VALIDATION OF THE EULER FLOW SOLVER
STA 2 STA 1 STATOA
T O A «10 m JR
nff
a
o n o m i n a l s u m « Î M l o n ? ) t 40 0 l « ) n 101 Q0#& O fl/O O M O R o to rFigure 4.1: United Technologies Research Center Large Scale Rotating Rig (Schem atic Diagram Reproduced from Dring et al.^ 1981 Report)
4.2.2 Num erical Analysis
In both cascades, the high aspect ratio (see table 4.1) of the blades isolated the end-wall effects and gave rise to a smooth and nearly two-dimensional flow near the mid-span
(see Dring et a l, 1982).
In addition, it is also noted that the steady state flow over the rotor had only a weak dependence on the axial gap from the adjacent row of vanes upstream. Based on these
observations, two-dimensional simulations of the flows past the mid-span sections of both blades are performed separately for the validations. In both computations, viscous modelling is included. The viscous shear stresses are approximated with a constant wall
friction factor, C/ and distributed with an algebraic power law constant, n. The chosen
constants, C /= 0.01 and « = 70 are typical values suggested by Denton (1986) which
are also confirmed by numerical experimentation here. The UTRC experiments were
carried out at three flow coefficients {Vj rco =0.68, jrco =0.78 and Jrco =0.96). In
the current analysis, the flow condition corresponding to jrco =0.78 is used.
4.2.2.1 Grid Definition
Simple sheared H-grid topology is employed to define the computational domains for the cascades. The blunt leading-edges of both cascades are modelled correctly but their blunt trailing-edges are replaced by short wedges simulating the recirculating flow zone downstream o f the edges. This is a common practice to ensure that the flow leaves the blade smoothly and to eradicate non-physical prediction of the steady state of the unsteady vortex shedding. This was described recently by Dawes and Denton (1998).
The grid definitions for both cascades are similar and each employs 1911 grid points; 21 points in the blade-to-blade direction, 91 points in the stream-wise direction with 51 points from the blade leading-edge to its trailing-edge for the stator and 71 points for the rotor. Non-uniform pitch-wise grid distribution is used in which more grids are concentrated near the blade surfaces and the finest cells adjacent to the blade walls are about 1/6 that at mid-pitch.
Figure 4.2 shows the generated grids; on the left is the computational domain generated for the stator and on the right that for the rotor.
stator Rotor
Figure 4.2: Computational Meshes for UTRC Stator and Rotor Cascades
The experimental flow conditions measured upstream and downstream of the two airfoils are implemented as the inlet and outlet boundary conditions in the computations. At the upstream boundary, the inlet total pressure, temperature and absolute inlet angle are imposed and assumed to be uniform in the tangential direction. At the exit, the static pressure is fixed.
In the flow computation of the rotor section, a constant rotating tangential velocity of 29.44 m/s is specified to simulate the nominal operating rotational speed of 410 rpm.
4.2.2.2 Com parisons with Experimental Data
The comparisons between the experimental and computed pressure coefficient, Cp,
along the pressure and suction sides of the stator and rotor cascades are shown in figure 4.3 and 4.4 respectively.
Both figures show good correlation between the numerical and experimental results except for some discrepancies near the leading- and trailing-edges. The differences in the results near the leading-edges arise as a result of modelling the leading-edge with
the simple sheared H-type grid. Employing O or C-type grid topology would lead to better leading-edge resolution. However, for the reasons given in Chapter 3, H-grid is applied here.
Despite the inaccuracies near the leading-edges in these cases, the errors incurred at the front do not convect downstream nor adversely affect the solution substantially; from the figures, the solutions (blue lines) can be observed to match the experimental distributions (circles) satisfactorily.
O Experimental Data Calculated Data 8 6 d 8 o 2
r
0 2 0 20 4 0 6 0 8 0 100% Axial C h o rd from L.E.
Figure 4.3: Validation: UTRC Stator
Comparison o f Numerical and Experimental Pressure Coefficient, Cp
1 2 -1 O Experimental Data Calculated Data 1 0- d 1 Ü 8 Ü 2 2 a. 0 20 4 0 6 0 8 0 100
% Axial C h o rd from L.E.
Figure 4.4; Validation: UTRC Rotor
4.3 MEL ANNULAR TURBINE NOZZLE
The first three-dimensional test case is a low hub-to-tip ratio annular turbine nozzle guide vane. As was mentioned at the start of this chapter, it is taken from AGARD Report 275, which is meant to serve as the basis for validation of computational codes. As such, the test case (a sixth-scale prototype) has well-defined experimental boundary conditions that can be applied directly in the flow simulation, and is chosen because it has the characteristics of a real working transonic machine. In particular, it has all the features o f a last stage L.P. steam turbine nozzle; namely, low hub-tip radius ratio, high turning, high casing flare, highly turbulent flow (see table 4.2) which is transonic at the hub and subsonic at the casing. Furthermore, this nozzle has the added complications of leaning leading- and trailing-edges in the meridional plane and a non-uniform profile cross-section.