Detached eddy simulation of compressible flow with rapid expanded divergent contour

Detached eddy simulation of compressible flow with rapid expanded divergent contour

Khaled Bensayah El-Ahcene Mahfoudi 

CORIA UMR 6614 CNRS, Rouen, 76000, France

Corresponding Author Email: 
bensayahkha@yahoo.fr
Page: 
359-366
|
DOI: 
https://doi.org/10.18280/ijht.360148
Received: 
11 July 2017
| |
Accepted: 
2 January 2018
| | Citation

OPEN ACCESS

Abstract: 

Due to the large number of correlations and relationships between variables and the physical phenomena involved, compressible flow simulations become very difficult or impossible if all the necessary scales and mechanisms are included and solved. Several research efforts have been made toward a more accurate flow field predictions and the current study aims to add to that knowledge base by exploring the capability of Delayed Detached Eddy Simulation employing the SST turbulence model to simulate the transonic region of over-expanded nozzle with small radius of curvature. An analysis was made of the transonic flow in axisymmetric nozzle, the paper shows the potential for using DES turbulence model to identify important internal radial flow downstream the throat region, where most RANS models fail to predict with high accuracy and in detail the structure of the flow. With small radius of curvature, the sonic line begins upstream of the throat and ends downstream due to turning flow near the wall transonic region. Comparison of the computational results with experimental data and some developed prediction methods are presented and good agreements are obtained.

Keywords: 

compressible flow, detached eddy simulation, SST model, nozzle, over-expanded, Shock

1. Introduction
2. Turbulence Models and Numerical Code
3. Results and Discussion
4. Conclusions
Acknowledgement
Nomenclature
  References

[1] Yuan H, He Y. (2009). Transonic potential flows in a convergent divergent approximate nozzle. J. Math. Anal. Appl 353(2): 614-626. https://doi.org/10.1016/j.jmaa.2008.12.005

[2] Theodore von Karman. (1947). The similarity law of transonic flow. J. Math. And Phys 26: 182-190. https://doi.org/10.1002/sapm1947261182

[3] Kuz’min AG. (2002). Boundary Value Problems for Transonic Flow. John Wiley & sons, West Sussex, 2002. 

[4] Leith VSFO, Soviero PAO, Bastos-Netto D. (2005). Numerical evaluation of the flow inside the transonic nozzle of a direct-connect supersonic combustion re-search facility. 18th ICME, Nov. 6-11, Ouro Oreto, MG, Proceedings of COBEM. mtc-m16b.sid.inpe.br

[5] Wenxiang C. (2009). Applying numerical solution to analyze the performance of nozzles. ICEET’2009, 16-18 Oct. https://doi.org/10.1109/ICEET.2009.515

[6] Sauer R. (1947). General characteristics of the flow through nozzles at near critical speeds. NACA-TM-1147.

[7] Oswatitsch K, Rothstein W. (1949). Flow pattern in a converging-diverging nozzle. NACA-TM-1215.

[8] Hall IM. (1962). Transonic flow in two-dimensional and axially-symmetric nozzles. Quarterly Journal of Me-chanics and Applied Mathematics 15(4): 487-508. https://doi.org/10.1093/qjmam/15.4.487

[9] Thompson PA. (1972). Compressible Fluid Dynamics. McGraw-Hill Inc, US.

[10] Zucrow MJ, Hoffman JD. (1976). Gas Dynamics. Vol. I, John Wiley and Sons, New York. 

[11] Lalmi D, Hadef R. (2017). Numerical study of the swirl direction effect at the turbulent diffusion flame char-acteristics, International Journal of Heat and Technol-ogy 35(1): 520-528. https://doi.org/10.18280/ijht.350308.

[12] Wilcox DC. (1988). Reassessment of the scale-determining equation for advanced turbulence models. AIAA Journal 26(11): 1299-1310. https://doi.org/10.2514/3.10041 

[13] Cui WZ, Zhang XT, Li ZX, Li H, Liu Y. (2017). Three-dimensional numerical simulation of flow around combined pier based on detached eddy simulation at high Reynolds numbers, International Journal of Heat and Technology 35(1): 91-96. https://doi.org/10.18280/ijht.350112. 

[14] Suzen YB, Hoffmann KA. (1998). Investigation of supersonic jet exhaust flow by one- and two-equation turbulence models. 36th AIAA Aerospace Sciences Meeting and Exhibit. https://doi.org/10.2514/6.1998-322

[15] Silton SI. (2005). Navier–Stokes computation for a spinning projectile from subsonic to supersonic. Journal of Spacecraft and Rockets, March 42(2): pp. 223-231.  https://doi.org/10.2514/1.4175

[16] Menter FR, Kuntz M. (2003). A zonal SST-DES formulation. In: DES-Workshop. Technical University, St. Petersburg.

[17] Xiao ZX, Chen HX, Zhang YF, Huang JB, Fu S. (2006). Study of delayed-detached eddy simulation with weakly nonlinear turbulence model. Journal of Aircraft, September 43(5): pp. 1377-1385. https://doi.org/10.2514/1.20127.

[18] Fu S, Xiao ZX, Chen HX, Zhang YF, Huang JB. (2007). Simulation of wing-body junction flows with hybrid RANS/LES methods. Int. J. Heat Fluid Flow 28(6): 1379–1390. https://doi.org/10.1016/j.ijheatfluidflow.2007.05.007

[19] Spalart P, Jou WH, Strelets M, Allmaras SR. (1997). Comments on the feasibility of les for wings and on a hybrid RANS/LES approach. Proceedings of the 1st AFSOR International Conference on DNS/LES, edited by C. Liu and Z. Liu, Greyden, Columbus, OH, 1998: 137–147.

[20] Strelets M. (2001). Detached eddy simulation of mas-sively separated flows. 39th Aerospace Sciences Meet-ing and Exhibit. https://doi.org/10.2514/6.2001-879   

[21] Squires KD, Forsythe JR, Morton SA, Strang WZ, Wurtzler KE, Tomaro RF, Grismer MJ, Spalart PR. (2002). Progress on detached-eddy simulation of mas-sively separated flows. 40th AIAA Aerospace Sciences Meeting & Exhibit. https://doi.org/10.2514/6.2002-1021

[22] Forsythe JR, Squires KD, Wurtzler KE, Spalart PR. (2002). Detached-eddy simulation of fighter aircraft at high alpha. 40th AIAA Aerospace Sciences Meeting & Exhibit. https://doi.org/10.2514/6.2002-591

[23] Deck S, Garnier E, Guillen P. (2002) Turbulence model-ling applied to space launcher configurations. Journal of Turbulence 3(3): 1–21. https://doi.org/10.1088/1468-5248/3/1/057

[24] Back LH, Massier PF, Gier HL. (1965). Comparison of measured and predicted flows through conical super-sonic nozzles, with emphasis on the transonic region. AIAA Journal 3(9): 1606-1614. https://doi.org/10.2514/3.3216

[25] Back LH, Massier PF, Cuffel RF. (1967). Flow phe-nomena and convective heat transfer in a conical su-personic nozzle. Journal of Spacecraft and Rockets 4(8): 1040-1047. https://doi.org/10.2514/3.29015

[26] Back LH, Cuffel RF. (1966). Detection of oblique shocks in a conical nozzle with a circular-arc throat. AIAA Journal 4(12): 2219-2221. https://doi.org/10.2514/3.3881

[27] Cuffel RF, Back LH, Massier PF. (1968). Transonic flow field in a supersonic nozzle with small throat radius of curvature. AIAA paper 7(7):1364-1366. https://doi.org/10.2514/3.5349

[28] Kliegel JR, Levine JN. (1969). Transonic flow in small throat radius of curvature nozzles. AIAA Journal 7(7): 1375-1378. https://doi.org/10.2514/3.5355

[29] Hopkins DF, Hill DE. (1966). Effect of small radius of curvature on transonic flow in axisymmetric nozzles. AIAA Journal 4(8): 1337-1343. https://doi.org/10.2514/3.3674

[30] Friedrichs KO. (1944). Theoretical studies on the flow through nozzles and related problems. Rept. 82.1R, AMG-NYU 43, 1944, New York Univ.

[31] Shelton SV. (1967). Work done at the Jet Propulsion Laboratory, Pasadena, California, Unpublished report.

[32] Crocco L. (1965). A suggestion for the numerical solu-tion of the steady Navier-Stokes equations. AIAA Journal 3(10): 1824-1832. https://doi.org/10.2514/3.3266

[33] Prozan RJ. (1968). Private communication, Lockheed Missiles and Space Co, Huntsville, Alabama.

[34] Saunders LM. (1966). Numerical solution of the flow field in the throat region of a nozzle. BSVD-P-66-TN-001 (NASA CR 82601), Brown Engi-neering Co, Huntsville, Alabama.