Adverse Pressure Gradient Case Research Articles

A wind tunnel study of adverse pressure gradient impact on wind turbine wake dynamics

Wind tunnel experiments were conducted to investigate the impact of an adverse streamwise pressure gradient on the wake dynamics of a small-scale horizontal-axis wind turbine. The study used high-frequency constant temperature hotwire anemometry to measure wake velocities up to 7 rotor diameters (dT) downstream. Two cases were studied: zero pressure gradient (ZPG) and adverse pressure gradient (APG). Experimental conditions included a Reynolds number based on the rotor diameter of Re≈6.7×104 and an inflow velocity of 7 m/s. The results show significant differences between the ZPG and APG cases as the wake progresses downstream. The APG case exhibits a higher maximum velocity deficit in the far wake and a more distorted, oval-shaped wake than the ZPG case. Turbulence intensity trends also differ, with a decreasing trend in the ZPG case and an increasing trend in the APG case. Energy spectra analysis at specific wake locations offers insights into flow structure development. In both cases, small-scale (high-frequency) energy decreases as the wake advances, while large-scale (low-frequency) energy increases. Specifically, the adverse pressure gradient attenuates certain large-scale flow structures λx/dT∈[0.05,0.2], corresponding to f∈[20,100]Hz near the rotor tip height and narrows downstream. Additionally, in the APG case, energy increases in the lower half of the wake for flow structures ranging from λx/dT∈[0.04,0.5], or f∈[10,100]Hz near the rotor, narrowing further downstream. The results suggest that an adverse pressure gradient enhances turbulence and hinders velocity recovery toward freestream conditions in the wake of a wind turbine.

Heat Transfer of Power-Law Fluids in Plane Couette–Poiseuille Flows with Viscous Dissipation

Analytical expressions for the velocity and temperature profiles, bulk temperature and Nusselt numbers, in a fully-developed laminar Couette–Poiseuille flow between parallel plates of a power-law fluid with constant, and distinct, wall heat fluxes, in the presence of viscous dissipation are deduced and presented. Both favorable and adverse pressure gradient cases were analyzed. The walls’ shear stresses ratio, which arises naturally when the dimensionless hydrodynamic solution is obtained, together with the fluid power-law index Brinkman number and the walls’ heat fluxes ratio are the independent variables in the heat transfer solutions. With the exception of Newtonian fluids, there are in general two distinct analytical solutions, one for positive and another for negative values of the walls’ shear stresses ratio. The existence of singular points are also observed, where for a given value of the power-law index, there are values of the walls’ shear stresses ratio for which the Nusselt number becomes independent of the Brinkman number. It was also found that in a Couette–Poiseuille flow, for each value of the power-law index there exists a certain negative value of the walls’ shear stresses ratio that makes the Nusselt numbers at both walls identically zero.

Pressure gradient effects on wake-flow instabilities behind isolated roughness elements on re-entry capsules

Laminar-turbulent transition caused by modal disturbance growth in the wake flow of isolated roughness elements on blunt re-entry capsules is studied numerically at typical cold hypersonic wind-tunnel conditions. Two fundamentally different heat shield shapes are considered. On the sphere-cone forebody the wake flow of the roughness is exposed to an adverse pressure gradient, whereas the spherical heat shield exhibits a strongly favorable pressure gradient. The pressure gradient effects on the development of the stationary wake flow and its modal instability characteristics are discussed for various heights and diameters of the cylindrical roughness element. Regions of increased shear develop in its wake, which persist longer in the adverse pressure gradient case. Consequently, the results of spatial two-dimensional eigenvalue analyses reveal that the unstable wake-flow region extends much further downstream and the wake-mode instabilities are considerably more amplified. The disturbance kinetic energy production terms are used to assess the contributions of the different shear-layer regions to the mode growth and its dependence on the pressure gradient.

On the impact of adverse pressure gradient on the supersonic turbulent boundary layer

By employing the particle image velocimetry, the mean and turbulent characteristics of a Mach 2.95 turbulent boundary layer are experimentally investigated without the impact of curvature. The physical mechanism with which the streamwise adverse pressure gradient affects the supersonic boundary layer is revealed. The data are compared to that of the concave boundary layer with similar streamwise distributions of wall static pressure to clarify the separate impacts of the adverse pressure gradient and the concave curvature. The logarithmic law is observed to be well preserved for both of the cases. The dip below the logarithmic law is not observed in present investigation. Theoretical analysis indicates that it could be the result of compromise between the opposite impacts of the compression wave and the increased turbulent intensity. Compared to the zero pressure gradient boundary layer, the principal strain rate and the turbulent intensities are increased by the adverse pressure gradient. The shear layer formed due the hairpin packets could be sharpened by the compression wave, which leads to higher principal strain rate and the associated turbulent level. Due to the additional impact of the centrifugal instability brought by the concave wall, even higher turbulent intensities than that of the adverse pressure gradient case are introduced. The existence of velocity modes within the zero pressure gradient boundary layer suggests that the large scale motions are statistically well organized. The generation of new velocity modes due to the adverse pressure gradient indicates that the turbulent structure is changed by the adverse pressure gradient, through which more turbulence production that cannot be effectively predicted by the Reynolds-stress transport equations could be brought.

Effects of compound angle on film cooling effectiveness with different streamwise pressure gradient and convex curvature

Streamwise pressure gradient and surface curvature are two important characteristics of turbine flow and compound angle film cooling is an efficient way to improve cooling performance. Compound angle film cooling effectiveness with those two effects was investigated using PSP technology. The corresponding numerical studies were validated and carried out to investigate the physical mechanism of the interaction between the coolant jet and the main flow. Compound angle increases film cooling effectiveness for high blowing ratios in the near hole region, but the stronger interaction between the jet and the main flow makes the coolant dissipate faster. On the flat surface, the favorable pressure gradient leads to a maximum of 50% increase of film cooling effectiveness compared with the adverse pressure gradient case. On the convex surface, the cooling jet is pushed to the wall by the radial pressure gradient in the free stream which makes film cooling effectiveness 20–50% higher than the flat wall case. The compound angle film cooling performance under strong favorable pressure gradient for the convex surface is quite different from the flat wall case and thus streamwise pressure gradient and surface curvature should be taken into consideration in gas turbine film cooling design.

Large-Eddy Simulation of Film Cooling in an Adverse Pressure Gradient Flow

In order to analyze the interaction of multiple rows of film cooling holes in flows at adverse pressure gradients, large-eddy simulations (LESs) are performed. The considered three-row cooling configuration consists of inclined cooling holes at an angle of 30 deg with a lateral pitch of p/D=3 and a streamwise spacing of l/D=6. The cooling holes possess a fan-shaped exit geometry with lateral and streamwise expansions. For each cooling row the complete internal flow is computed. Air and CO2 are injected in order to investigate the influence of an increased density ratio on the film cooling physics at adverse pressure gradients. The CO2 injected at the same blowing rate as air shows a higher magnitude of the Reynolds shear stress component and, thus, an enhanced mixing downstream of the cooling holes. The LES results of the air and CO2 configurations are compared to the corresponding particle-image velocimetry (PIV) measurements and show a convincing agreement in terms of the averaged streamwise velocity and streamwise velocity fluctuations. Furthermore, the cooling effectiveness is investigated for a zero and an adverse pressure gradient configuration with a temperature ratio at gas turbine conditions. For the adverse pressure gradient case, reduced temperature levels off the wall are observed. However, the cooling effectiveness shows only minor differences compared to the zero pressure gradient flow. The turbulent Schmidt number at CO2 injection shows large variations. Just downstream of the injection it attains low values, whereas high values are detected in the upper mixing zone of the cooling flow and the freestream at each film cooling row.

Experiment and simulation of mixed flows in a trapezoidal microchannel

This paper presents experimental and numerical results of mixed electroosmotic and pressure driven flows in a trapezoidal shaped microchannel. A micro particle image velocimetry (μPIV) technique is utilized to acquire velocity profiles across the microchannel for pressure, electroosmotic and mixed electroosmotic-pressure driven flows. In mixed flow studies, both favorable and adverse pressure gradient cases are considered. Flow results obtained from the μPIV technique are compared with 3D numerical predictions, and an excellent agreement is obtained between them. In the numerical technique, the electric double layer is not resolved to avoid expensive computation, rather a slip velocity is assigned at the channel surface based on the electric field and electroosmotic mobility. This study shows that a trapezoidal microchannel provides a tapered-cosine velocity profile if there is any pressure gradient in the flow direction. This result is significantly different from that observed in rectangular microchannels. Our experimental results verify that velocity distribution in mixed flow can be decomposed into pressure and electroosmotic driven components.

Linear and nonlinear development of localized disturbances in zero and adverse pressure gradient boundary-layers

Localized disturbances in laminar boundary-layers at Reynolds number Reδ*=950 were studied using direct numerical simulation. Instability mechanisms in both an adverse and zero pressure gradient were investigated by introducing three different three-dimensional disturbances. The first disturbance was centered around a pair of oblique waves in Fourier space, the second around a plane wave, while the third was axisymmetric. For small amplitudes, the first disturbance developed into a wave-packet of oblique waves in adverse pressure gradient and into a streaky structure with a trailing wave-packet in a zero pressure gradient. The second disturbance developed into a wave-packet centered around plane waves in both pressure gradients. The third disturbance developed into a wave-packet of plane waves in adverse pressure gradient and, due to the transient growth mechanism, into a streaky structure in a zero pressure gradient. For finite-amplitude plane wave-packets in a zero pressure gradient, a subharmonic secondary instability was observed which subsequently developed into an elongated Λ structure. The secondary instability was less significant in adverse pressure gradient due to the large growth rate of the primary instability. Breakdown was observed as high-frequency oscillations on the spike over the head of the Λ vortices. Providing the initial amplitude was sufficiently large, the vortex pair yielded the fastest route to turbulence. The main growth mechanism in this scenario, in addition to the exponential growth in the adverse pressure gradient case, was the nonlinear excitation of transient growth of streaks by interacting oblique modes. Disturbances dominated by streaks needed substantially larger amplitudes before secondary instability or breakdown occurred. In that case, breakdown was shifted from the spike to an instability of the rear part of the streaks.

Direct numerical simulation of self-similar turbulent boundary layers in adverse pressure gradients

Direct numerical simulations of the Navier–Stokes equations have been carried out with the objective of studying turbulent boundary layers in adverse pressure gradients. The boundary layer flows concerned are of the equilibrium type which makes the analysis simpler and the results can be compared with earlier experiments and simulations. This type of turbulent boundary layers also permits an analysis of the equation of motion to predict separation. The linear analysis based on the assumption of asymptotically high Reynolds number gives results that are not applicable to finite Reynolds number flows. A different non-linear approach is presented to obtain a useful relation between the freestream variation and other mean flow parameters. Comparison of turbulent statistics from the zero pressure gradient case and two adverse pressure gradient cases shows the development of an outer peak in the turbulent energy in agreement with experiment. The turbulent flows have also been investigated using a differential Reynolds stress model. Profiles for velocity and turbulence quantities obtained from the direct numerical simulations were used as initial data. The initial transients in the model predictions vanished rapidly. The model predictions are compared with the direct simulations and low Reynolds number effects are investigated.

The Effects of Adverse Pressure Gradients on Momentum and Thermal Structures in Transitional Boundary Layers: Part 2—Fluctuation Quantities

The effects of adverse pressure gradients on the thermal and momentum characteristics of a heated transitional boundary layer were investigated with free-stream turbulence ranging from 0.3 to 0.6 percent. Boundary layer measurements were conducted for two constant-K cases, K1 = −0.51 × 10−6 and K2 = −1.05 × 10−6. The fluctuation quantities, u′, ν′, t′, the Reynolds shear stress (uν), and the Reynolds heat fluxes (νt and ut) were measured. In general, u′/U∞, ν′/U∞, and νt have higher values across the boundary layer for the adverse pressure-gradient cases than they do for the baseline case (K = 0). The development of ν′ for the adverse pressure gradients was more actively involved than that of the baseline. In the early transition region, the Reynolds shear stress distribution for the K2 case showed a near-wall region of high-turbulent shear generated at Y+ = 7. At stations farther downstream, this near-wall shear reduced in magnitude, while a second region of high-turbulent shear developed at Y+ = 70. For the baseline case, however, the maximum turbulent shear in the transition region was generated at Y+ = 70, and no near-wall high-shear region was seen. Stronger adverse pressure gradients appear to produce more uniform and higher t′ in the near-wall region (Y+ < 20) in both transitional and turbulent boundary layers. The instantaneous velocity signals did not show any clear turbulent/nonturbulent demarcations in the transition region. Increasingly stronger adverse pressure gradients seemed to produce large non turbulent unsteadiness (or instability waves) at a similar magnitude as the turbulent fluctuations such that the production of turbulent spots was obscured. The turbulent spots could not be identified visually or through conventional conditional-sampling schemes. In addition, the streamwise evolution of eddy viscosity, turbulent thermal diffusivity, and Prt, are also presented.

Supersonic flux-split procedure for second moments of turbulence

A finite volume procedure which combines flux-difference splitting and flux-vector splitting is presented in this paper. The diffusive fluxes are treated explicitly to preserve the upwinding structure of the split Euler fluxes. This procedure is extended in this paper from its essentially laminar or eddy viscosity form to include the equations for the six components of the Reynolds stress tensor and an additional equation for the solenoidal dissipation. The models used for the unclosed terms are presented as are the extensions of the numerical procedures to cover the turbulence equations. To validate the proposed procedures, a compressible turbulent flow over a flat plate at Mach number M∞ = 2.87 and Reynolds number per unit length Re/m of 6.5X10 7 was calculated and compared with experimental measurements. Also simulated was the case when the foregoing boundary-layer flow was made to pass over a ramp. A strong adverse pressure gradient case in which boundary-layer thickness-to-curvature ratio (δ/R c ) is 0.1 was considered. In this case, the supersonic turbulent boundary layer experiences the combined effects of an adverse pressure gradient, bulk compression, and concave streamline curvature.

Turbulent Near Wake of a Flat Plate : Part 3, Effect of Pressure Gradients

The turbulent near wakes starting from the turbulent boundary layers on both sides of a flat plate and subjected to pressure gradients have been investigated. The experiments have been conducted in zero, adverse, favourable and mixed pressure gradients, and the results show that the total pressure along a streamline of the near wake in a pressure gradient changes at a rate nearly equal to that along the same streamline in zero pressure gradient, which suggests that the transverse gradients of Reynolds stress are little affected by pressure gradients in the turbulent near wakes. On the basis of the experimental results a model to predict the development of a near wake in a pressure gradient has been presented. The calculated results agree well with the experimental data except for a strong adverse pressure gradient case.

Measurements of the low wave number components of turbulent boundary layer wall pressure fluctuations with zero and adverse pressure gradients

Two rectangular plates with approximately clamped boundary conditions were used as spatial filters to measure the low wave number components of the wall pressure fluctuations beneath a turbulent boundary layer. The plates were designed to provide low wave number measurements at higher frequencies and wave numbers than previous plate experiments in order to provide data comparable to measurements made using microphone arrays. Measurements were made in the lower test section wall of the MIT low turbulence subsonic wind tunnel under zero pressure gradient and adverse pressure gradient conditions. The zero pressure gradient data lies in the wave number frequency range 2.5 <ωδ*/U∞<10 and 0.5 <k1δ*<1.8 while the adverse gradient data lies in the range 4.5 <ωδ*/U∞<23 and 0.9 <k1δ*<4.6. Momentum thickness Reynolds numbers ranged from 6000 to 11 000 for the zero pressure gradient case and 11 000 to 16 000 for the adverse pressure gradient case. When normalized on outer variables the adverse gradient data do not exhibit increased levels from those of the zero pressure gradient data. [Work supported by the Sonar Technology Program, Office of Naval Research.]

A family of integral methods for predicting turbulent boundary layers

A family of integral methods for predicting the development of two-dimensional incompressible turbulent boundary layers in arbitrary pressure gradients is described. The momentum integral equation and a wall friction relation are used in each method. A third equation must be selected from A) the energy integral equation, B) the entrainment equation, or C) the moment of momentum integral equation. It is shown that an over-all comparison of all three methods with a wide range of experimental results is generally satisfactory. The use of B gives the best agreement for adverse pressure gradient cases whereas the use of A and C predicts equilibrium and relaxing flows better.