Approximate solution of the shear flow boundary layer on a flat plate.
Nonsimilar solution of incompressible boundary layer over flat plate in presence of shear flow, using approximate method
SHEAR FLOW↗
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Calculation of turbulent boundary layers with heat transfer and pressure gradient utilizing a compressibility transformation. Part 2: Constant property turbulent boundary layer flow with simultaneous mass transfer and pressure gradient
An analysis of the incompressible turbulent boundary layer, developing under the combined effects of mass transfer and pressure gradient, is presented in this paper. A strip-integral method is employed whereby two of the three governing equations are obtained by integrating the combined momentum and continuity equation to 50 percent and 100 percent, respectively, of the boundary-layer height. The latter equation is the usual momentum-integral equation; the former equation requires specification of shear. Accordingly, Clauser's equilibrium eddy-viscosity law is assumed valid at this point. The third and final equation is obtained by specifying that Stevenson's velocity profiles apply throughout the domain of interest, from which a skin-friction law can be derived. Comparisons of the numerical results with the experiments of McQuaid, which include combined effects of variable pressure gradient and mass transfer, show good agreement.
Boccio, J.↗
Shooting method for solution of boundary-layer flows with massive blowing
A modified, bidirectional shooting method is presented for solving boundary-layer equations under conditions of massive blowing. Unlike the conventional shooting method, which is unstable when the blowing rate increases, the proposed method avoids the unstable direction and is capable of solving complex boundary-layer problems involving mass and energy balance on the surface.
Liu, T.-M.↗
Heat transfer and fluid mechanics measurements in transitional boundary layer flows
Experimental results are presented to document hydrodynamic and thermal development of flat-plate boundary layers undergoing natural transition. Local heat transfer coefficients, skin friction coefficients and profiles of velocity, temperature and Reynolds normal and shear stresses are presented. A case with no transition and transitional cases with 0.68% and 2.0% free-stream disturbance intensities were investigated. The locations of transition are consistent with earlier data. A late-laminar state with significant levels of turbulence is documented. In late-transitional and early-turbulent flows, turbulent Prandtl number and conduction layer thickness values exceed, and the Reynolds analogy factor is less than, values previously measured in fully turbulent flows.
Wang, T.↗
Heat transfer and fluid mechanics measurements in transitional boundary layer flows
Experimental results are presented to document hydrodynamic and thermal development of flat-plate boundary layers undergoing natural transition. Local heat transfer coefficients, skin friction coefficients and profiles of velocity, temperature and Reynolds normal and shear stresses are presented. A case with no transition and transitional cases with 0.68 percent and 2.0 percent free-stream disturbance intensities were investigated. The locations of transition are consistent with earlier data. A late-laminar state with significant levels of turbulence is documented. In late-transitional and early-turbulent flows, turbulent Prandtl number and conduction layer thickness values exceed, and the Reynolds analogy factor is less than, values previously measured in fully turbulent flows.
Wang, T.↗
Studies on the influence on flexural wall deformations on the development of the flow boundary layer
Flexural wave-like deformations can be used to excite boundary layer waves which in turn lead to the onset of turbulence in the boundary layer. The investigations were performed with flow velocities between 5 m/s and 40 m/s. With four different flexural wave transmissions a frequency range from 0.2 kc/s to 1.5 kc/s and a phase velocity range from 3.5 m/s to 12 m/s was covered. The excitation of boundary layer waves becomes most effective if the phase velocity of the flexural wave coincides with the phase velocity region of unstable boundary layer waves.
Schilz, W.↗
Prediction of laminar and turbulent boundary layer flow separation in V/STOL engine inlets
The paper provides a theoretical description of the development of the boundary layer on the lip and diffuser surface of a subsonic inlet at arbitrary operating conditions of mass flow rate, freestream velocity and incidence angle. Both laminar separation on the lip and turbulent separation in the diffuser are discussed. The agreement of the theoretical results with model experimental data illustrates the capability of the theory to predict separation. The effects of throat Mach number, inlet size, and surface roughness on boundary-layer development and separation are illustrated.
Chou, D. C.↗
Computation of a Synthetic Jet in a Turbulent Cross-Flow Boundary Layer
A series of unsteady Reynolds-averaged Navier-Stokes computations are performed for the flow of a synthetic jet issuing into a turbulent boundary layer through a circular orifice. This is one of the validation test cases from a synthetic jet validation workshop held in March 2004. Several numerical parameters are investigated, and the effects of three different turbulence models are explored. Both long-time-averaged and time-dependent phase-averaged results are compared to experiment. On the whole, qualitative comparisons of the mean flow quantities are fairly good. There are many differences evident in the quantitative comparisons. The calculations do not exhibit a strong dependence on the type of turbulence model employed.
Rumsey, Christopher L.↗
Boundary Layer Flow Control by an Array of Ramp-Shaped Vortex Generators
Flow field survey results for the effect of ramp-shaped vortex generators (VG) on a turbulent boundary layer are presented. The experiments are carried out in a low-speed wind tunnel and the data are acquired primarily by hot-wire anemometry. Distributions of mean velocity and turbulent stresses as well as streamwise vorticity, on cross-sectional planes at various downstream locations, are obtained. These detailed flow field properties, including the boundary layer characteristics, are documented with the primary objective of aiding possible computational investigations. The results show that VG orientation with apex upstream, that produces a downwash directly behind it, yields a stronger pair of streamwise vortices. This is in contrast to the case with apex downstream that produces a pair of vortices of opposite sense. Thus, an array of VG s with the former orientation, usually considered for film-cooling application, may also be superior for mixing enhancement and boundary layer separation control. (See CASI ID 20120009374 for Supplemental CD-ROM.)
Zaman, K. B. M. Q.↗
Boundary Layer Flow Control by an Array of Ramp-Shaped Vortex Generators
Flow field survey results for the effect of ramp-shaped vortex generators (VG) on a turbulent boundary layer are presented. The experiments are carried out in a low-speed wind tunnel and the data are acquired primarily by hot-wire anemometry. Distributions of mean velocity and turbulent stresses as well as streamwise vorticity, on cross-sectional planes at various downstream locations, are obtained. These detailed flow field properties, including the boundary layer characteristics, are documented with the primary objective of aiding possible computational investigations. The results show that VG orientation with apex upstream, that produces a downwash directly behind it, yields a stronger pair of streamwise vortices. This is in contrast to the case with apex downstream that produces a pair of vortices of opposite sense. Thus, an array of VG s with the former orientation, usually considered for film-cooling application, may also be superior for mixing enhancement and boundary layer separation control. The data files can be found on a supplemental CD.
Zaman, K. B. M. Q.↗
Hybrid suction surface for turbulent boundary layer flow
A hybrid suction surface which combines favorable aspects of both uniformly porous and discrete opening suction surfaces has been evaluated experimentally for use with incompressible turbulent boundary layers. The surface consisted of an array of closely spaced slots aligned in the direction of the freestream flow. Direct drag and mean boundary layer velocity profile measurements showed that the slotted surface had nominally the same suction characteristics as a uniformly porous surface.
Wilkinson, S. P.↗
Standardization of computational experiments in unsteady turbulent boundary-layer flow
Numerical experiments are proposed as standard cases to be computed by all who plan to analyze unsteady turbulent boundary layer behavior. In this way, differences between the results obtained by various methods can be compared in a completely defined environment. The test cases range in difficulty from time relaxation study of the steady flow on a flat plate to the analysis of unsteady reversed flow. Initial and boundary conditions are fully defined for each case and representative outputs are presented. It is recommended that tabulated samples of computations of these test cases be published in a compendium of results.
Carr, L. W.↗
Laminar boundary-layer flow of non-Newtonian fluid
A solution for the two-dimensional and axisymmetric laminar boundary-layer momentum equation of power-law non-Newtonian fluid is presented. The analysis makes use of the Merk-Chao series solution method originally devised for the flow of Newtonian fluid. The universal functions for the leading term in the series are tabulated for n from 0.2 to 2. Equations governing the universal functions associated with the second and the third terms are provided. The solution together with either Lighthill's formula or Chao's formula constitutes a simple yet general procedure for the calculation of wall shear and surface heat transfer rate. The theory was applied to flows over a circular cylinder and a sphere and the results compared with published data.
Lin, F. N.↗
Calculation of skin-friction coefficients for low Reynolds number turbulent boundary layer flows
An analysis is presented of the reliability of various generally accepted empirical expressions for the prediction of the skin-friction coefficient C/sub f/ of turbulent boundary layers at low Reynolds numbers in zero-pressure-gradient flows on a smooth flat plate. The skin-friction coefficients predicted from these expressions were compared to the skin-friction coefficients of experimental profiles that were determined from a graphical method formulated from the law of the wall. These expressions are found to predict values that are consistently different than those obtained from the graphical method over the range 600 Re/sub theta 2000. A curve-fitted empirical relationship was developed from the present data and yields a better estimated value of C/sub f/ in this range. The data, covering the range 200 Re/sub theta 7000, provide insight into the nature of transitional flows. They show that fully developed turbulent boundary layers occur at Reynolds numbers Re/sub theta/ down to 425. Below this level there appears to be a well-ordered evolutionary process from the laminar to the turbulent profiles. These profiles clearly display the development of the turbulent core region and the shrinking of the laminar sublayer with increasing values of Re/sub theta/.
Barr, P. K.↗
Three-dimensional shear-driven boundary layer flow with streamwise adverse pressure gradient
The effects of adverse pressure gradient on a three-dimensional turbulent boundary layer are studied in an axisymmetric forward-facing step geometry. Velocity measurements made using a three-component laser Doppler velocimeter include mean flow as well as Reynolds stresses and velocity triple-product correlations. Turbulent Prandtl mixing-lengths are extracted from the data, showing the effects of curvature. Streamwise pressure gradient was seen to alter streamwise velocity and Reynolds stress without significantly affecting transverse velocity and Reynolds stress. Transverse-strain was seen to have the effect of reducing the streamwise component of Reynolds stress.
Driver, David M.↗
Low-Reynolds-number k-epsilon model for unsteady turbulent boundary-layer flows
An assessment of the near-wall and low-Reynolds-number functions used in low-Reynolds-number k-epsilon models suggests that they are not suitable for the near-wall region of unsteady turbulent boundary layers, where the flow is characterized by rapid changes in phase. An improved low-Reynolds-number k-epsilon model is developed in this paper. The near-wall and low-Reynolds-number functions in this model are formulated as functions of the local turbulent Reynolds numbers instead of the inner variable y(+). The present model also has the correct asymptotic behavior in the near-wall region. The turbulence model has been incorporated in an unsteady boundary-layer code and validated for unsteady turbulent boundary layers with and without adverse pressure gradients. The predictions agree well with the experimental data and the theoretical analysis. For the cases tested, the present model correctly predicts the unsteady near-wall flow and the unsteady shin friction at various frequencies.
Fan, Sixin↗
A Simple Method for Determining Heat Transfer, Skin Friction, and Boundary-Layer Thickness for Hypersonic Laminar Boundary-Layer Flows in a Pressure Gradient
A procedure based on the method of similar solutions is presented by which the skin friction, heat transfer, and boundary-layer thickness in a laminar hypersonic flow with pressure gradient may be rapidly evaluated if the pressure distribution is known. This solution, which at present is. restricted to power-law variations of pressure with surface distance, is presented for a wide range of exponents in the power law corresponding to both favorable and adverse pressure gradients. This theory has been compared to results from heat-transfer experiments on blunt-nose flat plates and a hemisphere cylinder at free-stream Mach numbers of 4 and 6.8. The flat-plate experiments included tests made at a Mach number of 6.8 over a range of angle of attack of +/- 10 deg. Reasonable agreement of the experimental and theoretical heat-transfer coefficients has been obtained as well as good correlation of the experimental results over the entire range of angle of attack studied. A similar comparison of theory with experiment was not feasible for boundary-layer-thickness data; however, the hypersonic similarity theory was found to account satisfactorily for the variation in boundary-layer thickness due to local pressure distribution for several sets of measurements.
Bertram, Mitchel H.↗
Three-dimensional boundary layer flow with streamwise adverse pressure gradient
The present study examines the effects of a strong adverse pressure gradient on a 3D turbulent boundary layer in an axisymmetric spinning cylinder geometry. Velocity measurements made with a three-component laser Doppler velocimeter include all three mean flow components, all six Reynolds stress components, and all ten triple-product correlations. Total Reynolds shear stress diminishes as the flow becomes 3D. Lower levels of shear stress were found to persist under adverse pressure gradient conditions. This low stress level was observed to roughly correlate with the magnitude of the crossflow. Variations in the pressure gradient do not alter this correlation. It is inferred that a 3D boundary layer is more prone to separate than a 2D boundary layer.
Driver, David M.↗