Study of Unforced and Modulated Film-Cooling Jets Using Proper Orthogonal Decomposition—Part I: Unforced Jets

Bidan, Guillaume; Vézier, Clementine; Nikitopoulos, Dimitris E.

doi:10.1115/1.4006599

Cited by 22 publications

(15 citation statements)

References 26 publications

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“…As validation, we compare the results obtained from our direct numerical simulation with the experimental measurements carried out by Bidan et al [21] for a 35-deg inclined jet in crossflow. The computational domain consists of a pipe with length of 7D with a 35-deg angle with the crossflow and a mainstream domain that expands the volume of 21D in the streamwise direction, 10D in the wall-normal direction and 6D in the spanwise direction.…”

Section: Resultsmentioning

confidence: 87%

“…6, timeaveraged streamwise velocity profiles are compared with those of experimental measurements in Ref. [21] at three different streamwise sections on the centerline plane. Overall good agreement is obtained.…”

Section: Resultsmentioning

confidence: 99%

“…Error convergence forg N ðnÞ with increasing polynomial order Comparison of time-averaged u 1 velocity in the midplane with experimental data[21] at BR 5 0:15…”

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confidence: 99%

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Optimization of Forcing Parameters of Film Cooling Effectiveness

Babaee

Acharya

Wan

2013

Volume 3B: Heat Transfer

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An optimization strategy is described that combines high-fidelity simulations with response surface construction, and is applied to pulsed film cooling for turbine blades. The response surface is constructed for the film cooling effectiveness as a function of duty cycle, in the range of DC between 0.05 and 1, and pulsation frequency St in the range of 0.2–2, using a pseudo-spectral projection method. The jet is fully modulated and the blowing ratio, when the jet is on, is 1.5 in all cases. Overall 73 direct numerical simulations (DNS) using spectral element method were performed to sample the film cooling effectiveness on a Clenshaw-Curtis grid in the design space. The geometry includes a 35-degree delivery tube and a plenum. It is observed that in the parameter space explored a global optimum exists, and in the present study, the best film cooling effectiveness is found at DC = 0.14 and St = 1.03. In the same range of DC and St, four other local optimums were found. The physical mechanisms leading to the forcing parameters of the global optimum are explored and ingestion of the crossflow into the delivery tube is observed to play an important role in this process. The gradient-based optimization algorithms are argued to be unsuitable for the current problem due to the non-convexity of the objective function.

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Section: Resultsmentioning

confidence: 87%

Section: Resultsmentioning

confidence: 99%

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Optimization of Forcing Parameters of Film Cooling Effectiveness

Babaee

Acharya

Wan

2013

Volume 3B: Heat Transfer

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“…Indeed, in the mid-field (2<X j <10), the iso-surfaces of the temperature fluctuation exhibit hairpin like shapes showing the convective effect of the hairpin vortices while in the far field (10<X j ) elongated tube-like isosurfaces suggest the side vortices participate in mixing in the wall region. More details on the formation of the vortical structures and their impact on the wall temperature can be found in 30 .…”

Section: Instantaneous Flow Fieldsmentioning

confidence: 99%

Film-Cooling Jets Analyzed with Proper Orthogonal Decomposition and Dynamic Mode Decomposition

Bidan

Nikitopoulos

2013

43rd Fluid Dynamics Conference

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Film cooling jets were simulated using Large Eddy Simulation (LES) at blowing ratios of 0.150, 0.50 and 1.0. The results were analyzed using Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) as a statistical analysis tool and the first step toward reduced order modeling. The results of both decompositions are presented and put in perspective with dominant vortical structures and heat transfer mechanisms observed in the instantaneous velocity and temperature fields. Assessment of the performance of the decompositions is provided in terms of energy content and rendered dominant frequencies. Evolution of the dominant modes and decomposition metrics are discussed as the blowing ratio is increased. Nomenclature BR = Blowing ratio D j = Jet diameter, mm Re δ = Boundary layer Reynolds number (U ∞ .δ/ν) St = Strouhal number (f D j /U ∞ ) = Time averaged temperature, K ΔT = Normalized temperature fluctuation (T-)/(T j -T ∞ ) (T j , T ∞ jet and cross-flow temperatures resp.) U ∞= Average free-stream velocity, m.s -1 X j = Normalized streamwise coordinate (x/D j ) Y j = Normalized spanwise coordinate (y/D j ) Z j = Normalized vertical coordinate (z/D j ) δ = 99% Boundary layer thickness, mm ν = Air kinematic viscosity, m 2 .s -1 φ i , a i = Velocity POD shape function and temporal coefficient ψ i , b i = Temperature POD shape function and temporal coefficient Φ i , λ i = Velocity DMD shape function and eigenvalue Ψ i , μ i = Temperature DMD shape function and eigenvalue Λ 2 = Second invariant of the tensor S 2 +Ω 2 (S -stress tensor, Ω -rate of rotation tensor)

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“…Film cooling effectiveness, among other factors, is strongly dependent on the blowing ratio (the ratio of the averaged coolant velocity in the delivery tube to the crossflow velocity) as demonstrated by several experimental and numerical studies (see for e.g., Refs. [3,4]). The coolant film with very low blowing ratio (BR < 0.1) can be rapidly mixed out with the crossflow, which leads to the deterioration of film cooling performance.…”

Section: Introductionmentioning

confidence: 99%

Effect of Uncertainty in Blowing Ratio on Film Cooling Effectiveness

Babaee

Wan

Acharya

2013

Journal of Heat Transfer

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In this study, the effect of randomness of blowing ratio on film cooling performance is investigated by combining direct numerical simulations with a stochastic collocation approach. The geometry includes a 35-deg inclined jet with a plenum attached to it. The blowing ratio variations are assumed to have a truncated Gaussian distribution with mean of 0.3 and the standard variation of approximately 0.1. The parametric space is discretized using multi-element general polynomial chaos (ME-gPC) with five elements where general polynomial chaos of order 3 is used in each element. Direct numerical simulations were carried out using spectral element method to sample the governing equations in space and time. The probability density function of the film cooling effectiveness was obtained and the standard deviation of the adiabatic film cooling effectiveness on the blade surface was calculated. A maximum of 20% of variation in film cooling effectiveness was observed at 2.2 jet-diameter distance downstream of the exit hole. The spatially-averaged adiabatic film cooling effectiveness was 0.23 ± 0.02. The calculation of all the statistical properties were carried out as off-line post processing. A fast convergence of the polynomial expansion in the random space is observed which shows that the computational strategy is very cost-effective.

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Study of Unforced and Modulated Film-Cooling Jets Using Proper Orthogonal Decomposition—Part I: Unforced Jets

Cited by 22 publications

References 26 publications

Optimization of Forcing Parameters of Film Cooling Effectiveness

Optimization of Forcing Parameters of Film Cooling Effectiveness

Film-Cooling Jets Analyzed with Proper Orthogonal Decomposition and Dynamic Mode Decomposition

Effect of Uncertainty in Blowing Ratio on Film Cooling Effectiveness

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