Owe Eld Research Articles

Simulations of Normal Shock-Wave/Boundary-Layer Interaction Control Using Mesoflaps

Computations were performed to investigate the e owe elds of normal shock-wave/boundary-layer interactions with mesoe ap control. The passive control (no feedback included) concept involves placing a mesoe ap streamwise array beneath the interaction and allowing high-pressure air from the e ow downstream of the shock wave to recirculate through a cavity into the low-pressuree ow upstream of the wave. The case of a normal shock at a Mach number of 1.4 interacting with the turbulentboundary layer on a e at wall was e rst considered, and thepredictions yielded reasonable comparison with experimental results. A number of e xed-dee ection mesoe ap simulations were then performed to understand the correlations between e ap dee ections, downstream boundary-layer characteristics, andstagnation pressurerecovery.Theprescribedsteady-statedee ectionswerebased on qualitativeaeroelastic experimental observations. It was found that the magnitude of the dee ection of the upstream mesoe aps is key to providing a signie cantly increased “ lambda-foot” benee t, which is critical for improved stagnation pressure recovery. The number of e aps and their locations were also found to affect the stagnation pressure recovery and downstream boundary-layer characteristics signie cantly. However, it was found that cavity depth does not play a signie cant role in stagnation pressure recovery.

Dynamics and Control of an Isolated Jet in Crossflow

Experimental results from a systematic exploration of the dynamics and control of large-scale, organized structures in an isolated, circular jet issuing into a uniform crosse ow with a jet-to-crosse ow velocity (or blowing) ratio of 6 are presented. Surveys of the unsteady e owe eld were conducted using a single sensor hot-e lm probe, and the instantaneous and time-averaged scalar e elds were explored using Mie scattering-based e ow visualization. A spinning mechanical valve was used to modulate the jet e ow with a single frequency. The forced e ow response illustrates the e ow receptivity to high frequencies near the jet exit (associated with the jet instabilities) and to low frequencies farther downstream (where the counter-rotating vortex pair dynamics are dominant). Open-loop forcing in a jet Strouhal number around SrD =0.1 was recognized and demonstrated to be effective in organizing unsteadiness and enhancing mixing and entrainment in the e owe eld. Measurements of the time-averaged velocity and scalare eldsareusedtodemonstrateincreasedmassentrainmentandmixingasaresultoftheunsteady forcing.

Influence of Orifice Orientation on a Synthetic Jet-Boundary-Layer Interaction

Themeanstreamwisevelocitye elddownstreamofasyntheticjetembeddedin aturbulentboundarylayer( Reµ = 830) was investigated experimentally. Of particular interest was the change in the mean e owe eld resulting from changes in the yaw orientation of the rectangular synthetic jet orie ce. Three yaw angles ( ¯ = 0, 10, 20 deg) were considered.Time-averagedandphase-averagedhot-wiremeasurementswereobtainedattwopositionsdownstream of the synthetic jet actuator. The measurements show that when the orie ce is aligned with the mean freestream velocity (¯ = 0 deg), a e ow structure consistent with a weak counter-rotating vortex pair was observed in the boundary layer. For ¯ = 10 deg, the mean streamwise velocity contours suggest the presence of a single vortex in the boundary layer, whereas for ¯ = 20 deg, the e ow structure resembles a horseshoe vortex formed as a result of e ow blockage by the jet.

Flow Visualization of Numerically Simulated Blast Waves Discharging from Open-Ended Duct

In this study a high-resolution Euler solver is used to investigate the e owe elds of different-intensity planar blast waves discharging from an open-ended duct. Acoustic waves and a vortex pair generated by blast/vortex interactions near the 90-deg sharp corner of the duct at different blast Mach numbers are studied in detail by using computational shadowgraghs, computational schlieren pictures, and computational interferograms. It is found that the schlieren technique provides a better method for the study of acoustic waves than the other two techniques. The number of sounds generated by blast/vortex interaction as well as its nature is dependent on the strength of the blast wave. Moreover, the mechanism of vorticity generation induced by blast-wave diffraction is explored. It is found that the compressibility term, the vorticity scaled down by the e uid dilatation, is more dominant than the baroclinic term in the vorticity transport equation during the second shock/vortex interaction. The compressibility term is mainly contributed by the rollup of the slipstream, but not by the e uid dilatation. The induced vortex pair caused by blast-wave diffraction rotates cyclically after the second shock/vortex interaction. The circulation (or strength) of the two vortices increases to a maximum value when the second shock begins to interact with the major vortex, and it decreases to a constant value when the second shock has moved far downstream.

Analysis of Flow Conditions in Freejet Experiments for Studying Airfoil Self-Noise

A new set of mean wall pressure data has been collected on a controlled diffusion airfoil at a chord Reynolds number of 1.2 £ £105 in a freejet anechoic wind tunnel. Comparisons of the experimental data with Reynoldsaveraged Navier‐ Stokes (RANS) simulationsin freeairshow signie cant e owe eld and pressure loading differences, indicatingsubstantialjetinterferenceeffects.Toanalyzetheseeffects,asystematicRANS-basedcomputationale uid dynamicsstudyoftheexperimentale owconditionshasbeencarriedout,whichquantie esthestrongine uenceofthe e nite jet (nozzle) width on the aerodynamic loading and e ow characteristics. When the jet width is not sufe ciently large compared to the frontal wetted area of the airfoil, the airfoil pressure distribution is found to be closer to the distribution on a cascade than that of an isolated proe le. The airfoil lift is signie cantly reduced. Accounting for the actual wind-tunnel setup recovers the wall pressure distribution on the airfoil without further empirical angle-of-attack corrections. These jet interference effects could be responsible for the discrepancies among some earlier experimental and computational studies of airfoil self-noise. They should be accounted for in future noise computations to ensure that the experimental e ow conditions are simulated accurately.

Verification and Validation for Laminar Hypersonic Flowfields, Part 2: Validation

A validation methodology is applied to the laminar Mach 8 e ow over a spherically blunted cone. Validation of the overall computational model is performed via surface pressure comparisons with experimental data. Careful attention is paid to the submodels in the computational simulations and the assumptions in the experimental data analysis. The computational submodels for molecular viscosity and thermal conductivity are validated by comparisons to experimental data, whereasthevibrational nonequilibrium submodel is validated by comparing to published results using the vibrational master equation. The thermodynamic state of the hypersonic wind-tunnel nozzleisexamined,and argumentsaremadeforthepresenceofasignie cantamountofvibrationalnonequilibrium in thetunnel. Afterextensiveinvestigation, a 1.4% errorwasdiscovered in thefreestream static pressure originally reported in the experiment. Accounting for this error, along with the experimental uncertainty and estimated numerical error, agreement was found for surface pressure within 1.5%. The remaining errors are likely due to e owe eld nonuniformities in the tunnel, which are estimated using tunnel pitot calibration data and the method of characteristics.

Adaptive Harmonic Balance Solutions to Euler's Equation

A new adaptive harmonic balance method is presented and applied to a variety of subsonic and supersonic onedimensional e owe elds containing strong moving shocks. The adaptive method augments the frequency content in each cell as required to capture the local e ow physics. Augmentation automatically adjusts with grid density, resulting in lower frequency content on coarse grids that cannot adequately resolve high-frequency terms. A study of the effect of augmentation thresholds, increments, and scheduling on the performance and accuracy of the adaptive method is presented, and optimal parameters identie ed. When optimal parameters are used, the new adaptive harmonic balancemethod produces solutions equivalent to a nonadapted harmonic balance solution, but with up to a 50% reduction in run time.

Rotor-Wake Modeling for Simulation of Helicopter Flight Mechanics in Autorotation

Rotorcrafte ightmechanicssimulationstypicallyusee nite-stateinducedvelocitymodelstomimictheeffectofthe rotorwakeon bladeloads. However, with recent developmentsin computational methods coupled e ight mechanics and comprehensive rotor-wake analyses have become more tractable. This paper compares results from a e nitestate induced velocity model with a vorticity transport wakemodel that computes thee owe eld in a domain around the aircraft. The study focuses on e ight mechanics in autorotation. Simple parameter estimation using three- and e ve-state induced velocity model structures facilitates interpretation of the vorticity transport induced velocity e eld as well as providing a direct comparison with the e nite-state model. Comparisons of performance, trim, and control response indicate that there is little difference between the two models where the autorotative descent is shallow. However, as airspeed reduces the descent angle steepens, and clear discrepancies become apparent. These are directly related to a single parameter in the e nite-state model. It is concluded that e nite-state models are adequate for much of the autorotation regime, but for low speeds in steep descents the improved resolution of the rotor ine ow provided by more comprehensive rotor-wake models might be essential.

Control of Supersonic Impinging Jet Flows Using Supersonic Microjets

Supersonic impinging jets, such as those occurring in the next generation of short takeoff and vertical landing aircraft, generate a highly oscillatory e ow with very high unsteady loads on the nearby aircraft structures and the landing surfaces. These high-pressure and acoustic loads are also accompanied by a dramatic loss in lift during hover.Previousstudies of supersonic impinging jets suggestthatthehighly unsteady behavioroftheimpinging jets is due to a feedback loop between the e uid and acoustic e elds, which leads to these adverse effects. A unique active control technique was attempted with the aim of disrupting the feedback loop, diminishing the e ow unsteadiness, and ultimatelyreducing theadverseeffectsofthise ow.Flowcontrolwasimplementedbyplacingacirculararray of 400-πm-diamsupersonicmicrojetsaroundtheperipheryofthemainjet.Thiscontrolapproachwasverysuccessful in disrupting the feedback loop in that the activation of the microjets led to dramatic reductions in the lift loss (40%), unsteady pressure loads (11 dB), and near-e eld noise (8 dB). This relatively simple and highly effective control technique makes it a suitable candidate for implementation in practical aircraft systems. NUNDERSTANDINGoftheimpingingjete owe eld isnecessary for the design of efe cient short takeoff and vertical landing (STOVL) aircraft. When such STOVL aircraft are operating in hovermode,thatis,in closeproximityto theground,thedownwardpointing lift jets produce high-speed, hot e ow that impinges on the landing surface and generates the direct lift force. It is well known that in this cone guration several e ow-induced effects can emerge, which substantially diminish the performance of the aircraft. In particular, a signie cant lift loss can be induced due to e ow entrainment bytheliftingjetsfromtheambientenvironmentinthe vicinityofthe airframe. Other adverse phenomena include severe ground erosion on the landing surface and hot gas ingestion into the engine inlets. In addition, the impinging e owe eld usually generates signie cantly highernoiselevelsrelativetothatofafreejetoperatingundersimilar conditions. Increased overall sound pressure levels (OASPL) associated with the high-speed impinging jets can pose an environment pollution problem and adversely affect the integrity of structural elements in the vicinity of the nozzle exhaust due to acoustic loading. Moreover, the noise and the highly unsteady pressure e eld are frequently dominated by high-amplitude discrete tones, which may match the resonant frequencies of the aircraft panels, thus further exacerbating the sonic fatigue problem. These problems become more pronounced when the impinging jets are supersonic, the operating regime of the STOVL version of the future joint strike e ghter. In addition, the presence of multiple impinging jets can potentially further aggravate these effects due to the strong coupling between the jets and the emergence of an upward-moving fountain e ow e owing opposite to the lift jets. 1 A

Shock/Vortex Interactions Induced by Blast Waves

The problem of blast-wave propagation in an open-ended duct with a 90-deg sharp convex (expansion) corner is numerically investigated by the use of a high-resolution Euler solver. The complicated e owe elds induced by the blast-wave diffraction around the corner and by a secondary shock/vortex interaction are explored. Both a two-dimensional case and an axisymmetric case are considered. It is found that two vortices near the corner in the two-dimensionalcase(ortwo ring vorticesin theaxisymmetriccase) areinduced by theblast-wavediffraction.One vortexisstrongerandislocatedfartherdownstream thantheother.Thesetwovorticesrotatein oppositedirections. In the axisymmetric e ow, the major ring vortex is located farther downstream than that for the corresponding two-dimensional case, resulting in a lower pressure at the vortex centers. This is due to the relieving effect that is represented by an extra nonvanishing term in the vorticity transport equation in the axisymmetric case. The trajectories of the major planar vortex or ring vortex induced by different blast intensities are explored. Basically, the planar major vortex (or the major ring vortex in the axisymmetric case) moves downstream before a critical time and then turns toward the duct centerline after the critical time. The critical time roughly corresponds to the formation of a minor vortex.

Hydroxyl Formation Mechanisms and Models in High-Altitude Hypersonic Flows

The formation of vibrationally hot OH isexamined for a raree ed e ow about a sphere at 80 and 100 km using the direct simulation Monte Carlo method. Four main processes are considered leading to OH production in the e ow, which include water dissociation, exchange reaction between water and atomic oxygen, and exchange reactions between hydrogen (H and H 2) and oxygen (O 2 and O). The principal mechanism of OH production at 100 km is shown to be the H+O 2 !OH+O reaction, with the maximum OH temperature greater than 5000 K. Water dissociation is found to be the most important source of OH at 80 km, with the maximum vibrational temperature of approximately 2500 K. The molecular dynamics results incorporated into the direct simulation Monte Carlo method areused to simulate waterdissociation by N 2 and arecompared to theresultsobtained by theconventional total collision energy model. The OH spatial distribution along the stagnation line predicted by the molecular dynamics approach is signie cantly different than that obtained with the total collisional energy model. I. Introduction T HE modeling of ultraviolet emissions from hypersonic bow shocks provides an indication of the e owe eld gas properties and compliments the usual hypersonic e ight surface diagnostics of temperature and pressure. Moreover, the prediction of ultraviolet radiation from hypersonic vehicles is an important engineering application relevant to the prediction of passive optical signatures. Despite the strong operational and scientie c reasons for measuring opticalemissionsfromhypersonicvehicles,suchdataarerare.Spectral radiation from high-energy raree ed e ows provides a sensitive metric for the evaluation of energy exchange and chemical reaction models. The bow shock ultraviolet e ight experiments 1 (BSUV) obtained spectra of OH( A 2 6 C i X 2 5) UV radiation between altitudes of 100 and 80 km. These experiments indicate that the OH( A) species formed in raree ed, high-energy e ows have internal energies much greater than that of the bulk e ow. Because there are so few collisions in these e ows, the spectral data may be used to test the ability of theory to model near-nascent distributions of chemically produced radiating species and energy exchange. The UV spectra of OH(A) are well dee ned and originate from a single excited electronic state. Under raree ed conditions, the OH( A) UV spectra are sensitive to the chemical processes involved in OH formation. UV radiation from the OH ( A) system has been studied extensively in the combustion and atmospheric sciences communities. 2 Earlier work 3 demonstrated thesensitivity oftheOHspectrato variationinthevibrationaltemperature.Itwasshownthattheratioofthe peakheightsat2800 ƒ

Navier-Stokes and Direct Simulation Monte Carlo Predictions for Laminar Hypersonic Separation

Axisymmetric direct simulation Monte Carlo (DSMC) and Navier‐Stokes simulations are performed as part of a code validation effort for hypersonice ows. The e owe eld examined herein is the Mach 11 laminar e ow over a 25 ‐ 55-deg blunted biconic. Experimental data are available for surface pressure and heat e ux at a Knudsen number Kn=0.019 based on the nose radius. Simulations at a reduced freestream density (Kn=0.057) are performed to explore the region of viability of the numerical methods for hypersonic separated e ows. A detailed and careful effort is made to address the numerical accuracy of these simulations, including iterative and grid convergence studiesforNavier ‐Stokesandtemporal,grid,andparticleconvergencestudiesforDSMC.Goodagreementisfound between the DSMC and Navier ‐Stokes simulation approaches for surface properties as well as velocity proe les within the recirculation zone for the reduced density case. The results obtained indicate that the failure of earlier DSMC simulations at Kn=0.019 is due to insufe cient grid ree nement within the recirculation zone. Furthermore, it is shown that accurate simulations of the biconic at the experimental conditions with the DSMC method are not yet possible due to the extreme computational cost. Nomenclature d = molecular diameter, m f = general solution variable Kn = Knudsen number based on nose radius, ¸=RN L = characteristic length scale, m n = number density, particles/m 3 p = pressure, N/m 2 , order of accuracy q = heat e ux, W/m 2

Thrust Generation Caused by Flapping Airfoils in a Biplane Configuration

Unsteady, viscous e ows over e apping airfoils in a biplane cone guration are computed on moving overset grids. The overset grid solutions are obtained in parallel in a distributed memory environment. Unsteady e owe elds are described by particle traces. Time-averaged thrust values are obtained from the integration of the unsteady drag coefe cient. It isshown thatairfoilsin abiplanecone guration andoscillatingina combinedpitchand plungemotion with a proper phase shift between them produce 20 ‐40% more thrust than a single e apping airfoil. Turbulence in the e ow further augments the thrust generation. For a maximum thrust at a given e apping frequency, an optimization of the e apping motion parameters is needed.

Prediction of Lobed Mixer Vortical Structures with a k - e Turbulence Model

Numerical simulations of an incompressible planar shear layer and a lobed mixer e owe eld are presented and validated against the detailed experimental measurements of McCormick and Bennett (McCormick, D. C., and Bennett, J. C., Jr., “ Vortical and Turbulent Structure of a Lobed Mixer Free Shear Layer,” AIAA Journal, Vol. 32, No. 9, 1994, pp. 1852 ‐1859). The study focused on quantifying the predictability of these e ows using the standard k‐≤ turbulence model. Simulations for the planar shear layer showed that, whereas the self-similar behavior can be captured by the model, the measured near-e eld development of the shear layer could not be reproduced in the simulations. Inconsistencies between simulations and experiments arise as a result of the Kelvin ‐Helmholtz instability that is not captured in the simulations. Predictions for the lobed mixer shear layer revealed a lag of 1 :75 lobe heights in the shear-layer development with respect to the measured data. Global parameters such as momentum thickness and streamwise circulation generally showed an underprediction of 20% and an overprediction of 65% with respect to measured values, respectively. Good prediction of the primary Reynolds shear stresses that control the variation of the momentum thickness was obtained. An analysis for the equation of the streamwise component ofvorticity revealedthattheimportantcontribution tothestreamwisecirculation decay rateisthesecondary shear stress and the normal stress anisotropy. Neither is well predicted by the k‐≤ model, leading to poorer predictions of the streamwise circulation decay rate.

Application of Proper Orthogonal Decomposition to a Supersonic Axisymmetric Jet

Results are presented from the application of the snapshot proper orthogonal decomposition (POD) method to a spatiotemporal e owe eld generated from large eddy simulations (LES) of a Mach 1.4 ideally expanded jet. This is part of ongoing research in the development and use of the POD method in conjunction with advanced laser-based optical measurementsin high-speed e ows.ThePOD application goal istwofold: to extract dynamically signie cant information on the large-scale coherent structures in a high-speed jet and to facilitate low-dimensional modeling of the jet. It was found that the spatial eigenmodes obtained using weakly correlated snapshots, but spanning tens of convective timescale and uncorrelated snapshots, are similar. It was also found that a shortduration temporally resolved LES data (simulating data obtainable from pulse burst laser-based measurements ) could be used to calculate the time evolution coefe cients of the eigenmodes. The use of a few modes (namely, 12) was sufe cient for a reasonable reconstruction of the spatiotemporal e owe eld. The use of POD with a vector norm instead of a scalar norm did reduce the energy captured in the e rst few modes and also changed their rank order, but did not substantially alter the reconstructed e ow. In the early jet development region, the e rst and dominant mode was found to be axisymmetric, followed by either another axisymmetric or asymmetric (probably helical ) mode, whereas higher modes in this region and all ofthemodes fartherdownstream weremorecomplex and threedimensional. The POD modes and their temporal coefe cients obtained at various streamwise locations suggest that the large-scale jet structures undergo a process of disorganization near the end of potential core, followed by reorganization farther downstream.

Two-Dimensional Model for Simulating Shock-Wave Interaction with Rigid Porous Materials

A two-dimensional numerical model for predicting the characteristics of the e owe eld during an unsteady interaction between a shock wave moving through air and a rigid saturated porous matrix is developed. The numerical modelincludesa Lagrangianschemecombined with aremeshand an interfacetrackingtechnique.Thepredictions of the numerical simulations are compared with the predictions of a two-dimensional analytical model for regular ree ection from a rigid porous surface in pseudosteady e ow. The numerical and the physical model are also validated by comparing the one- and two-dimensional predictions of the model with experimental results. In general the predictions of the numerical simulations reveal very good to excellent agreement with both the experimental results and the predictions of the analytical model. Nomenclature C® = specie c heat capacities ratio for the ® phase c® = shape factor for the ® phase

Aeroelasticity of Composite Aerovehicle Wings in Supersonic Flows

A comprehensive aeroelastic model developed toward investigating the static divergence, e utter, and dynamic aeroelastic response of composite aerovehicle wings to sharp-edged gust and blast loads in supersonic e owe eld is presented. The aerovehicle wings are modeled as an anisotropic composite thin-walled beam structure featuring circumferentially asymmetric stiffness lay up that generates preferred elastic couplings. A number of nonclassical effects, such as transverse shear, warping restraint, and three-dimensional strain effects, are incorporated in the structural model. Based on the concept of two-dimensional indicial functions considered in conjunction with the aerodynamicstriptheoryextendedtothree-dimensionalwingmodel,theunsteadyaerodynamicloadsinsupersonic e ows are derived. The effect of elastic tailoring and the implications of transverse shear, warping restraint on divergence and dynamic response of selected wing cone gurations are investigated, and pertinent conclusions are outlined. Nomenclature AR = wing aspect ratio, L=b a.s/ = geometric quantity; see Eq. (2) and Fig. 3 aij = one-dimensional global stiffness coefe cients a1 = undisturbed speed of sound b;d = semichord and semidepth of the beam normal cross section, respectively bi = inertia coefe cient Eij = Young’ s modulus of orthotropic materials in the material coordinate system h.s/ = wall thickness as the function of the midline

Effect of Geometrical Parameters on the Mixing Performance of Cantilevered Ramp Injectors

A cantilevered ramp fuel-injection strategy is considered as a means to deliver rapid mixing for use in scramjets and shock-induced combustion ramjets (shcramjets). The primary objective is to perform parametric studies of the injector array spacing, injection angle, and sweeping angle at a convective Mach number of 1.5. Analysis of the three-dimensional steady-state hypersonic e owe elds is accomplished through the WARP code, using the Yee‐Roe e ux-limiting scheme and theWilcox k-! turbulencemodel, along with the Wilcox dilatational dissipation correction. A closer array spacing is shown to increase signie cantly the mixing efe ciency in the near e eld, and a direct relationship between initial fuel/air contact surface and mixing efe ciency growth is apparent. A change in the injector angle from 4 to 16 deg induces a 9% augmentation in the mixing efe ciency but more than a twofold increase in the thrust potential losses. A sweeping angle of i3.5 deg is observed to result into signie cantly better fuel penetration, translating into a 28% increase in the mixing efe ciency for a sweep angle decreased from 3.5 to i3.5 deg. It is observed that an air cushion between the wall and the hydrogen is sufe ciently thick to prevent fuel penetrating the boundary layer when 1 ) the fuel is injected at an angle of »10 deg or more, 2 ) an array spacing of at least the height of the injector is used, and 3 ) a swept ramp cone guration is avoided.

Numerical Prediction of Laminar Shock/Shock Interactions in Hypersonic Flow

Results are presented of a series of numerical simulations of experiments conducted at the ONERA ChalaisMeudon ResearchCenterandattheCalspan— University at Buffalo Research Centeron shock/shock interactions. The e owe eld characteristics are described with the aid of the numerical predictions, and the computed values of surface pressure and heat transfer are compared with the experimental measurements for purposes of verie cation andvalidation.Issuesrelatedtoboundaryconditions,gridconvergence,andtimeunsteadinessofthecomputational e uid dynamicssimulations are addressed, and thedife culties that characterize thevalidation of the computational results are put in evidence. Nomenclature F = e ux vector h = enthalpy, J/kg M = Mach number n = normal unit vector p = pressure, Pa R = radius, reference length, m Re = Reynolds number S = surface,m 2 T = temperature, K t = time, s U = primitive variables vector u; v = velocity components in the x and y directions, m/s V = velocity, m/s V = volume, m 3 W = conservative variables vector X = axis oriented in the direction between two cells x; y = Cartesian body axes, m 1n = distance from the wall of the e rst cell center, m µ = angular measurement, deg π = dynamic viscosity, kg/m ¢s Ω = density, kg/m 3 Subscripts c = cell cyl = cylinder I = inviscid t = time derivative V = viscous w = wall conditions X = space derivative 1 = freestream conditions Superscript 0 = stagnation conditions

Low-Reynolds-Number k-e Modeling of Nonstationary Solid Boundary Flows

Animprovedlow-Reynolds-number k‐~modelisadoptedto predictturbulente owswitha nonstationary boundary.Theperformanceoftheadoptedmodelise rstcontrastedwithdirectnumericalsimulationdataoftheturbulent plane Couette ‐Poiseuille e ow. Detailed e ow structure is captured accurately by the model, in particularthe reduction of theshearstress and, hence, the turbulent kinetic energy due to thepresence of the moving wall. The validity of the present model in computing complex e ows within rotating disk cavities is further examined. Flows with two different rotational Reynolds numbers are investigated, and the predicted mean and turbulence results are also contrasted with measurements. The ine uence of rotation on the e owe eld and turbulence modeling is investigated by sensitizing the turbulence model coefe cient to rotational Richardson number, and the effect is found to be marginal. Because the internal e ow structure of the rotating disk cavities is induced by the diffusive transport of thetangential momentum from therotorinto theinterior, thepredicted thickness of the Ekman layer isfound to be critical to the correct predictions. The adopted model reproduces correctly the gradual thickening of the Ekman layers from small to large radii, which is due to the transition from laminar to turbulent regimes, especially on the rotor side within the disk cavities. The elevated level of turbulence on the stator side compared to that on the rotor side is also predicted correctly by the present model.