Freestream Pressure Gradient Research Articles

A Critical Assessment of Reynolds Analogy for Turbine Flows

The application of Reynolds analogy 2St/cf≅1 for turbine flows is critically evaluated using experimental data collected in a low-speed wind tunnel. Independent measurements of St and cf over a wide variety of test conditions permit assessments of the variation of the Reynolds analogy factor (i.e., 2St/cf) with Reynolds number, freestream pressure gradient, surface roughness, and freestream turbulence. While the factor is fairly independent of Reynolds number, it increases with positive (adverse) pressure gradient and decreases with negative (favorable) pressure gradient. This variation can be traced directly to the governing equations for momentum and energy which dictate a more direct influence of pressure gradient on wall shear than on energy (heat) transfer. Surface roughness introduces a large pressure drag component to the net skin friction measurement without a corresponding mechanism for a comparable increase in heat transfer. Accordingly, the Reynolds analogy factor decreases dramatically with surface roughness (by as much as 50% as roughness elements become more prominent). Freestream turbulence has the opposite effect of increasing heat transfer more than skin friction, thus the Reynolds analogy factor increases with turbulence level (by up to 35% at a level of 11% freestream turbulence). Physical mechanisms responsible for the observed variations are offered in each case. Finally, synergies resulting from the combinations of pressure gradient and freestream turbulence with surface roughness are evaluated. With this added insight, the Reynolds analogy remains a useful tool for qualitative assessments of complex turbine flows where both heat load management and aerodynamic efficiency are critical design parameters.

The Effect of Real Turbine Roughness With Pressure Gradient on Heat Transfer

Experimental measurements of heat transfer (St) are reported for low speed flow over scaled turbine roughness models at three different freestream pressure gradients: adverse, zero (nominally), and favorable. The roughness models were scaled from surface measurements taken on actual, in-service land-based turbine hardware and include samples of fuel deposits, TBC spallation, erosion, and pitting as well as a smooth control surface. All St measurements were made in a developing turbulent boundary layer at the same value of Reynolds number Rex≅900,000. An integral boundary layer method used to estimate cf for the smooth wall cases allowed the calculation of the Reynolds analogy 2St/cf. Results indicate that for a smooth wall, Reynolds analogy varies appreciably with pressure gradient. Smooth surface heat transfer is considerably less sensitive to pressure gradients than skin friction. For the rough surfaces with adverse pressure gradient, St is less sensitive to roughness than with zero or favorable pressure gradient. Roughness-induced Stanton number increases at zero pressure gradient range from 16–44% (depending on roughness type), while increases with adverse pressure gradient are 7% less on average for the same roughness type. Hot-wire measurements show a corresponding drop in roughness-induced momentum deficit and streamwise turbulent kinetic energy generation in the adverse pressure gradient boundary layer compared with the other pressure gradient conditions. The combined effects of roughness and pressure gradient are different than their individual effects added together. Specifically, for adverse pressure gradient the combined effect on heat transfer is 9% less than that estimated by adding their separate effects. For favorable pressure gradient, the additive estimate is 6% lower than the result with combined effects. Identical measurements on a “simulated” roughness surface composed of cones in an ordered array show a behavior unlike that of the scaled “real” roughness models. St calculations made using a discrete-element roughness model show promising agreement with the experimental data. Predictions and data combine to underline the importance of accounting for pressure gradient and surface roughness effects simultaneously rather than independently for accurate performance calculations in turbines.

Modelling Bypass Transition with Low-Reynolds-Number Nonlinear Eddy-Viscosity Closure

The ability of two nonlinear, low-Reynolds-number eddy-viscosity models, one cubic and the other quadratic, to predict transitional boundary layers is investigated. The latter model distinguishes itself by its ability to return the correct wall-asymptotic variation of all the Reynolds-stress components. The choice of low-Reynolds-number models is motivated by the fact that transitional flows in turbomachinery can feature both transition and relaminarisation in different parts of the same flow, the latter demanding the inclusion of closure terms that represent the effects of viscosity on turbulence. Four flat-plate boundary layers are considered, each subjected to different combinations of free-stream turbulence and pressure gradient. A fifth flow is that around a VKI turbine blade. The models are first applied on their own. Whilst returning qualitative features of the transition process, the models do not provide an adequate quantitative description. In particular, neither model is able to predict the distinctive rise in turbulence intensity in the boundary layer well upstream of the location at which the skin friction and shear stress rise, taken to signify the onset of transition. It is then shown that the combination of the models with conventional intermittency-factor-based formulations is ineffective. This finally leads to a proposal which involves the introduction of modifications that combine a separate transport equation for the pre-transitional laminar fluctuation energy with an intermittency-type factor, governed by a correlation function. This factor is used to ‘blend’ pre-transitional fluctuation energy and turbulence-energy components, and it also features in the eddy-viscosity relation. The resulting modified model is shown to procure a substantial improvement in the representation of the transition process, including the pre-transitional rise in turbulence intensity and shear stress. To assist the assessment of the physical realism of the pre-transitional model, a large eddy simulation of a transitional flat-plate boundary layer was undertaken, and turbulence/fluctuation-energy budgets derived from the simulation are included.

Transition to Turbulence in the Boundary Layer on a Plate in the Presence of a Negative Free-Stream Pressure Gradient

Transition to turbulence in the boundary layer on a flat plate is investigated numerically for an incompressible fluid flow with a given negative free-stream pressure gradient. The transition is investigated using the three-parameter turbulence model developed by the authors. The calculation results are compared with the available experimental data.

Momentum transfer on power law stretching plate with free stream pressure gradient

The similarity solution of laminar boundary layer driven by the stretching surface boundary and pressure gradient, each proportional to the same power law of the downstream coordinate, based on composite reference velocity (sum of the velocities of stretching boundary and free stream) has been formulated by single set of equations, containing two parameters: β measuring the stretch rate of the moving boundary, and ϵ the ratio of free stream velocity to composite reference velocity. The closed form exact and asymptotic solutions in special cases, approximate integral solution and general numerical solutions have been obtained. For β>0 and 0⩽ ϵ⩽1 solutions are unique. For β<0 solutions are dual for 0< ϵ< ϵ 0( β), unique solution for ϵ=0 and ϵ= ϵ 0( β) and no solution exists ϵ> ϵ 0( β).

A NEW LOW-REYNOLDS-NUMBER TURBULENCE MODEL FOR PREDICTION OF TRANSITION ON GAS TURBINE BLADES

A new low-Reynolds-number (LRN) turbulence model is developed for the prediction of transition. In the definition of the LRN functions in the new model, only local quantities are used so that the model potentially can be used for a wide range of flows. The performance of the new model in predicting boundary layer transition is demonstrated by reference to a wide range of experimental data for boundary layers with free-stream turbulence and pressure gradient.

Local Measurement of Loss Using Heated Thin-Film Sensors

A calibration equation is derived linking the nondimensional entropy generation rate per unit area with the nondimensional aerodynamic wall shear stress and free-stream pressure gradient. It is proposed that the latter quantities, which can be measured from surface sensors, be used to measure the profile entropy generation rate. It is shown that the equation is accurate for a wide range of well-defined laminar profiles. To measure the dimensional entropy generation rate per unit area requires measurement of the thickness of the boundary layer. A general profile equation is given and used to show the range of accuracy of a further simplification to the calibration. For flows with low free-stream pressure gradients, the entropy generation rate is very simply related to the wall shear stress, if both are expressed without units. An array of heated thin film sensors is calibrated for the measurement of wall shear stress, thus demonstrating the feasibility of using them to measure profile entropy generation rate.

An investigation of external flows with various pressures and surfaces

Flow and convective heat transfer characteristics are considered by solving the mass, momentum and energy equations for two dimensional laminar and turbulent boundary layers at zero, favourable and adverse pressure gradients, including the influence of unheated starting length, surface curvature and free stream pressure gradients. The numerical predictions have been compared with approximate methods and experimental results. Results showed that Stanton numbers in laminar flat plates increased in all favourable pressure gradients and but increased only in moderate favourable pressure gradients of concave walls. On the other hand, Stanton numbers decreased both with adverse pressure gradients in laminar flow and with favorable pressures in tubulent flows.

The Origin of Turbulent Spots

It has been suggested that a turbulent spot is formed when a transient separation occurs in the laminar boundary layer and this criterion has been successfully used by Johnson and Ercan (1996, ASME Paper No. 96-GT-44; 1997, ASME Paper No. 97-GT-475) to predict bypass transition for boundary layers subjected to a wide range of free-stream turbulence levels and streamwise pressure gradients. In the current paper experimental results are presented that support the premise that the formation of turbulent spots is associated with transient separation. Near-wall hot-wire signals in laminar and transitional boundary layers are analyzed statistically to produce probability distributions for signal level and trough frequency. In the laminar period the signal level is normally distributed, but during the inter-turbulent periods in the transitional boundary layer, the distribution is truncated at the lower end, i.e., the lowest velocity periods in the signal disappear, suggesting that these are replaced during transition by the turbulent periods. The number of these events (troughs) also correlates with the number of turbulent spots during early transition. A linear perturbation theory is also used in the paper to compute the streamlines through a turbulent spot and its associated calmed region. The results indicate that a hairpin vortex dominates the flow and entrains a low-momentum fluid stream from upstream with a high-momentum stream from downstream and then ejects the combined stream into the turbulent spot. The hairpin can only exist if a local separation occurs beneath its nose and the current results suggest that this separation is induced when the instantaneous velocity in the near-wall signal drops below 50 percent of the mean. [S0889-504X(00)01001-1]

The effects of freestream pressure gradient on a corner boundary layer

The effects of freestream pressure gradient on a corner boundary layer

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.

The effects of freestream pressure gradient on a corner boundary layer

The incompressible boundary layer in the corner formed by two intersecting perpendicular semi-infinite planes is investigated; the freestream flow, aligned with the corner, is of the form xn,x repr...

Capturing of transition by the RNG based algebraic turbulence model

This paper concerns the RNG based algebraic turbulence model. This model has characteristics to capture transitional process from laminar to turbulent flow. This is determined by the argument of the Heaviside function, which becomes a threshold for the occurrence of turbulence. It is supposed that proper modeling of this argument will lead to correctly capture transition location. In the present paper, this argument is modeled in such a way that the form of cubic equation for the turbulent kinematic viscosity be maintained. Moreover, the length scale which is required to calculate the turbulent kinematic viscosity is newly proposed, taking into account the freestream pressure gradient. The validation is performed by comparing the calculated results with the empirical expressions as well as the experimental data. This model can simulate the streamwise intermittency effect, by which a sudden increase of skin friction is prevented. Moreover, the transition location can be predicted within reasonable accuracy compared with the experimental data.

Calculation of Transitional Boundary Layers With an Improved Low-Reynolds-Number Version of the k–ε Turbulence Model

Several well-known low-Reynolds-number versions of the k–ε models are analyzed critically for laminar to turbulent transitional flows as well as near-wall turbulent flows from a theoretical and numerical standpoint. After examining apparent problems associated with the modeling of low-Reynolds-number wall damping functions used in these models, an improved version of the k–ε model is proposed by defining the wall damping factors as a function of some quantity (turbulence Reynolds number Ret) that is only a rather general indicator of the degree of turbulent activity at any location in the flow rather than a specific function of the location itself, and by considering the wall limiting behavior, the free-stream asymptotic behavior, and the balance between production and destruction of turbulence. This new model is applied to the prediction of (1) transitional boundary layers influenced by the free-stream turbulence, pressure gradient, and heat transfer; (2) external heat transfer distribution on the gas turbine rotor and stator blade under different inlet Reynolds number and free-stream turbulence conditions. It is demonstrated that the present model yields improved predictions.

Flame structure and stabilization in a divergent flow. Eddy structure behind a circular cylinder in a cold divergent flow.

In order to elucidate the effects of positive pressure gradient on flame structure and stabilization mechanism, it is first necessary to clarify those on turbulence characteristics and eddy structure not only in a cold shear layer, but also in a cold wake flow behind a bluff body. In this study, the influences of pressure gradient in the flow direction on the surface pressure around a circular cylinder and the eddy-shedding process are investigated in a two-dimensional cold air flow without combustion. Flow visualization and an FFT analysis of the oscillating surface pressure are made to examine time-averaged and fluctuating properties concerning the eddy-shedding process. It is found that increasing the free stream pressure gradient causes a transition of the wake flow pattern from an alternative eddy-shedding type to a symmetric one without Karman vortex. An increase in the pressure gradient extends the wake region, and simultaneously lowers the pressure drag force, which may be regarded as one of the most important characteristics of the divergent flow.

The Effect of Pressure Gradient and Freestream Turbulence Intensity on the Length of Transitional Boundary Layers

The paper presents the results of an experimental investigation aimed at an elucidation of the individual and collective influence of freestream turbulence intensity and pressure gradient on the length of the transitional boundary layer. A correlation for the transition length Reynolds number is developed and used, in an intermittency-based computational scheme, to predict the transitional boundary layer behaviour in a number of practical flows representative of the suction surface of gas turbine blading.

Free-Stream Turbulence and Pressure Gradient Effects on Heat Transfer and Boundary Layer Development on Highly Cooled Surfaces

Heat transfer and boundary layer measurements were derived from flows over a cooled flat plate with various free-stream turbulence intensities (Tu = 1.6–11 percent), favorable pressure gradients (k = νe/ue2•due/dx = 0÷6•10−6) and cooling intensities (Tw/Te = 1.0–0.53). Special interest is directed towards the effects of the dominant parameters, including the influence on laminar to turbulent boundary layer transition. It is shown, that free-stream turbulence and pressure gradients are of primary importance. The increase of heat transfer due to wall cooling can be explained primarily by property variations as transition, and the influence of free-stream parameters are not affected.

Film Cooling From Two Rows of Holes Inclined in the Streamwise and Spanwise Directions

This paper describes the results of an experimental investigation into the film cooling effectiveness of two rows of holes inclined in the stream and spanwise directions. The effects of hole and row spacings and combinations of inclinations are investigated in the presence of free-stream pressure gradients and turbulence for a typical range of blowing rates.

The measurements of drag resulting from small surface irregularities immersed in turbulent boundary layers

Different methods for measuring the drag of small two-dimensional surface irregularities are considered. The pressure distribution technique is employed to measure the drag of small backward-facing steps in six different free stream pressure gradient flows. Results obtained show that Gaudet and Johnson's logarithmic drag coefficient relationship for zero pressure gradient is valid over a wide range of pressure gradients.

Boundary Layer Calculation for Analysis and Design

A simple, semiempirical method for calculating the laminar, transition, and turbulent boundary layer with arbitrary free stream pressure gradient is developed. Good correlation is obtained with data on general two dimensional turbulent flows, diffuser flows, and the cylinder in cross-flow. However only for the diffuser has the boundary layer flow been coupled with the potential core so that only the inlet conditions and geometry are required. In other cases the free stream velocity distribution must be known or calculable. Skin friction coefficient, momentum thickness Reynolds number, and free stream pressure gradient parameter correlation employs a simple lag theory. With the integral momentum equation the complete boundary layer parameters are obtained as functions of the distance along a surface.