Numerical Study of Deterministic Fluxes in Compressor Passages

Abstract

Computational fluid dynamics (CFD) has been widely adopted in the compressor design process, but it remains a challenge to predict the flow details, performance, and stage matching for multistage, high-speed machines accurately. The Reynolds Averaged Navier-Stokes (RANS) simulation with mixing plane for bladerow coupling is still the workhorse in the industry and the unsteady bladerow interaction is discarded. This paper examines these discarded unsteady effects via deterministic fluxes using semi-analytical and unsteady RANS (URANS) calculations. The study starts from a planar duct under periodic perturbations. The study shows that under large perturbations, the mixing plane produces dubious values of flow quantities (e.g., whirl angle). The performance of the mixing plane can be considerably improved by including deterministic fluxes into the mixing plane formulation. This demonstrates the effect of deterministic fluxes at the bladerow interface. Furthermore, the front stages of a 19-blade row compressor are investigated and URANS solutions are compared with RANS mixing plane solutions. The magnitudes of divergence of Reynolds stresses (RS) and deterministic stresses (DS) are compared. The effect of deterministic fluxes is demonstrated on whirl angle and radial profiles of total pressure and so on. The enhanced spanwise mixing due to deterministic fluxes is also observed. The effect of deterministic fluxes is confirmed via the nonlinear harmonic (NLH) method which includes the deterministic fluxes in the mean flow, and the study of multistage compressor shows that unsteady effects, which are quantified by deterministic fluxes, are indispensable to have credible predictions of the flow details and performance of compressor even at its design stage.

Favre-Averaged Nonlinear Harmonic Method for Compressible Periodic Flows

“…This is 450 time steps for the 15 deg sector and is equivalent to 10,800 time steps if the whole wheel is the case. The choice of the time step is based on the previous URANS study of the same compressor [33]. The mesh for the FNLH is identical to the steady simulation with mixing plane.…”

Computation of Multistage Flows Using a Fourier Approach

“…For the time-mean flow, the mixing plane is modified to include the contribution of deterministic fluxes in the convective fluxes of the momentum and energy equations. For a more detailed study of R-S or S-R interface treatment, readers can refer to Wang et al [5,12] for more details.…”

“…Quasi-3D non-reflective treatment for the mean flow and the linearized flow is used for the bladerow interface [31]. The mean flow is coupled with a reformulated mixing plane which includes deterministic fluxes [5,27] in the flux averaging. Phase shift is applied on the periodic boundaries of the linearized solution so that only one passage is required in multi-bladerow computations.…”

“…The first test case is the mid-span stream tube of the front 1.5 stages of an 8-stage compressor, and the stream tube accounts for roughly 4.8% of the span height. The code has been extensively validated on this compressor both for RANS [35] and URANS [5]. The configuration of the geometry is shown in Fig.…”

“…Such effect is embodied by the deterministic stresses [3,4] in the momentum equation and by additional terms in the energy equation. Together these additional terms are denoted as deterministic fluxes [5] in the following text. If the stochastic fluctuation is modelled by a suitable turbulence model (e.g.…”