Development and Application of a Multistage Navier-Stokes Solver: Part I — Multistage Modeling Using Bodyforces and Deterministic Stresses

Abstract

A novel multistage compressor performance analysis method based on the three-dimensional Reynolds averaged Navier-Stokes equations is presented in this paper. This approach is a “continuous interface plane approach” where deterministic stresses are used to ensure continuous physical properties across interface planes. The average unsteady effects due to neighboring blades and/or vanes are approximated using deterministic stresses along with the application of bodyforces. Bodyforces are used to account for the “potential” interaction between closely coupled (staged) rows. Deterministic stresses account for the “average” wake blockage and mixing effects both axially and radially. The attempt here is to implement an approximate technique for incorporating periodic unsteady flow physics that provides for a robust multistage design procedure incorporating reasonable computational efficiency. The present paper gives the theoretical development of the stress/bodyforce models incorporated in the code, and demonstrates the usefulness of these models in practical compressor applications. Compressor performance prediction capability is then established through a rigorous code/model validation effort using the power of networked workstations. The numerical results are compared with experimental data in terms of one-dimensional performance parameters such as total pressure ratio and circumferentially averaged radial profiles deemed critical to compressor design. This methodology allows the designer to design from hub to tip with a high level of confidence in the procedure.

On the Role of the Deterministic and Circumferential Stresses in Throughflow Calculations

“…neglecting the purely temporal part of the deterministic stresses and retaining only the spatial part [3]. Some approaches based on this assumption compute explicitly the terms required for the closure and neglect the viscous terms [15], [6]. Bardoux [6] has presented some results obtained on the same CME2 compressor that is studied here.…”

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

“…To accelerate the convergence, local time stepping [23], implicit residual smoothing [24] and multigrid [25] are employed. The mixing plane method [18] is employed in the steady simulation and the continuous interface plane method [3] is used in the time-averaging simulation for the interblade row coupling. The domain scaling method is employed in the unsteady simulation [26].…”

“…Adamczyk et al [2] proposed the first model using overlapping grids for all blade rows without interface planes. Rhie et al [3] demonstrated a continuous interface plane approach using overlapping grids for downstream row only. LeJambre et al [4] employed this type of analysis in a multistage axial compressor design study and effectively improved a baseline design using results from the averagepassage-based flow simulation.…”

“…V(1) is the spatial velocity fluctuation of the time-average flow relative to the axisymmetrical flow in a frame of reference fixed to the blade row 1, V(2) is the spatial velocity fluctuation of the time-average flow relative to the axisymmetrical flow in a frame of reference fixed to the blade row 2, and V(3) is purely unsteady in either frame of reference.…”

Computational Study of Asynchronous Vibrations in a 1.5 Stage Transonic Compressor

“…Responding to this limitation, several researchers have worked on the Mixing-plane method [1][2][3][4][5][6][7] to approximate the unsteady flow field that occurs in multistage turbomachines with a steady flow. The idea is that by adding a mixing layer between adjacent blade rows, the flow can essentially "mix" and thus smooth out the unsteady variations that would occur in a real multistage machine.…”