Method for solving the equations describing the interaction of a three-dimensional boundary layer with an outer inviscid flow

G. L. Korolev

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 3, pp. 506-529

Résumé

A new method is developed for solving the three-dimensional time-independent equations describing the interaction of a laminar boundary layer with an outer inviscid flow. The method also applies to the interaction of plane flows. By applying the method, the problem of the three-dimensional viscous supersonic gas flow over a roughness element (a hump and a cavity) is solved for the first time within the framework of the classical triple-deck theory. The asymptotic height of the roughness element corresponding to the nonseparated flow is determined, and separated flow patterns are constructed.

Bibliographie

[1] Neiland V. Ya., “K teorii otryva laminarnogo pogranichnogo sloya v sverkhzvukovom potoke”, Izv. AN SSSR. Mekhan. zhidkosti i gaza, 1969, no. 4, 53–57 | Zbl

[2] Stewartson K., Williams P. G., “Self-induced separation”, Proc. Roy. Soc. London. Ser. A, 312:1509 (1969), 181–206 | DOI | Zbl

[3] Sychev V. V., Ruban A. I., Sychev Vik. V., Korolev G. L., Asimptoticheskaya teoriya otryvnykh techenii, Nauka, M., 1987

[4] Neiland V. Ya., Bogolepov V. V., Dudin G. N., Lipatov I. I., Asimptoticheskaya teoriya sverkhzvukovykh techenii vyazkogo gaza, Fizmatlit, M., 2004

[5] Bodonyi R. J., Kluwick A., “Transonic trailing-edge flow”, Quart. J. Mech. and Appl. Math., 51 (1998), 297–310 | DOI | MR | Zbl

[6] Bogdanov A. N., Diesperov V. N., Zhuk V. I. i dr., Asimptoticheskie modeli vyazkikh transzvukovykh techenii, Ann. dokl. Vses. s'ezda po teor. i prikl. mekhan. 23–29 avgusta. Perm, 2003, 106–107 pp.

[7] Diesperov V. N., Korolev G. L., “Vozniknovenie sverkhzvukovykh zon i zon lokalnogo otryva pri transzvukovom statsionarnom obtekanii nerovnosti poverkhnosti v rezhime svobodnogo vzaimodeistviya”, Izv. RAN. Mekhan. zhidkosti i gaza, 2003, no. 1, 50–59 | Zbl

[8] Ryzhov O. S., “O nestatsionarnom prostranstvennom pogranichnom sloe, svobodno vzaimodeistvuyuschem s vneshnim potokom”, Prikl. matem. i mekhan., 44:6 (1980), 1035–1052 | MR | Zbl

[9] Smith F. T., “On the high Reynolds number theory of laminar flows”, IMA J. Appl. Math., 28:3 (1982), 207–281 | DOI | MR | Zbl

[10] Duck P. W., Burgraf O. R., “Spectral solutions for the three-dimensional triple-deck flow over surface topography”, J. Fluid Mech., 162 (1986), 1–22 | DOI | MR | Zbl

[11] Lyzhin V. D., Dudin G. H., “Ob odnom metode rascheta rezhima silnogo vyazkogo vzaimodeistviya na treugolnom kryle”, Izv. AN SSSR. Mekhan. zhidkosti i gaza, 1983, no. 4, 119–124 | Zbl

[12] Lipatov I. I., Vinogradov I. V., “Three-dimensional flow near surface distortions for the compensation regime”, Philos. Trans. Roy. Soc. London. Ser. A, 358:777 (2000), 3143–3153 | DOI | MR | Zbl

[13] Zhuk V. I., Volny Tollmina–Shlikhtinga i solitony, Nauka, M., 2001

[14] Smith F. T., “A three-dimensional boundary layer separation”, J. Fluid Mech., 99 (1991), 185–201 | DOI | MR

[15] Delery J. M., Farmery M. J., A finite difference method for inverse solutions of 3-d turbulent boundary-layer flow, AIAA 83-0301. AIAA 21-st Aerospace Science Meeting. Jan. 10–13, Reno, Nevada, 1983 | Zbl

[16] Bodonyi R. J., Duck P. W., “A numerical method for treating strongly interactive three-dimensional viscous-inviscid flows”, Internat. J. Comput. Fluids, 16:3 (1988), 279–290 | DOI | Zbl

[17] Karas O. V., Kovalev B. E., “Primenenie obratnogo metoda rascheta trekhmernogo pogranichnogo sloya k zadache obtekaniya kryla s uchetom vliyaniya vyazkosti”, Uch. zap. TsAGI, 20:5 (1989), 1–11

[18] Timoshin S. N., Smith F. T., “Singularities encountered in three-dimensional boundary layers under adverse or favourable pressure gradient”, Philos. Trans. Roy. Soc. London. Ser. A, 352:1698 (1995), 45–87 | DOI | MR | Zbl

[19] Smith F. T., Sykes R. I., Brighton P. W. M., “A two-dimensional boundary layer encountering a three-dimensional hump”, J. Fluid Mech., 83:1 (1977), 163–176 | DOI | Zbl

[20] Bogolepov V. V., “Issledovanie malykh prostranstvennykh vozmuschenii laminarnogo pogranichnogo sloya”, Prikl. mekhan. i tekhn. fiz., 1987, no. 5, 69–79 | MR

[21] Krasilschikova E. A., Krylo konechnogo razmakha v szhimaemom potoke, Gostekhteorizdat, M., L., 1952

[22] Bodonyi R. J., Kluwick A., “Supercritical transonic trailing-edge flow”, Quart. J. Mech. and Appl. Math., 35:2 (1982), 265–277 | DOI | MR | Zbl

[23] Sychev V. V., Ruban A. I., “Giperzvukovoe vyazkoe techenie gaza okolo kryla malogo udlineniya”, Uch. zap. TsAGI, 5:5 (1973), 42–51

[24] Smith F. T., “Steady and unsteady 3-D interactive boundary layers”, Comput. and Fluids, 20:3 (1991), 243–268 | DOI | Zbl

[25] Sychev Vik. V., “O prostranstvennykh techeniyakh okolo nerovnostei na poverkhnosti osesimmetrichnogo tela”, Uch. zap. TsAGI, 24:1 (1993), 12–28 | MR

[26] Zhuk V. I., Ryzhov O. S., “O lokalno-nevyazkikh vozmuscheniyakh v pogranichnom sloe s samoindutsirovannym davleniem”, Dokl. AN SSSR, 263:1 (1982), 56–59 | MR | Zbl

[27] Korolev G. L., “Ob odnom metode resheniya zadach asimptoticheskoi teorii vzaimodeistviya pogranichnogo sloya s vneshnim potokom”, Zh. vychisl. matem. i matem. fiz., 27:8 (1987), 1224–1232