Moderate Adverse Pressure Gradient Research Articles

Direct numerical simulation of adverse pressure gradient turbulent boundary layer up to [formula omitted

A direct numerical simulation of a moderate adverse pressure gradient turbulent boundary layer flow on a flat plate was performed on a fairly long domain with a Reynolds number from Reθ≃2000 to Reθ≃8000. The mean streamwise velocity profile does not exhibit a clear log region even at the highest Reynolds number. The Reynolds stresses exhibit a well defined peak in the outer region which moves away from the wall before to stabilise at a wall distance y of 0.45 boundary layer thickness after evolving over 20 local boundary layer thicknesses. These outer peaks are the consequences of an excess of production over dissipation and they all scale with the shear stress velocity for wall distance 0.2δ<y<0.85δ. The different terms of the Reynolds stresses equations are analysed in the outer region and the analysis confirms that the leading terms are the same as for a zero pressure gradient turbulent boundary layer except that the production and dissipation are not negligible in the outer region. The most significant contribution of scales smaller than two Taylor scales is on the pressure strain term of the shear stress equation. The probability of the occurrence of small scale vortices conditioned by the presence of an ejection or a sweep shows that the shear stress contained in ejections is associated with the production and transport of near wall vortices away from the wall. The local mean shear generated by the sweeps increases the production of near wall vortices. Lastly, the large scale structures analysed by means of two point correlations of the streamwise fluctuating velocity are shown to be strongly modified by the adverse pressure gradient. The correlation reveals a decoupling between the near wall streaks and the large scale streamwise structures enhanced by the adverse pressure gradient.

Investigation on shock-induced separation loss mitigation method considering radial equilibrium in a transonic compressor rotor

AbstractA shock-induced separation loss reduction method, using local blade suction surface shape modification (smooth ramp structure) with constant adverse pressure gradient with the consideration of radial equilibrium effect to split a single shock foot into multiple weaker shock wave configuration, is investigated on the NASA Rotor 37 for promoting aerodynamic performance of a transonic compressor rotor. Numerical investigation on baseline blade and improved one with blade modification on suction side has been conducted employing the Reynolds-averaged Navier–Stokes method to reveal flow physics of ramp structure. The results indicate that the passage shock foot of baseline is replaced with a family of compression waves and a weaker shock foot generating moderate adverse pressure gradient on ramp profile, which is beneficial for mitigating the shock foot and shrinking flow separation region as well. In addition, the radial secondary flow of low-momentum fluids within boundary layer is decreased significantly in the region of passage shock-wave/boundary-layer interaction on blade suction side, which mitigates the mass flow and mixing intensity of tip leakage flow. With the reduction of flow separation loss induced by passage shock, the adiabatic efficiency and total pressure ratio of improved rotor are superior to baseline model. This study herein implies a potential application of ramp profile in design method of transonic and supersonic compressors.

Passage shock wave/boundary layer interaction control for transonic compressors using bumps

Flow separation due to shock wave/boundary layer interaction is dominated in blade passage with supersonic relative incoming flow, which always accompanies aerodynamic performance penalties. A loss reduction method for smearing the passage shock foot via Shock Control Bump (SCB) located on transonic compressor rotor blade suction side is implemented to shrink the region of boundary layer separation. The curved windward section of SCB with constant adverse pressure gradient is constructed ahead of passage shock-impingement point at design rotor speed of Rotor 37 to get the improved model. Numerical investigations on both two models have been conducted employing Reynolds-Averaged Navier-Stokes (RANS) method to reveal flow physics of SCB. Comparisons and analyses on simulation results have also been carried out, showing that passage shock foot of baseline is replaced with a family of compression waves and a weaker shock foot for moderate adverse pressure gradient as well as suppression of boundary layer separations and secondary flow of low-momentum fluid within boundary layer. It is found that adiabatic efficiency and total pressure ratio of improved blade exceeds those of baseline at 95%-100% design rotor speed, and then slightly worsens with decrease of rotatory speed till both equal below 60% rated speed. The investigated conclusion implies a potential promise for future practical applications of SCB in both transonic and supersonic compressors.

Contribution of large-scale motions to the skin friction in a moderate adverse pressure gradient turbulent boundary layer

Direct numerical simulation of a turbulent boundary layer (TBL) subjected to a moderate adverse pressure gradient (APG,$\unicode[STIX]{x1D6FD}=1.45$) is performed to explore the contribution of large scales to the skin friction, where$\unicode[STIX]{x1D6FD}$is the Clauser pressure gradient parameter. The Reynolds number based on the momentum thickness develops from$Re_{\unicode[STIX]{x1D703}}\approx 110$to 6000 with an equilibrium region in$Re_{\unicode[STIX]{x1D703}}=4000$–5500. The spanwise wavelength ($\unicode[STIX]{x1D706}_{z}$) spectra of the streamwise and spanwise velocity fluctuations show that the large-scale energy is significantly enhanced throughout the boundary layer. We quantify the superposition and amplitude modulation effects of these enhanced large scales on the skin friction coefficient ($C_{f}$) by employing two approaches: (i) spanwise co-spectra of$\langle v\unicode[STIX]{x1D714}_{z}\rangle$and$\langle -w\unicode[STIX]{x1D714}_{y}\rangle$; (ii) conditionally averaged$\langle v\unicode[STIX]{x1D714}_{z}\rangle$and$\langle -w\unicode[STIX]{x1D714}_{y}\rangle$. The velocity–vorticity correlations$\langle v\unicode[STIX]{x1D714}_{z}\rangle$and$\langle -w\unicode[STIX]{x1D714}_{y}\rangle$are related to the advective transport and the vortex stretching, respectively. Although$\langle v\unicode[STIX]{x1D714}_{z}\rangle$negatively contributes to$C_{f}$, the positive contribution of the large scales ($\unicode[STIX]{x1D706}_{z}&gt;0.5\unicode[STIX]{x1D6FF}$) is observed in the co-spectra of weighted$\langle v\unicode[STIX]{x1D714}_{z}\rangle$. For the co-spectra of weighted$\langle -w\unicode[STIX]{x1D714}_{y}\rangle$, we observe an outer peak at$\unicode[STIX]{x1D706}_{z}\approx 0.75\unicode[STIX]{x1D6FF}$and the superposition of the large scales in the buffer region, leading to the enhancement of$C_{f}$. The magnitude of$\langle v\unicode[STIX]{x1D714}_{z}\rangle$and$\langle -w\unicode[STIX]{x1D714}_{y}\rangle$depends on the large-scale streamwise velocity fluctuations ($u_{L}$). In particular, the negative-$u_{L}$events amplify$\langle v\unicode[STIX]{x1D714}_{z}\rangle$in the outer region, and$\langle -w\unicode[STIX]{x1D714}_{y}\rangle$is enhanced by the positive-$u_{L}$events. As a result, the skin friction induced by$\langle v\unicode[STIX]{x1D714}_{z}\rangle$and$\langle -w\unicode[STIX]{x1D714}_{y}\rangle$increases in the present APG TBL.

The Effects of Inflow Uncertainties on the Characteristics of Developing Turbulent Flow in Rectangular Pipe and Asymmetric Diffuser

In the current paper nondeterministic computational fluid dynamics (CFD) computations of three-dimensional (3D), developing, and statistically steady turbulent flow through an asymmetric diffuser with moderate adverse pressure gradient are presented. The inflow condition is assumed to be uncertain. The inlet streamwise velocity is supposed to be a stochastic process and described by the Karhunen–Loève (KL) expansion. In addition, the inlet turbulence intensity and turbulent length scale are assumed to be uncertain. The nonintrusive polynomial chaos (NIPC) expansion is used to propagate the inflow uncertainties in the flow field. The developed code is verified using a Monte Carlo (MC) simulation with 1000 Latin Hypercube samples on a planar asymmetric diffuser. A very good agreement is observed between the results of MC and polynomial chaos expansion methods. The verified uncertainty quantification method is then applied to stochastic developing turbulent flow through a 3D asymmetric diffuser. It was observed that the eigenvalues of covariance kernel rapidly decay due to the large correlation lengths and thus a few terms in the truncated KL expansion are used to describe the stochastic inlet velocity. For the KL expansion, the mean and the standard deviation are set to those measured experimentally. The uncertain inlet condition has a significant influence on the numerical results of velocity and turbulence fields specially in the developing region before the shear layers meet. It is concluded that one of the reasons for discrepancies between experimental and deterministic CFD results is the uncertainty in inflow condition. A sensitivity analysis is also performed using the Sobol’ indices and contribution of each uncertain parameter on outputs variance is presented.

Computation of Developing Turbulent Flow through a Straight Asymmetric Diffuser with Moderate Adverse Pressure Gradient

In this paper, numerical investigation of three-dimensional, developing turbulent flow, subjected to a moderate adverse pressure gradient, has been investigated using various turbulence models, namely: the low-Re , the SST , the and a variant of Reynolds stress model. The results are compared with the detailed velocity and pressure measurements. Since the inlet condition is uncertain, a study was first performed to investigate the sensitivity of the results to the inlet boundary condition. The results showed the importance of including the contraction effects. It is seen that the developing flow inside the straight duct, is highly sensitive to the inlet boundary condition. The comparisons indicate that all turbulence models are able to predict a correct trend for the centerline velocity and pressure recovery inside the straight duct and diffuser but the low-Re and RSM turbulence models yield more realistic results. The SST model largely overpredicts the centerline velocity and boundary layer thickness in the straight duct. The comparisons of the numerical results also revealed that the RSM model, due to its anisotropic formulation, is able to reproduce the secondary flows. As expected, the RSM model demonstrates the best performance in prediction of the flow field and pressure recovery in the asymmetric diffuser.

Computations of periodic turbulent boundary layers with moderate adverse pressure gradient

Computations of periodic turbulent boundary layers with moderate adverse pressure gradient

Computations of periodic turbulent boundary layers with moderate adverse pressure gradient

In this computational study a two-equation eddy-viscosity model of turbulence is used to predict the development of boundary layers with periodic variation of the free-stream velocity and time-mean adverse pressure gradient. Transport equations are solved for q, the square root of the turbulence kinetic energy and ζ, its dissipation rate. Comparisons with reliable experimental data on such flows verified that the model can satisfactorily reproduce the time-average prime variables as well as their amplitudes. The predicted boundary-layer integral parameters were also found to be in good agreement with comparable data in the literature. Additional comparisons are made with the computed development of the same flow at constant pressure. The effects of the pressure gradient isolated and studied in this way were generally found to be similar to those of nonperiodic flow in similar conditions.

Turbulent boundary layer in an adverse pressure gradient - Effectiveness of riblets

Measurements of skin friction by means of a drag balance and of velocity profiles by means of a hot wire have been carried out in the boundary layer over a flat plate in a wind tunnel. A convergent/divergent test section produces a moderate adverse pressure gradient in the divergent part. The purpose of the present study is to investigate the characteristics of this boundary layer and to examine the effectiveness of riblets for skin-friction reduction. We find that the mean velocity follows a logarithmic profile that is shifted downward with respect to the logarithmic law for a zero-pressure-gradient boundary layer. The profile of the streamwise velocity fiuctuations exhibits two maxima. Application of riblets in this case leads to a skin-friction reduction of 13%, which implies a considerable increase over the 6% obtained in the zero-pressure-gradient boundary layer. Measurements with a hot wire show that only close to the wall is the mean velocity affected by the presence of riblets and that streamwise velocity fluctuations are reduced here.

Characteristics of the Three Dimensional flow with an Adverse Pressure Gradient

The three dimensional flow field of an open channel flow with a moderate adverse pressure gradient was measured by a Hot-film anemometer. It is found that the intensity of the secondary flow which normalized by a mean bulk velocity increases in the flow direction. The secondary flow affects on mean velocity profiles and friction velocity distributions. In particularly, as the intensity of the Reynolds stress increases in the flow direction, the production of turbulence energy is increased. Therefore, the intensity of the turbulence energy increases.

An experimental study on open channel flows with moderate adverse pressure gradients

An experimental study on open channel flows with moderate adverse pressure gradients

Behavior of the Johnson-King turbulence model in axisymmetric supersonic flows

A series of systematic tests are carried out on the Johnson-King turbulence model (JKM) for applied compressible aerodynamics. Two-dimensional flows with a moderate adverse pressure gradient and without separation at various Mach numbers are used for the tests. The results are compared with the Baldwin-Lomax model (BLM) as well as the measurements. The agreement of the results of both models and the measured data becomes poorer at higher Mach numbers. Overall, the performance of the JKM is slightly better than BLM except with respect to the prediction of the skin friction coefficient. The ordinary differential equation (ODE) in the JKM is effective in improving the prediction. However, the effects of the ODE are not as significant as in flows with separation. Use of the JKM even in nonseparated flows may improve accuracy of prediction, which has not been clearly established before this work.

Wall-wakes in moderate adverse pressure gradients

The flow past an obstacle attached perpendiculary to a surface (wall) is postulated to possess the characteristics of boundary layer flow in the vicinity of the wall and free-wake flow away from the wall. Analytical analyses of wall-wake flows with adverse pressure gradient (without causing separaton of the boundary layer) are made to obtain expressions for variations of free stream velocity and the chatacteristic length and velocity scales of the self preserving flow. Experiments are conducted in a wind tunnel for three arbitrary adverse pressure gradient flows. The experimental observations clearly indicate that wall-wakes in adverse pressure gradient can be adequately described by the two-layer model proposed.

Supersonic Turbulent Boundary Layer in Adverse Pressure Gradient. Part 11: Data Analysis

Experimental measurements of the mean profile characteristics of the supersonic turbulent boundary layer in a moderate adverse pressure gradient are analyzed. Turbulent boundary-layer equations applicable to compressible flow over a surface with longitudinal curvature are evaluated by numerical integration using the tabulated profile data. Curvature corrections to the equation for conservation of streamwise momentum are shown to be small but of the same order of magnitude as the wall shear stress. The data are shown to correlate in law of the wall dimentionless coordinates using an integral compressibility transformation that follows directly from Prandtl's mixing length approximation of the Reynolds stress. Values of skin-friction coefficient determined using the experimental data are compared to other experimental data and to values predicted using the Spalding-Chi method.

Supersonic Turbulent Boundary Layer in Adverse Pressure Gradient. Part I: The Experiment

Experimental measurements of the mean profile characteristics of the supersonic turbulent boundary layer in a region of moderate adverse pressure gradient along the curved surface of an isentropic ramp model are reported. Detailed surveys of impact pressure, static pressure and total temperature were made through the boundary layer and local values of wall shear stress were obtained using the Preston tube technique. The measurements were made for a nominal tunnel nozzle setting of Mach 3.5, closely adiabatic wall, and momentum thickness Reynolds number of 1.9 to 4.2 x 10. In addition to the mean profile data, fluctuation data were obtained using constant temperature hot wire anemometry at one station in the region of zero pressure gradient and at one station in the region of adverse pressure gradient.