Where 𝑃e 𝑃f⁄ is the ratio of the wall surface to the freesteam pressure, and 𝑃h 𝑃i⁄ is the ratio of the total pressure of the jet to the total pressure of the crossflow. 𝑃e is obtained along streamwise off-center line axis apart from the center line by 25 mm at both sides. It can be seen that the numerical calculation results are basically consistent with the experimental results.

(a)

(b) Fig. 2 Comparison of wall pressure distribution between experiment and numerical calculation

3 Results and discussion

3.1 Effect of the secondary jet pressure

Fig. 3 shows the temperature field distribution of different secondary jet pressures. It can be seen from the figure that as the jet pressure increases, the bow shock gradually increases, which causes the total pressure loss at the downstream to increase, but from the mixing effect, by increasing the jet pressure, the mixing effect of two supersonic flows have been greatly enhanced. The turbulent transitions in advance due to the greater disturbance caused by the larger jet pressure. At a jet pressure of 300 kPa, the vortex scale is largest and the most chaotic.

Fig. 3 Temperature distribution cloud map under different jet pressures

There are many ways to define the thickness of the shear layer. In this paper, the thickness of the shear layer

is defined by Vorticity thickness proposed by Brown and Roshko [9], which is defined as follows:

𝛿j =klmkn

|!k/!p|qrs (6)

Where 𝑈] − 𝑈T represents the speed difference between the two supersonic flows.

A certain number of observation positions are set along the streamwise, and the thickness of the shear layer at these positions is calculated. Fig. 4(a) shows the distribution of shear layer thickness along the streamwise for different secondary jet pressures, where the free flow inlet position is x=0 mm. The figure reveals that as


Paper ID:180 5

the jet pressure increases, the shear layer thickness increases, and the shear layer thickness growth rate also increases, indicating that the larger pressure jet promotes the development of the shear layer.

According to the study by Brown et al., the normalized shear layer thickness growth rate is used to characterize the relationship between shear layer development and convective Mach number. The normalized shear layer thickness growth rate is the normalized parameter of the incompressible shear layer thickness growth rate with the same density ratio and speed ratio, and the relative growth rate is obtained. The thickness growth rate for the incompressible shear layer can be determined by:

Auvu+KMwh

= 𝐶v(]mx)5]y√H>

]yx√H (7)

Where r is the ratio of the two gas flow velocities, s is the density ratio, and 𝐶v is a constant, which is related

to the inflow condition. Using Auvu+KMwh

as a characteristic parameter, the normalized shear layer thickness growth rate is obtained.

The shear layer thickness is linearly fitted in the flow direction, and the growth rate of the thickness of the shear layer and the growth rate of the thickness of the non-dimensional shear layer with the jet pressure are obtained, shown in Fig. 4(b). The thickness growth rate of the shear layer increases as the jet pressure increases, and the larger jet pressure favors the intensive mixing of the supersonic-supersonic shear layer.

(a)

(b)

Fig. 4 Mixing layer thickness along the streamwise direction. Mixed layer thickness growth rate under different jet pressures.

Total pressure loss (η) is an important indicator for measuring the effect of mixing enhancement. In Fig.

5(a), the distribution of total pressure loss along the flow direction can be divided into development stage and stable stage. The range of x=0~45mm is the development stage, and the rapid increase of total pressure loss is the characteristic of this stage, which is caused by many shock near the secondary jet. The increase in jet pressure causes the shock to become stronger and the total pressure loss to increase; After the development phase, the flow enters a stable phase, in which the flow is gradually stabilizing and will grow slowly in most cases. The small shock structure in the flow field is the main cause of the increase in total pressure loss during the stable phase. The average total pressure loss is defined as the average of the total pressure loss during the stabilization phase. Table. 3 gives the specific values for each average total pressure loss. Fig. 5 (b) shows that the average total pressure loss increases with increasing jet pressure, and a larger jet pressure results in greater energy loss.


Paper ID:180 6

(a)

(b)

Fig. 5 total pressure loss along the streamwise direction. average total pressure loss under different jet pressures.

Table 3 Average total pressure loss value Pj 80kPa 180kPa 300kPa

average total pressure loss 0.138 0.24 0.277 The turbulence intensity σ distributed in the y direction is obtained at x = 150 mm. σ/ΔU represents the

dimensionless turbulence intensity, and ΔU represents the difference between the velocity of the primary flow and the secondary flow. When the pressure of the secondary jet increases, the peak value of the turbulence intensity increases correspondingly in Fig. 6, which indicates that increasing the pressure of the secondary lateral jet is beneficial to increasing the mixing effect of the shear layer. The peak position of the turbulence intensity gradually shifts downward as the jet pressure increases. This demonstrates that an increase in jet pressure deflects the shear layer position toward the secondary flow.

Fig. 6 Transverse turbulence intensity along the transverse direction

3.2 Effect of the secondary jet total temperature

Fig. 7 shows the temperature distribution of different jet temperatures. With the increase of the total temperature of the secondary jet, the temperature of the shear layer increases, the scale of the quasi-ordered structures increases, the mixing area becomes thicker, and the mixing effect of the shear layer is significantly enhanced, however, the bow shock does not change much.


Paper ID:180 7

Fig. 7 Temperature distribution cloud map under different jet total temperature.

The development of the shear layer thickness in the streamwise of the different jet total temperature

conditions is shown in Fig. 8. As the total temperature of the jet increases, the thickness of the shear layer increases, and the growth rate of the shear layer becomes larger, indicating that the high temperature can promote the mixing of the super-super shear layer.

(a)

(b)

Fig. 8 Mixing layer thickness along the streamwise direction. Mixed layer thickness growth rate under different jet total temperature.

In Fig. 9, with the increase of the total temperature of the jet, the total pressure loss increases slightly.

Considering the change of the shape of the bow shock in Fig. 7, it can be further confirmed that the total pressure loss in the flow field is mostly caused by the bow shock. The average total pressure loss values of each case are shown in Table 4.

(a)

(b)

Fig. 9 total pressure loss along the streamwise direction. average total pressure loss under different jet total temperature.

Table 4.Average total pressure loss value Tj

* 295K 600K 1000K average total pressure loss 0.138 0.154 0.167

Fig. 10 shows the distribution of the dimensionless turbulence intensity along the Y direction at different jet

temperatures. As the total temperature of the jet increases, the peak of the dimensionless turbulence intensity increases. This will enable a faster development of the shear layer with higher total jet temperature conditions,


Paper ID:180 8

and promote the mixing of the shear layer finally.

Fig. 10 Transverse turbulence intensity along the transverse direction

3.3 Effect of jet Mach number

The temperature distribution for different jet Mach numbers has been given in Fig. 11. The larger jet Mach number increases the shock angle, which will increase the total pressure loss of the downstream flow field. This is because the increase of the Mach number directly increases the momentum flux of the secondary jet inlet, which increase barriers to incoming flow.

When the jet velocity is small, many small shock structures can be seen downstream. Comparing the cases where the jet Mach number is 0.4, 0.6 and 1, the increase of the jet velocity will lengthen the laminar flow region and delay the flow transition. This indicates that the increase in jet Mach number will inhibit the mixing of the shear layer when the jet Mach number is within a certain subsonic range. When the jet Mach number is supersonic, a higher jet velocity will accelerate the transition of the shear layer. It can be seen from the case, in which the jet Mach number is 2, the laminar flow region of the shear layer is very short, and the vortex structure is more irregular. Unlike the subsonic secondary jet, the jet Mach number of the supersonic secondary jet promotes the mixing of the shear layer.

Fig. 11 Temperature distribution cloud map under different jet Mach number.

As is shown in the Fig. 11, the growth rate of the supersonic-supersonic shear layer showed a trend of

decreasing first and then increasing. The shear layer thickness growth rate is the smallest when the jet Mach number is 1 in the five sets of conditions, which is consistent with the previous conclusion.


Paper ID:180 9

(a)

(b)

Fig. 12 Mixing layer thickness along the streamwise direction. Mixed layer thickness growth rate under different jet Mach number.

In terms of total pressure loss, when the jet Mach number is increased, the total pressure loss growth rate in

the development stage increases, and the total pressure loss in the steady phase also increases. Fig. 13 (b) reveals that there is a linear relationship between the mean total pressure loss and the jet Mach number. The average total pressure loss values are shown in Table 5.

Fig. 13 total pressure loss along the streamwise direction. average total pressure loss under different jet Mach number.

Table 5. Average total pressure loss value

Maj 0.4 0.6 1 1.5 2 average total pressure loss 0.079 0.1 0.138 0.2 0.237

The dimensionless turbulence intensity along the Y direction under different jet Mach numbers were

comparing in Fig. 14. Like the growth rate of the shear layer thickness, the peak of the dimensionless turbulence intensity first decreases and then increases, and the turbulence intensity has the smallest turbulence intensity peak when the jet Mach number is 1. This suggests that a smaller subsonic jet and a larger supersonic jet are beneficial for accelerating the development of turbulence and the mixing effect of the shear layer, which is consistent with previous conclusions.


Paper ID:180 10

Fig 14 Transverse turbulence intensity along the transverse direction

3.4 Vortex structure

According to the previous temperature cloud analysis results, the flow field has a quasi-order structure. However, the study of the quasi-order structure must consider its identification. The quasi-order structure in the flow field mostly appears in the form of vortex structure, so the quasi-order structure identification method is mostly based on vortex structure recognition. Hunt et al. [10] mathematically define the vortex as the region where the second invariant Q in the flow field is positive. This method will be used in this section to analyze the vortex structure. The Q criterion expression is as follows:

Q = ]T(‖𝑆T‖ − ‖ΩT‖) (8)

Fig. 15 is an iso-surface map of the Q criterion for Cases 1 to 5, which stained with the local Mach number.

By comparing Case1~3, increasing the jet pressure leads to a significant increase in vortex structure. The vortex structure in Case1 basically maintains two-dimensional flow characteristics, and only a few vortex structures begin to have a deformation trend. Since the initial mesh scale is smaller in the upstream part of the calculation domain, the displayed vortex structure will be finer, but the flow upstream is mainly laminar flow, so the vortex structure displayed is mainly in two-dimensional form. As the jet pressure increases, the downstream large-scale vortex flowing in Case2 has begun to break, and Λ vortex structure appears, which is similar to the two-dimensional quasi-order structure. The vortex structure began to appear at a very early position in Case3, but it is found that this vortex structure still has some order in the spanwise direction. After the vortex structure, the vortex structure begins to become more messy. A vortex structure shaped like a U-shape can be observed downstream of Case3, which is generally called the hairpin vortex. In Case1 and Case4~5, it can be seen that the vortex structure does not exhibit more shapes as the total temperature of the jet increases. However, the higher total temperature of the jet increases the number of vortices and the vortex structure is more broken.

(a)


Paper ID:180 11

(b)

(c)

(d)

(e) Fig 15 The Q criterion iso-surface with Ma staining: (a) Case1, (b) Case2, (c) Case3, (d) Case4, (e) Case5.

4. Summary

In this paper, the method of numerical calculation is used to study the mixing effect of supersonic-sonic shear flow by means of lateral jet gas. Firstly, a test is carried out in this paper, where the experimental results are compared with the numerical calculations to verify the feasibility of the current large eddy simulation to obtain the characteristics of the flow field. Then, 9 shear flow intensification hybrid calculations under different secondary jet conditions were calculated. The effects of secondary jet pressure, total temperature and jet Mach number were studied by analyzing the supersonic-supersonic shear layer temperature distribution, shear layer thickness, turbulence intensity and total pressure loss under various conditions. The results are as follows:

(1) The secondary jet pressure increases, the shear layer thickness growth rate and the shear layer turbulence intensity increase, which can enhance the mixing effect, but the total pressure loss also increases, which damages the performance of the scramjet engine.

(2) The effect of total jet temperature on shear layer thickness growth rate, turbulence intensity and total pressure loss is similar to jet pressure.

(3) When the jet Mach number increases, the total pressure loss increases, the shear layer thickness growth rate and the turbulence intensity decreased initially, followed by an increase, and When the jet Mach number reaches 1, their values are the smallest;


Paper ID:180 12

References

[1] Zukoski, E. E., and Spaid, F. W., “Secondary Injection of Gases into a Supersonic Flow.” AIAA Journal, Vol. 2, No. 10, 1964, pp. 1689-1696.

[2] E. E. Zukoski and F. W. Spaid, “Secondary Injection of Gases into a Supersonic Flow,” AIAA J., Vol.2, 1964, pp.1689-1696.

[3] Aso S, Okuyama S, Kawai M, Ando Y, Experimental study on mixing phenomena in supersonic flows with slot injection. In: 29th Aerospace Sciences Meeting, Reno, Nevada 1991. AIAA Paper 91-0016.

[4] You, Y.C., Ludeke, H., Hannemann, K., 2012. On the flow physics of a low momentum flux ratio jet in a supersonic turbulent crossflow. 97:24001.

[5] Lee, S.H., 2006a. Characteristics of dual transverse injection in scramjet combustor, Part 1: Mixing. Journal of Propulsion and Power, 22(5):1012-1019.

[6] Abdelhafez, A., Gupta, A.K., Balar, R., Yu, K.H., 2007. Evaluation of Oblique and Traverse Fuel Injection in a Supersonic Combustor. AIAA Paper 2007-5026.

[7] Le Ribault, C., “Large Eddy simulation of passive scalar in compressible mixing layers,” International Journal of Heat and Mass Transfer, 2008. 51(13-14): p. 3514-3524.

[8] Zhang Chenxi, LiuYang, Yu Xiao-jing. Mixing enhancement using secondary gas ejection method in supersonic-subsonic shear layer. AIAA Paper 2017-2421.

[9] Brown G L, Roshko A. On density effects and large structure in turbulent mixing layers [J]. J. Fluid Mech., 1974, 64: 775-816.

[10] Hunt J C R, Wray A A, & Moin P. Eddies, streams, and convergence zones in turbulent flows [C]. Studying Turbulence Using Numerical Simulation Databases, 2, 1988.

Documents

Numerical imulation of supersonic-supersonic shear flow ... · vertically upward into the primary stream. The supersonic flow enters the flow domain from the upper and lower sides