Modeling turbomachinery unsteadiness with lumped deterministic stresses

Sondak, Douglas L.; Dorney, Daniel J.; Davis, Roger L.

doi:10.2514/6.1996-2570

Cited by 23 publications

(13 citation statements)

References 2 publications

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“…The LDST technique has been used in this latter fashion by Sondak et al 1 and Busby et al 2 to model rotor-stator interaction unsteadiness in turbomachinery. They performed unsteady inviscid simulations to extract the lumped deterministic stress field and then applied it as a source term in steady viscous calculations to model unsteady flow effects.…”

Section: Nomenclaturementioning

confidence: 99%

Neural Network Modeling of Deterministic Unsteadiness Source Terms

et al. 2006

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A neural-network-based lumped deterministic source term technique is presented that results in the prediction of an approximate time-average solution when used to modify a steady-state solver. Three different neural networks are developed for simple cavity flows using Mach number, cavity length-to-depth ratio, and aft wall translation as parameters. The results indicate that axial force data can be reproduced with less than 15% error as compared to the time average of a fully unsteady calculation. Computation times for the resultant neural network lumped deterministic source term approach were up to two orders of magnitude less than the comparable unsteady solution and were essentially identical to that of a steady-state calculation, although it must be noted that a database of unsteady calculations is required to develop the technique. The lumped deterministic source terms did not appear to affect the robustness of the steady-state solver adversely. NomenclatureA = control surface area a, a n i = neural network output neuron b l i = neural network bias c, c i = neural network input neuron D = cavity length E = error vector function e = neural network error vector e t = total energy F = force vector f = function k = turbulent kinetic energy L = cavity length L/D = cavity length-to-depth ratio M = Mach number n = normal direction vector n j i = neural network neuron P = primitive variable vector p= y-direction velocity .Sekar@wpafb.af.mi. Associate Fellow AIAA.[W]= weight factor matrix w = z-direction velocity (x, y, z) = Cartesian coordinate directions y + = nondimensional turbulent near-wall distance γ = ratio of specific heats ε = turbulent dissipation μ = molecular viscosity μ t = turbulent viscosity ρ = density υ = kinematic viscosity Subscripts wall = wall value 0 = stagnation conditions Superscripts -= time average = = derived quantity time average ∼ = deterministic fluctuation = stochastic fluctuation

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Section: Nomenclaturementioning

confidence: 99%

Neural Network Modeling of Deterministic Unsteadiness Source Terms

et al. 2006

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“…Many efforts have been made on this and then various models have been proposed in recent years [2][3][4][5][6][7][8][9][10]. These studies showed that the models employed in the APES obviously improve the numerical results in comparison with mixing plane method.…”

Section: List Of Symbolsmentioning

confidence: 99%

“…Only DC in momentum equations was modeled in some models [7,9,10], though there is also DC in energy equation. Some models [5,6] are reducedorder models, belonging to simplified unsteady calculations and are still too time consuming in comparison with the mixing plane method. Hence, more research work should be conducted to study the influence of DC on the time-averaged flow and to model the DC.…”

Section: List Of Symbolsmentioning

confidence: 99%

Study of modeling unsteady blade row interaction in a transonic compressor stage part 2: influence of deterministic correlations on time-averaged flow prediction

Liu

2012

Acta Mech Sin

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The average-passage equation system (APES) provides a rigorous mathematical framework for accounting for the unsteady blade row interaction through multistage compressors in steady state environment by introducing deterministic correlations (DC) that need to be modeled to close the equation system. The primary purpose of this study was to provide insight into the DC characteristics and the influence of DC on the time-averaged flow field of the APES. In Part 2 of this two-part paper, the influence of DC on the time-averaged flow field was systematically studied. Several time-averaging computations were conducted with various boundary conditions and DC for the downstream stator in a transonic compressor stage, by employing the CFD solver developed in Part 1 of this two-part paper. These results were compared with the time-averaged unsteady flow field and the steady one. The study indicated that the circumferentialaveraged DC can take into account major part of the unsteady effects on spanwise redistribution of flow fields in compressors. Furthermore, it demonstrated that both deterministic stresses and deterministic enthalpy fluxes are necessary to reproduce the time-averaged flow field.

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“…Li & Tourlidakis [5] improved this model by introducing the blade blockage through a different approach for the body force modeling and concluded that the implementation of the deterministic stresses is beneficial to the flow prediction but the improvement in accuracy for low-speed axial flow compressor rear stages is not significant. Sondak et al [6] developed a "lumped" DC model based on lower-order (inviscid) time-dependent simulations and the model saved 63 % CPU time compared with that based on a fully coupled unsteady viscous simulation. He [7] developed a nonlinear harmonic method, showing that this method is much more efficient than the nonlinear time-marching methods while still modeling dominant nonlinear effects.…”

Section: Introductionmentioning

confidence: 99%

Study of modeling unsteady blade row interaction in a transonic compressor stage part 1: code development and deterministic correlation analysis

Liu

2012

Acta Mech Sin

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The average-passage equation system (APES) provides a rigorous mathematical framework for accounting for the unsteady blade row interaction through multistage compressors in steady state environment by introducing deterministic correlations (DC) that need to be modeled to close the equation system. The primary purpose of this study is to provide insight into the DC characteristics and the influence of DC on the time-averaged flow field of the APES. In Part 1 of this two-part paper, firstly a 3D viscous unsteady and time-averaging flow CFD solver is developed to investigate the APES technique. Then steady and unsteady simulations are conducted in a transonic compressor stage. The results from both simulations are compared to highlight the significance of the unsteady interactions. Furthermore, the distribution characteristics of DC are studied and the DC at the rotor/stator interface are compared with their spatial correlations (SC). Lastly, steady and time-averaging (employing APES with DC) simulations for the downstream stator alone are conducted employing DC derived from the unsteady results. The results from steady and time-averaging simulations are compared with the time-averaged unsteady results. The comparisons demonstrate that the simulation employing APES with DC can reproduce the time-averaged field and the 3D viscous time-averaging flow solver is validated.

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Modeling turbomachinery unsteadiness with lumped deterministic stresses

Cited by 23 publications

References 2 publications

Neural Network Modeling of Deterministic Unsteadiness Source Terms

Neural Network Modeling of Deterministic Unsteadiness Source Terms

Study of modeling unsteady blade row interaction in a transonic compressor stage part 2: influence of deterministic correlations on time-averaged flow prediction

Study of modeling unsteady blade row interaction in a transonic compressor stage part 1: code development and deterministic correlation analysis

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