Streamwise Evolution Research Articles

Performance of Rough-Ribbed Low-Pressure Turbine Blades Under Varying Loading and Operating Conditions

Abstract In this research, we pursue the efficacy of riblets in reducing blade profile loss of Low-Pressure Turbine (LPT) blades under various design and off-design conditions. We adopt a strategy in which surface roughness is employed in the transitional regime to minimize the separation bubble-related losses and flush mounted riblets downstream to mitigate the boundary layer losses due to an increase in the turbulent wetted area. Several high-fidelity scale resolving simulations are carried out to test the efficacy of this ‘rough-ribbed’ LPT blade for loadings ranging from low-lift (LL), high-lift (HL) and ultra-high-lift (UHL) conditions. Furthermore, two exit Reynolds numbers - 83,000 and 166,000 pertaining to engine-relevant design and off-design conditions, respectively, are considered. The streamwise evolution of skin friction coefficient, boundary layer integral parameters, instantaneous flow features and second-order statistics are analyzed to determine the design and off-design performance of riblets. The results demonstrate the efficacy of scallop-shaped riblets in reducing the profile loss and the blockage due to boundary layers with loading and Reynolds number. This resulted in a net skin-friction reduction of 3.4% for LL and 8% for UHL loading at cruise and a corresponding reduction in the trailing edge momentum thickness from 10% to 15%. Furthermore, the study highlights the necessity to optimize the riblet ramp to achieve skin friction reduction under off-design conditions.

Spectral proper orthogonal decomposition analysis of a spatially developing underexpanded round jet at Re = 45 000

This study conducts a comprehensive analysis of the coherent structures within a spatially developing underexpanded axisymmetric jet at a Reynolds number of 45 000, utilizing high-fidelity implicit large eddy simulations (iLES) in conjunction with spectral proper orthogonal decomposition (SPOD). In the frequency–wavenumber space, the global SPOD analysis identifies three distinct coherent structures, corresponding to three different mechanisms, namely, Kelvin–Helmholtz (KH), Orr, and lift-up. Their salient characteristics are discussed in detail. Local SPOD analysis further explores the streamwise evolution of these coherent structures, revealing that the influence of KH mechanism is confined to the near field, while the lift-up mechanism persists and dominates the energy content beyond the potential core, with the streaks of azimuthal wavenumbers one and two being the most energetic. The reconstruction of turbulent kinetic energy (TKE) and Reynolds shear stress from SPOD modes is assessed, and the first few azimuthal modes with low wavenumbers and frequencies are found crucial for capturing the dominant features of the flow. It is found that only the m = 0 and m = 1 modes contribute to the TKE at the centerline. The Reynolds shear stress reconstruction quality is comparable to TKE, but with a negligible contribution from the m = 0 mode. The azimuthal mode m = 1 captures the slope of the actual Reynolds shear stress profile in the vicinity of centerline, while m = 2 and higher modes capture the peak location of the actual profile.

Characterizing disturbance growth and transition of laminar separation bubbles subjected to varying freestream turbulence

The spatial manifestation of a boundary layer subjected to an adverse pressure gradient for varying freestream turbulence (FST) is discussed here through experiments and a wall-resolved large eddy simulation (LES). Three levels of FST, i.e., 1.02%, 2.1%, and 3.5%, are considered at a Reynolds number of 0.2 × 106 based on the inlet velocity and plate length. A laminar separation bubble (LSB) appears for FST levels of 1.02%, where the shear layer becomes unstable via the Kelvin-Helmholtz (K-H) mechanism. Bubble suppression is apparent, where transition occurs via the Klebanoff mode (K-mode), bypassing the K-H instability as the FST level is increased to 3.5%. The streamwise evolution of fluctuations reveals an exponential growth at a low FST of 1.02%, whereas it changes to algebraic at a higher FST level of 3.5%. Notably, a dual growth of velocity fluctuations, i.e., an algebraic growth in the initial part of LSB followed by an exponential growth, illustrates the coexistence of K-H instability and K-mode at an FST level of 2.1%: a finding corroborated by LES. Additionally, local linear stability analysis and the evolution of intermittency provide valuable insights into the growth of modal and non-modal instabilities and their interactions.

Modeling the transport and mixing of suspended sediment in ecological flows with submerged vegetation: A random displacement model-based analysis

Aquatic vegetation in rivers influences the flow structure, impacting the sediment transport in the river and further changing the ecosystem and geomorphologic evolution of the river. In this paper, an improved random displacement model (RDM) is proposed to investigate the concentration of suspended sediment (CSS) in flows with flexible submerged vegetation. Considering the effect of sediment resuspension on sediment transport, a probability model of sediment resuspension is embedded into the RDM so that the simulation process is more consistent with the natural cases. For the streamwise development of flow with flexible submerged vegetation, the flow is divided into a flow adjustment region and a fully developed region in the longitudinal direction. The vertical distributions of the flow velocity and turbulence diffusion coefficient were analyzed in these two regions, and they were incorporated into the RDM to simulate the along-flow development of the CSS. The simulated concentrations were compared with the experimental data. The mean relative errors (MREs) were below 15%, the root mean square errors (RMSEs) were below 0.20, and the Nash–Sutcliffe efficiencies (NSEs) ranged from 0.71 to 0.99, indicating that the improved RDM is plausible and reliable. In addition, the along-flow distribution of the sediment transport rate (STR) was analyzed. The rate exhibited a decreasing trend during the flow adjustment region and tended to stabilize during the fully developed region. This study provides a new way of thinking for research on sediment transport in rivers with aquatic vegetation, which is of great significance for achieving the sustainable development of river ecosystems and the optimal design of river channels.

Film hole layout optimization for multi-row film cooling plate in continuous parameter space under non-uniform inlet temperature distribution

Film cooling is an advanced external cooling technology for protecting gas turbine blades from excessive temperatures. To counteract non-uniform heat loads caused by hot streak and swirl effects at the combustion chamber outlet, fine design of film hole positions is necessary. However, the complexity due to the numerous film holes and their positional parameters presents challenges in the independent optimization of film hole positions in a continuous parameter space. This study proposed an optimization method grounded in the divide and conquer approach to address optimization for film hole layout. The film hole layout was decomposed into multiple single rows and optimized systematically by iteratively refining the single-row film hole layout along the streamwise direction using the expectation maximization algorithm. Optimized layouts for five different inlet temperature distributions were obtained using the proposed method and adiabatic wall temperature distributions were compared and analyzed for optimized and staggered layouts. Additionally, the cooling performance of the optimized layout was evaluated against the staggered layout under conjugate heat transfer conditions and the robustness of the optimized layout under various blowing ratios and peak temperature positions was tested. The results demonstrated that the proposed method can optimize the positions of 52 film holes within 0.3h, and it was generalized to various inlet temperature distributions. By enhancing lateral interactions among downstream film jets, the lifting effect of kidney vortex in the optimized layout was weakened, bringing the film jets closer to the wall and significantly increasing coolant coverage during streamwise development. Comparative analysis reveals the superior cooling performance of the optimized layout at the blowing ratio of 1.0, evidenced by a 15.1% reduction in total input heat transfer rate and a 12.3% enhancement in overall cooling efficiency relative to the staggered layout. Under conditions with blowing ratios ranging from 0.5 to 1.5 and peak temperature position deviations, the average wall temperature of the optimized layout consistently remained lower than the staggered layout, indicating the robustness of the optimized layout to variations in blowing ratio and hot streak position.

Experimental Study On Pressure-Velocity Relation Of Near-Field Tip Vortex Using Tomographic PIV

The non-cavitating tip vortex in the near field of an elliptical hydrofoil is studied using tomographic particle image velocimetry (TPIV). By investigating the distributions of the axial velocity difference and streamwise vorticity, the formation and development of the near-field tip vortex are clearly revealed. In the near field, the axial flow within the tip vortex manifests a jet-like profile, and the majority of the vorticity is contained within the vortex core. A special position is identified during the streamwise evolution of the tip vortex, where the vortex core circulation reaches its local maximum for the first time and tip vortex cavitation (TVC) might be more prone to incept. In the vicinity of this crucial position, a concise relation between the static pressure along the tip vortex center line and the local velocity is derived by combining the three-dimensional measured velocity fields with the governing equations. Based on the Reynolds-averaged Navier-Stokes equation, it is revealed that the mean static pressure along the vortex center line is directly related to the local mean axial velocity, whereas the local velocity fluctuation has little impact on the mean static pressure. It is the first attempt to combine the three-dimensional measurement with the governing equations to investigate the near-field tip vortex flow, which might provide valuable insights for understanding and predicting tip vortex cavitation inception.

On the generation of free-stream turbulence at low Reynolds number: A numerical study

We investigate the generation of free-stream perturbations at a relatively low characteristic Reynolds number of 1000 by means of direct numerical simulations using a synthetic turbulence generation method. This approach consists of generating turbulent fluctuations by means of digital filtering and a source term formulation in the Navier–Stokes equations. To assess its validity in the framework of decaying turbulence, we compare the results with those obtained with a physically-based, grid-induced turbulent flow in terms of spatial decay, evolution of characteristic length-scales and energy spectra. Also, we highlight relevant differences such as those in the streamwise development length and the anisotropy of the largest scales. Then, we characterize the generated perturbations when systematically varying the input parameters, namely the initial integral length-scale and turbulence intensity. Here, we notice differences in the streamwise decay of the turbulence intensity and the development length as we vary these parameters. By inspecting the evolution of the characteristic length-scales and the micro-scale Reynolds number, we also identify that the effective scale separation is highly sensitive to these variations.

Effect of Tip Gap Size on the Tip Flow Structure and Turbulence Generation in a Low Reynolds Number Compressor Cascade

Abstract Efficient and compact axial compressors are currently undergoing rapid development for use in microcooling systems and small-scale vehicles. Limited experimental work concentrates on the inner flow field of the compressors working at such low Reynolds numbers (Re∼104). This study examines the vortical structures and the resulting turbulence production in the transitional flow over a C4 compressor blade at a Reynolds number Re of 24,000, with a specific focus on the impact of tip clearance. The particle image velocimetry measurements reveal the tip flow structures in detail, including the tip leakage vortex (TLV) and its induced complex vortical structures. The tip secondary flow at the low Reynolds number can be divided as the tip leakage flow (TLF)/vortex and transitional boundary layer both at the end walls and the blade surfaces. The TLV propagates at the highest spanwise positions and farthest pitchwise positions at the middle tip gap size (τ/C = 3%) for the three tip gap sizes investigated. The tip flow fluctuations decrease from τ/C = 5% to τ/C = 3% and then increase from τ/C = 3% to τ/C = 1%. The spatial distribution, streamwise evolution, and individual Reynolds normal stress components contributing to the turbulent kinetic energy (TKE) are discussed. The primary contributors to the turbulence generation are examined to elucidate the flow mechanism leading to the distinct anisotropic turbulence structure in the tip region with various tip gap sizes.

Interaction of stream-wise vortices generated by swirler grid

A system of stream-wise vortices has been created using a grid of swirling elements with alternating orientations (like a chessboard). The particle image velocimetry method has been used to map the velocity field in several planes perpendicular to the stream. The mesh-based Reynolds number is 1.35×104 and 2.71×104, respectively. The stream-wise development of turbulent kinetic energy (TKE) shows first an increase in a distance of x≈10M, followed by power-law decay. Individual vortices are detected in each snapshot. The radial profile of TKE transformed to a vortex coordinate system is almost constant, either with maximum as in static frame or zero as observed by previous research. The properties of detected vortices are studied statistically: the meandering amplitude expressed as the standard deviation of vortex positions grows roughly as ∼ex, i.e., faster than expected random-walk growth ∼x. Vortex circulation decays exponentially as predicted by classical Helmholtz theorem. The interaction between neighboring vortices is expressed via correlation of selected quantities. Correlation of energy develops downstream from anticorrelation to a positive correlation. The strongest correlation is observed between the first vortex circulation and the second vortex position perpendicular to their connection line. Other correlations are weak.

Planar wall plumes bounded by vertical and inclined surfaces

Planar wall plumes are gravity-driven flows where a fluid of lower (or higher) density than the ambient rises (or lowers) along a vertical or inclined wall. This study investigates planar wall plumes at five different wall slopes, ranging from a vertical wall (θ=90°) to a shallow inclination of θ=3°, using highly resolved direct numerical simulations. The three-dimensional turbulent structure of these supercritical flows is investigated in detail along with the streamwise evolution of the depth-averaged quantities. Simulations were performed in very large domains in order to focus attention on the behavior of the plumes in the near self-similar state, far downstream of the inlet. In the self-similar state, key quantities such as the entrainment rate, the basal drag coefficient, the Richardson number (or equivalently the Froude number), and the shape factors reach constant values, which dependent only on the slope. The present simulations, along with earlier results for subcritical currents at shallower slopes, provide a complete description of this dependency.

Three-dimensional characteristics of separation vortex generated by crossing shock/boundary layer interaction

Three-dimensional characteristics of separation vortex generated by crossing shock/boundary layer interaction

Response of a Turbulent Boundary Layer to an Imposed Synthetic Large-Scale Structure

The dynamic response of a zero-pressure gradient turbulent boundary layer (TBL) to an active flow control actuator was experimentally investigated. The experimental TBL had a sufficiently low momentum thickness Reynolds number, such that there were no energetic organized large-scale structures in the outer region, as evidenced from measurements of the premultiplied wavenumber–frequency spectra. The periodically pulsed plasma actuator, placed inside the outer region of TBL, introduced a synthetic large-scale structure, and the boundary-layer response to this synthetic structure downstream of the actuator at select wall-normal and streamwise locations was investigated. The turbulence amplitude modulating effect of the synthetic large-scale structure, within the inner and log-linear regions of the boundary layer, was isolated and analyzed using a phase-locked analysis. The dynamic interaction of the synthetic large-scale structure and smaller-scale turbulent motions was quantified using a modulation coefficient, and a strong positive correlation within the inner and log regions of the boundary layer was measured. The streamwise development of the synthetic large-scale structure and its modulating effect on the near-wall turbulence across several streamwise locations are described. Profiles of the phase speed at these streamwise locations were extracted and were found to be constant within the log region, further confirming a strong coupling between the near-wall fluctuations in turbulence intensity and the synthetic large-scale motions introduced in the outer region. Overall, the turbulence amplitude modulation effect induced by the synthetic large-scale structure was found to be dynamically similar to the large-scale modulation measured in canonical TBLs at higher Reynolds numbers.

Effects of Riblet Dimensions on the Transitional Boundary Layers Over High-Lift Turbine Blades

Abstract Substantial research exists in the literature on reducing the profile loss of transitional boundary layers over low-pressure turbine (LPT) blades via different mechanisms such as freestream turbulence, upstream wakes, and surface roughness. These mechanisms have proven to be beneficial in mitigating the separation bubble-related losses in ultra-high-lift blade designs, despite an increase in the loss due to increased turbulent wetted area (TWA). In this work, we adopt a strategy of employing surface roughness in the transitional regime to minimize the separation bubble-related losses and flush-mounted riblets downstream to further mitigate the skin-friction drag and boundary layer losses due to an increase in the TWA. Several high-fidelity scale-resolving simulations are performed on this “rough-ribbed blade surface” to discern the effect of varying the riblet spacing (s+) and height (h+). The streamwise evolution of skin-friction coefficient, boundary layer integral parameters, and shape factor are compared and contrasted among riblets of different dimensions. The instantaneous flow features and second-order statistics such as the Reynolds stress, turbulent kinetic energy, and its production are analyzed for different test cases to determine the impact of riblets on these quantities. When compared to the roughness alone configuration, the scalloped shape riblets with s+ = 17 and h+ = 22 reduced the net skin-friction drag by 7.3% and the trailing edge momentum thickness by 14.5%, thereby demonstrating the efficacy of riblets in reducing the mixing losses under adverse pressure gradients. Through an analysis of flow blockage introduced by the application of riblets, the deleterious effects of increasing the riblet height along with the necessity of optimizing the riblet ramp are highlighted.

Characteristic stages of heat transfer for supercritical CO2 flowing downward in a vertical tube under cooling conditions

The present work investigates the streamwise development stages of supercritical carbon dioxide downward cooling flow and heat transfer in a vertical tube through direct numerical simulation. The tube has a diameter of 2 mm and an inlet Reynolds number of 5400. The formation mechanisms of flow stages are investigated by studying turbulence statistics and momentum balance analysis. The results indicate that there are three distinct development stages for both flow and heat transfer, including a deterioration stage, a recovery stage, and a re-deterioration stage. The last stage only occurs in some flows and is less well-understood than the first two stages. In the flow deterioration stage, both the weakening of the external buoyancy effect (due to mean flow modification) and the negative influence of the structural effect (direct interactions between the fluctuating density and the thermal field) contribute to flow laminarization. In the flow recovery stage, the increase in buoyancy further reduces the streamwise pressure gradient, increasing near-wall velocity. At this point, the velocity profile becomes M-shaped, accompanied by turbulence regeneration. As the bulk temperature drops around pseudo-critical temperature, a sudden global deceleration occurs due to the increased fluid density, which weakens both the external and structural effects and causes a decrease in turbulence, and hence the flow and heat transfer enter the re-deterioration stage. Moreover, the inlet temperature and wall heat flux have a pronounced effect on the development stages, which affects the duration distance of the deterioration stage and the corresponding enthalpy value at the beginning of the recovery stage.

Hydrodynamics of turbidity currents evolving over a plane bed

In this paper, we investigate the hydrodynamics of turbidity currents evolving over a plane bed. The analytical framework encompasses the depth-averaged conservation equations for fluid mass, sediment mass, momentum, and turbulent kinetic energy (TKE). The analysis incorporates self-similar distributions of streamwise velocity, sediment concentration, and TKE. Using the self-similar distributions of streamwise velocity and sediment concentration, the distributions of turbulent diffusivity, Reynolds shear stress, and TKE production rate are determined. The analytical model of turbidity currents enables the prediction of streamwise evolutions of flow depth, depth-averaged velocity, depth-averaged sediment concentration, and depth-averaged TKE. The self-acceleration and subsidence of turbidity currents are found to depend on the initial conditions. Additionally, the model results demonstrate the sensitivity of turbidity current hydrodynamics to grain size and longitudinal bed slope. Importantly, increased grain size and longitudinal bed slope contribute to enhanced self-acceleration, leading to a decrease in the subsidence rate of turbidity currents. The model predictions satisfactorily capture the available experimental data.

A unified description of mean velocity in transitional- and turbulence-developed boundary layers

This study presents a unified algebraic model based on the multi-layer mixing length to quantify the mean velocity of the transitional and fully turbulent boundary layer. Mean velocity profiles from direct numerical simulations of the zero-pressure-gradient boundary layer are being investigated. By using the gradient descent method, three parameters in the multi-layer mixing length are optimized and determined at each streamwise location. It turns out that the multi-layer mixing length model describes mean velocity profiles well, and the corresponding relative deviation is around 2%. This value is not less than, or even better than, the compared Nickels’ model [Nickels, J. Fluid Mech. 521, 217–239 (2004)]. Moreover, the variation of the three optimal parameters with Rex is similar to the streamwise development of the friction coefficient. This similarity offers a supplementary way to comprehend the transition process. The results confirm that the multi-layer length function is suitable for modeling transitional boundary layers.

Scaling of boundary-layer disturbances exposed to free-stream turbulence

We present theoretical results related to the experimental findings of Matsubara & Alfredsson (J. Fluid Mech., vol. 430, 2001, pp. 149–168) on the scaling of the energy spectra of the Klebanoff modes, i.e. streamwise-elongated vortical disturbances generated by free-stream turbulence in a flat-plate transitional boundary layer. The scaling is explained by a model that describes the streamwise evolution of the streamwise and spanwise energy spectra. The theoretical framework is based on the quasi-steady asymptotic solution of the boundary-region equations, on an axial-symmetric model of the free-stream spectrum, and on the spectral response of the boundary layer to the external perturbations.

Particle segregation within bidisperse turbidity current evolution

Multigrain/polydispersity has a significant impact on turbidity current (TC). Despite the fact that several researches have looked into this effect, the impact of the fluid–particle interactions is not fully understood. Motivated by this, we employ the Eulerian–Lagrangian computational fluid dynamics–discrete element method model to investigate the dynamics of the bidisperse lock-exchange TC. Results show that, because the coarse particles will settle faster and stop moving forward, the two phases of bidisperse transport and fine component transport can be distinguished in the evolution of the bidisperse TC. During the bidisperse transport stage, the upper interface of each component is primarily determined by their own settling and transport characteristics and does not strongly depend on the relative fine particle volume fraction $\phi _F$ . Fine particles are primarily responsible for the vortical structures near the upper interface of the TC head, and the increase of $\phi _F$ promotes their streamwise development. In comparison, fragmented vortical coherent structures are closely related to the presence of coarse particles, which can be seen in the lower layers. Bidisperse segregation alters the collision process between dispersed phases, which differs from monodisperse TC. The collisions and segregation-induced flow establish interconnections between the two dispersed phases. In the latter stage, the transport of fine particles is inhibited by both the lift force and the contact force produced by the collision with the deposited materials. As $\phi _F$ rises, the negative contact force weakens, and its change is essentially balanced by the rise in negative lift force.

Secondary flows induced by two-dimensional surface temperature heterogeneity in stably stratified channel flow

The structure and impact of thermally induced secondary motions in stably stratified channel flows with two-dimensional surface temperature inhomogeneities is studied using direct numerical simulation (DNS). Starting from a configuration with only spanwise varying surface temperature, where the streamwise direction is homogeneous (Bon & Meyers, J. Fluid Mech., 2022, pp. 1–38), we study cases where the periodic temperature strip length $l_x/h$ (with $h$ the half-channel height) assumes finite values. The patch width ( $l_y/h =\{{\rm \pi} /4, {\rm \pi}/8$ }) and length are varied at fixed stability and two different Reynolds numbers. Results indicate that for the investigated patch widths, the streamwise development of the secondary flows depends on the patch aspect ratio ( $a=l_x/l_y$ ), while they reach a fully developed state after approximately $25l_y$ . The strength of the secondary motions, and their impact on momentum and heat transfer through the dispersive fluxes, is strongly reduced as the length of the temperature strips decreases, and becomes negligible when $a\lesssim 1$ . We demonstrate that upward dispersive and turbulent heat transport in locally unstably stratified regions above the high-temperature patches lead to reduced overall downward heat transfer. Comparison to local Monin–Obukhov similarity theory (MOST) reveals that scaled velocity and temperature gradients in homogeneous stably stratified channel flow at $Re_\tau =550$ agree reasonably well with empirical correlations obtained from meteorological data. For thermally heterogeneous cases with strips of finite length, the similarity functions only collapse higher above the surface, where dispersive fluxes are negligible. Lastly, we show that mean profiles of all simulations collapse when using outer-layer scaling based on displacement thickness.

Data-driven estimation of entropy production by large scale motions in an intermediate turbine duct

In modern gas turbines, the physics of three-dimensional inflow for aggressive intermediate turbine ducts are strongly associated with large-scale coherent motions, which contribute to the production of irreversible aerodynamic and thermodynamic energy losses. To address this problem, an extended data-driven approach for estimating the irreversible losses through viscosity dissipation and heat transfer in turbulent flows is proposed. An aggressive intermediate turbine duct connected to a high-pressure turbine is numerically investigated using the detached-eddy simulation framework. The influence of tip leakage vortices and rotor wakes on the aerodynamics in the duct is assessed through quadruple proper orthogonal decomposition analysis. The entropy production rate corresponding to the coherent structures is then identified, and the irreversible losses in the duct subject to unsteady flow motions are quantitatively evaluated. The results indicate that the coherent structures in the intermediate turbine duct are strongly associated with the upstream conditions, including the tip leakage flow and rotor wakes. Direct viscous dissipation accounts for the majority of the irreversible losses, with coherent perturbed dissipation contributing to 7.25% and 5.54% of the total for tip gap sizes of 1.5% and 3.5% span, respectively. The streamwise development of coherent perturbations is restricted compared with that in the mean structure, and the stochastic part contributes little to the viscous dissipation. The proposed method provides a systematic procedure for estimating the irreversible energy losses in unsteady turbulent flow, and highlights the significance of unsteady aero-thermodynamics in the design of turbomachinery.