[ { "id": "authors:640fg-thd43", "collection": "authors", "collection_id": "640fg-thd43", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20160108-110033407", "type": "monograph", "title": "Periodic Cavity Oscillations, Shear flow Instabilities and Nonequilibrium Turbulent Wakes", "author": [ { "family_name": "Behrens", "given_name": "Wilhelm", "clpid": "Behrens-W" }, { "family_name": "Sarohia", "given_name": "Virendra", "clpid": "Saohia-V" } ], "publisher": "Caltech Library", "publication_date": "1972-10-01" }, { "id": "authors:zcmv9-s6s08", "collection": "authors", "collection_id": "zcmv9-s6s08", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170731-130155026", "type": "article", "title": "Total temperature thermocouple probe based on recovery temperature of circular cylinder", "author": [ { "family_name": "Behrens", "given_name": "Wihelm", "clpid": "Behrens-W" } ], "abstract": "A total temperature probe based on the recovery temperature of a circular cylinder is described which combines the advantages of both hot wire and shielded thermocouple probe. It is mechanically very simple and durable and may be used in low and high speed flow, from continuum to the free molecule regime and is suitable for wake and boundary layer investigations with large total temperature gradients. As an example of the use of the probe, measurements of total temperature in the hypersonic near wake of a cold cylinder (77\u00b0K) are discussed.", "doi": "10.1016/0017-9310(71)90072-X", "issn": "0017-9310", "publisher": "Elsevier", "publication": "International Journal of Heat and Mass Transfer", "publication_date": "1971-10", "series_number": "10", "volume": "14", "issue": "10", "pages": "1621-1630" }, { "id": "authors:j04bk-3z022", "collection": "authors", "collection_id": "j04bk-3z022", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170731-140852664", "type": "article", "title": "Transition and Turbulence Phenomena in Supersonic Wakes of Wedges", "author": [ { "family_name": "Behrens", "given_name": "Wilhelm", "clpid": "Behrens-W" }, { "family_name": "Lewis", "given_name": "John E.", "clpid": "Lewis-J-E" }, { "family_name": "Webb", "given_name": "Wilmot H.", "clpid": "Webb-W-H" } ], "abstract": "At supersonic speeds the wake of a blunt body may be divided into an inner viscous wake stemming from the body boundary layers and an outer \"inviscid\" wake produced by the bow shock. In such wakes, as in the wake of a cylinder, at low Reynolds numbers the onset of transition occurs thousands of diameters downstream of the body in the outer, shock-induced wake. As the Reynolds number is increased, transition occurs in the inner wake. For the same Mach number and at high Reynolds numbers transition on the wake of a wedge occurs further downstream than in the case of a cylinder, but the slender body transition curve crosses the blunt body transition curve. The question arises, where does transition occur in slender body wakes as the Reynolds number is decreased further? What effect does the much weaker outer shock-induced wake have on transition and, is the outer wake unstable enough to become turbulent?", "doi": "10.2514/3.50011", "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "1971-10", "series_number": "10", "volume": "9", "issue": "10", "pages": "2083-2084" }, { "id": "authors:n9kq0-5wr07", "collection": "authors", "collection_id": "n9kq0-5wr07", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170731-132632622", "type": "article", "title": "Experimental Investigation of the Effects of Base Mass Addition on the Near Wake of a Slender Body", "author": [ { "family_name": "Lewis", "given_name": "John E.", "clpid": "Lewis-J-E" }, { "family_name": "Behrens", "given_name": "Wilhelm", "clpid": "Behrens-W" }, { "family_name": "Collins", "given_name": "Donald J.", "clpid": "Collins-D-J" } ], "abstract": "The near wake of a two-dimensional wedge was studied at Mach 4. Static pressure, Pitot pressure, total temperature, injectant concentration and hot-wire fluctuations were measured. Helium, argon, and SF_6 were injected into the base, and their diffusion in laminar and turbulent wakes was studied. The locations of the wake stagnation points as a function of injection rate, and the critical rates required to eliminate the recirculating flow were determined. It was found that the near-wake flow with injection does not scale with the mass flux, nor do the momentum or the volume fluxes serve to correlate the data over the entire range of injection. Fluctuation measurements show that SF_6 has a destabilizing effect on the wake, whereas helium has a stabilizing influence, compared to the wake without injection. Model cooling (T_w/T_0\u221e = 0.25) resulted in a forward shift of the rear stagnation point and a pronounced decrease in both the velocity defect and the wake width but had a lesser effect on the distribution of the injected species.", "doi": "10.2514/3.49953", "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "1971-08", "series_number": "8", "volume": "9", "issue": "8", "pages": "1506-1513" }, { "id": "authors:ahkx1-xgc75", "collection": "authors", "collection_id": "ahkx1-xgc75", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170801-083712062", "type": "book_section", "title": "An experimental study of hypersonic wakes behind wedges at angle of attack", "author": [ { "family_name": "Behrens", "given_name": "W.", "clpid": "Behrens-W" } ], "abstract": "Experimental measurements of mean flow properties of hypersonic wakes behind wedges of 20\u00b0 included angle were conducted for angles of attack up to 25\u00b0 at Mach number 6, with Reynolds number based on wedge base height ranging from 7,000 to 55,000. The near and far wake structures were determined, including streamlines and velocity profiles, over a down-stream distance of 60 base heights. The base pressure is insensitive to incidence within about 17\u00b0. At higher incidence, flow separation occurs on the leeward surface. The near wake flow field changes accordingly. The far viscous wake (x/H > 4) changes with increasing incidence because of the increasing differences of the inviscid flow quantities at the leeward and windward edges of the viscous wake. The wake static pressure, which increases with incidence, viscous wake edge velocities, edge Mach number, edge temperatures and flow inclination of the real flow (directed towards the leeward side) compare favorably with a simple inviscid shock expansion model. In the laminar wake flows the wake widths, minimum velocities, minimum Mach numbers and maximum temperatures change little with incidence. However, in the transitional wake flows, the \"break-away\" phenomenon is observed and transition from laminar to turbulent flow moves upstream as angle of attach increases.", "doi": "10.2514/6.1971-563", "publisher": "AIAA", "publication_date": "1971-06" }, { "id": "authors:vxa81-41g12", "collection": "authors", "collection_id": "vxa81-41g12", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170731-133752887", "type": "article", "title": "Experimental stability studies in wakes of two-dimensional slender bodies at hypersonic speeds", "author": [ { "family_name": "Behrens", "given_name": "W.", "clpid": "Behrens-W" }, { "family_name": "Ko", "given_name": "D. R. S.", "clpid": "Ko-D-R-S" } ], "abstract": "Experimental stability studies were conducted in the transition region from laminar to turbulent flow in wakes of slender wedges and a flat plate at Mach number 6. As in low-speed flat plate wakes, transition from laminar to turbulent flow may be divided into a linear and a nonlinear instability region. Inviscid linear stability theory predicts well the growth of fluctuations and amplitude distribution in the linear region. In the nonlinear region similarities with low-speed wakes exist. Characteristic persisting peaks in the power spectra are observed. Based on these peak frequencies a nearly universal Strouhal number of fb_0/u\u221e = 0.3 was found for both incompressible and hypersonic wake flows. A theoretical approach to predict the development of mean flow and flow fluctuations in the nonlinear region as employed by Ko, Kubota, and Lees in slender body low-speed wakes appears equally applicable for hypersonic wakes.", "doi": "10.2514/3.6285", "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "1971-05", "series_number": "5", "volume": "9", "issue": "5", "pages": "851-857" }, { "id": "authors:s7s5c-vvj29", "collection": "authors", "collection_id": "s7s5c-vvj29", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170731-145242715", "type": "book_section", "title": "Separation of a supersonic turbulent boundary layer by a forward facing step", "author": [ { "family_name": "Behrens", "given_name": "W.", "clpid": "Behrens-W" } ], "abstract": "The mean flow and fluctuations were measured in the undistributed turbulent boundary layer, the separated flow region and on top of the step. The freestream Mach number was 4.0 and the boundary layer Reynolds number based on momentum thickness was 4,100. The model was large enough to allow reversed flow profile measurements and to insure two-dimensionality of the separated flow. For an aspect ratio (span between fences/step height) of 9.4, the back flow profiles show three-dimensionality effects. The mean flowfield is described in detail. In the \"separation region\" large normal and axial pressure gradients exist. The angle of the inviscid flow after separation is 12 1/2\u00b0 In the nearly constant pressure separated flow region the forward velocity profiles up to 2H of the step are similar and nearly similar closer to the step. The entrainment rate of the forward flow \u03bb_e = \u03c1_0v_0/ \u03c1_eu_e = .010. Close correspondence of the forward flow with the turbulent boundary layer with injection at the same \u03bb_e was found. The reversed flow velocity reaches 0.37 u_e, close to the step (< 1H) and decays slowly to zero at separation (x/H = 4.25). The center of the recirculating vortex is closer to the step than 0.7H. On top of the step the mean turbulent boundary layer attains nearly similarity shape within one step height wheras the fluctuation distributions lag considerably. In the separated flow region most of the fluctuation energy is in random large scale low frequency fluctuations.", "doi": "10.2514/6.1971-127", "publisher": "AIAA", "publication_date": "1971-01" }, { "id": "authors:82m1a-zt078", "collection": "authors", "collection_id": "82m1a-zt078", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170807-141808618", "type": "article", "title": "Linear instability of far-wake flow", "author": [ { "family_name": "Behrens", "given_name": "Wilhelm", "clpid": "Behrens-W" }, { "family_name": "Kubota", "given_name": "Toshi", "clpid": "Kubota-Toshi" } ], "abstract": "Measurements of the mean wake flow behind circular cylinders at Mach 6, described in Ref. 1, showed that in a certain Reynolds number range (Re_d \u2243 300-4000) the inner wake stemming from the body boundary layers is laminar and loses its identity within 60 diam, and the outer wake, stemming from the bow shock, is also laminar within a certain downstream distance, and may be calculated from a laminar linear theory, but does not become similar (Gaussian) within 2400 diam. Experimental study of the stability of these wakes is presented in Ref. 2.", "doi": "10.2514/3.5868", "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "1970-06", "series_number": "6", "volume": "8", "issue": "6", "pages": "1178-1179" }, { "id": "authors:fk1td-tff45", "collection": "authors", "collection_id": "fk1td-tff45", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170807-153908350", "type": "book_section", "title": "Experimental investigation of the effects of base mass addition on the near wake of a slender body", "author": [ { "family_name": "Lewis", "given_name": "John E.", "clpid": "Lewis-J-E" }, { "family_name": "Behrens", "given_name": "Wilhelm", "clpid": "Behrens-W" }, { "family_name": "Collins", "given_name": "Donald J.", "clpid": "Collins-D-J" } ], "abstract": "The near wake of a two-dimensional wedge was studied at Mach 4. Static pressure, Pitot pressure, total temperature, injectant concentration and hot-wire fluctuations were measured. Helium, argon and SF_6 were injected into the base, and their diffusion in laminar and turbulent wakes was studies. The locations of the wake stagnation points as a function of injection rate, and the critical rates required to eliminate the recirculation flow were determined. It was found that the Tear-wake flow with injection does not scale with the mass flux, nor do the momentum or the volume fluxes serve to correlate the data over the entire range of injection. Fluctuation measurements show that SF_6 has a destabilizing effect on the wake, whereas helium has a stabilizing influence, compared to the wake without injection. Model cooling (T_W/T_0\u221e = 0.25) resulted in a forward shift of the rear stagnation point and a pronounced decrease in both the velocity defect and the wake width but had a lesser effect on the distribution of the injected species.", "doi": "10.2514/6.1970-110", "publisher": "AIAA", "publication_date": "1970-01" }, { "id": "authors:tvkpr-p0e56", "collection": "authors", "collection_id": "tvkpr-p0e56", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170731-130924236", "type": "article", "title": "Fluctuation measurements in the near wake of a wedge with and without base injection", "author": [ { "family_name": "Lewis", "given_name": "John E.", "clpid": "Lewis-J-E" }, { "family_name": "Behrens", "given_name": "Wilhelm", "clpid": "Behrens-W" } ], "abstract": "An experimental investigation of the turbulent and transitional near wake of an adiabatic, slender wedge with and without base injection was performed in the Jet Propulsion Laboratory (JPL) supersonic wind tunnel at Mach 4. Two different quantities were measured with a constant current hot-wire anemometer: the mean square fluctuation intensity [f = 0.1 to 80 KC (see Nomenclature)], and the frequency spectrum of the fluctuations (f = 5 to 200 KC, bandwidth \u0394f = 0.2 KC). The various flow regions of the near wake were identified and the growth and decay of flow fluctuations were determined. The flow fluctuations of the turbulent boundary-layer remnant were found to decay rapidly during the expansion, and the inner shear layers and the reverse flow region, which they bound, were shown to be laminar. Base injection was found to stabilize the near wake and to delay wake transition.", "doi": "10.2514/3.5184", "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "1969-04", "series_number": "4", "volume": "7", "issue": "4", "pages": "664-670" }, { "id": "authors:dx8sd-h5736", "collection": "authors", "collection_id": "dx8sd-h5736", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170731-154902517", "type": "article", "title": "Far wake behind cylinders at hypersonic speeds: II. Stability", "author": [ { "family_name": "Behrens", "given_name": "W.", "clpid": "Behrens-W" } ], "abstract": "At Reynolds numbers below 10^4 the inner viscous wake behind cylinders at Mach 6 is entirely laminar. At these low Reynolds numbers the outer wake caused by the bow shock becomes transitional thousands of diameters downstream. Flowfield measurements (Part I) indicated strong deviations from the behavior of laminar steady flow from a certain point on, suggesting a division into linear and nonlinear wake instability regions. Fluctuation measurements confirm this supposition at four Reynolds numbers. Wake instabilities were investigated experimentally up to a distance of 12,000 dimeters behind the cylinder in a Reynolds number range of 200 to 4,000. Additional measurements were performed in the regime where both inner and outer wake instabilities occur. In the linear region close correspondence with linear inviscid stability theory was found. The nonlinear instability region is a long stretched-out region in comparison with the wake at low speeds behind a flat plate. A further increase of the fundamentally instability component and a sudden growth of the first harmonic is observed. A tentative picture is given of the onset of nonlinearity and/or transition in the inner and outer wakes behind blunt bodies at hypersonic speeds.", "doi": "10.2514/3.4482", "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "1968-02", "series_number": "2", "volume": "6", "issue": "2", "pages": "225-232" }, { "id": "authors:tayhb-2fd86", "collection": "authors", "collection_id": "tayhb-2fd86", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170807-145720584", "type": "book_section", "title": "Fluctuation measurements in the near wake of a slender wedge at Mach 4.0 with and without base injection", "author": [ { "family_name": "Behrens", "given_name": "W.", "clpid": "Behrens-W" }, { "family_name": "Lewis", "given_name": "John E.", "clpid": "Lewis-J-E" } ], "abstract": "An experimental investigation of the turbulent and transitional near wake of an adiabatic, slender wedge with and without base injection was performed in the JPL Supersonic Wind Tunnel at Mach 4. Two different quantities were measured with a constant current hot wire anemometer, the mean square fluctuation intensity (f \u2013 0.1 to 80 KC), and the frequency spectrum of the fluctuations (f = 5 to 200 KC, bandwidth 0.2 KC). The various flow regions of the near wake were identified and the growth and decay of flow fluctuations were determined. Helium and nitrogen were used as injectants and similar effects were obtained when He = N2. The flow fluctuations of the turbulent boundary layer remnant rapidly decayed during the expansion, and the inner shear layers and the reverse flow region which they bound were laminar. Base injection was found to significantly alter the near wake instability mechanism, which resulted in the delay of wake transition.", "doi": "10.2514/6.1968-100", "publisher": "AIAA", "publication_date": "1968-01" }, { "id": "authors:1qary-3m188", "collection": "authors", "collection_id": "1qary-3m188", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170731-152129563", "type": "article", "title": "The far wake behind cylinders at hypersonic speeds. Part I: Flowfield", "author": [ { "family_name": "Behrens", "given_name": "W.", "clpid": "Behrens-W" } ], "abstract": "The flowfield in the wake of circular cylinders was studies experimentally at a Mach number of 6 to a distance of 2400 diam downstream. In the Reynolds number range considered (Re_d \u2248 300-4000), the inner wake stemming from the cylinder boundary layer is laminar and loses its identity within 60 diam, so that only the outer wake caused by the bow shock is of importance. The flowfield was defined experimentally by Pitot pressure, static pressure, and mean-flow hot-wire measurements. Experiments show that the outer wake can be considered inviscid in the first 100 diam but viscosity is essential thereafter. Within a certain region the experimental results compare well with laminar linear theory but the wake profiles do not become similar within 2400 diam. In one case (Re_d \u2248 960), rapid deviations from steady laminar behavior were observed beyond x/d = 1600, indicating breakdown of this flow because of strong nonlinear instabilities that increase \"the effective diffusivity.\" The stability problem of these wakes is considered in Pt. II of this study (to be published in AIAA Journal).", "doi": "10.2514/3.4398", "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "1967-12", "series_number": "12", "volume": "5", "issue": "12", "pages": "2135-2141" }, { "id": "authors:hpgrg-3pn34", "collection": "authors", "collection_id": "hpgrg-3pn34", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170807-144358436", "type": "article", "title": "Reply by Authors to A. Goldburg", "author": [ { "family_name": "Behrens", "given_name": "Wilhelm", "clpid": "Behrens-W" }, { "family_name": "Lees", "given_name": "Lester", "clpid": "Lees-L" } ], "abstract": "Goldburg has apparently misunderstood the significance of the local minimum critical Reynolds number (Re_f, d)min, er. When the effective turbulent diffusivity \u03b5_T is smaller than the kinematic viscosity, v_i, the work done by the Reynolds stresses is more than counterbalanced by the rate of viscous dissipation. Thus, turbulence in the wake cannot exist when (\u03b5_T/u_fd) < (v_f/u_jd), or when Re_f, d < (Re_f, d)min, er, any more than turbulent flow in a pipe can exist below a critical Reynolds number of 2000. If one chooses to call this \"quenching,\" that is a problem in semantics and not in fluid mechanics.", "doi": "10.2514/3.55155", "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "1965-05", "series_number": "5", "volume": "3", "issue": "5", "pages": "991-992" }, { "id": "authors:nvdpv-z0d17", "collection": "authors", "collection_id": "nvdpv-z0d17", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20170731-144425203", "type": "article", "title": "Viscous interaction effects on a static pressure probe at M = 6", "author": [ { "family_name": "Behrens", "given_name": "W.", "clpid": "Behrens-W" } ], "abstract": "The purpose of this investigation was to find the relation between measured static pressure and true static pressure as a function of the viscous interaction parameter \u03c7. The results obtained make possible accurate interpretation of measured static pressure data.", "doi": "10.2514/3.2193", "issn": "0001-1452", "publisher": "AIAA", "publication": "AIAA Journal", "publication_date": "1963-12", "series_number": "12", "volume": "1", "issue": "12", "pages": "2864-2866" } ]